LMFDB - Embedded newform 324.3.o.a.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			65.5
Character	$\chi$	$=$	324.65
Dual form			324.3.o.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.61407 + 1.47195i) q^{3} +(7.35484 + 5.47548i) q^{5} +(2.16180 + 1.42184i) q^{7} +(4.66673 - 7.69556i) q^{9} +O(q^{10})$	\(q+(-2.61407 + 1.47195i) q^{3} +(7.35484 + 5.47548i) q^{5} +(2.16180 + 1.42184i) q^{7} +(4.66673 - 7.69556i) q^{9} +(1.90463 + 16.2951i) q^{11} +(5.51865 - 18.4336i) q^{13} +(-27.2857 - 3.48733i) q^{15} +(2.42175 - 0.427020i) q^{17} +(-0.578712 + 3.28204i) q^{19} +(-7.74398 - 0.534727i) q^{21} +(2.97065 + 4.51665i) q^{23} +(16.9428 + 56.5928i) q^{25} +(-0.871702 + 26.9859i) q^{27} +(-20.3292 - 19.1797i) q^{29} +(1.91430 + 32.8672i) q^{31} +(-28.9645 - 39.7932i) q^{33} +(8.11447 + 22.2943i) q^{35} +(-32.4429 - 11.8083i) q^{37} +(12.7071 + 56.3099i) q^{39} +(18.6748 + 78.7953i) q^{41} +(-11.9365 + 27.6720i) q^{43} +(76.4600 - 31.0470i) q^{45} +(64.6646 + 3.76628i) q^{47} +(-16.7561 - 38.8451i) q^{49} +(-5.70208 + 4.68095i) q^{51} +(-25.5689 + 14.7622i) q^{53} +(-75.2155 + 130.277i) q^{55} +(-3.31820 - 9.43132i) q^{57} +(8.73474 - 74.7305i) q^{59} +(17.6094 - 8.84378i) q^{61} +(21.0304 - 10.0009i) q^{63} +(141.522 - 105.359i) q^{65} +(-52.8216 - 55.9876i) q^{67} +(-14.4138 - 7.43420i) q^{69} +(-45.5910 - 54.3333i) q^{71} +(35.3645 + 29.6743i) q^{73} +(-127.591 - 122.999i) q^{75} +(-19.0517 + 37.9350i) q^{77} +(-110.642 - 26.2225i) q^{79} +(-37.4432 - 71.8262i) q^{81} +(21.6720 - 91.4413i) q^{83} +(20.1497 + 10.1196i) q^{85} +(81.3735 + 20.2134i) q^{87} +(60.8048 - 72.4644i) q^{89} +(38.1398 - 32.0031i) q^{91} +(-53.3830 - 83.0995i) q^{93} +(-22.2271 + 20.9702i) q^{95} +(84.6863 + 113.753i) q^{97} +(134.289 + 61.3879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{31}{54}\right)$

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
$3$	−2.61407	+	1.47195i	−0.871357	+	0.490650i
$3$	−2.61407	+	1.47195i	−0.871357	+	0.490650i
$4$		0			0
$5$	7.35484	+	5.47548i	1.47097	+	1.09510i	0.973790	+	0.227447i	$0.0730380\pi$
$5$	7.35484	+	5.47548i	1.47097	+	1.09510i	0.497178	+	0.867648i	$0.334369\pi$
$6$		0			0
$7$	2.16180	+	1.42184i	0.308829	+	0.203120i	0.694457	−	0.719534i	$-0.255645\pi$
$7$	2.16180	+	1.42184i	0.308829	+	0.203120i	−0.385628	+	0.922654i	$0.626015\pi$
$8$		0			0
$9$	4.66673	−	7.69556i	0.518526	−	0.855062i
$10$		0			0
$11$	1.90463	+	16.2951i	0.173148	+	1.48138i	0.748316	+	0.663342i	$0.230863\pi$
$11$	1.90463	+	16.2951i	0.173148	+	1.48138i	−0.575168	+	0.818035i	$0.695063\pi$
$12$		0			0
$13$	5.51865	−	18.4336i	0.424512	−	1.41797i	−0.432015	−	0.901866i	$-0.642197\pi$
$13$	5.51865	−	18.4336i	0.424512	−	1.41797i	0.856527	−	0.516102i	$-0.172617\pi$
$14$		0			0
$15$	−27.2857	−	3.48733i	−1.81905	−	0.232489i
$16$		0			0
$17$	2.42175	−	0.427020i	0.142456	−	0.0251188i	−0.101965	−	0.994788i	$-0.532513\pi$
$17$	2.42175	−	0.427020i	0.142456	−	0.0251188i	0.244421	+	0.969669i	$0.421402\pi$
$18$		0			0
$19$	−0.578712	+	3.28204i	−0.0304586	+	0.172739i	−0.996242	−	0.0866096i	$-0.972397\pi$
$19$	−0.578712	+	3.28204i	−0.0304586	+	0.172739i	0.965784	+	0.259349i	$0.0835078\pi$
$20$		0			0
$21$	−7.74398	−	0.534727i	−0.368761	−	0.0254632i
$22$		0			0
$23$	2.97065	+	4.51665i	0.129158	+	0.196376i	0.894277	−	0.447513i	$-0.147690\pi$
$23$	2.97065	+	4.51665i	0.129158	+	0.196376i	−0.765119	+	0.643889i	$0.777320\pi$
$24$		0			0
$25$	16.9428	+	56.5928i	0.677711	+	2.26371i
$26$		0			0
$27$	−0.871702	+	26.9859i	−0.0322853	+	0.999479i
$28$		0			0
$29$	−20.3292	−	19.1797i	−0.701008	−	0.661367i	0.250808	−	0.968037i	$-0.419304\pi$
$29$	−20.3292	−	19.1797i	−0.701008	−	0.661367i	−0.951816	+	0.306670i	$0.900785\pi$
$30$		0			0
$31$	1.91430	+	32.8672i	0.0617515	+	1.06023i	0.876805	+	0.480847i	$0.159671\pi$
$31$	1.91430	+	32.8672i	0.0617515	+	1.06023i	−0.815053	+	0.579386i	$0.803292\pi$
$32$		0			0
$33$	−28.9645	−	39.7932i	−0.877711	−	1.20585i
$34$		0			0
$35$	8.11447	+	22.2943i	0.231842	+	0.636980i
$36$		0			0
$37$	−32.4429	−	11.8083i	−0.876835	−	0.319142i	−0.135903	−	0.990722i	$-0.543394\pi$
$37$	−32.4429	−	11.8083i	−0.876835	−	0.319142i	−0.740932	+	0.671580i	$0.765616\pi$
$38$		0			0
$39$	12.7071	+	56.3099i	0.325824	+	1.44384i
$40$		0			0
$41$	18.6748	+	78.7953i	0.455483	+	1.92184i	0.380885	+	0.924622i	$0.375619\pi$
$41$	18.6748	+	78.7953i	0.455483	+	1.92184i	0.0745983	+	0.997214i	$0.476233\pi$
$42$		0			0
$43$	−11.9365	+	27.6720i	−0.277594	+	0.643536i	−0.998789	−	0.0491965i	$-0.984334\pi$
$43$	−11.9365	+	27.6720i	−0.277594	+	0.643536i	0.721195	+	0.692732i	$0.243593\pi$
$44$		0			0
$45$	76.4600	−	31.0470i	1.69911	−	0.689934i
$46$		0			0
$47$	64.6646	+	3.76628i	1.37584	+	0.0801336i	0.730057	−	0.683386i	$-0.239493\pi$
$47$	64.6646	+	3.76628i	1.37584	+	0.0801336i	0.645784	+	0.763520i	$0.276530\pi$
$48$		0			0
$49$	−16.7561	−	38.8451i	−0.341962	−	0.792757i
$50$		0			0
$51$	−5.70208	+	4.68095i	−0.111805	+	0.0917834i
$52$		0			0
$53$	−25.5689	+	14.7622i	−0.482432	+	0.278532i	−0.721429	−	0.692488i	$-0.756515\pi$
$53$	−25.5689	+	14.7622i	−0.482432	+	0.278532i	0.238998	+	0.971020i	$0.423181\pi$
$54$		0			0
$55$	−75.2155	+	130.277i	−1.36755	+	2.36867i
$56$		0			0
$57$	−3.31820	−	9.43132i	−0.0582141	−	0.165462i
$58$		0			0
$59$	8.73474	−	74.7305i	0.148046	−	1.26662i	−0.691119	−	0.722741i	$-0.742882\pi$
$59$	8.73474	−	74.7305i	0.148046	−	1.26662i	0.839165	−	0.543877i	$-0.183044\pi$
$60$		0			0
$61$	17.6094	−	8.84378i	0.288679	−	0.144980i	−0.298567	−	0.954389i	$-0.596509\pi$
$61$	17.6094	−	8.84378i	0.288679	−	0.144980i	0.587246	+	0.809409i	$0.300212\pi$
$62$		0			0
$63$	21.0304	−	10.0009i	0.333816	−	0.158745i
$64$		0			0
$65$	141.522	−	105.359i	2.17725	−	1.62091i
$66$		0			0
$67$	−52.8216	−	55.9876i	−0.788382	−	0.835636i	0.201209	−	0.979548i	$-0.435513\pi$
$67$	−52.8216	−	55.9876i	−0.788382	−	0.835636i	−0.989590	+	0.143913i	$0.954032\pi$
$68$		0			0
$69$	−14.4138	−	7.43420i	−0.208895	−	0.107742i
$70$		0			0
$71$	−45.5910	−	54.3333i	−0.642127	−	0.765257i	0.342577	−	0.939490i	$-0.388700\pi$
$71$	−45.5910	−	54.3333i	−0.642127	−	0.765257i	−0.984705	+	0.174232i	$0.944256\pi$
$72$		0			0
$73$	35.3645	+	29.6743i	0.484445	+	0.406498i	0.852031	−	0.523492i	$-0.175371\pi$
$73$	35.3645	+	29.6743i	0.484445	+	0.406498i	−0.367586	+	0.929990i	$0.619815\pi$
$74$		0			0
$75$	−127.591	−	122.999i	−1.70122	−	1.63998i
$76$		0			0
$77$	−19.0517	+	37.9350i	−0.247424	+	0.492662i
$78$		0			0
$79$	−110.642	−	26.2225i	−1.40053	−	0.331931i	−0.540141	−	0.841574i	$-0.681629\pi$
$79$	−110.642	−	26.2225i	−1.40053	−	0.331931i	−0.860386	+	0.509643i	$0.829777\pi$
$80$		0			0
$81$	−37.4432	−	71.8262i	−0.462262	−	0.886743i
$82$		0			0
$83$	21.6720	−	91.4413i	0.261108	−	1.10170i	−0.671555	−	0.740955i	$-0.734373\pi$
