LMFDB - Embedded newform 525.2.q.f.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.f.374.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.192865 - 0.334053i) q^{2} +(0.983691 - 1.42561i) q^{3} +(0.925606 + 1.60320i) q^{4} +(-0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} +1.48553 q^{8} +(-1.06470 - 2.80471i) q^{9} +O(q^{10})$	\(q+(0.192865 - 0.334053i) q^{2} +(0.983691 - 1.42561i) q^{3} +(0.925606 + 1.60320i) q^{4} +(-0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} +1.48553 q^{8} +(-1.06470 - 2.80471i) q^{9} +(-2.20164 + 1.27112i) q^{11} +(3.19604 + 0.257501i) q^{12} +3.06718 q^{13} +(1.01854 + 0.0640110i) q^{14} +(-1.56470 + 2.71015i) q^{16} +(5.59565 - 3.23065i) q^{17} +(-1.14227 - 0.185264i) q^{18} +(1.03570 + 0.597960i) q^{19} +(4.53570 + 0.653796i) q^{21} +0.980620i q^{22} +(-1.52800 + 2.64657i) q^{23} +(1.46130 - 2.11778i) 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} +(-0.353622 + 4.38907i) q^{33} -2.49232i q^{34} +(3.51101 - 4.30299i) q^{36} +(3.07619 + 1.77604i) q^{37} +(0.399500 - 0.230652i) q^{38} +(3.01716 - 4.37259i) q^{39} +2.31252 q^{41} +(1.09318 - 1.38907i) 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} +(0.898757 - 11.1552i) q^{51} +(2.83900 + 4.91730i) q^{52} +(-6.62740 - 11.4790i) q^{53} +(-1.38775 + 1.44618i) 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} +(5.39378 - 5.82298i) q^{63} -4.64717 q^{64} +(1.39798 + 0.964627i) q^{66} +(-3.04782 + 1.75966i) q^{67} +(10.3587 + 5.98062i) q^{68} +(2.26989 + 4.78173i) q^{69} +0.921861i q^{71} +(-1.58165 - 4.16649i) 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} +(-6.73281 + 5.97238i) q^{81} +(0.446004 - 0.772502i) q^{82} -2.11171i q^{83} +(3.15010 + 7.87677i) q^{84} +(-1.82436 - 1.05330i) q^{86} +(-11.0774 - 7.64357i) q^{87} +(-3.27061 + 1.88829i) q^{88} +(-9.41507 + 16.3074i) q^{89} +(3.60871 + 7.26845i) q^{91} -5.65729 q^{92} +(-0.956152 + 11.8675i) q^{93} +(-1.07571 + 0.621062i) q^{94} +(7.21343 + 0.581177i) 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} + 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	$ 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * 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	$0.123121\pi$
$3$	0.983691	−	1.42561i	0.567934	−	0.823074i
$3$	0.983691	−	1.42561i	0.567934	−	0.823074i
$4$	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
$9$	−1.06470	−	2.80471i	−0.354901	−	0.934904i
$10$		0			0
$11$	−2.20164	+	1.27112i	−0.663821	+	0.383257i	−0.793731	−	0.608269i	$-0.791864\pi$
$11$	−2.20164	+	1.27112i	−0.663821	+	0.383257i	0.129910	+	0.991526i	$0.458531\pi$
$12$	3.19604	+	0.257501i	0.922616	+	0.0743340i
$13$	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	0.367907	−	0.929863i	$-0.380074\pi$
$17$	5.59565	−	3.23065i	1.35715	−	0.783548i	0.989238	+	0.146314i	$0.0467411\pi$
$18$	−1.14227	−	0.185264i	−0.269235	−	0.0436672i
$19$	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
$21$	4.53570	+	0.653796i	0.989770	+	0.142670i
$22$			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	$0.269882\pi$
$24$	1.46130	−	2.11778i	0.298287	−	0.432290i
$25$		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	$-0.743474\pi$
$29$		−	7.77029i		−	1.44291i	0.692463	−	0.721454i	$-0.256526\pi$
$30$		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
$33$	−0.353622	+	4.38907i	−0.0615576	+	0.764039i
$34$		−	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
$39$	3.01716	−	4.37259i	0.483132	−	0.700175i
$40$		0			0
$41$	2.31252			0.361154			0.180577	−	0.983561i	$-0.442203\pi$
$41$	2.31252			0.361154			0.180577	+	0.983561i	$0.442203\pi$
$42$	1.09318	−	1.38907i	0.168682	−	0.214338i
$43$		−	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	0.282624	−	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
$51$	0.898757	−	11.1552i	0.125851	−	1.56203i
$52$	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	$-0.530850\pi$
$54$	−1.38775	+	1.44618i	−0.188849	+	0.196800i
$55$		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	0.965696	−	0.259674i	$-0.0836150\pi$
$59$	1.98146	+	3.43199i	0.257964	+	0.446807i	−0.707732	+	0.706481i	$0.750282\pi$
