LMFDB - Embedded newform 2646.2.h.o.667.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (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:	$21.1284163748$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.o.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.58836 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.58836 q^{5} +1.00000 q^{8} +(-0.794182 - 1.37556i) q^{10} +1.58836 q^{11} +(-2.40545 - 4.16635i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.69963 - 4.67589i) q^{17} +(3.54944 - 6.14781i) q^{19} +(-0.794182 + 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} -0.300372 q^{23} -2.47710 q^{25} +(-2.40545 + 4.16635i) q^{26} +(-4.13781 + 7.16689i) q^{29} +(-1.35600 + 2.34867i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.69963 + 4.67589i) q^{34} +(0.500000 - 0.866025i) q^{37} -7.09888 q^{38} +1.58836 q^{40} +(2.93818 + 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(-0.794182 + 1.37556i) q^{44} +(0.150186 + 0.260130i) q^{46} +(-1.33310 - 2.30900i) q^{47} +(1.23855 + 2.14523i) q^{50} +4.81089 q^{52} +(-2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +8.27561 q^{58} +(-3.23855 + 5.60933i) q^{59} +(-2.23855 - 3.87728i) q^{61} +2.71201 q^{62} +1.00000 q^{64} +(-3.82072 - 6.61769i) q^{65} +(5.02654 - 8.70623i) q^{67} +5.39926 q^{68} -12.7207 q^{71} +(-8.02654 - 13.9024i) q^{73} -1.00000 q^{74} +(3.54944 + 6.14781i) q^{76} +(-4.19344 - 7.26325i) q^{79} +(-0.794182 - 1.37556i) q^{80} +(2.93818 - 5.08907i) q^{82} +(1.18292 - 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +1.66621 q^{86} +1.58836 q^{88} +(1.60507 - 2.78007i) q^{89} +(0.150186 - 0.260130i) q^{92} +(-1.33310 + 2.30900i) q^{94} +(5.63781 - 9.76497i) q^{95} +(-0.712008 + 1.23323i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + q^{10} - 2 q^{11} - 8 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} - 14 q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} + 3 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} - 9 q^{47} + 2 q^{50} + 16 q^{52} - 15 q^{53} + 26 q^{55} - 10 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 8 q^{68} - 14 q^{71} - 19 q^{73} - 6 q^{74} + 3 q^{76} + 5 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} - 9 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 6 * q^8 + q^10 - 2 * q^11 - 8 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 - 14 * q^23 - 4 * q^25 - 8 * q^26 + 5 * q^29 - 20 * q^31 - 3 * q^32 - 4 * q^34 + 3 * q^37 - 6 * q^38 - 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 - 9 * q^47 + 2 * q^50 + 16 * q^52 - 15 * q^53 + 26 * q^55 - 10 * q^58 - 14 * q^59 - 8 * q^61 + 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 + 8 * q^68 - 14 * q^71 - 19 * q^73 - 6 * q^74 + 3 * q^76 + 5 * q^79 + q^80 + 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 - 9 * q^89 + 7 * q^92 - 9 * q^94 + 4 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	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
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.794182	−	1.37556i	−0.251142	−	0.434991i
$11$	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	−0.978697	−	0.205308i	$-0.934180\pi$
$13$	−2.40545	−	4.16635i	−0.667151	−	1.15554i	0.311547	−	0.950231i	$-0.399153\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.69963	−	4.67589i	−0.654756	−	1.13407i	−0.981955	−	0.189115i	$-0.939438\pi$
$17$	−2.69963	−	4.67589i	−0.654756	−	1.13407i	0.327199	−	0.944955i	$-0.393895\pi$
$18$		0			0
$19$	3.54944	−	6.14781i	0.814298	−	1.41041i	−0.0955331	−	0.995426i	$-0.530456\pi$
$19$	3.54944	−	6.14781i	0.814298	−	1.41041i	0.909831	−	0.414979i	$-0.136211\pi$
$20$	−0.794182	+	1.37556i	−0.177584	+	0.307585i
$21$		0			0
$22$	−0.794182	−	1.37556i	−0.169320	−	0.293271i
$23$	−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
$26$	−2.40545	+	4.16635i	−0.471747	+	0.817089i
$27$		0			0
$28$		0			0
$29$	−4.13781	+	7.16689i	−0.768371	+	1.33086i	0.170074	+	0.985431i	$0.445599\pi$
$29$	−4.13781	+	7.16689i	−0.768371	+	1.33086i	−0.938446	+	0.345427i	$0.887734\pi$
$30$		0			0
$31$	−1.35600	+	2.34867i	−0.243545	+	0.421833i	−0.961722	−	0.274028i	$-0.911644\pi$
$31$	−1.35600	+	2.34867i	−0.243545	+	0.421833i	0.718176	+	0.695861i	$0.244977\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−2.69963	+	4.67589i	−0.462982	+	0.801909i
$35$		0			0
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−7.09888			−1.15159
$39$		0			0
$40$	1.58836			0.251142
$41$	2.93818	+	5.08907i	0.458866	+	0.794780i	0.998901	−	0.0468628i	$-0.0149223\pi$
$41$	2.93818	+	5.08907i	0.458866	+	0.794780i	−0.540035	+	0.841643i	$0.681589\pi$
$42$		0			0
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	−0.922531	−	0.385922i	$-0.873883\pi$
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	0.795484	+	0.605974i	$0.207217\pi$
$44$	−0.794182	+	1.37556i	−0.119727	+	0.207374i
$45$		0			0
$46$	0.150186	+	0.260130i	0.0221437	+	0.0383540i
$47$	−1.33310	−	2.30900i	−0.194453	−	0.336803i	0.752268	−	0.658857i	$-0.228960\pi$
$47$	−1.33310	−	2.30900i	−0.194453	−	0.336803i	−0.946721	+	0.322055i	$0.895627\pi$
$48$		0			0
$49$		0			0
$50$	1.23855	+	2.14523i	0.175157	+	0.303382i
$51$		0			0
$52$	4.81089			0.667151
$53$	−2.44437	−	4.23377i	−0.335760	−	0.581553i	0.647871	−	0.761750i	$-0.275660\pi$
$53$	−2.44437	−	4.23377i	−0.335760	−	0.581553i	−0.983630	+	0.180197i	$0.942326\pi$
$54$		0			0
$55$	2.52290			0.340188
$56$		0			0
$57$		0			0
$58$	8.27561			1.08664
$59$	−3.23855	+	5.60933i	−0.421623	+	0.730273i	−0.996098	−	0.0882491i	$-0.971873\pi$
$59$	−3.23855	+	5.60933i	−0.421623	+	0.730273i	0.574475	+	0.818522i	$0.305206\pi$
$60$		0			0
$61$	−2.23855	−	3.87728i	−0.286617	−	0.496435i	0.686383	−	0.727240i	$-0.259197\pi$
$61$	−2.23855	−	3.87728i	−0.286617	−	0.496435i	−0.973000	+	0.230805i	$0.925864\pi$
$62$	2.71201			0.344425
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.82072	−	6.61769i	−0.473902	−	0.820823i
$66$		0			0
$67$	5.02654	−	8.70623i	0.614090	−	1.06363i	−0.376454	−	0.926435i	$-0.622857\pi$
$67$	5.02654	−	8.70623i	0.614090	−	1.06363i	0.990543	−	0.137199i	$-0.0438101\pi$
$68$	5.39926			0.654756
$69$		0			0
$70$		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	−0.766527	−	0.642213i	$-0.778017\pi$
$73$	−8.02654	−	13.9024i	−0.939436	−	1.62715i	−0.172909	−	0.984938i	$-0.555317\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	3.54944	+	6.14781i	0.407149	+	0.705203i
$77$		0			0
$78$		0			0
$79$	−4.19344	−	7.26325i	−0.471799	−	0.817179i	0.527681	−	0.849443i	$-0.323062\pi$
$79$	−4.19344	−	7.26325i	−0.471799	−	0.817179i	−0.999479	+	0.0322635i	$0.989728\pi$
$80$	−0.794182	−	1.37556i	−0.0887922	−	0.153793i
$81$		0			0
$82$	2.93818	−	5.08907i	0.324467	−	0.561994i