$83$	21.6720	−	91.4413i	0.261108	−	1.10170i	0.932663	−	0.360748i	$-0.117478\pi$
$84$		0			0
$85$	20.1497	+	10.1196i	0.237056	+	0.119054i
$86$		0			0
$87$	81.3735	+	20.2134i	0.935328	+	0.232337i
$88$		0			0
$89$	60.8048	−	72.4644i	0.683200	−	0.814206i	−0.307315	−	0.951608i	$-0.599431\pi$
$89$	60.8048	−	72.4644i	0.683200	−	0.814206i	0.990515	+	0.137401i	$0.0438750\pi$
$90$		0			0
$91$	38.1398	−	32.0031i	0.419119	−	0.351683i
$92$		0			0
$93$	−53.3830	−	83.0995i	−0.574010	−	0.893543i
$94$		0			0
$95$	−22.2271	+	20.9702i	−0.233969	+	0.220739i
$96$		0			0
$97$	84.6863	+	113.753i	0.873054	+	1.17272i	0.983872	+	0.178875i	$0.0572457\pi$
$97$	84.6863	+	113.753i	0.873054	+	1.17272i	−0.110818	+	0.993841i	$0.535347\pi$
$98$		0			0
$99$	134.289	+	61.3879i	1.35645	+	0.620080i
$100$		0			0
$101$	3.32962	+	6.62981i	0.0329665	+	0.0656417i	0.909513	−	0.415676i	$-0.136455\pi$
$101$	3.32962	+	6.62981i	0.0329665	+	0.0656417i	−0.876546	+	0.481317i	$0.840159\pi$
$102$		0			0
$103$	−45.0910	−	5.27038i	−0.437777	−	0.0511688i	−0.105650	−	0.994403i	$-0.533692\pi$
$103$	−45.0910	−	5.27038i	−0.437777	−	0.0511688i	−0.332127	+	0.943235i	$0.607766\pi$
$104$		0			0
$105$	−54.0279	−	46.3348i	−0.514551	−	0.441284i
$106$		0			0
$107$	64.4406	+	37.2048i	0.602249	+	0.347708i	0.769926	−	0.638134i	$-0.220293\pi$
$107$	64.4406	+	37.2048i	0.602249	+	0.347708i	−0.167677	+	0.985842i	$0.553627\pi$
$108$		0			0
$109$	28.5195	+	49.3972i	0.261646	+	0.453185i	0.966680	−	0.255989i	$-0.0824012\pi$
$109$	28.5195	+	49.3972i	0.261646	+	0.453185i	−0.705033	+	0.709174i	$0.749068\pi$
$110$		0			0
$111$	102.189	−	16.8867i	0.920624	−	0.152132i
$112$		0			0
$113$	124.881	−	53.8682i	1.10514	−	0.476710i	0.236236	−	0.971696i	$-0.424086\pi$
$113$	124.881	−	53.8682i	1.10514	−	0.476710i	0.868901	+	0.494986i	$0.164827\pi$
$114$		0			0
$115$	−2.88217	+	49.4849i	−0.0250623	+	0.430304i
$116$		0			0
$117$	−116.103	−	128.494i	−0.992330	−	1.09824i
$118$		0			0
$119$	5.84250	+	2.52021i	0.0490967	+	0.0211782i
$120$		0			0
$121$	−144.166	+	34.1679i	−1.19145	+	0.282380i
$122$		0			0
$123$	−164.800	−	178.488i	−1.33984	−	1.45112i
$124$		0			0
$125$	−106.860	+	293.595i	−0.854879	+	2.34876i
$126$		0			0
$127$	125.934	−	45.8361i	0.991604	−	0.360914i	0.205263	−	0.978707i	$-0.434195\pi$
$127$	125.934	−	45.8361i	0.991604	−	0.360914i	0.786341	+	0.617792i	$0.211973\pi$
$128$		0			0
$129$	−9.52883	−	89.9066i	−0.0738669	−	0.696951i
$130$		0			0
$131$	−208.470	+	12.1420i	−1.59137	+	0.0926868i	−0.830801	−	0.556570i	$-0.812117\pi$
$131$	−208.470	+	12.1420i	−1.59137	+	0.0926868i	−0.760570	+	0.649256i	$0.775080\pi$
$132$		0			0
$133$	−5.91760	+	6.27229i	−0.0444932	+	0.0471601i
$134$		0			0
$135$	−154.172	+	193.704i	−1.14202	+	1.43485i
$136$		0			0
$137$	164.825	−	49.3452i	1.20310	−	0.360184i	0.378339	−	0.925667i	$-0.376495\pi$
$137$	164.825	−	49.3452i	1.20310	−	0.360184i	0.824760	+	0.565483i	$0.191310\pi$
$138$		0			0
$139$	−26.7418	+	17.5884i	−0.192387	+	0.126535i	−0.642048	−	0.766664i	$-0.721915\pi$
$139$	−26.7418	+	17.5884i	−0.192387	+	0.126535i	0.449661	+	0.893199i	$0.351545\pi$
$140$		0			0
$141$	−174.581	+	85.3376i	−1.23817	+	0.605231i
$142$		0			0
$143$	310.889	+	54.8181i	2.17405	+	0.383344i
$144$		0			0
$145$	−44.5006	−	252.376i	−0.306901	−	1.74052i
$146$		0			0
$147$	100.980	+	76.8797i	0.686937	+	0.522991i
$148$		0			0
$149$	94.4698	+	28.2824i	0.634025	+	0.189815i	0.587658	−	0.809110i	$-0.300050\pi$
$149$	94.4698	+	28.2824i	0.634025	+	0.189815i	0.0463677	+	0.998924i	$0.485235\pi$
$150$		0			0
$151$	1.12008	−	0.130919i	0.00741777	−	0.000867012i	−0.112383	−	0.993665i	$-0.535848\pi$
$151$	1.12008	−	0.130919i	0.00741777	−	0.000867012i	0.119801	+	0.992798i	$0.461774\pi$
$152$		0			0
$153$	8.01551	−	20.6295i	0.0523889	−	0.134833i
$154$		0			0
$155$	−165.884	+	252.215i	−1.07022	+	1.62719i
$156$		0			0
$157$	83.8996	−	112.697i	0.534392	−	0.717813i	−0.450152	−	0.892952i	$-0.648630\pi$
$157$	83.8996	−	112.697i	0.534392	−	0.717813i	0.984544	+	0.175139i	$0.0560374\pi$
$158$		0			0
$159$	45.1097	−	76.2255i	0.283709	−	0.479406i
$160$		0			0
$161$			13.9879i			0.0868812i
$162$		0			0
$163$	211.418			1.29705			0.648523	−	0.761195i	$-0.275387\pi$
$163$	211.418			1.29705			0.648523	+	0.761195i	$0.275387\pi$
$164$		0			0
$165$	4.85746	−	451.267i	0.0294391	−	2.73495i
$166$		0			0
$167$	−187.010	−	139.224i	−1.11982	−	0.833675i	−0.132306	−	0.991209i	$-0.542238\pi$
$167$	−187.010	−	139.224i	−1.11982	−	0.833675i	−0.987514	+	0.157534i	$0.949646\pi$
$168$		0			0
$169$	−168.144	−	110.590i	−0.994936	−	0.654380i
$170$		0			0
$171$	22.5564	+	19.7699i	0.131909	+	0.115614i
$172$		0			0
$173$	2.63088	+	22.5086i	0.0152074	+	0.130107i	0.998709	−	0.0507899i	$-0.0161739\pi$
$173$	2.63088	+	22.5086i	0.0152074	+	0.130107i	−0.983502	+	0.180897i	$0.942100\pi$
$174$		0			0
$175$	−43.8390	+	146.432i	−0.250509	+	0.836757i
$176$		0			0
$177$	87.1662	+	208.208i	0.492464	+	1.17632i
$178$		0			0
$179$	286.613	−	50.5377i	1.60119	−	0.282333i	0.699474	−	0.714658i	$-0.253418\pi$
$179$	286.613	−	50.5377i	1.60119	−	0.282333i	0.901718	+	0.432324i	$0.142306\pi$
$180$		0			0
$181$	39.5528	−	224.315i	0.218524	−	1.23931i	−0.656163	−	0.754619i	$-0.727821\pi$
$181$	39.5528	−	224.315i	0.218524	−	1.23931i	0.874686	−	0.484689i	$-0.161067\pi$
$182$		0			0
$183$	−33.0147	+	49.0384i	−0.180408	+	0.267970i
$184$		0			0
$185$	−173.957	−	264.488i	−0.940307	−	1.42967i
$186$		0			0
$187$	11.5709	+	38.6495i	0.0618764	+	0.206682i
$188$		0			0
$189$	−40.2541	+	57.0988i	−0.212985	+	0.302110i
$190$		0			0
$191$	−105.227	−	99.2761i	−0.550924	−	0.519770i	0.359666	−	0.933081i	$-0.382891\pi$
$191$	−105.227	−	99.2761i	−0.550924	−	0.519770i	−0.910590	+	0.413311i	$0.864372\pi$
$192$		0			0
$193$	7.66984	+	131.686i	0.0397401	+	0.682311i	0.958077	+	0.286511i	$0.0924956\pi$
$193$	7.66984	+	131.686i	0.0397401	+	0.682311i	−0.918337	+	0.395800i	$0.870467\pi$
$194$		0			0
$195$	−214.864	+	483.728i	−1.10187	+	2.48066i
$196$		0			0
$197$	−0.663587	−	1.82319i	−0.00336846	−	0.00925477i	0.937997	−	0.346643i	$-0.112679\pi$
$197$	−0.663587	−	1.82319i	−0.00336846	−	0.00925477i	−0.941365	+	0.337389i	$0.890456\pi$
$198$		0			0
$199$	231.669	+	84.3205i	1.16416	+	0.423721i	0.850583	−	0.525840i	$-0.176249\pi$
$199$	231.669	+	84.3205i	1.16416	+	0.423721i	0.313581	+	0.949561i	$0.398471\pi$
$200$		0			0
$201$	220.490	+	68.6049i	1.09697	+	0.341318i
$202$		0			0
$203$	−16.6774	−	70.3675i	−0.0821547	−	0.346638i
$204$		0			0
$205$	−294.091	+	681.781i	−1.43459	+	3.32576i
$206$		0			0
$207$	48.6213	−	1.78279i	0.234886	−	0.00861250i
$208$		0			0
$209$	−54.5836	−	3.17913i	−0.261165	−	0.0152112i
$210$		0			0
$211$	−133.335	−	309.105i	−0.631918	−	1.46495i	−0.869674	−	0.493626i	$-0.835671\pi$
