LMFDB - Embedded newform 1815.2.c.f.364.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.4
Root			$-1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.f.364.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.456850i q^{2} +1.00000i q^{3} +1.79129 q^{4} +(2.00000 + 1.00000i) q^{5} +0.456850 q^{6} +0.913701i q^{7} -1.73205i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.456850i q^{2} +1.00000i q^{3} +1.79129 q^{4} +(2.00000 + 1.00000i) q^{5} +0.456850 q^{6} +0.913701i q^{7} -1.73205i q^{8} -1.00000 q^{9} +(0.456850 - 0.913701i) q^{10} +1.79129i q^{12} +0.913701i q^{13} +0.417424 q^{14} +(-1.00000 + 2.00000i) q^{15} +2.79129 q^{16} +7.02355i q^{17} +0.456850i q^{18} -5.29150 q^{19} +(3.58258 + 1.79129i) q^{20} -0.913701 q^{21} +0.582576i q^{23} +1.73205 q^{24} +(3.00000 + 4.00000i) q^{25} +0.417424 q^{26} -1.00000i q^{27} +1.63670i q^{28} -4.37780 q^{29} +(0.913701 + 0.456850i) q^{30} +2.58258 q^{31} -4.73930i q^{32} +3.20871 q^{34} +(-0.913701 + 1.82740i) q^{35} -1.79129 q^{36} +9.58258i q^{37} +2.41742i q^{38} -0.913701 q^{39} +(1.73205 - 3.46410i) q^{40} +6.92820 q^{41} +0.417424i q^{42} -4.37780i q^{43} +(-2.00000 - 1.00000i) q^{45} +0.266150 q^{46} +6.58258i q^{47} +2.79129i q^{48} +6.16515 q^{49} +(1.82740 - 1.37055i) q^{50} -7.02355 q^{51} +1.63670i q^{52} -5.00000i q^{53} -0.456850 q^{54} +1.58258 q^{56} -5.29150i q^{57} +2.00000i q^{58} +3.58258 q^{59} +(-1.79129 + 3.58258i) q^{60} +8.66025 q^{61} -1.17985i q^{62} -0.913701i q^{63} +3.41742 q^{64} +(-0.913701 + 1.82740i) q^{65} -14.7477i q^{67} +12.5812i q^{68} -0.582576 q^{69} +(0.834849 + 0.417424i) q^{70} -9.16515 q^{71} +1.73205i q^{72} -15.6838i q^{73} +4.37780 q^{74} +(-4.00000 + 3.00000i) q^{75} -9.47860 q^{76} +0.417424i q^{78} +2.64575 q^{79} +(5.58258 + 2.79129i) q^{80} +1.00000 q^{81} -3.16515i q^{82} +12.2197i q^{83} -1.63670 q^{84} +(-7.02355 + 14.0471i) q^{85} -2.00000 q^{86} -4.37780i q^{87} -16.7477 q^{89} +(-0.456850 + 0.913701i) q^{90} -0.834849 q^{91} +1.04356i q^{92} +2.58258i q^{93} +3.00725 q^{94} +(-10.5830 - 5.29150i) q^{95} +4.73930 q^{96} -3.58258i q^{97} -2.81655i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9	$ 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9} + 40 q^{14} - 8 q^{15} + 4 q^{16} - 8 q^{20} + 24 q^{25} + 40 q^{26} - 16 q^{31} + 44 q^{34} + 4 q^{36} - 16 q^{45} - 24 q^{49} - 24 q^{56} - 8 q^{59} + 4 q^{60} + 64 q^{64} + 32 q^{69} + 80 q^{70} - 32 q^{75} + 8 q^{80} + 8 q^{81} - 16 q^{86} - 24 q^{89} - 80 q^{91}+O(q^{100}) $ 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9 + 40 * q^14 - 8 * q^15 + 4 * q^16 - 8 * q^20 + 24 * q^25 + 40 * q^26 - 16 * q^31 + 44 * q^34 + 4 * q^36 - 16 * q^45 - 24 * q^49 - 24 * q^56 - 8 * q^59 + 4 * q^60 + 64 * q^64 + 32 * q^69 + 80 * q^70 - 32 * q^75 + 8 * q^80 + 8 * q^81 - 16 * q^86 - 24 * q^89 - 80 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	0.456850i		−	0.323042i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$		−	0.456850i		−	0.323042i	0.986869	−	0.161521i	$-0.0516399\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.79129			0.895644
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	0.456850			0.186508
$7$			0.913701i			0.345346i	0.984979	+	0.172673i	$0.0552404\pi$
$7$			0.913701i			0.345346i	−0.984979	+	0.172673i	$0.944760\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−1.00000			−0.333333
$10$	0.456850	−	0.913701i	0.144469	−	0.288937i
$11$		0			0
$11$		0			0
$12$			1.79129i			0.517100i
$13$			0.913701i			0.253415i	0.991940	+	0.126707i	$0.0404409\pi$
$13$			0.913701i			0.253415i	−0.991940	+	0.126707i	$0.959559\pi$
$14$	0.417424			0.111561
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	2.79129			0.697822
$17$			7.02355i			1.70346i	0.523979	+	0.851731i	$0.324447\pi$
$17$			7.02355i			1.70346i	−0.523979	+	0.851731i	$0.675553\pi$
$18$			0.456850i			0.107681i
$19$	−5.29150			−1.21395			−0.606977	−	0.794719i	$-0.707618\pi$
$19$	−5.29150			−1.21395			−0.606977	+	0.794719i	$0.707618\pi$
$20$	3.58258	+	1.79129i	0.801088	+	0.400544i
$21$	−0.913701			−0.199386
$22$		0			0
$23$			0.582576i			0.121475i	0.998154	+	0.0607377i	$0.0193453\pi$
$23$			0.582576i			0.121475i	−0.998154	+	0.0607377i	$0.980655\pi$
$24$	1.73205			0.353553
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	0.417424			0.0818636
$27$		−	1.00000i		−	0.192450i
$28$			1.63670i			0.309307i
$29$	−4.37780			−0.812937			−0.406469	−	0.913665i	$-0.633240\pi$
$29$	−4.37780			−0.812937			−0.406469	+	0.913665i	$0.633240\pi$
$30$	0.913701	+	0.456850i	0.166818	+	0.0834091i
$31$	2.58258			0.463844			0.231922	−	0.972734i	$-0.425499\pi$
$31$	2.58258			0.463844			0.231922	+	0.972734i	$0.425499\pi$
$32$		−	4.73930i		−	0.837798i
$33$		0			0
$34$	3.20871			0.550290
$35$	−0.913701	+	1.82740i	−0.154444	+	0.308887i
$36$	−1.79129			−0.298548
$37$			9.58258i			1.57537i	0.616081	+	0.787683i	$0.288719\pi$
$37$			9.58258i			1.57537i	−0.616081	+	0.787683i	$0.711281\pi$
$38$			2.41742i			0.392158i
$39$	−0.913701			−0.146309
$40$	1.73205	−	3.46410i	0.273861	−	0.547723i
$41$	6.92820			1.08200			0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820			1.08200			0.541002	+	0.841021i	$0.318045\pi$
$42$			0.417424i			0.0644100i
$43$		−	4.37780i		−	0.667609i	−0.942642	−	0.333804i	$-0.891668\pi$
$43$		−	4.37780i		−	0.667609i	0.942642	−	0.333804i	$-0.108332\pi$
$44$		0			0
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	0.266150			0.0392417
$47$			6.58258i			0.960167i	0.877223	+	0.480084i	$0.159394\pi$
$47$			6.58258i			0.960167i	−0.877223	+	0.480084i	$0.840606\pi$
$48$			2.79129i			0.402888i
$49$	6.16515			0.880736
$50$	1.82740	−	1.37055i	0.258434	−	0.193825i
$51$	−7.02355			−0.983494
$52$			1.63670i			0.226970i
$53$		−	5.00000i		−	0.686803i	−0.939189	−	0.343401i	$-0.888421\pi$
$53$		−	5.00000i		−	0.686803i	0.939189	−	0.343401i	$-0.111579\pi$
$54$	−0.456850			−0.0621694
$55$		0			0
$56$	1.58258			0.211481
$57$		−	5.29150i		−	0.700877i
$58$			2.00000i			0.262613i
$59$	3.58258			0.466412			0.233206	−	0.972427i	$-0.425078\pi$
$59$	3.58258			0.466412			0.233206	+	0.972427i	$0.425078\pi$
$60$	−1.79129	+	3.58258i	−0.231254	+	0.462509i
$61$	8.66025			1.10883			0.554416	−	0.832240i	$-0.312942\pi$
$61$	8.66025			1.10883			0.554416	+	0.832240i	$0.312942\pi$
$62$		−	1.17985i		−	0.149841i
$63$		−	0.913701i		−	0.115115i
$64$	3.41742			0.427178
$65$	−0.913701	+	1.82740i	−0.113331	+	0.226661i
$66$		0			0
$67$		−	14.7477i		−	1.80172i	−0.434108	−	0.900861i	$-0.642936\pi$
$67$		−	14.7477i		−	1.80172i	0.434108	−	0.900861i	$-0.357064\pi$
$68$			12.5812i			1.52570i
$69$	−0.582576			−0.0701339
$70$	0.834849	+	0.417424i	0.0997835	+	0.0498917i
