LMFDB - Embedded newform 1008.2.t.h.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.h.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29418 - 1.15113i) q^{3} +1.58836 q^{5} +(2.64400 + 0.0963576i) q^{7} +(0.349814 + 2.97954i) q^{9} +O(q^{10})$	\(q+(-1.29418 - 1.15113i) q^{3} +1.58836 q^{5} +(2.64400 + 0.0963576i) q^{7} +(0.349814 + 2.97954i) q^{9} +1.58836 q^{11} +(2.40545 - 4.16635i) q^{13} +(-2.05563 - 1.82841i) q^{15} +(-2.69963 + 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-3.31089 - 3.16828i) q^{21} -0.300372 q^{23} -2.47710 q^{25} +(2.97710 - 4.25874i) q^{27} +(4.13781 + 7.16689i) q^{29} +(-1.35600 - 2.34867i) q^{31} +(-2.05563 - 1.82841i) q^{33} +(4.19963 + 0.153051i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-7.90909 + 2.62305i) q^{39} +(2.93818 - 5.08907i) q^{41} +(0.833104 + 1.44298i) q^{43} +(0.555632 + 4.73259i) q^{45} +(1.33310 - 2.30900i) q^{47} +(6.98143 + 0.509538i) q^{49} +(8.87636 - 2.94384i) q^{51} +(2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +(2.48329 - 12.0422i) q^{57} +(3.23855 + 5.60933i) q^{59} +(2.23855 - 3.87728i) q^{61} +(0.637806 + 7.91159i) q^{63} +(3.82072 - 6.61769i) q^{65} +(-5.02654 - 8.70623i) q^{67} +(0.388736 + 0.345766i) q^{69} -12.7207 q^{71} +(8.02654 - 13.9024i) q^{73} +(3.20582 + 2.85146i) q^{75} +(4.19963 + 0.153051i) q^{77} +(4.19344 - 7.26325i) q^{79} +(-8.75526 + 2.08457i) q^{81} +(-1.18292 - 2.04887i) q^{83} +(-4.28799 + 7.42702i) q^{85} +(2.89493 - 14.0384i) q^{87} +(1.60507 + 2.78007i) q^{89} +(6.76145 - 10.7840i) q^{91} +(-0.948699 + 4.60054i) q^{93} +(5.63781 + 9.76497i) q^{95} +(0.712008 + 1.23323i) q^{97} +(0.555632 + 4.73259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q - 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^9	$ 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9} - 2 q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} - 4 q^{25} + 7 q^{27} - 5 q^{29} - 20 q^{31} - 12 q^{33} + 13 q^{35} + 3 q^{37} - q^{39} + 6 q^{43} + 3 q^{45} + 9 q^{47} - 12 q^{49} + 18 q^{51} + 15 q^{53} + 26 q^{55} + 22 q^{57} + 14 q^{59} + 8 q^{61} - 26 q^{63} - 12 q^{65} - q^{67} + 3 q^{69} - 14 q^{71} + 19 q^{73} + 25 q^{75} + 13 q^{77} - 5 q^{79} - 40 q^{81} - 2 q^{83} - 2 q^{85} + 36 q^{87} - 9 q^{89} + 46 q^{91} + 37 q^{93} + 4 q^{95} + 28 q^{97} + 3 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^9 - 2 * q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 - 4 * q^25 + 7 * q^27 - 5 * q^29 - 20 * q^31 - 12 * q^33 + 13 * q^35 + 3 * q^37 - q^39 + 6 * q^43 + 3 * q^45 + 9 * q^47 - 12 * q^49 + 18 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 + 14 * q^59 + 8 * q^61 - 26 * q^63 - 12 * q^65 - q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 + 25 * q^75 + 13 * q^77 - 5 * q^79 - 40 * q^81 - 2 * q^83 - 2 * q^85 + 36 * q^87 - 9 * q^89 + 46 * q^91 + 37 * q^93 + 4 * q^95 + 28 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.29418	−	1.15113i	−0.747196	−	0.664603i
$3$	−1.29418	−	1.15113i	−0.747196	−	0.664603i
$4$		0			0
$5$	1.58836			0.710338			0.355169	−	0.934802i	$-0.384423\pi$
$5$	1.58836			0.710338			0.355169	+	0.934802i	$0.384423\pi$
$6$		0			0
$7$	2.64400	+	0.0963576i	0.999337	+	0.0364197i
$7$	2.64400	+	0.0963576i	0.999337	+	0.0364197i
$8$		0			0
$9$	0.349814	+	2.97954i	0.116605	+	0.993178i
$10$		0			0
$11$	1.58836			0.478910			0.239455	−	0.970907i	$-0.423031\pi$
$11$	1.58836			0.478910			0.239455	+	0.970907i	$0.423031\pi$
$12$		0			0
$13$	2.40545	−	4.16635i	0.667151	−	1.15554i	−0.311547	−	0.950231i	$-0.600847\pi$
$13$	2.40545	−	4.16635i	0.667151	−	1.15554i	0.978697	−	0.205308i	$-0.0658196\pi$
$14$		0			0
$15$	−2.05563	−	1.82841i	−0.530762	−	0.472093i
$16$		0			0
$17$	−2.69963	+	4.67589i	−0.654756	+	1.13407i	0.327199	+	0.944955i	$0.393895\pi$
$17$	−2.69963	+	4.67589i	−0.654756	+	1.13407i	−0.981955	+	0.189115i	$0.939438\pi$
$18$		0			0
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	0.909831	+	0.414979i	$0.136211\pi$
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	−0.0955331	+	0.995426i	$0.530456\pi$
$20$		0			0
$21$	−3.31089	−	3.16828i	−0.722496	−	0.691375i
$22$		0			0
$23$	−0.300372			−0.0626319			−0.0313159	−	0.999510i	$-0.509970\pi$
$23$	−0.300372			−0.0626319			−0.0313159	+	0.999510i	$0.509970\pi$
$24$		0			0
$25$	−2.47710			−0.495420
$26$		0			0
$27$	2.97710	−	4.25874i	0.572943	−	0.819595i
$28$		0			0
$29$	4.13781	+	7.16689i	0.768371	+	1.33086i	0.938446	+	0.345427i	$0.112266\pi$
$29$	4.13781	+	7.16689i	0.768371	+	1.33086i	−0.170074	+	0.985431i	$0.554401\pi$
$30$		0			0
$31$	−1.35600	−	2.34867i	−0.243545	−	0.421833i	0.718176	−	0.695861i	$-0.244977\pi$
$31$	−1.35600	−	2.34867i	−0.243545	−	0.421833i	−0.961722	+	0.274028i	$0.911644\pi$
$32$		0			0
$33$	−2.05563	−	1.82841i	−0.357840	−	0.318285i
$34$		0			0
$35$	4.19963	+	0.153051i	0.709867	+	0.0258703i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−7.90909	+	2.62305i	−1.26647	+	0.420024i
$40$		0			0
$41$	2.93818	−	5.08907i	0.458866	−	0.794780i	−0.540035	−	0.841643i	$-0.681589\pi$
$41$	2.93818	−	5.08907i	0.458866	−	0.794780i	0.998901	+	0.0468628i	$0.0149223\pi$
$42$		0			0
$43$	0.833104	+	1.44298i	0.127047	+	0.220052i	0.922531	−	0.385922i	$-0.126117\pi$
$43$	0.833104	+	1.44298i	0.127047	+	0.220052i	−0.795484	+	0.605974i	$0.792783\pi$
$44$		0			0
$45$	0.555632	+	4.73259i	0.0828287	+	0.705492i
$46$		0			0
$47$	1.33310	−	2.30900i	0.194453	−	0.336803i	−0.752268	−	0.658857i	$-0.771040\pi$
$47$	1.33310	−	2.30900i	0.194453	−	0.336803i	0.946721	+	0.322055i	$0.104373\pi$
$48$		0			0
$49$	6.98143	+	0.509538i	0.997347	+	0.0727912i
$50$		0			0
$51$	8.87636	−	2.94384i	1.24294	−	0.412220i
$52$		0			0
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	−0.647871	−	0.761750i	$-0.724340\pi$
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	0.983630	+	0.180197i	$0.0576736\pi$
$54$		0			0
$55$	2.52290			0.340188
$56$		0			0
$57$	2.48329	−	12.0422i	0.328920	−	1.59503i
$58$		0			0
$59$	3.23855	+	5.60933i	0.421623	+	0.730273i	0.996098	−	0.0882491i	$-0.0281271\pi$
$59$	3.23855	+	5.60933i	0.421623	+	0.730273i	−0.574475	+	0.818522i	$0.694794\pi$
$60$		0			0
$61$	2.23855	−	3.87728i	0.286617	−	0.496435i	−0.686383	−	0.727240i	$-0.740803\pi$
$61$	2.23855	−	3.87728i	0.286617	−	0.496435i	0.973000	+	0.230805i	$0.0741360\pi$
$62$		0			0
$63$	0.637806	+	7.91159i	0.0803560	+	0.996766i
$64$		0			0
$65$	3.82072	−	6.61769i	0.473902	−	0.820823i
$66$		0			0
$67$	−5.02654	−	8.70623i	−0.614090	−	1.06363i	−0.990543	−	0.137199i	$-0.956190\pi$
$67$	−5.02654	−	8.70623i	−0.614090	−	1.06363i	0.376454	−	0.926435i	$-0.377143\pi$
$68$		0			0
$69$	0.388736	+	0.345766i	0.0467983	+	0.0416253i
$70$		0			0
$71$	−12.7207			−1.50967			−0.754833	−	0.655917i	$-0.772282\pi$
$71$	−12.7207			−1.50967			−0.754833	+	0.655917i	$0.772282\pi$
$72$		0			0
$73$	8.02654	−	13.9024i	0.939436	−	1.62715i	0.172909	−	0.984938i	$-0.444683\pi$
$73$	8.02654	−	13.9024i	0.939436	−	1.62715i	0.766527	−	0.642213i	$-0.221983\pi$
$74$		0			0
