LMFDB - Embedded newform 684.3.s.a.445.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.5
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72361 + 1.25776i) q^{3} +(0.340706 + 0.590120i) q^{5} +(-2.79581 - 4.84248i) q^{7} +(5.83609 - 6.85128i) q^{9} +O(q^{10})$	\(q+(-2.72361 + 1.25776i) q^{3} +(0.340706 + 0.590120i) q^{5} +(-2.79581 - 4.84248i) q^{7} +(5.83609 - 6.85128i) q^{9} +(7.44896 + 12.9020i) q^{11} -2.36780i q^{13} +(-1.67018 - 1.17873i) q^{15} +(-8.72908 + 15.1192i) q^{17} +(-17.2199 - 8.02967i) q^{19} +(13.7054 + 9.67258i) q^{21} -10.4486 q^{23} +(12.2678 - 21.2485i) q^{25} +(-7.27796 + 26.0006i) q^{27} +(-37.6328 - 21.7273i) q^{29} +(28.9832 + 16.7334i) q^{31} +(-36.5156 - 25.7710i) q^{33} +(1.90510 - 3.29973i) q^{35} -30.3219i q^{37} +(2.97813 + 6.44897i) q^{39} +(48.7811 - 28.1638i) q^{41} -62.4810 q^{43} +(6.03147 + 1.10972i) q^{45} +(43.3232 - 75.0381i) q^{47} +(8.86690 - 15.3579i) q^{49} +(4.75828 - 52.1579i) q^{51} +(43.7359 - 25.2509i) q^{53} +(-5.07582 + 8.79157i) q^{55} +(56.9996 + 0.211226i) q^{57} +(13.9077 - 8.02962i) q^{59} +(0.219952 - 0.380967i) q^{61} +(-49.4938 - 9.10628i) q^{63} +(1.39729 - 0.806726i) q^{65} -41.0728i q^{67} +(28.4580 - 13.1419i) q^{69} +(62.9245 + 36.3295i) q^{71} +(38.3367 - 66.4012i) q^{73} +(-6.68729 + 73.3026i) q^{75} +(41.6518 - 72.1430i) q^{77} +120.760i q^{79} +(-12.8802 - 79.9694i) q^{81} +(-53.7042 - 93.0184i) q^{83} -11.8962 q^{85} +(129.825 + 11.8437i) q^{87} +(-122.606 + 70.7865i) q^{89} +(-11.4661 + 6.61993i) q^{91} +(-99.9854 - 9.12151i) q^{93} +(-1.12845 - 12.8976i) q^{95} -171.665i q^{97} +(131.868 + 24.2621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.72361	+	1.25776i	−0.907870	+	0.419253i
$3$	−2.72361	+	1.25776i	−0.907870	+	0.419253i
$4$		0			0
$5$	0.340706	+	0.590120i	0.0681412	+	0.118024i	0.898083	−	0.439826i	$-0.144960\pi$
$5$	0.340706	+	0.590120i	0.0681412	+	0.118024i	−0.829942	+	0.557850i	$0.811626\pi$
$6$		0			0
$7$	−2.79581	−	4.84248i	−0.399401	−	0.691783i	0.594251	−	0.804280i	$-0.297449\pi$
$7$	−2.79581	−	4.84248i	−0.399401	−	0.691783i	−0.993652	+	0.112496i	$0.964115\pi$
$8$		0			0
$9$	5.83609	−	6.85128i	0.648454	−	0.761254i
$10$		0			0
$11$	7.44896	+	12.9020i	0.677179	+	1.17291i	0.975827	+	0.218545i	$0.0701309\pi$
$11$	7.44896	+	12.9020i	0.677179	+	1.17291i	−0.298648	+	0.954363i	$0.596536\pi$
$12$		0			0
$13$		−	2.36780i		−	0.182139i	−0.995845	−	0.0910694i	$-0.970971\pi$
$13$		−	2.36780i		−	0.182139i	0.995845	−	0.0910694i	$-0.0290285\pi$
$14$		0			0
$15$	−1.67018	−	1.17873i	−0.111345	−	0.0785821i
$16$		0			0
$17$	−8.72908	+	15.1192i	−0.513475	+	0.889365i	0.486403	+	0.873735i	$0.338309\pi$
$17$	−8.72908	+	15.1192i	−0.513475	+	0.889365i	−0.999878	+	0.0156303i	$0.995025\pi$
$18$		0			0
$19$	−17.2199	−	8.02967i	−0.906310	−	0.422614i
$19$	−17.2199	−	8.02967i	−0.906310	−	0.422614i
$20$		0			0
$21$	13.7054	+	9.67258i	0.652636	+	0.460599i
$22$		0			0
$23$	−10.4486			−0.454289			−0.227144	−	0.973861i	$-0.572939\pi$
$23$	−10.4486			−0.454289			−0.227144	+	0.973861i	$0.572939\pi$
$24$		0			0
$25$	12.2678	−	21.2485i	0.490714	−	0.849941i
$26$		0			0
$27$	−7.27796	+	26.0006i	−0.269554	+	0.962985i
$28$		0			0
$29$	−37.6328	−	21.7273i	−1.29768	−	0.749217i	−0.317679	−	0.948198i	$-0.602903\pi$
$29$	−37.6328	−	21.7273i	−1.29768	−	0.749217i	−0.980003	+	0.198981i	$0.936237\pi$
$30$		0			0
$31$	28.9832	+	16.7334i	0.934940	+	0.539788i	0.888371	−	0.459127i	$-0.151838\pi$
$31$	28.9832	+	16.7334i	0.934940	+	0.539788i	0.0465698	+	0.998915i	$0.485171\pi$
$32$		0			0
$33$	−36.5156	−	25.7710i	−1.10653	−	0.780938i
$34$		0			0
$35$	1.90510	−	3.29973i	0.0544314	−	0.0942780i
$36$		0			0
$37$		−	30.3219i		−	0.819510i	−0.912196	−	0.409755i	$-0.865614\pi$
$37$		−	30.3219i		−	0.819510i	0.912196	−	0.409755i	$-0.134386\pi$
$38$		0			0
$39$	2.97813	+	6.44897i	0.0763622	+	0.165358i
$40$		0			0
$41$	48.7811	−	28.1638i	1.18978	−	0.686921i	0.231525	−	0.972829i	$-0.425628\pi$
$41$	48.7811	−	28.1638i	1.18978	−	0.686921i	0.958257	+	0.285908i	$0.0922951\pi$
$42$		0			0
$43$	−62.4810			−1.45305			−0.726523	−	0.687142i	$-0.758865\pi$
$43$	−62.4810			−1.45305			−0.726523	+	0.687142i	$0.758865\pi$
$44$		0			0
$45$	6.03147	+	1.10972i	0.134033	+	0.0246604i
$46$		0			0
$47$	43.3232	−	75.0381i	0.921771	−	1.59655i	0.125098	−	0.992144i	$-0.460075\pi$
$47$	43.3232	−	75.0381i	0.921771	−	1.59655i	0.796673	−	0.604410i	$-0.206591\pi$
$48$		0			0
$49$	8.86690	−	15.3579i	0.180957	−	0.313427i
$50$		0			0
$51$	4.75828	−	52.1579i	0.0932996	−	1.02270i
$52$		0			0
$53$	43.7359	−	25.2509i	0.825206	−	0.476433i	−0.0270024	−	0.999635i	$-0.508596\pi$
$53$	43.7359	−	25.2509i	0.825206	−	0.476433i	0.852208	+	0.523202i	$0.175263\pi$
$54$		0			0
$55$	−5.07582	+	8.79157i	−0.0922876	+	0.159847i
$56$		0			0
$57$	56.9996	+	0.211226i	0.999993	+	0.00370572i
$58$		0			0
$59$	13.9077	−	8.02962i	0.235724	−	0.136095i	−0.377486	−	0.926015i	$-0.623211\pi$
$59$	13.9077	−	8.02962i	0.235724	−	0.136095i	0.613210	+	0.789920i	$0.289878\pi$
$60$		0			0
$61$	0.219952	−	0.380967i	0.00360576	−	0.00624536i	−0.864217	−	0.503119i	$-0.832186\pi$
$61$	0.219952	−	0.380967i	0.00360576	−	0.00624536i	0.867823	+	0.496874i	$0.165519\pi$
$62$		0			0
$63$	−49.4938	−	9.10628i	−0.785616	−	0.144544i
$64$		0			0
$65$	1.39729	−	0.806726i	0.0214968	−	0.0124112i
$66$		0			0
$67$		−	41.0728i		−	0.613027i	−0.951866	−	0.306513i	$-0.900838\pi$
$67$		−	41.0728i		−	0.613027i	0.951866	−	0.306513i	$-0.0991624\pi$
$68$		0			0
$69$	28.4580	−	13.1419i	0.412435	−	0.190462i
$70$		0			0
$71$	62.9245	+	36.3295i	0.886260	+	0.511683i	0.872717	−	0.488226i	$-0.162356\pi$
$71$	62.9245	+	36.3295i	0.886260	+	0.511683i	0.0135429	+	0.999908i	$0.495689\pi$
$72$		0			0
$73$	38.3367	−	66.4012i	0.525161	−	0.909605i	−0.474410	−	0.880304i	$-0.657339\pi$
$73$	38.3367	−	66.4012i	0.525161	−	0.909605i	0.999571	−	0.0293009i	$-0.00932811\pi$
$74$		0			0
$75$	−6.68729	+	73.3026i	−0.0891638	+	0.977368i
$76$		0			0
$77$	41.6518	−	72.1430i	0.540932	−	0.936922i
$78$		0			0
$79$			120.760i			1.52861i	0.644856	+	0.764304i	$0.276918\pi$
$79$			120.760i			1.52861i	−0.644856	+	0.764304i	$0.723082\pi$
$80$		0			0
$81$	−12.8802	−	79.9694i	−0.159014	−	0.987276i
$82$		0			0
$83$	−53.7042	−	93.0184i	−0.647038	−	1.12070i	−0.983827	−	0.179123i	$-0.942674\pi$
$83$	−53.7042	−	93.0184i	−0.647038	−	1.12070i	0.336788	−	0.941580i	$-0.390659\pi$
$84$		0			0
$85$	−11.8962			−0.139955
$86$		0			0