$71$	−9.16515			−1.08770			−0.543852	−	0.839181i	$-0.683035\pi$
$71$	−9.16515			−1.08770			−0.543852	+	0.839181i	$0.683035\pi$
$72$			1.73205i			0.204124i
$73$		−	15.6838i		−	1.83565i	−0.396984	−	0.917825i	$-0.629943\pi$
$73$		−	15.6838i		−	1.83565i	0.396984	−	0.917825i	$-0.370057\pi$
$74$	4.37780			0.508909
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$	−9.47860			−1.08727
$77$		0			0
$78$			0.417424i			0.0472640i
$79$	2.64575			0.297670			0.148835	−	0.988862i	$-0.452448\pi$
$79$	2.64575			0.297670			0.148835	+	0.988862i	$0.452448\pi$
$80$	5.58258	+	2.79129i	0.624151	+	0.312075i
$81$	1.00000			0.111111
$82$		−	3.16515i		−	0.349532i
$83$			12.2197i			1.34129i	0.741780	+	0.670643i	$0.233982\pi$
$83$			12.2197i			1.34129i	−0.741780	+	0.670643i	$0.766018\pi$
$84$	−1.63670			−0.178579
$85$	−7.02355	+	14.0471i	−0.761811	+	1.52362i
$86$	−2.00000			−0.215666
$87$		−	4.37780i		−	0.469350i
$88$		0			0
$89$	−16.7477			−1.77526			−0.887628	−	0.460562i	$-0.847648\pi$
$89$	−16.7477			−1.77526			−0.887628	+	0.460562i	$0.847648\pi$
$90$	−0.456850	+	0.913701i	−0.0481562	+	0.0963125i
$91$	−0.834849			−0.0875159
$92$			1.04356i			0.108799i
$93$			2.58258i			0.267801i
$94$	3.00725			0.310174
$95$	−10.5830	−	5.29150i	−1.08579	−	0.542897i
$96$	4.73930			0.483703
$97$		−	3.58258i		−	0.363755i	−0.983321	−	0.181878i	$-0.941782\pi$
$97$		−	3.58258i		−	0.363755i	0.983321	−	0.181878i	$-0.0582175\pi$
$98$		−	2.81655i		−	0.284515i
$99$		0			0
$100$	5.37386	+	7.16515i	0.537386	+	0.716515i
$101$	5.29150			0.526524			0.263262	−	0.964724i	$-0.415202\pi$
$101$	5.29150			0.526524			0.263262	+	0.964724i	$0.415202\pi$
$102$			3.20871i			0.317710i
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	1.58258			0.155184
$105$	−1.82740	−	0.913701i	−0.178336	−	0.0891680i
$106$	−2.28425			−0.221866
$107$			1.00905i			0.0975486i	0.998810	+	0.0487743i	$0.0155315\pi$
$107$			1.00905i			0.0975486i	−0.998810	+	0.0487743i	$0.984468\pi$
$108$		−	1.79129i		−	0.172367i
$109$	−5.10080			−0.488568			−0.244284	−	0.969704i	$-0.578553\pi$
$109$	−5.10080			−0.488568			−0.244284	+	0.969704i	$0.578553\pi$
$110$		0			0
$111$	−9.58258			−0.909538
$112$			2.55040i			0.240990i
$113$			3.00000i			0.282216i	0.989994	+	0.141108i	$0.0450665\pi$
$113$			3.00000i			0.282216i	−0.989994	+	0.141108i	$0.954933\pi$
$114$	−2.41742			−0.226413
$115$	−0.582576	+	1.16515i	−0.0543255	+	0.108651i
$116$	−7.84190			−0.728102
$117$		−	0.913701i		−	0.0844716i
$118$		−	1.63670i		−	0.150671i
$119$	−6.41742			−0.588284
$120$	3.46410	+	1.73205i	0.316228	+	0.158114i
$121$		0			0
$122$		−	3.95644i		−	0.358199i
$123$			6.92820i			0.624695i
$124$	4.62614			0.415439
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−0.417424			−0.0371871
$127$			6.01450i			0.533701i	0.963738	+	0.266850i	$0.0859830\pi$
$127$			6.01450i			0.533701i	−0.963738	+	0.266850i	$0.914017\pi$
$128$		−	11.0399i		−	0.975795i
$129$	4.37780			0.385444
$130$	0.834849	+	0.417424i	0.0732211	+	0.0366105i
$131$	1.82740			0.159661			0.0798304	−	0.996808i	$-0.474562\pi$
$131$	1.82740			0.159661			0.0798304	+	0.996808i	$0.474562\pi$
$132$		0			0
$133$		−	4.83485i		−	0.419235i
$134$	−6.73750			−0.582032
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	12.1652			1.04315
$137$		−	4.16515i		−	0.355853i	−0.984044	−	0.177926i	$-0.943061\pi$
$137$		−	4.16515i		−	0.355853i	0.984044	−	0.177926i	$-0.0569389\pi$
$138$			0.266150i			0.0226562i
$139$	20.1570			1.70969			0.854846	−	0.518883i	$-0.173652\pi$
$139$	20.1570			1.70969			0.854846	+	0.518883i	$0.173652\pi$
$140$	−1.63670	+	3.27340i	−0.138326	+	0.276653i
$141$	−6.58258			−0.554353
$142$			4.18710i			0.351374i
$143$		0			0
$144$	−2.79129			−0.232607
$145$	−8.75560	−	4.37780i	−0.727113	−	0.363557i
$146$	−7.16515			−0.592992
$147$			6.16515i			0.508493i
$148$			17.1652i			1.41097i
$149$	14.7701			1.21001			0.605007	−	0.796220i	$-0.293170\pi$
$149$	14.7701			1.21001			0.605007	+	0.796220i	$0.293170\pi$
$150$	1.37055	+	1.82740i	0.111905	+	0.149207i
$151$	−5.91915			−0.481694			−0.240847	−	0.970563i	$-0.577425\pi$
$151$	−5.91915			−0.481694			−0.240847	+	0.970563i	$0.577425\pi$
$152$			9.16515i			0.743392i
$153$		−	7.02355i		−	0.567821i
$154$		0			0
$155$	5.16515	+	2.58258i	0.414875	+	0.207437i
$156$	−1.63670			−0.131041
$157$			12.4174i			0.991018i	0.868603	+	0.495509i	$0.165019\pi$
$157$			12.4174i			0.991018i	−0.868603	+	0.495509i	$0.834981\pi$
$158$		−	1.20871i		−	0.0961600i
$159$	5.00000			0.396526
$160$	4.73930	−	9.47860i	0.374675	−	0.749349i
$161$	−0.532300			−0.0419511
$162$		−	0.456850i		−	0.0358935i
$163$		−	17.5826i		−	1.37717i	−0.725154	−	0.688587i	$-0.758231\pi$
$163$		−	17.5826i		−	1.37717i	0.725154	−	0.688587i	$-0.241769\pi$
$164$	12.4104			0.969090
$165$		0			0
$166$	5.58258			0.433292
$167$		−	18.3296i		−	1.41838i	−0.705015	−	0.709192i	$-0.749060\pi$
$167$		−	18.3296i		−	1.41838i	0.705015	−	0.709192i	$-0.250940\pi$
$168$			1.58258i			0.122098i
$169$	12.1652			0.935781
$170$	6.41742	+	3.20871i	0.492194	+	0.246097i
$171$	5.29150			0.404651
$172$		−	7.84190i		−	0.597940i
$173$		−	15.6838i		−	1.19242i	−0.802829	−	0.596209i	$-0.796673\pi$
$173$		−	15.6838i		−	1.19242i	0.802829	−	0.596209i	$-0.203327\pi$
$174$	−2.00000			−0.151620
$175$	−3.65480	+	2.74110i	−0.276277	+	0.207208i
$176$		0			0
$177$			3.58258i			0.269283i
$178$			7.65120i			0.573482i
$179$	10.7477			0.803323			0.401661	−	0.915788i	$-0.368433\pi$
$179$	10.7477			0.803323			0.401661	+	0.915788i	$0.368433\pi$
$180$	−3.58258	−	1.79129i	−0.267029	−	0.133515i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$			0.381401i			0.0282713i
$183$			8.66025i			0.640184i
$184$	1.00905			0.0743882
$185$	−9.58258	+	19.1652i	−0.704525	+	1.40905i
$186$	1.17985			0.0865108
$187$		0			0
$188$			11.7913i			0.859968i
$189$	0.913701			0.0664619
$190$	−2.41742	+	4.83485i	−0.175378	+	0.350757i
$191$	−19.9129			−1.44085			−0.720423	−	0.693535i	$-0.756052\pi$
$191$	−19.9129			−1.44085			−0.720423	+	0.693535i	$0.756052\pi$
$192$			3.41742i			0.246631i
$193$			13.1334i			0.945363i	0.881233	+	0.472682i	$0.156714\pi$
$193$			13.1334i			0.945363i	−0.881233	+	0.472682i	$0.843286\pi$
$194$	−1.63670			−0.117508
$195$	−1.82740	−	0.913701i	−0.130863	−	0.0654315i
$196$	11.0436			0.788826
$197$			6.92820i			0.493614i	0.969065	+	0.246807i	$0.0793814\pi$
$197$			6.92820i			0.493614i	−0.969065	+	0.246807i	$0.920619\pi$
$198$		0			0
$199$	17.4174			1.23469			0.617344	−	0.786693i	$-0.288209\pi$
$199$	17.4174			1.23469			0.617344	+	0.786693i	$0.288209\pi$
$200$	6.92820	−	5.19615i	0.489898	−	0.367423i
$201$	14.7477			1.04022
$202$		−	2.41742i		−	0.170089i
$203$		−	4.00000i		−	0.280745i
$204$	−12.5812			−0.880861
$205$	13.8564	+	6.92820i	0.967773	+	0.483887i