$60$		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
$63$	5.39378	−	5.82298i	0.679552	−	0.733627i
$64$	−4.64717			−0.580896
$65$		0			0
$66$	1.39798	+	0.964627i	0.172079	+	0.118737i
$67$	−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	$0.0174210\pi$
$71$			0.921861i			0.109405i	−0.998503	+	0.0547024i	$0.982579\pi$
$72$	−1.58165	−	4.16649i	−0.186399	−	0.491025i
$73$	−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
$81$	−6.73281	+	5.97238i	−0.748090	+	0.663597i
$82$	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	$-0.0369737\pi$
$84$	3.15010	+	7.87677i	0.343705	+	0.859426i
$85$		0			0
$86$	−1.82436	−	1.05330i	−0.196726	−	0.113580i
$87$	−11.0774	−	7.64357i	−1.18762	−	0.819477i
$88$	−3.27061	+	1.88829i	−0.348648	+	0.201292i
$89$	−9.41507	+	16.3074i	−0.997996	+	1.72858i	−0.444197	+	0.895929i	$0.646511\pi$
$89$	−9.41507	+	16.3074i	−0.997996	+	1.72858i	−0.553799	+	0.832651i	$0.686822\pi$
$90$		0			0
$91$	3.60871	+	7.26845i	0.378296	+	0.761941i
$92$	−5.65729			−0.589813
$93$	−0.956152	+	11.8675i	−0.0991483	+	1.23061i
$94$	−1.07571	+	0.621062i	−0.110951	+	0.0640576i
$95$		0			0
$96$	7.21343	+	0.581177i	0.736218	+	0.0593161i
$97$	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	0.638646	−	0.769501i	$-0.279495\pi$
$101$	−3.48815	−	6.04166i	−0.347084	−	0.601167i	−0.985730	+	0.168333i	$0.946162\pi$
$102$	−3.55307	−	2.45168i	−0.351806	−	0.242752i
$103$	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	$0.387597\pi$
$107$	−6.61684	+	11.4607i	−0.639674	+	1.10795i	−0.985504	+	0.169651i	$0.945736\pi$
$108$	−2.68062	−	9.23812i	−0.257943	−	0.888939i
$109$	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	$0.609723\pi$
$114$	0.0641665	−	0.796420i	0.00600975	−	0.0745916i
$115$		0			0
$116$	12.4573	−	7.19223i	1.15663	−	0.667782i
$117$	−3.26564	−	8.60256i	−0.301909	−	0.795307i
$118$	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
$123$	2.27480	−	3.29674i	0.205112	−	0.297257i
$124$	−11.0202	−	6.36254i	−0.989648	−	0.571373i
$125$		0			0
$126$	−0.904910	−	2.92486i	−0.0806158	−	0.260567i
$127$		−	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
$129$	−7.78567	−	5.37223i	−0.685490	−	0.472999i
$130$		0			0
$131$	−7.83183	+	13.5651i	−0.684270	+	1.18519i	0.289395	+	0.957210i	$0.406546\pi$
$131$	−7.83183	+	13.5651i	−0.684270	+	1.18519i	−0.973666	+	0.227981i	$0.926787\pi$
$132$	−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	$0.913428\pi$
$138$	2.03513	+	0.163968i	0.173242	+	0.0139579i
$139$			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
$144$	9.26713	+	1.50304i	0.772261	+	0.125253i
$145$		0			0
$146$	−0.114345			−0.00946324
$147$	3.78717	+	11.5177i	0.312361	+	0.949964i
$148$			6.57565i			0.540515i
$149$	−16.1925	−	9.34874i	−1.32654	−	0.765879i	−0.341778	−	0.939781i	$-0.611029\pi$
$149$	−16.1925	−	9.34874i	−1.32654	−	0.765879i	−0.984763	+	0.173902i	$0.944362\pi$
$150$		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
$156$	9.80283	+	0.789801i	0.784854	+	0.0632347i
$157$	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
$159$	−22.8838	−	1.84372i	−1.81481	−	0.146217i
$160$		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	$-0.940402\pi$
$167$		−	4.81089i		−	0.372278i	0.982523	−	0.186139i	$-0.0595975\pi$
$168$	6.73792	+	0.971234i	0.519842	+	0.0749323i
$169$	−3.59239			−0.276338
$170$		0			0
$171$	0.574394	−	3.54148i	0.0439250	−	0.270824i
$172$	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
$177$	6.84181	+	0.551236i	0.514262	+	0.0414335i
$178$	3.63168	+	6.29026i	0.272206	+	0.471475i
$179$	17.2931	−	9.98420i	1.29255	−	0.746254i	0.313444	−	0.949607i	$-0.398517\pi$
$179$	17.2931	−	9.98420i	1.29255	−	0.746254i	0.979106	+	0.203353i	$0.0651838\pi$
$180$		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
$186$	3.77997	+	2.60824i	0.277161	+	0.191245i
$187$	−8.21309	+	14.2255i	−0.600601	+	1.04027i
$188$		−	5.96124i		−	0.434768i
$189$	−2.99547	−	13.4174i	−0.217888	−	0.975974i
$190$		0			0
$191$	−7.48332	−	4.32049i	−0.541474	−	0.312620i	0.204202	−	0.978929i	$-0.434540\pi$
$191$	−7.48332	−	4.32049i	−0.541474	−	0.312620i	−0.745676	+	0.666309i	$0.767873\pi$
$192$	−4.57138	+	6.62503i	−0.329911	+	0.478120i
