LMFDB - Embedded newform 320.3.r.a.271.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(111,320)]

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([2, 3, 0]))

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

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

chi := DirichletCharacter("320.111");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.r (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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			271.13
Character	$\chi$	$=$	320.271
Dual form			320.3.r.a.111.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05924 + 2.05924i) q^{3} +(1.58114 + 1.58114i) q^{5} -10.3931 q^{7} -0.519079i q^{9} +O(q^{10})$	\(q+(2.05924 + 2.05924i) q^{3} +(1.58114 + 1.58114i) q^{5} -10.3931 q^{7} -0.519079i q^{9} +(-14.0477 + 14.0477i) q^{11} +(-9.77323 + 9.77323i) q^{13} +6.51188i q^{15} +7.10104 q^{17} +(16.6198 + 16.6198i) q^{19} +(-21.4020 - 21.4020i) q^{21} -24.8307 q^{23} +5.00000i q^{25} +(19.6020 - 19.6020i) q^{27} +(11.2993 - 11.2993i) q^{29} +7.04353i q^{31} -57.8551 q^{33} +(-16.4330 - 16.4330i) q^{35} +(11.2634 + 11.2634i) q^{37} -40.2508 q^{39} +62.6084i q^{41} +(37.0749 - 37.0749i) q^{43} +(0.820736 - 0.820736i) q^{45} +0.176089i q^{47} +59.0176 q^{49} +(14.6227 + 14.6227i) q^{51} +(-32.3810 - 32.3810i) q^{53} -44.4227 q^{55} +68.4483i q^{57} +(-25.8843 + 25.8843i) q^{59} +(-36.8700 + 36.8700i) q^{61} +5.39487i q^{63} -30.9057 q^{65} +(12.8767 + 12.8767i) q^{67} +(-51.1323 - 51.1323i) q^{69} +64.6644 q^{71} +19.2006i q^{73} +(-10.2962 + 10.2962i) q^{75} +(146.000 - 146.000i) q^{77} -48.9106i q^{79} +76.0588 q^{81} +(18.5930 + 18.5930i) q^{83} +(11.2277 + 11.2277i) q^{85} +46.5359 q^{87} +43.4973i q^{89} +(101.575 - 101.575i) q^{91} +(-14.5043 + 14.5043i) q^{93} +52.5565i q^{95} -115.574 q^{97} +(7.29186 + 7.29186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) $ 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	2.05924	+	2.05924i	0.686413	+	0.686413i	0.961437	−	0.275025i	$-0.0886860\pi$
$3$	2.05924	+	2.05924i	0.686413	+	0.686413i	−0.275025	+	0.961437i	$0.588686\pi$
$4$		0			0
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$		0			0
$7$	−10.3931			−1.48474			−0.742368	−	0.669993i	$-0.766297\pi$
$7$	−10.3931			−1.48474			−0.742368	+	0.669993i	$0.766297\pi$
$8$		0			0
$9$		−	0.519079i		−	0.0576755i
$10$		0			0
$11$	−14.0477	+	14.0477i	−1.27706	+	1.27706i	−0.334759	+	0.942304i	$0.608655\pi$
$11$	−14.0477	+	14.0477i	−1.27706	+	1.27706i	−0.942304	+	0.334759i	$0.891345\pi$
$12$		0			0
$13$	−9.77323	+	9.77323i	−0.751787	+	0.751787i	−0.974813	−	0.223026i	$-0.928407\pi$
$13$	−9.77323	+	9.77323i	−0.751787	+	0.751787i	0.223026	+	0.974813i	$0.428407\pi$
$14$		0			0
$15$			6.51188i			0.434125i
$16$		0			0
$17$	7.10104			0.417709			0.208854	−	0.977947i	$-0.433027\pi$
$17$	7.10104			0.417709			0.208854	+	0.977947i	$0.433027\pi$
$18$		0			0
$19$	16.6198	+	16.6198i	0.874727	+	0.874727i	0.992983	−	0.118256i	$-0.0377303\pi$
$19$	16.6198	+	16.6198i	0.874727	+	0.874727i	−0.118256	+	0.992983i	$0.537730\pi$
$20$		0			0
$21$	−21.4020	−	21.4020i	−1.01914	−	1.01914i
$22$		0			0
$23$	−24.8307			−1.07959			−0.539797	−	0.841795i	$-0.681499\pi$
$23$	−24.8307			−1.07959			−0.539797	+	0.841795i	$0.681499\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	19.6020	−	19.6020i	0.726002	−	0.726002i
$28$		0			0
$29$	11.2993	−	11.2993i	0.389631	−	0.389631i	−0.484925	−	0.874556i	$-0.661153\pi$
$29$	11.2993	−	11.2993i	0.389631	−	0.389631i	0.874556	+	0.484925i	$0.161153\pi$
$30$		0			0
$31$			7.04353i			0.227211i	0.993526	+	0.113605i	$0.0362399\pi$
$31$			7.04353i			0.227211i	−0.993526	+	0.113605i	$0.963760\pi$
$32$		0			0
$33$	−57.8551			−1.75318
$34$		0			0
$35$	−16.4330	−	16.4330i	−0.469515	−	0.469515i
$36$		0			0
$37$	11.2634	+	11.2634i	0.304417	+	0.304417i	0.842739	−	0.538322i	$-0.180942\pi$
$37$	11.2634	+	11.2634i	0.304417	+	0.304417i	−0.538322	+	0.842739i	$0.680942\pi$
$38$		0			0
$39$	−40.2508			−1.03207
$40$		0			0
$41$			62.6084i			1.52704i	0.645787	+	0.763518i	$0.276529\pi$
$41$			62.6084i			1.52704i	−0.645787	+	0.763518i	$0.723471\pi$
$42$		0			0
$43$	37.0749	−	37.0749i	0.862206	−	0.862206i	−0.129388	−	0.991594i	$-0.541301\pi$
$43$	37.0749	−	37.0749i	0.862206	−	0.862206i	0.991594	+	0.129388i	$0.0413013\pi$
$44$		0			0
$45$	0.820736	−	0.820736i	0.0182386	−	0.0182386i
$46$		0			0
$47$			0.176089i			0.00374658i	0.999998	+	0.00187329i	$0.000596286\pi$
$47$			0.176089i			0.00374658i	−0.999998	+	0.00187329i	$0.999404\pi$
$48$		0			0
$49$	59.0176			1.20444
$50$		0			0
$51$	14.6227	+	14.6227i	0.286720	+	0.286720i
$52$		0			0
$53$	−32.3810	−	32.3810i	−0.610963	−	0.610963i	0.332234	−	0.943197i	$-0.392198\pi$
$53$	−32.3810	−	32.3810i	−0.610963	−	0.610963i	−0.943197	+	0.332234i	$0.892198\pi$
$54$		0			0
$55$	−44.4227			−0.807686
$56$		0			0
$57$			68.4483i			1.20085i
$58$		0			0
$59$	−25.8843	+	25.8843i	−0.438718	+	0.438718i	−0.891580	−	0.452863i	$-0.850403\pi$
$59$	−25.8843	+	25.8843i	−0.438718	+	0.438718i	0.452863	+	0.891580i	$0.350403\pi$
$60$		0			0
$61$	−36.8700	+	36.8700i	−0.604426	+	0.604426i	−0.941484	−	0.337058i	$-0.890568\pi$
$61$	−36.8700	+	36.8700i	−0.604426	+	0.604426i	0.337058	+	0.941484i	$0.390568\pi$
$62$		0			0
$63$			5.39487i			0.0856328i
$64$		0			0
$65$	−30.9057			−0.475472
$66$		0			0
$67$	12.8767	+	12.8767i	0.192190	+	0.192190i	0.796642	−	0.604452i	$-0.206608\pi$
$67$	12.8767	+	12.8767i	0.192190	+	0.192190i	−0.604452	+	0.796642i	$0.706608\pi$
$68$		0			0
$69$	−51.1323	−	51.1323i	−0.741047	−	0.741047i
$70$		0			0
$71$	64.6644			0.910767			0.455383	−	0.890295i	$-0.349502\pi$
$71$	64.6644			0.910767			0.455383	+	0.890295i	$0.349502\pi$
$72$		0			0
$73$			19.2006i			0.263022i	0.991315	+	0.131511i	$0.0419828\pi$
$73$			19.2006i			0.263022i	−0.991315	+	0.131511i	$0.958017\pi$
$74$		0			0
$75$	−10.2962	+	10.2962i	−0.137283	+	0.137283i
$76$		0			0
$77$	146.000	−	146.000i	1.89610	−	1.89610i
$78$		0			0
$79$		−	48.9106i		−	0.619121i	−0.950880	−	0.309561i	$-0.899818\pi$
$79$		−	48.9106i		−	0.619121i	0.950880	−	0.309561i	$-0.100182\pi$
