LMFDB - Embedded newform 588.3.g.d.295.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,2,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.489494783471841.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 18 x^{8} - 22 x^{7} + 33 x^{6} - 44 x^{5} + 72 x^{4} + \cdots + 64 $ x^12 - 3x^11 + 7x^10 - 11x^9 + 18x^8 - 22x^7 + 33x^6 - 44x^5 + 72x^4 - 88x^3 + 112x^2 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.2
Root			$1.19375 + 0.758257i$ of defining polynomial
Character	$\chi$	$=$	588.295
Dual form			588.3.g.d.295.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.83926 + 0.785573i) q^{2} -1.73205i q^{3} +(2.76575 - 2.88975i) q^{4} +8.17539 q^{5} +(1.36065 + 3.18569i) q^{6} +(-2.81683 + 7.48769i) q^{8} -3.00000 q^{9} +(-15.0367 + 6.42236i) q^{10} -15.5659i q^{11} +(-5.00519 - 4.79042i) q^{12} +20.4200 q^{13} -14.1602i q^{15} +(-0.701254 - 15.9846i) q^{16} +5.97018 q^{17} +(5.51778 - 2.35672i) q^{18} -4.19049i q^{19} +(22.6111 - 23.6248i) q^{20} +(12.2282 + 28.6297i) q^{22} +29.3602i q^{23} +(12.9691 + 4.87889i) q^{24} +41.8370 q^{25} +(-37.5577 + 16.0414i) q^{26} +5.19615i q^{27} -7.89812 q^{29} +(11.1239 + 26.0443i) q^{30} -35.3829i q^{31} +(13.8469 + 28.8490i) q^{32} -26.9609 q^{33} +(-10.9807 + 4.69002i) q^{34} +(-8.29725 + 8.66924i) q^{36} -49.2518 q^{37} +(3.29194 + 7.70740i) q^{38} -35.3685i q^{39} +(-23.0286 + 61.2148i) q^{40} +4.11644 q^{41} -19.6131i q^{43} +(-44.9815 - 43.0514i) q^{44} -24.5262 q^{45} +(-23.0646 - 54.0010i) q^{46} +30.5134i q^{47} +(-27.6862 + 1.21461i) q^{48} +(-76.9490 + 32.8660i) q^{50} -10.3407i q^{51} +(56.4767 - 59.0087i) q^{52} +40.4284 q^{53} +(-4.08196 - 9.55707i) q^{54} -127.257i q^{55} -7.25815 q^{57} +(14.5267 - 6.20455i) q^{58} +83.1502i q^{59} +(-40.9193 - 39.1635i) q^{60} +3.43067 q^{61} +(27.7959 + 65.0783i) q^{62} +(-48.1310 - 42.1830i) q^{64} +166.942 q^{65} +(49.5881 - 21.1798i) q^{66} +5.17488i q^{67} +(16.5120 - 17.2523i) q^{68} +50.8534 q^{69} -75.1139i q^{71} +(8.45048 - 22.4631i) q^{72} +21.5545 q^{73} +(90.5868 - 38.6909i) q^{74} -72.4638i q^{75} +(-12.1095 - 11.5899i) q^{76} +(27.7846 + 65.0519i) q^{78} -62.5091i q^{79} +(-5.73302 - 130.681i) q^{80} +9.00000 q^{81} +(-7.57121 + 3.23377i) q^{82} -58.0935i q^{83} +48.8086 q^{85} +(15.4075 + 36.0736i) q^{86} +13.6799i q^{87} +(116.553 + 43.8464i) q^{88} +135.578 q^{89} +(45.1100 - 19.2671i) q^{90} +(84.8435 + 81.2030i) q^{92} -61.2850 q^{93} +(-23.9705 - 56.1221i) q^{94} -34.2589i q^{95} +(49.9679 - 23.9835i) q^{96} -61.8562 q^{97} +46.6977i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{4} - 8 q^{5} + 12 q^{6} - 10 q^{8} - 36 q^{9} - 28 q^{10} - 24 q^{12} + 24 q^{13} - 14 q^{16} + 40 q^{17} - 6 q^{18} + 20 q^{20} - 88 q^{22} + 36 q^{24} + 180 q^{25} - 100 q^{26} + 72 q^{29}+ \cdots + 264 q^{97}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^4 - 8 * q^5 + 12 * q^6 - 10 * q^8 - 36 * q^9 - 28 * q^10 - 24 * q^12 + 24 * q^13 - 14 * q^16 + 40 * q^17 - 6 * q^18 + 20 * q^20 - 88 * q^22 + 36 * q^24 + 180 * q^25 - 100 * q^26 + 72 * q^29 + 72 * q^30 + 142 * q^32 + 100 * q^34 - 6 * q^36 - 88 * q^37 - 128 * q^38 + 28 * q^40 + 200 * q^41 - 40 * q^44 + 24 * q^45 - 24 * q^46 - 48 * q^48 - 346 * q^50 + 364 * q^52 + 104 * q^53 - 36 * q^54 + 148 * q^58 + 96 * q^60 - 104 * q^61 - 64 * q^62 - 70 * q^64 + 176 * q^65 - 24 * q^66 - 188 * q^68 + 192 * q^69 + 30 * q^72 - 312 * q^73 + 4 * q^74 - 432 * q^76 + 48 * q^78 + 564 * q^80 + 108 * q^81 - 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 + 552 * q^89 + 84 * q^90 + 232 * q^92 - 48 * q^93 + 144 * q^94 + 108 * q^96 + 264 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.83926	+	0.785573i	−0.919630	+	0.392787i
$2$	−1.83926	+	0.785573i	−0.919630	+	0.392787i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.76575	−	2.88975i	0.691437	−	0.722436i
$5$	8.17539			1.63508			0.817539	−	0.575874i	$-0.195338\pi$
$5$	8.17539			1.63508			0.817539	+	0.575874i	$0.195338\pi$
$6$	1.36065	+	3.18569i	0.226775	+	0.530948i
$7$		0			0
$7$		0			0
$8$	−2.81683	+	7.48769i	−0.352103	+	0.935961i
$9$	−3.00000			−0.333333
$10$	−15.0367	+	6.42236i	−1.50367	+	0.642236i
$11$		−	15.5659i		−	1.41508i	−0.706672	−	0.707541i	$-0.749805\pi$
$11$		−	15.5659i		−	1.41508i	0.706672	−	0.707541i	$-0.250195\pi$
$12$	−5.00519	−	4.79042i	−0.417099	−	0.399202i
$13$	20.4200			1.57077			0.785386	−	0.619006i	$-0.212464\pi$
$13$	20.4200			1.57077			0.785386	+	0.619006i	$0.212464\pi$
$14$		0			0
$15$		−	14.1602i		−	0.944012i
$16$	−0.701254	−	15.9846i	−0.0438284	−	0.999039i
$17$	5.97018			0.351187			0.175594	−	0.984463i	$-0.443816\pi$
$17$	5.97018			0.351187			0.175594	+	0.984463i	$0.443816\pi$
$18$	5.51778	−	2.35672i	0.306543	−	0.130929i
$19$		−	4.19049i		−	0.220552i	−0.993901	−	0.110276i	$-0.964826\pi$
$19$		−	4.19049i		−	0.220552i	0.993901	−	0.110276i	$-0.0351735\pi$
$20$	22.6111	−	23.6248i	1.13055	−	1.18124i
$21$		0			0
$22$	12.2282	+	28.6297i	0.555825	+	1.30135i
$23$			29.3602i			1.27653i	0.769817	+	0.638265i	$0.220348\pi$
$23$			29.3602i			1.27653i	−0.769817	+	0.638265i	$0.779652\pi$
$24$	12.9691	+	4.87889i	0.540377	+	0.203287i
$25$	41.8370			1.67348
$26$	−37.5577	+	16.0414i	−1.44453	+	0.616978i
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−7.89812			−0.272349			−0.136174	−	0.990685i	$-0.543481\pi$
$29$	−7.89812			−0.272349			−0.136174	+	0.990685i	$0.543481\pi$
$30$	11.1239	+	26.0443i	0.370795	+	0.868142i
$31$		−	35.3829i		−	1.14138i	−0.821164	−	0.570692i	$-0.806675\pi$
$31$		−	35.3829i		−	1.14138i	0.821164	−	0.570692i	$-0.193325\pi$
$32$	13.8469	+	28.8490i	0.432715	+	0.901531i
$33$	−26.9609			−0.816998
$34$	−10.9807	+	4.69002i	−0.322962	+	0.137942i
$35$		0			0
$36$	−8.29725	+	8.66924i	−0.230479	+	0.240812i
$37$	−49.2518			−1.33113			−0.665565	−	0.746340i	$-0.731809\pi$
$37$	−49.2518			−1.33113			−0.665565	+	0.746340i	$0.731809\pi$
$38$	3.29194	+	7.70740i	0.0866300	+	0.202826i
$39$		−	35.3685i		−	0.906886i
$40$	−23.0286	+	61.2148i	−0.575716	+	1.53037i
$41$	4.11644			0.100401			0.0502005	−	0.998739i	$-0.484014\pi$
$41$	4.11644			0.100401			0.0502005	+	0.998739i	$0.484014\pi$
$42$		0			0
$43$		−	19.6131i		−	0.456118i	−0.973647	−	0.228059i	$-0.926762\pi$
$43$		−	19.6131i		−	0.456118i	0.973647	−	0.228059i	$-0.0732380\pi$
$44$	−44.9815	−	43.0514i	−1.02231	−	0.978441i
$45$	−24.5262			−0.545026
$46$	−23.0646	−	54.0010i	−0.501404	−	1.17394i
$47$			30.5134i			0.649222i	0.945848	+	0.324611i	$0.105233\pi$
$47$			30.5134i			0.649222i	−0.945848	+	0.324611i	$0.894767\pi$
$48$	−27.6862	+	1.21461i	−0.576795	+	0.0253043i
$49$		0			0
$50$	−76.9490	+	32.8660i	−1.53898	+	0.657320i
$51$		−	10.3407i		−	0.202758i
$52$	56.4767	−	59.0087i	1.08609	−	1.13478i
$53$	40.4284			0.762799			0.381400	−	0.924410i	$-0.375442\pi$
$53$	40.4284			0.762799			0.381400	+	0.924410i	$0.375442\pi$
$54$	−4.08196	−	9.55707i	−0.0755918	−	0.176983i
$55$		−	127.257i		−	2.31377i
$56$		0			0
$57$	−7.25815			−0.127336
$58$	14.5267	−	6.20455i	0.250460	−	0.106975i
$59$			83.1502i			1.40932i	0.709543	+	0.704662i	$0.248902\pi$
$59$			83.1502i			1.40932i	−0.709543	+	0.704662i	$0.751098\pi$
$60$	−40.9193	−	39.1635i	−0.681989	−	0.652726i
$61$	3.43067			0.0562405			0.0281202	−	0.999605i	$-0.491048\pi$
$61$	3.43067			0.0562405			0.0281202	+	0.999605i	$0.491048\pi$
$62$	27.7959	+	65.0783i	0.448320	+	1.04965i
$63$		0			0
$64$	−48.1310	−	42.1830i	−0.752047	−	0.659110i
