LMFDB - Embedded newform 40.3.l.b.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(17,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("40.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.l (of order $4$, degree $2$, 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:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 21x^{2} + 100 $ x^4 + 21*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.2
Root			$-2.70156i$ of defining polynomial
Character	$\chi$	$=$	40.17
Dual form			40.3.l.b.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.70156 - 2.70156i) q^{3} +(-4.70156 - 1.70156i) q^{5} +(6.70156 + 6.70156i) q^{7} -5.59688i q^{9} +O(q^{10})$	\(q+(2.70156 - 2.70156i) q^{3} +(-4.70156 - 1.70156i) q^{5} +(6.70156 + 6.70156i) q^{7} -5.59688i q^{9} -1.40312 q^{11} +(-14.4031 + 14.4031i) q^{13} +(-17.2984 + 8.10469i) q^{15} +(-2.40312 - 2.40312i) q^{17} -22.8062i q^{19} +36.2094 q^{21} +(-0.104686 + 0.104686i) q^{23} +(19.2094 + 16.0000i) q^{25} +(9.19375 + 9.19375i) q^{27} -45.6125i q^{29} -2.59688 q^{31} +(-3.79063 + 3.79063i) q^{33} +(-20.1047 - 42.9109i) q^{35} +(10.6125 + 10.6125i) q^{37} +77.8219i q^{39} -44.6281 q^{41} +(26.7016 - 26.7016i) q^{43} +(-9.52343 + 26.3141i) q^{45} +(-10.4922 - 10.4922i) q^{47} +40.8219i q^{49} -12.9844 q^{51} +(-3.00000 + 3.00000i) q^{53} +(6.59688 + 2.38750i) q^{55} +(-61.6125 - 61.6125i) q^{57} +41.1938i q^{59} -57.4031 q^{61} +(37.5078 - 37.5078i) q^{63} +(92.2250 - 43.2094i) q^{65} +(34.7016 + 34.7016i) q^{67} +0.565633i q^{69} +45.4031 q^{71} +(11.3875 - 11.3875i) q^{73} +(95.1203 - 8.67032i) q^{75} +(-9.40312 - 9.40312i) q^{77} -86.4500i q^{79} +100.047 q^{81} +(-81.7172 + 81.7172i) q^{83} +(7.20937 + 15.3875i) q^{85} +(-123.225 - 123.225i) q^{87} +91.2250i q^{89} -193.047 q^{91} +(-7.01562 + 7.01562i) q^{93} +(-38.8062 + 107.225i) q^{95} +(49.0000 + 49.0000i) q^{97} +7.85311i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 6 q^{5} + 14 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 - 6 * q^5 + 14 * q^7	$ 4 q - 2 q^{3} - 6 q^{5} + 14 q^{7} + 20 q^{11} - 32 q^{13} - 82 q^{15} + 16 q^{17} + 68 q^{21} + 38 q^{23} + 88 q^{27} - 36 q^{31} - 92 q^{33} - 42 q^{35} - 60 q^{37} + 52 q^{41} + 94 q^{43} + 154 q^{45} - 106 q^{47} - 180 q^{51} - 12 q^{53} + 52 q^{55} - 144 q^{57} - 204 q^{61} + 86 q^{63} + 164 q^{65} + 126 q^{67} + 156 q^{71} + 148 q^{73} + 214 q^{75} - 12 q^{77} + 16 q^{81} - 186 q^{83} - 48 q^{85} - 288 q^{87} - 388 q^{91} + 100 q^{93} - 104 q^{95} + 196 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 6 * q^5 + 14 * q^7 + 20 * q^11 - 32 * q^13 - 82 * q^15 + 16 * q^17 + 68 * q^21 + 38 * q^23 + 88 * q^27 - 36 * q^31 - 92 * q^33 - 42 * q^35 - 60 * q^37 + 52 * q^41 + 94 * q^43 + 154 * q^45 - 106 * q^47 - 180 * q^51 - 12 * q^53 + 52 * q^55 - 144 * q^57 - 204 * q^61 + 86 * q^63 + 164 * q^65 + 126 * q^67 + 156 * q^71 + 148 * q^73 + 214 * q^75 - 12 * q^77 + 16 * q^81 - 186 * q^83 - 48 * q^85 - 288 * q^87 - 388 * q^91 + 100 * q^93 - 104 * q^95 + 196 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.70156	−	2.70156i	0.900521	−	0.900521i	−0.0949603	−	0.995481i	$-0.530272\pi$
$3$	2.70156	−	2.70156i	0.900521	−	0.900521i	0.995481	+	0.0949603i	$0.0302724\pi$
$4$		0			0
$5$	−4.70156	−	1.70156i	−0.940312	−	0.340312i
$5$	−4.70156	−	1.70156i	−0.940312	−	0.340312i
$6$		0			0
$7$	6.70156	+	6.70156i	0.957366	+	0.957366i	0.999128	−	0.0417616i	$-0.0132970\pi$
$7$	6.70156	+	6.70156i	0.957366	+	0.957366i	−0.0417616	+	0.999128i	$0.513297\pi$
$8$		0			0
$9$		−	5.59688i		−	0.621875i
$10$		0			0
$11$	−1.40312			−0.127557			−0.0637784	−	0.997964i	$-0.520315\pi$
$11$	−1.40312			−0.127557			−0.0637784	+	0.997964i	$0.520315\pi$
$12$		0			0
$13$	−14.4031	+	14.4031i	−1.10793	+	1.10793i	−0.114511	+	0.993422i	$0.536530\pi$
$13$	−14.4031	+	14.4031i	−1.10793	+	1.10793i	−0.993422	+	0.114511i	$0.963470\pi$
$14$		0			0
$15$	−17.2984	+	8.10469i	−1.15323	+	0.540312i
$16$		0			0
$17$	−2.40312	−	2.40312i	−0.141360	−	0.141360i	0.632885	−	0.774246i	$-0.281870\pi$
$17$	−2.40312	−	2.40312i	−0.141360	−	0.141360i	−0.774246	+	0.632885i	$0.781870\pi$
$18$		0			0
$19$		−	22.8062i		−	1.20033i	−0.799877	−	0.600164i	$-0.795102\pi$
$19$		−	22.8062i		−	1.20033i	0.799877	−	0.600164i	$-0.204898\pi$
$20$		0			0
$21$	36.2094			1.72426
$22$		0			0
$23$	−0.104686	+	0.104686i	−0.00455158	+	0.00455158i	−0.709379	−	0.704827i	$-0.751024\pi$
$23$	−0.104686	+	0.104686i	−0.00455158	+	0.00455158i	0.704827	+	0.709379i	$0.251024\pi$
$24$		0			0
$25$	19.2094	+	16.0000i	0.768375	+	0.640000i
$26$		0			0
$27$	9.19375	+	9.19375i	0.340509	+	0.340509i
$28$		0			0
$29$		−	45.6125i		−	1.57284i	−0.617689	−	0.786422i	$-0.711931\pi$
$29$		−	45.6125i		−	1.57284i	0.617689	−	0.786422i	$-0.288069\pi$
$30$		0			0
$31$	−2.59688			−0.0837702			−0.0418851	−	0.999122i	$-0.513336\pi$
$31$	−2.59688			−0.0837702			−0.0418851	+	0.999122i	$0.513336\pi$
$32$		0			0
$33$	−3.79063	+	3.79063i	−0.114867	+	0.114867i
$34$		0			0
$35$	−20.1047	−	42.9109i	−0.574420	−	1.22603i
$36$		0			0
$37$	10.6125	+	10.6125i	0.286824	+	0.286824i	0.835823	−	0.548999i	$-0.184991\pi$
$37$	10.6125	+	10.6125i	0.286824	+	0.286824i	−0.548999	+	0.835823i	$0.684991\pi$
$38$		0			0
$39$			77.8219i			1.99543i
$40$		0			0
$41$	−44.6281			−1.08849			−0.544245	−	0.838926i	$-0.683184\pi$
$41$	−44.6281			−1.08849			−0.544245	+	0.838926i	$0.683184\pi$
$42$		0			0
$43$	26.7016	−	26.7016i	0.620967	−	0.620967i	−0.324812	−	0.945779i	$-0.605301\pi$
$43$	26.7016	−	26.7016i	0.620967	−	0.620967i	0.945779	+	0.324812i	$0.105301\pi$
$44$		0			0
$45$	−9.52343	+	26.3141i	−0.211632	+	0.584757i
$46$		0			0
$47$	−10.4922	−	10.4922i	−0.223238	−	0.223238i	0.586622	−	0.809861i	$-0.300457\pi$
$47$	−10.4922	−	10.4922i	−0.223238	−	0.223238i	−0.809861	+	0.586622i	$0.800457\pi$
$48$		0			0
$49$			40.8219i			0.833099i
$50$		0			0
$51$	−12.9844			−0.254596
$52$		0			0
$53$	−3.00000	+	3.00000i	−0.0566038	+	0.0566038i	−0.734842	−	0.678238i	$-0.762744\pi$
$53$	−3.00000	+	3.00000i	−0.0566038	+	0.0566038i	0.678238	+	0.734842i	$0.262744\pi$
$54$		0			0
$55$	6.59688	+	2.38750i	0.119943	+	0.0434091i
$56$		0			0
$57$	−61.6125	−	61.6125i	−1.08092	−	1.08092i
$58$		0			0
$59$			41.1938i			0.698199i	0.937086	+	0.349100i	$0.113513\pi$
$59$			41.1938i			0.698199i	−0.937086	+	0.349100i	$0.886487\pi$
$60$		0			0
$61$	−57.4031			−0.941035			−0.470517	−	0.882391i	$-0.655933\pi$
$61$	−57.4031			−0.941035			−0.470517	+	0.882391i	$0.655933\pi$
$62$		0			0
$63$	37.5078	−	37.5078i	0.595362	−	0.595362i