$80$		0			0
$81$	76.0588			0.938998
$82$		0			0
$83$	18.5930	+	18.5930i	0.224012	+	0.224012i	0.810185	−	0.586174i	$-0.199366\pi$
$83$	18.5930	+	18.5930i	0.224012	+	0.224012i	−0.586174	+	0.810185i	$0.699366\pi$
$84$		0			0
$85$	11.2277	+	11.2277i	0.132091	+	0.132091i
$86$		0			0
$87$	46.5359			0.534895
$88$		0			0
$89$			43.4973i			0.488734i	0.969683	+	0.244367i	$0.0785801\pi$
$89$			43.4973i			0.488734i	−0.969683	+	0.244367i	$0.921420\pi$
$90$		0			0
$91$	101.575	−	101.575i	1.11620	−	1.11620i
$92$		0			0
$93$	−14.5043	+	14.5043i	−0.155960	+	0.155960i
$94$		0			0
$95$			52.5565i			0.553226i
$96$		0			0
$97$	−115.574			−1.19148			−0.595741	−	0.803177i	$-0.703141\pi$
$97$	−115.574			−1.19148			−0.595741	+	0.803177i	$0.703141\pi$
$98$		0			0
$99$	7.29186	+	7.29186i	0.0736552	+	0.0736552i
$100$		0			0
$101$	90.9433	+	90.9433i	0.900428	+	0.900428i	0.995473	−	0.0950446i	$-0.0302994\pi$
$101$	90.9433	+	90.9433i	0.900428	+	0.900428i	−0.0950446	+	0.995473i	$0.530299\pi$
$102$		0			0
$103$	−41.0401			−0.398447			−0.199224	−	0.979954i	$-0.563842\pi$
$103$	−41.0401			−0.398447			−0.199224	+	0.979954i	$0.563842\pi$
$104$		0			0
$105$		−	67.6790i		−	0.644562i
$106$		0			0
$107$	91.4653	−	91.4653i	0.854816	−	0.854816i	−0.135906	−	0.990722i	$-0.543395\pi$
$107$	91.4653	−	91.4653i	0.854816	−	0.854816i	0.990722	+	0.135906i	$0.0433946\pi$
$108$		0			0
$109$	76.9281	−	76.9281i	0.705762	−	0.705762i	−0.259879	−	0.965641i	$-0.583683\pi$
$109$	76.9281	−	76.9281i	0.705762	−	0.705762i	0.965641	+	0.259879i	$0.0836827\pi$
$110$		0			0
$111$			46.3881i			0.417911i
$112$		0			0
$113$	37.6147			0.332873			0.166437	−	0.986052i	$-0.446774\pi$
$113$	37.6147			0.332873			0.166437	+	0.986052i	$0.446774\pi$
$114$		0			0
$115$	−39.2608	−	39.2608i	−0.341398	−	0.341398i
$116$		0			0
$117$	5.07308	+	5.07308i	0.0433597	+	0.0433597i
$118$		0			0
$119$	−73.8022			−0.620187
$120$		0			0
$121$		−	273.675i		−	2.26178i
$122$		0			0
$123$	−128.926	+	128.926i	−1.04818	+	1.04818i
$124$		0			0
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$		0			0
$127$			76.6673i			0.603680i	0.953359	+	0.301840i	$0.0976008\pi$
$127$			76.6673i			0.603680i	−0.953359	+	0.301840i	$0.902399\pi$
$128$		0			0
$129$	152.692			1.18366
$130$		0			0
$131$	12.4149	+	12.4149i	0.0947700	+	0.0947700i	0.752902	−	0.658132i	$-0.228653\pi$
$131$	12.4149	+	12.4149i	0.0947700	+	0.0947700i	−0.658132	+	0.752902i	$0.728653\pi$
$132$		0			0
$133$	−172.732	−	172.732i	−1.29874	−	1.29874i
$134$		0			0
$135$	61.9871			0.459164
$136$		0			0
$137$			31.3649i			0.228941i	0.993427	+	0.114470i	$0.0365171\pi$
$137$			31.3649i			0.228941i	−0.993427	+	0.114470i	$0.963483\pi$
$138$		0			0
$139$	−9.05252	+	9.05252i	−0.0651260	+	0.0651260i	−0.738920	−	0.673794i	$-0.764664\pi$
$139$	−9.05252	+	9.05252i	−0.0651260	+	0.0651260i	0.673794	+	0.738920i	$0.264664\pi$
$140$		0			0
$141$	−0.362609	+	0.362609i	−0.00257170	+	0.00257170i
$142$		0			0
$143$		−	274.583i		−	1.92016i
$144$		0			0
$145$	35.7315			0.246424
$146$		0			0
$147$	121.531	+	121.531i	0.826743	+	0.826743i
$148$		0			0
$149$	165.486	+	165.486i	1.11064	+	1.11064i	0.993063	+	0.117581i	$0.0375141\pi$
$149$	165.486	+	165.486i	1.11064	+	1.11064i	0.117581	+	0.993063i	$0.462486\pi$
$150$		0			0
$151$	192.683			1.27605			0.638024	−	0.770016i	$-0.279752\pi$
$151$	192.683			1.27605			0.638024	+	0.770016i	$0.279752\pi$
$152$		0			0
$153$		−	3.68600i		−	0.0240915i
$154$		0			0
$155$	−11.1368	+	11.1368i	−0.0718503	+	0.0718503i
$156$		0			0
$157$	−65.5629	+	65.5629i	−0.417598	+	0.417598i	−0.884375	−	0.466777i	$-0.845415\pi$
$157$	−65.5629	+	65.5629i	−0.417598	+	0.417598i	0.466777	+	0.884375i	$0.345415\pi$
$158$		0			0
$159$		−	133.360i		−	0.838745i
$160$		0			0
$161$	258.069			1.60291
$162$		0			0
$163$	−164.309	−	164.309i	−1.00803	−	1.00803i	−0.999967	−	0.00806604i	$-0.997432\pi$
$163$	−164.309	−	164.309i	−1.00803	−	1.00803i	−0.00806604	−	0.999967i	$-0.502568\pi$
$164$		0			0
$165$	−91.4769	−	91.4769i	−0.554406	−	0.554406i
$166$		0			0
$167$	−107.045			−0.640987			−0.320494	−	0.947251i	$-0.603849\pi$
$167$	−107.045			−0.640987			−0.320494	+	0.947251i	$0.603849\pi$
$168$		0			0
$169$		−	22.0320i		−	0.130367i
$170$		0			0
$171$	8.62700	−	8.62700i	0.0504503	−	0.0504503i
$172$		0			0
$173$	−216.322	+	216.322i	−1.25042	+	1.25042i	−0.294886	+	0.955533i	$0.595282\pi$
$173$	−216.322	+	216.322i	−1.25042	+	1.25042i	−0.955533	+	0.294886i	$0.904718\pi$
$174$		0			0
$175$		−	51.9657i		−	0.296947i
$176$		0			0
$177$	−106.604			−0.602283
$178$		0			0
$179$	149.660	+	149.660i	0.836091	+	0.836091i	0.988342	−	0.152251i	$-0.0486522\pi$
$179$	149.660	+	149.660i	0.836091	+	0.836091i	−0.152251	+	0.988342i	$0.548652\pi$
$180$		0			0
$181$	117.050	+	117.050i	0.646684	+	0.646684i	0.952190	−	0.305506i	$-0.0988256\pi$
$181$	117.050	+	117.050i	0.646684	+	0.646684i	−0.305506	+	0.952190i	$0.598826\pi$
$182$		0			0
$183$	−151.848			−0.829771
$184$		0			0
$185$			35.6180i			0.192530i
$186$		0			0
$187$	−99.7533	+	99.7533i	−0.533440	+	0.533440i
$188$		0			0
$189$	−203.727	+	203.727i	−1.07792	+	1.07792i
$190$		0			0
$191$			264.175i			1.38312i	0.722321	+	0.691558i	$0.243075\pi$
$191$			264.175i			1.38312i	−0.722321	+	0.691558i	$0.756925\pi$
$192$		0			0
$193$	−350.764			−1.81743			−0.908715	−	0.417418i	$-0.862935\pi$
$193$	−350.764			−1.81743			−0.908715	+	0.417418i	$0.862935\pi$
$194$		0			0
$195$	−63.6421	−	63.6421i	−0.326370	−	0.326370i
$196$		0			0
$197$	165.437	+	165.437i	0.839782	+	0.839782i	0.988830	−	0.149048i	$-0.0476208\pi$
$197$	165.437	+	165.437i	0.839782	+	0.839782i	−0.149048	+	0.988830i	$0.547621\pi$
$198$		0			0
$199$	140.603			0.706547			0.353274	−	0.935520i	$-0.385068\pi$
$199$	140.603			0.706547			0.353274	+	0.935520i	$0.385068\pi$
$200$		0			0
$201$			53.0324i			0.263843i
$202$		0			0
$203$	−117.435	+	117.435i	−0.578499	+	0.578499i
$204$		0			0
$205$	−98.9926	+	98.9926i	−0.482891	+	0.482891i
$206$		0			0
$207$			12.8891i			0.0622661i
$208$		0			0
$209$	−466.940			−2.23416
$210$		0			0
