LMFDB - Embedded newform 483.3.b.a.323.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(323,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.323");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.b (of order $2$, degree $1$, 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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.9
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.80

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.36083i q^{2} +(-2.11593 + 2.12669i) q^{3} -7.29519 q^{4} +8.80778i q^{5} +(7.14745 + 7.11130i) q^{6} +2.64575 q^{7} +11.0746i q^{8} +(-0.0456396 - 8.99988i) q^{9} +O(q^{10})$	\(q-3.36083i q^{2} +(-2.11593 + 2.12669i) q^{3} -7.29519 q^{4} +8.80778i q^{5} +(7.14745 + 7.11130i) q^{6} +2.64575 q^{7} +11.0746i q^{8} +(-0.0456396 - 8.99988i) q^{9} +29.6015 q^{10} +13.4482i q^{11} +(15.4361 - 15.5146i) q^{12} -1.25970 q^{13} -8.89192i q^{14} +(-18.7314 - 18.6367i) q^{15} +8.03899 q^{16} -22.6883i q^{17} +(-30.2471 + 0.153387i) q^{18} -22.4891 q^{19} -64.2544i q^{20} +(-5.59824 + 5.62670i) q^{21} +45.1971 q^{22} +4.79583i q^{23} +(-23.5522 - 23.4330i) q^{24} -52.5770 q^{25} +4.23363i q^{26} +(19.2366 + 18.9461i) q^{27} -19.3012 q^{28} -16.9752i q^{29} +(-62.6348 + 62.9532i) q^{30} +31.1584 q^{31} +17.2806i q^{32} +(-28.6002 - 28.4555i) q^{33} -76.2516 q^{34} +23.3032i q^{35} +(0.332950 + 65.6558i) q^{36} -59.4859 q^{37} +75.5820i q^{38} +(2.66544 - 2.67899i) q^{39} -97.5423 q^{40} -40.9829i q^{41} +(18.9104 + 18.8147i) q^{42} -26.1594 q^{43} -98.1070i q^{44} +(79.2690 - 0.401984i) q^{45} +16.1180 q^{46} -40.8096i q^{47} +(-17.0100 + 17.0964i) q^{48} +7.00000 q^{49} +176.703i q^{50} +(48.2511 + 48.0070i) q^{51} +9.18974 q^{52} +89.0976i q^{53} +(63.6747 - 64.6508i) q^{54} -118.449 q^{55} +29.3005i q^{56} +(47.5854 - 47.8273i) q^{57} -57.0507 q^{58} -86.6905i q^{59} +(136.649 + 135.958i) q^{60} -46.6485 q^{61} -104.718i q^{62} +(-0.120751 - 23.8115i) q^{63} +90.2330 q^{64} -11.0952i q^{65} +(-95.6341 + 96.1203i) q^{66} -43.3792 q^{67} +165.516i q^{68} +(-10.1993 - 10.1477i) q^{69} +78.3181 q^{70} -23.5293i q^{71} +(99.6698 - 0.505439i) q^{72} -115.077 q^{73} +199.922i q^{74} +(111.250 - 111.815i) q^{75} +164.062 q^{76} +35.5806i q^{77} +(-9.00364 - 8.95810i) q^{78} +16.4630 q^{79} +70.8057i q^{80} +(-80.9958 + 0.821503i) q^{81} -137.737 q^{82} -67.8180i q^{83} +(40.8402 - 41.0478i) q^{84} +199.834 q^{85} +87.9174i q^{86} +(36.1010 + 35.9184i) q^{87} -148.933 q^{88} +24.1825i q^{89} +(-1.35100 - 266.410i) q^{90} -3.33285 q^{91} -34.9865i q^{92} +(-65.9291 + 66.2643i) q^{93} -137.154 q^{94} -198.079i q^{95} +(-36.7504 - 36.5646i) q^{96} +101.618 q^{97} -23.5258i q^{98} +(121.032 - 0.613770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	3.36083i		−	1.68042i	−0.542265	−	0.840208i	$-0.682433\pi$
$2$		−	3.36083i		−	1.68042i	0.542265	−	0.840208i	$-0.317567\pi$
$3$	−2.11593	+	2.12669i	−0.705312	+	0.708897i
$3$	−2.11593	+	2.12669i	−0.705312	+	0.708897i
$4$	−7.29519			−1.82380
$5$			8.80778i			1.76156i	0.473529	+	0.880778i	$0.342980\pi$
$5$			8.80778i			1.76156i	−0.473529	+	0.880778i	$0.657020\pi$
$6$	7.14745	+	7.11130i	1.19124	+	1.18522i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$			11.0746i			1.38432i
$9$	−0.0456396	−	8.99988i	−0.00507107	−	0.999987i
$10$	29.6015			2.96015
$11$			13.4482i			1.22256i	0.791413	+	0.611281i	$0.209346\pi$
$11$			13.4482i			1.22256i	−0.791413	+	0.611281i	$0.790654\pi$
$12$	15.4361	−	15.5146i	1.28634	−	1.29288i
$13$	−1.25970			−0.0968999			−0.0484500	−	0.998826i	$-0.515428\pi$
$13$	−1.25970			−0.0968999			−0.0484500	+	0.998826i	$0.515428\pi$
$14$		−	8.89192i		−	0.635137i
$15$	−18.7314	−	18.6367i	−1.24876	−	1.24245i
$16$	8.03899			0.502437
$17$		−	22.6883i		−	1.33461i	−0.744786	−	0.667304i	$-0.767448\pi$
$17$		−	22.6883i		−	1.33461i	0.744786	−	0.667304i	$-0.232552\pi$
$18$	−30.2471	+	0.153387i	−1.68039	+	0.00852150i
$19$	−22.4891			−1.18364			−0.591818	−	0.806072i	$-0.701589\pi$
$19$	−22.4891			−1.18364			−0.591818	+	0.806072i	$0.701589\pi$
$20$		−	64.2544i		−	3.21272i
$21$	−5.59824	+	5.62670i	−0.266583	+	0.267938i
$22$	45.1971			2.05441
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−23.5522	−	23.4330i	−0.981341	−	0.976377i
$25$	−52.5770			−2.10308
$26$			4.23363i			0.162832i
$27$	19.2366	+	18.9461i	0.712465	+	0.701708i
$28$	−19.3012			−0.689330
$29$		−	16.9752i		−	0.585351i	−0.956212	−	0.292676i	$-0.905454\pi$
$29$		−	16.9752i		−	0.585351i	0.956212	−	0.292676i	$-0.0945456\pi$
$30$	−62.6348	+	62.9532i	−2.08783	+	2.09844i
$31$	31.1584			1.00511			0.502554	−	0.864546i	$-0.332394\pi$
$31$	31.1584			1.00511			0.502554	+	0.864546i	$0.332394\pi$
$32$			17.2806i			0.540018i
$33$	−28.6002	−	28.4555i	−0.866671	−	0.862288i
$34$	−76.2516			−2.24270
$35$			23.3032i			0.665806i
$36$	0.332950	+	65.6558i	0.00924860	+	1.82377i
$37$	−59.4859			−1.60773			−0.803863	−	0.594814i	$-0.797226\pi$
$37$	−59.4859			−1.60773			−0.803863	+	0.594814i	$0.797226\pi$
$38$			75.5820i			1.98900i
$39$	2.66544	−	2.67899i	0.0683446	−	0.0686921i
$40$	−97.5423			−2.43856
$41$		−	40.9829i		−	0.999584i	−0.866145	−	0.499792i	$-0.833410\pi$
$41$		−	40.9829i		−	0.999584i	0.866145	−	0.499792i	$-0.166590\pi$
$42$	18.9104	+	18.8147i	0.450247	+	0.447970i
$43$	−26.1594			−0.608359			−0.304179	−	0.952615i	$-0.598382\pi$
$43$	−26.1594			−0.608359			−0.304179	+	0.952615i	$0.598382\pi$
$44$		−	98.1070i		−	2.22971i
$45$	79.2690	−	0.401984i	1.76153	−	0.00893298i
$46$	16.1180			0.350391
$47$		−	40.8096i		−	0.868290i	−0.900843	−	0.434145i	$-0.857051\pi$
$47$		−	40.8096i		−	0.868290i	0.900843	−	0.434145i	$-0.142949\pi$
$48$	−17.0100	+	17.0964i	−0.354374	+	0.356176i
$49$	7.00000			0.142857
$50$			176.703i			3.53405i
$51$	48.2511	+	48.0070i	0.946100	+	0.941314i
$52$	9.18974			0.176726
$53$			89.0976i			1.68109i	0.541744	+	0.840543i	$0.317764\pi$
$53$			89.0976i			1.68109i	−0.541744	+	0.840543i	$0.682236\pi$
$54$	63.6747	−	64.6508i	1.17916	−	1.19724i
$55$	−118.449			−2.15361
$56$			29.3005i			0.523224i
$57$	47.5854	−	47.8273i	0.834832	−	0.839076i
$58$	−57.0507			−0.983634
$59$		−	86.6905i		−	1.46933i	−0.678430	−	0.734665i	$-0.737339\pi$
$59$		−	86.6905i		−	1.46933i	0.678430	−	0.734665i	$-0.262661\pi$
$60$	136.649	+	135.958i	2.27749	+	2.26597i
$61$	−46.6485			−0.764729			−0.382364	−	0.924012i	$-0.624890\pi$
$61$	−46.6485			−0.764729			−0.382364	+	0.924012i	$0.624890\pi$
$62$		−	104.718i		−	1.68900i
$63$	−0.120751	−	23.8115i	−0.00191668	−	0.377960i
$64$	90.2330			1.40989
$65$		−	11.0952i		−	0.170695i
$66$	−95.6341	+	96.1203i	−1.44900	+	1.45637i
$67$	−43.3792			−0.647451			−0.323725	−	0.946151i	$-0.604935\pi$
$67$	−43.3792			−0.647451			−0.323725	+	0.946151i	$0.604935\pi$
$68$			165.516i			2.43405i
$69$	−10.1993	−	10.1477i	−0.147815	−	0.147068i
$70$	78.3181			1.11883
$71$		−	23.5293i		−	0.331398i	−0.986176	−	0.165699i	$-0.947012\pi$
$71$		−	23.5293i		−	0.331398i	0.986176	−	0.165699i	$-0.0529881\pi$
$72$	99.6698	−	0.505439i	1.38430	−	0.00701998i
$73$	−115.077			−1.57640			−0.788201	−	0.615418i	$-0.788987\pi$
$73$	−115.077			−1.57640			−0.788201	+	0.615418i	$0.788987\pi$