$75$	3.20582	+	2.85146i	0.370176	+	0.329258i
$76$		0			0
$77$	4.19963	+	0.153051i	0.478592	+	0.0174418i
$78$		0			0
$79$	4.19344	−	7.26325i	0.471799	−	0.817179i	−0.527681	−	0.849443i	$-0.676938\pi$
$79$	4.19344	−	7.26325i	0.471799	−	0.817179i	0.999479	+	0.0322635i	$0.0102716\pi$
$80$		0			0
$81$	−8.75526	+	2.08457i	−0.972807	+	0.231619i
$82$		0			0
$83$	−1.18292	−	2.04887i	−0.129842	−	0.224893i	0.793773	−	0.608214i	$-0.208114\pi$
$83$	−1.18292	−	2.04887i	−0.129842	−	0.224893i	−0.923615	+	0.383321i	$0.874780\pi$
$84$		0			0
$85$	−4.28799	+	7.42702i	−0.465098	+	0.805573i
$86$		0			0
$87$	2.89493	−	14.0384i	0.310369	−	1.50507i
$88$		0			0
$89$	1.60507	+	2.78007i	0.170138	+	0.294687i	0.938468	−	0.345367i	$-0.112245\pi$
$89$	1.60507	+	2.78007i	0.170138	+	0.294687i	−0.768330	+	0.640054i	$0.778912\pi$
$90$		0			0
$91$	6.76145	−	10.7840i	0.708793	−	1.13047i
$92$		0			0
$93$	−0.948699	+	4.60054i	−0.0983755	+	0.477053i
$94$		0			0
$95$	5.63781	+	9.76497i	0.578427	+	1.00186i
$96$		0			0
$97$	0.712008	+	1.23323i	0.0722934	+	0.125216i	0.899906	−	0.436084i	$-0.143635\pi$
$97$	0.712008	+	1.23323i	0.0722934	+	0.125216i	−0.827613	+	0.561300i	$0.810302\pi$
$98$		0			0
$99$	0.555632	+	4.73259i	0.0558431	+	0.475643i
$100$		0			0
$101$	12.0334			1.19737			0.598685	−	0.800985i	$-0.295690\pi$
$101$	12.0334			1.19737			0.598685	+	0.800985i	$0.295690\pi$
$102$		0			0
$103$	6.09888			0.600941			0.300470	−	0.953791i	$-0.402856\pi$
$103$	6.09888			0.600941			0.300470	+	0.953791i	$0.402856\pi$
$104$		0			0
$105$	−5.25890	−	5.03238i	−0.513216	−	0.491110i
$106$		0			0
$107$	1.54325	+	2.67299i	0.149192	+	0.258408i	0.930929	−	0.365200i	$-0.118999\pi$
$107$	1.54325	+	2.67299i	0.149192	+	0.258408i	−0.781737	+	0.623608i	$0.785666\pi$
$108$		0			0
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	−0.806023	−	0.591884i	$-0.798384\pi$
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	0.915598	+	0.402095i	$0.131718\pi$
$110$		0			0
$111$	0.349814	−	1.69636i	0.0332029	−	0.161011i
$112$		0			0
$113$	−9.73236	+	16.8569i	−0.915543	+	1.58577i	−0.109440	+	0.993993i	$0.534906\pi$
$113$	−9.73236	+	16.8569i	−0.915543	+	1.58577i	−0.806104	+	0.591774i	$0.798428\pi$
$114$		0			0
$115$	−0.477100			−0.0444898
$116$		0			0
$117$	13.2553	+	5.70966i	1.22545	+	0.527858i
$118$		0			0
$119$	−7.58836	+	12.1029i	−0.695624	+	1.10947i
$120$		0			0
$121$	−8.47710			−0.770645
$122$		0			0
$123$	−9.66071	+	3.20397i	−0.871077	+	0.288892i
$124$		0			0
$125$	−11.8764			−1.06225
$126$		0			0
$127$	13.4400			1.19260			0.596302	−	0.802760i	$-0.296636\pi$
$127$	13.4400			1.19260			0.596302	+	0.802760i	$0.296636\pi$
$128$		0			0
$129$	0.582863	−	2.82648i	0.0513182	−	0.248858i
$130$		0			0
$131$	3.17673			0.277552			0.138776	−	0.990324i	$-0.455683\pi$
$131$	3.17673			0.277552			0.138776	+	0.990324i	$0.455683\pi$
$132$		0			0
$133$	8.79232	+	16.5968i	0.762391	+	1.43913i
$134$		0			0
$135$	4.72872	−	6.76443i	0.406983	−	0.582190i
$136$		0			0
$137$	−21.2632			−1.81664			−0.908320	−	0.418275i	$-0.862635\pi$
$137$	−21.2632			−1.81664			−0.908320	+	0.418275i	$0.862635\pi$
$138$		0			0
$139$	−6.52654	+	11.3043i	−0.553574	+	0.958818i	0.444439	+	0.895809i	$0.353403\pi$
$139$	−6.52654	+	11.3043i	−0.553574	+	0.958818i	−0.998013	+	0.0630092i	$0.979930\pi$
$140$		0			0
$141$	−4.38323	+	1.45370i	−0.369135	+	0.122424i
$142$		0			0
$143$	3.82072	−	6.61769i	0.319505	−	0.553399i
$144$		0			0
$145$	6.57234	+	11.3836i	0.545803	+	0.945359i
$146$		0			0
$147$	−8.44870	−	8.69595i	−0.696837	−	0.717230i
$148$		0			0
$149$	5.20877			0.426719			0.213360	−	0.976974i	$-0.431559\pi$
$149$	5.20877			0.426719			0.213360	+	0.976974i	$0.431559\pi$
$150$		0			0
$151$	0.522900			0.0425530			0.0212765	−	0.999774i	$-0.493227\pi$
$151$	0.522900			0.0425530			0.0212765	+	0.999774i	$0.493227\pi$
$152$		0			0
$153$	−14.8764	−	6.40794i	−1.20268	−	0.518052i
$154$		0			0
$155$	−2.15383	−	3.73054i	−0.173000	−	0.299644i
$156$		0			0
$157$	−4.43199	−	7.67643i	−0.353711	−	0.612646i	0.633185	−	0.774000i	$-0.281747\pi$
$157$	−4.43199	−	7.67643i	−0.353711	−	0.612646i	−0.986897	+	0.161354i	$0.948414\pi$
$158$		0			0
$159$	−8.03706	+	2.66549i	−0.637381	+	0.211387i
$160$		0			0
$161$	−0.794182	−	0.0289431i	−0.0625903	−	0.00228104i
$162$		0			0
$163$	−10.9814	−	19.0204i	−0.860132	−	1.48979i	−0.871801	−	0.489860i	$-0.837048\pi$
$163$	−10.9814	−	19.0204i	−0.860132	−	1.48979i	0.0116689	−	0.999932i	$-0.496286\pi$
$164$		0			0
$165$	−3.26509	−	2.90418i	−0.254187	−	0.226090i
$166$		0			0
$167$	−1.65019	+	2.85821i	−0.127695	+	0.221175i	−0.922783	−	0.385319i	$-0.874091\pi$
$167$	−1.65019	+	2.85821i	−0.127695	+	0.221175i	0.795088	+	0.606494i	$0.207425\pi$
$168$		0			0
$169$	−5.07234	−	8.78555i	−0.390180	−	0.675812i
$170$		0			0
$171$	−17.0760	+	12.7263i	−1.30583	+	0.973203i
$172$		0			0
$173$	−9.55377	+	16.5476i	−0.726360	+	1.25809i	0.232052	+	0.972703i	$0.425456\pi$
$173$	−9.55377	+	16.5476i	−0.726360	+	1.25809i	−0.958412	+	0.285389i	$0.907877\pi$
$174$		0			0
$175$	−6.54944	−	0.238687i	−0.495091	−	0.0180431i
$176$		0			0
$177$	2.26578	−	10.9875i	0.170307	−	0.825870i
$178$		0			0
$179$	8.03706	−	13.9206i	0.600718	−	1.04047i	−0.391994	−	0.919968i	$-0.628215\pi$
$179$	8.03706	−	13.9206i	0.600718	−	1.04047i	0.992712	−	0.120507i	$-0.0384520\pi$
$180$		0			0
$181$	8.05308			0.598581			0.299291	−	0.954162i	$-0.403250\pi$
$181$	8.05308			0.598581			0.299291	+	0.954162i	$0.403250\pi$
$182$		0			0
$183$	−7.36033	+	2.44105i	−0.544092	+	0.180448i
$184$		0			0
$185$	0.794182	+	1.37556i	0.0583894	+	0.101133i
$186$		0			0
$187$	−4.28799	+	7.42702i	−0.313569	+	0.543118i
$188$		0			0
$189$	8.28180	−	10.9732i	0.602412	−	0.798185i
$190$		0			0
$191$	−11.9814	+	20.7524i	−0.866946	+	1.50159i	−0.00184390	+	0.999998i	$0.500587\pi$
$191$	−11.9814	+	20.7524i	−0.866946	+	1.50159i	−0.865102	+	0.501596i	$0.832746\pi$
$192$		0			0
$193$	−4.88255	−	8.45682i	−0.351453	−	0.608735i	0.635051	−	0.772470i	$-0.280979\pi$
$193$	−4.88255	−	8.45682i	−0.351453	−	0.608735i	−0.986504	+	0.163735i	$0.947646\pi$
$194$		0			0
$195$	−12.5625	+	4.16635i	−0.899620	+	0.298359i
$196$		0			0
$197$	−18.2436			−1.29980			−0.649900	−	0.760020i	$-0.725189\pi$
$197$	−18.2436			−1.29980			−0.649900	+	0.760020i	$0.725189\pi$
$198$		0			0
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	0.343601	+	0.939116i	$0.388353\pi$
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	−0.985098	+	0.171991i	$0.944980\pi$
$200$		0			0
$201$	−3.51671	+	17.0536i	−0.248050	+	1.20287i
$202$		0			0
$203$	10.2498	+	19.3479i	0.719392	+	1.35796i
$204$		0			0
$205$	4.66690	−	8.08330i	0.325950	−	0.564562i
$206$		0			0
$207$	−0.105074	−	0.894969i	−0.00730317	−	0.0622046i
$208$		0			0
$209$	5.63781	+	9.76497i	0.389975	+	0.675457i
$210$		0			0
$211$	−0.166208	+	0.287880i	−0.0114422	+	0.0198185i	−0.871690	−	0.490058i	$-0.836976\pi$
$211$	−0.166208	+	0.287880i	−0.0114422	+	0.0198185i	0.860248	+	0.509877i	$0.170309\pi$
$212$		0			0
$213$	16.4629	+	14.6431i	1.12802	+	1.00333i
$214$		0			0