$211$	−280.563	−	280.563i	−1.32968	−	1.32968i	−0.905643	−	0.424040i	$-0.860612\pi$
$211$	−280.563	−	280.563i	−1.32968	−	1.32968i	−0.424040	−	0.905643i	$-0.639388\pi$
$212$		0			0
$213$	133.159	+	133.159i	0.625162	+	0.625162i
$214$		0			0
$215$	117.241			0.545307
$216$		0			0
$217$		−	73.2044i		−	0.337348i
$218$		0			0
$219$	−39.5386	+	39.5386i	−0.180542	+	0.180542i
$220$		0			0
$221$	−69.4001	+	69.4001i	−0.314028	+	0.314028i
$222$		0			0
$223$			227.136i			1.01855i	0.860604	+	0.509275i	$0.170086\pi$
$223$			227.136i			1.01855i	−0.860604	+	0.509275i	$0.829914\pi$
$224$		0			0
$225$	2.59540			0.0115351
$226$		0			0
$227$	−16.8393	−	16.8393i	−0.0741820	−	0.0741820i	0.669042	−	0.743224i	$-0.266704\pi$
$227$	−16.8393	−	16.8393i	−0.0741820	−	0.0741820i	−0.743224	+	0.669042i	$0.766704\pi$
$228$		0			0
$229$	−186.956	−	186.956i	−0.816400	−	0.816400i	0.169184	−	0.985584i	$-0.445887\pi$
$229$	−186.956	−	186.956i	−0.816400	−	0.816400i	−0.985584	+	0.169184i	$0.945887\pi$
$230$		0			0
$231$	601.296			2.60302
$232$		0			0
$233$		−	43.8154i		−	0.188049i	−0.995570	−	0.0940245i	$-0.970027\pi$
$233$		−	43.8154i		−	0.188049i	0.995570	−	0.0940245i	$-0.0299732\pi$
$234$		0			0
$235$	−0.278421	+	0.278421i	−0.00118477	+	0.00118477i
$236$		0			0
$237$	100.719	−	100.719i	0.424973	−	0.424973i
$238$		0			0
$239$			101.703i			0.425534i	0.977103	+	0.212767i	$0.0682475\pi$
$239$			101.703i			0.425534i	−0.977103	+	0.212767i	$0.931752\pi$
$240$		0			0
$241$	101.753			0.422211			0.211105	−	0.977463i	$-0.432294\pi$
$241$	101.753			0.422211			0.211105	+	0.977463i	$0.432294\pi$
$242$		0			0
$243$	−19.7952	−	19.7952i	−0.0814617	−	0.0814617i
$244$		0			0
$245$	93.3149	+	93.3149i	0.380877	+	0.380877i
$246$		0			0
$247$	−324.859			−1.31522
$248$		0			0
$249$			76.5747i			0.307529i
$250$		0			0
$251$	−250.137	+	250.137i	−0.996562	+	0.996562i	−0.999994	−	0.00343190i	$-0.998908\pi$
$251$	−250.137	+	250.137i	−0.996562	+	0.996562i	0.00343190	+	0.999994i	$0.498908\pi$
$252$		0			0
$253$	348.814	−	348.814i	1.37871	−	1.37871i
$254$		0			0
$255$			46.2412i			0.181338i
$256$		0			0
$257$	−30.7854			−0.119788			−0.0598938	−	0.998205i	$-0.519076\pi$
$257$	−30.7854			−0.119788			−0.0598938	+	0.998205i	$0.519076\pi$
$258$		0			0
$259$	−117.062	−	117.062i	−0.451978	−	0.451978i
$260$		0			0
$261$	−5.86523	−	5.86523i	−0.0224721	−	0.0224721i
$262$		0			0
$263$	−33.6453			−0.127929			−0.0639644	−	0.997952i	$-0.520374\pi$
$263$	−33.6453			−0.127929			−0.0639644	+	0.997952i	$0.520374\pi$
$264$		0			0
$265$		−	102.398i		−	0.386407i
$266$		0			0
$267$	−89.5713	+	89.5713i	−0.335473	+	0.335473i
$268$		0			0
$269$	181.278	−	181.278i	0.673897	−	0.673897i	−0.284715	−	0.958612i	$-0.591899\pi$
$269$	181.278	−	181.278i	0.673897	−	0.673897i	0.958612	+	0.284715i	$0.0918990\pi$
$270$		0			0
$271$		−	116.847i		−	0.431172i	−0.976485	−	0.215586i	$-0.930834\pi$
$271$		−	116.847i		−	0.431172i	0.976485	−	0.215586i	$-0.0691661\pi$
$272$		0			0
$273$	418.333			1.53235
$274$		0			0
$275$	−70.2385	−	70.2385i	−0.255413	−	0.255413i
$276$		0			0
$277$	−147.875	−	147.875i	−0.533845	−	0.533845i	0.387870	−	0.921714i	$-0.373211\pi$
$277$	−147.875	−	147.875i	−0.533845	−	0.533845i	−0.921714	+	0.387870i	$0.873211\pi$
$278$		0			0
$279$	3.65615			0.0131045
$280$		0			0
$281$		−	483.500i		−	1.72064i	−0.509754	−	0.860320i	$-0.670264\pi$
$281$		−	483.500i		−	1.72064i	0.509754	−	0.860320i	$-0.329736\pi$
$282$		0			0
$283$	−63.7806	+	63.7806i	−0.225373	+	0.225373i	−0.810757	−	0.585383i	$-0.800944\pi$
$283$	−63.7806	+	63.7806i	−0.225373	+	0.225373i	0.585383	+	0.810757i	$0.300944\pi$
$284$		0			0
$285$	−108.226	+	108.226i	−0.379741	+	0.379741i
$286$		0			0
$287$		−	650.699i		−	2.26724i
$288$		0			0
$289$	−238.575			−0.825520
$290$		0			0
$291$	−237.994	−	237.994i	−0.817848	−	0.817848i
$292$		0			0
$293$	175.050	+	175.050i	0.597440	+	0.597440i	0.939631	−	0.342191i	$-0.111169\pi$
$293$	175.050	+	175.050i	0.597440	+	0.597440i	−0.342191	+	0.939631i	$0.611169\pi$
$294$		0			0
$295$	−81.8535			−0.277469
$296$		0			0
$297$			550.727i			1.85430i
$298$		0			0
$299$	242.676	−	242.676i	0.811625	−	0.811625i
$300$		0			0
$301$	−385.325	+	385.325i	−1.28015	+	1.28015i
$302$		0			0
$303$			374.548i			1.23613i
$304$		0			0
$305$	−116.593			−0.382273
$306$		0			0
$307$	413.683	+	413.683i	1.34750	+	1.34750i	0.888367	+	0.459133i	$0.151840\pi$
$307$	413.683	+	413.683i	1.34750	+	1.34750i	0.459133	+	0.888367i	$0.348160\pi$
$308$		0			0
$309$	−84.5113	−	84.5113i	−0.273499	−	0.273499i
$310$		0			0
$311$	−363.740			−1.16958			−0.584791	−	0.811184i	$-0.698823\pi$
$311$	−363.740			−1.16958			−0.584791	+	0.811184i	$0.698823\pi$
$312$		0			0
$313$		−	281.938i		−	0.900760i	−0.892837	−	0.450380i	$-0.851288\pi$
$313$		−	281.938i		−	0.900760i	0.892837	−	0.450380i	$-0.148712\pi$
$314$		0			0
$315$	−8.53003	+	8.53003i	−0.0270795	+	0.0270795i
$316$		0			0
$317$	271.946	−	271.946i	0.857873	−	0.857873i	−0.133215	−	0.991087i	$-0.542530\pi$
$317$	271.946	−	271.946i	0.857873	−	0.857873i	0.991087	+	0.133215i	$0.0425299\pi$
$318$		0			0
$319$			317.458i			0.995166i
$320$		0			0
$321$	376.697			1.17351
$322$		0			0
$323$	118.018	+	118.018i	0.365381	+	0.365381i
$324$		0			0
$325$	−48.8661	−	48.8661i	−0.150357	−	0.150357i
$326$		0			0
$327$	316.826			0.968888
$328$		0			0
$329$		−	1.83012i		−	0.00556267i
$330$		0			0
$331$	87.1363	−	87.1363i	0.263252	−	0.263252i	−0.563122	−	0.826374i	$-0.690400\pi$
$331$	87.1363	−	87.1363i	0.263252	−	0.263252i	0.826374	+	0.563122i	$0.190400\pi$
$332$		0			0
$333$	5.84660	−	5.84660i	0.0175574	−	0.0175574i
$334$		0			0
$335$			40.7197i			0.121551i
$336$		0			0
$337$	480.244			1.42506			0.712528	−	0.701644i	$-0.247550\pi$
$337$	480.244			1.42506			0.712528	+	0.701644i	$0.247550\pi$
$338$		0			0
$339$	77.4576	+	77.4576i	0.228488	+	0.228488i
$340$		0			0
$341$	−98.9453	−	98.9453i	−0.290162	−	0.290162i
$342$		0			0
$343$	−104.114			−0.303539
$344$		0			0
$345$		−	161.694i		−	0.468680i
$346$		0			0
$347$	−108.368	+	108.368i	−0.312299	+	0.312299i	−0.845800	−	0.533501i	$-0.820876\pi$
$347$	−108.368	+	108.368i	−0.312299	+	0.312299i	0.533501	+	0.845800i	$0.320876\pi$