$83$	1.18292	−	2.04887i	0.129842	−	0.224893i	−0.793773	−	0.608214i	$-0.791886\pi$
$83$	1.18292	−	2.04887i	0.129842	−	0.224893i	0.923615	+	0.383321i	$0.125220\pi$
$84$		0			0
$85$	−4.28799	−	7.42702i	−0.465098	−	0.805573i
$86$	1.66621			0.179672
$87$		0			0
$88$	1.58836			0.169320
$89$	1.60507	−	2.78007i	0.170138	−	0.294687i	−0.768330	−	0.640054i	$-0.778912\pi$
$89$	1.60507	−	2.78007i	0.170138	−	0.294687i	0.938468	+	0.345367i	$0.112245\pi$
$90$		0			0
$91$		0			0
$92$	0.150186	−	0.260130i	0.0156580	−	0.0271204i
$93$		0			0
$94$	−1.33310	+	2.30900i	−0.137499	+	0.238156i
$95$	5.63781	−	9.76497i	0.578427	−	1.00186i
$96$		0			0
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	−0.899906	−	0.436084i	$-0.856365\pi$
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	0.827613	+	0.561300i	$0.189698\pi$
$98$		0			0
$99$		0			0
$100$	1.23855	−	2.14523i	0.123855	−	0.214523i
$101$	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	$0.402856\pi$
$104$	−2.40545	−	4.16635i	−0.235873	−	0.408545i
$105$		0			0
$106$	−2.44437	+	4.23377i	−0.237418	+	0.411220i
$107$	1.54325	−	2.67299i	0.149192	−	0.258408i	−0.781737	−	0.623608i	$-0.785666\pi$
$107$	1.54325	−	2.67299i	0.149192	−	0.258408i	0.930929	+	0.365200i	$0.118999\pi$
$108$		0			0
$109$	1.14400	+	1.98146i	0.109575	+	0.189789i	0.915598	−	0.402095i	$-0.131718\pi$
$109$	1.14400	+	1.98146i	0.109575	+	0.189789i	−0.806023	+	0.591884i	$0.798384\pi$
$110$	−1.26145	−	2.18490i	−0.120275	−	0.208322i
$111$		0			0
$112$		0			0
$113$	9.73236	+	16.8569i	0.915543	+	1.58577i	0.806104	+	0.591774i	$0.201572\pi$
$113$	9.73236	+	16.8569i	0.915543	+	1.58577i	0.109440	+	0.993993i	$0.465094\pi$
$114$		0			0
$115$	−0.477100			−0.0444898
$116$	−4.13781	−	7.16689i	−0.384186	−	0.665429i
$117$		0			0
$118$	6.47710			0.596265
$119$		0			0
$120$		0			0
$121$	−8.47710			−0.770645
$122$	−2.23855	+	3.87728i	−0.202669	+	0.351033i
$123$		0			0
$124$	−1.35600	−	2.34867i	−0.121773	−	0.210917i
$125$	−11.8764			−1.06225
$126$		0			0
$127$	−13.4400			−1.19260			−0.596302	−	0.802760i	$-0.703364\pi$
$127$	−13.4400			−1.19260			−0.596302	+	0.802760i	$0.703364\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−3.82072	+	6.61769i	−0.335100	+	0.580410i
$131$	−3.17673			−0.277552			−0.138776	−	0.990324i	$-0.544317\pi$
$131$	−3.17673			−0.277552			−0.138776	+	0.990324i	$0.544317\pi$
$132$		0			0
$133$		0			0
$134$	−10.0531			−0.868454
$135$		0			0
$136$	−2.69963	−	4.67589i	−0.231491	−	0.400955i
$137$	21.2632			1.81664			0.908320	−	0.418275i	$-0.137365\pi$
$137$	21.2632			1.81664			0.908320	+	0.418275i	$0.137365\pi$
$138$		0			0
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	−0.998013	−	0.0630092i	$-0.979930\pi$
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	0.444439	−	0.895809i	$-0.353403\pi$
$140$		0			0
$141$		0			0
$142$	6.36033	+	11.0164i	0.533747	+	0.924478i
$143$	−3.82072	−	6.61769i	−0.319505	−	0.553399i
$144$		0			0
$145$	−6.57234	+	11.3836i	−0.545803	+	0.945359i
$146$	−8.02654	+	13.9024i	−0.664281	+	1.15057i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−5.20877			−0.426719			−0.213360	−	0.976974i	$-0.568441\pi$
$149$	−5.20877			−0.426719			−0.213360	+	0.976974i	$0.568441\pi$
$150$		0			0
$151$	−0.522900			−0.0425530			−0.0212765	−	0.999774i	$-0.506773\pi$
$151$	−0.522900			−0.0425530			−0.0212765	+	0.999774i	$0.506773\pi$
$152$	3.54944	−	6.14781i	0.287898	−	0.498654i
$153$		0			0
$154$		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	$-0.718253\pi$
$157$	4.43199	−	7.67643i	0.353711	−	0.612646i	0.986897	+	0.161354i	$0.0515862\pi$
$158$	−4.19344	+	7.26325i	−0.333612	+	0.577833i
$159$		0			0
$160$	−0.794182	+	1.37556i	−0.0627856	+	0.108748i
$161$		0			0
$162$		0			0
$163$	10.9814	−	19.0204i	0.860132	−	1.48979i	−0.0116689	−	0.999932i	$-0.503714\pi$
$163$	10.9814	−	19.0204i	0.860132	−	1.48979i	0.871801	−	0.489860i	$-0.162952\pi$
$164$	−5.87636			−0.458866
$165$		0			0
$166$	−2.36584			−0.183624
$167$	1.65019	+	2.85821i	0.127695	+	0.221175i	0.922783	−	0.385319i	$-0.125909\pi$
$167$	1.65019	+	2.85821i	0.127695	+	0.221175i	−0.795088	+	0.606494i	$0.792575\pi$
$168$		0			0
$169$	−5.07234	+	8.78555i	−0.390180	+	0.675812i
$170$	−4.28799	+	7.42702i	−0.328874	+	0.569626i
$171$		0			0
$172$	−0.833104	−	1.44298i	−0.0635236	−	0.110026i
$173$	−9.55377	−	16.5476i	−0.726360	−	1.25809i	−0.958412	−	0.285389i	$-0.907877\pi$
$173$	−9.55377	−	16.5476i	−0.726360	−	1.25809i	0.232052	−	0.972703i	$-0.425456\pi$
$174$		0			0
$175$		0			0
$176$	−0.794182	−	1.37556i	−0.0598637	−	0.103687i
$177$		0			0
$178$	−3.21015			−0.240611
$179$	8.03706	+	13.9206i	0.600718	+	1.04047i	0.992712	+	0.120507i	$0.0384520\pi$
$179$	8.03706	+	13.9206i	0.600718	+	1.04047i	−0.391994	+	0.919968i	$0.628215\pi$
$180$		0			0
$181$	−8.05308			−0.598581			−0.299291	−	0.954162i	$-0.596750\pi$
$181$	−8.05308			−0.598581			−0.299291	+	0.954162i	$0.596750\pi$
$182$		0			0
$183$		0			0
$184$	−0.300372			−0.0221437
$185$	0.794182	−	1.37556i	0.0583894	−	0.101133i
$186$		0			0
$187$	−4.28799	−	7.42702i	−0.313569	−	0.543118i
$188$	2.66621			0.194453
$189$		0			0
$190$	−11.2756			−0.818019
$191$	−11.9814	−	20.7524i	−0.866946	−	1.50159i	−0.865102	−	0.501596i	$-0.832746\pi$
$191$	−11.9814	−	20.7524i	−0.866946	−	1.50159i	−0.00184390	−	0.999998i	$-0.500587\pi$
$192$		0			0
$193$	−4.88255	+	8.45682i	−0.351453	+	0.608735i	−0.986504	−	0.163735i	$-0.947646\pi$
$193$	−4.88255	+	8.45682i	−0.351453	+	0.608735i	0.635051	+	0.772470i	$0.280979\pi$
$194$	1.42402			0.102238
$195$		0			0
$196$		0			0
$197$	18.2436			1.29980			0.649900	−	0.760020i	$-0.274811\pi$
$197$	18.2436			1.29980			0.649900	+	0.760020i	$0.274811\pi$
$198$		0			0
$199$	−9.04944	−	15.6741i	−0.641498	−	1.11111i	−0.985098	−	0.171991i	$-0.944980\pi$
$199$	−9.04944	−	15.6741i	−0.641498	−	1.11111i	0.343601	−	0.939116i	$-0.388353\pi$
$200$	−2.47710			−0.175157
$201$		0			0
$202$	−6.01671	−	10.4212i	−0.423334	−	0.733236i
$203$		0			0
$204$		0			0
$205$	4.66690	+	8.08330i	0.325950	+	0.564562i
$206$	−3.04944	−	5.28179i	−0.212465	−	0.368000i
$207$		0			0
$208$	−2.40545	+	4.16635i	−0.166788	+	0.288885i
$209$	5.63781	−	9.76497i	0.389975	−	0.675457i
$210$		0			0
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	0.871690	−	0.490058i	$-0.163024\pi$
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	−0.860248	+	0.509877i	$0.829691\pi$
$212$	4.88874			0.335760
$213$		0			0
$214$	−3.08650			−0.210989
$215$	−1.32327	+	2.29197i	−0.0902464	+	0.156311i
$216$		0			0
$217$		0			0
$218$	1.14400	−	1.98146i	0.0774812	−	0.134201i
$219$		0			0
$220$	−1.26145	+	2.18490i	−0.0850469	+	0.147306i
$221$	−12.9876	+	22.4952i	−0.873642	+	1.51319i
$222$		0			0
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	−0.952348	−	0.305013i	$-0.901339\pi$
