LMFDB - Embedded newform 354.4.c.a.353.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,4,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	354.c (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:	$20.8866761420$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.12
Character	$\chi$	$=$	354.353
Dual form			354.4.c.a.353.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +(-1.90975 + 4.83248i) q^{3} +4.00000 q^{4} -5.55280i q^{5} +(3.81949 - 9.66496i) q^{6} +16.8053 q^{7} -8.00000 q^{8} +(-19.7057 - 18.4576i) q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +(-1.90975 + 4.83248i) q^{3} +4.00000 q^{4} -5.55280i q^{5} +(3.81949 - 9.66496i) q^{6} +16.8053 q^{7} -8.00000 q^{8} +(-19.7057 - 18.4576i) q^{9} +11.1056i q^{10} -29.9926 q^{11} +(-7.63899 + 19.3299i) q^{12} +44.4463i q^{13} -33.6106 q^{14} +(26.8338 + 10.6045i) q^{15} +16.0000 q^{16} -29.8647i q^{17} +(39.4115 + 36.9153i) q^{18} +60.7611 q^{19} -22.2112i q^{20} +(-32.0938 + 81.2112i) q^{21} +59.9853 q^{22} +12.0075 q^{23} +(15.2780 - 38.6598i) q^{24} +94.1664 q^{25} -88.8925i q^{26} +(126.829 - 59.9782i) q^{27} +67.2211 q^{28} +182.868i q^{29} +(-53.6676 - 21.2089i) q^{30} +48.1002i q^{31} -32.0000 q^{32} +(57.2784 - 144.939i) q^{33} +59.7294i q^{34} -93.3165i q^{35} +(-78.8229 - 73.8305i) q^{36} +47.9852i q^{37} -121.522 q^{38} +(-214.786 - 84.8811i) q^{39} +44.4224i q^{40} +345.220i q^{41} +(64.1877 - 162.422i) q^{42} +171.705i q^{43} -119.971 q^{44} +(-102.492 + 109.422i) q^{45} -24.0150 q^{46} -611.923 q^{47} +(-30.5559 + 77.3197i) q^{48} -60.5825 q^{49} -188.333 q^{50} +(144.321 + 57.0340i) q^{51} +177.785i q^{52} +20.9097i q^{53} +(-253.658 + 119.956i) q^{54} +166.543i q^{55} -134.442 q^{56} +(-116.038 + 293.627i) q^{57} -365.736i q^{58} +(-250.470 + 377.682i) q^{59} +(107.335 + 42.4178i) q^{60} +24.9730i q^{61} -96.2004i q^{62} +(-331.160 - 310.186i) q^{63} +64.0000 q^{64} +246.801 q^{65} +(-114.557 + 289.878i) q^{66} -48.4157i q^{67} -119.459i q^{68} +(-22.9313 + 58.0260i) q^{69} +186.633i q^{70} +89.7055i q^{71} +(157.646 + 147.661i) q^{72} +262.627i q^{73} -95.9705i q^{74} +(-179.834 + 455.057i) q^{75} +243.044 q^{76} -504.035 q^{77} +(429.571 + 169.762i) q^{78} -762.943 q^{79} -88.8449i q^{80} +(47.6319 + 727.442i) q^{81} -690.440i q^{82} +47.0013 q^{83} +(-128.375 + 324.845i) q^{84} -165.833 q^{85} -343.410i q^{86} +(-883.706 - 349.232i) q^{87} +239.941 q^{88} -237.332 q^{89} +(204.983 - 218.844i) q^{90} +746.932i q^{91} +48.0300 q^{92} +(-232.443 - 91.8592i) q^{93} +1223.85 q^{94} -337.394i q^{95} +(61.1119 - 154.639i) q^{96} +1120.03i q^{97} +121.165 q^{98} +(591.027 + 553.593i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$	−1.90975	+	4.83248i	−0.367531	+	0.930011i
$3$	−1.90975	+	4.83248i	−0.367531	+	0.930011i
$4$	4.00000			0.500000
$5$		−	5.55280i		−	0.496658i	−0.968676	−	0.248329i	$-0.920119\pi$
$5$		−	5.55280i		−	0.496658i	0.968676	−	0.248329i	$-0.0798814\pi$
$6$	3.81949	−	9.66496i	0.259884	−	0.657617i
$7$	16.8053			0.907400			0.453700	−	0.891154i	$-0.350104\pi$
$7$	16.8053			0.907400			0.453700	+	0.891154i	$0.350104\pi$
$8$	−8.00000			−0.353553
$9$	−19.7057	−	18.4576i	−0.729842	−	0.683616i
$10$			11.1056i			0.351190i
$11$	−29.9926			−0.822102			−0.411051	−	0.911612i	$-0.634838\pi$
$11$	−29.9926			−0.822102			−0.411051	+	0.911612i	$0.634838\pi$
$12$	−7.63899	+	19.3299i	−0.183765	+	0.465006i
$13$			44.4463i			0.948244i	0.880459	+	0.474122i	$0.157235\pi$
$13$			44.4463i			0.948244i	−0.880459	+	0.474122i	$0.842765\pi$
$14$	−33.6106			−0.641629
$15$	26.8338	+	10.6045i	0.461898	+	0.182537i
$16$	16.0000			0.250000
$17$		−	29.8647i		−	0.426074i	−0.977044	−	0.213037i	$-0.931665\pi$
$17$		−	29.8647i		−	0.426074i	0.977044	−	0.213037i	$-0.0683355\pi$
$18$	39.4115	+	36.9153i	0.516076	+	0.483389i
$19$	60.7611			0.733661			0.366830	−	0.930288i	$-0.380443\pi$
$19$	60.7611			0.733661			0.366830	+	0.930288i	$0.380443\pi$
$20$		−	22.2112i		−	0.248329i
$21$	−32.0938	+	81.2112i	−0.333498	+	0.843892i
$22$	59.9853			0.581314
$23$	12.0075			0.108858			0.0544291	−	0.998518i	$-0.482666\pi$
$23$	12.0075			0.108858			0.0544291	+	0.998518i	$0.482666\pi$
$24$	15.2780	−	38.6598i	0.129942	−	0.328809i
$25$	94.1664			0.753331
$26$		−	88.8925i		−	0.670510i
$27$	126.829	−	59.9782i	0.904010	−	0.427511i
$28$	67.2211			0.453700
$29$			182.868i			1.17096i	0.810688	+	0.585478i	$0.199093\pi$
$29$			182.868i			1.17096i	−0.810688	+	0.585478i	$0.800907\pi$
$30$	−53.6676	−	21.2089i	−0.326611	−	0.129073i
$31$			48.1002i			0.278679i	0.990245	+	0.139339i	$0.0444979\pi$
$31$			48.1002i			0.278679i	−0.990245	+	0.139339i	$0.955502\pi$
$32$	−32.0000			−0.176777
$33$	57.2784	−	144.939i	0.302148	−	0.764564i
$34$			59.7294i			0.301280i
$35$		−	93.3165i		−	0.450667i
$36$	−78.8229	−	73.8305i	−0.364921	−	0.341808i
$37$			47.9852i			0.213209i	0.994302	+	0.106604i	$0.0339978\pi$
$37$			47.9852i			0.213209i	−0.994302	+	0.106604i	$0.966002\pi$
$38$	−121.522			−0.518776
$39$	−214.786	−	84.8811i	−0.881878	−	0.348509i
$40$			44.4224i			0.175595i
$41$			345.220i			1.31498i	0.753462	+	0.657491i	$0.228382\pi$
$41$			345.220i			1.31498i	−0.753462	+	0.657491i	$0.771618\pi$
$42$	64.1877	−	162.422i	0.235818	−	0.596722i
$43$			171.705i			0.608949i	0.952521	+	0.304474i	$0.0984808\pi$
$43$			171.705i			0.608949i	−0.952521	+	0.304474i	$0.901519\pi$
$44$	−119.971			−0.411051
$45$	−102.492	+	109.422i	−0.339523	+	0.362482i
$46$	−24.0150			−0.0769744
$47$	−611.923			−1.89911			−0.949554	−	0.313603i	$-0.898464\pi$
$47$	−611.923			−1.89911			−0.949554	+	0.313603i	$0.898464\pi$
$48$	−30.5559	+	77.3197i	−0.0918827	+	0.232503i
$49$	−60.5825			−0.176625
$50$	−188.333			−0.532685
$51$	144.321	+	57.0340i	0.396253	+	0.156595i
$52$			177.785i			0.474122i
$53$			20.9097i			0.0541919i	0.999633	+	0.0270959i	$0.00862596\pi$
$53$			20.9097i			0.0541919i	−0.999633	+	0.0270959i	$0.991374\pi$
$54$	−253.658	+	119.956i	−0.639232	+	0.302296i
$55$			166.543i			0.408304i
$56$	−134.442			−0.320814
$57$	−116.038	+	293.627i	−0.269643	+	0.682313i
$58$		−	365.736i		−	0.827991i
$59$	−250.470	+	377.682i	−0.552685	+	0.833390i
$59$	−250.470	+	377.682i	−0.552685	+	0.833390i
$60$	107.335	+	42.4178i	0.230949	+	0.0912686i
$61$			24.9730i			0.0524175i	0.999656	+	0.0262088i	$0.00834346\pi$
$61$			24.9730i			0.0524175i	−0.999656	+	0.0262088i	$0.991657\pi$
$62$		−	96.2004i		−	0.197056i
$63$	−331.160	−	310.186i	−0.662259	−	0.620313i
$64$	64.0000			0.125000
$65$	246.801			0.470953
$66$	−114.557	+	289.878i	−0.213651	+	0.540629i
$67$		−	48.4157i		−	0.0882823i	−0.999025	−	0.0441412i	$-0.985945\pi$
$67$		−	48.4157i		−	0.0882823i	0.999025	−	0.0441412i	$-0.0140551\pi$
$68$		−	119.459i		−	0.213037i
$69$	−22.9313	+	58.0260i	−0.0400088	+	0.101239i
$70$			186.633i			0.318670i
$71$			89.7055i			0.149945i	0.997186	+	0.0749724i	$0.0238869\pi$
$71$			89.7055i			0.149945i	−0.997186	+	0.0749724i	$0.976113\pi$
$72$	157.646	+	147.661i	0.258038	+	0.241695i
$73$			262.627i			0.421071i	0.977586	+	0.210536i	$0.0675208\pi$
$73$			262.627i			0.421071i	−0.977586	+	0.210536i	$0.932479\pi$
$74$		−	95.9705i		−	0.150761i
$75$	−179.834	+	455.057i	−0.276872	+	0.700606i
$76$	243.044			0.366830
$77$	−504.035			−0.745975
