LMFDB - Embedded newform 845.2.b.d.339.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(339,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, 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("845.339");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.49843600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} + 10x^{2} + 1 $ x^6 + 8x^4 + 10x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.5
Root			$1.18733i$ of defining polynomial
Character	$\chi$	$=$	845.339
Dual form			845.2.b.d.339.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18733i q^{2} -0.345110i q^{3} +0.590239 q^{4} +(1.44045 - 1.71029i) q^{5} +0.409761 q^{6} +2.02956i q^{7} +3.07548i q^{8} +2.88090 q^{9} +O(q^{10})$	\(q+1.18733i q^{2} -0.345110i q^{3} +0.590239 q^{4} +(1.44045 - 1.71029i) q^{5} +0.409761 q^{6} +2.02956i q^{7} +3.07548i q^{8} +2.88090 q^{9} +(2.03069 + 1.71029i) q^{10} +3.88090 q^{11} -0.203698i q^{12} -2.40976 q^{14} +(-0.590239 - 0.497113i) q^{15} -2.47114 q^{16} -5.45014i q^{17} +3.42059i q^{18} -5.88090 q^{19} +(0.850210 - 1.00948i) q^{20} +0.700420 q^{21} +4.60792i q^{22} +0.345110i q^{23} +1.06138 q^{24} +(-0.850210 - 4.92718i) q^{25} -2.02956i q^{27} +1.19792i q^{28} -3.00000 q^{29} +(0.590239 - 0.700811i) q^{30} +1.18048 q^{31} +3.21689i q^{32} -1.33934i q^{33} +6.47114 q^{34} +(3.47114 + 2.92347i) q^{35} +1.70042 q^{36} +5.45014i q^{37} -6.98259i q^{38} +(5.25997 + 4.43007i) q^{40} +0.180479 q^{41} +0.831632i q^{42} +1.33934i q^{43} +2.29066 q^{44} +(4.14979 - 4.92718i) q^{45} -0.409761 q^{46} +12.2807i q^{47} +0.852815i q^{48} +2.88090 q^{49} +(5.85021 - 1.00948i) q^{50} -1.88090 q^{51} -2.42636i q^{53} +2.40976 q^{54} +(5.59024 - 6.63748i) q^{55} -6.24186 q^{56} +2.02956i q^{57} -3.56200i q^{58} +7.06138 q^{59} +(-0.348383 - 0.293416i) q^{60} +6.76180 q^{61} +1.40162i q^{62} +5.84695i q^{63} -8.76180 q^{64} +1.59024 q^{66} -4.40422i q^{67} -3.21689i q^{68} +0.119101 q^{69} +(-3.47114 + 4.12140i) q^{70} -1.88090 q^{71} +8.86014i q^{72} -8.86014i q^{73} -6.47114 q^{74} +(-1.70042 + 0.293416i) q^{75} -3.47114 q^{76} +7.87651i q^{77} -11.1805 q^{79} +(-3.55955 + 4.22637i) q^{80} +7.94228 q^{81} +0.214289i q^{82} -7.83540i q^{83} +0.413416 q^{84} +(-9.32135 - 7.85066i) q^{85} -1.59024 q^{86} +1.03533i q^{87} +11.9356i q^{88} -12.2419 q^{89} +(5.85021 + 4.92718i) q^{90} +0.203698i q^{92} -0.407395i q^{93} -14.5813 q^{94} +(-8.47114 + 10.0581i) q^{95} +1.11018 q^{96} -5.80585i q^{97} +3.42059i q^{98} +11.1805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9	$ 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9} - 7 q^{10} - 22 q^{14} + 4 q^{15} + 16 q^{16} - 12 q^{19} + q^{20} - 4 q^{21} - 32 q^{24} - q^{25} - 18 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{36} + 35 q^{40} - 14 q^{41} - 2 q^{44} + 29 q^{45} - 10 q^{46} - 6 q^{49} + 31 q^{50} + 12 q^{51} + 22 q^{54} + 26 q^{55} + 16 q^{56} + 4 q^{59} - 48 q^{60} - 6 q^{61} - 6 q^{64} + 2 q^{66} + 24 q^{69} + 10 q^{70} + 12 q^{71} - 8 q^{74} - 2 q^{75} + 10 q^{76} - 52 q^{79} - 33 q^{80} - 14 q^{81} - 90 q^{84} - 21 q^{85} - 2 q^{86} - 20 q^{89} + 31 q^{90} - 56 q^{94} - 20 q^{95} + 6 q^{96} + 52 q^{99}+O(q^{100}) $ 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9 - 7 * q^10 - 22 * q^14 + 4 * q^15 + 16 * q^16 - 12 * q^19 + q^20 - 4 * q^21 - 32 * q^24 - q^25 - 18 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^34 - 10 * q^35 + 2 * q^36 + 35 * q^40 - 14 * q^41 - 2 * q^44 + 29 * q^45 - 10 * q^46 - 6 * q^49 + 31 * q^50 + 12 * q^51 + 22 * q^54 + 26 * q^55 + 16 * q^56 + 4 * q^59 - 48 * q^60 - 6 * q^61 - 6 * q^64 + 2 * q^66 + 24 * q^69 + 10 * q^70 + 12 * q^71 - 8 * q^74 - 2 * q^75 + 10 * q^76 - 52 * q^79 - 33 * q^80 - 14 * q^81 - 90 * q^84 - 21 * q^85 - 2 * q^86 - 20 * q^89 + 31 * q^90 - 56 * q^94 - 20 * q^95 + 6 * q^96 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.18733i			0.839571i	0.907623	+	0.419786i	$0.137895\pi$
$2$			1.18733i			0.839571i	−0.907623	+	0.419786i	$0.862105\pi$
$3$		−	0.345110i		−	0.199249i	−0.995025	−	0.0996247i	$-0.968236\pi$
$3$		−	0.345110i		−	0.199249i	0.995025	−	0.0996247i	$-0.0317642\pi$
$4$	0.590239			0.295120
$5$	1.44045	−	1.71029i	0.644189	−	0.764867i
$5$	1.44045	−	1.71029i	0.644189	−	0.764867i
$6$	0.409761			0.167284
$7$			2.02956i			0.767100i	0.923520	+	0.383550i	$0.125299\pi$
$7$			2.02956i			0.767100i	−0.923520	+	0.383550i	$0.874701\pi$
$8$			3.07548i			1.08735i
$9$	2.88090			0.960300
$10$	2.03069	+	1.71029i	0.642160	+	0.540842i
$11$	3.88090			1.17014			0.585068	−	0.810985i	$-0.301068\pi$
$11$	3.88090			1.17014			0.585068	+	0.810985i	$0.301068\pi$
$12$		−	0.203698i		−	0.0588024i
$13$		0			0
$13$		0			0
$14$	−2.40976			−0.644036
$15$	−0.590239	−	0.497113i	−0.152399	−	0.128354i
$16$	−2.47114			−0.617785
$17$		−	5.45014i		−	1.32185i	−0.750450	−	0.660927i	$-0.770163\pi$
$17$		−	5.45014i		−	1.32185i	0.750450	−	0.660927i	$-0.229837\pi$
$18$			3.42059i			0.806240i
$19$	−5.88090			−1.34917			−0.674585	−	0.738197i	$-0.735678\pi$
$19$	−5.88090			−1.34917			−0.674585	+	0.738197i	$0.735678\pi$
$20$	0.850210	−	1.00948i	0.190113	−	0.225727i
$21$	0.700420			0.152844
$22$			4.60792i			0.982412i
$23$			0.345110i			0.0719604i	0.999353	+	0.0359802i	$0.0114553\pi$
$23$			0.345110i			0.0719604i	−0.999353	+	0.0359802i	$0.988545\pi$
$24$	1.06138			0.216653
$25$	−0.850210	−	4.92718i	−0.170042	−	0.985437i
$26$		0			0
$27$		−	2.02956i		−	0.390588i
$28$			1.19792i			0.226386i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	0.590239	−	0.700811i	0.107762	−	0.127950i
$31$	1.18048			0.212020			0.106010	−	0.994365i	$-0.466192\pi$
$31$	1.18048			0.212020			0.106010	+	0.994365i	$0.466192\pi$
$32$			3.21689i			0.568671i
$33$		−	1.33934i		−	0.233149i
$34$	6.47114			1.10979
$35$	3.47114	+	2.92347i	0.586730	+	0.494157i
$36$	1.70042			0.283403
$37$			5.45014i			0.895998i	0.894034	+	0.447999i	$0.147863\pi$
$37$			5.45014i			0.895998i	−0.894034	+	0.447999i	$0.852137\pi$
$38$		−	6.98259i		−	1.13273i
$39$		0			0
$40$	5.25997	+	4.43007i	0.831674	+	0.700456i
$41$	0.180479			0.0281861			0.0140930	−	0.999901i	$-0.495514\pi$
$41$	0.180479			0.0281861			0.0140930	+	0.999901i	$0.495514\pi$
$42$			0.831632i			0.128324i
$43$			1.33934i			0.204247i	0.994772	+	0.102123i	$0.0325637\pi$
$43$			1.33934i			0.204247i	−0.994772	+	0.102123i	$0.967436\pi$
$44$	2.29066			0.345330
$45$	4.14979	−	4.92718i	0.618614	−	0.734501i
$46$	−0.409761			−0.0604159
$47$			12.2807i			1.79133i	0.444731	+	0.895664i	$0.353299\pi$
$47$			12.2807i			1.79133i	−0.444731	+	0.895664i	$0.646701\pi$
$48$			0.852815i			0.123093i
$49$	2.88090			0.411557
$50$	5.85021	−	1.00948i	0.827345	−	0.142762i
$51$	−1.88090			−0.263379
$52$		0			0
$53$		−	2.42636i		−	0.333286i	−0.986017	−	0.166643i	$-0.946707\pi$
$53$		−	2.42636i		−	0.333286i	0.986017	−	0.166643i	$-0.0532928\pi$
$54$	2.40976			0.327927
$55$	5.59024	−	6.63748i	0.753788	−	0.894997i
$56$	−6.24186			−0.834103
$57$			2.02956i			0.268821i
$58$		−	3.56200i		−	0.467714i
$59$	7.06138			0.919313			0.459657	−	0.888097i	$-0.347973\pi$
$59$	7.06138			0.919313			0.459657	+	0.888097i	$0.347973\pi$
$60$	−0.348383	−	0.293416i	−0.0449760	−	0.0378798i
$61$	6.76180			0.865760			0.432880	−	0.901452i	$-0.357497\pi$