$65$	166.942			2.56833
$66$	49.5881	−	21.1798i	0.751335	−	0.320906i
$67$			5.17488i			0.0772369i	0.999254	+	0.0386185i	$0.0122957\pi$
$67$			5.17488i			0.0772369i	−0.999254	+	0.0386185i	$0.987704\pi$
$68$	16.5120	−	17.2523i	0.242824	−	0.253710i
$69$	50.8534			0.737005
$70$		0			0
$71$		−	75.1139i		−	1.05794i	−0.848640	−	0.528971i	$-0.822578\pi$
$71$		−	75.1139i		−	1.05794i	0.848640	−	0.528971i	$-0.177422\pi$
$72$	8.45048	−	22.4631i	0.117368	−	0.311987i
$73$	21.5545			0.295267			0.147634	−	0.989042i	$-0.452834\pi$
$73$	21.5545			0.295267			0.147634	+	0.989042i	$0.452834\pi$
$74$	90.5868	−	38.6909i	1.22415	−	0.522850i
$75$		−	72.4638i		−	0.966183i
$76$	−12.1095	−	11.5899i	−0.159335	−	0.152498i
$77$		0			0
$78$	27.7846	+	65.0519i	0.356212	+	0.833999i
$79$		−	62.5091i		−	0.791254i	−0.918411	−	0.395627i	$-0.870527\pi$
$79$		−	62.5091i		−	0.791254i	0.918411	−	0.395627i	$-0.129473\pi$
$80$	−5.73302	−	130.681i	−0.0716628	−	1.63351i
$81$	9.00000			0.111111
$82$	−7.57121	+	3.23377i	−0.0923318	+	0.0394362i
$83$		−	58.0935i		−	0.699922i	−0.936764	−	0.349961i	$-0.886195\pi$
$83$		−	58.0935i		−	0.699922i	0.936764	−	0.349961i	$-0.113805\pi$
$84$		0			0
$85$	48.8086			0.574218
$86$	15.4075	+	36.0736i	0.179157	+	0.419460i
$87$			13.6799i			0.157241i
$88$	116.553	+	43.8464i	1.32446	+	0.498255i
$89$	135.578			1.52334			0.761672	−	0.647963i	$-0.224379\pi$
$89$	135.578			1.52334			0.761672	+	0.647963i	$0.224379\pi$
$90$	45.1100	−	19.2671i	0.501222	−	0.214079i
$91$		0			0
$92$	84.8435	+	81.2030i	0.922212	+	0.882641i
$93$	−61.2850			−0.658978
$94$	−23.9705	−	56.1221i	−0.255006	−	0.597044i
$95$		−	34.2589i		−	0.360620i
$96$	49.9679	−	23.9835i	0.520499	−	0.249828i
$97$	−61.8562			−0.637693			−0.318846	−	0.947806i	$-0.603295\pi$
$97$	−61.8562			−0.637693			−0.318846	+	0.947806i	$0.603295\pi$
$98$		0			0
$99$			46.6977i			0.471694i
$100$	115.711	−	120.898i	1.15711	−	1.20898i
$101$	−11.4853			−0.113716			−0.0568580	−	0.998382i	$-0.518108\pi$
$101$	−11.4853			−0.113716			−0.0568580	+	0.998382i	$0.518108\pi$
$102$	8.12334	+	19.0192i	0.0796406	+	0.186462i
$103$		−	122.726i		−	1.19151i	−0.803164	−	0.595757i	$-0.796852\pi$
$103$		−	122.726i		−	1.19151i	0.803164	−	0.595757i	$-0.203148\pi$
$104$	−57.5197	+	152.899i	−0.553074	+	1.47018i
$105$		0			0
$106$	−74.3582	+	31.7594i	−0.701493	+	0.299617i
$107$			85.1425i			0.795724i	0.917445	+	0.397862i	$0.130248\pi$
$107$			85.1425i			0.795724i	−0.917445	+	0.397862i	$0.869752\pi$
$108$	15.0156	+	14.3713i	0.139033	+	0.133067i
$109$	−52.4816			−0.481482			−0.240741	−	0.970589i	$-0.577390\pi$
$109$	−52.4816			−0.481482			−0.240741	+	0.970589i	$0.577390\pi$
$110$	99.9699	+	234.059i	0.908817	+	2.12781i
$111$			85.3066i			0.768528i
$112$		0			0
$113$	92.5191			0.818753			0.409376	−	0.912366i	$-0.365746\pi$
$113$	92.5191			0.818753			0.409376	+	0.912366i	$0.365746\pi$
$114$	13.3496	−	5.70180i	0.117102	−	0.0500158i
$115$			240.031i			2.08723i
$116$	−21.8442	+	22.8235i	−0.188312	+	0.196755i
$117$	−61.2601			−0.523591
$118$	−65.3205	−	152.935i	−0.553564	−	1.29606i
$119$		0			0
$120$	106.027	+	39.8868i	0.883559	+	0.332390i
$121$	−121.297			−1.00246
$122$	−6.30989	+	2.69504i	−0.0517204	+	0.0220905i
$123$		−	7.12989i		−	0.0579666i
$124$	−102.248	−	97.8603i	−0.824577	−	0.789196i
$125$	137.649			1.10119
$126$		0			0
$127$		−	215.557i		−	1.69730i	−0.528954	−	0.848651i	$-0.677415\pi$
$127$		−	215.557i		−	1.69730i	0.528954	−	0.848651i	$-0.322585\pi$
$128$	121.663	+	39.7751i	0.950494	+	0.310743i
$129$	−33.9709			−0.263340
$130$	−307.049	+	131.145i	−2.36192	+	1.00881i
$131$			1.12631i			0.00859781i	0.999991	+	0.00429891i	$0.00136839\pi$
$131$			1.12631i			0.00859781i	−0.999991	+	0.00429891i	$0.998632\pi$
$132$	−74.5672	+	77.9102i	−0.564903	+	0.590229i
$133$		0			0
$134$	−4.06524	−	9.51794i	−0.0303376	−	0.0710294i
$135$			42.4806i			0.314671i
$136$	−16.8170	+	44.7029i	−0.123654	+	0.328698i
$137$	−94.6501			−0.690876			−0.345438	−	0.938441i	$-0.612270\pi$
$137$	−94.6501			−0.690876			−0.345438	+	0.938441i	$0.612270\pi$
$138$	−93.5325	+	39.9490i	−0.677772	+	0.289486i
$139$		−	57.2889i		−	0.412150i	−0.978536	−	0.206075i	$-0.933931\pi$
$139$		−	57.2889i		−	0.412150i	0.978536	−	0.206075i	$-0.0660691\pi$
$140$		0			0
$141$	52.8508			0.374829
$142$	59.0074	+	138.154i	0.415545	+	0.972915i
$143$		−	317.856i		−	2.22277i
$144$	2.10376	+	47.9539i	0.0146095	+	0.333013i
$145$	−64.5702			−0.445312
$146$	−39.6444	+	16.9327i	−0.271537	+	0.115977i
$147$		0			0
$148$	−136.218	+	142.325i	−0.920393	+	0.961656i
$149$	−142.469			−0.956169			−0.478085	−	0.878314i	$-0.658669\pi$
$149$	−142.469			−0.956169			−0.478085	+	0.878314i	$0.658669\pi$
$150$	56.9256	+	133.280i	0.379504	+	0.888531i
$151$		−	105.397i		−	0.697993i	−0.937124	−	0.348997i	$-0.886522\pi$
$151$		−	105.397i		−	0.697993i	0.937124	−	0.348997i	$-0.113478\pi$
$152$	31.3771	+	11.8039i	0.206428	+	0.0776572i
$153$	−17.9106			−0.117062
$154$		0			0
$155$		−	289.269i		−	1.86625i
$156$	−102.206	−	97.8205i	−0.655167	−	0.627055i
$157$	277.604			1.76818			0.884089	−	0.467318i	$-0.154780\pi$
$157$	277.604			1.76818			0.884089	+	0.467318i	$0.154780\pi$
$158$	49.1054	+	114.970i	0.310794	+	0.727661i
$159$		−	70.0240i		−	0.440402i
$160$	113.204	+	235.852i	0.707523	+	1.47407i
$161$		0			0
$162$	−16.5533	+	7.07016i	−0.102181	+	0.0436429i
$163$		−	0.173725i		−	0.00106579i	−1.00000		0.000532897i	$-0.999830\pi$
$163$		−	0.173725i		−	0.00106579i	1.00000		0.000532897i	$-0.000169627\pi$
$164$	11.3851	−	11.8955i	0.0694211	−	0.0725334i
$165$	−220.416			−1.33585
$166$	45.6367	+	106.849i	0.274920	+	0.643669i
$167$			168.587i			1.00950i	0.863265	+	0.504750i	$0.168415\pi$
$167$			168.587i			1.00950i	−0.863265	+	0.504750i	$0.831585\pi$
$168$		0			0
$169$	247.978			1.46733
$170$	−89.7716	+	38.3427i	−0.528068	+	0.225545i
$171$			12.5715i			0.0735174i
$172$	−56.6768	−	54.2449i	−0.329516	−	0.315377i
$173$	8.35807			0.0483125			0.0241563	−	0.999708i	$-0.492310\pi$
$173$	8.35807			0.0483125			0.0241563	+	0.999708i	$0.492310\pi$
$174$	−10.7466	−	25.1610i	−0.0617620	−	0.144603i
$175$		0			0
$176$	−248.815	+	10.9156i	−1.41372	+	0.0620207i
$177$	144.020			0.813674
$178$	−249.362	+	106.506i	−1.40091	+	0.598349i
$179$			185.600i			1.03687i	0.855117	+	0.518435i	$0.173485\pi$
$179$			185.600i			1.03687i	−0.855117	+	0.518435i	$0.826515\pi$
$180$	−67.8332	+	70.8744i	−0.376851	+	0.393746i
$181$	−236.102			−1.30443			−0.652216	−	0.758033i	$-0.726161\pi$
$181$	−236.102			−1.30443			−0.652216	+	0.758033i	$0.726161\pi$
$182$		0			0
$183$		−	5.94209i		−	0.0324705i
$184$	−219.840	−	82.7026i	−1.19478	−	0.449470i
$185$	−402.652			−2.17650
$186$	112.719	−	48.1438i	0.606016	−	0.258838i
$187$		−	92.9313i		−	0.496959i
$188$	88.1761	+	84.3926i	0.469022	+	0.448897i
$189$		0			0
$190$	26.9129	+	63.0110i	0.141647	+	0.331637i
$191$			347.719i			1.82052i	0.414036	+	0.910260i	$0.364119\pi$
$191$			347.719i			1.82052i	−0.414036	+	0.910260i	$0.635881\pi$
$192$	−73.0632	+	83.3653i	−0.380537	+	0.434194i
$193$	286.487			1.48439			0.742194	−	0.670185i	$-0.233785\pi$
$193$	286.487			1.48439			0.742194	+	0.670185i	$0.233785\pi$
$194$	113.770	−	48.5926i	0.586441	−	0.250477i
$195$		−	289.152i		−	1.48283i
$196$		0			0
$197$	−325.318			−1.65136			−0.825680	−	0.564139i	$-0.809208\pi$
$197$	−325.318			−1.65136			−0.825680	+	0.564139i	$0.809208\pi$