$211$	−133.335	−	309.105i	−0.631918	−	1.46495i	0.237757	−	0.971325i	$-0.423588\pi$
$212$		0			0
$213$	199.154	+	74.9234i	0.934995	+	0.351753i
$214$		0			0
$215$	−239.309	+	138.165i	−1.11307	+	0.642629i
$216$		0			0
$217$	−42.5936	+	73.7742i	−0.196284	+	0.339973i
$218$		0			0
$219$	−136.124	−	25.5161i	−0.621572	−	0.116512i
$220$		0			0
$221$	5.49329	−	46.9981i	0.0248565	−	0.212661i
$222$		0			0
$223$	108.396	−	54.4385i	0.486080	−	0.244119i	−0.188842	−	0.982007i	$-0.560473\pi$
$223$	108.396	−	54.4385i	0.486080	−	0.244119i	0.674922	+	0.737889i	$0.264177\pi$
$224$		0			0
$225$	514.581	+	133.720i	2.28703	+	0.594309i
$226$		0			0
$227$	−117.879	+	87.7578i	−0.519291	+	0.386598i	−0.824653	−	0.565638i	$-0.808630\pi$
$227$	−117.879	+	87.7578i	−0.519291	+	0.386598i	0.305362	+	0.952236i	$0.401222\pi$
$228$		0			0
$229$	61.6777	+	65.3745i	0.269335	+	0.285478i	0.847898	−	0.530159i	$-0.177868\pi$
$229$	61.6777	+	65.3745i	0.269335	+	0.285478i	−0.578563	+	0.815638i	$0.696386\pi$
$230$		0			0
$231$	−6.03595	−	127.208i	−0.0261297	−	0.550683i
$232$		0			0
$233$	223.982	+	266.932i	0.961298	+	1.14563i	0.989281	+	0.146022i	$0.0466470\pi$
$233$	223.982	+	266.932i	0.961298	+	1.14563i	−0.0279834	+	0.999608i	$0.508909\pi$
$234$		0			0
$235$	454.976	+	381.770i	1.93607	+	1.62455i
$236$		0			0
$237$	327.823	−	94.3112i	1.38322	−	0.397938i
$238$		0			0
$239$	55.4982	−	110.506i	0.232210	−	0.462369i	−0.747106	−	0.664705i	$-0.768557\pi$
$239$	55.4982	−	110.506i	0.232210	−	0.462369i	0.979316	+	0.202337i	$0.0648535\pi$
$240$		0			0
$241$	−409.705	−	97.1020i	−1.70002	−	0.402913i	−0.737766	−	0.675057i	$-0.764119\pi$
$241$	−409.705	−	97.1020i	−1.70002	−	0.402913i	−0.962257	+	0.272144i	$0.912267\pi$
$242$		0			0
$243$	203.604	+	132.644i	0.837875	+	0.545861i
$244$		0			0
$245$	89.4567	−	377.448i	0.365130	−	1.54060i
$246$		0			0
$247$	57.3061	+	28.7802i	0.232008	+	0.116519i
$248$		0			0
$249$	77.9448	+	270.934i	0.313031	+	1.08809i
$250$		0			0
$251$	−87.4266	+	104.191i	−0.348313	+	0.415103i	−0.911548	−	0.411193i	$-0.865112\pi$
$251$	−87.4266	+	104.191i	−0.348313	+	0.415103i	0.563235	+	0.826297i	$0.309557\pi$
$252$		0			0
$253$	−67.9415	+	57.0096i	−0.268543	+	0.225335i
$254$		0			0
$255$	−67.5684	+	3.20609i	−0.264974	+	0.0125729i
$256$		0			0
$257$	33.1761	−	31.3000i	0.129090	−	0.121790i	−0.618990	−	0.785399i	$-0.712458\pi$
$257$	33.1761	−	31.3000i	0.129090	−	0.121790i	0.748079	+	0.663609i	$0.230976\pi$
$258$		0			0
$259$	−53.3457	−	71.6557i	−0.205968	−	0.276663i
$260$		0			0
$261$	−242.469	+	66.9385i	−0.929001	+	0.256470i
$262$		0			0
$263$	12.2130	+	24.3182i	0.0464374	+	0.0924645i	0.915655	−	0.401966i	$-0.131673\pi$
$263$	12.2130	+	24.3182i	0.0464374	+	0.0924645i	−0.869217	+	0.494430i	$0.835377\pi$
$264$		0			0
$265$	−268.885	−	31.4282i	−1.01466	−	0.118597i
$266$		0			0
$267$	−52.2843	+	278.929i	−0.195821	+	1.04468i
$268$		0			0
$269$	−125.773	−	72.6152i	−0.467558	−	0.269945i	0.247659	−	0.968847i	$-0.420339\pi$
$269$	−125.773	−	72.6152i	−0.467558	−	0.269945i	−0.715217	+	0.698902i	$0.753672\pi$
$270$		0			0
$271$	−217.713	−	377.090i	−0.803370	−	1.39148i	−0.917386	−	0.397998i	$-0.869705\pi$
$271$	−217.713	−	377.090i	−0.803370	−	1.39148i	0.114017	−	0.993479i	$-0.463628\pi$
$272$		0			0
$273$	−52.5933	+	139.798i	−0.192649	+	0.512082i
$274$		0			0
$275$	−889.919	+	383.874i	−3.23607	+	1.39590i
$276$		0			0
$277$	2.73450	−	46.9495i	0.00987183	−	0.169493i	−0.989769	−	0.142681i	$-0.954428\pi$
$277$	2.73450	−	46.9495i	0.00987183	−	0.169493i	0.999641	−	0.0268115i	$-0.00853538\pi$
$278$		0			0
$279$	261.865	+	138.651i	0.938584	+	0.496957i
$280$		0			0
$281$	176.050	+	75.9404i	0.626511	+	0.270250i	0.685573	−	0.728004i	$-0.259552\pi$
$281$	176.050	+	75.9404i	0.626511	+	0.270250i	−0.0590621	+	0.998254i	$0.518811\pi$
$282$		0			0
$283$	12.5946	−	2.98497i	0.0445037	−	0.0105476i	−0.208304	−	0.978064i	$-0.566794\pi$
$283$	12.5946	−	2.98497i	0.0445037	−	0.0105476i	0.252807	+	0.967517i	$0.418646\pi$
$284$		0			0
$285$	27.2362	−	87.5347i	0.0955655	−	0.307139i
$286$		0			0
$287$	−71.6630	+	196.892i	−0.249697	+	0.686036i
$288$		0			0
$289$	−265.889	+	96.7755i	−0.920030	+	0.334863i
$290$		0			0
$291$	−388.815	−	172.706i	−1.33613	−	0.593490i
$292$		0			0
$293$	−282.337	+	16.4443i	−0.963609	+	0.0561238i	−0.532729	−	0.846286i	$-0.678834\pi$
$293$	−282.337	+	16.4443i	−0.963609	+	0.0561238i	−0.430879	+	0.902410i	$0.641797\pi$
$294$		0			0
$295$	473.428	−	501.804i	1.60484	−	1.70103i
$296$		0			0
$297$	−441.400	+	37.1937i	−1.48620	+	0.125231i
$298$		0			0
$299$	99.6520	−	29.8338i	0.333284	−	0.0997787i
$300$		0			0
$301$	−65.1497	+	42.8496i	−0.216444	+	0.142357i
$302$		0			0
$303$	−18.4626	−	12.4298i	−0.0609327	−	0.0410224i
$304$		0			0
$305$	177.938	+	31.3754i	0.583405	+	0.102870i
$306$		0			0
$307$	−47.8807	−	271.545i	−0.155963	−	0.884512i	−0.957900	−	0.287103i	$-0.907308\pi$
$307$	−47.8807	−	271.545i	−0.155963	−	0.884512i	0.801937	−	0.597409i	$-0.203803\pi$
$308$		0			0
$309$	125.629	−	52.5945i	0.406566	−	0.170209i
$310$		0			0
$311$	−96.2193	−	28.8062i	−0.309387	−	0.0926243i	0.128346	−	0.991729i	$-0.459033\pi$
$311$	−96.2193	−	28.8062i	−0.309387	−	0.0926243i	−0.437733	+	0.899105i	$0.644218\pi$
$312$		0			0
$313$	232.509	−	27.1764i	0.742841	−	0.0868257i	0.263750	−	0.964591i	$-0.415041\pi$
$313$	232.509	−	27.1764i	0.742841	−	0.0868257i	0.479091	+	0.877765i	$0.340966\pi$
$314$		0			0
$315$	209.435	+	41.5963i	0.664874	+	0.132052i
$316$		0			0
$317$	186.925	−	284.206i	0.589669	−	0.896548i	−0.410212	−	0.911990i	$-0.634545\pi$
$317$	186.925	−	284.206i	0.589669	−	0.896548i	0.999881	+	0.0154422i	$0.00491559\pi$
$318$		0			0
$319$	273.816	−	367.798i	0.858356	−	1.15297i
$320$		0			0
$321$	−223.216	−	2.40271i	−0.695377	−	0.00748506i
$322$		0			0
$323$			8.19541i			0.0253728i
$324$		0			0
$325$	1136.71			3.49757
$326$		0			0
$327$	−147.262	−	87.1485i	−0.450343	−	0.266509i
$328$		0			0
$329$	134.437	+	100.085i	0.408623	+	0.304209i
$330$		0			0
$331$	91.5328	+	60.2020i	0.276534	+	0.181879i	0.680199	−	0.733028i	$-0.261893\pi$
$331$	91.5328	+	60.2020i	0.276534	+	0.181879i	−0.403665	+	0.914907i	$0.632264\pi$
$332$		0			0
$333$	−242.273	+	194.560i	−0.727548	+	0.584265i
$334$		0			0
$335$	−81.9355	−	701.003i	−0.244584	−	2.09255i
$336$		0			0
$337$	108.367	−	361.973i	0.321565	−	1.07410i	−0.632514	−	0.774549i	$-0.717977\pi$
$337$	108.367	−	361.973i	0.321565	−	1.07410i	0.954079	−	0.299554i	$-0.0968378\pi$
$338$		0			0
$339$	−247.155	+	324.633i	−0.729072	+	0.957620i
$340$		0			0
$341$	−531.930	+	93.7936i	−1.55991	+	0.275055i
$342$		0			0
$343$	41.0242	−	232.660i	0.119604	−	0.678309i
$344$		0			0
$345$	−65.3051	−	133.600i	−0.189290	−	0.387245i
$346$		0			0
$347$	118.277	+	179.831i	0.340855	+	0.518245i	0.964717	−	0.263290i	$-0.0848075\pi$
