LMFDB - Embedded newform 320.3.i.a.177.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(177,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("320.177");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.i (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			177.3
Character	$\chi$	$=$	320.177
Dual form			320.3.i.a.273.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.94472i q^{3} +(-3.37360 + 3.69037i) q^{5} +(-3.22480 + 3.22480i) q^{7} -15.4503 q^{9} +O(q^{10})$	\(q-4.94472i q^{3} +(-3.37360 + 3.69037i) q^{5} +(-3.22480 + 3.22480i) q^{7} -15.4503 q^{9} +(7.67097 + 7.67097i) q^{11} +22.2152i q^{13} +(18.2478 + 16.6815i) q^{15} +(-3.76038 - 3.76038i) q^{17} +(0.809445 + 0.809445i) q^{19} +(15.9458 + 15.9458i) q^{21} +(-12.2839 - 12.2839i) q^{23} +(-2.23764 - 24.8997i) q^{25} +31.8948i q^{27} +(27.1574 + 27.1574i) q^{29} -25.5557 q^{31} +(37.9308 - 37.9308i) q^{33} +(-1.02151 - 22.7799i) q^{35} +8.62466i q^{37} +109.848 q^{39} +73.4504i q^{41} +17.5521 q^{43} +(52.1231 - 57.0172i) q^{45} +(-17.4590 - 17.4590i) q^{47} +28.2013i q^{49} +(-18.5940 + 18.5940i) q^{51} -29.3309 q^{53} +(-54.1875 + 2.42991i) q^{55} +(4.00248 - 4.00248i) q^{57} +(-72.6508 + 72.6508i) q^{59} +(19.7110 - 19.7110i) q^{61} +(49.8241 - 49.8241i) q^{63} +(-81.9821 - 74.9451i) q^{65} -14.0319 q^{67} +(-60.7406 + 60.7406i) q^{69} +91.3292i q^{71} +(-42.7665 - 42.7665i) q^{73} +(-123.122 + 11.0645i) q^{75} -49.4747 q^{77} -46.7110i q^{79} +18.6585 q^{81} +82.9430i q^{83} +(26.5632 - 1.19117i) q^{85} +(134.286 - 134.286i) q^{87} +131.145 q^{89} +(-71.6395 - 71.6395i) q^{91} +126.366i q^{93} +(-5.71789 + 0.256406i) q^{95} +(-30.5363 - 30.5363i) q^{97} +(-118.519 - 118.519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^5 - 108 * q^9	$ 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 380 * q^95 - 4 * q^97 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	4.94472i		−	1.64824i	−0.566415	−	0.824120i	$-0.691670\pi$
$3$		−	4.94472i		−	1.64824i	0.566415	−	0.824120i	$-0.308330\pi$
$4$		0			0
$5$	−3.37360	+	3.69037i	−0.674720	+	0.738074i
$5$	−3.37360	+	3.69037i	−0.674720	+	0.738074i
$6$		0			0
$7$	−3.22480	+	3.22480i	−0.460686	+	0.460686i	−0.898880	−	0.438194i	$-0.855618\pi$
$7$	−3.22480	+	3.22480i	−0.460686	+	0.460686i	0.438194	+	0.898880i	$0.355618\pi$
$8$		0			0
$9$	−15.4503			−1.71670
$10$		0			0
$11$	7.67097	+	7.67097i	0.697361	+	0.697361i	0.963841	−	0.266480i	$-0.0858605\pi$
$11$	7.67097	+	7.67097i	0.697361	+	0.697361i	−0.266480	+	0.963841i	$0.585861\pi$
$12$		0			0
$13$			22.2152i			1.70886i	0.519568	+	0.854429i	$0.326093\pi$
$13$			22.2152i			1.70886i	−0.519568	+	0.854429i	$0.673907\pi$
$14$		0			0
$15$	18.2478	+	16.6815i	1.21652	+	1.11210i
$16$		0			0
$17$	−3.76038	−	3.76038i	−0.221199	−	0.221199i	0.587804	−	0.809003i	$-0.299993\pi$
$17$	−3.76038	−	3.76038i	−0.221199	−	0.221199i	−0.809003	+	0.587804i	$0.799993\pi$
$18$		0			0
$19$	0.809445	+	0.809445i	0.0426024	+	0.0426024i	0.728087	−	0.685485i	$-0.240410\pi$
$19$	0.809445	+	0.809445i	0.0426024	+	0.0426024i	−0.685485	+	0.728087i	$0.740410\pi$
$20$		0			0
$21$	15.9458	+	15.9458i	0.759322	+	0.759322i
$22$		0			0
$23$	−12.2839	−	12.2839i	−0.534083	−	0.534083i	0.387701	−	0.921785i	$-0.373269\pi$
$23$	−12.2839	−	12.2839i	−0.534083	−	0.534083i	−0.921785	+	0.387701i	$0.873269\pi$
$24$		0			0
$25$	−2.23764	−	24.8997i	−0.0895055	−	0.995986i
$26$		0			0
$27$			31.8948i			1.18129i
$28$		0			0
$29$	27.1574	+	27.1574i	0.936464	+	0.936464i	0.998099	−	0.0616350i	$-0.0196315\pi$
$29$	27.1574	+	27.1574i	0.936464	+	0.936464i	−0.0616350	+	0.998099i	$0.519631\pi$
$30$		0			0
$31$	−25.5557			−0.824379			−0.412189	−	0.911098i	$-0.635236\pi$
$31$	−25.5557			−0.824379			−0.412189	+	0.911098i	$0.635236\pi$
$32$		0			0
$33$	37.9308	−	37.9308i	1.14942	−	1.14942i
$34$		0			0
$35$	−1.02151	−	22.7799i	−0.0291861	−	0.650855i
$36$		0			0
$37$			8.62466i			0.233099i	0.993185	+	0.116550i	$0.0371834\pi$
$37$			8.62466i			0.233099i	−0.993185	+	0.116550i	$0.962817\pi$
$38$		0			0
$39$	109.848			2.81661
$40$		0			0
$41$			73.4504i			1.79147i	0.444585	+	0.895737i	$0.353351\pi$
$41$			73.4504i			1.79147i	−0.444585	+	0.895737i	$0.646649\pi$
$42$		0			0
$43$	17.5521			0.408188			0.204094	−	0.978951i	$-0.434575\pi$
$43$	17.5521			0.408188			0.204094	+	0.978951i	$0.434575\pi$
$44$		0			0
$45$	52.1231	−	57.0172i	1.15829	−	1.26705i
$46$		0			0
$47$	−17.4590	−	17.4590i	−0.371469	−	0.371469i	0.496543	−	0.868012i	$-0.334602\pi$
$47$	−17.4590	−	17.4590i	−0.371469	−	0.371469i	−0.868012	+	0.496543i	$0.834602\pi$
$48$		0			0
$49$			28.2013i			0.575536i
$50$		0			0
$51$	−18.5940	+	18.5940i	−0.364589	+	0.364589i
$52$		0			0
$53$	−29.3309			−0.553413			−0.276707	−	0.960954i	$-0.589243\pi$
$53$	−29.3309			−0.553413			−0.276707	+	0.960954i	$0.589243\pi$
$54$		0			0
$55$	−54.1875	+	2.42991i	−0.985227	+	0.0441803i
$56$		0			0
$57$	4.00248	−	4.00248i	0.0702190	−	0.0702190i
$58$		0			0
$59$	−72.6508	+	72.6508i	−1.23137	+	1.23137i	−0.267931	+	0.963438i	$0.586340\pi$
$59$	−72.6508	+	72.6508i	−1.23137	+	1.23137i	−0.963438	+	0.267931i	$0.913660\pi$
$60$		0			0
$61$	19.7110	−	19.7110i	0.323132	−	0.323132i	−0.526835	−	0.849967i	$-0.676622\pi$
$61$	19.7110	−	19.7110i	0.323132	−	0.323132i	0.849967	+	0.526835i	$0.176622\pi$
$62$		0			0
$63$	49.8241	−	49.8241i	0.790859	−	0.790859i
$64$		0			0
$65$	−81.9821	−	74.9451i	−1.26126	−	1.15300i
$66$		0			0
$67$	−14.0319			−0.209431			−0.104716	−	0.994502i	$-0.533393\pi$
$67$	−14.0319			−0.209431			−0.104716	+	0.994502i	$0.533393\pi$
$68$		0			0
$69$	−60.7406	+	60.7406i	−0.880298	+	0.880298i
$70$		0			0
$71$			91.3292i			1.28633i	0.765729	+	0.643163i	$0.222378\pi$
$71$			91.3292i			1.28633i	−0.765729	+	0.643163i	$0.777622\pi$
$72$		0			0
$73$	−42.7665	−	42.7665i	−0.585843	−	0.585843i	0.350660	−	0.936503i	$-0.385957\pi$
$73$	−42.7665	−	42.7665i	−0.585843	−	0.585843i	−0.936503	+	0.350660i	$0.885957\pi$
$74$		0			0
$75$	−123.122	+	11.0645i	−1.64163	+	0.147527i
$76$		0			0
$77$	−49.4747			−0.642529
$78$		0			0
$79$		−	46.7110i		−	0.591278i	−0.955300	−	0.295639i	$-0.904467\pi$
$79$		−	46.7110i		−	0.591278i	0.955300	−	0.295639i	$-0.0955326\pi$
$80$		0			0
$81$	18.6585			0.230352
$82$		0			0
$83$			82.9430i			0.999313i	0.866224	+	0.499656i	$0.166540\pi$