$87$	129.825	+	11.8437i	1.49224	+	0.136135i
$88$		0			0
$89$	−122.606	+	70.7865i	−1.37759	+	0.795354i	−0.991869	−	0.127259i	$-0.959382\pi$
$89$	−122.606	+	70.7865i	−1.37759	+	0.795354i	−0.385725	+	0.922614i	$0.626049\pi$
$90$		0			0
$91$	−11.4661	+	6.61993i	−0.126001	+	0.0727465i
$92$		0			0
$93$	−99.9854	−	9.12151i	−1.07511	−	0.0980808i
$94$		0			0
$95$	−1.12845	−	12.8976i	−0.0118784	−	0.135764i
$96$		0			0
$97$		−	171.665i		−	1.76974i	−0.465836	−	0.884871i	$-0.654246\pi$
$97$		−	171.665i		−	1.76974i	0.465836	−	0.884871i	$-0.345754\pi$
$98$		0			0
$99$	131.868	+	24.2621i	1.33200	+	0.245072i
$100$		0			0
$101$	95.2105	−	164.910i	0.942679	−	1.63277i	0.182345	−	0.983235i	$-0.441631\pi$
$101$	95.2105	−	164.910i	0.942679	−	1.63277i	0.760334	−	0.649533i	$-0.225035\pi$
$102$		0			0
$103$	−82.2476	−	47.4857i	−0.798520	−	0.461026i	0.0444333	−	0.999012i	$-0.485852\pi$
$103$	−82.2476	−	47.4857i	−0.798520	−	0.461026i	−0.842953	+	0.537987i	$0.819185\pi$
$104$		0			0
$105$	−1.03848	+	11.3833i	−0.00989031	+	0.108413i
$106$		0			0
$107$			21.9122i			0.204787i	0.994744	+	0.102393i	$0.0326500\pi$
$107$			21.9122i			0.204787i	−0.994744	+	0.102393i	$0.967350\pi$
$108$		0			0
$109$	−170.338	−	98.3447i	−1.56273	−	0.902245i	−0.996979	−	0.0776724i	$-0.975251\pi$
$109$	−170.338	−	98.3447i	−1.56273	−	0.902245i	−0.565756	−	0.824573i	$-0.691415\pi$
$110$		0			0
$111$	38.1376	+	82.5850i	0.343582	+	0.744009i
$112$		0			0
$113$	4.06724	+	2.34822i	0.0359933	+	0.0207807i	0.517889	−	0.855448i	$-0.326718\pi$
$113$	4.06724	+	2.34822i	0.0359933	+	0.0207807i	−0.481895	+	0.876229i	$0.660051\pi$
$114$		0			0
$115$	−3.55992	−	6.16596i	−0.0309558	−	0.0536170i
$116$		0			0
$117$	−16.2225	−	13.8187i	−0.138654	−	0.118109i
$118$		0			0
$119$	97.6193			0.820331
$120$		0			0
$121$	−50.4742	+	87.4238i	−0.417142	+	0.722511i
$122$		0			0
$123$	−97.4373	+	138.062i	−0.792173	+	1.12245i
$124$		0			0
$125$	33.7542			0.270034
$126$		0			0
$127$	−180.051	+	103.952i	−1.41772	+	0.818523i	−0.996099	−	0.0882482i	$-0.971873\pi$
$127$	−180.051	+	103.952i	−1.41772	+	0.818523i	−0.421624	+	0.906771i	$0.638540\pi$
$128$		0			0
$129$	170.174	−	78.5860i	1.31918	−	0.609194i
$130$		0			0
$131$	−101.507	−	175.815i	−0.774861	−	1.34210i	−0.934873	−	0.354983i	$-0.884487\pi$
$131$	−101.507	−	175.815i	−0.774861	−	1.34210i	0.160012	−	0.987115i	$-0.448847\pi$
$132$		0			0
$133$	9.25996	+	105.836i	0.0696238	+	0.795763i
$134$		0			0
$135$	−17.8231	+	4.56369i	−0.132023	+	0.0338051i
$136$		0			0
$137$	44.5917	−	77.2351i	0.325487	−	0.563760i	−0.656124	−	0.754653i	$-0.727805\pi$
$137$	44.5917	−	77.2351i	0.325487	−	0.563760i	0.981611	+	0.190894i	$0.0611385\pi$
$138$		0			0
$139$	−165.847			−1.19315			−0.596573	−	0.802559i	$-0.703471\pi$
$139$	−165.847			−1.19315			−0.596573	+	0.802559i	$0.703471\pi$
$140$		0			0
$141$	−23.6158	+	258.865i	−0.167488	+	1.83592i
$142$		0			0
$143$	30.5494	−	17.6377i	0.213632	−	0.123340i
$144$		0			0
$145$		−	29.6105i		−	0.204210i
$146$		0			0
$147$	−4.83341	+	52.9814i	−0.0328804	+	0.360418i
$148$		0			0
$149$	77.9783	+	135.062i	0.523344	+	0.906459i	0.999631	+	0.0271686i	$0.00864909\pi$
$149$	77.9783	+	135.062i	0.523344	+	0.906459i	−0.476287	+	0.879290i	$0.658018\pi$
$150$		0			0
$151$	255.830	−	147.703i	1.69424	−	0.978168i	0.743212	−	0.669056i	$-0.233302\pi$
$151$	255.830	−	147.703i	1.69424	−	0.978168i	0.951026	−	0.309112i	$-0.100032\pi$
$152$		0			0
$153$	52.6423	+	148.042i	0.344067	+	0.967597i
$154$		0			0
$155$			22.8047i			0.147127i
$156$		0			0
$157$	34.2907	+	59.3933i	0.218412	+	0.378301i	0.954323	−	0.298778i	$-0.0965789\pi$
$157$	34.2907	+	59.3933i	0.218412	+	0.378301i	−0.735910	+	0.677079i	$0.763246\pi$
$158$		0			0
$159$	−87.3599	+	123.783i	−0.549434	+	0.778509i
$160$		0			0
$161$	29.2124	+	50.5974i	0.181444	+	0.314269i
$162$		0			0
$163$	54.7677			0.335998			0.167999	−	0.985787i	$-0.446269\pi$
$163$	54.7677			0.335998			0.167999	+	0.985787i	$0.446269\pi$
$164$		0			0
$165$	2.76686	−	30.3290i	0.0167689	−	0.183812i
$166$		0			0
$167$			104.833i			0.627745i	0.949465	+	0.313873i	$0.101627\pi$
$167$			104.833i			0.627745i	−0.949465	+	0.313873i	$0.898373\pi$
$168$		0			0
$169$	163.394			0.966825
$170$		0			0
$171$	−155.510	+	71.1164i	−0.909417	+	0.415886i
$172$		0			0
$173$			115.208i			0.665940i	0.942937	+	0.332970i	$0.108051\pi$
$173$			115.208i			0.665940i	−0.942937	+	0.332970i	$0.891949\pi$
$174$		0			0
$175$	−137.194			−0.783966
$176$		0			0
$177$	−27.7798	+	39.3621i	−0.156948	+	0.222385i
$178$		0			0
$179$			136.922i			0.764928i	0.923970	+	0.382464i	$0.124924\pi$
$179$			136.922i			0.764928i	−0.923970	+	0.382464i	$0.875076\pi$
$180$		0			0
$181$	−80.6052	+	46.5374i	−0.445332	+	0.257113i	−0.705857	−	0.708354i	$-0.749438\pi$
$181$	−80.6052	+	46.5374i	−0.445332	+	0.257113i	0.260524	+	0.965467i	$0.416105\pi$
$182$		0			0
$183$	−0.119897	+	1.31425i	−0.000655176	+	0.00718170i
$184$		0			0
$185$	17.8936	−	10.3309i	0.0967220	−	0.0558425i
$186$		0			0
$187$	−260.090			−1.39086
$188$		0			0
$189$	146.255	−	37.4493i	0.773837	−	0.198145i
$190$		0			0
$191$	−17.8353	−	30.8917i	−0.0933786	−	0.161737i	0.815552	−	0.578684i	$-0.196433\pi$
$191$	−17.8353	−	30.8917i	−0.0933786	−	0.161737i	−0.908931	+	0.416947i	$0.863100\pi$
$192$		0			0
$193$	−127.581	+	73.6587i	−0.661039	+	0.381651i	−0.792673	−	0.609647i	$-0.791311\pi$
$193$	−127.581	+	73.6587i	−0.661039	+	0.381651i	0.131634	+	0.991298i	$0.457978\pi$
$194$		0			0
$195$	−2.79100	+	3.95466i	−0.0143128	+	0.0202803i
$196$		0			0
$197$	91.9844			0.466926			0.233463	−	0.972366i	$-0.424994\pi$
$197$	91.9844			0.466926			0.233463	+	0.972366i	$0.424994\pi$
$198$		0			0
$199$	79.6590	+	137.973i	0.400296	+	0.693334i	0.993762	−	0.111526i	$-0.0355738\pi$
$199$	79.6590	+	137.973i	0.400296	+	0.693334i	−0.593465	+	0.804860i	$0.702241\pi$
$200$		0			0
$201$	51.6596	+	111.866i	0.257013	+	0.556548i
$202$		0			0
$203$			242.982i			1.19695i
$204$		0			0
$205$	33.2400	+	19.1911i	0.162146	+	0.0936153i
$206$		0			0
$207$	−60.9792	+	71.5866i	−0.294586	+	0.345829i
$208$		0			0
$209$	−24.6716	−	281.983i	−0.118046	−	1.34920i
$210$		0			0
$211$	−237.914	+	137.360i	−1.12755	+	0.650993i	−0.943318	−	0.331889i	$-0.892314\pi$
$211$	−237.914	+	137.360i	−1.12755	+	0.650993i	−0.184235	+	0.982882i	$0.558981\pi$
$212$		0			0
$213$	−217.075	−	19.8034i	−1.01913	−	0.0929739i
$214$		0			0
$215$	−21.2877	−	36.8713i	−0.0990124	−	0.171494i
$216$		0			0
$217$		−	187.134i		−	0.862368i