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	0.740323	+	0.672251i	$0.234672\pi$
$224$		0			0
$225$		0			0
$226$	9.73236	−	16.8569i	0.647387	−	1.12131i
$227$	−23.3090			−1.54707			−0.773537	−	0.633751i	$-0.781515\pi$
$227$	−23.3090			−1.54707			−0.773537	+	0.633751i	$0.781515\pi$
$228$		0			0
$229$	4.95420			0.327383			0.163691	−	0.986512i	$-0.447660\pi$
$229$	4.95420			0.327383			0.163691	+	0.986512i	$0.447660\pi$
$230$	0.238550	+	0.413181i	0.0157295	+	0.0272443i
$231$		0			0
$232$	−4.13781	+	7.16689i	−0.271660	+	0.470529i
$233$	7.13781	−	12.3630i	0.467613	−	0.809930i	−0.531702	−	0.846932i	$-0.678447\pi$
$233$	7.13781	−	12.3630i	0.467613	−	0.809930i	0.999315	+	0.0370017i	$0.0117807\pi$
$234$		0			0
$235$	−2.11745	−	3.66754i	−0.138127	−	0.239244i
$236$	−3.23855	−	5.60933i	−0.210812	−	0.365136i
$237$		0			0
$238$		0			0
$239$	−2.48762	−	4.30868i	−0.160911	−	0.278706i	0.774285	−	0.632837i	$-0.218110\pi$
$239$	−2.48762	−	4.30868i	−0.160911	−	0.278706i	−0.935196	+	0.354132i	$0.884776\pi$
$240$		0			0
$241$	13.0000			0.837404			0.418702	−	0.908124i	$-0.362485\pi$
$241$	13.0000			0.837404			0.418702	+	0.908124i	$0.362485\pi$
$242$	4.23855	+	7.34138i	0.272464	+	0.471922i
$243$		0			0
$244$	4.47710			0.286617
$245$		0			0
$246$		0			0
$247$	−34.1520			−2.17304
$248$	−1.35600	+	2.34867i	−0.0861063	+	0.149141i
$249$		0			0
$250$	5.93818	+	10.2852i	0.375563	+	0.650495i
$251$	2.43268			0.153549			0.0767746	−	0.997048i	$-0.475538\pi$
$251$	2.43268			0.153549			0.0767746	+	0.997048i	$0.475538\pi$
$252$		0			0
$253$	−0.477100			−0.0299950
$254$	6.71998	+	11.6393i	0.421649	+	0.730318i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−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
$259$		0			0
$260$	7.64145			0.473902
$261$		0			0
$262$	1.58836	+	2.75113i	0.0981295	+	0.169965i
$263$	−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
$267$		0			0
$268$	5.02654	+	8.70623i	0.307045	+	0.531817i
$269$	11.4523	+	19.8360i	0.698262	+	1.20942i	0.969069	+	0.246791i	$0.0793761\pi$
$269$	11.4523	+	19.8360i	0.698262	+	1.20942i	−0.270807	+	0.962634i	$0.587291\pi$
$270$		0			0
$271$	−7.00364	+	12.1307i	−0.425441	+	0.736885i	−0.996462	−	0.0840504i	$-0.973214\pi$
$271$	−7.00364	+	12.1307i	−0.425441	+	0.736885i	0.571021	+	0.820936i	$0.306548\pi$
$272$	−2.69963	+	4.67589i	−0.163689	+	0.283518i
$273$		0			0
$274$	−10.6316	−	18.4145i	−0.642279	−	1.11246i
$275$	−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	$0.176572\pi$
$278$	−6.52654	+	11.3043i	−0.391436	+	0.677987i
$279$		0			0
$280$		0			0
$281$	8.79782	−	15.2383i	0.524834	−	0.909039i	−0.474748	−	0.880122i	$-0.657461\pi$
$281$	8.79782	−	15.2383i	0.524834	−	0.909039i	0.999582	−	0.0289175i	$-0.00920600\pi$
$282$		0			0
$283$	−9.26145	+	16.0413i	−0.550536	+	0.953556i	0.447700	+	0.894184i	$0.352243\pi$
$283$	−9.26145	+	16.0413i	−0.550536	+	0.953556i	−0.998236	+	0.0593725i	$0.981090\pi$
$284$	6.36033	−	11.0164i	0.377416	−	0.653704i
$285$		0			0
$286$	−3.82072	+	6.61769i	−0.225924	+	0.391312i
$287$		0			0
$288$		0			0
$289$	−6.07598	+	10.5239i	−0.357411	+	0.619054i
$290$	13.1447			0.771882
$291$		0			0
$292$	16.0531			0.939436
$293$	−7.04256	−	12.1981i	−0.411431	−	0.712619i	0.583616	−	0.812030i	$-0.301638\pi$
$293$	−7.04256	−	12.1981i	−0.411431	−	0.712619i	−0.995046	+	0.0994108i	$0.968304\pi$
$294$		0			0
$295$	−5.14400	+	8.90966i	−0.299495	+	0.518741i
$296$	0.500000	−	0.866025i	0.0290619	−	0.0503367i
$297$		0			0
$298$	2.60439	+	4.51093i	0.150868	+	0.261311i
$299$	0.722528	+	1.25146i	0.0417849	+	0.0723736i
$300$		0			0
$301$		0			0
$302$	0.261450	+	0.452845i	0.0150448	+	0.0260583i
$303$		0			0
$304$	−7.09888			−0.407149
$305$	−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
$309$		0			0
$310$	4.30766			0.244658
$311$	−0.405446	+	0.702253i	−0.0229907	+	0.0398211i	−0.877292	−	0.479957i	$-0.840652\pi$
$311$	−0.405446	+	0.702253i	−0.0229907	+	0.0398211i	0.854301	+	0.519778i	$0.173985\pi$
$312$		0			0
$313$	5.28799	+	9.15907i	0.298895	+	0.517701i	0.975883	−	0.218292i	$-0.0700486\pi$
$313$	5.28799	+	9.15907i	0.298895	+	0.517701i	−0.676988	+	0.735994i	$0.736715\pi$
$314$	−8.86398			−0.500223
$315$		0			0
$316$	8.38688			0.471799
$317$	6.09820	+	10.5624i	0.342509	+	0.593243i	0.984898	−	0.173136i	$-0.0553900\pi$
$317$	6.09820	+	10.5624i	0.342509	+	0.593243i	−0.642389	+	0.766379i	$0.722057\pi$
$318$		0			0
$319$	−6.57234	+	11.3836i	−0.367981	+	0.637361i
$320$	1.58836			0.0887922
$321$		0			0
$322$		0			0
$323$	−38.3287			−2.13267
$324$		0			0
$325$	5.95853	+	10.3205i	0.330520	+	0.572477i
$326$	−21.9629			−1.21641
$327$		0			0
$328$	2.93818	+	5.08907i	0.162234	+	0.280997i
$329$		0			0
$330$		0			0
$331$	7.83310	+	13.5673i	0.430546	+	0.745728i	0.996920	−	0.0784202i	$-0.0249876\pi$
$331$	7.83310	+	13.5673i	0.430546	+	0.745728i	−0.566374	+	0.824148i	$0.691654\pi$
$332$	1.18292	+	2.04887i	0.0649211	+	0.112447i
$333$		0			0
$334$	1.65019	−	2.85821i	0.0902942	−	0.156394i
$335$	7.98398	−	13.8287i	0.436211	−	0.755540i
$336$		0			0
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	0.728200	−	0.685364i	$-0.240357\pi$
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	−0.957643	+	0.287958i	$0.907024\pi$
$338$	10.1447			0.551798
$339$		0			0
$340$	8.57598			0.465098
$341$	−2.15383	+	3.73054i	−0.116636	+	0.202020i
$342$		0			0
$343$		0			0
$344$	−0.833104	+	1.44298i	−0.0449179	+	0.0778002i
$345$		0			0
$346$	−9.55377	+	16.5476i	−0.513614	+	0.889606i
$347$	0.283662	−	0.491316i	0.0152277	−	0.0263752i	−0.858311	−	0.513130i	$-0.828486\pi$
$347$	0.283662	−	0.491316i	0.0152277	−	0.0263752i	0.873539	+	0.486754i	$0.161819\pi$
$348$		0			0
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	−0.865928	−	0.500169i	$-0.833271\pi$
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	0.866123	+	0.499831i	$0.166605\pi$
$350$		0			0
$351$		0			0
$352$	−0.794182	+	1.37556i	−0.0423300	+	0.0733178i
$353$	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
$356$	1.60507	+	2.78007i	0.0850688	+	0.147343i
$357$		0			0
$358$	8.03706	−	13.9206i	0.424772	−	0.735727i
$359$	0.398568	−	0.690339i	0.0210356	−	0.0364347i	−0.855316	−	0.518107i	$-0.826637\pi$
$359$	0.398568	−	0.690339i	0.0210356	−	0.0364347i	0.876352	+	0.481672i	$0.159970\pi$
$360$		0			0
$361$	−15.6971	−	27.1881i	−0.826162	−	1.43095i
$362$	4.02654	+	6.97418i	0.211630	+	0.366555i
$363$		0			0
$364$		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	$0.368041\pi$
$368$	0.150186	+	0.260130i	0.00782898	+	0.0135602i
$369$		0			0
$370$	−1.58836			−0.0825751
$371$		0			0
$372$		0			0
$373$	10.2422			0.530321			0.265160	−	0.964204i	$-0.414575\pi$
$373$	10.2422			0.530321			0.265160	+	0.964204i	$0.414575\pi$