$61$	6.76180			0.865760			0.432880	+	0.901452i	$0.357497\pi$
$62$			1.40162i			0.178006i
$63$			5.84695i			0.736646i
$64$	−8.76180			−1.09522
$65$		0			0
$66$	1.59024			0.195745
$67$		−	4.40422i		−	0.538062i	−0.963132	−	0.269031i	$-0.913297\pi$
$67$		−	4.40422i		−	0.538062i	0.963132	−	0.269031i	$-0.0867033\pi$
$68$		−	3.21689i		−	0.390105i
$69$	0.119101			0.0143381
$70$	−3.47114	+	4.12140i	−0.414880	+	0.492601i
$71$	−1.88090			−0.223222			−0.111611	−	0.993752i	$-0.535601\pi$
$71$	−1.88090			−0.223222			−0.111611	+	0.993752i	$0.535601\pi$
$72$			8.86014i			1.04418i
$73$		−	8.86014i		−	1.03700i	−0.855077	−	0.518501i	$-0.826490\pi$
$73$		−	8.86014i		−	1.03700i	0.855077	−	0.518501i	$-0.173510\pi$
$74$	−6.47114			−0.752255
$75$	−1.70042	+	0.293416i	−0.196348	+	0.0338808i
$76$	−3.47114			−0.398167
$77$			7.87651i			0.897611i
$78$		0			0
$79$	−11.1805			−1.25790			−0.628951	−	0.777445i	$-0.716515\pi$
$79$	−11.1805			−1.25790			−0.628951	+	0.777445i	$0.716515\pi$
$80$	−3.55955	+	4.22637i	−0.397970	+	0.472523i
$81$	7.94228			0.882475
$82$			0.214289i			0.0236642i
$83$		−	7.83540i		−	0.860047i	−0.902818	−	0.430024i	$-0.858505\pi$
$83$		−	7.83540i		−	0.860047i	0.902818	−	0.430024i	$-0.141495\pi$
$84$	0.413416			0.0451073
$85$	−9.32135	−	7.85066i	−1.01104	−	0.851523i
$86$	−1.59024			−0.171480
$87$			1.03533i			0.110999i
$88$			11.9356i			1.27234i
$89$	−12.2419			−1.29763			−0.648817	−	0.760944i	$-0.724736\pi$
$89$	−12.2419			−1.29763			−0.648817	+	0.760944i	$0.724736\pi$
$90$	5.85021	+	4.92718i	0.616666	+	0.519371i
$91$		0			0
$92$			0.203698i			0.0212369i
$93$		−	0.407395i		−	0.0422449i
$94$	−14.5813			−1.50395
$95$	−8.47114	+	10.0581i	−0.869120	+	1.03194i
$96$	1.11018			0.113307
$97$		−	5.80585i		−	0.589494i	−0.955575	−	0.294747i	$-0.904765\pi$
$97$		−	5.80585i		−	0.589494i	0.955575	−	0.294747i	$-0.0952354\pi$
$98$			3.42059i			0.345532i
$99$	11.1805			1.12368
$100$	−0.501828	−	2.90822i	−0.0501828	−	0.290822i
$101$	−5.94228			−0.591279			−0.295639	−	0.955300i	$-0.595533\pi$
$101$	−5.94228			−0.591279			−0.295639	+	0.955300i	$0.595533\pi$
$102$		−	2.23325i		−	0.221125i
$103$			6.43378i			0.633939i	0.948436	+	0.316970i	$0.102665\pi$
$103$			6.43378i			0.633939i	−0.948436	+	0.316970i	$0.897335\pi$
$104$		0			0
$105$	1.00892	−	1.19792i	0.0984605	−	0.116905i
$106$	2.88090			0.279818
$107$			17.6792i			1.70911i	0.519360	+	0.854555i	$0.326170\pi$
$107$			17.6792i			1.70911i	−0.519360	+	0.854555i	$0.673830\pi$
$108$		−	1.19792i		−	0.115270i
$109$	−5.76180			−0.551880			−0.275940	−	0.961175i	$-0.588989\pi$
$109$	−5.76180			−0.551880			−0.275940	+	0.961175i	$0.588989\pi$
$110$	7.88090	+	6.63748i	0.751414	+	0.632859i
$111$	1.88090			0.178527
$112$		−	5.01532i		−	0.473903i
$113$			4.75992i			0.447776i	0.974615	+	0.223888i	$0.0718750\pi$
$113$			4.75992i			0.447776i	−0.974615	+	0.223888i	$0.928125\pi$
$114$	−2.40976			−0.225695
$115$	0.590239	+	0.497113i	0.0550401	+	0.0463561i
$116$	−1.77072			−0.164407
$117$		0			0
$118$			8.38421i			0.771829i
$119$	11.0614			1.01399
$120$	1.52886	−	1.81527i	0.139565	−	0.165711i
$121$	4.06138			0.369216
$122$			8.02851i			0.726867i
$123$		−	0.0622851i		−	0.00561605i
$124$	0.696765			0.0625714
$125$	−9.65162	−	5.64325i	−0.863267	−	0.504748i
$126$	−6.94228			−0.618467
$127$		−	16.7061i		−	1.48243i	−0.671268	−	0.741215i	$-0.734250\pi$
$127$		−	16.7061i		−	1.48243i	0.671268	−	0.741215i	$-0.265750\pi$
$128$		−	3.96940i		−	0.350848i
$129$	0.462218			0.0406961
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$		−	0.790529i		−	0.0688068i
$133$		−	11.9356i		−	1.03495i
$134$	5.22928			0.451741
$135$	−3.47114	−	2.92347i	−0.298748	−	0.251613i
$136$	16.7618			1.43731
$137$			1.97786i			0.168980i	0.996424	+	0.0844901i	$0.0269261\pi$
$137$			1.97786i			0.168980i	−0.996424	+	0.0844901i	$0.973074\pi$
$138$			0.141412i			0.0120378i
$139$	−8.70042			−0.737960			−0.368980	−	0.929437i	$-0.620293\pi$
$139$	−8.70042			−0.737960			−0.368980	+	0.929437i	$0.620293\pi$
$140$	2.04880	+	1.72555i	0.173155	+	0.145836i
$141$	4.23820			0.356921
$142$		−	2.23325i		−	0.187411i
$143$		0			0
$144$	−7.11910			−0.593258
$145$	−4.32135	+	5.13088i	−0.358868	+	0.426097i
$146$	10.5199			0.870637
$147$		−	0.994227i		−	0.0820025i
$148$			3.21689i			0.264427i
$149$	−22.3032			−1.82715			−0.913576	−	0.406668i	$-0.866691\pi$
$149$	−22.3032			−1.82715			−0.913576	+	0.406668i	$0.866691\pi$
$150$	−0.348383	−	2.01897i	−0.0284453	−	0.164848i
$151$	−19.1626			−1.55943			−0.779717	−	0.626132i	$-0.784637\pi$
$151$	−19.1626			−1.55943			−0.779717	+	0.626132i	$0.784637\pi$
$152$		−	18.0866i		−	1.46701i
$153$		−	15.7013i		−	1.26938i
$154$	−9.35204			−0.753609
$155$	1.70042	−	2.01897i	0.136581	−	0.162167i
$156$		0			0
$157$		−	6.20265i		−	0.495025i	−0.968885	−	0.247513i	$-0.920387\pi$
$157$		−	6.20265i		−	0.495025i	0.968885	−	0.247513i	$-0.0796132\pi$
$158$		−	13.2750i		−	1.05610i
$159$	−0.837361			−0.0664071
$160$	5.50183	+	4.63377i	0.434958	+	0.366332i
$161$	−0.700420			−0.0552008
$162$			9.43013i			0.740901i
$163$		−	11.9356i		−	0.934870i	−0.884027	−	0.467435i	$-0.845178\pi$
$163$		−	11.9356i		−	0.934870i	0.884027	−	0.467435i	$-0.154822\pi$
$164$	0.106526			0.00831826
$165$	−2.29066	−	1.92925i	−0.178328	−	0.150192i
$166$	9.30323			0.722071
$167$		−	2.02956i		−	0.157052i	−0.996912	−	0.0785259i	$-0.974979\pi$
$167$		−	2.02956i		−	0.157052i	0.996912	−	0.0785259i	$-0.0250213\pi$
$168$			2.15413i			0.166195i
$169$		0			0
$170$	9.32135	−	11.0675i	0.714915	−	0.848842i
$171$	−16.9423			−1.29561
$172$			0.790529i			0.0602773i
$173$		−	1.33934i		−	0.101828i	−0.998703	−	0.0509139i	$-0.983787\pi$
$173$		−	1.33934i		−	0.101828i	0.998703	−	0.0509139i	$-0.0162134\pi$
$174$	−1.22928			−0.0931916
$175$	10.0000	−	1.72555i	0.755929	−	0.130439i
$176$	−9.59024			−0.722891
$177$		−	2.43695i		−	0.183173i
$178$		−	14.5352i		−	1.08946i
$179$	−20.2240			−1.51161			−0.755807	−	0.654794i	$-0.772755\pi$
$179$	−20.2240			−1.51161			−0.755807	+	0.654794i	$0.772755\pi$
$180$	2.44937	−	2.90822i	0.182565	−	0.216766i
$181$	19.8232			1.47345			0.736723	−	0.676195i	$-0.236372\pi$
$181$	19.8232			1.47345			0.736723	+	0.676195i	$0.236372\pi$
$182$		0			0
$183$		−	2.33356i		−	0.172502i
$184$	−1.06138			−0.0782458
$185$	9.32135	+	7.85066i	0.685319	+	0.577192i
$186$	0.483714			0.0354676
$187$		−	21.1515i		−	1.54675i
$188$			7.24857i			0.528656i
$189$	4.11910			0.299621
$190$	−11.9423	−	10.0581i	−0.866384	−	0.729689i
$191$	1.53778			0.111270			0.0556350	−	0.998451i	$-0.482282\pi$
$191$	1.53778			0.111270			0.0556350	+	0.998451i	$0.482282\pi$
$192$			3.02378i			0.218223i
$193$		−	21.2032i		−	1.52624i	−0.646259	−	0.763118i	$-0.723667\pi$
$193$		−	21.2032i		−	1.52624i	0.646259	−	0.763118i	$-0.276333\pi$
$194$	6.89347			0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$		−	9.25695i		−	0.659530i	−0.944063	−	0.329765i	$-0.893030\pi$
$197$		−	9.25695i		−	0.659530i	0.944063	−	0.329765i	$-0.106970\pi$
$198$			13.2750i			0.943410i
$199$	17.4045			1.23377			0.616886	−	0.787053i	$-0.288394\pi$
$199$	17.4045			1.23377			0.616886	+	0.787053i	$0.288394\pi$
$200$	15.1534	−	2.61480i	1.07151	−	0.184894i
$201$	−1.51994			−0.107208
$202$		−	7.05546i		−	0.496421i