$78$	429.571	+	169.762i	0.623582	+	0.246433i
$79$	−762.943			−1.08655			−0.543277	−	0.839553i	$-0.682817\pi$
$79$	−762.943			−1.08655			−0.543277	+	0.839553i	$0.682817\pi$
$80$		−	88.8449i		−	0.124164i
$81$	47.6319	+	727.442i	0.0653387	+	0.997863i
$82$		−	690.440i		−	0.929833i
$83$	47.0013			0.0621574			0.0310787	−	0.999517i	$-0.490106\pi$
$83$	47.0013			0.0621574			0.0310787	+	0.999517i	$0.490106\pi$
$84$	−128.375	+	324.845i	−0.166749	+	0.421946i
$85$	−165.833			−0.211613
$86$		−	343.410i		−	0.430592i
$87$	−883.706	−	349.232i	−1.08900	−	0.430363i
$88$	239.941			0.290657
$89$	−237.332			−0.282665			−0.141332	−	0.989962i	$-0.545139\pi$
$89$	−237.332			−0.282665			−0.141332	+	0.989962i	$0.545139\pi$
$90$	204.983	−	218.844i	0.240079	−	0.256313i
$91$			746.932i			0.860437i
$92$	48.0300			0.0544291
$93$	−232.443	−	91.8592i	−0.259175	−	0.102423i
$94$	1223.85			1.34287
$95$		−	337.394i		−	0.364378i
$96$	61.1119	−	154.639i	0.0649709	−	0.164404i
$97$			1120.03i			1.17239i	0.810171	+	0.586193i	$0.199374\pi$
$97$			1120.03i			1.17239i	−0.810171	+	0.586193i	$0.800626\pi$
$98$	121.165			0.124893
$99$	591.027	+	553.593i	0.600005	+	0.562002i
$100$	376.665			0.376665
$101$	1492.10			1.47000			0.734998	−	0.678070i	$-0.237183\pi$
$101$	1492.10			1.47000			0.734998	+	0.678070i	$0.237183\pi$
$102$	−288.641	−	114.068i	−0.280193	−	0.110730i
$103$			842.378i			0.805844i	0.915234	+	0.402922i	$0.132005\pi$
$103$			842.378i			0.805844i	−0.915234	+	0.402922i	$0.867995\pi$
$104$		−	355.570i		−	0.335255i
$105$	450.950	+	178.211i	0.419126	+	0.165634i
$106$		−	41.8194i		−	0.0383194i
$107$			16.8432i			0.0152177i	0.999971	+	0.00760884i	$0.00242199\pi$
$107$			16.8432i			0.0152177i	−0.999971	+	0.00760884i	$0.997578\pi$
$108$	507.316	−	239.913i	0.452005	−	0.213756i
$109$			1746.40i			1.53463i	0.641271	+	0.767314i	$0.278407\pi$
$109$			1746.40i			1.53463i	−0.641271	+	0.767314i	$0.721593\pi$
$110$		−	333.087i		−	0.288714i
$111$	−231.888	−	91.6397i	−0.198287	−	0.0783608i
$112$	268.885			0.226850
$113$	−468.120			−0.389709			−0.194854	−	0.980832i	$-0.562423\pi$
$113$	−468.120			−0.389709			−0.194854	+	0.980832i	$0.562423\pi$
$114$	232.077	−	587.254i	0.190666	−	0.482468i
$115$		−	66.6753i		−	0.0540653i
$116$			731.472i			0.585478i
$117$	820.373	−	875.846i	0.648235	−	0.692069i
$118$	500.940	−	755.364i	0.390808	−	0.589296i
$119$		−	501.885i		−	0.386619i
$120$	−214.671	−	84.8356i	−0.163305	−	0.0645366i
$121$	−431.441			−0.324148
$122$		−	49.9461i		−	0.0370648i
$123$	−1668.27	−	659.283i	−1.22295	−	0.483297i
$124$			192.401i			0.139339i
$125$		−	1216.99i		−	0.870806i
$126$	662.321	+	620.371i	0.468288	+	0.438628i
$127$	−901.184			−0.629663			−0.314831	−	0.949148i	$-0.601948\pi$
$127$	−901.184			−0.629663			−0.314831	+	0.949148i	$0.601948\pi$
$128$	−128.000			−0.0883883
$129$	−829.762	−	327.913i	−0.566329	−	0.223808i
$130$	−493.603			−0.333014
$131$	1853.34			1.23609			0.618043	−	0.786144i	$-0.287926\pi$
$131$	1853.34			1.23609			0.618043	+	0.786144i	$0.287926\pi$
$132$	229.113	−	579.755i	0.151074	−	0.382282i
$133$	1021.11			0.665724
$134$			96.8314i			0.0624250i
$135$	−333.047	−	704.257i	−0.212327	−	0.448984i
$136$			238.918i			0.150640i
$137$		−	743.121i		−	0.463424i	−0.972784	−	0.231712i	$-0.925567\pi$
$137$		−	743.121i		−	0.463424i	0.972784	−	0.231712i	$-0.0744327\pi$
$138$	45.8626	−	116.052i	0.0282905	−	0.0715870i
$139$	−54.3986			−0.0331945			−0.0165972	−	0.999862i	$-0.505283\pi$
$139$	−54.3986			−0.0331945			−0.0165972	+	0.999862i	$0.505283\pi$
$140$		−	373.266i		−	0.225334i
$141$	1168.62	−	2957.10i	0.697981	−	1.76619i
$142$		−	179.411i		−	0.106027i
$143$		−	1333.06i		−	0.779554i
$144$	−315.292	−	295.322i	−0.182461	−	0.170904i
$145$	1015.43			0.581565
$146$		−	525.255i		−	0.297742i
$147$	115.697	−	292.764i	0.0649153	−	0.164264i
$148$			191.941i			0.106604i
$149$	1356.96			0.746085			0.373042	−	0.927814i	$-0.378315\pi$
$149$	1356.96			0.746085			0.373042	+	0.927814i	$0.378315\pi$
$150$	359.668	−	910.114i	0.195778	−	0.495403i
$151$		−	650.275i		−	0.350455i	−0.984528	−	0.175227i	$-0.943934\pi$
$151$		−	650.275i		−	0.350455i	0.984528	−	0.175227i	$-0.0560660\pi$
$152$	−486.089			−0.259388
$153$	−551.232	+	588.506i	−0.291271	+	0.310967i
$154$	1008.07			0.527484
$155$	267.091			0.138408
$156$	−859.143	−	339.524i	−0.440939	−	0.174255i
$157$		−	3611.70i		−	1.83595i	−0.396634	−	0.917977i	$-0.629822\pi$
$157$		−	3611.70i		−	1.83595i	0.396634	−	0.917977i	$-0.370178\pi$
$158$	1525.89			0.768310
$159$	−101.046	−	39.9322i	−0.0503990	−	0.0199172i
$160$			177.690i			0.0877976i
$161$	201.790			0.0987779
$162$	−95.2638	−	1454.88i	−0.0462014	−	0.705596i
$163$	−2664.60			−1.28041			−0.640206	−	0.768203i	$-0.721151\pi$
$163$	−2664.60			−1.28041			−0.640206	+	0.768203i	$0.721151\pi$
$164$			1380.88i			0.657491i
$165$	−804.817	−	318.056i	−0.379727	−	0.150064i
$166$	−94.0026			−0.0439519
$167$			2490.52i			1.15403i	0.816735	+	0.577013i	$0.195782\pi$
$167$			2490.52i			1.15403i	−0.816735	+	0.577013i	$0.804218\pi$
$168$	256.751	−	649.690i	0.117909	−	0.298361i
$169$	221.529			0.100833
$170$	331.666			0.149633
$171$	−1197.34	−	1121.51i	−0.535456	−	0.501542i
$172$			686.821i			0.304474i
$173$	−836.030			−0.367412			−0.183706	−	0.982981i	$-0.558809\pi$
$173$	−836.030			−0.367412			−0.183706	+	0.982981i	$0.558809\pi$
$174$	1767.41	+	698.463i	0.770041	+	0.304312i
$175$	1582.49			0.683572
$176$	−479.882			−0.205526
$177$	−1346.81	−	1931.67i	−0.571933	−	0.820300i
$178$	474.664			0.199874
$179$	−1339.97			−0.559520			−0.279760	−	0.960070i	$-0.590255\pi$
$179$	−1339.97			−0.559520			−0.279760	+	0.960070i	$0.590255\pi$
$180$	−409.966	+	437.688i	−0.169762	+	0.181241i
$181$	4412.80			1.81216			0.906081	−	0.423105i	$-0.139060\pi$
$181$	4412.80			1.81216			0.906081	+	0.423105i	$0.139060\pi$
$182$		−	1493.86i		−	0.608421i
$183$	−120.682	−	47.6922i	−0.0487489	−	0.0192651i
$184$	−96.0601			−0.0384872
$185$	266.453			0.105892
$186$	464.886	+	183.718i	0.183264	+	0.0724241i
$187$			895.721i			0.350276i
$188$	−2447.69			−0.949554
$189$	2131.40	−	1007.95i	0.820299	−	0.387924i
$190$			674.789i			0.257654i
$191$	2265.08			0.858093			0.429046	−	0.903283i	$-0.358850\pi$
$191$	2265.08			0.858093			0.429046	+	0.903283i	$0.358850\pi$
$192$	−122.224	+	309.279i	−0.0459414	+	0.116251i
$193$	1267.75			0.472822			0.236411	−	0.971653i	$-0.424029\pi$
$193$	1267.75			0.472822			0.236411	+	0.971653i	$0.424029\pi$
$194$		−	2240.05i		−	0.829003i
$195$	−471.328	+	1192.66i	−0.173090	+	0.437992i
$196$	−242.330			−0.0883127
$197$			3551.01i			1.28426i	0.766596	+	0.642130i	$0.221949\pi$
$197$			3551.01i			1.28426i	−0.766596	+	0.642130i	$0.778051\pi$
$198$	−1182.05	−	1107.19i	−0.424267	−	0.397395i
$199$	−1153.88			−0.411039			−0.205519	−	0.978653i	$-0.565888\pi$
$199$	−1153.88			−0.411039			−0.205519	+	0.978653i	$0.565888\pi$
$200$	−753.331			−0.266343
$201$	233.968	+	92.4617i	0.0821036	+	0.0324465i
$202$	−2984.20			−1.03944
$203$			3073.15i			1.06253i
$204$	577.282	+	228.136i	0.198127	+	0.0782977i
$205$	1916.94			0.653097
$206$		−	1684.76i		−	0.569818i
$207$	−236.617	−	221.630i	−0.0794493	−	0.0744172i
$208$			711.140i			0.237061i
$209$	−1822.39			−0.603144
$210$	−901.900	−	356.422i	−0.296367	−	0.117121i