$193$	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	$-0.363348\pi$
$197$	11.6843			0.832475			0.416238	+	0.909256i	$0.363348\pi$
$198$	2.75036	−	1.04407i	0.195459	−	0.0741989i
$199$	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
$201$	−0.489531	+	6.07595i	−0.0345289	+	0.428564i
$202$	−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
$207$	9.04972	+	1.46778i	0.628999	+	0.102018i
$208$	−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
$213$	1.31421	+	0.906827i	0.0900482	+	0.0621347i
$214$	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
$219$	−0.511785	−	0.0412339i	−0.0345832	−	0.00278633i
$220$		0			0
$221$	17.1629	−	9.90900i	1.15450	−	0.666551i
$222$	0.190585	−	2.36550i	0.0127912	−	0.158762i
$223$	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	−0.552587	−	0.833455i	$-0.686359\pi$
$227$	−1.61344	+	0.931518i	−0.107087	+	0.0618270i	0.445500	+	0.895282i	$0.353026\pi$
$228$	3.15615	+	2.17780i	0.209021	+	0.144228i
$229$	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
$231$	−10.8170	+	4.32599i	−0.711709	+	0.284629i
$232$		−	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	$0.150339\pi$
$234$	−3.50354	−	0.568240i	−0.229033	−	0.0371470i
$235$		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	$-0.941062\pi$
$239$		−	5.69230i		−	0.368205i	0.982907	−	0.184102i	$-0.0589378\pi$
$240$		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
$243$	1.89125	+	15.4733i	0.121324	+	0.992613i
$244$		−	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
$249$	−3.01047	−	2.07727i	−0.190781	−	0.131642i
$250$		0			0
$251$	5.32590			0.336168			0.168084	−	0.985773i	$-0.446242\pi$
$251$	5.32590			0.336168			0.168084	+	0.985773i	$0.446242\pi$
$252$	14.3279	+	3.25750i	0.902573	+	0.205203i
$253$		−	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
$261$	−21.7934	+	8.27307i	−1.34898	+	0.512090i
$262$	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	$0.682214\pi$
$264$	−0.525316	+	6.52009i	−0.0323309	+	0.401284i
$265$		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	$-0.896624\pi$
$269$	−12.3042	−	21.3115i	−0.750201	−	1.29939i	0.197525	−	0.980298i	$-0.436710\pi$
$270$		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
$273$	13.9118	+	2.00531i	0.841981	+	0.121367i
$274$	−2.24819			−0.135818
$275$		0			0
$276$	−5.56503	+	8.06507i	−0.334975	+	0.485460i
$277$	−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	$0.249758\pi$
$281$			23.6885i			1.41314i	−0.707643	+	0.706570i	$0.750242\pi$
$282$	−0.172777	+	2.14447i	−0.0102887	+	0.127701i
$283$	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
$291$	12.1675	−	17.6336i	0.713270	−	1.03370i
$292$	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	$-0.0588580\pi$
$294$	4.57793	+	0.956251i	0.266990	+	0.0557697i
$295$		0			0
$296$	4.56977	+	2.63836i	0.265613	+	0.153352i
$297$	12.6866	−	3.68125i	0.736149	−	0.213608i
$298$	−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
$303$	−12.0443	−	0.970393i	−0.691926	−	0.0557476i
$304$	−3.24112	+	1.87126i	−0.185891	+	0.107324i
$305$		0			0
$306$	−6.99025	+	2.65359i	−0.399606	+	0.151696i
$307$	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	$0.00457602\pi$
$311$	9.03624	+	15.6512i	0.512398	+	0.887499i	−0.487499	+	0.873124i	$0.662091\pi$
$312$	4.48208	−	6.49562i	0.253748	−	0.367742i
$313$	−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	−0.826628	−	0.562748i	$-0.809744\pi$
$317$	1.31825	−	2.28327i	0.0740402	−	0.128241i	0.900669	+	0.434507i	$0.143077\pi$
$318$	−5.02940	+	7.28882i	−0.282035	+	0.408737i
$319$	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
$324$	−15.8068	−	5.26595i	−0.878157	−	0.292553i
$325$		0			0
$326$	−5.49299	+	3.17138i	−0.304228	+	0.175646i
$327$	4.31894	+	0.347971i	0.238838	+	0.0192429i
$328$	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
$333$	1.70604	−	10.5188i	0.0934906	−	0.576426i
$334$	−1.60709	−	0.927855i	−0.0879362	−	0.0507700i
$335$		0			0
$336$	−8.86891	+	11.2694i	−0.483839	+	0.614797i
$337$		−	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
$339$	−7.06708	+	10.2419i	−0.383831	+	0.556264i
$340$		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	$0.762779\pi$