$218$		0			0
$219$	−20.8976	+	229.069i	−0.0954229	+	1.04598i
$220$		0			0
$221$	35.7993	+	20.6687i	0.161988	+	0.0935237i
$222$		0			0
$223$			128.065i			0.574281i	0.957888	+	0.287141i	$0.0927047\pi$
$223$			128.065i			0.574281i	−0.957888	+	0.287141i	$0.907295\pi$
$224$		0			0
$225$	−73.9835	−	208.059i	−0.328815	−	0.924705i
$226$		0			0
$227$	79.1787	−	45.7138i	0.348805	−	0.201383i	−0.315354	−	0.948974i	$-0.602123\pi$
$227$	79.1787	−	45.7138i	0.348805	−	0.201383i	0.664159	+	0.747592i	$0.268790\pi$
$228$		0			0
$229$	−17.3912	+	30.1225i	−0.0759442	+	0.131539i	−0.901496	−	0.432786i	$-0.857530\pi$
$229$	−17.3912	+	30.1225i	−0.0759442	+	0.131539i	0.825552	+	0.564326i	$0.190864\pi$
$230$		0			0
$231$	−22.7047	+	248.877i	−0.0982886	+	1.07739i
$232$		0			0
$233$	46.6581	−	80.8142i	0.200249	−	0.346842i	−0.748359	−	0.663293i	$-0.769158\pi$
$233$	46.6581	−	80.8142i	0.200249	−	0.346842i	0.948609	+	0.316452i	$0.102491\pi$
$234$		0			0
$235$	59.0420			0.251243
$236$		0			0
$237$	−151.887	−	328.903i	−0.640874	−	1.38778i
$238$		0			0
$239$	206.209	−	357.165i	0.862801	−	1.49441i	−0.00641358	−	0.999979i	$-0.502042\pi$
$239$	206.209	−	357.165i	0.862801	−	1.49441i	0.869214	−	0.494435i	$-0.164625\pi$
$240$		0			0
$241$	−148.987	−	86.0178i	−0.618204	−	0.356920i	0.157966	−	0.987445i	$-0.449507\pi$
$241$	−148.987	−	86.0178i	−0.618204	−	0.356920i	−0.776169	+	0.630524i	$0.782840\pi$
$242$		0			0
$243$	135.663	+	201.605i	0.558283	+	0.829651i
$244$		0			0
$245$	12.0840			0.0493226
$246$		0			0
$247$	−19.0127	+	40.7733i	−0.0769744	+	0.165074i
$248$		0			0
$249$	263.264	+	185.799i	1.05728	+	0.746180i
$250$		0			0
$251$	186.771	+	323.497i	0.744108	+	1.28883i	0.950610	+	0.310387i	$0.100459\pi$
$251$	186.771	+	323.497i	0.744108	+	1.28883i	−0.206502	+	0.978446i	$0.566208\pi$
$252$		0			0
$253$	−77.8316	−	134.808i	−0.307635	−	0.532839i
$254$		0			0
$255$	32.4006	−	14.9626i	0.127061	−	0.0586767i
$256$		0			0
$257$		−	130.571i		−	0.508058i	−0.967197	−	0.254029i	$-0.918244\pi$
$257$		−	130.571i		−	0.508058i	0.967197	−	0.254029i	$-0.0817559\pi$
$258$		0			0
$259$	−146.833	+	84.7742i	−0.566924	+	0.327314i
$260$		0			0
$261$	−368.488	+	131.030i	−1.41183	+	0.502032i
$262$		0			0
$263$	−25.3716			−0.0964699			−0.0482349	−	0.998836i	$-0.515360\pi$
$263$	−25.3716			−0.0964699			−0.0482349	+	0.998836i	$0.515360\pi$
$264$		0			0
$265$	29.8022	+	17.2063i	0.112461	+	0.0649295i
$266$		0			0
$267$	244.898	−	347.003i	0.917221	−	1.29964i
$268$		0			0
$269$	−128.863	−	74.3993i	−0.479046	−	0.276577i	0.240973	−	0.970532i	$-0.422534\pi$
$269$	−128.863	−	74.3993i	−0.479046	−	0.276577i	−0.720019	+	0.693954i	$0.755867\pi$
$270$		0			0
$271$	198.014	−	342.970i	0.730678	−	1.26557i	−0.225916	−	0.974147i	$-0.572537\pi$
$271$	198.014	−	342.970i	0.730678	−	1.26557i	0.956594	−	0.291425i	$-0.0941292\pi$
$272$		0			0
$273$	22.9028	−	32.4516i	0.0838929	−	0.118870i
$274$		0			0
$275$	365.531			1.32920
$276$		0			0
$277$	137.542	+	238.230i	0.496541	+	0.860035i	0.999992	−	0.00398925i	$-0.00126982\pi$
$277$	137.542	+	238.230i	0.496541	+	0.860035i	−0.503451	+	0.864024i	$0.667936\pi$
$278$		0			0
$279$	283.794	−	100.914i	1.01718	−	0.361699i
$280$		0			0
$281$	321.322	+	185.515i	1.14349	+	0.660197i	0.947294	−	0.320367i	$-0.103806\pi$
$281$	321.322	+	185.515i	1.14349	+	0.660197i	0.196201	+	0.980564i	$0.437140\pi$
$282$		0			0
$283$	49.0115	+	84.8904i	0.173185	+	0.299966i	0.939532	−	0.342462i	$-0.111261\pi$
$283$	49.0115	+	84.8904i	0.173185	+	0.299966i	−0.766346	+	0.642428i	$0.777927\pi$
$284$		0			0
$285$	19.2955	+	33.7086i	0.0677034	+	0.118276i
$286$		0			0
$287$	−272.765	−	157.481i	−0.950401	−	0.548714i
$288$		0			0
$289$	−7.89361	−	13.6721i	−0.0273135	−	0.0473084i
$290$		0			0
$291$	215.913	+	467.548i	0.741969	+	1.60669i
$292$		0			0
$293$	−341.458	−	197.141i	−1.16538	−	0.672835i	−0.212796	−	0.977097i	$-0.568257\pi$
$293$	−341.458	−	197.141i	−1.16538	−	0.672835i	−0.952588	+	0.304262i	$0.901590\pi$
$294$		0			0
$295$	9.47689	+	5.47148i	0.0321250	+	0.0185474i
$296$		0			0
$297$	−389.673	+	99.7775i	−1.31203	+	0.335951i
$298$		0			0
$299$			24.7403i			0.0827436i
$300$		0			0
$301$	174.685	+	302.563i	0.580349	+	1.00519i
$302$		0			0
$303$	−51.8999	+	568.901i	−0.171287	+	1.87756i
$304$		0			0
$305$	0.299755			0.000982805
$306$		0			0
$307$	−450.819	−	260.280i	−1.46847	−	0.847819i	−0.469090	−	0.883150i	$-0.655418\pi$
$307$	−450.819	−	260.280i	−1.46847	−	0.847819i	−0.999376	+	0.0353313i	$0.988751\pi$
$308$		0			0
$309$	283.736	+	25.8848i	0.918238	+	0.0837695i
$310$		0			0
$311$	−89.2653	+	154.612i	−0.287027	+	0.497145i	−0.973099	−	0.230389i	$-0.926000\pi$
$311$	−89.2653	+	154.612i	−0.287027	+	0.497145i	0.686072	+	0.727534i	$0.259334\pi$
$312$		0			0
$313$	95.6595	−	165.687i	0.305621	−	0.529352i	−0.671778	−	0.740752i	$-0.734469\pi$
$313$	95.6595	−	165.687i	0.305621	−	0.529352i	0.977399	+	0.211401i	$0.0678025\pi$
$314$		0			0
$315$	−11.4890	−	32.3099i	−0.0364732	−	0.102571i
$316$		0			0
$317$	142.358	+	82.1907i	0.449080	+	0.259277i	0.707442	−	0.706772i	$-0.249849\pi$
$317$	142.358	+	82.1907i	0.449080	+	0.259277i	−0.258361	+	0.966048i	$0.583183\pi$
$318$		0			0
$319$		−	647.384i		−	2.02942i
$320$		0			0
$321$	−27.5602	−	59.6802i	−0.0858574	−	0.185920i
$322$		0			0
$323$	271.716	−	190.259i	0.841226	−	0.589038i
$324$		0			0
$325$	−50.3123	−	29.0478i	−0.154807	−	0.0893780i
$326$		0			0
$327$	587.628	+	53.6084i	1.79703	+	0.163940i
$328$		0			0
$329$	−484.494			−1.47263
$330$		0			0
$331$	86.5524	−	49.9711i	0.261488	−	0.150970i	−0.363525	−	0.931584i	$-0.618427\pi$
$331$	86.5524	−	49.9711i	0.261488	−	0.150970i	0.625013	+	0.780614i	$0.285094\pi$
$332$		0			0
$333$	−207.744	−	176.961i	−0.623855	−	0.531415i
$334$		0			0
$335$	24.2379	−	13.9938i	0.0723519	−	0.0417724i
$336$		0			0
$337$	−385.329	+	222.470i	−1.14341	+	0.660148i	−0.947273	−	0.320429i	$-0.896173\pi$
$337$	−385.329	+	222.470i	−1.14341	+	0.660148i	−0.196137	+	0.980576i	$0.562840\pi$
$338$		0			0
$339$	−14.0311	−	1.28003i	−0.0413896	−	0.00377591i
$340$		0			0
$341$			498.587i			1.46213i
$342$		0			0
$343$	−373.150			−1.08790
$344$		0			0
$345$	17.4511	+	12.3161i	0.0505829	+	0.0356990i
$346$		0			0
$347$	25.7406	+	44.5839i	0.0741803	+	0.128484i	0.900730	−	0.434380i	$-0.143033\pi$
$347$	25.7406	+	44.5839i	0.0741803	+	0.128484i	−0.826549	+	0.562864i	$0.809699\pi$
$348$		0			0
$349$	−46.4841	−	80.5128i	−0.133192	−	0.230696i	0.791713	−	0.610893i	$-0.209189\pi$