$64$		0			0
$65$	92.2250	−	43.2094i	1.41885	−	0.664760i
$66$		0			0
$67$	34.7016	+	34.7016i	0.517934	+	0.517934i	0.916946	−	0.399012i	$-0.130647\pi$
$67$	34.7016	+	34.7016i	0.517934	+	0.517934i	−0.399012	+	0.916946i	$0.630647\pi$
$68$		0			0
$69$			0.565633i			0.00819759i
$70$		0			0
$71$	45.4031			0.639481			0.319740	−	0.947505i	$-0.396404\pi$
$71$	45.4031			0.639481			0.319740	+	0.947505i	$0.396404\pi$
$72$		0			0
$73$	11.3875	−	11.3875i	0.155993	−	0.155993i	−0.624795	−	0.780789i	$-0.714818\pi$
$73$	11.3875	−	11.3875i	0.155993	−	0.155993i	0.780789	+	0.624795i	$0.214818\pi$
$74$		0			0
$75$	95.1203	−	8.67032i	1.26827	−	0.115604i
$76$		0			0
$77$	−9.40312	−	9.40312i	−0.122118	−	0.122118i
$78$		0			0
$79$		−	86.4500i		−	1.09430i	−0.837033	−	0.547152i	$-0.815712\pi$
$79$		−	86.4500i		−	1.09430i	0.837033	−	0.547152i	$-0.184288\pi$
$80$		0			0
$81$	100.047			1.23515
$82$		0			0
$83$	−81.7172	+	81.7172i	−0.984544	+	0.984544i	−0.999882	−	0.0153380i	$-0.995118\pi$
$83$	−81.7172	+	81.7172i	−0.984544	+	0.984544i	0.0153380	+	0.999882i	$0.495118\pi$
$84$		0			0
$85$	7.20937	+	15.3875i	0.0848161	+	0.181029i
$86$		0			0
$87$	−123.225	−	123.225i	−1.41638	−	1.41638i
$88$		0			0
$89$			91.2250i			1.02500i	0.858687	+	0.512500i	$0.171281\pi$
$89$			91.2250i			1.02500i	−0.858687	+	0.512500i	$0.828719\pi$
$90$		0			0
$91$	−193.047			−2.12139
$92$		0			0
$93$	−7.01562	+	7.01562i	−0.0754368	+	0.0754368i
$94$		0			0
$95$	−38.8062	+	107.225i	−0.408487	+	1.12868i
$96$		0			0
$97$	49.0000	+	49.0000i	0.505155	+	0.505155i	0.913035	−	0.407881i	$-0.133732\pi$
$97$	49.0000	+	49.0000i	0.505155	+	0.505155i	−0.407881	+	0.913035i	$0.633732\pi$
$98$		0			0
$99$			7.85311i			0.0793244i
$100$		0			0
$101$	60.0312			0.594369			0.297184	−	0.954820i	$-0.403952\pi$
$101$	60.0312			0.594369			0.297184	+	0.954820i	$0.403952\pi$
$102$		0			0
$103$	61.5078	−	61.5078i	0.597163	−	0.597163i	−0.342393	−	0.939557i	$-0.611238\pi$
$103$	61.5078	−	61.5078i	0.597163	−	0.597163i	0.939557	+	0.342393i	$0.111238\pi$
$104$		0			0
$105$	−170.241	−	61.6125i	−1.62134	−	0.586786i
$106$		0			0
$107$	67.5391	+	67.5391i	0.631206	+	0.631206i	0.948371	−	0.317164i	$-0.102731\pi$
$107$	67.5391	+	67.5391i	0.631206	+	0.631206i	−0.317164	+	0.948371i	$0.602731\pi$
$108$		0			0
$109$			19.0469i			0.174742i	0.996176	+	0.0873709i	$0.0278465\pi$
$109$			19.0469i			0.174742i	−0.996176	+	0.0873709i	$0.972153\pi$
$110$		0			0
$111$	57.3406			0.516582
$112$		0			0
$113$	8.82187	−	8.82187i	0.0780696	−	0.0780696i	−0.666994	−	0.745063i	$-0.732419\pi$
$113$	8.82187	−	8.82187i	0.0780696	−	0.0780696i	0.745063	+	0.666994i	$0.232419\pi$
$114$		0			0
$115$	0.670320	−	0.314059i	0.00582887	−	0.00273095i
$116$		0			0
$117$	80.6125	+	80.6125i	0.688996	+	0.688996i
$118$		0			0
$119$		−	32.2094i		−	0.270667i
$120$		0			0
$121$	−119.031			−0.983729
$122$		0			0
$123$	−120.566	+	120.566i	−0.980208	+	0.980208i
$124$		0			0
$125$	−63.0891	−	107.911i	−0.504713	−	0.863287i
$126$		0			0
$127$	14.7016	+	14.7016i	0.115760	+	0.115760i	0.762614	−	0.646854i	$-0.223916\pi$
$127$	14.7016	+	14.7016i	0.115760	+	0.115760i	−0.646854	+	0.762614i	$0.723916\pi$
$128$		0			0
$129$		−	144.272i		−	1.11839i
$130$		0			0
$131$	237.884			1.81591			0.907956	−	0.419066i	$-0.137643\pi$
$131$	237.884			1.81591			0.907956	+	0.419066i	$0.137643\pi$
$132$		0			0
$133$	152.837	−	152.837i	1.14915	−	1.14915i
$134$		0			0
$135$	−27.5813	−	58.8687i	−0.204306	−	0.436065i
$136$		0			0
$137$	86.6125	+	86.6125i	0.632208	+	0.632208i	0.948621	−	0.316413i	$-0.102479\pi$
$137$	86.6125	+	86.6125i	0.632208	+	0.632208i	−0.316413	+	0.948621i	$0.602479\pi$
$138$		0			0
$139$		−	246.806i		−	1.77558i	−0.460244	−	0.887792i	$-0.652238\pi$
$139$		−	246.806i		−	1.77558i	0.460244	−	0.887792i	$-0.347762\pi$
$140$		0			0
$141$	−56.6906			−0.402061
$142$		0			0
$143$	20.2094	−	20.2094i	0.141324	−	0.141324i
$144$		0			0
$145$	−77.6125	+	214.450i	−0.535259	+	1.47897i
$146$		0			0
$147$	110.283	+	110.283i	0.750223	+	0.750223i
$148$		0			0
$149$			121.853i			0.817806i	0.912578	+	0.408903i	$0.134089\pi$
$149$			121.853i			0.817806i	−0.912578	+	0.408903i	$0.865911\pi$
$150$		0			0
$151$	245.528			1.62601			0.813007	−	0.582254i	$-0.197829\pi$
$151$	245.528			1.62601			0.813007	+	0.582254i	$0.197829\pi$
$152$		0			0
$153$	−13.4500	+	13.4500i	−0.0879084	+	0.0879084i
$154$		0			0
$155$	12.2094	+	4.41875i	0.0787701	+	0.0285080i
$156$		0			0
$157$	−146.466	−	146.466i	−0.932902	−	0.932902i	0.0649843	−	0.997886i	$-0.479300\pi$
$157$	−146.466	−	146.466i	−0.932902	−	0.932902i	−0.997886	+	0.0649843i	$0.979300\pi$
$158$		0			0
$159$			16.2094i			0.101946i
$160$		0			0
$161$	−1.40312			−0.00871506
$162$		0			0
$163$	−174.973	+	174.973i	−1.07346	+	1.07346i	−0.0763776	+	0.997079i	$0.524335\pi$
$163$	−174.973	+	174.973i	−1.07346	+	1.07346i	−0.997079	+	0.0763776i	$0.975665\pi$
$164$		0			0
$165$	24.2719	−	11.3719i	0.147102	−	0.0689205i
$166$		0			0
$167$	−203.330	−	203.330i	−1.21754	−	1.21754i	−0.968490	−	0.249053i	$-0.919881\pi$
$167$	−203.330	−	203.330i	−1.21754	−	1.21754i	−0.249053	−	0.968490i	$-0.580119\pi$
$168$		0			0
$169$		−	245.900i		−	1.45503i
$170$		0			0
$171$	−127.644			−0.746455
$172$		0			0
$173$	−168.612	+	168.612i	−0.974639	+	0.974639i	−0.999686	−	0.0250476i	$-0.992026\pi$
$173$	−168.612	+	168.612i	−0.974639	+	0.974639i	0.0250476	+	0.999686i	$0.492026\pi$
$174$		0			0
$175$	21.5078	+	235.958i	0.122902	+	1.34833i
$176$		0			0
$177$	111.287	+	111.287i	0.628743	+	0.628743i
$178$		0			0
$179$			27.5813i			0.154085i	0.997028	+	0.0770426i	$0.0245477\pi$
$179$			27.5813i			0.154085i	−0.997028	+	0.0770426i	$0.975452\pi$
$180$		0			0
$181$	−88.3875			−0.488329			−0.244164	−	0.969734i	$-0.578514\pi$
$181$	−88.3875			−0.488329			−0.244164	+	0.969734i	$0.578514\pi$
$182$		0			0
$183$	−155.078	+	155.078i	−0.847421	+	0.847421i
$184$		0			0
$185$	−31.8375	−	67.9531i	−0.172095	−	0.367314i
$186$		0			0
$187$	3.37188	+	3.37188i	0.0180315	+	0.0180315i
$188$		0			0
$189$			123.225i			0.651984i
$190$		0			0
$191$	−79.4969			−0.416214			−0.208107	−	0.978106i	$-0.566730\pi$
$191$	−79.4969			−0.416214			−0.208107	+	0.978106i	$0.566730\pi$
$192$		0			0
$193$	104.822	−	104.822i	0.543118	−	0.543118i	−0.381323	−	0.924442i	$-0.624532\pi$
$193$	104.822	−	104.822i	0.543118	−	0.543118i	0.924442	+	0.381323i	$0.124532\pi$
$194$		0			0
$195$	132.419	−	365.884i	0.679070	−	1.87633i
$196$		0			0
$197$	68.1625	+	68.1625i	0.346003	+	0.346003i	0.858618	−	0.512616i	$-0.171323\pi$