$198$	−36.6845	−	85.8892i	−0.185275	−	0.433784i
$199$			149.317i			0.750336i	0.926957	+	0.375168i	$0.122415\pi$
$199$			149.317i			0.750336i	−0.926957	+	0.375168i	$0.877585\pi$
$200$	−117.847	+	313.262i	−0.589237	+	1.56631i
$201$	8.96315			0.0445928
$202$	21.1245	−	9.02256i	0.104577	−	0.0446661i
$203$		0			0
$204$	−29.8819	−	28.5997i	−0.146480	−	0.140195i
$205$	33.6535			0.164164
$206$	96.4103	+	225.725i	0.468011	+	1.09575i
$207$		−	88.0806i		−	0.425510i
$208$	−14.3196	−	326.407i	−0.0688444	−	1.56926i
$209$	−65.2288			−0.312099
$210$		0			0
$211$			236.005i			1.11851i	0.828997	+	0.559254i	$0.188912\pi$
$211$			236.005i			1.11851i	−0.828997	+	0.559254i	$0.811088\pi$
$212$	111.815	−	116.828i	0.527428	−	0.551074i
$213$	−130.101			−0.610803
$214$	−66.8856	−	156.599i	−0.312550	−	0.731772i
$215$		−	160.345i		−	0.745789i
$216$	−38.9072	−	14.6367i	−0.180126	−	0.0677623i
$217$		0			0
$218$	96.5272	−	41.2281i	0.442785	−	0.189120i
$219$		−	37.3335i		−	0.170473i
$220$	−367.741	−	351.962i	−1.67155	−	1.59983i
$221$	121.911			0.551635
$222$	−67.0146	−	156.901i	−0.301867	−	0.706761i
$223$			250.848i			1.12488i	0.826838	+	0.562440i	$0.190137\pi$
$223$			250.848i			1.12488i	−0.826838	+	0.562440i	$0.809863\pi$
$224$		0			0
$225$	−125.511			−0.557826
$226$	−170.167	+	72.6805i	−0.752949	+	0.321595i
$227$			229.377i			1.01047i	0.862981	+	0.505236i	$0.168594\pi$
$227$			229.377i			1.01047i	−0.862981	+	0.505236i	$0.831406\pi$
$228$	−20.0742	+	20.9742i	−0.0880448	+	0.0919921i
$229$	179.553			0.784073			0.392036	−	0.919950i	$-0.371771\pi$
$229$	179.553			0.784073			0.392036	+	0.919950i	$0.371771\pi$
$230$	−188.562	−	441.479i	−0.819834	−	1.91948i
$231$		0			0
$232$	22.2476	−	59.1386i	0.0958949	−	0.254908i
$233$	−217.847			−0.934967			−0.467483	−	0.884002i	$-0.654839\pi$
$233$	−217.847			−0.934967			−0.467483	+	0.884002i	$0.654839\pi$
$234$	112.673	−	48.1243i	0.481510	−	0.205659i
$235$			249.459i			1.06153i
$236$	240.283	+	229.973i	1.01815	+	0.974460i
$237$	−108.269			−0.456831
$238$		0			0
$239$			149.425i			0.625208i	0.949884	+	0.312604i	$0.101201\pi$
$239$			149.425i			0.625208i	−0.949884	+	0.312604i	$0.898799\pi$
$240$	−226.345	+	9.92989i	−0.943105	+	0.0413745i
$241$	18.5618			0.0770199			0.0385099	−	0.999258i	$-0.487739\pi$
$241$	18.5618			0.0770199			0.0385099	+	0.999258i	$0.487739\pi$
$242$	223.097	−	95.2878i	0.921889	−	0.393751i
$243$		−	15.5885i		−	0.0641500i
$244$	9.48837	−	9.91376i	0.0388868	−	0.0406302i
$245$		0			0
$246$	5.60105	+	13.1137i	0.0227685	+	0.0533078i
$247$		−	85.5700i		−	0.346437i
$248$	264.936	+	99.6675i	1.06829	+	0.401885i
$249$	−100.621			−0.404100
$250$	−253.172	+	108.133i	−1.01269	+	0.432533i
$251$		−	23.6892i		−	0.0943794i	−0.998886	−	0.0471897i	$-0.984973\pi$
$251$		−	23.6892i		−	0.0943794i	0.998886	−	0.0471897i	$-0.0150265\pi$
$252$		0			0
$253$	457.018			1.80640
$254$	169.336	+	396.466i	0.666677	+	1.56089i
$255$		−	84.5389i		−	0.331525i
$256$	−255.016	+	22.4186i	−0.996158	+	0.0875725i
$257$	81.4025			0.316741			0.158371	−	0.987380i	$-0.449376\pi$
$257$	81.4025			0.316741			0.158371	+	0.987380i	$0.449376\pi$
$258$	62.4812	−	26.6866i	0.242175	−	0.103436i
$259$		0			0
$260$	461.719	−	482.419i	1.77584	−	1.85546i
$261$	23.6944			0.0907830
$262$	−0.884801	−	2.07158i	−0.00337710	−	0.00790680i
$263$			205.306i			0.780629i	0.920682	+	0.390315i	$0.127634\pi$
$263$			205.306i			0.780629i	−0.920682	+	0.390315i	$0.872366\pi$
$264$	75.9442	−	201.875i	0.287668	−	0.764678i
$265$	330.518			1.24724
$266$		0			0
$267$		−	234.827i		−	0.879503i
$268$	14.9541	+	14.3124i	0.0557988	+	0.0534045i
$269$	−379.751			−1.41171			−0.705856	−	0.708355i	$-0.749437\pi$
$269$	−379.751			−1.41171			−0.705856	+	0.708355i	$0.749437\pi$
$270$	−33.3716	−	78.1328i	−0.123598	−	0.289381i
$271$			510.275i			1.88293i	0.337105	+	0.941467i	$0.390552\pi$
$271$			510.275i			1.88293i	−0.337105	+	0.941467i	$0.609448\pi$
$272$	−4.18661	−	95.4311i	−0.0153920	−	0.350850i
$273$		0			0
$274$	174.086	−	74.3545i	0.635350	−	0.271367i
$275$		−	651.230i		−	2.36811i
$276$	140.648	−	146.953i	0.509593	−	0.532439i
$277$	−402.982			−1.45481			−0.727404	−	0.686210i	$-0.759273\pi$
$277$	−402.982			−1.45481			−0.727404	+	0.686210i	$0.759273\pi$
$278$	45.0046	+	105.369i	0.161887	+	0.379026i
$279$			106.149i			0.380461i
$280$		0			0
$281$	−338.807			−1.20572			−0.602860	−	0.797847i	$-0.705972\pi$
$281$	−338.807			−1.20572			−0.602860	+	0.797847i	$0.705972\pi$
$282$	−97.2064	+	41.5182i	−0.344704	+	0.147228i
$283$			124.413i			0.439621i	0.975543	+	0.219811i	$0.0705440\pi$
$283$			124.413i			0.439621i	−0.975543	+	0.219811i	$0.929456\pi$
$284$	−217.060	−	207.746i	−0.764296	−	0.731501i
$285$	−59.3382			−0.208204
$286$	249.699	+	584.620i	0.873075	+	2.04413i
$287$		0			0
$288$	−41.5406	−	86.5470i	−0.144238	−	0.300510i
$289$	−253.357			−0.876668
$290$	118.761	−	50.7246i	0.409522	−	0.174912i
$291$			107.138i			0.368172i
$292$	59.6144	−	62.2871i	0.204159	−	0.213312i
$293$	221.231			0.755054			0.377527	−	0.925999i	$-0.376775\pi$
$293$	221.231			0.755054			0.377527	+	0.925999i	$0.376775\pi$
$294$		0			0
$295$			679.785i			2.30436i
$296$	138.734	−	368.782i	0.468695	−	1.24589i
$297$	80.8828			0.272333
$298$	262.038	−	111.920i	0.879322	−	0.375570i
$299$			599.536i			2.00514i
$300$	−209.402	−	200.417i	−0.698006	−	0.668055i
$301$		0			0
$302$	82.7970	+	193.852i	0.274162	+	0.641895i
$303$			19.8932i			0.0656540i
$304$	−66.9835	+	2.93860i	−0.220340	+	0.00966645i
$305$	28.0471			0.0919576
$306$	32.9421	−	14.0700i	0.107654	−	0.0459805i
$307$			1.58892i			0.00517563i	0.999997	+	0.00258782i	$0.000823728\pi$
$307$			1.58892i			0.00517563i	−0.999997	+	0.00258782i	$0.999176\pi$
$308$		0			0
$309$	−212.568			−0.687921
$310$	227.242	+	532.041i	0.733038	+	1.71626i
$311$		−	125.075i		−	0.402171i	−0.979574	−	0.201086i	$-0.935553\pi$
$311$		−	125.075i		−	0.402171i	0.979574	−	0.201086i	$-0.0644469\pi$
$312$	264.829	+	99.6270i	0.848810	+	0.319317i
$313$	222.134			0.709694			0.354847	−	0.934924i	$-0.384533\pi$
$313$	222.134			0.709694			0.354847	+	0.934924i	$0.384533\pi$
$314$	−510.586	+	218.078i	−1.62607	+	0.694517i
$315$		0			0
$316$	−180.635	−	172.884i	−0.571631	−	0.547103i
$317$	465.905			1.46973			0.734866	−	0.678212i	$-0.237245\pi$
$317$	465.905			1.46973			0.734866	+	0.678212i	$0.237245\pi$
$318$	55.0089	+	128.792i	0.172984	+	0.405007i
$319$			122.941i			0.385396i
$320$	−393.489	−	344.863i	−1.22965	−	1.07770i
$321$	147.471			0.459412
$322$		0			0
$323$		−	25.0180i		−	0.0774551i
$324$	24.8917	−	26.0077i	0.0768264	−	0.0802707i
$325$	854.312			2.62865
$326$	0.136473	+	0.319525i	0.000418630	+	0.000980137i
$327$			90.9007i			0.277984i
$328$	−11.5953	+	30.8227i	−0.0353515	+	0.0939715i
$329$		0			0
$330$	405.402	−	173.153i	1.22849	−	0.524706i
$331$			344.994i			1.04228i	0.853472	+	0.521139i	$0.174493\pi$
$331$			344.994i			1.04228i	−0.853472	+	0.521139i	$0.825507\pi$
$332$	−167.876	−	160.672i	−0.505649	−	0.483952i
$333$	147.755			0.443710
$334$	−132.437	−	310.074i	−0.396518	−	0.928367i
$335$			42.3066i			0.126288i
$336$		0			0
$337$	−518.977			−1.53999			−0.769996	−	0.638049i	$-0.779742\pi$
$337$	−518.977			−1.53999			−0.769996	+	0.638049i	$0.779742\pi$
$338$	−456.096	+	194.805i	−1.34940	+	0.576345i
$339$		−	160.248i		−	0.472707i
$340$	134.992	−	141.044i	0.397036	−	0.414836i
$341$	−550.767			−1.61515
$342$	−9.87581	−	23.1222i	−0.0288767	−	0.0676088i
