LMFDB - Embedded newform 230.5.d.a.91.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(91,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.d (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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.14
Character	$\chi$	$=$	230.91
Dual form			230.5.d.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843 q^{2} +7.33271 q^{3} +8.00000 q^{4} -11.1803i q^{5} -20.7400 q^{6} +75.6542i q^{7} -22.6274 q^{8} -27.2314 q^{9} +O(q^{10})$	\(q-2.82843 q^{2} +7.33271 q^{3} +8.00000 q^{4} -11.1803i q^{5} -20.7400 q^{6} +75.6542i q^{7} -22.6274 q^{8} -27.2314 q^{9} +31.6228i q^{10} -34.1889i q^{11} +58.6617 q^{12} -197.432 q^{13} -213.982i q^{14} -81.9822i q^{15} +64.0000 q^{16} -398.477i q^{17} +77.0220 q^{18} -103.242i q^{19} -89.4427i q^{20} +554.750i q^{21} +96.7007i q^{22} +(-296.326 - 438.214i) q^{23} -165.920 q^{24} -125.000 q^{25} +558.423 q^{26} -793.629 q^{27} +605.234i q^{28} +467.608 q^{29} +231.881i q^{30} -705.269 q^{31} -181.019 q^{32} -250.697i q^{33} +1127.06i q^{34} +845.840 q^{35} -217.851 q^{36} -1178.93i q^{37} +292.012i q^{38} -1447.71 q^{39} +252.982i q^{40} +2869.05 q^{41} -1569.07i q^{42} +1322.67i q^{43} -273.511i q^{44} +304.456i q^{45} +(838.137 + 1239.46i) q^{46} -2467.58 q^{47} +469.293 q^{48} -3322.56 q^{49} +353.553 q^{50} -2921.91i q^{51} -1579.46 q^{52} -3210.85i q^{53} +2244.72 q^{54} -382.243 q^{55} -1711.86i q^{56} -757.043i q^{57} -1322.60 q^{58} -6472.33 q^{59} -655.857i q^{60} -6608.69i q^{61} +1994.80 q^{62} -2060.17i q^{63} +512.000 q^{64} +2207.36i q^{65} +709.078i q^{66} +5225.76i q^{67} -3187.81i q^{68} +(-2172.87 - 3213.30i) q^{69} -2392.40 q^{70} -5696.69 q^{71} +616.176 q^{72} -7364.21 q^{73} +3334.51i q^{74} -916.589 q^{75} -825.936i q^{76} +2586.53 q^{77} +4094.75 q^{78} +1905.16i q^{79} -715.542i q^{80} -3613.71 q^{81} -8114.90 q^{82} +2724.40i q^{83} +4438.00i q^{84} -4455.11 q^{85} -3741.08i q^{86} +3428.84 q^{87} +773.606i q^{88} +4252.33i q^{89} -861.132i q^{90} -14936.6i q^{91} +(-2370.61 - 3505.71i) q^{92} -5171.53 q^{93} +6979.37 q^{94} -1154.28 q^{95} -1327.36 q^{96} +5482.74i q^{97} +9397.61 q^{98} +931.010i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.82843			−0.707107
$2$	−2.82843			−0.707107
$3$	7.33271			0.814745			0.407373	−	0.913262i	$-0.366445\pi$
$3$	7.33271			0.814745			0.407373	+	0.913262i	$0.366445\pi$
$4$	8.00000			0.500000
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$	−20.7400			−0.576112
$7$			75.6542i			1.54396i	0.635645	+	0.771982i	$0.280734\pi$