$206$	−2.74110			−0.190982
$207$		−	0.582576i		−	0.0404918i
$208$			2.55040i			0.176838i
$209$		0			0
$210$	−0.417424	+	0.834849i	−0.0288050	+	0.0576100i
$211$	6.30055			0.433748			0.216874	−	0.976200i	$-0.430414\pi$
$211$	6.30055			0.433748			0.216874	+	0.976200i	$0.430414\pi$
$212$		−	8.95644i		−	0.615131i
$213$		−	9.16515i		−	0.627986i
$214$	0.460985			0.0315123
$215$	4.37780	−	8.75560i	0.298564	−	0.597127i
$216$	−1.73205			−0.117851
$217$			2.35970i			0.160187i
$218$			2.33030i			0.157828i
$219$	15.6838			1.05981
$220$		0			0
$221$	−6.41742			−0.431683
$222$			4.37780i			0.293819i
$223$		−	23.1652i		−	1.55125i	−0.631192	−	0.775627i	$-0.717434\pi$
$223$		−	23.1652i		−	1.55125i	0.631192	−	0.775627i	$-0.282566\pi$
$224$	4.33030			0.289331
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	1.37055			0.0911677
$227$			18.3296i			1.21658i	0.793717	+	0.608288i	$0.208143\pi$
$227$			18.3296i			1.21658i	−0.793717	+	0.608288i	$0.791857\pi$
$228$		−	9.47860i		−	0.627736i
$229$	22.1652			1.46471			0.732357	−	0.680921i	$-0.238420\pi$
$229$	22.1652			1.46471			0.732357	+	0.680921i	$0.238420\pi$
$230$	0.532300	+	0.266150i	0.0350988	+	0.0175494i
$231$		0			0
$232$			7.58258i			0.497820i
$233$			10.6784i			0.699562i	0.936831	+	0.349781i	$0.113744\pi$
$233$			10.6784i			0.699562i	−0.936831	+	0.349781i	$0.886256\pi$
$234$	−0.417424			−0.0272879
$235$	−6.58258	+	13.1652i	−0.429400	+	0.858800i
$236$	6.41742			0.417739
$237$			2.64575i			0.171860i
$238$			2.93180i			0.190040i
$239$	−16.5975			−1.07360			−0.536802	−	0.843708i	$-0.680368\pi$
$239$	−16.5975			−1.07360			−0.536802	+	0.843708i	$0.680368\pi$
$240$	−2.79129	+	5.58258i	−0.180177	+	0.360354i
$241$	−28.1896			−1.81585			−0.907925	−	0.419133i	$-0.862334\pi$
$241$	−28.1896			−1.81585			−0.907925	+	0.419133i	$0.862334\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	15.5130			0.993119
$245$	12.3303	+	6.16515i	0.787754	+	0.393877i
$246$	3.16515			0.201803
$247$		−	4.83485i		−	0.307634i
$248$		−	4.47315i		−	0.284045i
$249$	−12.2197			−0.774392
$250$	5.02535	−	0.913701i	0.317831	−	0.0577875i
$251$	−1.58258			−0.0998913			−0.0499456	−	0.998752i	$-0.515905\pi$
$251$	−1.58258			−0.0998913			−0.0499456	+	0.998752i	$0.515905\pi$
$252$		−	1.63670i		−	0.103102i
$253$		0			0
$254$	2.74773			0.172408
$255$	−14.0471	−	7.02355i	−0.879664	−	0.439832i
$256$	1.79129			0.111955
$257$			13.0000i			0.810918i	0.914113	+	0.405459i	$0.132888\pi$
$257$			13.0000i			0.810918i	−0.914113	+	0.405459i	$0.867112\pi$
$258$		−	2.00000i		−	0.124515i
$259$	−8.75560			−0.544047
$260$	−1.63670	+	3.27340i	−0.101504	+	0.203008i
$261$	4.37780			0.270979
$262$		−	0.834849i		−	0.0515771i
$263$		−	11.4014i		−	0.703038i	−0.936181	−	0.351519i	$-0.885665\pi$
$263$		−	11.4014i		−	0.703038i	0.936181	−	0.351519i	$-0.114335\pi$
$264$		0			0
$265$	5.00000	−	10.0000i	0.307148	−	0.614295i
$266$	−2.20880			−0.135430
$267$		−	16.7477i		−	1.02494i
$268$		−	26.4174i		−	1.61370i
$269$	−19.1652			−1.16852			−0.584260	−	0.811567i	$-0.698615\pi$
$269$	−19.1652			−1.16852			−0.584260	+	0.811567i	$0.698615\pi$
$270$	−0.913701	−	0.456850i	−0.0556060	−	0.0278030i
$271$	23.4304			1.42329			0.711647	−	0.702538i	$-0.247950\pi$
$271$	23.4304			1.42329			0.711647	+	0.702538i	$0.247950\pi$
$272$			19.6048i			1.18871i
$273$		−	0.834849i		−	0.0505273i
$274$	−1.90285			−0.114955
$275$		0			0
$276$	−1.04356			−0.0628150
$277$		−	26.0761i		−	1.56676i	−0.621542	−	0.783381i	$-0.713493\pi$
$277$		−	26.0761i		−	1.56676i	0.621542	−	0.783381i	$-0.286507\pi$
$278$		−	9.20871i		−	0.552302i
$279$	−2.58258			−0.154615
$280$	3.16515	+	1.58258i	0.189154	+	0.0945770i
$281$	−25.5438			−1.52382			−0.761908	−	0.647685i	$-0.775737\pi$
$281$	−25.5438			−1.52382			−0.761908	+	0.647685i	$0.775737\pi$
$282$			3.00725i			0.179079i
$283$		−	29.5402i		−	1.75598i	−0.478676	−	0.877992i	$-0.658883\pi$
$283$		−	29.5402i		−	1.75598i	0.478676	−	0.877992i	$-0.341117\pi$
$284$	−16.4174			−0.974195
$285$	5.29150	−	10.5830i	0.313442	−	0.626883i
$286$		0			0
$287$			6.33030i			0.373666i
$288$			4.73930i			0.279266i
$289$	−32.3303			−1.90178
$290$	−2.00000	+	4.00000i	−0.117444	+	0.234888i
$291$	3.58258			0.210014
$292$		−	28.0942i		−	1.64409i
$293$			27.9989i			1.63571i	0.575424	+	0.817856i	$0.304837\pi$
$293$			27.9989i			1.63571i	−0.575424	+	0.817856i	$0.695163\pi$
$294$	2.81655			0.164265
$295$	7.16515	+	3.58258i	0.417171	+	0.208586i
$296$	16.5975			0.964711
$297$		0			0
$298$		−	6.74773i		−	0.390885i
$299$	−0.532300			−0.0307837
$300$	−7.16515	+	5.37386i	−0.413680	+	0.310260i
$301$	4.00000			0.230556
$302$			2.70417i			0.155607i
$303$			5.29150i			0.303989i
$304$	−14.7701			−0.847124
$305$	17.3205	+	8.66025i	0.991769	+	0.495885i
$306$	−3.20871			−0.183430
$307$			6.92820i			0.395413i	0.980261	+	0.197707i	$0.0633494\pi$
$307$			6.92820i			0.395413i	−0.980261	+	0.197707i	$0.936651\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$	1.17985	−	2.35970i	0.0670110	−	0.134022i
$311$	−15.5826			−0.883607			−0.441803	−	0.897112i	$-0.645661\pi$
$311$	−15.5826			−0.883607			−0.441803	+	0.897112i	$0.645661\pi$
$312$			1.58258i			0.0895957i
$313$		−	11.5826i		−	0.654686i	−0.944906	−	0.327343i	$-0.893847\pi$
$313$		−	11.5826i		−	0.654686i	0.944906	−	0.327343i	$-0.106153\pi$
$314$	5.67290			0.320140
$315$	0.913701	−	1.82740i	0.0514812	−	0.102962i
$316$	4.73930			0.266607
$317$			7.83485i			0.440049i	0.975494	+	0.220024i	$0.0706137\pi$
$317$			7.83485i			0.440049i	−0.975494	+	0.220024i	$0.929386\pi$
$318$		−	2.28425i		−	0.128094i
$319$		0			0
$320$	6.83485	+	3.41742i	0.382080	+	0.191040i
$321$	−1.00905			−0.0563197
$322$			0.243181i			0.0135520i
$323$		−	37.1652i		−	2.06792i
$324$	1.79129			0.0995160
$325$	−3.65480	+	2.74110i	−0.202732	+	0.152049i
$326$	−8.03260			−0.444885
$327$		−	5.10080i		−	0.282075i
$328$		−	12.0000i		−	0.662589i
$329$	−6.01450			−0.331590
$330$		0			0
$331$	5.41742			0.297769			0.148884	−	0.988855i	$-0.452432\pi$
$331$	5.41742			0.297769			0.148884	+	0.988855i	$0.452432\pi$
$332$			21.8890i			1.20132i
$333$		−	9.58258i		−	0.525122i
$334$	−8.37386			−0.458197
$335$	14.7477	−	29.4955i	0.805754	−	1.61151i
$336$	−2.55040			−0.139136
$337$		−	0.190700i		−	0.0103881i	−0.999987	−	0.00519406i	$-0.998347\pi$
$337$		−	0.190700i		−	0.0103881i	0.999987	−	0.00519406i	$-0.00165333\pi$
$338$		−	5.55765i		−	0.302296i
$339$	−3.00000			−0.162938
$340$	−12.5812	+	25.1624i	−0.682312	+	1.36462i
$341$		0			0
$342$		−	2.41742i		−	0.130719i
$343$			12.0290i			0.649505i
$344$	−7.58258			−0.408825
$345$	−1.16515	−	0.582576i	−0.0627296	−	0.0313648i
$346$	−7.16515			−0.385201
$347$		−	11.4014i		−	0.612057i	−0.952022	−	0.306028i	$-0.901000\pi$