$197$	68.1625	+	68.1625i	0.346003	+	0.346003i	−0.512616	+	0.858618i	$0.671323\pi$
$198$		0			0
$199$			250.512i			1.25886i	0.777059	+	0.629428i	$0.216711\pi$
$199$			250.512i			1.25886i	−0.777059	+	0.629428i	$0.783289\pi$
$200$		0			0
$201$	187.497			0.932820
$202$		0			0
$203$	305.675	−	305.675i	1.50579	−	1.50579i
$204$		0			0
$205$	209.822	+	75.9375i	1.02352	+	0.370427i
$206$		0			0
$207$	0.585917	+	0.585917i	0.00283051	+	0.00283051i
$208$		0			0
$209$			32.0000i			0.153110i
$210$		0			0
$211$	−332.628			−1.57644			−0.788218	−	0.615396i	$-0.788996\pi$
$211$	−332.628			−1.57644			−0.788218	+	0.615396i	$0.788996\pi$
$212$		0			0
$213$	122.659	−	122.659i	0.575866	−	0.575866i
$214$		0			0
$215$	−170.973	+	80.1047i	−0.795225	+	0.372580i
$216$		0			0
$217$	−17.4031	−	17.4031i	−0.0801987	−	0.0801987i
$218$		0			0
$219$		−	61.5281i		−	0.280950i
$220$		0			0
$221$	69.2250			0.313235
$222$		0			0
$223$	187.602	−	187.602i	0.841263	−	0.841263i	−0.147761	−	0.989023i	$-0.547207\pi$
$223$	187.602	−	187.602i	0.841263	−	0.841263i	0.989023	+	0.147761i	$0.0472065\pi$
$224$		0			0
$225$	89.5500	−	107.512i	0.398000	−	0.477833i
$226$		0			0
$227$	−152.167	−	152.167i	−0.670340	−	0.670340i	0.287454	−	0.957794i	$-0.407191\pi$
$227$	−152.167	−	152.167i	−0.670340	−	0.670340i	−0.957794	+	0.287454i	$0.907191\pi$
$228$		0			0
$229$			196.062i			0.856168i	0.903739	+	0.428084i	$0.140811\pi$
$229$			196.062i			0.856168i	−0.903739	+	0.428084i	$0.859189\pi$
$230$		0			0
$231$	−50.8062			−0.219940
$232$		0			0
$233$	−60.7906	+	60.7906i	−0.260904	+	0.260904i	−0.825421	−	0.564517i	$-0.809062\pi$
$233$	−60.7906	+	60.7906i	−0.260904	+	0.260904i	0.564517	+	0.825421i	$0.309062\pi$
$234$		0			0
$235$	31.4766	+	67.1828i	0.133943	+	0.285884i
$236$		0			0
$237$	−233.550	−	233.550i	−0.985443	−	0.985443i
$238$		0			0
$239$			178.388i			0.746391i	0.927753	+	0.373196i	$0.121738\pi$
$239$			178.388i			0.746391i	−0.927753	+	0.373196i	$0.878262\pi$
$240$		0			0
$241$	89.8219			0.372705			0.186352	−	0.982483i	$-0.440333\pi$
$241$	89.8219			0.372705			0.186352	+	0.982483i	$0.440333\pi$
$242$		0			0
$243$	187.539	−	187.539i	0.771766	−	0.771766i
$244$		0			0
$245$	69.4609	−	191.927i	0.283514	−	0.783374i
$246$		0			0
$247$	328.481	+	328.481i	1.32988	+	1.32988i
$248$		0			0
$249$			441.528i			1.77321i
$250$		0			0
$251$	−5.46561			−0.0217753			−0.0108877	−	0.999941i	$-0.503466\pi$
$251$	−5.46561			−0.0217753			−0.0108877	+	0.999941i	$0.503466\pi$
$252$		0			0
$253$	0.146888	−	0.146888i	0.000580585	−	0.000580585i
$254$		0			0
$255$	61.0469	+	22.0937i	0.239399	+	0.0866421i
$256$		0			0
$257$	−340.078	−	340.078i	−1.32326	−	1.32326i	−0.911120	−	0.412141i	$-0.864781\pi$
$257$	−340.078	−	340.078i	−1.32326	−	1.32326i	−0.412141	−	0.911120i	$-0.635219\pi$
$258$		0			0
$259$			142.241i			0.549192i
$260$		0			0
$261$	−255.287			−0.978113
$262$		0			0
$263$	−29.3609	+	29.3609i	−0.111638	+	0.111638i	−0.760719	−	0.649081i	$-0.775154\pi$
$263$	−29.3609	+	29.3609i	−0.111638	+	0.111638i	0.649081	+	0.760719i	$0.275154\pi$
$264$		0			0
$265$	19.2094	−	9.00000i	0.0724882	−	0.0339623i
$266$		0			0
$267$	246.450	+	246.450i	0.923034	+	0.923034i
$268$		0			0
$269$		−	403.047i		−	1.49832i	−0.662392	−	0.749158i	$-0.730458\pi$
$269$		−	403.047i		−	1.49832i	0.662392	−	0.749158i	$-0.269542\pi$
$270$		0			0
$271$	−308.984			−1.14016			−0.570082	−	0.821588i	$-0.693089\pi$
$271$	−308.984			−1.14016			−0.570082	+	0.821588i	$0.693089\pi$
$272$		0			0
$273$	−521.528	+	521.528i	−1.91036	+	1.91036i
$274$		0			0
$275$	−26.9531	−	22.4500i	−0.0980114	−	0.0816363i
$276$		0			0
$277$	9.59688	+	9.59688i	0.0346458	+	0.0346458i	0.724217	−	0.689572i	$-0.242201\pi$
$277$	9.59688	+	9.59688i	0.0346458	+	0.0346458i	−0.689572	+	0.724217i	$0.742201\pi$
$278$		0			0
$279$			14.5344i			0.0520946i
$280$		0			0
$281$	−268.628			−0.955972			−0.477986	−	0.878367i	$-0.658633\pi$
$281$	−268.628			−0.955972			−0.477986	+	0.878367i	$0.658633\pi$
$282$		0			0
$283$	−116.942	+	116.942i	−0.413223	+	0.413223i	−0.882860	−	0.469637i	$-0.844385\pi$
$283$	−116.942	+	116.942i	−0.413223	+	0.413223i	0.469637	+	0.882860i	$0.344385\pi$
$284$		0			0
$285$	184.837	+	394.512i	0.648553	+	1.38425i
$286$		0			0
$287$	−299.078	−	299.078i	−1.04208	−	1.04208i
$288$		0			0
$289$		−	277.450i		−	0.960035i
$290$		0			0
$291$	264.753			0.909804
$292$		0			0
$293$	−133.691	+	133.691i	−0.456282	+	0.456282i	−0.897433	−	0.441151i	$-0.854570\pi$
$293$	−133.691	+	133.691i	−0.456282	+	0.456282i	0.441151	+	0.897433i	$0.354570\pi$
$294$		0			0
$295$	70.0937	−	193.675i	0.237606	−	0.656525i
$296$		0			0
$297$	−12.9000	−	12.9000i	−0.0434343	−	0.0434343i
$298$		0			0
$299$		−	3.01562i		−	0.0100857i
$300$		0			0
$301$	357.884			1.18898
$302$		0			0
$303$	162.178	−	162.178i	0.535241	−	0.535241i
$304$		0			0
$305$	269.884	+	97.6750i	0.884867	+	0.320246i
$306$		0			0
$307$	−109.298	−	109.298i	−0.356021	−	0.356021i	0.506323	−	0.862344i	$-0.331004\pi$
$307$	−109.298	−	109.298i	−0.356021	−	0.356021i	−0.862344	+	0.506323i	$0.831004\pi$
$308$		0			0
$309$		−	332.334i		−	1.07552i
$310$		0			0
$311$	428.691			1.37843			0.689213	−	0.724559i	$-0.257956\pi$
$311$	428.691			1.37843			0.689213	+	0.724559i	$0.257956\pi$
$312$		0			0
$313$	299.334	−	299.334i	0.956340	−	0.956340i	−0.0427462	−	0.999086i	$-0.513611\pi$
$313$	299.334	−	299.334i	0.956340	−	0.956340i	0.999086	+	0.0427462i	$0.0136107\pi$
$314$		0			0
$315$	−240.167	+	112.523i	−0.762435	+	0.357217i
$316$		0			0
$317$	412.109	+	412.109i	1.30003	+	1.30003i	0.928369	+	0.371661i	$0.121212\pi$
$317$	412.109	+	412.109i	1.30003	+	1.30003i	0.371661	+	0.928369i	$0.378788\pi$
$318$		0			0
$319$			64.0000i			0.200627i
$320$		0			0
$321$	364.922			1.13683
$322$		0			0
$323$	−54.8062	+	54.8062i	−0.169679	+	0.169679i
$324$		0			0
$325$	−507.125	+	46.2250i	−1.56038	+	0.142231i
$326$		0			0
$327$	51.4563	+	51.4563i	0.157359	+	0.157359i
$328$		0			0
$329$		−	140.628i		−	0.427441i
$330$		0			0
$331$	12.9219			0.0390390			0.0195195	−	0.999809i	$-0.493786\pi$
$331$	12.9219			0.0390390			0.0195195	+	0.999809i	$0.493786\pi$
$332$		0			0
$333$	59.3968	−	59.3968i	0.178369	−	0.178369i
$334$		0			0
$335$	−104.105	−	222.198i	−0.310760	−	0.663279i
$336$		0			0
$337$	−61.3250	−	61.3250i	−0.181973	−	0.181973i	0.610242	−	0.792215i	$-0.291072\pi$
$337$	−61.3250	−	61.3250i	−0.181973	−	0.181973i	−0.792215	+	0.610242i	$0.791072\pi$
$338$		0			0
$339$		−	47.6657i		−	0.140607i
$340$		0			0
$341$	3.64374			0.0106855
$342$		0			0
