LMFDB - Embedded newform 684.3.be.a.425.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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, 1, 2]))

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

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (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			425.1
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99940 - 0.0599360i) q^{3} +(1.93690 + 1.11827i) q^{5} +(1.30590 - 2.26189i) q^{7} +(8.99282 + 0.359544i) q^{9} +O(q^{10})$	\(q+(-2.99940 - 0.0599360i) q^{3} +(1.93690 + 1.11827i) q^{5} +(1.30590 - 2.26189i) q^{7} +(8.99282 + 0.359544i) q^{9} +(9.01402 + 5.20424i) q^{11} +0.912775 q^{13} +(-5.74251 - 3.47023i) q^{15} +(-9.51759 + 5.49498i) q^{17} +(-18.2448 - 5.30348i) q^{19} +(-4.05249 + 6.70603i) q^{21} -5.05129i q^{23} +(-9.99895 - 17.3187i) q^{25} +(-26.9515 - 1.61741i) q^{27} +(22.7955 - 13.1610i) q^{29} +(20.3381 + 35.2267i) q^{31} +(-26.7247 - 16.1499i) q^{33} +(5.05879 - 2.92070i) q^{35} +65.4978 q^{37} +(-2.73778 - 0.0547081i) q^{39} +(46.4873 + 26.8395i) q^{41} -21.8403 q^{43} +(17.0161 + 10.7528i) q^{45} +(14.4776 - 8.35864i) q^{47} +(21.0893 + 36.5277i) q^{49} +(28.8764 - 15.9112i) q^{51} +(27.5234 + 15.8907i) q^{53} +(11.6395 + 20.1602i) q^{55} +(54.4056 + 17.0008i) q^{57} +(-22.5690 - 13.0302i) q^{59} +(28.6677 + 49.6539i) q^{61} +(12.5570 - 19.8712i) q^{63} +(1.76795 + 1.02073i) q^{65} +34.6740 q^{67} +(-0.302754 + 15.1508i) q^{69} +(31.4924 - 18.1821i) q^{71} +(-3.45130 - 5.97783i) q^{73} +(28.9528 + 52.5450i) q^{75} +(23.5428 - 13.5924i) q^{77} -58.3887 q^{79} +(80.7415 + 6.46663i) q^{81} +(-8.31103 - 4.79838i) q^{83} -24.5795 q^{85} +(-69.1616 + 38.1088i) q^{87} +(135.141 + 78.0237i) q^{89} +(1.19199 - 2.06459i) q^{91} +(-58.8909 - 106.878i) q^{93} +(-29.4076 - 30.6749i) q^{95} +95.3902 q^{97} +(79.1902 + 50.0418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.99940	−	0.0599360i	−0.999800	−	0.0199787i
$3$	−2.99940	−	0.0599360i	−0.999800	−	0.0199787i
$4$		0			0
$5$	1.93690	+	1.11827i	0.387380	+	0.223654i	0.681024	−	0.732261i	$-0.261535\pi$
$5$	1.93690	+	1.11827i	0.387380	+	0.223654i	−0.293644	+	0.955915i	$0.594868\pi$
$6$		0			0
$7$	1.30590	−	2.26189i	0.186557	−	0.323126i	−0.757543	−	0.652785i	$-0.773600\pi$
$7$	1.30590	−	2.26189i	0.186557	−	0.323126i	0.944100	+	0.329659i	$0.106934\pi$
$8$		0			0
$9$	8.99282	+	0.359544i	0.999202	+	0.0399494i
$10$		0			0
$11$	9.01402	+	5.20424i	0.819456	+	0.473113i	0.850229	−	0.526413i	$-0.176463\pi$
$11$	9.01402	+	5.20424i	0.819456	+	0.473113i	−0.0307728	+	0.999526i	$0.509797\pi$
$12$		0			0
$13$	0.912775			0.0702135			0.0351067	−	0.999384i	$-0.488823\pi$
$13$	0.912775			0.0702135			0.0351067	+	0.999384i	$0.488823\pi$
$14$		0			0
$15$	−5.74251	−	3.47023i	−0.382834	−	0.231349i
$16$		0			0
$17$	−9.51759	+	5.49498i	−0.559858	+	0.323234i	−0.753089	−	0.657919i	$-0.771437\pi$
$17$	−9.51759	+	5.49498i	−0.559858	+	0.323234i	0.193230	+	0.981153i	$0.438103\pi$
$18$		0			0
$19$	−18.2448	−	5.30348i	−0.960253	−	0.279130i
$19$	−18.2448	−	5.30348i	−0.960253	−	0.279130i
$20$		0			0
$21$	−4.05249	+	6.70603i	−0.192976	+	0.319335i
$22$		0			0
$23$		−	5.05129i		−	0.219621i	−0.993953	−	0.109811i	$-0.964976\pi$
$23$		−	5.05129i		−	0.219621i	0.993953	−	0.109811i	$-0.0350244\pi$
$24$		0			0
$25$	−9.99895	−	17.3187i	−0.399958	−	0.692747i
$26$		0			0
$27$	−26.9515	−	1.61741i	−0.998204	−	0.0599041i
$28$		0			0
$29$	22.7955	−	13.1610i	0.786051	−	0.453827i	−0.0525196	−	0.998620i	$-0.516725\pi$
$29$	22.7955	−	13.1610i	0.786051	−	0.453827i	0.838570	+	0.544793i	$0.183392\pi$
$30$		0			0
$31$	20.3381	+	35.2267i	0.656069	+	1.13635i	0.981625	+	0.190822i	$0.0611154\pi$
$31$	20.3381	+	35.2267i	0.656069	+	1.13635i	−0.325555	+	0.945523i	$0.605551\pi$
$32$		0			0
$33$	−26.7247	−	16.1499i	−0.809840	−	0.489390i
$34$		0			0
$35$	5.05879	−	2.92070i	0.144537	−	0.0834485i
$36$		0			0
$37$	65.4978			1.77021			0.885106	−	0.465390i	$-0.154086\pi$
$37$	65.4978			1.77021			0.885106	+	0.465390i	$0.154086\pi$
$38$		0			0
$39$	−2.73778	−	0.0547081i	−0.0701995	−	0.00140277i
$40$		0			0
$41$	46.4873	+	26.8395i	1.13384	+	0.654621i	0.944897	−	0.327368i	$-0.106162\pi$
$41$	46.4873	+	26.8395i	1.13384	+	0.654621i	0.188940	+	0.981989i	$0.439495\pi$
$42$		0			0
$43$	−21.8403			−0.507914			−0.253957	−	0.967215i	$-0.581732\pi$
$43$	−21.8403			−0.507914			−0.253957	+	0.967215i	$0.581732\pi$
$44$		0			0
$45$	17.0161	+	10.7528i	0.378136	+	0.238951i
$46$		0			0
$47$	14.4776	−	8.35864i	0.308034	−	0.177843i	−0.338012	−	0.941142i	$-0.609755\pi$
$47$	14.4776	−	8.35864i	0.308034	−	0.177843i	0.646046	+	0.763298i	$0.276421\pi$
$48$		0			0
$49$	21.0893	+	36.5277i	0.430393	+	0.745462i
$50$		0			0
$51$	28.8764	−	15.9112i	0.566204	−	0.311984i
$52$		0			0
$53$	27.5234	+	15.8907i	0.519310	+	0.299824i	0.736652	−	0.676272i	$-0.236405\pi$
$53$	27.5234	+	15.8907i	0.519310	+	0.299824i	−0.217342	+	0.976095i	$0.569739\pi$
$54$		0			0
$55$	11.6395	+	20.1602i	0.211627	+	0.366549i
$56$		0			0
$57$	54.4056	+	17.0008i	0.954485	+	0.298259i
$58$		0			0
$59$	−22.5690	−	13.0302i	−0.382526	−	0.220851i	0.296391	−	0.955067i	$-0.404217\pi$
$59$	−22.5690	−	13.0302i	−0.382526	−	0.220851i	−0.678917	+	0.734215i	$0.737550\pi$
$60$		0			0
$61$	28.6677	+	49.6539i	0.469962	+	0.813999i	0.999410	−	0.0343438i	$-0.0109341\pi$
$61$	28.6677	+	49.6539i	0.469962	+	0.813999i	−0.529448	+	0.848343i	$0.677601\pi$
$62$		0			0
$63$	12.5570	−	19.8712i	0.199317	−	0.315416i
$64$		0			0
$65$	1.76795	+	1.02073i	0.0271993	+	0.0157035i
$66$		0			0
$67$	34.6740			0.517522			0.258761	−	0.965941i	$-0.416686\pi$
$67$	34.6740			0.517522			0.258761	+	0.965941i	$0.416686\pi$
$68$		0			0
$69$	−0.302754	+	15.1508i	−0.00438774	+	0.219577i
$70$		0			0
$71$	31.4924	−	18.1821i	0.443555	−	0.256086i	−0.261550	−	0.965190i	$-0.584234\pi$
$71$	31.4924	−	18.1821i	0.443555	−	0.256086i	0.705104	+	0.709104i	$0.250900\pi$
$72$		0			0
$73$	−3.45130	−	5.97783i	−0.0472781	−	0.0818881i	0.841418	−	0.540385i	$-0.181721\pi$
$73$	−3.45130	−	5.97783i	−0.0472781	−	0.0818881i	−0.888696	+	0.458497i	$0.848388\pi$
$74$		0			0
$75$	28.9528	+	52.5450i	0.386038	+	0.700600i
$76$		0			0
$77$	23.5428	−	13.5924i	0.305751	−	0.176525i
$78$		0			0
$79$	−58.3887			−0.739097			−0.369548	−	0.929211i	$-0.620488\pi$
$79$	−58.3887			−0.739097			−0.369548	+	0.929211i	$0.620488\pi$
$80$		0			0
$81$	80.7415	+	6.46663i	0.996808	+	0.0798350i
$82$		0			0
$83$	−8.31103	−	4.79838i	−0.100133	−	0.0578118i	0.449097	−	0.893483i	$-0.351746\pi$
