LMFDB - Embedded newform 1512.2.c.d.757.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.12
Root			$0.156434 + 0.987688i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.d.757.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.437016 + 1.34500i) q^{2} +(-1.61803 + 1.17557i) q^{4} +4.29757i q^{5} -1.00000 q^{7} +(-2.28825 - 1.66251i) q^{8} +O(q^{10})$	\(q+(0.437016 + 1.34500i) q^{2} +(-1.61803 + 1.17557i) q^{4} +4.29757i q^{5} -1.00000 q^{7} +(-2.28825 - 1.66251i) q^{8} +(-5.78022 + 1.87811i) q^{10} +1.60758i q^{11} +6.02967i q^{13} +(-0.437016 - 1.34500i) q^{14} +(1.23607 - 3.80423i) q^{16} +3.16228 q^{17} +3.07768i q^{19} +(-5.05210 - 6.95362i) q^{20} +(-2.16219 + 0.702537i) q^{22} +5.95080 q^{23} -13.4691 q^{25} +(-8.10989 + 2.63506i) q^{26} +(1.61803 - 1.17557i) q^{28} -3.53972i q^{29} -2.08831 q^{31} +5.65685 q^{32} +(1.38197 + 4.25325i) q^{34} -4.29757i q^{35} +4.48276i q^{37} +(-4.13948 + 1.34500i) q^{38} +(7.14475 - 9.83390i) q^{40} -6.69568 q^{41} -12.2811i q^{43} +(-1.88982 - 2.60111i) q^{44} +(2.60059 + 8.00380i) q^{46} +3.82734 q^{47} +1.00000 q^{49} +(-5.88622 - 18.1159i) q^{50} +(-7.08831 - 9.75621i) q^{52} -8.63711i q^{53} -6.90868 q^{55} +(2.28825 + 1.66251i) q^{56} +(4.76091 - 1.54691i) q^{58} -1.55265i q^{59} +3.64886i q^{61} +(-0.912623 - 2.80876i) q^{62} +(2.47214 + 7.60845i) q^{64} -25.9129 q^{65} +0.772361i q^{67} +(-5.11667 + 3.71748i) q^{68} +(5.78022 - 1.87811i) q^{70} +7.36501 q^{71} +1.32739 q^{73} +(-6.02930 + 1.95904i) q^{74} +(-3.61803 - 4.97980i) q^{76} -1.60758i q^{77} +12.7401 q^{79} +(16.3489 + 5.31209i) q^{80} +(-2.92612 - 9.00567i) q^{82} +7.08446i q^{83} +13.5901i q^{85} +(16.5180 - 5.36702i) q^{86} +(2.67261 - 3.67853i) q^{88} +9.73307 q^{89} -6.02967i q^{91} +(-9.62859 + 6.99558i) q^{92} +(1.67261 + 5.14776i) q^{94} -13.2266 q^{95} -10.1803 q^{97} +(0.437016 + 1.34500i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} - 16 q^{7}+O(q^{10}) $ 16 * q - 8 * q^4 - 16 * q^7	$ 16 q - 8 q^{4} - 16 q^{7} - 20 q^{10} - 16 q^{16} + 20 q^{22} - 32 q^{25} + 8 q^{28} + 40 q^{31} + 40 q^{34} + 40 q^{40} + 4 q^{46} + 16 q^{49} - 40 q^{52} - 72 q^{55} - 32 q^{64} + 20 q^{70} + 24 q^{73} - 40 q^{76} + 24 q^{79} - 28 q^{82} + 40 q^{88} + 24 q^{94} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^4 - 16 * q^7 - 20 * q^10 - 16 * q^16 + 20 * q^22 - 32 * q^25 + 8 * q^28 + 40 * q^31 + 40 * q^34 + 40 * q^40 + 4 * q^46 + 16 * q^49 - 40 * q^52 - 72 * q^55 - 32 * q^64 + 20 * q^70 + 24 * q^73 - 40 * q^76 + 24 * q^79 - 28 * q^82 + 40 * q^88 + 24 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	0.437016	+	1.34500i	0.309017	+	0.951057i
$2$	0.437016	+	1.34500i	0.309017	+	0.951057i
$3$		0			0
$3$		0			0
$4$	−1.61803	+	1.17557i	−0.809017	+	0.587785i
$5$			4.29757i			1.92193i	0.276666	+	0.960966i	$0.410770\pi$
$5$			4.29757i			1.92193i	−0.276666	+	0.960966i	$0.589230\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.28825	−	1.66251i	−0.809017	−	0.587785i
$9$		0			0
$10$	−5.78022	+	1.87811i	−1.82787	+	0.593910i
$11$			1.60758i			0.484703i	0.970189	+	0.242351i	$0.0779187\pi$
$11$			1.60758i			0.484703i	−0.970189	+	0.242351i	$0.922081\pi$
$12$		0			0
$13$			6.02967i			1.67233i	0.548478	+	0.836165i	$0.315208\pi$
$13$			6.02967i			1.67233i	−0.548478	+	0.836165i	$0.684792\pi$
$14$	−0.437016	−	1.34500i	−0.116797	−	0.359466i
$15$		0			0
$16$	1.23607	−	3.80423i	0.309017	−	0.951057i
$17$	3.16228			0.766965			0.383482	−	0.923548i	$-0.374725\pi$
$17$	3.16228			0.766965			0.383482	+	0.923548i	$0.374725\pi$
$18$		0			0
$19$			3.07768i			0.706069i	0.935610	+	0.353035i	$0.114850\pi$
$19$			3.07768i			0.706069i	−0.935610	+	0.353035i	$0.885150\pi$
$20$	−5.05210	−	6.95362i	−1.12968	−	1.55488i
$21$		0			0
$22$	−2.16219	+	0.702537i	−0.460980	+	0.149781i
$23$	5.95080			1.24083			0.620413	−	0.784275i	$-0.286965\pi$
$23$	5.95080			1.24083			0.620413	+	0.784275i	$0.286965\pi$
$24$		0			0
$25$	−13.4691			−2.69382
$26$	−8.10989	+	2.63506i	−1.59048	+	0.516778i
$27$		0			0
$28$	1.61803	−	1.17557i	0.305780	−	0.222162i
$29$		−	3.53972i		−	0.657310i	−0.944450	−	0.328655i	$-0.893405\pi$
$29$		−	3.53972i		−	0.657310i	0.944450	−	0.328655i	$-0.106595\pi$
$30$		0			0
$31$	−2.08831			−0.375071			−0.187535	−	0.982258i	$-0.560050\pi$
$31$	−2.08831			−0.375071			−0.187535	+	0.982258i	$0.560050\pi$
$32$	5.65685			1.00000
$33$		0			0
$34$	1.38197	+	4.25325i	0.237005	+	0.729427i
$35$		−	4.29757i		−	0.726422i
$36$		0			0
$37$			4.48276i			0.736961i	0.929636	+	0.368480i	$0.120122\pi$
$37$			4.48276i			0.736961i	−0.929636	+	0.368480i	$0.879878\pi$
$38$	−4.13948	+	1.34500i	−0.671512	+	0.218187i
$39$		0			0
$40$	7.14475	−	9.83390i	1.12968	−	1.55488i
$41$	−6.69568			−1.04569			−0.522845	−	0.852428i	$-0.675129\pi$
$41$	−6.69568			−1.04569			−0.522845	+	0.852428i	$0.675129\pi$
$42$		0			0
$43$		−	12.2811i		−	1.87284i	−0.350875	−	0.936422i	$-0.614116\pi$
$43$		−	12.2811i		−	1.87284i	0.350875	−	0.936422i	$-0.385884\pi$
$44$	−1.88982	−	2.60111i	−0.284901	−	0.392133i
$45$		0			0
$46$	2.60059	+	8.00380i	0.383437	+	1.18010i
$47$	3.82734			0.558275			0.279138	−	0.960251i	$-0.409951\pi$
$47$	3.82734			0.558275			0.279138	+	0.960251i	$0.409951\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−5.88622	−	18.1159i	−0.832437	−	2.56198i
$51$		0			0
$52$	−7.08831	−	9.75621i	−0.982971	−	1.35294i
$53$		−	8.63711i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$53$		−	8.63711i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$54$		0			0
$55$	−6.90868			−0.931566
$56$	2.28825	+	1.66251i	0.305780	+	0.222162i
$57$		0			0
$58$	4.76091	−	1.54691i	0.625139	−	0.203120i
$59$		−	1.55265i		−	0.202137i	−0.994879	−	0.101069i	$-0.967774\pi$
$59$		−	1.55265i		−	0.202137i	0.994879	−	0.101069i	$-0.0322262\pi$
$60$		0			0
$61$			3.64886i			0.467189i	0.972334	+	0.233594i	$0.0750487\pi$
$61$			3.64886i			0.467189i	−0.972334	+	0.233594i	$0.924951\pi$
$62$	−0.912623	−	2.80876i	−0.115903	−	0.356713i
$63$		0			0
$64$	2.47214	+	7.60845i	0.309017	+	0.951057i
$65$	−25.9129			−3.21411
$66$		0			0
$67$			0.772361i			0.0943590i	0.998886	+	0.0471795i	$0.0150233\pi$
$67$			0.772361i			0.0943590i	−0.998886	+	0.0471795i	$0.984977\pi$
$68$	−5.11667	+	3.71748i	−0.620488	+	0.450811i
$69$		0			0
$70$	5.78022	−	1.87811i	0.690868	−	0.224477i
$71$	7.36501			0.874066			0.437033	−	0.899446i	$-0.356029\pi$
$71$	7.36501			0.874066			0.437033	+	0.899446i	$0.356029\pi$
$72$		0			0
$73$	1.32739			0.155359			0.0776797	−	0.996978i	$-0.475249\pi$
$73$	1.32739			0.155359			0.0776797	+	0.996978i	$0.475249\pi$