$83$			82.9430i			0.999313i	−0.866224	+	0.499656i	$0.833460\pi$
$84$		0			0
$85$	26.5632	−	1.19117i	0.312508	−	0.0140137i
$86$		0			0
$87$	134.286	−	134.286i	1.54352	−	1.54352i
$88$		0			0
$89$	131.145			1.47354			0.736768	−	0.676146i	$-0.236351\pi$
$89$	131.145			1.47354			0.736768	+	0.676146i	$0.236351\pi$
$90$		0			0
$91$	−71.6395	−	71.6395i	−0.787247	−	0.787247i
$92$		0			0
$93$			126.366i			1.35877i
$94$		0			0
$95$	−5.71789	+	0.256406i	−0.0601884	+	0.00269901i
$96$		0			0
$97$	−30.5363	−	30.5363i	−0.314807	−	0.314807i	0.531962	−	0.846769i	$-0.321455\pi$
$97$	−30.5363	−	30.5363i	−0.314807	−	0.314807i	−0.846769	+	0.531962i	$0.821455\pi$
$98$		0			0
$99$	−118.519	−	118.519i	−1.19716	−	1.19716i
$100$		0			0
$101$	22.0905	+	22.0905i	0.218718	+	0.218718i	0.807958	−	0.589240i	$-0.200573\pi$
$101$	22.0905	+	22.0905i	0.218718	+	0.218718i	−0.589240	+	0.807958i	$0.700573\pi$
$102$		0			0
$103$	−5.06551	−	5.06551i	−0.0491797	−	0.0491797i	0.682089	−	0.731269i	$-0.261072\pi$
$103$	−5.06551	−	5.06551i	−0.0491797	−	0.0491797i	−0.731269	+	0.682089i	$0.761072\pi$
$104$		0			0
$105$	−112.640	+	5.05110i	−1.07276	+	0.0481057i
$106$		0			0
$107$		−	54.6933i		−	0.511153i	−0.966789	−	0.255576i	$-0.917735\pi$
$107$		−	54.6933i		−	0.511153i	0.966789	−	0.255576i	$-0.0822652\pi$
$108$		0			0
$109$	−81.8934	−	81.8934i	−0.751316	−	0.751316i	0.223409	−	0.974725i	$-0.428281\pi$
$109$	−81.8934	−	81.8934i	−0.751316	−	0.751316i	−0.974725	+	0.223409i	$0.928281\pi$
$110$		0			0
$111$	42.6466			0.384203
$112$		0			0
$113$	−19.1764	+	19.1764i	−0.169703	+	0.169703i	−0.786849	−	0.617146i	$-0.788289\pi$
$113$	−19.1764	+	19.1764i	−0.169703	+	0.169703i	0.617146	+	0.786849i	$0.288289\pi$
$114$		0			0
$115$	86.7732	−	3.89115i	0.754550	−	0.0338361i
$116$		0			0
$117$		−	343.230i		−	2.93359i
$118$		0			0
$119$	24.2530			0.203807
$120$		0			0
$121$		−	3.31247i		−	0.0273758i
$122$		0			0
$123$	363.192			2.95278
$124$		0			0
$125$	99.4378	+	75.7438i	0.795502	+	0.605950i
$126$		0			0
$127$	−100.021	−	100.021i	−0.787565	−	0.787565i	0.193529	−	0.981094i	$-0.438007\pi$
$127$	−100.021	−	100.021i	−0.787565	−	0.787565i	−0.981094	+	0.193529i	$0.938007\pi$
$128$		0			0
$129$		−	86.7901i		−	0.672792i
$130$		0			0
$131$	48.8021	−	48.8021i	0.372535	−	0.372535i	−0.495865	−	0.868400i	$-0.665149\pi$
$131$	48.8021	−	48.8021i	0.372535	−	0.372535i	0.868400	+	0.495865i	$0.165149\pi$
$132$		0			0
$133$	−5.22060			−0.0392526
$134$		0			0
$135$	−117.704	−	107.600i	−0.871879	−	0.797040i
$136$		0			0
$137$	116.195	−	116.195i	0.848135	−	0.848135i	−0.141765	−	0.989900i	$-0.545278\pi$
$137$	116.195	−	116.195i	0.848135	−	0.848135i	0.989900	+	0.141765i	$0.0452778\pi$
$138$		0			0
$139$	25.5977	−	25.5977i	0.184156	−	0.184156i	−0.609008	−	0.793164i	$-0.708432\pi$
$139$	25.5977	−	25.5977i	0.184156	−	0.184156i	0.793164	+	0.609008i	$0.208432\pi$
$140$		0			0
$141$	−86.3301	+	86.3301i	−0.612270	+	0.612270i
$142$		0			0
$143$	−170.412	+	170.412i	−1.19169	+	1.19169i
$144$		0			0
$145$	−191.839	+	8.60260i	−1.32303	+	0.0593283i
$146$		0			0
$147$	139.448			0.948623
$148$		0			0
$149$	−11.6294	+	11.6294i	−0.0780497	+	0.0780497i	−0.745054	−	0.667004i	$-0.767576\pi$
$149$	−11.6294	+	11.6294i	−0.0780497	+	0.0780497i	0.667004	+	0.745054i	$0.267576\pi$
$150$		0			0
$151$			84.9872i			0.562829i	0.959586	+	0.281414i	$0.0908036\pi$
$151$			84.9872i			0.562829i	−0.959586	+	0.281414i	$0.909196\pi$
$152$		0			0
$153$	58.0989	+	58.0989i	0.379732	+	0.379732i
$154$		0			0
$155$	86.2149	−	94.3101i	0.556225	−	0.608452i
$156$		0			0
$157$	128.249			0.816874			0.408437	−	0.912787i	$-0.366074\pi$
$157$	128.249			0.816874			0.408437	+	0.912787i	$0.366074\pi$
$158$		0			0
$159$			145.033i			0.912158i
$160$		0			0
$161$	79.2265			0.492090
$162$		0			0
$163$			82.0115i			0.503138i	0.967839	+	0.251569i	$0.0809466\pi$
$163$			82.0115i			0.503138i	−0.967839	+	0.251569i	$0.919053\pi$
$164$		0			0
$165$	12.0153	+	267.942i	0.0728197	+	1.62389i
$166$		0			0
$167$	−131.169	+	131.169i	−0.785444	+	0.785444i	−0.980744	−	0.195299i	$-0.937432\pi$
$167$	−131.169	+	131.169i	−0.785444	+	0.785444i	0.195299	+	0.980744i	$0.437432\pi$
$168$		0			0
$169$	−324.513			−1.92020
$170$		0			0
$171$	−12.5061	−	12.5061i	−0.0731354	−	0.0731354i
$172$		0			0
$173$		−	58.5238i		−	0.338288i	−0.985591	−	0.169144i	$-0.945900\pi$
$173$		−	58.5238i		−	0.338288i	0.985591	−	0.169144i	$-0.0541003\pi$
$174$		0			0
$175$	87.5124	+	73.0806i	0.500071	+	0.417603i
$176$		0			0
$177$	359.238	+	359.238i	2.02959	+	2.02959i
$178$		0			0
$179$	−114.264	−	114.264i	−0.638347	−	0.638347i	0.311801	−	0.950147i	$-0.399068\pi$
$179$	−114.264	−	114.264i	−0.638347	−	0.638347i	−0.950147	+	0.311801i	$0.899068\pi$
$180$		0			0
$181$	74.0068	+	74.0068i	0.408878	+	0.408878i	0.881347	−	0.472470i	$-0.156637\pi$
$181$	74.0068	+	74.0068i	0.408878	+	0.408878i	−0.472470	+	0.881347i	$0.656637\pi$
$182$		0			0
$183$	−97.4656	−	97.4656i	−0.532599	−	0.532599i
$184$		0			0
$185$	−31.8282	−	29.0962i	−0.172044	−	0.157277i
$186$		0			0
$187$		−	57.6915i		−	0.308511i
$188$		0			0
$189$	−102.855	−	102.855i	−0.544204	−	0.544204i
$190$		0			0
$191$	−92.5178			−0.484387			−0.242193	−	0.970228i	$-0.577867\pi$
$191$	−92.5178			−0.484387			−0.242193	+	0.970228i	$0.577867\pi$
$192$		0			0
$193$	52.8692	−	52.8692i	0.273934	−	0.273934i	−0.556748	−	0.830682i	$-0.687951\pi$
$193$	52.8692	−	52.8692i	0.273934	−	0.273934i	0.830682	+	0.556748i	$0.187951\pi$
$194$		0			0
$195$	−370.582	+	405.379i	−1.90042	+	2.07887i
$196$		0			0
$197$		−	99.4134i		−	0.504637i	−0.967644	−	0.252318i	$-0.918807\pi$
$197$		−	99.4134i		−	0.504637i	0.967644	−	0.252318i	$-0.0811930\pi$
$198$		0			0
$199$	−265.168			−1.33250			−0.666252	−	0.745727i	$-0.732102\pi$
$199$	−265.168			−1.33250			−0.666252	+	0.745727i	$0.732102\pi$
$200$		0			0
$201$			69.3838i			0.345193i
$202$		0			0
$203$	−175.155			−0.862832
$204$		0			0
$205$	−271.059	−	247.792i	−1.32224	−	1.20874i
$206$		0			0
$207$	189.790	+	189.790i	0.916860	+	0.916860i
$208$		0			0
$209$			12.4185i			0.0594184i
$210$		0			0
$211$	226.573	−	226.573i	1.07380	−	1.07380i	0.0767547	−	0.997050i	$-0.475544\pi$
$211$	226.573	−	226.573i	1.07380	−	1.07380i	0.997050	−	0.0767547i	$-0.0244558\pi$