$343$		0			0
$344$	146.857	+	55.2467i	0.426909	+	0.160601i
$345$	415.746			1.20506
$346$	−15.3727	+	6.56587i	−0.0444296	+	0.0189765i
$347$		−	355.873i		−	1.02557i	−0.858517	−	0.512785i	$-0.828614\pi$
$347$		−	355.873i		−	1.02557i	0.858517	−	0.512785i	$-0.171386\pi$
$348$	39.5315	+	37.8353i	0.113596	+	0.108722i
$349$	−677.606			−1.94156			−0.970782	−	0.239961i	$-0.922865\pi$
$349$	−677.606			−1.94156			−0.970782	+	0.239961i	$0.922865\pi$
$350$		0			0
$351$			106.106i			0.302295i
$352$	449.060	−	215.539i	1.27574	−	0.612327i
$353$	430.655			1.21999			0.609993	−	0.792407i	$-0.291172\pi$
$353$	430.655			1.21999			0.609993	+	0.792407i	$0.291172\pi$
$354$	−264.891	+	113.138i	−0.748279	+	0.319600i
$355$		−	614.085i		−	1.72982i
$356$	374.974	−	391.785i	1.05330	−	1.10052i
$357$		0			0
$358$	−145.802	−	341.366i	−0.407269	−	0.953536i
$359$		−	284.240i		−	0.791756i	−0.918303	−	0.395878i	$-0.870440\pi$
$359$		−	284.240i		−	0.791756i	0.918303	−	0.395878i	$-0.129560\pi$
$360$	69.0859	−	183.644i	0.191905	−	0.510123i
$361$	343.440			0.951357
$362$	434.253	−	185.476i	1.19959	−	0.512363i
$363$			210.093i			0.578769i
$364$		0			0
$365$	176.217			0.482785
$366$	4.66795	+	10.9291i	0.0127540	+	0.0298608i
$367$		−	518.559i		−	1.41297i	−0.707730	−	0.706484i	$-0.750280\pi$
$367$		−	518.559i		−	1.41297i	0.707730	−	0.706484i	$-0.249720\pi$
$368$	469.312	−	20.5890i	1.27530	−	0.0559482i
$369$	−12.3493			−0.0334670
$370$	740.582	−	316.313i	2.00157	−	0.854900i
$371$		0			0
$372$	−169.499	+	177.098i	−0.455642	+	0.476070i
$373$	491.802			1.31850			0.659252	−	0.751922i	$-0.270873\pi$
$373$	491.802			1.31850			0.659252	+	0.751922i	$0.270873\pi$
$374$	73.0043	+	170.925i	0.195199	+	0.457018i
$375$		−	238.415i		−	0.635772i
$376$	−228.475	−	85.9511i	−0.607647	−	0.228593i
$377$	−161.280			−0.427798
$378$		0			0
$379$			289.092i			0.762776i	0.924415	+	0.381388i	$0.124554\pi$
$379$			289.092i			0.762776i	−0.924415	+	0.381388i	$0.875446\pi$
$380$	−98.9995	−	94.7516i	−0.260525	−	0.249346i
$381$	−373.356			−0.979937
$382$	−273.159	−	639.546i	−0.715076	−	1.67420i
$383$			155.917i			0.407095i	0.979065	+	0.203548i	$0.0652472\pi$
$383$			155.917i			0.407095i	−0.979065	+	0.203548i	$0.934753\pi$
$384$	68.8925	−	210.727i	0.179408	−	0.548768i
$385$		0			0
$386$	−526.923	+	225.056i	−1.36509	+	0.583047i
$387$			58.8393i			0.152039i
$388$	−171.079	+	178.749i	−0.440925	+	0.460692i
$389$	−212.764			−0.546951			−0.273475	−	0.961879i	$-0.588173\pi$
$389$	−212.764			−0.546951			−0.273475	+	0.961879i	$0.588173\pi$
$390$	227.150	+	531.825i	0.582435	+	1.36365i
$391$			175.286i			0.448301i
$392$		0			0
$393$	1.95083			0.00496395
$394$	598.344	−	255.561i	1.51864	−	0.648632i
$395$		−	511.036i		−	1.29376i
$396$	134.944	+	129.154i	0.340769	+	0.326147i
$397$	−101.368			−0.255335			−0.127667	−	0.991817i	$-0.540749\pi$
$397$	−101.368			−0.255335			−0.127667	+	0.991817i	$0.540749\pi$
$398$	−117.299	−	274.633i	−0.294722	−	0.690031i
$399$		0			0
$400$	−29.3383	−	668.748i	−0.0733458	−	1.67187i
$401$	488.472			1.21814			0.609068	−	0.793118i	$-0.291544\pi$
$401$	488.472			1.21814			0.609068	+	0.793118i	$0.291544\pi$
$402$	−16.4856	+	7.04121i	−0.0410088	+	0.0175154i
$403$		−	722.520i		−	1.79285i
$404$	−31.7655	+	33.1897i	−0.0786276	+	0.0821526i
$405$	73.5785			0.181675
$406$		0			0
$407$			766.648i			1.88366i
$408$	77.4277	+	29.1278i	0.189774	+	0.0713918i
$409$	390.757			0.955397			0.477698	−	0.878524i	$-0.341471\pi$
$409$	390.757			0.955397			0.477698	+	0.878524i	$0.341471\pi$
$410$	−61.8976	+	26.4373i	−0.150970	+	0.0644812i
$411$			163.939i			0.398878i
$412$	−354.647	−	339.430i	−0.860794	−	0.823858i
$413$		0			0
$414$	69.1937	+	162.003i	0.167135	+	0.391312i
$415$		−	474.937i		−	1.14443i
$416$	282.754	+	589.097i	0.679697	+	1.41610i
$417$	−99.2273			−0.237955
$418$	119.973	−	51.2420i	0.287016	−	0.122588i
$419$		−	23.8867i		−	0.0570089i	−0.999594	−	0.0285044i	$-0.990926\pi$
$419$		−	23.8867i		−	0.0570089i	0.999594	−	0.0285044i	$-0.00907447\pi$
$420$		0			0
$421$	157.877			0.375004			0.187502	−	0.982264i	$-0.439961\pi$
$421$	157.877			0.375004			0.187502	+	0.982264i	$0.439961\pi$
$422$	−185.399	−	434.074i	−0.439335	−	1.02861i
$423$		−	91.5403i		−	0.216407i
$424$	−113.880	+	302.715i	−0.268584	+	0.713951i
$425$	249.774			0.587704
$426$	239.290	−	102.204i	0.561713	−	0.239915i
$427$		0			0
$428$	246.040	+	235.483i	0.574860	+	0.550193i
$429$	−550.543			−1.28332
$430$	125.962	+	294.915i	0.292936	+	0.685850i
$431$			164.911i			0.382624i	0.981529	+	0.191312i	$0.0612742\pi$
$431$			164.911i			0.382624i	−0.981529	+	0.191312i	$0.938726\pi$
$432$	83.0585	−	3.64382i	0.192265	−	0.00843477i
$433$	149.686			0.345696			0.172848	−	0.984949i	$-0.444703\pi$
$433$	149.686			0.345696			0.172848	+	0.984949i	$0.444703\pi$
$434$		0			0
$435$			111.839i			0.257101i
$436$	−145.151	+	151.658i	−0.332915	+	0.347840i
$437$	123.034			0.281542
$438$	29.3282	+	68.6660i	0.0669594	+	0.156772i
$439$			430.660i			0.981002i	0.871441	+	0.490501i	$0.163186\pi$
$439$			430.660i			0.981002i	−0.871441	+	0.490501i	$0.836814\pi$
$440$	952.863	+	358.462i	2.16560	+	0.814685i
$441$		0			0
$442$	−224.227	+	95.7703i	−0.507300	+	0.216675i
$443$			611.766i			1.38096i	0.723350	+	0.690481i	$0.242601\pi$
$443$			611.766i			1.38096i	−0.723350	+	0.690481i	$0.757399\pi$
$444$	246.514	+	235.937i	0.555212	+	0.531389i
$445$	1108.40			2.49079
$446$	−197.060	−	461.375i	−0.441838	−	1.03447i
$447$			246.764i			0.552045i
$448$		0			0
$449$	14.7665			0.0328876			0.0164438	−	0.999865i	$-0.494766\pi$
$449$	14.7665			0.0328876			0.0164438	+	0.999865i	$0.494766\pi$
$450$	230.847	−	98.5980i	0.512994	−	0.219107i
$451$		−	64.0762i		−	0.142076i
$452$	255.885	−	267.356i	0.566116	−	0.591497i
$453$	−182.553			−0.402987
$454$	−180.192	−	421.884i	−0.396900	−	0.929259i
$455$		0			0
$456$	20.4449	−	54.3467i	0.0448354	−	0.119181i
$457$	−873.183			−1.91069			−0.955343	−	0.295501i	$-0.904514\pi$
$457$	−873.183			−1.91069			−0.955343	+	0.295501i	$0.904514\pi$
$458$	−330.244	+	141.052i	−0.721057	+	0.307973i
$459$			31.0220i			0.0675860i
$460$	693.629	+	663.866i	1.50789	+	1.44319i
$461$	12.2874			0.0266538			0.0133269	−	0.999911i	$-0.495758\pi$
$461$	12.2874			0.0266538			0.0133269	+	0.999911i	$0.495758\pi$
$462$		0			0
$463$		−	126.041i		−	0.272228i	−0.990693	−	0.136114i	$-0.956539\pi$
$463$		−	126.041i		−	0.272228i	0.990693	−	0.136114i	$-0.0434613\pi$
$464$	5.53859	+	126.248i	0.0119366	+	0.272087i
$465$	−501.029			−1.07748
$466$	400.678	−	171.135i	0.859823	−	0.367242i
$467$		−	532.644i		−	1.14056i	−0.821449	−	0.570282i	$-0.806834\pi$
$467$		−	532.644i		−	1.14056i	0.821449	−	0.570282i	$-0.193166\pi$
$468$	−169.430	+	177.026i	−0.362030	+	0.378261i
$469$		0			0
$470$	−195.968	−	458.820i	−0.416954	−	0.976213i
$471$		−	480.824i		−	1.02086i
$472$	−622.603	−	234.220i	−1.31907	−	0.496228i
$473$	−305.295			−0.645445
$474$	199.135	−	85.0531i	0.420115	−	0.179437i
$475$		−	175.318i		−	0.369090i
$476$		0			0
$477$	−121.285			−0.254266
$478$	−117.384	−	274.831i	−0.245573	−	0.574959i
$479$		−	363.063i		−	0.757961i	−0.925405	−	0.378980i	$-0.876275\pi$
$479$		−	363.063i		−	0.757961i	0.925405	−	0.378980i	$-0.123725\pi$
$480$	408.507	−	196.074i	0.851056	−	0.408488i
$481$	−1005.72			−2.09090
$482$	−34.1399	+	14.5816i	−0.0708298	+	0.0302524i
$483$		0			0
$484$	−335.478	+	350.518i	−0.693136	+	0.724211i