$203$		−	6.08867i		−	0.427341i
$204$	−1.11018			−0.0777282
$205$	0.259971	−	0.308672i	0.0181571	−	0.0215586i
$206$	−7.63904			−0.532237
$207$			0.994227i			0.0691036i
$208$		0			0
$209$	−22.8232			−1.57871
$210$	1.42234	+	1.19792i	0.0981505	+	0.0826646i
$211$	−7.28174			−0.501296			−0.250648	−	0.968078i	$-0.580644\pi$
$211$	−7.28174			−0.501296			−0.250648	+	0.968078i	$0.580644\pi$
$212$		−	1.43213i		−	0.0983594i
$213$			0.649117i			0.0444768i
$214$	−20.9911			−1.43492
$215$	2.29066	+	1.92925i	0.156222	+	0.131574i
$216$	6.24186			0.424705
$217$			2.39585i			0.162641i
$218$		−	6.84118i		−	0.463343i
$219$	−3.05772			−0.206622
$220$	3.29958	−	3.91770i	0.222458	−	0.264131i
$221$		0			0
$222$			2.23325i			0.149886i
$223$			19.4670i			1.30361i	0.758388	+	0.651804i	$0.225987\pi$
$223$			19.4670i			1.30361i	−0.758388	+	0.651804i	$0.774013\pi$
$224$	−6.52886			−0.436228
$225$	−2.44937	−	14.1947i	−0.163291	−	0.946315i
$226$	−5.65162			−0.375940
$227$			4.81162i			0.319358i	0.987169	+	0.159679i	$0.0510460\pi$
$227$			4.81162i			0.319358i	−0.987169	+	0.159679i	$0.948954\pi$
$228$			1.19792i			0.0793345i
$229$	−1.52360			−0.100682			−0.0503410	−	0.998732i	$-0.516031\pi$
$229$	−1.52360			−0.100682			−0.0503410	+	0.998732i	$0.516031\pi$
$230$	−0.590239	+	0.700811i	−0.0389192	+	0.0462101i
$231$	2.71826			0.178848
$232$		−	9.22643i		−	0.605745i
$233$			13.9652i			0.914889i	0.889238	+	0.457445i	$0.151235\pi$
$233$			13.9652i			0.914889i	−0.889238	+	0.457445i	$0.848765\pi$
$234$		0			0
$235$	21.0037	+	17.6898i	1.37013	+	1.15395i
$236$	4.16790			0.271307
$237$			3.85849i			0.250636i
$238$			13.1335i			0.851321i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	1.45856	+	1.22844i	0.0941499	+	0.0792952i
$241$	−17.4659			−1.12508			−0.562538	−	0.826771i	$-0.690175\pi$
$241$	−17.4659			−1.12508			−0.562538	+	0.826771i	$0.690175\pi$
$242$			4.82221i			0.309983i
$243$		−	8.82963i		−	0.566421i
$244$	3.99108			0.255503
$245$	4.14979	−	4.92718i	0.265120	−	0.314786i
$246$	0.0739531			0.00471508
$247$		0			0
$248$			3.63054i			0.230539i
$249$	−2.70408			−0.171364
$250$	6.70042	−	11.4597i	0.423772	−	0.724774i
$251$	9.29958			0.586984			0.293492	−	0.955961i	$-0.405183\pi$
$251$	9.29958			0.586984			0.293492	+	0.955961i	$0.405183\pi$
$252$			3.45110i			0.217399i
$253$			1.33934i			0.0842034i
$254$	19.8358			1.24461
$255$	−2.70934	+	3.21689i	−0.169665	+	0.201449i
$256$	−12.8106			−0.800663
$257$			10.8897i			0.679281i	0.940555	+	0.339640i	$0.110305\pi$
$257$			10.8897i			0.679281i	−0.940555	+	0.339640i	$0.889695\pi$
$258$			0.548807i			0.0341673i
$259$	−11.0614			−0.687321
$260$		0			0
$261$	−8.64270			−0.534970
$262$			11.8733i			0.733537i
$263$			13.4406i			0.828785i	0.910098	+	0.414392i	$0.136006\pi$
$263$			13.4406i			0.828785i	−0.910098	+	0.414392i	$0.863994\pi$
$264$	4.11910			0.253513
$265$	−4.14979	−	3.49505i	−0.254920	−	0.214699i
$266$	14.1716			0.868914
$267$			4.22479i			0.258553i
$268$		−	2.59955i		−	0.158793i
$269$	−3.66054			−0.223187			−0.111593	−	0.993754i	$-0.535595\pi$
$269$	−3.66054			−0.223187			−0.111593	+	0.993754i	$0.535595\pi$
$270$	3.47114	−	4.12140i	0.211247	−	0.250820i
$271$	22.0037			1.33663			0.668313	−	0.743880i	$-0.267017\pi$
$271$	22.0037			1.33663			0.668313	+	0.743880i	$0.267017\pi$
$272$			13.4681i			0.816621i
$273$		0			0
$274$	−2.34838			−0.141871
$275$	−3.29958	−	19.1219i	−0.198972	−	1.15309i
$276$	0.0702980			0.00423144
$277$			9.89547i			0.594561i	0.954790	+	0.297281i	$0.0960797\pi$
$277$			9.89547i			0.594561i	−0.954790	+	0.297281i	$0.903920\pi$
$278$		−	10.3303i		−	0.619570i
$279$	3.40084			0.203603
$280$	−8.99108	+	10.6754i	−0.537320	+	0.637978i
$281$	4.06138			0.242281			0.121141	−	0.992635i	$-0.461345\pi$
$281$	4.06138			0.242281			0.121141	+	0.992635i	$0.461345\pi$
$282$			5.03216i			0.299661i
$283$			6.08867i			0.361934i	0.983489	+	0.180967i	$0.0579227\pi$
$283$			6.08867i			0.361934i	−0.983489	+	0.180967i	$0.942077\pi$
$284$	−1.11018			−0.0658771
$285$	3.47114	+	2.92347i	0.205613	+	0.173172i
$286$		0			0
$287$			0.366292i			0.0216215i
$288$			9.26754i			0.546095i
$289$	−12.7041			−0.747299
$290$	−6.09207	−	5.13088i	−0.357738	−	0.301296i
$291$	−2.00366			−0.117456
$292$		−	5.22960i		−	0.306039i
$293$			9.79208i			0.572060i	0.958221	+	0.286030i	$0.0923356\pi$
$293$			9.79208i			0.572060i	−0.958221	+	0.286030i	$0.907664\pi$
$294$	1.18048			0.0688469
$295$	10.1716	−	12.0770i	0.592211	−	0.703152i
$296$	−16.7618			−0.974260
$297$		−	7.87651i		−	0.457041i
$298$		−	26.4814i		−	1.53402i
$299$		0			0
$300$	−1.00366	+	0.173186i	−0.0579461	+	0.00999888i
$301$	−2.71826			−0.156678
$302$		−	22.7524i		−	1.30926i
$303$			2.05074i			0.117812i
$304$	14.5325			0.833497
$305$	9.74003	−	11.5647i	0.557712	−	0.662191i
$306$	18.6427			1.06573
$307$		−	22.1046i		−	1.26158i	−0.775955	−	0.630788i	$-0.782732\pi$
$307$		−	22.1046i		−	1.26158i	0.775955	−	0.630788i	$-0.217268\pi$
$308$			4.64902i			0.264903i
$309$	2.22036			0.126312
$310$	2.39719	+	2.01897i	0.136151	+	0.114670i
$311$	7.63904			0.433170			0.216585	−	0.976264i	$-0.430508\pi$
$311$	7.63904			0.433170			0.216585	+	0.976264i	$0.430508\pi$
$312$		0			0
$313$		−	26.1425i		−	1.47766i	−0.673891	−	0.738831i	$-0.735378\pi$
$313$		−	26.1425i		−	1.47766i	0.673891	−	0.738831i	$-0.264622\pi$
$314$	7.36461			0.415609
$315$	10.0000	+	8.42223i	0.563436	+	0.474539i
$316$	−6.59916			−0.371232
$317$			11.8428i			0.665159i	0.943075	+	0.332580i	$0.107919\pi$
$317$			11.8428i			0.665159i	−0.943075	+	0.332580i	$0.892081\pi$
$318$		−	0.994227i		−	0.0557535i
$319$	−11.6427			−0.651866
$320$	−12.6209	+	14.9852i	−0.705531	+	0.837701i
$321$	6.10126			0.340539
$322$		−	0.831632i		−	0.0463451i
$323$			32.0518i			1.78341i
$324$	4.68785			0.260436
$325$		0			0
$326$	14.1716			0.784890
$327$			1.98845i			0.109962i
$328$			0.555059i			0.0306480i
$329$	−24.9244			−1.37413
$330$	2.29066	−	2.71978i	0.126097	−	0.149719i
$331$	−12.7004			−0.698078			−0.349039	−	0.937108i	$-0.613492\pi$
$331$	−12.7004			−0.698078			−0.349039	+	0.937108i	$0.613492\pi$
$332$		−	4.62476i		−	0.253817i
$333$			15.7013i			0.860427i
$334$	2.40976			0.131856
$335$	−7.53252	−	6.34406i	−0.411545	−	0.346613i
$336$	−1.73084			−0.0944248
$337$		−	15.2939i		−	0.833113i	−0.909110	−	0.416556i	$-0.863237\pi$
$337$		−	15.2939i		−	0.833113i	0.909110	−	0.416556i	$-0.136763\pi$
$338$		0			0
$339$	1.64270			0.0892191
$340$	−5.50183	−	4.63377i	−0.298378	−	0.251301i
$341$	4.58132			0.248092
$342$		−	20.1161i		−	1.08776i
$343$			20.0538i			1.08281i
$344$	−4.11910			−0.222087
$345$	0.171559	−	0.203698i	0.00923642	−	0.0109667i
$346$	1.59024			0.0854918
$347$			12.2396i			0.657058i	0.944494	+	0.328529i	$0.106553\pi$
$347$			12.2396i			0.657058i	−0.944494	+	0.328529i	$0.893447\pi$
$348$			0.611093i			0.0327580i
$349$	−18.7004			−1.00101			−0.500505	−	0.865733i	$-0.666852\pi$
$349$	−18.7004			−1.00101			−0.500505	+	0.865733i	$0.666852\pi$
$350$	2.04880	+	11.8733i	0.109513	+	0.634656i
$351$		0			0
$352$			12.4844i			0.665422i
$353$		−	1.30883i		−	0.0696617i	−0.999393	−	0.0348309i	$-0.988911\pi$
$353$		−	1.30883i		−	0.0696617i	0.999393	−	0.0348309i	$-0.0110893\pi$
$354$	2.89347			0.153786
$355$	−2.70934	+	3.21689i	−0.143797	+	0.170735i