$348$	2.00086	−	24.8341i	0.107257	−	1.33125i
$349$		−	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	$0.284735\pi$
$354$	1.50369	−	2.17921i	0.0799203	−	0.115824i
$355$		0			0
$356$	−34.8586			−1.84750
$357$	27.4924	−	10.9948i	1.45505	−	0.581909i
$358$		−	7.70242i		−	0.407086i
$359$	−4.16181	−	2.40282i	−0.219652	−	0.126816i	0.386137	−	0.922441i	$-0.373809\pi$
$359$	−4.16181	−	2.40282i	−0.219652	−	0.126816i	−0.605789	+	0.795625i	$0.707142\pi$
$360$		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
$366$	−0.501174	+	6.22045i	−0.0261968	+	0.325148i
$367$	−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
$369$	−2.46214	−	6.48594i	−0.128174	−	0.337644i
$370$		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
$378$	−5.05985	−	1.58711i	−0.260250	−	0.0816322i
$379$	−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
$381$	−15.9618	−	11.0139i	−0.817747	−	0.564258i
$382$	−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
$387$	−15.3174	+	5.81467i	−0.778626	+	0.295576i
$388$	11.4490	+	19.8303i	0.581236	+	1.00673i
$389$	2.13457	−	1.23239i	0.108227	−	0.0624848i	−0.444910	−	0.895576i	$-0.646764\pi$
$389$	2.13457	−	1.23239i	0.108227	−	0.0624848i	0.553136	+	0.833091i	$0.313431\pi$
$390$		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
$396$	−2.26037	+	13.9366i	−0.113588	+	0.700339i
$397$	−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
$399$	4.30667	+	3.38930i	0.215603	+	0.169677i
$400$		0			0
$401$	−5.40992	−	3.12342i	−0.270158	−	0.155976i	0.358801	−	0.933414i	$-0.383186\pi$
$401$	−5.40992	−	3.12342i	−0.270158	−	0.155976i	−0.628960	+	0.777438i	$0.716519\pi$
$402$	1.93527	+	1.33537i	0.0965226	+	0.0666022i
$403$	−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
$408$	1.33513	−	16.5713i	0.0660988	−	0.820403i
$409$	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
$411$	−10.0625	−	0.810722i	−0.496346	−	0.0399899i
$412$	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
$417$	17.1593	+	11.8402i	0.840295	+	0.579817i
$418$	−0.586372	+	1.01563i	−0.0286804	+	0.0496759i
$419$	12.0419			0.588284			0.294142	−	0.955762i	$-0.404966\pi$
$419$	12.0419			0.588284			0.294142	+	0.955762i	$0.404966\pi$
$420$		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
$423$	−1.54664	+	9.53594i	−0.0752000	+	0.463653i
$424$	−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
$429$	−1.08462	+	13.4621i	−0.0523660	+	0.649955i
$430$		0			0
$431$	−28.2346	+	16.3013i	−1.36001	+	0.785205i	−0.989625	−	0.143672i	$-0.954109\pi$
$431$	−28.2346	+	16.3013i	−1.36001	+	0.785205i	−0.370389	+	0.928877i	$0.620776\pi$
$432$	11.2587	−	11.7327i	0.541686	−	0.564492i
$433$	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
$438$	−0.112480	+	0.163011i	−0.00537450	+	0.00778895i
$439$	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
$441$	20.1451	+	5.93084i	0.959291	+	0.282421i
$442$		−	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	$0.290059\pi$
$444$	9.37428	+	6.46841i	0.444884	+	0.306977i
$445$		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	$0.311839\pi$
$449$			35.1881i			1.66063i	−0.557294	+	0.830315i	$0.688161\pi$
$450$		0			0
$451$	−5.09134	+	2.93948i	−0.239742	+	0.138415i
$452$	−6.64978	−	11.5178i	−0.312779	−	0.541750i
$453$	10.2735	+	0.827721i	0.482690	+	0.0388897i
$454$			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
$459$	−32.2439	+	9.35619i	−1.50502	+	0.436710i
$460$		0			0
$461$	13.5161			0.629506			0.314753	−	0.949174i	$-0.398078\pi$
$461$	13.5161			0.629506			0.314753	+	0.949174i	$0.398078\pi$
$462$	−0.641126	+	4.44780i	−0.0298279	+	0.206930i
$463$		−	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	0.304435	−	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
$471$	11.0714	+	0.892008i	0.510143	+	0.0411016i
$472$	2.94352	+	5.09833i	0.135487	+	0.234670i
$473$	6.94197	+	12.0238i	0.319192	+	0.552857i
$474$	−5.52391	−	0.445055i	−0.253722	−	0.0204420i
$475$		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	0.996989	−	0.0775419i	$-0.0247071\pi$
$479$	9.44037	+	16.3512i	0.431341	+	0.747105i	−0.565648	+	0.824647i	$0.691374\pi$
$480$		0			0
