LMFDB - Embedded newform 354.4.c.b.353.11

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			353.11
Character	$\chi$	$=$	354.353
Dual form			354.4.c.b.353.12

$q$-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	$0.0798814\pi$
$5$			5.55280i			0.496658i	−0.968676	+	0.248329i	$0.920119\pi$
$6$	−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	$-0.365162\pi$
$11$	29.9926			0.822102			0.411051	+	0.911612i	$0.365162\pi$
$12$	−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	$0.0683355\pi$
$17$			29.8647i			0.426074i	−0.977044	+	0.213037i	$0.931665\pi$
$18$	−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	$-0.517334\pi$
$23$	−12.0075			−0.108858			−0.0544291	+	0.998518i	$0.517334\pi$
$24$	−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	$-0.800907\pi$
$29$		−	182.868i		−	1.17096i	0.810688	−	0.585478i	$-0.199093\pi$
$30$	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	$-0.771618\pi$
$41$		−	345.220i		−	1.31498i	0.753462	−	0.657491i	$-0.228382\pi$
$42$	−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	$-0.101536\pi$
$47$	611.923			1.89911			0.949554	+	0.313603i	$0.101536\pi$
$48$	−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	$-0.991374\pi$
$53$		−	20.9097i		−	0.0541919i	0.999633	−	0.0270959i	$-0.00862596\pi$
$54$	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	$-0.976113\pi$
$71$		−	89.7055i		−	0.149945i	0.997186	−	0.0749724i	$-0.0238869\pi$
$72$	−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	$-0.509894\pi$
$83$	−47.0013			−0.0621574			−0.0310787	+	0.999517i	$0.509894\pi$
$84$	−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	$-0.454861\pi$
$89$	237.332			0.282665			0.141332	+	0.989962i	$0.454861\pi$
$90$	−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	$-0.762817\pi$
$101$	−1492.10			−1.47000			−0.734998	+	0.678070i	$0.762817\pi$
$102$	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	$-0.997578\pi$
$107$		−	16.8432i		−	0.0152177i	0.999971	−	0.00760884i	$-0.00242199\pi$
$108$	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	$-0.437577\pi$
$113$	468.120			0.389709			0.194854	+	0.980832i	$0.437577\pi$
$114$	−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	$-0.712074\pi$
$131$	−1853.34			−1.23609			−0.618043	+	0.786144i	$0.712074\pi$
$132$	−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	$0.0744327\pi$
$137$			743.121i			0.463424i	−0.972784	+	0.231712i	$0.925567\pi$
$138$	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	$-0.621685\pi$
$149$	−1356.96			−0.746085			−0.373042	+	0.927814i	$0.621685\pi$
$150$	−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	$-0.804218\pi$
$167$		−	2490.52i		−	1.15403i	0.816735	−	0.577013i	$-0.195782\pi$
$168$	−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	$-0.441191\pi$
$173$	836.030			0.367412			0.183706	+	0.982981i	$0.441191\pi$
$174$	−1767.41	+	698.463i	−0.770041	+	0.304312i
$175$	1582.49			0.683572
$176$	479.882			0.205526
$177$	−2303.48	−	489.115i	−0.978191	−	0.207707i
$178$	474.664			0.199874
$179$	1339.97			0.559520			0.279760	−	0.960070i	$-0.409745\pi$
$179$	1339.97			0.559520			0.279760	+	0.960070i	$0.409745\pi$
$180$	−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	$-0.641150\pi$
$191$	−2265.08			−0.858093			−0.429046	+	0.903283i	$0.641150\pi$
$192$	−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	$-0.778051\pi$
$197$		−	3551.01i		−	1.28426i	0.766596	−	0.642130i	$-0.221949\pi$
$198$	−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	$-0.685946\pi$
$227$	−3772.40			−1.10301			−0.551504	+	0.834172i	$0.685946\pi$
$228$	−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	$-0.838176\pi$
$233$	−6213.59			−1.74706			−0.873531	+	0.486768i	$0.838176\pi$
$234$	−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	$-0.830634\pi$
$239$		−	3748.99i		−	1.01465i	0.861754	−	0.507326i	$-0.169366\pi$
$240$	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	$0.0631513\pi$
$251$			1567.55i			0.394194i	−0.980384	+	0.197097i	$0.936849\pi$
$252$	−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	$-0.908863\pi$
$257$		−	2327.14i		−	0.564836i	0.959291	−	0.282418i	$-0.0911366\pi$
$258$	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	$-0.989242\pi$
$263$		−	288.250i		−	0.0675827i	0.999429	−	0.0337914i	$-0.0107582\pi$
$264$	−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	$-0.309138\pi$
$269$	4979.48			1.12864			0.564320	+	0.825556i	$0.309138\pi$
