LMFDB - Embedded newform 525.2.q.e.299.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 $ x^16 + 11x^14 + 85x^12 + 332x^10 + 940x^8 + 1064x^6 + 880x^4 + 128*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.4
Root			$0.192865 - 0.334053i$ of defining polynomial
Character	$\chi$	$=$	525.299
Dual form			525.2.q.e.374.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.192865 + 0.334053i) q^{2} +(-1.72646 + 0.139098i) q^{3} +(0.925606 + 1.60320i) q^{4} +(0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} -1.48553 q^{8} +(2.96130 - 0.480295i) q^{9} +O(q^{10})$	\(q+(-0.192865 + 0.334053i) q^{2} +(-1.72646 + 0.139098i) q^{3} +(0.925606 + 1.60320i) q^{4} +(0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} -1.48553 q^{8} +(2.96130 - 0.480295i) q^{9} +(2.20164 - 1.27112i) q^{11} +(-1.82102 - 2.63910i) q^{12} +3.06718 q^{13} +(-1.01854 - 0.0640110i) q^{14} +(-1.56470 + 2.71015i) q^{16} +(-5.59565 + 3.23065i) q^{17} +(-0.410689 + 1.08186i) q^{18} +(1.03570 + 0.597960i) q^{19} +(-2.36090 - 3.92761i) q^{21} +0.980620i q^{22} +(1.52800 - 2.64657i) q^{23} +(2.56470 - 0.206635i) q^{24} +(-0.591553 + 1.02460i) q^{26} +(-5.04575 + 1.24112i) q^{27} +(-2.71015 + 4.07971i) q^{28} +7.77029i q^{29} +(-5.95299 + 3.43696i) q^{31} +(-2.08909 - 3.61840i) q^{32} +(-3.62423 + 2.50078i) q^{33} -2.49232i q^{34} +(3.51101 + 4.30299i) q^{36} +(3.07619 + 1.77604i) q^{37} +(-0.399500 + 0.230652i) q^{38} +(-5.29536 + 0.426640i) q^{39} -2.31252 q^{41} +(1.76737 - 0.0311648i) q^{42} -5.46130i q^{43} +(4.07571 + 2.35311i) q^{44} +(0.589395 + 1.02086i) q^{46} +(2.78876 + 1.61009i) q^{47} +(2.32442 - 4.89660i) q^{48} +(-4.23143 + 5.57629i) q^{49} +(9.21127 - 6.35593i) q^{51} +(2.83900 + 4.91730i) q^{52} +(6.62740 + 11.4790i) q^{53} +(0.558552 - 1.92492i) q^{54} +(-1.74781 - 3.52034i) q^{56} +(-1.87126 - 0.888288i) q^{57} +(-2.59569 - 1.49862i) q^{58} +(-1.98146 - 3.43199i) q^{59} +(-8.08933 - 4.67038i) q^{61} -2.65148i q^{62} +(4.62232 + 6.45245i) q^{63} -4.64717 q^{64} +(-0.136403 - 1.69300i) q^{66} +(-3.04782 + 1.75966i) q^{67} +(-10.3587 - 5.98062i) q^{68} +(-2.26989 + 4.78173i) q^{69} -0.921861i q^{71} +(-4.39911 + 0.713493i) q^{72} +(-0.148218 - 0.256722i) q^{73} +(-1.18658 + 0.685073i) q^{74} +2.21390i q^{76} +(5.60260 + 3.72180i) q^{77} +(0.878771 - 1.85121i) q^{78} +(4.14741 - 7.18352i) q^{79} +(8.53863 - 2.84460i) q^{81} +(0.446004 - 0.772502i) q^{82} +2.11171i q^{83} +(4.11147 - 7.42041i) q^{84} +(1.82436 + 1.05330i) q^{86} +(-1.08084 - 13.4151i) q^{87} +(-3.27061 + 1.88829i) q^{88} +(9.41507 - 16.3074i) q^{89} +(3.60871 + 7.26845i) q^{91} +5.65729 q^{92} +(9.79951 - 6.76182i) q^{93} +(-1.07571 + 0.621062i) q^{94} +(4.11003 + 5.95643i) q^{96} +12.3692 q^{97} +(-1.04668 - 2.48899i) q^{98} +(5.90923 - 4.82161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9	$ 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9} - 24 q^{14} + 2 q^{16} - 18 q^{19} - 44 q^{21} + 14 q^{24} + 12 q^{26} - 42 q^{31} + 18 q^{36} - 30 q^{39} + 60 q^{41} - 14 q^{46} + 8 q^{49} + 24 q^{51} - 14 q^{54} + 42 q^{56} - 24 q^{59} + 30 q^{61} - 76 q^{64} - 32 q^{66} - 26 q^{69} + 108 q^{74} + 58 q^{79} + 56 q^{81} + 102 q^{84} - 18 q^{86} - 6 q^{89} - 6 q^{91} + 48 q^{94} - 84 q^{96} + 68 q^{99}+O(q^{100}) $ 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9 - 24 * q^14 + 2 * q^16 - 18 * q^19 - 44 * q^21 + 14 * q^24 + 12 * q^26 - 42 * q^31 + 18 * q^36 - 30 * q^39 + 60 * q^41 - 14 * q^46 + 8 * q^49 + 24 * q^51 - 14 * q^54 + 42 * q^56 - 24 * q^59 + 30 * q^61 - 76 * q^64 - 32 * q^66 - 26 * q^69 + 108 * q^74 + 58 * q^79 + 56 * q^81 + 102 * q^84 - 18 * q^86 - 6 * q^89 - 6 * q^91 + 48 * q^94 - 84 * q^96 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.192865	+	0.334053i	−0.136376	+	0.236211i	−0.926122	−	0.377223i	$-0.876879\pi$
$2$	−0.192865	+	0.334053i	−0.136376	+	0.236211i	0.789746	+	0.613434i	$0.210212\pi$
$3$	−1.72646	+	0.139098i	−0.996770	+	0.0803085i
$3$	−1.72646	+	0.139098i	−0.996770	+	0.0803085i
$4$	0.925606	+	1.60320i	0.462803	+	0.801598i
$5$		0			0
$5$		0			0
$6$	0.286507	−	0.603555i	0.116966	−	0.246400i
$7$	1.17656	+	2.36975i	0.444696	+	0.895681i
$7$	1.17656	+	2.36975i	0.444696	+	0.895681i
$8$	−1.48553			−0.525214
$9$	2.96130	−	0.480295i	0.987101	−	0.160098i
$10$		0			0
$11$	2.20164	−	1.27112i	0.663821	−	0.383257i	−0.129910	−	0.991526i	$-0.541469\pi$
$11$	2.20164	−	1.27112i	0.663821	−	0.383257i	0.793731	+	0.608269i	$0.208136\pi$
$12$	−1.82102	−	2.63910i	−0.525683	−	0.761842i
$13$	3.06718			0.850683			0.425342	−	0.905033i	$-0.360154\pi$
$13$	3.06718			0.850683			0.425342	+	0.905033i	$0.360154\pi$
$14$	−1.01854	−	0.0640110i	−0.272216	−	0.0171077i
$15$		0			0
$16$	−1.56470	+	2.71015i	−0.391176	+	0.677537i
$17$	−5.59565	+	3.23065i	−1.35715	+	0.783548i	−0.989238	−	0.146314i	$-0.953259\pi$
$17$	−5.59565	+	3.23065i	−1.35715	+	0.783548i	−0.367907	+	0.929863i	$0.619926\pi$
$18$	−0.410689	+	1.08186i	−0.0968004	+	0.254998i
$19$	1.03570	+	0.597960i	0.237605	+	0.137181i	0.614076	−	0.789247i	$-0.289529\pi$
$19$	1.03570	+	0.597960i	0.237605	+	0.137181i	−0.376470	+	0.926429i	$0.622862\pi$
$20$		0			0
$21$	−2.36090	−	3.92761i	−0.515191	−	0.857075i
$22$			0.980620i			0.209069i
$23$	1.52800	−	2.64657i	0.318609	−	0.551848i	−0.661589	−	0.749867i	$-0.730118\pi$
$23$	1.52800	−	2.64657i	0.318609	−	0.551848i	0.980198	+	0.198019i	$0.0634509\pi$
$24$	2.56470	−	0.206635i	0.523518	−	0.0421792i
$25$		0			0
$26$	−0.591553	+	1.02460i	−0.116013	+	0.200941i
$27$	−5.04575	+	1.24112i	−0.971056	+	0.238854i
$28$	−2.71015	+	4.07971i	−0.512170	+	0.770992i
$29$			7.77029i			1.44291i	0.692463	+	0.721454i	$0.256526\pi$
$29$			7.77029i			1.44291i	−0.692463	+	0.721454i	$0.743474\pi$
$30$		0			0
$31$	−5.95299	+	3.43696i	−1.06919	+	0.617297i	−0.927960	−	0.372680i	$-0.878439\pi$
$31$	−5.95299	+	3.43696i	−1.06919	+	0.617297i	−0.141229	+	0.989977i	$0.545105\pi$
$32$	−2.08909	−	3.61840i	−0.369302	−	0.639649i
$33$	−3.62423	+	2.50078i	−0.630898	+	0.435330i
$34$		−	2.49232i		−	0.427430i
$35$		0			0
$36$	3.51101	+	4.30299i	0.585168	+	0.717165i
$37$	3.07619	+	1.77604i	0.505722	+	0.291979i	0.731074	−	0.682299i	$-0.239020\pi$
$37$	3.07619	+	1.77604i	0.505722	+	0.291979i	−0.225351	+	0.974278i	$0.572353\pi$
$38$	−0.399500	+	0.230652i	−0.0648075	+	0.0374166i
$39$	−5.29536	+	0.426640i	−0.847936	+	0.0683171i
$40$		0			0
$41$	−2.31252			−0.361154			−0.180577	−	0.983561i	$-0.557797\pi$
$41$	−2.31252			−0.361154			−0.180577	+	0.983561i	$0.557797\pi$
$42$	1.76737	−	0.0311648i	0.272710	−	0.00480884i
$43$		−	5.46130i		−	0.832841i	−0.909172	−	0.416420i	$-0.863284\pi$
$43$		−	5.46130i		−	0.832841i	0.909172	−	0.416420i	$-0.136716\pi$
$44$	4.07571	+	2.35311i	0.614437	+	0.354745i
$45$		0			0
$46$	0.589395	+	1.02086i	0.0869016	+	0.150518i
$47$	2.78876	+	1.61009i	0.406782	+	0.234856i	0.689406	−	0.724375i	$-0.257871\pi$
$47$	2.78876	+	1.61009i	0.406782	+	0.234856i	−0.282624	+	0.959231i	$0.591205\pi$
$48$	2.32442	−	4.89660i	0.335501	−	0.706763i
$49$	−4.23143	+	5.57629i	−0.604490	+	0.796613i
$50$		0			0
$51$	9.21127	−	6.35593i	1.28984	−	0.890008i
$52$	2.83900	+	4.91730i	0.393699	+	0.681906i
$53$	6.62740	+	11.4790i	0.910344	+	1.57676i	0.813579	+	0.581455i	$0.197516\pi$
$53$	6.62740	+	11.4790i	0.910344	+	1.57676i	0.0967651	+	0.995307i	$0.469150\pi$
$54$	0.558552	−	1.92492i	0.0760092	−	0.261948i
$55$		0			0
$56$	−1.74781	−	3.52034i	−0.233561	−	0.470425i
$57$	−1.87126	−	0.888288i	−0.247855	−	0.117657i
$58$	−2.59569	−	1.49862i	−0.340830	−	0.196779i
$59$	−1.98146	−	3.43199i	−0.257964	−	0.446807i	0.707732	−	0.706481i	$-0.249718\pi$
$59$	−1.98146	−	3.43199i	−0.257964	−	0.446807i	−0.965696	+	0.259674i	$0.916385\pi$
$60$		0			0
$61$	−8.08933	−	4.67038i	−1.03573	−	0.597981i	−0.117111	−	0.993119i	$-0.537363\pi$
$61$	−8.08933	−	4.67038i	−1.03573	−	0.597981i	−0.918622	+	0.395138i	$0.870697\pi$
$62$		−	2.65148i		−	0.336739i
$63$	4.62232	+	6.45245i	0.582357	+	0.812933i
$64$	−4.64717			−0.580896
$65$		0			0
$66$	−0.136403	−	1.69300i	−0.0167900	−	0.208394i
$67$	−3.04782	+	1.75966i	−0.372350	+	0.214977i	−0.674485	−	0.738289i	$-0.735634\pi$
$67$	−3.04782	+	1.75966i	−0.372350	+	0.214977i	0.302134	+	0.953265i	$0.402301\pi$
$68$	−10.3587	−	5.98062i	−1.25618	−	0.725257i
$69$	−2.26989	+	4.78173i	−0.273262	+	0.575652i
$70$		0			0