$211$			4380.52i			1.42923i	0.699518	+	0.714615i	$0.253398\pi$
$211$			4380.52i			1.42923i	−0.699518	+	0.714615i	$0.746602\pi$
$212$			83.6388i			0.0270959i
$213$	−433.500	−	171.315i	−0.139450	−	0.0551094i
$214$		−	33.6864i		−	0.0107605i
$215$	953.445			0.302439
$216$	−1014.63	+	479.825i	−0.319616	+	0.151148i
$217$			808.337i			0.252873i
$218$		−	3492.79i		−	1.08515i
$219$	−1269.14	−	501.552i	−0.391601	−	0.154757i
$220$			666.173i			0.204152i
$221$	1327.37			0.404022
$222$	463.775	+	183.279i	0.140210	+	0.0554095i
$223$	−1377.62			−0.413688			−0.206844	−	0.978374i	$-0.566319\pi$
$223$	−1377.62			−0.413688			−0.206844	+	0.978374i	$0.566319\pi$
$224$	−537.769			−0.160407
$225$	−1855.62	−	1738.09i	−0.549813	−	0.514989i
$226$	936.241			0.275566
$227$	3772.40			1.10301			0.551504	−	0.834172i	$-0.314054\pi$
$227$	3772.40			1.10301			0.551504	+	0.834172i	$0.314054\pi$
$228$	−464.153	+	1174.51i	−0.134821	+	0.341156i
$229$		−	3033.91i		−	0.875486i	−0.899100	−	0.437743i	$-0.855778\pi$
$229$		−	3033.91i		−	0.875486i	0.899100	−	0.437743i	$-0.144222\pi$
$230$			133.351i			0.0382299i
$231$	962.579	−	2435.74i	0.274169	−	0.693766i
$232$		−	1462.94i		−	0.413996i
$233$	6213.59			1.74706			0.873531	−	0.486768i	$-0.161824\pi$
$233$	6213.59			1.74706			0.873531	+	0.486768i	$0.161824\pi$
$234$	−1640.75	+	1751.69i	−0.458371	+	0.489366i
$235$			3397.89i			0.943207i
$236$	−1001.88	+	1510.73i	−0.276343	+	0.416695i
$237$	1457.03	−	3686.91i	0.399343	−	1.01051i
$238$			1003.77i			0.273381i
$239$			3748.99i			1.01465i	0.861754	+	0.507326i	$0.169366\pi$
$239$			3748.99i			1.01465i	−0.861754	+	0.507326i	$0.830634\pi$
$240$	429.341	+	169.671i	0.115474	+	0.0456343i
$241$	−3617.25			−0.966836			−0.483418	−	0.875390i	$-0.660605\pi$
$241$	−3617.25			−0.966836			−0.483418	+	0.875390i	$0.660605\pi$
$242$	862.883			0.229207
$243$	−3606.32	−	1159.05i	−0.952038	−	0.305980i
$244$			99.8921i			0.0262088i
$245$			336.403i			0.0877224i
$246$	3336.54	+	1318.57i	0.864755	+	0.341743i
$247$			2700.60i			0.695689i
$248$		−	384.802i		−	0.0985279i
$249$	−89.7605	+	227.133i	−0.0228448	+	0.0578070i
$250$			2433.98i			0.615753i
$251$		−	1567.55i		−	0.394194i	−0.980384	−	0.197097i	$-0.936849\pi$
$251$		−	1567.55i		−	0.394194i	0.980384	−	0.197097i	$-0.0631513\pi$
$252$	−1324.64	−	1240.74i	−0.331129	−	0.310157i
$253$	−360.137			−0.0894925
$254$	1802.37			0.445239
$255$	316.699	−	801.384i	0.0777743	−	0.196802i
$256$	256.000			0.0625000
$257$			2327.14i			0.564836i	0.959291	+	0.282418i	$0.0911366\pi$
$257$			2327.14i			0.564836i	−0.959291	+	0.282418i	$0.908863\pi$
$258$	1659.52	+	655.827i	0.400455	+	0.158256i
$259$			806.406i			0.193466i
$260$	987.206			0.235477
$261$	3375.31	−	3603.55i	0.800484	−	0.854613i
$262$	−3706.69			−0.874045
$263$			288.250i			0.0675827i	0.999429	+	0.0337914i	$0.0107582\pi$
$263$			288.250i			0.0675827i	−0.999429	+	0.0337914i	$0.989242\pi$
$264$	−458.227	+	1159.51i	−0.106825	+	0.270314i
$265$	116.107			0.0269148
$266$	−2042.21			−0.470738
$267$	453.244	−	1146.90i	0.103888	−	0.262881i
$268$		−	193.663i		−	0.0441412i
$269$	−4979.48			−1.12864			−0.564320	−	0.825556i	$-0.690862\pi$
$269$	−4979.48			−1.12864			−0.564320	+	0.825556i	$0.690862\pi$
$270$	666.094	+	1408.51i	0.150138	+	0.317479i
$271$	3392.62			0.760469			0.380234	−	0.924890i	$-0.375843\pi$
$271$	3392.62			0.760469			0.380234	+	0.924890i	$0.375843\pi$
$272$		−	477.835i		−	0.106518i
$273$	−3609.53	−	1426.45i	−0.800216	−	0.316237i
$274$			1486.24i			0.327690i
$275$	−2824.30			−0.619315
$276$	−91.7252	+	232.104i	−0.0200044	+	0.0506197i
$277$	3918.03			0.849862			0.424931	−	0.905226i	$-0.360298\pi$
$277$	3918.03			0.849862			0.424931	+	0.905226i	$0.360298\pi$
$278$	108.797			0.0234720
$279$	887.815	−	947.850i	0.190509	−	0.203392i
$280$			746.532i			0.159335i
$281$		−	3769.82i		−	0.800315i	−0.916446	−	0.400157i	$-0.868955\pi$
$281$		−	3769.82i		−	0.800315i	0.916446	−	0.400157i	$-0.131045\pi$
$282$	−2337.23	+	5914.21i	−0.493547	+	1.24889i
$283$		−	3936.77i		−	0.826914i	−0.910524	−	0.413457i	$-0.864321\pi$
$283$		−	3936.77i		−	0.826914i	0.910524	−	0.413457i	$-0.135679\pi$
$284$			358.822i			0.0749724i
$285$	1630.45	+	644.338i	0.338876	+	0.133920i
$286$			2666.12i			0.551228i
$287$			5801.52i			1.19322i
$288$	630.583	+	590.644i	0.129019	+	0.120847i
$289$	4021.10			0.818461
$290$	−2030.86			−0.411228
$291$	−5412.51	−	2138.97i	−1.09033	−	0.430888i
$292$			1050.51i			0.210536i
$293$			2291.88i			0.456973i	0.973547	+	0.228487i	$0.0733778\pi$
$293$			2291.88i			0.456973i	−0.973547	+	0.228487i	$0.926622\pi$
$294$	−231.394	+	585.527i	−0.0459020	+	0.116152i
$295$	2097.19	+	1390.81i	0.413910	+	0.274496i
$296$		−	383.882i		−	0.0753807i
$297$	−3803.94	+	1798.90i	−0.743188	+	0.351458i
$298$	−2713.92			−0.527562
$299$			533.689i			0.103224i
$300$	−719.336	+	1820.23i	−0.138436	+	0.350303i
$301$			2885.55i			0.552560i
$302$			1300.55i			0.247809i
$303$	−2849.53	+	7210.54i	−0.540269	+	1.36711i
$304$	972.177			0.183415
$305$	138.670			0.0260336
$306$	1102.46	−	1177.01i	0.205960	−	0.219887i
$307$	4142.93			0.770193			0.385097	−	0.922876i	$-0.374168\pi$
$307$	4142.93			0.770193			0.385097	+	0.922876i	$0.374168\pi$
$308$	−2016.14			−0.372988
$309$	−4070.77	−	1608.73i	−0.749444	−	0.296173i
$310$	−534.182			−0.0978693
$311$		−	810.589i		−	0.147795i	−0.997266	−	0.0738976i	$-0.976456\pi$
$311$		−	810.589i		−	0.147795i	0.997266	−	0.0738976i	$-0.0235438\pi$
$312$	1718.29	+	679.049i	0.311791	+	0.123217i
$313$		−	2975.72i		−	0.537373i	−0.963228	−	0.268686i	$-0.913410\pi$
$313$		−	2975.72i		−	0.537373i	0.963228	−	0.268686i	$-0.0865896\pi$
$314$			7223.39i			1.29822i
$315$	−1722.40	+	1838.87i	−0.308083	+	0.328916i
$316$	−3051.77			−0.543277
$317$			6181.31i			1.09520i	0.836742	+	0.547598i	$0.184458\pi$
$317$			6181.31i			1.09520i	−0.836742	+	0.547598i	$0.815542\pi$
$318$	202.091	+	79.8645i	0.0356375	+	0.0140836i
$319$		−	5484.69i		−	0.962646i
$320$		−	355.380i		−	0.0620822i
$321$	−81.3943	−	32.1662i	−0.0141526	−	0.00559297i
$322$	−403.579			−0.0698465
$323$		−	1814.61i		−	0.312594i
$324$	190.528	+	2909.77i	0.0326693	+	0.498932i
$325$			4185.34i			0.714342i
$326$	5329.19			0.905389
$327$	−8439.43	−	3335.18i	−1.42722	−	0.564023i
$328$		−	2761.76i		−	0.464917i
$329$	−10283.5			−1.72325
$330$	1609.63	+	636.111i	0.268507	+	0.106111i
$331$	123.581			0.0205216			0.0102608	−	0.999947i	$-0.496734\pi$
$331$	123.581			0.0205216			0.0102608	+	0.999947i	$0.496734\pi$
$332$	188.005			0.0310787
$333$	885.694	−	945.584i	0.145753	−	0.155609i
$334$		−	4981.05i		−	0.816020i
$335$	−268.843			−0.0438461
$336$	−513.501	+	1299.38i	−0.0833744	+	0.210973i
$337$			8654.36i			1.39891i	0.714676	+	0.699456i	$0.246574\pi$
$337$			8654.36i			1.39891i	−0.714676	+	0.699456i	$0.753426\pi$
$338$	−443.059			−0.0712995
$339$	893.991	−	2262.18i	0.143230	−	0.362433i
$340$	−663.331			−0.105806
$341$		−	1442.65i		−	0.229103i
$342$	2394.68	+	2243.01i	0.378625	+	0.354644i
$343$	−6782.32			−1.06767
$344$		−	1373.64i		−	0.215296i
$345$	322.207	+	127.333i	0.0502813	+	0.0198707i
$346$	1672.06			0.259799
$347$	−3853.12			−0.596098			−0.298049	−	0.954551i	$-0.596336\pi$
$347$	−3853.12			−0.596098			−0.298049	+	0.954551i	$0.596336\pi$
