LMFDB - Embedded newform 525.2.q.e.299.5

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			299.5
Root			$-0.192865 + 0.334053i$ of defining polynomial
Character	$\chi$	$=$	525.299
Dual form			525.2.q.e.374.5

$q$-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	−0.789746	−	0.613434i	$-0.789788\pi$
$2$	0.192865	−	0.334053i	0.136376	−	0.236211i	0.926122	+	0.377223i	$0.123121\pi$
$3$	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	$-0.639846\pi$
$13$	−3.06718			−0.850683			−0.425342	+	0.905033i	$0.639846\pi$
$14$	−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	0.367907	−	0.929863i	$-0.380074\pi$
$17$	5.59565	−	3.23065i	1.35715	−	0.783548i	0.989238	+	0.146314i	$0.0467411\pi$
$18$	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	−0.980198	−	0.198019i	$-0.936549\pi$
$23$	−1.52800	+	2.64657i	−0.318609	+	0.551848i	0.661589	+	0.749867i	$0.269882\pi$
$24$	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	0.225351	−	0.974278i	$-0.427647\pi$
$37$	−3.07619	−	1.77604i	−0.505722	−	0.291979i	−0.731074	+	0.682299i	$0.760980\pi$
$38$	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	$0.136716\pi$
$43$			5.46130i			0.832841i	−0.909172	+	0.416420i	$0.863284\pi$
$44$	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	0.282624	−	0.959231i	$-0.408795\pi$
$47$	−2.78876	−	1.61009i	−0.406782	−	0.234856i	−0.689406	+	0.724375i	$0.742129\pi$
$48$	−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	$-0.802484\pi$
$53$	−6.62740	−	11.4790i	−0.910344	−	1.57676i	−0.0967651	−	0.995307i	$-0.530850\pi$
$54$	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	−0.302134	−	0.953265i	$-0.597699\pi$
$67$	3.04782	−	1.75966i	0.372350	−	0.214977i	0.674485	+	0.738289i	$0.264366\pi$
$68$	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	0.874569	−	0.484901i	$-0.161144\pi$
$73$	0.148218	+	0.256722i	0.0173477	+	0.0300470i	−0.857221	+	0.514948i	$0.827811\pi$
$74$	−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	$-0.963026\pi$
$83$		−	2.11171i		−	0.231790i	0.993261	−	0.115895i	$-0.0369737\pi$
$84$	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	$-0.716106\pi$
$97$	−12.3692			−1.25590			−0.627952	+	0.778252i	$0.716106\pi$
$98$	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	−0.943876	−	0.330299i	$-0.892850\pi$
$103$	−1.88659	+	3.26767i	−0.185891	+	0.321973i	0.757985	+	0.652272i	$0.226184\pi$
$104$	−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	$0.387597\pi$
$107$	−6.61684	+	11.4607i	−0.639674	+	1.10795i	−0.985504	+	0.169651i	$0.945736\pi$
$108$	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	$-0.609723\pi$
$113$	−7.18425			−0.675837			−0.337919	+	0.941175i	$0.609723\pi$
$114$	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	$0.165478\pi$
$127$			11.1965i			0.993528i	−0.867886	+	0.496764i	$0.834522\pi$
$128$	−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	0.714265	−	0.699875i	$-0.246761\pi$
$137$	−2.91420	−	5.04755i	−0.248977	−	0.431241i	−0.963242	+	0.268634i	$0.913428\pi$
$138$	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	0.709241	−	0.704966i	$-0.249038\pi$
$157$	−3.20639	−	5.55364i	−0.255898	−	0.443228i	−0.965139	+	0.261738i	$0.915704\pi$
$158$	−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	0.940223	−	0.340560i	$-0.110617\pi$