$215$	1.32327	+	2.29197i	0.0902464	+	0.156311i
$216$		0			0
$217$	−3.35896	−	6.34053i	−0.228021	−	0.430423i
$218$		0			0
$219$	−26.3912	+	8.75264i	−1.78335	+	0.591449i
$220$		0			0
$221$	12.9876	+	22.4952i	0.873642	+	1.51319i
$222$		0			0
$223$	−3.16621	−	5.48403i	−0.212025	−	0.367238i	0.740323	−	0.672251i	$-0.234672\pi$
$223$	−3.16621	−	5.48403i	−0.212025	−	0.367238i	−0.952348	+	0.305013i	$0.901339\pi$
$224$		0			0
$225$	−0.866524	−	7.38061i	−0.0577683	−	0.492040i
$226$		0			0
$227$	23.3090			1.54707			0.773537	−	0.633751i	$-0.218485\pi$
$227$	23.3090			1.54707			0.773537	+	0.633751i	$0.218485\pi$
$228$		0			0
$229$	−4.95420			−0.327383			−0.163691	−	0.986512i	$-0.552340\pi$
$229$	−4.95420			−0.327383			−0.163691	+	0.986512i	$0.552340\pi$
$230$		0			0
$231$	−5.25890	−	5.03238i	−0.346010	−	0.331106i
$232$		0			0
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	0.531702	−	0.846932i	$-0.321553\pi$
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	−0.999315	+	0.0370017i	$0.988219\pi$
$234$		0			0
$235$	2.11745	−	3.66754i	0.138127	−	0.239244i
$236$		0			0
$237$	−13.7880	+	4.57279i	−0.895626	+	0.297034i
$238$		0			0
$239$	−2.48762	+	4.30868i	−0.160911	+	0.278706i	−0.935196	−	0.354132i	$-0.884776\pi$
$239$	−2.48762	+	4.30868i	−0.160911	+	0.278706i	0.774285	+	0.632837i	$0.218110\pi$
$240$		0			0
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$		0			0
$243$	13.7305	+	7.38061i	0.880812	+	0.473466i
$244$		0			0
$245$	11.0891	+	0.809332i	0.708454	+	0.0517063i
$246$		0			0
$247$	34.1520			2.17304
$248$		0			0
$249$	−0.827603	+	4.01330i	−0.0524472	+	0.254333i
$250$		0			0
$251$	−2.43268			−0.153549			−0.0767746	−	0.997048i	$-0.524462\pi$
$251$	−2.43268			−0.153549			−0.0767746	+	0.997048i	$0.524462\pi$
$252$		0			0
$253$	−0.477100			−0.0299950
$254$		0			0
$255$	14.0989	−	4.67589i	0.882906	−	0.292816i
$256$		0			0
$257$	−0.987620			−0.0616061			−0.0308030	−	0.999525i	$-0.509806\pi$
$257$	−0.987620			−0.0616061			−0.0308030	+	0.999525i	$0.509806\pi$
$258$		0			0
$259$	1.23855	+	2.33795i	0.0769597	+	0.145273i
$260$		0			0
$261$	−19.9065	+	14.8358i	−1.23218	+	0.918314i
$262$		0			0
$263$	−17.1854			−1.05970			−0.529848	−	0.848092i	$-0.677751\pi$
$263$	−17.1854			−1.05970			−0.529848	+	0.848092i	$0.677751\pi$
$264$		0			0
$265$	3.88255	−	6.72477i	0.238503	−	0.413099i
$266$		0			0
$267$	1.12296	−	5.44556i	0.0687237	−	0.333263i
$268$		0			0
$269$	11.4523	−	19.8360i	0.698262	−	1.20942i	−0.270807	−	0.962634i	$-0.587291\pi$
$269$	11.4523	−	19.8360i	0.698262	−	1.20942i	0.969069	−	0.246791i	$-0.0793761\pi$
$270$		0			0
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	0.571021	−	0.820936i	$-0.306548\pi$
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	−0.996462	+	0.0840504i	$0.973214\pi$
$272$		0			0
$273$	−21.1643	+	6.17323i	−1.28092	+	0.373621i
$274$		0			0
$275$	−3.93454			−0.237261
$276$		0			0
$277$	28.2953			1.70010			0.850049	−	0.526703i	$-0.176572\pi$
$277$	28.2953			1.70010			0.850049	+	0.526703i	$0.176572\pi$
$278$		0			0
$279$	6.52359	−	4.86186i	0.390557	−	0.291072i
$280$		0			0
$281$	−8.79782	−	15.2383i	−0.524834	−	0.909039i	−0.999582	−	0.0289175i	$-0.990794\pi$
$281$	−8.79782	−	15.2383i	−0.524834	−	0.909039i	0.474748	−	0.880122i	$-0.342539\pi$
$282$		0			0
$283$	−9.26145	−	16.0413i	−0.550536	−	0.953556i	−0.998236	−	0.0593725i	$-0.981090\pi$
$283$	−9.26145	−	16.0413i	−0.550536	−	0.953556i	0.447700	−	0.894184i	$-0.352243\pi$
$284$		0			0
$285$	3.94437	−	19.1275i	0.233644	−	1.13301i
$286$		0			0
$287$	8.25890	−	13.1724i	0.487508	−	0.777541i
$288$		0			0
$289$	−6.07598	−	10.5239i	−0.357411	−	0.619054i
$290$		0			0
$291$	0.498141	−	2.41564i	0.0292015	−	0.141607i
$292$		0			0
$293$	−7.04256	+	12.1981i	−0.411431	+	0.712619i	−0.995046	−	0.0994108i	$-0.968304\pi$
$293$	−7.04256	+	12.1981i	−0.411431	+	0.712619i	0.583616	+	0.812030i	$0.301638\pi$
$294$		0			0
$295$	5.14400	+	8.90966i	0.299495	+	0.518741i
$296$		0			0
$297$	4.72872	−	6.76443i	0.274388	−	0.392512i
$298$		0			0
$299$	−0.722528	+	1.25146i	−0.0417849	+	0.0723736i
$300$		0			0
$301$	2.06368	+	3.89550i	0.118949	+	0.224533i
$302$		0			0
$303$	−15.5734	−	13.8520i	−0.894671	−	0.795776i
$304$		0			0
$305$	3.55563	−	6.15854i	0.203595	−	0.352637i
$306$		0			0
$307$	5.85532			0.334180			0.167090	−	0.985942i	$-0.446563\pi$
$307$	5.85532			0.334180			0.167090	+	0.985942i	$0.446563\pi$
$308$		0			0
$309$	−7.89307	−	7.02059i	−0.449021	−	0.399387i
$310$		0			0
$311$	0.405446	+	0.702253i	0.0229907	+	0.0398211i	0.877292	−	0.479957i	$-0.159348\pi$
$311$	0.405446	+	0.702253i	0.0229907	+	0.0398211i	−0.854301	+	0.519778i	$0.826015\pi$
$312$		0			0
$313$	−5.28799	+	9.15907i	−0.298895	+	0.517701i	−0.975883	−	0.218292i	$-0.929951\pi$
$313$	−5.28799	+	9.15907i	−0.298895	+	0.517701i	0.676988	+	0.735994i	$0.263285\pi$
$314$		0			0
$315$	1.01307	+	12.5665i	0.0570799	+	0.708041i
$316$		0			0
$317$	−6.09820	+	10.5624i	−0.342509	+	0.593243i	−0.984898	−	0.173136i	$-0.944610\pi$
$317$	−6.09820	+	10.5624i	−0.342509	+	0.593243i	0.642389	+	0.766379i	$0.277943\pi$
$318$		0			0
$319$	6.57234	+	11.3836i	0.367981	+	0.637361i
$320$		0			0
$321$	1.07970	−	5.23582i	0.0602631	−	0.292235i
$322$		0			0
$323$	−38.3287			−2.13267
$324$		0			0
$325$	−5.95853	+	10.3205i	−0.330520	+	0.572477i
$326$		0			0
$327$	−3.76145	+	1.24748i	−0.208009	+	0.0689860i
$328$		0			0
$329$	3.74721	−	5.97654i	0.206590	−	0.329497i
$330$		0			0
$331$	−7.83310	+	13.5673i	−0.430546	+	0.745728i	−0.996920	−	0.0784202i	$-0.975012\pi$
$331$	−7.83310	+	13.5673i	−0.430546	+	0.745728i	0.566374	+	0.824148i	$0.308346\pi$
$332$		0			0
$333$	−2.40545	+	1.79272i	−0.131818	+	0.0982402i
$334$		0			0
$335$	−7.98398	−	13.8287i	−0.436211	−	0.755540i
$336$		0			0
$337$	−4.21201	+	7.29541i	−0.229443	+	0.397406i	−0.957643	−	0.287958i	$-0.907024\pi$
$337$	−4.21201	+	7.29541i	−0.229443	+	0.397406i	0.728200	+	0.685364i	$0.240357\pi$
$338$		0			0
$339$	31.9999	−	10.6128i	1.73800	−	0.576407i
$340$		0			0
$341$	−2.15383	−	3.73054i	−0.116636	−	0.202020i
$342$		0			0
$343$	18.4098	+	2.01993i	0.994035	+	0.109066i
$344$		0			0
$345$	0.617454	+	0.549202i	0.0332426	+	0.0295681i
$346$		0			0
$347$	0.283662	+	0.491316i	0.0152277	+	0.0263752i	0.873539	−	0.486754i	$-0.161819\pi$
$347$	0.283662	+	0.491316i	0.0152277	+	0.0263752i	−0.858311	+	0.513130i	$0.828486\pi$
$348$		0			0
$349$	−0.00364189	−	0.00630794i	−0.000194946	−	0.000337656i	0.865928	−	0.500169i	$-0.166729\pi$
$349$	−0.00364189	−	0.00630794i	−0.000194946	−	0.000337656i	−0.866123	+	0.499831i	$0.833395\pi$
$350$		0			0
$351$	−10.5822	−	22.6478i	−0.564835	−	1.20885i
$352$		0			0
$353$	6.65383			0.354148			0.177074	−	0.984198i	$-0.443337\pi$
$353$	6.65383			0.354148			0.177074	+	0.984198i	$0.443337\pi$
$354$		0			0
$355$	−20.2051			−1.07237
$356$		0			0
$357$	23.7527	−	6.92820i	1.25713	−	0.366679i
$358$		0			0
$359$	0.398568	+	0.690339i	0.0210356	+	0.0364347i	0.876352	−	0.481672i	$-0.159970\pi$
$359$	0.398568	+	0.690339i	0.0210356	+	0.0364347i	−0.855316	+	0.518107i	$0.826637\pi$