$348$	−3534.82	−	1396.93i	−0.544501	−	0.215181i
$349$		−	7666.84i		−	1.17592i	−0.808889	−	0.587961i	$-0.799931\pi$
$349$		−	7666.84i		−	1.17592i	0.808889	−	0.587961i	$-0.200069\pi$
$350$	−3164.98			−0.483359
$351$	2665.81	+	5637.08i	0.405385	+	0.857222i
$352$	959.765			0.145328
$353$	839.813			0.126625			0.0633127	−	0.997994i	$-0.479833\pi$
$353$	839.813			0.126625			0.0633127	+	0.997994i	$0.479833\pi$
$354$	2693.61	+	3863.34i	0.404418	+	0.580040i
$355$	498.117			0.0744713
$356$	−949.328			−0.141332
$357$	2425.35	+	958.473i	0.359560	+	0.142095i
$358$	2679.94			0.395640
$359$		−	7378.43i		−	1.08473i	−0.840143	−	0.542366i	$-0.817529\pi$
$359$		−	7378.43i		−	1.08473i	0.840143	−	0.542366i	$-0.182471\pi$
$360$	819.933	−	875.377i	0.120040	−	0.128157i
$361$	−3167.09			−0.461742
$362$	−8825.61			−1.28139
$363$	823.944	−	2084.93i	0.119135	−	0.301462i
$364$			2987.73i			0.430218i
$365$	1458.32			0.209128
$366$	241.363	+	95.3843i	0.0344707	+	0.0136225i
$367$		−	6664.44i		−	0.947904i	−0.880551	−	0.473952i	$-0.842827\pi$
$367$		−	6664.44i		−	0.947904i	0.880551	−	0.473952i	$-0.157173\pi$
$368$	192.120			0.0272145
$369$	6371.94	−	6802.81i	0.898943	−	0.959730i
$370$	−532.905			−0.0748768
$371$			351.393i			0.0491737i
$372$	−929.773	−	367.437i	−0.129587	−	0.0512116i
$373$	−3534.53			−0.490646			−0.245323	−	0.969441i	$-0.578894\pi$
$373$	−3534.53			−0.490646			−0.245323	+	0.969441i	$0.578894\pi$
$374$		−	1791.44i		−	0.247683i
$375$	5881.07	+	2324.14i	0.809859	+	0.320048i
$376$	4895.38			0.671436
$377$	−8127.80			−1.11035
$378$	−4262.80	+	2015.90i	−0.580039	+	0.274304i
$379$	3508.65			0.475533			0.237767	−	0.971322i	$-0.423585\pi$
$379$	3508.65			0.475533			0.237767	+	0.971322i	$0.423585\pi$
$380$		−	1349.58i		−	0.182189i
$381$	1721.03	−	4354.96i	0.231421	−	0.585594i
$382$	−4530.17			−0.606763
$383$			6546.79i			0.873434i	0.899599	+	0.436717i	$0.143859\pi$
$383$			6546.79i			0.873434i	−0.899599	+	0.436717i	$0.856141\pi$
$384$	244.448	−	618.557i	0.0324855	−	0.0822022i
$385$			2798.81i			0.370495i
$386$	−2535.50			−0.334336
$387$	3169.27	−	3383.58i	0.416287	−	0.444436i
$388$			4480.11i			0.586193i
$389$		−	6914.77i		−	0.901266i	−0.892709	−	0.450633i	$-0.851198\pi$
$389$		−	6914.77i		−	0.901266i	0.892709	−	0.450633i	$-0.148802\pi$
$390$	942.657	−	2385.33i	0.122393	−	0.309707i
$391$		−	358.601i		−	0.0463816i
$392$	484.660			0.0624465
$393$	−3539.42	+	8956.25i	−0.454300	+	1.14957i
$394$		−	7102.03i		−	0.908109i
$395$			4236.48i			0.539646i
$396$	2364.11	+	2214.37i	0.300002	+	0.281001i
$397$		−	14003.2i		−	1.77028i	−0.465322	−	0.885142i	$-0.654061\pi$
$397$		−	14003.2i		−	1.77028i	0.465322	−	0.885142i	$-0.345939\pi$
$398$	2307.77			0.290648
$399$	−1950.06	+	4934.48i	−0.244674	+	0.619130i
$400$	1506.66			0.188333
$401$	8402.96			1.04644			0.523222	−	0.852197i	$-0.324730\pi$
$401$	8402.96			1.04644			0.523222	+	0.852197i	$0.324730\pi$
$402$	−467.936	−	184.923i	−0.0580560	−	0.0229431i
$403$	−2137.87			−0.264256
$404$	5968.40			0.734998
$405$	4039.34	−	264.491i	0.495597	−	0.0324510i
$406$		−	6146.30i		−	0.751319i
$407$		−	1439.20i		−	0.175279i
$408$	−1154.56	−	456.272i	−0.140097	−	0.0553648i
$409$		−	14040.7i		−	1.69748i	−0.528811	−	0.848740i	$-0.677362\pi$
$409$		−	14040.7i		−	1.69748i	0.528811	−	0.848740i	$-0.322638\pi$
$410$	−3833.88			−0.461809
$411$	3591.12	+	1419.17i	0.430990	+	0.170323i
$412$			3369.51i			0.402922i
$413$	−4209.22	+	6347.05i	−0.501507	+	0.756218i
$414$	473.234	+	443.260i	0.0561791	+	0.0526209i
$415$		−	260.989i		−	0.0308709i
$416$		−	1422.28i		−	0.167628i
$417$	103.888	−	262.880i	0.0122000	−	0.0308712i
$418$	3644.77			0.426487
$419$	9817.23			1.14464			0.572318	−	0.820031i	$-0.306044\pi$
$419$	9817.23			1.14464			0.572318	+	0.820031i	$0.306044\pi$
$420$	1803.80	+	712.843i	0.209563	+	0.0828171i
$421$			2102.13i			0.243353i	0.992570	+	0.121676i	$0.0388270\pi$
$421$			2102.13i			0.243353i	−0.992570	+	0.121676i	$0.961173\pi$
$422$		−	8761.04i		−	1.01062i
$423$	12058.4	+	11294.6i	1.38605	+	1.29826i
$424$		−	167.278i		−	0.0191597i
$425$		−	2812.25i		−	0.320975i
$426$	867.000	+	342.629i	0.0986063	+	0.0389682i
$427$			419.679i			0.0475637i
$428$			67.3727i			0.00760884i
$429$	6441.99	+	2545.81i	0.724994	+	0.286510i
$430$	−1906.89			−0.213857
$431$	7897.78			0.882651			0.441326	−	0.897347i	$-0.354508\pi$
$431$	7897.78			0.882651			0.441326	+	0.897347i	$0.354508\pi$
$432$	2029.27	−	959.651i	0.226002	−	0.106878i
$433$	−137.599			−0.0152715			−0.00763575	−	0.999971i	$-0.502431\pi$
$433$	−137.599			−0.0152715			−0.00763575	+	0.999971i	$0.502431\pi$
$434$		−	1616.67i		−	0.178808i
$435$	−1939.21	+	4907.05i	−0.213743	+	0.540862i
$436$			6985.59i			0.767314i
$437$	729.589			0.0798650
$438$	2538.28	+	1003.10i	0.276904	+	0.109430i
$439$	−11229.9			−1.22090			−0.610449	−	0.792055i	$-0.709011\pi$
$439$	−11229.9			−1.22090			−0.610449	+	0.792055i	$0.709011\pi$
$440$		−	1332.35i		−	0.144357i
$441$	1193.82	+	1118.21i	0.128909	+	0.120744i
$442$	−2654.75			−0.285687
$443$	3910.61			0.419410			0.209705	−	0.977765i	$-0.432750\pi$
$443$	3910.61			0.419410			0.209705	+	0.977765i	$0.432750\pi$
$444$	−927.551	−	366.559i	−0.0991433	−	0.0391804i
$445$			1317.86i			0.140388i
$446$	2755.24			0.292521
$447$	−2591.45	+	6557.49i	−0.274209	+	0.693867i
$448$	1075.54			0.113425
$449$		−	13823.1i		−	1.45290i	−0.687219	−	0.726451i	$-0.741169\pi$
$449$		−	13823.1i		−	1.45290i	0.687219	−	0.726451i	$-0.258831\pi$
$450$	3711.23	+	3476.18i	0.388776	+	0.364152i
$451$		−	10354.1i		−	1.08105i
$452$	−1872.48			−0.194854
$453$	3142.44	+	1241.86i	0.325927	+	0.128803i
$454$	−7544.79			−0.779944
$455$	4147.57			0.427343
$456$	928.306	−	2349.01i	0.0953332	−	0.241234i
$457$		−	10050.8i		−	1.02879i	−0.857552	−	0.514397i	$-0.828016\pi$
$457$		−	10050.8i		−	1.02879i	0.857552	−	0.514397i	$-0.171984\pi$
$458$			6067.82i			0.619062i
$459$	−1791.23	−	3787.71i	−0.182151	−	0.385175i
$460$		−	266.701i		−	0.0270326i
$461$			7797.77i			0.787805i	0.919152	+	0.393903i	$0.128875\pi$
$461$			7797.77i			0.787805i	−0.919152	+	0.393903i	$0.871125\pi$
$462$	−1925.16	+	4871.48i	−0.193867	+	0.490566i
$463$			13435.3i			1.34857i	0.738470	+	0.674286i	$0.235549\pi$
$463$			13435.3i			1.34857i	−0.738470	+	0.674286i	$0.764451\pi$
$464$			2925.89i			0.292739i
$465$	−510.076	+	1290.71i	−0.0508693	+	0.128721i
$466$	−12427.2			−1.23536
$467$	−12420.0			−1.23069			−0.615343	−	0.788259i	$-0.710983\pi$
$467$	−12420.0			−1.23069			−0.615343	+	0.788259i	$0.710983\pi$
$468$	3281.49	−	3503.39i	0.324117	−	0.346034i
$469$		−	813.639i		−	0.0801074i
$470$		−	6795.77i		−	0.666948i
$471$	17453.5	+	6897.43i	1.70746	+	0.674770i
$472$	2003.76	−	3021.46i	0.195404	−	0.294648i
$473$		−	5149.89i		−	0.500618i
$474$	−2914.06	+	7373.82i	−0.282378	+	0.714537i
$475$	5721.65			0.552689
$476$		−	2007.54i		−	0.193310i
$477$	385.944	−	412.041i	0.0370464	−	0.0395515i
$478$		−	7497.97i		−	0.717467i
$479$		−	2912.40i		−	0.277810i	−0.990306	−	0.138905i	$-0.955642\pi$
$479$		−	2912.40i		−	0.277810i	0.990306	−	0.138905i	$-0.0443583\pi$
$480$	−858.682	−	339.342i	−0.0816527	−	0.0322683i
$481$	−2132.76			−0.202174
$482$	7234.50			0.683656
$483$	−385.367	+	975.144i	−0.0363039	+	0.0918646i
