LMFDB - Embedded newform 1512.2.c.d.757.9

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

$q$-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	$-0.589230\pi$
$5$		−	4.29757i		−	1.92193i	0.276666	−	0.960966i	$-0.410770\pi$
$6$		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	$-0.922081\pi$
$11$		−	1.60758i		−	0.484703i	0.970189	−	0.242351i	$-0.0779187\pi$
$12$		0			0
$13$		−	6.02967i		−	1.67233i	−0.548478	−	0.836165i	$-0.684792\pi$
$13$		−	6.02967i		−	1.67233i	0.548478	−	0.836165i	$-0.315208\pi$
$14$	−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	$-0.885150\pi$
$19$		−	3.07768i		−	0.706069i	0.935610	−	0.353035i	$-0.114850\pi$
$20$	−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	$0.106595\pi$
$29$			3.53972i			0.657310i	−0.944450	+	0.328655i	$0.893405\pi$
$30$		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	$-0.879878\pi$
$37$		−	4.48276i		−	0.736961i	0.929636	−	0.368480i	$-0.120122\pi$
$38$	−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	$0.385884\pi$
$43$			12.2811i			1.87284i	−0.350875	+	0.936422i	$0.614116\pi$
$44$	−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	$0.202135\pi$
$53$			8.63711i			1.18640i	−0.805056	+	0.593199i	$0.797865\pi$
$54$		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	$0.0322262\pi$
$59$			1.55265i			0.202137i	−0.994879	+	0.101069i	$0.967774\pi$
$60$		0			0
$61$		−	3.64886i		−	0.467189i	−0.972334	−	0.233594i	$-0.924951\pi$
$61$		−	3.64886i		−	0.467189i	0.972334	−	0.233594i	$-0.0750487\pi$
$62$	−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	$-0.984977\pi$
$67$		−	0.772361i		−	0.0943590i	0.998886	−	0.0471795i	$-0.0150233\pi$
$68$	−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	$-0.872886\pi$
$83$		−	7.08446i		−	0.777620i	0.921318	−	0.388810i	$-0.127114\pi$
$84$		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	$-0.983721\pi$
$101$		−	1.02749i		−	0.102239i	0.998693	−	0.0511194i	$-0.0162789\pi$
$102$		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	$0.283754\pi$
$107$			16.0949i			1.55595i	−0.628294	+	0.777976i	$0.716246\pi$
$108$		0			0
$109$		−	20.2686i		−	1.94138i	−0.240327	−	0.970692i	$-0.577255\pi$
$109$		−	20.2686i		−	1.94138i	0.240327	−	0.970692i	$-0.422745\pi$
$110$	−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	$-0.855908\pi$
$131$		−	10.0120i		−	0.874752i	0.899279	−	0.437376i	$-0.144092\pi$
$132$		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	$0.0905042\pi$
$139$			6.61437i			0.561024i	−0.959851	+	0.280512i	$0.909496\pi$
$140$	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	$0.244949\pi$
$149$			16.9866i			1.39160i	−0.718238	+	0.695798i	$0.755051\pi$
$150$		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	$0.136066\pi$
$157$			10.3889i			0.829127i	−0.910020	+	0.414563i	$0.863934\pi$
$158$	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	$-0.846042\pi$
$163$		−	11.8743i		−	0.930067i	0.885293	−	0.465034i	$-0.153958\pi$
$164$	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	$-0.640479\pi$
$173$		−	23.7854i		−	1.80837i	0.427142	−	0.904185i	$-0.359521\pi$
$174$		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	$-0.688710\pi$
$179$		−	22.1919i		−	1.65870i	0.558728	−	0.829351i	$-0.311290\pi$
$180$		0			0
$181$		−	8.60253i		−	0.639421i	−0.947515	−	0.319711i	$-0.896414\pi$
$181$		−	8.60253i		−	0.639421i	0.947515	−	0.319711i	$-0.103586\pi$
$182$	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	$-0.705259\pi$
$197$		−	22.4345i		−	1.59839i	0.601072	−	0.799195i	$-0.294741\pi$
$198$		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	$-0.905411\pi$
$211$		−	8.50651i		−	0.585612i	0.956172	−	0.292806i	$-0.0945890\pi$
$212$	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	$0.116997\pi$
$227$			10.8279i			0.718671i	−0.933208	+	0.359336i	$0.883003\pi$
$228$		0			0
$229$			24.9251i			1.64710i	0.567245	+	0.823549i	$0.308009\pi$
$229$			24.9251i			1.64710i	−0.567245	+	0.823549i	$0.691991\pi$
$230$	−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	$-0.792550\pi$
$251$		−	19.2193i		−	1.21311i	0.795040	−	0.606556i	$-0.207450\pi$
$252$		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	$0.142592\pi$
$269$			14.2078i			0.866266i	−0.901330	+	0.433133i	$0.857408\pi$
$270$		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	$-0.862460\pi$