$360$		0			0
$361$	−15.6971	+	27.1881i	−0.826162	+	1.43095i
$362$		0			0
$363$	10.9709	+	9.75822i	0.575823	+	0.512174i
$364$		0			0
$365$	12.7491	−	22.0820i	0.667317	−	1.15583i
$366$		0			0
$367$	15.4327			0.805579			0.402790	−	0.915293i	$-0.368041\pi$
$367$	15.4327			0.805579			0.402790	+	0.915293i	$0.368041\pi$
$368$		0			0
$369$	16.1909	+	6.97418i	0.842864	+	0.363061i
$370$		0			0
$371$	6.87085	−	10.9585i	0.356717	−	0.568939i
$372$		0			0
$373$	10.2422			0.530321			0.265160	−	0.964204i	$-0.414575\pi$
$373$	10.2422			0.530321			0.265160	+	0.964204i	$0.414575\pi$
$374$		0			0
$375$	15.3702	+	13.6712i	0.793712	+	0.705977i
$376$		0			0
$377$	39.8131			2.05048
$378$		0			0
$379$	−25.0087			−1.28461			−0.642304	−	0.766450i	$-0.722021\pi$
$379$	−25.0087			−1.28461			−0.642304	+	0.766450i	$0.722021\pi$
$380$		0			0
$381$	−17.3938	−	15.4711i	−0.891109	−	0.792608i
$382$		0			0
$383$	6.26695			0.320226			0.160113	−	0.987099i	$-0.448814\pi$
$383$	6.26695			0.320226			0.160113	+	0.987099i	$0.448814\pi$
$384$		0			0
$385$	6.67054	+	0.243101i	0.339962	+	0.0123896i
$386$		0			0
$387$	−4.00797	+	2.98704i	−0.203737	+	0.151840i
$388$		0			0
$389$	−21.6342			−1.09690			−0.548448	−	0.836185i	$-0.684781\pi$
$389$	−21.6342			−1.09690			−0.548448	+	0.836185i	$0.684781\pi$
$390$		0			0
$391$	0.810892	−	1.40451i	0.0410086	−	0.0710290i
$392$		0			0
$393$	−4.11126	−	3.65682i	−0.207386	−	0.184462i
$394$		0			0
$395$	6.66071	−	11.5367i	0.335137	−	0.580473i
$396$		0			0
$397$	2.05308	+	3.55605i	0.103041	+	0.178473i	0.912936	−	0.408102i	$-0.133809\pi$
$397$	2.05308	+	3.55605i	0.103041	+	0.178473i	−0.809895	+	0.586575i	$0.800476\pi$
$398$		0			0
$399$	7.72617	−	31.6004i	0.386792	−	1.58200i
$400$		0			0
$401$	16.7417			0.836041			0.418021	−	0.908438i	$-0.362724\pi$
$401$	16.7417			0.836041			0.418021	+	0.908438i	$0.362724\pi$
$402$		0			0
$403$	−13.0472			−0.649926
$404$		0			0
$405$	−13.9065	+	3.31105i	−0.691022	+	0.164527i
$406$		0			0
$407$	0.794182	+	1.37556i	0.0393661	+	0.0681842i
$408$		0			0
$409$	4.38255	+	7.59079i	0.216703	+	0.375341i	0.953798	−	0.300449i	$-0.0971364\pi$
$409$	4.38255	+	7.59079i	0.216703	+	0.375341i	−0.737095	+	0.675789i	$0.763803\pi$
$410$		0			0
$411$	27.5185	+	24.4767i	1.35739	+	1.20735i
$412$		0			0
$413$	8.02221	+	15.1431i	0.394747	+	0.745144i
$414$		0			0
$415$	−1.87890	−	3.25436i	−0.0922318	−	0.159750i
$416$		0			0
$417$	21.4592	−	7.11695i	1.05086	−	0.348518i
$418$		0			0
$419$	0.210149	−	0.363988i	0.0102664	−	0.0177820i	−0.860847	−	0.508865i	$-0.830065\pi$
$419$	0.210149	−	0.363988i	0.0102664	−	0.0177820i	0.871113	+	0.491083i	$0.163399\pi$
$420$		0			0
$421$	3.28799	+	5.69497i	0.160247	+	0.277556i	0.934957	−	0.354761i	$-0.115438\pi$
$421$	3.28799	+	5.69497i	0.160247	+	0.277556i	−0.774710	+	0.632316i	$0.782104\pi$
$422$		0			0
$423$	7.34610	+	3.16431i	0.357179	+	0.153854i
$424$		0			0
$425$	6.68725	−	11.5827i	0.324379	−	0.561841i
$426$		0			0
$427$	6.29232	−	10.0358i	0.304507	−	0.485667i
$428$		0			0
$429$	−12.5625	+	4.16635i	−0.606524	+	0.201154i
$430$		0			0
$431$	−11.0439	+	19.1287i	−0.531968	+	0.921395i	0.467336	+	0.884080i	$0.345214\pi$
$431$	−11.0439	+	19.1287i	−0.531968	+	0.921395i	−0.999304	+	0.0373155i	$0.988119\pi$
$432$		0			0
$433$	−9.43268			−0.453306			−0.226653	−	0.973976i	$-0.572778\pi$
$433$	−9.43268			−0.453306			−0.226653	+	0.973976i	$0.572778\pi$
$434$		0			0
$435$	4.59820	−	22.2981i	0.220467	−	1.06911i
$436$		0			0
$437$	−1.06615	−	1.84663i	−0.0510010	−	0.0883363i
$438$		0			0
$439$	−15.6032	+	27.0256i	−0.744701	+	1.28986i	0.205634	+	0.978629i	$0.434074\pi$
$439$	−15.6032	+	27.0256i	−0.744701	+	1.28986i	−0.950334	+	0.311231i	$0.899259\pi$
$440$		0			0
$441$	0.924016	+	20.9797i	0.0440007	+	0.999031i
$442$		0			0
$443$	6.52723	−	11.3055i	0.310118	−	0.537140i	−0.668270	−	0.743919i	$-0.732965\pi$
$443$	6.52723	−	11.3055i	0.310118	−	0.537140i	0.978388	+	0.206779i	$0.0662981\pi$
$444$		0			0
$445$	2.54944	+	4.41576i	0.120855	+	0.209327i
$446$		0			0
$447$	−6.74110	−	5.99596i	−0.318843	−	0.283599i
$448$		0			0
$449$	−9.91706			−0.468015			−0.234008	−	0.972235i	$-0.575184\pi$
$449$	−9.91706			−0.468015			−0.234008	+	0.972235i	$0.575184\pi$
$450$		0			0
$451$	4.66690	−	8.08330i	0.219756	−	0.380628i
$452$		0			0
$453$	−0.676728	−	0.601924i	−0.0317955	−	0.0282809i
$454$		0			0
$455$	10.7396	−	17.1290i	0.503482	−	0.803019i
$456$		0			0
$457$	12.2615	−	21.2375i	0.573566	−	0.993446i	−0.422629	−	0.906303i	$-0.638893\pi$
$457$	12.2615	−	21.2375i	0.573566	−	0.993446i	0.996196	−	0.0871436i	$-0.0277739\pi$
$458$		0			0
$459$	11.8764	+	25.4176i	0.554341	+	1.18639i
$460$		0			0
$461$	1.75526	+	3.04020i	0.0817506	+	0.141596i	0.904002	−	0.427528i	$-0.140616\pi$
$461$	1.75526	+	3.04020i	0.0817506	+	0.141596i	−0.822251	+	0.569125i	$0.807282\pi$
$462$		0			0
$463$	−8.69413	+	15.0587i	−0.404050	+	0.699836i	−0.994210	−	0.107451i	$-0.965731\pi$
$463$	−8.69413	+	15.0587i	−0.404050	+	0.699836i	0.590160	+	0.807286i	$0.299065\pi$
$464$		0			0
$465$	−1.50688	+	7.30733i	−0.0698798	+	0.338869i
$466$		0			0
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	0.668370	−	0.743829i	$-0.266992\pi$
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	−0.978360	+	0.206911i	$0.933659\pi$
$468$		0			0
$469$	−12.4512	−	23.5036i	−0.574945	−	1.08529i
$470$		0			0
$471$	−3.10074	+	15.0365i	−0.142875	+	0.692844i
$472$		0			0
$473$	1.32327	+	2.29197i	0.0608441	+	0.105385i
$474$		0			0
$475$	−8.79232	−	15.2287i	−0.403419	−	0.698743i
$476$		0			0
$477$	13.4697	+	5.80205i	0.616737	+	0.265658i
$478$		0			0
$479$	−20.8058			−0.950641			−0.475321	−	0.879813i	$-0.657668\pi$
$479$	−20.8058			−0.950641			−0.475321	+	0.879813i	$0.657668\pi$
$480$		0			0
$481$	4.81089			0.219358
$482$		0			0
$483$	0.994499	+	0.951662i	0.0452513	+	0.0433021i
$484$		0			0
$485$	1.13093	+	1.95882i	0.0513528	+	0.0889456i
$486$		0			0
$487$	−16.2472	+	28.1410i	−0.736231	+	1.27519i	0.217950	+	0.975960i	$0.430063\pi$
$487$	−16.2472	+	28.1410i	−0.736231	+	1.27519i	−0.954181	+	0.299230i	$0.903270\pi$
$488$		0			0
$489$	−7.68292	+	37.2569i	−0.347434	+	1.68481i
$490$		0			0
$491$	9.66071	−	16.7328i	0.435982	−	0.755142i	−0.561394	−	0.827549i	$-0.689735\pi$
$491$	9.66071	−	16.7328i	0.435982	−	0.755142i	0.997375	+	0.0724067i	$0.0230679\pi$
$492$		0			0
$493$	−44.6822			−2.01238
$494$		0			0
$495$	0.882546	+	7.51707i	0.0396675	+	0.337867i
$496$		0			0
$497$	−33.6334	−	1.22573i	−1.50866	−	0.0549816i
$498$		0			0
$499$	11.1506			0.499169			0.249585	−	0.968353i	$-0.419706\pi$
$499$	11.1506			0.499169			0.249585	+	0.968353i	$0.419706\pi$
$500$		0			0
$501$	5.42580	−	1.79947i	0.242407	−	0.0803942i
$502$		0			0
$503$	40.7651			1.81763			0.908813	−	0.417204i	$-0.136990\pi$
$503$	40.7651			1.81763			0.908813	+	0.417204i	$0.136990\pi$
$504$		0			0
$505$	19.1135			0.850537
$506$		0			0
$507$	−3.54875	+	17.2090i	−0.157606	+	0.764279i
$508$		0			0
$509$	1.44506			0.0640510			0.0320255	−	0.999487i	$-0.489804\pi$