$74$	−6.02930	+	1.95904i	−0.700891	+	0.227733i
$75$		0			0
$76$	−3.61803	−	4.97980i	−0.415017	−	0.571222i
$77$		−	1.60758i		−	0.183200i
$78$		0			0
$79$	12.7401			1.43337			0.716685	−	0.697397i	$-0.245659\pi$
$79$	12.7401			1.43337			0.716685	+	0.697397i	$0.245659\pi$
$80$	16.3489	+	5.31209i	1.82787	+	0.593910i
$81$		0			0
$82$	−2.92612	−	9.00567i	−0.323136	−	0.994510i
$83$			7.08446i			0.777620i	0.921318	+	0.388810i	$0.127114\pi$
$83$			7.08446i			0.777620i	−0.921318	+	0.388810i	$0.872886\pi$
$84$		0			0
$85$			13.5901i			1.47405i
$86$	16.5180	−	5.36702i	1.78118	−	0.578741i
$87$		0			0
$88$	2.67261	−	3.67853i	0.284901	−	0.392133i
$89$	9.73307			1.03170			0.515852	−	0.856678i	$-0.327475\pi$
$89$	9.73307			1.03170			0.515852	+	0.856678i	$0.327475\pi$
$90$		0			0
$91$		−	6.02967i		−	0.632081i
$92$	−9.62859	+	6.99558i	−1.00385	+	0.729340i
$93$		0			0
$94$	1.67261	+	5.14776i	0.172517	+	0.530951i
$95$	−13.2266			−1.35702
$96$		0			0
$97$	−10.1803			−1.03366			−0.516828	−	0.856089i	$-0.672887\pi$
$97$	−10.1803			−1.03366			−0.516828	+	0.856089i	$0.672887\pi$
$98$	0.437016	+	1.34500i	0.0441453	+	0.135865i
$99$		0			0
$100$	21.7935	−	15.8339i	2.17935	−	1.58339i
$101$			1.02749i			0.102239i	0.998693	+	0.0511194i	$0.0162789\pi$
$101$			1.02749i			0.102239i	−0.998693	+	0.0511194i	$0.983721\pi$
$102$		0			0
$103$	−0.965118			−0.0950959			−0.0475479	−	0.998869i	$-0.515141\pi$
$103$	−0.965118			−0.0950959			−0.0475479	+	0.998869i	$0.515141\pi$
$104$	10.0244	−	13.7974i	0.982971	−	1.35294i
$105$		0			0
$106$	11.6169	−	3.77455i	1.12833	−	0.366617i
$107$		−	16.0949i		−	1.55595i	−0.628294	−	0.777976i	$-0.716246\pi$
$107$		−	16.0949i		−	1.55595i	0.628294	−	0.777976i	$-0.283754\pi$
$108$		0			0
$109$			20.2686i			1.94138i	0.240327	+	0.970692i	$0.422745\pi$
$109$			20.2686i			1.94138i	−0.240327	+	0.970692i	$0.577255\pi$
$110$	−3.01920	−	9.29215i	−0.287870	−	0.885972i
$111$		0			0
$112$	−1.23607	+	3.80423i	−0.116797	+	0.359466i
$113$	−0.951214			−0.0894826			−0.0447413	−	0.998999i	$-0.514246\pi$
$113$	−0.951214			−0.0894826			−0.0447413	+	0.998999i	$0.514246\pi$
$114$		0			0
$115$			25.5740i			2.38478i
$116$	4.16119	+	5.72739i	0.386357	+	0.531775i
$117$		0			0
$118$	2.08831	−	0.678531i	0.192244	−	0.0624639i
$119$	−3.16228			−0.289886
$120$		0			0
$121$	8.41570			0.765063
$122$	−4.90770	+	1.59461i	−0.444323	+	0.144369i
$123$		0			0
$124$	3.37895	−	2.45495i	0.303439	−	0.220461i
$125$		−	36.3966i		−	3.25541i
$126$		0			0
$127$	−11.6132			−1.03050			−0.515250	−	0.857040i	$-0.672301\pi$
$127$	−11.6132			−1.03050			−0.515250	+	0.857040i	$0.672301\pi$
$128$	−9.15298	+	6.65003i	−0.809017	+	0.587785i
$129$		0			0
$130$	−11.3244	−	34.8528i	−0.993213	−	3.05680i
$131$			10.0120i			0.874752i	0.899279	+	0.437376i	$0.144092\pi$
$131$			10.0120i			0.874752i	−0.899279	+	0.437376i	$0.855908\pi$
$132$		0			0
$133$		−	3.07768i		−	0.266869i
$134$	−1.03882	+	0.337534i	−0.0897407	+	0.0291585i
$135$		0			0
$136$	−7.23607	−	5.25731i	−0.620488	−	0.450811i
$137$	−8.40383			−0.717988			−0.358994	−	0.933340i	$-0.616880\pi$
$137$	−8.40383			−0.717988			−0.358994	+	0.933340i	$0.616880\pi$
$138$		0			0
$139$		−	6.61437i		−	0.561024i	−0.959851	−	0.280512i	$-0.909496\pi$
$139$		−	6.61437i		−	0.561024i	0.959851	−	0.280512i	$-0.0905042\pi$
$140$	5.05210	+	6.95362i	0.426980	+	0.587688i
$141$		0			0
$142$	3.21863	+	9.90592i	0.270101	+	0.831286i
$143$	−9.69316			−0.810583
$144$		0			0
$145$	15.2122			1.26330
$146$	0.580091	+	1.78534i	0.0480087	+	0.147755i
$147$		0			0
$148$	−5.26980	−	7.25325i	−0.433175	−	0.596214i
$149$		−	16.9866i		−	1.39160i	−0.718238	−	0.695798i	$-0.755051\pi$
$149$		−	16.9866i		−	1.39160i	0.718238	−	0.695798i	$-0.244949\pi$
$150$		0			0
$151$	−11.5256			−0.937937			−0.468968	−	0.883215i	$-0.655374\pi$
$151$	−11.5256			−0.937937			−0.468968	+	0.883215i	$0.655374\pi$
$152$	5.11667	−	7.04250i	0.415017	−	0.571222i
$153$		0			0
$154$	2.16219	−	0.702537i	0.174234	−	0.0566120i
$155$		−	8.97464i		−	0.720860i
$156$		0			0
$157$		−	10.3889i		−	0.829127i	−0.910020	−	0.414563i	$-0.863934\pi$
$157$		−	10.3889i		−	0.829127i	0.910020	−	0.414563i	$-0.136066\pi$
$158$	5.56761	+	17.1354i	0.442936	+	1.36322i
$159$		0			0
$160$			24.3107i			1.92193i
$161$	−5.95080			−0.468988
$162$		0			0
$163$			11.8743i			0.930067i	0.885293	+	0.465034i	$0.153958\pi$
$163$			11.8743i			0.930067i	−0.885293	+	0.465034i	$0.846042\pi$
$164$	10.8338	−	7.87124i	0.845980	−	0.614641i
$165$		0			0
$166$	−9.52858	+	3.09602i	−0.739561	+	0.240298i
$167$	15.0596			1.16535			0.582673	−	0.812706i	$-0.302007\pi$
$167$	15.0596			1.16535			0.582673	+	0.812706i	$0.302007\pi$
$168$		0			0
$169$	−23.3570			−1.79669
$170$	−18.2787	+	5.93910i	−1.40191	+	0.455508i
$171$		0			0
$172$	14.4373	+	19.8712i	1.10083	+	1.51516i
$173$			23.7854i			1.80837i	0.427142	+	0.904185i	$0.359521\pi$
$173$			23.7854i			1.80837i	−0.427142	+	0.904185i	$0.640479\pi$
$174$		0			0
$175$	13.4691			1.01817
$176$	6.11559	+	1.98707i	0.460980	+	0.149781i
$177$		0			0
$178$	4.25351	+	13.0910i	0.318814	+	0.981209i
$179$			22.1919i			1.65870i	0.558728	+	0.829351i	$0.311290\pi$
$179$			22.1919i			1.65870i	−0.558728	+	0.829351i	$0.688710\pi$
$180$		0			0
$181$			8.60253i			0.639421i	0.947515	+	0.319711i	$0.103586\pi$
$181$			8.60253i			0.639421i	−0.947515	+	0.319711i	$0.896414\pi$
$182$	8.10989	−	2.63506i	0.601145	−	0.195324i
$183$		0			0
$184$	−13.6169	−	9.89324i	−1.00385	−	0.729340i
$185$	−19.2650			−1.41639
$186$		0			0
$187$			5.08361i			0.371750i
$188$	−6.19277	+	4.49931i	−0.451654	+	0.328146i
$189$		0			0
$190$	−5.78022	−	17.7897i	−0.419341	−	1.29060i
$191$	−8.72989			−0.631673			−0.315836	−	0.948814i	$-0.602285\pi$
$191$	−8.72989			−0.631673			−0.315836	+	0.948814i	$0.602285\pi$
$192$		0			0
$193$	−12.8708			−0.926459			−0.463229	−	0.886238i	$-0.653309\pi$
$193$	−12.8708			−0.926459			−0.463229	+	0.886238i	$0.653309\pi$
$194$	−4.44897	−	13.6925i	−0.319418	−	0.983066i
$195$		0			0
$196$	−1.61803	+	1.17557i	−0.115574	+	0.0839693i
$197$			22.4345i			1.59839i	0.601072	+	0.799195i	$0.294741\pi$
$197$			22.4345i			1.59839i	−0.601072	+	0.799195i	$0.705259\pi$
$198$		0			0
$199$	−14.9799			−1.06189			−0.530947	−	0.847405i	$-0.678164\pi$
$199$	−14.9799			−1.06189			−0.530947	+	0.847405i	$0.678164\pi$
$200$	30.8207	+	22.3925i	2.17935	+	1.58339i
$201$		0			0
$202$	−1.38197	+	0.449028i	−0.0972348	+	0.0315935i
$203$			3.53972i			0.248440i
$204$		0			0
$205$		−	28.7752i		−	2.00974i
$206$	−0.421772	−	1.29808i	−0.0293862	−	0.0904416i