$83$	−8.31103	−	4.79838i	−0.100133	−	0.0578118i	−0.549230	+	0.835671i	$0.685079\pi$
$84$		0			0
$85$	−24.5795			−0.289170
$86$		0			0
$87$	−69.1616	+	38.1088i	−0.794961	+	0.438032i
$88$		0			0
$89$	135.141	+	78.0237i	1.51844	+	0.876671i	0.999765	+	0.0216992i	$0.00690760\pi$
$89$	135.141	+	78.0237i	1.51844	+	0.876671i	0.518674	+	0.854972i	$0.326426\pi$
$90$		0			0
$91$	1.19199	−	2.06459i	0.0130988	−	0.0226878i
$92$		0			0
$93$	−58.8909	−	106.878i	−0.633236	−	1.14923i
$94$		0			0
$95$	−29.4076	−	30.6749i	−0.309554	−	0.322894i
$96$		0			0
$97$	95.3902			0.983404			0.491702	−	0.870764i	$-0.336375\pi$
$97$	95.3902			0.983404			0.491702	+	0.870764i	$0.336375\pi$
$98$		0			0
$99$	79.1902	+	50.0418i	0.799901	+	0.505472i
$100$		0			0
$101$	42.1242	−	24.3204i	0.417072	−	0.240796i	−0.276752	−	0.960941i	$-0.589258\pi$
$101$	42.1242	−	24.3204i	0.417072	−	0.240796i	0.693824	+	0.720145i	$0.255925\pi$
$102$		0			0
$103$	102.218	+	177.048i	0.992412	+	1.71891i	0.602688	+	0.797977i	$0.294097\pi$
$103$	102.218	+	177.048i	0.992412	+	1.71891i	0.389725	+	0.920931i	$0.372570\pi$
$104$		0			0
$105$	−15.3484	+	8.45713i	−0.146175	+	0.0805441i
$106$		0			0
$107$		−	193.373i		−	1.80722i	−0.428353	−	0.903612i	$-0.640906\pi$
$107$		−	193.373i		−	1.80722i	0.428353	−	0.903612i	$-0.359094\pi$
$108$		0			0
$109$	50.6137	+	87.6656i	0.464346	+	0.804271i	0.999172	−	0.0406912i	$-0.0129560\pi$
$109$	50.6137	+	87.6656i	0.464346	+	0.804271i	−0.534826	+	0.844963i	$0.679623\pi$
$110$		0			0
$111$	−196.454	−	3.92568i	−1.76986	−	0.0353665i
$112$		0			0
$113$	120.372	−	69.4967i	1.06524	−	0.615015i	0.138361	−	0.990382i	$-0.455817\pi$
$113$	120.372	−	69.4967i	1.06524	−	0.615015i	0.926876	+	0.375367i	$0.122483\pi$
$114$		0			0
$115$	5.64870	−	9.78384i	0.0491191	−	0.0850768i
$116$		0			0
$117$	8.20842	+	0.328183i	0.0701574	+	0.00280499i
$118$		0			0
$119$			28.7036i			0.241207i
$120$		0			0
$121$	−6.33167	−	10.9668i	−0.0523278	−	0.0906345i
$122$		0			0
$123$	−137.825	−	83.2886i	−1.12053	−	0.677143i
$124$		0			0
$125$		−	100.640i		−	0.805116i
$126$		0			0
$127$	32.3301	−	55.9973i	0.254568	−	0.440924i	−0.710210	−	0.703989i	$-0.751400\pi$
$127$	32.3301	−	55.9973i	0.254568	−	0.440924i	0.964778	+	0.263066i	$0.0847335\pi$
$128$		0			0
$129$	65.5079	+	1.30902i	0.507813	+	0.0101475i
$130$		0			0
$131$	84.5188	+	48.7970i	0.645182	+	0.372496i	0.786608	−	0.617453i	$-0.211835\pi$
$131$	84.5188	+	48.7970i	0.645182	+	0.372496i	−0.141426	+	0.989949i	$0.545169\pi$
$132$		0			0
$133$	−35.8218	+	34.3419i	−0.269337	+	0.258209i
$134$		0			0
$135$	−50.3937	−	33.2718i	−0.373286	−	0.246458i
$136$		0			0
$137$	−186.625	+	107.748i	−1.36222	+	0.786480i	−0.989919	−	0.141631i	$-0.954765\pi$
$137$	−186.625	+	107.748i	−1.36222	+	0.786480i	−0.372303	+	0.928111i	$0.621432\pi$
$138$		0			0
$139$	−95.8818			−0.689797			−0.344899	−	0.938640i	$-0.612087\pi$
$139$	−95.8818			−0.689797			−0.344899	+	0.938640i	$0.612087\pi$
$140$		0			0
$141$	−43.9251	+	24.2032i	−0.311525	+	0.171654i
$142$		0			0
$143$	8.22777	+	4.75031i	0.0575369	+	0.0332189i
$144$		0			0
$145$	58.8701			0.406000
$146$		0			0
$147$	−61.0658	−	110.825i	−0.415414	−	0.753912i
$148$		0			0
$149$	−61.4921	−	35.5025i	−0.412699	−	0.238272i	0.279250	−	0.960218i	$-0.409914\pi$
$149$	−61.4921	−	35.5025i	−0.412699	−	0.238272i	−0.691949	+	0.721947i	$0.743248\pi$
$150$		0			0
$151$	19.3277	−	33.4766i	0.127998	−	0.221700i	−0.794903	−	0.606737i	$-0.792478\pi$
$151$	19.3277	−	33.4766i	0.127998	−	0.221700i	0.922901	+	0.385037i	$0.125811\pi$
$152$		0			0
$153$	−87.5656	+	45.9934i	−0.572324	+	0.300610i
$154$		0			0
$155$			90.9741i			0.586930i
$156$		0			0
$157$	−124.680	+	215.953i	−0.794143	+	1.37550i	0.129239	+	0.991614i	$0.458747\pi$
$157$	−124.680	+	215.953i	−0.794143	+	1.37550i	−0.923382	+	0.383883i	$0.874587\pi$
$158$		0			0
$159$	−81.6014	−	49.3121i	−0.513216	−	0.310139i
$160$		0			0
$161$	−11.4254	−	6.59648i	−0.0709654	−	0.0409719i
$162$		0			0
$163$	−68.7055			−0.421506			−0.210753	−	0.977539i	$-0.567592\pi$
$163$	−68.7055			−0.421506			−0.210753	+	0.977539i	$0.567592\pi$
$164$		0			0
$165$	−33.7032	−	61.1661i	−0.204262	−	0.370704i
$166$		0			0
$167$		−	35.7218i		−	0.213903i	−0.994264	−	0.106952i	$-0.965891\pi$
$167$		−	35.7218i		−	0.213903i	0.994264	−	0.106952i	$-0.0341090\pi$
$168$		0			0
$169$	−168.167			−0.995070
$170$		0			0
$171$	−162.165	−	54.2530i	−0.948336	−	0.317269i
$172$		0			0
$173$		−	122.883i		−	0.710309i	−0.934808	−	0.355154i	$-0.884428\pi$
$173$		−	122.883i		−	0.710309i	0.934808	−	0.355154i	$-0.115572\pi$
$174$		0			0
$175$	−52.2305			−0.298460
$176$		0			0
$177$	66.9126	+	40.4356i	0.378037	+	0.228450i
$178$		0			0
$179$		−	142.388i		−	0.795463i	−0.917502	−	0.397732i	$-0.869798\pi$
$179$		−	142.388i		−	0.795463i	0.917502	−	0.397732i	$-0.130202\pi$
$180$		0			0
$181$	−58.9258	+	102.062i	−0.325557	+	0.563881i	−0.981625	−	0.190821i	$-0.938885\pi$
$181$	−58.9258	+	102.062i	−0.325557	+	0.563881i	0.656068	+	0.754702i	$0.272218\pi$
$182$		0			0
$183$	−83.0099	−	150.650i	−0.453606	−	0.823226i
$184$		0			0
$185$	126.863	+	73.2442i	0.685744	+	0.395915i
$186$		0			0
$187$	−114.389			−0.611705
$188$		0			0
$189$	−38.8544	+	58.8490i	−0.205579	+	0.311371i
$190$		0			0
$191$	26.7649	+	15.4527i	0.140130	+	0.0809043i	0.568426	−	0.822734i	$-0.307553\pi$
$191$	26.7649	+	15.4527i	0.140130	+	0.0809043i	−0.428296	+	0.903639i	$0.640886\pi$
$192$		0			0
$193$	21.6838	−	37.5574i	0.112351	−	0.194598i	−0.804367	−	0.594133i	$-0.797495\pi$
$193$	21.6838	−	37.5574i	0.112351	−	0.194598i	0.916718	+	0.399535i	$0.130828\pi$
$194$		0			0
$195$	−5.24162	−	3.16754i	−0.0268801	−	0.0162438i
$196$		0			0
$197$		−	194.898i		−	0.989332i	−0.869083	−	0.494666i	$-0.835290\pi$
$197$		−	194.898i		−	0.989332i	0.869083	−	0.494666i	$-0.164710\pi$
$198$		0			0
$199$	1.35743	−	2.35113i	0.00682124	−	0.0118147i	−0.862595	−	0.505896i	$-0.831162\pi$
$199$	1.35743	−	2.35113i	0.00682124	−	0.0118147i	0.869416	+	0.494081i	$0.164495\pi$
$200$		0			0
$201$	−104.001	−	2.07822i	−0.517419	−	0.0103394i
$202$		0			0
$203$		−	68.7477i		−	0.338658i
$204$		0			0
$205$	60.0275	+	103.971i	0.292817	+	0.507174i
$206$		0			0
$207$	1.81616	−	45.4253i	0.00877373	−	0.219446i
$208$		0			0
$209$	−136.858	−	142.756i	−0.654825	−	0.683044i
$210$		0			0
$211$	−173.330	+	300.217i	−0.821470	+	1.42283i	0.0831169	+	0.996540i	$0.473513\pi$
$211$	−173.330	+	300.217i	−0.821470	+	1.42283i	−0.904587	+	0.426289i	$0.859821\pi$
$212$		0			0