$374$	−4.28799	+	7.42702i	−0.221727	+	0.384042i
$375$		0			0
$376$	−1.33310	−	2.30900i	−0.0687496	−	0.119078i
$377$	39.8131			2.05048
$378$		0			0
$379$	25.0087			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$379$	25.0087			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$380$	5.63781	+	9.76497i	0.289213	+	0.500932i
$381$		0			0
$382$	−11.9814	+	20.7524i	−0.613023	+	1.06179i
$383$	−6.26695			−0.320226			−0.160113	−	0.987099i	$-0.551186\pi$
$383$	−6.26695			−0.320226			−0.160113	+	0.987099i	$0.551186\pi$
$384$		0			0
$385$		0			0
$386$	9.76509			0.497030
$387$		0			0
$388$	−0.712008	−	1.23323i	−0.0361467	−	0.0626080i
$389$	21.6342			1.09690			0.548448	−	0.836185i	$-0.315219\pi$
$389$	21.6342			1.09690			0.548448	+	0.836185i	$0.315219\pi$
$390$		0			0
$391$	0.810892	+	1.40451i	0.0410086	+	0.0710290i
$392$		0			0
$393$		0			0
$394$	−9.12178	−	15.7994i	−0.459549	−	0.795962i
$395$	−6.66071	−	11.5367i	−0.335137	−	0.580473i
$396$		0			0
$397$	−2.05308	+	3.55605i	−0.103041	+	0.178473i	−0.912936	−	0.408102i	$-0.866191\pi$
$397$	−2.05308	+	3.55605i	−0.103041	+	0.178473i	0.809895	+	0.586575i	$0.199524\pi$
$398$	−9.04944	+	15.6741i	−0.453608	+	0.785671i
$399$		0			0
$400$	1.23855	+	2.14523i	0.0619275	+	0.107262i
$401$	−16.7417			−0.836041			−0.418021	−	0.908438i	$-0.637276\pi$
$401$	−16.7417			−0.836041			−0.418021	+	0.908438i	$0.637276\pi$
$402$		0			0
$403$	13.0472			0.649926
$404$	−6.01671	+	10.4212i	−0.299343	+	0.518476i
$405$		0			0
$406$		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	$-0.902864\pi$
$409$	−4.38255	+	7.59079i	−0.216703	+	0.375341i	0.737095	+	0.675789i	$0.236197\pi$
$410$	4.66690	−	8.08330i	0.230482	−	0.399206i
$411$		0			0
$412$	−3.04944	+	5.28179i	−0.150235	+	0.260215i
$413$		0			0
$414$		0			0
$415$	1.87890	−	3.25436i	0.0922318	−	0.159750i
$416$	4.81089			0.235873
$417$		0			0
$418$	−11.2756			−0.551508
$419$	−0.210149	−	0.363988i	−0.0102664	−	0.0177820i	0.860847	−	0.508865i	$-0.169935\pi$
$419$	−0.210149	−	0.363988i	−0.0102664	−	0.0177820i	−0.871113	+	0.491083i	$0.836601\pi$
$420$		0			0
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	−0.774710	−	0.632316i	$-0.782104\pi$
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	0.934957	+	0.354761i	$0.115438\pi$
$422$	0.166208	−	0.287880i	0.00809086	−	0.0140138i
$423$		0			0
$424$	−2.44437	−	4.23377i	−0.118709	−	0.205610i
$425$	6.68725	+	11.5827i	0.324379	+	0.561841i
$426$		0			0
$427$		0			0
$428$	1.54325	+	2.67299i	0.0745959	+	0.129204i
$429$		0			0
$430$	2.64654			0.127628
$431$	−11.0439	−	19.1287i	−0.531968	−	0.921395i	−0.999304	−	0.0373155i	$-0.988119\pi$
$431$	−11.0439	−	19.1287i	−0.531968	−	0.921395i	0.467336	−	0.884080i	$-0.345214\pi$
$432$		0			0
$433$	9.43268			0.453306			0.226653	−	0.973976i	$-0.427222\pi$
$433$	9.43268			0.453306			0.226653	+	0.973976i	$0.427222\pi$
$434$		0			0
$435$		0			0
$436$	−2.28799			−0.109575
$437$	−1.06615	+	1.84663i	−0.0510010	+	0.0883363i
$438$		0			0
$439$	−15.6032	−	27.0256i	−0.744701	−	1.28986i	−0.950334	−	0.311231i	$-0.899259\pi$
$439$	−15.6032	−	27.0256i	−0.744701	−	1.28986i	0.205634	−	0.978629i	$-0.434074\pi$
$440$	2.52290			0.120275
$441$		0			0
$442$	25.9752			1.23552
$443$	6.52723	+	11.3055i	0.310118	+	0.537140i	0.978388	−	0.206779i	$-0.0662981\pi$
$443$	6.52723	+	11.3055i	0.310118	+	0.537140i	−0.668270	+	0.743919i	$0.732965\pi$
$444$		0			0
$445$	2.54944	−	4.41576i	0.120855	−	0.209327i
$446$	6.33242			0.299849
$447$		0			0
$448$		0			0
$449$	9.91706			0.468015			0.234008	−	0.972235i	$-0.424816\pi$
$449$	9.91706			0.468015			0.234008	+	0.972235i	$0.424816\pi$
$450$		0			0
$451$	4.66690	+	8.08330i	0.219756	+	0.380628i
$452$	−19.4647			−0.915543
$453$		0			0
$454$	11.6545	+	20.1862i	0.546974	+	0.947386i
$455$		0			0
$456$		0			0
$457$	12.2615	+	21.2375i	0.573566	+	0.993446i	0.996196	+	0.0871436i	$0.0277739\pi$
$457$	12.2615	+	21.2375i	0.573566	+	0.993446i	−0.422629	+	0.906303i	$0.638893\pi$
$458$	−2.47710	−	4.29046i	−0.115747	−	0.200480i
$459$		0			0
$460$	0.238550	−	0.413181i	0.0111224	−	0.0192646i
$461$	1.75526	−	3.04020i	0.0817506	−	0.141596i	−0.822251	−	0.569125i	$-0.807282\pi$
$461$	1.75526	−	3.04020i	0.0817506	−	0.141596i	0.904002	+	0.427528i	$0.140616\pi$
$462$		0			0
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	0.994210	−	0.107451i	$-0.0342687\pi$
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	−0.590160	+	0.807286i	$0.700935\pi$
$464$	8.27561			0.384186
$465$		0			0
$466$	−14.2756			−0.661305
$467$	6.69894	−	11.6029i	0.309990	−	0.536918i	−0.668370	−	0.743829i	$-0.733008\pi$
$467$	6.69894	−	11.6029i	0.309990	−	0.536918i	0.978360	+	0.206911i	$0.0663410\pi$
$468$		0			0
$469$		0			0
$470$	−2.11745	+	3.66754i	−0.0976709	+	0.169171i
$471$		0			0
$472$	−3.23855	+	5.60933i	−0.149066	+	0.258190i
$473$	−1.32327	+	2.29197i	−0.0608441	+	0.105385i
$474$		0			0
$475$	−8.79232	+	15.2287i	−0.403419	+	0.698743i
$476$		0			0
$477$		0			0
$478$	−2.48762	+	4.30868i	−0.113781	+	0.197075i
$479$	20.8058			0.950641			0.475321	−	0.879813i	$-0.342332\pi$
$479$	20.8058			0.950641			0.475321	+	0.879813i	$0.342332\pi$
$480$		0			0
$481$	−4.81089			−0.219358
$482$	−6.50000	−	11.2583i	−0.296067	−	0.512803i
$483$		0			0
$484$	4.23855	−	7.34138i	0.192661	−	0.333699i
$485$	−1.13093	+	1.95882i	−0.0513528	+	0.0889456i
$486$		0			0
$487$	16.2472	+	28.1410i	0.736231	+	1.27519i	0.954181	+	0.299230i	$0.0967298\pi$
$487$	16.2472	+	28.1410i	0.736231	+	1.27519i	−0.217950	+	0.975960i	$0.569937\pi$
$488$	−2.23855	−	3.87728i	−0.101334	−	0.175516i
$489$		0			0
$490$		0			0
$491$	9.66071	+	16.7328i	0.435982	+	0.755142i	0.997375	−	0.0724067i	$-0.0230679\pi$
$491$	9.66071	+	16.7328i	0.435982	+	0.755142i	−0.561394	+	0.827549i	$0.689735\pi$
$492$		0			0
$493$	44.6822			2.01238
$494$	17.0760	+	29.5765i	0.768285	+	1.33071i
$495$		0			0
$496$	2.71201			0.121773
$497$		0			0
$498$		0			0
$499$	−11.1506			−0.499169			−0.249585	−	0.968353i	$-0.580294\pi$
$499$	−11.1506			−0.499169			−0.249585	+	0.968353i	$0.580294\pi$
$500$	5.93818	−	10.2852i	0.265563	−	0.459969i
$501$		0			0
$502$	−1.21634	−	2.10676i	−0.0542878	−	0.0940293i
$503$	−40.7651			−1.81763			−0.908813	−	0.417204i	$-0.863010\pi$
$503$	−40.7651			−1.81763			−0.908813	+	0.417204i	$0.863010\pi$
$504$		0			0
$505$	19.1135			0.850537
$506$	0.238550	+	0.413181i	0.0106048	+	0.0183681i
$507$		0			0
$508$	6.71998	−	11.6393i	0.298151	−	0.516413i
$509$	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
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	0.493810	+	0.855304i	0.0217810	+	0.0377259i
$515$	9.68725			0.426871
$516$		0			0
$517$	−2.11745	−	3.66754i	−0.0931255	−	0.161298i
$518$		0			0
$519$		0			0
$520$	−3.82072	−	6.61769i	−0.167550	−	0.290205i