$212$		0			0
$213$	451.597			2.12017
$214$		0			0
$215$	−59.2137	+	64.7736i	−0.275413	+	0.301273i
$216$		0			0
$217$	82.4122	−	82.4122i	0.379780	−	0.379780i
$218$		0			0
$219$	−211.469	+	211.469i	−0.965610	+	0.965610i
$220$		0			0
$221$	83.5374	−	83.5374i	0.377997	−	0.377997i
$222$		0			0
$223$	238.888	−	238.888i	1.07125	−	1.07125i	0.0739871	−	0.997259i	$-0.476428\pi$
$223$	238.888	−	238.888i	1.07125	−	1.07125i	0.997259	−	0.0739871i	$-0.0235724\pi$
$224$		0			0
$225$	34.5721	+	384.707i	0.153654	+	1.70981i
$226$		0			0
$227$	442.991			1.95150			0.975751	−	0.218884i	$-0.0702416\pi$
$227$	442.991			1.95150			0.975751	+	0.218884i	$0.0702416\pi$
$228$		0			0
$229$	−218.763	+	218.763i	−0.955297	+	0.955297i	−0.999043	−	0.0437454i	$-0.986071\pi$
$229$	−218.763	+	218.763i	−0.955297	+	0.955297i	0.0437454	+	0.999043i	$0.486071\pi$
$230$		0			0
$231$			244.639i			1.05904i
$232$		0			0
$233$	181.998	+	181.998i	0.781108	+	0.781108i	0.980018	−	0.198910i	$-0.0637401\pi$
$233$	181.998	+	181.998i	0.781108	+	0.781108i	−0.198910	+	0.980018i	$0.563740\pi$
$234$		0			0
$235$	123.330	−	5.53046i	0.524809	−	0.0235339i
$236$		0			0
$237$	−230.973			−0.974569
$238$		0			0
$239$			41.3149i			0.172866i	0.996258	+	0.0864328i	$0.0275468\pi$
$239$			41.3149i			0.172866i	−0.996258	+	0.0864328i	$0.972453\pi$
$240$		0			0
$241$	223.654			0.928023			0.464012	−	0.885829i	$-0.346410\pi$
$241$	223.654			0.928023			0.464012	+	0.885829i	$0.346410\pi$
$242$		0			0
$243$			194.792i			0.801614i
$244$		0			0
$245$	−104.073	−	95.1399i	−0.424788	−	0.388326i
$246$		0			0
$247$	−17.9819	+	17.9819i	−0.0728014	+	0.0728014i
$248$		0			0
$249$	410.130			1.64711
$250$		0			0
$251$	329.376	+	329.376i	1.31226	+	1.31226i	0.919749	+	0.392507i	$0.128392\pi$
$251$	329.376	+	329.376i	1.31226	+	1.31226i	0.392507	+	0.919749i	$0.371608\pi$
$252$		0			0
$253$		−	188.459i		−	0.744898i
$254$		0			0
$255$	−5.88999	−	131.348i	−0.0230980	−	0.515089i
$256$		0			0
$257$	−102.275	−	102.275i	−0.397958	−	0.397958i	0.479555	−	0.877512i	$-0.340798\pi$
$257$	−102.275	−	102.275i	−0.397958	−	0.397958i	−0.877512	+	0.479555i	$0.840798\pi$
$258$		0			0
$259$	−27.8128	−	27.8128i	−0.107386	−	0.107386i
$260$		0			0
$261$	−419.590	−	419.590i	−1.60762	−	1.60762i
$262$		0			0
$263$	149.290	+	149.290i	0.567642	+	0.567642i	0.931467	−	0.363826i	$-0.118530\pi$
$263$	149.290	+	149.290i	0.567642	+	0.567642i	−0.363826	+	0.931467i	$0.618530\pi$
$264$		0			0
$265$	98.9508	−	108.242i	0.373399	−	0.408460i
$266$		0			0
$267$		−	648.474i		−	2.42874i
$268$		0			0
$269$	169.168	+	169.168i	0.628876	+	0.628876i	0.947785	−	0.318909i	$-0.103316\pi$
$269$	169.168	+	169.168i	0.628876	+	0.628876i	−0.318909	+	0.947785i	$0.603316\pi$
$270$		0			0
$271$	389.998			1.43911			0.719554	−	0.694437i	$-0.244346\pi$
$271$	389.998			1.43911			0.719554	+	0.694437i	$0.244346\pi$
$272$		0			0
$273$	−354.237	+	354.237i	−1.29757	+	1.29757i
$274$		0			0
$275$	173.840	−	208.169i	0.632144	−	0.756979i
$276$		0			0
$277$			290.668i			1.04934i	0.851305	+	0.524671i	$0.175812\pi$
$277$			290.668i			1.04934i	−0.851305	+	0.524671i	$0.824188\pi$
$278$		0			0
$279$	394.843			1.41521
$280$		0			0
$281$			235.390i			0.837688i	0.908058	+	0.418844i	$0.137565\pi$
$281$			235.390i			0.837688i	−0.908058	+	0.418844i	$0.862435\pi$
$282$		0			0
$283$	−468.675			−1.65609			−0.828047	−	0.560659i	$-0.810548\pi$
$283$	−468.675			−1.65609			−0.828047	+	0.560659i	$0.810548\pi$
$284$		0			0
$285$	1.26786	+	28.2734i	0.00444862	+	0.0992049i
$286$		0			0
$287$	−236.863	−	236.863i	−0.825307	−	0.825307i
$288$		0			0
$289$		−	260.719i		−	0.902142i
$290$		0			0
$291$	−150.993	+	150.993i	−0.518878	+	0.518878i
$292$		0			0
$293$	179.844			0.613801			0.306901	−	0.951742i	$-0.400708\pi$
$293$	179.844			0.613801			0.306901	+	0.951742i	$0.400708\pi$
$294$		0			0
$295$	−23.0134	−	513.203i	−0.0780116	−	1.73967i
$296$		0			0
$297$	−244.664	+	244.664i	−0.823785	+	0.823785i
$298$		0			0
$299$	272.889	−	272.889i	0.912673	−	0.912673i
$300$		0			0
$301$	−56.6020	+	56.6020i	−0.188047	+	0.188047i
$302$		0			0
$303$	109.231	−	109.231i	0.360500	−	0.360500i
$304$		0			0
$305$	6.24382	+	139.238i	0.0204715	+	0.456519i
$306$		0			0
$307$	−110.106			−0.358653			−0.179326	−	0.983790i	$-0.557392\pi$
$307$	−110.106			−0.358653			−0.179326	+	0.983790i	$0.557392\pi$
$308$		0			0
$309$	−25.0475	+	25.0475i	−0.0810599	+	0.0810599i
$310$		0			0
$311$		−	53.7610i		−	0.172865i	−0.996258	−	0.0864325i	$-0.972453\pi$
$311$		−	53.7610i		−	0.172865i	0.996258	−	0.0864325i	$-0.0275467\pi$
$312$		0			0
$313$	−165.965	−	165.965i	−0.530241	−	0.530241i	0.390403	−	0.920644i	$-0.372336\pi$
$313$	−165.965	−	165.965i	−0.530241	−	0.530241i	−0.920644	+	0.390403i	$0.872336\pi$
$314$		0			0
$315$	15.7827	+	351.956i	0.0501037	+	1.11732i
$316$		0			0
$317$	−40.4315			−0.127544			−0.0637721	−	0.997964i	$-0.520313\pi$
$317$	−40.4315			−0.127544			−0.0637721	+	0.997964i	$0.520313\pi$
$318$		0			0
$319$			416.648i			1.30611i
$320$		0			0
$321$	−270.443			−0.842503
$322$		0			0
$323$		−	6.08764i		−	0.0188472i
$324$		0			0
$325$	553.150	−	49.7094i	1.70200	−	0.152952i
$326$		0			0
$327$	−404.940	+	404.940i	−1.23835	+	1.23835i
$328$		0			0
$329$	112.604			0.342261
$330$		0			0
$331$	107.944	+	107.944i	0.326116	+	0.326116i	0.851107	−	0.524992i	$-0.175932\pi$
$331$	107.944	+	107.944i	0.326116	+	0.326116i	−0.524992	+	0.851107i	$0.675932\pi$
$332$		0			0
$333$		−	133.253i		−	0.400160i
$334$		0			0
$335$	47.3380	−	51.7828i	0.141307	−	0.154576i
$336$		0			0
$337$	−119.972	−	119.972i	−0.356000	−	0.356000i	0.506336	−	0.862336i	$-0.330999\pi$
$337$	−119.972	−	119.972i	−0.356000	−	0.356000i	−0.862336	+	0.506336i	$0.830999\pi$
$338$		0			0
$339$	94.8219	+	94.8219i	0.279711	+	0.279711i
$340$		0			0
$341$	−196.037	−	196.037i	−0.574889	−	0.574889i
$342$		0			0
$343$	−248.959	−	248.959i	−0.725828	−	0.725828i
$344$		0			0
$345$	−19.2406	−	429.070i	−0.0557700	−	1.24368i
$346$		0			0
$347$			165.996i			0.478375i	0.970973	+	0.239188i	$0.0768811\pi$
$347$			165.996i			0.478375i	−0.970973	+	0.239188i	$0.923119\pi$
$348$		0			0
$349$	201.279	+	201.279i	0.576730	+	0.576730i	0.934001	−	0.357271i	$-0.116293\pi$
$349$	201.279	+	201.279i	0.576730	+	0.576730i	−0.357271	+	0.934001i	$0.616293\pi$