$207$		0			0
$208$	22.9382	+	7.45309i	1.59048	+	0.516778i
$209$	−4.94761			−0.342234
$210$		0			0
$211$			8.50651i			0.585612i	0.956172	+	0.292806i	$0.0945890\pi$
$211$			8.50651i			0.585612i	−0.956172	+	0.292806i	$0.905411\pi$
$212$	10.1535	+	13.9751i	0.697347	+	0.959816i
$213$		0			0
$214$	21.6476	−	7.03373i	1.47980	−	0.480816i
$215$	52.7787			3.59948
$216$		0			0
$217$	2.08831			0.141763
$218$	−27.2613	+	8.85772i	−1.84637	+	0.599921i
$219$		0			0
$220$	11.1785	−	8.12164i	0.753653	−	0.547561i
$221$			19.0675i			1.28262i
$222$		0			0
$223$	16.3214			1.09296			0.546479	−	0.837473i	$-0.315968\pi$
$223$	16.3214			1.09296			0.546479	+	0.837473i	$0.315968\pi$
$224$	−5.65685			−0.377964
$225$		0			0
$226$	−0.415696	−	1.27938i	−0.0276517	−	0.0851031i
$227$		−	10.8279i		−	0.718671i	−0.933208	−	0.359336i	$-0.883003\pi$
$227$		−	10.8279i		−	0.718671i	0.933208	−	0.359336i	$-0.116997\pi$
$228$		0			0
$229$		−	24.9251i		−	1.64710i	−0.567245	−	0.823549i	$-0.691991\pi$
$229$		−	24.9251i		−	1.64710i	0.567245	−	0.823549i	$-0.308009\pi$
$230$	−34.3969	+	11.1762i	−2.26807	+	0.736939i
$231$		0			0
$232$	−5.88481	+	8.09975i	−0.386357	+	0.531775i
$233$	−13.5950			−0.890641			−0.445321	−	0.895371i	$-0.646910\pi$
$233$	−13.5950			−0.890641			−0.445321	+	0.895371i	$0.646910\pi$
$234$		0			0
$235$			16.4483i			1.07297i
$236$	1.82525	+	2.51224i	0.118813	+	0.163533i
$237$		0			0
$238$	−1.38197	−	4.25325i	−0.0895796	−	0.275698i
$239$	3.82998			0.247741			0.123870	−	0.992298i	$-0.460469\pi$
$239$	3.82998			0.247741			0.123870	+	0.992298i	$0.460469\pi$
$240$		0			0
$241$	5.32509			0.343019			0.171509	−	0.985182i	$-0.445136\pi$
$241$	5.32509			0.343019			0.171509	+	0.985182i	$0.445136\pi$
$242$	3.67779	+	11.3191i	0.236418	+	0.727618i
$243$		0			0
$244$	−4.28949	−	5.90398i	−0.274607	−	0.377963i
$245$			4.29757i			0.274562i
$246$		0			0
$247$	−18.5574			−1.18078
$248$	4.77856	+	3.47182i	0.303439	+	0.220461i
$249$		0			0
$250$	48.9534	−	15.9059i	3.09608	−	1.00598i
$251$			19.2193i			1.21311i	0.795040	+	0.606556i	$0.207450\pi$
$251$			19.2193i			1.21311i	−0.795040	+	0.606556i	$0.792550\pi$
$252$		0			0
$253$			9.56636i			0.601432i
$254$	−5.07513	−	15.6197i	−0.318442	−	0.980064i
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$	0.655642			0.0408979			0.0204489	−	0.999791i	$-0.493490\pi$
$257$	0.655642			0.0408979			0.0204489	+	0.999791i	$0.493490\pi$
$258$		0			0
$259$		−	4.48276i		−	0.278545i
$260$	41.9280	−	30.4625i	2.60027	−	1.88920i
$261$		0			0
$262$	−13.4661	+	4.37540i	−0.831939	+	0.270313i
$263$	25.8211			1.59220			0.796098	−	0.605168i	$-0.206894\pi$
$263$	25.8211			1.59220			0.796098	+	0.605168i	$0.206894\pi$
$264$		0			0
$265$	37.1186			2.28018
$266$	4.13948	−	1.34500i	0.253808	−	0.0824671i
$267$		0			0
$268$	−0.907965	−	1.24971i	−0.0554628	−	0.0763380i
$269$		−	14.2078i		−	0.866266i	−0.901330	−	0.433133i	$-0.857408\pi$
$269$		−	14.2078i		−	0.866266i	0.901330	−	0.433133i	$-0.142592\pi$
$270$		0			0
$271$	3.52786			0.214302			0.107151	−	0.994243i	$-0.465827\pi$
$271$	3.52786			0.214302			0.107151	+	0.994243i	$0.465827\pi$
$272$	3.90879	−	12.0300i	0.237005	−	0.729427i
$273$		0			0
$274$	−3.67261	−	11.3031i	−0.221870	−	0.682847i
$275$		−	21.6526i		−	1.30570i
$276$		0			0
$277$			13.9396i			0.837548i	0.908091	+	0.418774i	$0.137540\pi$
$277$			13.9396i			0.837548i	−0.908091	+	0.418774i	$0.862460\pi$
$278$	8.89631	−	2.89059i	0.533565	−	0.173366i
$279$		0			0
$280$	−7.14475	+	9.83390i	−0.426980	+	0.587688i
$281$	20.4105			1.21759			0.608793	−	0.793329i	$-0.291654\pi$
$281$	20.4105			1.21759			0.608793	+	0.793329i	$0.291654\pi$
$282$		0			0
$283$			29.6867i			1.76469i	0.470600	+	0.882347i	$0.344037\pi$
$283$			29.6867i			1.76469i	−0.470600	+	0.882347i	$0.655963\pi$
$284$	−11.9168	+	8.65809i	−0.707134	+	0.513763i
$285$		0			0
$286$	−4.23607	−	13.0373i	−0.250484	−	0.770910i
$287$	6.69568			0.395233
$288$		0			0
$289$	−7.00000			−0.411765
$290$	6.64798	+	20.4604i	0.390383	+	1.20147i
$291$		0			0
$292$	−2.14776	+	1.56044i	−0.125688	+	0.0913179i
$293$			16.4504i			0.961044i	0.876983	+	0.480522i	$0.159553\pi$
$293$			16.4504i			0.961044i	−0.876983	+	0.480522i	$0.840447\pi$
$294$		0			0
$295$	6.67261			0.388494
$296$	7.45262	−	10.2577i	0.433175	−	0.596214i
$297$		0			0
$298$	22.8469	−	7.42341i	1.32349	−	0.430027i
$299$			35.8813i			2.07507i
$300$		0			0
$301$			12.2811i			0.707869i
$302$	−5.03685	−	15.5018i	−0.289838	−	0.892031i
$303$		0			0
$304$	11.7082	+	3.80423i	0.671512	+	0.218187i
$305$	−15.6812			−0.897905
$306$		0			0
$307$		−	19.8393i		−	1.13229i	−0.824306	−	0.566145i	$-0.808434\pi$
$307$		−	19.8393i		−	1.13229i	0.824306	−	0.566145i	$-0.191566\pi$
$308$	1.88982	+	2.60111i	0.107683	+	0.148212i
$309$		0			0
$310$	12.0709	−	3.92206i	0.685579	−	0.222758i
$311$	32.3919			1.83677			0.918387	−	0.395683i	$-0.129492\pi$
$311$	32.3919			1.83677			0.918387	+	0.395683i	$0.129492\pi$
$312$		0			0
$313$	−6.02156			−0.340359			−0.170179	−	0.985413i	$-0.554435\pi$
$313$	−6.02156			−0.340359			−0.170179	+	0.985413i	$0.554435\pi$
$314$	13.9731	−	4.54013i	0.788546	−	0.256214i
$315$		0			0
$316$	−20.6139	+	14.9768i	−1.15962	+	0.842514i
$317$			5.23318i			0.293925i	0.989142	+	0.146962i	$0.0469496\pi$
$317$			5.23318i			0.293925i	−0.989142	+	0.146962i	$0.953050\pi$
$318$		0			0
$319$	5.69038			0.318600
$320$	−32.6979	+	10.6242i	−1.82787	+	0.593910i
$321$		0			0
$322$	−2.60059	−	8.00380i	−0.144925	−	0.446034i
$323$			9.73249i			0.541530i
$324$		0			0
$325$		−	81.2144i		−	4.50496i
$326$	−15.9709	+	5.18926i	−0.884547	+	0.287407i
$327$		0			0
$328$	15.3214	+	11.1316i	0.845980	+	0.614641i
$329$	−3.82734			−0.211008
$330$		0			0
$331$			16.5740i			0.910988i	0.890239	+	0.455494i	$0.150537\pi$
$331$			16.5740i			0.910988i	−0.890239	+	0.455494i	$0.849463\pi$
$332$	−8.32828	−	11.4629i	−0.457074	−	0.629108i
$333$		0			0
$334$	6.58129	+	20.2551i	0.360112	+	1.10831i
$335$	−3.31928			−0.181352
$336$		0			0
$337$	1.70020			0.0926159			0.0463080	−	0.998927i	$-0.485254\pi$
$337$	1.70020			0.0926159			0.0463080	+	0.998927i	$0.485254\pi$
$338$	−10.2074	−	31.4150i	−0.555207	−	1.70875i
$339$		0			0
$340$	−15.9761	−	21.9893i	−0.866428	−	1.19254i
$341$		−	3.35711i		−	0.181798i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−20.4174	+	28.1021i	−1.10083	+	1.51516i
$345$		0			0
$346$	−31.9913	+	10.3946i	−1.71986	+	0.558817i
$347$		−	24.0032i		−	1.28856i	−0.764790	−	0.644279i	$-0.777157\pi$
$347$		−	24.0032i		−	1.28856i	0.764790	−	0.644279i	$-0.222843\pi$