$347$		−	11.4014i		−	0.612057i	0.952022	−	0.306028i	$-0.0990003\pi$
$348$		−	7.84190i		−	0.420370i
$349$	−8.85095			−0.473781			−0.236890	−	0.971536i	$-0.576128\pi$
$349$	−8.85095			−0.473781			−0.236890	+	0.971536i	$0.576128\pi$
$350$	1.25227	+	1.66970i	0.0669368	+	0.0892491i
$351$	0.913701			0.0487697
$352$		0			0
$353$		−	15.3303i		−	0.815950i	−0.912993	−	0.407975i	$-0.866235\pi$
$353$		−	15.3303i		−	0.815950i	0.912993	−	0.407975i	$-0.133765\pi$
$354$	1.63670			0.0869897
$355$	−18.3303	−	9.16515i	−0.972871	−	0.486436i
$356$	−30.0000			−1.59000
$357$		−	6.41742i		−	0.339646i
$358$		−	4.91010i		−	0.259507i
$359$	24.2487			1.27980			0.639899	−	0.768459i	$-0.278976\pi$
$359$	24.2487			1.27980			0.639899	+	0.768459i	$0.278976\pi$
$360$	−1.73205	+	3.46410i	−0.0912871	+	0.182574i
$361$	9.00000			0.473684
$362$			4.56850i			0.240115i
$363$		0			0
$364$	−1.49545			−0.0783831
$365$	15.6838	−	31.3676i	0.820928	−	1.64186i
$366$	3.95644			0.206806
$367$		−	25.9129i		−	1.35264i	−0.736607	−	0.676321i	$-0.763573\pi$
$367$		−	25.9129i		−	1.35264i	0.736607	−	0.676321i	$-0.236427\pi$
$368$			1.62614i			0.0847682i
$369$	−6.92820			−0.360668
$370$	8.75560	+	4.37780i	0.455182	+	0.227591i
$371$	4.56850			0.237185
$372$			4.62614i			0.239854i
$373$			14.2378i			0.737206i	0.929587	+	0.368603i	$0.120164\pi$
$373$			14.2378i			0.737206i	−0.929587	+	0.368603i	$0.879836\pi$
$374$		0			0
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$	11.4014			0.587980
$377$		−	4.00000i		−	0.206010i
$378$		−	0.417424i		−	0.0214700i
$379$	−6.58258			−0.338124			−0.169062	−	0.985605i	$-0.554074\pi$
$379$	−6.58258			−0.338124			−0.169062	+	0.985605i	$0.554074\pi$
$380$	−18.9572	−	9.47860i	−0.972484	−	0.486242i
$381$	−6.01450			−0.308132
$382$			9.09720i			0.465453i
$383$		−	33.4955i		−	1.71154i	−0.517358	−	0.855769i	$-0.673085\pi$
$383$		−	33.4955i		−	1.71154i	0.517358	−	0.855769i	$-0.326915\pi$
$384$	11.0399			0.563375
$385$		0			0
$386$	6.00000			0.305392
$387$			4.37780i			0.222536i
$388$		−	6.41742i		−	0.325795i
$389$	7.58258			0.384452			0.192226	−	0.981351i	$-0.438429\pi$
$389$	7.58258			0.384452			0.192226	+	0.981351i	$0.438429\pi$
$390$	−0.417424	+	0.834849i	−0.0211371	+	0.0422742i
$391$	−4.09175			−0.206929
$392$		−	10.6784i		−	0.539338i
$393$			1.82740i			0.0921802i
$394$	3.16515			0.159458
$395$	5.29150	+	2.64575i	0.266244	+	0.133122i
$396$		0			0
$397$			2.00000i			0.100377i	0.998740	+	0.0501886i	$0.0159822\pi$
$397$			2.00000i			0.100377i	−0.998740	+	0.0501886i	$0.984018\pi$
$398$		−	7.95715i		−	0.398856i
$399$	4.83485			0.242045
$400$	8.37386	+	11.1652i	0.418693	+	0.558258i
$401$	10.3303			0.515871			0.257935	−	0.966162i	$-0.416958\pi$
$401$	10.3303			0.515871			0.257935	+	0.966162i	$0.416958\pi$
$402$		−	6.73750i		−	0.336036i
$403$			2.35970i			0.117545i
$404$	9.47860			0.471578
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	−1.82740			−0.0906924
$407$		0			0
$408$			12.1652i			0.602265i
$409$	3.36875			0.166574			0.0832870	−	0.996526i	$-0.473458\pi$
$409$	3.36875			0.166574			0.0832870	+	0.996526i	$0.473458\pi$
$410$	3.16515	−	6.33030i	0.156316	−	0.312631i
$411$	4.16515			0.205452
$412$		−	10.7477i		−	0.529503i
$413$			3.27340i			0.161074i
$414$	−0.266150			−0.0130806
$415$	−12.2197	+	24.4394i	−0.599842	+	1.19968i
$416$	4.33030			0.212311
$417$			20.1570i			0.987091i
$418$		0			0
$419$	−32.3303			−1.57944			−0.789719	−	0.613468i	$-0.789774\pi$
$419$	−32.3303			−1.57944			−0.789719	+	0.613468i	$0.789774\pi$
$420$	−3.27340	−	1.63670i	−0.159726	−	0.0798628i
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$		−	2.87841i		−	0.140119i
$423$		−	6.58258i		−	0.320056i
$424$	−8.66025			−0.420579
$425$	−28.0942	+	21.0707i	−1.36277	+	1.02208i
$426$	−4.18710			−0.202866
$427$			7.91288i			0.382931i
$428$			1.80750i			0.0873688i
$429$		0			0
$430$	−4.00000	−	2.00000i	−0.192897	−	0.0964486i
$431$	−32.4720			−1.56412			−0.782061	−	0.623202i	$-0.785831\pi$
$431$	−32.4720			−1.56412			−0.782061	+	0.623202i	$0.785831\pi$
$432$		−	2.79129i		−	0.134296i
$433$		−	14.7477i		−	0.708731i	−0.935107	−	0.354365i	$-0.884697\pi$
$433$		−	14.7477i		−	0.708731i	0.935107	−	0.354365i	$-0.115303\pi$
$434$	1.07803			0.0517471
$435$	4.37780	−	8.75560i	0.209900	−	0.419799i
$436$	−9.13701			−0.437583
$437$		−	3.08270i		−	0.147466i
$438$		−	7.16515i		−	0.342364i
$439$	4.47315			0.213492			0.106746	−	0.994286i	$-0.465957\pi$
$439$	4.47315			0.213492			0.106746	+	0.994286i	$0.465957\pi$
$440$		0			0
$441$	−6.16515			−0.293579
$442$			2.93180i			0.139452i
$443$		−	36.0000i		−	1.71041i	−0.518289	−	0.855206i	$-0.673431\pi$
$443$		−	36.0000i		−	1.71041i	0.518289	−	0.855206i	$-0.326569\pi$
$444$	−17.1652			−0.814622
$445$	−33.4955	−	16.7477i	−1.58784	−	0.793918i
$446$	−10.5830			−0.501120
$447$			14.7701i			0.698602i
$448$			3.12250i			0.147524i
$449$	2.83485			0.133785			0.0668924	−	0.997760i	$-0.478692\pi$
$449$	2.83485			0.133785			0.0668924	+	0.997760i	$0.478692\pi$
$450$	−1.82740	+	1.37055i	−0.0861445	+	0.0646084i
$451$		0			0
$452$			5.37386i			0.252765i
$453$		−	5.91915i		−	0.278106i
$454$	8.37386			0.393005
$455$	−1.66970	−	0.834849i	−0.0782766	−	0.0391383i
$456$	−9.16515			−0.429198
$457$		−	40.5046i		−	1.89473i	−0.320161	−	0.947363i	$-0.603737\pi$
$457$		−	40.5046i		−	1.89473i	0.320161	−	0.947363i	$-0.396263\pi$
$458$		−	10.1262i		−	0.473164i
$459$	7.02355			0.327831
$460$	−1.04356	+	2.08712i	−0.0486563	+	0.0973125i
$461$	23.5257			1.09570			0.547851	−	0.836576i	$-0.315446\pi$
$461$	23.5257			1.09570			0.547851	+	0.836576i	$0.315446\pi$
$462$		0			0
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	−12.2197			−0.567286
$465$	−2.58258	+	5.16515i	−0.119764	+	0.239528i
$466$	4.87841			0.225988
$467$			13.7477i			0.636169i	0.948062	+	0.318084i	$0.103040\pi$
$467$			13.7477i			0.636169i	−0.948062	+	0.318084i	$0.896960\pi$
$468$		−	1.63670i		−	0.0756565i
$469$	13.4750			0.622218
$470$	6.01450	+	3.00725i	0.277428	+	0.138714i
$471$	−12.4174			−0.572165
$472$		−	6.20520i		−	0.285618i
$473$		0			0
$474$	1.20871			0.0555180
$475$	−15.8745	−	21.1660i	−0.728372	−	0.971163i
$476$	−11.4955			−0.526893
$477$			5.00000i			0.228934i
$478$			7.58258i			0.346819i
$479$	24.9717			1.14099			0.570493	−	0.821302i	$-0.306752\pi$
$479$	24.9717			1.14099			0.570493	+	0.821302i	$0.306752\pi$
$480$	9.47860	+	4.73930i	0.432637	+	0.216319i
$481$	−8.75560			−0.399221
$482$			12.8784i			0.586595i
$483$		−	0.532300i		−	0.0242205i
$484$		0			0
$485$	3.58258	−	7.16515i	0.162676	−	0.325353i
$486$	0.456850			0.0207231
$487$			21.9129i			0.992967i	0.868046	+	0.496484i	$0.165376\pi$
$487$			21.9129i			0.992967i	−0.868046	+	0.496484i	$0.834624\pi$
$488$		−	15.0000i		−	0.679018i