$270$	−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	$0.131045\pi$
$281$			3769.82i			0.800315i	−0.916446	+	0.400157i	$0.868955\pi$
$282$	−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	$-0.926622\pi$
$293$		−	2291.88i		−	0.456973i	0.973547	−	0.228487i	$-0.0733778\pi$
$294$	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	$0.0235438\pi$
$311$			810.589i			0.147795i	−0.997266	+	0.0738976i	$0.976456\pi$
$312$	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	$-0.815542\pi$
$317$		−	6181.31i		−	1.09520i	0.836742	−	0.547598i	$-0.184458\pi$
$318$	−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	$-0.403664\pi$
$347$	3853.12			0.596098			0.298049	+	0.954551i	$0.403664\pi$
$348$	−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	$-0.520167\pi$
$353$	−839.813			−0.126625			−0.0633127	+	0.997994i	$0.520167\pi$
$354$	−4606.95	−	978.230i	−0.691686	−	0.146871i
$355$	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	$0.182471\pi$
$359$			7378.43i			1.08473i	−0.840143	+	0.542366i	$0.817529\pi$
$360$	−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	$-0.856141\pi$
$383$		−	6546.79i		−	0.873434i	0.899599	−	0.436717i	$-0.143859\pi$
$384$	−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	$0.148802\pi$
$389$			6914.77i			0.901266i	−0.892709	+	0.450633i	$0.851198\pi$
$390$	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	$-0.675270\pi$
$401$	−8402.96			−1.04644			−0.523222	+	0.852197i	$0.675270\pi$
$402$	−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	$-0.693956\pi$
$419$	−9817.23			−1.14464			−0.572318	+	0.820031i	$0.693956\pi$
$420$	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	$-0.645492\pi$
$431$	−7897.78			−0.882651			−0.441326	+	0.897347i	$0.645492\pi$
$432$	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	$-0.567250\pi$
$443$	−3910.61			−0.419410			−0.209705	+	0.977765i	$0.567250\pi$
$444$	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	$0.258831\pi$
$449$			13823.1i			1.45290i	−0.687219	+	0.726451i	$0.741169\pi$
$450$	−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	$-0.871125\pi$
$461$		−	7797.77i		−	0.787805i	0.919152	−	0.393903i	$-0.128875\pi$
$462$	−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	$-0.289017\pi$
$467$	12420.0			1.23069			0.615343	+	0.788259i	$0.289017\pi$
$468$	−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	$0.0443583\pi$
$479$			2912.40i			0.277810i	−0.990306	+	0.138905i	$0.955642\pi$
$480$	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	$0.00655112\pi$
$491$			447.803i			0.0411590i	−0.999788	+	0.0205795i	$0.993449\pi$
$492$	−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	$-0.444289\pi$
$503$	3928.76			0.348260			0.174130	+	0.984723i	$0.444289\pi$
$504$	−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	$-0.710909\pi$
$509$	−14128.5			−1.23032			−0.615161	+	0.788401i	$0.710909\pi$
$510$	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	$0.225459\pi$
$521$			15472.6i			1.30109i	−0.759468	+	0.650544i	$0.774541\pi$
$522$	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
$531$	2035.42	+	12065.6i	0.166346	+	0.986067i
$532$	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	$-0.976880\pi$
$557$		−	1907.98i		−	0.145141i	0.997363	−	0.0725706i	$-0.0231203\pi$
$558$	−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	$-0.344711\pi$
$563$	12523.3			0.937465			0.468733	+	0.883340i	$0.344711\pi$
$564$	−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	$-0.764492\pi$
$569$	−20048.5			−1.47711			−0.738557	+	0.674191i	$0.764492\pi$
$570$	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	$-0.568732\pi$
$587$	−6094.18			−0.428507			−0.214254	+	0.976778i	$0.568732\pi$
$588$	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	$-0.701106\pi$
$593$		−	23306.1i		−	1.61394i	0.590594	−	0.806969i	$-0.298894\pi$
$594$	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	$-0.911895\pi$
$599$		−	8012.39i		−	0.546540i	0.961937	−	0.273270i	$-0.0881052\pi$
$600$	−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	$0.0125777\pi$
$617$			1210.86i			0.0790072i	−0.999219	+	0.0395036i	$0.987422\pi$
$618$	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	$0.0110495\pi$
$641$			1126.48i			0.0694122i	−0.999398	+	0.0347061i	$0.988950\pi$
$642$	−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	$0.247456\pi$
$647$			23087.3i			1.40287i	−0.712736	+	0.701433i	$0.752544\pi$