$343$	54.8062	−	54.8062i	0.159785	−	0.159785i
$344$		0			0
$345$	0.962460	−	2.65936i	0.00278974	−	0.00770829i
$346$		0			0
$347$	179.183	+	179.183i	0.516377	+	0.516377i	0.916473	−	0.400096i	$-0.131023\pi$
$347$	179.183	+	179.183i	0.516377	+	0.516377i	−0.400096	+	0.916473i	$0.631023\pi$
$348$		0			0
$349$		−	240.962i		−	0.690437i	−0.938522	−	0.345218i	$-0.887805\pi$
$349$		−	240.962i		−	0.690437i	0.938522	−	0.345218i	$-0.112195\pi$
$350$		0			0
$351$	−264.837			−0.754523
$352$		0			0
$353$	141.900	−	141.900i	0.401983	−	0.401983i	−0.476948	−	0.878931i	$-0.658257\pi$
$353$	141.900	−	141.900i	0.401983	−	0.401983i	0.878931	+	0.476948i	$0.158257\pi$
$354$		0			0
$355$	−213.466	−	77.2562i	−0.601312	−	0.217623i
$356$		0			0
$357$	−87.0156	−	87.0156i	−0.243741	−	0.243741i
$358$		0			0
$359$		−	238.325i		−	0.663858i	−0.943304	−	0.331929i	$-0.892301\pi$
$359$		−	238.325i		−	0.663858i	0.943304	−	0.331929i	$-0.107699\pi$
$360$		0			0
$361$	−159.125			−0.440789
$362$		0			0
$363$	−321.570	+	321.570i	−0.885869	+	0.885869i
$364$		0			0
$365$	−72.9156	+	34.1625i	−0.199769	+	0.0935959i
$366$		0			0
$367$	259.477	+	259.477i	0.707021	+	0.707021i	0.965908	−	0.258887i	$-0.0833557\pi$
$367$	259.477	+	259.477i	0.707021	+	0.707021i	−0.258887	+	0.965908i	$0.583356\pi$
$368$		0			0
$369$			249.778i			0.676905i
$370$		0			0
$371$	−40.2094			−0.108381
$372$		0			0
$373$	−310.350	+	310.350i	−0.832037	+	0.832037i	−0.987795	−	0.155758i	$-0.950218\pi$
$373$	−310.350	+	310.350i	−0.832037	+	0.832037i	0.155758	+	0.987795i	$0.450218\pi$
$374$		0			0
$375$	−461.967	−	121.089i	−1.23191	−	0.322904i
$376$		0			0
$377$	656.962	+	656.962i	1.74261	+	1.74261i
$378$		0			0
$379$			90.1562i			0.237879i	0.992901	+	0.118940i	$0.0379495\pi$
$379$			90.1562i			0.237879i	−0.992901	+	0.118940i	$0.962051\pi$
$380$		0			0
$381$	79.4344			0.208489
$382$		0			0
$383$	−209.298	+	209.298i	−0.546471	+	0.546471i	−0.925418	−	0.378947i	$-0.876286\pi$
$383$	−209.298	+	209.298i	−0.546471	+	0.546471i	0.378947	+	0.925418i	$0.376286\pi$
$384$		0			0
$385$	28.2094	+	60.2094i	0.0732711	+	0.156388i
$386$		0			0
$387$	−149.445	−	149.445i	−0.386164	−	0.386164i
$388$		0			0
$389$			193.372i			0.497100i	0.968619	+	0.248550i	$0.0799540\pi$
$389$			193.372i			0.497100i	−0.968619	+	0.248550i	$0.920046\pi$
$390$		0			0
$391$	0.503149			0.00128683
$392$		0			0
$393$	642.659	−	642.659i	1.63527	−	1.63527i
$394$		0			0
$395$	−147.100	+	406.450i	−0.372405	+	1.02899i
$396$		0			0
$397$	80.2250	+	80.2250i	0.202078	+	0.202078i	0.800890	−	0.598812i	$-0.204360\pi$
$397$	80.2250	+	80.2250i	0.202078	+	0.202078i	−0.598812	+	0.800890i	$0.704360\pi$
$398$		0			0
$399$		−	825.800i		−	2.06967i
$400$		0			0
$401$	−727.800			−1.81496			−0.907481	−	0.420093i	$-0.861998\pi$
$401$	−727.800			−1.81496			−0.907481	+	0.420093i	$0.861998\pi$
$402$		0			0
$403$	37.4031	−	37.4031i	0.0928117	−	0.0928117i
$404$		0			0
$405$	−470.377	−	170.236i	−1.16142	−	0.420336i
$406$		0			0
$407$	−14.8907	−	14.8907i	−0.0365864	−	0.0365864i
$408$		0			0
$409$			355.403i			0.868956i	0.900682	+	0.434478i	$0.143067\pi$
$409$			355.403i			0.868956i	−0.900682	+	0.434478i	$0.856933\pi$
$410$		0			0
$411$	467.978			1.13863
$412$		0			0
$413$	−276.062	+	276.062i	−0.668432	+	0.668432i
$414$		0			0
$415$	523.245	−	245.152i	1.26083	−	0.590727i
$416$		0			0
$417$	−666.762	−	666.762i	−1.59895	−	1.59895i
$418$		0			0
$419$			767.644i			1.83209i	0.401081	+	0.916043i	$0.368635\pi$
$419$			767.644i			1.83209i	−0.401081	+	0.916043i	$0.631365\pi$
$420$		0			0
$421$	446.722			1.06110			0.530549	−	0.847655i	$-0.321986\pi$
$421$	446.722			1.06110			0.530549	+	0.847655i	$0.321986\pi$
$422$		0			0
$423$	−58.7235	+	58.7235i	−0.138826	+	0.138826i
$424$		0			0
$425$	−7.71252	−	84.6125i	−0.0181471	−	0.199088i
$426$		0			0
$427$	−384.691	−	384.691i	−0.900915	−	0.900915i
$428$		0			0
$429$		−	109.194i		−	0.254531i
$430$		0			0
$431$	303.791			0.704851			0.352425	−	0.935840i	$-0.385357\pi$
$431$	303.791			0.704851			0.352425	+	0.935840i	$0.385357\pi$
$432$		0			0
$433$	−610.350	+	610.350i	−1.40958	+	1.40958i	−0.647625	+	0.761959i	$0.724238\pi$
$433$	−610.350	+	610.350i	−1.40958	+	1.40958i	−0.761959	+	0.647625i	$0.775762\pi$
$434$		0			0
$435$	369.675	+	789.025i	0.849828	+	1.81385i
$436$		0			0
$437$	2.38750	+	2.38750i	0.00546339	+	0.00546339i
$438$		0			0
$439$		−	737.925i		−	1.68092i	−0.541872	−	0.840461i	$-0.682284\pi$
$439$		−	737.925i		−	1.68092i	0.541872	−	0.840461i	$-0.317716\pi$
$440$		0			0
$441$	228.475			0.518084
$442$		0			0
$443$	481.508	−	481.508i	1.08693	−	1.08693i	0.0910817	−	0.995843i	$-0.470968\pi$
$443$	481.508	−	481.508i	1.08693	−	1.08693i	0.995843	−	0.0910817i	$-0.0290324\pi$
$444$		0			0
$445$	155.225	−	428.900i	0.348820	−	0.963820i
$446$		0			0
$447$	329.194	+	329.194i	0.736451	+	0.736451i
$448$		0			0
$449$		−	568.428i		−	1.26599i	−0.774157	−	0.632993i	$-0.781826\pi$
$449$		−	568.428i		−	1.26599i	0.774157	−	0.632993i	$-0.218174\pi$
$450$		0			0
$451$	62.6188			0.138844
$452$		0			0
$453$	663.309	−	663.309i	1.46426	−	1.46426i
$454$		0			0
$455$	907.622	+	328.481i	1.99477	+	0.721937i
$456$		0			0
$457$	−108.791	−	108.791i	−0.238054	−	0.238054i	0.577990	−	0.816044i	$-0.303837\pi$
$457$	−108.791	−	108.791i	−0.238054	−	0.238054i	−0.816044	+	0.577990i	$0.803837\pi$
$458$		0			0
$459$		−	44.1875i		−	0.0962690i
$460$		0			0
$461$	348.281			0.755491			0.377745	−	0.925910i	$-0.376699\pi$
$461$	348.281			0.755491			0.377745	+	0.925910i	$0.376699\pi$
$462$		0			0
$463$	−307.330	+	307.330i	−0.663779	+	0.663779i	−0.956269	−	0.292490i	$-0.905516\pi$
$463$	−307.330	+	307.330i	−0.663779	+	0.663779i	0.292490	+	0.956269i	$0.405516\pi$
$464$		0			0
$465$	44.9219	−	21.0469i	0.0966062	−	0.0452621i
$466$		0			0
$467$	50.3453	+	50.3453i	0.107806	+	0.107806i	0.758952	−	0.651146i	$-0.225712\pi$
$467$	50.3453	+	50.3453i	0.107806	+	0.107806i	−0.651146	+	0.758952i	$0.725712\pi$
$468$		0			0
$469$			465.109i			0.991704i
$470$		0			0
$471$	−791.372			−1.68020
$472$		0			0
$473$	−37.4656	+	37.4656i	−0.0792085	+	0.0792085i
$474$		0			0
$475$	364.900	−	438.094i	0.768210	−	0.922303i
$476$		0			0
$477$	16.7906	+	16.7906i	0.0352005	+	0.0352005i
$478$		0			0
$479$			445.862i			0.930819i	0.885095	+	0.465410i	$0.154093\pi$
$479$			445.862i			0.930819i	−0.885095	+	0.465410i	$0.845907\pi$
$480$		0			0
$481$	−305.706			−0.635564
$482$		0			0
$483$	−3.79063	+	3.79063i	−0.00784809	+	0.00784809i
$484$		0			0
$485$	−147.000	−	313.753i	−0.303093	−	0.646914i
$486$		0			0