$350$		0			0
$351$	−708.548			−2.01866
$352$		0			0
$353$	−5.16188	+	5.16188i	−0.0146229	+	0.0146229i	−0.714380	−	0.699758i	$-0.753291\pi$
$353$	−5.16188	+	5.16188i	−0.0146229	+	0.0146229i	0.699758	+	0.714380i	$0.253291\pi$
$354$		0			0
$355$	−337.038	−	308.108i	−0.949403	−	0.867910i
$356$		0			0
$357$		−	119.924i		−	0.335922i
$358$		0			0
$359$	81.8547			0.228008			0.114004	−	0.993480i	$-0.463632\pi$
$359$	81.8547			0.228008			0.114004	+	0.993480i	$0.463632\pi$
$360$		0			0
$361$		−	359.690i		−	0.996370i
$362$		0			0
$363$	−16.3792			−0.0451218
$364$		0			0
$365$	302.102	−	13.5471i	0.827676	−	0.0371152i
$366$		0			0
$367$	−120.769	−	120.769i	−0.329071	−	0.329071i	0.523162	−	0.852233i	$-0.324752\pi$
$367$	−120.769	−	120.769i	−0.329071	−	0.329071i	−0.852233	+	0.523162i	$0.824752\pi$
$368$		0			0
$369$		−	1134.83i		−	3.07542i
$370$		0			0
$371$	94.5864	−	94.5864i	0.254950	−	0.254950i
$372$		0			0
$373$	−320.574			−0.859447			−0.429724	−	0.902960i	$-0.641389\pi$
$373$	−320.574			−0.859447			−0.429724	+	0.902960i	$0.641389\pi$
$374$		0			0
$375$	374.532	−	491.692i	0.998752	−	1.31118i
$376$		0			0
$377$	−603.307	+	603.307i	−1.60028	+	1.60028i
$378$		0			0
$379$	−3.16506	+	3.16506i	−0.00835109	+	0.00835109i	−0.711270	−	0.702919i	$-0.751880\pi$
$379$	−3.16506	+	3.16506i	−0.00835109	+	0.00835109i	0.702919	+	0.711270i	$0.251880\pi$
$380$		0			0
$381$	−494.575	+	494.575i	−1.29810	+	1.29810i
$382$		0			0
$383$	−401.423	+	401.423i	−1.04810	+	1.04810i	−0.0493197	+	0.998783i	$0.515705\pi$
$383$	−401.423	+	401.423i	−1.04810	+	1.04810i	−0.998783	+	0.0493197i	$0.984295\pi$
$384$		0			0
$385$	166.908	−	182.580i	0.433527	−	0.474234i
$386$		0			0
$387$	−271.184			−0.700735
$388$		0			0
$389$	−179.440	+	179.440i	−0.461286	+	0.461286i	−0.899077	−	0.437791i	$-0.855761\pi$
$389$	−179.440	+	179.440i	−0.461286	+	0.461286i	0.437791	+	0.899077i	$0.355761\pi$
$390$		0			0
$391$			92.3844i			0.236277i
$392$		0			0
$393$	−241.313	−	241.313i	−0.614028	−	0.614028i
$394$		0			0
$395$	172.381	+	157.584i	0.436407	+	0.398947i
$396$		0			0
$397$	321.234			0.809154			0.404577	−	0.914504i	$-0.367419\pi$
$397$	321.234			0.809154			0.404577	+	0.914504i	$0.367419\pi$
$398$		0			0
$399$			25.8144i			0.0646978i
$400$		0			0
$401$	649.404			1.61946			0.809730	−	0.586802i	$-0.199613\pi$
$401$	649.404			1.61946			0.809730	+	0.586802i	$0.199613\pi$
$402$		0			0
$403$		−	567.725i		−	1.40875i
$404$		0			0
$405$	−62.9465	+	68.8569i	−0.155423	+	0.170017i
$406$		0			0
$407$	−66.1595	+	66.1595i	−0.162554	+	0.162554i
$408$		0			0
$409$	−20.3455			−0.0497444			−0.0248722	−	0.999691i	$-0.507918\pi$
$409$	−20.3455			−0.0497444			−0.0248722	+	0.999691i	$0.507918\pi$
$410$		0			0
$411$	−574.550	−	574.550i	−1.39793	−	1.39793i
$412$		0			0
$413$		−	468.569i		−	1.13455i
$414$		0			0
$415$	−306.090	−	279.816i	−0.737566	−	0.674256i
$416$		0			0
$417$	−126.573	−	126.573i	−0.303533	−	0.303533i
$418$		0			0
$419$	−204.233	−	204.233i	−0.487430	−	0.487430i	0.420064	−	0.907494i	$-0.362008\pi$
$419$	−204.233	−	204.233i	−0.487430	−	0.487430i	−0.907494	+	0.420064i	$0.862008\pi$
$420$		0			0
$421$	−74.3563	−	74.3563i	−0.176618	−	0.176618i	0.613262	−	0.789880i	$-0.289857\pi$
$421$	−74.3563	−	74.3563i	−0.176618	−	0.176618i	−0.789880	+	0.613262i	$0.789857\pi$
$422$		0			0
$423$	269.747	+	269.747i	0.637699	+	0.637699i
$424$		0			0
$425$	−85.2178	+	102.047i	−0.200513	+	0.240110i
$426$		0			0
$427$			127.128i			0.297725i
$428$		0			0
$429$	842.639	+	842.639i	1.96419	+	1.96419i
$430$		0			0
$431$	−30.9498			−0.0718092			−0.0359046	−	0.999355i	$-0.511431\pi$
$431$	−30.9498			−0.0718092			−0.0359046	+	0.999355i	$0.511431\pi$
$432$		0			0
$433$	−68.9194	+	68.9194i	−0.159167	+	0.159167i	−0.782198	−	0.623030i	$-0.785901\pi$
$433$	−68.9194	+	68.9194i	−0.159167	+	0.159167i	0.623030	+	0.782198i	$0.285901\pi$
$434$		0			0
$435$	42.5375	+	948.592i	0.0977873	+	2.18067i
$436$		0			0
$437$		−	19.8863i		−	0.0455064i
$438$		0			0
$439$	755.005			1.71983			0.859914	−	0.510439i	$-0.170517\pi$
$439$	755.005			1.71983			0.859914	+	0.510439i	$0.170517\pi$
$440$		0			0
$441$		−	435.718i		−	0.988022i
$442$		0			0
$443$	109.778			0.247806			0.123903	−	0.992294i	$-0.460459\pi$
$443$	109.778			0.247806			0.123903	+	0.992294i	$0.460459\pi$
$444$		0			0
$445$	−442.430	+	483.972i	−0.994224	+	1.08758i
$446$		0			0
$447$	57.5042	+	57.5042i	0.128645	+	0.128645i
$448$		0			0
$449$			491.218i			1.09403i	0.837124	+	0.547013i	$0.184235\pi$
$449$			491.218i			1.09403i	−0.837124	+	0.547013i	$0.815765\pi$
$450$		0			0
$451$	−563.436	+	563.436i	−1.24930	+	1.24930i
$452$		0			0
$453$	420.238			0.927678
$454$		0			0
$455$	506.059	−	22.6931i	1.11222	−	0.0498749i
$456$		0			0
$457$	468.944	−	468.944i	1.02614	−	1.02614i	0.0264867	−	0.999649i	$-0.491568\pi$
$457$	468.944	−	468.944i	1.02614	−	1.02614i	0.999649	−	0.0264867i	$-0.00843195\pi$
$458$		0			0
$459$	119.937	−	119.937i	0.261300	−	0.261300i
$460$		0			0
$461$	−78.6933	+	78.6933i	−0.170701	+	0.170701i	−0.787287	−	0.616586i	$-0.788515\pi$
$461$	−78.6933	+	78.6933i	−0.170701	+	0.170701i	0.616586	+	0.787287i	$0.288515\pi$
$462$		0			0
$463$	382.322	−	382.322i	0.825749	−	0.825749i	−0.161176	−	0.986926i	$-0.551529\pi$
$463$	382.322	−	382.322i	0.825749	−	0.825749i	0.986926	+	0.161176i	$0.0515288\pi$
$464$		0			0
$465$	−466.337	−	426.309i	−1.00288	−	0.916793i
$466$		0			0
$467$	374.594			0.802129			0.401065	−	0.916050i	$-0.368640\pi$
$467$	374.594			0.802129			0.401065	+	0.916050i	$0.368640\pi$
$468$		0			0
$469$	45.2501	−	45.2501i	0.0964820	−	0.0964820i
$470$		0			0
$471$		−	634.157i		−	1.34640i
$472$		0			0
$473$	134.641	+	134.641i	0.284654	+	0.284654i
$474$		0			0
$475$	18.3437	−	21.9661i	0.0386182	−	0.0462445i
$476$		0			0
$477$	453.171			0.950043
$478$		0			0
$479$		−	450.432i		−	0.940359i	−0.882571	−	0.470179i	$-0.844189\pi$
$479$		−	450.432i		−	0.940359i	0.882571	−	0.470179i	$-0.155811\pi$
$480$		0			0
$481$	−191.598			−0.398333
$482$		0			0
$483$		−	391.753i		−	0.811082i
$484$		0			0
$485$	215.707	−	9.67290i	0.444757	−	0.0199441i
$486$		0			0
$487$	−292.281	+	292.281i	−0.600166	+	0.600166i	−0.940357	−	0.340190i	$-0.889508\pi$
$487$	−292.281	+	292.281i	−0.600166	+	0.600166i	0.340190	+	0.940357i	$0.389508\pi$