$163$	14.2405	+	8.22174i	1.11540	+	0.643976i	0.175177	+	0.984537i	$0.443950\pi$
$164$	−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	$-0.940402\pi$
$167$		−	4.81089i		−	0.372278i	0.982523	−	0.186139i	$-0.0595975\pi$
$168$	−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	0.707294	−	0.706919i	$-0.249916\pi$
$173$	5.90215	+	3.40761i	0.448732	+	0.259075i	−0.258563	+	0.965994i	$0.583249\pi$
$174$	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	−0.999789	−	0.0205300i	$-0.993465\pi$
$193$	−20.5873	+	11.8861i	−1.48190	+	0.855578i	−0.482115	+	0.876108i	$0.660131\pi$
$194$	−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	$-0.363348\pi$
$197$	11.6843			0.832475			0.416238	+	0.909256i	$0.363348\pi$
$198$	−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	$-0.577572\pi$
$223$	−7.20662			−0.482591			−0.241296	+	0.970452i	$0.577572\pi$
$224$	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	−0.552587	−	0.833455i	$-0.686359\pi$
$227$	−1.61344	+	0.931518i	−0.107087	+	0.0618270i	0.445500	+	0.895282i	$0.353026\pi$
$228$	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	−0.839250	−	0.543746i	$-0.817005\pi$
$233$	0.782650	−	1.35559i	0.0512731	−	0.0888077i	0.890523	+	0.454938i	$0.150339\pi$
$234$	−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	0.665188	−	0.746676i	$-0.268352\pi$
$257$	5.62922	+	3.25003i	0.351141	+	0.202731i	−0.314047	+	0.949408i	$0.601685\pi$
$258$	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	0.998807	−	0.0488236i	$-0.0155472\pi$
$263$	7.41326	+	12.8401i	0.457121	+	0.791757i	−0.541686	+	0.840581i	$0.682214\pi$
$264$	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	0.0756131	−	0.997137i	$-0.475909\pi$
$277$	16.2600	−	9.38769i	0.976966	−	0.564052i	0.901353	+	0.433086i	$0.142575\pi$
$278$	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	0.781278	−	0.624184i	$-0.214568\pi$
$283$	−2.52204	−	4.36831i	−0.149920	−	0.259669i	−0.931198	+	0.364515i	$0.881235\pi$
$284$	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	$-0.941142\pi$
$293$		−	6.29421i		−	0.367712i	0.982953	−	0.183856i	$-0.0588580\pi$
$294$	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	$-0.651332\pi$
$307$	−16.0397			−0.915432			−0.457716	+	0.889099i	$0.651332\pi$
$308$	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	$-0.656916\pi$
$313$	9.31104	−	16.1272i	0.526291	−	0.911563i	0.999531	−	0.0306290i	$-0.00975103\pi$
$314$	−2.47361			−0.139594
$315$		0			0
$316$	15.3555			0.863812
$317$	1.31825	−	2.28327i	0.0740402	−	0.128241i	−0.826628	−	0.562748i	$-0.809744\pi$
$317$	1.31825	−	2.28327i	0.0740402	−	0.128241i	0.900669	+	0.434507i	$0.143077\pi$
$318$	−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	$0.0159776\pi$
$337$			1.84215i			0.100348i	−0.998740	+	0.0501741i	$0.984022\pi$
$338$	−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	0.954759	−	0.297379i	$-0.0961126\pi$
$347$	4.09520	+	7.09309i	0.219842	+	0.380777i	−0.734918	+	0.678156i	$0.762779\pi$
$348$	−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	−0.362477	−	0.931993i	$-0.618069\pi$
$353$	4.94910	−	2.85736i	0.263414	−	0.152082i	0.625891	+	0.779911i	$0.284735\pi$
$354$	−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	$0.0549932\pi$
$367$	12.2881	+	21.2836i	0.641433	+	1.11099i	−0.343680	+	0.939087i	$0.611673\pi$