$348$		0			0
$349$	82.3704	−	82.3704i	0.236018	−	0.236018i	−0.579181	−	0.815199i	$-0.696627\pi$
$349$	82.3704	−	82.3704i	0.236018	−	0.236018i	0.815199	+	0.579181i	$0.196627\pi$
$350$		0			0
$351$			383.151i			1.09160i
$352$		0			0
$353$	−401.677			−1.13790			−0.568948	−	0.822373i	$-0.692650\pi$
$353$	−401.677			−1.13790			−0.568948	+	0.822373i	$0.692650\pi$
$354$		0			0
$355$	102.243	+	102.243i	0.288010	+	0.288010i
$356$		0			0
$357$	−151.976	−	151.976i	−0.425704	−	0.425704i
$358$		0			0
$359$	276.390			0.769890			0.384945	−	0.922940i	$-0.374220\pi$
$359$	276.390			0.769890			0.384945	+	0.922940i	$0.374220\pi$
$360$		0			0
$361$			191.437i			0.530295i
$362$		0			0
$363$	563.563	−	563.563i	1.55251	−	1.55251i
$364$		0			0
$365$	−30.3588	+	30.3588i	−0.0831748	+	0.0831748i
$366$		0			0
$367$		−	669.742i		−	1.82491i	−0.409177	−	0.912455i	$-0.634184\pi$
$367$		−	669.742i		−	1.82491i	0.409177	−	0.912455i	$-0.365816\pi$
$368$		0			0
$369$	32.4987			0.0880725
$370$		0			0
$371$	336.541	+	336.541i	0.907118	+	0.907118i
$372$		0			0
$373$	−79.6410	−	79.6410i	−0.213515	−	0.213515i	0.592244	−	0.805759i	$-0.298242\pi$
$373$	−79.6410	−	79.6410i	−0.213515	−	0.213515i	−0.805759	+	0.592244i	$0.798242\pi$
$374$		0			0
$375$	−32.5594			−0.0868251
$376$		0			0
$377$			220.861i			0.585839i
$378$		0			0
$379$	180.062	−	180.062i	0.475097	−	0.475097i	−0.428463	−	0.903559i	$-0.640945\pi$
$379$	180.062	−	180.062i	0.475097	−	0.475097i	0.903559	+	0.428463i	$0.140945\pi$
$380$		0			0
$381$	−157.876	+	157.876i	−0.414373	+	0.414373i
$382$		0			0
$383$		−	146.777i		−	0.383229i	−0.981470	−	0.191615i	$-0.938628\pi$
$383$		−	146.777i		−	0.383229i	0.981470	−	0.191615i	$-0.0613724\pi$
$384$		0			0
$385$	461.692			1.19920
$386$		0			0
$387$	−19.2448	−	19.2448i	−0.0497281	−	0.0497281i
$388$		0			0
$389$	343.044	+	343.044i	0.881861	+	0.881861i	0.993724	−	0.111863i	$-0.0356818\pi$
$389$	343.044	+	343.044i	0.881861	+	0.881861i	−0.111863	+	0.993724i	$0.535682\pi$
$390$		0			0
$391$	−176.324			−0.450956
$392$		0			0
$393$			51.1303i			0.130103i
$394$		0			0
$395$	77.3344	−	77.3344i	0.195783	−	0.195783i
$396$		0			0
$397$	−40.3574	+	40.3574i	−0.101656	+	0.101656i	−0.756106	−	0.654450i	$-0.772900\pi$
$397$	−40.3574	+	40.3574i	−0.101656	+	0.101656i	0.654450	+	0.756106i	$0.272900\pi$
$398$		0			0
$399$		−	711.394i		−	1.78294i
$400$		0			0
$401$	−451.974			−1.12712			−0.563559	−	0.826076i	$-0.690568\pi$
$401$	−451.974			−1.12712			−0.563559	+	0.826076i	$0.690568\pi$
$402$		0			0
$403$	−68.8380	−	68.8380i	−0.170814	−	0.170814i
$404$		0			0
$405$	120.260	+	120.260i	0.296937	+	0.296937i
$406$		0			0
$407$	−316.450			−0.777518
$408$		0			0
$409$			638.957i			1.56224i	0.624380	+	0.781121i	$0.285352\pi$
$409$			638.957i			1.56224i	−0.624380	+	0.781121i	$0.714648\pi$
$410$		0			0
$411$	−64.5878	+	64.5878i	−0.157148	+	0.157148i
$412$		0			0
$413$	269.020	−	269.020i	0.651380	−	0.651380i
$414$		0			0
$415$			58.7962i			0.141677i
$416$		0			0
$417$	−37.2826			−0.0894066
$418$		0			0
$419$	244.970	+	244.970i	0.584654	+	0.584654i	0.936179	−	0.351525i	$-0.114337\pi$
$419$	244.970	+	244.970i	0.584654	+	0.584654i	−0.351525	+	0.936179i	$0.614337\pi$
$420$		0			0
$421$	−168.087	−	168.087i	−0.399256	−	0.399256i	0.478715	−	0.877970i	$-0.341103\pi$
$421$	−168.087	−	168.087i	−0.399256	−	0.399256i	−0.877970	+	0.478715i	$0.841103\pi$
$422$		0			0
$423$	0.0914041			0.000216085
$424$		0			0
$425$			35.5052i			0.0835417i
$426$		0			0
$427$	383.195	−	383.195i	0.897413	−	0.897413i
$428$		0			0
$429$	565.431	−	565.431i	1.31802	−	1.31802i
$430$		0			0
$431$			62.2481i			0.144427i	0.997389	+	0.0722135i	$0.0230063\pi$
$431$			62.2481i			0.144427i	−0.997389	+	0.0722135i	$0.976994\pi$
$432$		0			0
$433$	270.015			0.623590			0.311795	−	0.950149i	$-0.399070\pi$
$433$	270.015			0.623590			0.311795	+	0.950149i	$0.399070\pi$
$434$		0			0
$435$	73.5797	+	73.5797i	0.169149	+	0.169149i
$436$		0			0
$437$	−412.681	−	412.681i	−0.944351	−	0.944351i
$438$		0			0
$439$	−501.545			−1.14247			−0.571236	−	0.820786i	$-0.693536\pi$
$439$	−501.545			−1.14247			−0.571236	+	0.820786i	$0.693536\pi$
$440$		0			0
$441$		−	30.6348i		−	0.0694666i
$442$		0			0
$443$	72.6881	−	72.6881i	0.164081	−	0.164081i	−0.620291	−	0.784372i	$-0.712985\pi$
$443$	72.6881	−	72.6881i	0.164081	−	0.164081i	0.784372	+	0.620291i	$0.212985\pi$
$444$		0			0
$445$	−68.7753	+	68.7753i	−0.154551	+	0.154551i
$446$		0			0
$447$			681.550i			1.52472i
$448$		0			0
$449$	270.002			0.601342			0.300671	−	0.953728i	$-0.402789\pi$
$449$	270.002			0.601342			0.300671	+	0.953728i	$0.402789\pi$
$450$		0			0
$451$	−879.504	−	879.504i	−1.95012	−	1.95012i
$452$		0			0
$453$	396.781	+	396.781i	0.875896	+	0.875896i
$454$		0			0
$455$	321.207			0.705950
$456$		0			0
$457$		−	764.553i		−	1.67298i	−0.547980	−	0.836492i	$-0.684603\pi$
$457$		−	764.553i		−	1.67298i	0.547980	−	0.836492i	$-0.315397\pi$
$458$		0			0
$459$	139.195	−	139.195i	0.303257	−	0.303257i
$460$		0			0
$461$	−117.608	+	117.608i	−0.255115	+	0.255115i	−0.823064	−	0.567949i	$-0.807737\pi$
$461$	−117.608	+	117.608i	−0.255115	+	0.255115i	0.567949	+	0.823064i	$0.307737\pi$
$462$		0			0
$463$		−	524.036i		−	1.13183i	−0.824465	−	0.565914i	$-0.808524\pi$
$463$		−	524.036i		−	1.13183i	0.824465	−	0.565914i	$-0.191476\pi$
$464$		0			0
$465$	−45.8666			−0.0986379
$466$		0			0
$467$	327.269	+	327.269i	0.700789	+	0.700789i	0.964580	−	0.263791i	$-0.0849728\pi$
$467$	327.269	+	327.269i	0.700789	+	0.700789i	−0.263791	+	0.964580i	$0.584973\pi$
$468$		0			0
$469$	−133.830	−	133.830i	−0.285351	−	0.285351i
$470$		0			0
$471$	−270.019			−0.573289
$472$		0			0
$473$			1041.63i			2.20218i
$474$		0			0
$475$	−83.0991	+	83.0991i	−0.174945	+	0.174945i
$476$		0			0
$477$	−16.8083	+	16.8083i	−0.0352375	+	0.0352375i
$478$		0			0
$479$			257.109i			0.536761i	0.963313	+	0.268381i	$0.0864885\pi$
$479$			257.109i			0.536761i	−0.963313	+	0.268381i	$0.913512\pi$
$480$		0			0
$481$	−220.160			−0.457713
$482$		0			0
$483$	531.425	+	531.425i	1.10026	+	1.10026i