$213$	−95.5480	+	52.6480i	−0.448582	+	0.247174i
$214$		0			0
$215$	−42.3025	−	24.4234i	−0.196756	−	0.113597i
$216$		0			0
$217$	106.238			0.489578
$218$		0			0
$219$	9.99356	+	18.1368i	0.0456327	+	0.0828163i
$220$		0			0
$221$	−8.68742	+	5.01568i	−0.0393096	+	0.0226954i
$222$		0			0
$223$	85.1109			0.381663			0.190832	−	0.981623i	$-0.438882\pi$
$223$	85.1109			0.381663			0.190832	+	0.981623i	$0.438882\pi$
$224$		0			0
$225$	−83.6918	−	159.339i	−0.371964	−	0.708172i
$226$		0			0
$227$	−230.450	−	133.050i	−1.01520	−	0.586124i	−0.102488	−	0.994734i	$-0.532680\pi$
$227$	−230.450	−	133.050i	−1.01520	−	0.586124i	−0.912709	+	0.408610i	$0.866014\pi$
$228$		0			0
$229$	−47.2542	−	81.8466i	−0.206350	−	0.357409i	0.744212	−	0.667943i	$-0.232825\pi$
$229$	−47.2542	−	81.8466i	−0.206350	−	0.357409i	−0.950562	+	0.310535i	$0.899492\pi$
$230$		0			0
$231$	−71.4290	+	39.3581i	−0.309216	+	0.170382i
$232$		0			0
$233$	238.339	−	137.605i	1.02292	−	0.590580i	0.107968	−	0.994154i	$-0.465566\pi$
$233$	238.339	−	137.605i	1.02292	−	0.590580i	0.914947	+	0.403574i	$0.132232\pi$
$234$		0			0
$235$	37.3889			0.159102
$236$		0			0
$237$	175.131	+	3.49958i	0.738949	+	0.0147662i
$238$		0			0
$239$	154.005	−	88.9146i	0.644371	−	0.372028i	−0.141925	−	0.989877i	$-0.545329\pi$
$239$	154.005	−	88.9146i	0.644371	−	0.372028i	0.786296	+	0.617850i	$0.211996\pi$
$240$		0			0
$241$	90.2117	+	156.251i	0.374322	+	0.648345i	0.990225	−	0.139477i	$-0.0445420\pi$
$241$	90.2117	+	156.251i	0.374322	+	0.648345i	−0.615903	+	0.787822i	$0.711209\pi$
$242$		0			0
$243$	−241.788	−	24.2354i	−0.995014	−	0.0997340i
$244$		0			0
$245$			94.3339i			0.385036i
$246$		0			0
$247$	−16.6534	−	4.84088i	−0.0674227	−	0.0195987i
$248$		0			0
$249$	24.6405	+	14.8904i	0.0989580	+	0.0598008i
$250$		0			0
$251$	204.777	+	118.228i	0.815844	+	0.471028i	0.848981	−	0.528423i	$-0.177216\pi$
$251$	204.777	+	118.228i	0.815844	+	0.471028i	−0.0331370	+	0.999451i	$0.510550\pi$
$252$		0			0
$253$	26.2881	−	45.5324i	0.103906	−	0.179970i
$254$		0			0
$255$	73.7237	+	1.47320i	0.289113	+	0.00577724i
$256$		0			0
$257$			40.2045i			0.156438i	0.996936	+	0.0782188i	$0.0249233\pi$
$257$			40.2045i			0.156438i	−0.996936	+	0.0782188i	$0.975077\pi$
$258$		0			0
$259$	85.5336	−	148.149i	0.330246	−	0.572002i
$260$		0			0
$261$	209.727	−	110.158i	0.803553	−	0.422062i
$262$		0			0
$263$			407.203i			1.54830i	0.633002	+	0.774150i	$0.281823\pi$
$263$			407.203i			1.54830i	−0.633002	+	0.774150i	$0.718177\pi$
$264$		0			0
$265$	35.5401	+	61.5572i	0.134113	+	0.232291i
$266$		0			0
$267$	−400.666	−	242.124i	−1.50062	−	0.906833i
$268$		0			0
$269$	411.714	−	237.703i	1.53054	−	0.883655i	0.531199	−	0.847247i	$-0.321742\pi$
$269$	411.714	−	237.703i	1.53054	−	0.883655i	0.999337	−	0.0364078i	$-0.0115915\pi$
$270$		0			0
$271$	1.43602	+	2.48726i	0.00529897	+	0.00917808i	0.868663	−	0.495404i	$-0.164980\pi$
$271$	1.43602	+	2.48726i	0.00529897	+	0.00917808i	−0.863364	+	0.504582i	$0.831647\pi$
$272$		0			0
$273$	−3.69901	+	6.12110i	−0.0135495	+	0.0224216i
$274$		0			0
$275$		−	208.148i		−	0.756901i
$276$		0			0
$277$	52.5685	−	91.0512i	0.189778	−	0.328705i	−0.755398	−	0.655266i	$-0.772557\pi$
$277$	52.5685	−	91.0512i	0.189778	−	0.328705i	0.945176	+	0.326561i	$0.105890\pi$
$278$		0			0
$279$	170.232	+	324.100i	0.610149	+	1.16165i
$280$		0			0
$281$	−241.073	+	139.183i	−0.857910	+	0.495314i	−0.863312	−	0.504671i	$-0.831614\pi$
$281$	−241.073	+	139.183i	−0.857910	+	0.495314i	0.00540212	+	0.999985i	$0.498280\pi$
$282$		0			0
$283$	−104.594	+	181.161i	−0.369588	+	0.640146i	−0.989501	−	0.144525i	$-0.953835\pi$
$283$	−104.594	+	181.161i	−0.369588	+	0.640146i	0.619913	+	0.784671i	$0.287168\pi$
$284$		0			0
$285$	86.3668	+	93.7690i	0.303041	+	0.329014i
$286$		0			0
$287$	121.416	−	70.0993i	0.423051	−	0.244248i
$288$		0			0
$289$	−84.1104	+	145.683i	−0.291039	+	0.504095i
$290$		0			0
$291$	−286.113	−	5.71731i	−0.983207	−	0.0196471i
$292$		0			0
$293$	−403.308	+	232.850i	−1.37648	+	0.794710i	−0.991734	−	0.128312i	$-0.959044\pi$
$293$	−403.308	+	232.850i	−1.37648	+	0.794710i	−0.384745	+	0.923023i	$0.625711\pi$
$294$		0			0
$295$	−29.1426	−	50.4765i	−0.0987885	−	0.171107i
$296$		0			0
$297$	−234.524	−	154.842i	−0.789643	−	0.521352i
$298$		0			0
$299$		−	4.61069i		−	0.0154204i
$300$		0			0
$301$	−28.5213	+	49.4003i	−0.0947550	+	0.164121i
$302$		0			0
$303$	−127.805	+	70.4220i	−0.421799	+	0.232416i
$304$		0			0
$305$			128.233i			0.420436i
$306$		0			0
$307$	63.2296	+	109.517i	0.205960	+	0.356733i	0.950438	−	0.310914i	$-0.100635\pi$
$307$	63.2296	+	109.517i	0.205960	+	0.356733i	−0.744478	+	0.667647i	$0.767302\pi$
$308$		0			0
$309$	−295.983	−	537.163i	−0.957873	−	1.73839i
$310$		0			0
$311$	522.948	−	301.924i	1.68151	−	0.970817i	0.720843	−	0.693099i	$-0.243755\pi$
$311$	522.948	−	301.924i	1.68151	−	0.970817i	0.960662	−	0.277719i	$-0.0895783\pi$
$312$		0			0
$313$	−163.727	−	283.583i	−0.523089	−	0.906017i	−0.999639	−	0.0268697i	$-0.991446\pi$
$313$	−163.727	−	283.583i	−0.523089	−	0.906017i	0.476550	−	0.879148i	$-0.341887\pi$
$314$		0			0
$315$	46.5429	−	24.4464i	0.147755	−	0.0776077i
$316$		0			0
$317$	−36.6359	+	21.1518i	−0.115571	+	0.0667248i	−0.556671	−	0.830733i	$-0.687922\pi$
$317$	−36.6359	+	21.1518i	−0.115571	+	0.0667248i	0.441100	+	0.897458i	$0.354588\pi$
$318$		0			0
$319$	273.972			0.858845
$320$		0			0
$321$	−11.5900	+	580.003i	−0.0361059	+	1.80686i
$322$		0			0
$323$	202.789	−	49.7786i	0.627830	−	0.154113i
$324$		0			0
$325$	−9.12679	−	15.8081i	−0.0280824	−	0.0486402i
$326$		0			0
$327$	−146.557	−	265.978i	−0.448185	−	0.813388i
$328$		0			0
$329$		−	43.6622i		−	0.132712i
$330$		0			0
$331$	−228.357	+	395.526i	−0.689901	+	1.19494i	0.281968	+	0.959424i	$0.409013\pi$
$331$	−228.357	+	395.526i	−0.689901	+	1.19494i	−0.971869	+	0.235520i	$0.924321\pi$
$332$		0			0
$333$	589.010	+	23.5494i	1.76880	+	0.0707189i
$334$		0			0
$335$	67.1600	+	38.7749i	0.200478	+	0.115746i
$336$		0			0
$337$	232.175	−	402.139i	0.688948	−	1.19329i	−0.283231	−	0.959052i	$-0.591406\pi$
$337$	232.175	−	402.139i	0.688948	−	1.19329i	0.972179	−	0.234240i	$-0.0752603\pi$
$338$		0			0
$339$	−365.209	+	201.234i	−1.07731	+	0.593610i
$340$		0			0
$341$			423.379i			1.24158i
$342$		0			0
$343$	238.140			0.694286
$344$		0			0
$345$	−17.5291	+	29.0071i	−0.0508091	+	0.0840785i
$346$		0			0
$347$	−415.648	−	239.975i	−1.19783	−	0.691570i	−0.237762	−	0.971323i	$-0.576414\pi$
$347$	−415.648	−	239.975i	−1.19783	−	0.691570i	−0.960072	+	0.279753i	$0.909747\pi$