$368$	−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	−0.230461	−	0.973082i	$-0.574023\pi$
$373$	−22.9519	−	13.2513i	−1.18840	−	0.686126i	−0.957944	+	0.286956i	$0.907357\pi$
$374$	−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	0.0751982	−	0.997169i	$-0.476041\pi$
$383$	−14.6930	−	8.48299i	−0.750776	−	0.433461i	−0.825974	+	0.563708i	$0.809374\pi$
$384$	−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	−0.820874	−	0.571109i	$-0.806513\pi$
$397$	1.67684	−	2.90437i	0.0841582	−	0.145766i	0.905032	+	0.425343i	$0.139847\pi$
$398$		−	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	$-0.533535\pi$
$433$	−4.37644			−0.210318			−0.105159	+	0.994455i	$0.533535\pi$
$434$	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	−0.990773	−	0.135533i	$-0.956725\pi$
$443$	−7.95622	+	13.7806i	−0.378011	+	0.654735i	0.612762	+	0.790268i	$0.290059\pi$
$444$	−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	0.756968	−	0.653451i	$-0.226680\pi$
$457$	12.1755	+	7.02954i	0.569547	+	0.328828i	−0.187421	+	0.982280i	$0.560013\pi$
$458$	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	$0.136045\pi$
$463$			17.8381i			0.829009i	−0.910047	+	0.414504i	$0.863955\pi$
$464$	−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	0.304435	−	0.952533i	$-0.401532\pi$
$467$	−7.95827	−	4.59471i	−0.368265	−	0.212618i	−0.672700	+	0.739915i	$0.734866\pi$
$468$	−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	−0.393746	−	0.919219i	$-0.628821\pi$
$487$	4.53386	−	2.61762i	0.205449	−	0.118616i	0.599194	+	0.800604i	$0.295488\pi$
$488$	−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	$0.362170\pi$
$503$			40.7156i			1.81542i	−0.419602	+	0.907708i	$0.637830\pi$
$504$	−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	−0.914214	−	0.405232i	$-0.867191\pi$
$523$	−2.42791	+	4.20527i	−0.106165	+	0.183884i	0.808048	+	0.589116i	$0.200524\pi$
$524$	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	$0.283726\pi$
$547$			36.3881i			1.55584i	−0.628362	+	0.777921i	$0.716274\pi$
$548$	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	0.621157	−	0.783686i	$-0.286663\pi$
$557$	−8.68779	−	15.0477i	−0.368114	−	0.637591i	−0.989271	+	0.146095i	$0.953330\pi$
$558$	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	−0.0672735	−	0.997735i	$-0.521430\pi$
$563$	18.1078	−	10.4546i	0.763153	−	0.440607i	0.830427	+	0.557128i	$0.188097\pi$
$564$	−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	0.510635	−	0.859797i	$-0.329410\pi$
$577$	−11.7531	−	20.3570i	−0.489289	−	0.847473i	−0.999924	+	0.0123245i	$0.996077\pi$
$578$	−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	$0.168439\pi$
$587$			24.4613i			1.00963i	−0.863229	+	0.504813i	$0.831561\pi$
$588$	−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	0.565199	−	0.824955i	$-0.308799\pi$
$593$	3.24770	+	1.87506i	0.133367	+	0.0769995i	−0.431832	+	0.901954i	$0.642133\pi$
$594$	−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	$-0.474552\pi$
$607$	22.2522	−	38.5420i	0.903190	−	1.56437i	0.823329	−	0.567565i	$-0.192114\pi$
$608$			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	0.414705	−	0.909956i	$-0.363885\pi$
$613$	34.9125	−	20.1567i	1.41010	−	0.814123i	0.995397	+	0.0958333i	$0.0305516\pi$
$614$	−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	$-0.225384\pi$