$484$		0			0
$485$	−182.738	−	182.738i	−0.376780	−	0.376780i
$486$		0			0
$487$	−538.554			−1.10586			−0.552930	−	0.833227i	$-0.686490\pi$
$487$	−538.554			−1.10586			−0.552930	+	0.833227i	$0.686490\pi$
$488$		0			0
$489$		−	676.705i		−	1.38385i
$490$		0			0
$491$	−31.0314	+	31.0314i	−0.0632004	+	0.0632004i	−0.738001	−	0.674800i	$-0.764230\pi$
$491$	−31.0314	+	31.0314i	−0.0632004	+	0.0632004i	0.674800	+	0.738001i	$0.264230\pi$
$492$		0			0
$493$	80.2368	−	80.2368i	0.162752	−	0.162752i
$494$		0			0
$495$			23.0589i			0.0465836i
$496$		0			0
$497$	−672.067			−1.35225
$498$		0			0
$499$	−160.845	−	160.845i	−0.322335	−	0.322335i	0.527327	−	0.849662i	$-0.323194\pi$
$499$	−160.845	−	160.845i	−0.322335	−	0.322335i	−0.849662	+	0.527327i	$0.823194\pi$
$500$		0			0
$501$	−220.431	−	220.431i	−0.439982	−	0.439982i
$502$		0			0
$503$	787.428			1.56546			0.782732	−	0.622359i	$-0.213826\pi$
$503$	787.428			1.56546			0.782732	+	0.622359i	$0.213826\pi$
$504$		0			0
$505$			287.588i			0.569481i
$506$		0			0
$507$	45.3691	−	45.3691i	0.0894854	−	0.0894854i
$508$		0			0
$509$	−108.575	+	108.575i	−0.213310	+	0.213310i	−0.805672	−	0.592362i	$-0.798196\pi$
$509$	−108.575	+	108.575i	−0.213310	+	0.213310i	0.592362	+	0.805672i	$0.298196\pi$
$510$		0			0
$511$		−	199.555i		−	0.390518i
$512$		0			0
$513$	651.565			1.27011
$514$		0			0
$515$	−64.8900	−	64.8900i	−0.126000	−	0.126000i
$516$		0			0
$517$	−2.47364	−	2.47364i	−0.00478461	−	0.00478461i
$518$		0			0
$519$	−890.918			−1.71661
$520$		0			0
$521$		−	294.967i		−	0.566156i	−0.959097	−	0.283078i	$-0.908645\pi$
$521$		−	294.967i		−	0.566156i	0.959097	−	0.283078i	$-0.0913555\pi$
$522$		0			0
$523$	−95.9563	+	95.9563i	−0.183473	+	0.183473i	−0.792867	−	0.609394i	$-0.791413\pi$
$523$	−95.9563	+	95.9563i	−0.183473	+	0.183473i	0.609394	+	0.792867i	$0.291413\pi$
$524$		0			0
$525$	107.010	−	107.010i	0.203828	−	0.203828i
$526$		0			0
$527$			50.0164i			0.0949078i
$528$		0			0
$529$	87.5627			0.165525
$530$		0			0
$531$	13.4360	+	13.4360i	0.0253032	+	0.0253032i
$532$		0			0
$533$	−611.887	−	611.887i	−1.14800	−	1.14800i
$534$		0			0
$535$	289.239			0.540633
$536$		0			0
$537$			616.372i			1.14781i
$538$		0			0
$539$	−829.060	+	829.060i	−1.53815	+	1.53815i
$540$		0			0
$541$	286.845	−	286.845i	0.530212	−	0.530212i	−0.390423	−	0.920635i	$-0.627671\pi$
$541$	286.845	−	286.845i	0.530212	−	0.530212i	0.920635	+	0.390423i	$0.127671\pi$
$542$		0			0
$543$			482.067i			0.887784i
$544$		0			0
$545$	243.268			0.446363
$546$		0			0
$547$	285.464	+	285.464i	0.521872	+	0.521872i	0.918136	−	0.396264i	$-0.129694\pi$
$547$	285.464	+	285.464i	0.521872	+	0.521872i	−0.396264	+	0.918136i	$0.629694\pi$
$548$		0			0
$549$	19.1384	+	19.1384i	0.0348605	+	0.0348605i
$550$		0			0
$551$	375.584			0.681641
$552$		0			0
$553$			508.335i			0.919231i
$554$		0			0
$555$	−73.3460	+	73.3460i	−0.132155	+	0.132155i
$556$		0			0
$557$	168.107	−	168.107i	0.301808	−	0.301808i	−0.539913	−	0.841721i	$-0.681543\pi$
$557$	168.107	−	168.107i	0.301808	−	0.301808i	0.841721	+	0.539913i	$0.181543\pi$
$558$		0			0
$559$			724.682i			1.29639i
$560$		0			0
$561$	−410.832			−0.732320
$562$		0			0
$563$	400.369	+	400.369i	0.711136	+	0.711136i	0.966773	−	0.255637i	$-0.0822852\pi$
$563$	400.369	+	400.369i	0.711136	+	0.711136i	−0.255637	+	0.966773i	$0.582285\pi$
$564$		0			0
$565$	59.4740	+	59.4740i	0.105264	+	0.105264i
$566$		0			0
$567$	−790.491			−1.39416
$568$		0			0
$569$			741.052i			1.30238i	0.758916	+	0.651188i	$0.225729\pi$
$569$			741.052i			1.30238i	−0.758916	+	0.651188i	$0.774271\pi$
$570$		0			0
$571$	91.1623	−	91.1623i	0.159654	−	0.159654i	−0.622760	−	0.782413i	$-0.713989\pi$
$571$	91.1623	−	91.1623i	0.159654	−	0.159654i	0.782413	+	0.622760i	$0.213989\pi$
$572$		0			0
$573$	−544.000	+	544.000i	−0.949388	+	0.949388i
$574$		0			0
$575$		−	124.153i		−	0.215919i
$576$		0			0
$577$	−725.837			−1.25795			−0.628975	−	0.777426i	$-0.716525\pi$
$577$	−725.837			−1.25795			−0.628975	+	0.777426i	$0.716525\pi$
$578$		0			0
$579$	−722.306	−	722.306i	−1.24751	−	1.24751i
$580$		0			0
$581$	−193.240	−	193.240i	−0.332598	−	0.332598i
$582$		0			0
$583$	909.757			1.56048
$584$		0			0
$585$			16.0425i			0.0274231i
$586$		0			0
$587$	−327.120	+	327.120i	−0.557274	+	0.557274i	−0.928530	−	0.371256i	$-0.878927\pi$
$587$	−327.120	+	327.120i	−0.557274	+	0.557274i	0.371256	+	0.928530i	$0.378927\pi$
$588$		0			0
$589$	−117.062	+	117.062i	−0.198747	+	0.198747i
$590$		0			0
$591$			681.349i			1.15287i
$592$		0			0
$593$	−195.537			−0.329742			−0.164871	−	0.986315i	$-0.552721\pi$
$593$	−195.537			−0.329742			−0.164871	+	0.986315i	$0.552721\pi$
$594$		0			0
$595$	−116.692	−	116.692i	−0.196120	−	0.196120i
$596$		0			0
$597$	289.535	+	289.535i	0.484983	+	0.484983i
$598$		0			0
$599$	−730.188			−1.21901			−0.609506	−	0.792782i	$-0.708632\pi$
$599$	−730.188			−1.21901			−0.609506	+	0.792782i	$0.708632\pi$
$600$		0			0
$601$			477.101i			0.793845i	0.917852	+	0.396922i	$0.129922\pi$
$601$			477.101i			0.793845i	−0.917852	+	0.396922i	$0.870078\pi$
$602$		0			0
$603$	6.68403	−	6.68403i	0.0110846	−	0.0110846i
$604$		0			0
$605$	432.719	−	432.719i	0.715238	−	0.715238i
$606$		0			0
$607$			810.479i			1.33522i	0.744511	+	0.667610i	$0.232683\pi$
$607$			810.479i			1.33522i	−0.744511	+	0.667610i	$0.767317\pi$
$608$		0			0
$609$	−483.654			−0.794178
$610$		0			0
$611$	−1.72096	−	1.72096i	−0.00281663	−	0.00281663i
$612$		0			0
$613$	306.486	+	306.486i	0.499976	+	0.499976i	0.911431	−	0.411454i	$-0.134979\pi$
$613$	306.486	+	306.486i	0.499976	+	0.499976i	−0.411454	+	0.911431i	$0.634979\pi$
$614$		0			0
$615$	−407.699			−0.662925
$616$		0			0
$617$		−	241.465i		−	0.391353i	−0.980669	−	0.195676i	$-0.937310\pi$
$617$		−	241.465i		−	0.391353i	0.980669	−	0.195676i	$-0.0626902\pi$
$618$		0			0
$619$	43.0837	−	43.0837i	0.0696022	−	0.0696022i	−0.671449	−	0.741051i	$-0.734328\pi$
$619$	43.0837	−	43.0837i	0.0696022	−	0.0696022i	0.741051	+	0.671449i	$0.234328\pi$
$620$		0			0
$621$	−486.732	+	486.732i	−0.783788	+	0.783788i
$622$		0			0