$481$	9.43523	+	5.44743i	0.430210	+	0.248382i
$482$		−	5.14291i		−	0.234253i
$483$	−8.66085	+	11.0050i	−0.394082	+	0.500746i
$484$	−8.39897			−0.381772
$485$		0			0
$486$	5.53366	+	2.35249i	0.251012	+	0.106711i
$487$	−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	$-0.854814\pi$
$491$		−	19.5201i		−	0.880930i	0.897770	−	0.440465i	$-0.145186\pi$
$492$	7.39088	+	0.595474i	0.333207	+	0.0268460i
$493$	−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
$501$	−6.85844	−	4.73243i	−0.306413	−	0.211430i
$502$	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	$0.637830\pi$
$504$	8.01263	−	8.65022i	0.356911	−	0.385312i
$505$		0			0
$506$	−2.59528	−	1.49838i	−0.115374	−	0.0666113i
$507$	−3.53381	+	5.12134i	−0.156942	+	0.227447i
$508$	17.9502	−	10.3635i	0.796410	−	0.459807i
$509$	−8.86384	+	15.3526i	−0.392883	+	0.680493i	−0.992828	−	0.119548i	$-0.961856\pi$
$509$	−8.86384	+	15.3526i	−0.392883	+	0.680493i	0.599946	+	0.800041i	$0.295189\pi$
$510$		0			0
$511$	0.433979	−	0.653288i	0.0191981	−	0.0288998i
$512$	−22.3729			−0.988751
$513$	−4.48373	−	4.30258i	−0.197962	−	0.189964i
$514$	2.17136	−	1.25364i	0.0957747	−	0.0552956i
$515$		0			0
$516$	1.40629	−	17.4545i	0.0619084	−	0.768393i
$517$	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	0.901959	−	0.431822i	$-0.142129\pi$
$521$	1.75780	+	3.04461i	0.0770108	+	0.133387i	−0.824948	+	0.565208i	$0.808796\pi$
$522$	−1.43956	+	8.87574i	−0.0630078	+	0.388481i
$523$	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
$528$	−11.3417	−	7.82596i	−0.493584	−	0.340581i
$529$	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
$534$	12.5399	+	1.01032i	0.542654	+	0.0437209i
$535$		0			0
$536$	−4.52763	+	2.61403i	−0.195564	+	0.112909i
$537$	2.77757	−	34.4746i	0.119861	−	1.48769i
$538$	−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
$543$	−7.39615	−	5.10346i	−0.317399	−	0.219011i
$544$	23.3796	+	13.4982i	1.00239	+	0.578731i
$545$		0			0
$546$	3.35299	−	4.26052i	0.143495	−	0.182333i
$547$		−	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
$549$	−4.48632	+	27.6608i	−0.191471	+	1.18053i
$550$		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	$0.953330\pi$
$558$	7.43665	−	2.82305i	0.314818	−	0.119509i
$559$		−	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	$0.188097\pi$
$564$	−8.49838	−	5.86402i	−0.357846	−	0.246920i
$565$		0			0
$566$	1.94566			0.0817822
$567$	−22.0746	−	8.92824i	−0.927045	−	0.374951i
$568$			1.36945i			0.0574610i
$569$	24.8873	+	14.3687i	1.04333	+	0.602367i	0.920775	−	0.390094i	$-0.127558\pi$
$569$	24.8873	+	14.3687i	1.04333	+	0.602367i	0.122556	+	0.992462i	$0.460891\pi$
$570$		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
$576$	4.94786	+	13.0340i	0.206161	+	0.543082i
$577$	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
$579$	3.30667	−	41.0416i	0.137420	−	1.70563i
$580$		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	$0.831561\pi$
$588$	−14.9597	+	16.7324i	−0.616928	+	0.690034i
$589$	−8.22067			−0.338727
$590$		0			0
$591$	11.4938	−	16.6573i	0.472791	−	0.685189i
$592$	−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
$597$	1.96501	−	24.3892i	0.0804224	−	0.998184i
$598$	1.80778	+	3.13117i	0.0739257	+	0.128043i
$599$	−28.6663	+	16.5505i	−1.17127	+	0.676235i	−0.953980	−	0.299871i	$-0.903056\pi$
$599$	−28.6663	+	16.5505i	−1.17127	+	0.676235i	−0.217294	+	0.976106i	$0.569723\pi$
$600$		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
$606$	−2.64709	+	3.83627i	−0.107531	+	0.155838i
$607$	−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
$609$	5.08019	−	35.2437i	0.205860	−	1.42815i
$610$		0			0
$611$	−8.55364	−	4.93844i	−0.346043	−	0.199788i
$612$	5.74492	−	35.4209i	0.232225	−	1.43180i
$613$	−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	$-0.225384\pi$
$617$	37.7372			1.51924			0.759621	+	0.650366i	$0.225384\pi$
$618$	−2.51274	−	0.202448i	−0.101077	−	0.00814365i
$619$	−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
$621$	10.9946	−	11.4575i	0.441198	−	0.459774i
$622$	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
$627$	−2.99073	+	4.33429i	−0.119438	+	0.173095i
$628$	−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