$348$		0			0
$349$	115.688	−	200.378i	0.331484	−	0.574148i	−0.651319	−	0.758804i	$-0.725784\pi$
$349$	115.688	−	200.378i	0.331484	−	0.574148i	0.982803	+	0.184657i	$0.0591173\pi$
$350$		0			0
$351$	−24.6007	−	1.47633i	−0.0700874	−	0.00420608i
$352$		0			0
$353$	1.54484	+	0.891915i	0.00437632	+	0.00252667i	0.502187	−	0.864759i	$-0.332529\pi$
$353$	1.54484	+	0.891915i	0.00437632	+	0.00252667i	−0.497810	+	0.867286i	$0.665862\pi$
$354$		0			0
$355$	81.3301			0.229099
$356$		0			0
$357$	1.72038	−	86.0936i	0.00481899	−	0.241158i
$358$		0			0
$359$	−85.5489	+	49.3917i	−0.238298	+	0.137581i	−0.614394	−	0.788999i	$-0.710599\pi$
$359$	−85.5489	+	49.3917i	−0.238298	+	0.137581i	0.376096	+	0.926581i	$0.377266\pi$
$360$		0			0
$361$	304.746	+	193.522i	0.844172	+	0.536072i
$362$		0			0
$363$	18.3339	+	33.2732i	0.0505066	+	0.0916618i
$364$		0			0
$365$		−	15.4379i		−	0.0422958i
$366$		0			0
$367$	−11.1336	−	19.2839i	−0.0303367	−	0.0525447i	0.850458	−	0.526042i	$-0.176325\pi$
$367$	−11.1336	−	19.2839i	−0.0303367	−	0.0525447i	−0.880795	+	0.473498i	$0.842991\pi$
$368$		0			0
$369$	408.402	+	258.077i	1.10678	+	0.699395i
$370$		0			0
$371$	71.8857	−	41.5032i	0.193762	−	0.111869i
$372$		0			0
$373$	−293.673	−	508.657i	−0.787328	−	1.36369i	−0.927599	−	0.373578i	$-0.878131\pi$
$373$	−293.673	−	508.657i	−0.787328	−	1.36369i	0.140271	−	0.990113i	$-0.455203\pi$
$374$		0			0
$375$	−6.03194	+	301.858i	−0.0160852	+	0.804956i
$376$		0			0
$377$	20.8071	−	12.0130i	0.0551914	−	0.0318647i
$378$		0			0
$379$	−366.161			−0.966123			−0.483062	−	0.875586i	$-0.660475\pi$
$379$	−366.161			−0.966123			−0.483062	+	0.875586i	$0.660475\pi$
$380$		0			0
$381$	−100.327	+	166.021i	−0.263326	+	0.435750i
$382$		0			0
$383$	−524.985	−	303.100i	−1.37072	−	0.791385i	−0.379700	−	0.925110i	$-0.623973\pi$
$383$	−524.985	−	303.100i	−1.37072	−	0.791385i	−0.991018	+	0.133725i	$0.957306\pi$
$384$		0			0
$385$	60.8001			0.157922
$386$		0			0
$387$	−196.406	−	7.85256i	−0.507509	−	0.0202909i
$388$		0			0
$389$	−527.958	+	304.817i	−1.35722	+	0.783590i	−0.989248	−	0.146247i	$-0.953280\pi$
$389$	−527.958	+	304.817i	−1.35722	+	0.783590i	−0.367970	+	0.929838i	$0.619947\pi$
$390$		0			0
$391$	27.7567	+	48.0761i	0.0709891	+	0.122957i
$392$		0			0
$393$	−250.581	−	151.427i	−0.637611	−	0.385312i
$394$		0			0
$395$	−113.093	−	65.2942i	−0.286311	−	0.165302i
$396$		0			0
$397$	4.32872	+	7.49756i	0.0109036	+	0.0188855i	0.871426	−	0.490528i	$-0.163196\pi$
$397$	4.32872	+	7.49756i	0.0109036	+	0.0188855i	−0.860522	+	0.509413i	$0.829863\pi$
$398$		0			0
$399$	109.502	−	100.858i	0.274441	−	0.252777i
$400$		0			0
$401$	99.1045	+	57.2180i	0.247143	+	0.142688i	0.618456	−	0.785820i	$-0.287759\pi$
$401$	99.1045	+	57.2180i	0.247143	+	0.142688i	−0.371312	+	0.928508i	$0.621092\pi$
$402$		0			0
$403$	18.5642	+	32.1541i	0.0460649	+	0.0797868i
$404$		0			0
$405$	149.157	+	102.816i	0.368288	+	0.253866i
$406$		0			0
$407$	590.399	+	340.867i	1.45061	+	0.837510i
$408$		0			0
$409$	23.8711			0.0583646			0.0291823	−	0.999574i	$-0.490710\pi$
$409$	23.8711			0.0583646			0.0291823	+	0.999574i	$0.490710\pi$
$410$		0			0
$411$	566.220	−	311.993i	1.37766	−	0.759107i
$412$		0			0
$413$	−58.9458	+	34.0324i	−0.142726	+	0.0824028i
$414$		0			0
$415$	−10.7318	−	18.5880i	−0.0258597	−	0.0447902i
$416$		0			0
$417$	287.588	+	5.74678i	0.689660	+	0.0137812i
$418$		0			0
$419$	243.314	−	140.478i	0.580703	−	0.335269i	−0.180710	−	0.983536i	$-0.557839\pi$
$419$	243.314	−	140.478i	0.580703	−	0.335269i	0.761413	+	0.648268i	$0.224506\pi$
$420$		0			0
$421$	−514.291			−1.22159			−0.610797	−	0.791787i	$-0.709151\pi$
$421$	−514.291			−1.22159			−0.610797	+	0.791787i	$0.709151\pi$
$422$		0			0
$423$	133.200	−	69.9624i	0.314893	−	0.165396i
$424$		0			0
$425$	190.332	+	109.888i	0.447839	+	0.258560i
$426$		0			0
$427$	149.749			0.350699
$428$		0			0
$429$	−24.3937	−	14.7412i	−0.0568617	−	0.0343618i
$430$		0			0
$431$	263.180	+	151.947i	0.610625	+	0.352545i	0.773210	−	0.634150i	$-0.218650\pi$
$431$	263.180	+	151.947i	0.610625	+	0.352545i	−0.162585	+	0.986695i	$0.551983\pi$
$432$		0			0
$433$	236.247	−	409.191i	0.545604	−	0.945014i	−0.452965	−	0.891528i	$-0.649634\pi$
$433$	236.247	−	409.191i	0.545604	−	0.945014i	0.998569	−	0.0534853i	$-0.0170330\pi$
$434$		0			0
$435$	−176.575	−	3.52844i	−0.405919	−	0.00811135i
$436$		0			0
$437$	−26.7894	+	92.1598i	−0.0613030	+	0.210892i
$438$		0			0
$439$	−338.757			−0.771657			−0.385828	−	0.922571i	$-0.626084\pi$
$439$	−338.757			−0.771657			−0.385828	+	0.922571i	$0.626084\pi$
$440$		0			0
$441$	176.518	+	336.069i	0.400269	+	0.762061i
$442$		0			0
$443$	61.1347	−	35.2962i	0.138002	−	0.0796753i	−0.429410	−	0.903110i	$-0.641278\pi$
$443$	61.1347	−	35.2962i	0.138002	−	0.0796753i	0.567411	+	0.823435i	$0.307945\pi$
$444$		0			0
$445$	174.503	+	302.248i	0.392142	+	0.679209i
$446$		0			0
$447$	182.312	+	110.172i	0.407856	+	0.246469i
$448$		0			0
$449$		−	195.529i		−	0.435476i	−0.976007	−	0.217738i	$-0.930132\pi$
$449$		−	195.529i		−	0.435476i	0.976007	−	0.217738i	$-0.0698678\pi$
$450$		0			0
$451$	279.358	+	483.863i	0.619420	+	1.07287i
$452$		0			0
$453$	−59.9781	+	99.2515i	−0.132402	+	0.219098i
$454$		0			0
$455$	4.61754	−	2.66594i	0.0101484	−	0.00585921i
$456$		0			0
$457$	49.0934	−	85.0323i	0.107425	−	0.186066i	−0.807301	−	0.590140i	$-0.799073\pi$
$457$	49.0934	−	85.0323i	0.107425	−	0.186066i	0.914727	+	0.404073i	$0.132406\pi$
$458$		0			0
$459$	265.401	−	132.704i	0.578216	−	0.289116i
$460$		0			0
$461$		−	188.076i		−	0.407973i	−0.978974	−	0.203987i	$-0.934610\pi$
$461$		−	188.076i		−	0.407973i	0.978974	−	0.203987i	$-0.0653899\pi$
$462$		0			0
$463$	205.254	+	355.510i	0.443313	+	0.767840i	0.997933	−	0.0642632i	$-0.0204697\pi$
$463$	205.254	+	355.510i	0.443313	+	0.767840i	−0.554620	+	0.832104i	$0.687136\pi$
$464$		0			0
$465$	5.45263	−	272.868i	0.0117261	−	0.586813i
$466$		0			0
$467$		−	352.331i		−	0.754457i	−0.926120	−	0.377229i	$-0.876877\pi$
$467$		−	352.331i		−	0.754457i	0.926120	−	0.377229i	$-0.123123\pi$
$468$		0			0
$469$	45.2808	−	78.4286i	0.0965475	−	0.167225i
$470$		0			0
$471$	386.910	−	640.257i	0.821465	−	1.35936i
$472$		0			0
$473$	−196.869	−	113.662i	−0.416213	−	0.240301i
$474$		0			0
$475$	90.5796	+	369.005i	0.190694	+	0.776853i
$476$		0			0
$477$	241.800	+	152.798i	0.506918	+	0.320331i
$478$		0			0
$479$	−29.5006	+	17.0322i	−0.0615879	+	0.0355578i	−0.530478	−	0.847699i	$-0.677987\pi$