$489$	17.5826			0.795112
$490$	2.81655	−	5.63310i	0.127239	−	0.254478i
$491$	8.94630			0.403741			0.201871	−	0.979412i	$-0.435298\pi$
$491$	8.94630			0.403741			0.201871	+	0.979412i	$0.435298\pi$
$492$			12.4104i			0.559504i
$493$		−	30.7477i		−	1.38481i
$494$	−2.20880			−0.0993787
$495$		0			0
$496$	7.20871			0.323681
$497$		−	8.37420i		−	0.375634i
$498$			5.58258i			0.250161i
$499$	−24.0000			−1.07439			−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000			−1.07439			−0.537194	+	0.843459i	$0.680516\pi$
$500$	3.58258	+	19.7042i	0.160218	+	0.881197i
$501$	18.3296			0.818904
$502$			0.723000i			0.0322691i
$503$		−	35.6501i		−	1.58956i	−0.606899	−	0.794779i	$-0.707587\pi$
$503$		−	35.6501i		−	1.58956i	0.606899	−	0.794779i	$-0.292413\pi$
$504$	−1.58258			−0.0704935
$505$	10.5830	+	5.29150i	0.470938	+	0.235469i
$506$		0			0
$507$			12.1652i			0.540273i
$508$			10.7737i			0.478006i
$509$	−3.91288			−0.173435			−0.0867176	−	0.996233i	$-0.527638\pi$
$509$	−3.91288			−0.173435			−0.0867176	+	0.996233i	$0.527638\pi$
$510$	−3.20871	+	6.41742i	−0.142084	+	0.284168i
$511$	14.3303			0.633935
$512$		−	22.8981i		−	1.01196i
$513$			5.29150i			0.233626i
$514$	5.93905			0.261960
$515$	6.00000	−	12.0000i	0.264392	−	0.528783i
$516$	7.84190			0.345221
$517$		0			0
$518$			4.00000i			0.175750i
$519$	15.6838			0.688443
$520$	3.16515	+	1.58258i	0.138801	+	0.0694005i
$521$	26.4174			1.15737			0.578684	−	0.815552i	$-0.303566\pi$
$521$	26.4174			1.15737			0.578684	+	0.815552i	$0.303566\pi$
$522$		−	2.00000i		−	0.0875376i
$523$			26.9898i			1.18018i	0.807337	+	0.590091i	$0.200908\pi$
$523$			26.9898i			1.18018i	−0.807337	+	0.590091i	$0.799092\pi$
$524$	3.27340			0.142999
$525$	−2.74110	−	3.65480i	−0.119631	−	0.159509i
$526$	−5.20871			−0.227111
$527$			18.1389i			0.790141i
$528$		0			0
$529$	22.6606			0.985244
$530$	−4.56850	−	2.28425i	−0.198443	−	0.0992215i
$531$	−3.58258			−0.155471
$532$		−	8.66061i		−	0.375485i
$533$			6.33030i			0.274196i
$534$	−7.65120			−0.331100
$535$	−1.00905	+	2.01810i	−0.0436251	+	0.0872501i
$536$	−25.5438			−1.10332
$537$			10.7477i			0.463799i
$538$			8.75560i			0.377481i
$539$		0			0
$540$	1.79129	−	3.58258i	0.0770848	−	0.154170i
$541$	−38.2958			−1.64647			−0.823233	−	0.567704i	$-0.807832\pi$
$541$	−38.2958			−1.64647			−0.823233	+	0.567704i	$0.807832\pi$
$542$		−	10.7042i		−	0.459783i
$543$		−	10.0000i		−	0.429141i
$544$	33.2867			1.42716
$545$	−10.2016	−	5.10080i	−0.436989	−	0.218494i
$546$	−0.381401			−0.0163224
$547$		−	12.9427i		−	0.553390i	−0.960958	−	0.276695i	$-0.910761\pi$
$547$		−	12.9427i		−	0.553390i	0.960958	−	0.276695i	$-0.0892392\pi$
$548$		−	7.46099i		−	0.318717i
$549$	−8.66025			−0.369611
$550$		0			0
$551$	23.1652			0.986869
$552$			1.00905i			0.0429481i
$553$			2.41742i			0.102799i
$554$	−11.9129			−0.506130
$555$	−19.1652	−	9.58258i	−0.813515	−	0.406758i
$556$	36.1069			1.53127
$557$			13.9518i			0.591155i	0.955319	+	0.295577i	$0.0955120\pi$
$557$			13.9518i			0.591155i	−0.955319	+	0.295577i	$0.904488\pi$
$558$			1.17985i			0.0499470i
$559$	4.00000			0.169182
$560$	−2.55040	+	5.10080i	−0.107774	+	0.215548i
$561$		0			0
$562$			11.6697i			0.492256i
$563$			36.6591i			1.54500i	0.635016	+	0.772499i	$0.280993\pi$
$563$			36.6591i			1.54500i	−0.635016	+	0.772499i	$0.719007\pi$
$564$	−11.7913			−0.496503
$565$	−3.00000	+	6.00000i	−0.126211	+	0.252422i
$566$	−13.4955			−0.567256
$567$			0.913701i			0.0383718i
$568$			15.8745i			0.666080i
$569$	−2.55040			−0.106918			−0.0534592	−	0.998570i	$-0.517025\pi$
$569$	−2.55040			−0.106918			−0.0534592	+	0.998570i	$0.517025\pi$
$570$	−4.83485	−	2.41742i	−0.202510	−	0.101255i
$571$	34.0134			1.42342			0.711708	−	0.702476i	$-0.247922\pi$
$571$	34.0134			1.42342			0.711708	+	0.702476i	$0.247922\pi$
$572$		0			0
$573$		−	19.9129i		−	0.831872i
$574$	2.89200			0.120710
$575$	−2.33030	+	1.74773i	−0.0971803	+	0.0728853i
$576$	−3.41742			−0.142393
$577$			24.0000i			0.999133i	0.866276	+	0.499567i	$0.166507\pi$
$577$			24.0000i			0.999133i	−0.866276	+	0.499567i	$0.833493\pi$
$578$			14.7701i			0.614355i
$579$	−13.1334			−0.545806
$580$	−15.6838	−	7.84190i	−0.651235	−	0.325617i
$581$	−11.1652			−0.463209
$582$		−	1.63670i		−	0.0678434i
$583$		0			0
$584$	−27.1652			−1.12410
$585$	0.913701	−	1.82740i	0.0377769	−	0.0755537i
$586$	12.7913			0.528403
$587$		−	4.25227i		−	0.175510i	−0.996142	−	0.0877550i	$-0.972031\pi$
$587$		−	4.25227i		−	0.175510i	0.996142	−	0.0877550i	$-0.0279693\pi$
$588$			11.0436i			0.455429i
$589$	−13.6657			−0.563086
$590$	1.63670	−	3.27340i	0.0673819	−	0.134764i
$591$	−6.92820			−0.284988
$592$			26.7477i			1.09932i
$593$		−	17.5112i		−	0.719099i	−0.933126	−	0.359550i	$-0.882930\pi$
$593$		−	17.5112i		−	0.719099i	0.933126	−	0.359550i	$-0.117070\pi$
$594$		0			0
$595$	−12.8348	−	6.41742i	−0.526177	−	0.263089i
$596$	26.4575			1.08374
$597$			17.4174i			0.712848i
$598$			0.243181i			0.00994442i
$599$	−31.9129			−1.30392			−0.651962	−	0.758251i	$-0.726054\pi$
$599$	−31.9129			−1.30392			−0.651962	+	0.758251i	$0.726054\pi$
$600$	5.19615	+	6.92820i	0.212132	+	0.282843i
$601$	17.5112			0.714297			0.357149	−	0.934048i	$-0.383749\pi$
$601$	17.5112			0.714297			0.357149	+	0.934048i	$0.383749\pi$
$602$		−	1.82740i		−	0.0744793i
$603$			14.7477i			0.600574i
$604$	−10.6029			−0.431426
$605$		0			0
$606$	2.41742			0.0982011
$607$			13.5148i			0.548549i	0.961651	+	0.274275i	$0.0884377\pi$
$607$			13.5148i			0.548549i	−0.961651	+	0.274275i	$0.911562\pi$
$608$			25.0780i			1.01705i
$609$	4.00000			0.162088
$610$	3.95644	−	7.91288i	0.160192	−	0.320383i
$611$	−6.01450			−0.243321
$612$		−	12.5812i		−	0.508565i
$613$			1.44600i			0.0584034i	0.999574	+	0.0292017i	$0.00929651\pi$
$613$			1.44600i			0.0584034i	−0.999574	+	0.0292017i	$0.990703\pi$
$614$	3.16515			0.127735
$615$	−6.92820	+	13.8564i	−0.279372	+	0.558744i
$616$		0			0
$617$			35.4955i			1.42899i	0.699639	+	0.714497i	$0.253344\pi$
$617$			35.4955i			1.42899i	−0.699639	+	0.714497i	$0.746656\pi$
$618$		−	2.74110i		−	0.110263i
$619$	9.49545			0.381655			0.190827	−	0.981624i	$-0.438883\pi$
$619$	9.49545			0.381655			0.190827	+	0.981624i	$0.438883\pi$
$620$	9.25227	+	4.62614i	0.371580	+	0.185790i
$621$	0.582576			0.0233780
$622$			7.11890i			0.285442i
$623$		−	15.3024i		−	0.613078i
$624$	−2.55040			−0.102098
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−5.29150			−0.211491
$627$		0			0
$628$			22.2432i			0.887600i
$629$	−67.3037			−2.68358
$630$	−0.834849	−	0.417424i	−0.0332612	−	0.0166306i
$631$	−20.5826			−0.819379			−0.409690	−	0.912225i	$-0.634363\pi$
$631$	−20.5826			−0.819379			−0.409690	+	0.912225i	$0.634363\pi$
$632$		−	4.58258i		−	0.182285i