$74$			199.922i			2.70165i
$75$	111.250	−	111.815i	1.48333	−	1.49087i
$76$	164.062			2.15871
$77$			35.5806i			0.462085i
$78$	−9.00364	−	8.95810i	−0.115431	−	0.114847i
$79$	16.4630			0.208393			0.104196	−	0.994557i	$-0.466773\pi$
$79$	16.4630			0.208393			0.104196	+	0.994557i	$0.466773\pi$
$80$			70.8057i			0.885071i
$81$	−80.9958	+	0.821503i	−0.999949	+	0.0101420i
$82$	−137.737			−1.67972
$83$		−	67.8180i		−	0.817084i	−0.912739	−	0.408542i	$-0.866037\pi$
$83$		−	67.8180i		−	0.817084i	0.912739	−	0.408542i	$-0.133963\pi$
$84$	40.8402	−	41.0478i	0.486193	−	0.488664i
$85$	199.834			2.35099
$86$			87.9174i			1.02230i
$87$	36.1010	+	35.9184i	0.414954	+	0.412855i
$88$	−148.933			−1.69242
$89$			24.1825i			0.271714i	0.990728	+	0.135857i	$0.0433787\pi$
$89$			24.1825i			0.271714i	−0.990728	+	0.135857i	$0.956621\pi$
$90$	−1.35100	−	266.410i	−0.0150111	−	2.96011i
$91$	−3.33285			−0.0366247
$92$		−	34.9865i		−	0.380288i
$93$	−65.9291	+	66.2643i	−0.708915	+	0.712519i
$94$	−137.154			−1.45909
$95$		−	198.079i		−	2.08504i
$96$	−36.7504	−	36.5646i	−0.382817	−	0.380881i
$97$	101.618			1.04761			0.523804	−	0.851839i	$-0.324512\pi$
$97$	101.618			1.04761			0.523804	+	0.851839i	$0.324512\pi$
$98$		−	23.5258i		−	0.240059i
$99$	121.032	−	0.613770i	1.22255	−	0.00619970i
$100$	383.559			3.83559
$101$			168.522i			1.66854i	0.551358	+	0.834269i	$0.314110\pi$
$101$			168.522i			1.66854i	−0.551358	+	0.834269i	$0.685890\pi$
$102$	161.343	−	162.164i	1.58180	−	1.58984i
$103$	44.4417			0.431473			0.215736	−	0.976452i	$-0.430785\pi$
$103$	44.4417			0.431473			0.215736	+	0.976452i	$0.430785\pi$
$104$		−	13.9506i		−	0.134140i
$105$	−49.5587	−	49.3081i	−0.471988	−	0.469601i
$106$	299.442			2.82492
$107$			37.7991i			0.353263i	0.984277	+	0.176631i	$0.0565201\pi$
$107$			37.7991i			0.353263i	−0.984277	+	0.176631i	$0.943480\pi$
$108$	−140.334	−	138.215i	−1.29939	−	1.27977i
$109$	−133.261			−1.22257			−0.611287	−	0.791409i	$-0.709348\pi$
$109$	−133.261			−1.22257			−0.611287	+	0.791409i	$0.709348\pi$
$110$			398.086i			3.61897i
$111$	125.868	−	126.508i	1.13395	−	1.13971i
$112$	21.2692			0.189903
$113$		−	137.728i		−	1.21883i	−0.792850	−	0.609417i	$-0.791404\pi$
$113$		−	137.728i		−	1.21883i	0.792850	−	0.609417i	$-0.208596\pi$
$114$	−160.740	−	159.927i	−1.41000	−	1.40286i
$115$	−42.2406			−0.367310
$116$			123.837i			1.06756i
$117$	0.0574922	+	11.3371i	0.000491386	+	0.0968987i
$118$	−291.352			−2.46909
$119$		−	60.0277i		−	0.504434i
$120$	206.393	−	207.443i	1.71994	−	1.72869i
$121$	−59.8538			−0.494659
$122$			156.778i			1.28506i
$123$	87.1581	+	86.7172i	0.708603	+	0.705018i
$124$	−227.306			−1.83311
$125$		−	242.893i		−	1.94314i
$126$	−80.0263	+	0.405824i	−0.635129	+	0.00322083i
$127$	−188.414			−1.48358			−0.741788	−	0.670634i	$-0.766022\pi$
$127$	−188.414			−1.48358			−0.741788	+	0.670634i	$0.766022\pi$
$128$		−	234.136i		−	1.82918i
$129$	55.3516	−	55.6331i	0.429083	−	0.431264i
$130$	−37.2889			−0.286838
$131$		−	23.6717i		−	0.180700i	−0.995910	−	0.0903501i	$-0.971201\pi$
$131$		−	23.6717i		−	0.180700i	0.995910	−	0.0903501i	$-0.0287986\pi$
$132$	208.643	+	207.588i	1.58063	+	1.57264i
$133$	−59.5005			−0.447372
$134$			145.790i			1.08799i
$135$	−166.873	+	169.431i	−1.23610	+	1.25505i
$136$	251.263			1.84752
$137$			146.853i			1.07192i	0.844243	+	0.535961i	$0.180051\pi$
$137$			146.853i			1.07192i	−0.844243	+	0.535961i	$0.819949\pi$
$138$	−34.1046	+	34.2780i	−0.247135	+	0.248391i
$139$	58.7282			0.422505			0.211252	−	0.977432i	$-0.432246\pi$
$139$	58.7282			0.422505			0.211252	+	0.977432i	$0.432246\pi$
$140$		−	170.001i		−	1.21429i
$141$	86.7895	+	86.3505i	0.615528	+	0.612415i
$142$	−79.0780			−0.556887
$143$		−	16.9407i		−	0.118466i
$144$	−0.366896	−	72.3499i	−0.00254789	−	0.502430i
$145$	149.514			1.03113
$146$			386.755i			2.64901i
$147$	−14.8115	+	14.8868i	−0.100759	+	0.101271i
$148$	433.960			2.93217
$149$			72.8827i			0.489146i	0.969631	+	0.244573i	$0.0786477\pi$
$149$			72.8827i			0.489146i	−0.969631	+	0.244573i	$0.921352\pi$
$150$	−375.792	−	373.891i	−2.50528	−	2.49261i
$151$	−199.486			−1.32110			−0.660550	−	0.750782i	$-0.729677\pi$
$151$	−199.486			−1.32110			−0.660550	+	0.750782i	$0.729677\pi$
$152$		−	249.057i		−	1.63853i
$153$	−204.192	+	1.03549i	−1.33459	+	0.00676789i
$154$	119.580			0.776495
$155$			274.436i			1.77056i
$156$	−19.4449	+	19.5437i	−0.124647	+	0.125280i
$157$	−87.3963			−0.556664			−0.278332	−	0.960485i	$-0.589782\pi$
$157$	−87.3963			−0.556664			−0.278332	+	0.960485i	$0.589782\pi$
$158$		−	55.3295i		−	0.350187i
$159$	−189.483	−	188.525i	−1.19172	−	1.18569i
$160$	−152.203			−0.951272
$161$			12.6886i			0.0788110i
$162$	2.76093	+	272.213i	0.0170428	+	1.68033i
$163$	21.5835			0.132414			0.0662070	−	0.997806i	$-0.478910\pi$
$163$	21.5835			0.132414			0.0662070	+	0.997806i	$0.478910\pi$
$164$			298.978i			1.82304i
$165$	250.630	−	251.904i	1.51897	−	1.52669i
$166$	−227.925			−1.37304
$167$		−	38.9542i		−	0.233258i	−0.993176	−	0.116629i	$-0.962791\pi$
$167$		−	38.9542i		−	0.233258i	0.993176	−	0.116629i	$-0.0372089\pi$
$168$	−62.3132	−	61.9980i	−0.370912	−	0.369036i
$169$	−167.413			−0.990610
$170$		−	671.608i		−	3.95063i
$171$	1.02639	+	202.399i	0.00600230	+	1.18362i
$172$	190.838			1.10952
$173$			199.498i			1.15317i	0.817038	+	0.576584i	$0.195615\pi$
$173$			199.498i			1.15317i	−0.817038	+	0.576584i	$0.804385\pi$
$174$	120.716	−	121.329i	0.693768	−	0.697295i
$175$	−139.106			−0.794890
$176$			108.110i			0.614260i
$177$	184.364	+	183.431i	1.04160	+	1.03634i
$178$	81.2734			0.456592
$179$		−	201.014i		−	1.12298i	−0.827482	−	0.561492i	$-0.810227\pi$
$179$		−	201.014i		−	1.12298i	0.827482	−	0.561492i	$-0.189773\pi$
$180$	−578.282	+	2.93255i	−3.21268	+	0.0162919i
$181$	214.081			1.18277			0.591385	−	0.806389i	$-0.298581\pi$
$181$	214.081			1.18277			0.591385	+	0.806389i	$0.298581\pi$
$182$			11.2011i			0.0615448i
$183$	98.7051	−	99.2069i	0.539372	−	0.542114i
$184$	−53.1117			−0.288651
$185$		−	523.939i		−	2.83210i
$186$	222.703	+	221.576i	1.19733	+	1.19127i
$187$	305.117			1.63164
$188$			297.714i			1.58358i
$189$	50.8951	+	50.1267i	0.269286	+	0.265221i
$190$	−665.710			−3.50373
$191$			266.977i			1.39778i	0.715228	+	0.698891i	$0.246323\pi$
$191$			266.977i			1.39778i	−0.715228	+	0.698891i	$0.753677\pi$
$192$	−190.927	+	191.898i	−0.994412	+	0.999468i
$193$	34.2214			0.177313			0.0886564	−	0.996062i	$-0.471743\pi$
$193$	34.2214			0.177313			0.0886564	+	0.996062i	$0.471743\pi$
$194$		−	341.521i		−	1.76042i
$195$	23.5960	+	23.4766i	0.121005	+	0.120393i
$196$	−51.0663			−0.260542
$197$		−	74.5456i		−	0.378404i	−0.981938	−	0.189202i	$-0.939410\pi$
$197$		−	74.5456i		−	0.378404i	0.981938	−	0.189202i	$-0.0605901\pi$
$198$	−2.06278	−	406.769i	−0.0104181	−	2.05439i
$199$	299.642			1.50574			0.752870	−	0.658169i	$-0.228669\pi$
$199$	299.642			1.50574			0.752870	+	0.658169i	$0.228669\pi$
$200$		−	582.268i		−	2.91134i
$201$	91.7876	−	92.2542i	0.456654	−	0.458976i
$202$	566.375			2.80384
$203$		−	44.9121i		−	0.221242i
$204$	−352.001	−	350.220i	−1.72549	−	1.71677i
$205$	360.969			1.76082
$206$		−	149.361i		−	0.725053i