$509$	1.44506			0.0640510			0.0320255	+	0.999487i	$0.489804\pi$
$510$		0			0
$511$	22.5617	−	35.9844i	0.998073	−	1.59186i
$512$		0			0
$513$	36.7490	+	3.18650i	1.62251	+	0.140687i
$514$		0			0
$515$	9.68725			0.426871
$516$		0			0
$517$	2.11745	−	3.66754i	0.0931255	−	0.161298i
$518$		0			0
$519$	31.4127	−	10.4180i	1.37887	−	0.457301i
$520$		0			0
$521$	9.64214	−	16.7007i	0.422430	−	0.731670i	−0.573747	−	0.819033i	$-0.694511\pi$
$521$	9.64214	−	16.7007i	0.422430	−	0.731670i	0.996177	+	0.0873630i	$0.0278440\pi$
$522$		0			0
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	0.918173	+	0.396180i	$0.129665\pi$
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	−0.115984	+	0.993251i	$0.537002\pi$
$524$		0			0
$525$	8.20141	+	7.84814i	0.357939	+	0.342521i
$526$		0			0
$527$	14.6428			0.637851
$528$		0			0
$529$	−22.9098			−0.996077
$530$		0			0
$531$	−15.5803	+	11.6116i	−0.676128	+	0.503900i
$532$		0			0
$533$	−14.1353	−	24.4830i	−0.612266	−	1.06048i
$534$		0			0
$535$	2.45125	+	4.24568i	0.105977	+	0.183557i
$536$		0			0
$537$	−26.4258	+	8.76411i	−1.14036	+	0.378199i
$538$		0			0
$539$	11.0891	+	0.809332i	0.477639	+	0.0348604i
$540$		0			0
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	0.828967	−	0.559298i	$-0.188929\pi$
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	−0.898849	+	0.438258i	$0.855596\pi$
$542$		0			0
$543$	−10.4222	−	9.27012i	−0.447258	−	0.397819i
$544$		0			0
$545$	1.81708	−	3.14728i	0.0778352	−	0.134815i
$546$		0			0
$547$	2.95853	+	5.12432i	0.126498	+	0.219100i	0.922317	−	0.386433i	$-0.126293\pi$
$547$	2.95853	+	5.12432i	0.126498	+	0.219100i	−0.795820	+	0.605534i	$0.792960\pi$
$548$		0			0
$549$	12.3356	+	5.31351i	0.526470	+	0.226775i
$550$		0			0
$551$	−29.3738	+	50.8769i	−1.25137	+	2.16743i
$552$		0			0
$553$	11.7873	−	18.7999i	0.501247	−	0.799454i
$554$		0			0
$555$	0.555632	−	2.69443i	0.0235853	−	0.114372i
$556$		0			0
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	−0.456235	−	0.889859i	$-0.650802\pi$
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	0.998758	−	0.0498188i	$-0.0158644\pi$
$558$		0			0
$559$	8.01594			0.339038
$560$		0			0
$561$	14.0989	−	4.67589i	0.595255	−	0.197416i
$562$		0			0
$563$	−23.3189	−	40.3895i	−0.982773	−	1.70221i	−0.651443	−	0.758698i	$-0.725836\pi$
$563$	−23.3189	−	40.3895i	−0.982773	−	1.70221i	−0.331330	−	0.943515i	$-0.607497\pi$
$564$		0			0
$565$	−15.4585	+	26.7750i	−0.650345	+	1.12643i
$566$		0			0
$567$	−23.3497	+	4.66795i	−0.980597	+	0.196035i
$568$		0			0
$569$	−15.5989	+	27.0181i	−0.653939	+	1.13266i	0.328219	+	0.944602i	$0.393551\pi$
$569$	−15.5989	+	27.0181i	−0.653939	+	1.13266i	−0.982159	+	0.188054i	$0.939782\pi$
$570$		0			0
$571$	−7.83812	−	13.5760i	−0.328015	−	0.568139i	0.654103	−	0.756406i	$-0.273046\pi$
$571$	−7.83812	−	13.5760i	−0.328015	−	0.568139i	−0.982118	+	0.188267i	$0.939713\pi$
$572$		0			0
$573$	39.3948	−	13.0653i	1.64574	−	0.545811i
$574$		0			0
$575$	0.744051			0.0310291
$576$		0			0
$577$	6.99567	−	12.1169i	0.291234	−	0.504431i	−0.682868	−	0.730542i	$-0.739268\pi$
$577$	6.99567	−	12.1169i	0.291234	−	0.504431i	0.974102	+	0.226110i	$0.0726010\pi$
$578$		0			0
$579$	−3.41597	+	16.5651i	−0.141963	+	0.688422i
$580$		0			0
$581$	−2.93021	−	5.53120i	−0.121565	−	0.229473i
$582$		0			0
$583$	3.88255	−	6.72477i	0.160799	−	0.278511i
$584$		0			0
$585$	21.0542	+	9.06902i	0.870483	+	0.374958i
$586$		0			0
$587$	−1.44801	−	2.50803i	−0.0597658	−	0.103517i	0.834594	−	0.550865i	$-0.185702\pi$
$587$	−1.44801	−	2.50803i	−0.0597658	−	0.103517i	−0.894360	+	0.447348i	$0.852369\pi$
$588$		0			0
$589$	9.62612	−	16.6729i	0.396637	−	0.686996i
$590$		0			0
$591$	23.6105	+	21.0007i	0.971206	+	0.863852i
$592$		0			0
$593$	−2.04394	−	3.54021i	−0.0839346	−	0.145379i	0.821002	−	0.570925i	$-0.193415\pi$
$593$	−2.04394	−	3.54021i	−0.0839346	−	0.145379i	−0.904937	+	0.425546i	$0.860082\pi$
$594$		0			0
$595$	−12.0531	+	19.2238i	−0.494128	+	0.788100i
$596$		0			0
$597$	29.7545	−	9.86807i	1.21777	−	0.403873i
$598$		0			0
$599$	−9.88255	−	17.1171i	−0.403790	−	0.699385i	0.590390	−	0.807118i	$-0.298974\pi$
$599$	−9.88255	−	17.1171i	−0.403790	−	0.699385i	−0.994180	+	0.107734i	$0.965641\pi$
$600$		0			0
$601$	−13.4320	−	23.2649i	−0.547902	−	0.948994i	−0.998418	−	0.0562261i	$-0.982093\pi$
$601$	−13.4320	−	23.2649i	−0.547902	−	0.948994i	0.450516	−	0.892768i	$-0.351240\pi$
$602$		0			0
$603$	24.1822	−	18.0223i	0.984773	−	0.733926i
$604$		0			0
$605$	−13.4647			−0.547419
$606$		0			0
$607$	15.2422			0.618661			0.309331	−	0.950955i	$-0.399895\pi$
$607$	15.2422			0.618661			0.309331	+	0.950955i	$0.399895\pi$
$608$		0			0
$609$	9.00688	−	36.8385i	0.364977	−	1.49277i
$610$		0			0
$611$	−6.41342	−	11.1084i	−0.259459	−	0.449396i
$612$		0			0
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	−0.892189	−	0.451662i	$-0.850831\pi$
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	0.837246	+	0.546827i	$0.184165\pi$
$614$		0			0
$615$	−15.3447	+	5.08907i	−0.618759	+	0.205211i
$616$		0			0
$617$	−9.21812	+	15.9663i	−0.371108	+	0.642777i	−0.989736	−	0.142906i	$-0.954355\pi$
$617$	−9.21812	+	15.9663i	−0.371108	+	0.642777i	0.618629	+	0.785684i	$0.287689\pi$
$618$		0			0
$619$	−0.107546			−0.00432262			−0.00216131	−	0.999998i	$-0.500688\pi$
$619$	−0.107546			−0.00432262			−0.00216131	+	0.999998i	$0.500688\pi$
$620$		0			0
$621$	−0.894237	+	1.27921i	−0.0358845	+	0.0513328i
$622$		0			0
$623$	3.97593	+	7.50516i	0.159292	+	0.300688i
$624$		0			0
$625$	−6.47848			−0.259139
$626$		0			0
$627$	3.94437	−	19.1275i	0.157523	−	0.763878i
$628$		0			0
$629$	−5.39926			−0.215282
$630$		0			0
$631$	−35.7266			−1.42225			−0.711126	−	0.703064i	$-0.751815\pi$
$631$	−35.7266			−1.42225			−0.711126	+	0.703064i	$0.751815\pi$
$632$		0			0
$633$	0.546489	−	0.181243i	0.0217210	−	0.00720376i
$634$		0			0
$635$	21.3475			0.847152
$636$		0			0
$637$	18.9164	−	27.8615i	0.749494	−	1.10391i
$638$		0			0
$639$	−4.44987	−	37.9017i	−0.176034	−	1.49937i
$640$		0			0
$641$	17.3128			0.683813			0.341906	−	0.939734i	$-0.388927\pi$
$641$	17.3128			0.683813			0.341906	+	0.939734i	$0.388927\pi$
$642$		0			0
$643$	−14.4821	+	25.0838i	−0.571119	+	0.989207i	0.425332	+	0.905037i	$0.360157\pi$
$643$	−14.4821	+	25.0838i	−0.571119	+	0.989207i	−0.996451	+	0.0841700i	$0.973176\pi$
$644$		0			0
$645$	0.925798	−	4.48949i	0.0364533	−	0.176773i
$646$		0			0
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	−0.890056	−	0.455851i	$-0.849335\pi$
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	0.839807	+	0.542886i	$0.182668\pi$
$648$		0			0
$649$	5.14400	+	8.90966i	0.201920	+	0.349735i
$650$		0			0
$651$	−2.95165	+	12.0724i	−0.115684	+	0.473154i
$652$		0			0
$653$	29.9766			1.17308			0.586538	−	0.809922i	$-0.300491\pi$
$653$	29.9766			1.17308			0.586538	+	0.809922i	$0.300491\pi$
$654$		0			0
$655$	5.04580			0.197156
$656$		0			0
$657$	44.2304	+	19.0521i	1.72559	+	0.743294i
$658$		0			0
$659$	7.63162	+	13.2183i	0.297286	+	0.514914i	0.975514	−	0.219937i	$-0.0705853\pi$
