LMFDB - Embedded newform 605.2.b.g.364.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(364,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("605.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.b (of order $2$, degree $1$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1480160000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 27x^{4} + 31x^{2} + 11 $ x^8 + 9x^6 + 27x^4 + 31*x^2 + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.1
Root			$-2.02368i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.g.364.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02368i q^{2} +2.62059i q^{3} -2.09529 q^{4} +(-0.294963 + 2.21653i) q^{5} +5.30325 q^{6} +0.965823i q^{7} +0.192845i q^{8} -3.86752 q^{9} +O(q^{10})$	\(q-2.02368i q^{2} +2.62059i q^{3} -2.09529 q^{4} +(-0.294963 + 2.21653i) q^{5} +5.30325 q^{6} +0.965823i q^{7} +0.192845i q^{8} -3.86752 q^{9} +(4.48555 + 0.596911i) q^{10} -5.49092i q^{12} +4.52509i q^{13} +1.95452 q^{14} +(-5.80862 - 0.772978i) q^{15} -3.80033 q^{16} -3.33669i q^{17} +7.82663i q^{18} -3.27759 q^{19} +(0.618034 - 4.64428i) q^{20} -2.53103 q^{21} +3.36643i q^{23} -0.505368 q^{24} +(-4.82599 - 1.30759i) q^{25} +9.15736 q^{26} -2.27341i q^{27} -2.02368i q^{28} -4.91300 q^{29} +(-1.56426 + 11.7548i) q^{30} -0.418365 q^{31} +8.07636i q^{32} -6.75241 q^{34} +(-2.14077 - 0.284882i) q^{35} +8.10358 q^{36} +6.33755i q^{37} +6.63281i q^{38} -11.8584 q^{39} +(-0.427446 - 0.0568821i) q^{40} +5.78564 q^{41} +5.12200i q^{42} +2.26205i q^{43} +(1.14077 - 8.57246i) q^{45} +6.81258 q^{46} +4.32424i q^{47} -9.95913i q^{48} +6.06719 q^{49} +(-2.64614 + 9.76628i) q^{50} +8.74411 q^{51} -9.48140i q^{52} +2.66070i q^{53} -4.60066 q^{54} -0.186254 q^{56} -8.58924i q^{57} +9.94235i q^{58} +10.1253 q^{59} +(12.1708 + 1.61962i) q^{60} -2.47086 q^{61} +0.846638i q^{62} -3.73534i q^{63} +8.74332 q^{64} +(-10.0300 - 1.33473i) q^{65} -9.60059i q^{67} +6.99135i q^{68} -8.82204 q^{69} +(-0.576511 + 4.33225i) q^{70} -5.45311 q^{71} -0.745831i q^{72} -1.43554i q^{73} +12.8252 q^{74} +(3.42666 - 12.6470i) q^{75} +6.86752 q^{76} +23.9977i q^{78} -1.00396 q^{79} +(1.12096 - 8.42354i) q^{80} -5.64486 q^{81} -11.7083i q^{82} -7.39542i q^{83} +5.30325 q^{84} +(7.39587 + 0.984200i) q^{85} +4.57768 q^{86} -12.8750i q^{87} +12.1964 q^{89} +(-17.3479 - 2.30857i) q^{90} -4.37044 q^{91} -7.05365i q^{92} -1.09637i q^{93} +8.75089 q^{94} +(0.966768 - 7.26487i) q^{95} -21.1649 q^{96} -3.01924i q^{97} -12.2781i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} - 8 q^{25} + 10 q^{26} - 24 q^{29} - 22 q^{30} + 14 q^{31} - 8 q^{34} - 14 q^{35} + 20 q^{36} - 30 q^{39} - 24 q^{40} + 34 q^{41} + 6 q^{45} + 24 q^{46} + 30 q^{49} - 16 q^{50} + 54 q^{51} - 20 q^{54} - 10 q^{56} + 6 q^{59} + 34 q^{60} + 20 q^{61} - 14 q^{64} - 20 q^{65} - 32 q^{69} + 8 q^{70} - 42 q^{71} + 4 q^{74} - 20 q^{75} + 28 q^{76} - 16 q^{79} - 28 q^{80} - 36 q^{81} + 6 q^{84} + 4 q^{85} + 46 q^{86} + 12 q^{89} - 46 q^{90} + 20 q^{91} + 42 q^{94} - 26 q^{95} - 8 q^{96}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 - 12 * q^19 - 4 * q^20 + 4 * q^21 - 2 * q^24 - 8 * q^25 + 10 * q^26 - 24 * q^29 - 22 * q^30 + 14 * q^31 - 8 * q^34 - 14 * q^35 + 20 * q^36 - 30 * q^39 - 24 * q^40 + 34 * q^41 + 6 * q^45 + 24 * q^46 + 30 * q^49 - 16 * q^50 + 54 * q^51 - 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 + 20 * q^61 - 14 * q^64 - 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 + 4 * q^74 - 20 * q^75 + 28 * q^76 - 16 * q^79 - 28 * q^80 - 36 * q^81 + 6 * q^84 + 4 * q^85 + 46 * q^86 + 12 * q^89 - 46 * q^90 + 20 * q^91 + 42 * q^94 - 26 * q^95 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.02368i		−	1.43096i	−0.698633	−	0.715480i	$-0.746208\pi$
$2$		−	2.02368i		−	1.43096i	0.698633	−	0.715480i	$-0.253792\pi$
$3$			2.62059i			1.51300i	0.653993	+	0.756501i	$0.273093\pi$
$3$			2.62059i			1.51300i	−0.653993	+	0.756501i	$0.726907\pi$
$4$	−2.09529			−1.04765
$5$	−0.294963	+	2.21653i	−0.131911	+	0.991262i
$5$	−0.294963	+	2.21653i	−0.131911	+	0.991262i
$6$	5.30325			2.16504
$7$			0.965823i			0.365047i	0.983202	+	0.182523i	$0.0584265\pi$
$7$			0.965823i			0.365047i	−0.983202	+	0.182523i	$0.941573\pi$
$8$			0.192845i			0.0681809i
$9$	−3.86752			−1.28917
$10$	4.48555	+	0.596911i	1.41846	+	0.188760i
$11$		0			0
$11$		0			0
$12$		−	5.49092i		−	1.58509i
$13$			4.52509i			1.25504i	0.778602	+	0.627518i	$0.215929\pi$
$13$			4.52509i			1.25504i	−0.778602	+	0.627518i	$0.784071\pi$
$14$	1.95452			0.522367
$15$	−5.80862	−	0.772978i	−1.49978	−	0.199582i
$16$	−3.80033			−0.950083
$17$		−	3.33669i		−	0.809266i	−0.914479	−	0.404633i	$-0.867399\pi$
$17$		−	3.33669i		−	0.809266i	0.914479	−	0.404633i	$-0.132601\pi$
$18$			7.82663i			1.84475i
$19$	−3.27759			−0.751931			−0.375965	−	0.926634i	$-0.622689\pi$
$19$	−3.27759			−0.751931			−0.375965	+	0.926634i	$0.622689\pi$
$20$	0.618034	−	4.64428i	0.138197	−	1.03849i
$21$	−2.53103			−0.552316
$22$		0			0
$23$			3.36643i			0.701948i	0.936385	+	0.350974i	$0.114149\pi$
$23$			3.36643i			0.701948i	−0.936385	+	0.350974i	$0.885851\pi$
$24$	−0.505368			−0.103158
$25$	−4.82599	−	1.30759i	−0.965199	−	0.261517i
$26$	9.15736			1.79591
$27$		−	2.27341i		−	0.437518i
$28$		−	2.02368i		−	0.382440i
$29$	−4.91300			−0.912321			−0.456160	−	0.889898i	$-0.650776\pi$
$29$	−4.91300			−0.912321			−0.456160	+	0.889898i	$0.650776\pi$
$30$	−1.56426	+	11.7548i	−0.285594	+	2.14613i
$31$	−0.418365			−0.0751406			−0.0375703	−	0.999294i	$-0.511962\pi$
$31$	−0.418365			−0.0751406			−0.0375703	+	0.999294i	$0.511962\pi$
$32$			8.07636i			1.42771i
$33$		0			0
$34$	−6.75241			−1.15803
$35$	−2.14077	−	0.284882i	−0.361857	−	0.0481538i
$36$	8.10358			1.35060
$37$			6.33755i			1.04189i	0.853591	+	0.520944i	$0.174420\pi$
$37$			6.33755i			1.04189i	−0.853591	+	0.520944i	$0.825580\pi$
$38$			6.63281i			1.07598i
$39$	−11.8584			−1.89887
$40$	−0.427446	−	0.0568821i	−0.0675851	−	0.00899385i
$41$	5.78564			0.903565			0.451782	−	0.892128i	$-0.350788\pi$
$41$	5.78564			0.903565			0.451782	+	0.892128i	$0.350788\pi$
$42$			5.12200i			0.790343i
$43$			2.26205i			0.344960i	0.985013	+	0.172480i	$0.0551780\pi$
$43$			2.26205i			0.344960i	−0.985013	+	0.172480i	$0.944822\pi$
$44$		0			0
$45$	1.14077	−	8.57246i	0.170057	−	1.27791i
$46$	6.81258			1.00446
$47$			4.32424i			0.630755i	0.948966	+	0.315378i	$0.102131\pi$
$47$			4.32424i			0.630755i	−0.948966	+	0.315378i	$0.897869\pi$
$48$		−	9.95913i		−	1.43748i
$49$	6.06719			0.866741
$50$	−2.64614	+	9.76628i	−0.374221	+	1.38116i
$51$	8.74411			1.22442
$52$		−	9.48140i		−	1.31483i
$53$			2.66070i			0.365475i	0.983162	+	0.182738i	$0.0584959\pi$
$53$			2.66070i			0.365475i	−0.983162	+	0.182738i	$0.941504\pi$
$54$	−4.60066			−0.626071
$55$		0			0
$56$	−0.186254			−0.0248892
$57$		−	8.58924i		−	1.13767i
$58$			9.94235i			1.30549i
$59$	10.1253			1.31820			0.659100	−	0.752055i	$-0.270937\pi$
$59$	10.1253			1.31820			0.659100	+	0.752055i	$0.270937\pi$
$60$	12.1708	+	1.61962i	1.57124	+	0.209092i
$61$	−2.47086			−0.316361			−0.158180	−	0.987410i	$-0.550563\pi$