$207$	43.1619	−	0.218880i	0.208512	−	0.00105739i
$208$	−10.1267			−0.0486861
$209$		−	302.437i		−	1.44707i
$210$	−165.716	+	166.559i	−0.789124	+	0.793136i
$211$	−166.678			−0.789945			−0.394973	−	0.918693i	$-0.629246\pi$
$211$	−166.678			−0.789945			−0.394973	+	0.918693i	$0.629246\pi$
$212$		−	649.983i		−	3.06596i
$213$	50.0396	+	49.7864i	0.234928	+	0.233739i
$214$	127.036			0.593628
$215$		−	230.407i		−	1.07166i
$216$	−209.820	+	213.036i	−0.971388	+	0.986280i
$217$	82.4373			0.379895
$218$			447.866i			2.05443i
$219$	243.496	−	244.734i	1.11185	−	1.11751i
$220$	864.105			3.92775
$221$			28.5805i			0.129323i
$222$	−425.172	−	423.022i	−1.91519	−	1.90550i
$223$	224.307			1.00586			0.502931	−	0.864327i	$-0.332255\pi$
$223$	224.307			1.00586			0.502931	+	0.864327i	$0.332255\pi$
$224$			45.7201i			0.204108i
$225$	2.39960	+	473.187i	0.0106649	+	2.10305i
$226$	−462.881			−2.04815
$227$			130.679i			0.575678i	0.957679	+	0.287839i	$0.0929369\pi$
$227$			130.679i			0.575678i	−0.957679	+	0.287839i	$0.907063\pi$
$228$	−347.144	+	348.909i	−1.52256	+	1.53030i
$229$	196.328			0.857329			0.428665	−	0.903464i	$-0.358984\pi$
$229$	196.328			0.857329			0.428665	+	0.903464i	$0.358984\pi$
$230$			141.964i			0.617233i
$231$	−75.6689	−	75.2861i	−0.327571	−	0.325914i
$232$	187.993			0.810314
$233$		−	287.857i		−	1.23544i	−0.786399	−	0.617719i	$-0.788057\pi$
$233$		−	287.857i		−	1.23544i	0.786399	−	0.617719i	$-0.211943\pi$
$234$	38.1022	−	0.193222i	0.162830	−	0.000825733i
$235$	359.442			1.52954
$236$			632.423i			2.67976i
$237$	−34.8347	+	35.0118i	−0.146982	+	0.147729i
$238$	−201.743			−0.847659
$239$		−	49.8279i		−	0.208485i	−0.994552	−	0.104242i	$-0.966758\pi$
$239$		−	49.8279i		−	0.208485i	0.994552	−	0.104242i	$-0.0332418\pi$
$240$	−150.582	−	149.820i	−0.627424	−	0.624251i
$241$	146.862			0.609384			0.304692	−	0.952451i	$-0.401446\pi$
$241$	146.862			0.609384			0.304692	+	0.952451i	$0.401446\pi$
$242$			201.158i			0.831233i
$243$	169.635	−	173.991i	0.698086	−	0.716014i
$244$	340.309			1.39471
$245$			61.6545i			0.251651i
$246$	291.442	−	292.924i	1.18472	−	1.19075i
$247$	28.3295			0.114694
$248$			345.065i			1.39139i
$249$	144.228	+	143.498i	0.579229	+	0.576299i
$250$	−816.321			−3.26528
$251$		−	163.645i		−	0.651970i	−0.945375	−	0.325985i	$-0.894304\pi$
$251$		−	163.645i		−	0.651970i	0.945375	−	0.325985i	$-0.105696\pi$
$252$	0.880902	+	173.709i	0.00349564	+	0.689321i
$253$	−64.4952			−0.254922
$254$			633.228i			2.49303i
$255$	−422.835	+	424.985i	−1.65818	+	1.66661i
$256$	−425.958			−1.66390
$257$			458.217i			1.78295i	0.453073	+	0.891473i	$0.350328\pi$
$257$			458.217i			1.78295i	−0.453073	+	0.891473i	$0.649672\pi$
$258$	−186.973	−	186.028i	−0.724703	−	0.721037i
$259$	−157.385			−0.607663
$260$			80.9412i			0.311312i
$261$	−152.775	+	0.774741i	−0.585344	+	0.00296836i
$262$	−79.5566			−0.303651
$263$		−	171.278i		−	0.651247i	−0.945499	−	0.325624i	$-0.894426\pi$
$263$		−	171.278i		−	0.651247i	0.945499	−	0.325624i	$-0.105574\pi$
$264$	315.132	−	316.734i	1.19368	−	1.19975i
$265$	−784.752			−2.96133
$266$			199.971i			0.751771i
$267$	−51.4288	−	51.1687i	−0.192617	−	0.191643i
$268$	316.459			1.18082
$269$			497.294i			1.84868i	0.381576	+	0.924338i	$0.375382\pi$
$269$			497.294i			1.84868i	−0.381576	+	0.924338i	$0.624618\pi$
$270$	569.430	+	560.833i	2.10900	+	2.07716i
$271$	54.4266			0.200836			0.100418	−	0.994945i	$-0.467982\pi$
$271$	54.4266			0.200836			0.100418	+	0.994945i	$0.467982\pi$
$272$		−	182.391i		−	0.670556i
$273$	7.05209	−	7.08795i	0.0258318	−	0.0259632i
$274$	493.549			1.80127
$275$		−	707.066i		−	2.57115i
$276$	74.4055	+	74.0291i	0.269585	+	0.268221i
$277$	−481.596			−1.73861			−0.869307	−	0.494273i	$-0.835434\pi$
$277$	−481.596			−1.73861			−0.869307	+	0.494273i	$0.835434\pi$
$278$		−	197.375i		−	0.709984i
$279$	−1.42206	−	280.422i	−0.00509698	−	1.00510i
$280$	−258.073			−0.921688
$281$			318.923i			1.13496i	0.823389	+	0.567478i	$0.192081\pi$
$281$			318.923i			1.13496i	−0.823389	+	0.567478i	$0.807919\pi$
$282$	290.209	−	291.685i	1.02911	−	1.03434i
$283$	−11.1618			−0.0394411			−0.0197206	−	0.999806i	$-0.506278\pi$
$283$	−11.1618			−0.0394411			−0.0197206	+	0.999806i	$0.506278\pi$
$284$			171.651i			0.604403i
$285$	421.253	+	419.122i	1.47808	+	1.47060i
$286$	−56.9347			−0.199072
$287$		−	108.431i		−	0.377807i
$288$	155.523	−	0.788679i	0.540011	−	0.00273847i
$289$	−225.760			−0.781177
$290$		−	502.491i		−	1.73273i
$291$	−215.017	+	216.110i	−0.738891	+	0.742647i
$292$	839.510			2.87503
$293$			446.376i			1.52347i	0.647889	+	0.761735i	$0.275652\pi$
$293$			446.376i			1.52347i	−0.647889	+	0.761735i	$0.724348\pi$
$294$	50.0322	+	49.7791i	0.170177	+	0.169317i
$295$	763.551			2.58831
$296$		−	658.780i		−	2.22561i
$297$	−254.791	+	258.697i	−0.857882	+	0.871033i
$298$	244.946			0.821968
$299$		−	6.04130i		−	0.0202050i
$300$	−811.586	+	815.713i	−2.70529	+	2.71904i
$301$	−69.2113			−0.229938
$302$			670.439i			2.22000i
$303$	−358.395	−	356.582i	−1.18282	−	1.17684i
$304$	−180.789			−0.594702
$305$		−	410.869i		−	1.34711i
$306$	3.48010	+	686.256i	0.0113729	+	2.24267i
$307$	23.9467			0.0780024			0.0390012	−	0.999239i	$-0.487582\pi$
$307$	23.9467			0.0780024			0.0390012	+	0.999239i	$0.487582\pi$
$308$		−	259.567i		−	0.842749i
$309$	−94.0357	+	94.5138i	−0.304323	+	0.305870i
$310$	922.334			2.97527
$311$			125.208i			0.402598i	0.979530	+	0.201299i	$0.0645163\pi$
$311$			125.208i			0.402598i	−0.979530	+	0.201299i	$0.935484\pi$
$312$	29.6687	+	29.5186i	0.0950918	+	0.0946108i
$313$	−224.695			−0.717876			−0.358938	−	0.933361i	$-0.616861\pi$
$313$	−224.695			−0.717876			−0.358938	+	0.933361i	$0.616861\pi$
$314$			293.724i			0.935427i
$315$	209.726	−	1.06355i	0.665797	−	0.00337635i
$316$	−120.101			−0.380066
$317$		−	22.8063i		−	0.0719441i	−0.999353	−	0.0359721i	$-0.988547\pi$
$317$		−	22.8063i		−	0.0719441i	0.999353	−	0.0359721i	$-0.0114527\pi$
$318$	−633.600	+	636.821i	−1.99245	+	2.00258i
$319$	228.286			0.715629
$320$			794.753i			2.48360i
$321$	−80.3871	−	79.9805i	−0.250427	−	0.249160i
$322$	42.6442			0.132435
$323$			510.239i			1.57969i
$324$	590.880	−	5.99301i	1.82370	−	0.0184970i
$325$	66.2312			0.203788
$326$		−	72.5385i		−	0.222511i
$327$	281.971	−	283.404i	0.862295	−	0.866679i
$328$	453.868			1.38374
$329$		−	107.972i		−	0.328183i
$330$	−846.607	−	842.324i	−2.56547	−	2.55250i
$331$	269.039			0.812806			0.406403	−	0.913694i	$-0.366783\pi$
$331$	269.039			0.812806			0.406403	+	0.913694i	$0.366783\pi$
$332$			494.745i			1.49020i
$333$	2.71491	+	535.366i	0.00815289	+	1.60771i
$334$	−130.918			−0.391971
$335$		−	382.075i		−	1.14052i
$336$	−45.0042	+	45.2330i	−0.133941	+	0.134622i
$337$	−349.479			−1.03703			−0.518515	−	0.855069i	$-0.673515\pi$
$337$	−349.479			−1.03703			−0.518515	+	0.855069i	$0.673515\pi$
$338$			562.647i			1.66464i
$339$	292.905	+	291.424i	0.864028	+	0.859657i
$340$	−1457.83			−4.28772
$341$			419.024i			1.22881i
$342$	680.229	−	3.44953i	1.98897	−	0.0100864i
$343$	18.5203			0.0539949
$344$		−	289.704i		−	0.842163i
$345$	89.3785	−	89.8329i	0.259068	−	0.260385i
$346$	670.479			1.93780