$349$	−46.4841	−	80.5128i	−0.133192	−	0.230696i	−0.924905	+	0.380197i	$0.875856\pi$
$350$		0			0
$351$	61.5643	+	17.2328i	0.175397	+	0.0490962i
$352$		0			0
$353$	−332.939	−	576.668i	−0.943171	−	1.63362i	−0.759373	−	0.650655i	$-0.774494\pi$
$353$	−332.939	−	576.668i	−0.943171	−	1.63362i	−0.183797	−	0.982964i	$-0.558839\pi$
$354$		0			0
$355$			49.5107i			0.139467i
$356$		0			0
$357$	−265.877	+	122.782i	−0.744753	+	0.343926i
$358$		0			0
$359$	−17.3255	+	30.0087i	−0.0482605	+	0.0835897i	−0.889147	−	0.457623i	$-0.848701\pi$
$359$	−17.3255	+	30.0087i	−0.0482605	+	0.0835897i	0.840886	+	0.541212i	$0.182034\pi$
$360$		0			0
$361$	232.049	+	276.540i	0.642794	+	0.766039i
$362$		0			0
$363$	27.5138	−	301.592i	0.0757956	−	0.830833i
$364$		0			0
$365$	52.2462			0.143140
$366$		0			0
$367$	−223.471	+	387.063i	−0.608912	+	1.05467i	0.382508	+	0.923952i	$0.375060\pi$
$367$	−223.471	+	387.063i	−0.608912	+	1.05467i	−0.991420	+	0.130715i	$0.958273\pi$
$368$		0			0
$369$	91.7327	−	498.579i	0.248598	−	1.35116i
$370$		0			0
$371$	−244.555	−	141.194i	−0.659177	−	0.380576i
$372$		0			0
$373$	359.861	+	207.766i	0.964775	+	0.557013i	0.897639	−	0.440731i	$-0.145281\pi$
$373$	359.861	+	207.766i	0.964775	+	0.557013i	0.0671357	+	0.997744i	$0.478614\pi$
$374$		0			0
$375$	−91.9333	+	42.4547i	−0.245155	+	0.113212i
$376$		0			0
$377$	−51.4460	+	89.1071i	−0.136462	+	0.236358i
$378$		0			0
$379$			485.460i			1.28090i	0.768001	+	0.640449i	$0.221252\pi$
$379$			485.460i			1.28090i	−0.768001	+	0.640449i	$0.778748\pi$
$380$		0			0
$381$	359.641	−	509.586i	0.943939	−	1.33750i
$382$		0			0
$383$	−148.710	+	85.8577i	−0.388276	+	0.224172i	−0.681413	−	0.731899i	$-0.738634\pi$
$383$	−148.710	+	85.8577i	−0.388276	+	0.224172i	0.293137	+	0.956071i	$0.405301\pi$
$384$		0			0
$385$	56.7641			0.147439
$386$		0			0
$387$	−364.645	+	428.075i	−0.942234	+	1.10614i
$388$		0			0
$389$	141.077	−	244.352i	0.362665	−	0.628154i	−0.625734	−	0.780037i	$-0.715200\pi$
$389$	141.077	−	244.352i	0.362665	−	0.628154i	0.988398	+	0.151883i	$0.0485337\pi$
$390$		0			0
$391$	91.2070	−	157.975i	0.233266	−	0.404029i
$392$		0			0
$393$	497.597	+	351.180i	1.26615	+	0.893588i
$394$		0			0
$395$	−71.2630	+	41.1437i	−0.180413	+	0.104161i
$396$		0			0
$397$	252.435	−	437.231i	0.635857	−	1.10134i	−0.350476	−	0.936572i	$-0.613980\pi$
$397$	252.435	−	437.231i	0.635857	−	1.10134i	0.986333	−	0.164765i	$-0.0526866\pi$
$398$		0			0
$399$	−158.337	−	276.610i	−0.396835	−	0.693259i
$400$		0			0
$401$	36.8889	−	21.2978i	0.0919923	−	0.0531118i	−0.453298	−	0.891359i	$-0.649753\pi$
$401$	36.8889	−	21.2978i	0.0919923	−	0.0531118i	0.545290	+	0.838247i	$0.316419\pi$
$402$		0			0
$403$	39.6215	−	68.6264i	0.0983163	−	0.170289i
$404$		0			0
$405$	42.8032	−	34.8469i	0.105687	−	0.0860418i
$406$		0			0
$407$	391.213	−	225.867i	0.961210	−	0.554955i
$408$		0			0
$409$		−	404.458i		−	0.988896i	−0.869207	−	0.494448i	$-0.835370\pi$
$409$		−	404.458i		−	0.988896i	0.869207	−	0.494448i	$-0.164630\pi$
$410$		0			0
$411$	−24.3072	+	266.444i	−0.0591417	+	0.648281i
$412$		0			0
$413$	−77.7666	−	44.8986i	−0.188297	−	0.108713i
$414$		0			0
$415$	36.5947	−	63.3839i	0.0881800	−	0.152732i
$416$		0			0
$417$	451.703	−	208.596i	1.08322	−	0.500230i
$418$		0			0
$419$	−216.308	+	374.657i	−0.516249	+	0.894169i	0.483573	+	0.875304i	$0.339339\pi$
$419$	−216.308	+	374.657i	−0.516249	+	0.894169i	−0.999822	+	0.0188652i	$0.993995\pi$
$420$		0			0
$421$		−	23.5995i		−	0.0560557i	−0.999607	−	0.0280279i	$-0.991077\pi$
$421$		−	23.5995i		−	0.0560557i	0.999607	−	0.0280279i	$-0.00892272\pi$
$422$		0			0
$423$	−261.269	−	734.749i	−0.617657	−	1.73699i
$424$		0			0
$425$	214.174	+	370.960i	0.503938	+	0.872847i
$426$		0			0
$427$	−2.45977			−0.00576059
$428$		0			0
$429$	−61.0206	+	86.4619i	−0.142239	+	0.201543i
$430$		0			0
$431$	89.7445	−	51.8140i	0.208224	−	0.120218i	−0.392262	−	0.919854i	$-0.628307\pi$
$431$	89.7445	−	51.8140i	0.208224	−	0.120218i	0.600486	+	0.799636i	$0.294974\pi$
$432$		0			0
$433$	−464.495	+	268.176i	−1.07274	+	0.619344i	−0.928928	−	0.370261i	$-0.879268\pi$
$433$	−464.495	+	268.176i	−1.07274	+	0.619344i	−0.143808	+	0.989606i	$0.545935\pi$
$434$		0			0
$435$	37.2429	+	80.6474i	0.0856158	+	0.185396i
$436$		0			0
$437$	179.924	+	83.8992i	0.411726	+	0.191989i
$438$		0			0
$439$		−	260.499i		−	0.593392i	−0.954972	−	0.296696i	$-0.904115\pi$
$439$		−	260.499i		−	0.593392i	0.954972	−	0.296696i	$-0.0958848\pi$
$440$		0			0
$441$	−53.4735	−	150.380i	−0.121255	−	0.340997i
$442$		0			0
$443$	244.994	−	424.342i	0.553034	−	0.957882i	−0.445020	−	0.895521i	$-0.646803\pi$
$443$	244.994	−	424.342i	0.553034	−	0.957882i	0.998054	−	0.0623617i	$-0.0198632\pi$
$444$		0			0
$445$	−83.5452	−	48.2348i	−0.187742	−	0.108393i
$446$		0			0
$447$	−382.258	−	269.779i	−0.855164	−	0.603533i
$448$		0			0
$449$			783.722i			1.74548i	0.488182	+	0.872742i	$0.337660\pi$
$449$			783.722i			1.74548i	−0.488182	+	0.872742i	$0.662340\pi$
$450$		0			0
$451$	726.737	+	419.582i	1.61139	+	0.930336i
$452$		0			0
$453$	−511.005	+	724.058i	−1.12805	+	1.59836i
$454$		0			0
$455$	−7.81311	−	4.51090i	−0.0171717	−	0.00991407i
$456$		0			0
$457$	−166.574	−	288.514i	−0.364493	−	0.631321i	0.624201	−	0.781264i	$-0.285425\pi$
$457$	−166.574	−	288.514i	−0.364493	−	0.631321i	−0.988695	+	0.149942i	$0.952091\pi$
$458$		0			0
$459$	−329.579	−	336.998i	−0.718036	−	0.734201i
$460$		0			0
$461$	−473.007			−1.02605			−0.513023	−	0.858375i	$-0.671474\pi$
$461$	−473.007			−1.02605			−0.513023	+	0.858375i	$0.671474\pi$
$462$		0			0
$463$	151.128	−	261.762i	0.326411	−	0.565360i	−0.655386	−	0.755294i	$-0.727494\pi$
$463$	151.128	−	261.762i	0.326411	−	0.565360i	0.981797	+	0.189934i	$0.0608274\pi$
$464$		0			0
$465$	−28.6828	−	62.1112i	−0.0616835	−	0.133572i
$466$		0			0
$467$	420.810			0.901093			0.450546	−	0.892753i	$-0.351229\pi$
$467$	420.810			0.901093			0.450546	+	0.892753i	$0.351229\pi$
$468$		0			0
$469$	−198.894	+	114.832i	−0.424082	+	0.244844i
$470$		0			0
$471$	−168.097	−	118.635i	−0.356894	−	0.251878i
$472$		0			0
$473$	−465.419	−	806.129i	−0.983972	−	1.70429i
$474$		0			0
$475$	−381.869	+	267.390i	−0.803936	+	0.562927i
$476$		0			0
$477$	82.2453	−	447.014i	0.172422	−	0.937136i
$478$		0			0
$479$	186.508	−	323.041i	0.389369	−	0.674407i	−0.602996	−	0.797745i	$-0.706026\pi$
$479$	186.508	−	323.041i	0.389369	−	0.674407i	0.992365	+	0.123337i	$0.0393597\pi$
$480$		0			0