$61$	−2.47086			−0.316361			−0.158180	+	0.987410i	$0.550563\pi$
$62$			0.846638i			0.107523i
$63$		−	3.73534i		−	0.470608i
$64$	8.74332			1.09292
$65$	−10.0300	−	1.33473i	−1.24407	−	0.165553i
$66$		0			0
$67$		−	9.60059i		−	1.17290i	−0.809986	−	0.586449i	$-0.800525\pi$
$67$		−	9.60059i		−	1.17290i	0.809986	−	0.586449i	$-0.199475\pi$
$68$			6.99135i			0.847826i
$69$	−8.82204			−1.06205
$70$	−0.576511	+	4.33225i	−0.0689062	+	0.517803i
$71$	−5.45311			−0.647165			−0.323582	−	0.946200i	$-0.604887\pi$
$71$	−5.45311			−0.647165			−0.323582	+	0.946200i	$0.604887\pi$
$72$		−	0.745831i		−	0.0878970i
$73$		−	1.43554i		−	0.168018i	−0.996465	−	0.0840088i	$-0.973228\pi$
$73$		−	1.43554i		−	0.168018i	0.996465	−	0.0840088i	$-0.0267724\pi$
$74$	12.8252			1.49090
$75$	3.42666	−	12.6470i	0.395676	−	1.46035i
$76$	6.86752			0.787758
$77$		0			0
$78$			23.9977i			2.71721i
$79$	−1.00396			−0.112954			−0.0564770	−	0.998404i	$-0.517987\pi$
$79$	−1.00396			−0.112954			−0.0564770	+	0.998404i	$0.517987\pi$
$80$	1.12096	−	8.42354i	0.125327	−	0.941780i
$81$	−5.64486			−0.627207
$82$		−	11.7083i		−	1.29297i
$83$		−	7.39542i		−	0.811752i	−0.913928	−	0.405876i	$-0.866966\pi$
$83$		−	7.39542i		−	0.811752i	0.913928	−	0.405876i	$-0.133034\pi$
$84$	5.30325			0.578632
$85$	7.39587	+	0.984200i	0.802195	+	0.106751i
$86$	4.57768			0.493624
$87$		−	12.8750i		−	1.38034i
$88$		0			0
$89$	12.1964			1.29282			0.646410	−	0.762991i	$-0.276270\pi$
$89$	12.1964			1.29282			0.646410	+	0.762991i	$0.276270\pi$
$90$	−17.3479	−	2.30857i	−1.82863	−	0.243344i
$91$	−4.37044			−0.458147
$92$		−	7.05365i		−	0.735394i
$93$		−	1.09637i		−	0.113688i
$94$	8.75089			0.902586
$95$	0.966768	−	7.26487i	0.0991883	−	0.745360i
$96$	−21.1649			−2.16013
$97$		−	3.01924i		−	0.306557i	−0.988183	−	0.153279i	$-0.951017\pi$
$97$		−	3.01924i		−	0.306557i	0.988183	−	0.153279i	$-0.0489832\pi$
$98$		−	12.2781i		−	1.24027i
$99$		0			0
$100$	10.1119	+	2.73978i	1.01119	+	0.273978i
$101$	15.1962			1.51208			0.756039	−	0.654526i	$-0.227132\pi$
$101$	15.1962			1.51208			0.756039	+	0.654526i	$0.227132\pi$
$102$		−	17.6953i		−	1.75210i
$103$			9.74692i			0.960392i	0.877161	+	0.480196i	$0.159435\pi$
$103$			9.74692i			0.960392i	−0.877161	+	0.480196i	$0.840565\pi$
$104$	−0.872641			−0.0855695
$105$	0.746560	−	5.61010i	0.0728568	−	0.547490i
$106$	5.38441			0.522980
$107$			7.64179i			0.738760i	0.929278	+	0.369380i	$0.120430\pi$
$107$			7.64179i			0.738760i	−0.929278	+	0.369380i	$0.879570\pi$
$108$			4.76346i			0.458364i
$109$	9.85576			0.944010			0.472005	−	0.881596i	$-0.343530\pi$
$109$	9.85576			0.944010			0.472005	+	0.881596i	$0.343530\pi$
$110$		0			0
$111$	−16.6082			−1.57638
$112$		−	3.67045i		−	0.346825i
$113$		−	5.01861i		−	0.472111i	−0.971740	−	0.236056i	$-0.924145\pi$
$113$		−	5.01861i		−	0.472111i	0.971740	−	0.236056i	$-0.0758547\pi$
$114$	−17.3819			−1.62796
$115$	−7.46178	−	0.992971i	−0.695814	−	0.0925950i
$116$	10.2942			0.955790
$117$		−	17.5009i		−	1.61796i
$118$		−	20.4904i		−	1.88629i
$119$	3.22265			0.295420
$120$	0.149065	−	1.12016i	0.0136077	−	0.102256i
$121$		0			0
$122$			5.00023i			0.452700i
$123$			15.1618i			1.36709i
$124$	0.876598			0.0787208
$125$	4.32179	−	10.3113i	0.386553	−	0.922267i
$126$	−7.55914			−0.673422
$127$			7.09040i			0.629172i	0.949229	+	0.314586i	$0.101866\pi$
$127$			7.09040i			0.629172i	−0.949229	+	0.314586i	$0.898134\pi$
$128$		−	1.54101i		−	0.136207i
$129$	−5.92792			−0.521925
$130$	−2.70108	+	20.2975i	−0.236900	+	1.78021i
$131$	7.21704			0.630556			0.315278	−	0.948999i	$-0.397902\pi$
$131$	7.21704			0.630556			0.315278	+	0.948999i	$0.397902\pi$
$132$		0			0
$133$		−	3.16557i		−	0.274490i
$134$	−19.4285			−1.67837
$135$	5.03908	+	0.670572i	0.433695	+	0.0577136i
$136$	0.643464			0.0551766
$137$			8.49079i			0.725417i	0.931903	+	0.362709i	$0.118148\pi$
$137$			8.49079i			0.725417i	−0.931903	+	0.362709i	$0.881852\pi$
$138$			17.8530i			1.51975i
$139$	−7.74016			−0.656512			−0.328256	−	0.944589i	$-0.606461\pi$
$139$	−7.74016			−0.656512			−0.328256	+	0.944589i	$0.606461\pi$
$140$	4.48555	+	0.596911i	0.379098	+	0.0504482i
$141$	−11.3321			−0.954334
$142$			11.0354i			0.926067i
$143$		0			0
$144$	14.6978			1.22482
$145$	1.44915	−	10.8898i	0.120346	−	0.904348i
$146$	−2.90508			−0.240426
$147$			15.8996i			1.31138i
$148$		−	13.2790i		−	1.09153i
$149$	16.8833			1.38313			0.691567	−	0.722312i	$-0.256921\pi$
$149$	16.8833			1.38313			0.691567	+	0.722312i	$0.256921\pi$
$150$	−25.5935	−	6.93447i	−2.08970	−	0.566197i
$151$	−12.2826			−0.999548			−0.499774	−	0.866156i	$-0.666584\pi$
$151$	−12.2826			−0.999548			−0.499774	+	0.866156i	$0.666584\pi$
$152$		−	0.632067i		−	0.0512674i
$153$			12.9047i			1.04328i
$154$		0			0
$155$	0.123402	−	0.927318i	0.00991190	−	0.0744840i
$156$	24.8469			1.98934
$157$			4.20971i			0.335972i	0.985789	+	0.167986i	$0.0537263\pi$
$157$			4.20971i			0.335972i	−0.985789	+	0.167986i	$0.946274\pi$
$158$			2.03169i			0.161633i
$159$	−6.97261			−0.552964
$160$	−17.9015	−	2.38223i	−1.41524	−	0.188331i
$161$	−3.25137			−0.256244
$162$			11.4234i			0.897508i
$163$			16.5736i			1.29814i	0.760728	+	0.649071i	$0.224842\pi$
$163$			16.5736i			1.29814i	−0.760728	+	0.649071i	$0.775158\pi$
$164$	−12.1226			−0.946617
$165$		0			0
$166$	−14.9660			−1.16159
$167$			9.16678i			0.709347i	0.934990	+	0.354674i	$0.115408\pi$
$167$			9.16678i			0.709347i	−0.934990	+	0.354674i	$0.884592\pi$
$168$		−	0.488096i		−	0.0376574i
$169$	−7.47647			−0.575113
$170$	1.99171	−	14.9669i	0.152757	−	1.14791i
$171$	12.6761			0.969369
$172$		−	4.73967i		−	0.361396i
$173$			4.10967i			0.312452i	0.987721	+	0.156226i	$0.0499329\pi$
$173$			4.10967i			0.312452i	−0.987721	+	0.156226i	$0.950067\pi$
$174$	−26.0549			−1.97521
$175$	1.26290	−	4.66106i	0.0954661	−	0.352343i
$176$		0			0
$177$			26.5343i			1.99444i
$178$		−	24.6817i		−	1.84997i
$179$	16.2961			1.21802			0.609012	−	0.793161i	$-0.291566\pi$
$179$	16.2961			1.21802			0.609012	+	0.793161i	$0.291566\pi$
$180$	−2.39026	+	17.9618i	−0.178159	+	1.33880i
$181$	−5.54689			−0.412297			−0.206149	−	0.978521i	$-0.566093\pi$
$181$	−5.54689			−0.412297			−0.206149	+	0.978521i	$0.566093\pi$
$182$			8.84439i			0.655589i
$183$		−	6.47512i		−	0.478654i
$184$	−0.649198			−0.0478595
$185$	−14.0474	−	1.86934i	−1.03278	−	0.137437i
$186$	−2.21870			−0.162683
$187$		0			0
$188$		−	9.06056i		−	0.660809i
$189$	2.19571			0.159715
$190$	−14.7018	−	1.95643i	−1.06658	−	0.141934i
$191$	21.8161			1.57856			0.789280	−	0.614034i	$-0.210454\pi$
$191$	21.8161			1.57856			0.789280	+	0.614034i	$0.210454\pi$
$192$			22.9127i			1.65358i
$193$		−	22.4789i		−	1.61807i	−0.587762	−	0.809034i	$-0.699991\pi$
$193$		−	22.4789i		−	1.61807i	0.587762	−	0.809034i	$-0.300009\pi$
$194$	−6.10999			−0.438672
$195$	3.49780	−	26.2846i	0.250483	−	1.88228i
$196$	−12.7125			−0.908038
$197$		−	25.7479i		−	1.83446i	−0.398358	−	0.917230i	$-0.630420\pi$
$197$		−	25.7479i		−	1.83446i	0.398358	−	0.917230i	$-0.369580\pi$
$198$		0			0
$199$	−16.9671			−1.20277			−0.601385	−	0.798960i	$-0.705384\pi$
$199$	−16.9671			−1.20277			−0.601385	+	0.798960i	$0.705384\pi$