$485$	−505.698			−1.04268
$486$	12.2459	+	28.6712i	0.0251973	+	0.0589943i
$487$			871.471i			1.78947i	0.446600	+	0.894734i	$0.352635\pi$
$487$			871.471i			1.78947i	−0.446600	+	0.894734i	$0.647365\pi$
$488$	−9.66360	+	25.6878i	−0.0198025	+	0.0526389i
$489$	−0.300900			−0.000615337
$490$		0			0
$491$		−	296.111i		−	0.603077i	−0.953454	−	0.301539i	$-0.902500\pi$
$491$		−	296.111i		−	0.603077i	0.953454	−	0.301539i	$-0.0975002\pi$
$492$	−20.6036	−	19.7195i	−0.0418772	−	0.0400803i
$493$	−47.1532			−0.0956455
$494$	67.2215	+	157.385i	0.136076	+	0.318594i
$495$			381.772i			0.771256i
$496$	−565.583	+	24.8124i	−1.14029	+	0.0500250i
$497$		0			0
$498$	185.068	−	79.0451i	0.371623	−	0.158725i
$499$		−	102.398i		−	0.205206i	−0.994722	−	0.102603i	$-0.967283\pi$
$499$		−	102.398i		−	0.205206i	0.994722	−	0.102603i	$-0.0327171\pi$
$500$	380.702	−	397.770i	0.761404	−	0.795540i
$501$	292.001			0.582835
$502$	18.6096	+	43.5706i	0.0370709	+	0.0867941i
$503$		−	218.310i		−	0.434016i	−0.976170	−	0.217008i	$-0.930370\pi$
$503$		−	218.310i		−	0.434016i	0.976170	−	0.217008i	$-0.0696297\pi$
$504$		0			0
$505$	−93.8970			−0.185935
$506$	−840.575	+	359.021i	−1.66121	+	0.709528i
$507$		−	429.510i		−	0.847160i
$508$	−622.906	−	596.178i	−1.22619	−	1.17358i
$509$	−663.088			−1.30273			−0.651363	−	0.758766i	$-0.725803\pi$
$509$	−663.088			−1.30273			−0.651363	+	0.758766i	$0.725803\pi$
$510$	66.4115	+	155.489i	0.130219	+	0.304880i
$511$		0			0
$512$	451.430	−	241.568i	0.881699	−	0.471812i
$513$	21.7744			0.0424453
$514$	−149.720	+	63.9476i	−0.291285	+	0.124412i
$515$		−	1003.33i		−	1.94822i
$516$	−93.9549	+	98.1672i	−0.182083	+	0.190246i
$517$	474.969			0.918703
$518$		0			0
$519$		−	14.4766i		−	0.0278933i
$520$	−470.246	+	1250.01i	−0.904319	+	2.40386i
$521$	573.342			1.10046			0.550232	−	0.835012i	$-0.314539\pi$
$521$	573.342			1.10046			0.550232	+	0.835012i	$0.314539\pi$
$522$	−43.5801	+	18.6136i	−0.0834867	+	0.0356583i
$523$			737.920i			1.41094i	0.708742	+	0.705468i	$0.249263\pi$
$523$			737.920i			1.41094i	−0.708742	+	0.705468i	$0.750737\pi$
$524$	3.25476	+	3.11510i	0.00621137	+	0.00594485i
$525$		0			0
$526$	−161.282	−	377.610i	−0.306621	−	0.717890i
$527$		−	211.242i		−	0.400840i
$528$	18.9065	+	430.960i	0.0358077	+	0.816213i
$529$	−333.021			−0.629530
$530$	−607.907	+	259.646i	−1.14700	+	0.489897i
$531$		−	249.450i		−	0.469775i
$532$		0			0
$533$	84.0579			0.157707
$534$	184.474	+	431.908i	0.345457	+	0.808817i
$535$			696.073i			1.30107i
$536$	−38.7479	−	14.5767i	−0.0722908	−	0.0271954i
$537$	321.468			0.598637
$538$	698.460	−	298.322i	1.29825	−	0.554501i
$539$		0			0
$540$	122.758	+	117.491i	0.227330	+	0.217575i
$541$	−204.530			−0.378060			−0.189030	−	0.981971i	$-0.560534\pi$
$541$	−204.530			−0.378060			−0.189030	+	0.981971i	$0.560534\pi$
$542$	−400.858	−	938.528i	−0.739591	−	1.73160i
$543$			408.941i			0.753114i
$544$	82.6684	+	172.234i	0.151964	+	0.316606i
$545$	−429.057			−0.787261
$546$		0			0
$547$		−	706.043i		−	1.29076i	−0.763864	−	0.645378i	$-0.776700\pi$
$547$		−	706.043i		−	1.29076i	0.763864	−	0.645378i	$-0.223300\pi$
$548$	−261.778	+	273.515i	−0.477698	+	0.499114i
$549$	−10.2920			−0.0187468
$550$	511.589	+	1197.78i	0.930161	+	2.17778i
$551$			33.0970i			0.0600672i
$552$	−143.245	+	380.774i	−0.259502	+	0.689808i
$553$		0			0
$554$	741.188	−	316.572i	1.33788	−	0.571429i
$555$			697.415i			1.25660i
$556$	−165.550	−	158.447i	−0.297752	−	0.284976i
$557$	−701.852			−1.26006			−0.630029	−	0.776572i	$-0.716957\pi$
$557$	−701.852			−1.26006			−0.630029	+	0.776572i	$0.716957\pi$
$558$	−83.3876	−	195.235i	−0.149440	−	0.349884i
$559$		−	400.500i		−	0.716458i
$560$		0			0
$561$	−160.962			−0.286919
$562$	623.154	−	266.158i	1.10882	−	0.473590i
$563$			817.730i			1.45245i	0.687456	+	0.726226i	$0.258727\pi$
$563$			817.730i			1.45245i	−0.687456	+	0.726226i	$0.741273\pi$
$564$	146.172	−	152.725i	0.259171	−	0.270790i
$565$	756.379			1.33872
$566$	−97.7354	−	228.828i	−0.172677	−	0.404289i
$567$		0			0
$568$	562.429	+	211.583i	0.990193	+	0.372505i
$569$	368.297			0.647271			0.323635	−	0.946182i	$-0.395095\pi$
$569$	368.297			0.647271			0.323635	+	0.946182i	$0.395095\pi$
$570$	109.138	−	46.6145i	0.191471	−	0.0817798i
$571$			737.145i			1.29097i	0.763772	+	0.645486i	$0.223345\pi$
$571$			737.145i			1.29097i	−0.763772	+	0.645486i	$0.776655\pi$
$572$	−918.524	−	879.111i	−1.60581	−	1.53691i
$573$	602.268			1.05108
$574$		0			0
$575$			1228.34i			2.13625i
$576$	144.393	+	126.549i	0.250682	+	0.219703i
$577$	−660.019			−1.14388			−0.571940	−	0.820295i	$-0.693809\pi$
$577$	−660.019			−1.14388			−0.571940	+	0.820295i	$0.693809\pi$
$578$	465.989	−	199.030i	0.806209	−	0.344343i
$579$		−	496.210i		−	0.857011i
$580$	−178.585	+	186.591i	−0.307905	+	0.321709i
$581$		0			0
$582$	−84.1648	−	197.055i	−0.144613	−	0.338582i
$583$		−	629.304i		−	1.07942i
$584$	−60.7153	+	161.394i	−0.103965	+	0.276359i
$585$	−500.825			−0.856111
$586$	−406.901	+	173.793i	−0.694370	+	0.296575i
$587$			704.445i			1.20008i	0.799971	+	0.600038i	$0.204848\pi$
$587$			704.445i			1.20008i	−0.799971	+	0.600038i	$0.795152\pi$
$588$		0			0
$589$	−148.272			−0.251735
$590$	−534.021	−	1250.30i	−0.905120	−	2.11915i
$591$			563.467i			0.953413i
$592$	34.5380	+	787.271i	0.0583412	+	1.32985i
$593$	273.204			0.460716			0.230358	−	0.973106i	$-0.426010\pi$
$593$	273.204			0.460716			0.230358	+	0.973106i	$0.426010\pi$
$594$	−148.764	+	63.5393i	−0.250445	+	0.106969i
$595$		0			0
$596$	−394.034	+	411.700i	−0.661131	+	0.690771i
$597$	258.624			0.433207
$598$	−470.980	−	1102.70i	−0.787591	−	1.84398i
$599$		−	499.570i		−	0.834007i	−0.908905	−	0.417004i	$-0.863080\pi$
$599$		−	499.570i		−	0.834007i	0.908905	−	0.417004i	$-0.136920\pi$
$600$	542.586	+	204.118i	0.904310	+	0.340196i
$601$	−193.513			−0.321984			−0.160992	−	0.986956i	$-0.551469\pi$
$601$	−193.513			−0.321984			−0.160992	+	0.986956i	$0.551469\pi$
$602$		0			0
$603$		−	15.5246i		−	0.0257456i
$604$	−304.570	−	291.502i	−0.504256	−	0.482619i
$605$	−991.652			−1.63909
$606$	−15.6275	−	36.5887i	−0.0257880	−	0.0603774i
$607$			860.598i			1.41779i	0.705315	+	0.708894i	$0.250806\pi$
$607$			860.598i			1.41779i	−0.705315	+	0.708894i	$0.749194\pi$
$608$	120.891	−	58.0252i	0.198835	−	0.0954363i
$609$		0			0
$610$	−51.5858	+	22.0330i	−0.0845669	+	0.0361197i
$611$			623.086i			1.01978i
$612$	−49.5361	+	51.7569i	−0.0809413	+	0.0845701i
$613$	−87.4688			−0.142690			−0.0713448	−	0.997452i	$-0.522729\pi$
$613$	−87.4688			−0.142690			−0.0713448	+	0.997452i	$0.522729\pi$
$614$	−1.24821	−	2.92243i	−0.00203292	−	0.00475966i
$615$		−	58.2896i		−	0.0947799i
$616$		0			0
$617$	20.7265			0.0335923			0.0167962	−	0.999859i	$-0.494653\pi$
$617$	20.7265			0.0335923			0.0167962	+	0.999859i	$0.494653\pi$
$618$	390.967	−	166.987i	0.632633	−	0.270206i
$619$			16.2753i			0.0262930i	0.999914	+	0.0131465i	$0.00418477\pi$
$619$			16.2753i			0.0262930i	−0.999914	+	0.0131465i	$0.995815\pi$
$620$	−835.914	−	800.046i	−1.34825	−	1.29040i
$621$	−152.560			−0.245668
$622$	98.2558	+	230.046i	0.157967	+	0.369849i
$623$		0			0
$624$	−565.353	+	24.8023i	−0.906014	+	0.0397473i
$625$	79.4077			0.127052
$626$	−408.562	+	174.503i	−0.652656	+	0.278758i
$627$			112.980i			0.180191i
$628$	767.783	−	802.205i	1.22258	−	1.27740i
$629$	−294.042			−0.467476
$630$		0			0