$481$	−71.7963			−0.149265
$482$		0			0
$483$	−143.202	−	101.065i	−0.296485	−	0.209245i
$484$		0			0
$485$	101.303	−	58.4873i	0.208872	−	0.120592i
$486$		0			0
$487$		−	666.331i		−	1.36824i	−0.729371	−	0.684118i	$-0.760187\pi$
$487$		−	666.331i		−	1.36824i	0.729371	−	0.684118i	$-0.239813\pi$
$488$		0			0
$489$	−149.166	+	68.8845i	−0.305042	+	0.140868i
$490$		0			0
$491$	−278.509	−	482.392i	−0.567228	−	0.982468i	−0.996839	−	0.0794534i	$-0.974683\pi$
$491$	−278.509	−	482.392i	−0.567228	−	0.982468i	0.429611	−	0.903014i	$-0.358651\pi$
$492$		0			0
$493$	656.999	−	379.319i	1.33266	−	0.769409i
$494$		0			0
$495$	30.6106	+	86.0843i	0.0618397	+	0.173908i
$496$		0			0
$497$		−	406.281i		−	0.817467i
$498$		0			0
$499$	312.553	+	541.357i	0.626358	+	1.08488i	0.988277	+	0.152675i	$0.0487886\pi$
$499$	312.553	+	541.357i	0.626358	+	1.08488i	−0.361918	+	0.932210i	$0.617878\pi$
$500$		0			0
$501$	−131.855	−	285.525i	−0.263184	−	0.569911i
$502$		0			0
$503$	99.7875	+	172.837i	0.198385	+	0.343613i	0.948005	−	0.318256i	$-0.103097\pi$
$503$	99.7875	+	172.837i	0.198385	+	0.343613i	−0.749620	+	0.661868i	$0.769764\pi$
$504$		0			0
$505$	129.755			0.256941
$506$		0			0
$507$	−445.020	+	205.510i	−0.877751	+	0.405344i
$508$		0			0
$509$			176.640i			0.347034i	0.984831	+	0.173517i	$0.0555131\pi$
$509$			176.640i			0.347034i	−0.984831	+	0.173517i	$0.944487\pi$
$510$		0			0
$511$	−428.729			−0.838999
$512$		0			0
$513$	334.102	−	389.288i	0.651271	−	0.758845i
$514$		0			0
$515$		−	64.7146i		−	0.125659i
$516$		0			0
$517$	1290.85			2.49682
$518$		0			0
$519$	−144.903	−	313.780i	−0.279197	−	0.604587i
$520$		0			0
$521$			143.921i			0.276240i	0.990415	+	0.138120i	$0.0441060\pi$
$521$			143.921i			0.276240i	−0.990415	+	0.138120i	$0.955894\pi$
$522$		0			0
$523$	22.5109	−	12.9967i	0.0430419	−	0.0248503i	−0.478325	−	0.878183i	$-0.658756\pi$
$523$	22.5109	−	12.9967i	0.0430419	−	0.0248503i	0.521367	+	0.853333i	$0.325422\pi$
$524$		0			0
$525$	373.663	−	172.557i	0.711739	−	0.328680i
$526$		0			0
$527$	−505.992	+	292.135i	−0.960137	+	0.554336i
$528$		0			0
$529$	−419.826			−0.793622
$530$		0			0
$531$	26.1534	−	142.147i	0.0492531	−	0.267697i
$532$		0			0
$533$	−66.6863	−	115.504i	−0.125115	−	0.216705i
$534$		0			0
$535$	−12.9308	+	7.46561i	−0.0241698	+	0.0139544i
$536$		0			0
$537$	−172.215	−	372.922i	−0.320698	−	0.694455i
$538$		0			0
$539$	264.197			0.490161
$540$		0			0
$541$	387.168	+	670.595i	0.715653	+	1.23955i	0.962707	+	0.270546i	$0.0872041\pi$
$541$	387.168	+	670.595i	0.715653	+	1.23955i	−0.247054	+	0.969002i	$0.579463\pi$
$542$		0			0
$543$	161.004	−	228.132i	0.296509	−	0.420132i
$544$		0			0
$545$		−	134.027i		−	0.245920i
$546$		0			0
$547$	14.4722	+	8.35552i	0.0264574	+	0.0152752i	0.513170	−	0.858287i	$-0.328471\pi$
$547$	14.4722	+	8.35552i	0.0264574	+	0.0152752i	−0.486713	+	0.873562i	$0.661804\pi$
$548$		0			0
$549$	−1.32646	−	3.73031i	−0.00241614	−	0.00679473i
$550$		0			0
$551$	473.569	+	676.321i	0.859472	+	1.22744i
$552$		0			0
$553$	584.779	−	337.622i	1.05747	−	0.610528i
$554$		0			0
$555$	−35.7414	+	50.6430i	−0.0643988	+	0.0912486i
$556$		0			0
$557$	269.959	+	467.583i	0.484666	+	0.839467i	0.999845	−	0.0176161i	$-0.00560766\pi$
$557$	269.959	+	467.583i	0.484666	+	0.839467i	−0.515178	+	0.857083i	$0.672274\pi$
$558$		0			0
$559$			147.943i			0.264656i
$560$		0			0
$561$	708.384	−	327.131i	1.26272	−	0.583121i
$562$		0			0
$563$	−504.214	−	291.108i	−0.895585	−	0.517066i	−0.0198195	−	0.999804i	$-0.506309\pi$
$563$	−504.214	−	291.108i	−0.895585	−	0.517066i	−0.875765	+	0.482738i	$0.839642\pi$
$564$		0			0
$565$			3.20022i			0.00566410i
$566$		0			0
$567$	−351.240	+	285.951i	−0.619471	+	0.504323i
$568$		0			0
$569$	−520.303	+	300.397i	−0.914417	+	0.527939i	−0.881850	−	0.471531i	$-0.843702\pi$
$569$	−520.303	+	300.397i	−0.914417	+	0.527939i	−0.0325670	+	0.999470i	$0.510368\pi$
$570$		0			0
$571$	263.244	−	455.953i	0.461023	−	0.798516i	−0.537989	−	0.842952i	$-0.680816\pi$
$571$	263.244	−	455.953i	0.461023	−	0.798516i	0.999012	+	0.0444360i	$0.0141491\pi$
$572$		0			0
$573$	87.4307	+	61.7043i	0.152584	+	0.107686i
$574$		0			0
$575$	−128.182	+	222.018i	−0.222926	+	0.386119i
$576$		0			0
$577$	679.846			1.17824			0.589121	−	0.808045i	$-0.299474\pi$
$577$	679.846			1.17824			0.589121	+	0.808045i	$0.299474\pi$
$578$		0			0
$579$	254.835	−	361.083i	0.440129	−	0.623632i
$580$		0			0
$581$	−300.293	+	520.123i	−0.516856	+	0.895221i
$582$		0			0
$583$	651.575	+	376.187i	1.11762	+	0.645260i
$584$		0			0
$585$	2.62760	−	14.2813i	0.00449162	−	0.0244126i
$586$		0			0
$587$	431.522			0.735130			0.367565	−	0.929998i	$-0.380191\pi$
$587$	431.522			0.735130			0.367565	+	0.929998i	$0.380191\pi$
$588$		0			0
$589$	−364.723	−	520.873i	−0.619223	−	0.884334i
$590$		0			0
$591$	−250.529	+	115.694i	−0.423908	+	0.195760i
$592$		0			0
$593$	−184.931	−	320.310i	−0.311856	−	0.540151i	0.666908	−	0.745140i	$-0.267617\pi$
$593$	−184.931	−	320.310i	−0.311856	−	0.540151i	−0.978764	+	0.204989i	$0.934284\pi$
$594$		0			0
$595$	33.2595	+	57.6072i	0.0558983	+	0.0968188i
$596$		0			0
$597$	−390.497	−	275.594i	−0.654099	−	0.461631i
$598$		0			0
$599$		−	740.472i		−	1.23618i	−0.786107	−	0.618090i	$-0.787907\pi$
$599$		−	740.472i		−	1.23618i	0.786107	−	0.618090i	$-0.212093\pi$
$600$		0			0
$601$	15.1465	−	8.74483i	0.0252021	−	0.0145505i	−0.487346	−	0.873209i	$-0.662035\pi$
$601$	15.1465	−	8.74483i	0.0252021	−	0.0145505i	0.512548	+	0.858658i	$0.328702\pi$
$602$		0			0
$603$	−281.401	−	239.704i	−0.466669	−	0.397520i
$604$		0			0
$605$	−68.7874			−0.113698
$606$		0			0
$607$	601.906	+	347.510i	0.991607	+	0.572505i	0.905754	−	0.423803i	$-0.139305\pi$
$607$	601.906	+	347.510i	0.991607	+	0.572505i	0.0858530	+	0.996308i	$0.472638\pi$
$608$		0			0
$609$	−305.612	−	661.787i	−0.501826	−	1.08668i
$610$		0			0
$611$	−177.675	−	102.581i	−0.290795	−	0.167890i
$612$		0			0
$613$	140.459	−	243.281i	0.229133	−	0.396870i	−0.728418	−	0.685133i	$-0.759744\pi$
$613$	140.459	−	243.281i	0.229133	−	0.396870i	0.957551	+	0.288263i	$0.0930776\pi$
$614$		0			0
$615$	−114.671	−	10.4612i	−0.186456	−	0.0170101i
$616$		0			0
$617$	−425.784			−0.690087			−0.345044	−	0.938587i	$-0.612136\pi$
$617$	−425.784			−0.690087			−0.345044	+	0.938587i	$0.612136\pi$
$618$		0			0
$619$	−268.153	−	464.455i	−0.433204	−	0.750332i	0.563943	−	0.825814i	$-0.309284\pi$
$619$	−268.153	−	464.455i	−0.433204	−	0.750332i	−0.997147	+	0.0754821i	$0.975950\pi$