$71$		−	0.921861i		−	0.109405i	−0.998503	−	0.0547024i	$-0.982579\pi$
$71$		−	0.921861i		−	0.109405i	0.998503	−	0.0547024i	$-0.0174210\pi$
$72$	−4.39911	+	0.713493i	−0.518440	+	0.0840859i
$73$	−0.148218	−	0.256722i	−0.0173477	−	0.0300470i	0.857221	−	0.514948i	$-0.172189\pi$
$73$	−0.148218	−	0.256722i	−0.0173477	−	0.0300470i	−0.874569	+	0.484901i	$0.838856\pi$
$74$	−1.18658	+	0.685073i	−0.137937	+	0.0796381i
$75$		0			0
$76$			2.21390i			0.253952i
$77$	5.60260	+	3.72180i	0.638475	+	0.424139i
$78$	0.878771	−	1.85121i	0.0995012	−	0.209608i
$79$	4.14741	−	7.18352i	0.466620	−	0.808210i	−0.532653	−	0.846334i	$-0.678805\pi$
$79$	4.14741	−	7.18352i	0.466620	−	0.808210i	0.999273	+	0.0381242i	$0.0121383\pi$
$80$		0			0
$81$	8.53863	−	2.84460i	0.948737	−	0.316066i
$82$	0.446004	−	0.772502i	0.0492529	−	0.0853085i
$83$			2.11171i			0.231790i	0.993261	+	0.115895i	$0.0369737\pi$
$83$			2.11171i			0.231790i	−0.993261	+	0.115895i	$0.963026\pi$
$84$	4.11147	−	7.42041i	0.448598	−	0.809633i
$85$		0			0
$86$	1.82436	+	1.05330i	0.196726	+	0.113580i
$87$	−1.08084	−	13.4151i	−0.115878	−	1.43825i
$88$	−3.27061	+	1.88829i	−0.348648	+	0.201292i
$89$	9.41507	−	16.3074i	0.997996	−	1.72858i	0.444197	−	0.895929i	$-0.353489\pi$
$89$	9.41507	−	16.3074i	0.997996	−	1.72858i	0.553799	−	0.832651i	$-0.313178\pi$
$90$		0			0
$91$	3.60871	+	7.26845i	0.378296	+	0.761941i
$92$	5.65729			0.589813
$93$	9.79951	−	6.76182i	1.01616	−	0.701168i
$94$	−1.07571	+	0.621062i	−0.110951	+	0.0640576i
$95$		0			0
$96$	4.11003	+	5.95643i	0.419478	+	0.607925i
$97$	12.3692			1.25590			0.627952	−	0.778252i	$-0.283894\pi$
$97$	12.3692			1.25590			0.627952	+	0.778252i	$0.283894\pi$
$98$	−1.04668	−	2.48899i	−0.105730	−	0.251426i
$99$	5.90923	−	4.82161i	0.593900	−	0.484590i
$100$		0			0
$101$	3.48815	+	6.04166i	0.347084	+	0.601167i	0.985730	−	0.168333i	$-0.0538385\pi$
$101$	3.48815	+	6.04166i	0.347084	+	0.601167i	−0.638646	+	0.769501i	$0.720505\pi$
$102$	0.346678	+	4.30289i	0.0343263	+	0.426049i
$103$	1.88659	−	3.26767i	0.185891	−	0.321973i	−0.757985	−	0.652272i	$-0.773816\pi$
$103$	1.88659	−	3.26767i	0.185891	−	0.321973i	0.943876	+	0.330299i	$0.107150\pi$
$104$	−4.55639			−0.446791
$105$		0			0
$106$	−5.11279			−0.496598
$107$	6.61684	−	11.4607i	0.639674	−	1.10795i	−0.345830	−	0.938297i	$-0.612403\pi$
$107$	6.61684	−	11.4607i	0.639674	−	1.10795i	0.985504	−	0.169651i	$-0.0542640\pi$
$108$	−6.66014	−	6.94054i	−0.640872	−	0.667854i
$109$	1.25081	+	2.16647i	0.119806	+	0.207510i	0.919691	−	0.392644i	$-0.128439\pi$
$109$	1.25081	+	2.16647i	0.119806	+	0.207510i	−0.799885	+	0.600154i	$0.795106\pi$
$110$		0			0
$111$	−5.55795	−	2.63836i	−0.527537	−	0.250422i
$112$	−8.26333	−	0.519317i	−0.780812	−	0.0490709i
$113$	7.18425			0.675837			0.337919	−	0.941175i	$-0.390277\pi$
$113$	7.18425			0.675837			0.337919	+	0.941175i	$0.390277\pi$
$114$	0.657637	−	0.453780i	0.0615933	−	0.0425004i
$115$		0			0
$116$	−12.4573	+	7.19223i	−1.15663	+	0.667782i
$117$	9.08286	−	1.47315i	0.839710	−	0.136193i
$118$	1.52862			0.140721
$119$	−14.2394	−	9.45925i	−1.30533	−	0.867128i
$120$		0			0
$121$	−2.26851	+	3.92917i	−0.206228	+	0.357197i
$122$	3.12030	−	1.80151i	0.282499	−	0.163101i
$123$	3.99246	−	0.321667i	0.359988	−	0.0290037i
$124$	−11.0202	−	6.36254i	−0.989648	−	0.571373i
$125$		0			0
$126$	−3.04694	+	0.299642i	−0.271443	+	0.0266943i
$127$		−	11.1965i		−	0.993528i	−0.867886	−	0.496764i	$-0.834522\pi$
$127$		−	11.1965i		−	0.993528i	0.867886	−	0.496764i	$-0.165478\pi$
$128$	5.07445	−	8.78920i	0.448522	−	0.776863i
$129$	0.759659	+	9.42870i	0.0668842	+	0.830151i
$130$		0			0
$131$	7.83183	−	13.5651i	0.684270	−	1.18519i	−0.289395	−	0.957210i	$-0.593454\pi$
$131$	7.83183	−	13.5651i	0.684270	−	1.18519i	0.973666	−	0.227981i	$-0.0732125\pi$
$132$	−7.36385	−	3.49562i	−0.640941	−	0.304255i
$133$	−0.198460	+	3.15788i	−0.0172086	+	0.273823i
$134$		−	1.35751i		−	0.117271i
$135$		0			0
$136$	8.31252	−	4.79923i	0.712792	−	0.411531i
$137$	2.91420	+	5.04755i	0.248977	+	0.431241i	0.963242	−	0.268634i	$-0.0865723\pi$
$137$	2.91420	+	5.04755i	0.248977	+	0.431241i	−0.714265	+	0.699875i	$0.753239\pi$
$138$	−1.15957	−	1.68049i	−0.0987088	−	0.143053i
$139$			12.0365i			1.02092i	0.859900	+	0.510462i	$0.170525\pi$
$139$			12.0365i			1.02092i	−0.859900	+	0.510462i	$0.829475\pi$
$140$		0			0
$141$	−5.03863	−	2.39184i	−0.424330	−	0.201429i
$142$	0.307950	+	0.177795i	0.0258426	+	0.0149202i
$143$	6.75285	−	3.89876i	0.564701	−	0.326030i
$144$	−3.33189	+	8.77709i	−0.277658	+	0.731424i
$145$		0			0
$146$	0.114345			0.00946324
$147$	6.52973	−	10.2158i	0.538563	−	0.842585i
$148$			6.57565i			0.540515i
$149$	16.1925	+	9.34874i	1.32654	+	0.765879i	0.984763	−	0.173902i	$-0.0556377\pi$
$149$	16.1925	+	9.34874i	1.32654	+	0.765879i	0.341778	+	0.939781i	$0.388971\pi$
$150$		0			0
$151$	2.97531	+	5.15339i	0.242127	+	0.419377i	0.961320	−	0.275434i	$-0.0888215\pi$
$151$	2.97531	+	5.15339i	0.242127	+	0.419377i	−0.719193	+	0.694811i	$0.755488\pi$
$152$	−1.53856	−	0.888288i	−0.124794	−	0.0720497i
$153$	−15.0188	+	12.2545i	−1.21419	+	0.990718i
$154$	−2.32383	+	1.15376i	−0.187259	+	0.0929722i
$155$		0			0
$156$	−5.58540	−	8.09460i	−0.447190	−	0.648086i
$157$	3.20639	+	5.55364i	0.255898	+	0.443228i	0.965139	−	0.261738i	$-0.0842955\pi$
$157$	3.20639	+	5.55364i	0.255898	+	0.443228i	−0.709241	+	0.704966i	$0.750962\pi$
$158$	1.59978	+	2.77091i	0.127272	+	0.220441i
$159$	−13.0386	−	18.8961i	−1.03403	−	1.49856i
$160$		0			0
$161$	8.06948	+	0.507134i	0.635964	+	0.0399678i
$162$	−0.696562	+	3.40098i	−0.0547271	+	0.267206i
$163$	−14.2405	−	8.22174i	−1.11540	−	0.643976i	−0.175177	−	0.984537i	$-0.556050\pi$
$163$	−14.2405	−	8.22174i	−1.11540	−	0.643976i	−0.940223	+	0.340560i	$0.889383\pi$
$164$	−2.14048	−	3.70742i	−0.167143	−	0.289501i
$165$		0			0
$166$	−0.705423	−	0.407276i	−0.0547514	−	0.0316108i
$167$			4.81089i			0.372278i	0.982523	+	0.186139i	$0.0595975\pi$
$167$			4.81089i			0.372278i	−0.982523	+	0.186139i	$0.940402\pi$
$168$	3.50719	+	5.83459i	0.270586	+	0.450148i
$169$	−3.59239			−0.276338
$170$		0			0
$171$	3.35421	+	1.27330i	0.256503	+	0.0973718i
$172$	8.75554	−	5.05501i	0.667604	−	0.385441i
$173$	−5.90215	−	3.40761i	−0.448732	−	0.259075i	0.258563	−	0.965994i	$-0.416751\pi$
$173$	−5.90215	−	3.40761i	−0.448732	−	0.259075i	−0.707294	+	0.706919i	$0.750084\pi$
$174$	4.68980	+	2.22625i	0.355533	+	0.168771i
$175$		0			0
$176$			7.95571i			0.599684i
$177$	3.89829	+	5.64957i	0.293014	+	0.424647i
$178$	3.63168	+	6.29026i	0.272206	+	0.471475i
$179$	−17.2931	+	9.98420i	−1.29255	+	0.746254i	−0.979106	−	0.203353i	$-0.934816\pi$
$179$	−17.2931	+	9.98420i	−1.29255	+	0.746254i	−0.313444	+	0.949607i	$0.601483\pi$
$180$		0			0
$181$		−	5.18808i		−	0.385627i	−0.981235	−	0.192813i	$-0.938239\pi$
$181$		−	5.18808i		−	0.385627i	0.981235	−	0.192813i	$-0.0617612\pi$
$182$	−3.12404	−	0.196333i	−0.231569	−	0.0145532i
$183$	14.6155	+	6.93799i	1.08041	+	0.512871i
$184$	−2.26989	+	3.93156i	−0.167338	+	0.289838i
$185$		0			0
$186$	0.368817	+	4.57767i	0.0270430	+	0.335651i
$187$	−8.21309	+	14.2255i	−0.600601	+	1.04027i
$188$			5.96124i			0.434768i
$189$	−8.87776	−	10.4969i	−0.645762	−	0.763539i
$190$		0			0
$191$	7.48332	+	4.32049i	0.541474	+	0.312620i	0.745676	−	0.666309i	$-0.232127\pi$
$191$	7.48332	+	4.32049i	0.541474	+	0.312620i	−0.204202	+	0.978929i	$0.565460\pi$
$192$	8.02313	−	0.646414i	0.579020	−	0.0466509i
$193$	20.5873	−	11.8861i	1.48190	−	0.855578i	0.482115	−	0.876108i	$-0.339869\pi$
$193$	20.5873	−	11.8861i	1.48190	−	0.855578i	0.999789	+	0.0205300i	$0.00653536\pi$
$194$	−2.38559	+	4.13197i	−0.171276	+	0.296658i
$195$		0			0
$196$	−12.8565	−	1.62237i	−0.918323	−	0.115883i
$197$	−11.6843			−0.832475			−0.416238	−	0.909256i	$-0.636652\pi$
$197$	−11.6843			−0.832475			−0.416238	+	0.909256i	$0.636652\pi$
$198$	0.470987	+	2.90391i	0.0334716	+	0.206372i
$199$	12.2341	−	7.06338i	0.867254	−	0.500709i	0.000819396	−	1.00000i	$-0.499739\pi$
$199$	12.2341	−	7.06338i	0.867254	−	0.500709i	0.866435	+	0.499290i	$0.166406\pi$
$200$		0			0
$201$	5.01716	−	3.46192i	0.353883	−	0.244185i
$202$	−2.69098			−0.189336
$203$	−18.4137	+	9.14219i	−1.29239	+	0.641656i
$204$	18.7158	+	8.88440i	1.31037	+	0.622032i
$205$		0			0
$206$	0.727715	+	1.26044i	0.0507023	+	0.0878190i