$633$			6.30055i			0.250425i
$634$	3.57935			0.142154
$635$	−6.01450	+	12.0290i	−0.238678	+	0.477357i
$636$	8.95644			0.355146
$637$			5.63310i			0.223192i
$638$		0			0
$639$	9.16515			0.362568
$640$	11.0399	−	22.0797i	0.436389	−	0.872777i
$641$	23.5826			0.931456			0.465728	−	0.884928i	$-0.345793\pi$
$641$	23.5826			0.931456			0.465728	+	0.884928i	$0.345793\pi$
$642$			0.460985i			0.0181936i
$643$		−	18.3303i		−	0.722877i	−0.932396	−	0.361438i	$-0.882286\pi$
$643$		−	18.3303i		−	0.722877i	0.932396	−	0.361438i	$-0.117714\pi$
$644$	−0.953502			−0.0375732
$645$	8.75560	+	4.37780i	0.344752	+	0.172376i
$646$	−16.9789			−0.668026
$647$		−	32.5826i		−	1.28095i	−0.767978	−	0.640477i	$-0.778737\pi$
$647$		−	32.5826i		−	1.28095i	0.767978	−	0.640477i	$-0.221263\pi$
$648$		−	1.73205i		−	0.0680414i
$649$		0			0
$650$	1.25227	+	1.66970i	0.0491182	+	0.0654909i
$651$	−2.35970			−0.0924840
$652$		−	31.4955i		−	1.23346i
$653$			8.33030i			0.325990i	0.986627	+	0.162995i	$0.0521154\pi$
$653$			8.33030i			0.325990i	−0.986627	+	0.162995i	$0.947885\pi$
$654$	−2.33030			−0.0911220
$655$	3.65480	+	1.82740i	0.142805	+	0.0714025i
$656$	19.3386			0.755046
$657$			15.6838i			0.611884i
$658$			2.74773i			0.107118i
$659$	−35.9361			−1.39987			−0.699936	−	0.714205i	$-0.746788\pi$
$659$	−35.9361			−1.39987			−0.699936	+	0.714205i	$0.746788\pi$
$660$		0			0
$661$	−21.1652			−0.823229			−0.411614	−	0.911358i	$-0.635035\pi$
$661$	−21.1652			−0.823229			−0.411614	+	0.911358i	$0.635035\pi$
$662$		−	2.47495i		−	0.0961917i
$663$		−	6.41742i		−	0.249232i
$664$	21.1652			0.821367
$665$	4.83485	−	9.66970i	0.187487	−	0.374975i
$666$	−4.37780			−0.169636
$667$		−	2.55040i		−	0.0987519i
$668$		−	32.8335i		−	1.27037i
$669$	23.1652			0.895616
$670$	−13.4750	−	6.73750i	−0.520585	−	0.260292i
$671$		0			0
$672$			4.33030i			0.167045i
$673$			7.46050i			0.287581i	0.989608	+	0.143791i	$0.0459292\pi$
$673$			7.46050i			0.287581i	−0.989608	+	0.143791i	$0.954071\pi$
$674$	−0.0871215			−0.00335580
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	21.7913			0.838126
$677$			5.10080i			0.196040i	0.995184	+	0.0980199i	$0.0312509\pi$
$677$			5.10080i			0.196040i	−0.995184	+	0.0980199i	$0.968749\pi$
$678$			1.37055i			0.0526357i
$679$	3.27340			0.125622
$680$	24.3303	+	12.1652i	0.933025	+	0.466512i
$681$	−18.3296			−0.702390
$682$		0			0
$683$		−	10.3303i		−	0.395278i	−0.980275	−	0.197639i	$-0.936673\pi$
$683$		−	10.3303i		−	0.395278i	0.980275	−	0.197639i	$-0.0633274\pi$
$684$	9.47860			0.362423
$685$	4.16515	−	8.33030i	0.159142	−	0.318285i
$686$	5.49545			0.209817
$687$			22.1652i			0.845653i
$688$		−	12.2197i		−	0.465872i
$689$	4.56850			0.174046
$690$	−0.266150	+	0.532300i	−0.0101322	+	0.0202643i
$691$	−21.4174			−0.814757			−0.407379	−	0.913259i	$-0.633557\pi$
$691$	−21.4174			−0.814757			−0.407379	+	0.913259i	$0.633557\pi$
$692$		−	28.0942i		−	1.06798i
$693$		0			0
$694$	−5.20871			−0.197720
$695$	40.3139	+	20.1570i	1.52919	+	0.764597i
$696$	−7.58258			−0.287417
$697$			48.6606i			1.84315i
$698$			4.04356i			0.153051i
$699$	−10.6784			−0.403892
$700$	−6.54680	+	4.91010i	−0.247446	+	0.185584i
$701$	46.3284			1.74980			0.874900	−	0.484303i	$-0.160927\pi$
$701$	46.3284			1.74980			0.874900	+	0.484303i	$0.160927\pi$
$702$		−	0.417424i		−	0.0157547i
$703$		−	50.7062i		−	1.91242i
$704$		0			0
$705$	−13.1652	−	6.58258i	−0.495828	−	0.247914i
$706$	−7.00365			−0.263586
$707$			4.83485i			0.181833i
$708$			6.41742i			0.241182i
$709$	−11.0000			−0.413114			−0.206557	−	0.978435i	$-0.566226\pi$
$709$	−11.0000			−0.413114			−0.206557	+	0.978435i	$0.566226\pi$
$710$	−4.18710	+	8.37420i	−0.157139	+	0.314278i
$711$	−2.64575			−0.0992234
$712$			29.0079i			1.08712i
$713$			1.50455i			0.0563457i
$714$	−2.93180			−0.109720
$715$		0			0
$716$	19.2523			0.719491
$717$		−	16.5975i		−	0.619845i
$718$		−	11.0780i		−	0.413428i
$719$	45.4955			1.69669			0.848347	−	0.529441i	$-0.177598\pi$
$719$	45.4955			1.69669			0.848347	+	0.529441i	$0.177598\pi$
$720$	−5.58258	−	2.79129i	−0.208050	−	0.104025i
$721$	5.48220			0.204168
$722$		−	4.11165i		−	0.153020i
$723$		−	28.1896i		−	1.04838i
$724$	−17.9129			−0.665727
$725$	−13.1334	−	17.5112i	−0.487762	−	0.650350i
$726$		0			0
$727$		−	23.4955i		−	0.871398i	−0.900092	−	0.435699i	$-0.856501\pi$
$727$		−	23.4955i		−	0.871398i	0.900092	−	0.435699i	$-0.143499\pi$
$728$			1.44600i			0.0535923i
$729$	−1.00000			−0.0370370
$730$	−14.3303	−	7.16515i	−0.530388	−	0.265194i
$731$	30.7477			1.13725
$732$			15.5130i			0.573377i
$733$		−	17.7019i		−	0.653835i	−0.945053	−	0.326917i	$-0.893990\pi$
$733$		−	17.7019i		−	0.653835i	0.945053	−	0.326917i	$-0.106010\pi$
$734$	−11.8383			−0.436960
$735$	−6.16515	+	12.3303i	−0.227405	+	0.454810i
$736$	2.76100			0.101772
$737$		0			0
$738$			3.16515i			0.116511i
$739$	18.1389			0.667249			0.333624	−	0.942706i	$-0.391728\pi$
$739$	18.1389			0.667249			0.333624	+	0.942706i	$0.391728\pi$
$740$	−17.1652	+	34.3303i	−0.631004	+	1.26201i
$741$	4.83485			0.177613
$742$		−	2.08712i		−	0.0766206i
$743$			0.436950i			0.0160301i	0.999968	+	0.00801506i	$0.00255130\pi$
$743$			0.436950i			0.0160301i	−0.999968	+	0.00801506i	$0.997449\pi$
$744$	4.47315			0.163994
$745$	29.5402	+	14.7701i	1.08227	+	0.541135i
$746$	6.50455			0.238148
$747$		−	12.2197i		−	0.447096i
$748$		0			0
$749$	−0.921970			−0.0336881
$750$	0.913701	+	5.02535i	0.0333636	+	0.183500i
$751$	−11.7477			−0.428681			−0.214340	−	0.976759i	$-0.568760\pi$
$751$	−11.7477			−0.428681			−0.214340	+	0.976759i	$0.568760\pi$
$752$			18.3739i			0.670026i
$753$		−	1.58258i		−	0.0576723i
$754$	−1.82740			−0.0665500
$755$	−11.8383	−	5.91915i	−0.430840	−	0.215420i
$756$	1.63670			0.0595262
$757$			33.4955i			1.21741i	0.793395	+	0.608706i	$0.208311\pi$
$757$			33.4955i			1.21741i	−0.793395	+	0.608706i	$0.791689\pi$
$758$			3.00725i			0.109228i
$759$		0			0
$760$	−9.16515	+	18.3303i	−0.332455	+	0.664910i
$761$	48.3465			1.75256			0.876280	−	0.481802i	$-0.160018\pi$
$761$	48.3465			1.75256			0.876280	+	0.481802i	$0.160018\pi$
$762$			2.74773i			0.0995396i
$763$		−	4.66061i		−	0.168725i
$764$	−35.6697			−1.29048
$765$	7.02355	−	14.0471i	0.253937	−	0.507874i
$766$	−15.3024			−0.552898
$767$			3.27340i			0.118196i
$768$			1.79129i			0.0646375i
$769$	22.8981			0.825725			0.412863	−	0.910793i	$-0.364529\pi$
$769$	22.8981			0.825725			0.412863	+	0.910793i	$0.364529\pi$
$770$		0			0
$771$	−13.0000			−0.468184
$772$			23.5257i			0.846709i
$773$		−	6.16515i		−	0.221745i	−0.993835	−	0.110873i	$-0.964635\pi$
$773$		−	6.16515i		−	0.221745i	0.993835	−	0.110873i	$-0.0353645\pi$
$774$	2.00000			0.0718885
$775$	7.74773	+	10.3303i	0.278307	+	0.371075i
$776$	−6.20520			−0.222754
$777$		−	8.75560i		−	0.314106i