$200$	0.252161	−	0.930668i	0.0178305	−	0.0658082i
$201$	25.1592			1.77460
$202$		−	30.7523i		−	2.16372i
$203$		−	4.74509i		−	0.333040i
$204$	−18.3215			−1.28276
$205$	−1.70655	+	12.8240i	−0.119191	+	0.895669i
$206$	19.7247			1.37428
$207$		−	13.0197i		−	0.904932i
$208$		−	17.1969i		−	1.19239i
$209$		0			0
$210$	−11.3531	−	1.51080i	−0.783436	−	0.104255i
$211$	−5.82637			−0.401104			−0.200552	−	0.979683i	$-0.564274\pi$
$211$	−5.82637			−0.401104			−0.200552	+	0.979683i	$0.564274\pi$
$212$		−	5.57495i		−	0.382889i
$213$		−	14.2904i		−	0.979161i
$214$	15.4646			1.05714
$215$	−5.01390	−	0.667222i	−0.341945	−	0.0455041i
$216$	0.438415			0.0298304
$217$		−	0.404067i		−	0.0274298i
$218$		−	19.9449i		−	1.35084i
$219$	3.76197			0.254211
$220$		0			0
$221$	15.0988			1.01566
$222$			33.6097i			2.25573i
$223$		−	19.0223i		−	1.27383i	−0.770936	−	0.636913i	$-0.780211\pi$
$223$		−	19.0223i		−	1.27383i	0.770936	−	0.636913i	$-0.219789\pi$
$224$	−7.80033			−0.521182
$225$	18.6646	+	5.05712i	1.24431	+	0.337141i
$226$	−10.1561			−0.675572
$227$			28.4659i			1.88935i	0.328008	+	0.944675i	$0.393623\pi$
$227$			28.4659i			1.88935i	−0.328008	+	0.944675i	$0.606377\pi$
$228$			17.9970i			1.19188i
$229$	25.3914			1.67791			0.838954	−	0.544202i	$-0.183168\pi$
$229$	25.3914			1.67791			0.838954	+	0.544202i	$0.183168\pi$
$230$	−2.00946	+	15.1003i	−0.132500	+	0.995682i
$231$		0			0
$232$		−	0.947446i		−	0.0622029i
$233$		−	12.5174i		−	0.820043i	−0.912076	−	0.410022i	$-0.865521\pi$
$233$		−	12.5174i		−	0.820043i	0.912076	−	0.410022i	$-0.134479\pi$
$234$	−35.4162			−2.31523
$235$	−9.58480	−	1.27549i	−0.625244	−	0.0832038i
$236$	−21.2155			−1.38101
$237$		−	2.63096i		−	0.170899i
$238$		−	6.52163i		−	0.422734i
$239$	−20.3876			−1.31876			−0.659381	−	0.751809i	$-0.729182\pi$
$239$	−20.3876			−1.31876			−0.659381	+	0.751809i	$0.729182\pi$
$240$	22.0747	+	2.93757i	1.42491	+	0.189620i
$241$	−22.7935			−1.46826			−0.734129	−	0.679010i	$-0.762409\pi$
$241$	−22.7935			−1.46826			−0.734129	+	0.679010i	$0.762409\pi$
$242$		0			0
$243$		−	21.6131i		−	1.38648i
$244$	5.17717			0.331435
$245$	−1.78959	+	13.4481i	−0.114333	+	0.859167i
$246$	30.6827			1.95626
$247$		−	14.8314i		−	0.943700i
$248$		−	0.0806795i		−	0.00512316i
$249$	19.3804			1.22818
$250$	−20.8667	−	8.74594i	−1.31973	−	0.553142i
$251$	16.9528			1.07005			0.535025	−	0.844836i	$-0.320302\pi$
$251$	16.9528			1.07005			0.535025	+	0.844836i	$0.320302\pi$
$252$			7.82663i			0.493031i
$253$		0			0
$254$	14.3487			0.900320
$255$	−2.57919	+	19.3816i	−0.161515	+	1.21372i
$256$	14.3681			0.898009
$257$			4.73584i			0.295414i	0.989031	+	0.147707i	$0.0471892\pi$
$257$			4.73584i			0.295414i	−0.989031	+	0.147707i	$0.952811\pi$
$258$			11.9962i			0.746853i
$259$	−6.12096			−0.380338
$260$	21.0158	+	2.79666i	1.30334	+	0.173442i
$261$	19.0011			1.17614
$262$		−	14.6050i		−	0.902300i
$263$			18.1037i			1.11632i	0.829732	+	0.558162i	$0.188493\pi$
$263$			18.1037i			1.11632i	−0.829732	+	0.558162i	$0.811507\pi$
$264$		0			0
$265$	−5.89751	−	0.784807i	−0.362281	−	0.0482103i
$266$	−6.40612			−0.392784
$267$			31.9619i			1.95604i
$268$			20.1160i			1.22878i
$269$	2.29802			0.140113			0.0700563	−	0.997543i	$-0.477682\pi$
$269$	2.29802			0.140113			0.0700563	+	0.997543i	$0.477682\pi$
$270$	1.35702	−	10.1975i	0.0825859	−	0.620600i
$271$	0.805688			0.0489421			0.0244710	−	0.999701i	$-0.492210\pi$
$271$	0.805688			0.0489421			0.0244710	+	0.999701i	$0.492210\pi$
$272$			12.6805i			0.768870i
$273$		−	11.4532i		−	0.693176i
$274$	17.1827			1.03804
$275$		0			0
$276$	18.4848			1.11265
$277$		−	11.8329i		−	0.710970i	−0.934682	−	0.355485i	$-0.884316\pi$
$277$		−	11.8329i		−	0.710970i	0.934682	−	0.355485i	$-0.115684\pi$
$278$			15.6636i			0.939442i
$279$	1.61803			0.0968692
$280$	0.0549380	−	0.412837i	0.00328317	−	0.0246717i
$281$	6.22929			0.371608			0.185804	−	0.982587i	$-0.440511\pi$
$281$	6.22929			0.371608			0.185804	+	0.982587i	$0.440511\pi$
$282$			22.9325i			1.36561i
$283$			8.64565i			0.513930i	0.966421	+	0.256965i	$0.0827226\pi$
$283$			8.64565i			0.513930i	−0.966421	+	0.256965i	$0.917277\pi$
$284$	11.4259			0.678000
$285$	19.0383	+	2.53351i	1.12773	+	0.150072i
$286$		0			0
$287$			5.58790i			0.329843i
$288$		−	31.2354i		−	1.84057i
$289$	5.86649			0.345088
$290$	−22.0375	−	2.93262i	−1.29409	−	0.172210i
$291$	7.91221			0.463822
$292$			3.00788i			0.176023i
$293$		−	5.81048i		−	0.339452i	−0.985491	−	0.169726i	$-0.945712\pi$
$293$		−	5.81048i		−	0.339452i	0.985491	−	0.169726i	$-0.0542883\pi$
$294$	32.1758			1.87653
$295$	−2.98659	+	22.4430i	−0.173886	+	1.30668i
$296$	−1.22216			−0.0710369
$297$		0			0
$298$		−	34.1665i		−	1.97921i
$299$	−15.2334			−0.880970
$300$	−7.17985	+	26.4991i	−0.414529	+	1.52993i
$301$	−2.18474			−0.125926
$302$			24.8562i			1.43031i
$303$			39.8231i			2.28778i
$304$	12.4559			0.714397
$305$	0.728811	−	5.47673i	0.0417316	−	0.313596i
$306$	26.1150			1.49290
$307$			18.4721i			1.05426i	0.849785	+	0.527130i	$0.176732\pi$
$307$			18.4721i			1.05426i	−0.849785	+	0.527130i	$0.823268\pi$
$308$		0			0
$309$	−25.5427			−1.45307
$310$	−1.87660	−	0.249727i	−0.106584	−	0.0141835i
$311$	−11.3314			−0.642543			−0.321271	−	0.946987i	$-0.604110\pi$
$311$	−11.3314			−0.642543			−0.321271	+	0.946987i	$0.604110\pi$
$312$		−	2.28684i		−	0.129467i
$313$			5.11499i			0.289116i	0.989496	+	0.144558i	$0.0461760\pi$
$313$			5.11499i			0.289116i	−0.989496	+	0.144558i	$0.953824\pi$
$314$	8.51913			0.480762
$315$	8.27948	+	1.10179i	0.466496	+	0.0620786i
$316$	2.10358			0.118336
$317$			11.8133i			0.663501i	0.943367	+	0.331750i	$0.107639\pi$
$317$			11.8133i			0.663501i	−0.943367	+	0.331750i	$0.892361\pi$
$318$			14.1104i			0.791270i
$319$		0			0
$320$	−2.57896	+	19.3798i	−0.144168	+	1.08337i
$321$	−20.0260			−1.11774
$322$			6.57975i			0.366675i
$323$			10.9363i			0.608512i
$324$	11.8276			0.657092
$325$	5.91695	−	21.8381i	0.328214	−	1.21136i
$326$	33.5396			1.85759
$327$			25.8279i			1.42829i
$328$			1.11573i			0.0616059i
$329$	−4.17645			−0.230255
$330$		0			0
$331$	29.2692			1.60878			0.804391	−	0.594100i	$-0.202492\pi$
$331$	29.2692			1.60878			0.804391	+	0.594100i	$0.202492\pi$
$332$			15.4956i			0.850430i
$333$		−	24.5106i		−	1.34317i
$334$	18.5507			1.01505
$335$	21.2800	+	2.83182i	1.16265	+	0.154719i
$336$	9.61876			0.524746
$337$		−	26.6441i		−	1.45140i	−0.688013	−	0.725698i	$-0.741517\pi$
$337$		−	26.6441i		−	1.45140i	0.688013	−	0.725698i	$-0.258483\pi$
$338$			15.1300i			0.822964i
$339$	13.1517			0.714305
$340$	−15.4965	−	2.06219i	−0.840417	−	0.111838i
$341$		0			0
$342$		−	25.6525i		−	1.38713i
$343$			12.6206i			0.681448i
$344$	−0.436225			−0.0235197
$345$	2.60217	−	19.5543i	0.140096	−	1.05277i
$346$	8.31667			0.447107
$347$			4.31128i			0.231442i	0.993282	+	0.115721i	$0.0369178\pi$
$347$			4.31128i			0.231442i	−0.993282	+	0.115721i	$0.963082\pi$
$348$			26.9769i			1.44611i
$349$	13.1695			0.704947			0.352473	−	0.935822i	$-0.385341\pi$
$349$	13.1695			0.704947			0.352473	+	0.935822i	$0.385341\pi$
$350$	−9.43250	−	2.55571i	−0.504188	−	0.136608i
$351$	10.2874			0.549100
$352$		0			0