$348$		0			0
$349$		−	21.3679i		−	1.14380i	−0.820324	−	0.571898i	$-0.806207\pi$
$349$		−	21.3679i		−	1.14380i	0.820324	−	0.571898i	$-0.193793\pi$
$350$	5.88622	+	18.1159i	0.314632	+	0.968337i
$351$		0			0
$352$			9.09383i			0.484703i
$353$	25.1560			1.33892			0.669460	−	0.742849i	$-0.266526\pi$
$353$	25.1560			1.33892			0.669460	+	0.742849i	$0.266526\pi$
$354$		0			0
$355$			31.6517i			1.67990i
$356$	−15.7484	+	11.4419i	−0.834666	+	0.606420i
$357$		0			0
$358$	−29.8481	+	9.69822i	−1.57752	+	0.512567i
$359$	−18.1318			−0.956957			−0.478479	−	0.878099i	$-0.658812\pi$
$359$	−18.1318			−0.956957			−0.478479	+	0.878099i	$0.658812\pi$
$360$		0			0
$361$	9.52786			0.501467
$362$	−11.5704	+	3.75944i	−0.608126	+	0.197592i
$363$		0			0
$364$	7.08831	+	9.75621i	0.371528	+	0.511365i
$365$			5.70456i			0.298590i
$366$		0			0
$367$	−29.6249			−1.54641			−0.773203	−	0.634158i	$-0.781347\pi$
$367$	−29.6249			−1.54641			−0.773203	+	0.634158i	$0.781347\pi$
$368$	7.35559	−	22.6382i	0.383437	−	1.18010i
$369$		0			0
$370$	−8.41910	−	25.9113i	−0.437688	−	1.34707i
$371$			8.63711i			0.448416i
$372$		0			0
$373$			29.3696i			1.52070i	0.649514	+	0.760349i	$0.274972\pi$
$373$			29.3696i			1.52070i	−0.649514	+	0.760349i	$0.725028\pi$
$374$	−6.83743	+	2.22162i	−0.353555	+	0.114877i
$375$		0			0
$376$	−8.75790	−	6.36298i	−0.451654	−	0.328146i
$377$	21.3434			1.09924
$378$		0			0
$379$		−	16.1375i		−	0.828930i	−0.910065	−	0.414465i	$-0.863969\pi$
$379$		−	16.1375i		−	0.828930i	0.910065	−	0.414465i	$-0.136031\pi$
$380$	21.4010	−	15.5488i	1.09785	−	0.797634i
$381$		0			0
$382$	−3.81510	−	11.7417i	−0.195198	−	0.600757i
$383$	21.9227			1.12020			0.560099	−	0.828426i	$-0.310763\pi$
$383$	21.9227			1.12020			0.560099	+	0.828426i	$0.310763\pi$
$384$		0			0
$385$	6.90868			0.352099
$386$	−5.62474	−	17.3112i	−0.286292	−	0.881115i
$387$		0			0
$388$	16.4721	−	11.9677i	0.836246	−	0.607568i
$389$		−	27.7725i		−	1.40812i	−0.710140	−	0.704061i	$-0.751368\pi$
$389$		−	27.7725i		−	1.40812i	0.710140	−	0.704061i	$-0.248632\pi$
$390$		0			0
$391$	18.8181			0.951671
$392$	−2.28825	−	1.66251i	−0.115574	−	0.0839693i
$393$		0			0
$394$	−30.1743	+	9.80423i	−1.52016	+	0.493930i
$395$			54.7514i			2.75484i
$396$		0			0
$397$			27.6193i			1.38617i	0.720855	+	0.693086i	$0.243749\pi$
$397$			27.6193i			1.38617i	−0.720855	+	0.693086i	$0.756251\pi$
$398$	−6.54644	−	20.1479i	−0.328143	−	1.00992i
$399$		0			0
$400$	−16.6487	+	51.2396i	−0.832437	+	2.56198i
$401$	10.4439			0.521546			0.260773	−	0.965400i	$-0.416023\pi$
$401$	10.4439			0.521546			0.260773	+	0.965400i	$0.416023\pi$
$402$		0			0
$403$		−	12.5918i		−	0.627242i
$404$	−1.20788	−	1.66251i	−0.0600944	−	0.0827129i
$405$		0			0
$406$	−4.76091	+	1.54691i	−0.236280	+	0.0767721i
$407$	−7.20638			−0.357207
$408$		0			0
$409$	15.1424			0.748745			0.374373	−	0.927278i	$-0.377858\pi$
$409$	15.1424			0.748745			0.374373	+	0.927278i	$0.377858\pi$
$410$	38.7025	−	12.5752i	1.91138	−	0.621045i
$411$		0			0
$412$	1.56159	−	1.13456i	0.0769342	−	0.0558960i
$413$			1.55265i			0.0764007i
$414$		0			0
$415$	−30.4460			−1.49453
$416$			34.1090i			1.67233i
$417$		0			0
$418$	−2.16219	−	6.65453i	−0.105756	−	0.325484i
$419$		−	19.9623i		−	0.975222i	−0.873061	−	0.487611i	$-0.837869\pi$
$419$		−	19.9623i		−	0.975222i	0.873061	−	0.487611i	$-0.162131\pi$
$420$		0			0
$421$			12.8339i			0.625486i	0.949838	+	0.312743i	$0.101248\pi$
$421$			12.8339i			0.625486i	−0.949838	+	0.312743i	$0.898752\pi$
$422$	−11.4412	+	3.71748i	−0.556950	+	0.180964i
$423$		0			0
$424$	−14.3593	+	19.7638i	−0.697347	+	0.959816i
$425$	−42.5931			−2.06607
$426$		0			0
$427$		−	3.64886i		−	0.176581i
$428$	18.9207	+	26.0421i	0.914566	+	1.25879i
$429$		0			0
$430$	23.0652	+	70.9872i	1.11230	+	3.42331i
$431$	−2.66364			−0.128303			−0.0641514	−	0.997940i	$-0.520434\pi$
$431$	−2.66364			−0.128303			−0.0641514	+	0.997940i	$0.520434\pi$
$432$		0			0
$433$	−19.2122			−0.923280			−0.461640	−	0.887067i	$-0.652739\pi$
$433$	−19.2122			−0.923280			−0.461640	+	0.887067i	$0.652739\pi$
$434$	0.912623	+	2.80876i	0.0438073	+	0.134825i
$435$		0			0
$436$	−23.8272	−	32.7954i	−1.14112	−	1.57061i
$437$			18.3147i			0.876109i
$438$		0			0
$439$	−35.1209			−1.67623			−0.838114	−	0.545495i	$-0.816342\pi$
$439$	−35.1209			−1.67623			−0.838114	+	0.545495i	$0.816342\pi$
$440$	15.8088	+	11.4857i	0.753653	+	0.547561i
$441$		0			0
$442$	−25.6457	+	8.33280i	−1.21984	+	0.396351i
$443$			8.40943i			0.399544i	0.979842	+	0.199772i	$0.0640202\pi$
$443$			8.40943i			0.399544i	−0.979842	+	0.199772i	$0.935980\pi$
$444$		0			0
$445$			41.8286i			1.98286i
$446$	7.13269	+	21.9522i	0.337743	+	1.03947i
$447$		0			0
$448$	−2.47214	−	7.60845i	−0.116797	−	0.359466i
$449$	−4.81067			−0.227030			−0.113515	−	0.993536i	$-0.536211\pi$
$449$	−4.81067			−0.227030			−0.113515	+	0.993536i	$0.536211\pi$
$450$		0			0
$451$		−	10.7638i		−	0.506848i
$452$	1.53910	−	1.11822i	0.0723930	−	0.0525966i
$453$		0			0
$454$	14.5635	−	4.73195i	0.683497	−	0.222082i
$455$	25.9129			1.21482
$456$		0			0
$457$	−37.8291			−1.76957			−0.884785	−	0.465999i	$-0.845695\pi$
$457$	−37.8291			−1.76957			−0.884785	+	0.465999i	$0.845695\pi$
$458$	33.5242	−	10.8927i	1.56648	−	0.508981i
$459$		0			0
$460$	−30.0640	−	41.3795i	−1.40174	−	1.92933i
$461$			10.5113i			0.489558i	0.969579	+	0.244779i	$0.0787154\pi$
$461$			10.5113i			0.489558i	−0.969579	+	0.244779i	$0.921285\pi$
$462$		0			0
$463$	4.76163			0.221292			0.110646	−	0.993860i	$-0.464708\pi$
$463$	4.76163			0.221292			0.110646	+	0.993860i	$0.464708\pi$
$464$	−13.4659	−	4.37534i	−0.625139	−	0.203120i
$465$		0			0
$466$	−5.94125	−	18.2853i	−0.275223	−	0.847050i
$467$			19.7216i			0.912609i	0.889824	+	0.456305i	$0.150827\pi$
$467$			19.7216i			0.912609i	−0.889824	+	0.456305i	$0.849173\pi$
$468$		0			0
$469$		−	0.772361i		−	0.0356643i
$470$	−22.1229	+	7.18816i	−1.02045	+	0.331565i
$471$		0			0
$472$	−2.58129	+	3.55284i	−0.118813	+	0.163533i
$473$	19.7428			0.907773
$474$		0			0
$475$		−	41.4537i		−	1.90203i
$476$	5.11667	−	3.71748i	0.234522	−	0.170390i
$477$		0			0
$478$	1.67376	+	5.15131i	0.0765561	+	0.235615i
$479$	2.49558			0.114026			0.0570131	−	0.998373i	$-0.481842\pi$
$479$	2.49558			0.114026			0.0570131	+	0.998373i	$0.481842\pi$
$480$		0			0
$481$	−27.0296			−1.23244
$482$	2.32715	+	7.16222i	0.105999	+	0.326230i
$483$		0			0
$484$	−13.6169	+	9.89324i	−0.618949	+	0.449693i
$485$		−	43.7507i		−	1.98662i
$486$		0			0
$487$	−10.0178			−0.453951			−0.226976	−	0.973900i	$-0.572884\pi$