$356$	−7.22563			−0.382957
$357$		−	3.81739i		−	0.202038i
$358$		−	24.0127i		−	1.26911i
$359$	29.4082			1.55210			0.776051	−	0.630670i	$-0.217220\pi$
$359$	29.4082			1.55210			0.776051	+	0.630670i	$0.217220\pi$
$360$	15.1534	+	12.7626i	0.798657	+	0.672647i
$361$	15.5850			0.820262
$362$			23.5367i			1.23706i
$363$		−	1.40162i		−	0.0735661i
$364$		0			0
$365$	−15.1534	−	12.7626i	−0.793168	−	0.668024i
$366$	2.77072			0.144828
$367$		−	33.4322i		−	1.74515i	−0.488484	−	0.872573i	$-0.662450\pi$
$367$		−	33.4322i		−	1.74515i	0.488484	−	0.872573i	$-0.337550\pi$
$368$		−	0.852815i		−	0.0444560i
$369$	0.519941			0.0270671
$370$	−9.32135	+	11.0675i	−0.484594	+	0.575374i
$371$	4.92444			0.255664
$372$		−	0.240461i		−	0.0124673i
$373$			34.4781i			1.78521i	0.450841	+	0.892604i	$0.351124\pi$
$373$			34.4781i			1.78521i	−0.450841	+	0.892604i	$0.648876\pi$
$374$	25.1138			1.29861
$375$	−1.94754	+	3.33087i	−0.100571	+	0.172005i
$376$	−37.7691			−1.94779
$377$		0			0
$378$			4.89075i			0.251553i
$379$	17.4045			0.894009			0.447004	−	0.894532i	$-0.352491\pi$
$379$	17.4045			0.894009			0.447004	+	0.894532i	$0.352491\pi$
$380$	−5.00000	+	5.93667i	−0.256495	+	0.304545i
$381$	−5.76545			−0.295373
$382$			1.82586i			0.0934191i
$383$		−	1.74673i		−	0.0892538i	−0.999004	−	0.0446269i	$-0.985790\pi$
$383$		−	1.74673i		−	0.0892538i	0.999004	−	0.0446269i	$-0.0142099\pi$
$384$	−1.36988			−0.0699063
$385$	13.4711	+	11.3457i	0.686553	+	0.578231i
$386$	25.1752			1.28138
$387$			3.85849i			0.196138i
$388$		−	3.42684i		−	0.173971i
$389$	−22.0435			−1.11765			−0.558826	−	0.829285i	$-0.688748\pi$
$389$	−22.0435			−1.11765			−0.558826	+	0.829285i	$0.688748\pi$
$390$		0			0
$391$	1.88090			0.0951212
$392$			8.86014i			0.447505i
$393$		−	3.45110i		−	0.174085i
$394$	10.9911			0.553723
$395$	−16.1049	+	19.1219i	−0.810326	+	0.962127i
$396$	6.59916			0.331620
$397$		−	22.5319i		−	1.13084i	−0.824802	−	0.565422i	$-0.808713\pi$
$397$		−	22.5319i		−	1.13084i	0.824802	−	0.565422i	$-0.191287\pi$
$398$			20.6649i			1.03584i
$399$	−4.11910			−0.206213
$400$	2.10099	+	12.1758i	0.105049	+	0.608788i
$401$	−3.70408			−0.184973			−0.0924863	−	0.995714i	$-0.529481\pi$
$401$	−3.70408			−0.184973			−0.0924863	+	0.995714i	$0.529481\pi$
$402$		−	1.80468i		−	0.0900091i
$403$		0			0
$404$	−3.50737			−0.174498
$405$	11.4404	−	13.5836i	0.568481	−	0.674976i
$406$	7.22928			0.358783
$407$			21.1515i			1.04844i
$408$		−	5.78466i		−	0.286384i
$409$	13.4837			0.666727			0.333363	−	0.942798i	$-0.391816\pi$
$409$	13.4837			0.666727			0.333363	+	0.942798i	$0.391816\pi$
$410$	0.366496	+	0.308672i	0.0181000	+	0.0152442i
$411$	0.682580			0.0336692
$412$			3.79747i			0.187088i
$413$			14.3315i			0.705205i
$414$	−1.18048			−0.0580174
$415$	−13.4008	−	11.2865i	−0.657821	−	0.554033i
$416$		0			0
$417$			3.00260i			0.147038i
$418$		−	27.0987i		−	1.32544i
$419$	−16.8232			−0.821866			−0.410933	−	0.911666i	$-0.634797\pi$
$419$	−16.8232			−0.821866			−0.410933	+	0.911666i	$0.634797\pi$
$420$	0.595504	−	0.707062i	0.0290576	−	0.0345011i
$421$	17.1013			0.833464			0.416732	−	0.909029i	$-0.363175\pi$
$421$	17.1013			0.833464			0.416732	+	0.909029i	$0.363175\pi$
$422$		−	8.64585i		−	0.420874i
$423$			35.3795i			1.72021i
$424$	7.46222			0.362397
$425$	−26.8539	+	4.63377i	−1.30260	+	0.224771i
$426$	−0.770718			−0.0373414
$427$			13.7235i			0.664124i
$428$			10.4349i			0.504392i
$429$		0			0
$430$	−2.29066	+	2.71978i	−0.110465	+	0.131159i
$431$	9.66054			0.465332			0.232666	−	0.972557i	$-0.425255\pi$
$431$	9.66054			0.465332			0.232666	+	0.972557i	$0.425255\pi$
$432$			5.01532i			0.241300i
$433$		−	24.7727i		−	1.19050i	−0.803541	−	0.595249i	$-0.797053\pi$
$433$		−	24.7727i		−	1.19050i	0.803541	−	0.595249i	$-0.202947\pi$
$434$	−2.84467			−0.136549
$435$	1.77072	+	1.49134i	0.0848994	+	0.0715043i
$436$	−3.40084			−0.162871
$437$		−	2.02956i		−	0.0970869i
$438$		−	3.63054i		−	0.173474i
$439$	−7.06138			−0.337021			−0.168511	−	0.985700i	$-0.553896\pi$
$439$	−7.06138			−0.337021			−0.168511	+	0.985700i	$0.553896\pi$
$440$	20.4134	+	17.1927i	0.973171	+	0.819628i
$441$	8.29958			0.395218
$442$		0			0
$443$			38.2438i			1.81702i	0.417865	+	0.908509i	$0.362778\pi$
$443$			38.2438i			1.81702i	−0.417865	+	0.908509i	$0.637222\pi$
$444$	1.11018			0.0526869
$445$	−17.6338	+	20.9372i	−0.835921	+	0.992517i
$446$	−23.1138			−1.09447
$447$			7.69707i			0.364059i
$448$		−	17.7826i		−	0.840147i
$449$	12.4801			0.588970			0.294485	−	0.955656i	$-0.404852\pi$
$449$	12.4801			0.588970			0.294485	+	0.955656i	$0.404852\pi$
$450$	16.8539	−	2.90822i	0.794499	−	0.137095i
$451$	0.700420			0.0329815
$452$			2.80950i			0.132148i
$453$			6.61322i			0.310716i
$454$	−5.71300			−0.268124
$455$		0			0
$456$	−6.24186			−0.292302
$457$			8.23221i			0.385086i	0.981289	+	0.192543i	$0.0616735\pi$
$457$			8.23221i			0.385086i	−0.981289	+	0.192543i	$0.938326\pi$
$458$		−	1.80902i		−	0.0845298i
$459$	−11.0614			−0.516301
$460$	0.348383	+	0.293416i	0.0162434	+	0.0136806i
$461$	−4.54144			−0.211516			−0.105758	−	0.994392i	$-0.533727\pi$
$461$	−4.54144			−0.211516			−0.105758	+	0.994392i	$0.533727\pi$
$462$			3.22748i			0.150156i
$463$			1.98845i			0.0924113i	0.998932	+	0.0462056i	$0.0147130\pi$
$463$			1.98845i			0.0924113i	−0.998932	+	0.0462056i	$0.985287\pi$
$464$	7.41342			0.344159
$465$	−0.696765	−	0.586832i	−0.0323117	−	0.0272137i
$466$	−16.5813			−0.768115
$467$		−	32.8043i		−	1.51800i	−0.651091	−	0.759000i	$-0.725688\pi$
$467$		−	32.8043i		−	1.51800i	0.651091	−	0.759000i	$-0.274312\pi$
$468$		0			0
$469$	8.93862			0.412747
$470$	−21.0037	+	24.9383i	−0.968826	+	1.15032i
$471$	−2.14060			−0.0986335
$472$			21.7171i			0.999611i
$473$			5.19783i			0.238997i
$474$	−4.58132			−0.210427
$475$	5.00000	+	28.9763i	0.229416	+	1.32952i
$476$	6.52886			0.299250
$477$		−	6.99010i		−	0.320055i
$478$		−	4.74933i		−	0.217229i
$479$	30.8053			1.40753			0.703766	−	0.710432i	$-0.251500\pi$
$479$	30.8053			1.40753			0.703766	+	0.710432i	$0.251500\pi$
$480$	1.59916	−	1.89874i	0.0729913	−	0.0866650i
$481$		0			0
$482$		−	20.7378i		−	0.944582i
$483$			0.241722i			0.0109987i
$484$	2.39719			0.108963
$485$	−9.92970	−	8.36303i	−0.450885	−	0.379746i
$486$	10.4837			0.475551
$487$		−	22.3251i		−	1.01165i	−0.862637	−	0.505824i	$-0.831189\pi$
$487$		−	22.3251i		−	1.01165i	0.862637	−	0.505824i	$-0.168811\pi$
$488$			20.7958i			0.941380i
$489$	−4.11910			−0.186272
$490$	5.85021	+	4.92718i	0.264286	+	0.222587i
$491$	10.6826			0.482098			0.241049	−	0.970513i	$-0.422509\pi$
$491$	10.6826			0.482098			0.241049	+	0.970513i	$0.422509\pi$
$492$		−	0.0367631i		−	0.00165741i
$493$			16.3504i			0.736386i
$494$		0			0
$495$	16.1049	−	19.1219i	0.723862	−	0.859466i
$496$	−2.91713			−0.130983
$497$		−	3.81739i		−	0.171233i
$498$		−	3.21064i		−	0.143872i
$499$	−18.8195			−0.842477			−0.421239	−	0.906950i	$-0.638405\pi$
$499$	−18.8195			−0.842477			−0.421239	+	0.906950i	$0.638405\pi$
$500$	−5.69677	−	3.33087i	−0.254767	−	0.148961i
$501$	−0.700420			−0.0312925
$502$			11.0417i			0.492815i
$503$			5.68128i			0.253316i	0.991946	+	0.126658i	$0.0404250\pi$
$503$			5.68128i			0.253316i	−0.991946	+	0.126658i	$0.959575\pi$
$504$	−17.9822			−0.800989