$633$	4.42502	−	6.41292i	0.175879	−	0.254891i
$634$	−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
$639$	2.58555	−	0.981510i	0.102283	−	0.0388279i
$640$		0			0
$641$	−13.5251	+	7.80872i	−0.534209	+	0.308426i	−0.742729	−	0.669592i	$-0.766469\pi$
$641$	−13.5251	+	7.80872i	−0.534209	+	0.308426i	0.208519	+	0.978018i	$0.433136\pi$
$642$	8.81293	+	0.710047i	0.347819	+	0.0280233i
$643$	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	−0.609201	−	0.793016i	$-0.708510\pi$
$647$	−5.77475	+	3.33405i	−0.227029	+	0.131075i	0.382172	+	0.924091i	$0.375176\pi$
$648$	−10.0018	+	8.87215i	−0.392908	+	0.348531i
$649$	−8.72495	−	5.03735i	−0.342484	−	0.197733i
$650$		0			0
$651$	−29.2480	+	11.6970i	−1.14632	+	0.458441i
$652$		−	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	$-0.165031\pi$
$654$	0.949214	−	1.37564i	0.0371172	−	0.0537918i
$655$		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	$-0.955836\pi$
$659$		−	7.10057i		−	0.276599i	0.990390	−	0.138299i	$-0.0441636\pi$
$660$		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
$663$	2.75665	−	34.2149i	0.107059	−	1.32880i
$664$		−	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
$669$	7.08909	−	10.2738i	0.274080	−	0.397208i
$670$		0			0
$671$	23.7464			0.916721
$672$	7.10976	+	17.7778i	0.274265	+	0.685794i
$673$			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	0.963945	−	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
$681$	−0.259145	+	3.21645i	−0.00993047	+	0.123255i
$682$	−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	$0.695587\pi$
$684$	6.20936	−	2.35715i	0.237421	−	0.0901279i
$685$		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
$693$	−4.47347	+	19.6763i	−0.169933	+	0.747440i
$694$	3.15929			0.119925
$695$		0			0
$696$	−16.4558	−	11.3548i	−0.623755	−	0.430401i
$697$	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	$0.189527\pi$
$701$			29.6988i			1.12171i	−0.827915	+	0.560854i	$0.810473\pi$
$702$	−4.25648	+	4.43569i	−0.160651	+	0.167414i
$703$	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
$711$	−24.5635	−	3.98396i	−0.921202	−	0.149410i
$712$	−13.9864	+	24.2251i	−0.524162	+	0.907875i
$713$		−	21.0067i		−	0.786706i
$714$	1.62947	−	11.3044i	0.0609814	−	0.423057i
$715$		0			0
$716$	32.0133	+	18.4829i	1.19639	+	0.690737i
$717$	−8.11498	−	5.59947i	−0.303060	−	0.209116i
$718$	−1.60534	+	0.926842i	−0.0599107	+	0.0345895i
$719$	25.5863	−	44.3167i	0.954207	−	1.65273i	0.218034	−	0.975941i	$-0.430036\pi$
$719$	25.5863	−	44.3167i	0.954207	−	1.65273i	0.736173	−	0.676794i	$-0.236631\pi$
$720$		0			0
$721$	9.96323	+	0.626148i	0.371050	+	0.0233190i
$722$	−6.77720			−0.252221
$723$	1.85459	−	23.0187i	0.0689728	−	0.856074i
$724$	8.31751	−	4.80211i	0.309118	−	0.178469i
$725$		0			0
$726$	3.02141	+	0.243431i	0.112135	+	0.00903459i
$727$	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
$732$	−24.6512	−	17.0097i	−0.911134	−	0.628697i
$733$	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
$738$	−2.64151	−	0.428427i	−0.0972352	−	0.0157706i
$739$	−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	$0.477685\pi$
$744$	−1.42039	+	17.6296i	−0.0520741	+	0.646332i
$745$		0			0
$746$	8.85325	−	5.11143i	0.324141	−	0.187143i
$747$	−5.92274	+	2.24835i	−0.216702	+	0.0822628i
$748$	−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
$753$	5.23904	−	7.59263i	0.190921	−	0.276691i
$754$	−7.96145	−	4.59654i	−0.289939	−	0.167396i
$755$		0			0
$756$	18.7381	−	17.2216i	0.681500	−	0.626342i
$757$			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
$759$	−11.0756	−	7.64236i	−0.402020	−	0.277400i
$760$		0			0
$761$	5.34875	−	9.26431i	0.193892	−	0.335831i	−0.752645	−	0.658427i	$-0.771222\pi$
$761$	5.34875	−	9.26431i	0.193892	−	0.335831i	0.946537	+	0.322596i	$0.104556\pi$
$762$	−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
$768$	−9.28763	−	0.748293i	−0.335139	−	0.0270017i
$769$			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	$0.198302\pi$
$774$	−1.01179	+	6.23826i	−0.0363679	+	0.224230i
$775$		0			0
$776$	18.3748			0.659618
$777$	12.7915	+	10.0668i	0.458892	+	0.361144i
$778$		−	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