$487$	−10.0178			−0.453951			−0.226976	+	0.973900i	$0.572884\pi$
$488$	6.06626	−	8.34949i	0.274607	−	0.377963i
$489$		0			0
$490$	−5.78022	+	1.87811i	−0.261124	+	0.0848442i
$491$		−	4.23469i		−	0.191109i	−0.995424	−	0.0955544i	$-0.969538\pi$
$491$		−	4.23469i		−	0.191109i	0.995424	−	0.0955544i	$-0.0304624\pi$
$492$		0			0
$493$		−	11.1936i		−	0.504134i
$494$	−8.10989	−	24.9597i	−0.364881	−	1.12299i
$495$		0			0
$496$	−2.58129	+	7.94438i	−0.115903	+	0.356713i
$497$	−7.36501			−0.330366
$498$		0			0
$499$			10.1176i			0.452925i	0.974020	+	0.226463i	$0.0727161\pi$
$499$			10.1176i			0.452925i	−0.974020	+	0.226463i	$0.927284\pi$
$500$	42.7868	+	58.8910i	1.91348	+	2.63369i
$501$		0			0
$502$	−25.8499	+	8.39915i	−1.15374	+	0.374873i
$503$	21.6693			0.966186			0.483093	−	0.875569i	$-0.339513\pi$
$503$	21.6693			0.966186			0.483093	+	0.875569i	$0.339513\pi$
$504$		0			0
$505$	−4.41570			−0.196496
$506$	−12.8667	+	4.18065i	−0.571996	+	0.185853i
$507$		0			0
$508$	18.7905	−	13.6521i	0.833692	−	0.605713i
$509$		−	13.8362i		−	0.613280i	−0.951826	−	0.306640i	$-0.900795\pi$
$509$		−	13.8362i		−	0.613280i	0.951826	−	0.306640i	$-0.0992048\pi$
$510$		0			0
$511$	−1.32739			−0.0587203
$512$	6.99226	−	21.5200i	0.309017	−	0.951057i
$513$		0			0
$514$	0.286526	+	0.881837i	0.0126381	+	0.0388962i
$515$		−	4.14766i		−	0.182768i
$516$		0			0
$517$			6.15275i			0.270597i
$518$	6.02930	−	1.95904i	0.264912	−	0.0860751i
$519$		0			0
$520$	59.2952	+	43.0805i	2.60027	+	1.88920i
$521$	−19.5067			−0.854603			−0.427302	−	0.904109i	$-0.640536\pi$
$521$	−19.5067			−0.854603			−0.427302	+	0.904109i	$0.640536\pi$
$522$		0			0
$523$		−	0.616566i		−	0.0269606i	−0.999909	−	0.0134803i	$-0.995709\pi$
$523$		−	0.616566i		−	0.0269606i	0.999909	−	0.0134803i	$-0.00429104\pi$
$524$	−11.7698	−	16.1997i	−0.514166	−	0.707689i
$525$		0			0
$526$	11.2842	+	34.7293i	0.492015	+	1.51427i
$527$	−6.60380			−0.287666
$528$		0			0
$529$	12.4120			0.539651
$530$	16.2214	+	49.9244i	0.704613	+	2.16858i
$531$		0			0
$532$	3.61803	+	4.97980i	0.156862	+	0.215902i
$533$		−	40.3727i		−	1.74874i
$534$		0			0
$535$	69.1690			2.99044
$536$	1.28406	−	1.76735i	0.0554628	−	0.0763380i
$537$		0			0
$538$	19.1095	−	6.20905i	0.823868	−	0.267691i
$539$			1.60758i			0.0692433i
$540$		0			0
$541$		−	33.0638i		−	1.42152i	−0.703432	−	0.710762i	$-0.748350\pi$
$541$		−	33.0638i		−	1.42152i	0.703432	−	0.710762i	$-0.251650\pi$
$542$	1.54173	+	4.74497i	0.0662231	+	0.203814i
$543$		0			0
$544$	17.8885			0.766965
$545$	−87.1059			−3.73121
$546$		0			0
$547$		−	45.6463i		−	1.95170i	−0.218450	−	0.975848i	$-0.570100\pi$
$547$		−	45.6463i		−	1.95170i	0.218450	−	0.975848i	$-0.429900\pi$
$548$	13.5977	−	9.87930i	0.580864	−	0.422023i
$549$		0			0
$550$	29.1227	−	9.46255i	1.24180	−	0.403485i
$551$	10.8941			0.464106
$552$		0			0
$553$	−12.7401			−0.541763
$554$	−18.7487	+	6.09182i	−0.796555	+	0.258816i
$555$		0			0
$556$	7.77566	+	10.7023i	0.329762	+	0.453878i
$557$		−	0.0518694i		−	0.00219778i	−0.999999	−	0.00109889i	$-0.999650\pi$
$557$		−	0.0518694i		−	0.00219778i	0.999999	−	0.00109889i	$-0.000349787\pi$
$558$		0			0
$559$	74.0508			3.13201
$560$	−16.3489	−	5.31209i	−0.690868	−	0.224477i
$561$		0			0
$562$	8.91970	+	27.4520i	0.376255	+	1.15799i
$563$			10.9105i			0.459822i	0.973212	+	0.229911i	$0.0738436\pi$
$563$			10.9105i			0.459822i	−0.973212	+	0.229911i	$0.926156\pi$
$564$		0			0
$565$		−	4.08791i		−	0.171980i
$566$	−39.9286	+	12.9736i	−1.67832	+	0.545320i
$567$		0			0
$568$	−16.8529	−	12.2444i	−0.707134	−	0.513763i
$569$	−26.2746			−1.10149			−0.550745	−	0.834673i	$-0.685656\pi$
$569$	−26.2746			−1.10149			−0.550745	+	0.834673i	$0.685656\pi$
$570$		0			0
$571$		−	24.4590i		−	1.02358i	−0.859111	−	0.511789i	$-0.828983\pi$
$571$		−	24.4590i		−	1.02358i	0.859111	−	0.511789i	$-0.171017\pi$
$572$	15.6839	−	11.3950i	0.655775	−	0.476449i
$573$		0			0
$574$	2.92612	+	9.00567i	0.122134	+	0.375889i
$575$	−80.1520			−3.34257
$576$		0			0
$577$	−10.2538			−0.426873			−0.213436	−	0.976957i	$-0.568466\pi$
$577$	−10.2538			−0.426873			−0.213436	+	0.976957i	$0.568466\pi$
$578$	−3.05911	−	9.41498i	−0.127242	−	0.391612i
$579$		0			0
$580$	−24.6139	+	17.8830i	−1.02204	+	0.742552i
$581$		−	7.08446i		−	0.293913i
$582$		0			0
$583$	13.8848			0.575050
$584$	−3.03740	−	2.20680i	−0.125688	−	0.0913179i
$585$		0			0
$586$	−22.1258	+	7.18910i	−0.914007	+	0.296979i
$587$		−	25.3720i		−	1.04722i	−0.851959	−	0.523608i	$-0.824586\pi$
$587$		−	25.3720i		−	1.04722i	0.851959	−	0.523608i	$-0.175414\pi$
$588$		0			0
$589$		−	6.42714i		−	0.264826i
$590$	2.91604	+	8.97464i	0.120051	+	0.369480i
$591$		0			0
$592$	17.0534	+	5.54099i	0.700891	+	0.227733i
$593$	7.14310			0.293332			0.146666	−	0.989186i	$-0.453146\pi$
$593$	7.14310			0.293332			0.146666	+	0.989186i	$0.453146\pi$
$594$		0			0
$595$		−	13.5901i		−	0.557140i
$596$	19.9689	+	27.4849i	0.817959	+	1.12582i
$597$		0			0
$598$	−48.2603	+	15.6807i	−1.97351	+	0.641232i
$599$	3.00175			0.122648			0.0613242	−	0.998118i	$-0.480468\pi$
$599$	3.00175			0.122648			0.0613242	+	0.998118i	$0.480468\pi$
$600$		0			0
$601$	21.2516			0.866871			0.433435	−	0.901185i	$-0.357301\pi$
$601$	21.2516			0.866871			0.433435	+	0.901185i	$0.357301\pi$
$602$	−16.5180	+	5.36702i	−0.673223	+	0.218743i
$603$		0			0
$604$	18.6487	−	13.5491i	0.758807	−	0.551305i
$605$			36.1671i			1.47040i
$606$		0			0
$607$	24.0614			0.976623			0.488312	−	0.872669i	$-0.337613\pi$
$607$	24.0614			0.976623			0.488312	+	0.872669i	$0.337613\pi$
$608$			17.4100i			0.706069i
$609$		0			0
$610$	−6.85295	−	21.0912i	−0.277468	−	0.853958i
$611$			23.0776i			0.933620i
$612$		0			0
$613$			20.9197i			0.844939i	0.906377	+	0.422469i	$0.138837\pi$
$613$			20.9197i			0.844939i	−0.906377	+	0.422469i	$0.861163\pi$
$614$	26.6838	−	8.67010i	1.07687	−	0.349897i
$615$		0			0
$616$	−2.67261	+	3.67853i	−0.107683	+	0.148212i
$617$	3.95122			0.159070			0.0795350	−	0.996832i	$-0.474656\pi$
$617$	3.95122			0.159070			0.0795350	+	0.996832i	$0.474656\pi$
$618$		0			0
$619$		−	23.8651i		−	0.959220i	−0.877482	−	0.479610i	$-0.840778\pi$
$619$		−	23.8651i		−	0.959220i	0.877482	−	0.479610i	$-0.159222\pi$
$620$	10.5503	+	14.5213i	0.423711	+	0.583188i
$621$		0			0
$622$	14.1558	+	43.5670i	0.567594	+	1.74688i
$623$	−9.73307			−0.389947
$624$		0			0
$625$	89.0716			3.56286
$626$	−2.63152	−	8.09898i	−0.105177	−	0.323700i
$627$		0			0
$628$	12.2129	+	16.8096i	0.487348	+	0.670778i
$629$			14.1757i			0.565223i
$630$		0			0
$631$	36.3725			1.44797			0.723983	−	0.689818i	$-0.242310\pi$