$487$	−322.136	−	322.136i	−0.661470	−	0.661470i	0.294256	−	0.955727i	$-0.404928\pi$
$487$	−322.136	−	322.136i	−0.661470	−	0.661470i	−0.955727	+	0.294256i	$0.904928\pi$
$488$		0			0
$489$			945.403i			1.93334i
$490$		0			0
$491$	−362.953			−0.739212			−0.369606	−	0.929189i	$-0.620507\pi$
$491$	−362.953			−0.739212			−0.369606	+	0.929189i	$0.620507\pi$
$492$		0			0
$493$	−109.612	+	109.612i	−0.222338	+	0.222338i
$494$		0			0
$495$	13.3626	−	36.9219i	0.0269951	−	0.0745897i
$496$		0			0
$497$	304.272	+	304.272i	0.612217	+	0.612217i
$498$		0			0
$499$		−	555.831i		−	1.11389i	−0.830549	−	0.556945i	$-0.811973\pi$
$499$		−	555.831i		−	1.11389i	0.830549	−	0.556945i	$-0.188027\pi$
$500$		0			0
$501$	−1098.62			−2.19285
$502$		0			0
$503$	−173.717	+	173.717i	−0.345362	+	0.345362i	−0.858379	−	0.513017i	$-0.828528\pi$
$503$	−173.717	+	173.717i	−0.345362	+	0.345362i	0.513017	+	0.858379i	$0.328528\pi$
$504$		0			0
$505$	−282.241	−	102.147i	−0.558892	−	0.202271i
$506$		0			0
$507$	−664.314	−	664.314i	−1.31028	−	1.31028i
$508$		0			0
$509$			213.737i			0.419916i	0.977710	+	0.209958i	$0.0673328\pi$
$509$			213.737i			0.419916i	−0.977710	+	0.209958i	$0.932667\pi$
$510$		0			0
$511$	152.628			0.298685
$512$		0			0
$513$	209.675	−	209.675i	0.408723	−	0.408723i
$514$		0			0
$515$	−393.842	+	184.523i	−0.764742	+	0.358298i
$516$		0			0
$517$	14.7218	+	14.7218i	0.0284755	+	0.0284755i
$518$		0			0
$519$			911.034i			1.75536i
$520$		0			0
$521$	312.094			0.599028			0.299514	−	0.954092i	$-0.403175\pi$
$521$	312.094			0.599028			0.299514	+	0.954092i	$0.403175\pi$
$522$		0			0
$523$	−197.655	+	197.655i	−0.377925	+	0.377925i	−0.870353	−	0.492428i	$-0.836109\pi$
$523$	−197.655	+	197.655i	−0.377925	+	0.377925i	0.492428	+	0.870353i	$0.336109\pi$
$524$		0			0
$525$	695.559	+	579.350i	1.32487	+	1.10352i
$526$		0			0
$527$	6.24062	+	6.24062i	0.0118418	+	0.0118418i
$528$		0			0
$529$			528.978i			0.999959i
$530$		0			0
$531$	230.556			0.434193
$532$		0			0
$533$	642.784	−	642.784i	1.20597	−	1.20597i
$534$		0			0
$535$	−202.617	−	432.461i	−0.378724	−	0.808338i
$536$		0			0
$537$	74.5125	+	74.5125i	0.138757	+	0.138757i
$538$		0			0
$539$		−	57.2782i		−	0.106267i
$540$		0			0
$541$	172.031			0.317988			0.158994	−	0.987280i	$-0.449175\pi$
$541$	172.031			0.317988			0.158994	+	0.987280i	$0.449175\pi$
$542$		0			0
$543$	−238.784	+	238.784i	−0.439750	+	0.439750i
$544$		0			0
$545$	32.4094	−	89.5500i	0.0594668	−	0.164312i
$546$		0			0
$547$	−60.9422	−	60.9422i	−0.111412	−	0.111412i	0.649203	−	0.760615i	$-0.275102\pi$
$547$	−60.9422	−	60.9422i	−0.111412	−	0.111412i	−0.760615	+	0.649203i	$0.775102\pi$
$548$		0			0
$549$			321.278i			0.585206i
$550$		0			0
$551$	−1040.25			−1.88793
$552$		0			0
$553$	579.350	−	579.350i	1.04765	−	1.04765i
$554$		0			0
$555$	−269.591	−	97.5687i	−0.485749	−	0.175799i
$556$		0			0
$557$	−441.575	−	441.575i	−0.792774	−	0.792774i	0.189171	−	0.981944i	$-0.439420\pi$
$557$	−441.575	−	441.575i	−0.792774	−	0.792774i	−0.981944	+	0.189171i	$0.939420\pi$
$558$		0			0
$559$			769.172i			1.37598i
$560$		0			0
$561$	18.2187			0.0324754
$562$		0			0
$563$	502.764	−	502.764i	0.893009	−	0.893009i	−0.101796	−	0.994805i	$-0.532459\pi$
$563$	502.764	−	502.764i	0.893009	−	0.893009i	0.994805	+	0.101796i	$0.0324590\pi$
$564$		0			0
$565$	−56.4875	+	26.4656i	−0.0999779	+	0.0468418i
$566$		0			0
$567$	670.470	+	670.470i	1.18249	+	1.18249i
$568$		0			0
$569$		−	518.753i		−	0.911693i	−0.890059	−	0.455846i	$-0.849337\pi$
$569$		−	518.753i		−	0.911693i	0.890059	−	0.455846i	$-0.150663\pi$
$570$		0			0
$571$	1034.07			1.81098			0.905492	−	0.424363i	$-0.139502\pi$
$571$	1034.07			1.81098			0.905492	+	0.424363i	$0.139502\pi$
$572$		0			0
$573$	−214.766	+	214.766i	−0.374809	+	0.374809i
$574$		0			0
$575$	−3.68594	+	0.335978i	−0.00641033	+	0.000584309i
$576$		0			0
$577$	220.172	+	220.172i	0.381580	+	0.381580i	0.871671	−	0.490091i	$-0.163036\pi$
$577$	220.172	+	220.172i	0.381580	+	0.381580i	−0.490091	+	0.871671i	$0.663036\pi$
$578$		0			0
$579$		−	566.366i		−	0.978179i
$580$		0			0
$581$	−1095.27			−1.88514
$582$		0			0
$583$	4.20937	−	4.20937i	0.00722019	−	0.00722019i
$584$		0			0
$585$	−241.837	−	516.172i	−0.413397	−	0.882345i
$586$		0			0
$587$	−547.517	−	547.517i	−0.932738	−	0.932738i	0.0651384	−	0.997876i	$-0.479251\pi$
$587$	−547.517	−	547.517i	−0.932738	−	0.932738i	−0.997876	+	0.0651384i	$0.979251\pi$
$588$		0			0
$589$			59.2250i			0.100552i
$590$		0			0
$591$	368.291			0.623165
$592$		0			0
$593$	−165.450	+	165.450i	−0.279005	+	0.279005i	−0.832712	−	0.553707i	$-0.813213\pi$
$593$	−165.450	+	165.450i	−0.279005	+	0.279005i	0.553707	+	0.832712i	$0.313213\pi$
$594$		0			0
$595$	−54.8062	+	151.434i	−0.0921113	+	0.254512i
$596$		0			0
$597$	676.775	+	676.775i	1.13363	+	1.13363i
$598$		0			0
$599$		−	997.987i		−	1.66609i	−0.553206	−	0.833045i	$-0.686596\pi$
$599$		−	997.987i		−	1.66609i	0.553206	−	0.833045i	$-0.313404\pi$
$600$		0			0
$601$	691.372			1.15037			0.575185	−	0.818024i	$-0.304930\pi$
$601$	691.372			1.15037			0.575185	+	0.818024i	$0.304930\pi$
$602$		0			0
$603$	194.220	−	194.220i	0.322090	−	0.322090i
$604$		0			0
$605$	559.633	+	202.539i	0.925013	+	0.334775i
$606$		0			0
$607$	115.833	+	115.833i	0.190828	+	0.190828i	0.796054	−	0.605226i	$-0.206917\pi$
$607$	115.833	+	115.833i	0.190828	+	0.190828i	−0.605226	+	0.796054i	$0.706917\pi$
$608$		0			0
$609$		−	1651.60i		−	2.71199i
$610$		0			0
$611$	302.241			0.494665
$612$		0			0
$613$	−72.7906	+	72.7906i	−0.118745	+	0.118745i	−0.763982	−	0.645237i	$-0.776758\pi$
$613$	−72.7906	+	72.7906i	−0.118745	+	0.118745i	0.645237	+	0.763982i	$0.276758\pi$
$614$		0			0
$615$	771.997	−	361.697i	1.25528	−	0.588125i
$616$		0			0
$617$	17.5344	+	17.5344i	0.0284188	+	0.0284188i	0.721173	−	0.692755i	$-0.243603\pi$
$617$	17.5344	+	17.5344i	0.0284188	+	0.0284188i	−0.692755	+	0.721173i	$0.743603\pi$
$618$		0			0
$619$			1026.99i			1.65912i	0.558419	+	0.829559i	$0.311408\pi$
$619$			1026.99i			1.65912i	−0.558419	+	0.829559i	$0.688592\pi$
$620$		0			0
$621$	−1.92492			−0.00309971
$622$		0			0
$623$	−611.350	+	611.350i	−0.981300	+	0.981300i
$624$		0			0
$625$	113.000	+	614.700i	0.180800	+	0.983520i
$626$		0			0
$627$	86.4500	+	86.4500i	0.137879	+	0.137879i
$628$		0			0
$629$		−	51.0063i		−	0.0810911i
$630$		0			0
$631$	246.241			0.390239			0.195119	−	0.980780i	$-0.437491\pi$
$631$	246.241			0.390239			0.195119	+	0.980780i	$0.437491\pi$
$632$		0			0
$633$	−898.616	+	898.616i	−1.41961	+	1.41961i
$634$		0			0