$659$	7.63162	+	13.2183i	0.297286	+	0.514914i	−0.678228	+	0.734851i	$0.737252\pi$
$660$		0			0
$661$	13.6261	+	23.6011i	0.529994	+	0.917977i	0.999388	+	0.0349881i	$0.0111393\pi$
$661$	13.6261	+	23.6011i	0.529994	+	0.917977i	−0.469393	+	0.882989i	$0.655527\pi$
$662$		0			0
$663$	9.08650	−	44.0633i	0.352891	−	1.71128i
$664$		0			0
$665$	13.9654	+	26.3618i	0.541555	+	1.02227i
$666$		0			0
$667$	−1.24288	−	2.15273i	−0.0481245	−	0.0833541i
$668$		0			0
$669$	−2.21517	+	10.7420i	−0.0856433	+	0.415311i
$670$		0			0
$671$	3.55563	−	6.15854i	0.137264	−	0.237748i
$672$		0			0
$673$	23.2280	+	40.2320i	0.895372	+	1.55083i	0.833344	+	0.552755i	$0.186423\pi$
$673$	23.2280	+	40.2320i	0.895372	+	1.55083i	0.0620280	+	0.998074i	$0.480243\pi$
$674$		0			0
$675$	−7.37457	+	10.5493i	−0.283847	+	0.406044i
$676$		0			0
$677$	−2.54944	+	4.41576i	−0.0979830	+	0.169712i	−0.910850	−	0.412738i	$-0.864572\pi$
$677$	−2.54944	+	4.41576i	−0.0979830	+	0.169712i	0.812867	+	0.582450i	$0.197906\pi$
$678$		0			0
$679$	1.76371	+	3.32927i	0.0676852	+	0.127766i
$680$		0			0
$681$	−30.1661	−	26.8317i	−1.15597	−	1.02819i
$682$		0			0
$683$	7.77197	−	13.4614i	0.297386	−	0.515088i	−0.678151	−	0.734923i	$-0.737218\pi$
$683$	7.77197	−	13.4614i	0.297386	−	0.515088i	0.975537	+	0.219835i	$0.0705518\pi$
$684$		0			0
$685$	−33.7738			−1.29043
$686$		0			0
$687$	6.41164	+	5.70291i	0.244619	+	0.217580i
$688$		0			0
$689$	−11.7596	−	20.3682i	−0.448005	−	0.775967i
$690$		0			0
$691$	11.6483	−	20.1755i	0.443123	−	0.767512i	−0.554796	−	0.831986i	$-0.687204\pi$
$691$	11.6483	−	20.1755i	0.443123	−	0.767512i	0.997919	+	0.0644744i	$0.0205371\pi$
$692$		0			0
$693$	1.01307	+	12.5665i	0.0384833	+	0.477361i
$694$		0			0
$695$	−10.3665	+	17.9553i	−0.393225	+	0.681085i
$696$		0			0
$697$	15.8640	+	27.4772i	0.600891	+	1.04077i
$698$		0			0
$699$	−4.99381	+	24.2165i	−0.188883	+	0.915954i
$700$		0			0
$701$	−45.6464			−1.72404			−0.862020	−	0.506874i	$-0.830801\pi$
$701$	−45.6464			−1.72404			−0.862020	+	0.506874i	$0.830801\pi$
$702$		0			0
$703$	−3.54944	+	6.14781i	−0.133870	+	0.231869i
$704$		0			0
$705$	−6.96217	+	2.30900i	−0.262211	+	0.0869621i
$706$		0			0
$707$	31.8163	+	1.15951i	1.19658	+	0.0436079i
$708$		0			0
$709$	−9.00069	+	15.5897i	−0.338028	+	0.585482i	−0.984062	−	0.177827i	$-0.943093\pi$
$709$	−9.00069	+	15.5897i	−0.338028	+	0.585482i	0.646034	+	0.763309i	$0.276427\pi$
$710$		0			0
$711$	23.1080	+	9.95371i	0.866619	+	0.373293i
$712$		0			0
$713$	0.407305	+	0.705474i	0.0152537	+	0.0264202i
$714$		0			0
$715$	6.06870	−	10.5113i	0.226957	−	0.393100i
$716$		0			0
$717$	8.17928	−	2.71266i	0.305461	−	0.101306i
$718$		0			0
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	−0.972595	−	0.232506i	$-0.925307\pi$
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	0.284941	−	0.958545i	$-0.408026\pi$
$720$		0			0
$721$	16.1254	+	0.587674i	0.600542	+	0.0218861i
$722$		0			0
$723$	16.8244	+	14.9646i	0.625705	+	0.556541i
$724$		0			0
$725$	−10.2498	−	17.7531i	−0.380666	−	0.659334i
$726$		0			0
$727$	−15.2429	−	26.4014i	−0.565327	−	0.979175i	−0.997019	−	0.0771543i	$-0.975417\pi$
$727$	−15.2429	−	26.4014i	−0.565327	−	0.979175i	0.431692	−	0.902021i	$-0.357917\pi$
$728$		0			0
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$		0			0
$731$	−8.99628			−0.332739
$732$		0			0
$733$	6.15059			0.227177			0.113589	−	0.993528i	$-0.463765\pi$
$733$	6.15059			0.227177			0.113589	+	0.993528i	$0.463765\pi$
$734$		0			0
$735$	−13.4196	−	13.8123i	−0.494990	−	0.509475i
$736$		0			0
$737$	−7.98398	−	13.8287i	−0.294094	−	0.509385i
$738$		0			0
$739$	20.3912	−	35.3186i	0.750103	−	1.29922i	−0.197670	−	0.980269i	$-0.563337\pi$
$739$	20.3912	−	35.3186i	0.750103	−	1.29922i	0.947772	−	0.318947i	$-0.103329\pi$
$740$		0			0
$741$	−44.1989	−	39.3132i	−1.62369	−	1.44421i
$742$		0			0
$743$	−7.25271	+	12.5621i	−0.266076	+	0.460858i	−0.967845	−	0.251547i	$-0.919061\pi$
$743$	−7.25271	+	12.5621i	−0.266076	+	0.460858i	0.701769	+	0.712405i	$0.252394\pi$
$744$		0			0
$745$	8.27342			0.303115
$746$		0			0
$747$	5.69089	−	4.24127i	0.208219	−	0.155180i
$748$		0			0
$749$	3.82279	+	7.21608i	0.139682	+	0.263670i
$750$		0			0
$751$	−4.18911			−0.152863			−0.0764314	−	0.997075i	$-0.524353\pi$
$751$	−4.18911			−0.152863			−0.0764314	+	0.997075i	$0.524353\pi$
$752$		0			0
$753$	3.14833	+	2.80032i	0.114731	+	0.102049i
$754$		0			0
$755$	0.830556			0.0302270
$756$		0			0
$757$	2.38688			0.0867525			0.0433763	−	0.999059i	$-0.486189\pi$
$757$	2.38688			0.0867525			0.0433763	+	0.999059i	$0.486189\pi$
$758$		0			0
$759$	0.617454	+	0.549202i	0.0224122	+	0.0199348i
$760$		0			0
$761$	3.63416			0.131738			0.0658692	−	0.997828i	$-0.479018\pi$
$761$	3.63416			0.131738			0.0658692	+	0.997828i	$0.479018\pi$
$762$		0			0
$763$	3.21565	−	5.12874i	0.116414	−	0.185673i
$764$		0			0
$765$	−23.6291	−	10.1781i	−0.854311	−	0.367992i
$766$		0			0
$767$	31.1606			1.12515
$768$		0			0
$769$	−19.9672	+	34.5842i	−0.720035	+	1.24714i	0.240950	+	0.970538i	$0.422541\pi$
$769$	−19.9672	+	34.5842i	−0.720035	+	1.24714i	−0.960985	+	0.276600i	$0.910792\pi$
$770$		0			0
$771$	1.27816	+	1.13688i	0.0460318	+	0.0409436i
$772$		0			0
$773$	18.0698	−	31.2978i	0.649925	−	1.12570i	−0.333215	−	0.942851i	$-0.608133\pi$
$773$	18.0698	−	31.2978i	0.649925	−	1.12570i	0.983140	−	0.182853i	$-0.0585332\pi$
$774$		0			0
$775$	3.35896	+	5.81788i	0.120657	+	0.208985i
$776$		0			0
$777$	1.08836	−	4.45146i	0.0390448	−	0.159695i
$778$		0			0
$779$	41.7156			1.49462
$780$		0			0
$781$	−20.2051			−0.722994
$782$		0			0
$783$	42.8406	+	3.71470i	1.53100	+	0.132753i
$784$		0			0
$785$	−7.03961	−	12.1930i	−0.251254	−	0.435186i
$786$		0			0
$787$	−22.3189	−	38.6574i	−0.795582	−	1.37799i	−0.922469	−	0.386071i	$-0.873832\pi$
$787$	−22.3189	−	38.6574i	−0.795582	−	1.37799i	0.126888	−	0.991917i	$-0.459501\pi$
$788$		0			0
$789$	22.2410	+	19.7826i	0.791801	+	0.704278i
$790$		0			0
$791$	−27.3566	+	43.6319i	−0.972689	+	1.55137i
$792$		0			0
$793$	−10.7694	−	18.6532i	−0.382433	−	0.662394i
$794$		0			0
$795$	−12.7658	+	4.23377i	−0.452756	+	0.150156i
$796$		0			0
$797$	26.2836	−	45.5245i	0.931012	−	1.61256i	0.149418	−	0.988774i	$-0.452260\pi$
$797$	26.2836	−	45.5245i	0.931012	−	1.61256i	0.781595	−	0.623786i	$-0.214407\pi$
$798$		0			0
$799$	7.19777	+	12.4669i	0.254639	+	0.441047i
$800$		0			0
$801$	−7.72184	+	5.75488i	−0.272838	+	0.203339i
$802$		0			0
$803$	12.7491	−	22.0820i	0.449905	−	0.779258i
$804$		0			0
$805$	−1.26145	−	0.0459722i	−0.0444603	−	0.00162031i
$806$		0			0
$807$	−37.6552	+	12.4883i	−1.32553	+	0.439611i
$808$		0			0
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	−0.706042	−	0.708170i	$-0.749521\pi$
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	0.966314	+	0.257365i	$0.0828544\pi$
$810$		0			0
$811$	−27.0704			−0.950571			−0.475285	−	0.879832i	$-0.657655\pi$
$811$	−27.0704			−0.950571			−0.475285	+	0.879832i	$0.657655\pi$
$812$		0			0
$813$	−4.89995	+	23.7614i	−0.171849	+	0.833348i
$814$		0			0
$815$	−17.4425	−	30.2113i	−0.610984	−	1.05826i