$347$		−	427.625i		−	1.23235i	−0.787610	−	0.616174i	$-0.788682\pi$
$347$		−	427.625i		−	1.23235i	0.787610	−	0.616174i	$-0.211318\pi$
$348$	−263.364	−	262.031i	−0.756792	−	0.752964i
$349$	−180.741			−0.517883			−0.258941	−	0.965893i	$-0.583374\pi$
$349$	−180.741			−0.517883			−0.258941	+	0.965893i	$0.583374\pi$
$350$			467.511i			1.33575i
$351$	−24.2323	−	23.8664i	−0.0690378	−	0.0679954i
$352$	−232.392			−0.660205
$353$		−	437.689i		−	1.23991i	−0.784637	−	0.619956i	$-0.787150\pi$
$353$		−	437.689i		−	1.23991i	0.784637	−	0.619956i	$-0.212850\pi$
$354$	616.482	−	619.616i	1.74147	−	1.75033i
$355$	207.241			0.583777
$356$		−	176.416i		−	0.495551i
$357$	127.660	+	127.015i	0.357592	+	0.355783i
$358$	−675.575			−1.88708
$359$			355.471i			0.990170i	0.868845	+	0.495085i	$0.164863\pi$
$359$			355.471i			0.990170i	−0.868845	+	0.495085i	$0.835137\pi$
$360$	4.45180	+	877.870i	0.0123661	+	2.43853i
$361$	144.758			0.400993
$362$		−	719.492i		−	1.98755i
$363$	126.647	−	127.291i	0.348889	−	0.350663i
$364$	24.3138			0.0667960
$365$		−	1013.58i		−	2.77692i
$366$	−333.418	−	331.731i	−0.910977	−	0.906369i
$367$	−192.877			−0.525551			−0.262775	−	0.964857i	$-0.584638\pi$
$367$	−192.877			−0.525551			−0.262775	+	0.964857i	$0.584638\pi$
$368$			38.5536i			0.104765i
$369$	−368.842	+	1.87045i	−0.999571	+	0.00506896i
$370$	−1760.87			−4.75911
$371$			235.730i			0.635391i
$372$	480.965	−	483.410i	1.29292	−	1.29949i
$373$	165.001			0.442363			0.221181	−	0.975233i	$-0.429009\pi$
$373$	165.001			0.442363			0.221181	+	0.975233i	$0.429009\pi$
$374$		−	1025.45i		−	2.74184i
$375$	516.558	+	513.945i	1.37749	+	1.37052i
$376$	451.948			1.20199
$377$			21.3836i			0.0567205i
$378$	168.467	−	171.050i	0.445681	−	0.452513i
$379$	−166.186			−0.438486			−0.219243	−	0.975670i	$-0.570359\pi$
$379$	−166.186			−0.438486			−0.219243	+	0.975670i	$0.570359\pi$
$380$			1445.02i			3.80269i
$381$	398.672	−	400.699i	1.04638	−	1.05170i
$382$	897.263			2.34886
$383$			39.7220i			0.103713i	0.998655	+	0.0518564i	$0.0165138\pi$
$383$			39.7220i			0.103713i	−0.998655	+	0.0518564i	$0.983486\pi$
$384$	497.934	+	495.416i	1.29670	+	1.29015i
$385$	−313.386			−0.813989
$386$		−	115.012i		−	0.297959i
$387$	1.19391	+	235.432i	0.00308503	+	0.608351i
$388$	−741.323			−1.91063
$389$			497.565i			1.27909i	0.768755	+	0.639543i	$0.220876\pi$
$389$			497.565i			1.27909i	−0.768755	+	0.639543i	$0.779124\pi$
$390$	78.9010	−	79.3021i	0.202310	−	0.203339i
$391$	108.809			0.278285
$392$			77.5219i			0.197760i
$393$	50.3425	+	50.0878i	0.128098	+	0.127450i
$394$	−250.535			−0.635876
$395$			145.003i			0.367096i
$396$	−882.952	+	4.47757i	−2.22968	+	0.0113070i
$397$	324.752			0.818015			0.409007	−	0.912531i	$-0.365875\pi$
$397$	324.752			0.818015			0.409007	+	0.912531i	$0.365875\pi$
$398$		−	1007.05i		−	2.53027i
$399$	125.899	−	126.539i	0.315537	−	0.317141i
$400$	−422.666			−1.05667
$401$			523.788i			1.30621i	0.757269	+	0.653103i	$0.226533\pi$
$401$			523.788i			1.30621i	−0.757269	+	0.653103i	$0.773467\pi$
$402$	−310.051	−	308.482i	−0.771271	−	0.767369i
$403$	−39.2502			−0.0973949
$404$		−	1229.40i		−	3.04307i
$405$	−7.23562	−	713.394i	−0.0178657	−	1.76147i
$406$	−150.942			−0.371779
$407$		−	799.977i		−	1.96555i
$408$	−531.657	+	534.360i	−1.30308	+	1.30970i
$409$	−213.151			−0.521151			−0.260576	−	0.965453i	$-0.583912\pi$
$409$	−213.151			−0.521151			−0.260576	+	0.965453i	$0.583912\pi$
$410$		−	1213.16i		−	2.95892i
$411$	−312.312	−	310.732i	−0.759882	−	0.756039i
$412$	−324.210			−0.786918
$413$		−	229.361i		−	0.555355i
$414$	−0.735619	−	145.060i	−0.00177686	−	0.350386i
$415$	597.326			1.43934
$416$		−	21.7683i		−	0.0523277i
$417$	−124.265	+	124.897i	−0.297998	+	0.299513i
$418$	−1016.44			−2.43168
$419$			765.067i			1.82594i	0.408031	+	0.912968i	$0.366216\pi$
$419$			765.067i			1.82594i	−0.408031	+	0.912968i	$0.633784\pi$
$420$	361.540	+	359.711i	0.860810	+	0.856456i
$421$	−676.407			−1.60667			−0.803334	−	0.595529i	$-0.796942\pi$
$421$	−676.407			−1.60667			−0.803334	+	0.595529i	$0.796942\pi$
$422$			560.178i			1.32744i
$423$	−367.282	+	1.86254i	−0.868278	+	0.00440316i
$424$	−986.717			−2.32716
$425$			1192.89i			2.80679i
$426$	167.324	−	168.175i	0.392779	−	0.394776i
$427$	−123.420			−0.289040
$428$		−	275.752i		−	0.644279i
$429$	36.0276	+	35.8453i	0.0839804	+	0.0835556i
$430$	−774.358			−1.80083
$431$			552.492i			1.28188i	0.767589	+	0.640942i	$0.221456\pi$
$431$			552.492i			1.28188i	−0.767589	+	0.640942i	$0.778544\pi$
$432$	154.642	+	152.307i	0.357969	+	0.352564i
$433$	−278.861			−0.644021			−0.322011	−	0.946736i	$-0.604359\pi$
$433$	−278.861			−0.644021			−0.322011	+	0.946736i	$0.604359\pi$
$434$		−	277.058i		−	0.638382i
$435$	−316.361	+	317.970i	−0.727268	+	0.730965i
$436$	972.160			2.22973
$437$		−	107.854i		−	0.246805i
$438$	−822.510	−	818.349i	−1.87788	−	1.86838i
$439$	−385.077			−0.877169			−0.438584	−	0.898690i	$-0.644520\pi$
$439$	−385.077			−0.877169			−0.438584	+	0.898690i	$0.644520\pi$
$440$		−	1311.77i		−	2.98129i
$441$	−0.319477	−	62.9992i	−0.000724439	−	0.142855i
$442$	96.0541			0.217317
$443$			316.586i			0.714641i	0.933982	+	0.357321i	$0.116310\pi$
$443$			316.586i			0.714641i	−0.933982	+	0.357321i	$0.883690\pi$
$444$	−918.232	+	922.900i	−2.06809	+	2.07860i
$445$	−212.994			−0.478639
$446$		−	753.859i		−	1.69027i
$447$	−154.999	−	154.215i	−0.346754	−	0.345000i
$448$	238.734			0.532889
$449$		−	366.885i		−	0.817116i	−0.912732	−	0.408558i	$-0.866032\pi$
$449$		−	366.885i		−	0.817116i	0.912732	−	0.408558i	$-0.133968\pi$
$450$	1590.30	−	8.06464i	3.53401	−	0.0179214i
$451$	551.146			1.22205
$452$			1004.75i			2.22290i
$453$	422.100	−	424.246i	0.931788	−	0.936525i
$454$	439.190			0.967379
$455$		−	29.3550i		−	0.0645165i
$456$	529.667	+	526.987i	1.16155	+	1.15567i
$457$	−489.078			−1.07019			−0.535097	−	0.844791i	$-0.679725\pi$
$457$	−489.078			−1.07019			−0.535097	+	0.844791i	$0.679725\pi$
$458$		−	659.827i		−	1.44067i
$459$	429.855	−	436.445i	0.936504	−	0.950861i
$460$	308.153			0.669899
$461$		−	93.5290i		−	0.202883i	−0.994842	−	0.101441i	$-0.967655\pi$
$461$		−	93.5290i		−	0.202883i	0.994842	−	0.101441i	$-0.0323454\pi$
$462$	−253.024	+	254.310i	−0.547671	+	0.550455i
$463$	−198.131			−0.427928			−0.213964	−	0.976842i	$-0.568638\pi$
$463$	−198.131			−0.427928			−0.213964	+	0.976842i	$0.568638\pi$
$464$		−	136.463i		−	0.294102i
$465$	−583.641	−	580.689i	−1.25514	−	1.24879i
$466$	−967.439			−2.07605
$467$		−	536.580i		−	1.14899i	−0.818506	−	0.574497i	$-0.805198\pi$
$467$		−	536.580i		−	1.14899i	0.818506	−	0.574497i	$-0.194802\pi$
$468$	−0.419416	−	82.7066i	−0.000896188	−	0.176723i
$469$	−114.771			−0.244713
$470$		−	1208.02i		−	2.57026i
$471$	184.925	−	185.865i	0.392622	−	0.394618i
$472$	960.059			2.03402
$473$		−	351.797i		−	0.743757i
$474$	117.669	+	117.074i	0.248246	+	0.246991i
$475$	1182.41			2.48928
$476$			437.913i			0.919985i
$477$	801.868	−	4.06638i	1.68107	−	0.00852491i
$478$	−167.463			−0.350341
$479$		−	276.134i		−	0.576481i	−0.957558	−	0.288240i	$-0.906930\pi$
$479$		−	276.134i		−	0.576481i	0.957558	−	0.288240i	$-0.0930702\pi$
$480$	322.053	−	323.690i	0.670943	−	0.674354i