$631$			1050.90i			1.66546i	0.553681	+	0.832729i	$0.313223\pi$
$631$			1050.90i			1.66546i	−0.553681	+	0.832729i	$0.686777\pi$
$632$	468.048	+	176.077i	0.740583	+	0.278603i
$633$	408.773			0.645770
$634$	−856.920	+	366.002i	−1.35161	+	0.577291i
$635$		−	1762.26i		−	2.77522i
$636$	−202.351	−	193.669i	−0.318163	−	0.304511i
$637$		0			0
$638$	−96.5794	−	226.121i	−0.151378	−	0.354422i
$639$			225.342i			0.352647i
$640$	994.644	+	325.177i	1.55413	+	0.508089i
$641$	113.722			0.177413			0.0887063	−	0.996058i	$-0.471727\pi$
$641$	113.722			0.177413			0.0887063	+	0.996058i	$0.471727\pi$
$642$	−271.238	+	115.849i	−0.422488	+	0.180451i
$643$		−	51.0660i		−	0.0794184i	−0.999211	−	0.0397092i	$-0.987357\pi$
$643$		−	51.0660i		−	0.0794184i	0.999211	−	0.0397092i	$-0.0126431\pi$
$644$		0			0
$645$	−277.725			−0.430581
$646$	19.6535	+	46.0146i	0.0304233	+	0.0712300i
$647$			854.686i			1.32100i	0.750827	+	0.660499i	$0.229655\pi$
$647$			854.686i			1.32100i	−0.750827	+	0.660499i	$0.770345\pi$
$648$	−25.3514	+	67.3892i	−0.0391226	+	0.103996i
$649$	1294.31			1.99431
$650$	−1571.30	+	671.125i	−2.41739	+	1.03250i
$651$		0			0
$652$	−0.502020	−	0.480479i	−0.000769969	−	0.000736931i
$653$	−341.101			−0.522361			−0.261180	−	0.965290i	$-0.584112\pi$
$653$	−341.101			−0.522361			−0.261180	+	0.965290i	$0.584112\pi$
$654$	−71.4092	−	167.190i	−0.109188	−	0.255642i
$655$			9.20805i			0.0140581i
$656$	−2.88667	−	65.7998i	−0.00440042	−	0.100305i
$657$	−64.6636			−0.0984225
$658$		0			0
$659$		−	1282.35i		−	1.94590i	−0.231009	−	0.972952i	$-0.574203\pi$
$659$		−	1282.35i		−	1.94590i	0.231009	−	0.972952i	$-0.425797\pi$
$660$	−609.616	+	636.946i	−0.923660	+	0.965070i
$661$	−292.351			−0.442286			−0.221143	−	0.975241i	$-0.570979\pi$
$661$	−292.351			−0.442286			−0.221143	+	0.975241i	$0.570979\pi$
$662$	−271.018	−	634.534i	−0.409393	−	0.958510i
$663$		−	211.157i		−	0.318487i
$664$	434.986	+	163.639i	0.655100	+	0.246445i
$665$		0			0
$666$	−271.760	+	116.073i	−0.408049	+	0.174283i
$667$		−	231.890i		−	0.347662i
$668$	487.172	+	466.268i	0.729300	+	0.698006i
$669$	434.482			0.649450
$670$	−33.2349	−	77.8128i	−0.0496044	−	0.116139i
$671$		−	53.4015i		−	0.0795849i
$672$		0			0
$673$	493.361			0.733077			0.366538	−	0.930403i	$-0.380543\pi$
$673$	493.361			0.733077			0.366538	+	0.930403i	$0.380543\pi$
$674$	954.533	−	407.694i	1.41622	−	0.604888i
$675$			217.391i			0.322061i
$676$	685.845	−	716.593i	1.01456	−	1.06005i
$677$	−118.821			−0.175511			−0.0877553	−	0.996142i	$-0.527969\pi$
$677$	−118.821			−0.175511			−0.0877553	+	0.996142i	$0.527969\pi$
$678$	125.886	+	294.737i	0.185673	+	0.434715i
$679$		0			0
$680$	−137.485	+	365.463i	−0.202184	+	0.537446i
$681$	397.293			0.583396
$682$	1013.00	−	432.668i	1.48534	−	0.634410i
$683$			807.926i			1.18291i	0.806339	+	0.591454i	$0.201446\pi$
$683$			807.926i			1.18291i	−0.806339	+	0.591454i	$0.798554\pi$
$684$	36.3284	+	34.7696i	0.0531117	+	0.0508327i
$685$	−773.801			−1.12964
$686$		0			0
$687$		−	310.994i		−	0.452685i
$688$	−313.508	+	13.7538i	−0.455680	+	0.0199909i
$689$	825.549			1.19818
$690$	−764.665	+	326.599i	−1.10821	+	0.473332i
$691$		−	668.758i		−	0.967812i	−0.875120	−	0.483906i	$-0.839218\pi$
$691$		−	668.758i		−	0.967812i	0.875120	−	0.483906i	$-0.160782\pi$
$692$	23.1163	−	24.1527i	0.0334051	−	0.0349027i
$693$		0			0
$694$	279.564	+	654.543i	0.402830	+	0.943145i
$695$		−	468.359i		−	0.673898i
$696$	−102.431	−	38.5340i	−0.147171	−	0.0553650i
$697$	24.5759			0.0352596
$698$	1246.29	−	532.309i	1.78552	−	0.762620i
$699$			377.323i			0.539803i
$700$		0			0
$701$	−208.430			−0.297333			−0.148666	−	0.988887i	$-0.547498\pi$
$701$	−208.430			−0.297333			−0.148666	+	0.988887i	$0.547498\pi$
$702$	−83.3537	−	195.156i	−0.118737	−	0.278000i
$703$			206.389i			0.293584i
$704$	−656.617	+	749.202i	−0.932694	+	1.06421i
$705$	432.076			0.612874
$706$	−792.087	+	338.311i	−1.12194	+	0.479194i
$707$		0			0
$708$	398.324	−	416.182i	0.562605	−	0.587828i
$709$	775.472			1.09375			0.546877	−	0.837213i	$-0.315816\pi$
$709$	775.472			1.09375			0.546877	+	0.837213i	$0.315816\pi$
$710$	482.409	+	1129.46i	0.679449	+	1.59079i
$711$			187.527i			0.263751i
$712$	−381.899	+	1015.16i	−0.536374	+	1.42579i
$713$	1038.85			1.45701
$714$		0			0
$715$		−	2598.60i		−	3.63440i
$716$	536.336	+	513.322i	0.749072	+	0.716931i
$717$	258.811			0.360964
$718$	223.292	+	522.792i	0.310991	+	0.728122i
$719$			512.869i			0.713309i	0.934236	+	0.356654i	$0.116083\pi$
$719$			512.869i			0.713309i	−0.934236	+	0.356654i	$0.883917\pi$
$720$	17.1991	+	392.042i	0.0238876	+	0.544502i
$721$		0			0
$722$	−631.675	+	269.797i	−0.874896	+	0.373680i
$723$		−	32.1500i		−	0.0444674i
$724$	−653.000	+	682.275i	−0.901933	+	0.942369i
$725$	−330.433			−0.455770
$726$	−165.043	−	386.415i	−0.227332	−	0.532253i
$727$			491.795i			0.676472i	0.941061	+	0.338236i	$0.109830\pi$
$727$			491.795i			0.676472i	−0.941061	+	0.338236i	$0.890170\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−324.108	+	138.431i	−0.443984	+	0.189632i
$731$		−	117.094i		−	0.160183i
$732$	−17.1711	−	16.4343i	−0.0234578	−	0.0224513i
$733$	235.137			0.320787			0.160393	−	0.987053i	$-0.448724\pi$
$733$	235.137			0.320787			0.160393	+	0.987053i	$0.448724\pi$
$734$	407.366	+	953.764i	0.554994	+	1.29941i
$735$		0			0
$736$	−847.012	+	406.547i	−1.15083	+	0.552374i
$737$	80.5516			0.109297
$738$	22.7136	−	9.70130i	0.0307773	−	0.0131454i
$739$		−	604.116i		−	0.817477i	−0.912651	−	0.408739i	$-0.865969\pi$
$739$		−	604.116i		−	0.817477i	0.912651	−	0.408739i	$-0.134031\pi$
$740$	−1113.64	+	1163.56i	−1.50491	+	1.57238i
$741$	−148.212			−0.200016
$742$		0			0
$743$		−	310.216i		−	0.417519i	−0.977967	−	0.208759i	$-0.933057\pi$
$743$		−	310.216i		−	0.417519i	0.977967	−	0.208759i	$-0.0669425\pi$
$744$	172.629	−	458.883i	0.232028	−	0.616778i
$745$	−1164.74			−1.56341
$746$	−904.552	+	386.347i	−1.21254	+	0.517891i
$747$			174.281i			0.233307i
$748$	−268.548	−	257.025i	−0.359021	−	0.343616i
$749$		0			0
$750$	187.292	+	438.506i	0.249723	+	0.584675i
$751$			1276.52i			1.69976i	0.526978	+	0.849879i	$0.323325\pi$
$751$			1276.52i			1.69976i	−0.526978	+	0.849879i	$0.676675\pi$
$752$	487.746	−	21.3977i	0.648598	−	0.0284544i
$753$	−41.0309			−0.0544899
$754$	296.635	−	126.697i	0.393416	−	0.168033i
$755$		−	861.661i		−	1.14127i
$756$		0			0
$757$	971.918			1.28391			0.641954	−	0.766743i	$-0.278124\pi$
$757$	971.918			1.28391			0.641954	+	0.766743i	$0.278124\pi$
$758$	−227.103	−	531.715i	−0.299608	−	0.701471i
$759$		−	791.578i		−	1.04292i
$760$	256.520	+	96.5014i	0.337526	+	0.126975i
$761$	−1004.09			−1.31944			−0.659719	−	0.751512i	$-0.729325\pi$
$761$	−1004.09			−1.31944			−0.659719	+	0.751512i	$0.729325\pi$
$762$	686.699	−	293.299i	0.901180	−	0.384906i
$763$		0			0
$764$	1004.82	+	961.705i	1.31521	+	1.25878i
$765$	−146.426			−0.191406
$766$	−122.485	−	286.773i	−0.159902	−	0.374377i
$767$			1697.93i			2.21373i
$768$	38.8301	+	441.702i	0.0505600	+	0.575132i
$769$	23.8844			0.0310590			0.0155295	−	0.999879i	$-0.495057\pi$
$769$	23.8844			0.0310590			0.0155295	+	0.999879i	$0.495057\pi$
$770$		0			0
$771$		−	140.993i		−	0.182871i
$772$	792.351	−	827.874i	1.02636	−	1.07238i
$773$	−822.514			−1.06405			−0.532027	−	0.846727i	$-0.678569\pi$
$773$	−822.514			−1.06405			−0.532027	+	0.846727i	$0.678569\pi$
$774$	−46.2225	−	108.221i	−0.0597190	−	0.139820i
$775$		−	1480.31i		−	1.91008i