$648$	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	$-0.736102\pi$
$653$		−	24606.1i		−	1.47460i	0.675568	−	0.737298i	$-0.263898\pi$
$654$	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	$-0.363330\pi$
$659$	14084.9			0.832579			0.416289	+	0.909232i	$0.363330\pi$
$660$	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	$-0.942686\pi$
$677$		−	6309.18i		−	0.358171i	0.983834	−	0.179085i	$-0.0573138\pi$
$678$	−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	$-0.295912\pi$
$683$	21352.7			1.19625			0.598125	+	0.801403i	$0.295912\pi$
$684$	−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	$-0.797345\pi$
$701$	−29847.6			−1.60817			−0.804086	+	0.594513i	$0.797345\pi$
$702$	−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
$708$	−9213.90	−	1956.46i	−0.489096	−	0.103853i
$709$	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	$-0.208812\pi$
$719$	30555.4			1.58488			0.792438	+	0.609953i	$0.208812\pi$
$720$	−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	$0.203198\pi$
$743$			24136.6i			1.19177i	−0.803070	+	0.595884i	$0.796802\pi$
$744$	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	$-0.636836\pi$
$761$		−	38166.1i		−	1.81803i	0.416765	−	0.909014i	$-0.363164\pi$
$762$	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	$-0.381254\pi$
$773$	15665.6			0.728916			0.364458	+	0.931220i	$0.381254\pi$
$774$	−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	$-0.520698\pi$
$797$	−2924.05			−0.129956			−0.0649781	+	0.997887i	$0.520698\pi$
$798$	−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	$-0.276407\pi$
$809$	29733.1			1.29216			0.646081	+	0.763269i	$0.276407\pi$
$810$	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	$-0.508394\pi$
$821$	−1240.60			−0.0527373			−0.0263686	+	0.999652i	$0.508394\pi$
$822$	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	$-0.901515\pi$
$827$		−	14483.0i		−	0.608975i	0.952516	−	0.304487i	$-0.0984852\pi$
$828$	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	$-0.446422\pi$
$839$	8142.54			0.335056			0.167528	+	0.985867i	$0.446422\pi$
$840$	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	$-0.288580\pi$
$857$	30930.2			1.23285			0.616426	+	0.787413i	$0.288580\pi$
$858$	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	$-0.656426\pi$
$863$	−23926.7			−0.943769			−0.471885	+	0.881660i	$0.656426\pi$
$864$	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	$-0.496527\pi$
$881$	570.605			0.0218209			0.0109104	+	0.999940i	$0.496527\pi$
$882$	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
$885$	2715.96	−	12790.7i	0.103159	−	0.485826i
$886$	−7821.22			−0.296568
$887$	1442.79			0.0546156			0.0273078	−	0.999627i	$-0.491307\pi$
$887$	1442.79			0.0546156			0.0273078	+	0.999627i	$0.491307\pi$
$888$	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	$0.262111\pi$
$911$			40336.9i			1.46698i	−0.679698	+	0.733492i	$0.737889\pi$
$912$	−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	$-0.505807\pi$
$929$	−1033.02			−0.0364824			−0.0182412	+	0.999834i	$0.505807\pi$
$930$	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	$-0.773793\pi$
$941$	−43757.1			−1.51588			−0.757939	+	0.652326i	$0.773793\pi$
$942$	−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	$0.140477\pi$
$947$			24895.4i			0.854269i	−0.904188	+	0.427134i	$0.859523\pi$
$948$	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	$0.0917608\pi$
$953$			16728.0i			0.568598i	−0.958736	+	0.284299i	$0.908239\pi$
$954$	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	$-0.974211\pi$
$971$		−	4897.37i		−	0.161858i	0.996720	−	0.0809289i	$-0.0257887\pi$
$972$	−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	$-0.920131\pi$
$977$	−59163.6			−1.93737			−0.968685	+	0.248291i	$0.920131\pi$
$978$	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	$-0.395254\pi$
$983$	19919.6			0.646323			0.323162	+	0.946344i	$0.395254\pi$
$984$	−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.b.353.11	yes	30
3.2	odd	2		354.4.c.a.353.12	yes	30
59.58	odd	2		354.4.c.a.353.11	✓	30
177.176	even	2	inner	354.4.c.b.353.12	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.11	✓	30	59.58	odd	2
354.4.c.a.353.12	yes	30	3.2	odd	2
354.4.c.b.353.11	yes	30	1.1	even	1	trivial
354.4.c.b.353.12	yes	30	177.176	even	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
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

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