$481$	74.9343			0.155789
$482$		−	493.577i		−	1.02402i
$483$	−26.9847	−	26.8482i	−0.0558689	−	0.0555863i
$484$	436.644			0.902158
$485$			895.030i			1.84542i
$486$	−584.756	−	570.114i	−1.20320	−	1.17307i
$487$	435.366			0.893974			0.446987	−	0.894540i	$-0.352497\pi$
$487$	435.366			0.893974			0.446987	+	0.894540i	$0.352497\pi$
$488$		−	516.611i		−	1.05863i
$489$	−45.6693	+	45.9014i	−0.0933932	+	0.0938680i
$490$	207.210			0.422878
$491$			386.456i			0.787079i	0.919308	+	0.393540i	$0.128750\pi$
$491$			386.456i			0.787079i	−0.919308	+	0.393540i	$0.871250\pi$
$492$	−635.835	−	632.618i	−1.29235	−	1.28581i
$493$	−385.139			−0.781214
$494$		−	95.2105i		−	0.192734i
$495$	5.40596	+	1066.02i	0.0109211	+	2.15359i
$496$	250.482			0.505003
$497$		−	62.2527i		−	0.125257i
$498$	482.274	−	484.726i	0.968422	−	0.973345i
$499$	424.635			0.850972			0.425486	−	0.904965i	$-0.360103\pi$
$499$	424.635			0.850972			0.425486	+	0.904965i	$0.360103\pi$
$500$			1771.95i			3.54389i
$501$	82.8435	+	82.4245i	0.165356	+	0.164520i
$502$	−549.982			−1.09558
$503$			829.310i			1.64873i	0.566060	+	0.824364i	$0.308467\pi$
$503$			829.310i			1.64873i	−0.566060	+	0.824364i	$0.691533\pi$
$504$	263.701	−	1.33727i	0.523217	−	0.00265330i
$505$	−1484.31			−2.93922
$506$			216.758i			0.428375i
$507$	354.235	−	356.036i	0.698689	−	0.702241i
$508$	1374.52			2.70574
$509$			719.837i			1.41422i	0.707104	+	0.707109i	$0.250001\pi$
$509$			719.837i			1.41422i	−0.707104	+	0.707109i	$0.749999\pi$
$510$	1428.30	+	1421.08i	2.80059	+	2.78643i
$511$	−304.466			−0.595824
$512$			495.031i			0.966858i
$513$	−432.612	−	426.080i	−0.843299	−	0.830566i
$514$	1539.99			2.99609
$515$			391.433i			0.760063i
$516$	−403.801	+	405.853i	−0.782559	+	0.786538i
$517$	548.815			1.06154
$518$			528.944i			1.02113i
$519$	−424.271	−	422.125i	−0.817477	−	0.813342i
$520$	122.874			0.236296
$521$		−	100.206i		−	0.192334i	−0.995365	−	0.0961670i	$-0.969342\pi$
$521$		−	100.206i		−	0.192334i	0.995365	−	0.0961670i	$-0.0306583\pi$
$522$	2.60377	+	513.450i	0.00498807	+	0.983621i
$523$	−441.459			−0.844090			−0.422045	−	0.906575i	$-0.638688\pi$
$523$	−441.459			−0.844090			−0.422045	+	0.906575i	$0.638688\pi$
$524$			172.690i			0.329560i
$525$	294.339	−	295.835i	0.560645	−	0.563496i
$526$	−575.637			−1.09437
$527$		−	706.931i		−	1.34143i
$528$	−229.916	−	228.753i	−0.435447	−	0.433245i
$529$	−23.0000			−0.0434783
$530$			2637.42i			4.97626i
$531$	−780.204	+	3.95652i	−1.46931	+	0.00745108i
$532$	434.067			0.815916
$533$			51.6262i			0.0968596i
$534$	−171.969	+	172.843i	−0.322040	+	0.323677i
$535$	−332.927			−0.622293
$536$		−	480.406i		−	0.896279i
$537$	427.495	+	425.333i	0.796081	+	0.792054i
$538$	1671.32			3.10654
$539$			94.1373i			0.174652i
$540$	1217.37	−	1236.03i	2.25439	−	2.28895i
$541$	−156.494			−0.289268			−0.144634	−	0.989485i	$-0.546200\pi$
$541$	−156.494			−0.289268			−0.144634	+	0.989485i	$0.546200\pi$
$542$		−	182.919i		−	0.337488i
$543$	−452.982	+	455.285i	−0.834222	+	0.838463i
$544$	392.067			0.720712
$545$		−	1173.73i		−	2.15363i
$546$	−23.8214	−	23.7009i	−0.0436289	−	0.0434082i
$547$	−265.209			−0.484843			−0.242421	−	0.970171i	$-0.577942\pi$
$547$	−265.209			−0.484843			−0.242421	+	0.970171i	$0.577942\pi$
$548$		−	1071.32i		−	1.95497i
$549$	2.12902	+	419.831i	0.00387799	+	0.764719i
$550$	−2376.33			−4.32060
$551$			381.756i			0.692843i
$552$	112.381	−	112.952i	0.203589	−	0.204624i
$553$	43.5571			0.0787651
$554$			1618.56i			2.92159i
$555$	1114.26	+	1108.62i	2.00767	+	1.99751i
$556$	−428.433			−0.770563
$557$		−	701.165i		−	1.25882i	−0.777072	−	0.629412i	$-0.783296\pi$
$557$		−	701.165i		−	1.25882i	0.777072	−	0.629412i	$-0.216704\pi$
$558$	−942.450	+	4.77929i	−1.68898	+	0.00856504i
$559$	32.9530			0.0589499
$560$			187.334i			0.334525i
$561$	−645.607	+	648.890i	−1.15082	+	1.15667i
$562$	1071.84			1.90720
$563$		−	985.066i		−	1.74967i	−0.484418	−	0.874837i	$-0.660969\pi$
$563$		−	985.066i		−	1.74967i	0.484418	−	0.874837i	$-0.339031\pi$
$564$	−633.145	−	629.943i	−1.12260	−	1.11692i
$565$	1213.08			2.14704
$566$			37.5130i			0.0662775i
$567$	−214.295	+	2.17349i	−0.377945	+	0.00383332i
$568$	260.577			0.458762
$569$		−	690.429i		−	1.21341i	−0.794928	−	0.606704i	$-0.792491\pi$
$569$		−	690.429i		−	1.21341i	0.794928	−	0.606704i	$-0.207509\pi$
$570$	1408.60	−	1415.76i	2.47122	−	2.48379i
$571$	750.371			1.31413			0.657067	−	0.753832i	$-0.271797\pi$
$571$	750.371			1.31413			0.657067	+	0.753832i	$0.271797\pi$
$572$			123.585i			0.216058i
$573$	−567.777	−	564.905i	−0.990885	−	0.985872i
$574$	−364.417			−0.634873
$575$		−	252.151i		−	0.438523i
$576$	−4.11820	−	812.087i	−0.00714965	−	1.40987i
$577$	−902.929			−1.56487			−0.782434	−	0.622734i	$-0.786022\pi$
$577$	−902.929			−1.56487			−0.782434	+	0.622734i	$0.786022\pi$
$578$			758.742i			1.31270i
$579$	−72.4102	+	72.7783i	−0.125061	+	0.125697i
$580$	−1090.73			−1.88057
$581$		−	179.430i		−	0.308829i
$582$	726.310	+	722.636i	1.24796	+	1.24164i
$583$	−1198.20			−2.05523
$584$		−	1274.43i		−	2.18224i
$585$	−99.8551	+	0.506379i	−0.170692	+	0.000865605i
$586$	1500.20			2.56006
$587$		−	339.782i		−	0.578845i	−0.957202	−	0.289422i	$-0.906537\pi$
$587$		−	339.782i		−	0.578845i	0.957202	−	0.289422i	$-0.0934632\pi$
$588$	108.053	−	108.602i	0.183764	−	0.184698i
$589$	−700.723			−1.18968
$590$		−	2566.17i		−	4.34943i
$591$	158.536	+	157.734i	0.268250	+	0.266893i
$592$	−478.206			−0.807781
$593$		−	542.064i		−	0.914104i	−0.889440	−	0.457052i	$-0.848905\pi$
$593$		−	542.064i		−	0.914104i	0.889440	−	0.457052i	$-0.151095\pi$
$594$	869.436	+	856.309i	1.46370	+	1.44160i
$595$	528.711			0.888589
$596$		−	531.693i		−	0.892102i
$597$	−634.024	+	637.247i	−1.06202	+	1.06742i
$598$	−20.3038			−0.0339528
$599$			671.144i			1.12044i	0.828343	+	0.560221i	$0.189284\pi$
$599$			671.144i			1.12044i	−0.828343	+	0.560221i	$0.810716\pi$
$600$	1238.30	+	1232.04i	2.06384	+	2.05340i
$601$	331.609			0.551762			0.275881	−	0.961192i	$-0.411030\pi$
$601$	331.609			0.551762			0.275881	+	0.961192i	$0.411030\pi$
$602$			232.608i			0.386391i
$603$	1.97981	+	390.408i	0.00328327	+	0.647442i
$604$	1455.29			2.40942
$605$		−	527.179i		−	0.871370i
$606$	−1198.41	+	1204.51i	−1.97758	+	1.98763i
$607$	−587.174			−0.967337			−0.483669	−	0.875251i	$-0.660696\pi$
$607$	−587.174			−0.967337			−0.483669	+	0.875251i	$0.660696\pi$
$608$		−	388.624i		−	0.639184i
$609$	95.5143	+	95.0311i	0.156838	+	0.156045i
$610$	−1380.86			−2.26371
$611$			51.4078i			0.0841372i
$612$	1489.62	−	7.55407i	2.43402	−	0.0123432i
$613$	−564.973			−0.921652			−0.460826	−	0.887490i	$-0.652447\pi$
$613$	−564.973			−0.921652			−0.460826	+	0.887490i	$0.652447\pi$
$614$		−	80.4810i		−	0.131076i
$615$	−763.787	+	767.670i	−1.24193	+	1.24824i
$616$	−394.039			−0.639674
$617$		−	429.821i		−	0.696630i	−0.937377	−	0.348315i	$-0.886754\pi$
$617$		−	429.821i		−	0.696630i	0.937377	−	0.348315i	$-0.113246\pi$
$618$	317.645	+	316.038i	0.513988	+	0.511388i
$619$	−20.0286			−0.0323563			−0.0161782	−	0.999869i	$-0.505150\pi$
$619$	−20.0286			−0.0323563			−0.0161782	+	0.999869i	$0.505150\pi$