$479$	−29.5006	+	17.0322i	−0.0615879	+	0.0355578i	0.468890	+	0.883257i	$0.344654\pi$
$480$		0			0
$481$	59.7848			0.124293
$482$		0			0
$483$	33.8741	+	20.4703i	0.0701327	+	0.0423815i
$484$		0			0
$485$	184.761	+	106.672i	0.380951	+	0.219942i
$486$		0			0
$487$	−815.065			−1.67364			−0.836822	−	0.547475i	$-0.815589\pi$
$487$	−815.065			−1.67364			−0.836822	+	0.547475i	$0.815589\pi$
$488$		0			0
$489$	206.075	+	4.11794i	0.421422	+	0.00842114i
$490$		0			0
$491$	−567.947	−	327.904i	−1.15671	−	0.667830i	−0.206200	−	0.978510i	$-0.566110\pi$
$491$	−567.947	−	327.904i	−1.15671	−	0.667830i	−0.950514	+	0.310680i	$0.899443\pi$
$492$		0			0
$493$	−144.639	+	250.521i	−0.293385	+	0.508157i
$494$		0			0
$495$	97.4233	+	185.482i	0.196815	+	0.374711i
$496$		0			0
$497$		−	94.9762i		−	0.191099i
$498$		0			0
$499$	151.910	−	263.116i	0.304429	−	0.527286i	−0.672705	−	0.739911i	$-0.734868\pi$
$499$	151.910	−	263.116i	0.304429	−	0.527286i	0.977134	+	0.212625i	$0.0682011\pi$
$500$		0			0
$501$	−2.14103	+	107.144i	−0.00427350	+	0.213861i
$502$		0			0
$503$	220.195	+	127.130i	0.437764	+	0.252743i	0.702649	−	0.711537i	$-0.252001\pi$
$503$	220.195	+	127.130i	0.437764	+	0.252743i	−0.264885	+	0.964280i	$0.585334\pi$
$504$		0			0
$505$	108.787			0.215420
$506$		0			0
$507$	504.400	+	10.0793i	0.994871	+	0.0198802i
$508$		0			0
$509$		−	271.200i		−	0.532809i	−0.963861	−	0.266404i	$-0.914164\pi$
$509$		−	271.200i		−	0.532809i	0.963861	−	0.266404i	$-0.0858357\pi$
$510$		0			0
$511$	−18.0282			−0.0352803
$512$		0			0
$513$	483.147	+	172.446i	0.941808	+	0.336152i
$514$		0			0
$515$			457.231i			0.887827i
$516$		0			0
$517$	174.002			0.336560
$518$		0			0
$519$	−7.36515	+	368.577i	−0.0141910	+	0.710167i
$520$		0			0
$521$			764.752i			1.46785i	0.679229	+	0.733927i	$0.262315\pi$
$521$			764.752i			1.46785i	−0.679229	+	0.733927i	$0.737685\pi$
$522$		0			0
$523$	234.866	−	406.799i	0.449074	−	0.777819i	−0.549252	−	0.835657i	$-0.685087\pi$
$523$	234.866	−	406.799i	0.449074	−	0.777819i	0.998326	+	0.0578377i	$0.0184206\pi$
$524$		0			0
$525$	156.660	+	3.13049i	0.298400	+	0.00596284i
$526$		0			0
$527$	−387.140	−	223.515i	−0.734611	−	0.424128i
$528$		0			0
$529$	503.484			0.951767
$530$		0			0
$531$	−198.274	−	125.293i	−0.373398	−	0.235957i
$532$		0			0
$533$	42.4325	+	24.4984i	0.0796106	+	0.0459632i
$534$		0			0
$535$	216.243	−	374.544i	0.404192	−	0.700082i
$536$		0			0
$537$	−8.53417	+	427.078i	−0.0158923	+	0.795304i
$538$		0			0
$539$			439.015i			0.814498i
$540$		0			0
$541$	241.908	−	418.997i	0.447150	−	0.774486i	−0.551049	−	0.834473i	$-0.685772\pi$
$541$	241.908	−	418.997i	0.447150	−	0.774486i	0.998199	+	0.0599864i	$0.0191057\pi$
$542$		0			0
$543$	182.859	−	302.594i	0.336757	−	0.557264i
$544$		0			0
$545$			226.399i			0.415411i
$546$		0			0
$547$	207.598	+	359.571i	0.379522	+	0.657351i	0.990993	−	0.133916i	$-0.0427553\pi$
$547$	207.598	+	359.571i	0.379522	+	0.657351i	−0.611471	+	0.791267i	$0.709422\pi$
$548$		0			0
$549$	239.951	+	456.836i	0.437068	+	0.832124i
$550$		0			0
$551$	−485.698	+	119.224i	−0.881485	+	0.216378i
$552$		0			0
$553$	−76.2497	+	132.068i	−0.137884	+	0.238822i
$554$		0			0
$555$	−376.122	−	227.292i	−0.677698	−	0.409536i
$556$		0			0
$557$	831.480	+	480.055i	1.49278	+	0.861859i	0.999966	−	0.00827418i	$-0.00263378\pi$
$557$	831.480	+	480.055i	1.49278	+	0.861859i	0.492817	+	0.870133i	$0.335967\pi$
$558$		0			0
$559$	−19.9353			−0.0356624
$560$		0			0
$561$	343.098	+	6.85602i	0.611583	+	0.0122211i
$562$		0			0
$563$	−31.2391	+	18.0359i	−0.0554868	+	0.0320353i	−0.527487	−	0.849563i	$-0.676866\pi$
$563$	−31.2391	+	18.0359i	−0.0554868	+	0.0320353i	0.472000	+	0.881599i	$0.343532\pi$
$564$		0			0
$565$	310.864			0.550202
$566$		0			0
$567$	120.067	−	174.183i	0.211758	−	0.307201i
$568$		0			0
$569$	−141.307	−	81.5839i	−0.248344	−	0.143381i	0.370662	−	0.928768i	$-0.379131\pi$
$569$	−141.307	−	81.5839i	−0.248344	−	0.143381i	−0.619006	+	0.785387i	$0.712464\pi$
$570$		0			0
$571$	−229.873	−	398.152i	−0.402580	−	0.697289i	0.591457	−	0.806337i	$-0.298553\pi$
$571$	−229.873	−	398.152i	−0.402580	−	0.697289i	−0.994036	+	0.109048i	$0.965220\pi$
$572$		0			0
$573$	−79.3524	−	47.9531i	−0.138486	−	0.0836877i
$574$		0			0
$575$	−87.4817	+	50.5076i	−0.152142	+	0.0878392i
$576$		0			0
$577$	−421.023			−0.729675			−0.364838	−	0.931071i	$-0.618875\pi$
$577$	−421.023			−0.729675			−0.364838	+	0.931071i	$0.618875\pi$
$578$		0			0
$579$	−67.2894	+	111.350i	−0.116217	+	0.192315i
$580$		0			0
$581$	−21.7068	+	12.5324i	−0.0373610	+	0.0215704i
$582$		0			0
$583$	165.398	+	286.477i	0.283701	+	0.491385i
$584$		0			0
$585$	15.5319	+	9.81488i	0.0265502	+	0.0167776i
$586$		0			0
$587$			862.872i			1.46997i	0.678084	+	0.734984i	$0.262810\pi$
$587$			862.872i			1.46997i	−0.678084	+	0.734984i	$0.737190\pi$
$588$		0			0
$589$	−184.242	−	750.567i	−0.312804	−	1.27431i
$590$		0			0
$591$	−11.6814	+	584.579i	−0.0197656	+	0.989135i
$592$		0			0
$593$	101.112	+	58.3770i	0.170509	+	0.0984435i	0.582826	−	0.812597i	$-0.301947\pi$
$593$	101.112	+	58.3770i	0.170509	+	0.0984435i	−0.412317	+	0.911041i	$0.635280\pi$
$594$		0			0
$595$	−32.0983	+	55.5960i	−0.0539468	+	0.0934386i
$596$		0			0
$597$	−4.21238	+	6.97063i	−0.00705592	+	0.0116761i
$598$		0			0
$599$		−	456.915i		−	0.762796i	−0.924411	−	0.381398i	$-0.875443\pi$
$599$		−	456.915i		−	0.762796i	0.924411	−	0.381398i	$-0.124557\pi$
$600$		0			0
$601$	452.634	−	783.985i	0.753134	−	1.30447i	−0.193162	−	0.981167i	$-0.561874\pi$
$601$	452.634	−	783.985i	0.753134	−	1.30447i	0.946297	−	0.323300i	$-0.104792\pi$
$602$		0			0
$603$	311.817	+	12.4668i	0.517109	+	0.0206747i
$604$		0			0
$605$		−	28.3220i		−	0.0468133i
$606$		0			0
$607$	−128.308	−	222.237i	−0.211381	−	0.366123i	0.740766	−	0.671763i	$-0.234463\pi$
$607$	−128.308	−	222.237i	−0.211381	−	0.366123i	−0.952147	+	0.305640i	$0.901130\pi$
$608$		0			0
$609$	−4.12046	+	206.202i	−0.00676595	+	0.338591i
$610$		0			0
$611$	13.2148	−	7.62956i	0.0216281	−	0.0124870i
$612$		0			0
$613$	−224.574	−	388.974i	−0.366353	−	0.634542i	0.622639	−	0.782509i	$-0.286060\pi$
$613$	−224.574	−	388.974i	−0.366353	−	0.634542i	−0.988992	+	0.147967i	$0.952727\pi$
$614$		0			0
$615$	−173.815	−	315.448i	−0.282626	−	0.512923i
$616$		0			0
$617$		−	197.645i		−	0.320332i	−0.987090	−	0.160166i	$-0.948797\pi$
$617$		−	197.645i		−	0.320332i	0.987090	−	0.160166i	$-0.0512029\pi$
$618$		0			0
$619$	−198.212	+	343.312i	−0.320213	+	0.554624i	−0.980532	−	0.196361i	$-0.937088\pi$