$816$		0			0
$817$	−5.91411	+	10.2435i	−0.206908	+	0.358376i
$818$		0			0
$819$	34.4967	+	16.3736i	1.20541	+	0.572139i
$820$		0			0
$821$	−21.9091	+	37.9477i	−0.764632	+	1.32438i	0.175808	+	0.984424i	$0.443746\pi$
$821$	−21.9091	+	37.9477i	−0.764632	+	1.32438i	−0.940441	+	0.339958i	$0.889587\pi$
$822$		0			0
$823$	15.6712	+	27.1434i	0.546265	+	0.946158i	0.998526	+	0.0542727i	$0.0172840\pi$
$823$	15.6712	+	27.1434i	0.546265	+	0.946158i	−0.452262	+	0.891885i	$0.649383\pi$
$824$		0			0
$825$	5.09201	+	4.52915i	0.177281	+	0.157685i
$826$		0			0
$827$	14.7665			0.513480			0.256740	−	0.966480i	$-0.417352\pi$
$827$	14.7665			0.513480			0.256740	+	0.966480i	$0.417352\pi$
$828$		0			0
$829$	−15.0036	+	25.9871i	−0.521098	+	0.902568i	0.478601	+	0.878033i	$0.341144\pi$
$829$	−15.0036	+	25.9871i	−0.521098	+	0.902568i	−0.999699	+	0.0245357i	$0.992189\pi$
$830$		0			0
$831$	−36.6192	−	32.5715i	−1.27031	−	1.12989i
$832$		0			0
$833$	−21.2298	+	31.2689i	−0.735569	+	1.08340i
$834$		0			0
$835$	−2.62110	+	4.53987i	−0.0907068	+	0.157109i
$836$		0			0
$837$	−14.0393	−	1.21735i	−0.485270	−	0.0420777i
$838$		0			0
$839$	−18.0167	−	31.2059i	−0.622006	−	1.07735i	−0.989112	−	0.147167i	$-0.952985\pi$
$839$	−18.0167	−	31.2059i	−0.622006	−	1.07735i	0.367106	−	0.930179i	$-0.380349\pi$
$840$		0			0
$841$	−19.7429	+	34.1957i	−0.680789	+	1.17916i
$842$		0			0
$843$	−6.15521	+	29.8485i	−0.211997	+	1.02804i
$844$		0			0
$845$	−8.05673	−	13.9547i	−0.277160	−	0.480055i
$846$		0			0
$847$	−22.4134	−	0.816833i	−0.770134	−	0.0280667i
$848$		0			0
$849$	−6.47957	+	31.4215i	−0.222378	+	1.07838i
$850$		0			0
$851$	−0.150186	−	0.260130i	−0.00514831	−	0.00891713i
$852$		0			0
$853$	−12.2658	−	21.2450i	−0.419972	−	0.727413i	0.575964	−	0.817475i	$-0.304627\pi$
$853$	−12.2658	−	21.2450i	−0.419972	−	0.727413i	−0.995936	+	0.0900617i	$0.971294\pi$
$854$		0			0
$855$	−27.1229	+	20.2140i	−0.927583	+	0.691303i
$856$		0			0
$857$	29.0480			0.992260			0.496130	−	0.868248i	$-0.334754\pi$
$857$	29.0480			0.992260			0.496130	+	0.868248i	$0.334754\pi$
$858$		0			0
$859$	−25.2953			−0.863064			−0.431532	−	0.902098i	$-0.642027\pi$
$859$	−25.2953			−0.863064			−0.431532	+	0.902098i	$0.642027\pi$
$860$		0			0
$861$	−25.8516	+	7.54041i	−0.881020	+	0.256976i
$862$		0			0
$863$	1.34981	+	2.33795i	0.0459482	+	0.0795846i	0.888085	−	0.459680i	$-0.152036\pi$
$863$	1.34981	+	2.33795i	0.0459482	+	0.0795846i	−0.842137	+	0.539264i	$0.818702\pi$
$864$		0			0
$865$	−15.1749	+	26.2836i	−0.515961	+	0.893671i
$866$		0			0
$867$	−4.25093	+	20.6141i	−0.144369	+	0.700091i
$868$		0			0
$869$	6.66071	−	11.5367i	0.225949	−	0.391355i
$870$		0			0
$871$	−48.3643			−1.63876
$872$		0			0
$873$	−3.42539	+	2.55286i	−0.115932	+	0.0864011i
$874$		0			0
$875$	−31.4010	−	1.14438i	−1.06155	−	0.0386870i
$876$		0			0
$877$	−11.0916			−0.374537			−0.187268	−	0.982309i	$-0.559963\pi$
$877$	−11.0916			−0.374537			−0.187268	+	0.982309i	$0.559963\pi$
$878$		0			0
$879$	23.1559	−	7.67965i	0.781029	−	0.259028i
$880$		0			0
$881$	−40.3942			−1.36091			−0.680457	−	0.732788i	$-0.738219\pi$
$881$	−40.3942			−1.36091			−0.680457	+	0.732788i	$0.738219\pi$
$882$		0			0
$883$	33.2581			1.11923			0.559613	−	0.828754i	$-0.310950\pi$
$883$	33.2581			1.11923			0.559613	+	0.828754i	$0.310950\pi$
$884$		0			0
$885$	3.59888	−	17.4521i	0.120975	−	0.586646i
$886$		0			0
$887$	−40.5672			−1.36211			−0.681056	−	0.732231i	$-0.738479\pi$
$887$	−40.5672			−1.36211			−0.681056	+	0.732231i	$0.738479\pi$
$888$		0			0
$889$	35.5352	+	1.29504i	1.19181	+	0.0434343i
$890$		0			0
$891$	−13.9065	+	3.31105i	−0.465887	+	0.110924i
$892$		0			0
$893$	18.9271			0.633371
$894$		0			0
$895$	12.7658	−	22.1110i	0.426713	−	0.739089i
$896$		0			0
$897$	2.37567	−	0.787890i	0.0793212	−	0.0263069i
$898$		0			0
$899$	11.2218	−	19.4367i	0.374267	−	0.648249i
$900$		0			0
$901$	13.1978	+	22.8592i	0.439681	+	0.761551i
$902$		0			0
$903$	1.81344	−	7.41705i	0.0603475	−	0.246824i
$904$		0			0
$905$	12.7912			0.425195
$906$		0			0
$907$	−30.1135			−0.999901			−0.499950	−	0.866054i	$-0.666648\pi$
$907$	−30.1135			−0.999901			−0.499950	+	0.866054i	$0.666648\pi$
$908$		0			0
$909$	4.20946	+	35.8540i	0.139619	+	1.18920i
$910$		0			0
$911$	−14.6113	−	25.3075i	−0.484093	−	0.838473i	0.515740	−	0.856745i	$-0.327517\pi$
$911$	−14.6113	−	25.3075i	−0.484093	−	0.838473i	−0.999833	+	0.0182717i	$0.994184\pi$
$912$		0			0
$913$	−1.87890	−	3.25436i	−0.0621826	−	0.107704i
$914$		0			0
$915$	−11.6909	+	3.87728i	−0.386489	+	0.128179i
$916$		0			0
$917$	8.39926	+	0.306102i	0.277368	+	0.0101084i
$918$		0			0
$919$	5.52359	+	9.56714i	0.182206	+	0.315591i	0.942632	−	0.333835i	$-0.108343\pi$
$919$	5.52359	+	9.56714i	0.182206	+	0.315591i	−0.760425	+	0.649426i	$0.775009\pi$
$920$		0			0
$921$	−7.57784	−	6.74021i	−0.249698	−	0.222097i
$922$		0			0
$923$	−30.5989	+	52.9988i	−1.00717	+	1.74448i
$924$		0			0
$925$	−1.23855	−	2.14523i	−0.0407233	−	0.0705348i
$926$		0			0
$927$	2.13348	+	18.1718i	0.0700725	+	0.596842i
$928$		0			0
$929$	21.1669	−	36.6621i	0.694463	−	1.20285i	−0.275898	−	0.961187i	$-0.588975\pi$
$929$	21.1669	−	36.6621i	0.694463	−	1.20285i	0.970361	−	0.241659i	$-0.0776915\pi$
$930$		0			0
$931$	21.6476	+	44.7291i	0.709473	+	1.46594i
$932$		0			0
$933$	0.283662	−	1.37556i	0.00928666	−	0.0450339i
$934$		0			0
$935$	−6.81089	+	11.7968i	−0.222740	+	0.385797i
$936$		0			0
$937$	−11.7651			−0.384349			−0.192174	−	0.981361i	$-0.561554\pi$
$937$	−11.7651			−0.384349			−0.192174	+	0.981361i	$0.561554\pi$
$938$		0			0
$939$	17.3869	−	5.76636i	0.567399	−	0.188178i
$940$		0			0
$941$	−7.28799	−	12.6232i	−0.237582	−	0.411504i	0.722438	−	0.691436i	$-0.243021\pi$
$941$	−7.28799	−	12.6232i	−0.237582	−	0.411504i	−0.960020	+	0.279932i	$0.909688\pi$
$942$		0			0
$943$	−0.882546	+	1.52861i	−0.0287397	+	0.0497785i
$944$		0			0
$945$	13.1545	−	17.4295i	0.427916	−	0.566981i
$946$		0			0
$947$	3.12178	−	5.40709i	0.101444	−	0.175707i	−0.810836	−	0.585274i	$-0.800987\pi$
$947$	3.12178	−	5.40709i	0.101444	−	0.175707i	0.912280	+	0.409567i	$0.134320\pi$
$948$		0			0
$949$	−38.6148	−	66.8828i	−1.25349	−	2.17111i
$950$		0			0
$951$	20.0508	−	6.64985i	0.650192	−	0.215636i
$952$		0			0
$953$	28.0173			0.907570			0.453785	−	0.891111i	$-0.350073\pi$
$953$	28.0173			0.907570			0.453785	+	0.891111i	$0.350073\pi$
$954$		0			0
$955$	−19.0309	+	32.9624i	−0.615825	+	1.06664i
$956$		0			0
$957$	4.59820	−	22.2981i	0.148639	−	0.720795i
$958$		0			0
$959$	−56.2199	−	2.04887i	−1.81544	−	0.0661616i
$960$		0			0
$961$	11.8225	−	20.4772i	0.381371	−	0.660554i
$962$		0			0
$963$	−7.42442	+	5.53322i	−0.239249	+	0.178306i
$964$		0			0
$965$	−7.75526	−	13.4325i	−0.249651	−	0.432408i
$966$		0			0
$967$	−15.7837	+	27.3381i	−0.507568	+	0.879134i	0.492393	+	0.870373i	$0.336122\pi$
$967$	−15.7837	+	27.3381i	−0.507568	+	0.879134i	−0.999962	+	0.00876132i	$0.997211\pi$
$968$		0			0
$969$	49.6043	+	44.1212i	1.59352	+	1.41738i
$970$		0			0
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	0.817196	−	0.576359i	$-0.195527\pi$