$635$	−44.1047	−	94.1359i	−0.0694562	−	0.148246i
$636$		0			0
$637$	−587.962	−	587.962i	−0.923018	−	0.923018i
$638$		0			0
$639$		−	254.116i		−	0.397677i
$640$		0			0
$641$	825.822			1.28833			0.644167	−	0.764885i	$-0.277204\pi$
$641$	825.822			1.28833			0.644167	+	0.764885i	$0.277204\pi$
$642$		0			0
$643$	15.2453	−	15.2453i	0.0237096	−	0.0237096i	−0.695153	−	0.718862i	$-0.744663\pi$
$643$	15.2453	−	15.2453i	0.0237096	−	0.0237096i	0.718862	+	0.695153i	$0.244663\pi$
$644$		0			0
$645$	−245.488	+	678.303i	−0.380601	+	1.05163i
$646$		0			0
$647$	359.414	+	359.414i	0.555509	+	0.555509i	0.928025	−	0.372517i	$-0.121505\pi$
$647$	359.414	+	359.414i	0.555509	+	0.555509i	−0.372517	+	0.928025i	$0.621505\pi$
$648$		0			0
$649$		−	57.8000i		−	0.0890600i
$650$		0			0
$651$	−94.0312			−0.144441
$652$		0			0
$653$	−247.187	+	247.187i	−0.378541	+	0.378541i	−0.870576	−	0.492034i	$-0.836253\pi$
$653$	−247.187	+	247.187i	−0.378541	+	0.378541i	0.492034	+	0.870576i	$0.336253\pi$
$654$		0			0
$655$	−1118.43	−	404.775i	−1.70752	−	0.617977i
$656$		0			0
$657$	−63.7344	−	63.7344i	−0.0970083	−	0.0970083i
$658$		0			0
$659$		−	400.606i		−	0.607900i	−0.952688	−	0.303950i	$-0.901694\pi$
$659$		−	400.606i		−	0.607900i	0.952688	−	0.303950i	$-0.0983056\pi$
$660$		0			0
$661$	121.947			0.184488			0.0922442	−	0.995736i	$-0.470596\pi$
$661$	121.947			0.184488			0.0922442	+	0.995736i	$0.470596\pi$
$662$		0			0
$663$	187.016	−	187.016i	0.282075	−	0.282075i
$664$		0			0
$665$	−978.637	+	458.512i	−1.47164	+	0.689492i
$666$		0			0
$667$	4.77501	+	4.77501i	0.00715893	+	0.00715893i
$668$		0			0
$669$		−	1013.63i		−	1.51515i
$670$		0			0
$671$	80.5437			0.120035
$672$		0			0
$673$	−645.450	+	645.450i	−0.959064	+	0.959064i	−0.999194	−	0.0401306i	$-0.987223\pi$
$673$	−645.450	+	645.450i	−0.959064	+	0.959064i	0.0401306	+	0.999194i	$0.487223\pi$
$674$		0			0
$675$	29.5062	+	323.706i	0.0437129	+	0.479565i
$676$		0			0
$677$	−684.087	−	684.087i	−1.01047	−	1.01047i	−0.999945	−	0.0105243i	$-0.996650\pi$
$677$	−684.087	−	684.087i	−1.01047	−	1.01047i	−0.0105243	−	0.999945i	$-0.503350\pi$
$678$		0			0
$679$			656.753i			0.967236i
$680$		0			0
$681$	−822.178			−1.20731
$682$		0			0
$683$	164.252	−	164.252i	0.240485	−	0.240485i	−0.576565	−	0.817051i	$-0.695607\pi$
$683$	164.252	−	164.252i	0.240485	−	0.240485i	0.817051	+	0.576565i	$0.195607\pi$
$684$		0			0
$685$	−259.837	−	554.591i	−0.379325	−	0.809621i
$686$		0			0
$687$	529.675	+	529.675i	0.770997	+	0.770997i
$688$		0			0
$689$		−	86.4187i		−	0.125426i
$690$		0			0
$691$	−241.403			−0.349353			−0.174677	−	0.984626i	$-0.555888\pi$
$691$	−241.403			−0.349353			−0.174677	+	0.984626i	$0.555888\pi$
$692$		0			0
$693$	−52.6281	+	52.6281i	−0.0759425	+	0.0759425i
$694$		0			0
$695$	−419.956	+	1160.37i	−0.604253	+	1.66960i
$696$		0			0
$697$	107.247	+	107.247i	0.153869	+	0.153869i
$698$		0			0
$699$			328.459i			0.469899i
$700$		0			0
$701$	353.822			0.504739			0.252369	−	0.967631i	$-0.418790\pi$
$701$	353.822			0.504739			0.252369	+	0.967631i	$0.418790\pi$
$702$		0			0
$703$	242.031	−	242.031i	0.344283	−	0.344283i
$704$		0			0
$705$	266.534	+	96.4626i	0.378063	+	0.136826i
$706$		0			0
$707$	402.303	+	402.303i	0.569028	+	0.569028i
$708$		0			0
$709$			362.762i			0.511654i	0.966723	+	0.255827i	$0.0823477\pi$
$709$			362.762i			0.511654i	−0.966723	+	0.255827i	$0.917652\pi$
$710$		0			0
$711$	−483.850			−0.680520
$712$		0			0
$713$	0.271857	−	0.271857i	0.000381287	−	0.000381287i
$714$		0			0
$715$	−129.403	+	60.6281i	−0.180983	+	0.0847946i
$716$		0			0
$717$	481.925	+	481.925i	0.672141	+	0.672141i
$718$		0			0
$719$		−	1191.41i		−	1.65704i	−0.559959	−	0.828520i	$-0.689183\pi$
$719$		−	1191.41i		−	1.65704i	0.559959	−	0.828520i	$-0.310817\pi$
$720$		0			0
$721$	824.397			1.14341
$722$		0			0
$723$	242.659	−	242.659i	0.335628	−	0.335628i
$724$		0			0
$725$	729.800	−	876.187i	1.00662	−	1.20853i
$726$		0			0
$727$	304.502	+	304.502i	0.418847	+	0.418847i	0.884806	−	0.465959i	$-0.154291\pi$
$727$	304.502	+	304.502i	0.418847	+	0.418847i	−0.465959	+	0.884806i	$0.654291\pi$
$728$		0			0
$729$		−	112.875i		−	0.154835i
$730$		0			0
$731$	−128.334			−0.175560
$732$		0			0
$733$	−117.263	+	117.263i	−0.159976	+	0.159976i	−0.782556	−	0.622580i	$-0.786085\pi$
$733$	−117.263	+	117.263i	−0.159976	+	0.159976i	0.622580	+	0.782556i	$0.286085\pi$
$734$		0			0
$735$	−330.848	−	706.155i	−0.450134	−	0.960755i
$736$		0			0
$737$	−48.6906	−	48.6906i	−0.0660659	−	0.0660659i
$738$		0			0
$739$		−	692.669i		−	0.937305i	−0.883383	−	0.468653i	$-0.844740\pi$
$739$		−	692.669i		−	0.937305i	0.883383	−	0.468653i	$-0.155260\pi$
$740$		0			0
$741$	1774.82			2.39518
$742$		0			0
$743$	826.301	−	826.301i	1.11212	−	1.11212i	0.119251	−	0.992864i	$-0.461951\pi$
$743$	826.301	−	826.301i	1.11212	−	1.11212i	0.992864	−	0.119251i	$-0.0380493\pi$
$744$		0			0
$745$	207.341	−	572.900i	0.278310	−	0.768993i
$746$		0			0
$747$	457.361	+	457.361i	0.612264	+	0.612264i
$748$		0			0
$749$			905.234i			1.20859i
$750$		0			0
$751$	61.4031			0.0817618			0.0408809	−	0.999164i	$-0.486984\pi$
$751$	61.4031			0.0817618			0.0408809	+	0.999164i	$0.486984\pi$
$752$		0			0
$753$	−14.7657	+	14.7657i	−0.0196091	+	0.0196091i
$754$		0			0
$755$	−1154.37	−	417.781i	−1.52896	−	0.553353i
$756$		0			0
$757$	366.372	+	366.372i	0.483979	+	0.483979i	0.906400	−	0.422421i	$-0.138820\pi$
$757$	366.372	+	366.372i	0.483979	+	0.483979i	−0.422421	+	0.906400i	$0.638820\pi$
$758$		0			0
$759$		−	0.793654i		−	0.00104566i
$760$		0			0
$761$	−895.675			−1.17697			−0.588486	−	0.808508i	$-0.700276\pi$
$761$	−895.675			−1.17697			−0.588486	+	0.808508i	$0.700276\pi$
$762$		0			0
$763$	−127.644	+	127.644i	−0.167292	+	0.167292i
$764$		0			0
$765$	86.1219	−	40.3500i	0.112578	−	0.0527451i
$766$		0			0
$767$	−593.319	−	593.319i	−0.773558	−	0.773558i
$768$		0			0
$769$		−	241.675i		−	0.314272i	−0.987577	−	0.157136i	$-0.949774\pi$
$769$		−	241.675i		−	0.314272i	0.987577	−	0.157136i	$-0.0502261\pi$
$770$		0			0
$771$	−1837.48			−2.38325
$772$		0			0
$773$	359.459	−	359.459i	0.465019	−	0.465019i	−0.435278	−	0.900296i	$-0.643350\pi$
$773$	359.459	−	359.459i	0.465019	−	0.465019i	0.900296	+	0.435278i	$0.143350\pi$
$774$		0			0
$775$	−49.8844	−	41.5500i	−0.0643669	−	0.0536129i
$776$		0			0
$777$	384.272	+	384.272i	0.494558	+	0.494558i
$778$		0			0
$779$			1017.80i			1.30655i
$780$		0			0
$781$	−63.7062			−0.0815701
$782$		0			0
$783$	419.350	−	419.350i	0.535568	−	0.535568i
$784$		0			0
$785$	439.397	+	937.837i	0.559741	+	1.19470i