$778$		−	3.46410i		−	0.124194i
$779$	−36.6606			−1.31350
$780$	−3.27340	−	1.63670i	−0.117207	−	0.0586033i
$781$		0			0
$782$			1.86932i			0.0668467i
$783$			4.37780i			0.156450i
$784$	17.2087			0.614597
$785$	−12.4174	+	24.8348i	−0.443197	+	0.886394i
$786$	0.834849			0.0297781
$787$			46.8607i			1.67040i	0.549943	+	0.835202i	$0.314649\pi$
$787$			46.8607i			1.67040i	−0.549943	+	0.835202i	$0.685351\pi$
$788$			12.4104i			0.442102i
$789$	11.4014			0.405899
$790$	1.20871	−	2.41742i	0.0430040	−	0.0860081i
$791$	−2.74110			−0.0974623
$792$		0			0
$793$			7.91288i			0.280995i
$794$	0.913701			0.0324260
$795$	10.0000	+	5.00000i	0.354663	+	0.177332i
$796$	31.1996			1.10584
$797$		−	9.16515i		−	0.324646i	−0.986738	−	0.162323i	$-0.948101\pi$
$797$		−	9.16515i		−	0.324646i	0.986738	−	0.162323i	$-0.0518987\pi$
$798$		−	2.20880i		−	0.0781907i
$799$	−46.2331			−1.63561
$800$	18.9572	−	14.2179i	0.670239	−	0.502679i
$801$	16.7477			0.591752
$802$		−	4.71940i		−	0.166648i
$803$		0			0
$804$	26.4174			0.931671
$805$	−1.06460	−	0.532300i	−0.0375222	−	0.0187611i
$806$	1.07803			0.0379720
$807$		−	19.1652i		−	0.674645i
$808$		−	9.16515i		−	0.322429i
$809$	26.6482			0.936901			0.468451	−	0.883490i	$-0.344812\pi$
$809$	26.6482			0.936901			0.468451	+	0.883490i	$0.344812\pi$
$810$	0.456850	−	0.913701i	0.0160521	−	0.0321042i
$811$	−9.19255			−0.322794			−0.161397	−	0.986890i	$-0.551600\pi$
$811$	−9.19255			−0.322794			−0.161397	+	0.986890i	$0.551600\pi$
$812$		−	7.16515i		−	0.251448i
$813$			23.4304i			0.821739i
$814$		0			0
$815$	17.5826	−	35.1652i	0.615891	−	1.23178i
$816$	−19.6048			−0.686304
$817$			23.1652i			0.810446i
$818$		−	1.53901i		−	0.0538104i
$819$	0.834849			0.0291720
$820$	24.8208	+	12.4104i	0.866780	+	0.433390i
$821$	−12.0290			−0.419815			−0.209908	−	0.977721i	$-0.567316\pi$
$821$	−12.0290			−0.419815			−0.209908	+	0.977721i	$0.567316\pi$
$822$		−	1.90285i		−	0.0663695i
$823$		−	4.83485i		−	0.168532i	−0.996443	−	0.0842661i	$-0.973145\pi$
$823$		−	4.83485i		−	0.168532i	0.996443	−	0.0842661i	$-0.0268546\pi$
$824$	−10.3923			−0.362033
$825$		0			0
$826$	1.49545			0.0520335
$827$		−	10.7737i		−	0.374638i	−0.982299	−	0.187319i	$-0.940020\pi$
$827$		−	10.7737i		−	0.374638i	0.982299	−	0.187319i	$-0.0599799\pi$
$828$		−	1.04356i		−	0.0362662i
$829$	−10.1652			−0.353050			−0.176525	−	0.984296i	$-0.556486\pi$
$829$	−10.1652			−0.353050			−0.176525	+	0.984296i	$0.556486\pi$
$830$	11.1652	+	5.58258i	0.387548	+	0.193774i
$831$	26.0761			0.904570
$832$			3.12250i			0.108253i
$833$			43.3013i			1.50030i
$834$	9.20871			0.318872
$835$	18.3296	−	36.6591i	0.634321	−	1.26864i
$836$		0			0
$837$		−	2.58258i		−	0.0892669i
$838$			14.7701i			0.510225i
$839$	1.16515			0.0402255			0.0201127	−	0.999798i	$-0.493597\pi$
$839$	1.16515			0.0402255			0.0201127	+	0.999798i	$0.493597\pi$
$840$	−1.58258	+	3.16515i	−0.0546040	+	0.109208i
$841$	−9.83485			−0.339133
$842$			0.456850i			0.0157441i
$843$		−	25.5438i		−	0.879776i
$844$	11.2861			0.388484
$845$	24.3303	+	12.1652i	0.836988	+	0.418494i
$846$	−3.00725			−0.103391
$847$		0			0
$848$		−	13.9564i		−	0.479266i
$849$	29.5402			1.01382
$850$	9.62614	+	12.8348i	0.330174	+	0.440232i
$851$	−5.58258			−0.191368
$852$		−	16.4174i		−	0.562452i
$853$			24.8208i			0.849848i	0.905229	+	0.424924i	$0.139699\pi$
$853$			24.8208i			0.849848i	−0.905229	+	0.424924i	$0.860301\pi$
$854$	3.61500			0.123703
$855$	10.5830	+	5.29150i	0.361931	+	0.180966i
$856$	1.74773			0.0597361
$857$			5.38685i			0.184011i	0.995758	+	0.0920057i	$0.0293278\pi$
$857$			5.38685i			0.184011i	−0.995758	+	0.0920057i	$0.970672\pi$
$858$		0			0
$859$	26.3303			0.898378			0.449189	−	0.893437i	$-0.351713\pi$
$859$	26.3303			0.898378			0.449189	+	0.893437i	$0.351713\pi$
$860$	7.84190	−	15.6838i	0.267407	−	0.534813i
$861$	−6.33030			−0.215736
$862$			14.8348i			0.505277i
$863$			18.3303i			0.623971i	0.950087	+	0.311985i	$0.100994\pi$
$863$			18.3303i			0.623971i	−0.950087	+	0.311985i	$0.899006\pi$
$864$	−4.73930			−0.161234
$865$	15.6838	−	31.3676i	0.533265	−	1.06653i
$866$	−6.73750			−0.228950
$867$		−	32.3303i		−	1.09799i
$868$			4.22690i			0.143470i
$869$		0			0
$870$	−4.00000	−	2.00000i	−0.135613	−	0.0678064i
$871$	13.4750			0.456583
$872$			8.83485i			0.299186i
$873$			3.58258i			0.121252i
$874$	−1.40833			−0.0476376
$875$	−10.0507	+	1.82740i	−0.339776	+	0.0617774i
$876$	28.0942			0.949216
$877$		−	24.6301i		−	0.831700i	−0.909433	−	0.415850i	$-0.863484\pi$
$877$		−	24.6301i		−	0.831700i	0.909433	−	0.415850i	$-0.136516\pi$
$878$		−	2.04356i		−	0.0689668i
$879$	−27.9989			−0.944378
$880$		0			0
$881$	−3.49545			−0.117765			−0.0588824	−	0.998265i	$-0.518754\pi$
$881$	−3.49545			−0.117765			−0.0588824	+	0.998265i	$0.518754\pi$
$882$			2.81655i			0.0948382i
$883$			32.7477i			1.10205i	0.834489	+	0.551024i	$0.185763\pi$
$883$			32.7477i			1.10205i	−0.834489	+	0.551024i	$0.814237\pi$
$884$	−11.4955			−0.386634
$885$	−3.58258	+	7.16515i	−0.120427	+	0.240854i
$886$	−16.4466			−0.552535
$887$		−	47.2421i		−	1.58624i	−0.609069	−	0.793118i	$-0.708457\pi$
$887$		−	47.2421i		−	1.58624i	0.609069	−	0.793118i	$-0.291543\pi$
$888$			16.5975i			0.556976i
$889$	−5.49545			−0.184312
$890$	−7.65120	+	15.3024i	−0.256469	+	0.512938i
$891$		0			0
$892$		−	41.4955i		−	1.38937i
$893$		−	34.8317i		−	1.16560i
$894$	6.74773			0.225678
$895$	21.4955	+	10.7477i	0.718514	+	0.359257i
$896$	10.0871			0.336987
$897$		−	0.532300i		−	0.0177730i
$898$		−	1.29510i		−	0.0432181i
$899$	−11.3060			−0.377076
$900$	−5.37386	−	7.16515i	−0.179129	−	0.238838i
$901$	35.1178			1.16994
$902$		0			0
$903$			4.00000i			0.133112i
$904$	5.19615			0.172821
$905$	−20.0000	−	10.0000i	−0.664822	−	0.332411i
$906$	−2.70417			−0.0898399
$907$			10.8348i			0.359765i	0.983688	+	0.179883i	$0.0575718\pi$
$907$			10.8348i			0.359765i	−0.983688	+	0.179883i	$0.942428\pi$
$908$			32.8335i			1.08962i
$909$	−5.29150			−0.175508
$910$	−0.381401	+	0.762802i	−0.0126433	+	0.0252866i
$911$	25.5826			0.847589			0.423794	−	0.905758i	$-0.360698\pi$
$911$	25.5826			0.847589			0.423794	+	0.905758i	$0.360698\pi$
$912$		−	14.7701i		−	0.489087i
$913$		0			0
$914$	−18.5045			−0.612076
$915$	−8.66025	+	17.3205i	−0.286299	+	0.572598i
$916$	39.7042			1.31186
$917$			1.66970i			0.0551383i
$918$		−	3.20871i		−	0.105903i
$919$	−42.1413			−1.39011			−0.695057	−	0.718955i	$-0.744621\pi$
$919$	−42.1413			−1.39011			−0.695057	+	0.718955i	$0.744621\pi$
$920$	2.01810	+	1.00905i	0.0665348	+	0.0332674i
$921$	−6.92820			−0.228292
$922$		−	10.7477i		−	0.353958i
$923$		−	8.37420i		−	0.275640i
$924$		0			0
$925$	−38.3303	+	28.7477i	−1.26029	+	0.945219i
$926$	−1.82740			−0.0600521
$927$			6.00000i			0.197066i