$277$		−	13.9396i		−	0.837548i	0.908091	−	0.418774i	$-0.137540\pi$
$278$	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	$-0.655963\pi$
$283$		−	29.6867i		−	1.76469i	0.470600	−	0.882347i	$-0.344037\pi$
$284$	−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	$-0.840447\pi$
$293$		−	16.4504i		−	0.961044i	0.876983	−	0.480522i	$-0.159553\pi$
$294$		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	$0.191566\pi$
$307$			19.8393i			1.13229i	−0.824306	+	0.566145i	$0.808434\pi$
$308$	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	$-0.953050\pi$
$317$		−	5.23318i		−	0.293925i	0.989142	−	0.146962i	$-0.0469496\pi$
$318$		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	$-0.849463\pi$
$331$		−	16.5740i		−	0.910988i	0.890239	−	0.455494i	$-0.150537\pi$
$332$	−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	$0.222843\pi$
$347$			24.0032i			1.28856i	−0.764790	+	0.644279i	$0.777157\pi$
$348$		0			0
$349$			21.3679i			1.14380i	0.820324	+	0.571898i	$0.193793\pi$
$349$			21.3679i			1.14380i	−0.820324	+	0.571898i	$0.806207\pi$
$350$	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	$-0.725028\pi$
$373$		−	29.3696i		−	1.52070i	0.649514	−	0.760349i	$-0.274972\pi$
$374$	−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	$0.136031\pi$
$379$			16.1375i			0.828930i	−0.910065	+	0.414465i	$0.863969\pi$
$380$	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	$0.248632\pi$
$389$			27.7725i			1.40812i	−0.710140	+	0.704061i	$0.751368\pi$
$390$		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	$-0.756251\pi$
$397$		−	27.6193i		−	1.38617i	0.720855	−	0.693086i	$-0.243749\pi$
$398$	−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	$0.162131\pi$
$419$			19.9623i			0.975222i	−0.873061	+	0.487611i	$0.837869\pi$
$420$		0			0
$421$		−	12.8339i		−	0.625486i	−0.949838	−	0.312743i	$-0.898752\pi$
$421$		−	12.8339i		−	0.625486i	0.949838	−	0.312743i	$-0.101248\pi$
$422$	−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	$-0.935980\pi$
$443$		−	8.40943i		−	0.399544i	0.979842	−	0.199772i	$-0.0640202\pi$
$444$		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	$-0.921285\pi$
$461$		−	10.5113i		−	0.489558i	0.969579	−	0.244779i	$-0.0787154\pi$
$462$		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	$-0.849173\pi$
$467$		−	19.7216i		−	0.912609i	0.889824	−	0.456305i	$-0.150827\pi$
$468$		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	$0.0304624\pi$
$491$			4.23469i			0.191109i	−0.995424	+	0.0955544i	$0.969538\pi$
$492$		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	$-0.927284\pi$
$499$		−	10.1176i		−	0.452925i	0.974020	−	0.226463i	$-0.0727161\pi$
$500$	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	$0.0992048\pi$
$509$			13.8362i			0.613280i	−0.951826	+	0.306640i	$0.900795\pi$
$510$		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	$0.00429104\pi$
$523$			0.616566i			0.0269606i	−0.999909	+	0.0134803i	$0.995709\pi$
$524$	−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	$0.251650\pi$
$541$			33.0638i			1.42152i	−0.703432	+	0.710762i	$0.748350\pi$
$542$	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	$0.429900\pi$
$547$			45.6463i			1.95170i	−0.218450	+	0.975848i	$0.570100\pi$
$548$	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	$0.000349787\pi$
$557$			0.0518694i			0.00219778i	−0.999999	+	0.00109889i	$0.999650\pi$
$558$		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	$-0.926156\pi$
$563$		−	10.9105i		−	0.459822i	0.973212	−	0.229911i	$-0.0738436\pi$
$564$		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	$0.171017\pi$
$571$			24.4590i			1.02358i	−0.859111	+	0.511789i	$0.828983\pi$
$572$	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	$0.175414\pi$
$587$			25.3720i			1.04722i	−0.851959	+	0.523608i	$0.824586\pi$
$588$		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	$-0.861163\pi$
$613$		−	20.9197i		−	0.844939i	0.906377	−	0.422469i	$-0.138837\pi$
$614$	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	$0.159222\pi$
$619$			23.8651i			0.959220i	−0.877482	+	0.479610i	$0.840778\pi$
$620$	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	$0.0972114\pi$
$643$			15.2486i			0.601347i	−0.953727	+	0.300674i	$0.902789\pi$
$644$	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	$0.0582150\pi$