$620$		−	2002.06i		−	3.22913i
$621$	−90.8623	+	92.2553i	−0.146316	+	0.148559i
$622$	420.803			0.676532
$623$			63.9810i			0.102698i
$624$	21.4274	−	21.5364i	0.0343388	−	0.0345134i
$625$	824.920			1.31987
$626$			755.162i			1.20633i
$627$	643.191	+	639.938i	1.02582	+	1.02063i
$628$	637.572			1.01524
$629$			1349.63i			2.14568i
$630$	−3.57441	−	704.854i	−0.00567367	−	1.11882i
$631$	1132.60			1.79494			0.897468	−	0.441080i	$-0.145404\pi$
$631$	1132.60			1.79494			0.897468	+	0.441080i	$0.145404\pi$
$632$			182.321i			0.288483i
$633$	352.681	−	354.474i	0.557157	−	0.559990i
$634$	−76.6481			−0.120896
$635$		−	1659.51i		−	2.61340i
$636$	1382.31	+	1375.32i	2.17345	+	2.16246i
$637$	−8.81789			−0.0138428
$638$		−	767.229i		−	1.20255i
$639$	−211.761	+	1.07387i	−0.331394	+	0.00168054i
$640$	2062.22			3.22221
$641$			1216.82i			1.89832i	0.314801	+	0.949158i	$0.398062\pi$
$641$			1216.82i			1.89832i	−0.314801	+	0.949158i	$0.601938\pi$
$642$	−268.801	+	270.167i	−0.418693	+	0.420822i
$643$	−1003.87			−1.56123			−0.780617	−	0.625010i	$-0.785095\pi$
$643$	−1003.87			−1.56123			−0.780617	+	0.625010i	$0.785095\pi$
$644$		−	92.5655i		−	0.143735i
$645$	490.004	+	487.525i	0.759696	+	0.755853i
$646$	1714.83			2.65453
$647$			28.5595i			0.0441415i	0.999756	+	0.0220707i	$0.00702590\pi$
$647$			28.5595i			0.0441415i	−0.999756	+	0.0220707i	$0.992974\pi$
$648$	−9.09778	−	896.993i	−0.0140398	−	1.38425i
$649$	1165.83			1.79635
$650$		−	222.592i		−	0.342449i
$651$	−174.432	+	175.319i	−0.267945	+	0.269307i
$652$	−157.456			−0.241496
$653$		−	864.905i		−	1.32451i	−0.749279	−	0.662255i	$-0.769600\pi$
$653$		−	864.905i		−	1.32451i	0.749279	−	0.662255i	$-0.230400\pi$
$654$	−952.473	−	947.655i	−1.45638	−	1.44901i
$655$	208.495			0.318314
$656$		−	329.461i		−	0.502228i
$657$	5.25208	+	1035.68i	0.00799404	+	1.57638i
$658$	−362.876			−0.551483
$659$		−	1027.66i		−	1.55942i	−0.626141	−	0.779710i	$-0.715366\pi$
$659$		−	1027.66i		−	1.55942i	0.626141	−	0.779710i	$-0.284634\pi$
$660$	−1828.39	+	1837.69i	−2.77029	+	2.78437i
$661$	−1112.24			−1.68267			−0.841334	−	0.540516i	$-0.818229\pi$
$661$	−1112.24			−1.68267			−0.841334	+	0.540516i	$0.818229\pi$
$662$		−	904.194i		−	1.36585i
$663$	−60.7818	−	60.4744i	−0.0916770	−	0.0912133i
$664$	751.055			1.13111
$665$		−	524.067i		−	0.788071i
$666$	1799.27	−	9.12436i	2.70161	−	0.0137002i
$667$	81.4102			0.122054
$668$			284.178i			0.425416i
$669$	−474.619	+	477.032i	−0.709446	+	0.713053i
$670$	−1284.09			−1.91655
$671$		−	627.337i		−	0.934929i
$672$	−97.2325	−	96.7407i	−0.144691	−	0.143959i
$673$	226.047			0.335880			0.167940	−	0.985797i	$-0.446289\pi$
$673$	226.047			0.335880			0.167940	+	0.985797i	$0.446289\pi$
$674$			1174.54i			1.74264i
$675$	−1011.40	−	996.130i	−1.49837	−	1.47575i
$676$	1221.31			1.80667
$677$			96.1876i			0.142079i	0.997473	+	0.0710396i	$0.0226317\pi$
$677$			96.1876i			0.142079i	−0.997473	+	0.0710396i	$0.977368\pi$
$678$	979.426	−	984.406i	1.44458	−	1.45193i
$679$	268.856			0.395959
$680$			2213.07i			3.25452i
$681$	−277.914	−	276.508i	−0.408097	−	0.406033i
$682$	1408.27			2.06491
$683$			135.612i			0.198554i	0.995060	+	0.0992770i	$0.0316530\pi$
$683$			135.612i			0.198554i	−0.995060	+	0.0992770i	$0.968347\pi$
$684$	−7.48773	−	1476.54i	−0.0109470	−	2.15868i
$685$	−1293.45			−1.88825
$686$		−	62.2435i		−	0.0907339i
$687$	−415.418	+	417.530i	−0.604684	+	0.607759i
$688$	−210.295			−0.305662
$689$		−	112.236i		−	0.162897i
$690$	−301.913	−	300.386i	−0.437555	−	0.435342i
$691$	735.737			1.06474			0.532371	−	0.846511i	$-0.321301\pi$
$691$	735.737			1.06474			0.532371	+	0.846511i	$0.321301\pi$
$692$		−	1455.37i		−	2.10314i
$693$	320.221	−	1.62388i	0.462079	−	0.00234327i
$694$	−1437.17			−2.07086
$695$			517.265i			0.744266i
$696$	−397.780	+	399.803i	−0.571524	+	0.574429i
$697$	−929.834			−1.33405
$698$			607.440i			0.870258i
$699$	612.183	+	609.087i	0.875799	+	0.871369i
$700$	1014.80			1.44972
$701$		−	786.332i		−	1.12173i	−0.827908	−	0.560865i	$-0.810469\pi$
$701$		−	786.332i		−	1.12173i	0.827908	−	0.560865i	$-0.189531\pi$
$702$	−80.2109	+	81.4405i	−0.114261	+	0.116012i
$703$	1337.78			1.90296
$704$			1213.47i			1.72368i
$705$	−760.556	+	764.423i	−1.07880	+	1.08429i
$706$	−1471.00			−2.08357
$707$			445.868i			0.630648i
$708$	−1344.97	−	1338.17i	−1.89967	−	1.89007i
$709$	−667.393			−0.941316			−0.470658	−	0.882316i	$-0.655983\pi$
$709$	−667.393			−0.941316			−0.470658	+	0.882316i	$0.655983\pi$
$710$		−	696.502i		−	0.980988i
$711$	−0.751367	−	148.165i	−0.00105678	−	0.208390i
$712$	−267.811			−0.376139
$713$			149.430i			0.209580i
$714$	426.875	−	429.045i	0.597864	−	0.600903i
$715$	149.210			0.208685
$716$			1466.44i			2.04810i
$717$	105.969	+	105.433i	0.147794	+	0.147047i
$718$	1194.68			1.66390
$719$			215.327i			0.299481i	0.988725	+	0.149741i	$0.0478439\pi$
$719$			215.327i			0.299481i	−0.988725	+	0.149741i	$0.952156\pi$
$720$	637.243	−	3.23154i	0.885059	−	0.00448825i
$721$	117.582			0.163081
$722$		−	486.508i		−	0.673834i
$723$	−310.750	+	312.329i	−0.429806	+	0.431991i
$724$	−1561.76			−2.15713
$725$			892.505i			1.23104i
$726$	−427.802	−	425.638i	−0.589259	−	0.586278i
$727$	713.312			0.981172			0.490586	−	0.871393i	$-0.336783\pi$
$727$	713.312			0.981172			0.490586	+	0.871393i	$0.336783\pi$
$728$		−	36.9098i		−	0.0507003i
$729$	11.0900	+	728.916i	0.0152127	+	0.999884i
$730$	−3406.46			−4.66638
$731$			593.514i			0.811920i
$732$	−720.072	+	723.733i	−0.983705	+	0.988706i
$733$	89.2933			0.121819			0.0609095	−	0.998143i	$-0.480600\pi$
$733$	89.2933			0.121819			0.0609095	+	0.998143i	$0.480600\pi$
$734$			648.227i			0.883144i
$735$	−131.120	−	130.457i	−0.178395	−	0.177492i
$736$	−82.8747			−0.112601
$737$		−	583.372i		−	0.791549i
$738$	6.28625	+	1239.61i	0.00851796	+	1.67969i
$739$	−648.694			−0.877800			−0.438900	−	0.898536i	$-0.644632\pi$
$739$	−648.694			−0.877800			−0.438900	+	0.898536i	$0.644632\pi$
$740$			3822.23i			5.16517i
$741$	−59.9433	+	60.2480i	−0.0808951	+	0.0813064i
$742$	792.249			1.06772
$743$			416.240i			0.560216i	0.959969	+	0.280108i	$0.0903702\pi$
$743$			416.240i			0.560216i	−0.959969	+	0.280108i	$0.909630\pi$
$744$	−733.848	−	730.136i	−0.986354	−	0.981365i
$745$	−641.935			−0.861658
$746$		−	554.542i		−	0.743353i
$747$	−610.354	+	3.09519i	−0.817074	+	0.00414349i
$748$	−2225.88			−2.97578
$749$			100.007i			0.133521i
$750$	1727.28	−	1736.06i	2.30304	−	2.31475i
$751$	1120.12			1.49150			0.745752	−	0.666223i	$-0.232090\pi$
$751$	1120.12			1.49150			0.745752	+	0.666223i	$0.232090\pi$
$752$		−	328.068i		−	0.436260i
$753$	348.022	+	346.261i	0.462180	+	0.459842i
$754$	71.8668			0.0953140
$755$		−	1757.03i		−	2.32719i
$756$	−371.289	−	365.683i	−0.491124	−	0.483708i
$757$	76.0762			0.100497			0.0502485	−	0.998737i	$-0.483999\pi$
$757$	76.0762			0.100497			0.0502485	+	0.998737i	$0.483999\pi$
$758$			558.523i			0.736838i
$759$	136.468	−	137.162i	0.179799	−	0.180713i
$760$	2193.64			2.88636
$761$		−	341.557i		−	0.448827i	−0.974494	−	0.224413i	$-0.927953\pi$
$761$		−	341.557i		−	0.448827i	0.974494	−	0.224413i	$-0.0720466\pi$
$762$	−1346.68	−	1339.87i	−1.76730	−	1.75836i