$347$	118.277	+	179.831i	0.340855	+	0.518245i	−0.623862	+	0.781535i	$0.714437\pi$
$348$		0			0
$349$	80.4521	+	268.729i	0.230522	+	0.769997i	0.992484	+	0.122375i	$0.0390511\pi$
$349$	80.4521	+	268.729i	0.230522	+	0.769997i	−0.761962	+	0.647622i	$0.775764\pi$
$350$		0			0
$351$	492.637	+	164.995i	1.40352	+	0.470070i
$352$		0			0
$353$	361.019	+	340.604i	1.02272	+	0.964883i	0.999393	−	0.0348451i	$-0.0110938\pi$
$353$	361.019	+	340.604i	1.02272	+	0.964883i	0.0233234	+	0.999728i	$0.492575\pi$
$354$		0			0
$355$	−37.8142	−	649.246i	−0.106519	−	1.82886i
$356$		0			0
$357$	−18.9823	+	2.01186i	−0.0531718	+	0.00563546i
$358$		0			0
$359$	7.97397	+	21.9083i	0.0222116	+	0.0610259i	0.950303	−	0.311327i	$-0.100773\pi$
$359$	7.97397	+	21.9083i	0.0222116	+	0.0610259i	−0.928091	+	0.372353i	$0.878551\pi$
$360$		0			0
$361$	328.792	+	119.671i	0.910782	+	0.331497i
$362$		0			0
$363$	326.566	−	301.522i	0.899632	−	0.830640i
$364$		0			0
$365$	97.6191	+	411.888i	0.267450	+	1.12846i
$366$		0			0
$367$	56.6167	−	131.252i	0.154269	−	0.357636i	−0.823501	−	0.567314i	$-0.807982\pi$
$367$	56.6167	−	131.252i	0.154269	−	0.357636i	0.977770	+	0.209679i	$0.0672417\pi$
$368$		0			0
$369$	693.524	+	224.003i	1.87947	+	0.607055i
$370$		0			0
$371$	−76.2644	−	4.44189i	−0.205564	−	0.0119728i
$372$		0			0
$373$	−244.262	−	566.264i	−0.654859	−	1.51813i	−0.844090	−	0.536201i	$-0.819859\pi$
$373$	−244.262	−	566.264i	−0.654859	−	1.51813i	0.189231	−	0.981933i	$-0.439400\pi$
$374$		0			0
$375$	−152.818	−	924.771i	−0.407514	−	2.46606i
$376$		0			0
$377$	−465.740	+	268.895i	−1.23538	+	0.713249i
$378$		0			0
$379$	−338.338	+	586.019i	−0.892713	+	1.54622i	−0.0561038	+	0.998425i	$0.517868\pi$
$379$	−338.338	+	586.019i	−0.892713	+	1.54622i	−0.836609	+	0.547800i	$0.815466\pi$
$380$		0			0
$381$	−261.731	+	305.187i	−0.686959	+	0.801016i
$382$		0			0
$383$	1.60995	−	13.7740i	0.00420352	−	0.0359634i	−0.990974	−	0.134056i	$-0.957200\pi$
$383$	1.60995	−	13.7740i	0.00420352	−	0.0359634i	0.995177	+	0.0980922i	$0.0312740\pi$
$384$		0			0
$385$	−347.834	+	174.689i	−0.903465	+	0.453737i
$386$		0			0
$387$	157.247	+	220.996i	0.406323	+	0.571050i
$388$		0			0
$389$	−417.802	+	311.042i	−1.07404	+	0.799593i	−0.980598	−	0.196031i	$-0.937195\pi$
$389$	−417.802	+	311.042i	−1.07404	+	0.799593i	−0.0934427	+	0.995625i	$0.529787\pi$
$390$		0			0
$391$	9.12286	+	9.66967i	0.0233321	+	0.0247306i
$392$		0			0
$393$	527.082	−	338.597i	1.34118	−	0.861569i
$394$		0			0
$395$	−670.171	−	798.679i	−1.69664	−	2.02197i
$396$		0			0
$397$	−568.768	−	477.253i	−1.43266	−	1.20215i	−0.944117	−	0.329611i	$-0.893082\pi$
$397$	−568.768	−	477.253i	−1.43266	−	1.20215i	−0.488548	−	0.872537i	$-0.662473\pi$
$398$		0			0
$399$	6.23654	−	25.1066i	0.0156304	−	0.0629238i
$400$		0			0
$401$	87.1398	−	173.510i	0.217306	−	0.432692i	−0.758396	−	0.651794i	$-0.774016\pi$
$401$	87.1398	−	173.510i	0.217306	−	0.432692i	0.975702	+	0.219102i	$0.0703128\pi$
$402$		0			0
$403$	616.425	+	146.095i	1.52959	+	0.362520i
$404$		0			0
$405$	117.894	−	733.290i	0.291096	−	1.81059i
$406$		0			0
$407$	130.626	−	551.152i	0.320947	−	1.35418i
$408$		0			0
$409$	−611.565	−	307.140i	−1.49527	−	0.750953i	−0.501793	−	0.864988i	$-0.667326\pi$
$409$	−611.565	−	307.140i	−1.49527	−	0.750953i	−0.993477	+	0.114035i	$0.963622\pi$
$410$		0			0
$411$	−358.229	+	371.605i	−0.871605	+	0.904149i
$412$		0			0
$413$	125.138	−	149.133i	0.302996	−	0.361097i
$414$		0			0
$415$	660.079	−	553.872i	1.59055	−	1.33463i
$416$		0			0
$417$	44.0158	−	85.3399i	0.105554	−	0.204652i
$418$		0			0
$419$	−28.9193	+	27.2839i	−0.0690198	+	0.0651168i	−0.719979	−	0.693996i	$-0.755848\pi$
$419$	−28.9193	+	27.2839i	−0.0690198	+	0.0651168i	0.650959	+	0.759113i	$0.274367\pi$
$420$		0			0
$421$	254.401	+	341.720i	0.604278	+	0.811686i	0.994015	−	0.109240i	$-0.0348417\pi$
$421$	254.401	+	341.720i	0.604278	+	0.811686i	−0.389738	+	0.920926i	$0.627434\pi$
$422$		0			0
$423$	330.756	−	480.054i	0.781929	−	1.13488i
$424$		0			0
$425$	65.1975	+	129.819i	0.153406	+	0.305456i
$426$		0			0
$427$	50.6425	+	5.91926i	0.118601	+	0.0138624i
$428$		0			0
$429$	−893.375	+	314.314i	−2.08246	+	0.732667i
$430$		0			0
$431$	452.147	+	261.047i	1.04907	+	0.605678i	0.922388	−	0.386266i	$-0.126235\pi$
$431$	452.147	+	261.047i	1.04907	+	0.605678i	0.126678	+	0.991944i	$0.459569\pi$
$432$		0			0
$433$	−114.805	−	198.848i	−0.265138	−	0.459232i	0.702462	−	0.711721i	$-0.252084\pi$
$433$	−114.805	−	198.848i	−0.265138	−	0.459232i	−0.967600	+	0.252489i	$0.918751\pi$
$434$		0			0
$435$	487.812	+	594.225i	1.12141	+	1.36603i
$436$		0			0
$437$	−16.5430	+	7.13594i	−0.0378558	+	0.0163294i
$438$		0			0
$439$	−12.7902	+	219.600i	−0.0291349	+	0.500227i	0.951902	+	0.306404i	$0.0991259\pi$
$439$	−12.7902	+	219.600i	−0.0291349	+	0.500227i	−0.981036	+	0.193823i	$0.937911\pi$
$440$		0			0
$441$	−377.131	−	52.3319i	−0.855173	−	0.118666i
$442$		0			0
$443$	−209.963	−	90.5691i	−0.473957	−	0.204445i	0.145683	−	0.989331i	$-0.453462\pi$
$443$	−209.963	−	90.5691i	−0.473957	−	0.204445i	−0.619640	+	0.784886i	$0.712721\pi$
$444$		0			0
$445$	843.987	−	200.029i	1.89660	−	0.449503i
$446$		0			0
$447$	−288.581	+	65.1225i	−0.645595	+	0.145688i
$448$		0			0
$449$	300.809	−	826.465i	0.669952	−	1.84068i	0.145245	−	0.989396i	$-0.453603\pi$
$449$	300.809	−	826.465i	0.669952	−	1.84068i	0.524707	−	0.851283i	$-0.324175\pi$
$450$		0			0
$451$	−1248.41	+	454.385i	−2.76810	+	1.00751i
$452$		0			0
$453$	−2.73527	+	1.99094i	−0.00603812	+	0.00439500i
$454$		0			0
$455$	455.745	−	26.5441i	1.00164	−	0.0583387i
$456$		0			0
$457$	−445.066	+	471.742i	−0.973886	+	1.03226i	0.0255828	+	0.999673i	$0.491856\pi$
$457$	−445.066	+	471.742i	−0.973886	+	1.03226i	−0.999469	+	0.0325863i	$0.989626\pi$
$458$		0			0
$459$	9.41248	+	65.7254i	0.0205065	+	0.143193i
$460$		0			0
$461$	−19.1993	+	5.74789i	−0.0416471	+	0.0124683i	−0.307559	−	0.951529i	$-0.599512\pi$
$461$	−19.1993	+	5.74789i	−0.0416471	+	0.0124683i	0.265912	+	0.963997i	$0.414327\pi$
$462$		0			0
$463$	−194.327	+	127.811i	−0.419713	+	0.276049i	−0.741749	−	0.670678i	$-0.766003\pi$
$463$	−194.327	+	127.811i	−0.419713	+	0.276049i	0.322036	+	0.946727i	$0.395633\pi$
$464$		0			0
$465$	62.3860	−	903.481i	0.134163	−	1.94297i
$466$		0			0
$467$	−129.981	−	22.9192i	−0.278333	−	0.0490776i	0.0327392	−	0.999464i	$-0.489577\pi$
$467$	−129.981	−	22.9192i	−0.278333	−	0.0490776i	−0.311072	+	0.950386i	$0.600688\pi$
$468$		0			0
$469$	−34.5844	−	196.138i	−0.0737407	−	0.418205i
$470$		0			0
$471$	−53.4357	+	418.093i	−0.113452	+	0.887671i
$472$		0			0
$473$	−473.655	−	141.803i	−1.00138	−	0.299795i
$474$		0			0
$475$	−195.545	+	22.8559i	−0.411674	+	0.0481178i
$476$		0			0
$477$	−5.71977	+	265.658i	−0.0119911	+	0.556935i