$619$	−198.212	+	343.312i	−0.320213	+	0.554624i	0.660319	+	0.750985i	$0.270421\pi$
$620$		0			0
$621$	−8.17001	+	136.140i	−0.0131562	+	0.219227i
$622$		0			0
$623$	352.961	−	203.782i	0.566551	−	0.327098i
$624$		0			0
$625$	−137.432	+	238.038i	−0.219891	+	0.380862i
$626$		0			0
$627$	401.937	+	436.386i	0.641048	+	0.695990i
$628$		0			0
$629$	−623.381	+	359.909i	−0.991067	+	0.572193i
$630$		0			0
$631$	−154.867	+	268.238i	−0.245432	+	0.425100i	−0.962253	−	0.272157i	$-0.912263\pi$
$631$	−154.867	+	268.238i	−0.245432	+	0.425100i	0.716821	+	0.697257i	$0.245596\pi$
$632$		0			0
$633$	537.881	−	890.082i	0.849733	−	1.40613i
$634$		0			0
$635$	125.240	−	72.3075i	0.197229	−	0.113870i
$636$		0			0
$637$	19.2497	+	33.3415i	0.0302194	+	0.0523415i
$638$		0			0
$639$	289.742	−	152.186i	0.453431	−	0.238162i
$640$		0			0
$641$			1084.49i			1.69187i	0.533289	+	0.845933i	$0.320956\pi$
$641$			1084.49i			1.69187i	−0.533289	+	0.845933i	$0.679044\pi$
$642$		0			0
$643$	260.631	−	451.426i	0.405335	−	0.702062i	−0.589025	−	0.808115i	$-0.700488\pi$
$643$	260.631	−	451.426i	0.405335	−	0.702062i	0.994360	+	0.106053i	$0.0338214\pi$
$644$		0			0
$645$	125.418	+	75.7909i	0.194447	+	0.117505i
$646$		0			0
$647$		−	109.502i		−	0.169246i	−0.996413	−	0.0846232i	$-0.973031\pi$
$647$		−	109.502i		−	0.169246i	0.996413	−	0.0846232i	$-0.0269687\pi$
$648$		0			0
$649$	−135.625	−	234.909i	−0.208975	−	0.361956i
$650$		0			0
$651$	−318.651	−	6.36751i	−0.489480	−	0.00978111i
$652$		0			0
$653$	−421.496	+	243.351i	−0.645476	+	0.372666i	−0.786721	−	0.617309i	$-0.788223\pi$
$653$	−421.496	+	243.351i	−0.645476	+	0.372666i	0.141245	+	0.989975i	$0.454890\pi$
$654$		0			0
$655$	109.136	+	189.030i	0.166620	+	0.288595i
$656$		0			0
$657$	−28.8876	−	54.9985i	−0.0439690	−	0.0837115i
$658$		0			0
$659$	639.659	−	369.307i	0.970651	−	0.560406i	0.0712163	−	0.997461i	$-0.477312\pi$
$659$	639.659	−	369.307i	0.970651	−	0.560406i	0.899435	+	0.437055i	$0.143979\pi$
$660$		0			0
$661$	−388.929			−0.588394			−0.294197	−	0.955745i	$-0.595052\pi$
$661$	−388.929			−0.588394			−0.294197	+	0.955745i	$0.595052\pi$
$662$		0			0
$663$	26.3577	−	14.5234i	0.0397552	−	0.0219055i
$664$		0			0
$665$	−107.787	+	26.4583i	−0.162085	+	0.0397870i
$666$		0			0
$667$	−66.4799	−	115.146i	−0.0996700	−	0.172633i
$668$		0			0
$669$	−255.282	−	5.10121i	−0.381587	−	0.00762513i
$670$		0			0
$671$			596.775i			0.889382i
$672$		0			0
$673$	435.096	−	753.608i	0.646502	−	1.11977i	−0.337450	−	0.941343i	$-0.609564\pi$
$673$	435.096	−	753.608i	0.646502	−	1.11977i	0.983952	−	0.178431i	$-0.0571022\pi$
$674$		0			0
$675$	241.475	+	482.937i	0.357741	+	0.715462i
$676$		0			0
$677$	−859.080	−	495.990i	−1.26895	−	0.732629i	−0.294162	−	0.955756i	$-0.595040\pi$
$677$	−859.080	−	495.990i	−1.26895	−	0.732629i	−0.974790	+	0.223126i	$0.928374\pi$
$678$		0			0
$679$	124.570	−	215.762i	0.183461	−	0.317764i
$680$		0			0
$681$	683.236	+	412.883i	1.00328	+	0.606289i
$682$		0			0
$683$		−	260.321i		−	0.381144i	−0.981673	−	0.190572i	$-0.938966\pi$
$683$		−	260.321i		−	0.381144i	0.981673	−	0.190572i	$-0.0610343\pi$
$684$		0			0
$685$	−481.964			−0.703597
$686$		0			0
$687$	136.829	+	248.323i	0.199168	+	0.361460i
$688$		0			0
$689$	25.1227	+	14.5046i	0.0364626	+	0.0210517i
$690$		0			0
$691$	97.0956	−	168.175i	0.140515	−	0.243378i	−0.787176	−	0.616729i	$-0.788458\pi$
$691$	97.0956	−	168.175i	0.140515	−	0.243378i	0.927691	+	0.373350i	$0.121791\pi$
$692$		0			0
$693$	216.603	−	113.770i	0.312559	−	0.164170i
$694$		0			0
$695$	−185.713	−	107.222i	−0.267214	−	0.154276i
$696$		0			0
$697$	−589.929			−0.846384
$698$		0			0
$699$	−723.123	+	398.448i	−1.03451	+	0.570026i
$700$		0			0
$701$	−1199.67	+	692.631i	−1.71137	+	0.988061i	−0.778656	+	0.627451i	$0.784098\pi$
$701$	−1199.67	+	692.631i	−1.71137	+	0.988061i	−0.932716	+	0.360611i	$0.882568\pi$
$702$		0			0
$703$	−1195.00	−	347.366i	−1.69985	−	0.494120i
$704$		0			0
$705$	−112.144	−	2.24094i	−0.159070	−	0.00317864i
$706$		0			0
$707$		−	127.040i		−	0.179689i
$708$		0			0
$709$	−566.268	−	980.805i	−0.798685	−	1.38336i	−0.920473	−	0.390807i	$-0.872196\pi$
$709$	−566.268	−	980.805i	−0.798685	−	1.38336i	0.121787	−	0.992556i	$-0.461137\pi$
$710$		0			0
$711$	−525.078	−	20.9933i	−0.738507	−	0.0295265i
$712$		0			0
$713$	177.940	−	102.734i	0.249565	−	0.144087i
$714$		0			0
$715$	10.6242	+	18.4017i	0.0148591	+	0.0257367i
$716$		0			0
$717$	−467.251	+	257.460i	−0.651675	+	0.359080i
$718$		0			0
$719$	−212.442	+	122.653i	−0.295468	+	0.170589i	−0.640405	−	0.768037i	$-0.721234\pi$
$719$	−212.442	+	122.653i	−0.295468	+	0.170589i	0.344937	+	0.938626i	$0.387900\pi$
$720$		0			0
$721$	533.948			0.740566
$722$		0			0
$723$	−261.216	−	474.067i	−0.361295	−	0.655694i
$724$		0			0
$725$	−455.861	−	263.192i	−0.628774	−	0.363023i
$726$		0			0
$727$	394.815			0.543074			0.271537	−	0.962428i	$-0.412468\pi$
$727$	394.815			0.543074			0.271537	+	0.962428i	$0.412468\pi$
$728$		0			0
$729$	723.768	+	87.1834i	0.992823	+	0.119593i
$730$		0			0
$731$	207.867	−	120.012i	0.284360	−	0.164175i
$732$		0			0
$733$	−441.511	−	764.719i	−0.602334	−	1.04327i	−0.992467	−	0.122515i	$-0.960904\pi$
$733$	−441.511	−	764.719i	−0.602334	−	1.04327i	0.390133	−	0.920759i	$-0.372429\pi$
$734$		0			0
$735$	5.65400	−	282.945i	0.00769251	−	0.384959i
$736$		0			0
$737$	312.552	+	180.452i	0.424087	+	0.244847i
$738$		0			0
$739$	167.647	+	290.374i	0.226857	+	0.392928i	0.956875	−	0.290500i	$-0.0938217\pi$
$739$	167.647	+	290.374i	0.226857	+	0.392928i	−0.730018	+	0.683428i	$0.760488\pi$
$740$		0			0
$741$	49.6601	+	15.5179i	0.0670177	+	0.0209418i
$742$		0			0
$743$	−408.674	−	235.948i	−0.550032	−	0.317561i	0.199103	−	0.979979i	$-0.436197\pi$
$743$	−408.674	−	235.948i	−0.550032	−	0.317561i	−0.749135	+	0.662417i	$0.769531\pi$
$744$		0			0
$745$	−79.4027	−	137.530i	−0.106581	−	0.184603i
$746$		0			0
$747$	−73.0144	−	46.1391i	−0.0977435	−	0.0617659i
$748$		0			0
$749$	−437.387	−	252.526i	−0.583962	−	0.337150i
$750$		0			0
$751$	1017.73			1.35517			0.677586	−	0.735443i	$-0.263026\pi$
$751$	1017.73			1.35517			0.677586	+	0.735443i	$0.263026\pi$
$752$		0			0
$753$	−607.122	−	366.887i	−0.806271	−	0.487233i
$754$		0			0
$755$	74.8718	−	43.2273i	0.0991680	−	0.0572546i
$756$		0			0
$757$	−187.856	−	325.377i	−0.248159	−	0.429824i	0.714856	−	0.699272i	$-0.246492\pi$
$757$	−187.856	−	325.377i	−0.248159	−	0.429824i	−0.963015	+	0.269448i	$0.913159\pi$
$758$		0			0
$759$	−81.5777	+	134.994i	−0.107481	+	0.177858i
$760$		0			0