$207$	3.25373	−	8.57118i	0.226150	−	0.595738i
$208$	−4.79923	+	8.31252i	−0.332767	+	0.576369i
$209$	3.04032			0.210303
$210$		0			0
$211$	4.49838			0.309681			0.154841	−	0.987939i	$-0.450514\pi$
$211$	4.49838			0.309681			0.154841	+	0.987939i	$0.450514\pi$
$212$	−12.2687	+	21.2501i	−0.842620	+	1.45946i
$213$	0.128229	+	1.59155i	0.00878614	+	0.109051i
$214$	2.55232	+	4.42075i	0.174473	+	0.302196i
$215$		0			0
$216$	7.49562	−	1.84372i	0.510012	−	0.125449i
$217$	−15.1488	−	10.0633i	−1.02837	−	0.683143i
$218$	−0.964952			−0.0653548
$219$	0.291602	+	0.422602i	0.0197046	+	0.0285568i
$220$		0			0
$221$	−17.1629	+	9.90900i	−1.15450	+	0.666551i
$222$	1.95329	−	1.34780i	0.131096	−	0.0904584i
$223$	7.20662			0.482591			0.241296	−	0.970452i	$-0.422428\pi$
$223$	7.20662			0.482591			0.241296	+	0.970452i	$0.422428\pi$
$224$	6.11678	−	9.20786i	0.408695	−	0.615226i
$225$		0			0
$226$	−1.38559	+	2.39992i	−0.0921682	+	0.159640i
$227$	1.61344	−	0.931518i	0.107087	−	0.0618270i	−0.445500	−	0.895282i	$-0.646974\pi$
$227$	1.61344	−	0.931518i	0.107087	−	0.0618270i	0.552587	+	0.833455i	$0.313641\pi$
$228$	−0.307950	−	3.82220i	−0.0203945	−	0.253132i
$229$	17.4126	+	10.0532i	1.15066	+	0.664333i	0.949047	−	0.315133i	$-0.102049\pi$
$229$	17.4126	+	10.0532i	1.15066	+	0.664333i	0.201610	+	0.979466i	$0.435383\pi$
$230$		0			0
$231$	−10.1903	−	5.64622i	−0.670475	−	0.371494i
$232$		−	11.5430i		−	0.757836i
$233$	−0.782650	+	1.35559i	−0.0512731	+	0.0888077i	−0.890523	−	0.454938i	$-0.849661\pi$
$233$	−0.782650	+	1.35559i	−0.0512731	+	0.0888077i	0.839250	+	0.543746i	$0.182995\pi$
$234$	−1.25966	+	3.31827i	−0.0823465	+	0.216922i
$235$		0			0
$236$	3.66811	−	6.35334i	0.238773	−	0.413568i
$237$	−6.16110	+	12.9789i	−0.400207	+	0.843073i
$238$	5.90618	−	2.93236i	0.382841	−	0.190077i
$239$			5.69230i			0.368205i	0.982907	+	0.184102i	$0.0589378\pi$
$239$			5.69230i			0.368205i	−0.982907	+	0.184102i	$0.941062\pi$
$240$		0			0
$241$	11.5466	−	6.66646i	0.743785	−	0.429424i	−0.0796592	−	0.996822i	$-0.525383\pi$
$241$	11.5466	−	6.66646i	0.743785	−	0.429424i	0.823444	+	0.567398i	$0.192050\pi$
$242$	−0.875033	−	1.51560i	−0.0562492	−	0.0974266i
$243$	−14.3459	+	6.09878i	−0.920290	+	0.391237i
$244$		−	17.2917i		−	1.10699i
$245$		0			0
$246$	−0.662553	+	1.39573i	−0.0422428	+	0.0889884i
$247$	3.17667	+	1.83405i	0.202127	+	0.116698i
$248$	8.84335	−	5.10571i	0.561554	−	0.324213i
$249$	−0.293736	−	3.64578i	−0.0186147	−	0.231042i
$250$		0			0
$251$	−5.32590			−0.336168			−0.168084	−	0.985773i	$-0.553758\pi$
$251$	−5.32590			−0.336168			−0.168084	+	0.985773i	$0.553758\pi$
$252$	−6.06611	+	13.3829i	−0.382129	+	0.843044i
$253$		−	7.76907i		−	0.488437i
$254$	3.74022	+	2.15941i	0.234682	+	0.135494i
$255$		0			0
$256$	−2.68980	−	4.65887i	−0.168112	−	0.291179i
$257$	−5.62922	−	3.25003i	−0.351141	−	0.202731i	0.314047	−	0.949408i	$-0.398315\pi$
$257$	−5.62922	−	3.25003i	−0.351141	−	0.202731i	−0.665188	+	0.746676i	$0.731648\pi$
$258$	−3.29619	−	1.56470i	−0.205212	−	0.0974142i
$259$	−0.589458	+	9.37941i	−0.0366271	+	0.582808i
$260$		0			0
$261$	3.73203	+	23.0102i	0.231007	+	1.42430i
$262$	3.02098	+	5.23249i	0.186637	+	0.323264i
$263$	−7.41326	−	12.8401i	−0.457121	−	0.791757i	0.541686	−	0.840581i	$-0.317786\pi$
$263$	−7.41326	−	12.8401i	−0.457121	−	0.791757i	−0.998807	+	0.0488236i	$0.984453\pi$
$264$	5.38391	−	3.71498i	0.331357	−	0.228641i
$265$		0			0
$266$	−1.01662	−	0.675341i	−0.0623331	−	0.0414078i
$267$	−13.9864	+	29.4636i	−0.855953	+	1.80314i
$268$	−5.64216	−	3.25750i	−0.344650	−	0.198984i
$269$	12.3042	+	21.3115i	0.750201	+	1.29939i	0.947725	+	0.319088i	$0.103376\pi$
$269$	12.3042	+	21.3115i	0.750201	+	1.29939i	−0.197525	+	0.980298i	$0.563290\pi$
$270$		0			0
$271$	3.30121	+	1.90595i	0.200534	+	0.115778i	0.596905	−	0.802312i	$-0.296397\pi$
$271$	3.30121	+	1.90595i	0.200534	+	0.115778i	−0.396371	+	0.918091i	$0.629730\pi$
$272$		−	20.2201i		−	1.22602i
$273$	−7.24131	−	12.0467i	−0.438264	−	0.729100i
$274$	−2.24819			−0.135818
$275$		0			0
$276$	−9.76707	+	0.786920i	−0.587908	+	0.0473670i
$277$	−16.2600	+	9.38769i	−0.976966	+	0.564052i	−0.901353	−	0.433086i	$-0.857425\pi$
$277$	−16.2600	+	9.38769i	−0.976966	+	0.564052i	−0.0756131	+	0.997137i	$0.524091\pi$
$278$	−4.02083	−	2.32143i	−0.241153	−	0.139230i
$279$	−15.9779	+	13.0371i	−0.956570	+	0.780509i
$280$		0			0
$281$		−	23.6885i		−	1.41314i	−0.707643	−	0.706570i	$-0.750242\pi$
$281$		−	23.6885i		−	1.41314i	0.707643	−	0.706570i	$-0.249758\pi$
$282$	1.77078	−	1.22187i	0.105448	−	0.0727610i
$283$	2.52204	+	4.36831i	0.149920	+	0.259669i	0.931198	−	0.364515i	$-0.118765\pi$
$283$	2.52204	+	4.36831i	0.149920	+	0.259669i	−0.781278	+	0.624184i	$0.785432\pi$
$284$	1.47792	−	0.853280i	0.0876987	−	0.0506329i
$285$		0			0
$286$			3.00774i			0.177851i
$287$	−2.72080	−	5.48008i	−0.160604	−	0.323479i
$288$	−7.92431	−	9.71181i	−0.466945	−	0.572274i
$289$	12.3742	−	21.4328i	0.727895	−	1.26075i
$290$		0			0
$291$	−21.3549	+	1.72054i	−1.25185	+	0.100860i
$292$	0.274384	−	0.475246i	0.0160571	−	0.0278117i
$293$			6.29421i			0.367712i	0.982953	+	0.183856i	$0.0588580\pi$
$293$			6.29421i			0.367712i	−0.982953	+	0.183856i	$0.941142\pi$
$294$	2.15326	+	4.15155i	0.125581	+	0.242123i
$295$		0			0
$296$	−4.56977	−	2.63836i	−0.265613	−	0.153352i
$297$	−9.53134	+	9.14626i	−0.553065	+	0.530720i
$298$	−6.24594	+	3.60610i	−0.361818	+	0.208896i
$299$	4.68664	−	8.11750i	0.271036	−	0.469447i
$300$		0			0
$301$	12.9419	−	6.42553i	0.745960	−	0.370361i
$302$	−2.29534			−0.132082
$303$	−6.86253	−	9.94546i	−0.394242	−	0.571352i
$304$	−3.24112	+	1.87126i	−0.185891	+	0.107324i
$305$		0			0
$306$	−1.19705	−	7.38053i	−0.0684308	−	0.421917i
$307$	16.0397			0.915432			0.457716	−	0.889099i	$-0.348668\pi$
$307$	16.0397			0.915432			0.457716	+	0.889099i	$0.348668\pi$
$308$	−0.780986	+	12.4270i	−0.0445008	+	0.708093i
$309$	−2.80258	+	5.90390i	−0.159433	+	0.335861i
$310$		0			0
$311$	−9.03624	−	15.6512i	−0.512398	−	0.887499i	−0.999897	−	0.0143755i	$-0.995424\pi$
$311$	−9.03624	−	15.6512i	−0.512398	−	0.887499i	0.487499	−	0.873124i	$-0.337909\pi$
$312$	7.86641	−	0.633787i	0.445348	−	0.0358811i
$313$	−9.31104	+	16.1272i	−0.526291	+	0.911563i	0.473240	+	0.880934i	$0.343084\pi$
$313$	−9.31104	+	16.1272i	−0.526291	+	0.911563i	−0.999531	+	0.0306290i	$0.990249\pi$
$314$	−2.47361			−0.139594
$315$		0			0
$316$	15.3555			0.863812
$317$	−1.31825	+	2.28327i	−0.0740402	+	0.128241i	−0.900669	−	0.434507i	$-0.856923\pi$
$317$	−1.31825	+	2.28327i	−0.0740402	+	0.128241i	0.826628	+	0.562748i	$0.190256\pi$
$318$	8.82700	−	0.711181i	0.494994	−	0.0398810i
$319$	9.87698	+	17.1074i	0.553005	+	0.957832i
$320$		0			0
$321$	−9.82952	+	20.7068i	−0.548630	+	1.15574i
$322$	−1.72573	+	2.59782i	−0.0961713	+	0.144771i
$323$	−7.72720			−0.429953
$324$	12.4639	+	11.0561i	0.692436	+	0.614230i
$325$		0			0
$326$	5.49299	−	3.17138i	0.304228	−	0.175646i
$327$	−2.46082	−	3.56632i	−0.136084	−	0.197218i
$328$	3.43531			0.189683
$329$	−0.534381	+	8.50303i	−0.0294614	+	0.468787i
$330$		0			0
$331$	15.1704	−	26.2759i	0.833842	−	1.44426i	−0.0611286	−	0.998130i	$-0.519470\pi$
$331$	15.1704	−	26.2759i	0.833842	−	1.44426i	0.894970	−	0.446126i	$-0.147197\pi$
$332$	−3.38549	+	1.95461i	−0.185803	+	0.107273i
$333$	9.96255	+	3.78191i	0.545944	+	0.207248i
$334$	−1.60709	−	0.927855i	−0.0879362	−	0.0507700i
$335$		0			0
$336$	14.3385	−	0.252838i	0.782231	−	0.0137935i
$337$		−	1.84215i		−	0.100348i	−0.998740	−	0.0501741i	$-0.984022\pi$
$337$		−	1.84215i		−	0.100348i	0.998740	−	0.0501741i	$-0.0159776\pi$
$338$	0.692849	−	1.20005i	0.0376860	−	0.0652741i
$339$	−12.4033	+	0.999317i	−0.673654	+	0.0542755i
$340$		0			0
$341$	−8.73758	+	15.1339i	−0.473167	+	0.819549i
$342$	−1.07226	+	0.874907i	−0.0579812	+	0.0473096i
$343$	−18.1929	−	3.46661i	−0.982326	−	0.187180i
$344$			8.11293i			0.437420i
$345$		0			0
$346$	2.27664	−	1.31442i	0.122393	−	0.0706636i
$347$	−4.09520	−	7.09309i	−0.219842	−	0.380777i	0.734918	−	0.678156i	$-0.237221\pi$
$347$	−4.09520	−	7.09309i	−0.219842	−	0.380777i	−0.954759	+	0.297379i	$0.903887\pi$
$348$	20.5066	−	14.1499i	1.09927	−	0.758512i
$349$		−	36.3291i		−	1.94465i	−0.233627	−	0.972326i	$-0.575059\pi$
$349$		−	36.3291i		−	1.94465i	0.233627	−	0.972326i	$-0.424941\pi$
$350$		0			0
$351$	−15.4762	+	3.80674i	−0.826061	+	0.203189i