$521$	9.64214	+	16.7007i	0.422430	+	0.731670i	0.996177	−	0.0873630i	$-0.0278440\pi$
$521$	9.64214	+	16.7007i	0.422430	+	0.731670i	−0.573747	+	0.819033i	$0.694511\pi$
$522$		0			0
$523$	18.3454	−	31.7752i	0.802189	−	1.38943i	−0.115984	−	0.993251i	$-0.537002\pi$
$523$	18.3454	−	31.7752i	0.802189	−	1.38943i	0.918173	−	0.396180i	$-0.129665\pi$
$524$	1.58836	−	2.75113i	0.0693880	−	0.120184i
$525$		0			0
$526$	8.59269	+	14.8830i	0.374659	+	0.648929i
$527$	14.6428			0.637851
$528$		0			0
$529$	−22.9098			−0.996077
$530$	−3.88255	+	6.72477i	−0.168647	+	0.292105i
$531$		0			0
$532$		0			0
$533$	14.1353	−	24.4830i	0.612266	−	1.06048i
$534$		0			0
$535$	2.45125	−	4.24568i	0.105977	−	0.183557i
$536$	5.02654	−	8.70623i	0.217114	−	0.376052i
$537$		0			0
$538$	11.4523	−	19.8360i	0.493745	−	0.855192i
$539$		0			0
$540$		0			0
$541$	−1.62543	+	2.81532i	−0.0698825	+	0.121040i	−0.898849	−	0.438258i	$-0.855596\pi$
$541$	−1.62543	+	2.81532i	−0.0698825	+	0.121040i	0.828967	+	0.559298i	$0.188929\pi$
$542$	14.0073			0.601664
$543$		0			0
$544$	5.39926			0.231491
$545$	1.81708	+	3.14728i	0.0778352	+	0.134815i
$546$		0			0
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	−0.922317	−	0.386433i	$-0.873707\pi$
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	0.795820	+	0.605534i	$0.207040\pi$
$548$	−10.6316	+	18.4145i	−0.454160	+	0.786628i
$549$		0			0
$550$	1.96727	+	3.40741i	0.0838846	+	0.145292i
$551$	29.3738	+	50.8769i	1.25137	+	2.16743i
$552$		0			0
$553$		0			0
$554$	−14.1476	−	24.5044i	−0.601076	−	1.04109i
$555$		0			0
$556$	13.0531			0.553574
$557$	−12.8040	−	22.1772i	−0.542523	−	0.939678i	−0.998758	−	0.0498188i	$-0.984136\pi$
$557$	−12.8040	−	22.1772i	−0.542523	−	0.939678i	0.456235	−	0.889859i	$-0.349198\pi$
$558$		0			0
$559$	8.01594			0.339038
$560$		0			0
$561$		0			0
$562$	−17.5956			−0.742228
$563$	23.3189	−	40.3895i	0.982773	−	1.70221i	0.331330	−	0.943515i	$-0.392503\pi$
$563$	23.3189	−	40.3895i	0.982773	−	1.70221i	0.651443	−	0.758698i	$-0.274164\pi$
$564$		0			0
$565$	15.4585	+	26.7750i	0.650345	+	1.12643i
$566$	18.5229			0.778576
$567$		0			0
$568$	−12.7207			−0.533747
$569$	15.5989	+	27.0181i	0.653939	+	1.13266i	0.982159	+	0.188054i	$0.0602182\pi$
$569$	15.5989	+	27.0181i	0.653939	+	1.13266i	−0.328219	+	0.944602i	$0.606449\pi$
$570$		0			0
$571$	7.83812	−	13.5760i	0.328015	−	0.568139i	−0.654103	−	0.756406i	$-0.726954\pi$
$571$	7.83812	−	13.5760i	0.328015	−	0.568139i	0.982118	+	0.188267i	$0.0602869\pi$
$572$	7.64145			0.319505
$573$		0			0
$574$		0			0
$575$	0.744051			0.0310291
$576$		0			0
$577$	−6.99567	−	12.1169i	−0.291234	−	0.504431i	0.682868	−	0.730542i	$-0.260732\pi$
$577$	−6.99567	−	12.1169i	−0.291234	−	0.504431i	−0.974102	+	0.226110i	$0.927399\pi$
$578$	12.1520			0.505455
$579$		0			0
$580$	−6.57234	−	11.3836i	−0.272902	−	0.472680i
$581$		0			0
$582$		0			0
$583$	−3.88255	−	6.72477i	−0.160799	−	0.278511i
$584$	−8.02654	−	13.9024i	−0.332141	−	0.575285i
$585$		0			0
$586$	−7.04256	+	12.1981i	−0.290926	+	0.503898i
$587$	1.44801	−	2.50803i	0.0597658	−	0.103517i	−0.834594	−	0.550865i	$-0.814298\pi$
$587$	1.44801	−	2.50803i	0.0597658	−	0.103517i	0.894360	+	0.447348i	$0.147631\pi$
$588$		0			0
$589$	9.62612	+	16.6729i	0.396637	+	0.686996i
$590$	10.2880			0.423550
$591$		0			0
$592$	−1.00000			−0.0410997
$593$	−2.04394	+	3.54021i	−0.0839346	+	0.145379i	−0.904937	−	0.425546i	$-0.860082\pi$
$593$	−2.04394	+	3.54021i	−0.0839346	+	0.145379i	0.821002	+	0.570925i	$0.193415\pi$
$594$		0			0
$595$		0			0
$596$	2.60439	−	4.51093i	0.106680	−	0.184775i
$597$		0			0
$598$	0.722528	−	1.25146i	0.0295464	−	0.0511758i
$599$	−9.88255	+	17.1171i	−0.403790	+	0.699385i	−0.994180	−	0.107734i	$-0.965641\pi$
$599$	−9.88255	+	17.1171i	−0.403790	+	0.699385i	0.590390	+	0.807118i	$0.298974\pi$
$600$		0			0
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	−0.450516	−	0.892768i	$-0.648760\pi$
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	0.998418	−	0.0562261i	$-0.0179068\pi$
$602$		0			0
$603$		0			0
$604$	0.261450	−	0.452845i	0.0106383	−	0.0184260i
$605$	−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	$0.399895\pi$
$608$	3.54944	+	6.14781i	0.143949	+	0.249327i
$609$		0			0
$610$	−3.55563	+	6.15854i	−0.143963	+	0.249352i
$611$	−6.41342	+	11.1084i	−0.259459	+	0.449396i
$612$		0			0
$613$	−1.36033	−	2.35617i	−0.0549434	−	0.0951648i	0.837246	−	0.546827i	$-0.184165\pi$
$613$	−1.36033	−	2.35617i	−0.0549434	−	0.0951648i	−0.892189	+	0.451662i	$0.850831\pi$
$614$	−2.92766	−	5.07085i	−0.118151	−	0.204643i
$615$		0			0
$616$		0			0
$617$	9.21812	+	15.9663i	0.371108	+	0.642777i	0.989736	−	0.142906i	$-0.0456448\pi$
$617$	9.21812	+	15.9663i	0.371108	+	0.642777i	−0.618629	+	0.785684i	$0.712311\pi$
$618$		0			0
$619$	−0.107546			−0.00432262			−0.00216131	−	0.999998i	$-0.500688\pi$
$619$	−0.107546			−0.00432262			−0.00216131	+	0.999998i	$0.500688\pi$
$620$	−2.15383	−	3.73054i	−0.0864998	−	0.149822i
$621$		0			0
$622$	0.810892			0.0325138
$623$		0			0
$624$		0			0
$625$	−6.47848			−0.259139
$626$	5.28799	−	9.15907i	0.211351	−	0.366070i
$627$		0			0
$628$	4.43199	+	7.67643i	0.176856	+	0.306323i
$629$	−5.39926			−0.215282
$630$		0			0
$631$	35.7266			1.42225			0.711126	−	0.703064i	$-0.248185\pi$
$631$	35.7266			1.42225			0.711126	+	0.703064i	$0.248185\pi$
$632$	−4.19344	−	7.26325i	−0.166806	−	0.288916i
$633$		0			0
$634$	6.09820	−	10.5624i	0.242190	−	0.419486i
$635$	−21.3475			−0.847152
$636$		0			0
$637$		0			0
$638$	13.1447			0.520403
$639$		0			0
$640$	−0.794182	−	1.37556i	−0.0313928	−	0.0543739i
$641$	−17.3128			−0.683813			−0.341906	−	0.939734i	$-0.611073\pi$
$641$	−17.3128			−0.683813			−0.341906	+	0.939734i	$0.611073\pi$
$642$		0			0
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	−0.996451	−	0.0841700i	$-0.973176\pi$
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	0.425332	−	0.905037i	$-0.360157\pi$
$644$		0			0
$645$		0			0
$646$	19.1643	+	33.1936i	0.754011	+	1.30599i
$647$	1.27816	+	2.21384i	0.0502497	+	0.0870350i	0.890056	−	0.455851i	$-0.150665\pi$
$647$	1.27816	+	2.21384i	0.0502497	+	0.0870350i	−0.839807	+	0.542886i	$0.817332\pi$
$648$		0			0
$649$	−5.14400	+	8.90966i	−0.201920	+	0.349735i
$650$	5.95853	−	10.3205i	0.233713	−	0.404802i
$651$		0			0
$652$	10.9814	+	19.0204i	0.430066	+	0.744896i
$653$	−29.9766			−1.17308			−0.586538	−	0.809922i	$-0.699509\pi$
$653$	−29.9766			−1.17308			−0.586538	+	0.809922i	$0.699509\pi$
$654$		0			0
$655$	−5.04580			−0.197156
$656$	2.93818	−	5.08907i	0.114717	−	0.198695i
$657$		0			0
$658$		0			0
$659$	7.63162	−	13.2183i	0.297286	−	0.514914i	−0.678228	−	0.734851i	$-0.737252\pi$
$659$	7.63162	−	13.2183i	0.297286	−	0.514914i	0.975514	+	0.219937i	$0.0705853\pi$