$484$	−1725.77			−0.162074
$485$	6219.29			0.582275
$486$	7212.63	+	2318.10i	0.673193	+	0.216360i
$487$	−8159.22			−0.759198			−0.379599	−	0.925151i	$-0.623938\pi$
$487$	−8159.22			−0.759198			−0.379599	+	0.925151i	$0.623938\pi$
$488$		−	199.784i		−	0.0185324i
$489$	5088.70	−	12876.6i	0.470591	−	1.19080i
$490$		−	672.805i		−	0.0620291i
$491$		−	447.803i		−	0.0411590i	−0.999788	−	0.0205795i	$-0.993449\pi$
$491$		−	447.803i		−	0.0411590i	0.999788	−	0.0205795i	$-0.00655112\pi$
$492$	−6673.07	−	2637.13i	−0.611474	−	0.241648i
$493$	5461.30			0.498914
$494$		−	5401.21i		−	0.491927i
$495$	3073.99	−	3281.86i	0.279123	−	0.297997i
$496$			769.603i			0.0696697i
$497$			1507.53i			0.136060i
$498$	179.521	−	454.265i	0.0161537	−	0.0408757i
$499$	4343.63			0.389674			0.194837	−	0.980836i	$-0.437582\pi$
$499$	4343.63			0.389674			0.194837	+	0.980836i	$0.437582\pi$
$500$		−	4867.95i		−	0.435403i
$501$	−12035.4	−	4756.27i	−1.07326	−	0.424141i
$502$			3135.09i			0.278737i
$503$	−3928.76			−0.348260			−0.174130	−	0.984723i	$-0.555711\pi$
$503$	−3928.76			−0.348260			−0.174130	+	0.984723i	$0.555711\pi$
$504$	2649.28	+	2481.49i	0.234144	+	0.219314i
$505$		−	8285.34i		−	0.730085i
$506$	720.274			0.0632808
$507$	−423.065	+	1070.54i	−0.0370591	+	0.0937755i
$508$	−3604.74			−0.314831
$509$	14128.5			1.23032			0.615161	−	0.788401i	$-0.289091\pi$
$509$	14128.5			1.23032			0.615161	+	0.788401i	$0.289091\pi$
$510$	−633.398	+	1602.77i	−0.0549947	+	0.139160i
$511$			4413.53i			0.382080i
$512$	−512.000			−0.0441942
$513$	7706.27	−	3644.34i	0.663236	−	0.313648i
$514$		−	4654.28i		−	0.399400i
$515$	4677.56			0.400229
$516$	−3319.05	−	1311.65i	−0.283165	−	0.111904i
$517$	18353.2			1.56126
$518$		−	1612.81i		−	0.136801i
$519$	1596.61	−	4040.10i	0.135035	−	0.341697i
$520$	−1974.41			−0.166507
$521$		−	15472.6i		−	1.30109i	−0.759468	−	0.650544i	$-0.774541\pi$
$521$		−	15472.6i		−	1.30109i	0.759468	−	0.650544i	$-0.225459\pi$
$522$	−6750.62	+	7207.10i	−0.566028	+	0.604303i
$523$	−21126.1			−1.76631			−0.883153	−	0.469084i	$-0.844584\pi$
$523$	−21126.1			−1.76631			−0.883153	+	0.469084i	$0.844584\pi$
$524$	7413.37			0.618043
$525$	−3022.16	+	7647.36i	−0.251234	+	0.635730i
$526$		−	576.500i		−	0.0477882i
$527$	1436.50			0.118738
$528$	916.454	−	2319.02i	0.0755370	−	0.191141i
$529$	−12022.8			−0.988150
$530$	−232.215			−0.0190317
$531$	11906.8	−	2819.42i	0.973092	−	0.230419i
$532$	4084.43			0.332862
$533$	−15343.7			−1.24693
$534$	−906.488	+	2293.80i	−0.0734599	+	0.185885i
$535$	93.5269			0.00755798
$536$			387.325i			0.0312125i
$537$	2559.00	−	6475.38i	0.205641	−	0.520360i
$538$	9958.95			0.798069
$539$	1817.03			0.145204
$540$	−1332.19	−	2817.03i	−0.106163	−	0.224492i
$541$			23.4250i			0.00186158i	1.00000		0.000930792i	$0.000296280\pi$
$541$			23.4250i			0.00186158i	−1.00000		0.000930792i	$0.999704\pi$
$542$	−6785.24			−0.537733
$543$	−8427.34	+	21324.8i	−0.666025	+	1.68533i
$544$			955.670i			0.0753199i
$545$	9697.40			0.762185
$546$	7219.07	+	2852.90i	0.565838	+	0.223613i
$547$	−12020.5			−0.939599			−0.469800	−	0.882773i	$-0.655674\pi$
$547$	−12020.5			−0.939599			−0.469800	+	0.882773i	$0.655674\pi$
$548$		−	2972.48i		−	0.231712i
$549$	460.943	−	492.112i	0.0358334	−	0.0382565i
$550$	5648.60			0.437922
$551$			11111.3i			0.859084i
$552$	183.450	−	464.208i	0.0141452	−	0.0357935i
$553$	−12821.5			−0.985940
$554$	−7836.07			−0.600943
$555$	−508.857	+	1287.63i	−0.0389185	+	0.0984806i
$556$	−217.595			−0.0165972
$557$			1907.98i			0.145141i	0.997363	+	0.0725706i	$0.0231203\pi$
$557$			1907.98i			0.145141i	−0.997363	+	0.0725706i	$0.976880\pi$
$558$	−1775.63	+	1895.70i	−0.134710	+	0.143820i
$559$	−7631.66			−0.577432
$560$		−	1493.06i		−	0.112667i
$561$	−4328.56	−	1710.60i	−0.325761	−	0.128737i
$562$			7539.63i			0.565908i
$563$	−12523.3			−0.937465			−0.468733	−	0.883340i	$-0.655289\pi$
$563$	−12523.3			−0.937465			−0.468733	+	0.883340i	$0.655289\pi$
$564$	4674.47	−	11828.4i	0.348991	−	0.883096i
$565$			2599.38i			0.193552i
$566$			7873.54i			0.584716i
$567$	800.468	+	12224.9i	0.0592883	+	0.905461i
$568$		−	717.644i		−	0.0530135i
$569$	20048.5			1.47711			0.738557	−	0.674191i	$-0.235508\pi$
$569$	20048.5			1.47711			0.738557	+	0.674191i	$0.235508\pi$
$570$	−3260.90	−	1288.68i	−0.239622	−	0.0946960i
$571$			2123.35i			0.155620i	0.996968	+	0.0778102i	$0.0247928\pi$
$571$			2123.35i			0.155620i	−0.996968	+	0.0778102i	$0.975207\pi$
$572$		−	5332.24i		−	0.389777i
$573$	−4325.74	+	10946.0i	−0.315376	+	0.798036i
$574$		−	11603.0i		−	0.843731i
$575$	1130.70			0.0820062
$576$	−1261.17	−	1181.29i	−0.0912303	−	0.0854520i
$577$	−1128.24			−0.0814023			−0.0407012	−	0.999171i	$-0.512959\pi$
$577$	−1128.24			−0.0814023			−0.0407012	+	0.999171i	$0.512959\pi$
$578$	−8042.20			−0.578739
$579$	−2421.08	+	6126.38i	−0.173777	+	0.439730i
$580$	4061.72			0.290782
$581$	789.870			0.0564016
$582$	10825.0	+	4277.94i	0.770982	+	0.304684i
$583$		−	627.137i		−	0.0445512i
$584$		−	2101.02i		−	0.148871i
$585$	−4863.40	−	4555.37i	−0.343721	−	0.321951i
$586$		−	4583.77i		−	0.323129i
$587$	6094.18			0.428507			0.214254	−	0.976778i	$-0.431268\pi$
$587$	6094.18			0.428507			0.214254	+	0.976778i	$0.431268\pi$
$588$	462.789	−	1171.05i	0.0324576	−	0.0821318i
$589$			2922.62i			0.204456i
$590$	−4194.39	−	2781.62i	−0.292678	−	0.194098i
$591$	−17160.2	−	6781.54i	−1.19438	−	0.472005i
$592$			767.764i			0.0533022i
$593$			23306.1i			1.61394i	0.590594	+	0.806969i	$0.298894\pi$
$593$			23306.1i			1.61394i	−0.590594	+	0.806969i	$0.701106\pi$
$594$	7607.88	−	3597.81i	0.525514	−	0.248518i
$595$	−2786.87			−0.192018
$596$	5427.85			0.373042
$597$	2203.63	−	5576.12i	0.151069	−	0.382271i
$598$		−	1067.38i		−	0.0729905i
$599$			8012.39i			0.546540i	0.961937	+	0.273270i	$0.0881052\pi$
$599$			8012.39i			0.546540i	−0.961937	+	0.273270i	$0.911895\pi$
$600$	1438.67	−	3640.46i	0.0978892	−	0.247702i
$601$			26907.0i			1.82622i	0.407712	+	0.913111i	$0.366327\pi$
$601$			26907.0i			1.82622i	−0.407712	+	0.913111i	$0.633673\pi$
$602$		−	5771.11i		−	0.390719i
$603$	−893.639	+	954.066i	−0.0603512	+	0.0644322i
$604$		−	2601.10i		−	0.175227i
$605$			2395.71i			0.160991i
$606$	5699.07	−	14421.1i	0.382028	−	0.966694i
$607$	7555.52			0.505221			0.252611	−	0.967568i	$-0.418711\pi$
$607$	7555.52			0.505221			0.252611	+	0.967568i	$0.418711\pi$
$608$	−1944.35			−0.129694
$609$	−14850.9	−	5868.93i	−0.988161	−	0.390511i
$610$	−277.341			−0.0184085
$611$		−	27197.7i		−	1.80082i
$612$	−2204.93	+	2354.02i	−0.145635	+	0.155483i
$613$		−	26798.4i		−	1.76571i	−0.469650	−	0.882853i	$-0.655620\pi$
$613$		−	26798.4i		−	1.76571i	0.469650	−	0.882853i	$-0.344380\pi$
$614$	−8285.85			−0.544609
$615$	−3660.87	+	9263.57i	−0.240033	+	0.607387i
$616$	4032.28			0.263742
$617$		−	1210.86i		−	0.0790072i	−0.999219	−	0.0395036i	$-0.987422\pi$
$617$		−	1210.86i		−	0.0790072i	0.999219	−	0.0395036i	$-0.0125777\pi$
$618$	8141.55	+	3217.46i	0.529937	+	0.209426i
$619$	7048.07			0.457651			0.228825	−	0.973467i	$-0.426512\pi$
$619$	7048.07			0.457651			0.228825	+	0.973467i	$0.426512\pi$
$620$	1068.36			0.0692041
$621$	1522.90	−	720.188i	0.0984089	−	0.0465381i
$622$			1621.18i			0.104507i
$623$	−3988.43			−0.256490