$631$	36.3725			1.44797			0.723983	+	0.689818i	$0.242310\pi$
$632$	−29.1524	−	21.1805i	−1.15962	−	0.842514i
$633$		0			0
$634$	−7.03861	+	2.28698i	−0.279539	+	0.0908277i
$635$		−	49.9083i		−	1.98055i
$636$		0			0
$637$			6.02967i			0.238904i
$638$	2.48679	+	7.65354i	0.0984528	+	0.303006i
$639$		0			0
$640$	−28.5790	−	39.3356i	−1.12968	−	1.55488i
$641$	0.876669			0.0346264			0.0173132	−	0.999850i	$-0.494489\pi$
$641$	0.876669			0.0346264			0.0173132	+	0.999850i	$0.494489\pi$
$642$		0			0
$643$		−	15.2486i		−	0.601347i	−0.953727	−	0.300674i	$-0.902789\pi$
$643$		−	15.2486i		−	0.601347i	0.953727	−	0.300674i	$-0.0972114\pi$
$644$	9.62859	−	6.99558i	0.379420	−	0.275664i
$645$		0			0
$646$	−13.0902	+	4.25325i	−0.515026	+	0.167342i
$647$	−9.53027			−0.374673			−0.187337	−	0.982296i	$-0.559986\pi$
$647$	−9.53027			−0.374673			−0.187337	+	0.982296i	$0.559986\pi$
$648$		0			0
$649$	2.49600			0.0979765
$650$	109.233	−	35.4920i	4.28447	−	1.39211i
$651$		0			0
$652$	−13.9591	−	19.2130i	−0.546680	−	0.752440i
$653$		−	9.29496i		−	0.363740i	−0.983323	−	0.181870i	$-0.941785\pi$
$653$		−	9.29496i		−	0.363740i	0.983323	−	0.181870i	$-0.0582150\pi$
$654$		0			0
$655$	−43.0273			−1.68121
$656$	−8.27631	+	25.4719i	−0.323136	+	0.994510i
$657$		0			0
$658$	−1.67261	−	5.14776i	−0.0652051	−	0.200681i
$659$		−	36.1879i		−	1.40968i	−0.709366	−	0.704841i	$-0.751018\pi$
$659$		−	36.1879i		−	1.40968i	0.709366	−	0.704841i	$-0.248982\pi$
$660$		0			0
$661$		−	19.8091i		−	0.770483i	−0.922816	−	0.385242i	$-0.874118\pi$
$661$		−	19.8091i		−	0.770483i	0.922816	−	0.385242i	$-0.125882\pi$
$662$	−22.2919	+	7.24309i	−0.866401	+	0.281511i
$663$		0			0
$664$	11.7780	−	16.2110i	0.457074	−	0.629108i
$665$	13.2266			0.512904
$666$		0			0
$667$		−	21.0642i		−	0.815607i
$668$	−24.3669	+	17.7036i	−0.942785	+	0.684974i
$669$		0			0
$670$	−1.45058	−	4.46442i	−0.0560407	−	0.172476i
$671$	−5.86582			−0.226448
$672$		0			0
$673$	−0.186375			−0.00718421			−0.00359211	−	0.999994i	$-0.501143\pi$
$673$	−0.186375			−0.00718421			−0.00359211	+	0.999994i	$0.501143\pi$
$674$	0.743016	+	2.28677i	0.0286199	+	0.0880830i
$675$		0			0
$676$	37.7923	−	27.4577i	1.45355	−	1.05607i
$677$		−	3.31885i		−	0.127554i	−0.997964	−	0.0637770i	$-0.979685\pi$
$677$		−	3.31885i		−	0.127554i	0.997964	−	0.0637770i	$-0.0203146\pi$
$678$		0			0
$679$	10.1803			0.390686
$680$	22.5937	−	31.0975i	0.866428	−	1.19254i
$681$		0			0
$682$	4.51531	−	1.46711i	0.172900	−	0.0561786i
$683$		−	17.9992i		−	0.688720i	−0.938838	−	0.344360i	$-0.888096\pi$
$683$		−	17.9992i		−	0.688720i	0.938838	−	0.344360i	$-0.111904\pi$
$684$		0			0
$685$		−	36.1161i		−	1.37992i
$686$	−0.437016	−	1.34500i	−0.0166853	−	0.0513522i
$687$		0			0
$688$	−46.7199	−	15.1802i	−1.78118	−	0.578741i
$689$	52.0789			1.98405
$690$		0			0
$691$		−	3.67153i		−	0.139671i	−0.997559	−	0.0698357i	$-0.977752\pi$
$691$		−	3.67153i		−	0.139671i	0.997559	−	0.0698357i	$-0.0222475\pi$
$692$	−27.9614	−	38.4856i	−1.06293	−	1.46300i
$693$		0			0
$694$	32.2842	−	10.4898i	1.22549	−	0.398187i
$695$	28.4257			1.07825
$696$		0			0
$697$	−21.1736			−0.802007
$698$	28.7397	−	9.33811i	1.08782	−	0.353453i
$699$		0			0
$700$	−21.7935	+	15.8339i	−0.823717	+	0.598465i
$701$		−	7.06843i		−	0.266971i	−0.991051	−	0.133485i	$-0.957383\pi$
$701$		−	7.06843i		−	0.266971i	0.991051	−	0.133485i	$-0.0426169\pi$
$702$		0			0
$703$	−13.7965			−0.520345
$704$	−12.2312	+	3.97415i	−0.460980	+	0.149781i
$705$		0			0
$706$	10.9936	+	33.8348i	0.413749	+	1.27339i
$707$		−	1.02749i		−	0.0386426i
$708$		0			0
$709$			20.4607i			0.768417i	0.923246	+	0.384209i	$0.125526\pi$
$709$			20.4607i			0.768417i	−0.923246	+	0.384209i	$0.874474\pi$
$710$	−42.5714	+	13.8323i	−1.59768	+	0.519116i
$711$		0			0
$712$	−22.2717	−	16.1813i	−0.834666	−	0.606420i
$713$	−12.4271			−0.465398
$714$		0			0
$715$		−	41.6571i		−	1.55789i
$716$	−26.0882	−	35.9073i	−0.974961	−	1.34192i
$717$		0			0
$718$	−7.92387	−	24.3872i	−0.295716	−	0.910120i
$719$	−40.5191			−1.51111			−0.755554	−	0.655087i	$-0.772632\pi$
$719$	−40.5191			−1.51111			−0.755554	+	0.655087i	$0.772632\pi$
$720$		0			0
$721$	0.965118			0.0359429
$722$	4.16383	+	12.8149i	0.154962	+	0.476923i
$723$		0			0
$724$	−10.1129	−	13.9192i	−0.375842	−	0.517302i
$725$			47.6769i			1.77068i
$726$		0			0
$727$	6.87078			0.254823			0.127412	−	0.991850i	$-0.459333\pi$
$727$	6.87078			0.254823			0.127412	+	0.991850i	$0.459333\pi$
$728$	−10.0244	+	13.7974i	−0.371528	+	0.511365i
$729$		0			0
$730$	−7.67261	+	2.49298i	−0.283976	+	0.0922694i
$731$		−	38.8361i		−	1.43641i
$732$		0			0
$733$			18.5847i			0.686442i	0.939255	+	0.343221i	$0.111518\pi$
$733$			18.5847i			0.686442i	−0.939255	+	0.343221i	$0.888482\pi$
$734$	−12.9465	−	39.8454i	−0.477866	−	1.47072i
$735$		0			0
$736$	33.6628			1.24083
$737$	−1.24163			−0.0457360
$738$		0			0
$739$			4.69519i			0.172715i	0.996264	+	0.0863576i	$0.0275228\pi$
$739$			4.69519i			0.172715i	−0.996264	+	0.0863576i	$0.972477\pi$
$740$	31.1714	−	22.6473i	1.14588	−	0.832532i
$741$		0			0
$742$	−11.6169	+	3.77455i	−0.426469	+	0.138568i
$743$	−15.5867			−0.571821			−0.285911	−	0.958256i	$-0.592296\pi$
$743$	−15.5867			−0.571821			−0.285911	+	0.958256i	$0.592296\pi$
$744$		0			0
$745$	73.0011			2.67455
$746$	−39.5020	+	12.8350i	−1.44627	+	0.469922i
$747$		0			0
$748$	−5.97614	−	8.22545i	−0.218509	−	0.300752i
$749$			16.0949i			0.588095i
$750$		0			0
$751$	−18.7401			−0.683835			−0.341917	−	0.939730i	$-0.611076\pi$
$751$	−18.7401			−0.683835			−0.341917	+	0.939730i	$0.611076\pi$
$752$	4.73085	−	14.5601i	0.172517	−	0.530951i
$753$		0			0
$754$	9.32739	+	28.7068i	0.339684	+	1.04544i
$755$		−	49.5319i		−	1.80265i
$756$		0			0
$757$			24.9095i			0.905352i	0.891675	+	0.452676i	$0.149531\pi$
$757$			24.9095i			0.905352i	−0.891675	+	0.452676i	$0.850469\pi$
$758$	21.7049	−	7.05236i	0.788359	−	0.256153i
$759$		0			0
$760$	30.2656	+	21.9893i	1.09785	+	0.797634i
$761$	4.70991			0.170734			0.0853670	−	0.996350i	$-0.472794\pi$
$761$	4.70991			0.170734			0.0853670	+	0.996350i	$0.472794\pi$
$762$		0			0
$763$		−	20.2686i		−	0.733774i
$764$	14.1253	−	10.2626i	0.511034	−	0.371288i
$765$		0			0
$766$	9.58057	+	29.4860i	0.346160	+	1.06537i
$767$	9.36195			0.338040
$768$		0			0
$769$	13.8989			0.501208			0.250604	−	0.968090i	$-0.419371\pi$
$769$	13.8989			0.501208			0.250604	+	0.968090i	$0.419371\pi$
$770$	3.01920	+	9.29215i	0.108805	+	0.334866i
$771$		0			0
$772$	20.8254	−	15.1305i	0.749521	−	0.544559i
$773$			14.8995i			0.535899i	0.963433	+	0.267949i	$0.0863460\pi$