$761$	−554.683	+	320.246i	−0.728887	+	0.420823i	−0.818015	−	0.575197i	$-0.804925\pi$
$761$	−554.683	+	320.246i	−0.728887	+	0.420823i	0.0891278	+	0.996020i	$0.471592\pi$
$762$		0			0
$763$	264.386			0.346508
$764$		0			0
$765$	−221.039	−	8.83742i	−0.288939	−	0.0115522i
$766$		0			0
$767$	−20.6004	−	11.8937i	−0.0268585	−	0.0155067i
$768$		0			0
$769$	−886.170			−1.15237			−0.576183	−	0.817320i	$-0.695459\pi$
$769$	−886.170			−1.15237			−0.576183	+	0.817320i	$0.695459\pi$
$770$		0			0
$771$	2.40970	−	120.589i	0.00312542	−	0.156406i
$772$		0			0
$773$	356.974	+	206.099i	0.461803	+	0.266622i	0.712802	−	0.701365i	$-0.247426\pi$
$773$	356.974	+	206.099i	0.461803	+	0.266622i	−0.250999	+	0.967987i	$0.580759\pi$
$774$		0			0
$775$	406.720	−	704.460i	0.524800	−	0.908980i
$776$		0			0
$777$	−265.429	+	439.230i	−0.341608	+	0.565290i
$778$		0			0
$779$	−705.810	−	736.225i	−0.906046	−	0.945090i
$780$		0			0
$781$	378.497			0.484631
$782$		0			0
$783$	−635.659	+	317.838i	−0.811825	+	0.405924i
$784$		0			0
$785$	−482.987	+	278.853i	−0.615270	+	0.355226i
$786$		0			0
$787$	262.887	+	455.334i	0.334037	+	0.578569i	0.983299	−	0.181996i	$-0.0582557\pi$
$787$	262.887	+	455.334i	0.334037	+	0.578569i	−0.649262	+	0.760564i	$0.724922\pi$
$788$		0			0
$789$	24.4061	−	1221.37i	0.0309330	−	1.54799i
$790$		0			0
$791$		−	363.023i		−	0.458942i
$792$		0			0
$793$	26.1672	+	45.3229i	0.0329977	+	0.0571537i
$794$		0			0
$795$	−102.909	−	186.765i	−0.129446	−	0.234924i
$796$		0			0
$797$	−425.382	+	245.594i	−0.533729	+	0.308149i	−0.742534	−	0.669809i	$-0.766376\pi$
$797$	−425.382	+	245.594i	−0.533729	+	0.308149i	0.208805	+	0.977957i	$0.433043\pi$
$798$		0			0
$799$	−91.8612	+	159.108i	−0.114970	+	0.199134i
$800$		0			0
$801$	1187.25	+	750.242i	1.48220	+	0.936632i
$802$		0			0
$803$		−	71.8457i		−	0.0894716i
$804$		0			0
$805$	−14.7533	−	25.5534i	−0.0183270	−	0.0317434i
$806$		0			0
$807$	−1249.14	+	688.291i	−1.54788	+	0.852901i
$808$		0			0
$809$		−	1024.63i		−	1.26654i	−0.773931	−	0.633270i	$-0.781712\pi$
$809$		−	1024.63i		−	1.26654i	0.773931	−	0.633270i	$-0.218288\pi$
$810$		0			0
$811$	−427.052	+	739.675i	−0.526574	+	0.912053i	0.472947	+	0.881091i	$0.343190\pi$
$811$	−427.052	+	739.675i	−0.526574	+	0.912053i	−0.999521	+	0.0309618i	$0.990143\pi$
$812$		0			0
$813$	−4.15812	−	7.54636i	−0.00511454	−	0.00928212i
$814$		0			0
$815$	−133.076	−	76.8313i	−0.163283	−	0.0942715i
$816$		0			0
$817$	398.472	+	115.830i	0.487726	+	0.141774i
$818$		0			0
$819$	11.4617	−	18.1379i	0.0139947	−	0.0221464i
$820$		0			0
$821$	−1289.87	+	744.707i	−1.57110	+	0.907073i	−0.575061	+	0.818110i	$0.695022\pi$
$821$	−1289.87	+	744.707i	−1.57110	+	0.907073i	−0.996035	+	0.0889626i	$0.971645\pi$
$822$		0			0
$823$	−418.421			−0.508410			−0.254205	−	0.967150i	$-0.581814\pi$
$823$	−418.421			−0.508410			−0.254205	+	0.967150i	$0.581814\pi$
$824$		0			0
$825$	−12.4756	+	624.319i	−0.0151219	+	0.756750i
$826$		0			0
$827$	840.873	+	485.478i	1.01678	+	0.587036i	0.913168	−	0.407583i	$-0.133628\pi$
$827$	840.873	+	485.478i	1.01678	+	0.587036i	0.103607	+	0.994618i	$0.466962\pi$
$828$		0			0
$829$	−1204.76			−1.45327			−0.726637	−	0.687021i	$-0.758918\pi$
$829$	−1204.76			−1.45327			−0.726637	+	0.687021i	$0.758918\pi$
$830$		0			0
$831$	−163.131	+	269.948i	−0.196307	+	0.324848i
$832$		0			0
$833$	−401.438	−	231.770i	−0.481918	−	0.278235i
$834$		0			0
$835$	39.9466	−	69.1896i	0.0478403	−	0.0828618i
$836$		0			0
$837$	−491.168	−	982.308i	−0.586819	−	1.17361i
$838$		0			0
$839$			1105.55i			1.31770i	0.752274	+	0.658850i	$0.228957\pi$
$839$			1105.55i			1.31770i	−0.752274	+	0.658850i	$0.771043\pi$
$840$		0			0
$841$	−74.0776	+	128.306i	−0.0880827	+	0.152564i
$842$		0			0
$843$	731.416	−	403.018i	0.867634	−	0.478076i
$844$		0			0
$845$	−325.722	−	188.056i	−0.385470	−	0.222551i
$846$		0			0
$847$	−33.0741			−0.0390485
$848$		0			0
$849$	324.576	−	537.107i	0.382304	−	0.632634i
$850$		0			0
$851$		−	330.848i		−	0.388776i
$852$		0			0
$853$	−824.665			−0.966782			−0.483391	−	0.875405i	$-0.660595\pi$
$853$	−824.665			−0.966782			−0.483391	+	0.875405i	$0.660595\pi$
$854$		0			0
$855$	−253.429	−	286.427i	−0.296408	−	0.335003i
$856$		0			0
$857$			578.179i			0.674655i	0.941387	+	0.337327i	$0.109523\pi$
$857$			578.179i			0.674655i	−0.941387	+	0.337327i	$0.890477\pi$
$858$		0			0
$859$	−919.084			−1.06995			−0.534973	−	0.844869i	$-0.679678\pi$
$859$	−919.084			−1.06995			−0.534973	+	0.844869i	$0.679678\pi$
$860$		0			0
$861$	−368.375	+	202.979i	−0.427846	+	0.235748i
$862$		0			0
$863$			102.762i			0.119075i	0.998226	+	0.0595377i	$0.0189626\pi$
$863$			102.762i			0.119075i	−0.998226	+	0.0595377i	$0.981037\pi$
$864$		0			0
$865$	137.417	−	238.013i	0.158863	−	0.275159i
$866$		0			0
$867$	261.012	−	431.922i	0.301052	−	0.498180i
$868$		0			0
$869$	−526.316	−	303.869i	−0.605657	−	0.349676i
$870$		0			0
$871$	31.6496			0.0363370
$872$		0			0
$873$	857.826	+	34.2970i	0.982619	+	0.0392864i
$874$		0			0
$875$	−227.635	−	131.425i	−0.260154	−	0.150200i
$876$		0			0
$877$	356.759	−	617.924i	0.406795	−	0.704589i	−0.587734	−	0.809054i	$-0.699980\pi$
$877$	356.759	−	617.924i	0.406795	−	0.704589i	0.994529	+	0.104465i	$0.0333131\pi$
$878$		0			0
$879$	1223.64	−	674.238i	1.39208	−	0.767052i
$880$		0			0
$881$			132.789i			0.150725i	0.997156	+	0.0753626i	$0.0240114\pi$
$881$			132.789i			0.150725i	−0.997156	+	0.0753626i	$0.975989\pi$
$882$		0			0
$883$	−26.8525	+	46.5099i	−0.0304105	+	0.0526726i	−0.880830	−	0.473432i	$-0.843015\pi$
$883$	−26.8525	+	46.5099i	−0.0304105	+	0.0526726i	0.850420	+	0.526105i	$0.176348\pi$
$884$		0			0
$885$	84.3850	+	153.146i	0.0953503	+	0.173046i
$886$		0			0
$887$		−	336.682i		−	0.379574i	−0.981825	−	0.189787i	$-0.939220\pi$
$887$		−	336.682i		−	0.379574i	0.981825	−	0.189787i	$-0.0607797\pi$
$888$		0			0
$889$	−84.4397	−	146.254i	−0.0949828	−	0.164515i
$890$		0			0
$891$	694.151	+	478.489i	0.779069	+	0.537024i
$892$		0			0
$893$	−308.471	+	75.7202i	−0.345432	+	0.0847931i
$894$		0			0
$895$	159.228	−	275.791i	0.177908	−	0.308146i
$896$		0			0
$897$	−0.276347	+	13.8293i	−0.000308079	+	0.0154173i
$898$		0			0
$899$	927.235	+	535.340i	1.03141	+	0.595483i
$900$		0			0
$901$	−349.276			−0.387653
$902$		0			0
$903$	88.5076	−	146.462i	0.0980150	−	0.162195i
$904$		0			0
$905$	−228.267	+	131.790i	−0.252228	+	0.145624i
$906$		0			0
$907$	−151.672			−0.167224			−0.0836120	−	0.996498i	$-0.526646\pi$
$907$	−151.672			−0.167224			−0.0836120	+	0.996498i	$0.526646\pi$