$478$		0			0
$479$	204.550	−	311.003i	0.427036	−	0.649277i	−0.556320	−	0.830968i	$-0.687787\pi$
$479$	204.550	−	311.003i	0.427036	−	0.649277i	0.983356	+	0.181692i	$0.0581573\pi$
$480$		0			0
$481$	−396.710	+	532.874i	−0.824760	+	1.10785i
$482$		0			0
$483$	−20.5894	−	36.5653i	−0.0426282	−	0.0757046i
$484$		0			0
$485$			1300.34i			2.68111i
$486$		0			0
$487$	545.569			1.12027			0.560133	−	0.828403i	$-0.310750\pi$
$487$	545.569			1.12027			0.560133	+	0.828403i	$0.310750\pi$
$488$		0			0
$489$	−552.663	+	311.197i	−1.13019	+	0.636395i
$490$		0			0
$491$	−154.242	−	114.829i	−0.314139	−	0.233868i	0.428528	−	0.903528i	$-0.359032\pi$
$491$	−154.242	−	114.829i	−0.314139	−	0.233868i	−0.742667	+	0.669661i	$0.766440\pi$
$492$		0			0
$493$	−57.4225	−	37.7673i	−0.116476	−	0.0766072i
$494$		0			0
$495$	651.544	+	1186.79i	1.31625	+	2.39756i
$496$		0			0
$497$	−21.3056	−	182.281i	−0.0428684	−	0.366763i
$498$		0			0
$499$	100.380	−	335.293i	0.201163	−	0.671930i	−0.796565	−	0.604553i	$-0.793352\pi$
$499$	100.380	−	335.293i	0.201163	−	0.671930i	0.997728	−	0.0673768i	$-0.0214630\pi$
$500$		0			0
$501$	693.787	+	88.6716i	1.38480	+	0.176989i
$502$		0			0
$503$	−28.7858	+	5.07571i	−0.0572281	+	0.0100909i	−0.202189	−	0.979347i	$-0.564806\pi$
$503$	−28.7858	+	5.07571i	−0.0572281	+	0.0100909i	0.144961	+	0.989437i	$0.453694\pi$
$504$		0			0
$505$	−11.8126	+	66.9925i	−0.0233913	+	0.132658i
$506$		0			0
$507$	602.324	+	41.5909i	1.18802	+	0.0820333i
$508$		0			0
$509$	−382.853	−	582.099i	−0.752166	−	1.14361i	−0.985244	−	0.171155i	$-0.945250\pi$
$509$	−382.853	−	582.099i	−0.752166	−	1.14361i	0.233078	−	0.972458i	$-0.425120\pi$
$510$		0			0
$511$	34.2589	+	114.433i	0.0670428	+	0.223939i
$512$		0			0
$513$	−88.0645	−	18.4781i	−0.171666	−	0.0360196i
$514$		0			0
$515$	−302.780	−	285.658i	−0.587921	−	0.554675i
$516$		0			0
$517$	61.7899	+	1060.89i	0.119516	+	2.05202i
$518$		0			0
$519$	−40.0088	−	54.9665i	−0.0770882	−	0.105908i
$520$		0			0
$521$	263.282	+	723.361i	0.505340	+	1.38841i	0.885996	+	0.463693i	$0.153476\pi$
$521$	263.282	+	723.361i	0.505340	+	1.38841i	−0.380656	+	0.924717i	$0.624302\pi$
$522$		0			0
$523$	−390.531	−	142.142i	−0.746713	−	0.271781i	−0.0594913	−	0.998229i	$-0.518948\pi$
$523$	−390.531	−	142.142i	−0.746713	−	0.271781i	−0.687222	+	0.726447i	$0.741170\pi$
$524$		0			0
$525$	−100.943	−	447.314i	−0.192272	−	0.852026i
$526$		0			0
$527$	18.6709	+	78.7788i	0.0354287	+	0.149485i
$528$		0			0
$529$	197.951	−	458.902i	0.374198	−	0.867489i
$530$		0			0
$531$	−534.330	−	415.966i	−1.00627	−	0.783363i
$532$		0			0
$533$	1555.54	+	90.5999i	2.91846	+	0.169981i
$534$		0			0
$535$	270.237	+	626.479i	0.505115	+	1.17099i
$536$		0			0
$537$	−674.839	+	553.989i	−1.25668	+	1.03164i
$538$		0			0
$539$	601.073	−	347.029i	1.11516	−	0.643839i
$540$		0			0
$541$	−386.142	+	668.818i	−0.713756	+	1.23626i	0.249681	+	0.968328i	$0.419674\pi$
$541$	−386.142	+	668.818i	−0.713756	+	1.23626i	−0.963437	+	0.267934i	$0.913659\pi$
$542$		0			0
$543$	226.786	+	644.595i	0.417654	+	1.18710i
$544$		0			0
$545$	−60.7169	+	519.466i	−0.111407	+	0.953149i
$546$		0			0
$547$	−828.761	+	416.220i	−1.51510	+	0.760913i	−0.995613	−	0.0935635i	$-0.970174\pi$
$547$	−828.761	+	416.220i	−1.51510	+	0.760913i	−0.519490	+	0.854477i	$0.673878\pi$
$548$		0			0
$549$	14.1206	−	176.786i	0.0257206	−	0.322014i
$550$		0			0
$551$	74.7132	−	55.6219i	0.135596	−	0.100947i
$552$		0			0
$553$	−201.901	−	214.003i	−0.365101	−	0.386985i
$554$		0			0
$555$	844.048	+	435.336i	1.52081	+	0.784389i
$556$		0			0
$557$	49.5814	+	59.0889i	0.0890152	+	0.106084i	0.808713	−	0.588203i	$-0.200164\pi$
$557$	49.5814	+	59.0889i	0.0890152	+	0.106084i	−0.719698	+	0.694287i	$0.755720\pi$
$558$		0			0
$559$	444.221	+	372.746i	0.794671	+	0.666808i
$560$		0			0
$561$	−87.1372	−	84.0007i	−0.155325	−	0.149734i
$562$		0			0
$563$	278.692	−	554.921i	0.495012	−	0.985650i	−0.497949	−	0.867206i	$-0.665913\pi$
$563$	278.692	−	554.921i	0.495012	−	0.985650i	0.992961	−	0.118443i	$-0.0377904\pi$
$564$		0			0
$565$	1213.43	+	287.588i	2.14767	+	0.509006i
$566$		0			0
$567$	21.1806	−	208.512i	0.0373555	−	0.367747i
$568$		0			0
$569$	−193.097	+	814.738i	−0.339361	+	1.43188i	0.489294	+	0.872119i	$0.337254\pi$
$569$	−193.097	+	814.738i	−0.339361	+	1.43188i	−0.828656	+	0.559759i	$0.810894\pi$
$570$		0			0
$571$	50.7374	+	25.4813i	0.0888570	+	0.0446257i	0.492673	−	0.870215i	$-0.336020\pi$
$571$	50.7374	+	25.4813i	0.0888570	+	0.0446257i	−0.403816	+	0.914840i	$0.632316\pi$
$572$		0			0
$573$	421.199	+	104.627i	0.735077	+	0.182595i
$574$		0			0
$575$	−205.279	+	244.642i	−0.357007	+	0.425464i
$576$		0			0
$577$	−613.531	+	514.813i	−1.06331	+	0.892224i	−0.994430	−	0.105401i	$-0.966387\pi$
$577$	−613.531	+	514.813i	−1.06331	+	0.892224i	−0.0688815	+	0.997625i	$0.521943\pi$
$578$		0			0
$579$	−213.885	−	332.947i	−0.369404	−	0.575038i
$580$		0			0
$581$	176.865	−	166.864i	0.304416	−	0.287201i
$582$		0			0
$583$	−289.252	−	388.532i	−0.496143	−	0.666436i
$584$		0			0
$585$	−150.352	−	1580.77i	−0.257012	−	2.70217i
$586$		0			0
$587$	172.065	+	342.609i	0.293126	+	0.583661i	0.991201	−	0.132363i	$-0.0422564\pi$
$587$	172.065	+	342.609i	0.293126	+	0.583661i	−0.698076	+	0.716024i	$0.745960\pi$
$588$		0			0
$589$	−108.979	−	12.7379i	−0.185024	−	0.0216263i
$590$		0			0
$591$	4.41831	+	3.78918i	0.00747598	+	0.00641147i
$592$		0			0
$593$	29.0302	+	16.7606i	0.0489549	+	0.0282641i	0.524278	−	0.851547i	$-0.324335\pi$
$593$	29.0302	+	16.7606i	0.0489549	+	0.0282641i	−0.475323	+	0.879811i	$0.657669\pi$
$594$		0			0
$595$	29.1713	+	50.5262i	0.0490275	+	0.0849180i
$596$		0			0
$597$	−729.714	+	120.585i	−1.22230	+	0.201984i
$598$		0			0
$599$	−824.965	+	355.855i	−1.37724	+	0.594082i	−0.950622	−	0.310351i	$-0.899553\pi$
$599$	−824.965	+	355.855i	−1.37724	+	0.594082i	−0.426615	+	0.904433i	$0.640294\pi$
$600$		0			0
$601$	8.23677	−	141.420i	0.0137051	−	0.235308i	−0.984498	−	0.175393i	$-0.943880\pi$
$601$	8.23677	−	141.420i	0.0137051	−	0.235308i	0.998204	−	0.0599143i	$-0.0190827\pi$
$602$		0			0
$603$	−677.360	+	145.212i	−1.12332	+	0.240816i
$604$		0			0
$605$	−1247.40	−	538.077i	−2.06182	−	0.889384i
$606$		0			0
$607$	816.212	−	193.446i	1.34467	−	0.318692i	0.505622	−	0.862755i	$-0.331263\pi$
$607$	816.212	−	193.446i	1.34467	−	0.318692i	0.839044	+	0.544063i	$0.183115\pi$
$608$		0			0
$609$	147.173	+	159.397i	0.241664	+	0.261736i
$610$		0			0
$611$	426.287	−	1171.21i	0.697688	−	1.91688i
$612$		0			0
$613$	−42.2369	+	15.3730i	−0.0689019	+	0.0250783i	−0.376241	−	0.926522i	$-0.622784\pi$
$613$	−42.2369	+	15.3730i	−0.0689019	+	0.0250783i	0.307339	+	0.951600i	$0.400561\pi$
$614$		0			0
$615$	−234.770	−	2215.11i	−0.381740	−	3.60181i
$616$		0			0
$617$	703.586	−	40.9792i	1.14033	−	0.0664169i	0.522438	−	0.852677i	$-0.325022\pi$