$353$		−	25.4904i		−	1.35672i	−0.734732	−	0.678358i	$-0.762692\pi$
$353$		−	25.4904i		−	1.35672i	0.734732	−	0.678358i	$-0.237308\pi$
$354$	53.6970			2.85396
$355$	1.60846	−	12.0870i	0.0853684	−	0.641510i
$356$	−25.5551			−1.35442
$357$			8.44527i			0.446971i
$358$		−	32.9781i		−	1.74294i
$359$	−26.2741			−1.38670			−0.693348	−	0.720603i	$-0.743865\pi$
$359$	−26.2741			−1.38670			−0.693348	+	0.720603i	$0.743865\pi$
$360$	1.65315	+	0.219992i	0.0871289	+	0.0115946i
$361$	−8.25740			−0.434600
$362$			11.2252i			0.589981i
$363$		0			0
$364$	9.15736			0.479976
$365$	3.18192	+	0.423432i	0.166549	+	0.0221634i
$366$	−13.1036			−0.684935
$367$			2.01873i			0.105377i	0.998611	+	0.0526885i	$0.0167791\pi$
$367$			2.01873i			0.105377i	−0.998611	+	0.0526885i	$0.983221\pi$
$368$		−	12.7935i		−	0.666909i
$369$	−22.3761			−1.16485
$370$	−3.78296	+	28.4274i	−0.196667	+	1.47787i
$371$	−2.56976			−0.133416
$372$			2.29721i			0.119105i
$373$			8.87153i			0.459351i	0.973267	+	0.229675i	$0.0737664\pi$
$373$			8.87153i			0.459351i	−0.973267	+	0.229675i	$0.926234\pi$
$374$		0			0
$375$	27.0216	+	11.3257i	1.39539	+	0.584855i
$376$	−0.833908			−0.0430055
$377$		−	22.2318i		−	1.14499i
$378$		−	4.44343i		−	0.228545i
$379$	−21.0641			−1.08199			−0.540995	−	0.841026i	$-0.681952\pi$
$379$	−21.0641			−1.08199			−0.540995	+	0.841026i	$0.681952\pi$
$380$	−2.02566	+	15.2220i	−0.103914	+	0.780874i
$381$	−18.5811			−0.951937
$382$		−	44.1489i		−	2.25886i
$383$		−	25.9795i		−	1.32749i	−0.747958	−	0.663746i	$-0.768965\pi$
$383$		−	25.9795i		−	1.32749i	0.747958	−	0.663746i	$-0.231035\pi$
$384$	4.03836			0.206082
$385$		0			0
$386$	−45.4902			−2.31539
$387$		−	8.74853i		−	0.444713i
$388$			6.32620i			0.321164i
$389$	1.64381			0.0833444			0.0416722	−	0.999131i	$-0.486731\pi$
$389$	1.64381			0.0833444			0.0416722	+	0.999131i	$0.486731\pi$
$390$	−53.1916	−	7.07844i	−2.69346	−	0.358431i
$391$	11.2327			0.568063
$392$			1.17003i			0.0590952i
$393$			18.9129i			0.954032i
$394$	−52.1055			−2.62504
$395$	0.296130	−	2.22530i	0.0148999	−	0.111967i
$396$		0			0
$397$			16.7088i			0.838588i	0.907850	+	0.419294i	$0.137722\pi$
$397$			16.7088i			0.838588i	−0.907850	+	0.419294i	$0.862278\pi$
$398$			34.3361i			1.72111i
$399$	8.29568			0.415304
$400$	18.3404	+	4.96926i	0.917019	+	0.248463i
$401$	27.7920			1.38786			0.693932	−	0.720040i	$-0.255877\pi$
$401$	27.7920			1.38786			0.693932	+	0.720040i	$0.255877\pi$
$402$		−	50.9143i		−	2.53938i
$403$		−	1.89314i		−	0.0943041i
$404$	−31.8405			−1.58412
$405$	1.66503	−	12.5120i	0.0827358	−	0.621726i
$406$	−9.60255			−0.476567
$407$		0			0
$408$			1.68626i			0.0834822i
$409$	−39.4330			−1.94983			−0.974917	−	0.222569i	$-0.928556\pi$
$409$	−39.4330			−1.94983			−0.974917	+	0.222569i	$0.928556\pi$
$410$	25.9518	+	3.45351i	1.28167	+	0.170557i
$411$	−22.2509			−1.09756
$412$		−	20.4227i		−	1.00615i
$413$			9.77924i			0.481205i
$414$	−26.3478			−1.29492
$415$	16.3921	+	2.18137i	0.804659	+	0.107079i
$416$	−36.5463			−1.79183
$417$		−	20.2838i		−	0.993303i
$418$		0			0
$419$	−14.7812			−0.722111			−0.361055	−	0.932544i	$-0.617583\pi$
$419$	−14.7812			−0.722111			−0.361055	+	0.932544i	$0.617583\pi$
$420$	−1.56426	+	11.7548i	−0.0763282	+	0.573576i
$421$	−10.7773			−0.525252			−0.262626	−	0.964898i	$-0.584589\pi$
$421$	−10.7773			−0.525252			−0.262626	+	0.964898i	$0.584589\pi$
$422$			11.7907i			0.573964i
$423$		−	16.7241i		−	0.813152i
$424$	−0.513102			−0.0249184
$425$	−4.36301	+	16.1028i	−0.211637	+	0.781103i
$426$	−28.9192			−1.40114
$427$		−	2.38641i		−	0.115487i
$428$		−	16.0118i		−	0.773960i
$429$		0			0
$430$	−1.35025	+	10.1466i	−0.0651146	+	0.489310i
$431$	32.1916			1.55061			0.775307	−	0.631585i	$-0.217595\pi$
$431$	32.1916			1.55061			0.775307	+	0.631585i	$0.217595\pi$
$432$			8.63971i			0.415678i
$433$		−	0.382631i		−	0.0183881i	−0.999958	−	0.00919404i	$-0.997073\pi$
$433$		−	0.382631i		−	0.0183881i	0.999958	−	0.00919404i	$-0.00292659\pi$
$434$	−0.817703			−0.0392510
$435$	28.5377	+	3.79764i	1.36828	+	0.182083i
$436$	−20.6507			−0.988990
$437$		−	11.0338i		−	0.527817i
$438$		−	7.61305i		−	0.363765i
$439$	−26.5331			−1.26635			−0.633177	−	0.774007i	$-0.718249\pi$
$439$	−26.5331			−1.26635			−0.633177	+	0.774007i	$0.718249\pi$
$440$		0			0
$441$	−23.4649			−1.11738
$442$		−	30.5553i		−	1.45337i
$443$			14.5010i			0.688963i	0.938793	+	0.344482i	$0.111945\pi$
$443$			14.5010i			0.688963i	−0.938793	+	0.344482i	$0.888055\pi$
$444$	34.7990			1.65149
$445$	−3.59750	+	27.0337i	−0.170538	+	1.28152i
$446$	−38.4951			−1.82279
$447$			44.2443i			2.09268i
$448$			8.44450i			0.398965i
$449$	−10.1140			−0.477309			−0.238655	−	0.971105i	$-0.576706\pi$
$449$	−10.1140			−0.477309			−0.238655	+	0.971105i	$0.576706\pi$
$450$	10.2340	−	37.7713i	0.482435	−	1.78055i
$451$		0			0
$452$			10.5155i			0.494606i
$453$		−	32.1878i		−	1.51232i
$454$	57.6060			2.70358
$455$	1.28912	−	9.68720i	0.0604348	−	0.454143i
$456$	1.65639			0.0775676
$457$			39.0887i			1.82849i	0.405157	+	0.914247i	$0.367217\pi$
$457$			39.0887i			1.82849i	−0.405157	+	0.914247i	$0.632783\pi$
$458$		−	51.3841i		−	2.40102i
$459$	−7.58567			−0.354069
$460$	15.6346	+	2.08057i	0.728968	+	0.0970069i
$461$	39.1322			1.82257			0.911285	−	0.411776i	$-0.135092\pi$
$461$	39.1322			1.82257			0.911285	+	0.411776i	$0.135092\pi$
$462$		0			0
$463$			12.9189i			0.600392i	0.953878	+	0.300196i	$0.0970521\pi$
$463$			12.9189i			0.600392i	−0.953878	+	0.300196i	$0.902948\pi$
$464$	18.6710			0.866780
$465$	2.43012	+	0.323387i	0.112694	+	0.0149967i
$466$	−25.3313			−1.17345
$467$		−	11.2491i		−	0.520546i	−0.965535	−	0.260273i	$-0.916187\pi$
$467$		−	11.2491i		−	0.520546i	0.965535	−	0.260273i	$-0.0838126\pi$
$468$			36.6695i			1.69505i
$469$	9.27247			0.428163
$470$	−2.58119	+	19.3966i	−0.119061	+	0.894699i
$471$	−11.0320			−0.508326
$472$			1.95261i			0.0898762i
$473$		0			0
$474$	−5.32424			−0.244550
$475$	15.8176	+	4.28574i	0.725763	+	0.196643i
$476$	−6.75241			−0.309496
$477$		−	10.2903i		−	0.471160i
$478$			41.2580i			1.88710i
$479$	−20.9663			−0.957974			−0.478987	−	0.877822i	$-0.658996\pi$
$479$	−20.9663			−0.957974			−0.478987	+	0.877822i	$0.658996\pi$
$480$	6.24285	−	46.9125i	0.284946	−	2.14125i
$481$	−28.6780			−1.30761
$482$			46.1268i			2.10102i
$483$		−	8.52053i		−	0.387697i
$484$		0			0
$485$	6.69223	+	0.890564i	0.303879	+	0.0404384i
$486$	−43.7381			−1.98400
$487$			22.5691i			1.02270i	0.859371	+	0.511352i	$0.170855\pi$
$487$			22.5691i			1.02270i	−0.859371	+	0.511352i	$0.829145\pi$
$488$		−	0.476492i		−	0.0215698i
$489$	−43.4326			−1.96409
$490$	27.2147	+	3.62157i	1.22943	+	0.163606i
$491$	−20.0762			−0.906026			−0.453013	−	0.891504i	$-0.649651\pi$
$491$	−20.0762			−0.906026			−0.453013	+	0.891504i	$0.649651\pi$
$492$		−	31.7685i		−	1.43223i
$493$			16.3932i			0.738310i
$494$	−30.0141			−1.35040
$495$		0			0
$496$	1.58993			0.0713898
$497$		−	5.26674i		−	0.236245i
$498$		−	39.2198i		−	1.75748i
$499$	−4.65184			−0.208245			−0.104123	−	0.994564i	$-0.533203\pi$
$499$	−4.65184			−0.208245			−0.104123	+	0.994564i	$0.533203\pi$
$500$	−9.05543	+	21.6051i	−0.404971	+	0.966210i