$786$	10.4312	+	0.840427i	0.372068	+	0.0299770i
$787$	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
$789$	25.5973	+	2.06235i	0.911289	+	0.0734214i
$790$		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	$-0.191170\pi$
$798$	1.96281	−	0.784974i	0.0694828	−	0.0277878i
$799$	−20.8066			−0.736084
$800$		0			0
$801$	55.7618	+	9.04402i	1.97025	+	0.319555i
$802$	−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
$807$	−42.4853	−	3.42299i	−1.49555	−	0.120495i
$808$	−5.18176	−	8.97507i	−0.182294	−	0.315742i
$809$	−17.9862	+	10.3843i	−0.632360	+	0.365093i	−0.781666	−	0.623698i	$-0.785630\pi$
$809$	−17.9862	+	10.3843i	−0.632360	+	0.365093i	0.149305	+	0.988791i	$0.452296\pi$
$810$		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
$816$	28.8258	+	19.8903i	1.00911	+	0.696299i
$817$	3.26564	−	5.65626i	0.114250	−	0.197887i
$818$		−	4.54968i		−	0.159076i
$819$	16.5437	−	17.8602i	0.578084	−	0.624084i
$820$		0			0
$821$	12.7908	+	7.38477i	0.446402	+	0.257730i	0.706309	−	0.707903i	$-0.250359\pi$
$821$	12.7908	+	7.38477i	0.446402	+	0.257730i	−0.259907	+	0.965634i	$0.583692\pi$
$822$	−2.21153	+	3.20504i	−0.0771359	+	0.111789i
$823$	−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	$-0.340354\pi$
$827$	27.6521			0.961557			0.480779	+	0.876842i	$0.340354\pi$
$828$	6.02334	+	15.8671i	0.209326	+	0.551419i
$829$	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
$831$	−2.61162	+	32.4149i	−0.0905963	+	1.12446i
$832$	−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
$837$	34.3030	−	9.95368i	1.18569	−	0.344050i
$838$	2.32246	−	4.02262i	0.0802281	−	0.138959i
$839$	−26.4538			−0.913286			−0.456643	−	0.889650i	$-0.650948\pi$
$839$	−26.4538			−0.913286			−0.456643	+	0.889650i	$0.650948\pi$
$840$		0			0
$841$	−31.3775			−1.08198
$842$	2.20375	−	3.81701i	0.0759463	−	0.131543i
$843$	33.7705	+	23.3022i	1.16312	+	0.802570i
$844$	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
$849$	8.70840	+	0.701625i	0.298871	+	0.0240797i
$850$		0			0
$851$	−9.40081	+	5.42756i	−0.322256	+	0.186054i
$852$	−0.237380	+	2.94630i	−0.00813250	+	0.100939i
$853$	−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	−0.645081	−	0.764114i	$-0.723176\pi$
$857$	−8.95449	+	5.16988i	−0.305880	+	0.176600i	0.339202	+	0.940714i	$0.389843\pi$
$858$	4.28785	+	2.95869i	0.146385	+	0.101008i
$859$	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
$861$	10.4889	+	1.51191i	0.357460	+	0.0515259i
$862$			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	$0.0837013\pi$
$864$	−6.05014	−	20.8504i	−0.205830	−	0.709344i
$865$		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
$873$	−13.1696	−	34.6921i	−0.445722	−	1.17415i
$874$			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
$879$	−8.97306	−	6.19156i	−0.302654	−	0.208836i
$880$		0			0
$881$	−28.7481			−0.968548			−0.484274	−	0.874917i	$-0.660916\pi$
$881$	−28.7481			−0.968548			−0.484274	+	0.874917i	$0.660916\pi$
$882$	5.86651	−	5.58567i	0.197536	−	0.188079i
$883$		−	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	0.678706	−	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
$891$	7.23165	−	21.7073i	0.242269	−	0.727221i
$892$	6.67049	+	11.5536i	0.223345	+	0.386844i
$893$	−1.92554	−	3.33514i	−0.0644358	−	0.111606i
$894$	−1.00320	+	12.4515i	−0.0335522	+	0.416442i
$895$		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
$903$	3.57058	−	24.7708i	0.118821	−	0.824321i
$904$	−10.6724			−0.354959
$905$		0			0
$906$	2.25790	−	3.27225i	0.0750138	−	0.108713i
$907$	−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	$0.350116\pi$
$911$			53.7961i			1.78234i	−0.453665	+	0.891172i	$0.649884\pi$
$912$	−0.520579	+	6.46130i	−0.0172381	+	0.213955i
$913$	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
$921$	15.7781	−	22.8662i	0.519905	−	0.753468i
$922$	2.60678	−	4.51508i	0.0858498	−	0.148696i
$923$			2.82752i			0.0930688i
$924$	−16.9477	−	13.3377i	−0.557540	−	0.438778i
$925$		0			0
$926$	−5.95888	−	3.44036i	−0.195821	−	0.113057i
$927$	−11.1735	−	1.81224i	−0.366986	−	0.0595216i
$928$	28.1161	−	16.2328i	0.922955	−	0.532868i
$929$	26.4805	−	45.8655i	0.868796	−	1.50480i	0.00556817	−	0.999984i	$-0.498228\pi$