$505$	−8.55955	+	10.1630i	−0.380895	+	0.452249i
$506$	−1.59024			−0.0706948
$507$		0			0
$508$		−	9.86062i		−	0.437494i
$509$	−27.9244			−1.23773			−0.618864	−	0.785498i	$-0.712407\pi$
$509$	−27.9244			−1.23773			−0.618864	+	0.785498i	$0.712407\pi$
$510$	−3.81952	−	3.21689i	−0.169131	−	0.142446i
$511$	17.9822			0.795484
$512$		−	23.1492i		−	1.02306i
$513$			11.9356i			0.526970i
$514$	−12.9297			−0.570305
$515$	11.0037	+	9.26754i	0.484879	+	0.408376i
$516$	0.272820			0.0120102
$517$			47.6603i			2.09610i
$518$		−	13.1335i		−	0.577055i
$519$	−0.462218			−0.0202891
$520$		0			0
$521$	6.29958			0.275990			0.137995	−	0.990433i	$-0.455934\pi$
$521$	6.29958			0.275990			0.137995	+	0.990433i	$0.455934\pi$
$522$		−	10.2618i		−	0.449145i
$523$		−	22.8571i		−	0.999471i	−0.866178	−	0.499735i	$-0.833431\pi$
$523$		−	22.8571i		−	0.999471i	0.866178	−	0.499735i	$-0.166569\pi$
$524$	5.90239			0.257847
$525$	−0.595504	−	3.45110i	−0.0259899	−	0.150618i
$526$	−15.9585			−0.695824
$527$		−	6.43378i		−	0.280260i
$528$			3.30969i			0.144036i
$529$	22.8809			0.994822
$530$	4.14979	−	4.92718i	0.180255	−	0.214023i
$531$	20.3431			0.882816
$532$		−	7.04487i		−	0.305434i
$533$		0			0
$534$	−5.01623			−0.217074
$535$	30.2366	+	25.4660i	1.30724	+	1.10099i
$536$	13.5451			0.585059
$537$			6.97951i			0.301188i
$538$		−	4.34628i		−	0.187381i
$539$	11.1805			0.481577
$540$	−2.04880	−	1.72555i	−0.0881664	−	0.0742558i
$541$	−9.48006			−0.407580			−0.203790	−	0.979015i	$-0.565326\pi$
$541$	−9.48006			−0.407580			−0.203790	+	0.979015i	$0.565326\pi$
$542$			26.1257i			1.12219i
$543$		−	6.84118i		−	0.293583i
$544$	17.5325			0.751700
$545$	−8.29958	+	9.85437i	−0.355515	+	0.422115i
$546$		0			0
$547$			33.3911i			1.42770i	0.700299	+	0.713850i	$0.253050\pi$
$547$			33.3911i			1.42770i	−0.700299	+	0.713850i	$0.746950\pi$
$548$			1.16741i			0.0498694i
$549$	19.4801			0.831389
$550$	22.7041	−	3.91770i	0.968105	−	0.167051i
$551$	17.6427			0.751604
$552$			0.366292i			0.0155904i
$553$		−	22.6914i		−	0.964937i
$554$	−11.7492			−0.499177
$555$	2.70934	−	3.21689i	0.115005	−	0.136549i
$556$	−5.13533			−0.217787
$557$		−	37.7648i		−	1.60015i	−0.599903	−	0.800073i	$-0.704794\pi$
$557$		−	37.7648i		−	1.60015i	0.599903	−	0.800073i	$-0.295206\pi$
$558$			4.03793i			0.170939i
$559$		0			0
$560$	−8.57766	−	7.22431i	−0.362472	−	0.305283i
$561$	−7.29958			−0.308188
$562$			4.82221i			0.203413i
$563$		−	25.9008i		−	1.09159i	−0.837919	−	0.545794i	$-0.816228\pi$
$563$		−	25.9008i		−	1.09159i	0.837919	−	0.545794i	$-0.183772\pi$
$564$	2.50155			0.105334
$565$	8.14087	+	6.85643i	0.342489	+	0.288452i
$566$	−7.22928			−0.303869
$567$			16.1193i			0.676947i
$568$		−	5.78466i		−	0.242719i
$569$	21.5451			0.903217			0.451609	−	0.892216i	$-0.350850\pi$
$569$	21.5451			0.903217			0.451609	+	0.892216i	$0.350850\pi$
$570$	−3.47114	+	4.12140i	−0.145390	+	0.172626i
$571$	−2.22036			−0.0929192			−0.0464596	−	0.998920i	$-0.514794\pi$
$571$	−2.22036			−0.0929192			−0.0464596	+	0.998920i	$0.514794\pi$
$572$		0			0
$573$		−	0.530704i		−	0.0221705i
$574$	−0.434911			−0.0181528
$575$	1.70042	−	0.293416i	0.0709124	−	0.0122363i
$576$	−25.2419			−1.05174
$577$			6.20265i			0.258220i	0.991630	+	0.129110i	$0.0412120\pi$
$577$			6.20265i			0.258220i	−0.991630	+	0.129110i	$0.958788\pi$
$578$		−	15.0840i		−	0.627411i
$579$	−7.31742			−0.304102
$580$	−2.55063	+	3.02845i	−0.105909	+	0.125749i
$581$	15.9024			0.659742
$582$		−	2.37901i		−	0.0986130i
$583$		−	9.41646i		−	0.389990i
$584$	27.2492			1.12758
$585$		0			0
$586$	−11.6265			−0.480285
$587$			1.82894i			0.0754883i	0.999287	+	0.0377442i	$0.0120172\pi$
$587$			1.82894i			0.0754883i	−0.999287	+	0.0377442i	$0.987983\pi$
$588$		−	0.586832i		−	0.0242005i
$589$	−6.94228			−0.286052
$590$	14.3395	+	12.0770i	0.590346	+	0.497204i
$591$	−3.19466			−0.131411
$592$		−	13.4681i		−	0.553534i
$593$		−	0.0728761i		−	0.00299266i	−0.999999	−	0.00149633i	$-0.999524\pi$
$593$		−	0.0728761i		−	0.00299266i	0.999999	−	0.00149633i	$-0.000476297\pi$
$594$	9.35204			0.383719
$595$	15.9334	−	18.9182i	0.653204	−	0.775571i
$596$	−13.1642			−0.539229
$597$		−	6.00646i		−	0.245828i
$598$		0			0
$599$	14.5813			0.595777			0.297888	−	0.954601i	$-0.403718\pi$
$599$	14.5813			0.595777			0.297888	+	0.954601i	$0.403718\pi$
$600$	−0.902394	−	5.22960i	−0.0368401	−	0.213498i
$601$	−44.4082			−1.81145			−0.905723	−	0.423870i	$-0.860671\pi$
$601$	−44.4082			−1.81145			−0.905723	+	0.423870i	$0.860671\pi$
$602$		−	3.22748i		−	0.131542i
$603$		−	12.6881i		−	0.516700i
$604$	−11.3105			−0.460220
$605$	5.85021	−	6.94615i	0.237845	−	0.282401i
$606$	−2.43491			−0.0989115
$607$		−	36.2354i		−	1.47075i	−0.677660	−	0.735375i	$-0.737006\pi$
$607$		−	36.2354i		−	1.47075i	0.677660	−	0.735375i	$-0.262994\pi$
$608$		−	18.9182i		−	0.767235i
$609$	−2.10126			−0.0851474
$610$	13.7311	+	11.5647i	0.555956	+	0.468239i
$611$		0			0
$612$		−	9.26754i		−	0.374618i
$613$			3.35830i			0.135641i	0.997698	+	0.0678203i	$0.0216045\pi$
$613$			3.35830i			0.135641i	−0.997698	+	0.0678203i	$0.978396\pi$
$614$	26.2455			1.05918
$615$	−0.106526	−	0.0897185i	−0.00429553	−	0.00361780i
$616$	−24.2240			−0.976013
$617$			21.1820i			0.852754i	0.904546	+	0.426377i	$0.140210\pi$
$617$			21.1820i			0.852754i	−0.904546	+	0.426377i	$0.859790\pi$
$618$			2.63631i			0.106048i
$619$	−25.4082			−1.02124			−0.510620	−	0.859807i	$-0.670584\pi$
$619$	−25.4082			−1.02124			−0.510620	+	0.859807i	$0.670584\pi$
$620$	1.00366	−	1.19167i	0.0403078	−	0.0478587i
$621$	0.700420			0.0281069
$622$			9.07009i			0.363677i
$623$		−	24.8455i		−	0.995416i
$624$		0			0
$625$	−23.5543	+	8.37828i	−0.942171	+	0.335131i
$626$	31.0399			1.24060
$627$			7.87651i			0.314557i
$628$		−	3.66105i		−	0.146092i
$629$	29.7041			1.18438
$630$	−10.0000	+	11.8733i	−0.398410	+	0.473045i
$631$	43.5451			1.73350			0.866751	−	0.498740i	$-0.166204\pi$
$631$	43.5451			1.73350			0.866751	+	0.498740i	$0.166204\pi$
$632$		−	34.3853i		−	1.36777i
$633$			2.51300i			0.0998828i
$634$	−14.0614			−0.558449
$635$	−28.5724	−	24.0643i	−1.13386	−	0.954964i
$636$	−0.494244			−0.0195980
$637$		0			0
$638$		−	13.8238i		−	0.547288i
$639$	−5.41868			−0.214360
$640$	−6.78883	−	5.71771i	−0.268352	−	0.226012i
$641$	48.2854			1.90716			0.953579	−	0.301142i	$-0.0973679\pi$
$641$	48.2854			1.90716			0.953579	+	0.301142i	$0.0973679\pi$
$642$			7.24423i			0.285907i
$643$			42.3440i			1.66989i	0.550337	+	0.834943i	$0.314499\pi$
$643$			42.3440i			1.66989i	−0.550337	+	0.834943i	$0.685501\pi$
$644$	−0.413416			−0.0162909
$645$	0.665802	−	0.790529i	0.0262159	−	0.0311271i
$646$	−38.0561			−1.49730
$647$		−	34.4052i		−	1.35261i	−0.736622	−	0.676305i	$-0.763580\pi$
$647$		−	34.4052i		−	1.35261i	0.736622	−	0.676305i	$-0.236420\pi$
$648$			24.4263i			0.959556i
$649$	27.4045			1.07572
$650$		0			0
$651$	0.826831			0.0324061
$652$		−	7.04487i		−	0.275899i
$653$			14.3315i			0.560834i	0.959878	+	0.280417i	$0.0904727\pi$
$653$			14.3315i			0.560834i	−0.959878	+	0.280417i	$0.909527\pi$
$654$	−2.36096			−0.0923208
$655$	14.4045	−	17.1029i	0.562830	−	0.668267i
$656$	−0.445988			−0.0174129
$657$		−	25.5252i		−	0.995832i
$658$		−	29.5936i		−	1.15368i
$659$	−22.8232			−0.889065			−0.444532	−	0.895763i	$-0.646630\pi$