$660$		0			0
$661$	−13.6261	+	23.6011i	−0.529994	+	0.917977i	0.469393	+	0.882989i	$0.344473\pi$
$661$	−13.6261	+	23.6011i	−0.529994	+	0.917977i	−0.999388	+	0.0349881i	$0.988861\pi$
$662$	7.83310	−	13.5673i	0.304442	−	0.527309i
$663$		0			0
$664$	1.18292	−	2.04887i	0.0459061	−	0.0795117i
$665$		0			0
$666$		0			0
$667$	1.24288	−	2.15273i	0.0481245	−	0.0833541i
$668$	−3.30037			−0.127695
$669$		0			0
$670$	−15.9680			−0.616896
$671$	−3.55563	−	6.15854i	−0.137264	−	0.237748i
$672$		0			0
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.0620280	−	0.998074i	$-0.480243\pi$
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.833344	−	0.552755i	$-0.186423\pi$
$674$	−4.21201	+	7.29541i	−0.162240	+	0.281009i
$675$		0			0
$676$	−5.07234	−	8.78555i	−0.195090	−	0.337906i
$677$	−2.54944	−	4.41576i	−0.0979830	−	0.169712i	0.812867	−	0.582450i	$-0.197906\pi$
$677$	−2.54944	−	4.41576i	−0.0979830	−	0.169712i	−0.910850	+	0.412738i	$0.864572\pi$
$678$		0			0
$679$		0			0
$680$	−4.28799	−	7.42702i	−0.164437	−	0.284813i
$681$		0			0
$682$	4.30766			0.164949
$683$	7.77197	+	13.4614i	0.297386	+	0.515088i	0.975537	−	0.219835i	$-0.0705518\pi$
$683$	7.77197	+	13.4614i	0.297386	+	0.515088i	−0.678151	+	0.734923i	$0.737218\pi$
$684$		0			0
$685$	33.7738			1.29043
$686$		0			0
$687$		0			0
$688$	1.66621			0.0635236
$689$	−11.7596	+	20.3682i	−0.448005	+	0.775967i
$690$		0			0
$691$	11.6483	+	20.1755i	0.443123	+	0.767512i	0.997919	−	0.0644744i	$-0.0205371\pi$
$691$	11.6483	+	20.1755i	0.443123	+	0.767512i	−0.554796	+	0.831986i	$0.687204\pi$
$692$	19.1075			0.726360
$693$		0			0
$694$	−0.567323			−0.0215353
$695$	−10.3665	−	17.9553i	−0.393225	−	0.681085i
$696$		0			0
$697$	15.8640	−	27.4772i	0.600891	−	1.04077i
$698$	−0.00728378			−0.000275695
$699$		0			0
$700$		0			0
$701$	45.6464			1.72404			0.862020	−	0.506874i	$-0.169199\pi$
$701$	45.6464			1.72404			0.862020	+	0.506874i	$0.169199\pi$
$702$		0			0
$703$	−3.54944	−	6.14781i	−0.133870	−	0.231869i
$704$	1.58836			0.0598637
$705$		0			0
$706$	−3.32691	−	5.76238i	−0.125210	−	0.216870i
$707$		0			0
$708$		0			0
$709$	−9.00069	−	15.5897i	−0.338028	−	0.585482i	0.646034	−	0.763309i	$-0.276427\pi$
$709$	−9.00069	−	15.5897i	−0.338028	−	0.585482i	−0.984062	+	0.177827i	$0.943093\pi$
$710$	10.1025	+	17.4981i	0.379141	+	0.656692i
$711$		0			0
$712$	1.60507	−	2.78007i	0.0601527	−	0.104188i
$713$	0.407305	−	0.705474i	0.0152537	−	0.0264202i
$714$		0			0
$715$	−6.06870	−	10.5113i	−0.226957	−	0.393100i
$716$	−16.0741			−0.600718
$717$		0			0
$718$	−0.797135			−0.0297488
$719$	18.4389	−	31.9371i	0.687654	−	1.19105i	−0.284941	−	0.958545i	$-0.591974\pi$
$719$	18.4389	−	31.9371i	0.687654	−	1.19105i	0.972595	−	0.232506i	$-0.0746926\pi$
$720$		0			0
$721$		0			0
$722$	−15.6971	+	27.1881i	−0.584185	+	1.01184i
$723$		0			0
$724$	4.02654	−	6.97418i	0.149645	−	0.259193i
$725$	10.2498	−	17.7531i	0.380666	−	0.659334i
$726$		0			0
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	0.431692	+	0.902021i	$0.357917\pi$
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	−0.997019	+	0.0771543i	$0.975417\pi$
$728$		0			0
$729$		0			0
$730$	−12.7491	+	22.0820i	−0.471864	+	0.817293i
$731$	8.99628			0.332739
$732$		0			0
$733$	−6.15059			−0.227177			−0.113589	−	0.993528i	$-0.536235\pi$
$733$	−6.15059			−0.227177			−0.113589	+	0.993528i	$0.536235\pi$
$734$	−7.71634	−	13.3651i	−0.284815	−	0.493314i
$735$		0			0
$736$	0.150186	−	0.260130i	0.00553593	−	0.00958851i
$737$	7.98398	−	13.8287i	0.294094	−	0.509385i
$738$		0			0
$739$	−20.3912	−	35.3186i	−0.750103	−	1.29922i	−0.947772	−	0.318947i	$-0.896671\pi$
$739$	−20.3912	−	35.3186i	−0.750103	−	1.29922i	0.197670	−	0.980269i	$-0.436663\pi$
$740$	0.794182	+	1.37556i	0.0291947	+	0.0505667i
$741$		0			0
$742$		0			0
$743$	−7.25271	−	12.5621i	−0.266076	−	0.460858i	0.701769	−	0.712405i	$-0.252394\pi$
$743$	−7.25271	−	12.5621i	−0.266076	−	0.460858i	−0.967845	+	0.251547i	$0.919061\pi$
$744$		0			0
$745$	−8.27342			−0.303115
$746$	−5.12110	−	8.87000i	−0.187497	−	0.324754i
$747$		0			0
$748$	8.57598			0.313569
$749$		0			0
$750$		0			0
$751$	4.18911			0.152863			0.0764314	−	0.997075i	$-0.475647\pi$
$751$	4.18911			0.152863			0.0764314	+	0.997075i	$0.475647\pi$
$752$	−1.33310	+	2.30900i	−0.0486133	+	0.0842007i
$753$		0			0
$754$	−19.9065	−	34.4791i	−0.724953	−	1.25566i
$755$	−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	$0.486189\pi$
$758$	−12.5043	−	21.6581i	−0.454178	−	0.786659i
$759$		0			0
$760$	5.63781	−	9.76497i	0.204505	−	0.354213i
$761$	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
$763$		0			0
$764$	23.9629			0.866946
$765$		0			0
$766$	3.13348	+	5.42734i	0.113217	+	0.196098i
$767$	31.1606			1.12515
$768$		0			0
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	0.960985	+	0.276600i	$0.0892078\pi$
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	−0.240950	+	0.970538i	$0.577459\pi$
$770$		0			0
$771$		0			0
$772$	−4.88255	−	8.45682i	−0.175727	−	0.304368i
$773$	18.0698	+	31.2978i	0.649925	+	1.12570i	0.983140	+	0.182853i	$0.0585332\pi$
$773$	18.0698	+	31.2978i	0.649925	+	1.12570i	−0.333215	+	0.942851i	$0.608133\pi$
$774$		0			0
$775$	3.35896	−	5.81788i	0.120657	−	0.208985i
$776$	−0.712008	+	1.23323i	−0.0255596	+	0.0442705i
$777$		0			0
$778$	−10.8171	−	18.7357i	−0.387811	−	0.671709i
$779$	41.7156			1.49462
$780$		0			0
$781$	−20.2051			−0.722994
$782$	0.810892	−	1.40451i	0.0289974	−	0.0502251i
$783$		0			0
$784$		0			0
$785$	7.03961	−	12.1930i	0.251254	−	0.435186i
$786$		0			0
$787$	−22.3189	+	38.6574i	−0.795582	+	1.37799i	0.126888	+	0.991917i	$0.459501\pi$
$787$	−22.3189	+	38.6574i	−0.795582	+	1.37799i	−0.922469	+	0.386071i	$0.873832\pi$
$788$	−9.12178	+	15.7994i	−0.324950	+	0.562830i
$789$		0			0
$790$	−6.66071	+	11.5367i	−0.236977	+	0.410457i
$791$		0			0
$792$		0			0
$793$	−10.7694	+	18.6532i	−0.382433	+	0.662394i
$794$	4.10617			0.145722
$795$		0			0
$796$	18.0989			0.641498
$797$	26.2836	+	45.5245i	0.931012	+	1.61256i	0.781595	+	0.623786i	$0.214407\pi$
$797$	26.2836	+	45.5245i	0.931012	+	1.61256i	0.149418	+	0.988774i	$0.452260\pi$
$798$		0			0
$799$	−7.19777	+	12.4669i	−0.254639	+	0.441047i
$800$	1.23855	−	2.14523i	0.0437894	−	0.0758454i
$801$		0			0
$802$	8.37085	+	14.4987i	0.295585	+	0.511969i
$803$	−12.7491	−	22.0820i	−0.449905	−	0.779258i
$804$		0			0
$805$		0			0
$806$	−6.52359	−	11.2992i	−0.229784	−	0.397997i
$807$		0			0
$808$	12.0334			0.423334
$809$	−7.40290	−	12.8222i	−0.260272	−	0.450804i	0.706042	−	0.708170i	$-0.250479\pi$
$809$	−7.40290	−	12.8222i	−0.260272	−	0.450804i	−0.966314	+	0.257365i	$0.917146\pi$
$810$		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
$813$		0			0
$814$	−1.58836			−0.0556721