$763$	−352.574			−0.462089
$764$		−	1947.64i		−	2.54927i
$765$	−9.12034	−	1798.48i	−0.0119220	−	2.35096i
$766$	133.499			0.174281
$767$			109.204i			0.142378i
$768$	901.300	−	905.882i	1.17357	−	1.17953i
$769$	18.2545			0.0237380			0.0118690	−	0.999930i	$-0.496222\pi$
$769$	18.2545			0.0237380			0.0118690	+	0.999930i	$0.496222\pi$
$770$			1053.24i			1.36784i
$771$	−974.487	−	969.558i	−1.26393	−	1.25753i
$772$	−249.651			−0.323382
$773$			1015.39i			1.31357i	0.754077	+	0.656786i	$0.228085\pi$
$773$			1015.39i			1.31357i	−0.754077	+	0.656786i	$0.771915\pi$
$774$	791.247	−	4.01252i	1.02228	−	0.00518413i
$775$	−1638.22			−2.11383
$776$			1125.38i			1.45023i
$777$	333.016	−	334.709i	0.428592	−	0.430771i
$778$	1672.23			2.14940
$779$			921.668i			1.18314i
$780$	−172.137	−	171.266i	−0.220688	−	0.219572i
$781$	316.426			0.405155
$782$		−	365.690i		−	0.467634i
$783$	321.614	−	326.544i	0.410746	−	0.417042i
$784$	56.2729			0.0717767
$785$		−	769.767i		−	0.980595i
$786$	168.337	−	169.193i	0.214169	−	0.215258i
$787$	−1042.10			−1.32415			−0.662074	−	0.749438i	$-0.730324\pi$
$787$	−1042.10			−1.32415			−0.662074	+	0.749438i	$0.730324\pi$
$788$			543.824i			0.690132i
$789$	364.256	+	362.413i	0.461668	+	0.459332i
$790$	487.330			0.616874
$791$		−	364.395i		−	0.460676i
$792$	6.79724	+	1340.38i	0.00858237	+	1.69240i
$793$	58.7630			0.0741021
$794$		−	1091.44i		−	1.37461i
$795$	1660.48	−	1668.93i	2.08866	−	2.09928i
$796$	−2185.95			−2.74616
$797$		−	418.253i		−	0.524785i	−0.964961	−	0.262392i	$-0.915489\pi$
$797$		−	418.253i		−	0.524785i	0.964961	−	0.262392i	$-0.0845115\pi$
$798$	−425.277	−	423.126i	−0.532929	−	0.530233i
$799$	−925.902			−1.15883
$800$		−	908.561i		−	1.13570i
$801$	217.640	−	1.10368i	0.271710	−	0.00137788i
$802$	1760.36			2.19497
$803$		−	1547.58i		−	1.92725i
$804$	−669.607	+	673.011i	−0.832845	+	0.837079i
$805$	−111.758			−0.138830
$806$			131.913i			0.163664i
$807$	−1057.59	−	1052.24i	−1.31052	−	1.30389i
$808$	−1866.31			−2.30979
$809$			13.0448i			0.0161246i	0.999967	+	0.00806230i	$0.00256634\pi$
$809$			13.0448i			0.0161246i	−0.999967	+	0.00806230i	$0.997434\pi$
$810$	−2397.60	+	24.3177i	−2.95999	+	0.0300218i
$811$	−72.2248			−0.0890565			−0.0445283	−	0.999008i	$-0.514178\pi$
$811$	−72.2248			−0.0890565			−0.0445283	+	0.999008i	$0.514178\pi$
$812$			327.642i			0.403500i
$813$	−115.163	+	115.749i	−0.141652	+	0.142372i
$814$	−2688.59			−3.30293
$815$			190.103i			0.233255i
$816$	387.890	+	385.928i	0.475355	+	0.472951i
$817$	588.301			0.720075
$818$			716.364i			0.875751i
$819$	0.152110	+	29.9953i	0.000185727	+	0.0366243i
$820$	−2633.33			−3.21138
$821$		−	1004.82i		−	1.22389i	−0.790899	−	0.611947i	$-0.790386\pi$
$821$		−	1004.82i		−	1.22389i	0.790899	−	0.611947i	$-0.209614\pi$
$822$	−1044.32	+	1049.63i	−1.27046	+	1.27692i
$823$	−486.089			−0.590631			−0.295316	−	0.955400i	$-0.595425\pi$
$823$	−486.089			−0.590631			−0.295316	+	0.955400i	$0.595425\pi$
$824$			492.172i			0.597296i
$825$	1503.71	+	1496.11i	1.82268	+	1.81346i
$826$	−770.845			−0.933226
$827$			730.154i			0.882895i	0.897287	+	0.441448i	$0.145535\pi$
$827$			730.154i			0.882895i	−0.897287	+	0.441448i	$0.854465\pi$
$828$	−314.874	+	1.59677i	−0.380283	+	0.00192847i
$829$	−866.748			−1.04553			−0.522767	−	0.852476i	$-0.675100\pi$
$829$	−866.748			−1.04553			−0.522767	+	0.852476i	$0.675100\pi$
$830$		−	2007.51i		−	2.41869i
$831$	1019.03	−	1024.21i	1.22626	−	1.23250i
$832$	−113.666			−0.136618
$833$		−	158.818i		−	0.190658i
$834$	419.757	+	417.634i	0.503306	+	0.500760i
$835$	343.100			0.410898
$836$			2206.34i			2.63916i
$837$	599.380	+	590.330i	0.716105	+	0.705292i
$838$	2571.26			3.06833
$839$			401.463i			0.478501i	0.970958	+	0.239251i	$0.0769018\pi$
$839$			401.463i			0.478501i	−0.970958	+	0.239251i	$0.923098\pi$
$840$	546.065	−	548.841i	0.650078	−	0.653383i
$841$	552.843			0.657364
$842$			2273.29i			2.69987i
$843$	−678.250	−	674.819i	−0.804567	−	0.800498i
$844$	1215.95			1.44070
$845$		−	1474.54i		−	1.74502i
$846$	6.25967	+	1234.37i	0.00739913	+	1.45907i
$847$	−158.358			−0.186964
$848$			716.254i			0.844640i
$849$	23.6177	−	23.7378i	0.0278183	−	0.0279597i
$850$	4009.09			4.71657
$851$		−	285.284i		−	0.335234i
$852$	−365.048	−	363.201i	−0.428460	−	0.426293i
$853$	−2.24314			−0.00262971			−0.00131485	−	0.999999i	$-0.500419\pi$
$853$	−2.24314			−0.00262971			−0.00131485	+	0.999999i	$0.500419\pi$
$854$			414.794i			0.485708i
$855$	−1782.69	+	9.04025i	−2.08501	+	0.0105734i
$856$	−418.609			−0.489029
$857$			969.003i			1.13069i	0.824854	+	0.565346i	$0.191257\pi$
$857$			969.003i			1.13069i	−0.824854	+	0.565346i	$0.808743\pi$
$858$	120.470	−	121.083i	0.140408	−	0.141122i
$859$	413.425			0.481286			0.240643	−	0.970614i	$-0.422642\pi$
$859$	413.425			0.481286			0.240643	+	0.970614i	$0.422642\pi$
$860$			1680.86i			1.95449i
$861$	230.599	+	229.432i	0.267827	+	0.266472i
$862$	1856.83			2.15410
$863$			1303.40i			1.51031i	0.655545	+	0.755156i	$0.272439\pi$
$863$			1303.40i			1.51031i	−0.655545	+	0.755156i	$0.727561\pi$
$864$	−327.399	+	332.419i	−0.378935	+	0.384744i
$865$	−1757.13			−2.03137
$866$			937.206i			1.08222i
$867$	477.694	−	480.122i	0.550973	−	0.553774i
$868$	−601.395			−0.692852
$869$			221.398i			0.254773i
$870$	1068.64	+	1063.24i	1.22833	+	1.22211i
$871$	54.6447			0.0627379
$872$		−	1475.80i		−	1.69243i
$873$	−4.63781	−	914.551i	−0.00531250	−	1.04760i
$874$	−362.478			−0.414735
$875$		−	642.634i		−	0.734438i
$876$	−1776.35	+	1785.38i	−2.02780	+	2.03810i
$877$	349.859			0.398927			0.199464	−	0.979905i	$-0.436080\pi$
$877$	349.859			0.398927			0.199464	+	0.979905i	$0.436080\pi$
$878$			1294.18i			1.47401i
$879$	−949.305	−	944.504i	−1.07998	−	1.07452i
$880$	−952.208			−1.08205
$881$		−	595.225i		−	0.675624i	−0.941214	−	0.337812i	$-0.890313\pi$
$881$		−	595.225i		−	0.675624i	0.941214	−	0.337812i	$-0.109687\pi$
$882$	−211.730	+	1.07371i	−0.240056	+	0.00121736i
$883$	6.25613			0.00708509			0.00354254	−	0.999994i	$-0.498872\pi$
$883$	6.25613			0.00708509			0.00354254	+	0.999994i	$0.498872\pi$
$884$		−	208.500i		−	0.235859i
$885$	−1615.62	+	1623.84i	−1.82556	+	1.83485i
$886$	1063.99			1.20089
$887$			1090.79i			1.22975i	0.788624	+	0.614876i	$0.210794\pi$
$887$			1090.79i			1.22975i	−0.788624	+	0.614876i	$0.789206\pi$
$888$	1401.02	+	1393.94i	1.57773	+	1.56975i
$889$	−498.497			−0.560739
$890$			715.838i			0.804313i
$891$	−11.0477	−	1089.25i	−0.0123992	−	1.22250i
$892$	−1636.36			−1.83449
$893$			917.770i			1.02774i
$894$	−518.291	+	520.926i	−0.579743	+	0.582691i
$895$	1770.49			1.97820
$896$		−	619.465i		−	0.691367i
$897$	12.8480	+	12.7830i	0.0143233	+	0.0142508i
$898$	−1233.04			−1.37309
$899$		−	528.919i		−	0.588342i
$900$	−17.5055	−	3451.99i	−0.0194506	−	3.83554i
$901$	2021.48			2.24359
$902$		−	1852.31i		−	2.05356i
$903$	146.447	−	147.191i	0.162178	−	0.163002i
$904$	1525.28			1.68726
$905$			1885.58i			2.08352i
$906$	−1425.82	−	1418.61i	−1.57375	−	1.56579i
$907$	521.896			0.575409			0.287705	−	0.957719i	$-0.407108\pi$
$907$	521.896			0.575409			0.287705	+	0.957719i	$0.407108\pi$
$908$		−	953.328i		−	1.04992i