$659$	−22.8232			−0.889065			−0.444532	+	0.895763i	$0.646630\pi$
$660$	−1.35204	−	1.13872i	−0.0526280	−	0.0443245i
$661$	14.4187			0.560822			0.280411	−	0.959880i	$-0.409529\pi$
$661$	14.4187			0.560822			0.280411	+	0.959880i	$0.409529\pi$
$662$		−	15.0796i		−	0.586087i
$663$		0			0
$664$	24.0976			0.935168
$665$	−20.4134	−	17.1927i	−0.791598	−	0.666703i
$666$	−18.6427			−0.722390
$667$		−	1.03533i		−	0.0400881i
$668$		−	1.19792i		−	0.0463491i
$669$	6.71826			0.259743
$670$	7.53252	−	8.94361i	0.291007	−	0.345522i
$671$	26.2419			1.01306
$672$			2.25318i			0.0869181i
$673$			34.1741i			1.31731i	0.752443	+	0.658657i	$0.228875\pi$
$673$			34.1741i			1.31731i	−0.752443	+	0.658657i	$0.771125\pi$
$674$	18.1590			0.699458
$675$	−10.0000	+	1.72555i	−0.384900	+	0.0664164i
$676$		0			0
$677$			5.84695i			0.224716i	0.993668	+	0.112358i	$0.0358404\pi$
$677$			5.84695i			0.224716i	−0.993668	+	0.112358i	$0.964160\pi$
$678$			1.95043i			0.0749058i
$679$	11.7833			0.452201
$680$	24.1445	−	28.6676i	0.925900	−	1.09935i
$681$	1.66054			0.0636319
$682$			5.43955i			0.208291i
$683$			11.3488i			0.434249i	0.976144	+	0.217125i	$0.0696678\pi$
$683$			11.3488i			0.434249i	−0.976144	+	0.217125i	$0.930332\pi$
$684$	−10.0000			−0.382360
$685$	3.38273	+	2.84901i	0.129247	+	0.108855i
$686$	−23.8106			−0.909093
$687$			0.525808i			0.0200608i
$688$		−	3.30969i		−	0.126181i
$689$		0			0
$690$	0.241857	+	0.203698i	0.00920733	+	0.00775463i
$691$	−18.8232			−0.716067			−0.358034	−	0.933709i	$-0.616553\pi$
$691$	−18.8232			−0.716067			−0.358034	+	0.933709i	$0.616553\pi$
$692$		−	0.790529i		−	0.0300514i
$693$			22.6914i			0.861976i
$694$	−14.5325			−0.551647
$695$	−12.5325	+	14.8803i	−0.475385	+	0.564441i
$696$	−3.18413			−0.120694
$697$		−	0.983636i		−	0.0372579i
$698$		−	22.2036i		−	0.840420i
$699$	4.81952			0.182291
$700$	5.90239	−	1.01849i	0.223090	−	0.0384952i
$701$	19.1626			0.723763			0.361881	−	0.932224i	$-0.382135\pi$
$701$	19.1626			0.723763			0.361881	+	0.932224i	$0.382135\pi$
$702$		0			0
$703$		−	32.0518i		−	1.20885i
$704$	−34.0037			−1.28156
$705$	6.10492	−	7.24857i	0.229924	−	0.272997i
$706$	1.55401			0.0584860
$707$		−	12.0602i		−	0.453570i
$708$		−	1.43839i		−	0.0540578i
$709$	−23.4837			−0.881949			−0.440975	−	0.897520i	$-0.645367\pi$
$709$	−23.4837			−0.881949			−0.440975	+	0.897520i	$0.645367\pi$
$710$	−3.81952	−	3.21689i	−0.143344	−	0.120728i
$711$	−32.2098			−1.20796
$712$		−	37.6496i		−	1.41098i
$713$			0.407395i			0.0152571i
$714$	4.53252			0.169625
$715$		0			0
$716$	−11.9370			−0.446107
$717$			1.38044i			0.0515535i
$718$			34.9173i			1.30310i
$719$	14.1086			0.526161			0.263080	−	0.964774i	$-0.415262\pi$
$719$	14.1086			0.526161			0.263080	+	0.964774i	$0.415262\pi$
$720$	−10.2547	+	12.1758i	−0.382170	+	0.453764i
$721$	−13.0577			−0.486295
$722$			18.5046i			0.688668i
$723$			6.02765i			0.224171i
$724$	11.7004			0.434843
$725$	2.55063	+	14.7816i	0.0947280	+	0.548973i
$726$	1.66419			0.0617640
$727$			25.3762i			0.941153i	0.882359	+	0.470576i	$0.155954\pi$
$727$			25.3762i			0.941153i	−0.882359	+	0.470576i	$0.844046\pi$
$728$		0			0
$729$	20.7796			0.769616
$730$	15.1534	−	17.9922i	0.560854	−	0.665921i
$731$	7.29958			0.269985
$732$		−	1.37736i		−	0.0509087i
$733$			10.6692i			0.394074i	0.980396	+	0.197037i	$0.0631320\pi$
$733$			10.6692i			0.394074i	−0.980396	+	0.197037i	$0.936868\pi$
$734$	39.6952			1.46517
$735$	−1.70042	−	1.43213i	−0.0627209	−	0.0528251i
$736$	−1.11018			−0.0409218
$737$		−	17.0923i		−	0.629605i
$738$			0.617344i			0.0227247i
$739$	1.41503			0.0520526			0.0260263	−	0.999661i	$-0.491715\pi$
$739$	1.41503			0.0520526			0.0260263	+	0.999661i	$0.491715\pi$
$740$	5.50183	+	4.63377i	0.202251	+	0.170341i
$741$		0			0
$742$			5.84695i			0.214648i
$743$			29.8777i			1.09611i	0.836443	+	0.548053i	$0.184631\pi$
$743$			29.8777i			1.09611i	−0.836443	+	0.548053i	$0.815369\pi$
$744$	1.25293			0.0459348
$745$	−32.1267	+	38.1451i	−1.17703	+	1.39753i
$746$	−40.9370			−1.49881
$747$		−	22.5730i		−	0.825903i
$748$		−	12.4844i		−	0.456476i
$749$	−35.8809			−1.31106
$750$	−3.95485	−	2.31238i	−0.144411	−	0.0844362i
$751$	−19.9858			−0.729293			−0.364646	−	0.931146i	$-0.618810\pi$
$751$	−19.9858			−0.729293			−0.364646	+	0.931146i	$0.618810\pi$
$752$		−	30.3474i		−	1.10666i
$753$		−	3.20938i		−	0.116956i
$754$		0			0
$755$	−27.6028	+	32.7737i	−1.00457	+	1.19276i
$756$	2.43126			0.0884239
$757$		−	17.0923i		−	0.621232i	−0.950535	−	0.310616i	$-0.899465\pi$
$757$		−	17.0923i		−	0.621232i	0.950535	−	0.310616i	$-0.100535\pi$
$758$			20.6649i			0.750584i
$759$	0.462218			0.0167775
$760$	−30.9334	−	26.0528i	−1.12207	−	0.945034i
$761$	−42.2240			−1.53062			−0.765310	−	0.643662i	$-0.777414\pi$
$761$	−42.2240			−1.53062			−0.765310	+	0.643662i	$0.777414\pi$
$762$		−	6.84552i		−	0.247987i
$763$		−	11.6939i		−	0.423347i
$764$	0.907659			0.0328380
$765$	−26.8539	−	22.6170i	−0.970904	−	0.817718i
$766$	2.07395			0.0749350
$767$		0			0
$768$			4.42107i			0.159531i
$769$	23.7655			0.857004			0.428502	−	0.903541i	$-0.359041\pi$
$769$	23.7655			0.857004			0.428502	+	0.903541i	$0.359041\pi$
$770$	−13.4711	+	15.9947i	−0.485466	+	0.576410i
$771$	3.75814			0.135346
$772$		−	12.5149i		−	0.450422i
$773$			0.284086i			0.0102179i	0.999987	+	0.00510894i	$0.00162623\pi$
$773$			0.284086i			0.0102179i	−0.999987	+	0.00510894i	$0.998374\pi$
$774$	−4.58132			−0.164672
$775$	−1.00366	−	5.81644i	−0.0360524	−	0.208933i
$776$	17.8557			0.640984
$777$			3.81739i			0.136948i
$778$		−	26.1730i		−	0.938349i
$779$	−1.06138			−0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$			2.23325i			0.0798610i
$783$			6.08867i			0.217591i
$784$	−7.11910			−0.254254
$785$	−10.6084	−	8.93460i	−0.378628	−	0.318890i
$786$	4.09761			0.146157
$787$			24.1341i			0.860289i	0.902760	+	0.430145i	$0.141537\pi$
$787$			24.1341i			0.860289i	−0.902760	+	0.430145i	$0.858463\pi$
$788$		−	5.46381i		−	0.194640i
$789$	4.63849			0.165135
$790$	−22.7041	−	19.1219i	−0.807775	−	0.680327i
$791$	−9.66054			−0.343489
$792$			34.3853i			1.22183i
$793$		0			0
$794$	26.7529			0.949424
$795$	−1.20618	+	1.43213i	−0.0427787	+	0.0507926i
$796$	10.2728			0.364110
$797$		−	34.3442i		−	1.21653i	−0.793732	−	0.608267i	$-0.791865\pi$
$797$		−	34.3442i		−	1.21653i	0.793732	−	0.608267i	$-0.208135\pi$
$798$		−	4.89075i		−	0.173131i
$799$	66.9317			2.36787
$800$	15.8502	−	2.73503i	0.560390	−	0.0966980i
$801$	−35.2676			−1.24612
$802$		−	4.39797i		−	0.155298i
$803$		−	34.3853i		−	1.21343i
$804$	−0.897129			−0.0316393
$805$	−1.00892	+	1.19792i	−0.0355598	+	0.0422213i
$806$		0			0
$807$			1.26329i			0.0444698i
$808$		−	18.2753i		−	0.642924i
$809$	47.6862			1.67656			0.838279	−	0.545241i	$-0.183562\pi$
$809$	47.6862			1.67656			0.838279	+	0.545241i	$0.183562\pi$
$810$	16.1283	+	13.5836i	0.566691	+	0.477280i
$811$	24.5992			0.863793			0.431897	−	0.901923i	$-0.357845\pi$
$811$	24.5992			0.863793			0.431897	+	0.901923i	$0.357845\pi$
$812$		−	3.59377i		−	0.126117i
$813$		−	7.59368i		−	0.266322i
$814$	−25.1138			−0.880239
$815$	−20.4134	−	17.1927i	−0.715051	−	0.602233i
$816$	4.64796			0.162711
$817$		−	7.87651i		−	0.275564i
$818$			16.0097i			0.559765i
$819$		0			0
$820$	0.153445	−	0.182190i	0.00535853	−	0.00636236i