$7$			75.6542i			1.54396i	−0.635645	+	0.771982i	$0.719266\pi$
$8$	−22.6274			−0.353553
$9$	−27.2314			−0.336190
$10$			31.6228i			0.316228i
$11$		−	34.1889i		−	0.282553i	−0.989970	−	0.141276i	$-0.954879\pi$
$11$		−	34.1889i		−	0.282553i	0.989970	−	0.141276i	$-0.0451206\pi$
$12$	58.6617			0.407373
$13$	−197.432			−1.16824			−0.584119	−	0.811668i	$-0.698560\pi$
$13$	−197.432			−1.16824			−0.584119	+	0.811668i	$0.698560\pi$
$14$		−	213.982i		−	1.09175i
$15$		−	81.9822i		−	0.364365i
$16$	64.0000			0.250000
$17$		−	398.477i		−	1.37881i	−0.724375	−	0.689406i	$-0.757872\pi$
$17$		−	398.477i		−	1.37881i	0.724375	−	0.689406i	$-0.242128\pi$
$18$	77.0220			0.237722
$19$		−	103.242i		−	0.285989i	−0.989723	−	0.142994i	$-0.954327\pi$
$19$		−	103.242i		−	0.285989i	0.989723	−	0.142994i	$-0.0456731\pi$
$20$		−	89.4427i		−	0.223607i
$21$			554.750i			1.25794i
$22$			96.7007i			0.199795i
$23$	−296.326	−	438.214i	−0.560163	−	0.828383i
$23$	−296.326	−	438.214i	−0.560163	−	0.828383i
$24$	−165.920			−0.288056
$25$	−125.000			−0.200000
$26$	558.423			0.826069
$27$	−793.629			−1.08865
$28$			605.234i			0.771982i
$29$	467.608			0.556015			0.278007	−	0.960579i	$-0.410326\pi$
$29$	467.608			0.556015			0.278007	+	0.960579i	$0.410326\pi$
$30$			231.881i			0.257645i
$31$	−705.269			−0.733891			−0.366945	−	0.930242i	$-0.619596\pi$
$31$	−705.269			−0.733891			−0.366945	+	0.930242i	$0.619596\pi$
$32$	−181.019			−0.176777
$33$		−	250.697i		−	0.230209i
$34$			1127.06i			0.974967i
$35$	845.840			0.690481
$36$	−217.851			−0.168095
$37$		−	1178.93i		−	0.861158i	−0.902553	−	0.430579i	$-0.858309\pi$
$37$		−	1178.93i		−	0.861158i	0.902553	−	0.430579i	$-0.141691\pi$
$38$			292.012i			0.202225i
$39$	−1447.71			−0.951816
$40$			252.982i			0.158114i
$41$	2869.05			1.70675			0.853376	−	0.521296i	$-0.174551\pi$
$41$	2869.05			1.70675			0.853376	+	0.521296i	$0.174551\pi$
$42$		−	1569.07i		−	0.889496i
$43$			1322.67i			0.715344i	0.933847	+	0.357672i	$0.116429\pi$
$43$			1322.67i			0.715344i	−0.933847	+	0.357672i	$0.883571\pi$
$44$		−	273.511i		−	0.141276i
$45$			304.456i			0.150349i
$46$	838.137	+	1239.46i	0.396095	+	0.585755i
$47$	−2467.58			−1.11706			−0.558529	−	0.829485i	$-0.688634\pi$
$47$	−2467.58			−1.11706			−0.558529	+	0.829485i	$0.688634\pi$
$48$	469.293			0.203686
$49$	−3322.56			−1.38382
$50$	353.553			0.141421
$51$		−	2921.91i		−	1.12338i
$52$	−1579.46			−0.584119
$53$		−	3210.85i		−	1.14306i	−0.820582	−	0.571528i	$-0.806351\pi$
$53$		−	3210.85i		−	1.14306i	0.820582	−	0.571528i	$-0.193649\pi$
$54$	2244.72			0.769795
$55$	−382.243			−0.126361
$56$		−	1711.86i		−	0.545873i