$928$			20.7477i			0.681078i
$929$	−6.33030			−0.207690			−0.103845	−	0.994593i	$-0.533115\pi$
$929$	−6.33030			−0.207690			−0.103845	+	0.994593i	$0.533115\pi$
$930$	2.35970	+	1.17985i	0.0773776	+	0.0386888i
$931$	−32.6229			−1.06917
$932$			19.1280i			0.626559i
$933$		−	15.5826i		−	0.510151i
$934$	6.28065			0.205509
$935$		0			0
$936$	−1.58258			−0.0517281
$937$		−	2.93180i		−	0.0957778i	−0.998853	−	0.0478889i	$-0.984751\pi$
$937$		−	2.93180i		−	0.0957778i	0.998853	−	0.0478889i	$-0.0152493\pi$
$938$		−	6.15606i		−	0.201002i
$939$	11.5826			0.377983
$940$	−11.7913	+	23.5826i	−0.384589	+	0.769179i
$941$	23.9071			0.779350			0.389675	−	0.920953i	$-0.372587\pi$
$941$	23.9071			0.779350			0.389675	+	0.920953i	$0.372587\pi$
$942$			5.67290i			0.184833i
$943$			4.03620i			0.131437i
$944$	10.0000			0.325472
$945$	1.82740	+	0.913701i	0.0594454	+	0.0297227i
$946$		0			0
$947$		−	36.9129i		−	1.19951i	−0.800185	−	0.599754i	$-0.795265\pi$
$947$		−	36.9129i		−	1.19951i	0.800185	−	0.599754i	$-0.204735\pi$
$948$			4.73930i			0.153925i
$949$	14.3303			0.465181
$950$	−9.66970	+	7.25227i	−0.313726	+	0.235295i
$951$	−7.83485			−0.254062
$952$			11.1153i			0.360249i
$953$		−	45.6054i		−	1.47730i	−0.674087	−	0.738652i	$-0.735463\pi$
$953$		−	45.6054i		−	1.47730i	0.674087	−	0.738652i	$-0.264537\pi$
$954$	2.28425			0.0739554
$955$	−39.8258	−	19.9129i	−1.28873	−	0.644366i
$956$	−29.7309			−0.961566
$957$		0			0
$958$		−	11.4083i		−	0.368586i
$959$	3.80570			0.122892
$960$	−3.41742	+	6.83485i	−0.110297	+	0.220594i
$961$	−24.3303			−0.784848
$962$			4.00000i			0.128965i
$963$		−	1.00905i		−	0.0325162i
$964$	−50.4956			−1.62635
$965$	−13.1334	+	26.2668i	−0.422779	+	0.845559i
$966$	−0.243181			−0.00782423
$967$			16.0652i			0.516622i	0.966062	+	0.258311i	$0.0831660\pi$
$967$			16.0652i			0.516622i	−0.966062	+	0.258311i	$0.916834\pi$
$968$		0			0
$969$	37.1652			1.19392
$970$	−3.27340	−	1.63670i	−0.105103	−	0.0525513i
$971$	53.5826			1.71955			0.859773	−	0.510676i	$-0.170605\pi$
$971$	53.5826			1.71955			0.859773	+	0.510676i	$0.170605\pi$
$972$			1.79129i			0.0574556i
$973$			18.4174i			0.590436i
$974$	10.0109			0.320770
$975$	−2.74110	−	3.65480i	−0.0877855	−	0.117047i
$976$	24.1733			0.773767
$977$			17.8348i			0.570587i	0.958440	+	0.285294i	$0.0920911\pi$
$977$			17.8348i			0.570587i	−0.958440	+	0.285294i	$0.907909\pi$
$978$		−	8.03260i		−	0.256854i
$979$		0			0
$980$	22.0871	+	11.0436i	0.705547	+	0.352774i
$981$	5.10080			0.162856
$982$		−	4.08712i		−	0.130425i
$983$			24.0780i			0.767970i	0.923339	+	0.383985i	$0.125449\pi$
$983$			24.0780i			0.767970i	−0.923339	+	0.383985i	$0.874551\pi$
$984$	12.0000			0.382546
$985$	−6.92820	+	13.8564i	−0.220751	+	0.441502i
$986$	−14.0471			−0.447351
$987$		−	6.01450i		−	0.191444i
$988$		−	8.66061i		−	0.275531i
$989$	2.55040			0.0810980
$990$		0			0
$991$	−19.7477			−0.627307			−0.313654	−	0.949537i	$-0.601553\pi$
$991$	−19.7477			−0.627307			−0.313654	+	0.949537i	$0.601553\pi$
$992$		−	12.2396i		−	0.388608i
$993$			5.41742i			0.171917i
$994$	−3.82576			−0.121346
$995$	34.8348	+	17.4174i	1.10434	+	0.552169i
$996$	−21.8890			−0.693580
$997$			6.20520i			0.196521i	0.995161	+	0.0982604i	$0.0313278\pi$
$997$			6.20520i			0.196521i	−0.995161	+	0.0982604i	$0.968672\pi$
$998$			10.9644i			0.347072i
$999$	9.58258			0.303179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.f.364.4	yes	8
5.2	odd	4		9075.2.a.cz.1.3		4
5.3	odd	4		9075.2.a.cs.1.2		4
5.4	even	2	inner	1815.2.c.f.364.5	yes	8
11.10	odd	2	inner	1815.2.c.f.364.6	yes	8
55.32	even	4		9075.2.a.cz.1.2		4
55.43	even	4		9075.2.a.cs.1.3		4
55.54	odd	2	inner	1815.2.c.f.364.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.f.364.3	✓	8	55.54	odd	2	inner
1815.2.c.f.364.4	yes	8	1.1	even	1	trivial
1815.2.c.f.364.5	yes	8	5.4	even	2	inner
1815.2.c.f.364.6	yes	8	11.10	odd	2	inner
9075.2.a.cs.1.2		4	5.3	odd	4
9075.2.a.cs.1.3		4	55.43	even	4
9075.2.a.cz.1.2		4	55.32	even	4
9075.2.a.cz.1.3		4	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.456850i q^{2} +1.00000i q^{3} +1.79129 q^{4} +(2.00000 + 1.00000i) q^{5} +0.456850 q^{6} +0.913701i q^{7} -1.73205i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.456850i q^{2} +1.00000i q^{3} +1.79129 q^{4} +(2.00000 + 1.00000i) q^{5} +0.456850 q^{6} +0.913701i q^{7} -1.73205i q^{8} -1.00000 q^{9} +(0.456850 - 0.913701i) q^{10} +1.79129i q^{12} +0.913701i q^{13} +0.417424 q^{14} +(-1.00000 + 2.00000i) q^{15} +2.79129 q^{16} +7.02355i q^{17} +0.456850i q^{18} -5.29150 q^{19} +(3.58258 + 1.79129i) q^{20} -0.913701 q^{21} +0.582576i q^{23} +1.73205 q^{24} +(3.00000 + 4.00000i) q^{25} +0.417424 q^{26} -1.00000i q^{27} +1.63670i q^{28} -4.37780 q^{29} +(0.913701 + 0.456850i) q^{30} +2.58258 q^{31} -4.73930i q^{32} +3.20871 q^{34} +(-0.913701 + 1.82740i) q^{35} -1.79129 q^{36} +9.58258i q^{37} +2.41742i q^{38} -0.913701 q^{39} +(1.73205 - 3.46410i) q^{40} +6.92820 q^{41} +0.417424i q^{42} -4.37780i q^{43} +(-2.00000 - 1.00000i) q^{45} +0.266150 q^{46} +6.58258i q^{47} +2.79129i q^{48} +6.16515 q^{49} +(1.82740 - 1.37055i) q^{50} -7.02355 q^{51} +1.63670i q^{52} -5.00000i q^{53} -0.456850 q^{54} +1.58258 q^{56} -5.29150i q^{57} +2.00000i q^{58} +3.58258 q^{59} +(-1.79129 + 3.58258i) q^{60} +8.66025 q^{61} -1.17985i q^{62} -0.913701i q^{63} +3.41742 q^{64} +(-0.913701 + 1.82740i) q^{65} -14.7477i q^{67} +12.5812i q^{68} -0.582576 q^{69} +(0.834849 + 0.417424i) q^{70} -9.16515 q^{71} +1.73205i q^{72} -15.6838i q^{73} +4.37780 q^{74} +(-4.00000 + 3.00000i) q^{75} -9.47860 q^{76} +0.417424i q^{78} +2.64575 q^{79} +(5.58258 + 2.79129i) q^{80} +1.00000 q^{81} -3.16515i q^{82} +12.2197i q^{83} -1.63670 q^{84} +(-7.02355 + 14.0471i) q^{85} -2.00000 q^{86} -4.37780i q^{87} -16.7477 q^{89} +(-0.456850 + 0.913701i) q^{90} -0.834849 q^{91} +1.04356i q^{92} +2.58258i q^{93} +3.00725 q^{94} +(-10.5830 - 5.29150i) q^{95} +4.73930 q^{96} -3.58258i q^{97} -2.81655i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9	\( 8 q - 4 q^{4} + 16 q^{5} - 8 q^{9} + 40 q^{14} - 8 q^{15} + 4 q^{16} - 8 q^{20} + 24 q^{25} + 40 q^{26} - 16 q^{31} + 44 q^{34} + 4 q^{36} - 16 q^{45} - 24 q^{49} - 24 q^{56} - 8 q^{59} + 4 q^{60} + 64 q^{64} + 32 q^{69} + 80 q^{70} - 32 q^{75} + 8 q^{80} + 8 q^{81} - 16 q^{86} - 24 q^{89} - 80 q^{91}+O(q^{100}) \) 8 * q - 4 * q^4 + 16 * q^5 - 8 * q^9 + 40 * q^14 - 8 * q^15 + 4 * q^16 - 8 * q^20 + 24 * q^25 + 40 * q^26 - 16 * q^31 + 44 * q^34 + 4 * q^36 - 16 * q^45 - 24 * q^49 - 24 * q^56 - 8 * q^59 + 4 * q^60 + 64 * q^64 + 32 * q^69 + 80 * q^70 - 32 * q^75 + 8 * q^80 + 8 * q^81 - 16 * q^86 - 24 * q^89 - 80 * q^91

Introduction

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