$821$	17.2996			0.603759			0.301880	−	0.953346i	$-0.402386\pi$
$821$	17.2996			0.603759			0.301880	+	0.953346i	$0.402386\pi$
$822$			0.810450i			0.0282677i
$823$			32.5625i			1.13506i	0.823353	+	0.567529i	$0.192101\pi$
$823$			32.5625i			1.13506i	−0.823353	+	0.567529i	$0.807899\pi$
$824$	−19.7869			−0.689311
$825$	−6.59916	+	1.13872i	−0.229753	+	0.0396451i
$826$	−17.0162			−0.592070
$827$		−	15.4702i		−	0.537951i	−0.963147	−	0.268976i	$-0.913315\pi$
$827$		−	15.4702i		−	0.537951i	0.963147	−	0.268976i	$-0.0866851\pi$
$828$			0.586832i			0.0203938i
$829$	14.5236			0.504425			0.252213	−	0.967672i	$-0.418842\pi$
$829$	14.5236			0.504425			0.252213	+	0.967672i	$0.418842\pi$
$830$	13.4008	−	15.9113i	0.465150	−	0.552288i
$831$	3.41503			0.118466
$832$		0			0
$833$		−	15.7013i		−	0.544018i
$834$	−3.56509			−0.123449
$835$	−3.47114	−	2.92347i	−0.120124	−	0.101171i
$836$	−13.4711			−0.465909
$837$		−	2.39585i		−	0.0828127i
$838$		−	19.9747i		−	0.690015i
$839$	−0.815866			−0.0281668			−0.0140834	−	0.999901i	$-0.504483\pi$
$839$	−0.815866			−0.0281668			−0.0140834	+	0.999901i	$0.504483\pi$
$840$	3.68419	+	3.10291i	0.127117	+	0.107061i
$841$	−20.0000			−0.689655
$842$			20.3049i			0.699753i
$843$		−	1.40162i		−	0.0482744i
$844$	−4.29797			−0.147942
$845$		0			0
$846$	−42.0073			−1.44424
$847$			8.24280i			0.283226i
$848$			5.99587i			0.205899i
$849$	2.10126			0.0721151
$850$	−5.50183	−	31.8845i	−0.188711	−	1.09363i
$851$	−1.88090			−0.0644764
$852$			0.383134i			0.0131260i
$853$		−	20.0856i		−	0.687719i	−0.939021	−	0.343859i	$-0.888266\pi$
$853$		−	20.0856i		−	0.687719i	0.939021	−	0.343859i	$-0.111734\pi$
$854$	−16.2943			−0.557580
$855$	−24.4045	+	28.9763i	−0.834616	+	0.990968i
$856$	−54.3719			−1.85839
$857$			40.7886i			1.39331i	0.717406	+	0.696656i	$0.245329\pi$
$857$			40.7886i			1.39331i	−0.717406	+	0.696656i	$0.754671\pi$
$858$		0			0
$859$	40.1301			1.36922			0.684610	−	0.728909i	$-0.259972\pi$
$859$	40.1301			1.36922			0.684610	+	0.728909i	$0.259972\pi$
$860$	1.35204	+	1.13872i	0.0461041	+	0.0388300i
$861$	0.126411			0.00430808
$862$			11.4703i			0.390679i
$863$			20.8275i			0.708977i	0.935060	+	0.354489i	$0.115345\pi$
$863$			20.8275i			0.708977i	−0.935060	+	0.354489i	$0.884655\pi$
$864$	6.52886			0.222116
$865$	−2.29066	−	1.92925i	−0.0778848	−	0.0655964i
$866$	29.4134			0.999509
$867$			4.38430i			0.148899i
$868$			1.41412i			0.0479985i
$869$	−43.3903			−1.47192
$870$	−1.77072	+	2.10243i	−0.0600330	+	0.0712792i
$871$		0			0
$872$		−	17.7203i		−	0.600084i
$873$		−	16.7261i		−	0.566091i
$874$	2.40976			0.0815114
$875$	11.4533	−	19.5885i	0.387192	−	0.662212i
$876$	−1.80479			−0.0609782
$877$			46.5944i			1.57338i	0.617347	+	0.786691i	$0.288207\pi$
$877$			46.5944i			1.57338i	−0.617347	+	0.786691i	$0.711793\pi$
$878$		−	8.38421i		−	0.282953i
$879$	3.37935			0.113982
$880$	−13.8143	+	16.4021i	−0.465678	+	0.552916i
$881$	23.8447			0.803347			0.401674	−	0.915783i	$-0.368429\pi$
$881$	23.8447			0.803347			0.401674	+	0.915783i	$0.368429\pi$
$882$			9.85437i			0.331814i
$883$			37.2496i			1.25355i	0.779201	+	0.626774i	$0.215625\pi$
$883$			37.2496i			1.25355i	−0.779201	+	0.626774i	$0.784375\pi$
$884$		0			0
$885$	−4.16790	−	3.51031i	−0.140103	−	0.117998i
$886$	−45.4082			−1.52552
$887$			28.5795i			0.959605i	0.877377	+	0.479802i	$0.159292\pi$
$887$			28.5795i			0.959605i	−0.877377	+	0.479802i	$0.840708\pi$
$888$			5.78466i			0.194121i
$889$	33.9060			1.13717
$890$	−24.8594	−	20.9372i	−0.833289	−	0.701816i
$891$	30.8232			1.03262
$892$			11.4902i			0.384720i
$893$		−	72.2217i		−	2.41681i
$894$	−9.13899			−0.305653
$895$	−29.1317	+	34.5890i	−0.973765	+	1.15618i
$896$	8.05611			0.269136
$897$		0			0
$898$			14.8180i			0.494483i
$899$	−3.54144			−0.118114
$900$	−1.44571	−	8.37828i	−0.0481905	−	0.279276i
$901$	−13.2240			−0.440556
$902$			0.831632i			0.0276903i
$903$			0.938099i			0.0312180i
$904$	−14.6390			−0.486887
$905$	28.5543	−	33.9035i	0.949177	−	1.12699i
$906$	−7.85209			−0.260868
$907$			6.41386i			0.212969i	0.994314	+	0.106484i	$0.0339594\pi$
$907$			6.41386i			0.212969i	−0.994314	+	0.106484i	$0.966041\pi$
$908$			2.84001i			0.0942489i
$909$	−17.1191			−0.567805
$910$		0			0
$911$	22.2204			0.736193			0.368097	−	0.929788i	$-0.380010\pi$
$911$	22.2204			0.736193			0.368097	+	0.929788i	$0.380010\pi$
$912$		−	5.01532i		−	0.166074i
$913$		−	30.4084i		−	1.00637i
$914$	−9.77437			−0.323308
$915$	−3.99108	−	3.36138i	−0.131941	−	0.111124i
$916$	−0.899287			−0.0297133
$917$			20.2956i			0.670219i
$918$		−	13.1335i		−	0.433472i
$919$	−26.1264			−0.861831			−0.430915	−	0.902392i	$-0.641809\pi$
$919$	−26.1264			−0.861831			−0.430915	+	0.902392i	$0.641809\pi$
$920$	−1.52886	+	1.81527i	−0.0504051	+	0.0598476i
$921$	−7.62851			−0.251368
$922$		−	5.39220i		−	0.177583i
$923$		0			0
$924$	1.60442			0.0527817
$925$	26.8539	−	4.63377i	0.882950	−	0.152357i
$926$	−2.36096			−0.0775859
$927$			18.5351i			0.608772i
$928$		−	9.65067i		−	0.316799i
$929$	23.9423			0.785521			0.392760	−	0.919641i	$-0.371520\pi$
$929$	23.9423			0.785521			0.392760	+	0.919641i	$0.371520\pi$
$930$	0.696765	−	0.827293i	0.0228478	−	0.0271280i
$931$	−16.9423			−0.555261
$932$			8.24280i			0.270002i
$933$		−	2.63631i		−	0.0863089i
$934$	38.9496			1.27447
$935$	−36.1752	−	30.4676i	−1.18306	−	0.996397i
$936$		0			0
$937$		−	18.5046i		−	0.604518i	−0.953226	−	0.302259i	$-0.902259\pi$
$937$		−	18.5046i		−	0.604518i	0.953226	−	0.302259i	$-0.0977407\pi$
$938$			10.6131i			0.346531i
$939$	−9.02204			−0.294423
$940$	12.3972	+	10.4412i	0.404352	+	0.340554i
$941$	−14.3788			−0.468735			−0.234368	−	0.972148i	$-0.575302\pi$
$941$	−14.3788			−0.468735			−0.234368	+	0.972148i	$0.575302\pi$
$942$		−	2.54160i		−	0.0828098i
$943$			0.0622851i			0.00202828i
$944$	−17.4496			−0.567938
$945$	5.93336	−	7.04487i	0.193012	−	0.229170i
$946$	−6.17156			−0.200655
$947$			58.3188i			1.89511i	0.319596	+	0.947554i	$0.396453\pi$
$947$			58.3188i			1.89511i	−0.319596	+	0.947554i	$0.603547\pi$
$948$			2.27744i			0.0739677i
$949$		0			0
$950$	−34.4045	+	5.93667i	−1.11623	+	0.192611i
$951$	4.08708			0.132533
$952$			34.0190i			1.10256i
$953$			13.7995i			0.447010i	0.974703	+	0.223505i	$0.0717499\pi$
$953$			13.7995i			0.447010i	−0.974703	+	0.223505i	$0.928250\pi$
$954$	8.29958			0.268709
$955$	2.21510	−	2.63006i	0.0716788	−	0.0851067i
$956$	−2.36096			−0.0763588
$957$			4.01801i			0.129884i
$958$			36.5762i			1.18172i
$959$	−4.01419			−0.129625
$960$	5.17156	+	4.35561i	0.166911	+	0.140577i
$961$	−29.6065			−0.955047
$962$		0			0
$963$			50.9319i			1.64126i
$964$	−10.3090			−0.332032
$965$	−36.2636	−	30.5421i	−1.16737	−	0.983184i
$966$	−0.287005			−0.00923422
$967$			30.3474i			0.975906i	0.872870	+	0.487953i	$0.162256\pi$
$967$			30.3474i			0.975906i	−0.872870	+	0.487953i	$0.837744\pi$
$968$			12.4907i			0.401466i
$969$	11.0614			0.355343
$970$	9.92970	−	11.7899i	0.318824	−	0.378550i
$971$	44.1013			1.41528			0.707638	−	0.706575i	$-0.249761\pi$
$971$	44.1013			1.41528			0.707638	+	0.706575i	$0.249761\pi$
$972$		−	5.21160i		−	0.167162i
$973$		−	17.6580i		−	0.566089i
$974$	26.5074			0.849351
$975$		0			0
$976$	−16.7093			−0.534853