$620$		0			0
$621$	76.0448	−	271.671i	0.122455	−	0.437474i
$622$		0			0
$623$	685.565	+	395.811i	1.10043	+	0.635331i
$624$		0			0
$625$	−295.196	−	511.294i	−0.472313	−	0.818070i
$626$		0			0
$627$	421.863	+	736.982i	0.672827	+	1.17541i
$628$		0			0
$629$	458.443	+	264.682i	0.728844	+	0.420798i
$630$		0			0
$631$	42.3648	+	73.3780i	0.0671391	+	0.116288i	0.897641	−	0.440728i	$-0.145280\pi$
$631$	42.3648	+	73.3780i	0.0671391	+	0.116288i	−0.830502	+	0.557016i	$0.811946\pi$
$632$		0			0
$633$	475.219	−	673.351i	0.750740	−	1.06375i
$634$		0			0
$635$	−122.689	−	70.8344i	−0.193211	−	0.111550i
$636$		0			0
$637$	−36.3646	−	20.9951i	−0.0570872	−	0.0329593i
$638$		0			0
$639$	616.136	−	219.092i	0.964219	−	0.342866i
$640$		0			0
$641$			1011.89i			1.57862i	0.613996	+	0.789309i	$0.289561\pi$
$641$			1011.89i			1.57862i	−0.613996	+	0.789309i	$0.710439\pi$
$642$		0			0
$643$	−620.422	−	1074.60i	−0.964887	−	1.67123i	−0.709919	−	0.704283i	$-0.751269\pi$
$643$	−620.422	−	1074.60i	−0.964887	−	1.67123i	−0.254967	−	0.966950i	$-0.582065\pi$
$644$		0			0
$645$	104.354	+	73.6483i	0.161790	+	0.114183i
$646$		0			0
$647$	−491.485			−0.759637			−0.379819	−	0.925061i	$-0.624014\pi$
$647$	−491.485			−0.759637			−0.379819	+	0.925061i	$0.624014\pi$
$648$		0			0
$649$	207.196	+	119.625i	0.319254	+	0.184322i
$650$		0			0
$651$	235.369	+	509.680i	0.361550	+	0.782918i
$652$		0			0
$653$	−544.371	+	942.878i	−0.833646	+	1.44392i	0.0614817	+	0.998108i	$0.480417\pi$
$653$	−544.371	+	942.878i	−0.833646	+	1.44392i	−0.895128	+	0.445809i	$0.852916\pi$
$654$		0			0
$655$	69.1680	−	119.802i	0.105600	−	0.182905i
$656$		0			0
$657$	−231.197	−	650.179i	−0.351898	−	0.989618i
$658$		0			0
$659$	38.8040	+	22.4035i	0.0588831	+	0.0339962i	0.529153	−	0.848527i	$-0.322510\pi$
$659$	38.8040	+	22.4035i	0.0588831	+	0.0339962i	−0.470269	+	0.882523i	$0.655843\pi$
$660$		0			0
$661$			626.834i			0.948312i	0.880441	+	0.474156i	$0.157247\pi$
$661$			626.834i			0.948312i	−0.880441	+	0.474156i	$0.842753\pi$
$662$		0			0
$663$	−123.500	−	11.2667i	−0.186274	−	0.0169935i
$664$		0			0
$665$	−59.3013	+	41.5236i	−0.0891749	+	0.0624415i
$666$		0			0
$667$	393.212	+	227.021i	0.589523	+	0.340361i
$668$		0			0
$669$	−161.074	−	348.798i	−0.240769	−	0.521372i
$670$		0			0
$671$	6.55365			0.00976698
$672$		0			0
$673$	978.836	−	565.131i	1.45444	−	0.839719i	0.455708	−	0.890129i	$-0.349386\pi$
$673$	978.836	−	565.131i	1.45444	−	0.839719i	0.998729	+	0.0504103i	$0.0160529\pi$
$674$		0			0
$675$	463.189	+	473.617i	0.686207	+	0.701655i
$676$		0			0
$677$	−269.720	+	155.723i	−0.398405	+	0.230019i	−0.685796	−	0.727794i	$-0.740546\pi$
$677$	−269.720	+	155.723i	−0.398405	+	0.230019i	0.287390	+	0.957814i	$0.407212\pi$
$678$		0			0
$679$	−831.285	+	479.942i	−1.22428	+	0.706837i
$680$		0			0
$681$	−158.155	+	224.094i	−0.232239	+	0.329066i
$682$		0			0
$683$		−	30.4855i		−	0.0446348i	−0.999751	−	0.0223174i	$-0.992896\pi$
$683$		−	30.4855i		−	0.0446348i	0.999751	−	0.0223174i	$-0.00710443\pi$
$684$		0			0
$685$	60.7706			0.0887163
$686$		0			0
$687$	9.48008	−	103.916i	0.0137992	−	0.151260i
$688$		0			0
$689$	−59.7893	−	103.558i	−0.0867769	−	0.150302i
$690$		0			0
$691$	−231.091	−	400.262i	−0.334431	−	0.579251i	0.648945	−	0.760836i	$-0.275211\pi$
$691$	−231.091	−	400.262i	−0.334431	−	0.579251i	−0.983375	+	0.181585i	$0.941877\pi$
$692$		0			0
$693$	−251.189	−	706.401i	−0.362466	−	1.01934i
$694$		0			0
$695$	−56.5052	−	97.8699i	−0.0813024	−	0.140820i
$696$		0			0
$697$			983.375i			1.41087i
$698$		0			0
$699$	−25.4337	+	278.791i	−0.0363858	+	0.398842i
$700$		0			0
$701$	−640.659	+	1109.65i	−0.913922	+	1.58296i	−0.105449	+	0.994425i	$0.533628\pi$
$701$	−640.659	+	1109.65i	−0.913922	+	1.58296i	−0.808473	+	0.588534i	$0.799705\pi$
$702$		0			0
$703$	−243.475	+	522.139i	−0.346337	+	0.742730i
$704$		0			0
$705$	−160.807	+	74.2606i	−0.228095	+	0.105334i
$706$		0			0
$707$	−1064.76			−1.50603
$708$		0			0
$709$	59.5253	−	103.101i	0.0839567	−	0.145417i	−0.820989	−	0.570943i	$-0.806578\pi$
$709$	59.5253	−	103.101i	0.0839567	−	0.145417i	0.904946	+	0.425526i	$0.139911\pi$
$710$		0			0
$711$	827.362	+	704.767i	1.16366	+	0.991233i
$712$		0			0
$713$	−302.835	−	174.842i	−0.424733	−	0.245220i
$714$		0			0
$715$	20.8167	+	12.0185i	0.0291143	+	0.0168091i
$716$		0			0
$717$	−112.406	+	1232.14i	−0.156773	+	1.71847i
$718$		0			0
$719$	23.4411	−	40.6012i	0.0326024	−	0.0564690i	−0.849264	−	0.527969i	$-0.822954\pi$
$719$	23.4411	−	40.6012i	0.0326024	−	0.0564690i	0.881866	+	0.471500i	$0.156287\pi$
$720$		0			0
$721$			531.043i			0.736537i
$722$		0			0
$723$	513.972	+	46.8889i	0.710888	+	0.0648532i
$724$		0			0
$725$	−923.346	+	533.094i	−1.27358	+	0.735302i
$726$		0			0
$727$	−922.694			−1.26918			−0.634590	−	0.772849i	$-0.718831\pi$
$727$	−922.694			−1.26918			−0.634590	+	0.772849i	$0.718831\pi$
$728$		0			0
$729$	−623.063	−	378.463i	−0.854681	−	0.519153i
$730$		0			0
$731$	545.401	−	944.663i	0.746103	−	1.29229i
$732$		0			0
$733$	−379.867	+	657.948i	−0.518236	+	0.897610i	0.481540	+	0.876424i	$0.340078\pi$
$733$	−379.867	+	657.948i	−0.518236	+	0.897610i	−0.999776	+	0.0211862i	$0.993256\pi$
$734$		0			0
$735$	−32.9122	+	15.1988i	−0.0447785	+	0.0206786i
$736$		0			0
$737$	529.920	−	305.950i	0.719024	−	0.415128i
$738$		0			0
$739$	−455.753	+	789.387i	−0.616716	+	1.06818i	0.373365	+	0.927684i	$0.378204\pi$
$739$	−455.753	+	789.387i	−0.616716	+	1.06818i	−0.990081	+	0.140498i	$0.955130\pi$
$740$		0			0
$741$	0.500142	−	134.964i	0.000674956	−	0.182138i
$742$		0			0
$743$	−624.251	+	360.411i	−0.840176	+	0.485076i	−0.857324	−	0.514777i	$-0.827875\pi$
$743$	−624.251	+	360.411i	−0.840176	+	0.485076i	0.0171482	+	0.999853i	$0.494541\pi$
$744$		0			0
$745$	−53.1354	+	92.0332i	−0.0713226	+	0.123534i
$746$		0			0
$747$	−950.718	−	174.921i	−1.27271	−	0.234164i
$748$		0			0
$749$	106.109	−	61.2623i	0.141668	−	0.0817921i
$750$		0			0
$751$		−	204.996i		−	0.272964i	−0.990643	−	0.136482i	$-0.956420\pi$
$751$		−	204.996i		−	0.272964i	0.990643	−	0.136482i	$-0.0435796\pi$
$752$		0			0
$753$	−915.573	−	646.166i	−1.21590	−	0.858123i
$754$		0			0
$755$	174.326	+	100.647i	0.230895	+	0.133307i
$756$		0			0
$757$	−144.571	+	250.405i	−0.190979	+	0.330785i	−0.945575	−	0.325404i	$-0.894500\pi$
$757$	−144.571	+	250.405i	−0.190979	+	0.330785i	0.754596	+	0.656190i	$0.227833\pi$
$758$		0			0
$759$	381.539	+	269.272i	0.502686	+	0.354772i
$760$		0			0