$352$	−9.19885	−	5.31096i	−0.490300	−	0.283075i
$353$	−4.94910	+	2.85736i	−0.263414	+	0.152082i	−0.625891	−	0.779911i	$-0.715265\pi$
$353$	−4.94910	+	2.85736i	−0.263414	+	0.152082i	0.362477	+	0.931993i	$0.381931\pi$
$354$	−2.63910	+	0.212629i	−0.140266	+	0.0113011i
$355$		0			0
$356$	34.8586			1.84750
$357$	25.8995	+	14.3503i	1.37075	+	0.759499i
$358$		−	7.70242i		−	0.407086i
$359$	4.16181	+	2.40282i	0.219652	+	0.126816i	0.605789	−	0.795625i	$-0.292858\pi$
$359$	4.16181	+	2.40282i	0.219652	+	0.126816i	−0.386137	+	0.922441i	$0.626191\pi$
$360$		0			0
$361$	−8.78489	−	15.2159i	−0.462362	−	0.800835i
$362$	1.73309	+	1.00060i	0.0910892	+	0.0525904i
$363$	3.36994	−	7.09909i	0.176876	−	0.372605i
$364$	−8.31252	+	12.5132i	−0.435694	+	0.655870i
$365$		0			0
$366$	−5.13648	+	3.54426i	−0.268488	+	0.185261i
$367$	−12.2881	−	21.2836i	−0.641433	−	1.11099i	−0.985113	−	0.171908i	$-0.945007\pi$
$367$	−12.2881	−	21.2836i	−0.641433	−	1.11099i	0.343680	−	0.939087i	$-0.388327\pi$
$368$	4.78173	+	8.28219i	0.249265	+	0.431739i
$369$	−6.84806	+	1.11069i	−0.356496	+	0.0578201i
$370$		0			0
$371$	−19.4048	+	29.2110i	−1.00745	+	1.51656i
$372$	19.9110	+	9.45176i	1.03234	+	0.490051i
$373$	22.9519	+	13.2513i	1.18840	+	0.686126i	0.957944	−	0.286956i	$-0.0926434\pi$
$373$	22.9519	+	13.2513i	1.18840	+	0.686126i	0.230461	+	0.973082i	$0.425977\pi$
$374$	−3.16804	−	5.48721i	−0.163816	−	0.283737i
$375$		0			0
$376$	−4.14279	−	2.39184i	−0.213648	−	0.123350i
$377$			23.8329i			1.22746i
$378$	5.21874	−	0.941145i	0.268423	−	0.0484073i
$379$	−13.0939			−0.672588			−0.336294	−	0.941757i	$-0.609174\pi$
$379$	−13.0939			−0.672588			−0.336294	+	0.941757i	$0.609174\pi$
$380$		0			0
$381$	1.55741	+	19.3302i	0.0797887	+	0.990319i
$382$	−2.88655	+	1.66655i	−0.147689	+	0.0852680i
$383$	14.6930	+	8.48299i	0.750776	+	0.433461i	0.825974	−	0.563708i	$-0.190626\pi$
$383$	14.6930	+	8.48299i	0.750776	+	0.433461i	−0.0751982	+	0.997169i	$0.523959\pi$
$384$	−7.53825	+	15.8800i	−0.384685	+	0.810374i
$385$		0			0
$386$			9.16964i			0.466723i
$387$	−2.62303	−	16.1726i	−0.133336	−	0.822098i
$388$	11.4490	+	19.8303i	0.581236	+	1.00673i
$389$	−2.13457	+	1.23239i	−0.108227	+	0.0624848i	−0.553136	−	0.833091i	$-0.686569\pi$
$389$	−2.13457	+	1.23239i	−0.108227	+	0.0624848i	0.444910	+	0.895576i	$0.353236\pi$
$390$		0			0
$391$			19.7457i			0.998583i
$392$	6.28592	−	8.28375i	0.317487	−	0.418393i
$393$	−11.6344	+	24.5090i	−0.586879	+	1.23632i
$394$	2.25351	−	3.90319i	0.113530	−	0.196640i
$395$		0			0
$396$	13.1996	+	5.01074i	0.663305	+	0.251799i
$397$	−1.67684	+	2.90437i	−0.0841582	+	0.145766i	−0.905032	−	0.425343i	$-0.860153\pi$
$397$	−1.67684	+	2.90437i	−0.0841582	+	0.145766i	0.820874	+	0.571109i	$0.193487\pi$
$398$			5.44912i			0.273140i
$399$	−0.0966235	−	5.47954i	−0.00483723	−	0.274320i
$400$		0			0
$401$	5.40992	+	3.12342i	0.270158	+	0.155976i	0.628960	−	0.777438i	$-0.283481\pi$
$401$	5.40992	+	3.12342i	0.270158	+	0.155976i	−0.358801	+	0.933414i	$0.616814\pi$
$402$	0.188827	+	2.34368i	0.00941785	+	0.116892i
$403$	−18.2589	+	10.5418i	−0.909541	+	0.525124i
$404$	−6.45731	+	11.1844i	−0.321263	+	0.556444i
$405$		0			0
$406$	0.497384	−	7.91434i	0.0246848	−	0.392782i
$407$	9.03024			0.447612
$408$	−13.6836	+	9.44192i	−0.677441	+	0.467445i
$409$	10.2147	−	5.89748i	0.505086	−	0.291611i	−0.225726	−	0.974191i	$-0.572475\pi$
$409$	10.2147	−	5.89748i	0.505086	−	0.291611i	0.730811	+	0.682579i	$0.239142\pi$
$410$		0			0
$411$	−5.73335	−	8.30901i	−0.282805	−	0.409853i
$412$	6.98495			0.344124
$413$	5.80166	−	8.73350i	0.285481	−	0.429748i
$414$	2.23569	+	2.74000i	0.109878	+	0.134664i
$415$		0			0
$416$	−6.40761	−	11.0983i	−0.314159	−	0.544139i
$417$	−1.67426	−	20.7805i	−0.0819888	−	1.01763i
$418$	−0.586372	+	1.01563i	−0.0286804	+	0.0496759i
$419$	−12.0419			−0.588284			−0.294142	−	0.955762i	$-0.595034\pi$
$419$	−12.0419			−0.588284			−0.294142	+	0.955762i	$0.595034\pi$
$420$		0			0
$421$	11.4264			0.556888			0.278444	−	0.960453i	$-0.410181\pi$
$421$	11.4264			0.556888			0.278444	+	0.960453i	$0.410181\pi$
$422$	−0.867582	+	1.50270i	−0.0422332	+	0.0731501i
$423$	9.03168	+	3.42854i	0.439135	+	0.166701i
$424$	−9.84521	−	17.0524i	−0.478126	−	0.828138i
$425$		0			0
$426$	−0.556394	−	0.264120i	−0.0269574	−	0.0127967i
$427$	1.55007	−	24.6647i	0.0750133	−	1.19361i
$428$	24.4983			1.18417
$429$	−11.1162	+	7.67034i	−0.536694	+	0.370328i
$430$		0			0
$431$	28.2346	−	16.3013i	1.36001	−	0.785205i	0.370389	−	0.928877i	$-0.379224\pi$
$431$	28.2346	−	16.3013i	1.36001	−	0.785205i	0.989625	+	0.143672i	$0.0458909\pi$
$432$	4.53149	−	15.6167i	0.218022	−	0.751360i
$433$	4.37644			0.210318			0.105159	−	0.994455i	$-0.466465\pi$
$433$	4.37644			0.210318			0.105159	+	0.994455i	$0.466465\pi$
$434$	6.28335	−	3.11962i	0.301611	−	0.149747i
$435$		0			0
$436$	−2.31551	+	4.01059i	−0.110893	+	0.192072i
$437$	3.16508	−	1.82736i	0.151407	−	0.0874146i
$438$	−0.197411	+	0.0159052i	−0.00943268	+	0.000759979i
$439$	12.8416	+	7.41409i	0.612895	+	0.353855i	0.774098	−	0.633066i	$-0.218204\pi$
$439$	12.8416	+	7.41409i	0.612895	+	0.353855i	−0.161202	+	0.986921i	$0.551537\pi$
$440$		0			0
$441$	−9.85229	+	18.5454i	−0.469157	+	0.883115i
$442$		−	7.64441i		−	0.363607i
$443$	7.95622	−	13.7806i	0.378011	−	0.654735i	−0.612762	−	0.790268i	$-0.709941\pi$
$443$	7.95622	−	13.7806i	0.378011	−	0.654735i	0.990773	+	0.135533i	$0.0432747\pi$
$444$	−0.914662	−	11.3526i	−0.0434079	−	0.538769i
$445$		0			0
$446$	−1.38991	+	2.40739i	−0.0658141	+	0.113993i
$447$	−29.2560	−	13.8878i	−1.38376	−	0.656872i
$448$	−5.46765	−	11.0126i	−0.258322	−	0.520298i
$449$		−	35.1881i		−	1.66063i	−0.557294	−	0.830315i	$-0.688161\pi$
$449$		−	35.1881i		−	1.66063i	0.557294	−	0.830315i	$-0.311839\pi$
$450$		0			0
$451$	−5.09134	+	2.93948i	−0.239742	+	0.138415i
$452$	6.64978	+	11.5178i	0.312779	+	0.541750i
$453$	−5.85357	−	8.48324i	−0.275025	−	0.398577i
$454$			0.718630i			0.0337270i
$455$		0			0
$456$	2.77982	+	1.31958i	0.130177	+	0.0617950i
$457$	−12.1755	−	7.02954i	−0.569547	−	0.328828i	0.187421	−	0.982280i	$-0.439987\pi$
$457$	−12.1755	−	7.02954i	−0.569547	−	0.328828i	−0.756968	+	0.653451i	$0.773320\pi$
$458$	−6.71658	+	3.87782i	−0.313845	+	0.181199i
$459$	24.2247	−	23.2459i	1.13071	−	1.08503i
$460$		0			0
$461$	−13.5161			−0.629506			−0.314753	−	0.949174i	$-0.601922\pi$
$461$	−13.5161			−0.629506			−0.314753	+	0.949174i	$0.601922\pi$
$462$	3.85150	−	2.31515i	0.179188	−	0.107710i
$463$		−	17.8381i		−	0.829009i	−0.910047	−	0.414504i	$-0.863955\pi$
$463$		−	17.8381i		−	0.829009i	0.910047	−	0.414504i	$-0.136045\pi$
$464$	−21.0586	−	12.1582i	−0.977623	−	0.564431i
$465$		0			0
$466$	−0.301892	−	0.522893i	−0.0139849	−	0.0242225i
$467$	7.95827	+	4.59471i	0.368265	+	0.212618i	0.672700	−	0.739915i	$-0.265134\pi$
$467$	7.95827	+	4.59471i	0.368265	+	0.212618i	−0.304435	+	0.952533i	$0.598468\pi$
$468$	10.7689	+	13.1980i	0.497792	+	0.610080i
$469$	−7.75588	−	5.15223i	−0.358133	−	0.237908i
$470$		0			0
$471$	−6.30820	−	9.14211i	−0.290666	−	0.421246i
$472$	2.94352	+	5.09833i	0.135487	+	0.234670i
$473$	−6.94197	−	12.0238i	−0.319192	−	0.552857i
$474$	−3.14738	−	4.56132i	−0.144564	−	0.209508i
$475$		0			0
$476$	1.98494	−	31.5842i	0.0909794	−	1.44766i
$477$	25.1391	+	30.8097i	1.15104	+	1.41068i
$478$	−1.90153	−	1.09785i	−0.0869739	−	0.0502144i
$479$	−9.44037	−	16.3512i	−0.431341	−	0.747105i	0.565648	−	0.824647i	$-0.308626\pi$
$479$	−9.44037	−	16.3512i	−0.431341	−	0.747105i	−0.996989	+	0.0775419i	$0.975293\pi$
$480$		0			0
$481$	9.43523	+	5.44743i	0.430210	+	0.248382i
$482$			5.14291i			0.234253i
$483$	−14.0021	+	0.246907i	−0.637120	+	0.0112346i
$484$	−8.39897			−0.381772
$485$		0			0
$486$	0.729514	−	5.96853i	0.0330914	−	0.270738i
$487$	−4.53386	+	2.61762i	−0.205449	+	0.118616i	−0.599194	−	0.800604i	$-0.704512\pi$
$487$	−4.53386	+	2.61762i	−0.205449	+	0.118616i	0.393746	+	0.919219i	$0.371179\pi$
$488$	12.0170	+	6.93799i	0.543982	+	0.314068i
$489$	25.7292	+	12.2136i	1.16351	+	0.552320i
$490$		0			0
$491$			19.5201i			0.880930i	0.897770	+	0.440465i	$0.145186\pi$
$491$			19.5201i			0.880930i	−0.897770	+	0.440465i	$0.854814\pi$
$492$	4.21114	+	6.10295i	0.189853	+	0.275142i
$493$	−25.1031	−	43.4799i	−1.13059	−	1.95823i
$494$	−1.22534	+	0.707451i	−0.0551307	+	0.0318297i
$495$		0			0