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	−0.907740	+	0.419533i	$0.862194\pi$
$972$		0			0
$973$	−18.3454	+	29.2596i	−0.588127	+	0.938021i
$974$		0			0
$975$	19.5916	−	6.49755i	0.627433	−	0.208088i
$976$		0			0
$977$	−3.24652	−	5.62314i	−0.103865	−	0.179900i	0.809409	−	0.587246i	$-0.199788\pi$
$977$	−3.24652	−	5.62314i	−0.103865	−	0.179900i	−0.913274	+	0.407346i	$0.866454\pi$
$978$		0			0
$979$	2.54944	+	4.41576i	0.0814805	+	0.141128i
$980$		0			0
$981$	6.30401	+	2.71543i	0.201272	+	0.0866971i
$982$		0			0
$983$	30.3063			0.966620			0.483310	−	0.875449i	$-0.339434\pi$
$983$	30.3063			0.966620			0.483310	+	0.875449i	$0.339434\pi$
$984$		0			0
$985$	−28.9774			−0.923298
$986$		0			0
$987$	−11.7293	+	3.42122i	−0.373349	+	0.108899i
$988$		0			0
$989$	−0.250241	−	0.433430i	−0.00795720	−	0.0137823i
$990$		0			0
$991$	−11.1669	+	19.3416i	−0.354728	+	0.614407i	−0.987071	−	0.160281i	$-0.948760\pi$
$991$	−11.1669	+	19.3416i	−0.354728	+	0.614407i	0.632343	+	0.774688i	$0.282093\pi$
$992$		0			0
$993$	25.7552	−	8.54170i	0.817316	−	0.271063i
$994$		0			0
$995$	−14.3738	+	24.8962i	−0.455680	+	0.789262i
$996$		0			0
$997$	−8.76509			−0.277593			−0.138797	−	0.990321i	$-0.544323\pi$
$997$	−8.76509			−0.277593			−0.138797	+	0.990321i	$0.544323\pi$
$998$		0			0
$999$	5.17673	+	0.448873i	0.163784	+	0.0142017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.h.193.1		6
3.2	odd	2		3024.2.t.h.1873.1		6
4.3	odd	2		126.2.h.d.67.3	yes	6
7.2	even	3		1008.2.q.g.625.3		6
9.2	odd	6		3024.2.q.g.2881.3		6
9.7	even	3		1008.2.q.g.529.3		6
12.11	even	2		378.2.h.c.361.1		6
21.2	odd	6		3024.2.q.g.2305.3		6
28.3	even	6		882.2.f.o.589.1		6
28.11	odd	6		882.2.f.n.589.3		6
28.19	even	6		882.2.e.o.373.3		6
28.23	odd	6		126.2.e.c.121.1	yes	6
28.27	even	2		882.2.h.p.67.1		6
36.7	odd	6		126.2.e.c.25.1	✓	6
36.11	even	6		378.2.e.d.235.3		6
36.23	even	6		1134.2.g.l.487.3		6
36.31	odd	6		1134.2.g.m.487.1		6
63.2	odd	6		3024.2.t.h.289.1		6
63.16	even	3	inner	1008.2.t.h.961.1		6
84.11	even	6		2646.2.f.l.1765.3		6
84.23	even	6		378.2.e.d.37.3		6
84.47	odd	6		2646.2.e.p.1549.1		6
84.59	odd	6		2646.2.f.m.1765.1		6
84.83	odd	2		2646.2.h.o.361.3		6
252.11	even	6		2646.2.f.l.883.3		6
252.23	even	6		1134.2.g.l.163.3		6
252.31	even	6		7938.2.a.bw.1.1		3
252.47	odd	6		2646.2.h.o.667.3		6
252.59	odd	6		7938.2.a.bz.1.3		3
252.67	odd	6		7938.2.a.bv.1.3		3
252.79	odd	6		126.2.h.d.79.3	yes	6
252.83	odd	6		2646.2.e.p.2125.1		6
252.95	even	6		7938.2.a.ca.1.1		3
252.115	even	6		882.2.f.o.295.1		6
252.151	odd	6		882.2.f.n.295.3		6
252.187	even	6		882.2.h.p.79.1		6
252.191	even	6		378.2.h.c.289.1		6
252.223	even	6		882.2.e.o.655.3		6
252.227	odd	6		2646.2.f.m.883.1		6
252.247	odd	6		1134.2.g.m.163.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	36.7	odd	6
126.2.e.c.121.1	yes	6	28.23	odd	6
126.2.h.d.67.3	yes	6	4.3	odd	2
126.2.h.d.79.3	yes	6	252.79	odd	6
378.2.e.d.37.3		6	84.23	even	6
378.2.e.d.235.3		6	36.11	even	6
378.2.h.c.289.1		6	252.191	even	6
378.2.h.c.361.1		6	12.11	even	2
882.2.e.o.373.3		6	28.19	even	6
882.2.e.o.655.3		6	252.223	even	6
882.2.f.n.295.3		6	252.151	odd	6
882.2.f.n.589.3		6	28.11	odd	6
882.2.f.o.295.1		6	252.115	even	6
882.2.f.o.589.1		6	28.3	even	6
882.2.h.p.67.1		6	28.27	even	2
882.2.h.p.79.1		6	252.187	even	6
1008.2.q.g.529.3		6	9.7	even	3
1008.2.q.g.625.3		6	7.2	even	3
1008.2.t.h.193.1		6	1.1	even	1	trivial
1008.2.t.h.961.1		6	63.16	even	3	inner
1134.2.g.l.163.3		6	252.23	even	6
1134.2.g.l.487.3		6	36.23	even	6
1134.2.g.m.163.1		6	252.247	odd	6
1134.2.g.m.487.1		6	36.31	odd	6
2646.2.e.p.1549.1		6	84.47	odd	6
2646.2.e.p.2125.1		6	252.83	odd	6
2646.2.f.l.883.3		6	252.11	even	6
2646.2.f.l.1765.3		6	84.11	even	6
2646.2.f.m.883.1		6	252.227	odd	6
2646.2.f.m.1765.1		6	84.59	odd	6
2646.2.h.o.361.3		6	84.83	odd	2
2646.2.h.o.667.3		6	252.47	odd	6
3024.2.q.g.2305.3		6	21.2	odd	6
3024.2.q.g.2881.3		6	9.2	odd	6
3024.2.t.h.289.1		6	63.2	odd	6
3024.2.t.h.1873.1		6	3.2	odd	2
7938.2.a.bv.1.3		3	252.67	odd	6
7938.2.a.bw.1.1		3	252.31	even	6
7938.2.a.bz.1.3		3	252.59	odd	6
7938.2.a.ca.1.1		3	252.95	even	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29418 - 1.15113i) q^{3} +1.58836 q^{5} +(2.64400 + 0.0963576i) q^{7} +(0.349814 + 2.97954i) q^{9} +O(q^{10})\)	\(q+(-1.29418 - 1.15113i) q^{3} +1.58836 q^{5} +(2.64400 + 0.0963576i) q^{7} +(0.349814 + 2.97954i) q^{9} +1.58836 q^{11} +(2.40545 - 4.16635i) q^{13} +(-2.05563 - 1.82841i) q^{15} +(-2.69963 + 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-3.31089 - 3.16828i) q^{21} -0.300372 q^{23} -2.47710 q^{25} +(2.97710 - 4.25874i) q^{27} +(4.13781 + 7.16689i) q^{29} +(-1.35600 - 2.34867i) q^{31} +(-2.05563 - 1.82841i) q^{33} +(4.19963 + 0.153051i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-7.90909 + 2.62305i) q^{39} +(2.93818 - 5.08907i) q^{41} +(0.833104 + 1.44298i) q^{43} +(0.555632 + 4.73259i) q^{45} +(1.33310 - 2.30900i) q^{47} +(6.98143 + 0.509538i) q^{49} +(8.87636 - 2.94384i) q^{51} +(2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +(2.48329 - 12.0422i) q^{57} +(3.23855 + 5.60933i) q^{59} +(2.23855 - 3.87728i) q^{61} +(0.637806 + 7.91159i) q^{63} +(3.82072 - 6.61769i) q^{65} +(-5.02654 - 8.70623i) q^{67} +(0.388736 + 0.345766i) q^{69} -12.7207 q^{71} +(8.02654 - 13.9024i) q^{73} +(3.20582 + 2.85146i) q^{75} +(4.19963 + 0.153051i) q^{77} +(4.19344 - 7.26325i) q^{79} +(-8.75526 + 2.08457i) q^{81} +(-1.18292 - 2.04887i) q^{83} +(-4.28799 + 7.42702i) q^{85} +(2.89493 - 14.0384i) q^{87} +(1.60507 + 2.78007i) q^{89} +(6.76145 - 10.7840i) q^{91} +(-0.948699 + 4.60054i) q^{93} +(5.63781 + 9.76497i) q^{95} +(0.712008 + 1.23323i) q^{97} +(0.555632 + 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q - 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^9	\( 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9} - 2 q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} - 4 q^{25} + 7 q^{27} - 5 q^{29} - 20 q^{31} - 12 q^{33} + 13 q^{35} + 3 q^{37} - q^{39} + 6 q^{43} + 3 q^{45} + 9 q^{47} - 12 q^{49} + 18 q^{51} + 15 q^{53} + 26 q^{55} + 22 q^{57} + 14 q^{59} + 8 q^{61} - 26 q^{63} - 12 q^{65} - q^{67} + 3 q^{69} - 14 q^{71} + 19 q^{73} + 25 q^{75} + 13 q^{77} - 5 q^{79} - 40 q^{81} - 2 q^{83} - 2 q^{85} + 36 q^{87} - 9 q^{89} + 46 q^{91} + 37 q^{93} + 4 q^{95} + 28 q^{97} + 3 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^9 - 2 * q^11 + 8 * q^13 - 12 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 - 4 * q^25 + 7 * q^27 - 5 * q^29 - 20 * q^31 - 12 * q^33 + 13 * q^35 + 3 * q^37 - q^39 + 6 * q^43 + 3 * q^45 + 9 * q^47 - 12 * q^49 + 18 * q^51 + 15 * q^53 + 26 * q^55 + 22 * q^57 + 14 * q^59 + 8 * q^61 - 26 * q^63 - 12 * q^65 - q^67 + 3 * q^69 - 14 * q^71 + 19 * q^73 + 25 * q^75 + 13 * q^77 - 5 * q^79 - 40 * q^81 - 2 * q^83 - 2 * q^85 + 36 * q^87 - 9 * q^89 + 46 * q^91 + 37 * q^93 + 4 * q^95 + 28 * q^97 + 3 * q^99

Introduction

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