$617$	37.7372			1.51924			0.759621	+	0.650366i	$0.225384\pi$
$618$	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	$-0.696225\pi$
$643$	−29.3208			−1.15630			−0.578149	+	0.815931i	$0.696225\pi$
$644$	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	−0.609201	−	0.793016i	$-0.708510\pi$
$647$	−5.77475	+	3.33405i	−0.227029	+	0.131075i	0.382172	+	0.924091i	$0.375176\pi$
$648$	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	$-0.501636\pi$
$653$	22.0643	−	38.2165i	0.863444	−	1.49553i	0.868584	−	0.495542i	$-0.165031\pi$
$654$	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	$-0.907978\pi$
$673$		−	14.7915i		−	0.570171i	0.958502	−	0.285086i	$-0.0920220\pi$
$674$	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	0.963945	−	0.266103i	$-0.0857360\pi$
$677$	31.6255	+	18.2590i	1.21547	+	0.701749i	0.251521	+	0.967852i	$0.419069\pi$
$678$	−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	0.995875	−	0.0907317i	$-0.0289206\pi$
$683$	10.9597	+	18.9828i	0.419362	+	0.726356i	−0.576514	+	0.817088i	$0.695587\pi$
$684$	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	$-0.906928\pi$
$727$	−51.6371			−1.91511			−0.957556	+	0.288246i	$0.906928\pi$
$728$	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	−0.994352	−	0.106130i	$-0.966154\pi$
$733$	−10.9721	+	19.0043i	−0.405265	+	0.701940i	0.589087	+	0.808069i	$0.299487\pi$
$734$	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	$-0.477685\pi$
$743$	3.81873			0.140096			0.0700478	+	0.997544i	$0.477685\pi$
$744$	−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	$-0.825416\pi$
$757$		−	28.6903i		−	1.04277i	0.853323	−	0.521383i	$-0.174584\pi$
$758$	−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	−0.0992225	−	0.995065i	$-0.531636\pi$
$773$	19.8212	−	11.4438i	0.712918	−	0.411603i	0.812141	+	0.583462i	$0.198302\pi$
$774$	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	$-0.969877\pi$
$787$	−16.2597	−	28.1627i	−0.579597	−	1.00389i	0.415929	−	0.909397i	$-0.363457\pi$
$788$	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	$-0.808830\pi$
$797$		−	31.9080i		−	1.13024i	0.825009	−	0.565120i	$-0.191170\pi$
$798$	−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	−0.0255145	−	0.999674i	$-0.508122\pi$
$823$	23.7385	−	13.7054i	0.827472	−	0.477741i	0.852986	+	0.521933i	$0.174789\pi$
$824$	−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	$-0.340354\pi$
$827$	27.6521			0.961557			0.480779	+	0.876842i	$0.340354\pi$
$828$	−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	$-0.466917\pi$
$853$	6.05997			0.207490			0.103745	+	0.994604i	$0.466917\pi$
$854$	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	−0.645081	−	0.764114i	$-0.723176\pi$
$857$	−8.95449	+	5.16988i	−0.305880	+	0.176600i	0.339202	+	0.940714i	$0.389843\pi$
$858$	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	−0.707924	−	0.706289i	$-0.750368\pi$
$863$	7.57049	−	13.1125i	0.257702	−	0.446354i	0.965626	+	0.259935i	$0.0837013\pi$
$864$	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	0.758294	−	0.651913i	$-0.226033\pi$
$877$	16.9650	+	9.79476i	0.572868	+	0.330745i	−0.185426	+	0.982658i	$0.559367\pi$
$878$	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	$0.0309824\pi$
$883$			5.77550i			0.194361i	−0.995267	+	0.0971805i	$0.969018\pi$