$496$		−	21.5113i		−	0.965887i
$497$	2.18458	−	1.08462i	0.0979918	−	0.0486519i
$498$	1.27453	+	0.605021i	0.0571132	+	0.0271116i
$499$	−18.3175	+	31.7269i	−0.820005	+	1.42029i	0.0856728	+	0.996323i	$0.472696\pi$
$499$	−18.3175	+	31.7269i	−0.820005	+	1.42029i	−0.905678	+	0.423967i	$0.860637\pi$
$500$		0			0
$501$	−0.669188	−	8.30580i	−0.0298971	−	0.371076i
$502$	1.02718	−	1.77913i	0.0458453	−	0.0794064i
$503$		−	40.7156i		−	1.81542i	−0.419602	−	0.907708i	$-0.637830\pi$
$503$		−	40.7156i		−	1.81542i	0.419602	−	0.907708i	$-0.362170\pi$
$504$	−6.86660	−	9.58532i	−0.305863	−	0.426964i
$505$		0			0
$506$	2.59528	+	1.49838i	0.115374	+	0.0666113i
$507$	6.20211	−	0.499696i	0.275445	−	0.0221923i
$508$	17.9502	−	10.3635i	0.796410	−	0.459807i
$509$	8.86384	−	15.3526i	0.392883	−	0.680493i	−0.599946	−	0.800041i	$-0.704811\pi$
$509$	8.86384	−	15.3526i	0.392883	−	0.680493i	0.992828	+	0.119548i	$0.0381445\pi$
$510$		0			0
$511$	0.433979	−	0.653288i	0.0191981	−	0.0288998i
$512$	22.3729			0.988751
$513$	−5.96801	−	1.73173i	−0.263494	−	0.0764579i
$514$	2.17136	−	1.25364i	0.0957747	−	0.0552956i
$515$		0			0
$516$	−14.4129	+	9.94514i	−0.634493	+	0.437811i
$517$	8.18648			0.360041
$518$	−3.01953	−	2.00587i	−0.132671	−	0.0881330i
$519$	10.6638	+	5.06210i	0.468088	+	0.222202i
$520$		0			0
$521$	−1.75780	−	3.04461i	−0.0770108	−	0.133387i	0.824948	−	0.565208i	$-0.191204\pi$
$521$	−1.75780	−	3.04461i	−0.0770108	−	0.133387i	−0.901959	+	0.431822i	$0.857871\pi$
$522$	−8.40640	−	3.19118i	−0.367938	−	0.139674i
$523$	2.42791	−	4.20527i	0.106165	−	0.183884i	−0.808048	−	0.589116i	$-0.799476\pi$
$523$	2.42791	−	4.20527i	0.106165	−	0.183884i	0.914214	+	0.405232i	$0.132809\pi$
$524$	28.9968			1.26673
$525$		0			0
$526$	5.71904			0.249362
$527$	22.2073	−	38.4641i	0.967363	−	1.67552i
$528$	−1.10663	−	13.7352i	−0.0481597	−	0.597747i
$529$	6.83045	+	11.8307i	0.296976	+	0.514378i
$530$		0			0
$531$	−7.51608	−	9.21148i	−0.326170	−	0.399744i
$532$	−5.24639	+	2.60478i	−0.227460	+	0.112932i
$533$	−7.09290			−0.307228
$534$	−7.14491	−	10.3547i	−0.309190	−	0.448092i
$535$		0			0
$536$	4.52763	−	2.61403i	0.195564	−	0.112909i
$537$	28.4671	−	19.6427i	1.22844	−	0.847646i
$538$	−9.49222			−0.409239
$539$	−2.22797	+	17.6557i	−0.0959656	+	0.760483i
$540$		0			0
$541$	0.0193171	−	0.0334581i	0.000830506	−	0.00143848i	−0.865610	−	0.500719i	$-0.833069\pi$
$541$	0.0193171	−	0.0334581i	0.000830506	−	0.00143848i	0.866440	+	0.499281i	$0.166402\pi$
$542$	−1.27338	+	0.735184i	−0.0546962	+	0.0315789i
$543$	0.721653	+	8.95699i	0.0309691	+	0.384381i
$544$	23.3796	+	13.4982i	1.00239	+	0.578731i
$545$		0			0
$546$	5.42083	−	0.0955882i	0.231990	−	0.00409080i
$547$		−	36.3881i		−	1.55584i	−0.628362	−	0.777921i	$-0.716274\pi$
$547$		−	36.3881i		−	1.55584i	0.628362	−	0.777921i	$-0.283726\pi$
$548$	−5.39480	+	9.34408i	−0.230455	+	0.399159i
$549$	−26.1981	−	9.94514i	−1.11811	−	0.424448i
$550$		0			0
$551$	−4.64633	+	8.04767i	−0.197940	+	0.342842i
$552$	3.37199	−	7.10340i	0.143521	−	0.302341i
$553$	21.9028	+	1.37650i	0.931402	+	0.0585349i
$554$		−	7.24224i		−	0.307693i
$555$		0			0
$556$	−19.2969	+	11.1411i	−0.818370	+	0.472486i
$557$	8.68779	+	15.0477i	0.368114	+	0.637591i	0.989271	−	0.146095i	$-0.0466704\pi$
$557$	8.68779	+	15.0477i	0.368114	+	0.637591i	−0.621157	+	0.783686i	$0.713337\pi$
$558$	−1.27349	−	7.85185i	−0.0539113	−	0.332395i
$559$		−	16.7508i		−	0.708484i
$560$		0			0
$561$	12.2008	−	25.7021i	0.515118	−	1.08514i
$562$	7.91322	+	4.56870i	0.333799	+	0.192719i
$563$	−18.1078	+	10.4546i	−0.763153	+	0.440607i	−0.830427	−	0.557128i	$-0.811903\pi$
$563$	−18.1078	+	10.4546i	−0.763153	+	0.440607i	0.0672735	+	0.997735i	$0.478570\pi$
$564$	−0.829199	−	10.2918i	−0.0349156	−	0.433364i
$565$		0			0
$566$	−1.94566			−0.0817822
$567$	16.7872	+	16.8876i	0.704995	+	0.709213i
$568$			1.36945i			0.0574610i
$569$	−24.8873	−	14.3687i	−1.04333	−	0.602367i	−0.122556	−	0.992462i	$-0.539109\pi$
$569$	−24.8873	−	14.3687i	−1.04333	−	0.602367i	−0.920775	+	0.390094i	$0.872442\pi$
$570$		0			0
$571$	15.2499	+	26.4136i	0.638188	+	1.10537i	0.985830	+	0.167746i	$0.0536490\pi$
$571$	15.2499	+	26.4136i	0.638188	+	1.10537i	−0.347643	+	0.937627i	$0.613018\pi$
$572$	12.5009	+	7.21742i	0.522691	+	0.301776i
$573$	−13.5206	−	6.41823i	−0.564831	−	0.268125i
$574$	2.35539	+	0.148026i	0.0983119	+	0.00617850i
$575$		0			0
$576$	−13.7617	+	2.23201i	−0.573403	+	0.0930004i
$577$	11.7531	+	20.3570i	0.489289	+	0.847473i	0.999924	−	0.0123245i	$-0.00392310\pi$
$577$	11.7531	+	20.3570i	0.489289	+	0.847473i	−0.510635	+	0.859797i	$0.670590\pi$
$578$	4.77312	+	8.26728i	0.198536	+	0.343874i
$579$	−33.8897	+	23.3844i	−1.40841	+	0.971824i
$580$		0			0
$581$	−5.00423	+	2.48455i	−0.207610	+	0.103076i
$582$	3.54387	−	7.46549i	0.146898	−	0.309455i
$583$	29.1824	+	16.8485i	1.20861	+	0.697792i
$584$	0.220183	+	0.381368i	0.00911124	+	0.0157811i
$585$		0			0
$586$	−2.10260	−	1.21394i	−0.0868575	−	0.0501472i
$587$		−	24.4613i		−	1.00963i	−0.863229	−	0.504813i	$-0.831561\pi$
$587$		−	24.4613i		−	1.00963i	0.863229	−	0.504813i	$-0.168439\pi$
$588$	22.4219	+	1.01263i	0.924663	+	0.0417600i
$589$	−8.22067			−0.338727
$590$		0			0
$591$	20.1725	−	1.62527i	0.829786	−	0.0668548i
$592$	−9.62665	+	5.55795i	−0.395653	+	0.228430i
$593$	−3.24770	−	1.87506i	−0.133367	−	0.0769995i	0.431832	−	0.901954i	$-0.357867\pi$
$593$	−3.24770	−	1.87506i	−0.133367	−	0.0769995i	−0.565199	+	0.824955i	$0.691201\pi$
$594$	−1.21707	−	4.94797i	−0.0499369	−	0.203018i
$595$		0			0
$596$			34.6130i			1.41780i
$597$	−20.1392	+	13.8964i	−0.824242	+	0.568740i
$598$	1.80778	+	3.13117i	0.0739257	+	0.128043i
$599$	28.6663	−	16.5505i	1.17127	−	0.676235i	0.217294	−	0.976106i	$-0.430277\pi$
$599$	28.6663	−	16.5505i	1.17127	−	0.676235i	0.953980	+	0.299871i	$0.0969438\pi$
$600$		0			0
$601$		−	3.36032i		−	0.137070i	−0.997649	−	0.0685352i	$-0.978167\pi$
$601$		−	3.36032i		−	0.137070i	0.997649	−	0.0685352i	$-0.0218325\pi$
$602$	−0.349583	+	5.56255i	−0.0142480	+	0.226712i
$603$	−8.18036	+	6.67473i	−0.333130	+	0.271816i
$604$	−5.50793	+	9.54001i	−0.224114	+	0.388177i
$605$		0			0
$606$	4.64585	−	0.374310i	0.188725	−	0.0152053i
$607$	−22.2522	+	38.5420i	−0.903190	+	1.56437i	−0.0798612	+	0.996806i	$0.525448\pi$
$607$	−22.2522	+	38.5420i	−0.903190	+	1.56437i	−0.823329	+	0.567565i	$0.807886\pi$
$608$		−	4.99676i		−	0.202645i
$609$	30.5187	−	18.3449i	1.23668	−	0.743373i
$610$		0			0
$611$	8.55364	+	4.93844i	0.346043	+	0.199788i
$612$	−33.5478	−	12.7352i	−1.35609	−	0.514789i
$613$	−34.9125	+	20.1567i	−1.41010	+	0.814123i	−0.995397	−	0.0958333i	$-0.969448\pi$
$613$	−34.9125	+	20.1567i	−1.41010	+	0.814123i	−0.414705	+	0.909956i	$0.636115\pi$
$614$	−3.09349	+	5.35809i	−0.124843	+	0.216235i
$615$		0			0
$616$	−8.32283	−	5.52885i	−0.335336	−	0.222764i
$617$	−37.7372			−1.51924			−0.759621	−	0.650366i	$-0.774616\pi$
$617$	−37.7372			−1.51924			−0.759621	+	0.650366i	$0.774616\pi$
$618$	−1.43169	−	2.07487i	−0.0575911	−	0.0834635i
$619$	−12.7122	+	7.33941i	−0.510948	+	0.294996i	−0.733223	−	0.679988i	$-0.761985\pi$
$619$	−12.7122	+	7.33941i	−0.510948	+	0.294996i	0.222275	+	0.974984i	$0.428652\pi$
$620$		0			0
$621$	−4.42518	+	15.2504i	−0.177577	+	0.611976i
$622$	6.97111			0.279516
$623$	49.7218	+	3.12481i	1.99206	+	0.125193i
$624$	7.12941	−	15.0188i	0.285405	−	0.601232i
$625$		0			0
$626$	−3.59155	−	6.22075i	−0.143547	−	0.248631i
$627$	−5.24897	+	0.422903i	−0.209624	+	0.0168891i
$628$	−5.93571	+	10.2810i	−0.236861	+	0.410255i
$629$	−22.9511			−0.915118
$630$		0			0
$631$	−35.8363			−1.42662			−0.713311	−	0.700848i	$-0.752805\pi$
$631$	−35.8363			−1.42662			−0.713311	+	0.700848i	$0.752805\pi$
$632$	−6.16110	+	10.6713i	−0.245076	+	0.424483i
$633$	−7.76626	+	0.625717i	−0.308681	+	0.0248700i
$634$	−0.508489	−	0.880729i	−0.0201947	−	0.0349782i
$635$		0			0
$636$	18.2256	−	38.3939i	0.722691	−	1.52242i
$637$	−12.9786	+	17.1035i	−0.514230	+	0.677665i
$638$	−7.61971			−0.301667
$639$	−0.442765	−	2.72991i	−0.0175155	−	0.107994i
$640$		0			0
$641$	13.5251	−	7.80872i	0.534209	−	0.308426i	−0.208519	−	0.978018i	$-0.566864\pi$
$641$	13.5251	−	7.80872i	0.534209	−	0.308426i	0.742729	+	0.669592i	$0.233531\pi$
$642$	−5.02139	−	7.27720i	−0.198178	−	0.287208i
$643$	29.3208			1.15630			0.578149	−	0.815931i	$-0.303775\pi$