$501$	−24.0224			−1.07324
$502$		−	34.3071i		−	1.53120i
$503$		−	12.9972i		−	0.579517i	−0.957100	−	0.289759i	$-0.906425\pi$
$503$		−	12.9972i		−	0.579517i	0.957100	−	0.289759i	$-0.0935750\pi$
$504$	0.720340			0.0320865
$505$	−4.48232	+	33.6828i	−0.199460	+	1.49887i
$506$		0			0
$507$		−	19.5928i		−	0.870147i
$508$		−	14.8565i		−	0.659150i
$509$	−29.5445			−1.30954			−0.654769	−	0.755829i	$-0.727234\pi$
$509$	−29.5445			−1.30954			−0.654769	+	0.755829i	$0.727234\pi$
$510$	39.2222	+	5.21946i	1.73679	+	0.231122i
$511$	1.38648			0.0613343
$512$		−	32.1586i		−	1.42122i
$513$			7.45131i			0.328983i
$514$	9.58385			0.422725
$515$	−21.6043	−	2.87498i	−0.952000	−	0.126687i
$516$	12.4207			0.546793
$517$		0			0
$518$			12.3869i			0.544248i
$519$	−10.7698			−0.472741
$520$	0.257397	−	1.93423i	0.0112876	−	0.0848217i
$521$	−31.4512			−1.37790			−0.688952	−	0.724807i	$-0.741929\pi$
$521$	−31.4512			−1.37790			−0.688952	+	0.724807i	$0.741929\pi$
$522$		−	38.4522i		−	1.68301i
$523$		−	9.02021i		−	0.394426i	−0.980361	−	0.197213i	$-0.936811\pi$
$523$		−	9.02021i		−	0.394426i	0.980361	−	0.197213i	$-0.0631891\pi$
$524$	−15.1218			−0.660600
$525$	12.2147	+	3.30954i	0.533095	+	0.144440i
$526$	36.6362			1.59741
$527$			1.39595i			0.0608088i
$528$		0			0
$529$	11.6672			0.507269
$530$	−1.58820	+	11.9347i	−0.0689871	+	0.518410i
$531$	−39.1597			−1.69939
$532$			6.63281i			0.287569i
$533$			26.1806i			1.13401i
$534$	64.6808			2.79901
$535$	−16.9382	−	2.25405i	−0.732304	−	0.0974509i
$536$	1.85142			0.0799693
$537$			42.7054i			1.84287i
$538$		−	4.65046i		−	0.200496i
$539$		0			0
$540$	−10.5583	−	1.40504i	−0.454359	−	0.0604635i
$541$	−8.55013			−0.367599			−0.183799	−	0.982964i	$-0.558840\pi$
$541$	−8.55013			−0.367599			−0.183799	+	0.982964i	$0.558840\pi$
$542$		−	1.63046i		−	0.0700342i
$543$		−	14.5362i		−	0.623806i
$544$	26.9483			1.15540
$545$	−2.90708	+	21.8456i	−0.124526	+	0.935761i
$546$	−23.1776			−0.991908
$547$		−	33.9300i		−	1.45074i	−0.688358	−	0.725371i	$-0.741668\pi$
$547$		−	33.9300i		−	1.45074i	0.688358	−	0.725371i	$-0.258332\pi$
$548$		−	17.7907i		−	0.759981i
$549$	9.55608			0.407844
$550$		0			0
$551$	16.1028			0.686002
$552$		−	1.70128i		−	0.0724115i
$553$		−	0.969645i		−	0.0412335i
$554$	−23.9460			−1.01737
$555$	4.89879	−	36.8125i	0.207942	−	1.56260i
$556$	16.2179			0.687792
$557$		−	22.9406i		−	0.972025i	−0.873952	−	0.486013i	$-0.838451\pi$
$557$		−	22.9406i		−	0.972025i	0.873952	−	0.486013i	$-0.161549\pi$
$558$		−	3.27439i		−	0.138616i
$559$	−10.2360			−0.432937
$560$	8.13565	+	1.08265i	0.343794	+	0.0457501i
$561$		0			0
$562$		−	12.6061i		−	0.531757i
$563$		−	9.28262i		−	0.391216i	−0.980682	−	0.195608i	$-0.937332\pi$
$563$		−	9.28262i		−	0.391216i	0.980682	−	0.195608i	$-0.0626680\pi$
$564$	23.7440			0.999805
$565$	11.1239	+	1.48030i	0.467986	+	0.0622768i
$566$	17.4961			0.735414
$567$		−	5.45194i		−	0.228960i
$568$		−	1.05160i		−	0.0441243i
$569$	−30.9271			−1.29653			−0.648266	−	0.761414i	$-0.724506\pi$
$569$	−30.9271			−1.29653			−0.648266	+	0.761414i	$0.724506\pi$
$570$	5.12701	−	38.5275i	0.214747	−	1.61374i
$571$	−2.63736			−0.110370			−0.0551851	−	0.998476i	$-0.517575\pi$
$571$	−2.63736			−0.110370			−0.0551851	+	0.998476i	$0.517575\pi$
$572$		0			0
$573$			57.1712i			2.38836i
$574$	11.3081			0.471993
$575$	4.40189	−	16.2463i	0.183572	−	0.677520i
$576$	−33.8150			−1.40896
$577$		−	36.6305i		−	1.52495i	−0.647019	−	0.762474i	$-0.723985\pi$
$577$		−	36.6305i		−	1.52495i	0.647019	−	0.762474i	$-0.276015\pi$
$578$		−	11.8719i		−	0.493807i
$579$	58.9081			2.44814
$580$	−3.03640	+	22.8173i	−0.126080	+	0.947438i
$581$	7.14266			0.296328
$582$		−	16.0118i		−	0.663710i
$583$		0			0
$584$	0.276837			0.0114556
$585$	38.7912	+	5.16211i	1.60382	+	0.213427i
$586$	−11.7586			−0.485742
$587$			13.7524i			0.567623i	0.958880	+	0.283812i	$0.0915991\pi$
$587$			13.7524i			0.567623i	−0.958880	+	0.283812i	$0.908401\pi$
$588$		−	33.3144i		−	1.37386i
$589$	1.37123			0.0565005
$590$	45.4175	+	6.04390i	1.86981	+	0.248824i
$591$	67.4748			2.77554
$592$		−	24.0848i		−	0.989879i
$593$		−	20.1550i		−	0.827668i	−0.910352	−	0.413834i	$-0.864189\pi$
$593$		−	20.1550i		−	0.827668i	0.910352	−	0.413834i	$-0.135811\pi$
$594$		0			0
$595$	−0.950563	+	7.14310i	−0.0389693	+	0.292839i
$596$	−35.3755			−1.44904
$597$		−	44.4640i		−	1.81979i
$598$			30.8276i			1.26063i
$599$	−4.32318			−0.176640			−0.0883202	−	0.996092i	$-0.528150\pi$
$599$	−4.32318			−0.176640			−0.0883202	+	0.996092i	$0.528150\pi$
$600$	2.43890	+	0.660813i	0.0995678	+	0.0269776i
$601$	35.9895			1.46804			0.734021	−	0.679127i	$-0.237641\pi$
$601$	35.9895			1.46804			0.734021	+	0.679127i	$0.237641\pi$
$602$			4.42123i			0.180196i
$603$			37.1304i			1.51207i
$604$	25.7358			1.04717
$605$		0			0
$606$	80.5893			3.27372
$607$			39.6498i			1.60934i	0.593724	+	0.804669i	$0.297657\pi$
$607$			39.6498i			1.60934i	−0.593724	+	0.804669i	$0.702343\pi$
$608$		−	26.4710i		−	1.07354i
$609$	12.4349			0.503889
$610$	−11.0832	−	1.47488i	−0.448744	−	0.0597163i
$611$	−19.5676			−0.791620
$612$		−	27.0392i		−	1.09299i
$613$			3.81489i			0.154082i	0.997028	+	0.0770410i	$0.0245472\pi$
$613$			3.81489i			0.154082i	−0.997028	+	0.0770410i	$0.975453\pi$
$614$	37.3817			1.50860
$615$	−33.6066	−	4.47217i	−1.35515	−	0.180335i
$616$		0			0
$617$			28.4055i			1.14356i	0.820407	+	0.571781i	$0.193747\pi$
$617$			28.4055i			1.14356i	−0.820407	+	0.571781i	$0.806253\pi$
$618$			51.6904i			2.07929i
$619$	−24.0709			−0.967489			−0.483745	−	0.875209i	$-0.660724\pi$
$619$	−24.0709			−0.967489			−0.483745	+	0.875209i	$0.660724\pi$
$620$	−0.258564	+	1.94300i	−0.0103842	+	0.0780329i
$621$	7.65327			0.307115
$622$			22.9311i			0.919453i
$623$			11.7796i			0.471940i
$624$	45.0660			1.80408
$625$	21.5804	+	12.6208i	0.863217	+	0.504833i
$626$	10.3511			0.413714
$627$		0			0
$628$		−	8.82059i		−	0.351980i
$629$	21.1465			0.843165
$630$	2.22967	−	16.7550i	0.0888320	−	0.667537i
$631$	19.1216			0.761218			0.380609	−	0.924736i	$-0.375714\pi$
$631$	19.1216			0.761218			0.380609	+	0.924736i	$0.375714\pi$
$632$		−	0.193608i		−	0.00770131i
$633$		−	15.2686i		−	0.606871i
$634$	23.9064			0.949443
$635$	−15.7161	−	2.09141i	−0.623674	−	0.0829949i
$636$	14.6097			0.579311
$637$			27.4546i			1.08779i
$638$		0			0
$639$	21.0900			0.834307
$640$	3.41569	+	0.454540i	0.135017	+	0.0179673i
$641$	11.9790			0.473143			0.236571	−	0.971614i	$-0.423976\pi$
$641$	11.9790			0.473143			0.236571	+	0.971614i	$0.423976\pi$
$642$			40.5264i			1.59945i
$643$		−	25.7408i		−	1.01512i	−0.861617	−	0.507559i	$-0.830548\pi$
$643$		−	25.7408i		−	1.01512i	0.861617	−	0.507559i	$-0.169452\pi$
$644$	6.81258			0.268453
$645$	1.74852	−	13.1394i	0.0688478	−	0.517364i
$646$	22.1316			0.870757
$647$		−	9.30228i		−	0.365710i	−0.983140	−	0.182855i	$-0.941466\pi$
$647$		−	9.30228i		−	0.365710i	0.983140	−	0.182855i	$-0.0585339\pi$
$648$		−	1.08858i		−	0.0427636i
$649$		0			0
$650$	−44.1933	−	11.9740i	−1.73341	−	0.469661i
$651$	1.05889			0.0415014
$652$		−	34.7265i		−	1.35999i
$653$		−	37.4506i		−	1.46556i	−0.680468	−	0.732778i	$-0.738223\pi$