$617$	703.586	−	40.9792i	1.14033	−	0.0664169i	0.617896	+	0.786260i	$0.287985\pi$
$618$		0			0
$619$	306.113	−	324.461i	0.494529	−	0.524170i	−0.431252	−	0.902232i	$-0.641928\pi$
$619$	306.113	−	324.461i	0.494529	−	0.524170i	0.925780	+	0.378062i	$0.123409\pi$
$620$		0			0
$621$	−124.475	+	76.2284i	−0.200443	+	0.122751i
$622$		0			0
$623$	234.481	−	70.1989i	0.376374	−	0.112679i
$624$		0			0
$625$	−1159.61	+	762.687i	−1.85538	+	1.22030i
$626$		0			0
$627$	147.365	−	72.0338i	0.235032	−	0.114886i
$628$		0			0
$629$	−83.6110	−	14.7429i	−0.132927	−	0.0234386i
$630$		0			0
$631$	−49.5577	−	281.055i	−0.0785383	−	0.445413i	−0.998565	−	0.0535566i	$-0.982944\pi$
$631$	−49.5577	−	281.055i	−0.0785383	−	0.445413i	0.920027	−	0.391856i	$-0.128167\pi$
$632$		0			0
$633$	803.532	+	611.759i	1.26940	+	0.966444i
$634$		0			0
$635$	1177.20	+	352.430i	1.85386	+	0.555008i
$636$		0			0
$637$	−808.526	+	94.5032i	−1.26927	+	0.148357i
$638$		0			0
$639$	−630.886	+	97.2895i	−0.987302	+	0.152253i
$640$		0			0
$641$	−557.286	+	847.312i	−0.869401	+	1.32186i	0.0763880	+	0.997078i	$0.475661\pi$
$641$	−557.286	+	847.312i	−0.869401	+	1.32186i	−0.945789	+	0.324782i	$0.894709\pi$
$642$		0			0
$643$	−20.5039	+	27.5415i	−0.0318879	+	0.0428329i	−0.817781	−	0.575529i	$-0.804796\pi$
$643$	−20.5039	+	27.5415i	−0.0318879	+	0.0428329i	0.785893	+	0.618362i	$0.212203\pi$
$644$		0			0
$645$	422.199	−	713.424i	0.654572	−	1.10608i
$646$		0			0
$647$			386.838i			0.597895i	0.954270	+	0.298948i	$0.0966356\pi$
$647$			386.838i			0.597895i	−0.954270	+	0.298948i	$0.903364\pi$
$648$		0			0
$649$	1234.38			1.90197
$650$		0			0
$651$	2.75072	−	255.547i	0.00422537	−	0.392545i
$652$		0			0
$653$	285.718	+	212.709i	0.437546	+	0.325741i	0.793292	−	0.608842i	$-0.208366\pi$
$653$	285.718	+	212.709i	0.437546	+	0.325741i	−0.355746	+	0.934583i	$0.615773\pi$
$654$		0			0
$655$	−1599.74	−	1052.17i	−2.44236	−	1.60636i
$656$		0			0
$657$	393.397	−	133.667i	0.598778	−	0.203451i
$658$		0			0
$659$	132.851	+	1136.62i	0.201596	+	1.72476i	0.593569	+	0.804783i	$0.297719\pi$
$659$	132.851	+	1136.62i	0.201596	+	1.72476i	−0.391973	+	0.919977i	$0.628207\pi$
$660$		0			0
$661$	−17.6345	+	58.9034i	−0.0266785	+	0.0891125i	−0.970292	−	0.241937i	$-0.922217\pi$
$661$	−17.6345	+	58.9034i	−0.0266785	+	0.0891125i	0.943614	+	0.331049i	$0.107403\pi$
$662$		0			0
$663$	54.8190	+	130.942i	0.0826832	+	0.197500i
$664$		0			0
$665$	−77.8668	+	13.7300i	−0.117093	+	0.0206466i
$666$		0			0
$667$	26.2367	−	148.796i	0.0393354	−	0.223082i
$668$		0			0
$669$	−203.224	+	301.859i	−0.303773	+	0.451209i
$670$		0			0
$671$	177.650	+	270.104i	0.264754	+	0.402539i
$672$		0			0
$673$	−97.4590	−	325.536i	−0.144813	−	0.483708i	0.854551	−	0.519367i	$-0.173832\pi$
$673$	−97.4590	−	325.536i	−0.144813	−	0.483708i	−0.999364	+	0.0356587i	$0.988647\pi$
$674$		0			0
$675$	−1541.98	+	407.885i	−2.28441	+	0.604274i
$676$		0			0
$677$	790.504	+	745.802i	1.16766	+	1.10163i	0.993135	+	0.116975i	$0.0373197\pi$
$677$	790.504	+	745.802i	1.16766	+	1.10163i	0.174523	+	0.984653i	$0.444162\pi$
$678$		0			0
$679$	21.3359	+	366.323i	0.0314225	+	0.539503i
$680$		0			0
$681$	178.969	−	402.917i	0.262804	−	0.591655i
$682$		0			0
$683$	215.820	+	592.962i	0.315989	+	0.868172i	0.991416	+	0.130745i	$0.0417371\pi$
$683$	215.820	+	592.962i	0.315989	+	0.868172i	−0.675427	+	0.737427i	$0.736041\pi$
$684$		0			0
$685$	1482.45	+	539.567i	2.16416	+	0.787689i
$686$		0			0
$687$	−257.458	−	80.1073i	−0.374757	−	0.116604i
$688$		0			0
$689$	131.015	+	552.794i	0.190152	+	0.802313i
$690$		0			0
$691$	13.0336	−	30.2153i	0.0188619	−	0.0437269i	−0.908525	−	0.417831i	$-0.862790\pi$
$691$	13.0336	−	30.2153i	0.0188619	−	0.0437269i	0.927387	+	0.374104i	$0.122050\pi$
$692$		0			0
$693$	203.022	+	323.646i	0.292961	+	0.467021i
$694$		0			0
$695$	−292.987	−	17.0645i	−0.421564	−	0.0245533i
$696$		0			0
$697$	78.8729	+	182.848i	0.113161	+	0.262336i
$698$		0			0
$699$	−978.416	−	368.088i	−1.39974	−	0.526592i
$700$		0			0
$701$	487.235	−	281.305i	0.695057	−	0.401291i	−0.110447	−	0.993882i	$-0.535228\pi$
$701$	487.235	−	281.305i	0.695057	−	0.401291i	0.805504	+	0.592591i	$0.201895\pi$
$702$		0			0
$703$	57.5303	−	99.6454i	0.0818354	−	0.141743i
$704$		0			0
$705$	−1751.28	−	328.273i	−2.48409	−	0.465635i
$706$		0			0
$707$	−2.22856	+	19.0665i	−0.00315213	+	0.0269682i
$708$		0			0
$709$	169.594	−	85.1731i	0.239201	−	0.120131i	−0.325161	−	0.945659i	$-0.605418\pi$
$709$	169.594	−	85.1731i	0.239201	−	0.120131i	0.564362	+	0.825527i	$0.309122\pi$
$710$		0			0
$711$	−718.132	+	729.075i	−1.01003	+	1.02542i
$712$		0			0
$713$	−142.763	+	106.283i	−0.200228	+	0.149065i
$714$		0			0
$715$	1986.39	+	2105.45i	2.77816	+	2.94468i
$716$		0			0
$717$	17.5830	+	370.561i	0.0245230	+	0.516822i
$718$		0			0
$719$	−63.7972	−	76.0306i	−0.0887305	−	0.105745i	0.719852	−	0.694127i	$-0.244209\pi$
$719$	−63.7972	−	76.0306i	−0.0887305	−	0.105745i	−0.808583	+	0.588382i	$0.799765\pi$
$720$		0			0
$721$	−89.9842	−	75.5057i	−0.124805	−	0.104724i
$722$		0			0
$723$	1213.93	−	349.234i	1.67902	−	0.483035i
$724$		0			0
$725$	740.997	−	1475.45i	1.02206	−	2.03510i
$726$		0			0
$727$	370.614	+	87.8370i	0.509785	+	0.120821i	0.477455	−	0.878656i	$-0.341559\pi$
$727$	370.614	+	87.8370i	0.509785	+	0.120821i	0.0323295	+	0.999477i	$0.489707\pi$
$728$		0			0
$729$	−727.480	−	47.0474i	−0.997915	−	0.0645369i
$730$		0			0
$731$	−17.0908	+	72.1119i	−0.0233801	+	0.0986483i
$732$		0			0
$733$	−1036.27	−	520.435i	−1.41374	−	0.710007i	−0.432291	−	0.901734i	$-0.642295\pi$
$733$	−1036.27	−	520.435i	−1.41374	−	0.710007i	−0.981448	+	0.191727i	$0.938591\pi$
$734$		0			0
$735$	321.737	+	1118.35i	0.437738	+	1.52157i
$736$		0			0
$737$	811.721	−	967.371i	1.10138	−	1.31258i
$738$		0			0
$739$	−217.172	+	182.229i	−0.293873	+	0.246589i	−0.777789	−	0.628526i	$-0.783659\pi$
$739$	−217.172	+	182.229i	−0.293873	+	0.246589i	0.483916	+	0.875115i	$0.339214\pi$
$740$		0			0
$741$	−192.165	+	9.11815i	−0.259332	+	0.0123052i
$742$		0			0
$743$	614.867	−	580.097i	0.827546	−	0.780750i	−0.150616	−	0.988592i	$-0.548126\pi$
$743$	614.867	−	580.097i	0.827546	−	0.780750i	0.978162	+	0.207843i	$0.0666442\pi$
$744$		0			0
$745$	539.951	+	725.280i	0.724766	+	0.973530i
$746$		0			0
$747$	−602.554	−	593.510i	−0.806632	−	0.794525i
$748$		0			0
$749$	86.4086	+	172.054i	0.115365	+	0.229711i
$750$		0			0
$751$	−632.089	−	73.8806i	−0.841663	−	0.0983763i	−0.315674	−	0.948868i	$-0.602231\pi$
$751$	−632.089	−	73.8806i	−0.841663	−	0.0983763i	−0.525989	+	0.850491i	$0.676305\pi$
$752$		0			0
$753$	75.1755	−	401.050i	0.0998347	−	0.532603i
$754$		0			0
$755$	8.95488	+	5.17010i	0.0118608	+	0.00684781i
$756$		0			0
$757$	−548.823	−	950.590i	−0.724998	−	1.25573i	−0.958975	−	0.283491i	$-0.908507\pi$