$488$		0			0
$489$	405.524			0.829293
$490$		0			0
$491$	−434.376	−	434.376i	−0.884677	−	0.884677i	0.109329	−	0.994006i	$-0.465130\pi$
$491$	−434.376	−	434.376i	−0.884677	−	0.884677i	−0.994006	+	0.109329i	$0.965130\pi$
$492$		0			0
$493$		−	204.245i		−	0.414289i
$494$		0			0
$495$	837.212	−	37.5429i	1.69134	−	0.0758441i
$496$		0			0
$497$	−294.519	−	294.519i	−0.592593	−	0.592593i
$498$		0			0
$499$	36.0616	+	36.0616i	0.0722676	+	0.0722676i	0.742317	−	0.670049i	$-0.233727\pi$
$499$	36.0616	+	36.0616i	0.0722676	+	0.0722676i	−0.670049	+	0.742317i	$0.733727\pi$
$500$		0			0
$501$	648.595	+	648.595i	1.29460	+	1.29460i
$502$		0			0
$503$	196.896	+	196.896i	0.391444	+	0.391444i	0.875202	−	0.483758i	$-0.160729\pi$
$503$	196.896	+	196.896i	0.391444	+	0.391444i	−0.483758	+	0.875202i	$0.660729\pi$
$504$		0			0
$505$	−156.047	+	6.99756i	−0.309003	+	0.0138565i
$506$		0			0
$507$			1604.63i			3.16494i
$508$		0			0
$509$	−459.143	−	459.143i	−0.902049	−	0.902049i	0.0935638	−	0.995613i	$-0.470174\pi$
$509$	−459.143	−	459.143i	−0.902049	−	0.902049i	−0.995613	+	0.0935638i	$0.970174\pi$
$510$		0			0
$511$	275.827			0.539780
$512$		0			0
$513$	−25.8171	+	25.8171i	−0.0503257	+	0.0503257i
$514$		0			0
$515$	35.7826	−	1.60459i	0.0694807	−	0.00311571i
$516$		0			0
$517$		−	267.855i		−	0.518096i
$518$		0			0
$519$	−289.384			−0.557580
$520$		0			0
$521$			726.368i			1.39418i	0.716984	+	0.697090i	$0.245522\pi$
$521$			726.368i			1.39418i	−0.716984	+	0.697090i	$0.754478\pi$
$522$		0			0
$523$	−542.697			−1.03766			−0.518831	−	0.854877i	$-0.673633\pi$
$523$	−542.697			−1.03766			−0.518831	+	0.854877i	$0.673633\pi$
$524$		0			0
$525$	361.363	−	432.725i	0.688311	−	0.824237i
$526$		0			0
$527$	96.0993	+	96.0993i	0.182352	+	0.182352i
$528$		0			0
$529$		−	227.211i		−	0.429510i
$530$		0			0
$531$	1122.47	−	1122.47i	2.11389	−	2.11389i
$532$		0			0
$533$	−1631.71			−3.06137
$534$		0			0
$535$	201.839	+	184.513i	0.377268	+	0.344885i
$536$		0			0
$537$	−565.004	+	565.004i	−1.05215	+	1.05215i
$538$		0			0
$539$	−216.331	+	216.331i	−0.401357	+	0.401357i
$540$		0			0
$541$	727.376	−	727.376i	1.34450	−	1.34450i	0.452983	−	0.891519i	$-0.350360\pi$
$541$	727.376	−	727.376i	1.34450	−	1.34450i	0.891519	−	0.452983i	$-0.149640\pi$
$542$		0			0
$543$	365.943	−	365.943i	0.673929	−	0.673929i
$544$		0			0
$545$	578.493	−	25.9412i	1.06145	−	0.0475985i
$546$		0			0
$547$	−511.401			−0.934920			−0.467460	−	0.884014i	$-0.654831\pi$
$547$	−511.401			−0.934920			−0.467460	+	0.884014i	$0.654831\pi$
$548$		0			0
$549$	−304.541	+	304.541i	−0.554720	+	0.554720i
$550$		0			0
$551$			43.9649i			0.0797911i
$552$		0			0
$553$	150.634	+	150.634i	0.272394	+	0.272394i
$554$		0			0
$555$	−143.872	+	157.382i	−0.259230	+	0.283570i
$556$		0			0
$557$	−804.398			−1.44416			−0.722081	−	0.691809i	$-0.756814\pi$
$557$	−804.398			−1.44416			−0.722081	+	0.691809i	$0.756814\pi$
$558$		0			0
$559$			389.922i			0.697535i
$560$		0			0
$561$	−285.269			−0.508500
$562$		0			0
$563$			695.151i			1.23473i	0.786678	+	0.617363i	$0.211799\pi$
$563$			695.151i			1.23473i	−0.786678	+	0.617363i	$0.788201\pi$
$564$		0			0
$565$	−6.07446	−	135.461i	−0.0107513	−	0.239755i
$566$		0			0
$567$	−60.1701	+	60.1701i	−0.106120	+	0.106120i
$568$		0			0
$569$	−277.088			−0.486974			−0.243487	−	0.969904i	$-0.578291\pi$
$569$	−277.088			−0.486974			−0.243487	+	0.969904i	$0.578291\pi$
$570$		0			0
$571$	569.098	+	569.098i	0.996669	+	0.996669i	0.999994	−	0.00332578i	$-0.00105863\pi$
$571$	569.098	+	569.098i	0.996669	+	0.996669i	−0.00332578	+	0.999994i	$0.501059\pi$
$572$		0			0
$573$			457.475i			0.798386i
$574$		0			0
$575$	−278.378	+	333.352i	−0.484136	+	0.579743i
$576$		0			0
$577$	687.894	+	687.894i	1.19219	+	1.19219i	0.976451	+	0.215740i	$0.0692163\pi$
$577$	687.894	+	687.894i	1.19219	+	1.19219i	0.215740	+	0.976451i	$0.430784\pi$
$578$		0			0
$579$	−261.424	−	261.424i	−0.451509	−	0.451509i
$580$		0			0
$581$	−267.475	−	267.475i	−0.460370	−	0.460370i
$582$		0			0
$583$	−224.996	−	224.996i	−0.385929	−	0.385929i
$584$		0			0
$585$	1266.65	+	1157.92i	2.16521	+	1.97935i
$586$		0			0
$587$		−	78.2483i		−	0.133302i	−0.997776	−	0.0666510i	$-0.978769\pi$
$587$		−	78.2483i		−	0.133302i	0.997776	−	0.0666510i	$-0.0212314\pi$
$588$		0			0
$589$	−20.6860	−	20.6860i	−0.0351205	−	0.0351205i
$590$		0			0
$591$	−491.572			−0.831763
$592$		0			0
$593$	−296.118	+	296.118i	−0.499355	+	0.499355i	−0.911237	−	0.411882i	$-0.864872\pi$
$593$	−296.118	+	296.118i	−0.499355	+	0.499355i	0.411882	+	0.911237i	$0.364872\pi$
$594$		0			0
$595$	−81.8199	+	89.5024i	−0.137512	+	0.150424i
$596$		0			0
$597$			1311.18i			2.19629i
$598$		0			0
$599$	48.2788			0.0805990			0.0402995	−	0.999188i	$-0.487169\pi$
$599$	48.2788			0.0805990			0.0402995	+	0.999188i	$0.487169\pi$
$600$		0			0
$601$			592.230i			0.985408i	0.870197	+	0.492704i	$0.163992\pi$
$601$			592.230i			0.985408i	−0.870197	+	0.492704i	$0.836008\pi$
$602$		0			0
$603$	216.796			0.359530
$604$		0			0
$605$	12.2242	+	11.1749i	0.0202053	+	0.0184710i
$606$		0			0
$607$	289.382	+	289.382i	0.476741	+	0.476741i	0.904088	−	0.427346i	$-0.140552\pi$
$607$	289.382	+	289.382i	0.476741	+	0.476741i	−0.427346	+	0.904088i	$0.640552\pi$
$608$		0			0
$609$			866.092i			1.42215i
$610$		0			0
$611$	387.855	−	387.855i	0.634787	−	0.634787i
$612$		0			0
$613$	719.493			1.17373			0.586863	−	0.809687i	$-0.300363\pi$
$613$	719.493			1.17373			0.586863	+	0.809687i	$0.300363\pi$
$614$		0			0
$615$	−1225.26	+	1340.31i	−1.99230	+	2.17937i
$616$		0			0
$617$	370.007	−	370.007i	0.599687	−	0.599687i	−0.340542	−	0.940229i	$-0.610611\pi$
$617$	370.007	−	370.007i	0.599687	−	0.599687i	0.940229	+	0.340542i	$0.110611\pi$
$618$		0			0
$619$	−524.739	+	524.739i	−0.847721	+	0.847721i	−0.989848	−	0.142127i	$-0.954606\pi$
$619$	−524.739	+	524.739i	−0.847721	+	0.847721i	0.142127	+	0.989848i	$0.454606\pi$
$620$		0			0
$621$	391.793	−	391.793i	0.630907	−	0.630907i
$622$		0			0
$623$	−422.916	+	422.916i	−0.678837	+	0.678837i
$624$		0			0
$625$	−614.986	+	111.433i	−0.983978	+	0.178292i
$626$		0			0
$627$	61.4058			0.0979359
$628$		0			0
$629$	32.4320	−	32.4320i	0.0515612	−	0.0515612i
$630$		0			0
$631$		−	481.853i		−	0.763634i	−0.924238	−	0.381817i	$-0.875298\pi$