$786$		0			0
$787$	171.789	+	171.789i	0.218283	+	0.218283i	0.807775	−	0.589491i	$-0.200672\pi$
$787$	171.789	+	171.789i	0.218283	+	0.218283i	−0.589491	+	0.807775i	$0.700672\pi$
$788$		0			0
$789$			158.641i			0.201066i
$790$		0			0
$791$	118.241			0.149482
$792$		0			0
$793$	826.784	−	826.784i	1.04260	−	1.04260i
$794$		0			0
$795$	27.5813	−	76.2094i	0.0346934	−	0.0958608i
$796$		0			0
$797$	−547.891	−	547.891i	−0.687441	−	0.687441i	0.274224	−	0.961666i	$-0.411579\pi$
$797$	−547.891	−	547.891i	−0.687441	−	0.687441i	−0.961666	+	0.274224i	$0.911579\pi$
$798$		0			0
$799$			50.4281i			0.0631140i
$800$		0			0
$801$	510.575			0.637422
$802$		0			0
$803$	−15.9781	+	15.9781i	−0.0198980	+	0.0198980i
$804$		0			0
$805$	6.59688	+	2.38750i	0.00819488	+	0.00296584i
$806$		0			0
$807$	−1088.86	−	1088.86i	−1.34926	−	1.34926i
$808$		0			0
$809$			225.925i			0.279264i	0.990203	+	0.139632i	$0.0445920\pi$
$809$			225.925i			0.279264i	−0.990203	+	0.139632i	$0.955408\pi$
$810$		0			0
$811$	1083.03			1.33543			0.667715	−	0.744417i	$-0.267272\pi$
$811$	1083.03			1.33543			0.667715	+	0.744417i	$0.267272\pi$
$812$		0			0
$813$	−834.740	+	834.740i	−1.02674	+	1.02674i
$814$		0			0
$815$	1120.38	−	524.920i	1.37470	−	0.644074i
$816$		0			0
$817$	−608.962	−	608.962i	−0.745364	−	0.745364i
$818$		0			0
$819$			1080.46i			1.31924i
$820$		0			0
$821$	125.297			0.152615			0.0763074	−	0.997084i	$-0.475687\pi$
$821$	125.297			0.152615			0.0763074	+	0.997084i	$0.475687\pi$
$822$		0			0
$823$	−408.480	+	408.480i	−0.496330	+	0.496330i	−0.910293	−	0.413963i	$-0.864144\pi$
$823$	−408.480	+	408.480i	−0.496330	+	0.496330i	0.413963	+	0.910293i	$0.364144\pi$
$824$		0			0
$825$	−133.466	+	12.1655i	−0.161776	+	0.0147461i
$826$		0			0
$827$	705.508	+	705.508i	0.853093	+	0.853093i	0.990513	−	0.137420i	$-0.0438810\pi$
$827$	705.508	+	705.508i	0.853093	+	0.853093i	−0.137420	+	0.990513i	$0.543881\pi$
$828$		0			0
$829$		−	1040.20i		−	1.25476i	−0.778713	−	0.627380i	$-0.784127\pi$
$829$		−	1040.20i		−	1.25476i	0.778713	−	0.627380i	$-0.215873\pi$
$830$		0			0
$831$	51.8531			0.0623985
$832$		0			0
$833$	98.1000	−	98.1000i	0.117767	−	0.117767i
$834$		0			0
$835$	609.989	+	1301.95i	0.730526	+	1.55922i
$836$		0			0
$837$	−23.8750	−	23.8750i	−0.0285245	−	0.0285245i
$838$		0			0
$839$			154.512i			0.184163i	0.995751	+	0.0920813i	$0.0293520\pi$
$839$			154.512i			0.184163i	−0.995751	+	0.0920813i	$0.970648\pi$
$840$		0			0
$841$	−1239.50			−1.47384
$842$		0			0
$843$	−725.716	+	725.716i	−0.860873	+	0.860873i
$844$		0			0
$845$	−418.414	+	1156.11i	−0.495165	+	1.36818i
$846$		0			0
$847$	−797.695	−	797.695i	−0.941789	−	0.941789i
$848$		0			0
$849$			631.853i			0.744232i
$850$		0			0
$851$	−2.22197			−0.00261101
$852$		0			0
$853$	−572.141	+	572.141i	−0.670739	+	0.670739i	−0.957886	−	0.287147i	$-0.907293\pi$
$853$	−572.141	+	572.141i	−0.670739	+	0.670739i	0.287147	+	0.957886i	$0.407293\pi$
$854$		0			0
$855$	600.125	+	217.194i	0.701901	+	0.254028i
$856$		0			0
$857$	−81.2625	−	81.2625i	−0.0948221	−	0.0948221i	0.658105	−	0.752927i	$-0.271358\pi$
$857$	−81.2625	−	81.2625i	−0.0948221	−	0.0948221i	−0.752927	+	0.658105i	$0.771358\pi$
$858$		0			0
$859$			214.094i			0.249236i	0.992205	+	0.124618i	$0.0397705\pi$
$859$			214.094i			0.249236i	−0.992205	+	0.124618i	$0.960229\pi$
$860$		0			0
$861$	−1615.96			−1.87684
$862$		0			0
$863$	−72.8172	+	72.8172i	−0.0843768	+	0.0843768i	−0.748036	−	0.663659i	$-0.769003\pi$
$863$	−72.8172	+	72.8172i	−0.0843768	+	0.0843768i	0.663659	+	0.748036i	$0.269003\pi$
$864$		0			0
$865$	1079.65	−	505.837i	1.24815	−	0.584783i
$866$		0			0
$867$	−749.548	−	749.548i	−0.864531	−	0.864531i
$868$		0			0
$869$			121.300i			0.139586i
$870$		0			0
$871$	−999.622			−1.14767
$872$		0			0
$873$	274.247	−	274.247i	0.314143	−	0.314143i
$874$		0			0
$875$	300.377	−	1145.97i	0.343287	−	1.30968i
$876$		0			0
$877$	−922.841	−	922.841i	−1.05227	−	1.05227i	−0.998556	−	0.0537133i	$-0.982894\pi$
$877$	−922.841	−	922.841i	−1.05227	−	1.05227i	−0.0537133	−	0.998556i	$-0.517106\pi$
$878$		0			0
$879$			722.347i			0.821783i
$880$		0			0
$881$	364.922			0.414213			0.207107	−	0.978318i	$-0.433595\pi$
$881$	364.922			0.414213			0.207107	+	0.978318i	$0.433595\pi$
$882$		0			0
$883$	−274.786	+	274.786i	−0.311196	+	0.311196i	−0.845373	−	0.534177i	$-0.820622\pi$
$883$	−274.786	+	274.786i	−0.311196	+	0.311196i	0.534177	+	0.845373i	$0.320622\pi$
$884$		0			0
$885$	−333.862	−	712.588i	−0.377246	−	0.805184i
$886$		0			0
$887$	609.464	+	609.464i	0.687107	+	0.687107i	0.961592	−	0.274484i	$-0.0885072\pi$
$887$	609.464	+	609.464i	0.687107	+	0.687107i	−0.274484	+	0.961592i	$0.588507\pi$
$888$		0			0
$889$			197.047i			0.221650i
$890$		0			0
$891$	−140.378			−0.157551
$892$		0			0
$893$	−239.287	+	239.287i	−0.267959	+	0.267959i
$894$		0			0
$895$	46.9312	−	129.675i	0.0524371	−	0.144888i
$896$		0			0
$897$	−8.14689	−	8.14689i	−0.00908237	−	0.00908237i
$898$		0			0
$899$			118.450i			0.131757i
$900$		0			0
$901$	14.4187			0.0160030
$902$		0			0
$903$	966.847	−	966.847i	1.07071	−	1.07071i
$904$		0			0
$905$	415.559	+	150.397i	0.459182	+	0.166184i
$906$		0			0
$907$	112.439	+	112.439i	0.123968	+	0.123968i	0.766369	−	0.642401i	$-0.222062\pi$
$907$	112.439	+	112.439i	0.123968	+	0.123968i	−0.642401	+	0.766369i	$0.722062\pi$
$908$		0			0
$909$		−	335.987i		−	0.369623i
$910$		0			0
$911$	1469.90			1.61350			0.806752	−	0.590890i	$-0.201223\pi$
$911$	1469.90			1.61350			0.806752	+	0.590890i	$0.201223\pi$
$912$		0			0
$913$	114.659	−	114.659i	0.125585	−	0.125585i
$914$		0			0
$915$	992.984	−	465.234i	1.08523	−	0.508453i
$916$		0			0
$917$	1594.20	+	1594.20i	1.73849	+	1.73849i
$918$		0			0
$919$		−	503.662i		−	0.548055i	−0.961722	−	0.274027i	$-0.911644\pi$
$919$		−	503.662i		−	0.548055i	0.961722	−	0.274027i	$-0.0883559\pi$
$920$		0			0
$921$	−590.553			−0.641209
$922$		0			0
$923$	−653.947	+	653.947i	−0.708501	+	0.708501i
$924$		0			0
$925$	34.0595	+	373.659i	0.0368210	+	0.403956i
$926$		0			0
$927$	−344.252	−	344.252i	−0.371361	−	0.371361i
$928$		0			0
$929$			1016.43i			1.09411i	0.837097	+	0.547055i	$0.184251\pi$
$929$			1016.43i			1.09411i	−0.837097	+	0.547055i	$0.815749\pi$
$930$		0			0
$931$	930.994			0.999993
$932$		0			0
$933$	1158.13	−	1158.13i	1.24130	−	1.24130i
$934$		0			0
$935$	−10.1156	−	21.5906i	−0.0108189	−	0.0230915i
$936$		0			0
$937$	−678.841	−	678.841i	−0.724483	−	0.724483i	0.245032	−	0.969515i	$-0.421202\pi$
$937$	−678.841	−	678.841i	−0.724483	−	0.724483i	−0.969515	+	0.245032i	$0.921202\pi$