$773$			14.8995i			0.535899i	−0.963433	+	0.267949i	$0.913654\pi$
$774$		0			0
$775$	28.1276			1.01037
$776$	23.2951	+	16.9249i	0.836246	+	0.607568i
$777$		0			0
$778$	37.3539	−	12.1370i	1.33920	−	0.435134i
$779$		−	20.6072i		−	0.738329i
$780$		0			0
$781$			11.8398i			0.423662i
$782$	8.22380	+	25.3102i	0.294082	+	0.905092i
$783$		0			0
$784$	1.23607	−	3.80423i	0.0441453	−	0.135865i
$785$	44.6472			1.59353
$786$		0			0
$787$			10.1839i			0.363018i	0.983389	+	0.181509i	$0.0580981\pi$
$787$			10.1839i			0.363018i	−0.983389	+	0.181509i	$0.941902\pi$
$788$	−26.3733	−	36.2997i	−0.939510	−	1.29312i
$789$		0			0
$790$	−73.6404	+	23.9272i	−2.62001	+	0.851292i
$791$	0.951214			0.0338213
$792$		0			0
$793$	−22.0014			−0.781293
$794$	−37.1478	+	12.0701i	−1.31833	+	0.428351i
$795$		0			0
$796$	24.2379	−	17.6099i	0.859091	−	0.624166i
$797$			14.0210i			0.496648i	0.968677	+	0.248324i	$0.0798798\pi$
$797$			14.0210i			0.496648i	−0.968677	+	0.248324i	$0.920120\pi$
$798$		0			0
$799$	12.1031			0.428177
$800$	−76.1928			−2.69382
$801$		0			0
$802$	4.56417	+	14.0471i	0.161166	+	0.496019i
$803$			2.13388i			0.0753031i
$804$		0			0
$805$		−	25.5740i		−	0.901364i
$806$	16.9359	−	5.50282i	0.596543	−	0.193828i
$807$		0			0
$808$	1.70820	−	2.35114i	0.0600944	−	0.0827129i
$809$	28.0399			0.985831			0.492916	−	0.870077i	$-0.335931\pi$
$809$	28.0399			0.985831			0.492916	+	0.870077i	$0.335931\pi$
$810$		0			0
$811$		−	13.2362i		−	0.464785i	−0.972622	−	0.232393i	$-0.925345\pi$
$811$		−	13.2362i		−	0.464785i	0.972622	−	0.232393i	$-0.0746554\pi$
$812$	−4.16119	−	5.72739i	−0.146029	−	0.200992i
$813$		0			0
$814$	−3.14930	−	9.69256i	−0.110383	−	0.339724i
$815$	−51.0307			−1.78753
$816$		0			0
$817$	37.7972			1.32236
$818$	6.61749	+	20.3665i	0.231375	+	0.712099i
$819$		0			0
$820$	33.8272	+	46.5592i	1.18130	+	1.62592i
$821$		−	13.8343i		−	0.482821i	−0.970423	−	0.241411i	$-0.922390\pi$
$821$		−	13.8343i		−	0.482821i	0.970423	−	0.241411i	$-0.0776100\pi$
$822$		0			0
$823$	29.4862			1.02782			0.513912	−	0.857843i	$-0.328196\pi$
$823$	29.4862			1.02782			0.513912	+	0.857843i	$0.328196\pi$
$824$	2.20843	+	1.60452i	0.0769342	+	0.0558960i
$825$		0			0
$826$	−2.08831	+	0.678531i	−0.0726614	+	0.0236091i
$827$			28.9797i			1.00772i	0.863784	+	0.503861i	$0.168088\pi$
$827$			28.9797i			1.00772i	−0.863784	+	0.503861i	$0.831912\pi$
$828$		0			0
$829$			32.5800i			1.13155i	0.824560	+	0.565774i	$0.191423\pi$
$829$			32.5800i			1.13155i	−0.824560	+	0.565774i	$0.808577\pi$
$830$	−13.3054	−	40.9497i	−0.461836	−	1.42139i
$831$		0			0
$832$	−45.8765	+	14.9062i	−1.59048	+	0.516778i
$833$	3.16228			0.109566
$834$		0			0
$835$			64.7197i			2.23972i
$836$	8.00541	−	5.81627i	0.276873	−	0.201160i
$837$		0			0
$838$	26.8492	−	8.72384i	0.927491	−	0.301360i
$839$	19.8215			0.684313			0.342157	−	0.939643i	$-0.388843\pi$
$839$	19.8215			0.684313			0.342157	+	0.939643i	$0.388843\pi$
$840$		0			0
$841$	16.4704			0.567944
$842$	−17.2616	+	5.60862i	−0.594872	+	0.193286i
$843$		0			0
$844$	−10.0000	−	13.7638i	−0.344214	−	0.473770i
$845$		−	100.378i		−	3.45311i
$846$		0			0
$847$	−8.41570			−0.289167
$848$	−32.8575	−	10.6760i	−1.12833	−	0.366617i
$849$		0			0
$850$	−18.6139	−	57.2876i	−0.638450	−	1.96495i
$851$			26.6760i			0.914441i
$852$		0			0
$853$		−	17.4764i		−	0.598381i	−0.954193	−	0.299190i	$-0.903283\pi$
$853$		−	17.4764i		−	0.598381i	0.954193	−	0.299190i	$-0.0967166\pi$
$854$	4.90770	−	1.59461i	0.167938	−	0.0545664i
$855$		0			0
$856$	−26.7579	+	36.8291i	−0.914566	+	1.25879i
$857$	26.0767			0.890764			0.445382	−	0.895341i	$-0.353068\pi$
$857$	26.0767			0.890764			0.445382	+	0.895341i	$0.353068\pi$
$858$		0			0
$859$		−	40.6339i		−	1.38641i	−0.720740	−	0.693205i	$-0.756198\pi$
$859$		−	40.6339i		−	1.38641i	0.720740	−	0.693205i	$-0.243802\pi$
$860$	−85.3978	+	62.0451i	−2.91204	+	2.11572i
$861$		0			0
$862$	−1.16405	−	3.58258i	−0.0396477	−	0.122023i
$863$	41.4216			1.41001			0.705004	−	0.709204i	$-0.250945\pi$
$863$	41.4216			1.41001			0.705004	+	0.709204i	$0.250945\pi$
$864$		0			0
$865$	−102.219			−3.47556
$866$	−8.39604	−	25.8404i	−0.285309	−	0.878091i
$867$		0			0
$868$	−3.37895	+	2.45495i	−0.114689	+	0.0833264i
$869$			20.4806i			0.694758i
$870$		0			0
$871$	−4.65709			−0.157799
$872$	33.6968	−	46.3796i	1.14112	−	1.57061i
$873$		0			0
$874$	−24.6332	+	8.00380i	−0.833229	+	0.270733i
$875$			36.3966i			1.23043i
$876$		0			0
$877$		−	33.0093i		−	1.11464i	−0.830296	−	0.557322i	$-0.811829\pi$
$877$		−	33.0093i		−	1.11464i	0.830296	−	0.557322i	$-0.188171\pi$
$878$	−15.3484	−	47.2375i	−0.517983	−	1.59419i
$879$		0			0
$880$	−8.53960	+	26.2822i	−0.287870	+	0.885972i
$881$	−18.0587			−0.608414			−0.304207	−	0.952606i	$-0.598391\pi$
$881$	−18.0587			−0.608414			−0.304207	+	0.952606i	$0.598391\pi$
$882$		0			0
$883$			46.6771i			1.57081i	0.618983	+	0.785404i	$0.287545\pi$
$883$			46.6771i			1.57081i	−0.618983	+	0.785404i	$0.712455\pi$
$884$	−22.4152	−	30.8519i	−0.753904	−	1.03766i
$885$		0			0
$886$	−11.3107	+	3.67506i	−0.379989	+	0.123466i
$887$	−29.2001			−0.980444			−0.490222	−	0.871598i	$-0.663084\pi$
$887$	−29.2001			−0.980444			−0.490222	+	0.871598i	$0.663084\pi$
$888$		0			0
$889$	11.6132			0.389493
$890$	−56.2593	+	18.2798i	−1.88582	+	0.612739i
$891$		0			0
$892$	−26.4085	+	19.1869i	−0.884222	+	0.642425i
$893$			11.7793i			0.394181i
$894$		0			0
$895$	−95.3714			−3.18791
$896$	9.15298	−	6.65003i	0.305780	−	0.222162i
$897$		0			0
$898$	−2.10234	−	6.47034i	−0.0701560	−	0.215918i
$899$			7.39202i			0.246538i
$900$		0			0
$901$		−	27.3129i		−	0.909926i
$902$	14.4773	−	4.70396i	0.482042	−	0.156625i
$903$		0			0
$904$	2.17661	+	1.58140i	0.0723930	+	0.0525966i
$905$	−36.9700			−1.22892
$906$		0			0
$907$		−	9.06592i		−	0.301029i	−0.988608	−	0.150514i	$-0.951907\pi$
$907$		−	9.06592i		−	0.301029i	0.988608	−	0.150514i	$-0.0480930\pi$
$908$	12.7289	+	17.5199i	0.422424	+	0.581417i
$909$		0			0
$910$	11.3244	+	34.8528i	0.375399	+	1.15536i
$911$	−14.3571			−0.475673			−0.237837	−	0.971305i	$-0.576438\pi$
$911$	−14.3571			−0.475673			−0.237837	+	0.971305i	$0.576438\pi$
$912$		0			0
$913$	−11.3888			−0.376915
$914$	−16.5319	−	50.8800i	−0.546827	−	1.68296i
$915$		0			0
$916$	29.3012	+	40.3297i	0.968140	+	1.33253i
$917$		−	10.0120i		−	0.330625i
$918$		0			0
$919$	49.8788			1.64535			0.822675	−	0.568513i	$-0.192481\pi$
$919$	49.8788			1.64535			0.822675	+	0.568513i	$0.192481\pi$
$920$	42.5169	−	58.5195i	1.40174	−	1.92933i
$921$		0			0