$57$		−	757.043i		−	0.233008i
$58$	−1322.60			−0.393162
$59$	−6472.33			−1.85933			−0.929665	−	0.368406i	$-0.879904\pi$
$59$	−6472.33			−1.85933			−0.929665	+	0.368406i	$0.879904\pi$
$60$		−	655.857i		−	0.182183i
$61$		−	6608.69i		−	1.77605i	−0.459794	−	0.888026i	$-0.652077\pi$
$61$		−	6608.69i		−	1.77605i	0.459794	−	0.888026i	$-0.347923\pi$
$62$	1994.80			0.518939
$63$		−	2060.17i		−	0.519065i
$64$	512.000			0.125000
$65$			2207.36i			0.522452i
$66$			709.078i			0.162782i
$67$			5225.76i			1.16413i	0.813144	+	0.582063i	$0.197754\pi$
$67$			5225.76i			1.16413i	−0.813144	+	0.582063i	$0.802246\pi$
$68$		−	3187.81i		−	0.689406i
$69$	−2172.87	−	3213.30i	−0.456390	−	0.674921i
$70$	−2392.40			−0.488244
$71$	−5696.69			−1.13007			−0.565035	−	0.825067i	$-0.691138\pi$
$71$	−5696.69			−1.13007			−0.565035	+	0.825067i	$0.691138\pi$
$72$	616.176			0.118861
$73$	−7364.21			−1.38191			−0.690956	−	0.722897i	$-0.742810\pi$
$73$	−7364.21			−1.38191			−0.690956	+	0.722897i	$0.742810\pi$
$74$			3334.51i			0.608931i
$75$	−916.589			−0.162949
$76$		−	825.936i		−	0.142994i
$77$	2586.53			0.436251
$78$	4094.75			0.673036
$79$			1905.16i			0.305265i	0.988283	+	0.152633i	$0.0487752\pi$
$79$			1905.16i			0.305265i	−0.988283	+	0.152633i	$0.951225\pi$
$80$		−	715.542i		−	0.111803i
$81$	−3613.71			−0.550786
$82$	−8114.90			−1.20686
$83$			2724.40i			0.395470i	0.980255	+	0.197735i	$0.0633586\pi$
$83$			2724.40i			0.395470i	−0.980255	+	0.197735i	$0.936641\pi$
$84$			4438.00i			0.628968i
$85$	−4455.11			−0.616624
$86$		−	3741.08i		−	0.505825i
$87$	3428.84			0.453010
$88$			773.606i			0.0998975i
$89$			4252.33i			0.536843i	0.963302	+	0.268421i	$0.0865020\pi$
$89$			4252.33i			0.536843i	−0.963302	+	0.268421i	$0.913498\pi$
$90$		−	861.132i		−	0.106313i
$91$		−	14936.6i		−	1.80372i
$92$	−2370.61	−	3505.71i	−0.280081	−	0.414191i
$93$	−5171.53			−0.597934
$94$	6979.37			0.789879
$95$	−1154.28			−0.127898
$96$	−1327.36			−0.144028
$97$			5482.74i			0.582712i	0.956615	+	0.291356i	$0.0941064\pi$
$97$			5482.74i			0.582712i	−0.956615	+	0.291356i	$0.905894\pi$
$98$	9397.61			0.978510
$99$			931.010i			0.0949914i
$100$	−1000.00			−0.100000
$101$	19839.0			1.94481			0.972406	−	0.233296i	$-0.0749510\pi$
$101$	19839.0			1.94481			0.972406	+	0.233296i	$0.0749510\pi$
$102$			8264.42i			0.794350i
$103$			297.020i			0.0279970i	0.999902	+	0.0139985i	$0.00445601\pi$
$103$			297.020i			0.0279970i	−0.999902	+	0.0139985i	$0.995544\pi$
$104$	4467.38			0.413034
$105$	6202.30			0.562567
$106$			9081.64i			0.808263i
$107$			12365.7i			1.08007i	0.841643	+	0.540035i	$0.181589\pi$