$643$	29.3208			1.15630			0.578149	+	0.815931i	$0.303775\pi$
$644$	6.65612	+	13.4064i	0.262288	+	0.528285i
$645$		0			0
$646$	1.49031	−	2.58129i	0.0586355	−	0.101560i
$647$	5.77475	−	3.33405i	0.227029	−	0.131075i	−0.382172	−	0.924091i	$-0.624824\pi$
$647$	5.77475	−	3.33405i	0.227029	−	0.131075i	0.609201	+	0.793016i	$0.291490\pi$
$648$	−12.6844	+	4.22574i	−0.498290	+	0.166003i
$649$	−8.72495	−	5.03735i	−0.342484	−	0.197733i
$650$		0			0
$651$	27.5535	+	15.2667i	1.07991	+	0.598350i
$652$		−	30.4404i		−	1.19214i
$653$	−22.0643	+	38.2165i	−0.863444	+	1.49553i	0.00514013	+	0.999987i	$0.498364\pi$
$653$	−22.0643	+	38.2165i	−0.863444	+	1.49553i	−0.868584	+	0.495542i	$0.834969\pi$
$654$	1.66595	−	0.134223i	0.0651437	−	0.00524854i
$655$		0			0
$656$	3.61840	−	6.26726i	0.141275	−	0.244695i
$657$	−0.562222	−	0.689043i	−0.0219344	−	0.0268821i
$658$	−2.73740	−	1.81845i	−0.106715	−	0.0708906i
$659$			7.10057i			0.276599i	0.990390	+	0.138299i	$0.0441636\pi$
$659$			7.10057i			0.276599i	−0.990390	+	0.138299i	$0.955836\pi$
$660$		0			0
$661$	−20.5558	+	11.8679i	−0.799527	+	0.461607i	−0.843306	−	0.537434i	$-0.819394\pi$
$661$	−20.5558	+	11.8679i	−0.799527	+	0.461607i	0.0437789	+	0.999041i	$0.486060\pi$
$662$	5.85170	+	10.1354i	0.227433	+	0.393925i
$663$	28.2526	−	19.4948i	1.09724	−	0.757115i
$664$		−	3.13701i		−	0.121740i
$665$		0			0
$666$	−3.18479	+	2.59862i	−0.123408	+	0.100694i
$667$	20.5646	+	11.8730i	0.796265	+	0.459724i
$668$	−7.71281	+	4.45299i	−0.298418	+	0.172291i
$669$	−12.4419	+	1.00243i	−0.481033	+	0.0387562i
$670$		0			0
$671$	−23.7464			−0.916721
$672$	−9.27956	+	16.7478i	−0.357967	+	0.646061i
$673$			14.7915i			0.570171i	0.958502	+	0.285086i	$0.0920220\pi$
$673$			14.7915i			0.570171i	−0.958502	+	0.285086i	$0.907978\pi$
$674$	0.615374	+	0.355286i	0.0237033	+	0.0136851i
$675$		0			0
$676$	−3.32514	−	5.75931i	−0.127890	−	0.221512i
$677$	−31.6255	−	18.2590i	−1.21547	−	0.701749i	−0.251521	−	0.967852i	$-0.580931\pi$
$677$	−31.6255	−	18.2590i	−1.21547	−	0.701749i	−0.963945	+	0.266103i	$0.914264\pi$
$678$	2.05834	−	4.33609i	0.0790501	−	0.166526i
$679$	14.5531	+	29.3119i	0.558496	+	1.12489i
$680$		0			0
$681$	−2.65595	+	1.83265i	−0.101776	+	0.0702273i
$682$	−3.37035	−	5.83763i	−0.129058	−	0.223534i
$683$	−10.9597	−	18.9828i	−0.419362	−	0.726356i	0.576514	−	0.817088i	$-0.304413\pi$
$683$	−10.9597	−	18.9828i	−0.419362	−	0.726356i	−0.995875	+	0.0907317i	$0.971079\pi$
$684$	1.06333	+	6.55603i	0.0406573	+	0.250676i
$685$		0			0
$686$	4.66682	−	5.40881i	0.178180	−	0.206509i
$687$	−31.4605	−	14.9343i	−1.20029	−	0.569779i
$688$	14.8009	+	8.54532i	0.564280	+	0.325787i
$689$	20.3275	+	35.2082i	0.774414	+	1.34132i
$690$		0			0
$691$	27.2031	+	15.7057i	1.03485	+	0.597473i	0.918371	−	0.395720i	$-0.129505\pi$
$691$	27.2031	+	15.7057i	1.03485	+	0.597473i	0.116482	+	0.993193i	$0.462838\pi$
$692$		−	12.6164i		−	0.479604i
$693$	18.3785	+	8.33049i	0.698143	+	0.316449i
$694$	3.15929			0.119925
$695$		0			0
$696$	1.60561	+	19.9285i	0.0608607	+	0.755388i
$697$	12.9400	−	7.47093i	0.490139	−	0.282982i
$698$	12.1358	+	7.00663i	0.459348	+	0.265205i
$699$	1.16265	−	2.44923i	0.0439755	−	0.0926385i
$700$		0			0
$701$		−	29.6988i		−	1.12171i	−0.827915	−	0.560854i	$-0.810473\pi$
$701$		−	29.6988i		−	1.12171i	0.827915	−	0.560854i	$-0.189527\pi$
$702$	1.71318	−	5.90407i	0.0646598	−	0.222835i
$703$	2.12400	+	3.67888i	0.0801082	+	0.138751i
$704$	−10.2314	+	5.90711i	−0.385611	+	0.222633i
$705$		0			0
$706$		−	2.20435i		−	0.0829617i
$707$	−10.2132	+	15.3744i	−0.384107	+	0.578214i
$708$	−5.44908	+	11.4790i	−0.204789	+	0.431407i
$709$	6.66342	−	11.5414i	0.250250	−	0.433446i	−0.713344	−	0.700814i	$-0.752820\pi$
$709$	6.66342	−	11.5414i	0.250250	−	0.433446i	0.963595	+	0.267368i	$0.0861538\pi$
$710$		0			0
$711$	8.83153	−	23.2646i	0.331208	−	0.872490i
$712$	−13.9864	+	24.2251i	−0.524162	+	0.907875i
$713$			21.0067i			0.786706i
$714$	−9.78888	+	5.88413i	−0.366340	+	0.220208i
$715$		0			0
$716$	−32.0133	−	18.4829i	−1.19639	−	0.690737i
$717$	−0.791790	−	9.82752i	−0.0295700	−	0.367015i
$718$	−1.60534	+	0.926842i	−0.0599107	+	0.0345895i
$719$	−25.5863	+	44.3167i	−0.954207	+	1.65273i	−0.218034	+	0.975941i	$0.569964\pi$
$719$	−25.5863	+	44.3167i	−0.954207	+	1.65273i	−0.736173	+	0.676794i	$0.763369\pi$
$720$		0			0
$721$	9.96323	+	0.626148i	0.371050	+	0.0233190i
$722$	6.77720			0.252221
$723$	−19.0075	+	13.1155i	−0.706896	+	0.487769i
$724$	8.31751	−	4.80211i	0.309118	−	0.178469i
$725$		0			0
$726$	1.72152	+	2.49490i	0.0638917	+	0.0925946i
$727$	51.6371			1.91511			0.957556	−	0.288246i	$-0.0930721\pi$
$727$	51.6371			1.91511			0.957556	+	0.288246i	$0.0930721\pi$
$728$	−5.36085	−	10.7975i	−0.198686	−	0.400182i
$729$	23.9192	−	12.5248i	0.885898	−	0.463880i
$730$		0			0
$731$	17.6436	+	30.5596i	0.652571	+	1.13029i
$732$	2.40525	+	29.8534i	0.0889006	+	1.10341i
$733$	10.9721	−	19.0043i	0.405265	−	0.701940i	−0.589087	−	0.808069i	$-0.700513\pi$
$733$	10.9721	−	19.0043i	0.405265	−	0.701940i	0.994352	+	0.106130i	$0.0338459\pi$
$734$	9.47979			0.349905
$735$		0			0
$736$	−12.7685			−0.470652
$737$	−4.47347	+	7.74829i	−0.164783	+	0.285412i
$738$	0.949725	−	2.50183i	0.0349599	−	0.0920935i
$739$	−19.2874	−	33.4068i	−0.709500	−	1.22889i	−0.965043	−	0.262092i	$-0.915588\pi$
$739$	−19.2874	−	33.4068i	−0.709500	−	1.22889i	0.255543	−	0.966798i	$-0.417746\pi$
$740$		0			0
$741$	−5.73950	−	2.72454i	−0.210846	−	0.100089i
$742$	−6.01548	−	12.1160i	−0.220835	−	0.444793i
$743$	−3.81873			−0.140096			−0.0700478	−	0.997544i	$-0.522315\pi$
$743$	−3.81873			−0.140096			−0.0700478	+	0.997544i	$0.522315\pi$
$744$	−14.5575	+	10.0449i	−0.533703	+	0.368263i
$745$		0			0
$746$	−8.85325	+	5.11143i	−0.324141	+	0.187143i
$747$	1.01424	+	6.25342i	0.0371092	+	0.228801i
$748$	−30.4083			−1.11184
$749$	34.9441	+	2.19609i	1.27683	+	0.0802435i
$750$		0			0
$751$	−10.5271	+	18.2334i	−0.384139	+	0.665348i	−0.991649	−	0.128964i	$-0.958835\pi$
$751$	−10.5271	+	18.2334i	−0.384139	+	0.665348i	0.607511	+	0.794312i	$0.292168\pi$
$752$	−8.72717	+	5.03863i	−0.318247	+	0.183740i
$753$	9.19493	−	0.740824i	0.335082	−	0.0269971i
$754$	−7.96145	−	4.59654i	−0.289939	−	0.167396i
$755$		0			0
$756$	8.61133	−	23.9488i	0.313191	−	0.871010i
$757$			28.6903i			1.04277i	0.853323	+	0.521383i	$0.174584\pi$
$757$			28.6903i			1.04277i	−0.853323	+	0.521383i	$0.825416\pi$
$758$	2.52536	−	4.37405i	0.0917251	−	0.158873i
$759$	1.08067	+	13.4130i	0.0392257	+	0.486860i
$760$		0			0
$761$	−5.34875	+	9.26431i	−0.193892	+	0.335831i	−0.946537	−	0.322596i	$-0.895444\pi$
$761$	−5.34875	+	9.26431i	−0.193892	+	0.335831i	0.752645	+	0.658427i	$0.228778\pi$
$762$	−6.75769	−	3.20788i	−0.244805	−	0.116209i
$763$	−3.66234	+	5.51308i	−0.132585	+	0.199587i
$764$			15.9963i			0.578726i
$765$		0			0
$766$	−5.66753	+	3.27215i	−0.204776	+	0.118228i
$767$	−6.07750	−	10.5265i	−0.219446	−	0.380092i
$768$	5.29186	+	7.66918i	0.190953	+	0.276738i
$769$			38.6874i			1.39510i	0.716535	+	0.697551i	$0.245727\pi$
$769$			38.6874i			1.39510i	−0.716535	+	0.697551i	$0.754273\pi$
$770$		0			0
$771$	10.1707	+	4.82802i	0.366288	+	0.173877i
$772$	38.1114	+	22.0036i	1.37166	+	0.791928i
$773$	−19.8212	+	11.4438i	−0.712918	+	0.411603i	−0.812141	−	0.583462i	$-0.801698\pi$
$773$	−19.8212	+	11.4438i	−0.712918	+	0.411603i	0.0992225	+	0.995065i	$0.468364\pi$
$774$	5.90838	+	2.24290i	0.212372	+	0.0806193i
$775$		0			0
$776$	−18.3748			−0.659618
$777$	−0.286988	−	16.2751i	−0.0102956	−	0.583867i
$778$		−	0.950743i		−	0.0340858i
$779$	−2.39507	−	1.38279i	−0.0858121	−	0.0495437i
$780$		0			0
$781$	−1.17180	−	2.02961i	−0.0419302	−	0.0726252i
$782$	−6.59610	−	3.80826i	−0.235876	−	0.136183i
$783$	−9.64387	−	39.2070i	−0.344644	−	1.40114i
$784$	−8.49163	−	20.1930i	−0.303272	−	0.721180i
$785$		0			0
$786$	−5.94342	−	8.61345i	−0.211995	−	0.307232i
$787$	16.2597	+	28.1627i	0.579597	+	1.00389i	0.995525	+	0.0944937i	$0.0301232\pi$
$787$	16.2597	+	28.1627i	0.579597	+	1.00389i	−0.415929	+	0.909397i	$0.636543\pi$
$788$	−10.8151	−	18.7323i	−0.385272	−	0.667311i
$789$	14.5847	+	21.1368i	0.519230	+	0.752489i
$790$		0			0
$791$	8.45267	+	17.0249i	0.300542	+	0.605335i
$792$	−8.77834	+	7.16265i	−0.311925	+	0.254514i
$793$	−24.8115	−	14.3249i	−0.881081	−	0.508692i
$794$	−0.646809	−	1.12031i	−0.0229544	−	0.0397582i