$631$		−	481.853i		−	0.763634i	0.924238	−	0.381817i	$-0.124702\pi$
$632$		0			0
$633$	−1120.34	−	1120.34i	−1.76989	−	1.76989i
$634$		0			0
$635$	706.544	−	31.6833i	1.11267	−	0.0498950i
$636$		0			0
$637$	−626.496			−0.983510
$638$		0			0
$639$		−	1411.06i		−	2.20823i
$640$		0			0
$641$	602.798			0.940403			0.470202	−	0.882559i	$-0.344181\pi$
$641$	602.798			0.940403			0.470202	+	0.882559i	$0.344181\pi$
$642$		0			0
$643$			1220.05i			1.89744i	0.316118	+	0.948720i	$0.397621\pi$
$643$			1220.05i			1.89744i	−0.316118	+	0.948720i	$0.602379\pi$
$644$		0			0
$645$	320.288	+	292.795i	0.496570	+	0.453946i
$646$		0			0
$647$	674.538	−	674.538i	1.04256	−	1.04256i	0.0435096	−	0.999053i	$-0.486146\pi$
$647$	674.538	−	674.538i	1.04256	−	1.04256i	0.999053	−	0.0435096i	$-0.0138539\pi$
$648$		0			0
$649$	−1114.60			−1.71742
$650$		0			0
$651$	−407.506	−	407.506i	−0.625969	−	0.625969i
$652$		0			0
$653$			1069.12i			1.63724i	0.574336	+	0.818620i	$0.305260\pi$
$653$			1069.12i			1.63724i	−0.574336	+	0.818620i	$0.694740\pi$
$654$		0			0
$655$	15.4589	+	344.737i	0.0236014	+	0.526315i
$656$		0			0
$657$	660.755	+	660.755i	1.00572	+	1.00572i
$658$		0			0
$659$	−392.851	−	392.851i	−0.596131	−	0.596131i	0.343149	−	0.939281i	$-0.388506\pi$
$659$	−392.851	−	392.851i	−0.596131	−	0.596131i	−0.939281	+	0.343149i	$0.888506\pi$
$660$		0			0
$661$	−251.961	−	251.961i	−0.381182	−	0.381182i	0.490346	−	0.871528i	$-0.336871\pi$
$661$	−251.961	−	251.961i	−0.381182	−	0.381182i	−0.871528	+	0.490346i	$0.836871\pi$
$662$		0			0
$663$	−413.069	−	413.069i	−0.623031	−	0.623031i
$664$		0			0
$665$	17.6122	−	19.2659i	0.0264845	−	0.0289713i
$666$		0			0
$667$		−	667.200i		−	1.00030i
$668$		0			0
$669$	−1181.23	−	1181.23i	−1.76567	−	1.76567i
$670$		0			0
$671$	302.406			0.450679
$672$		0			0
$673$	−54.2702	+	54.2702i	−0.0806392	+	0.0806392i	−0.746276	−	0.665637i	$-0.768160\pi$
$673$	−54.2702	+	54.2702i	−0.0806392	+	0.0806392i	0.665637	+	0.746276i	$0.268160\pi$
$674$		0			0
$675$	794.170	−	71.3690i	1.17655	−	0.105732i
$676$		0			0
$677$		−	862.549i		−	1.27408i	−0.770832	−	0.637038i	$-0.780159\pi$
$677$		−	862.549i		−	1.27408i	0.770832	−	0.637038i	$-0.219841\pi$
$678$		0			0
$679$	196.947			0.290054
$680$		0			0
$681$		−	2190.47i		−	3.21654i
$682$		0			0
$683$	887.581			1.29953			0.649766	−	0.760134i	$-0.274867\pi$
$683$	887.581			1.29953			0.649766	+	0.760134i	$0.274867\pi$
$684$		0			0
$685$	36.8067	+	820.794i	0.0537323	+	1.19824i
$686$		0			0
$687$	1081.72	+	1081.72i	1.57456	+	1.57456i
$688$		0			0
$689$		−	651.591i		−	0.945705i
$690$		0			0
$691$	−810.243	+	810.243i	−1.17257	+	1.17257i	−0.190969	+	0.981596i	$0.561163\pi$
$691$	−810.243	+	810.243i	−1.17257	+	1.17257i	−0.981596	+	0.190969i	$0.938837\pi$
$692$		0			0
$693$	764.398			1.10303
$694$		0			0
$695$	8.10851	+	180.821i	0.0116669	+	0.260174i
$696$		0			0
$697$	276.202	−	276.202i	0.396272	−	0.396272i
$698$		0			0
$699$	899.930	−	899.930i	1.28745	−	1.28745i
$700$		0			0
$701$	768.186	−	768.186i	1.09584	−	1.09584i	0.100952	−	0.994891i	$-0.467811\pi$
$701$	768.186	−	768.186i	1.09584	−	1.09584i	0.994891	−	0.100952i	$-0.0321889\pi$
$702$		0			0
$703$	−6.98119	+	6.98119i	−0.00993057	+	0.00993057i
$704$		0			0
$705$	−27.3466	−	609.833i	−0.0387895	−	0.865011i
$706$		0			0
$707$	−142.475			−0.201521
$708$		0			0
$709$	587.694	−	587.694i	0.828906	−	0.828906i	−0.158459	−	0.987365i	$-0.550653\pi$
$709$	587.694	−	587.694i	0.828906	−	0.828906i	0.987365	+	0.158459i	$0.0506527\pi$
$710$		0			0
$711$			721.697i			1.01505i
$712$		0			0
$713$	313.925	+	313.925i	0.440287	+	0.440287i
$714$		0			0
$715$	−53.9809	−	1203.78i	−0.0754978	−	1.68361i
$716$		0			0
$717$	204.291			0.284924
$718$		0			0
$719$			735.293i			1.02266i	0.859384	+	0.511330i	$0.170847\pi$
$719$			735.293i			1.02266i	−0.859384	+	0.511330i	$0.829153\pi$
$720$		0			0
$721$	32.6705			0.0453128
$722$		0			0
$723$		−	1105.90i		−	1.52961i
$724$		0			0
$725$	615.443	−	736.980i	0.848886	−	1.01652i
$726$		0			0
$727$	−282.639	+	282.639i	−0.388775	+	0.388775i	−0.874250	−	0.485475i	$-0.838647\pi$
$727$	−282.639	+	282.639i	−0.388775	+	0.388775i	0.485475	+	0.874250i	$0.338647\pi$
$728$		0			0
$729$	1131.12			1.55160
$730$		0			0
$731$	−66.0025	−	66.0025i	−0.0902907	−	0.0902907i
$732$		0			0
$733$			1241.78i			1.69410i	0.531513	+	0.847050i	$0.321624\pi$
$733$			1241.78i			1.69410i	−0.531513	+	0.847050i	$0.678376\pi$
$734$		0			0
$735$	−470.440	+	514.613i	−0.640055	+	0.700153i
$736$		0			0
$737$	−107.638	−	107.638i	−0.146049	−	0.146049i
$738$		0			0
$739$	682.480	+	682.480i	0.923518	+	0.923518i	0.997276	−	0.0737578i	$-0.0234992\pi$
$739$	682.480	+	682.480i	0.923518	+	0.923518i	−0.0737578	+	0.997276i	$0.523499\pi$
$740$		0			0
$741$	88.9157	+	88.9157i	0.119994	+	0.119994i
$742$		0			0
$743$	−603.646	−	603.646i	−0.812444	−	0.812444i	0.172556	−	0.985000i	$-0.444797\pi$
$743$	−603.646	−	603.646i	−0.812444	−	0.812444i	−0.985000	+	0.172556i	$0.944797\pi$
$744$		0			0
$745$	−3.68382	−	82.1497i	−0.00494472	−	0.110268i
$746$		0			0
$747$		−	1281.49i		−	1.71552i
$748$		0			0
$749$	176.375	+	176.375i	0.235481	+	0.235481i
$750$		0			0
$751$	−849.499			−1.13116			−0.565578	−	0.824695i	$-0.691347\pi$
$751$	−849.499			−1.13116			−0.565578	+	0.824695i	$0.691347\pi$
$752$		0			0
$753$	1628.67	−	1628.67i	2.16291	−	2.16291i
$754$		0			0
$755$	−313.634	−	286.713i	−0.415409	−	0.379752i
$756$		0			0
$757$			410.039i			0.541663i	0.962627	+	0.270832i	$0.0872986\pi$
$757$			410.039i			0.541663i	−0.962627	+	0.270832i	$0.912701\pi$
$758$		0			0
$759$	−931.878			−1.22777
$760$		0			0
$761$			582.295i			0.765171i	0.923920	+	0.382585i	$0.124966\pi$
$761$			582.295i			0.765171i	−0.923920	+	0.382585i	$0.875034\pi$
$762$		0			0
$763$	528.180			0.692242
$764$		0			0
$765$	−410.409	+	18.4039i	−0.536482	+	0.0240573i
$766$		0			0
$767$	−1613.95	−	1613.95i	−2.10423	−	2.10423i
$768$		0			0
$769$			1386.11i			1.80249i	0.433311	+	0.901245i	$0.357345\pi$
$769$			1386.11i			1.80249i	−0.433311	+	0.901245i	$0.642655\pi$
$770$		0			0
$771$	−505.722	+	505.722i	−0.655930	+	0.655930i
$772$		0			0
$773$	−1124.50			−1.45473			−0.727363	−	0.686253i	$-0.759254\pi$
$773$	−1124.50			−1.45473			−0.727363	+	0.686253i	$0.759254\pi$
$774$		0			0