$776$	174.238	−	463.160i	0.224534	−	0.596856i
$777$		0			0
$778$	391.328	−	167.142i	0.502992	−	0.214835i
$779$		−	17.2499i		−	0.0221437i
$780$	−835.574	−	799.721i	−1.07125	−	1.02528i
$781$	−1169.22			−1.49707
$782$	−137.700	−	322.396i	−0.176087	−	0.412271i
$783$		−	41.0398i		−	0.0524136i
$784$		0			0
$785$	2269.52			2.89111
$786$	−3.58809	+	1.53252i	−0.00456500	+	0.00194977i
$787$		−	1555.47i		−	1.97646i	−0.152980	−	0.988229i	$-0.548887\pi$
$787$		−	1555.47i		−	1.97646i	0.152980	−	0.988229i	$-0.451113\pi$
$788$	−899.748	+	940.086i	−1.14181	+	1.19300i
$789$	355.600			0.450697
$790$	401.456	+	939.928i	0.508172	+	1.18978i
$791$		0			0
$792$	−349.658	−	131.539i	−0.441487	−	0.166085i
$793$	70.0544			0.0883410
$794$	186.442	−	79.6319i	0.234814	−	0.100292i
$795$		−	572.473i		−	0.720092i
$796$	431.488	+	412.973i	0.542070	+	0.518811i
$797$	−594.191			−0.745535			−0.372767	−	0.927925i	$-0.621591\pi$
$797$	−594.191			−0.745535			−0.372767	+	0.927925i	$0.621591\pi$
$798$		0			0
$799$			182.171i			0.227999i
$800$	579.311	+	1206.95i	0.724139	+	1.50869i
$801$	−406.733			−0.507781
$802$	−898.427	+	383.731i	−1.12023	+	0.478467i
$803$		−	335.516i		−	0.417828i
$804$	24.7898	−	25.9012i	0.0308331	−	0.0322154i
$805$		0			0
$806$	567.592	+	1328.90i	0.704209	+	1.64876i
$807$			657.747i			0.815052i
$808$	32.3522	−	85.9986i	0.0400398	−	0.106434i
$809$	1147.79			1.41878			0.709389	−	0.704817i	$-0.248971\pi$
$809$	1147.79			1.41878			0.709389	+	0.704817i	$0.248971\pi$
$810$	−135.330	+	57.8013i	−0.167074	+	0.0713596i
$811$		−	1214.93i		−	1.49806i	−0.662536	−	0.749030i	$-0.730520\pi$
$811$		−	1214.93i		−	1.49806i	0.662536	−	0.749030i	$-0.269480\pi$
$812$		0			0
$813$	883.822			1.08711
$814$	−602.258	−	1410.07i	−0.739875	−	1.73227i
$815$		−	1.42027i		−	0.00174266i
$816$	−165.292	+	7.25143i	−0.202563	+	0.00888656i
$817$	−82.1885			−0.100598
$818$	−718.704	+	306.968i	−0.878611	+	0.375267i
$819$		0			0
$820$	93.0772	−	97.2501i	0.113509	−	0.118598i
$821$	−1195.33			−1.45594			−0.727971	−	0.685608i	$-0.759536\pi$
$821$	−1195.33			−1.45594			−0.727971	+	0.685608i	$0.759536\pi$
$822$	−128.786	−	301.526i	−0.156674	−	0.366820i
$823$		−	810.829i		−	0.985212i	−0.870253	−	0.492606i	$-0.836044\pi$
$823$		−	810.829i		−	0.985212i	0.870253	−	0.492606i	$-0.163956\pi$
$824$	918.934	+	345.698i	1.11521	+	0.419536i
$825$	−1127.96			−1.36723
$826$		0			0
$827$		−	1268.19i		−	1.53349i	−0.641955	−	0.766743i	$-0.721876\pi$
$827$		−	1268.19i		−	1.53349i	0.641955	−	0.766743i	$-0.278124\pi$
$828$	−254.530	−	243.609i	−0.307404	−	0.294214i
$829$	1499.96			1.80936			0.904681	−	0.426089i	$-0.140109\pi$
$829$	1499.96			1.80936			0.904681	+	0.426089i	$0.140109\pi$
$830$	373.098	+	873.533i	0.449515	+	1.05245i
$831$			697.985i			0.839934i
$832$	−982.837	−	861.379i	−1.18129	−	1.03531i
$833$		0			0
$834$	182.505	−	77.9503i	0.218831	−	0.0934655i
$835$			1378.26i			1.65061i
$836$	−180.407	+	188.495i	−0.215797	+	0.225472i
$837$	183.855			0.219659
$838$	18.7648	+	43.9339i	0.0223923	+	0.0524270i
$839$			436.317i			0.520044i	0.965603	+	0.260022i	$0.0837298\pi$
$839$			436.317i			0.520044i	−0.965603	+	0.260022i	$0.916270\pi$
$840$		0			0
$841$	−778.620			−0.925826
$842$	−290.376	+	124.024i	−0.344865	+	0.147296i
$843$			586.831i			0.696122i
$844$	681.994	+	652.731i	0.808050	+	0.773378i
$845$	2027.32			2.39919
$846$	71.9116	+	168.366i	0.0850019	+	0.199015i
$847$		0			0
$848$	−28.3505	−	646.232i	−0.0334322	−	0.762066i
$849$	215.489			0.253816
$850$	−459.400	+	196.216i	−0.540470	+	0.230842i
$851$		−	1446.04i		−	1.69923i
$852$	−359.827	+	375.959i	−0.422332	+	0.441266i
$853$	729.996			0.855798			0.427899	−	0.903827i	$-0.359254\pi$
$853$	729.996			0.855798			0.427899	+	0.903827i	$0.359254\pi$
$854$		0			0
$855$			102.777i			0.120207i
$856$	−637.520	−	239.832i	−0.744767	−	0.280177i
$857$	284.649			0.332146			0.166073	−	0.986113i	$-0.446891\pi$
$857$	284.649			0.332146			0.166073	+	0.986113i	$0.446891\pi$
$858$	1012.59	−	432.492i	1.18018	−	0.504070i
$859$		−	251.786i		−	0.293116i	−0.989202	−	0.146558i	$-0.953181\pi$
$859$		−	251.786i		−	0.293116i	0.989202	−	0.146558i	$-0.0468195\pi$
$860$	−463.355	−	443.473i	−0.538785	−	0.515666i
$861$		0			0
$862$	−129.550	−	303.314i	−0.150289	−	0.351872i
$863$		−	695.096i		−	0.805441i	−0.915323	−	0.402721i	$-0.868065\pi$
$863$		−	695.096i		−	0.805441i	0.915323	−	0.402721i	$-0.131935\pi$
$864$	−149.904	+	71.9505i	−0.173500	+	0.0832760i
$865$	68.3305			0.0789947
$866$	−275.312	+	117.589i	−0.317912	+	0.135785i
$867$			438.827i			0.506144i
$868$		0			0
$869$	−973.010			−1.11969
$870$	−87.8576	−	205.701i	−0.100986	−	0.236437i
$871$			105.671i			0.121322i
$872$	147.831	−	392.966i	0.169531	−	0.450649i
$873$	185.569			0.212564
$874$	−226.291	+	96.6520i	−0.258914	+	0.110586i
$875$		0			0
$876$	−107.884	−	103.255i	−0.123156	−	0.117871i
$877$	1094.32			1.24780			0.623901	−	0.781503i	$-0.285547\pi$
$877$	1094.32			1.24780			0.623901	+	0.781503i	$0.285547\pi$
$878$	−338.315	−	792.095i	−0.385324	−	0.902159i
$879$		−	383.183i		−	0.435931i
$880$	−2034.16	+	89.2397i	−2.31155	+	0.101409i
$881$	26.3107			0.0298646			0.0149323	−	0.999889i	$-0.495247\pi$
$881$	26.3107			0.0298646			0.0149323	+	0.999889i	$0.495247\pi$
$882$		0			0
$883$		−	855.744i		−	0.969132i	−0.874755	−	0.484566i	$-0.838978\pi$
$883$		−	855.744i		−	0.969132i	0.874755	−	0.484566i	$-0.161022\pi$
$884$	337.176	−	352.293i	0.381421	−	0.398521i
$885$	1177.42			1.33042
$886$	−480.587	−	1125.20i	−0.542424	−	1.26997i
$887$		−	641.756i		−	0.723512i	−0.932273	−	0.361756i	$-0.882177\pi$
$887$		−	641.756i		−	0.723512i	0.932273	−	0.361756i	$-0.117823\pi$
$888$	−638.749	−	240.294i	−0.719312	−	0.270601i
$889$		0			0
$890$	−2038.63	+	870.729i	−2.29060	+	0.978347i
$891$		−	140.093i		−	0.157231i
$892$	724.888	+	693.784i	0.812655	+	0.777785i
$893$	127.866			0.143187
$894$	−193.851	−	453.863i	−0.216836	−	0.507677i
$895$			1517.35i			1.69536i
$896$		0			0
$897$	1038.43			1.15767
$898$	−27.1595	+	11.6002i	−0.0302444	+	0.0129178i
$899$			279.458i			0.310855i
$900$	−347.132	+	362.695i	−0.385702	+	0.402994i
$901$	241.365			0.267885
$902$	50.3365	+	117.853i	0.0558054	+	0.130657i
$903$		0			0
$904$	−260.610	+	692.754i	−0.288285	+	0.766321i
$905$	−1930.23			−2.13285
$906$	335.762	−	143.409i	0.370599	−	0.158288i
$907$			823.477i			0.907913i	0.891024	+	0.453957i	$0.149988\pi$
$907$			823.477i			0.907913i	−0.891024	+	0.453957i	$0.850012\pi$
$908$	662.841	+	634.399i	0.730001	+	0.698678i
$909$	34.4560			0.0379054
$910$		0			0
$911$			188.691i			0.207125i	0.994623	+	0.103563i	$0.0330242\pi$
$911$			188.691i			0.207125i	−0.994623	+	0.103563i	$0.966976\pi$
$912$	5.08980	+	116.019i	0.00558093	+	0.127214i
$913$	−904.278			−0.990447
$914$	1606.01	−	685.949i	1.75712	−	0.750491i
$915$		−	48.5789i		−	0.0530917i
$916$	496.598	−	518.862i	0.542137	−	0.566443i
$917$		0			0
$918$	−24.3700	−	57.0575i	−0.0265469	−	0.0621541i
$919$			32.5760i			0.0354472i	0.999843	+	0.0177236i	$0.00564189\pi$
$919$			32.5760i			0.0354472i	−0.999843	+	0.0177236i	$0.994358\pi$
$920$	−1797.28	−	676.126i	−1.95356	−	0.734919i
$921$	2.75209			0.00298815
$922$	−22.5997	+	9.65265i	−0.0245116	+	0.0104693i
$923$		−	1533.83i		−	1.66179i
$924$		0			0
$925$	−2060.55			−2.22762
$926$	99.0147	+	231.823i	0.106927	+	0.250349i
$927$			368.178i			0.397172i
$928$	−109.364	−	227.853i	−0.117849	−	0.245531i