$909$	1516.68	−	7.69129i	1.66852	−	0.00846127i
$910$	−98.6573			−0.108415
$911$		−	868.186i		−	0.953003i	−0.879174	−	0.476502i	$-0.841905\pi$
$911$		−	868.186i		−	0.953003i	0.879174	−	0.476502i	$-0.158095\pi$
$912$	382.538	−	384.483i	0.419450	−	0.421583i
$913$	912.029			0.998937
$914$			1643.71i			1.79837i
$915$	873.793	+	869.373i	0.954965	+	0.950135i
$916$	−1432.25			−1.56359
$917$		−	62.6295i		−	0.0682982i
$918$	−1466.82	−	1444.67i	−1.59784	−	1.57372i
$919$	1167.04			1.26990			0.634950	−	0.772553i	$-0.281021\pi$
$919$	1167.04			1.26990			0.634950	+	0.772553i	$0.281021\pi$
$920$		−	467.797i		−	0.508475i
$921$	−50.6697	+	50.9273i	−0.0550160	+	0.0552957i
$922$	−314.335			−0.340927
$923$			29.6398i			0.0321125i
$924$	552.019	+	549.226i	0.597423	+	0.594401i
$925$	3127.59			3.38118
$926$			665.884i			0.719097i
$927$	−2.02830	−	399.970i	−0.00218803	−	0.431467i
$928$	293.341			0.316100
$929$			841.414i			0.905720i	0.891582	+	0.452860i	$0.149596\pi$
$929$			841.414i			0.905720i	−0.891582	+	0.452860i	$0.850404\pi$
$930$	−1951.60	+	1961.52i	−2.09849	+	2.10916i
$931$	−157.423			−0.169091
$932$			2099.97i			2.25319i
$933$	−266.279	−	264.932i	−0.285401	−	0.283957i
$934$	−1803.36			−1.93079
$935$			2687.40i			2.87423i
$936$	−125.554	+	0.636701i	−0.134139	+	0.000680236i
$937$	784.059			0.836776			0.418388	−	0.908268i	$-0.362595\pi$
$937$	784.059			0.836776			0.418388	+	0.908268i	$0.362595\pi$
$938$			385.724i			0.411220i
$939$	475.440	−	477.857i	0.506326	−	0.508900i
$940$	−2622.20			−2.78957
$941$		−	350.364i		−	0.372332i	−0.982518	−	0.186166i	$-0.940394\pi$
$941$		−	350.364i		−	0.372332i	0.982518	−	0.186166i	$-0.0596062\pi$
$942$	−624.661	−	621.501i	−0.663122	−	0.659768i
$943$	196.547			0.208428
$944$		−	696.904i		−	0.738245i
$945$	−441.505	+	448.273i	−0.467201	+	0.474363i
$946$	−1182.33			−1.24982
$947$		−	931.588i		−	0.983725i	−0.870673	−	0.491863i	$-0.836316\pi$
$947$		−	931.588i		−	0.983725i	0.870673	−	0.491863i	$-0.163684\pi$
$948$	254.126	−	255.418i	0.268065	−	0.269428i
$949$	144.963			0.152753
$950$		−	3973.88i		−	4.18303i
$951$	48.5019	+	48.2566i	0.0510010	+	0.0507430i
$952$	664.780			0.698298
$953$			778.526i			0.816921i	0.912776	+	0.408460i	$0.133934\pi$
$953$			778.526i			0.816921i	−0.912776	+	0.408460i	$0.866066\pi$
$954$	−13.6664	−	2694.94i	−0.0143254	−	2.82489i
$955$	−2351.47			−2.46227
$956$			363.504i			0.380234i
$957$	−483.037	+	485.493i	−0.504741	+	0.507307i
$958$	−928.040			−0.968727
$959$			388.537i			0.405148i
$960$	−1690.19	−	1681.65i	−1.76062	−	1.75171i
$961$	9.84396			0.0102434
$962$		−	251.841i		−	0.261789i
$963$	340.188	−	1.72514i	0.353258	−	0.00179142i
$964$	−1071.38			−1.11139
$965$			301.414i			0.312347i
$966$	−90.2323	+	90.6910i	−0.0934082	+	0.0938830i
$967$	1465.67			1.51569			0.757846	−	0.652433i	$-0.226252\pi$
$967$	1465.67			1.51569			0.757846	+	0.652433i	$0.226252\pi$
$968$		−	662.854i		−	0.684767i
$969$	−1085.12	−	1079.63i	−1.11984	−	1.11417i
$970$	3008.04			3.10108
$971$		−	736.835i		−	0.758842i	−0.925224	−	0.379421i	$-0.876123\pi$
$971$		−	736.835i		−	0.758842i	0.925224	−	0.379421i	$-0.123877\pi$
$972$	−1237.52	+	1269.30i	−1.27317	+	1.30586i
$973$	155.380			0.159692
$974$		−	1463.19i		−	1.50225i
$975$	−140.141	+	140.853i	−0.143734	+	0.144465i
$976$	−375.006			−0.384228
$977$		−	1802.02i		−	1.84444i	−0.386663	−	0.922221i	$-0.626372\pi$
$977$		−	1802.02i		−	1.84444i	0.386663	−	0.922221i	$-0.373628\pi$
$978$	154.267	+	153.487i	0.157737	+	0.156939i
$979$	−325.211			−0.332187
$980$		−	449.781i		−	0.458960i
$981$	6.08196	+	1199.33i	0.00619976	+	1.22256i
$982$	1298.81			1.32262
$983$		−	725.398i		−	0.737943i	−0.929441	−	0.368971i	$-0.879710\pi$
$983$		−	725.398i		−	0.737943i	0.929441	−	0.368971i	$-0.120290\pi$
$984$	−960.355	+	965.238i	−0.975971	+	0.980933i
$985$	656.582			0.666580
$986$			1294.39i			1.31276i
$987$	229.623	+	228.462i	0.232648	+	0.231471i
$988$	−206.669			−0.209179
$989$		−	125.456i		−	0.126852i
$990$	3582.73	−	18.1685i	3.61892	−	0.0183520i
$991$	−11.3021			−0.0114047			−0.00570235	−	0.999984i	$-0.501815\pi$
$991$	−11.3021			−0.0114047			−0.00570235	+	0.999984i	$0.501815\pi$
$992$			538.434i			0.542777i
$993$	−569.269	+	572.163i	−0.573282	+	0.576196i
$994$	−209.221			−0.210484
$995$			2639.19i			2.65245i
$996$	−1052.17	−	1046.85i	−1.05640	−	1.05105i
$997$	−1484.68			−1.48914			−0.744571	−	0.667543i	$-0.767346\pi$
$997$	−1484.68			−1.48914			−0.744571	+	0.667543i	$0.767346\pi$
$998$		−	1427.13i		−	1.42999i
$999$	−1144.30	−	1127.03i	−1.14545	−	1.12815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.9	✓	88
3.2	odd	2	inner	483.3.b.a.323.80	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.9	✓	88	1.1	even	1	trivial
483.3.b.a.323.80	yes	88	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.36083i q^{2} +(-2.11593 + 2.12669i) q^{3} -7.29519 q^{4} +8.80778i q^{5} +(7.14745 + 7.11130i) q^{6} +2.64575 q^{7} +11.0746i q^{8} +(-0.0456396 - 8.99988i) q^{9} +O(q^{10})\)	\(q-3.36083i q^{2} +(-2.11593 + 2.12669i) q^{3} -7.29519 q^{4} +8.80778i q^{5} +(7.14745 + 7.11130i) q^{6} +2.64575 q^{7} +11.0746i q^{8} +(-0.0456396 - 8.99988i) q^{9} +29.6015 q^{10} +13.4482i q^{11} +(15.4361 - 15.5146i) q^{12} -1.25970 q^{13} -8.89192i q^{14} +(-18.7314 - 18.6367i) q^{15} +8.03899 q^{16} -22.6883i q^{17} +(-30.2471 + 0.153387i) q^{18} -22.4891 q^{19} -64.2544i q^{20} +(-5.59824 + 5.62670i) q^{21} +45.1971 q^{22} +4.79583i q^{23} +(-23.5522 - 23.4330i) q^{24} -52.5770 q^{25} +4.23363i q^{26} +(19.2366 + 18.9461i) q^{27} -19.3012 q^{28} -16.9752i q^{29} +(-62.6348 + 62.9532i) q^{30} +31.1584 q^{31} +17.2806i q^{32} +(-28.6002 - 28.4555i) q^{33} -76.2516 q^{34} +23.3032i q^{35} +(0.332950 + 65.6558i) q^{36} -59.4859 q^{37} +75.5820i q^{38} +(2.66544 - 2.67899i) q^{39} -97.5423 q^{40} -40.9829i q^{41} +(18.9104 + 18.8147i) q^{42} -26.1594 q^{43} -98.1070i q^{44} +(79.2690 - 0.401984i) q^{45} +16.1180 q^{46} -40.8096i q^{47} +(-17.0100 + 17.0964i) q^{48} +7.00000 q^{49} +176.703i q^{50} +(48.2511 + 48.0070i) q^{51} +9.18974 q^{52} +89.0976i q^{53} +(63.6747 - 64.6508i) q^{54} -118.449 q^{55} +29.3005i q^{56} +(47.5854 - 47.8273i) q^{57} -57.0507 q^{58} -86.6905i q^{59} +(136.649 + 135.958i) q^{60} -46.6485 q^{61} -104.718i q^{62} +(-0.120751 - 23.8115i) q^{63} +90.2330 q^{64} -11.0952i q^{65} +(-95.6341 + 96.1203i) q^{66} -43.3792 q^{67} +165.516i q^{68} +(-10.1993 - 10.1477i) q^{69} +78.3181 q^{70} -23.5293i q^{71} +(99.6698 - 0.505439i) q^{72} -115.077 q^{73} +199.922i q^{74} +(111.250 - 111.815i) q^{75} +164.062 q^{76} +35.5806i q^{77} +(-9.00364 - 8.95810i) q^{78} +16.4630 q^{79} +70.8057i q^{80} +(-80.9958 + 0.821503i) q^{81} -137.737 q^{82} -67.8180i q^{83} +(40.8402 - 41.0478i) q^{84} +199.834 q^{85} +87.9174i q^{86} +(36.1010 + 35.9184i) q^{87} -148.933 q^{88} +24.1825i q^{89} +(-1.35100 - 266.410i) q^{90} -3.33285 q^{91} -34.9865i q^{92} +(-65.9291 + 66.2643i) q^{93} -137.154 q^{94} -198.079i q^{95} +(-36.7504 - 36.5646i) q^{96} +101.618 q^{97} -23.5258i q^{98} +(121.032 - 0.613770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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