$815$	17.4425	−	30.2113i	0.610984	−	1.05826i
$816$		0			0
$817$	5.91411	+	10.2435i	0.206908	+	0.358376i
$818$	8.76509			0.306464
$819$		0			0
$820$	−9.33379			−0.325950
$821$	21.9091	+	37.9477i	0.764632	+	1.32438i	0.940441	+	0.339958i	$0.110413\pi$
$821$	21.9091	+	37.9477i	0.764632	+	1.32438i	−0.175808	+	0.984424i	$0.556254\pi$
$822$		0			0
$823$	−15.6712	+	27.1434i	−0.546265	+	0.946158i	0.452262	+	0.891885i	$0.350617\pi$
$823$	−15.6712	+	27.1434i	−0.546265	+	0.946158i	−0.998526	+	0.0542727i	$0.982716\pi$
$824$	6.09888			0.212465
$825$		0			0
$826$		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	0.999699	+	0.0245357i	$0.00781074\pi$
$829$	15.0036	+	25.9871i	0.521098	+	0.902568i	−0.478601	+	0.878033i	$0.658856\pi$
$830$	−3.75781			−0.130435
$831$		0			0
$832$	−2.40545	−	4.16635i	−0.0833938	−	0.144442i
$833$		0			0
$834$		0			0
$835$	2.62110	+	4.53987i	0.0907068	+	0.157109i
$836$	5.63781	+	9.76497i	0.194988	+	0.337728i
$837$		0			0
$838$	−0.210149	+	0.363988i	−0.00725946	+	0.0125738i
$839$	18.0167	−	31.2059i	0.622006	−	1.07735i	−0.367106	−	0.930179i	$-0.619651\pi$
$839$	18.0167	−	31.2059i	0.622006	−	1.07735i	0.989112	−	0.147167i	$-0.0470154\pi$
$840$		0			0
$841$	−19.7429	−	34.1957i	−0.680789	−	1.17916i
$842$	−6.57598			−0.226623
$843$		0			0
$844$	−0.332415			−0.0114422
$845$	−8.05673	+	13.9547i	−0.277160	+	0.480055i
$846$		0			0
$847$		0			0
$848$	−2.44437	+	4.23377i	−0.0839399	+	0.145388i
$849$		0			0
$850$	6.68725	−	11.5827i	0.229371	−	0.397282i
$851$	−0.150186	+	0.260130i	−0.00514831	+	0.00891713i
$852$		0			0
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	−0.575964	−	0.817475i	$-0.695373\pi$
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	0.995936	+	0.0900617i	$0.0287064\pi$
$854$		0			0
$855$		0			0
$856$	1.54325	−	2.67299i	0.0527473	−	0.0913610i
$857$	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	$0.642027\pi$
$860$	−1.32327	−	2.29197i	−0.0451232	−	0.0781557i
$861$		0			0
$862$	−11.0439	+	19.1287i	−0.376158	+	0.651525i
$863$	1.34981	−	2.33795i	0.0459482	−	0.0795846i	−0.842137	−	0.539264i	$-0.818702\pi$
$863$	1.34981	−	2.33795i	0.0459482	−	0.0795846i	0.888085	+	0.459680i	$0.152036\pi$
$864$		0			0
$865$	−15.1749	−	26.2836i	−0.515961	−	0.893671i
$866$	−4.71634	−	8.16894i	−0.160268	−	0.277592i
$867$		0			0
$868$		0			0
$869$	−6.66071	−	11.5367i	−0.225949	−	0.391355i
$870$		0			0
$871$	−48.3643			−1.63876
$872$	1.14400	+	1.98146i	0.0387406	+	0.0671007i
$873$		0			0
$874$	2.13231			0.0721263
$875$		0			0
$876$		0			0
$877$	−11.0916			−0.374537			−0.187268	−	0.982309i	$-0.559963\pi$
$877$	−11.0916			−0.374537			−0.187268	+	0.982309i	$0.559963\pi$
$878$	−15.6032	+	27.0256i	−0.526583	+	0.912069i
$879$		0			0
$880$	−1.26145	−	2.18490i	−0.0425235	−	0.0736528i
$881$	−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	$-0.689050\pi$
$883$	−33.2581			−1.11923			−0.559613	+	0.828754i	$0.689050\pi$
$884$	−12.9876	−	22.4952i	−0.436821	−	0.756596i
$885$		0			0
$886$	6.52723	−	11.3055i	0.219287	−	0.379816i
$887$	40.5672			1.36211			0.681056	−	0.732231i	$-0.261521\pi$
$887$	40.5672			1.36211			0.681056	+	0.732231i	$0.261521\pi$
$888$		0			0
$889$		0			0
$890$	−5.09888			−0.170915
$891$		0			0
$892$	−3.16621	−	5.48403i	−0.106012	−	0.183619i
$893$	−18.9271			−0.633371
$894$		0			0
$895$	12.7658	+	22.1110i	0.426713	+	0.739089i
$896$		0			0
$897$		0			0
$898$	−4.95853	−	8.58843i	−0.165468	−	0.286599i
$899$	−11.2218	−	19.4367i	−0.374267	−	0.648249i
$900$		0			0
$901$	−13.1978	+	22.8592i	−0.439681	+	0.761551i
$902$	4.66690	−	8.08330i	0.155391	−	0.269144i
$903$		0			0
$904$	9.73236	+	16.8569i	0.323693	+	0.560654i
$905$	−12.7912			−0.425195
$906$		0			0
$907$	30.1135			0.999901			0.499950	−	0.866054i	$-0.333352\pi$
$907$	30.1135			0.999901			0.499950	+	0.866054i	$0.333352\pi$
$908$	11.6545	−	20.1862i	0.386769	−	0.669903i
$909$		0			0
$910$		0			0
$911$	−14.6113	+	25.3075i	−0.484093	+	0.838473i	−0.999833	−	0.0182717i	$-0.994184\pi$
$911$	−14.6113	+	25.3075i	−0.484093	+	0.838473i	0.515740	+	0.856745i	$0.327517\pi$
$912$		0			0
$913$	1.87890	−	3.25436i	0.0621826	−	0.107704i
$914$	12.2615	−	21.2375i	0.405573	−	0.702473i
$915$		0			0
$916$	−2.47710	+	4.29046i	−0.0818457	+	0.141761i
$917$		0			0
$918$		0			0
$919$	−5.52359	+	9.56714i	−0.182206	+	0.315591i	−0.942632	−	0.333835i	$-0.891657\pi$
$919$	−5.52359	+	9.56714i	−0.182206	+	0.315591i	0.760425	+	0.649426i	$0.224991\pi$
$920$	−0.477100			−0.0157295
$921$		0			0
$922$	−3.51052			−0.115613
$923$	30.5989	+	52.9988i	1.00717	+	1.74448i
$924$		0			0
$925$	−1.23855	+	2.14523i	−0.0407233	+	0.0705348i
$926$	8.69413	−	15.0587i	0.285707	−	0.494859i
$927$		0			0
$928$	−4.13781	−	7.16689i	−0.135830	−	0.235265i
$929$	21.1669	+	36.6621i	0.694463	+	1.20285i	0.970361	+	0.241659i	$0.0776915\pi$
$929$	21.1669	+	36.6621i	0.694463	+	1.20285i	−0.275898	+	0.961187i	$0.588975\pi$
$930$		0			0
$931$		0			0
$932$	7.13781	+	12.3630i	0.233807	+	0.404965i
$933$		0			0
$934$	−13.3979			−0.438392
$935$	−6.81089	−	11.7968i	−0.222740	−	0.385797i
$936$		0			0
$937$	11.7651			0.384349			0.192174	−	0.981361i	$-0.438446\pi$
$937$	11.7651			0.384349			0.192174	+	0.981361i	$0.438446\pi$
$938$		0			0
$939$		0			0
$940$	4.23491			0.138127
$941$	−7.28799	+	12.6232i	−0.237582	+	0.411504i	−0.960020	−	0.279932i	$-0.909688\pi$
$941$	−7.28799	+	12.6232i	−0.237582	+	0.411504i	0.722438	+	0.691436i	$0.243021\pi$
$942$		0			0
$943$	−0.882546	−	1.52861i	−0.0287397	−	0.0497785i
$944$	6.47710			0.210812
$945$		0			0
$946$	2.64654			0.0860466
$947$	3.12178	+	5.40709i	0.101444	+	0.175707i	0.912280	−	0.409567i	$-0.134320\pi$
$947$	3.12178	+	5.40709i	0.101444	+	0.175707i	−0.810836	+	0.585274i	$0.800987\pi$
$948$		0			0
$949$	−38.6148	+	66.8828i	−1.25349	+	2.17111i
$950$	17.5846			0.570521
$951$		0			0
$952$		0			0
$953$	−28.0173			−0.907570			−0.453785	−	0.891111i	$-0.649927\pi$
$953$	−28.0173			−0.907570			−0.453785	+	0.891111i	$0.649927\pi$
$954$		0			0
$955$	−19.0309	−	32.9624i	−0.615825	−	1.06664i
$956$	4.97524			0.160911
$957$		0			0
$958$	−10.4029	−	18.0183i	−0.336102	−	0.582146i
$959$		0			0
$960$		0			0
$961$	11.8225	+	20.4772i	0.381371	+	0.660554i
$962$	2.40545	+	4.16635i	0.0775547	+	0.134329i
$963$		0			0
$964$	−6.50000	+	11.2583i	−0.209351	+	0.362606i
$965$	−7.75526	+	13.4325i	−0.249651	+	0.432408i
$966$		0			0
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	0.999962	+	0.00876132i	$0.00278885\pi$
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	−0.492393	+	0.870373i	$0.663878\pi$
$968$	−8.47710			−0.272464
$969$		0			0
$970$	2.26186			0.0726238
$971$	2.82141	−	4.88683i	0.0905434	−	0.156826i	−0.817196	−	0.576359i	$-0.804473\pi$
$971$	2.82141	−	4.88683i	0.0905434	−	0.156826i	0.907740	+	0.419533i	$0.137806\pi$