$653$			9.29496i			0.363740i	−0.983323	+	0.181870i	$0.941785\pi$
$654$		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	$0.248982\pi$
$659$			36.1879i			1.40968i	−0.709366	+	0.704841i	$0.751018\pi$
$660$		0			0
$661$			19.8091i			0.770483i	0.922816	+	0.385242i	$0.125882\pi$
$661$			19.8091i			0.770483i	−0.922816	+	0.385242i	$0.874118\pi$
$662$	−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	$0.0203146\pi$
$677$			3.31885i			0.127554i	−0.997964	+	0.0637770i	$0.979685\pi$
$678$		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	$0.111904\pi$
$683$			17.9992i			0.688720i	−0.938838	+	0.344360i	$0.888096\pi$
$684$		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	$0.0222475\pi$
$691$			3.67153i			0.139671i	−0.997559	+	0.0698357i	$0.977752\pi$
$692$	−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	$0.0426169\pi$
$701$			7.06843i			0.266971i	−0.991051	+	0.133485i	$0.957383\pi$
$702$		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	$-0.874474\pi$
$709$		−	20.4607i		−	0.768417i	0.923246	−	0.384209i	$-0.125526\pi$
$710$	−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	$-0.888482\pi$
$733$		−	18.5847i		−	0.686442i	0.939255	−	0.343221i	$-0.111518\pi$
$734$	−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	$-0.972477\pi$
$739$		−	4.69519i		−	0.172715i	0.996264	−	0.0863576i	$-0.0275228\pi$
$740$	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	$-0.850469\pi$
$757$		−	24.9095i		−	0.905352i	0.891675	−	0.452676i	$-0.149531\pi$
$758$	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	$-0.913654\pi$
$773$		−	14.8995i		−	0.535899i	0.963433	−	0.267949i	$-0.0863460\pi$
$774$		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	$-0.941902\pi$
$787$		−	10.1839i		−	0.363018i	0.983389	−	0.181509i	$-0.0580981\pi$
$788$	−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	$-0.920120\pi$
$797$		−	14.0210i		−	0.496648i	0.968677	−	0.248324i	$-0.0798798\pi$
$798$		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	$0.0746554\pi$
$811$			13.2362i			0.464785i	−0.972622	+	0.232393i	$0.925345\pi$
$812$	−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	$0.0776100\pi$
$821$			13.8343i			0.482821i	−0.970423	+	0.241411i	$0.922390\pi$
$822$		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	$-0.831912\pi$
$827$		−	28.9797i		−	1.00772i	0.863784	−	0.503861i	$-0.168088\pi$
$828$		0			0
$829$		−	32.5800i		−	1.13155i	−0.824560	−	0.565774i	$-0.808577\pi$
$829$		−	32.5800i		−	1.13155i	0.824560	−	0.565774i	$-0.191423\pi$
$830$	−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	$0.0967166\pi$
$853$			17.4764i			0.598381i	−0.954193	+	0.299190i	$0.903283\pi$
$854$	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	$0.243802\pi$
$859$			40.6339i			1.38641i	−0.720740	+	0.693205i	$0.756198\pi$
$860$	−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	$0.188171\pi$
$877$			33.0093i			1.11464i	−0.830296	+	0.557322i	$0.811829\pi$
$878$	−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	$-0.712455\pi$
$883$		−	46.6771i		−	1.57081i	0.618983	−	0.785404i	$-0.287545\pi$
$884$	−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	$0.0480930\pi$
$907$			9.06592i			0.301029i	−0.988608	+	0.150514i	$0.951907\pi$
$908$	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	$-0.782208\pi$
$941$		−	38.7781i		−	1.26413i	0.774915	−	0.632065i	$-0.217792\pi$
$942$		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	$-0.980577\pi$
$947$		−	3.75328i		−	0.121965i	0.998139	−	0.0609826i	$-0.0194234\pi$
$948$		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	$-0.970608\pi$
$971$		−	5.74652i		−	0.184415i	0.995740	−	0.0922073i	$-0.0293922\pi$
$972$		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	$-0.847356\pi$
$997$		−	29.1361i		−	0.922749i	0.887205	−	0.461375i	$-0.152644\pi$
$998$	−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.757.9	yes	16
3.2	odd	2	inner	1512.2.c.d.757.8	yes	16
4.3	odd	2		6048.2.c.d.3025.1		16
8.3	odd	2		6048.2.c.d.3025.16		16
8.5	even	2	inner	1512.2.c.d.757.12	yes	16
12.11	even	2		6048.2.c.d.3025.15		16
24.5	odd	2	inner	1512.2.c.d.757.5	✓	16
24.11	even	2		6048.2.c.d.3025.2		16

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

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Representations

Groups

Database

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