$977$		−	22.3220i		−	0.714143i	−0.934077	−	0.357071i	$-0.883775\pi$
$977$		−	22.3220i		−	0.714143i	0.934077	−	0.357071i	$-0.116225\pi$
$978$		−	4.89075i		−	0.156389i
$979$	−47.5094			−1.51841
$980$	2.44937	−	2.90822i	0.0782422	−	0.0928996i
$981$	−16.5992			−0.529970
$982$			12.6838i			0.404756i
$983$		−	4.03793i		−	0.128790i	−0.997924	−	0.0643950i	$-0.979488\pi$
$983$		−	4.03793i		−	0.128790i	0.997924	−	0.0643950i	$-0.0205118\pi$
$984$	0.191556			0.00610659
$985$	−15.8321	−	13.3342i	−0.504453	−	0.424862i
$986$	−19.4134			−0.618249
$987$			8.60167i			0.273794i
$988$		0			0
$989$	−0.462218			−0.0146977
$990$	22.7041	+	19.1219i	0.721583	+	0.607734i
$991$	29.6500			0.941864			0.470932	−	0.882170i	$-0.343918\pi$
$991$	29.6500			0.941864			0.470932	+	0.882170i	$0.343918\pi$
$992$			3.79747i			0.120570i
$993$			4.38304i			0.139092i
$994$	4.53252			0.143763
$995$	25.0703	−	29.7668i	0.794782	−	0.943671i
$996$	−1.59605			−0.0505728
$997$			22.1762i			0.702327i	0.936314	+	0.351164i	$0.114214\pi$
$997$			22.1762i			0.702327i	−0.936314	+	0.351164i	$0.885786\pi$
$998$		−	22.3450i		−	0.707320i
$999$	11.0614			0.349967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.b.d.339.5		6
5.2	odd	4		4225.2.a.br.1.2		6
5.3	odd	4		4225.2.a.br.1.5		6
5.4	even	2	inner	845.2.b.d.339.2		6
13.2	odd	12		845.2.l.f.654.4		24
13.3	even	3		65.2.n.a.9.2	✓	12
13.4	even	6		845.2.n.e.484.2		12
13.5	odd	4		845.2.d.d.844.9		12
13.6	odd	12		845.2.l.f.699.3		24
13.7	odd	12		845.2.l.f.699.9		24
13.8	odd	4		845.2.d.d.844.3		12
13.9	even	3		65.2.n.a.29.5	yes	12
13.10	even	6		845.2.n.e.529.5		12
13.11	odd	12		845.2.l.f.654.10		24
13.12	even	2		845.2.b.e.339.2		6
39.29	odd	6		585.2.bs.a.334.5		12
39.35	odd	6		585.2.bs.a.289.2		12
52.3	odd	6		1040.2.dh.a.529.3		12
52.35	odd	6		1040.2.dh.a.289.4		12
65.3	odd	12		325.2.e.e.126.2		12
65.4	even	6		845.2.n.e.484.5		12
65.9	even	6		65.2.n.a.29.2	yes	12
65.12	odd	4		4225.2.a.bq.1.5		6
65.19	odd	12		845.2.l.f.699.10		24
65.22	odd	12		325.2.e.e.276.5		12
65.24	odd	12		845.2.l.f.654.3		24
65.29	even	6		65.2.n.a.9.5	yes	12
65.34	odd	4		845.2.d.d.844.10		12
65.38	odd	4		4225.2.a.bq.1.2		6
65.42	odd	12		325.2.e.e.126.5		12
65.44	odd	4		845.2.d.d.844.4		12
65.48	odd	12		325.2.e.e.276.2		12
65.49	even	6		845.2.n.e.529.2		12
65.54	odd	12		845.2.l.f.654.9		24
65.59	odd	12		845.2.l.f.699.4		24
65.64	even	2		845.2.b.e.339.5		6
195.29	odd	6		585.2.bs.a.334.2		12
195.74	odd	6		585.2.bs.a.289.5		12
260.139	odd	6		1040.2.dh.a.289.3		12
260.159	odd	6		1040.2.dh.a.529.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	13.3	even	3
65.2.n.a.9.5	yes	12	65.29	even	6
65.2.n.a.29.2	yes	12	65.9	even	6
65.2.n.a.29.5	yes	12	13.9	even	3
325.2.e.e.126.2		12	65.3	odd	12
325.2.e.e.126.5		12	65.42	odd	12
325.2.e.e.276.2		12	65.48	odd	12
325.2.e.e.276.5		12	65.22	odd	12
585.2.bs.a.289.2		12	39.35	odd	6
585.2.bs.a.289.5		12	195.74	odd	6
585.2.bs.a.334.2		12	195.29	odd	6
585.2.bs.a.334.5		12	39.29	odd	6
845.2.b.d.339.2		6	5.4	even	2	inner
845.2.b.d.339.5		6	1.1	even	1	trivial
845.2.b.e.339.2		6	13.12	even	2
845.2.b.e.339.5		6	65.64	even	2
845.2.d.d.844.3		12	13.8	odd	4
845.2.d.d.844.4		12	65.44	odd	4
845.2.d.d.844.9		12	13.5	odd	4
845.2.d.d.844.10		12	65.34	odd	4
845.2.l.f.654.3		24	65.24	odd	12
845.2.l.f.654.4		24	13.2	odd	12
845.2.l.f.654.9		24	65.54	odd	12
845.2.l.f.654.10		24	13.11	odd	12
845.2.l.f.699.3		24	13.6	odd	12
845.2.l.f.699.4		24	65.59	odd	12
845.2.l.f.699.9		24	13.7	odd	12
845.2.l.f.699.10		24	65.19	odd	12
845.2.n.e.484.2		12	13.4	even	6
845.2.n.e.484.5		12	65.4	even	6
845.2.n.e.529.2		12	65.49	even	6
845.2.n.e.529.5		12	13.10	even	6
1040.2.dh.a.289.3		12	260.139	odd	6
1040.2.dh.a.289.4		12	52.35	odd	6
1040.2.dh.a.529.3		12	52.3	odd	6
1040.2.dh.a.529.4		12	260.159	odd	6
4225.2.a.bq.1.2		6	65.38	odd	4
4225.2.a.bq.1.5		6	65.12	odd	4
4225.2.a.br.1.2		6	5.2	odd	4
4225.2.a.br.1.5		6	5.3	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.18733i q^{2} -0.345110i q^{3} +0.590239 q^{4} +(1.44045 - 1.71029i) q^{5} +0.409761 q^{6} +2.02956i q^{7} +3.07548i q^{8} +2.88090 q^{9} +O(q^{10})\)	\(q+1.18733i q^{2} -0.345110i q^{3} +0.590239 q^{4} +(1.44045 - 1.71029i) q^{5} +0.409761 q^{6} +2.02956i q^{7} +3.07548i q^{8} +2.88090 q^{9} +(2.03069 + 1.71029i) q^{10} +3.88090 q^{11} -0.203698i q^{12} -2.40976 q^{14} +(-0.590239 - 0.497113i) q^{15} -2.47114 q^{16} -5.45014i q^{17} +3.42059i q^{18} -5.88090 q^{19} +(0.850210 - 1.00948i) q^{20} +0.700420 q^{21} +4.60792i q^{22} +0.345110i q^{23} +1.06138 q^{24} +(-0.850210 - 4.92718i) q^{25} -2.02956i q^{27} +1.19792i q^{28} -3.00000 q^{29} +(0.590239 - 0.700811i) q^{30} +1.18048 q^{31} +3.21689i q^{32} -1.33934i q^{33} +6.47114 q^{34} +(3.47114 + 2.92347i) q^{35} +1.70042 q^{36} +5.45014i q^{37} -6.98259i q^{38} +(5.25997 + 4.43007i) q^{40} +0.180479 q^{41} +0.831632i q^{42} +1.33934i q^{43} +2.29066 q^{44} +(4.14979 - 4.92718i) q^{45} -0.409761 q^{46} +12.2807i q^{47} +0.852815i q^{48} +2.88090 q^{49} +(5.85021 - 1.00948i) q^{50} -1.88090 q^{51} -2.42636i q^{53} +2.40976 q^{54} +(5.59024 - 6.63748i) q^{55} -6.24186 q^{56} +2.02956i q^{57} -3.56200i q^{58} +7.06138 q^{59} +(-0.348383 - 0.293416i) q^{60} +6.76180 q^{61} +1.40162i q^{62} +5.84695i q^{63} -8.76180 q^{64} +1.59024 q^{66} -4.40422i q^{67} -3.21689i q^{68} +0.119101 q^{69} +(-3.47114 + 4.12140i) q^{70} -1.88090 q^{71} +8.86014i q^{72} -8.86014i q^{73} -6.47114 q^{74} +(-1.70042 + 0.293416i) q^{75} -3.47114 q^{76} +7.87651i q^{77} -11.1805 q^{79} +(-3.55955 + 4.22637i) q^{80} +7.94228 q^{81} +0.214289i q^{82} -7.83540i q^{83} +0.413416 q^{84} +(-9.32135 - 7.85066i) q^{85} -1.59024 q^{86} +1.03533i q^{87} +11.9356i q^{88} -12.2419 q^{89} +(5.85021 + 4.92718i) q^{90} +0.203698i q^{92} -0.407395i q^{93} -14.5813 q^{94} +(-8.47114 + 10.0581i) q^{95} +1.11018 q^{96} -5.80585i q^{97} +3.42059i q^{98} +11.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9	\( 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9} - 7 q^{10} - 22 q^{14} + 4 q^{15} + 16 q^{16} - 12 q^{19} + q^{20} - 4 q^{21} - 32 q^{24} - q^{25} - 18 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{36} + 35 q^{40} - 14 q^{41} - 2 q^{44} + 29 q^{45} - 10 q^{46} - 6 q^{49} + 31 q^{50} + 12 q^{51} + 22 q^{54} + 26 q^{55} + 16 q^{56} + 4 q^{59} - 48 q^{60} - 6 q^{61} - 6 q^{64} + 2 q^{66} + 24 q^{69} + 10 q^{70} + 12 q^{71} - 8 q^{74} - 2 q^{75} + 10 q^{76} - 52 q^{79} - 33 q^{80} - 14 q^{81} - 90 q^{84} - 21 q^{85} - 2 q^{86} - 20 q^{89} + 31 q^{90} - 56 q^{94} - 20 q^{95} + 6 q^{96} + 52 q^{99}+O(q^{100}) \) 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9 - 7 * q^10 - 22 * q^14 + 4 * q^15 + 16 * q^16 - 12 * q^19 + q^20 - 4 * q^21 - 32 * q^24 - q^25 - 18 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^34 - 10 * q^35 + 2 * q^36 + 35 * q^40 - 14 * q^41 - 2 * q^44 + 29 * q^45 - 10 * q^46 - 6 * q^49 + 31 * q^50 + 12 * q^51 + 22 * q^54 + 26 * q^55 + 16 * q^56 + 4 * q^59 - 48 * q^60 - 6 * q^61 - 6 * q^64 + 2 * q^66 + 24 * q^69 + 10 * q^70 + 12 * q^71 - 8 * q^74 - 2 * q^75 + 10 * q^76 - 52 * q^79 - 33 * q^80 - 14 * q^81 - 90 * q^84 - 21 * q^85 - 2 * q^86 - 20 * q^89 + 31 * q^90 - 56 * q^94 - 20 * q^95 + 6 * q^96 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more