$107$			12365.7i			1.08007i	−0.841643	+	0.540035i	$0.818411\pi$
$108$	−6349.03			−0.544327
$109$		−	12718.6i		−	1.07050i	−0.844694	−	0.535250i	$-0.820217\pi$
$109$		−	12718.6i		−	1.07050i	0.844694	−	0.535250i	$-0.179783\pi$
$110$	1081.15			0.0893510
$111$		−	8644.72i		−	0.701625i
$112$			4841.87i			0.385991i
$113$		−	11813.4i		−	0.925165i	−0.886576	−	0.462583i	$-0.846923\pi$
$113$		−	11813.4i		−	0.925165i	0.886576	−	0.462583i	$-0.153077\pi$
$114$			2141.24i			0.164762i
$115$	−4899.39	+	3313.03i	−0.370464	+	0.250512i
$116$	3740.87			0.278007
$117$	5376.35			0.392750
$118$	18306.5			1.31474
$119$	30146.4			2.12884
$120$			1855.04i			0.128823i
$121$	13472.1			0.920164
$122$			18692.2i			1.25586i
$123$	21037.9			1.39057
$124$	−5642.15			−0.366945
$125$			1397.54i			0.0894427i
$126$			5827.04i			0.367034i
$127$	−12443.5			−0.771501			−0.385750	−	0.922603i	$-0.626057\pi$
$127$	−12443.5			−0.771501			−0.385750	+	0.922603i	$0.626057\pi$
$128$	−1448.15			−0.0883883
$129$			9698.77i			0.582824i
$130$		−	6243.35i		−	0.369429i
$131$	−14644.4			−0.853352			−0.426676	−	0.904405i	$-0.640316\pi$
$131$	−14644.4			−0.853352			−0.426676	+	0.904405i	$0.640316\pi$
$132$		−	2005.58i		−	0.115104i
$133$	7810.69			0.441556
$134$		−	14780.7i		−	0.823161i
$135$			8873.04i			0.486861i
$136$			9016.50i			0.487484i
$137$			24294.3i			1.29438i	0.762327	+	0.647192i	$0.224057\pi$
$137$			24294.3i			1.29438i	−0.762327	+	0.647192i	$0.775943\pi$
$138$	6145.81	+	9088.58i	0.322717	+	0.477241i
$139$	−22683.1			−1.17402			−0.587008	−	0.809581i	$-0.699694\pi$
$139$	−22683.1			−1.17402			−0.587008	+	0.809581i	$0.699694\pi$
$140$	6766.72			0.345241
$141$	−18094.0			−0.910117
$142$	16112.7			0.799081
$143$			6749.98i			0.330089i
$144$	−1742.81			−0.0840475
$145$		−	5228.02i		−	0.248657i
$146$	20829.1			0.977159
$147$	−24363.3			−1.12746
$148$		−	9431.40i		−	0.430579i
$149$			39128.9i			1.76248i	0.472666	+	0.881241i	$0.343292\pi$
$149$			39128.9i			1.76248i	−0.472666	+	0.881241i	$0.656708\pi$
$150$	2592.50			0.115222
$151$	21428.3			0.939798			0.469899	−	0.882720i	$-0.344290\pi$
$151$	21428.3			0.939798			0.469899	+	0.882720i	$0.344290\pi$
$152$			2336.10i			0.101112i
$153$			10851.1i			0.463543i
$154$	−7315.82			−0.308476
$155$			7885.15i			0.328206i
$156$	−11581.7			−0.475908
$157$			11663.7i			0.473193i	0.971608	+	0.236596i	$0.0760319\pi$
$157$			11663.7i			0.473193i	−0.971608	+	0.236596i	$0.923968\pi$
$158$		−	5388.61i		−	0.215855i
$159$		−	23544.2i		−	0.931300i
$160$			2023.86i			0.0790569i
$161$	33152.8	−	22418.3i	1.27899	−	0.864871i
$162$	10221.1			0.389465