$653$		−	37.4506i		−	1.46556i	0.680468	−	0.732778i	$-0.261777\pi$
$654$	52.2676			2.04382
$655$	−2.12876	+	15.9968i	−0.0831775	+	0.625046i
$656$	−21.9873			−0.858461
$657$			5.55198i			0.216604i
$658$			8.45182i			0.329486i
$659$	4.93753			0.192339			0.0961693	−	0.995365i	$-0.469341\pi$
$659$	4.93753			0.192339			0.0961693	+	0.995365i	$0.469341\pi$
$660$		0			0
$661$	−4.82155			−0.187537			−0.0937683	−	0.995594i	$-0.529891\pi$
$661$	−4.82155			−0.187537			−0.0937683	+	0.995594i	$0.529891\pi$
$662$		−	59.2317i		−	2.30210i
$663$			39.5679i			1.53669i
$664$	1.42617			0.0553460
$665$	7.01658	+	0.933727i	0.272091	+	0.0362084i
$666$	−49.6017			−1.92203
$667$		−	16.5392i		−	0.640402i
$668$		−	19.2071i		−	0.743145i
$669$	49.8497			1.92730
$670$	5.73070	−	43.0639i	0.221396	−	1.66370i
$671$		0			0
$672$		−	20.4415i		−	0.788548i
$673$			32.9141i			1.26874i	0.773028	+	0.634372i	$0.218741\pi$
$673$			32.9141i			1.26874i	−0.773028	+	0.634372i	$0.781259\pi$
$674$	−53.9192			−2.07689
$675$	−2.97268	+	10.9715i	−0.114419	+	0.422292i
$676$	15.6654			0.602515
$677$		−	17.1426i		−	0.658842i	−0.944183	−	0.329421i	$-0.893146\pi$
$677$		−	17.1426i		−	0.658842i	0.944183	−	0.329421i	$-0.106854\pi$
$678$		−	26.6150i		−	1.02214i
$679$	2.91605			0.111908
$680$	−0.189798	+	1.42626i	−0.00727842	+	0.0546944i
$681$	−74.5977			−2.85859
$682$		0			0
$683$			19.3586i			0.740737i	0.928885	+	0.370368i	$0.120769\pi$
$683$			19.3586i			0.740737i	−0.928885	+	0.370368i	$0.879231\pi$
$684$	−26.5602			−1.01556
$685$	−18.8201	−	2.50447i	−0.719078	−	0.0956908i
$686$	25.5401			0.975125
$687$			66.5405i			2.53868i
$688$		−	8.59655i		−	0.327740i
$689$	−12.0399			−0.458684
$690$	−39.5717	−	5.26598i	−1.50647	−	0.200472i
$691$	−9.14145			−0.347757			−0.173879	−	0.984767i	$-0.555630\pi$
$691$	−9.14145			−0.347757			−0.173879	+	0.984767i	$0.555630\pi$
$692$		−	8.61097i		−	0.327340i
$693$		0			0
$694$	8.72467			0.331184
$695$	2.28306	−	17.1563i	0.0866014	−	0.650775i
$696$	2.48287			0.0941130
$697$		−	19.3049i		−	0.731225i
$698$		−	26.6509i		−	1.00875i
$699$	32.8031			1.24073
$700$	−2.64614	+	9.76628i	−0.100015	+	0.369131i
$701$	−15.2935			−0.577626			−0.288813	−	0.957385i	$-0.593261\pi$
$701$	−15.2935			−0.577626			−0.288813	+	0.957385i	$0.593261\pi$
$702$		−	20.8184i		−	0.785741i
$703$		−	20.7719i		−	0.783428i
$704$		0			0
$705$	3.34254	−	25.1179i	0.125887	−	0.945994i
$706$	−51.5844			−1.94141
$707$			14.6768i			0.551979i
$708$		−	55.5971i		−	2.08947i
$709$	−42.9129			−1.61163			−0.805813	−	0.592170i	$-0.798271\pi$
$709$	−42.9129			−1.61163			−0.805813	+	0.592170i	$0.798271\pi$
$710$	−24.4602	−	3.25502i	−0.917975	−	0.122159i
$711$	3.88282			0.145617
$712$			2.35202i			0.0881456i
$713$		−	1.40839i		−	0.0527448i
$714$	17.0905			0.639598
$715$		0			0
$716$	−34.1450			−1.27606
$717$		−	53.4276i		−	1.99529i
$718$			53.1705i			1.98431i
$719$	−4.81326			−0.179504			−0.0897521	−	0.995964i	$-0.528607\pi$
$719$	−4.81326			−0.179504			−0.0897521	+	0.995964i	$0.528607\pi$
$720$	−4.33532	+	32.5782i	−0.161568	+	1.21412i
$721$	−9.41380			−0.350588
$722$			16.7104i			0.621895i
$723$		−	59.7325i		−	2.22147i
$724$	11.6224			0.431942
$725$	23.7101	+	6.42417i	0.880571	+	0.238588i
$726$		0			0
$727$		−	21.8922i		−	0.811937i	−0.913887	−	0.405969i	$-0.866934\pi$
$727$		−	21.8922i		−	0.811937i	0.913887	−	0.405969i	$-0.133066\pi$
$728$		−	0.842817i		−	0.0312369i
$729$	39.7047			1.47054
$730$	0.856892	−	6.43920i	0.0317150	−	0.238325i
$731$	7.54777			0.279164
$732$			13.5673i			0.501461i
$733$			48.0295i			1.77401i	0.461759	+	0.887005i	$0.347218\pi$
$733$			48.0295i			1.77401i	−0.461759	+	0.887005i	$0.652782\pi$
$734$	4.08528			0.150790
$735$	−35.2420	−	4.68980i	−1.29992	−	0.172986i
$736$	−27.1885			−1.00218
$737$		0			0
$738$			45.2820i			1.66685i
$739$	34.1074			1.25466			0.627330	−	0.778754i	$-0.284148\pi$
$739$	34.1074			1.25466			0.627330	+	0.778754i	$0.284148\pi$
$740$	29.4334	+	3.91682i	1.08199	+	0.143985i
$741$	38.8671			1.42782
$742$			5.20039i			0.190912i
$743$			26.4402i			0.969996i	0.874515	+	0.484998i	$0.161180\pi$
$743$			26.4402i			0.969996i	−0.874515	+	0.484998i	$0.838820\pi$
$744$	0.211428			0.00775134
$745$	−4.97995	+	37.4223i	−0.182451	+	1.37105i
$746$	17.9532			0.657312
$747$			28.6019i			1.04649i
$748$		0			0
$749$	−7.38062			−0.269682
$750$	22.9196	−	54.6832i	0.836904	−	1.99675i
$751$	45.9403			1.67639			0.838193	−	0.545374i	$-0.183612\pi$
$751$	45.9403			1.67639			0.838193	+	0.545374i	$0.183612\pi$
$752$		−	16.4335i		−	0.599270i
$753$			44.4264i			1.61899i
$754$	−44.9901			−1.63844
$755$	3.62292	−	27.2248i	0.131852	−	0.990813i
$756$	−4.60066			−0.167324
$757$		−	30.8557i		−	1.12147i	−0.827996	−	0.560735i	$-0.810519\pi$
$757$		−	30.8557i		−	1.12147i	0.827996	−	0.560735i	$-0.189481\pi$
$758$			42.6271i			1.54828i
$759$		0			0
$760$	1.40099	+	0.186436i	0.0508194	+	0.00676275i
$761$	−14.1975			−0.514658			−0.257329	−	0.966324i	$-0.582842\pi$
$761$	−14.1975			−0.514658			−0.257329	+	0.966324i	$0.582842\pi$
$762$			37.6022i			1.36218i
$763$			9.51892i			0.344608i
$764$	−45.7112			−1.65377
$765$	−28.6036	−	3.80641i	−1.03417	−	0.137621i
$766$	−52.5744			−1.89959
$767$			45.8179i			1.65439i
$768$			37.6531i			1.35869i
$769$	30.0208			1.08258			0.541290	−	0.840836i	$-0.317936\pi$
$769$	30.0208			1.08258			0.541290	+	0.840836i	$0.317936\pi$
$770$		0			0
$771$	−12.4107			−0.446961
$772$			47.0999i			1.69516i
$773$			30.4294i			1.09447i	0.836979	+	0.547234i	$0.184319\pi$
$773$			30.4294i			1.09447i	−0.836979	+	0.547234i	$0.815681\pi$
$774$	−17.7042			−0.636366
$775$	2.01903	+	0.547049i	0.0725256	+	0.0196506i
$776$	0.582245			0.0209014
$777$		−	16.0405i		−	0.575451i
$778$		−	3.32655i		−	0.119262i
$779$	−18.9630			−0.679418
$780$	−7.32892	+	55.0739i	−0.262417	+	1.97196i
$781$		0			0
$782$		−	22.7315i		−	0.812876i
$783$			11.1693i			0.399157i
$784$	−23.0573			−0.823476
$785$	−9.33095	−	1.24171i	−0.333036	−	0.0443185i
$786$	38.2738			1.36518
$787$			30.4648i			1.08595i	0.839748	+	0.542976i	$0.182702\pi$
$787$			30.4648i			1.08595i	−0.839748	+	0.542976i	$0.817298\pi$
$788$			53.9494i			1.92187i
$789$	−47.4425			−1.68900
$790$	−4.50330	−	0.599273i	−0.160220	−	0.0213212i
$791$	4.84709			0.172343
$792$		0			0
$793$		−	11.1809i		−	0.397044i
$794$	33.8132			1.19999
$795$	2.05666	−	15.4550i	0.0729423	−	0.548132i
$796$	35.5512			1.26008
$797$		−	33.0452i		−	1.17052i	−0.810846	−	0.585260i	$-0.800992\pi$
$797$		−	33.0452i		−	1.17052i	0.810846	−	0.585260i	$-0.199008\pi$
$798$		−	16.7878i		−	0.594283i
$799$	14.4287			0.510449
$800$	10.5605	−	38.9764i	0.373371	−	1.37803i
$801$	−47.1699			−1.66667
$802$		−	56.2421i		−	1.98598i
$803$		0			0
$804$	−52.7160			−1.85915
$805$	0.959034	−	7.20676i	0.0338015	−	0.254005i
$806$	−3.83112			−0.134945
$807$			6.02218i			0.211991i
$808$			2.93051i			0.103095i
$809$	−10.9895			−0.386371			−0.193186	−	0.981162i	$-0.561882\pi$
$809$	−10.9895			−0.386371			−0.193186	+	0.981162i	$0.561882\pi$
$810$	−25.3203	−	3.36948i	−0.889665	−	0.118392i
$811$	40.7587			1.43123			0.715615	−	0.698495i	$-0.246146\pi$