$623$		−	452.074i		−	0.725641i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−961.541	−	961.541i	−1.53356	−	1.53356i
$628$		0			0
$629$	79.9820	+	79.9820i	0.127157	+	0.127157i
$630$		0			0
$631$	−327.143			−0.518451			−0.259225	−	0.965817i	$-0.583467\pi$
$631$	−327.143			−0.518451			−0.259225	+	0.965817i	$0.583467\pi$
$632$		0			0
$633$		−	1155.49i		−	1.82542i
$634$		0			0
$635$	−121.222	+	121.222i	−0.190900	+	0.190900i
$636$		0			0
$637$	−576.792	+	576.792i	−0.905482	+	0.905482i
$638$		0			0
$639$		−	33.5660i		−	0.0525289i
$640$		0			0
$641$	−267.455			−0.417246			−0.208623	−	0.977996i	$-0.566898\pi$
$641$	−267.455			−0.417246			−0.208623	+	0.977996i	$0.566898\pi$
$642$		0			0
$643$	−324.978	−	324.978i	−0.505409	−	0.505409i	0.407704	−	0.913114i	$-0.366329\pi$
$643$	−324.978	−	324.978i	−0.505409	−	0.505409i	−0.913114	+	0.407704i	$0.866329\pi$
$644$		0			0
$645$	241.427	+	241.427i	0.374306	+	0.374306i
$646$		0			0
$647$	893.197			1.38052			0.690261	−	0.723561i	$-0.257496\pi$
$647$	893.197			1.38052			0.690261	+	0.723561i	$0.257496\pi$
$648$		0			0
$649$		−	727.231i		−	1.12054i
$650$		0			0
$651$	150.745	−	150.745i	0.231560	−	0.231560i
$652$		0			0
$653$	249.337	−	249.337i	0.381833	−	0.381833i	−0.489929	−	0.871762i	$-0.662977\pi$
$653$	249.337	−	249.337i	0.381833	−	0.381833i	0.871762	+	0.489929i	$0.162977\pi$
$654$		0			0
$655$			39.2593i			0.0599378i
$656$		0			0
$657$	9.96663			0.0151699
$658$		0			0
$659$	505.483	+	505.483i	0.767045	+	0.767045i	0.977585	−	0.210540i	$-0.0675223\pi$
$659$	505.483	+	505.483i	0.767045	+	0.767045i	−0.210540	+	0.977585i	$0.567522\pi$
$660$		0			0
$661$	720.088	+	720.088i	1.08939	+	1.08939i	0.995591	+	0.0938007i	$0.0299016\pi$
$661$	720.088	+	720.088i	1.08939	+	1.08939i	0.0938007	+	0.995591i	$0.470098\pi$
$662$		0			0
$663$	−285.823			−0.431105
$664$		0			0
$665$		−	546.227i		−	0.821394i
$666$		0			0
$667$	−280.569	+	280.569i	−0.420643	+	0.420643i
$668$		0			0
$669$	−467.728	+	467.728i	−0.699145	+	0.699145i
$670$		0			0
$671$		−	1035.88i		−	1.54378i
$672$		0			0
$673$	767.329			1.14016			0.570081	−	0.821588i	$-0.306912\pi$
$673$	767.329			1.14016			0.570081	+	0.821588i	$0.306912\pi$
$674$		0			0
$675$	98.0102	+	98.0102i	0.145200	+	0.145200i
$676$		0			0
$677$	650.823	+	650.823i	0.961333	+	0.961333i	0.999280	−	0.0379464i	$-0.0120816\pi$
$677$	650.823	+	650.823i	0.961333	+	0.961333i	−0.0379464	+	0.999280i	$0.512082\pi$
$678$		0			0
$679$	1201.18			1.76904
$680$		0			0
$681$		−	69.3523i		−	0.101839i
$682$		0			0
$683$	147.895	−	147.895i	0.216537	−	0.216537i	−0.590500	−	0.807038i	$-0.701070\pi$
$683$	147.895	−	147.895i	0.216537	−	0.216537i	0.807038	+	0.590500i	$0.201070\pi$
$684$		0			0
$685$	−49.5922	+	49.5922i	−0.0723974	+	0.0723974i
$686$		0			0
$687$		−	769.972i		−	1.12077i
$688$		0			0
$689$	632.934			0.918627
$690$		0			0
$691$	868.389	+	868.389i	1.25671	+	1.25671i	0.952653	+	0.304061i	$0.0983426\pi$
$691$	868.389	+	868.389i	1.25671	+	1.25671i	0.304061	+	0.952653i	$0.401657\pi$
$692$		0			0
$693$	−75.7854	−	75.7854i	−0.109358	−	0.109358i
$694$		0			0
$695$	−28.6266			−0.0411893
$696$		0			0
$697$			444.585i			0.637856i
$698$		0			0
$699$	90.2263	−	90.2263i	0.129079	−	0.129079i
$700$		0			0
$701$	712.136	−	712.136i	1.01589	−	1.01589i	0.0160148	−	0.999872i	$-0.494902\pi$
$701$	712.136	−	712.136i	1.01589	−	1.01589i	0.999872	−	0.0160148i	$-0.00509788\pi$
$702$		0			0
$703$			374.392i			0.532563i
$704$		0			0
$705$	−1.14667			−0.00162648
$706$		0			0
$707$	−945.187	−	945.187i	−1.33690	−	1.33690i
$708$		0			0
$709$	−553.104	−	553.104i	−0.780118	−	0.780118i	0.199732	−	0.979850i	$-0.435993\pi$
$709$	−553.104	−	553.104i	−0.780118	−	0.780118i	−0.979850	+	0.199732i	$0.935993\pi$
$710$		0			0
$711$	−25.3885			−0.0357081
$712$		0			0
$713$		−	174.896i		−	0.245295i
$714$		0			0
$715$	434.153	−	434.153i	0.607207	−	0.607207i
$716$		0			0
$717$	−209.430	+	209.430i	−0.292092	+	0.292092i
$718$		0			0
$719$		−	1389.67i		−	1.93278i	−0.257084	−	0.966389i	$-0.582762\pi$
$719$		−	1389.67i		−	1.93278i	0.257084	−	0.966389i	$-0.417238\pi$
$720$		0			0
$721$	426.536			0.591589
$722$		0			0
$723$	209.533	+	209.533i	0.289811	+	0.289811i
$724$		0			0
$725$	56.4965	+	56.4965i	0.0779262	+	0.0779262i
$726$		0			0
$727$	610.697			0.840023			0.420012	−	0.907519i	$-0.362026\pi$
$727$	610.697			0.840023			0.420012	+	0.907519i	$0.362026\pi$
$728$		0			0
$729$		−	766.056i		−	1.05083i
$730$		0			0
$731$	263.270	−	263.270i	0.360151	−	0.360151i
$732$		0			0
$733$	−355.943	+	355.943i	−0.485597	+	0.485597i	−0.906914	−	0.421316i	$-0.861568\pi$
$733$	−355.943	+	355.943i	−0.485597	+	0.485597i	0.421316	+	0.906914i	$0.361568\pi$
$734$		0			0
$735$			384.315i			0.522878i
$736$		0			0
$737$	−361.776			−0.490876
$738$		0			0
$739$	429.694	+	429.694i	0.581453	+	0.581453i	0.935302	−	0.353849i	$-0.115127\pi$
$739$	429.694	+	429.694i	0.581453	+	0.581453i	−0.353849	+	0.935302i	$0.615127\pi$
$740$		0			0
$741$	−668.961	−	668.961i	−0.902781	−	0.902781i
$742$		0			0
$743$	−362.510			−0.487900			−0.243950	−	0.969788i	$-0.578443\pi$
$743$	−362.510			−0.487900			−0.243950	+	0.969788i	$0.578443\pi$
$744$		0			0
$745$			523.313i			0.702433i
$746$		0			0
$747$	9.65123	−	9.65123i	0.0129200	−	0.0129200i
$748$		0			0
$749$	−950.612	+	950.612i	−1.26918	+	1.26918i
$750$		0			0
$751$		−	718.108i		−	0.956202i	−0.878305	−	0.478101i	$-0.841325\pi$
$751$		−	718.108i		−	0.956202i	0.878305	−	0.478101i	$-0.158675\pi$
$752$		0			0
$753$	−1030.18			−1.36811
$754$		0			0
$755$	304.659	+	304.659i	0.403522	+	0.403522i
$756$		0			0
$757$	−222.303	−	222.303i	−0.293664	−	0.293664i	0.544862	−	0.838526i	$-0.316582\pi$
$757$	−222.303	−	222.303i	−0.293664	−	0.293664i	−0.838526	+	0.544862i	$0.816582\pi$
$758$		0			0
$759$	1436.58			1.89273
$760$		0			0
$761$		−	1319.68i		−	1.73414i	−0.498191	−	0.867068i	$-0.666002\pi$
$761$		−	1319.68i		−	1.73414i	0.498191	−	0.867068i	$-0.333998\pi$
$762$		0			0
$763$	−799.525	+	799.525i	−1.04787	+	1.04787i
$764$		0			0
$765$	5.82808	−	5.82808i	0.00761841	−	0.00761841i
$766$		0			0
$767$		−	505.947i		−	0.659644i
$768$		0			0