$884$	−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	0.678706	−	0.734410i	$-0.262541\pi$
$887$	11.3781	+	6.56917i	0.382041	+	0.220571i	−0.296665	+	0.954982i	$0.595875\pi$
$888$	−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	−0.408657	−	0.912688i	$-0.634003\pi$
$907$	5.34345	−	3.08504i	0.177426	−	0.102437i	0.586083	+	0.810251i	$0.300669\pi$
$908$	−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	$-0.496531\pi$
$937$	0.667265			0.0217986			0.0108993	+	0.999941i	$0.496531\pi$
$938$	−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	$-0.481521\pi$
$947$	27.4984	−	47.6286i	0.893577	−	1.54772i	0.835556	−	0.549405i	$-0.185146\pi$
$948$	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	$-0.697300\pi$
$953$	−35.8657			−1.16180			−0.580902	+	0.813974i	$0.697300\pi$
$954$	−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	$-0.938832\pi$
$967$		−	11.8780i		−	0.381971i	0.981593	−	0.190986i	$-0.0611684\pi$
$968$	−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	0.973009	−	0.230768i	$-0.0741239\pi$
$977$	8.95992	+	15.5190i	0.286653	+	0.496498i	−0.686355	+	0.727266i	$0.740791\pi$
$978$	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	−0.950555	−	0.310556i	$-0.899485\pi$
$983$	−36.2715	+	20.9414i	−1.15688	+	0.667926i	−0.206328	+	0.978483i	$0.566151\pi$
$984$	−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	$0.0213757\pi$
$997$	17.5870	+	30.4616i	0.556986	+	0.964728i	−0.440760	+	0.897625i	$0.645291\pi$
$998$	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.299.5		16
3.2	odd	2		525.2.q.f.299.4		16
5.2	odd	4		105.2.s.d.26.2	yes	8
5.3	odd	4		525.2.t.f.26.3		8
5.4	even	2	inner	525.2.q.e.299.4		16
7.3	odd	6		525.2.q.f.374.5		16
15.2	even	4		105.2.s.c.26.3	✓	8
15.8	even	4		525.2.t.g.26.2		8
15.14	odd	2		525.2.q.f.299.5		16
21.17	even	6	inner	525.2.q.e.374.4		16
35.2	odd	12		735.2.b.c.146.4		8
35.3	even	12		525.2.t.g.101.2		8
35.12	even	12		735.2.b.d.146.4		8
35.17	even	12		105.2.s.c.101.3	yes	8
35.24	odd	6		525.2.q.f.374.4		16
35.27	even	4		735.2.s.l.656.2		8
35.32	odd	12		735.2.s.k.521.3		8
105.2	even	12		735.2.b.d.146.5		8
105.17	odd	12		105.2.s.d.101.2	yes	8
105.32	even	12		735.2.s.l.521.2		8
105.38	odd	12		525.2.t.f.101.3		8
105.47	odd	12		735.2.b.c.146.5		8
105.59	even	6	inner	525.2.q.e.374.5		16
105.62	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	15.2	even	4
105.2.s.c.101.3	yes	8	35.17	even	12
105.2.s.d.26.2	yes	8	5.2	odd	4
105.2.s.d.101.2	yes	8	105.17	odd	12
525.2.q.e.299.4		16	5.4	even	2	inner
525.2.q.e.299.5		16	1.1	even	1	trivial
525.2.q.e.374.4		16	21.17	even	6	inner
525.2.q.e.374.5		16	105.59	even	6	inner
525.2.q.f.299.4		16	3.2	odd	2
525.2.q.f.299.5		16	15.14	odd	2
525.2.q.f.374.4		16	35.24	odd	6
525.2.q.f.374.5		16	7.3	odd	6
525.2.t.f.26.3		8	5.3	odd	4
525.2.t.f.101.3		8	105.38	odd	12
525.2.t.g.26.2		8	15.8	even	4
525.2.t.g.101.2		8	35.3	even	12
735.2.b.c.146.4		8	35.2	odd	12
735.2.b.c.146.5		8	105.47	odd	12
735.2.b.d.146.4		8	35.12	even	12
735.2.b.d.146.5		8	105.2	even	12
735.2.s.k.521.3		8	35.32	odd	12
735.2.s.k.656.3		8	105.62	odd	4
735.2.s.l.521.2		8	105.32	even	12
735.2.s.l.656.2		8	35.27	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

Varieties

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Database

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