$811$	40.7587			1.43123			0.715615	+	0.698495i	$0.246146\pi$
$812$			9.94235i			0.348908i
$813$			2.11138i			0.0740494i
$814$		0			0
$815$	−36.7358	−	4.88858i	−1.28680	−	0.171240i
$816$	−33.2305			−1.16330
$817$		−	7.41408i		−	0.259386i
$818$			79.7998i			2.79013i
$819$	16.9027			0.590630
$820$	3.57572	−	26.8701i	0.124870	−	0.938345i
$821$	15.1076			0.527259			0.263630	−	0.964624i	$-0.415080\pi$
$821$	15.1076			0.527259			0.263630	+	0.964624i	$0.415080\pi$
$822$			45.0288i			1.57056i
$823$		−	36.4313i		−	1.26991i	−0.772548	−	0.634957i	$-0.781018\pi$
$823$		−	36.4313i		−	1.26991i	0.772548	−	0.634957i	$-0.218982\pi$
$824$	−1.87964			−0.0654805
$825$		0			0
$826$	19.7901			0.688585
$827$			3.80342i			0.132258i	0.997811	+	0.0661290i	$0.0210649\pi$
$827$			3.80342i			0.132258i	−0.997811	+	0.0661290i	$0.978935\pi$
$828$			27.2801i			0.948050i
$829$	27.3063			0.948386			0.474193	−	0.880421i	$-0.342740\pi$
$829$	27.3063			0.948386			0.474193	+	0.880421i	$0.342740\pi$
$830$	4.41441	−	33.1725i	0.153226	−	1.15143i
$831$	31.0092			1.07570
$832$			39.5644i			1.37165i
$833$		−	20.2443i		−	0.701424i
$834$	−41.0480			−1.42138
$835$	−20.3184	−	2.70386i	−0.703148	−	0.0935710i
$836$		0			0
$837$			0.951115i			0.0328754i
$838$			29.9125i			1.03331i
$839$	−28.3250			−0.977888			−0.488944	−	0.872315i	$-0.662618\pi$
$839$	−28.3250			−0.977888			−0.488944	+	0.872315i	$0.662618\pi$
$840$	1.08188	+	0.143970i	0.0373284	+	0.00496745i
$841$	−4.86246			−0.167671
$842$			21.8098i			0.751615i
$843$			16.3244i			0.562244i
$844$	12.2080			0.420215
$845$	2.20528	−	16.5718i	0.0758640	−	0.570087i
$846$	−33.8442			−1.16359
$847$		0			0
$848$		−	10.1115i		−	0.347232i
$849$	−22.6567			−0.777577
$850$	32.5871	+	8.82936i	1.11773	+	0.302845i
$851$	−21.3349			−0.731351
$852$			29.9426i			1.02582i
$853$		−	8.34318i		−	0.285665i	−0.989747	−	0.142833i	$-0.954379\pi$
$853$		−	8.34318i		−	0.285665i	0.989747	−	0.142833i	$-0.0456210\pi$
$854$	−4.82934			−0.165257
$855$	−3.73899	+	28.0970i	−0.127871	+	0.960898i
$856$	−1.47368			−0.0503694
$857$		−	8.59547i		−	0.293616i	−0.989165	−	0.146808i	$-0.953100\pi$
$857$		−	8.59547i		−	0.293616i	0.989165	−	0.146808i	$-0.0468999\pi$
$858$		0			0
$859$	−9.40807			−0.320999			−0.160500	−	0.987036i	$-0.551311\pi$
$859$	−9.40807			−0.320999			−0.160500	+	0.987036i	$0.551311\pi$
$860$	10.5056	+	1.39803i	0.358238	+	0.0476723i
$861$	−14.6436			−0.499054
$862$		−	65.1456i		−	2.21887i
$863$			10.3261i			0.351503i	0.984435	+	0.175752i	$0.0562356\pi$
$863$			10.3261i			0.351503i	−0.984435	+	0.175752i	$0.943764\pi$
$864$	18.3609			0.624649
$865$	−9.10920	−	1.21220i	−0.309722	−	0.0412160i
$866$	−0.774324			−0.0263126
$867$			15.3737i			0.522118i
$868$			0.846638i			0.0287368i
$869$		0			0
$870$	7.68522	−	57.7514i	0.260553	−	1.95795i
$871$	43.4435			1.47203
$872$			1.90063i			0.0643635i
$873$			11.6770i			0.395205i
$874$	−22.3288			−0.755285
$875$	9.95885	+	4.17409i	0.336671	+	0.141110i
$876$	−7.88244			−0.266323
$877$			29.8032i			1.00638i	0.864175	+	0.503191i	$0.167841\pi$
$877$			29.8032i			1.00638i	−0.864175	+	0.503191i	$0.832159\pi$
$878$			53.6945i			1.81210i
$879$	15.2269			0.513591
$880$		0			0
$881$	30.1175			1.01469			0.507343	−	0.861744i	$-0.330628\pi$
$881$	30.1175			1.01469			0.507343	+	0.861744i	$0.330628\pi$
$882$			47.4856i			1.59892i
$883$		−	50.3619i		−	1.69481i	−0.530945	−	0.847406i	$-0.678163\pi$
$883$		−	50.3619i		−	1.69481i	0.530945	−	0.847406i	$-0.321837\pi$
$884$	−31.6365			−1.06405
$885$	−58.8140	−	7.82663i	−1.97701	−	0.263089i
$886$	29.3454			0.985879
$887$			41.4054i			1.39026i	0.718885	+	0.695129i	$0.244653\pi$
$887$			41.4054i			1.39026i	−0.718885	+	0.695129i	$0.755347\pi$
$888$		−	3.20280i		−	0.107479i
$889$	−6.84808			−0.229677
$890$	54.7077	+	7.28019i	1.83381	+	0.244033i
$891$		0			0
$892$			39.8572i			1.33452i
$893$		−	14.1731i		−	0.474284i
$894$	89.5365			2.99455
$895$	−4.80673	+	36.1207i	−0.160671	+	1.20738i
$896$	1.48834			0.0497220
$897$		−	39.9205i		−	1.33291i
$898$			20.4675i			0.683010i
$899$	2.05543			0.0685523
$900$	−39.1079	−	10.5961i	−1.30360	−	0.353205i
$901$	8.87793			0.295767
$902$		0			0
$903$		−	5.72532i		−	0.190527i
$904$	0.967813			0.0321890
$905$	1.63613	−	12.2948i	0.0543867	−	0.408694i
$906$	−65.1380			−2.16406
$907$		−	4.63216i		−	0.153808i	−0.997038	−	0.0769041i	$-0.975496\pi$
$907$		−	4.63216i		−	0.153808i	0.997038	−	0.0769041i	$-0.0245035\pi$
$908$		−	59.6445i		−	1.97937i
$909$	−58.7716			−1.94933
$910$	−19.6038	−	2.60877i	−0.649861	−	0.0864797i
$911$	6.97855			0.231210			0.115605	−	0.993295i	$-0.463119\pi$
$911$	6.97855			0.231210			0.115605	+	0.993295i	$0.463119\pi$
$912$			32.6419i			1.08088i
$913$		0			0
$914$	79.1032			2.61650
$915$	14.3523	+	1.90992i	0.474472	+	0.0631400i
$916$	−53.2024			−1.75786
$917$			6.97038i			0.230182i
$918$			15.3510i			0.506658i
$919$	23.4207			0.772576			0.386288	−	0.922378i	$-0.373757\pi$
$919$	23.4207			0.772576			0.386288	+	0.922378i	$0.373757\pi$
$920$	0.191489	−	1.43897i	0.00631321	−	0.0474413i
$921$	−48.4079			−1.59510
$922$		−	79.1912i		−	2.60802i
$923$		−	24.6758i		−	0.812215i
$924$		0			0
$925$	8.28691	−	30.5850i	0.272472	−	1.00563i
$926$	26.1438			0.859137
$927$		−	37.6964i		−	1.23811i
$928$		−	39.6791i		−	1.30253i
$929$	18.0905			0.593529			0.296765	−	0.954951i	$-0.404092\pi$
$929$	18.0905			0.593529			0.296765	+	0.954951i	$0.404092\pi$
$930$	0.654433	−	4.91780i	0.0214597	−	0.161261i
$931$	−19.8858			−0.651729
$932$			26.2277i			0.859116i
$933$		−	29.6949i		−	0.972168i
$934$	−22.7646			−0.744881
$935$		0			0
$936$	3.37495			0.110314
$937$			11.0096i			0.359668i	0.983697	+	0.179834i	$0.0575561\pi$
$937$			11.0096i			0.359668i	−0.983697	+	0.179834i	$0.942444\pi$
$938$		−	18.7645i		−	0.612684i
$939$	−13.4043			−0.437433
$940$	20.0830	+	2.67253i	0.655034	+	0.0871682i
$941$	33.7808			1.10122			0.550612	−	0.834762i	$-0.314395\pi$
$941$	33.7808			1.10122			0.550612	+	0.834762i	$0.314395\pi$
$942$			22.3252i			0.727394i
$943$			19.4769i			0.634256i
$944$	−38.4795			−1.25240
$945$	−0.647654	+	4.86686i	−0.0210682	+	0.158319i
$946$		0			0
$947$		−	46.9853i		−	1.52682i	−0.645915	−	0.763409i	$-0.723524\pi$
$947$		−	46.9853i		−	1.52682i	0.645915	−	0.763409i	$-0.276476\pi$
$948$			5.51264i			0.179042i
$949$	6.49596			0.210868
$950$	8.67297	−	32.0099i	0.281388	−	1.03854i
$951$	−30.9579			−1.00388
$952$			0.621472i			0.0201420i
$953$		−	42.4907i		−	1.37641i	−0.725517	−	0.688204i	$-0.758400\pi$
$953$		−	42.4907i		−	1.37641i	0.725517	−	0.688204i	$-0.241600\pi$
$954$	−20.8243			−0.674212
$955$	−6.43495	+	48.3560i	−0.208230	+	1.56477i
$956$	42.7180			1.38160
$957$		0			0
$958$			42.4291i			1.37082i
$959$	−8.20060			−0.264811
$960$	−50.7867	−	6.75840i	−1.63913	−	0.218126i
$961$	−30.8250			−0.994354
$962$			58.0352i			1.87113i
$963$		−	29.5548i		−	0.952389i
$964$	47.7590			1.53822
$965$	49.8251	+	6.63044i	1.60393	+	0.213442i
$966$	−17.2428			−0.554780
$967$			54.1642i			1.74180i	0.491458	+	0.870901i	$0.336464\pi$
$967$			54.1642i			1.74180i	−0.491458	+	0.870901i	$0.663536\pi$
$968$		0			0