$769$	1346.98			1.75160			0.875800	−	0.482674i	$-0.160334\pi$
$769$	1346.98			1.75160			0.875800	+	0.482674i	$0.160334\pi$
$770$		0			0
$771$	−63.3945	−	63.3945i	−0.0822237	−	0.0822237i
$772$		0			0
$773$	543.589	+	543.589i	0.703220	+	0.703220i	0.965100	−	0.261881i	$-0.0843426\pi$
$773$	543.589	+	543.589i	0.703220	+	0.703220i	−0.261881	+	0.965100i	$0.584343\pi$
$774$		0			0
$775$	−35.2176			−0.0454421
$776$		0			0
$777$		−	482.118i		−	0.620487i
$778$		0			0
$779$	−1040.54	+	1040.54i	−1.33574	+	1.33574i
$780$		0			0
$781$	−908.386	+	908.386i	−1.16311	+	1.16311i
$782$		0			0
$783$		−	442.979i		−	0.565745i
$784$		0			0
$785$	−207.328			−0.264112
$786$		0			0
$787$	−31.2661	−	31.2661i	−0.0397283	−	0.0397283i	0.686964	−	0.726692i	$-0.258943\pi$
$787$	−31.2661	−	31.2661i	−0.0397283	−	0.0397283i	−0.726692	+	0.686964i	$0.758943\pi$
$788$		0			0
$789$	−69.2837	−	69.2837i	−0.0878120	−	0.0878120i
$790$		0			0
$791$	−390.935			−0.494229
$792$		0			0
$793$		−	720.677i		−	0.908799i
$794$		0			0
$795$	210.861	−	210.861i	0.265234	−	0.265234i
$796$		0			0
$797$	270.786	−	270.786i	0.339756	−	0.339756i	−0.516519	−	0.856275i	$-0.672773\pi$
$797$	270.786	−	270.786i	0.339756	−	0.339756i	0.856275	+	0.516519i	$0.172773\pi$
$798$		0			0
$799$			1.25042i			0.00156498i
$800$		0			0
$801$	22.5785			0.0281880
$802$		0			0
$803$	−269.724	−	269.724i	−0.335895	−	0.335895i
$804$		0			0
$805$	408.043	+	408.043i	0.506886	+	0.506886i
$806$		0			0
$807$	746.590			0.925143
$808$		0			0
$809$			544.465i			0.673010i	0.941682	+	0.336505i	$0.109245\pi$
$809$			544.465i			0.673010i	−0.941682	+	0.336505i	$0.890755\pi$
$810$		0			0
$811$	−451.927	+	451.927i	−0.557246	+	0.557246i	−0.928522	−	0.371276i	$-0.878920\pi$
$811$	−451.927	+	451.927i	−0.557246	+	0.557246i	0.371276	+	0.928522i	$0.378920\pi$
$812$		0			0
$813$	240.617	−	240.617i	0.295962	−	0.295962i
$814$		0			0
$815$		−	519.592i		−	0.637536i
$816$		0			0
$817$	1232.35			1.50839
$818$		0			0
$819$	−52.7253	−	52.7253i	−0.0643776	−	0.0643776i
$820$		0			0
$821$	433.211	+	433.211i	0.527663	+	0.527663i	0.919875	−	0.392212i	$-0.128290\pi$
$821$	433.211	+	433.211i	0.527663	+	0.527663i	−0.392212	+	0.919875i	$0.628290\pi$
$822$		0			0
$823$	787.997			0.957469			0.478734	−	0.877960i	$-0.341096\pi$
$823$	787.997			0.957469			0.478734	+	0.877960i	$0.341096\pi$
$824$		0			0
$825$		−	289.275i		−	0.350637i
$826$		0			0
$827$	994.198	−	994.198i	1.20217	−	1.20217i	0.228671	−	0.973504i	$-0.426562\pi$
$827$	994.198	−	994.198i	1.20217	−	1.20217i	0.973504	−	0.228671i	$-0.0734379\pi$
$828$		0			0
$829$	886.683	−	886.683i	1.06958	−	1.06958i	0.0721910	−	0.997391i	$-0.477001\pi$
$829$	886.683	−	886.683i	1.06958	−	1.06958i	0.997391	−	0.0721910i	$-0.0229991\pi$
$830$		0			0
$831$		−	609.019i		−	0.732875i
$832$		0			0
$833$	419.086			0.503105
$834$		0			0
$835$	−169.253	−	169.253i	−0.202698	−	0.202698i
$836$		0			0
$837$	138.068	+	138.068i	0.164955	+	0.164955i
$838$		0			0
$839$	306.867			0.365753			0.182876	−	0.983136i	$-0.441459\pi$
$839$	306.867			0.365753			0.182876	+	0.983136i	$0.441459\pi$
$840$		0			0
$841$			585.652i			0.696376i
$842$		0			0
$843$	995.641	−	995.641i	1.18107	−	1.18107i
$844$		0			0
$845$	34.8356	−	34.8356i	0.0412256	−	0.0412256i
$846$		0			0
$847$			2844.35i			3.35814i
$848$		0			0
$849$	−262.679			−0.309398
$850$		0			0
$851$	−279.678	−	279.678i	−0.328647	−	0.328647i
$852$		0			0
$853$	423.675	+	423.675i	0.496688	+	0.496688i	0.910405	−	0.413718i	$-0.135770\pi$
$853$	423.675	+	423.675i	0.496688	+	0.496688i	−0.413718	+	0.910405i	$0.635770\pi$
$854$		0			0
$855$	27.2810			0.0319076
$856$		0			0
$857$		−	811.440i		−	0.946838i	−0.880837	−	0.473419i	$-0.843020\pi$
$857$		−	811.440i		−	0.946838i	0.880837	−	0.473419i	$-0.156980\pi$
$858$		0			0
$859$	992.394	−	992.394i	1.15529	−	1.15529i	0.169814	−	0.985476i	$-0.445683\pi$
$859$	992.394	−	992.394i	1.15529	−	1.15529i	0.985476	−	0.169814i	$-0.0543166\pi$
$860$		0			0
$861$	1339.94	−	1339.94i	1.55626	−	1.55626i
$862$		0			0
$863$			1479.18i			1.71399i	0.515322	+	0.856997i	$0.327672\pi$
$863$			1479.18i			1.71399i	−0.515322	+	0.856997i	$0.672328\pi$
$864$		0			0
$865$	−684.071			−0.790834
$866$		0			0
$867$	−491.283	−	491.283i	−0.566647	−	0.566647i
$868$		0			0
$869$	687.081	+	687.081i	0.790657	+	0.790657i
$870$		0			0
$871$	−251.694			−0.288971
$872$		0			0
$873$			59.9919i			0.0687193i
$874$		0			0
$875$	82.1651	−	82.1651i	0.0939029	−	0.0939029i
$876$		0			0
$877$	491.849	−	491.849i	0.560831	−	0.560831i	−0.368712	−	0.929544i	$-0.620201\pi$
$877$	491.849	−	491.849i	0.560831	−	0.560831i	0.929544	+	0.368712i	$0.120201\pi$
$878$		0			0
$879$			720.939i			0.820181i
$880$		0			0
$881$	−508.703			−0.577416			−0.288708	−	0.957417i	$-0.593226\pi$
$881$	−508.703			−0.577416			−0.288708	+	0.957417i	$0.593226\pi$
$882$		0			0
$883$	−432.055	−	432.055i	−0.489304	−	0.489304i	0.418783	−	0.908086i	$-0.362457\pi$
$883$	−432.055	−	432.055i	−0.489304	−	0.489304i	−0.908086	+	0.418783i	$0.862457\pi$
$884$		0			0
$885$	−168.556	−	168.556i	−0.190459	−	0.190459i
$886$		0			0
$887$	147.316			0.166083			0.0830417	−	0.996546i	$-0.473537\pi$
$887$	147.316			0.166083			0.0830417	+	0.996546i	$0.473537\pi$
$888$		0			0
$889$		−	796.815i		−	0.896305i
$890$		0			0
$891$	−1068.45	+	1068.45i	−1.19916	+	1.19916i
$892$		0			0
$893$	−2.92657	+	2.92657i	−0.00327723	+	0.00327723i
$894$		0			0
$895$			473.267i			0.528790i
$896$		0			0
$897$	999.455			1.11422
$898$		0			0
$899$	79.5869	+	79.5869i	0.0885282	+	0.0885282i
$900$		0			0
$901$	−229.939	−	229.939i	−0.255204	−	0.255204i
$902$		0			0
$903$	−1586.95			−1.75742
$904$		0			0
$905$			370.144i			0.408999i
$906$		0			0
$907$	−1011.19	+	1011.19i	−1.11487	+	1.11487i	−0.122386	+	0.992483i	$0.539055\pi$
$907$	−1011.19	+	1011.19i	−1.11487	+	1.11487i	−0.992483	+	0.122386i	$0.960945\pi$
$908$		0			0
$909$	47.2068	−	47.2068i	0.0519326	−	0.0519326i
$910$		0			0
$911$			486.973i			0.534547i	0.963621	+	0.267274i	$0.0861227\pi$
$911$			486.973i			0.534547i	−0.963621	+	0.267274i	$0.913877\pi$
$912$		0			0
$913$	−522.377			−0.572154