$624$	−3436.57	−	1358.10i	−0.220469	−	0.0871273i
$625$	5013.10			0.320838
$626$			5951.44i			0.379980i
$627$	3480.30	−	8806.64i	0.221674	−	0.560931i
$628$		−	14446.8i		−	0.917977i
$629$	1433.06			0.0908427
$630$	3444.80	−	3677.74i	0.217848	−	0.232579i
$631$	−26270.5			−1.65739			−0.828694	−	0.559703i	$-0.810915\pi$
$631$	−26270.5			−1.65739			−0.828694	+	0.559703i	$0.810915\pi$
$632$	6103.55			0.384155
$633$	−21168.8	−	8365.69i	−1.32920	−	0.525286i
$634$		−	12362.6i		−	0.774420i
$635$			5004.10i			0.312727i
$636$	−404.183	−	159.729i	−0.0251995	−	0.00995859i
$637$		−	2692.67i		−	0.167484i
$638$			10969.4i			0.680693i
$639$	1655.75	−	1767.71i	0.102505	−	0.109436i
$640$			710.759i			0.0438988i
$641$		−	1126.48i		−	0.0694122i	−0.999398	−	0.0347061i	$-0.988950\pi$
$641$		−	1126.48i		−	0.0694122i	0.999398	−	0.0347061i	$-0.0110495\pi$
$642$	162.789	+	64.3324i	0.0100074	+	0.00395483i
$643$	4537.00			0.278261			0.139130	−	0.990274i	$-0.455569\pi$
$643$	4537.00			0.278261			0.139130	+	0.990274i	$0.455569\pi$
$644$	807.158			0.0493890
$645$	−1820.84	+	4607.51i	−0.111156	+	0.281272i
$646$			3629.22i			0.221037i
$647$		−	23087.3i		−	1.40287i	−0.712736	−	0.701433i	$-0.752544\pi$
$647$		−	23087.3i		−	1.40287i	0.712736	−	0.701433i	$-0.247456\pi$
$648$	−381.055	−	5819.54i	−0.0231007	−	0.352798i
$649$	7512.26	−	11327.7i	0.454364	−	0.685132i
$650$		−	8370.69i		−	0.505116i
$651$	−3906.27	−	1543.72i	−0.235175	−	0.0929388i
$652$	−10658.4			−0.640206
$653$			24606.1i			1.47460i	0.675568	+	0.737298i	$0.263898\pi$
$653$			24606.1i			1.47460i	−0.675568	+	0.737298i	$0.736102\pi$
$654$	16878.9	+	6670.35i	1.00920	+	0.398825i
$655$		−	10291.3i		−	0.613912i
$656$			5523.52i			0.328746i
$657$	4847.48	−	5175.26i	0.287851	−	0.307316i
$658$	20567.1			1.21852
$659$	−14084.9			−0.832579			−0.416289	−	0.909232i	$-0.636670\pi$
$659$	−14084.9			−0.832579			−0.416289	+	0.909232i	$0.636670\pi$
$660$	−3219.27	−	1272.22i	−0.189863	−	0.0750321i
$661$	16514.2			0.971749			0.485875	−	0.874029i	$-0.338501\pi$
$661$	16514.2			0.971749			0.485875	+	0.874029i	$0.338501\pi$
$662$	−247.163			−0.0145110
$663$	−2534.95	+	6414.51i	−0.148491	+	0.375745i
$664$	−376.010			−0.0219759
$665$		−	5670.01i		−	0.330637i
$666$	−1771.39	+	1891.17i	−0.103063	+	0.110032i
$667$			2195.79i			0.127468i
$668$			9962.09i			0.577013i
$669$	2630.91	−	6657.33i	0.152043	−	0.384734i
$670$	537.686			0.0310039
$671$		−	749.007i		−	0.0430925i
$672$	1027.00	−	2598.76i	0.0589546	−	0.149180i
$673$			9930.18i			0.568767i	0.958711	+	0.284384i	$0.0917890\pi$
$673$			9930.18i			0.568767i	−0.958711	+	0.284384i	$0.908211\pi$
$674$		−	17308.7i		−	0.989180i
$675$	11943.0	−	5647.93i	0.681019	−	0.322057i
$676$	886.117			0.0504163
$677$			6309.18i			0.358171i	0.983834	+	0.179085i	$0.0573138\pi$
$677$			6309.18i			0.358171i	−0.983834	+	0.179085i	$0.942686\pi$
$678$	−1787.98	+	4524.37i	−0.101279	+	0.256279i
$679$			18822.4i			1.06382i
$680$	1326.66			0.0748165
$681$	−7204.32	+	18230.0i	−0.405389	+	1.02581i
$682$			2885.30i			0.162000i
$683$	−21352.7			−1.19625			−0.598125	−	0.801403i	$-0.704088\pi$
$683$	−21352.7			−1.19625			−0.598125	+	0.801403i	$0.704088\pi$
$684$	−4789.37	−	4486.02i	−0.267728	−	0.250771i
$685$	−4126.41			−0.230163
$686$	13564.6			0.754957
$687$	14661.3	+	5794.00i	0.814212	+	0.321768i
$688$			2747.28i			0.152237i
$689$	−929.358			−0.0513871
$690$	−644.415	−	254.666i	−0.0355543	−	0.0140507i
$691$			16587.6i			0.913202i	0.889672	+	0.456601i	$0.150933\pi$
$691$			16587.6i			0.913202i	−0.889672	+	0.456601i	$0.849067\pi$
$692$	−3344.12			−0.183706
$693$	9932.38	+	9303.29i	0.544444	+	0.509961i
$694$	7706.23			0.421505
$695$			302.065i			0.0164863i
$696$	7069.65	+	2793.85i	0.385021	+	0.152156i
$697$	10309.9			0.560280
$698$			15333.7i			0.831502i
$699$	−11866.4	+	30027.0i	−0.642100	+	1.62479i
$700$	6329.97			0.341786
$701$	29847.6			1.60817			0.804086	−	0.594513i	$-0.202655\pi$
$701$	29847.6			1.60817			0.804086	+	0.594513i	$0.202655\pi$
$702$	−5331.61	−	11274.2i	−0.286651	−	0.606148i
$703$			2915.64i			0.156423i
$704$	−1919.53			−0.102763
$705$	−16420.2	−	6489.10i	−0.877193	−	0.346658i
$706$	−1679.63			−0.0895376
$707$	25075.2			1.33387
$708$	−5387.23	−	7726.68i	−0.285967	−	0.410150i
$709$	31965.9			1.69324			0.846618	−	0.532202i	$-0.178635\pi$
$709$	31965.9			1.69324			0.846618	+	0.532202i	$0.178635\pi$
$710$	−996.234			−0.0526591
$711$	15034.4	+	14082.1i	0.793013	+	0.742786i
$712$	1898.66			0.0999370
$713$			577.563i			0.0303365i
$714$	−4850.70	−	1916.95i	−0.254248	−	0.100476i
$715$	−7402.23			−0.387172
$716$	−5359.88			−0.279760
$717$	−18116.9	−	7159.62i	−0.943638	−	0.372916i
$718$			14756.9i			0.767021i
$719$	−30555.4			−1.58488			−0.792438	−	0.609953i	$-0.791188\pi$
$719$	−30555.4			−1.58488			−0.792438	+	0.609953i	$0.791188\pi$
$720$	−1639.87	+	1750.75i	−0.0848808	+	0.0906205i
$721$			14156.4i			0.731223i
$722$	6334.18			0.326501
$723$	6908.03	−	17480.3i	0.355342	−	0.899168i
$724$	17651.2			0.906081
$725$			17220.0i			0.882118i
$726$	−1647.89	+	4169.86i	−0.0842408	+	0.213165i
$727$	−33056.3			−1.68637			−0.843185	−	0.537623i	$-0.819322\pi$
$727$	−33056.3			−1.68637			−0.843185	+	0.537623i	$0.819322\pi$
$728$		−	5975.46i		−	0.304210i
$729$	12488.2	−	15214.0i	0.634468	−	0.772949i
$730$	−2916.64			−0.147876
$731$	5127.92			0.259457
$732$	−482.727	−	190.769i	−0.0243744	−	0.00963253i
$733$	2121.81			0.106918			0.0534591	−	0.998570i	$-0.482975\pi$
$733$	2121.81			0.106918			0.0534591	+	0.998570i	$0.482975\pi$
$734$			13328.9i			0.670269i
$735$	−1625.66	−	642.444i	−0.0815828	−	0.0322407i
$736$	−384.240			−0.0192436
$737$			1452.11i			0.0725771i
$738$	−12743.9	+	13605.6i	−0.635649	+	0.678631i
$739$		−	28678.6i		−	1.42755i	−0.700375	−	0.713775i	$-0.746984\pi$
$739$		−	28678.6i		−	1.42755i	0.700375	−	0.713775i	$-0.253016\pi$
$740$	1065.81			0.0529459
$741$	−13050.6	−	5157.47i	−0.646999	−	0.255687i
$742$		−	702.787i		−	0.0347711i
$743$		−	24136.6i		−	1.19177i	−0.803070	−	0.595884i	$-0.796802\pi$
$743$		−	24136.6i		−	1.19177i	0.803070	−	0.595884i	$-0.203198\pi$
$744$	1859.55	+	734.873i	0.0916321	+	0.0362121i
$745$		−	7534.94i		−	0.370549i
$746$	7069.05			0.346939
$747$	−926.195	−	867.532i	−0.0453650	−	0.0424918i
$748$			3582.89i			0.175138i
$749$			283.054i			0.0138085i
$750$	−11762.1	−	4648.28i	−0.572657	−	0.226308i
$751$		−	19222.6i		−	0.934012i	−0.884254	−	0.467006i	$-0.845333\pi$
$751$		−	19222.6i		−	0.934012i	0.884254	−	0.467006i	$-0.154667\pi$
$752$	−9790.76			−0.474777
$753$	7575.13	+	2993.62i	0.366605	+	0.144878i
$754$	16255.6			0.785138
$755$	−3610.85			−0.174056
$756$	8525.59	−	4031.80i	0.410149	−	0.193962i
$757$	−17368.8			−0.833921			−0.416960	−	0.908925i	$-0.636905\pi$
$757$	−17368.8			−0.833921			−0.416960	+	0.908925i	$0.636905\pi$
$758$	−7017.29			−0.336253
$759$	687.770	−	1740.35i	0.0328913	−	0.0832291i
$760$			2699.16i			0.128827i
$761$			38166.1i			1.81803i	0.416765	+	0.909014i	$0.363164\pi$
$761$			38166.1i			1.81803i	−0.416765	+	0.909014i	$0.636836\pi$
$762$	−3442.07	+	8709.91i	−0.163639	+	0.414077i
$763$			29348.7i			1.39252i
$764$	9060.33			0.429046
$765$	3267.86	+	3060.88i	0.154444	+	0.144662i
$766$		−	13093.6i		−	0.617611i