$795$		0			0
$796$	22.6480	+	13.0758i	0.802736	+	0.463460i
$797$			31.9080i			1.13024i	0.825009	+	0.565120i	$0.191170\pi$
$797$			31.9080i			1.13024i	−0.825009	+	0.565120i	$0.808830\pi$
$798$	1.84909	+	1.02454i	0.0654571	+	0.0362682i
$799$	−20.8066			−0.736084
$800$		0			0
$801$	20.0485	−	52.8131i	0.708380	−	1.86606i
$802$	−2.08677	+	1.20480i	−0.0736865	+	0.0425429i
$803$	−0.652648	−	0.376807i	−0.0230315	−	0.0132972i
$804$	10.1941	+	4.83912i	0.359516	+	0.170663i
$805$		0			0
$806$		−	8.13258i		−	0.286458i
$807$	−24.2071	−	35.0819i	−0.852129	−	1.23494i
$808$	−5.18176	−	8.97507i	−0.182294	−	0.315742i
$809$	17.9862	−	10.3843i	0.632360	−	0.365093i	−0.149305	−	0.988791i	$-0.547704\pi$
$809$	17.9862	−	10.3843i	0.632360	−	0.365093i	0.781666	+	0.623698i	$0.214370\pi$
$810$		0			0
$811$			5.77041i			0.202627i	0.994855	+	0.101313i	$0.0323044\pi$
$811$			5.77041i			0.202627i	−0.994855	+	0.101313i	$0.967696\pi$
$812$	−31.7005	−	21.0586i	−1.11247	−	0.739013i
$813$	−5.96450	−	2.83135i	−0.209184	−	0.0992998i
$814$	−1.74162	+	3.01657i	−0.0610437	+	0.105731i
$815$		0			0
$816$	2.81258	+	34.9090i	0.0984599	+	1.22206i
$817$	3.26564	−	5.65626i	0.114250	−	0.197887i
$818$			4.54968i			0.159076i
$819$	14.1775	+	19.7909i	0.495402	+	0.691548i
$820$		0			0
$821$	−12.7908	−	7.38477i	−0.446402	−	0.257730i	0.259907	−	0.965634i	$-0.416308\pi$
$821$	−12.7908	−	7.38477i	−0.446402	−	0.257730i	−0.706309	+	0.707903i	$0.749641\pi$
$822$	3.88141	−	0.312720i	0.135380	−	0.0109074i
$823$	−23.7385	+	13.7054i	−0.827472	+	0.477741i	−0.852986	−	0.521933i	$-0.825211\pi$
$823$	−23.7385	+	13.7054i	−0.827472	+	0.477741i	0.0255145	+	0.999674i	$0.491878\pi$
$824$	−2.80258	+	4.85422i	−0.0976326	+	0.169105i
$825$		0			0
$826$	1.79851	+	3.62245i	0.0625781	+	0.126041i
$827$	−27.6521			−0.961557			−0.480779	−	0.876842i	$-0.659646\pi$
$827$	−27.6521			−0.961557			−0.480779	+	0.876842i	$0.659646\pi$
$828$	16.7530	−	2.71717i	0.582205	−	0.0944281i
$829$	18.6252	−	10.7533i	0.646880	−	0.373476i	−0.140380	−	0.990098i	$-0.544832\pi$
$829$	18.6252	−	10.7533i	0.646880	−	0.373476i	0.787260	+	0.616621i	$0.211499\pi$
$830$		0			0
$831$	26.7663	−	18.4692i	0.928512	−	0.640688i
$832$	−14.2537			−0.494158
$833$	5.66257	−	44.8733i	0.196196	−	1.55477i
$834$	7.26469	+	3.44855i	0.251556	+	0.119414i
$835$		0			0
$836$	2.81414	+	4.87423i	0.0973289	+	0.168579i
$837$	25.7716	−	24.7304i	0.890798	−	0.854809i
$838$	2.32246	−	4.02262i	0.0802281	−	0.138959i
$839$	26.4538			0.913286			0.456643	−	0.889650i	$-0.349052\pi$
$839$	26.4538			0.913286			0.456643	+	0.889650i	$0.349052\pi$
$840$		0			0
$841$	−31.3775			−1.08198
$842$	−2.20375	+	3.81701i	−0.0759463	+	0.131543i
$843$	3.29504	+	40.8972i	0.113487	+	1.40858i
$844$	4.16373	+	7.21179i	0.143321	+	0.248240i
$845$		0			0
$846$	−2.88721	+	2.35581i	−0.0992644	+	0.0809944i
$847$	−11.9802	−	0.752905i	−0.411644	−	0.0258701i
$848$	−41.4797			−1.42442
$849$	−4.96182	−	7.19088i	−0.170289	−	0.246790i
$850$		0			0
$851$	9.40081	−	5.42756i	0.322256	−	0.186054i
$852$	−2.43288	+	1.67873i	−0.0833492	+	0.0575123i
$853$	−6.05997			−0.207490			−0.103745	−	0.994604i	$-0.533083\pi$
$853$	−6.05997			−0.207490			−0.103745	+	0.994604i	$0.533083\pi$
$854$	7.94034	+	5.27477i	0.271713	+	0.180499i
$855$		0			0
$856$	−9.82952	+	17.0252i	−0.335966	+	0.581910i
$857$	8.95449	−	5.16988i	0.305880	−	0.176600i	−0.339202	−	0.940714i	$-0.610157\pi$
$857$	8.95449	−	5.16988i	0.305880	−	0.176600i	0.645081	+	0.764114i	$0.276824\pi$
$858$	−0.418372	−	5.19273i	−0.0142830	−	0.177277i
$859$	30.7393	+	17.7473i	1.04881	+	0.605531i	0.922316	−	0.386436i	$-0.126294\pi$
$859$	30.7393	+	17.7473i	1.04881	+	0.605531i	0.126495	+	0.991967i	$0.459627\pi$
$860$		0			0
$861$	5.45962	+	9.08266i	0.186063	+	0.309536i
$862$			12.5758i			0.428334i
$863$	−7.57049	+	13.1125i	−0.257702	+	0.446354i	−0.965626	−	0.259935i	$-0.916299\pi$
$863$	−7.57049	+	13.1125i	−0.257702	+	0.446354i	0.707924	+	0.706289i	$0.249632\pi$
$864$	15.0319	+	15.6648i	0.511395	+	0.532926i
$865$		0			0
$866$	−0.844064	+	1.46196i	−0.0286824	+	0.0496795i
$867$	−18.3823	+	38.7240i	−0.624295	+	1.31514i
$868$	2.11169	−	33.6011i	0.0716756	−	1.14050i
$869$		−	21.0874i		−	0.715342i
$870$		0			0
$871$	−9.34821	+	5.39719i	−0.316752	+	0.182877i
$872$	−1.85812	−	3.21835i	−0.0629238	−	0.108987i
$873$	36.6290	−	5.94087i	1.23970	−	0.201068i
$874$			1.40974i			0.0476852i
$875$		0			0
$876$	−0.407605	+	0.858658i	−0.0137717	+	0.0290114i
$877$	−16.9650	−	9.79476i	−0.572868	−	0.330745i	0.185426	−	0.982658i	$-0.440633\pi$
$877$	−16.9650	−	9.79476i	−0.572868	−	0.330745i	−0.758294	+	0.651913i	$0.773967\pi$
$878$	−4.95339	+	2.85984i	−0.167169	+	0.0965150i
$879$	−0.875515	−	10.8667i	−0.0295304	−	0.366524i
$880$		0			0
$881$	28.7481			0.968548			0.484274	−	0.874917i	$-0.339084\pi$
$881$	28.7481			0.968548			0.484274	+	0.874917i	$0.339084\pi$
$882$	−4.29498	−	6.86795i	−0.144619	−	0.231256i
$883$		−	5.77550i		−	0.194361i	−0.995267	−	0.0971805i	$-0.969018\pi$
$883$		−	5.77550i		−	0.194361i	0.995267	−	0.0971805i	$-0.0309824\pi$
$884$	−31.7721	−	18.3437i	−1.06861	−	0.616964i
$885$		0			0
$886$	3.06896	+	5.31559i	0.103104	+	0.178581i
$887$	−11.3781	−	6.56917i	−0.382041	−	0.220571i	0.296665	−	0.954982i	$-0.404125\pi$
$887$	−11.3781	−	6.56917i	−0.382041	−	0.220571i	−0.678706	+	0.734410i	$0.737459\pi$
$888$	8.25651	+	3.91937i	0.277070	+	0.131525i
$889$	26.5329	−	13.1733i	0.889884	−	0.441818i
$890$		0			0
$891$	15.1832	−	17.1164i	0.508657	−	0.573422i
$892$	6.67049	+	11.5536i	0.223345	+	0.386844i
$893$	1.92554	+	3.33514i	0.0644358	+	0.111606i
$894$	10.2817	−	7.09457i	0.343873	−	0.237278i
$895$		0			0
$896$	26.7986	+	1.68418i	0.895278	+	0.0562646i
$897$	−6.96215	+	14.6664i	−0.232460	+	0.489698i
$898$	11.7547	+	6.78657i	0.392259	+	0.226471i
$899$	−26.7062	−	46.2565i	−0.890702	−	1.54274i
$900$		0			0
$901$	−74.1693	−	42.8217i	−2.47094	−	1.42660i
$902$		−	2.26770i		−	0.0755061i
$903$	−21.4499	+	12.8936i	−0.713807	+	0.429072i
$904$	−10.6724			−0.354959
$905$		0			0
$906$	3.96280	−	0.319278i	0.131655	−	0.0106073i
$907$	−5.34345	+	3.08504i	−0.177426	+	0.102437i	−0.586083	−	0.810251i	$-0.699331\pi$
$907$	−5.34345	+	3.08504i	−0.177426	+	0.102437i	0.408657	+	0.912688i	$0.365997\pi$
$908$	2.98681	+	1.72444i	0.0991208	+	0.0572274i
$909$	13.2313	+	16.2158i	0.438853	+	0.537845i
$910$		0			0
$911$		−	53.7961i		−	1.78234i	−0.453665	−	0.891172i	$-0.649884\pi$
$911$		−	53.7961i		−	1.78234i	0.453665	−	0.891172i	$-0.350116\pi$
$912$	5.33536	−	3.68149i	0.176672	−	0.121906i
$913$	2.68424	+	4.64924i	0.0888354	+	0.153867i
$914$	4.69648	−	2.71151i	0.155346	−	0.0896888i
$915$		0			0
$916$			37.2211i			1.22982i
$917$	41.3606	+	2.59934i	1.36585	+	0.0858379i
$918$	3.09327	+	12.5756i	0.102093	+	0.415058i
$919$	−0.310140	+	0.537179i	−0.0102306	+	0.0177199i	−0.871095	−	0.491114i	$-0.836590\pi$
$919$	−0.310140	+	0.537179i	−0.0102306	+	0.0177199i	0.860865	+	0.508834i	$0.169923\pi$
$920$		0			0
$921$	−27.6918	+	2.23109i	−0.912475	+	0.0735169i
$922$	2.60678	−	4.51508i	0.0858498	−	0.148696i
$923$		−	2.82752i		−	0.0930688i
$924$	−0.380236	−	21.5633i	−0.0125088	−	0.709380i
$925$		0			0
$926$	5.95888	+	3.44036i	0.195821	+	0.113057i
$927$	4.01732	−	10.5827i	0.131946	−	0.347580i
$928$	28.1161	−	16.2328i	0.922955	−	0.532868i
$929$	−26.4805	+	45.8655i	−0.868796	+	1.50480i	−0.00556817	+	0.999984i	$0.501772\pi$
$929$	−26.4805	+	45.8655i	−0.868796	+	1.50480i	−0.863228	+	0.504814i	$0.831561\pi$
$930$		0			0
$931$	−7.71688	+	3.24512i	−0.252911	+	0.106355i
$932$	−2.89770			−0.0949174
$933$	17.7777	+	25.7642i	0.582017	+	0.843483i
$934$	−3.06975	+	1.77232i	−0.100445	+	0.0579921i
$935$		0			0
$936$	−13.4929	+	2.18841i	−0.441028	+	0.0715305i
$937$	−0.667265			−0.0217986			−0.0108993	−	0.999941i	$-0.503469\pi$
$937$	−0.667265			−0.0217986			−0.0108993	+	0.999941i	$0.503469\pi$
$938$	3.21696	−	1.59719i	0.105037	−	0.0521500i
$939$	13.8318	−	29.1380i	0.451385	−	0.950884i
$940$		0			0
$941$	12.4842	+	21.6232i	0.406972	+	0.704896i	0.994549	−	0.104272i	$-0.0332514\pi$
$941$	12.4842	+	21.6232i	0.406972	+	0.704896i	−0.587577	+	0.809168i	$0.699918\pi$
$942$	4.27058	−	0.344075i	0.139143	−	0.0112106i
$943$	−3.53352	+	6.12023i	−0.115067	+	0.199302i
$944$	12.4016			0.403638
$945$		0			0
$946$	5.35547			0.174121