$761$	312.556	−	541.362i	0.410717	−	0.711383i	−0.584251	−	0.811573i	$-0.698612\pi$
$761$	312.556	−	541.362i	0.410717	−	0.711383i	0.994968	+	0.100190i	$0.0319450\pi$
$762$		0			0
$763$			1099.81i			1.44143i
$764$		0			0
$765$	−69.4273	+	81.5043i	−0.0907546	+	0.106542i
$766$		0			0
$767$	−19.0126	−	32.9307i	−0.0247882	−	0.0429345i
$768$		0			0
$769$	891.808			1.15970			0.579849	−	0.814724i	$-0.303112\pi$
$769$	891.808			1.15970			0.579849	+	0.814724i	$0.303112\pi$
$770$		0			0
$771$	164.227	+	355.624i	0.213005	+	0.461250i
$772$		0			0
$773$	−508.443	+	293.550i	−0.657753	+	0.379754i	−0.791420	−	0.611272i	$-0.790658\pi$
$773$	−508.443	+	293.550i	−0.657753	+	0.379754i	0.133667	+	0.991026i	$0.457325\pi$
$774$		0			0
$775$	711.121	−	410.566i	0.917576	−	0.529763i
$776$		0			0
$777$	293.291	−	415.573i	0.377466	−	0.534842i
$778$		0			0
$779$	−1066.15	+	93.2808i	−1.36861	+	0.119744i
$780$		0			0
$781$			1082.47i			1.38600i
$782$		0			0
$783$	838.813	−	820.345i	1.07128	−	1.04769i
$784$		0			0
$785$	−23.3661	+	40.4713i	−0.0297658	+	0.0515558i
$786$		0			0
$787$	−735.073	−	424.395i	−0.934020	−	0.539257i	−0.0459391	−	0.998944i	$-0.514628\pi$
$787$	−735.073	−	424.395i	−0.934020	−	0.539257i	−0.888081	+	0.459688i	$0.847961\pi$
$788$		0			0
$789$	69.1022	−	31.9113i	0.0875820	−	0.0404453i
$790$		0			0
$791$		−	26.2607i		−	0.0331994i
$792$		0			0
$793$	−0.902056	−	0.520802i	−0.00113752	−	0.000656749i
$794$		0			0
$795$	−102.811	−	9.37928i	−0.129322	−	0.0117978i
$796$		0			0
$797$	976.928	+	564.030i	1.22576	+	0.707691i	0.966139	−	0.258021i	$-0.0830703\pi$
$797$	976.928	+	564.030i	1.22576	+	0.707691i	0.259617	+	0.965712i	$0.416404\pi$
$798$		0			0
$799$	756.344	+	1310.03i	0.946613	+	1.63958i
$800$		0			0
$801$	−230.560	+	1253.12i	−0.287840	+	1.56445i
$802$		0			0
$803$	1142.28			1.42251
$804$		0			0
$805$	−19.9057	+	34.4777i	−0.0247276	+	0.0428294i
$806$		0			0
$807$	444.550	+	40.5556i	0.550867	+	0.0502548i
$808$		0			0
$809$	909.119			1.12376			0.561878	−	0.827220i	$-0.310079\pi$
$809$	909.119			1.12376			0.561878	+	0.827220i	$0.310079\pi$
$810$		0			0
$811$	645.717	−	372.805i	0.796199	−	0.459686i	−0.0459414	−	0.998944i	$-0.514629\pi$
$811$	645.717	−	372.805i	0.796199	−	0.459686i	0.842140	+	0.539258i	$0.181295\pi$
$812$		0			0
$813$	−107.939	+	1183.17i	−0.132766	+	1.45531i
$814$		0			0
$815$	18.6597	+	32.3195i	0.0228953	+	0.0396559i
$816$		0			0
$817$	1075.92	+	501.702i	1.31691	+	0.614078i
$818$		0			0
$819$	−21.5619	+	117.192i	−0.0263271	+	0.143091i
$820$		0			0
$821$	58.9196	−	102.052i	0.0717656	−	0.124302i	−0.827910	−	0.560862i	$-0.810470\pi$
$821$	58.9196	−	102.052i	0.0717656	−	0.124302i	0.899675	+	0.436560i	$0.143803\pi$
$822$		0			0
$823$	−446.415			−0.542424			−0.271212	−	0.962520i	$-0.587424\pi$
$823$	−446.415			−0.542424			−0.271212	+	0.962520i	$0.587424\pi$
$824$		0			0
$825$	−995.563	+	459.749i	−1.20674	+	0.557272i
$826$		0			0
$827$	−198.286	+	114.480i	−0.239765	+	0.138428i	−0.615069	−	0.788474i	$-0.710872\pi$
$827$	−198.286	+	114.480i	−0.239765	+	0.138428i	0.375304	+	0.926902i	$0.377538\pi$
$828$		0			0
$829$			705.074i			0.850511i	0.905073	+	0.425256i	$0.139816\pi$
$829$			705.074i			0.850511i	−0.905073	+	0.425256i	$0.860184\pi$
$830$		0			0
$831$	−674.246	−	475.850i	−0.811367	−	0.572623i
$832$		0			0
$833$	154.800	+	268.121i	0.185834	+	0.321874i
$834$		0			0
$835$	−61.8644	+	35.7174i	−0.0740891	+	0.0427754i
$836$		0			0
$837$	−646.017	+	631.794i	−0.771825	+	0.754832i
$838$		0			0
$839$			762.069i			0.908306i	0.890924	+	0.454153i	$0.150058\pi$
$839$			762.069i			0.908306i	−0.890924	+	0.454153i	$0.849942\pi$
$840$		0			0
$841$	523.651	+	906.991i	0.622653	+	1.07847i
$842$		0			0
$843$	−1108.49	−	101.126i	−1.31493	−	0.119959i
$844$		0			0
$845$	55.6692	+	96.4219i	0.0658807	+	0.114109i
$846$		0			0
$847$	564.464			0.666428
$848$		0			0
$849$	−240.260	−	169.564i	−0.282991	−	0.199721i
$850$		0			0
$851$			316.823i			0.372295i
$852$		0			0
$853$	−545.586			−0.639608			−0.319804	−	0.947484i	$-0.603617\pi$
$853$	−545.586			−0.639608			−0.319804	+	0.947484i	$0.603617\pi$
$854$		0			0
$855$	−94.9506	−	67.5400i	−0.111053	−	0.0789941i
$856$		0			0
$857$			107.063i			0.124927i	0.998047	+	0.0624636i	$0.0198957\pi$
$857$			107.063i			0.124927i	−0.998047	+	0.0624636i	$0.980104\pi$
$858$		0			0
$859$	844.828			0.983502			0.491751	−	0.870736i	$-0.336357\pi$
$859$	844.828			0.983502			0.491751	+	0.870736i	$0.336357\pi$
$860$		0			0
$861$	940.978	+	85.8440i	1.09289	+	0.0997027i
$862$		0			0
$863$			140.169i			0.162421i	0.996697	+	0.0812104i	$0.0258786\pi$
$863$			140.169i			0.162421i	−0.996697	+	0.0812104i	$0.974121\pi$
$864$		0			0
$865$	−67.9864	+	39.2520i	−0.0785970	+	0.0453780i
$866$		0			0
$867$	38.6953	+	27.3093i	0.0446313	+	0.0314986i
$868$		0			0
$869$	−1558.05	+	899.538i	−1.79292	+	1.03514i
$870$		0			0
$871$	−97.2523			−0.111656
$872$		0			0
$873$	−1176.13	−	1001.85i	−1.34722	−	1.14760i
$874$		0			0
$875$	−94.3704	−	163.454i	−0.107852	−	0.186805i
$876$		0			0
$877$	621.612	−	358.888i	0.708794	−	0.409222i	−0.101820	−	0.994803i	$-0.532467\pi$
$877$	621.612	−	358.888i	0.708794	−	0.409222i	0.810614	+	0.585581i	$0.199133\pi$
$878$		0			0
$879$	1177.95	+	107.463i	1.34010	+	0.122256i
$880$		0			0
$881$	973.635			1.10515			0.552574	−	0.833464i	$-0.313646\pi$
$881$	973.635			1.10515			0.552574	+	0.833464i	$0.313646\pi$
$882$		0			0
$883$	−810.466	−	1403.77i	−0.917855	−	1.58977i	−0.802667	−	0.596427i	$-0.796586\pi$
$883$	−810.466	−	1403.77i	−0.917855	−	1.58977i	−0.115188	−	0.993344i	$-0.536747\pi$
$884$		0			0
$885$	−32.6931	−	2.98254i	−0.0369414	−	0.00337011i
$886$		0			0
$887$		−	93.3587i		−	0.105252i	−0.998614	−	0.0526261i	$-0.983241\pi$
$887$		−	93.3587i		−	0.105252i	0.998614	−	0.0526261i	$-0.0167591\pi$
$888$		0			0
$889$	1006.78	+	581.262i	1.13248	+	0.653838i
$890$		0			0
$891$	935.820	−	761.869i	1.05030	−	0.855072i
$892$		0			0
$893$	−1348.55	+	944.275i	−1.51014	+	1.05742i
$894$		0			0
$895$	−80.8006	+	46.6502i	−0.0902800	+	0.0521232i
$896$		0			0
$897$	−31.1174	−	67.3830i	−0.0346905	−	0.0751204i
$898$		0			0
$899$	−727.145	−	1259.45i	−0.808837	−	1.40095i
$900$		0			0
$901$			881.670i			0.978546i
$902$		0			0
$903$	−856.325	−	604.352i	−0.948311	−	0.669272i
$904$		0			0
$905$	−54.9254	−	31.7112i	−0.0606910	−	0.0350400i
$906$		0			0
$907$		−	1442.46i		−	1.59036i	−0.606372	−	0.795181i	$-0.707376\pi$
$907$		−	1442.46i		−	1.59036i	0.606372	−	0.795181i	$-0.292624\pi$