$757$	−548.823	−	950.590i	−0.724998	−	1.25573i	0.233977	−	0.972242i	$-0.424826\pi$
$758$		0			0
$759$	93.6885	−	249.034i	0.123437	−	0.328108i
$760$		0			0
$761$	−687.361	+	296.498i	−0.903233	+	0.389617i	−0.796477	−	0.604668i	$-0.793306\pi$
$761$	−687.361	+	296.498i	−0.903233	+	0.389617i	−0.106756	+	0.994285i	$0.534046\pi$
$762$		0			0
$763$	−8.58140	+	147.337i	−0.0112469	+	0.193102i
$764$		0			0
$765$	171.909	−	107.838i	0.224718	−	0.140965i
$766$		0			0
$767$	−1329.35	−	573.424i	−1.73318	−	0.747619i
$768$		0			0
$769$	−121.445	+	28.7829i	−0.157926	+	0.0374291i	−0.308818	−	0.951121i	$-0.599933\pi$
$769$	−121.445	+	28.7829i	−0.157926	+	0.0374291i	0.150892	+	0.988550i	$0.451785\pi$
$770$		0			0
$771$	−40.6526	+	130.654i	−0.0527271	+	0.169460i
$772$		0			0
$773$	285.093	−	783.286i	0.368813	−	1.01331i	−0.607000	−	0.794702i	$-0.707627\pi$
$773$	285.093	−	783.286i	0.368813	−	1.01331i	0.975814	−	0.218604i	$-0.0701504\pi$
$774$		0			0
$775$	−1827.62	+	665.198i	−2.35821	+	0.858320i
$776$		0			0
$777$	244.923	+	108.791i	0.315216	+	0.140014i
$778$		0			0
$779$	−269.417	+	15.6917i	−0.345849	+	0.0201434i
$780$		0			0
$781$	798.535	−	846.398i	1.02245	−	1.08374i
$782$		0			0
$783$	535.302	−	531.884i	0.683655	−	0.679290i
$784$		0			0
$785$	1234.14	−	369.476i	1.57215	−	0.470670i
$786$		0			0
$787$	−181.521	+	119.388i	−0.230649	+	0.151700i	−0.659573	−	0.751640i	$-0.729263\pi$
$787$	−181.521	+	119.388i	−0.230649	+	0.151700i	0.428924	+	0.903340i	$0.358893\pi$
$788$		0			0
$789$	−67.7209	−	45.5924i	−0.0858313	−	0.0577851i
$790$		0			0
$791$	346.559	+	61.1077i	0.438128	+	0.0772537i
$792$		0			0
$793$	−65.8423	−	373.410i	−0.0830294	−	0.470883i
$794$		0			0
$795$	749.146	−	313.630i	0.942322	−	0.394503i
$796$		0			0
$797$	−244.668	−	73.2487i	−0.306986	−	0.0919055i	0.129605	−	0.991566i	$-0.458629\pi$
$797$	−244.668	−	73.2487i	−0.306986	−	0.0919055i	−0.436591	+	0.899660i	$0.643814\pi$
$798$		0			0
$799$	158.210	−	18.4921i	0.198010	−	0.0231440i
$800$		0			0
$801$	−273.894	−	806.099i	−0.341940	−	1.00637i
$802$		0			0
$803$	−416.191	+	632.788i	−0.518296	+	0.788030i
$804$		0			0
$805$	−76.5903	+	102.879i	−0.0951433	+	0.127800i
$806$		0			0
$807$	435.666	+	4.68953i	0.539859	+	0.00581106i
$808$		0			0
$809$		−	135.694i		−	0.167730i	−0.996477	−	0.0838650i	$-0.973274\pi$
$809$		−	135.694i		−	0.167730i	0.996477	−	0.0838650i	$-0.0267265\pi$
$810$		0			0
$811$	−546.446			−0.673793			−0.336897	−	0.941542i	$-0.609377\pi$
$811$	−546.446			−0.673793			−0.336897	+	0.941542i	$0.609377\pi$
$812$		0			0
$813$	1124.18	+	665.278i	1.38275	+	0.818300i
$814$		0			0
$815$	1554.95	+	1157.62i	1.90791	+	1.42039i
$816$		0			0
$817$	−83.9129	−	55.1904i	−0.102709	−	0.0675525i
$818$		0			0
$819$	−68.2935	−	442.857i	−0.0833864	−	0.540730i
$820$		0			0
$821$	−94.6288	−	809.601i	−0.115260	−	0.986116i	−0.919846	−	0.392279i	$-0.871687\pi$
$821$	−94.6288	−	809.601i	−0.115260	−	0.986116i	0.804586	−	0.593837i	$-0.202387\pi$
$822$		0			0
$823$	−297.481	+	993.656i	−0.361459	+	1.20736i	0.563122	+	0.826374i	$0.309600\pi$
$823$	−297.481	+	993.656i	−0.361459	+	1.20736i	−0.924581	+	0.380985i	$0.875585\pi$
$824$		0			0
$825$	1761.27	−	2313.39i	2.13487	−	2.80411i
$826$		0			0
$827$	−1044.14	+	184.110i	−1.26256	+	0.222624i	−0.764561	−	0.644551i	$-0.777044\pi$
$827$	−1044.14	+	184.110i	−1.26256	+	0.222624i	−0.498003	+	0.867175i	$0.665933\pi$
$828$		0			0
$829$	−34.9250	+	198.070i	−0.0421291	+	0.238926i	−0.998600	−	0.0529029i	$-0.983153\pi$
$829$	−34.9250	+	198.070i	−0.0421291	+	0.238926i	0.956471	+	0.291829i	$0.0942637\pi$
$830$		0			0
$831$	61.9591	+	126.754i	0.0745597	+	0.152532i
$832$		0			0
$833$	−57.1669	−	86.9180i	−0.0686277	−	0.104343i
$834$		0			0
$835$	−613.112	−	2047.94i	−0.734266	−	2.45262i
$836$		0			0
$837$	−888.621	+	23.0086i	−1.06167	+	0.0274894i
$838$		0			0
$839$	−678.224	−	639.871i	−0.808371	−	0.762659i	0.166354	−	0.986066i	$-0.446801\pi$
$839$	−678.224	−	639.871i	−0.808371	−	0.762659i	−0.974725	+	0.223407i	$0.928282\pi$
$840$		0			0
$841$	−3.48072	−	59.7617i	−0.00413879	−	0.0710603i
$842$		0			0
$843$	−571.986	+	60.6225i	−0.678513	+	0.0719128i
$844$		0			0
$845$	−631.140	−	1734.04i	−0.746911	−	2.05212i
$846$		0			0
$847$	−360.239	−	131.116i	−0.425312	−	0.154801i
$848$		0			0
$849$	−28.5294	+	26.3415i	−0.0336035	+	0.0310265i
$850$		0			0
$851$	−43.0427	−	181.611i	−0.0505789	−	0.213409i
$852$		0			0
$853$	−390.363	+	904.963i	−0.457635	+	1.06092i	0.520672	+	0.853757i	$0.325682\pi$
$853$	−390.363	+	904.963i	−0.457635	+	1.06092i	−0.978307	+	0.207161i	$0.933578\pi$
$854$		0			0
$855$	57.6493	+	268.912i	0.0674261	+	0.314517i
$856$		0			0
$857$	−671.252	−	39.0960i	−0.783257	−	0.0456195i	−0.338145	−	0.941094i	$-0.609799\pi$
$857$	−671.252	−	39.0960i	−0.783257	−	0.0456195i	−0.445113	+	0.895475i	$0.646836\pi$
$858$		0			0
$859$	−273.687	−	634.477i	−0.318611	−	0.738623i	−0.999978	−	0.00668074i	$-0.997873\pi$
$859$	−273.687	−	634.477i	−0.318611	−	0.738623i	0.681367	−	0.731942i	$-0.261386\pi$
$860$		0			0
$861$	−102.483	−	620.175i	−0.119028	−	0.720296i
$862$		0			0
$863$	234.173	−	135.200i	0.271347	−	0.156662i	−0.358153	−	0.933663i	$-0.616593\pi$
$863$	234.173	−	135.200i	0.271347	−	0.156662i	0.629500	+	0.777001i	$0.283260\pi$
$864$		0			0
$865$	−103.896	+	179.952i	−0.120110	+	0.208037i
$866$		0			0
$867$	552.603	−	644.353i	0.637374	−	0.743198i
$868$		0			0
$869$	216.569	−	1852.87i	0.249216	−	2.13218i
$870$		0			0
$871$	−1323.56	+	664.715i	−1.51958	+	0.763163i
$872$		0			0
$873$	1270.60	−	120.851i	1.45545	−	0.138432i
$874$		0			0
$875$	−648.455	+	482.757i	−0.741092	+	0.551722i
$876$		0			0
$877$	−1054.16	−	1117.34i	−1.20200	−	1.27405i	−0.952103	−	0.305777i	$-0.901084\pi$
$877$	−1054.16	−	1117.34i	−1.20200	−	1.27405i	−0.249900	−	0.968272i	$-0.580398\pi$
$878$		0			0
$879$	713.845	−	458.573i	0.812110	−	0.521698i
$880$		0			0
$881$	−280.841	−	334.693i	−0.318775	−	0.379901i	0.582733	−	0.812664i	$-0.301983\pi$
$881$	−280.841	−	334.693i	−0.318775	−	0.379901i	−0.901508	+	0.432762i	$0.857539\pi$
$882$		0			0
$883$	−942.500	−	790.852i	−1.06738	−	0.895642i	−0.0725715	−	0.997363i	$-0.523121\pi$
$883$	−942.500	−	790.852i	−1.06738	−	0.895642i	−0.994813	+	0.101721i	$0.967565\pi$
$884$		0			0
$885$	−498.944	+	2008.61i	−0.563778	+	2.26962i
$886$		0			0
$887$	−40.0929	+	79.8314i	−0.0452005	+	0.0900016i	−0.915099	−	0.403229i	$-0.867888\pi$
$887$	−40.0929	+	79.8314i	−0.0452005	+	0.0900016i	0.869899	+	0.493231i	$0.164184\pi$
$888$		0			0
$889$	337.416	+	79.9690i	0.379545	+	0.0899538i
$890$		0			0
$891$	1099.10	−	746.945i	1.23356	−	0.838322i
$892$		0			0
$893$	−49.7833	+	210.052i	−0.0557483	+	0.235221i
$894$		0			0
$895$	2384.72	+	1197.65i	2.66449	+	1.33816i
$896$		0			0