$922$	−14.1376	+	4.59359i	−0.465597	+	0.151282i
$923$			44.4086i			1.46173i
$924$		0			0
$925$		−	60.3788i		−	1.98524i
$926$	2.08091	+	6.40437i	0.0683829	+	0.210461i
$927$		0			0
$928$		−	20.0237i		−	0.657310i
$929$	−39.3069			−1.28962			−0.644809	−	0.764343i	$-0.723063\pi$
$929$	−39.3069			−1.28962			−0.644809	+	0.764343i	$0.723063\pi$
$930$		0			0
$931$			3.07768i			0.100867i
$932$	21.9973	−	15.9819i	0.720544	−	0.523506i
$933$		0			0
$934$	−26.5256	+	8.61868i	−0.867943	+	0.282012i
$935$	−21.8472			−0.714478
$936$		0			0
$937$	37.3504			1.22018			0.610092	−	0.792331i	$-0.291133\pi$
$937$	37.3504			1.22018			0.610092	+	0.792331i	$0.291133\pi$
$938$	1.03882	−	0.337534i	0.0339188	−	0.0110209i
$939$		0			0
$940$	−19.3361	−	26.6139i	−0.630674	−	0.868049i
$941$			38.7781i			1.26413i	0.774915	+	0.632065i	$0.217792\pi$
$941$			38.7781i			1.26413i	−0.774915	+	0.632065i	$0.782208\pi$
$942$		0			0
$943$	−39.8446			−1.29752
$944$	−5.90662	−	1.91918i	−0.192244	−	0.0624639i
$945$		0			0
$946$	8.62790	+	26.5539i	0.280517	+	0.863343i
$947$			3.75328i			0.121965i	0.998139	+	0.0609826i	$0.0194234\pi$
$947$			3.75328i			0.121965i	−0.998139	+	0.0609826i	$0.980577\pi$
$948$		0			0
$949$			8.00373i			0.259812i
$950$	55.7551	−	18.1159i	1.80893	−	0.587758i
$951$		0			0
$952$	7.23607	+	5.25731i	0.234522	+	0.170390i
$953$	46.5443			1.50772			0.753859	−	0.657036i	$-0.228190\pi$
$953$	46.5443			1.50772			0.753859	+	0.657036i	$0.228190\pi$
$954$		0			0
$955$		−	37.5173i		−	1.21403i
$956$	−6.19704	+	4.50241i	−0.200426	+	0.145618i
$957$		0			0
$958$	1.09061	+	3.35655i	0.0352360	+	0.108445i
$959$	8.40383			0.271374
$960$		0			0
$961$	−26.6390			−0.859322
$962$	−11.8124	−	36.3547i	−0.380845	−	1.17212i
$963$		0			0
$964$	−8.61617	+	6.26001i	−0.277508	+	0.201621i
$965$		−	55.3131i		−	1.78059i
$966$		0			0
$967$	−16.6487			−0.535388			−0.267694	−	0.963504i	$-0.586262\pi$
$967$	−16.6487			−0.535388			−0.267694	+	0.963504i	$0.586262\pi$
$968$	−19.2572	−	13.9912i	−0.618949	−	0.449693i
$969$		0			0
$970$	58.8446	−	19.1198i	1.88939	−	0.613899i
$971$			5.74652i			0.184415i	0.995740	+	0.0922073i	$0.0293922\pi$
$971$			5.74652i			0.184415i	−0.995740	+	0.0922073i	$0.970608\pi$
$972$		0			0
$973$			6.61437i			0.212047i
$974$	−4.37795	−	13.4739i	−0.140279	−	0.431733i
$975$		0			0
$976$	13.8811	+	4.51024i	0.444323	+	0.144369i
$977$	27.6236			0.883758			0.441879	−	0.897075i	$-0.354312\pi$
$977$	27.6236			0.883758			0.441879	+	0.897075i	$0.354312\pi$
$978$		0			0
$979$			15.6467i			0.500070i
$980$	−5.05210	−	6.95362i	−0.161383	−	0.222125i
$981$		0			0
$982$	5.69565	−	1.85063i	0.181755	−	0.0590559i
$983$	2.19812			0.0701091			0.0350545	−	0.999385i	$-0.488840\pi$
$983$	2.19812			0.0701091			0.0350545	+	0.999385i	$0.488840\pi$
$984$		0			0
$985$	−96.4138			−3.07200
$986$	15.0553	−	4.89177i	0.479460	−	0.155786i
$987$		0			0
$988$	30.0265	−	21.8156i	0.955272	−	0.694045i
$989$		−	73.0821i		−	2.32388i
$990$		0			0
$991$	2.62346			0.0833369			0.0416684	−	0.999131i	$-0.486733\pi$
$991$	2.62346			0.0833369			0.0416684	+	0.999131i	$0.486733\pi$
$992$	−11.8132			−0.375071
$993$		0			0
$994$	−3.21863	−	9.90592i	−0.102089	−	0.314197i
$995$		−	64.3770i		−	2.04089i
$996$		0			0
$997$			29.1361i			0.922749i	0.887205	+	0.461375i	$0.152644\pi$
$997$			29.1361i			0.922749i	−0.887205	+	0.461375i	$0.847356\pi$
$998$	−13.6081	+	4.42154i	−0.430757	+	0.139962i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.d.757.12	yes	16
3.2	odd	2	inner	1512.2.c.d.757.5	✓	16
4.3	odd	2		6048.2.c.d.3025.16		16
8.3	odd	2		6048.2.c.d.3025.1		16
8.5	even	2	inner	1512.2.c.d.757.9	yes	16
12.11	even	2		6048.2.c.d.3025.2		16
24.5	odd	2	inner	1512.2.c.d.757.8	yes	16
24.11	even	2		6048.2.c.d.3025.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.d.757.5	✓	16	3.2	odd	2	inner
1512.2.c.d.757.8	yes	16	24.5	odd	2	inner
1512.2.c.d.757.9	yes	16	8.5	even	2	inner
1512.2.c.d.757.12	yes	16	1.1	even	1	trivial
6048.2.c.d.3025.1		16	8.3	odd	2
6048.2.c.d.3025.2		16	12.11	even	2
6048.2.c.d.3025.15		16	24.11	even	2
6048.2.c.d.3025.16		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.437016 + 1.34500i) q^{2} +(-1.61803 + 1.17557i) q^{4} +4.29757i q^{5} -1.00000 q^{7} +(-2.28825 - 1.66251i) q^{8} +O(q^{10})\)	\(q+(0.437016 + 1.34500i) q^{2} +(-1.61803 + 1.17557i) q^{4} +4.29757i q^{5} -1.00000 q^{7} +(-2.28825 - 1.66251i) q^{8} +(-5.78022 + 1.87811i) q^{10} +1.60758i q^{11} +6.02967i q^{13} +(-0.437016 - 1.34500i) q^{14} +(1.23607 - 3.80423i) q^{16} +3.16228 q^{17} +3.07768i q^{19} +(-5.05210 - 6.95362i) q^{20} +(-2.16219 + 0.702537i) q^{22} +5.95080 q^{23} -13.4691 q^{25} +(-8.10989 + 2.63506i) q^{26} +(1.61803 - 1.17557i) q^{28} -3.53972i q^{29} -2.08831 q^{31} +5.65685 q^{32} +(1.38197 + 4.25325i) q^{34} -4.29757i q^{35} +4.48276i q^{37} +(-4.13948 + 1.34500i) q^{38} +(7.14475 - 9.83390i) q^{40} -6.69568 q^{41} -12.2811i q^{43} +(-1.88982 - 2.60111i) q^{44} +(2.60059 + 8.00380i) q^{46} +3.82734 q^{47} +1.00000 q^{49} +(-5.88622 - 18.1159i) q^{50} +(-7.08831 - 9.75621i) q^{52} -8.63711i q^{53} -6.90868 q^{55} +(2.28825 + 1.66251i) q^{56} +(4.76091 - 1.54691i) q^{58} -1.55265i q^{59} +3.64886i q^{61} +(-0.912623 - 2.80876i) q^{62} +(2.47214 + 7.60845i) q^{64} -25.9129 q^{65} +0.772361i q^{67} +(-5.11667 + 3.71748i) q^{68} +(5.78022 - 1.87811i) q^{70} +7.36501 q^{71} +1.32739 q^{73} +(-6.02930 + 1.95904i) q^{74} +(-3.61803 - 4.97980i) q^{76} -1.60758i q^{77} +12.7401 q^{79} +(16.3489 + 5.31209i) q^{80} +(-2.92612 - 9.00567i) q^{82} +7.08446i q^{83} +13.5901i q^{85} +(16.5180 - 5.36702i) q^{86} +(2.67261 - 3.67853i) q^{88} +9.73307 q^{89} -6.02967i q^{91} +(-9.62859 + 6.99558i) q^{92} +(1.67261 + 5.14776i) q^{94} -13.2266 q^{95} -10.1803 q^{97} +(0.437016 + 1.34500i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} - 16 q^{7}+O(q^{10}) \) 16 * q - 8 * q^4 - 16 * q^7	\( 16 q - 8 q^{4} - 16 q^{7} - 20 q^{10} - 16 q^{16} + 20 q^{22} - 32 q^{25} + 8 q^{28} + 40 q^{31} + 40 q^{34} + 40 q^{40} + 4 q^{46} + 16 q^{49} - 40 q^{52} - 72 q^{55} - 32 q^{64} + 20 q^{70} + 24 q^{73} - 40 q^{76} + 24 q^{79} - 28 q^{82} + 40 q^{88} + 24 q^{94} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^4 - 16 * q^7 - 20 * q^10 - 16 * q^16 + 20 * q^22 - 32 * q^25 + 8 * q^28 + 40 * q^31 + 40 * q^34 + 40 * q^40 + 4 * q^46 + 16 * q^49 - 40 * q^52 - 72 * q^55 - 32 * q^64 + 20 * q^70 + 24 * q^73 - 40 * q^76 + 24 * q^79 - 28 * q^82 + 40 * q^88 + 24 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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