$767$	−16786.6	−	11132.5i	−0.790257	−	0.524081i
$768$	−488.895	+	1237.11i	−0.0229707	+	0.0581257i
$769$			19736.8i			0.925523i	0.886483	+	0.462762i	$0.153141\pi$
$769$			19736.8i			0.925523i	−0.886483	+	0.462762i	$0.846859\pi$
$770$		−	5597.61i		−	0.261979i
$771$	−11245.9	−	4444.25i	−0.525304	−	0.207595i
$772$	5071.00			0.236411
$773$	−15665.6			−0.728916			−0.364458	−	0.931220i	$-0.618746\pi$
$773$	−15665.6			−0.728916			−0.364458	+	0.931220i	$0.618746\pi$
$774$	−6338.54	+	6767.15i	−0.294359	+	0.314264i
$775$			4529.42i			0.209937i
$776$		−	8960.22i		−	0.414501i
$777$	−3896.94	−	1540.03i	−0.179925	−	0.0711046i
$778$			13829.5i			0.637291i
$779$			20975.9i			0.964751i
$780$	−1885.31	+	4770.65i	−0.0865449	+	0.218996i
$781$		−	2690.50i		−	0.123270i
$782$			717.201i			0.0327968i
$783$	10968.1	+	23193.0i	0.500597	+	1.05856i
$784$	−969.320			−0.0441563
$785$	−20055.0			−0.911841
$786$	7078.83	−	17912.5i	0.321239	−	0.812872i
$787$	22590.9			1.02323			0.511613	−	0.859216i	$-0.329048\pi$
$787$	22590.9			1.02323			0.511613	+	0.859216i	$0.329048\pi$
$788$			14204.1i			0.642130i
$789$	−1392.96	−	550.485i	−0.0628527	−	0.0248387i
$790$		−	8472.95i		−	0.381587i
$791$	−7866.90			−0.353621
$792$	−4728.22	−	4428.74i	−0.212134	−	0.198698i
$793$	−1109.96			−0.0497046
$794$			28006.5i			1.25178i
$795$	−221.736	+	561.087i	−0.00989203	+	0.0250311i
$796$	−4615.54			−0.205519
$797$	2924.05			0.129956			0.0649781	−	0.997887i	$-0.479302\pi$
$797$	2924.05			0.129956			0.0649781	+	0.997887i	$0.479302\pi$
$798$	3900.11	−	9868.96i	0.173011	−	0.437791i
$799$			18274.9i			0.809160i
$800$	−3013.32			−0.133171
$801$	4676.80	+	4380.59i	0.206300	+	0.193234i
$802$	−16805.9			−0.739947
$803$		−	7876.89i		−	0.346164i
$804$	935.871	+	369.847i	0.0410518	+	0.0162232i
$805$		−	1120.50i		−	0.0490588i
$806$	4275.75			0.186857
$807$	9509.54	−	24063.2i	0.414810	−	1.04965i
$808$	−11936.8			−0.519722
$809$	−29733.1			−1.29216			−0.646081	−	0.763269i	$-0.723593\pi$
$809$	−29733.1			−1.29216			−0.646081	+	0.763269i	$0.723593\pi$
$810$	−8078.69	+	528.981i	−0.350440	+	0.0229463i
$811$		−	12705.9i		−	0.550141i	−0.961424	−	0.275070i	$-0.911299\pi$
$811$		−	12705.9i		−	0.550141i	0.961424	−	0.275070i	$-0.0887012\pi$
$812$			12292.6i			0.531263i
$813$	−6479.05	+	16394.8i	−0.279496	+	0.707244i
$814$			2878.41i			0.123941i
$815$			14796.0i			0.635927i
$816$	2309.13	+	912.544i	0.0990634	+	0.0391488i
$817$			10433.0i			0.446762i
$818$			28081.5i			1.20030i
$819$	13786.6	−	14718.8i	0.588208	−	0.627983i
$820$	7667.76			0.326548
$821$	1240.60			0.0527373			0.0263686	−	0.999652i	$-0.491606\pi$
$821$	1240.60			0.0527373			0.0263686	+	0.999652i	$0.491606\pi$
$822$	−7182.23	−	2838.35i	−0.304756	−	0.120436i
$823$			3847.92i			0.162977i	0.996674	+	0.0814885i	$0.0259674\pi$
$823$			3847.92i			0.162977i	−0.996674	+	0.0814885i	$0.974033\pi$
$824$		−	6739.02i		−	0.284909i
$825$	5393.69	−	13648.4i	0.227617	−	0.575970i
$826$	8418.44	−	12694.1i	0.354619	−	0.534727i
$827$			14483.0i			0.608975i	0.952516	+	0.304487i	$0.0984852\pi$
$827$			14483.0i			0.608975i	−0.952516	+	0.304487i	$0.901515\pi$
$828$	−946.467	−	886.521i	−0.0397246	−	0.0372086i
$829$	−10531.0			−0.441202			−0.220601	−	0.975364i	$-0.570802\pi$
$829$	−10531.0			−0.441202			−0.220601	+	0.975364i	$0.570802\pi$
$830$			521.978i			0.0218291i
$831$	−7482.45	+	18933.8i	−0.312351	+	0.790381i
$832$			2844.56i			0.118531i
$833$			1809.28i			0.0752554i
$834$	−207.775	+	525.761i	−0.00862670	+	0.0218293i
$835$	13829.4			0.573157
$836$	−7289.54			−0.301572
$837$	2884.96	+	6100.50i	0.119138	+	0.251929i
$838$	−19634.5			−0.809381
$839$	−8142.54			−0.335056			−0.167528	−	0.985867i	$-0.553578\pi$
$839$	−8142.54			−0.335056			−0.167528	+	0.985867i	$0.553578\pi$
$840$	−3607.60	−	1425.69i	−0.148183	−	0.0585605i
$841$	−9051.70			−0.371139
$842$		−	4204.26i		−	0.172077i
$843$	18217.6	+	7199.40i	0.744302	+	0.294140i
$844$			17522.1i			0.714615i
$845$		−	1230.11i		−	0.0500793i
$846$	−24116.8	−	22589.3i	−0.980085	−	0.918009i
$847$	−7250.49			−0.294132
$848$			334.555i			0.0135480i
$849$	19024.4	+	7518.23i	0.769039	+	0.303916i
$850$			5624.50i			0.226963i
$851$			576.183i			0.0232095i
$852$	−1734.00	−	685.259i	−0.0697252	−	0.0275547i
$853$	10420.7			0.418287			0.209144	−	0.977885i	$-0.432932\pi$
$853$	10420.7			0.418287			0.209144	+	0.977885i	$0.432932\pi$
$854$		−	839.358i		−	0.0336326i
$855$	−6227.50	+	6648.61i	−0.249095	+	0.265939i
$856$		−	134.745i		−	0.00538026i
$857$	−30930.2			−1.23285			−0.616426	−	0.787413i	$-0.711420\pi$
$857$	−30930.2			−1.23285			−0.616426	+	0.787413i	$0.711420\pi$
$858$	−12884.0	−	5091.62i	−0.512648	−	0.202593i
$859$			1754.22i			0.0696780i	0.999393	+	0.0348390i	$0.0110918\pi$
$859$			1754.22i			0.0696780i	−0.999393	+	0.0348390i	$0.988908\pi$
$860$	3813.78			0.151220
$861$	−28035.7	−	11079.4i	−1.10970	−	0.438544i
$862$	−15795.6			−0.624129
$863$	23926.7			0.943769			0.471885	−	0.881660i	$-0.343574\pi$
$863$	23926.7			0.943769			0.471885	+	0.881660i	$0.343574\pi$
$864$	−4058.53	+	1919.30i	−0.159808	+	0.0755740i
$865$			4642.31i			0.182478i
$866$	275.197			0.0107986
$867$	−7679.28	+	19431.9i	−0.300810	+	0.761178i
$868$			3233.35i			0.126437i
$869$	22882.7			0.893259
$870$	3878.43	−	9814.09i	0.151139	−	0.382447i
$871$	2151.90			0.0837132
$872$		−	13971.2i		−	0.542573i
$873$	20673.0	−	22071.0i	0.801462	−	0.855657i
$874$	−1459.18			−0.0564731
$875$		−	20451.8i		−	0.790169i
$876$	−5076.57	−	2006.21i	−0.195801	−	0.0773784i
$877$	−14997.3			−0.577449			−0.288724	−	0.957412i	$-0.593231\pi$
$877$	−14997.3			−0.577449			−0.288724	+	0.957412i	$0.593231\pi$
$878$	22459.8			0.863306
$879$	−11075.5	−	4376.92i	−0.424990	−	0.167952i
$880$			2664.69i			0.102076i
$881$	−570.605			−0.0218209			−0.0109104	−	0.999940i	$-0.503473\pi$
$881$	−570.605			−0.0218209			−0.0109104	+	0.999940i	$0.503473\pi$
$882$	−2387.64	−	2236.42i	−0.0911521	−	0.0853788i
$883$	30988.1			1.18101			0.590506	−	0.807034i	$-0.298928\pi$
$883$	30988.1			1.18101			0.590506	+	0.807034i	$0.298928\pi$
$884$	5309.50			0.202011
$885$	−10726.2	+	7478.55i	−0.407409	+	0.284055i
$886$	−7821.22			−0.296568
$887$	−1442.79			−0.0546156			−0.0273078	−	0.999627i	$-0.508693\pi$
$887$	−1442.79			−0.0546156			−0.0273078	+	0.999627i	$0.508693\pi$
$888$	1855.10	+	733.117i	0.0701049	+	0.0277047i
$889$	−15144.7			−0.571356
$890$		−	2635.72i		−	0.0992690i
$891$	−1428.61	−	21817.9i	−0.0537151	−	0.820345i
$892$	−5510.49			−0.206844
$893$	−37181.1			−1.39330
$894$	5182.91	−	13115.0i	0.193895	−	0.490638i
$895$			7440.59i			0.277890i
$896$	−2151.08			−0.0802036
$897$	−2579.04	−	1019.21i	−0.0959996	−	0.0379381i
$898$			27646.2i			1.02736i
$899$	−8795.98			−0.326321
$900$	−7422.47	−	6952.35i	−0.274906	−	0.257494i
$901$	624.462			0.0230897
$902$			20708.1i			0.764418i
$903$	−13944.4	−	5510.68i	−0.513887	−	0.203083i
$904$	3744.96			0.137783
$905$		−	24503.4i		−	0.900024i
$906$	−6284.88	−	2483.72i	−0.230465	−	0.0910774i
$907$	32917.7			1.20509			0.602544	−	0.798086i	$-0.294154\pi$
$907$	32917.7			1.20509			0.602544	+	0.798086i	$0.294154\pi$
$908$	15089.6			0.551504
$909$	−29402.9	−	27540.6i	−1.07286	−	1.00491i
$910$	−8295.14			−0.302177
$911$		−	40336.9i		−	1.46698i	−0.679698	−	0.733492i	$-0.737889\pi$