$929$	26.4805	−	45.8655i	0.868796	−	1.50480i	0.863228	−	0.504814i	$-0.168439\pi$
$930$		0			0
$931$	−7.71688	+	3.24512i	−0.252911	+	0.106355i
$932$	2.89770			0.0949174
$933$	31.2013	+	2.51385i	1.02149	+	0.0822998i
$934$	−3.06975	+	1.77232i	−0.100445	+	0.0579921i
$935$		0			0
$936$	−4.85121	−	12.7794i	−0.158567	−	0.417707i
$937$	−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	0.587577	−	0.809168i	$-0.300082\pi$
$941$	−12.4842	−	21.6232i	−0.406972	−	0.704896i	−0.994549	+	0.104272i	$0.966749\pi$
$942$	2.43327	−	3.52639i	0.0792801	−	0.114896i
$943$	−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	$-0.185146\pi$
$948$	15.1050	−	21.8908i	0.490589	−	0.710981i
$949$	−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	$0.697300\pi$
$954$	5.44361	+	14.3399i	0.176243	+	0.464271i
$955$		0			0
$956$	9.12588	−	5.26883i	0.295152	−	0.170406i
$957$	34.1043	+	2.74774i	1.10244	+	0.0888219i
$958$	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
$963$	39.1889	+	6.35607i	1.26285	+	0.204821i
$964$	21.3753	+	12.3410i	0.688451	+	0.397478i
$965$		0			0
$966$	2.00588	+	5.01567i	0.0645382	+	0.161376i
$967$			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
$969$	7.60118	−	11.0159i	0.244185	−	0.353883i
$970$		0			0
$971$	2.61333	−	4.52642i	0.0838658	−	0.145260i	−0.821042	−	0.570868i	$-0.806607\pi$
$971$	2.61333	−	4.52642i	0.0838658	−	0.145260i	0.904907	+	0.425609i	$0.139940\pi$
$972$	−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	$0.740791\pi$
$978$	−0.882267	+	10.9505i	−0.0282118	+	0.350158i
$979$		−	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	$0.566151\pi$
$984$	3.37929	−	4.89740i	0.107728	−	0.156123i
$985$		0			0
$986$	−19.3661			−0.616742
$987$	−11.5963	−	9.12617i	−0.369114	−	0.290489i
$988$			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
$996$	0.543767	−	6.74911i	0.0172299	−	0.213854i
$997$	−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
$999$	−13.3174	−	12.7794i	−0.421344	−	0.404322i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.192865 - 0.334053i) q^{2} +(0.983691 - 1.42561i) q^{3} +(0.925606 + 1.60320i) q^{4} +(-0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} +1.48553 q^{8} +(-1.06470 - 2.80471i) q^{9} +O(q^{10})\)	\(q+(0.192865 - 0.334053i) q^{2} +(0.983691 - 1.42561i) q^{3} +(0.925606 + 1.60320i) q^{4} +(-0.286507 - 0.603555i) q^{6} +(1.17656 + 2.36975i) q^{7} +1.48553 q^{8} +(-1.06470 - 2.80471i) q^{9} +(-2.20164 + 1.27112i) q^{11} +(3.19604 + 0.257501i) q^{12} +3.06718 q^{13} +(1.01854 + 0.0640110i) q^{14} +(-1.56470 + 2.71015i) q^{16} +(5.59565 - 3.23065i) q^{17} +(-1.14227 - 0.185264i) q^{18} +(1.03570 + 0.597960i) q^{19} +(4.53570 + 0.653796i) q^{21} +0.980620i q^{22} +(-1.52800 + 2.64657i) q^{23} +(1.46130 - 2.11778i) 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} +(-0.353622 + 4.38907i) q^{33} -2.49232i q^{34} +(3.51101 - 4.30299i) q^{36} +(3.07619 + 1.77604i) q^{37} +(0.399500 - 0.230652i) q^{38} +(3.01716 - 4.37259i) q^{39} +2.31252 q^{41} +(1.09318 - 1.38907i) 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} +(0.898757 - 11.1552i) q^{51} +(2.83900 + 4.91730i) q^{52} +(-6.62740 - 11.4790i) q^{53} +(-1.38775 + 1.44618i) 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} +(5.39378 - 5.82298i) q^{63} -4.64717 q^{64} +(1.39798 + 0.964627i) q^{66} +(-3.04782 + 1.75966i) q^{67} +(10.3587 + 5.98062i) q^{68} +(2.26989 + 4.78173i) q^{69} +0.921861i q^{71} +(-1.58165 - 4.16649i) 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} +(-6.73281 + 5.97238i) q^{81} +(0.446004 - 0.772502i) q^{82} -2.11171i q^{83} +(3.15010 + 7.87677i) q^{84} +(-1.82436 - 1.05330i) q^{86} +(-11.0774 - 7.64357i) q^{87} +(-3.27061 + 1.88829i) q^{88} +(-9.41507 + 16.3074i) q^{89} +(3.60871 + 7.26845i) q^{91} -5.65729 q^{92} +(-0.956152 + 11.8675i) q^{93} +(-1.07571 + 0.621062i) q^{94} +(7.21343 + 0.581177i) q^{96} +12.3692 q^{97} +(1.04668 + 2.48899i) q^{98} +(5.90923 + 4.82161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * q^96 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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