$972$		0			0
$973$		0			0
$974$	16.2472	−	28.1410i	0.520594	−	0.901696i
$975$		0			0
$976$	−2.23855	+	3.87728i	−0.0716542	+	0.124109i
$977$	3.24652	−	5.62314i	0.103865	−	0.179900i	−0.809409	−	0.587246i	$-0.800212\pi$
$977$	3.24652	−	5.62314i	0.103865	−	0.179900i	0.913274	+	0.407346i	$0.133546\pi$
$978$		0			0
$979$	2.54944	−	4.41576i	0.0814805	−	0.141128i
$980$		0			0
$981$		0			0
$982$	9.66071	−	16.7328i	0.308286	−	0.533966i
$983$	−30.3063			−0.966620			−0.483310	−	0.875449i	$-0.660566\pi$
$983$	−30.3063			−0.966620			−0.483310	+	0.875449i	$0.660566\pi$
$984$		0			0
$985$	28.9774			0.923298
$986$	−22.3411	−	38.6959i	−0.711485	−	1.23233i
$987$		0			0
$988$	17.0760	−	29.5765i	0.543259	−	0.940953i
$989$	0.250241	−	0.433430i	0.00795720	−	0.0137823i
$990$		0			0
$991$	11.1669	+	19.3416i	0.354728	+	0.614407i	0.987071	−	0.160281i	$-0.0512401\pi$
$991$	11.1669	+	19.3416i	0.354728	+	0.614407i	−0.632343	+	0.774688i	$0.717907\pi$
$992$	−1.35600	−	2.34867i	−0.0430532	−	0.0745703i
$993$		0			0
$994$		0			0
$995$	−14.3738	−	24.8962i	−0.455680	−	0.789262i
$996$		0			0
$997$	8.76509			0.277593			0.138797	−	0.990321i	$-0.455677\pi$
$997$	8.76509			0.277593			0.138797	+	0.990321i	$0.455677\pi$
$998$	5.57530	+	9.65670i	0.176483	+	0.305677i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.o.667.3		6
3.2	odd	2		882.2.h.p.79.1		6
7.2	even	3		2646.2.f.m.883.1		6
7.3	odd	6		378.2.e.d.235.3		6
7.4	even	3		2646.2.e.p.2125.1		6
7.5	odd	6		2646.2.f.l.883.3		6
7.6	odd	2		378.2.h.c.289.1		6
9.4	even	3		2646.2.e.p.1549.1		6
9.5	odd	6		882.2.e.o.373.3		6
21.2	odd	6		882.2.f.o.295.1		6
21.5	even	6		882.2.f.n.295.3		6
21.11	odd	6		882.2.e.o.655.3		6
21.17	even	6		126.2.e.c.25.1	✓	6
21.20	even	2		126.2.h.d.79.3	yes	6
28.3	even	6		3024.2.q.g.2881.3		6
28.27	even	2		3024.2.t.h.289.1		6
63.2	odd	6		7938.2.a.bw.1.1		3
63.4	even	3	inner	2646.2.h.o.361.3		6
63.5	even	6		882.2.f.n.589.3		6
63.13	odd	6		378.2.e.d.37.3		6
63.16	even	3		7938.2.a.bz.1.3		3
63.20	even	6		1134.2.g.m.163.1		6
63.23	odd	6		882.2.f.o.589.1		6
63.31	odd	6		378.2.h.c.361.1		6
63.32	odd	6		882.2.h.p.67.1		6
63.34	odd	6		1134.2.g.l.163.3		6
63.38	even	6		1134.2.g.m.487.1		6
63.40	odd	6		2646.2.f.l.1765.3		6
63.41	even	6		126.2.e.c.121.1	yes	6
63.47	even	6		7938.2.a.bv.1.3		3
63.52	odd	6		1134.2.g.l.487.3		6
63.58	even	3		2646.2.f.m.1765.1		6
63.59	even	6		126.2.h.d.67.3	yes	6
63.61	odd	6		7938.2.a.ca.1.1		3
84.59	odd	6		1008.2.q.g.529.3		6
84.83	odd	2		1008.2.t.h.961.1		6
252.31	even	6		3024.2.t.h.1873.1		6
252.59	odd	6		1008.2.t.h.193.1		6
252.139	even	6		3024.2.q.g.2305.3		6
252.167	odd	6		1008.2.q.g.625.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	21.17	even	6
126.2.e.c.121.1	yes	6	63.41	even	6
126.2.h.d.67.3	yes	6	63.59	even	6
126.2.h.d.79.3	yes	6	21.20	even	2
378.2.e.d.37.3		6	63.13	odd	6
378.2.e.d.235.3		6	7.3	odd	6
378.2.h.c.289.1		6	7.6	odd	2
378.2.h.c.361.1		6	63.31	odd	6
882.2.e.o.373.3		6	9.5	odd	6
882.2.e.o.655.3		6	21.11	odd	6
882.2.f.n.295.3		6	21.5	even	6
882.2.f.n.589.3		6	63.5	even	6
882.2.f.o.295.1		6	21.2	odd	6
882.2.f.o.589.1		6	63.23	odd	6
882.2.h.p.67.1		6	63.32	odd	6
882.2.h.p.79.1		6	3.2	odd	2
1008.2.q.g.529.3		6	84.59	odd	6
1008.2.q.g.625.3		6	252.167	odd	6
1008.2.t.h.193.1		6	252.59	odd	6
1008.2.t.h.961.1		6	84.83	odd	2
1134.2.g.l.163.3		6	63.34	odd	6
1134.2.g.l.487.3		6	63.52	odd	6
1134.2.g.m.163.1		6	63.20	even	6
1134.2.g.m.487.1		6	63.38	even	6
2646.2.e.p.1549.1		6	9.4	even	3
2646.2.e.p.2125.1		6	7.4	even	3
2646.2.f.l.883.3		6	7.5	odd	6
2646.2.f.l.1765.3		6	63.40	odd	6
2646.2.f.m.883.1		6	7.2	even	3
2646.2.f.m.1765.1		6	63.58	even	3
2646.2.h.o.361.3		6	63.4	even	3	inner
2646.2.h.o.667.3		6	1.1	even	1	trivial
3024.2.q.g.2305.3		6	252.139	even	6
3024.2.q.g.2881.3		6	28.3	even	6
3024.2.t.h.289.1		6	28.27	even	2
3024.2.t.h.1873.1		6	252.31	even	6
7938.2.a.bv.1.3		3	63.47	even	6
7938.2.a.bw.1.1		3	63.2	odd	6
7938.2.a.bz.1.3		3	63.16	even	3
7938.2.a.ca.1.1		3	63.61	odd	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.58836 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.58836 q^{5} +1.00000 q^{8} +(-0.794182 - 1.37556i) q^{10} +1.58836 q^{11} +(-2.40545 - 4.16635i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.69963 - 4.67589i) q^{17} +(3.54944 - 6.14781i) q^{19} +(-0.794182 + 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} -0.300372 q^{23} -2.47710 q^{25} +(-2.40545 + 4.16635i) q^{26} +(-4.13781 + 7.16689i) q^{29} +(-1.35600 + 2.34867i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.69963 + 4.67589i) q^{34} +(0.500000 - 0.866025i) q^{37} -7.09888 q^{38} +1.58836 q^{40} +(2.93818 + 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(-0.794182 + 1.37556i) q^{44} +(0.150186 + 0.260130i) q^{46} +(-1.33310 - 2.30900i) q^{47} +(1.23855 + 2.14523i) q^{50} +4.81089 q^{52} +(-2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +8.27561 q^{58} +(-3.23855 + 5.60933i) q^{59} +(-2.23855 - 3.87728i) q^{61} +2.71201 q^{62} +1.00000 q^{64} +(-3.82072 - 6.61769i) q^{65} +(5.02654 - 8.70623i) q^{67} +5.39926 q^{68} -12.7207 q^{71} +(-8.02654 - 13.9024i) q^{73} -1.00000 q^{74} +(3.54944 + 6.14781i) q^{76} +(-4.19344 - 7.26325i) q^{79} +(-0.794182 - 1.37556i) q^{80} +(2.93818 - 5.08907i) q^{82} +(1.18292 - 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +1.66621 q^{86} +1.58836 q^{88} +(1.60507 - 2.78007i) q^{89} +(0.150186 - 0.260130i) q^{92} +(-1.33310 + 2.30900i) q^{94} +(5.63781 - 9.76497i) q^{95} +(-0.712008 + 1.23323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + q^{10} - 2 q^{11} - 8 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} - 14 q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} + 3 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} - 9 q^{47} + 2 q^{50} + 16 q^{52} - 15 q^{53} + 26 q^{55} - 10 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 8 q^{68} - 14 q^{71} - 19 q^{73} - 6 q^{74} + 3 q^{76} + 5 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} - 9 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 6 * q^8 + q^10 - 2 * q^11 - 8 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 - 14 * q^23 - 4 * q^25 - 8 * q^26 + 5 * q^29 - 20 * q^31 - 3 * q^32 - 4 * q^34 + 3 * q^37 - 6 * q^38 - 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 - 9 * q^47 + 2 * q^50 + 16 * q^52 - 15 * q^53 + 26 * q^55 - 10 * q^58 - 14 * q^59 - 8 * q^61 + 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 + 8 * q^68 - 14 * q^71 - 19 * q^73 - 6 * q^74 + 3 * q^76 + 5 * q^79 + q^80 + 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 - 9 * q^89 + 7 * q^92 - 9 * q^94 + 4 * q^95 - 28 * q^97

Introduction

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