$897$	−216.583	+	224.670i	−0.241453	+	0.250469i
$898$		0			0
$899$	591.465	−	704.881i	0.657915	−	0.784072i
$900$		0			0
$901$	−55.6177	+	46.6688i	−0.0617289	+	0.0517967i
$902$		0			0
$903$	107.233	−	207.909i	0.118752	−	0.230242i
$904$		0			0
$905$	1519.14	−	1433.23i	1.67860	−	1.58368i
$906$		0			0
$907$	901.245	+	1210.58i	0.993655	+	1.33471i	0.941843	+	0.336054i	$0.109092\pi$
$907$	901.245	+	1210.58i	0.993655	+	1.33471i	0.0518126	+	0.998657i	$0.483500\pi$
$908$		0			0
$909$	66.5585	+	5.31630i	0.0732217	+	0.00584852i
$910$		0			0
$911$	351.522	+	699.937i	0.385864	+	0.768317i	0.999778	−	0.0210549i	$-0.00670247\pi$
$911$	351.522	+	699.937i	0.385864	+	0.768317i	−0.613915	+	0.789372i	$0.710406\pi$
$912$		0			0
$913$	1531.33	+	178.986i	1.67725	+	0.196042i
$914$		0			0
$915$	−511.327	+	179.899i	−0.558827	+	0.196611i
$916$		0			0
$917$	−467.934	−	270.162i	−0.510288	−	0.294615i
$918$		0			0
$919$	662.135	+	1146.85i	0.720495	+	1.24793i	0.960802	+	0.277237i	$0.0894187\pi$
$919$	662.135	+	1146.85i	0.720495	+	1.24793i	−0.240307	+	0.970697i	$0.577248\pi$
$920$		0			0
$921$	524.864	+	639.360i	0.569885	+	0.694202i
$922$		0			0
$923$	−1253.16	+	540.560i	−1.35770	+	0.585655i
$924$		0			0
$925$	118.589	−	2036.10i	0.128205	−	2.20119i
$926$		0			0
$927$	−250.986	+	322.405i	−0.270751	+	0.347794i
$928$		0			0
$929$	−219.294	−	94.5944i	−0.236054	−	0.101824i	0.274767	−	0.961511i	$-0.411399\pi$
$929$	−219.294	−	94.5944i	−0.236054	−	0.101824i	−0.510821	+	0.859687i	$0.670659\pi$
$930$		0			0
$931$	137.188	−	32.5142i	0.147356	−	0.0349240i
$932$		0			0
$933$	293.925	−	66.3285i	0.315032	−	0.0710917i
$934$		0			0
$935$	−126.522	+	347.617i	−0.135318	+	0.371783i
$936$		0			0
$937$	−438.936	+	159.760i	−0.468448	+	0.170501i	−0.565449	−	0.824783i	$-0.691297\pi$
$937$	−438.936	+	159.760i	−0.468448	+	0.170501i	0.0970009	+	0.995284i	$0.469075\pi$
$938$		0			0
$939$	−567.793	+	413.283i	−0.604679	+	0.440131i
$940$		0			0
$941$	−670.791	+	39.0692i	−0.712850	+	0.0415188i	−0.410737	−	0.911754i	$-0.634729\pi$
$941$	−670.791	+	39.0692i	−0.712850	+	0.0415188i	−0.302112	+	0.953272i	$0.597692\pi$
$942$		0			0
$943$	−300.414	+	318.420i	−0.318573	+	0.337667i
$944$		0			0
$945$	−608.706	+	199.542i	−0.644133	+	0.211156i
$946$		0			0
$947$	532.063	−	159.289i	0.561841	−	0.168204i	0.00672533	−	0.999977i	$-0.497859\pi$
$947$	532.063	−	159.289i	0.561841	−	0.168204i	0.555115	+	0.831773i	$0.312674\pi$
$948$		0			0
$949$	742.169	−	488.132i	0.782053	−	0.514365i
$950$		0			0
$951$	−70.2990	+	1018.08i	−0.0739211	+	1.07053i
$952$		0			0
$953$	642.645	+	113.316i	0.674339	+	0.118904i	0.500323	−	0.865839i	$-0.333215\pi$
$953$	642.645	+	113.316i	0.674339	+	0.118904i	0.174016	+	0.984743i	$0.444326\pi$
$954$		0			0
$955$	−230.341	−	1306.33i	−0.241194	−	1.36788i
$956$		0			0
$957$	−174.393	+	1364.49i	−0.182229	+	1.42580i
$958$		0			0
$959$	426.479	+	127.680i	0.444712	+	0.133138i
$960$		0			0
$961$	−122.087	+	14.2699i	−0.127042	+	0.0148490i
$962$		0			0
$963$	587.039	−	322.282i	0.609594	−	0.334664i
$964$		0			0
$965$	−664.634	+	1010.53i	−0.688740	+	1.04718i
$966$		0			0
$967$	883.875	−	1187.25i	0.914038	−	1.22777i	−0.0592646	−	0.998242i	$-0.518876\pi$
$967$	883.875	−	1187.25i	0.914038	−	1.22777i	0.973303	−	0.229524i	$-0.0737170\pi$
$968$		0			0
$969$	−12.0632	−	21.4234i	−0.0124491	−	0.0221088i
$970$		0			0
$971$		−	242.366i		−	0.249604i	−0.992182	−	0.124802i	$-0.960170\pi$
$971$		−	242.366i		−	0.249604i	0.992182	−	0.124802i	$-0.0398296\pi$
$972$		0			0
$973$	−82.8184			−0.0851166
$974$		0			0
$975$	−2971.44	+	1673.18i	−3.04763	+	1.71608i
$976$		0			0
$977$	174.832	+	130.158i	0.178948	+	0.133222i	0.682906	−	0.730506i	$-0.260716\pi$
$977$	174.832	+	130.158i	0.178948	+	0.133222i	−0.503958	+	0.863728i	$0.668123\pi$
$978$		0			0
$979$	1296.63	+	852.806i	1.32444	+	0.871099i
$980$		0			0
$981$	513.231	+	11.0502i	0.523172	+	0.0112642i
$982$		0			0
$983$	43.9356	+	375.893i	0.0446954	+	0.382393i	0.997010	+	0.0772750i	$0.0246219\pi$
$983$	43.9356	+	375.893i	0.0446954	+	0.382393i	−0.952314	+	0.305118i	$0.901304\pi$
$984$		0			0
$985$	5.10226	−	17.0427i	0.00517996	−	0.0173023i
$986$		0			0
$987$	−498.747	−	63.7439i	−0.505316	−	0.0645835i
$988$		0			0
$989$	−160.444	+	28.2906i	−0.162229	+	0.0286053i
$990$		0			0
$991$	−81.2735	+	460.925i	−0.0820116	+	0.465111i	0.915950	+	0.401293i	$0.131439\pi$
$991$	−81.2735	+	460.925i	−0.0820116	+	0.465111i	−0.997962	+	0.0638184i	$0.979672\pi$
$992$		0			0
$993$	−327.887	−	22.6409i	−0.330199	−	0.0228005i
$994$		0			0
$995$	1242.19	+	1888.66i	1.24843	+	1.89815i
$996$		0			0
$997$	−270.469	−	903.428i	−0.271282	−	0.906147i	−0.979720	−	0.200373i	$-0.935785\pi$
$997$	−270.469	−	903.428i	−0.271282	−	0.906147i	0.708437	−	0.705774i	$-0.249401\pi$
$998$		0			0
$999$	346.937	−	865.209i	0.347284	−	0.866075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.65.5	yes	324
81.5	odd	54	inner	324.3.o.a.5.5	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.5	✓	324	81.5	odd	54	inner
324.3.o.a.65.5	yes	324	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.61407 + 1.47195i) q^{3} +(7.35484 + 5.47548i) q^{5} +(2.16180 + 1.42184i) q^{7} +(4.66673 - 7.69556i) q^{9} +O(q^{10})\)	\(q+(-2.61407 + 1.47195i) q^{3} +(7.35484 + 5.47548i) q^{5} +(2.16180 + 1.42184i) q^{7} +(4.66673 - 7.69556i) q^{9} +(1.90463 + 16.2951i) q^{11} +(5.51865 - 18.4336i) q^{13} +(-27.2857 - 3.48733i) q^{15} +(2.42175 - 0.427020i) q^{17} +(-0.578712 + 3.28204i) q^{19} +(-7.74398 - 0.534727i) q^{21} +(2.97065 + 4.51665i) q^{23} +(16.9428 + 56.5928i) q^{25} +(-0.871702 + 26.9859i) q^{27} +(-20.3292 - 19.1797i) q^{29} +(1.91430 + 32.8672i) q^{31} +(-28.9645 - 39.7932i) q^{33} +(8.11447 + 22.2943i) q^{35} +(-32.4429 - 11.8083i) q^{37} +(12.7071 + 56.3099i) q^{39} +(18.6748 + 78.7953i) q^{41} +(-11.9365 + 27.6720i) q^{43} +(76.4600 - 31.0470i) q^{45} +(64.6646 + 3.76628i) q^{47} +(-16.7561 - 38.8451i) q^{49} +(-5.70208 + 4.68095i) q^{51} +(-25.5689 + 14.7622i) q^{53} +(-75.2155 + 130.277i) q^{55} +(-3.31820 - 9.43132i) q^{57} +(8.73474 - 74.7305i) q^{59} +(17.6094 - 8.84378i) q^{61} +(21.0304 - 10.0009i) q^{63} +(141.522 - 105.359i) q^{65} +(-52.8216 - 55.9876i) q^{67} +(-14.4138 - 7.43420i) q^{69} +(-45.5910 - 54.3333i) q^{71} +(35.3645 + 29.6743i) q^{73} +(-127.591 - 122.999i) q^{75} +(-19.0517 + 37.9350i) q^{77} +(-110.642 - 26.2225i) q^{79} +(-37.4432 - 71.8262i) q^{81} +(21.6720 - 91.4413i) q^{83} +(20.1497 + 10.1196i) q^{85} +(81.3735 + 20.2134i) q^{87} +(60.8048 - 72.4644i) q^{89} +(38.1398 - 32.0031i) q^{91} +(-53.3830 - 83.0995i) q^{93} +(-22.2271 + 20.9702i) q^{95} +(84.6863 + 113.753i) q^{97} +(134.289 + 61.3879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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