$938$		0			0
$939$		−	1617.34i		−	1.72241i
$940$		0			0
$941$	−603.987			−0.641857			−0.320928	−	0.947103i	$-0.603995\pi$
$941$	−603.987			−0.641857			−0.320928	+	0.947103i	$0.603995\pi$
$942$		0			0
$943$	4.67196	−	4.67196i	0.00495435	−	0.00495435i
$944$		0			0
$945$	209.675	−	579.350i	0.221878	−	0.613069i
$946$		0			0
$947$	1.02658	+	1.02658i	0.00108403	+	0.00108403i	0.707649	−	0.706565i	$-0.249756\pi$
$947$	1.02658	+	1.02658i	0.00108403	+	0.00108403i	−0.706565	+	0.707649i	$0.749756\pi$
$948$		0			0
$949$			328.031i			0.345660i
$950$		0			0
$951$	2226.68			2.34141
$952$		0			0
$953$	531.459	−	531.459i	0.557670	−	0.557670i	−0.370974	−	0.928643i	$-0.620976\pi$
$953$	531.459	−	531.459i	0.557670	−	0.557670i	0.928643	+	0.370974i	$0.120976\pi$
$954$		0			0
$955$	373.759	+	135.269i	0.391371	+	0.141643i
$956$		0			0
$957$	172.900	+	172.900i	0.180669	+	0.180669i
$958$		0			0
$959$			1160.88i			1.21051i
$960$		0			0
$961$	−954.256			−0.992983
$962$		0			0
$963$	378.008	−	378.008i	0.392531	−	0.392531i
$964$		0			0
$965$	−671.187	+	314.466i	−0.695531	+	0.325871i
$966$		0			0
$967$	−303.392	−	303.392i	−0.313746	−	0.313746i	0.532613	−	0.846359i	$-0.321210\pi$
$967$	−303.392	−	303.392i	−0.313746	−	0.313746i	−0.846359	+	0.532613i	$0.821210\pi$
$968$		0			0
$969$			296.125i			0.305599i
$970$		0			0
$971$	−1156.04			−1.19057			−0.595284	−	0.803516i	$-0.702960\pi$
$971$	−1156.04			−1.19057			−0.595284	+	0.803516i	$0.702960\pi$
$972$		0			0
$973$	1653.99	−	1653.99i	1.69988	−	1.69988i
$974$		0			0
$975$	−1245.15	+	1494.91i	−1.27708	+	1.53324i
$976$		0			0
$977$	−287.000	−	287.000i	−0.293756	−	0.293756i	0.544806	−	0.838562i	$-0.316603\pi$
$977$	−287.000	−	287.000i	−0.293756	−	0.293756i	−0.838562	+	0.544806i	$0.816603\pi$
$978$		0			0
$979$		−	128.000i		−	0.130746i
$980$		0			0
$981$	106.603			0.108668
$982$		0			0
$983$	−868.523	+	868.523i	−0.883544	+	0.883544i	−0.993893	−	0.110349i	$-0.964803\pi$
$983$	−868.523	+	868.523i	−0.883544	+	0.883544i	0.110349	+	0.993893i	$0.464803\pi$
$984$		0			0
$985$	−204.488	−	436.453i	−0.207602	−	0.443100i
$986$		0			0
$987$	−379.916	−	379.916i	−0.384920	−	0.384920i
$988$		0			0
$989$			5.59058i			0.00565276i
$990$		0			0
$991$	−1263.28			−1.27476			−0.637379	−	0.770551i	$-0.719981\pi$
$991$	−1263.28			−1.27476			−0.637379	+	0.770551i	$0.719981\pi$
$992$		0			0
$993$	34.9093	−	34.9093i	0.0351554	−	0.0351554i
$994$		0			0
$995$	426.263	−	1177.80i	0.428405	−	1.18372i
$996$		0			0
$997$	992.547	+	992.547i	0.995533	+	0.995533i	0.999990	−	0.00445673i	$-0.00141863\pi$
$997$	992.547	+	992.547i	0.995533	+	0.995533i	−0.00445673	+	0.999990i	$0.501419\pi$
$998$		0			0
$999$			195.137i			0.195333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.l.b.17.2	✓	4
3.2	odd	2		360.3.v.c.217.2		4
4.3	odd	2		80.3.p.d.17.1		4
5.2	odd	4		200.3.l.e.193.1		4
5.3	odd	4	inner	40.3.l.b.33.2	yes	4
5.4	even	2		200.3.l.e.57.1		4
8.3	odd	2		320.3.p.i.257.2		4
8.5	even	2		320.3.p.l.257.1		4
12.11	even	2		720.3.bh.l.577.2		4
15.2	even	4		1800.3.v.k.793.1		4
15.8	even	4		360.3.v.c.73.2		4
15.14	odd	2		1800.3.v.k.1657.1		4
20.3	even	4		80.3.p.d.33.1		4
20.7	even	4		400.3.p.i.193.2		4
20.19	odd	2		400.3.p.i.257.2		4
40.3	even	4		320.3.p.i.193.2		4
40.13	odd	4		320.3.p.l.193.1		4
60.23	odd	4		720.3.bh.l.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.l.b.17.2	✓	4	1.1	even	1	trivial
40.3.l.b.33.2	yes	4	5.3	odd	4	inner
80.3.p.d.17.1		4	4.3	odd	2
80.3.p.d.33.1		4	20.3	even	4
200.3.l.e.57.1		4	5.4	even	2
200.3.l.e.193.1		4	5.2	odd	4
320.3.p.i.193.2		4	40.3	even	4
320.3.p.i.257.2		4	8.3	odd	2
320.3.p.l.193.1		4	40.13	odd	4
320.3.p.l.257.1		4	8.5	even	2
360.3.v.c.73.2		4	15.8	even	4
360.3.v.c.217.2		4	3.2	odd	2
400.3.p.i.193.2		4	20.7	even	4
400.3.p.i.257.2		4	20.19	odd	2
720.3.bh.l.433.2		4	60.23	odd	4
720.3.bh.l.577.2		4	12.11	even	2
1800.3.v.k.793.1		4	15.2	even	4
1800.3.v.k.1657.1		4	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.70156 - 2.70156i) q^{3} +(-4.70156 - 1.70156i) q^{5} +(6.70156 + 6.70156i) q^{7} -5.59688i q^{9} +O(q^{10})\)	\(q+(2.70156 - 2.70156i) q^{3} +(-4.70156 - 1.70156i) q^{5} +(6.70156 + 6.70156i) q^{7} -5.59688i q^{9} -1.40312 q^{11} +(-14.4031 + 14.4031i) q^{13} +(-17.2984 + 8.10469i) q^{15} +(-2.40312 - 2.40312i) q^{17} -22.8062i q^{19} +36.2094 q^{21} +(-0.104686 + 0.104686i) q^{23} +(19.2094 + 16.0000i) q^{25} +(9.19375 + 9.19375i) q^{27} -45.6125i q^{29} -2.59688 q^{31} +(-3.79063 + 3.79063i) q^{33} +(-20.1047 - 42.9109i) q^{35} +(10.6125 + 10.6125i) q^{37} +77.8219i q^{39} -44.6281 q^{41} +(26.7016 - 26.7016i) q^{43} +(-9.52343 + 26.3141i) q^{45} +(-10.4922 - 10.4922i) q^{47} +40.8219i q^{49} -12.9844 q^{51} +(-3.00000 + 3.00000i) q^{53} +(6.59688 + 2.38750i) q^{55} +(-61.6125 - 61.6125i) q^{57} +41.1938i q^{59} -57.4031 q^{61} +(37.5078 - 37.5078i) q^{63} +(92.2250 - 43.2094i) q^{65} +(34.7016 + 34.7016i) q^{67} +0.565633i q^{69} +45.4031 q^{71} +(11.3875 - 11.3875i) q^{73} +(95.1203 - 8.67032i) q^{75} +(-9.40312 - 9.40312i) q^{77} -86.4500i q^{79} +100.047 q^{81} +(-81.7172 + 81.7172i) q^{83} +(7.20937 + 15.3875i) q^{85} +(-123.225 - 123.225i) q^{87} +91.2250i q^{89} -193.047 q^{91} +(-7.01562 + 7.01562i) q^{93} +(-38.8062 + 107.225i) q^{95} +(49.0000 + 49.0000i) q^{97} +7.85311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 6 q^{5} + 14 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 6 * q^5 + 14 * q^7	\( 4 q - 2 q^{3} - 6 q^{5} + 14 q^{7} + 20 q^{11} - 32 q^{13} - 82 q^{15} + 16 q^{17} + 68 q^{21} + 38 q^{23} + 88 q^{27} - 36 q^{31} - 92 q^{33} - 42 q^{35} - 60 q^{37} + 52 q^{41} + 94 q^{43} + 154 q^{45} - 106 q^{47} - 180 q^{51} - 12 q^{53} + 52 q^{55} - 144 q^{57} - 204 q^{61} + 86 q^{63} + 164 q^{65} + 126 q^{67} + 156 q^{71} + 148 q^{73} + 214 q^{75} - 12 q^{77} + 16 q^{81} - 186 q^{83} - 48 q^{85} - 288 q^{87} - 388 q^{91} + 100 q^{93} - 104 q^{95} + 196 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 6 * q^5 + 14 * q^7 + 20 * q^11 - 32 * q^13 - 82 * q^15 + 16 * q^17 + 68 * q^21 + 38 * q^23 + 88 * q^27 - 36 * q^31 - 92 * q^33 - 42 * q^35 - 60 * q^37 + 52 * q^41 + 94 * q^43 + 154 * q^45 - 106 * q^47 - 180 * q^51 - 12 * q^53 + 52 * q^55 - 144 * q^57 - 204 * q^61 + 86 * q^63 + 164 * q^65 + 126 * q^67 + 156 * q^71 + 148 * q^73 + 214 * q^75 - 12 * q^77 + 16 * q^81 - 186 * q^83 - 48 * q^85 - 288 * q^87 - 388 * q^91 + 100 * q^93 - 104 * q^95 + 196 * q^97

Introduction

L-functions

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