$908$		0			0
$909$	−574.185	−	1614.74i	−0.631666	−	1.77639i
$910$		0			0
$911$	967.610	−	558.650i	1.06214	−	0.613227i	0.136117	−	0.990693i	$-0.456538\pi$
$911$	967.610	−	558.650i	1.06214	−	0.613227i	0.926024	+	0.377466i	$0.123204\pi$
$912$		0			0
$913$	800.081	−	1385.78i	0.876321	−	1.51783i
$914$		0			0
$915$	−0.816416	+	0.377020i	−0.000892258	+	0.000412044i
$916$		0			0
$917$	−567.587	+	983.090i	−0.618961	+	1.07207i
$918$		0			0
$919$	−150.532			−0.163800			−0.0819002	−	0.996641i	$-0.526099\pi$
$919$	−150.532			−0.163800			−0.0819002	+	0.996641i	$0.526099\pi$
$920$		0			0
$921$	1555.22	+	141.881i	1.68863	+	0.154051i
$922$		0			0
$923$	86.0211	−	148.993i	0.0931972	−	0.161422i
$924$		0			0
$925$	−644.295	−	371.984i	−0.696535	−	0.402145i
$926$		0			0
$927$	−805.342	+	286.371i	−0.868761	+	0.308922i
$928$		0			0
$929$	−1219.21			−1.31239			−0.656193	−	0.754593i	$-0.727834\pi$
$929$	−1219.21			−1.31239			−0.656193	+	0.754593i	$0.727834\pi$
$930$		0			0
$931$	−276.006	+	193.263i	−0.296462	+	0.207587i
$932$		0			0
$933$	48.6592	−	533.377i	0.0521535	−	0.571680i
$934$		0			0
$935$	−88.6144	−	153.485i	−0.0947748	−	0.164155i
$936$		0			0
$937$	−584.150	−	1011.78i	−0.623426	−	1.07981i	−0.988843	−	0.148962i	$-0.952407\pi$
$937$	−584.150	−	1011.78i	−0.623426	−	1.07981i	0.365417	−	0.930844i	$-0.380926\pi$
$938$		0			0
$939$	−52.1447	+	571.583i	−0.0555321	+	0.608715i
$940$		0			0
$941$		−	757.255i		−	0.804735i	−0.915478	−	0.402367i	$-0.868187\pi$
$941$		−	757.255i		−	0.804735i	0.915478	−	0.402367i	$-0.131813\pi$
$942$		0			0
$943$	−509.696	+	294.273i	−0.540505	+	0.312061i
$944$		0			0
$945$	71.9297	+	73.5490i	0.0761161	+	0.0778296i
$946$		0			0
$947$	717.348			0.757495			0.378748	−	0.925500i	$-0.376355\pi$
$947$	717.348			0.757495			0.378748	+	0.925500i	$0.376355\pi$
$948$		0			0
$949$	−157.225	−	90.7739i	−0.165674	−	0.0956521i
$950$		0			0
$951$	−491.105	−	44.8027i	−0.516409	−	0.0471112i
$952$		0			0
$953$	143.573	+	82.8922i	0.150654	+	0.0869802i	0.573432	−	0.819253i	$-0.305612\pi$
$953$	143.573	+	82.8922i	0.150654	+	0.0869802i	−0.422778	+	0.906233i	$0.638945\pi$
$954$		0			0
$955$	12.1532	−	21.0500i	0.0127259	−	0.0220419i
$956$		0			0
$957$	814.252	+	1763.22i	0.850838	+	1.84244i
$958$		0			0
$959$	−498.679			−0.519999
$960$		0			0
$961$	79.5155	+	137.725i	0.0827424	+	0.143314i
$962$		0			0
$963$	150.127	+	127.881i	0.155895	+	0.132795i
$964$		0			0
$965$	−86.9350	−	50.1919i	−0.0900881	−	0.0520124i
$966$		0			0
$967$	−111.196	−	192.596i	−0.114990	−	0.199169i	0.802786	−	0.596268i	$-0.203350\pi$
$967$	−111.196	−	192.596i	−0.114990	−	0.199169i	−0.917776	+	0.397099i	$0.870017\pi$
$968$		0			0
$969$	−500.748	+	859.945i	−0.516767	+	0.887456i
$970$		0			0
$971$	1374.21	+	793.401i	1.41525	+	0.817097i	0.995877	−	0.0907152i	$-0.0289153\pi$
$971$	1374.21	+	793.401i	1.41525	+	0.817097i	0.419377	+	0.907812i	$0.362249\pi$
$972$		0			0
$973$	463.677	+	803.113i	0.476544	+	0.825398i
$974$		0			0
$975$	173.566	+	15.8342i	0.178017	+	0.0162402i
$976$		0			0
$977$	484.548	+	279.754i	0.495955	+	0.286340i	0.727042	−	0.686593i	$-0.240895\pi$
$977$	484.548	+	279.754i	0.495955	+	0.286340i	−0.231086	+	0.972933i	$0.574228\pi$
$978$		0			0
$979$	−1826.57	−	1054.57i	−1.86575	−	1.07719i
$980$		0			0
$981$	−1667.90	+	593.086i	−1.70020	+	0.604573i
$982$		0			0
$983$			879.650i			0.894863i	0.894318	+	0.447431i	$0.147661\pi$
$983$			879.650i			0.894863i	−0.894318	+	0.447431i	$0.852339\pi$
$984$		0			0
$985$	31.3396	+	54.2819i	0.0318169	+	0.0551085i
$986$		0			0
$987$	1319.57	−	609.377i	1.33695	−	0.617403i
$988$		0			0
$989$	652.842			0.660103
$990$		0			0
$991$	−470.061	−	271.390i	−0.474329	−	0.273854i	0.243721	−	0.969845i	$-0.421632\pi$
$991$	−470.061	−	271.390i	−0.474329	−	0.273854i	−0.718050	+	0.695991i	$0.754965\pi$
$992$		0			0
$993$	−172.883	+	244.964i	−0.174102	+	0.246691i
$994$		0			0
$995$	−54.2806	+	94.0168i	−0.0545534	+	0.0944892i
$996$		0			0
$997$	381.603	−	660.955i	0.382751	−	0.662944i	−0.608703	−	0.793398i	$-0.708310\pi$
$997$	381.603	−	660.955i	0.382751	−	0.662944i	0.991454	+	0.130454i	$0.0416434\pi$
$998$		0			0
$999$	788.387	+	220.681i	0.789177	+	0.220902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.5	✓	80
3.2	odd	2		2052.3.s.a.901.18		80
9.2	odd	6		2052.3.bl.a.1585.23		80
9.7	even	3		684.3.bl.a.673.21	yes	80
19.12	odd	6		684.3.bl.a.373.21	yes	80
57.50	even	6		2052.3.bl.a.145.23		80
171.88	odd	6	inner	684.3.s.a.601.5	yes	80
171.164	even	6		2052.3.s.a.829.18		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.5	✓	80	1.1	even	1	trivial
684.3.s.a.601.5	yes	80	171.88	odd	6	inner
684.3.bl.a.373.21	yes	80	19.12	odd	6
684.3.bl.a.673.21	yes	80	9.7	even	3
2052.3.s.a.829.18		80	171.164	even	6
2052.3.s.a.901.18		80	3.2	odd	2
2052.3.bl.a.145.23		80	57.50	even	6
2052.3.bl.a.1585.23		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.72361 + 1.25776i) q^{3} +(0.340706 + 0.590120i) q^{5} +(-2.79581 - 4.84248i) q^{7} +(5.83609 - 6.85128i) q^{9} +O(q^{10})\)	\(q+(-2.72361 + 1.25776i) q^{3} +(0.340706 + 0.590120i) q^{5} +(-2.79581 - 4.84248i) q^{7} +(5.83609 - 6.85128i) q^{9} +(7.44896 + 12.9020i) q^{11} -2.36780i q^{13} +(-1.67018 - 1.17873i) q^{15} +(-8.72908 + 15.1192i) q^{17} +(-17.2199 - 8.02967i) q^{19} +(13.7054 + 9.67258i) q^{21} -10.4486 q^{23} +(12.2678 - 21.2485i) q^{25} +(-7.27796 + 26.0006i) q^{27} +(-37.6328 - 21.7273i) q^{29} +(28.9832 + 16.7334i) q^{31} +(-36.5156 - 25.7710i) q^{33} +(1.90510 - 3.29973i) q^{35} -30.3219i q^{37} +(2.97813 + 6.44897i) q^{39} +(48.7811 - 28.1638i) q^{41} -62.4810 q^{43} +(6.03147 + 1.10972i) q^{45} +(43.3232 - 75.0381i) q^{47} +(8.86690 - 15.3579i) q^{49} +(4.75828 - 52.1579i) q^{51} +(43.7359 - 25.2509i) q^{53} +(-5.07582 + 8.79157i) q^{55} +(56.9996 + 0.211226i) q^{57} +(13.9077 - 8.02962i) q^{59} +(0.219952 - 0.380967i) q^{61} +(-49.4938 - 9.10628i) q^{63} +(1.39729 - 0.806726i) q^{65} -41.0728i q^{67} +(28.4580 - 13.1419i) q^{69} +(62.9245 + 36.3295i) q^{71} +(38.3367 - 66.4012i) q^{73} +(-6.68729 + 73.3026i) q^{75} +(41.6518 - 72.1430i) q^{77} +120.760i q^{79} +(-12.8802 - 79.9694i) q^{81} +(-53.7042 - 93.0184i) q^{83} -11.8962 q^{85} +(129.825 + 11.8437i) q^{87} +(-122.606 + 70.7865i) q^{89} +(-11.4661 + 6.61993i) q^{91} +(-99.9854 - 9.12151i) q^{93} +(-1.12845 - 12.8976i) q^{95} -171.665i q^{97} +(131.868 + 24.2621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more