$775$	57.1845	+	636.329i	0.0737864	+	0.821070i
$776$		0			0
$777$	−137.527	+	137.527i	−0.176997	+	0.176997i
$778$		0			0
$779$	−59.4541	+	59.4541i	−0.0763210	+	0.0763210i
$780$		0			0
$781$	−700.583	+	700.583i	−0.897033	+	0.897033i
$782$		0			0
$783$	−866.182	+	866.182i	−1.10623	+	1.10623i
$784$		0			0
$785$	−432.662	+	473.287i	−0.551161	+	0.602913i
$786$		0			0
$787$	785.121			0.997612			0.498806	−	0.866714i	$-0.333772\pi$
$787$	785.121			0.997612			0.498806	+	0.866714i	$0.333772\pi$
$788$		0			0
$789$	738.196	−	738.196i	0.935610	−	0.935610i
$790$		0			0
$791$		−	123.680i		−	0.156359i
$792$		0			0
$793$	437.884	+	437.884i	0.552186	+	0.552186i
$794$		0			0
$795$	−535.226	−	489.284i	−0.673240	−	0.615452i
$796$		0			0
$797$	−58.6173			−0.0735474			−0.0367737	−	0.999324i	$-0.511708\pi$
$797$	−58.6173			−0.0735474			−0.0367737	+	0.999324i	$0.511708\pi$
$798$		0			0
$799$			131.305i			0.164337i
$800$		0			0
$801$	−2026.22			−2.52961
$802$		0			0
$803$		−	656.122i		−	0.817088i
$804$		0			0
$805$	−267.278	+	292.375i	−0.332023	+	0.363198i
$806$		0			0
$807$	836.488	−	836.488i	1.03654	−	1.03654i
$808$		0			0
$809$	−361.896			−0.447337			−0.223669	−	0.974665i	$-0.571803\pi$
$809$	−361.896			−0.447337			−0.223669	+	0.974665i	$0.571803\pi$
$810$		0			0
$811$	−88.5414	−	88.5414i	−0.109176	−	0.109176i	0.650409	−	0.759584i	$-0.274598\pi$
$811$	−88.5414	−	88.5414i	−0.109176	−	0.109176i	−0.759584	+	0.650409i	$0.774598\pi$
$812$		0			0
$813$		−	1928.43i		−	2.37200i
$814$		0			0
$815$	−302.653	−	276.674i	−0.371353	−	0.339477i
$816$		0			0
$817$	14.2074	+	14.2074i	0.0173898	+	0.0173898i
$818$		0			0
$819$	1106.85	+	1106.85i	1.35147	+	1.35147i
$820$		0			0
$821$	−74.7330	−	74.7330i	−0.0910268	−	0.0910268i	0.660127	−	0.751154i	$-0.270502\pi$
$821$	−74.7330	−	74.7330i	−0.0910268	−	0.0910268i	−0.751154	+	0.660127i	$0.770502\pi$
$822$		0			0
$823$	−481.562	−	481.562i	−0.585131	−	0.585131i	0.351178	−	0.936309i	$-0.385781\pi$
$823$	−481.562	−	481.562i	−0.585131	−	0.585131i	−0.936309	+	0.351178i	$0.885781\pi$
$824$		0			0
$825$	−1029.34	−	859.589i	−1.24768	−	1.04193i
$826$		0			0
$827$			1232.64i			1.49049i	0.666789	+	0.745246i	$0.267668\pi$
$827$			1232.64i			1.49049i	−0.666789	+	0.745246i	$0.732332\pi$
$828$		0			0
$829$	−503.806	−	503.806i	−0.607727	−	0.607727i	0.334624	−	0.942352i	$-0.391391\pi$
$829$	−503.806	−	503.806i	−0.607727	−	0.607727i	−0.942352	+	0.334624i	$0.891391\pi$
$830$		0			0
$831$	1437.27			1.72957
$832$		0			0
$833$	106.048	−	106.048i	0.127308	−	0.127308i
$834$		0			0
$835$	−41.5502	−	926.575i	−0.0497607	−	1.10967i
$836$		0			0
$837$		−	815.096i		−	0.973830i
$838$		0			0
$839$	−949.352			−1.13153			−0.565764	−	0.824567i	$-0.691419\pi$
$839$	−949.352			−1.13153			−0.565764	+	0.824567i	$0.691419\pi$
$840$		0			0
$841$			634.054i			0.753929i
$842$		0			0
$843$	1163.94			1.38071
$844$		0			0
$845$	1094.78	−	1197.57i	1.29559	−	1.41725i
$846$		0			0
$847$	10.6821	+	10.6821i	0.0126116	+	0.0126116i
$848$		0			0
$849$			2317.47i			2.72964i
$850$		0			0
$851$	105.945	−	105.945i	0.124494	−	0.124494i
$852$		0			0
$853$	−331.721			−0.388887			−0.194444	−	0.980914i	$-0.562290\pi$
$853$	−331.721			−0.388887			−0.194444	+	0.980914i	$0.562290\pi$
$854$		0			0
$855$	88.3430	−	3.96154i	0.103325	−	0.00463338i
$856$		0			0
$857$	207.103	−	207.103i	0.241660	−	0.241660i	−0.575876	−	0.817537i	$-0.695339\pi$
$857$	207.103	−	207.103i	0.241660	−	0.241660i	0.817537	+	0.575876i	$0.195339\pi$
$858$		0			0
$859$	315.715	−	315.715i	0.367538	−	0.367538i	−0.499041	−	0.866579i	$-0.666314\pi$
$859$	315.715	−	315.715i	0.367538	−	0.367538i	0.866579	+	0.499041i	$0.166314\pi$
$860$		0			0
$861$	−1171.22	+	1171.22i	−1.36030	+	1.36030i
$862$		0			0
$863$	−278.969	+	278.969i	−0.323255	+	0.323255i	−0.850014	−	0.526760i	$-0.823407\pi$
$863$	−278.969	+	278.969i	−0.323255	+	0.323255i	0.526760	+	0.850014i	$0.323407\pi$
$864$		0			0
$865$	215.974	+	197.436i	0.249681	+	0.228250i
$866$		0			0
$867$	−1289.18			−1.48695
$868$		0			0
$869$	358.318	−	358.318i	0.412334	−	0.412334i
$870$		0			0
$871$		−	311.720i		−	0.357888i
$872$		0			0
$873$	471.794	+	471.794i	0.540428	+	0.540428i
$874$		0			0
$875$	−564.926	+	76.4085i	−0.645630	+	0.0873240i
$876$		0			0
$877$	−1338.50			−1.52623			−0.763114	−	0.646263i	$-0.776331\pi$
$877$	−1338.50			−1.52623			−0.763114	+	0.646263i	$0.776331\pi$
$878$		0			0
$879$		−	889.277i		−	1.01169i
$880$		0			0
$881$	−138.825			−0.157576			−0.0787881	−	0.996891i	$-0.525105\pi$
$881$	−138.825			−0.157576			−0.0787881	+	0.996891i	$0.525105\pi$
$882$		0			0
$883$			212.516i			0.240675i	0.992733	+	0.120337i	$0.0383976\pi$
$883$			212.516i			0.240675i	−0.992733	+	0.120337i	$0.961602\pi$
$884$		0			0
$885$	−2537.64	+	113.795i	−2.86740	+	0.128582i
$886$		0			0
$887$	−368.959	+	368.959i	−0.415963	+	0.415963i	−0.883810	−	0.467847i	$-0.845030\pi$
$887$	−368.959	+	368.959i	−0.415963	+	0.415963i	0.467847	+	0.883810i	$0.345030\pi$
$888$		0			0
$889$	645.095			0.725641
$890$		0			0
$891$	143.129	+	143.129i	0.160639	+	0.160639i
$892$		0			0
$893$		−	28.2643i		−	0.0316509i
$894$		0			0
$895$	807.158	−	36.1951i	0.901852	−	0.0404415i
$896$		0			0
$897$	−1349.36	−	1349.36i	−1.50430	−	1.50430i
$898$		0			0
$899$	−694.029	−	694.029i	−0.772001	−	0.772001i
$900$		0			0
$901$	110.295	+	110.295i	0.122414	+	0.122414i
$902$		0			0
$903$	279.881	+	279.881i	0.309946	+	0.309946i
$904$		0			0
$905$	−522.782	+	23.4430i	−0.577660	+	0.0259038i
$906$		0			0
$907$			783.206i			0.863513i	0.901990	+	0.431756i	$0.142106\pi$
$907$			783.206i			0.863513i	−0.901990	+	0.431756i	$0.857894\pi$
$908$		0			0
$909$	−341.304	−	341.304i	−0.375472	−	0.375472i
$910$		0			0
$911$	1463.16			1.60610			0.803052	−	0.595909i	$-0.203208\pi$
$911$	1463.16			1.60610			0.803052	+	0.595909i	$0.203208\pi$
$912$		0			0
$913$	−636.253	+	636.253i	−0.696882	+	0.696882i
$914$		0			0
$915$	688.494	−	30.8740i	0.752453	−	0.0337420i
$916$		0			0
$917$			314.754i			0.343244i
$918$		0			0
$919$	1217.73			1.32506			0.662529	−	0.749036i	$-0.269483\pi$
$919$	1217.73			1.32506			0.662529	+	0.749036i	$0.269483\pi$
$920$		0			0
$921$			544.445i			0.591146i
$922$		0			0
$923$	−2028.89			−2.19815
$924$		0			0
$925$	214.751	−	19.2989i	0.232163	−	0.0208636i
$926$		0			0