$947$	−27.4984	+	47.6286i	−0.893577	+	1.54772i	−0.0580209	+	0.998315i	$0.518479\pi$
$947$	−27.4984	+	47.6286i	−0.893577	+	1.54772i	−0.835556	+	0.549405i	$0.814854\pi$
$948$	−26.5105	+	2.13592i	−0.861022	+	0.0693715i
$949$	−0.454613	−	0.787412i	−0.0147574	−	0.0255605i
$950$		0			0
$951$	1.95830	−	4.12534i	0.0635022	−	0.133773i
$952$	21.1531	+	14.0520i	0.685577	+	0.455428i
$953$	35.8657			1.16180			0.580902	−	0.813974i	$-0.302700\pi$
$953$	35.8657			1.16180			0.580902	+	0.813974i	$0.302700\pi$
$954$	−15.1405	+	2.45564i	−0.490192	+	0.0795044i
$955$		0			0
$956$	−9.12588	+	5.26883i	−0.295152	+	0.170406i
$957$	−19.4318	−	28.1614i	−0.628140	−	0.910327i
$958$	7.28288			0.235299
$959$	−8.53270	+	12.8447i	−0.275535	+	0.414775i
$960$		0			0
$961$	8.12541	−	14.0736i	0.262110	−	0.453988i
$962$	−3.63946	+	2.10124i	−0.117341	+	0.0677468i
$963$	14.0900	−	37.1166i	0.454042	−	1.19607i
$964$	21.3753	+	12.3410i	0.688451	+	0.397478i
$965$		0			0
$966$	2.61805	−	4.72507i	0.0842343	−	0.152027i
$967$			11.8780i			0.381971i	0.981593	+	0.190986i	$0.0611684\pi$
$967$			11.8780i			0.381971i	−0.981593	+	0.190986i	$0.938832\pi$
$968$	3.36994	−	5.83690i	0.108314	−	0.187605i
$969$	13.3407	−	1.07484i	0.428564	−	0.0345289i
$970$		0			0
$971$	−2.61333	+	4.52642i	−0.0838658	+	0.145260i	−0.904907	−	0.425609i	$-0.860060\pi$
$971$	−2.61333	+	4.52642i	−0.0838658	+	0.145260i	0.821042	+	0.570868i	$0.193393\pi$
$972$	−23.0562	−	17.3542i	−0.739528	−	0.556637i
$973$	−28.5235	+	14.1616i	−0.914422	+	0.454001i
$974$		−	2.01940i		−	0.0647056i
$975$		0			0
$976$	25.3148	−	14.6155i	0.810308	−	0.467831i
$977$	−8.95992	−	15.5190i	−0.286653	−	0.496498i	0.686355	−	0.727266i	$-0.259209\pi$
$977$	−8.95992	−	15.5190i	−0.286653	−	0.496498i	−0.973009	+	0.230768i	$0.925876\pi$
$978$	−9.04227	+	6.23931i	−0.289140	+	0.199511i
$979$		−	47.8708i		−	1.52996i
$980$		0			0
$981$	4.74457	+	5.81481i	0.151482	+	0.185653i
$982$	−6.52074	−	3.76475i	−0.208085	−	0.120138i
$983$	36.2715	−	20.9414i	1.15688	−	0.667926i	0.206328	−	0.978483i	$-0.433849\pi$
$983$	36.2715	−	20.9414i	1.15688	−	0.667926i	0.950555	+	0.310556i	$0.100515\pi$
$984$	−5.93092	+	0.477846i	−0.189071	+	0.0152332i
$985$		0			0
$986$	19.3661			0.616742
$987$	−0.260172	−	14.7544i	−0.00828138	−	0.469639i
$988$			6.79044i			0.216033i
$989$	−14.4537	−	8.34485i	−0.459601	−	0.265351i
$990$		0			0
$991$	−4.88415	−	8.45960i	−0.155150	−	0.268728i	0.777964	−	0.628309i	$-0.216253\pi$
$991$	−4.88415	−	8.45960i	−0.155150	−	0.268728i	−0.933114	+	0.359581i	$0.882919\pi$
$992$	24.8726	+	14.3602i	0.789706	+	0.455937i
$993$	−22.5361	+	47.4744i	−0.715162	+	1.50656i
$994$	−0.0590093	+	0.938951i	−0.00187166	+	0.0297817i
$995$		0			0
$996$	5.57301	−	3.84547i	0.176588	−	0.121848i
$997$	−17.5870	−	30.4616i	−0.556986	−	0.964728i	−0.997746	−	0.0671032i	$-0.978624\pi$
$997$	−17.5870	−	30.4616i	−0.556986	−	0.964728i	0.440760	−	0.897625i	$-0.354709\pi$
$998$	−7.06563	−	12.2380i	−0.223659	−	0.387388i
$999$	−17.7260	−	5.14353i	−0.560825	−	0.162734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.e.299.4		16
3.2	odd	2		525.2.q.f.299.5		16
5.2	odd	4		525.2.t.f.26.3		8
5.3	odd	4		105.2.s.d.26.2	yes	8
5.4	even	2	inner	525.2.q.e.299.5		16
7.3	odd	6		525.2.q.f.374.4		16
15.2	even	4		525.2.t.g.26.2		8
15.8	even	4		105.2.s.c.26.3	✓	8
15.14	odd	2		525.2.q.f.299.4		16
21.17	even	6	inner	525.2.q.e.374.5		16
35.3	even	12		105.2.s.c.101.3	yes	8
35.13	even	4		735.2.s.l.656.2		8
35.17	even	12		525.2.t.g.101.2		8
35.18	odd	12		735.2.s.k.521.3		8
35.23	odd	12		735.2.b.c.146.4		8
35.24	odd	6		525.2.q.f.374.5		16
35.33	even	12		735.2.b.d.146.4		8
105.17	odd	12		525.2.t.f.101.3		8
105.23	even	12		735.2.b.d.146.5		8
105.38	odd	12		105.2.s.d.101.2	yes	8
105.53	even	12		735.2.s.l.521.2		8
105.59	even	6	inner	525.2.q.e.374.4		16
105.68	odd	12		735.2.b.c.146.5		8
105.83	odd	4		735.2.s.k.656.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.3	✓	8	15.8	even	4
105.2.s.c.101.3	yes	8	35.3	even	12
105.2.s.d.26.2	yes	8	5.3	odd	4
105.2.s.d.101.2	yes	8	105.38	odd	12
525.2.q.e.299.4		16	1.1	even	1	trivial
525.2.q.e.299.5		16	5.4	even	2	inner
525.2.q.e.374.4		16	105.59	even	6	inner
525.2.q.e.374.5		16	21.17	even	6	inner
525.2.q.f.299.4		16	15.14	odd	2
525.2.q.f.299.5		16	3.2	odd	2
525.2.q.f.374.4		16	7.3	odd	6
525.2.q.f.374.5		16	35.24	odd	6
525.2.t.f.26.3		8	5.2	odd	4
525.2.t.f.101.3		8	105.17	odd	12
525.2.t.g.26.2		8	15.2	even	4
525.2.t.g.101.2		8	35.17	even	12
735.2.b.c.146.4		8	35.23	odd	12
735.2.b.c.146.5		8	105.68	odd	12
735.2.b.d.146.4		8	35.33	even	12
735.2.b.d.146.5		8	105.23	even	12
735.2.s.k.521.3		8	35.18	odd	12
735.2.s.k.656.3		8	105.83	odd	4
735.2.s.l.521.2		8	105.53	even	12
735.2.s.l.656.2		8	35.13	even	4

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.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.192865 + 0.334053i) q^{2} +(-1.72646 + 0.139098i) q^{3} +(0.925606 + 1.60320i) q^{4} +(0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} -1.48553 q^{8} +(2.96130 - 0.480295i) q^{9} +O(q^{10})\)	\(q+(-0.192865 + 0.334053i) q^{2} +(-1.72646 + 0.139098i) q^{3} +(0.925606 + 1.60320i) q^{4} +(0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} -1.48553 q^{8} +(2.96130 - 0.480295i) q^{9} +(2.20164 - 1.27112i) q^{11} +(-1.82102 - 2.63910i) q^{12} +3.06718 q^{13} +(-1.01854 - 0.0640110i) q^{14} +(-1.56470 + 2.71015i) q^{16} +(-5.59565 + 3.23065i) q^{17} +(-0.410689 + 1.08186i) q^{18} +(1.03570 + 0.597960i) q^{19} +(-2.36090 - 3.92761i) q^{21} +0.980620i q^{22} +(1.52800 - 2.64657i) q^{23} +(2.56470 - 0.206635i) q^{24} +(-0.591553 + 1.02460i) q^{26} +(-5.04575 + 1.24112i) q^{27} +(-2.71015 + 4.07971i) q^{28} +7.77029i q^{29} +(-5.95299 + 3.43696i) q^{31} +(-2.08909 - 3.61840i) q^{32} +(-3.62423 + 2.50078i) q^{33} -2.49232i q^{34} +(3.51101 + 4.30299i) q^{36} +(3.07619 + 1.77604i) q^{37} +(-0.399500 + 0.230652i) q^{38} +(-5.29536 + 0.426640i) q^{39} -2.31252 q^{41} +(1.76737 - 0.0311648i) q^{42} -5.46130i q^{43} +(4.07571 + 2.35311i) q^{44} +(0.589395 + 1.02086i) q^{46} +(2.78876 + 1.61009i) q^{47} +(2.32442 - 4.89660i) q^{48} +(-4.23143 + 5.57629i) q^{49} +(9.21127 - 6.35593i) q^{51} +(2.83900 + 4.91730i) q^{52} +(6.62740 + 11.4790i) q^{53} +(0.558552 - 1.92492i) q^{54} +(-1.74781 - 3.52034i) q^{56} +(-1.87126 - 0.888288i) q^{57} +(-2.59569 - 1.49862i) q^{58} +(-1.98146 - 3.43199i) q^{59} +(-8.08933 - 4.67038i) q^{61} -2.65148i q^{62} +(4.62232 + 6.45245i) q^{63} -4.64717 q^{64} +(-0.136403 - 1.69300i) q^{66} +(-3.04782 + 1.75966i) q^{67} +(-10.3587 - 5.98062i) q^{68} +(-2.26989 + 4.78173i) q^{69} -0.921861i q^{71} +(-4.39911 + 0.713493i) q^{72} +(-0.148218 - 0.256722i) q^{73} +(-1.18658 + 0.685073i) q^{74} +2.21390i q^{76} +(5.60260 + 3.72180i) q^{77} +(0.878771 - 1.85121i) q^{78} +(4.14741 - 7.18352i) q^{79} +(8.53863 - 2.84460i) q^{81} +(0.446004 - 0.772502i) q^{82} +2.11171i q^{83} +(4.11147 - 7.42041i) q^{84} +(1.82436 + 1.05330i) q^{86} +(-1.08084 - 13.4151i) q^{87} +(-3.27061 + 1.88829i) q^{88} +(9.41507 - 16.3074i) q^{89} +(3.60871 + 7.26845i) q^{91} +5.65729 q^{92} +(9.79951 - 6.76182i) q^{93} +(-1.07571 + 0.621062i) q^{94} +(4.11003 + 5.95643i) q^{96} +12.3692 q^{97} +(-1.04668 - 2.48899i) q^{98} +(5.90923 - 4.82161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9	\( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9} - 24 q^{14} + 2 q^{16} - 18 q^{19} - 44 q^{21} + 14 q^{24} + 12 q^{26} - 42 q^{31} + 18 q^{36} - 30 q^{39} + 60 q^{41} - 14 q^{46} + 8 q^{49} + 24 q^{51} - 14 q^{54} + 42 q^{56} - 24 q^{59} + 30 q^{61} - 76 q^{64} - 32 q^{66} - 26 q^{69} + 108 q^{74} + 58 q^{79} + 56 q^{81} + 102 q^{84} - 18 q^{86} - 6 q^{89} - 6 q^{91} + 48 q^{94} - 84 q^{96} + 68 q^{99}+O(q^{100}) \) 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9 - 24 * q^14 + 2 * q^16 - 18 * q^19 - 44 * q^21 + 14 * q^24 + 12 * q^26 - 42 * q^31 + 18 * q^36 - 30 * q^39 + 60 * q^41 - 14 * q^46 + 8 * q^49 + 24 * q^51 - 14 * q^54 + 42 * q^56 - 24 * q^59 + 30 * q^61 - 76 * q^64 - 32 * q^66 - 26 * q^69 + 108 * q^74 + 58 * q^79 + 56 * q^81 + 102 * q^84 - 18 * q^86 - 6 * q^89 - 6 * q^91 + 48 * q^94 - 84 * q^96 + 68 * q^99

Introduction

L-functions

Modular forms

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Database

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