$929$	−877.630			−0.944704			−0.472352	−	0.881410i	$-0.656595\pi$
$929$	−877.630			−0.944704			−0.472352	+	0.881410i	$0.656595\pi$
$930$	921.522	−	393.595i	0.990883	−	0.423220i
$931$		0			0
$932$	−602.511	+	629.523i	−0.646471	+	0.675454i
$933$	−216.637			−0.232194
$934$	418.431	+	979.670i	0.447999	+	1.04890i
$935$		−	759.749i		−	0.812566i
$936$	172.559	−	458.697i	0.184358	−	0.490061i
$937$	233.999			0.249732			0.124866	−	0.992174i	$-0.460150\pi$
$937$	233.999			0.249732			0.124866	+	0.992174i	$0.460150\pi$
$938$		0			0
$939$		−	384.748i		−	0.409742i
$940$	720.874	+	689.942i	0.766887	+	0.733981i
$941$	−260.532			−0.276867			−0.138434	−	0.990372i	$-0.544207\pi$
$941$	−260.532			−0.276867			−0.138434	+	0.990372i	$0.544207\pi$
$942$	377.723	+	884.360i	0.400979	+	0.938812i
$943$			120.860i			0.128165i
$944$	1329.12	−	58.3094i	1.40797	−	0.0617684i
$945$		0			0
$946$	561.517	−	239.832i	0.593570	−	0.253522i
$947$		−	882.223i		−	0.931598i	−0.884891	−	0.465799i	$-0.845767\pi$
$947$		−	882.223i		−	0.931598i	0.884891	−	0.465799i	$-0.154233\pi$
$948$	−299.445	+	312.869i	−0.315870	+	0.330031i
$949$	440.144			0.463798
$950$	137.725	+	322.454i	0.144973	+	0.339426i
$951$		−	806.971i		−	0.848550i
$952$		0			0
$953$	−442.079			−0.463882			−0.231941	−	0.972730i	$-0.574508\pi$
$953$	−442.079			−0.463882			−0.231941	+	0.972730i	$0.574508\pi$
$954$	223.075	−	95.2783i	0.233831	−	0.0998724i
$955$			2842.74i			2.97669i
$956$	431.799	+	413.271i	0.451673	+	0.432292i
$957$	212.941			0.222508
$958$	285.213	+	667.768i	0.297717	+	0.697043i
$959$		0			0
$960$	−597.320	+	681.544i	−0.622208	+	0.709941i
$961$	−290.950			−0.302758
$962$	1849.79	−	790.069i	1.92285	−	0.821278i
$963$		−	255.427i		−	0.265241i
$964$	51.3373	−	53.6388i	0.0532544	−	0.0556420i
$965$	2342.14			2.42709
$966$		0			0
$967$			578.469i			0.598210i	0.954220	+	0.299105i	$0.0966880\pi$
$967$			578.469i			0.598210i	−0.954220	+	0.299105i	$0.903312\pi$
$968$	341.673	−	908.236i	0.352968	−	0.938260i
$969$	−43.3325			−0.0447187
$970$	930.110	−	397.263i	0.958877	−	0.409549i
$971$			1010.58i			1.04076i	0.853935	+	0.520379i	$0.174209\pi$
$971$			1010.58i			1.04076i	−0.853935	+	0.520379i	$0.825791\pi$
$972$	−45.0467	−	43.1138i	−0.0463443	−	0.0443557i
$973$		0			0
$974$	−684.604	−	1602.86i	−0.702879	−	1.64565i
$975$		−	1479.71i		−	1.51765i
$976$	−2.40577	−	54.8380i	−0.00246493	−	0.0561864i
$977$	210.284			0.215235			0.107617	−	0.994192i	$-0.465678\pi$
$977$	210.284			0.215235			0.107617	+	0.994192i	$0.465678\pi$
$978$	0.553433	−	0.236379i	0.000565882	−	0.000241696i
$979$		−	2110.39i		−	2.15566i
$980$		0			0
$981$	157.445			0.160494
$982$	232.617	+	544.625i	0.236881	+	0.554608i
$983$		−	593.862i		−	0.604132i	−0.953287	−	0.302066i	$-0.902324\pi$
$983$		−	593.862i		−	0.604132i	0.953287	−	0.302066i	$-0.0976764\pi$
$984$	53.3864	+	20.0837i	0.0542545	+	0.0204102i
$985$	−2659.60			−2.70010
$986$	86.7270	−	37.0423i	0.0879584	−	0.0375682i
$987$		0			0
$988$	−247.276	−	236.665i	−0.250279	−	0.239540i
$989$	575.844			0.582249
$990$	−299.910	−	702.177i	−0.302939	−	0.709270i
$991$		−	1183.14i		−	1.19389i	−0.802284	−	0.596943i	$-0.796382\pi$
$991$		−	1183.14i		−	1.19389i	0.802284	−	0.596943i	$-0.203618\pi$
$992$	1020.76	−	489.943i	1.02899	−	0.493894i
$993$	597.547			0.601760
$994$		0			0
$995$			1220.72i			1.22686i
$996$	−278.292	+	290.769i	−0.279410	+	0.291937i
$997$	−420.534			−0.421799			−0.210900	−	0.977508i	$-0.567639\pi$
$997$	−420.534			−0.421799			−0.210900	+	0.977508i	$0.567639\pi$
$998$	80.4409	+	188.336i	0.0806021	+	0.188713i
$999$		−	255.920i		−	0.256176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.d.295.2		12
4.3	odd	2	inner	588.3.g.d.295.1		12
7.6	odd	2		84.3.g.a.43.2	yes	12
21.20	even	2		252.3.g.b.127.11		12
28.27	even	2		84.3.g.a.43.1	✓	12
56.13	odd	2		1344.3.m.e.127.6		12
56.27	even	2		1344.3.m.e.127.12		12
84.83	odd	2		252.3.g.b.127.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.g.a.43.1	✓	12	28.27	even	2
84.3.g.a.43.2	yes	12	7.6	odd	2
252.3.g.b.127.11		12	21.20	even	2
252.3.g.b.127.12		12	84.83	odd	2
588.3.g.d.295.1		12	4.3	odd	2	inner
588.3.g.d.295.2		12	1.1	even	1	trivial
1344.3.m.e.127.6		12	56.13	odd	2
1344.3.m.e.127.12		12	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83926 + 0.785573i) q^{2} -1.73205i q^{3} +(2.76575 - 2.88975i) q^{4} +8.17539 q^{5} +(1.36065 + 3.18569i) q^{6} +(-2.81683 + 7.48769i) q^{8} -3.00000 q^{9} +(-15.0367 + 6.42236i) q^{10} -15.5659i q^{11} +(-5.00519 - 4.79042i) q^{12} +20.4200 q^{13} -14.1602i q^{15} +(-0.701254 - 15.9846i) q^{16} +5.97018 q^{17} +(5.51778 - 2.35672i) q^{18} -4.19049i q^{19} +(22.6111 - 23.6248i) q^{20} +(12.2282 + 28.6297i) q^{22} +29.3602i q^{23} +(12.9691 + 4.87889i) q^{24} +41.8370 q^{25} +(-37.5577 + 16.0414i) q^{26} +5.19615i q^{27} -7.89812 q^{29} +(11.1239 + 26.0443i) q^{30} -35.3829i q^{31} +(13.8469 + 28.8490i) q^{32} -26.9609 q^{33} +(-10.9807 + 4.69002i) q^{34} +(-8.29725 + 8.66924i) q^{36} -49.2518 q^{37} +(3.29194 + 7.70740i) q^{38} -35.3685i q^{39} +(-23.0286 + 61.2148i) q^{40} +4.11644 q^{41} -19.6131i q^{43} +(-44.9815 - 43.0514i) q^{44} -24.5262 q^{45} +(-23.0646 - 54.0010i) q^{46} +30.5134i q^{47} +(-27.6862 + 1.21461i) q^{48} +(-76.9490 + 32.8660i) q^{50} -10.3407i q^{51} +(56.4767 - 59.0087i) q^{52} +40.4284 q^{53} +(-4.08196 - 9.55707i) q^{54} -127.257i q^{55} -7.25815 q^{57} +(14.5267 - 6.20455i) q^{58} +83.1502i q^{59} +(-40.9193 - 39.1635i) q^{60} +3.43067 q^{61} +(27.7959 + 65.0783i) q^{62} +(-48.1310 - 42.1830i) q^{64} +166.942 q^{65} +(49.5881 - 21.1798i) q^{66} +5.17488i q^{67} +(16.5120 - 17.2523i) q^{68} +50.8534 q^{69} -75.1139i q^{71} +(8.45048 - 22.4631i) q^{72} +21.5545 q^{73} +(90.5868 - 38.6909i) q^{74} -72.4638i q^{75} +(-12.1095 - 11.5899i) q^{76} +(27.7846 + 65.0519i) q^{78} -62.5091i q^{79} +(-5.73302 - 130.681i) q^{80} +9.00000 q^{81} +(-7.57121 + 3.23377i) q^{82} -58.0935i q^{83} +48.8086 q^{85} +(15.4075 + 36.0736i) q^{86} +13.6799i q^{87} +(116.553 + 43.8464i) q^{88} +135.578 q^{89} +(45.1100 - 19.2671i) q^{90} +(84.8435 + 81.2030i) q^{92} -61.2850 q^{93} +(-23.9705 - 56.1221i) q^{94} -34.2589i q^{95} +(49.9679 - 23.9835i) q^{96} -61.8562 q^{97} +46.6977i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{4} - 8 q^{5} + 12 q^{6} - 10 q^{8} - 36 q^{9} - 28 q^{10} - 24 q^{12} + 24 q^{13} - 14 q^{16} + 40 q^{17} - 6 q^{18} + 20 q^{20} - 88 q^{22} + 36 q^{24} + 180 q^{25} - 100 q^{26} + 72 q^{29}+ \cdots + 264 q^{97}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^4 - 8 * q^5 + 12 * q^6 - 10 * q^8 - 36 * q^9 - 28 * q^10 - 24 * q^12 + 24 * q^13 - 14 * q^16 + 40 * q^17 - 6 * q^18 + 20 * q^20 - 88 * q^22 + 36 * q^24 + 180 * q^25 - 100 * q^26 + 72 * q^29 + 72 * q^30 + 142 * q^32 + 100 * q^34 - 6 * q^36 - 88 * q^37 - 128 * q^38 + 28 * q^40 + 200 * q^41 - 40 * q^44 + 24 * q^45 - 24 * q^46 - 48 * q^48 - 346 * q^50 + 364 * q^52 + 104 * q^53 - 36 * q^54 + 148 * q^58 + 96 * q^60 - 104 * q^61 - 64 * q^62 - 70 * q^64 + 176 * q^65 - 24 * q^66 - 188 * q^68 + 192 * q^69 + 30 * q^72 - 312 * q^73 + 4 * q^74 - 432 * q^76 + 48 * q^78 + 564 * q^80 + 108 * q^81 - 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 + 552 * q^89 + 84 * q^90 + 232 * q^92 - 48 * q^93 + 144 * q^94 + 108 * q^96 + 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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