$927$	78.2635	+	78.2635i	0.0844266	+	0.0844266i
$928$		0			0
$929$		−	169.265i		−	0.182201i	−0.995842	−	0.0911004i	$-0.970962\pi$
$929$		−	169.265i		−	0.182201i	0.995842	−	0.0911004i	$-0.0290384\pi$
$930$		0			0
$931$	−22.8274	+	22.8274i	−0.0245192	+	0.0245192i
$932$		0			0
$933$	−265.833			−0.284923
$934$		0			0
$935$	212.903	+	194.628i	0.227704	+	0.208159i
$936$		0			0
$937$	457.486	−	457.486i	0.488245	−	0.488245i	−0.419507	−	0.907752i	$-0.637797\pi$
$937$	457.486	−	457.486i	0.488245	−	0.488245i	0.907752	+	0.419507i	$0.137797\pi$
$938$		0			0
$939$	−820.653	+	820.653i	−0.873965	+	0.873965i
$940$		0			0
$941$	−206.539	+	206.539i	−0.219489	+	0.219489i	−0.808283	−	0.588794i	$-0.799603\pi$
$941$	−206.539	+	206.539i	−0.219489	+	0.219489i	0.588794	+	0.808283i	$0.299603\pi$
$942$		0			0
$943$	902.259	−	902.259i	0.956797	−	0.956797i
$944$		0			0
$945$	726.561	−	32.5810i	0.768848	−	0.0344772i
$946$		0			0
$947$	−952.719			−1.00604			−0.503019	−	0.864275i	$-0.667778\pi$
$947$	−952.719			−1.00604			−0.503019	+	0.864275i	$0.667778\pi$
$948$		0			0
$949$	950.065	−	950.065i	1.00112	−	1.00112i
$950$		0			0
$951$			199.923i			0.210224i
$952$		0			0
$953$	830.106	+	830.106i	0.871045	+	0.871045i	0.992586	−	0.121542i	$-0.0387838\pi$
$953$	830.106	+	830.106i	0.871045	+	0.871045i	−0.121542	+	0.992586i	$0.538784\pi$
$954$		0			0
$955$	312.118	−	341.425i	0.326825	−	0.357513i
$956$		0			0
$957$	2060.21			2.15278
$958$		0			0
$959$			749.409i			0.781448i
$960$		0			0
$961$	−307.904			−0.320400
$962$		0			0
$963$			845.027i			0.877494i
$964$		0			0
$965$	16.7473	+	373.467i	0.0173547	+	0.387012i
$966$		0			0
$967$	34.0691	−	34.0691i	0.0352318	−	0.0352318i	−0.689271	−	0.724503i	$-0.742069\pi$
$967$	34.0691	−	34.0691i	0.0352318	−	0.0352318i	0.724503	+	0.689271i	$0.242069\pi$
$968$		0			0
$969$	−30.1017			−0.0310647
$970$		0			0
$971$	84.7430	+	84.7430i	0.0872739	+	0.0872739i	0.749396	−	0.662122i	$-0.230344\pi$
$971$	84.7430	+	84.7430i	0.0872739	+	0.0872739i	−0.662122	+	0.749396i	$0.730344\pi$
$972$		0			0
$973$			165.095i			0.169676i
$974$		0			0
$975$	−245.799	−	2735.17i	−0.252102	−	2.80530i
$976$		0			0
$977$	28.0540	+	28.0540i	0.0287145	+	0.0287145i	0.721318	−	0.692604i	$-0.243537\pi$
$977$	28.0540	+	28.0540i	0.0287145	+	0.0287145i	−0.692604	+	0.721318i	$0.743537\pi$
$978$		0			0
$979$	1006.01	+	1006.01i	1.02759	+	1.02759i
$980$		0			0
$981$	1265.28	+	1265.28i	1.28978	+	1.28978i
$982$		0			0
$983$	359.158	+	359.158i	0.365370	+	0.365370i	0.865785	−	0.500416i	$-0.166819\pi$
$983$	359.158	+	359.158i	0.365370	+	0.365370i	−0.500416	+	0.865785i	$0.666819\pi$
$984$		0			0
$985$	366.872	+	335.381i	0.372459	+	0.340489i
$986$		0			0
$987$		−	556.795i		−	0.564129i
$988$		0			0
$989$	−215.608	−	215.608i	−0.218006	−	0.218006i
$990$		0			0
$991$	−301.699			−0.304439			−0.152219	−	0.988347i	$-0.548642\pi$
$991$	−301.699			−0.304439			−0.152219	+	0.988347i	$0.548642\pi$
$992$		0			0
$993$	533.755	−	533.755i	0.537517	−	0.537517i
$994$		0			0
$995$	894.571	−	978.568i	0.899067	−	0.983485i
$996$		0			0
$997$			701.351i			0.703461i	0.936101	+	0.351731i	$0.114407\pi$
$997$			701.351i			0.703461i	−0.936101	+	0.351731i	$0.885593\pi$
$998$		0			0
$999$	−275.082			−0.275357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.i.a.177.3		44
4.3	odd	2		80.3.i.a.37.1	yes	44
5.3	odd	4		320.3.t.a.113.20		44
8.3	odd	2		640.3.i.b.97.3		44
8.5	even	2		640.3.i.a.97.20		44
16.3	odd	4		80.3.t.a.77.12	yes	44
16.5	even	4		640.3.t.a.417.3		44
16.11	odd	4		640.3.t.b.417.20		44
16.13	even	4		320.3.t.a.17.20		44
20.3	even	4		80.3.t.a.53.12	yes	44
20.7	even	4		400.3.t.b.293.11		44
20.19	odd	2		400.3.i.b.357.22		44
40.3	even	4		640.3.t.b.353.20		44
40.13	odd	4		640.3.t.a.353.3		44
80.3	even	4		80.3.i.a.13.1	✓	44
80.13	odd	4	inner	320.3.i.a.273.20		44
80.19	odd	4		400.3.t.b.157.11		44
80.43	even	4		640.3.i.b.33.20		44
80.53	odd	4		640.3.i.a.33.3		44
80.67	even	4		400.3.i.b.93.22		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.1	✓	44	80.3	even	4
80.3.i.a.37.1	yes	44	4.3	odd	2
80.3.t.a.53.12	yes	44	20.3	even	4
80.3.t.a.77.12	yes	44	16.3	odd	4
320.3.i.a.177.3		44	1.1	even	1	trivial
320.3.i.a.273.20		44	80.13	odd	4	inner
320.3.t.a.17.20		44	16.13	even	4
320.3.t.a.113.20		44	5.3	odd	4
400.3.i.b.93.22		44	80.67	even	4
400.3.i.b.357.22		44	20.19	odd	2
400.3.t.b.157.11		44	80.19	odd	4
400.3.t.b.293.11		44	20.7	even	4
640.3.i.a.33.3		44	80.53	odd	4
640.3.i.a.97.20		44	8.5	even	2
640.3.i.b.33.20		44	80.43	even	4
640.3.i.b.97.3		44	8.3	odd	2
640.3.t.a.353.3		44	40.13	odd	4
640.3.t.a.417.3		44	16.5	even	4
640.3.t.b.353.20		44	40.3	even	4
640.3.t.b.417.20		44	16.11	odd	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-4.94472i q^{3} +(-3.37360 + 3.69037i) q^{5} +(-3.22480 + 3.22480i) q^{7} -15.4503 q^{9} +O(q^{10})\)	\(q-4.94472i q^{3} +(-3.37360 + 3.69037i) q^{5} +(-3.22480 + 3.22480i) q^{7} -15.4503 q^{9} +(7.67097 + 7.67097i) q^{11} +22.2152i q^{13} +(18.2478 + 16.6815i) q^{15} +(-3.76038 - 3.76038i) q^{17} +(0.809445 + 0.809445i) q^{19} +(15.9458 + 15.9458i) q^{21} +(-12.2839 - 12.2839i) q^{23} +(-2.23764 - 24.8997i) q^{25} +31.8948i q^{27} +(27.1574 + 27.1574i) q^{29} -25.5557 q^{31} +(37.9308 - 37.9308i) q^{33} +(-1.02151 - 22.7799i) q^{35} +8.62466i q^{37} +109.848 q^{39} +73.4504i q^{41} +17.5521 q^{43} +(52.1231 - 57.0172i) q^{45} +(-17.4590 - 17.4590i) q^{47} +28.2013i q^{49} +(-18.5940 + 18.5940i) q^{51} -29.3309 q^{53} +(-54.1875 + 2.42991i) q^{55} +(4.00248 - 4.00248i) q^{57} +(-72.6508 + 72.6508i) q^{59} +(19.7110 - 19.7110i) q^{61} +(49.8241 - 49.8241i) q^{63} +(-81.9821 - 74.9451i) q^{65} -14.0319 q^{67} +(-60.7406 + 60.7406i) q^{69} +91.3292i q^{71} +(-42.7665 - 42.7665i) q^{73} +(-123.122 + 11.0645i) q^{75} -49.4747 q^{77} -46.7110i q^{79} +18.6585 q^{81} +82.9430i q^{83} +(26.5632 - 1.19117i) q^{85} +(134.286 - 134.286i) q^{87} +131.145 q^{89} +(-71.6395 - 71.6395i) q^{91} +126.366i q^{93} +(-5.71789 + 0.256406i) q^{95} +(-30.5363 - 30.5363i) q^{97} +(-118.519 - 118.519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^5 - 108 * q^9	\( 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 380 * q^95 - 4 * q^97 + 92 * q^99

Introduction

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