$911$		−	40336.9i		−	1.46698i	0.679698	−	0.733492i	$-0.262111\pi$
$912$	−1856.61	+	4698.03i	−0.0674107	+	0.170578i
$913$	−1409.69			−0.0510997
$914$			20101.7i			0.727467i
$915$	−264.825	+	670.122i	−0.00956815	+	0.0242115i
$916$		−	12135.6i		−	0.437743i
$917$	31146.0			1.12163
$918$	3582.46	+	7575.43i	0.128800	+	0.272360i
$919$			44408.1i			1.59400i	0.603977	+	0.797002i	$0.293582\pi$
$919$			44408.1i			1.59400i	−0.603977	+	0.797002i	$0.706418\pi$
$920$			533.403i			0.0191150i
$921$	−7911.94	+	20020.6i	−0.283070	+	0.716289i
$922$		−	15595.5i		−	0.557063i
$923$	−3987.07			−0.142184
$924$	3850.32	−	9742.95i	0.137085	−	0.346883i
$925$			4518.60i			0.160617i
$926$		−	26870.5i		−	0.953585i
$927$	15548.3	−	16599.7i	0.550888	−	0.588139i
$928$		−	5851.78i		−	0.206998i
$929$	1033.02			0.0364824			0.0182412	−	0.999834i	$-0.494193\pi$
$929$	1033.02			0.0364824			0.0182412	+	0.999834i	$0.494193\pi$
$930$	1020.15	−	2581.42i	0.0359700	−	0.0910196i
$931$	−3681.06			−0.129583
$932$	24854.3			0.873531
$933$	3917.16	+	1548.02i	0.137451	+	0.0543193i
$934$	24840.1			0.870227
$935$	4973.77			0.173967
$936$	−6562.98	+	7006.77i	−0.229186	+	0.244683i
$937$		−	20876.9i		−	0.727874i	−0.931424	−	0.363937i	$-0.881432\pi$
$937$		−	20876.9i		−	0.727874i	0.931424	−	0.363937i	$-0.118568\pi$
$938$			1627.28i			0.0566445i
$939$	14380.1	+	5682.88i	0.499763	+	0.197501i
$940$			13591.5i			0.471604i
$941$	43757.1			1.51588			0.757939	−	0.652326i	$-0.226207\pi$
$941$	43757.1			1.51588			0.757939	+	0.652326i	$0.226207\pi$
$942$	−34906.9	−	13794.9i	−1.20736	−	0.477134i
$943$			4145.23i			0.143147i
$944$	−4007.52	+	6042.91i	−0.138171	+	0.208348i
$945$	−5596.95	−	11835.2i	−0.192665	−	0.407408i
$946$			10299.8i			0.353990i
$947$		−	24895.4i		−	0.854269i	−0.904188	−	0.427134i	$-0.859523\pi$
$947$		−	24895.4i		−	0.854269i	0.904188	−	0.427134i	$-0.140477\pi$
$948$	5828.11	−	14747.6i	0.199671	−	0.505254i
$949$	−11672.8			−0.399279
$950$	−11443.3			−0.390810
$951$	−29871.1	−	11804.7i	−1.01854	−	0.402518i
$952$			4015.08i			0.136691i
$953$		−	16728.0i		−	0.568598i	−0.958736	−	0.284299i	$-0.908239\pi$
$953$		−	16728.0i		−	0.568598i	0.958736	−	0.284299i	$-0.0917608\pi$
$954$	−771.887	+	824.082i	−0.0261958	+	0.0279671i
$955$		−	12577.6i		−	0.426178i
$956$			14995.9i			0.507326i
$957$	26504.7	+	10474.4i	0.895271	+	0.353802i
$958$			5824.81i			0.196442i
$959$		−	12488.4i		−	0.420511i
$960$	1717.36	+	678.685i	0.0577372	+	0.0228171i
$961$	27477.4			0.922338
$962$	4265.53			0.142959
$963$	310.885	−	331.907i	0.0104030	−	0.0111065i
$964$	−14469.0			−0.483418
$965$		−	7039.57i		−	0.234831i
$966$	770.734	−	1950.29i	0.0256708	−	0.0649581i
$967$			3553.23i			0.118163i	0.998253	+	0.0590817i	$0.0188173\pi$
$967$			3553.23i			0.118163i	−0.998253	+	0.0590817i	$0.981183\pi$
$968$	3451.53			0.114604
$969$	8769.08	+	3465.45i	0.290716	+	0.114888i
$970$	−12438.6			−0.411731
$971$			4897.37i			0.161858i	0.996720	+	0.0809289i	$0.0257887\pi$
$971$			4897.37i			0.161858i	−0.996720	+	0.0809289i	$0.974211\pi$
$972$	−14425.3	−	4636.20i	−0.476019	−	0.152990i
$973$	−914.185			−0.0301207
$974$	16318.4			0.536834
$975$	−20225.6	−	7992.95i	−0.664346	−	0.262543i
$976$			399.568i			0.0131044i
$977$	59163.6			1.93737			0.968685	−	0.248291i	$-0.0798690\pi$
$977$	59163.6			1.93737			0.968685	+	0.248291i	$0.0798690\pi$
$978$	−10177.4	+	25753.2i	−0.332758	+	0.842022i
$979$	7118.22			0.232379
$980$			1345.61i			0.0438612i
$981$	32234.3	−	34414.0i	1.04910	−	1.12004i
$982$			895.606i			0.0291038i
$983$	−19919.6			−0.646323			−0.323162	−	0.946344i	$-0.604746\pi$
$983$	−19919.6			−0.646323			−0.323162	+	0.946344i	$0.604746\pi$
$984$	13346.1	+	5274.26i	0.432378	+	0.170871i
$985$	19718.1			0.637838
$986$	−10922.6			−0.352785
$987$	19638.9	−	49695.0i	0.633348	−	1.60264i
$988$			10802.4i			0.347845i
$989$			2061.75i			0.0662891i
$990$	−6147.99	+	6563.72i	−0.197370	+	0.210716i
$991$		−	15278.2i		−	0.489736i	−0.969556	−	0.244868i	$-0.921255\pi$
$991$		−	15278.2i		−	0.489736i	0.969556	−	0.244868i	$-0.0787446\pi$
$992$		−	1539.21i		−	0.0492640i
$993$	−236.009	+	597.205i	−0.00754233	+	0.0190853i
$994$		−	3015.05i		−	0.0962089i
$995$			6407.29i			0.204146i
$996$	−359.042	+	908.531i	−0.0114224	+	0.0289035i
$997$	46689.2			1.48311			0.741555	−	0.670892i	$-0.234088\pi$
$997$	46689.2			1.48311			0.741555	+	0.670892i	$0.234088\pi$
$998$	−8687.26			−0.275541
$999$	2878.07	+	6085.92i	0.0911492	+	0.192743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.c.a.353.12	yes	30
3.2	odd	2		354.4.c.b.353.11	yes	30
59.58	odd	2		354.4.c.b.353.12	yes	30
177.176	even	2	inner	354.4.c.a.353.11	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.11	✓	30	177.176	even	2	inner
354.4.c.a.353.12	yes	30	1.1	even	1	trivial
354.4.c.b.353.11	yes	30	3.2	odd	2
354.4.c.b.353.12	yes	30	59.58	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +(-1.90975 + 4.83248i) q^{3} +4.00000 q^{4} -5.55280i q^{5} +(3.81949 - 9.66496i) q^{6} +16.8053 q^{7} -8.00000 q^{8} +(-19.7057 - 18.4576i) q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +(-1.90975 + 4.83248i) q^{3} +4.00000 q^{4} -5.55280i q^{5} +(3.81949 - 9.66496i) q^{6} +16.8053 q^{7} -8.00000 q^{8} +(-19.7057 - 18.4576i) q^{9} +11.1056i q^{10} -29.9926 q^{11} +(-7.63899 + 19.3299i) q^{12} +44.4463i q^{13} -33.6106 q^{14} +(26.8338 + 10.6045i) q^{15} +16.0000 q^{16} -29.8647i q^{17} +(39.4115 + 36.9153i) q^{18} +60.7611 q^{19} -22.2112i q^{20} +(-32.0938 + 81.2112i) q^{21} +59.9853 q^{22} +12.0075 q^{23} +(15.2780 - 38.6598i) q^{24} +94.1664 q^{25} -88.8925i q^{26} +(126.829 - 59.9782i) q^{27} +67.2211 q^{28} +182.868i q^{29} +(-53.6676 - 21.2089i) q^{30} +48.1002i q^{31} -32.0000 q^{32} +(57.2784 - 144.939i) q^{33} +59.7294i q^{34} -93.3165i q^{35} +(-78.8229 - 73.8305i) q^{36} +47.9852i q^{37} -121.522 q^{38} +(-214.786 - 84.8811i) q^{39} +44.4224i q^{40} +345.220i q^{41} +(64.1877 - 162.422i) q^{42} +171.705i q^{43} -119.971 q^{44} +(-102.492 + 109.422i) q^{45} -24.0150 q^{46} -611.923 q^{47} +(-30.5559 + 77.3197i) q^{48} -60.5825 q^{49} -188.333 q^{50} +(144.321 + 57.0340i) q^{51} +177.785i q^{52} +20.9097i q^{53} +(-253.658 + 119.956i) q^{54} +166.543i q^{55} -134.442 q^{56} +(-116.038 + 293.627i) q^{57} -365.736i q^{58} +(-250.470 + 377.682i) q^{59} +(107.335 + 42.4178i) q^{60} +24.9730i q^{61} -96.2004i q^{62} +(-331.160 - 310.186i) q^{63} +64.0000 q^{64} +246.801 q^{65} +(-114.557 + 289.878i) q^{66} -48.4157i q^{67} -119.459i q^{68} +(-22.9313 + 58.0260i) q^{69} +186.633i q^{70} +89.7055i q^{71} +(157.646 + 147.661i) q^{72} +262.627i q^{73} -95.9705i q^{74} +(-179.834 + 455.057i) q^{75} +243.044 q^{76} -504.035 q^{77} +(429.571 + 169.762i) q^{78} -762.943 q^{79} -88.8449i q^{80} +(47.6319 + 727.442i) q^{81} -690.440i q^{82} +47.0013 q^{83} +(-128.375 + 324.845i) q^{84} -165.833 q^{85} -343.410i q^{86} +(-883.706 - 349.232i) q^{87} +239.941 q^{88} -237.332 q^{89} +(204.983 - 218.844i) q^{90} +746.932i q^{91} +48.0300 q^{92} +(-232.443 - 91.8592i) q^{93} +1223.85 q^{94} -337.394i q^{95} +(61.1119 - 154.639i) q^{96} +1120.03i q^{97} +121.165 q^{98} +(591.027 + 553.593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more