$969$	−28.6596			−0.920680
$970$	1.80222	−	13.5430i	0.0578658	−	0.434838i
$971$	5.23848			0.168111			0.0840554	−	0.996461i	$-0.473213\pi$
$971$	5.23848			0.168111			0.0840554	+	0.996461i	$0.473213\pi$
$972$			45.2859i			1.45254i
$973$		−	7.47562i		−	0.239657i
$974$	45.6727			1.46345
$975$	57.2287	+	15.5059i	1.83279	+	0.496587i
$976$	9.39008			0.300569
$977$		−	7.78142i		−	0.248950i	−0.992223	−	0.124475i	$-0.960275\pi$
$977$		−	7.78142i		−	0.248950i	0.992223	−	0.124475i	$-0.0397246\pi$
$978$			87.8938i			2.81053i
$979$		0			0
$980$	3.74973	−	28.1777i	0.119781	−	0.900104i
$981$	−38.1173			−1.21699
$982$			40.6279i			1.29649i
$983$		−	51.5136i		−	1.64303i	−0.570188	−	0.821515i	$-0.693129\pi$
$983$		−	51.5136i		−	1.64303i	0.570188	−	0.821515i	$-0.306871\pi$
$984$	−2.92388			−0.0932098
$985$	57.0709	+	7.59467i	1.81843	+	0.241986i
$986$	33.1745			1.05649
$987$		−	10.9448i		−	0.348376i
$988$			31.0762i			0.988664i
$989$	−7.61503			−0.242144
$990$		0			0
$991$	−22.3382			−0.709596			−0.354798	−	0.934943i	$-0.615450\pi$
$991$	−22.3382			−0.709596			−0.354798	+	0.934943i	$0.615450\pi$
$992$		−	3.37887i		−	0.107279i
$993$			76.7028i			2.43409i
$994$	−10.6582			−0.338058
$995$	5.00468	−	37.6082i	0.158659	−	1.19226i
$996$	−40.6076			−1.28670
$997$			0.184546i			0.00584463i	0.999996	+	0.00292231i	$0.000930202\pi$
$997$			0.184546i			0.00584463i	−0.999996	+	0.00292231i	$0.999070\pi$
$998$			9.41386i			0.297990i
$999$	14.4079			0.455845

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.b.g.364.1		8
5.2	odd	4		3025.2.a.bl.1.8		8
5.3	odd	4		3025.2.a.bl.1.1		8
5.4	even	2	inner	605.2.b.g.364.8		8
11.2	odd	10		605.2.j.d.444.4		16
11.3	even	5		605.2.j.h.9.1		16
11.4	even	5		605.2.j.h.269.4		16
11.5	even	5		55.2.j.a.14.4	yes	16
11.6	odd	10		605.2.j.d.124.1		16
11.7	odd	10		605.2.j.g.269.1		16
11.8	odd	10		605.2.j.g.9.4		16
11.9	even	5		55.2.j.a.4.1	✓	16
11.10	odd	2		605.2.b.f.364.8		8
33.5	odd	10		495.2.ba.a.289.1		16
33.20	odd	10		495.2.ba.a.334.4		16
44.27	odd	10		880.2.cd.c.289.4		16
44.31	odd	10		880.2.cd.c.609.1		16
55.4	even	10		605.2.j.h.269.1		16
55.9	even	10		55.2.j.a.4.4	yes	16
55.14	even	10		605.2.j.h.9.4		16
55.19	odd	10		605.2.j.g.9.1		16
55.24	odd	10		605.2.j.d.444.1		16
55.27	odd	20		275.2.h.d.201.1		16
55.29	odd	10		605.2.j.g.269.4		16
55.32	even	4		3025.2.a.bk.1.1		8
55.38	odd	20		275.2.h.d.201.4		16
55.39	odd	10		605.2.j.d.124.4		16
55.42	odd	20		275.2.h.d.26.1		16
55.43	even	4		3025.2.a.bk.1.8		8
55.49	even	10		55.2.j.a.14.1	yes	16
55.53	odd	20		275.2.h.d.26.4		16
55.54	odd	2		605.2.b.f.364.1		8
165.104	odd	10		495.2.ba.a.289.4		16
165.119	odd	10		495.2.ba.a.334.1		16
220.119	odd	10		880.2.cd.c.609.4		16
220.159	odd	10		880.2.cd.c.289.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.1	✓	16	11.9	even	5
55.2.j.a.4.4	yes	16	55.9	even	10
55.2.j.a.14.1	yes	16	55.49	even	10
55.2.j.a.14.4	yes	16	11.5	even	5
275.2.h.d.26.1		16	55.42	odd	20
275.2.h.d.26.4		16	55.53	odd	20
275.2.h.d.201.1		16	55.27	odd	20
275.2.h.d.201.4		16	55.38	odd	20
495.2.ba.a.289.1		16	33.5	odd	10
495.2.ba.a.289.4		16	165.104	odd	10
495.2.ba.a.334.1		16	165.119	odd	10
495.2.ba.a.334.4		16	33.20	odd	10
605.2.b.f.364.1		8	55.54	odd	2
605.2.b.f.364.8		8	11.10	odd	2
605.2.b.g.364.1		8	1.1	even	1	trivial
605.2.b.g.364.8		8	5.4	even	2	inner
605.2.j.d.124.1		16	11.6	odd	10
605.2.j.d.124.4		16	55.39	odd	10
605.2.j.d.444.1		16	55.24	odd	10
605.2.j.d.444.4		16	11.2	odd	10
605.2.j.g.9.1		16	55.19	odd	10
605.2.j.g.9.4		16	11.8	odd	10
605.2.j.g.269.1		16	11.7	odd	10
605.2.j.g.269.4		16	55.29	odd	10
605.2.j.h.9.1		16	11.3	even	5
605.2.j.h.9.4		16	55.14	even	10
605.2.j.h.269.1		16	55.4	even	10
605.2.j.h.269.4		16	11.4	even	5
880.2.cd.c.289.1		16	220.159	odd	10
880.2.cd.c.289.4		16	44.27	odd	10
880.2.cd.c.609.1		16	44.31	odd	10
880.2.cd.c.609.4		16	220.119	odd	10
3025.2.a.bk.1.1		8	55.32	even	4
3025.2.a.bk.1.8		8	55.43	even	4
3025.2.a.bl.1.1		8	5.3	odd	4
3025.2.a.bl.1.8		8	5.2	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.02368i q^{2} +2.62059i q^{3} -2.09529 q^{4} +(-0.294963 + 2.21653i) q^{5} +5.30325 q^{6} +0.965823i q^{7} +0.192845i q^{8} -3.86752 q^{9} +O(q^{10})\)	\(q-2.02368i q^{2} +2.62059i q^{3} -2.09529 q^{4} +(-0.294963 + 2.21653i) q^{5} +5.30325 q^{6} +0.965823i q^{7} +0.192845i q^{8} -3.86752 q^{9} +(4.48555 + 0.596911i) q^{10} -5.49092i q^{12} +4.52509i q^{13} +1.95452 q^{14} +(-5.80862 - 0.772978i) q^{15} -3.80033 q^{16} -3.33669i q^{17} +7.82663i q^{18} -3.27759 q^{19} +(0.618034 - 4.64428i) q^{20} -2.53103 q^{21} +3.36643i q^{23} -0.505368 q^{24} +(-4.82599 - 1.30759i) q^{25} +9.15736 q^{26} -2.27341i q^{27} -2.02368i q^{28} -4.91300 q^{29} +(-1.56426 + 11.7548i) q^{30} -0.418365 q^{31} +8.07636i q^{32} -6.75241 q^{34} +(-2.14077 - 0.284882i) q^{35} +8.10358 q^{36} +6.33755i q^{37} +6.63281i q^{38} -11.8584 q^{39} +(-0.427446 - 0.0568821i) q^{40} +5.78564 q^{41} +5.12200i q^{42} +2.26205i q^{43} +(1.14077 - 8.57246i) q^{45} +6.81258 q^{46} +4.32424i q^{47} -9.95913i q^{48} +6.06719 q^{49} +(-2.64614 + 9.76628i) q^{50} +8.74411 q^{51} -9.48140i q^{52} +2.66070i q^{53} -4.60066 q^{54} -0.186254 q^{56} -8.58924i q^{57} +9.94235i q^{58} +10.1253 q^{59} +(12.1708 + 1.61962i) q^{60} -2.47086 q^{61} +0.846638i q^{62} -3.73534i q^{63} +8.74332 q^{64} +(-10.0300 - 1.33473i) q^{65} -9.60059i q^{67} +6.99135i q^{68} -8.82204 q^{69} +(-0.576511 + 4.33225i) q^{70} -5.45311 q^{71} -0.745831i q^{72} -1.43554i q^{73} +12.8252 q^{74} +(3.42666 - 12.6470i) q^{75} +6.86752 q^{76} +23.9977i q^{78} -1.00396 q^{79} +(1.12096 - 8.42354i) q^{80} -5.64486 q^{81} -11.7083i q^{82} -7.39542i q^{83} +5.30325 q^{84} +(7.39587 + 0.984200i) q^{85} +4.57768 q^{86} -12.8750i q^{87} +12.1964 q^{89} +(-17.3479 - 2.30857i) q^{90} -4.37044 q^{91} -7.05365i q^{92} -1.09637i q^{93} +8.75089 q^{94} +(0.966768 - 7.26487i) q^{95} -21.1649 q^{96} -3.01924i q^{97} -12.2781i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} - 8 q^{25} + 10 q^{26} - 24 q^{29} - 22 q^{30} + 14 q^{31} - 8 q^{34} - 14 q^{35} + 20 q^{36} - 30 q^{39} - 24 q^{40} + 34 q^{41} + 6 q^{45} + 24 q^{46} + 30 q^{49} - 16 q^{50} + 54 q^{51} - 20 q^{54} - 10 q^{56} + 6 q^{59} + 34 q^{60} + 20 q^{61} - 14 q^{64} - 20 q^{65} - 32 q^{69} + 8 q^{70} - 42 q^{71} + 4 q^{74} - 20 q^{75} + 28 q^{76} - 16 q^{79} - 28 q^{80} - 36 q^{81} + 6 q^{84} + 4 q^{85} + 46 q^{86} + 12 q^{89} - 46 q^{90} + 20 q^{91} + 42 q^{94} - 26 q^{95} - 8 q^{96}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 - 12 * q^19 - 4 * q^20 + 4 * q^21 - 2 * q^24 - 8 * q^25 + 10 * q^26 - 24 * q^29 - 22 * q^30 + 14 * q^31 - 8 * q^34 - 14 * q^35 + 20 * q^36 - 30 * q^39 - 24 * q^40 + 34 * q^41 + 6 * q^45 + 24 * q^46 + 30 * q^49 - 16 * q^50 + 54 * q^51 - 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 + 20 * q^61 - 14 * q^64 - 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 + 4 * q^74 - 20 * q^75 + 28 * q^76 - 16 * q^79 - 28 * q^80 - 36 * q^81 + 6 * q^84 + 4 * q^85 + 46 * q^86 + 12 * q^89 - 46 * q^90 + 20 * q^91 + 42 * q^94 - 26 * q^95 - 8 * q^96

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