$908$		0			0
$909$	387.560	−	203.564i	0.426358	−	0.223942i
$910$		0			0
$911$	601.083	+	347.036i	0.659806	+	0.380939i	0.792203	−	0.610257i	$-0.208934\pi$
$911$	601.083	+	347.036i	0.659806	+	0.380939i	−0.132397	+	0.991197i	$0.542267\pi$
$912$		0			0
$913$	−49.9439	−	86.5053i	−0.0547030	−	0.0947484i
$914$		0			0
$915$	7.68577	−	384.622i	0.00839975	−	0.420352i
$916$		0			0
$917$	220.746	−	127.448i	0.240727	−	0.138984i
$918$		0			0
$919$	654.831			0.712547			0.356274	−	0.934382i	$-0.384047\pi$
$919$	654.831			0.712547			0.356274	+	0.934382i	$0.384047\pi$
$920$		0			0
$921$	−183.087	−	332.275i	−0.198791	−	0.360776i
$922$		0			0
$923$	28.7455	−	16.5962i	0.0311435	−	0.0179807i
$924$		0			0
$925$	−654.909	−	1134.34i	−0.708010	−	1.22631i
$926$		0			0
$927$	855.575	+	1628.91i	0.922951	+	1.75718i
$928$		0			0
$929$		−	34.9242i		−	0.0375933i	−0.999823	−	0.0187967i	$-0.994016\pi$
$929$		−	34.9242i		−	0.0375933i	0.999823	−	0.0187967i	$-0.00598351\pi$
$930$		0			0
$931$	−191.046	−	778.287i	−0.205205	−	0.835968i
$932$		0			0
$933$	−1586.63	+	874.248i	−1.70057	+	0.937029i
$934$		0			0
$935$	−221.560	−	127.918i	−0.236962	−	0.136810i
$936$		0			0
$937$	−19.5119	+	33.7956i	−0.0208238	+	0.0360678i	−0.876250	−	0.481858i	$-0.839962\pi$
$937$	−19.5119	+	33.7956i	−0.0208238	+	0.0360678i	0.855426	+	0.517926i	$0.173296\pi$
$938$		0			0
$939$	474.086	+	860.394i	0.504884	+	0.916287i
$940$		0			0
$941$			14.0397i			0.0149200i	0.999972	+	0.00745999i	$0.00237461\pi$
$941$			14.0397i			0.0149200i	−0.999972	+	0.00745999i	$0.997625\pi$
$942$		0			0
$943$	135.574	−	234.821i	0.143769	−	0.249015i
$944$		0			0
$945$	−141.066	+	70.5350i	−0.149276	+	0.0746402i
$946$		0			0
$947$		−	616.423i		−	0.650921i	−0.945556	−	0.325461i	$-0.894481\pi$
$947$		−	616.423i		−	0.650921i	0.945556	−	0.325461i	$-0.105519\pi$
$948$		0			0
$949$	−3.15026	−	5.45642i	−0.00331956	−	0.00574965i
$950$		0			0
$951$	111.154	−	61.2468i	0.116881	−	0.0644026i
$952$		0			0
$953$	−697.352	+	402.617i	−0.731744	+	0.422473i	−0.819060	−	0.573708i	$-0.805504\pi$
$953$	−697.352	+	402.617i	−0.731744	+	0.422473i	0.0873157	+	0.996181i	$0.472171\pi$
$954$		0			0
$955$	34.5606	+	59.8607i	0.0361891	+	0.0626814i
$956$		0			0
$957$	−821.751	−	16.4208i	−0.858674	−	0.0171586i
$958$		0			0
$959$			562.831i			0.586894i
$960$		0			0
$961$	−346.780	+	600.641i	−0.360854	+	0.625017i
$962$		0			0
$963$	69.5261	−	1738.97i	0.0721975	−	1.80578i
$964$		0			0
$965$	83.9986	−	48.4966i	0.0870452	−	0.0502556i
$966$		0			0
$967$	122.473	−	212.130i	0.126653	−	0.219369i	−0.795725	−	0.605658i	$-0.792910\pi$
$967$	122.473	−	212.130i	0.126653	−	0.219369i	0.922378	+	0.386289i	$0.126243\pi$
$968$		0			0
$969$	−611.229	+	137.152i	−0.630784	+	0.141539i
$970$		0			0
$971$	903.998	−	521.923i	0.930997	−	0.537511i	0.0438700	−	0.999037i	$-0.486031\pi$
$971$	903.998	−	521.923i	0.930997	−	0.537511i	0.887127	+	0.461526i	$0.152698\pi$
$972$		0			0
$973$	−125.212	+	216.874i	−0.128687	+	0.222892i
$974$		0			0
$975$	26.4274	+	47.9618i	0.0271051	+	0.0491915i
$976$		0			0
$977$	1293.85	−	747.007i	1.32431	−	0.764592i	0.339899	−	0.940462i	$-0.389607\pi$
$977$	1293.85	−	747.007i	1.32431	−	0.764592i	0.984413	+	0.175870i	$0.0562738\pi$
$978$		0			0
$979$	812.109	+	1406.61i	0.829529	+	1.43679i
$980$		0			0
$981$	423.640	+	806.558i	0.431845	+	0.822180i
$982$		0			0
$983$			437.897i			0.445470i	0.974879	+	0.222735i	$0.0714985\pi$
$983$			437.897i			0.445470i	−0.974879	+	0.222735i	$0.928501\pi$
$984$		0			0
$985$	217.949	−	377.499i	0.221268	−	0.383247i
$986$		0			0
$987$	−2.61694	+	130.960i	−0.00265141	+	0.132685i
$988$		0			0
$989$			110.322i			0.111549i
$990$		0			0
$991$	98.5250	+	170.650i	0.0994198	+	0.172200i	0.911445	−	0.411423i	$-0.134968\pi$
$991$	98.5250	+	170.650i	0.0994198	+	0.172200i	−0.812025	+	0.583623i	$0.801635\pi$
$992$		0			0
$993$	708.642	−	1172.66i	0.713637	−	1.18092i
$994$		0			0
$995$	5.25840	−	3.03594i	0.00528482	−	0.00305119i
$996$		0			0
$997$	143.770	+	249.016i	0.144202	+	0.249766i	0.929075	−	0.369891i	$-0.120605\pi$
$997$	143.770	+	249.016i	0.144202	+	0.249766i	−0.784873	+	0.619657i	$0.787272\pi$
$998$		0			0
$999$	−1765.27	−	105.937i	−1.76703	−	0.106043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.1	yes	80
3.2	odd	2		2052.3.be.a.197.15		80
9.4	even	3		2052.3.m.a.881.15		80
9.5	odd	6		684.3.m.a.653.27	yes	80
19.11	even	3		684.3.m.a.353.27	✓	80
57.11	odd	6		2052.3.m.a.1493.26		80
171.49	even	3		2052.3.be.a.125.15		80
171.68	odd	6	inner	684.3.be.a.581.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.27	✓	80	19.11	even	3
684.3.m.a.653.27	yes	80	9.5	odd	6
684.3.be.a.425.1	yes	80	1.1	even	1	trivial
684.3.be.a.581.1	yes	80	171.68	odd	6	inner
2052.3.m.a.881.15		80	9.4	even	3
2052.3.m.a.1493.26		80	57.11	odd	6
2052.3.be.a.125.15		80	171.49	even	3
2052.3.be.a.197.15		80	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.99940 - 0.0599360i) q^{3} +(1.93690 + 1.11827i) q^{5} +(1.30590 - 2.26189i) q^{7} +(8.99282 + 0.359544i) q^{9} +O(q^{10})\)	\(q+(-2.99940 - 0.0599360i) q^{3} +(1.93690 + 1.11827i) q^{5} +(1.30590 - 2.26189i) q^{7} +(8.99282 + 0.359544i) q^{9} +(9.01402 + 5.20424i) q^{11} +0.912775 q^{13} +(-5.74251 - 3.47023i) q^{15} +(-9.51759 + 5.49498i) q^{17} +(-18.2448 - 5.30348i) q^{19} +(-4.05249 + 6.70603i) q^{21} -5.05129i q^{23} +(-9.99895 - 17.3187i) q^{25} +(-26.9515 - 1.61741i) q^{27} +(22.7955 - 13.1610i) q^{29} +(20.3381 + 35.2267i) q^{31} +(-26.7247 - 16.1499i) q^{33} +(5.05879 - 2.92070i) q^{35} +65.4978 q^{37} +(-2.73778 - 0.0547081i) q^{39} +(46.4873 + 26.8395i) q^{41} -21.8403 q^{43} +(17.0161 + 10.7528i) q^{45} +(14.4776 - 8.35864i) q^{47} +(21.0893 + 36.5277i) q^{49} +(28.8764 - 15.9112i) q^{51} +(27.5234 + 15.8907i) q^{53} +(11.6395 + 20.1602i) q^{55} +(54.4056 + 17.0008i) q^{57} +(-22.5690 - 13.0302i) q^{59} +(28.6677 + 49.6539i) q^{61} +(12.5570 - 19.8712i) q^{63} +(1.76795 + 1.02073i) q^{65} +34.6740 q^{67} +(-0.302754 + 15.1508i) q^{69} +(31.4924 - 18.1821i) q^{71} +(-3.45130 - 5.97783i) q^{73} +(28.9528 + 52.5450i) q^{75} +(23.5428 - 13.5924i) q^{77} -58.3887 q^{79} +(80.7415 + 6.46663i) q^{81} +(-8.31103 - 4.79838i) q^{83} -24.5795 q^{85} +(-69.1616 + 38.1088i) q^{87} +(135.141 + 78.0237i) q^{89} +(1.19199 - 2.06459i) q^{91} +(-58.8909 - 106.878i) q^{93} +(-29.4076 - 30.6749i) q^{95} +95.3902 q^{97} +(79.1902 + 50.0418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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