$914$		0			0
$915$	−240.093	−	240.093i	−0.262397	−	0.262397i
$916$		0			0
$917$	−129.030	−	129.030i	−0.140708	−	0.140708i
$918$		0			0
$919$	−277.022			−0.301438			−0.150719	−	0.988577i	$-0.548159\pi$
$919$	−277.022			−0.301438			−0.150719	+	0.988577i	$0.548159\pi$
$920$		0			0
$921$			1703.74i			1.84988i
$922$		0			0
$923$	−631.980	+	631.980i	−0.684702	+	0.684702i
$924$		0			0
$925$	−56.3171	+	56.3171i	−0.0608833	+	0.0608833i
$926$		0			0
$927$			21.3030i			0.0229806i
$928$		0			0
$929$	−1669.27			−1.79685			−0.898425	−	0.439128i	$-0.855287\pi$
$929$	−1669.27			−1.79685			−0.898425	+	0.439128i	$0.855287\pi$
$930$		0			0
$931$	980.861	+	980.861i	1.05356	+	1.05356i
$932$		0			0
$933$	−749.027	−	749.027i	−0.802815	−	0.802815i
$934$		0			0
$935$	−315.448			−0.337377
$936$		0			0
$937$		−	1122.11i		−	1.19755i	−0.800917	−	0.598776i	$-0.795654\pi$
$937$		−	1122.11i		−	1.19755i	0.800917	−	0.598776i	$-0.204346\pi$
$938$		0			0
$939$	580.577	−	580.577i	0.618293	−	0.618293i
$940$		0			0
$941$	696.516	−	696.516i	0.740187	−	0.740187i	−0.232427	−	0.972614i	$-0.574667\pi$
$941$	696.516	−	696.516i	0.740187	−	0.740187i	0.972614	+	0.232427i	$0.0746667\pi$
$942$		0			0
$943$		−	1554.61i		−	1.64858i
$944$		0			0
$945$	−644.241			−0.681737
$946$		0			0
$947$	65.1524	+	65.1524i	0.0687988	+	0.0687988i	0.740669	−	0.671870i	$-0.234509\pi$
$947$	65.1524	+	65.1524i	0.0687988	+	0.0687988i	−0.671870	+	0.740669i	$0.734509\pi$
$948$		0			0
$949$	−187.652	−	187.652i	−0.197736	−	0.197736i
$950$		0			0
$951$	1120.00			1.17771
$952$		0			0
$953$		−	9.49818i		−	0.00996661i	−0.999988	−	0.00498331i	$-0.998414\pi$
$953$		−	9.49818i		−	0.00996661i	0.999988	−	0.00498331i	$-0.00158624\pi$
$954$		0			0
$955$	−417.698	+	417.698i	−0.437380	+	0.437380i
$956$		0			0
$957$	−653.722	+	653.722i	−0.683095	+	0.683095i
$958$		0			0
$959$		−	325.980i		−	0.339916i
$960$		0			0
$961$	911.389			0.948375
$962$		0			0
$963$	−47.4777	−	47.4777i	−0.0493019	−	0.0493019i
$964$		0			0
$965$	−554.606	−	554.606i	−0.574722	−	0.574722i
$966$		0			0
$967$	1278.80			1.32244			0.661222	−	0.750190i	$-0.270038\pi$
$967$	1278.80			1.32244			0.661222	+	0.750190i	$0.270038\pi$
$968$		0			0
$969$			486.055i			0.501604i
$970$		0			0
$971$	−37.2611	+	37.2611i	−0.0383739	+	0.0383739i	−0.726033	−	0.687659i	$-0.758638\pi$
$971$	−37.2611	+	37.2611i	−0.0383739	+	0.0383739i	0.687659	+	0.726033i	$0.258638\pi$
$972$		0			0
$973$	94.0842	−	94.0842i	0.0966949	−	0.0966949i
$974$		0			0
$975$		−	201.254i		−	0.206414i
$976$		0			0
$977$	1006.12			1.02980			0.514902	−	0.857249i	$-0.327828\pi$
$977$	1006.12			1.02980			0.514902	+	0.857249i	$0.327828\pi$
$978$		0			0
$979$	−611.037	−	611.037i	−0.624144	−	0.624144i
$980$		0			0
$981$	−39.9318	−	39.9318i	−0.0407052	−	0.0407052i
$982$		0			0
$983$	−1218.44			−1.23951			−0.619754	−	0.784796i	$-0.712767\pi$
$983$	−1218.44			−1.23951			−0.619754	+	0.784796i	$0.712767\pi$
$984$		0			0
$985$			523.158i			0.531125i
$986$		0			0
$987$	3.76865	−	3.76865i	0.00381829	−	0.00381829i
$988$		0			0
$989$	−920.594	+	920.594i	−0.930833	+	0.930833i
$990$		0			0
$991$			247.969i			0.250221i	0.992143	+	0.125110i	$0.0399285\pi$
$991$			247.969i			0.250221i	−0.992143	+	0.125110i	$0.960071\pi$
$992$		0			0
$993$	358.869			0.361398
$994$		0			0
$995$	222.313	+	222.313i	0.223430	+	0.223430i
$996$		0			0
$997$	113.625	+	113.625i	0.113967	+	0.113967i	0.761791	−	0.647823i	$-0.224321\pi$
$997$	113.625	+	113.625i	0.113967	+	0.113967i	−0.647823	+	0.761791i	$0.724321\pi$
$998$		0			0
$999$	441.572			0.442014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.271.13		32
4.3	odd	2		80.3.r.a.11.6	✓	32
8.3	odd	2		640.3.r.a.31.13		32
8.5	even	2		640.3.r.b.31.4		32
16.3	odd	4	inner	320.3.r.a.111.13		32
16.5	even	4		640.3.r.a.351.13		32
16.11	odd	4		640.3.r.b.351.4		32
16.13	even	4		80.3.r.a.51.6	yes	32
20.3	even	4		400.3.k.g.299.14		32
20.7	even	4		400.3.k.h.299.3		32
20.19	odd	2		400.3.r.f.251.11		32
80.13	odd	4		400.3.k.h.99.3		32
80.29	even	4		400.3.r.f.51.11		32
80.77	odd	4		400.3.k.g.99.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.6	✓	32	4.3	odd	2
80.3.r.a.51.6	yes	32	16.13	even	4
320.3.r.a.111.13		32	16.3	odd	4	inner
320.3.r.a.271.13		32	1.1	even	1	trivial
400.3.k.g.99.14		32	80.77	odd	4
400.3.k.g.299.14		32	20.3	even	4
400.3.k.h.99.3		32	80.13	odd	4
400.3.k.h.299.3		32	20.7	even	4
400.3.r.f.51.11		32	80.29	even	4
400.3.r.f.251.11		32	20.19	odd	2
640.3.r.a.31.13		32	8.3	odd	2
640.3.r.a.351.13		32	16.5	even	4
640.3.r.b.31.4		32	8.5	even	2
640.3.r.b.351.4		32	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.r (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.05924 + 2.05924i) q^{3} +(1.58114 + 1.58114i) q^{5} -10.3931 q^{7} -0.519079i q^{9} +O(q^{10})\)	\(q+(2.05924 + 2.05924i) q^{3} +(1.58114 + 1.58114i) q^{5} -10.3931 q^{7} -0.519079i q^{9} +(-14.0477 + 14.0477i) q^{11} +(-9.77323 + 9.77323i) q^{13} +6.51188i q^{15} +7.10104 q^{17} +(16.6198 + 16.6198i) q^{19} +(-21.4020 - 21.4020i) q^{21} -24.8307 q^{23} +5.00000i q^{25} +(19.6020 - 19.6020i) q^{27} +(11.2993 - 11.2993i) q^{29} +7.04353i q^{31} -57.8551 q^{33} +(-16.4330 - 16.4330i) q^{35} +(11.2634 + 11.2634i) q^{37} -40.2508 q^{39} +62.6084i q^{41} +(37.0749 - 37.0749i) q^{43} +(0.820736 - 0.820736i) q^{45} +0.176089i q^{47} +59.0176 q^{49} +(14.6227 + 14.6227i) q^{51} +(-32.3810 - 32.3810i) q^{53} -44.4227 q^{55} +68.4483i q^{57} +(-25.8843 + 25.8843i) q^{59} +(-36.8700 + 36.8700i) q^{61} +5.39487i q^{63} -30.9057 q^{65} +(12.8767 + 12.8767i) q^{67} +(-51.1323 - 51.1323i) q^{69} +64.6644 q^{71} +19.2006i q^{73} +(-10.2962 + 10.2962i) q^{75} +(146.000 - 146.000i) q^{77} -48.9106i q^{79} +76.0588 q^{81} +(18.5930 + 18.5930i) q^{83} +(11.2277 + 11.2277i) q^{85} +46.5359 q^{87} +43.4973i q^{89} +(101.575 - 101.575i) q^{91} +(-14.5043 + 14.5043i) q^{93} +52.5565i q^{95} -115.574 q^{97} +(7.29186 + 7.29186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) \) 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

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