$163$	32325.1			1.21665			0.608323	−	0.793690i	$-0.291843\pi$
$163$	32325.1			1.21665			0.608323	+	0.793690i	$0.291843\pi$
$164$	22952.4			0.853376
$165$	−2802.88			−0.102952
$166$		−	7705.76i		−	0.279640i
$167$	−17057.6			−0.611625			−0.305812	−	0.952092i	$-0.598928\pi$
$167$	−17057.6			−0.611625			−0.305812	+	0.952092i	$0.598928\pi$
$168$		−	12552.6i		−	0.444748i
$169$	10418.5			0.364780
$170$	12600.9			0.436019
$171$			2811.42i			0.0961465i
$172$			10581.4i			0.357672i
$173$	−44731.0			−1.49457			−0.747286	−	0.664503i	$-0.768643\pi$
$173$	−44731.0			−1.49457			−0.747286	+	0.664503i	$0.768643\pi$
$174$	−9698.21			−0.320327
$175$		−	9456.77i		−	0.308793i
$176$		−	2188.09i		−	0.0706382i
$177$	−47459.7			−1.51488
$178$		−	12027.4i		−	0.379605i
$179$	42228.4			1.31795			0.658975	−	0.752165i	$-0.270990\pi$
$179$	42228.4			1.31795			0.658975	+	0.752165i	$0.270990\pi$
$180$			2435.65i			0.0751743i
$181$			30696.0i			0.936966i	0.883472	+	0.468483i	$0.155199\pi$
$181$			30696.0i			0.936966i	−0.883472	+	0.468483i	$0.844801\pi$
$182$			42247.0i			1.27542i
$183$		−	48459.6i		−	1.44703i
$184$	6705.09	+	9915.66i	0.198047	+	0.292877i
$185$	−13180.8			−0.385122
$186$	14627.3			0.422803
$187$	−13623.5			−0.389587
$188$	−19740.6			−0.558529
$189$		−	60041.4i		−	1.68084i
$190$	3264.80			0.0904376
$191$		−	49203.2i		−	1.34874i	−0.738395	−	0.674368i	$-0.764416\pi$
$191$		−	49203.2i		−	1.34874i	0.738395	−	0.674368i	$-0.235584\pi$
$192$	3754.35			0.101843
$193$	7645.71			0.205260			0.102630	−	0.994720i	$-0.467274\pi$
$193$	7645.71			0.205260			0.102630	+	0.994720i	$0.467274\pi$
$194$		−	15507.5i		−	0.412040i
$195$			16185.9i			0.425665i
$196$	−26580.5			−0.691911
$197$	−24674.2			−0.635785			−0.317892	−	0.948127i	$-0.602975\pi$
$197$	−24674.2			−0.635785			−0.317892	+	0.948127i	$0.602975\pi$
$198$		−	2633.29i		−	0.0671690i
$199$		−	50289.1i		−	1.26989i	−0.772556	−	0.634947i	$-0.781022\pi$
$199$		−	50289.1i		−	1.26989i	0.772556	−	0.634947i	$-0.218978\pi$
$200$	2828.43			0.0707107
$201$			38319.0i			0.948466i
$202$	−56113.2			−1.37519
$203$			35376.5i			0.858466i
$204$		−	23375.3i		−	0.561690i
$205$		−	32077.0i		−	0.763283i
$206$		−	840.101i		−	0.0197969i
$207$	8069.37	+	11933.2i	0.188321	+	0.278494i
$208$	−12635.7			−0.292059
$209$	−3529.73			−0.0808069
$210$	−17542.7			−0.397795
$211$	−2814.71			−0.0632220			−0.0316110	−	0.999500i	$-0.510064\pi$
$211$	−2814.71			−0.0632220			−0.0316110	+	0.999500i	$0.510064\pi$
$212$		−	25686.8i		−	0.571528i
$213$	−41772.1			−0.920720
$214$		−	34975.5i		−	0.763725i
$215$	14787.9			0.319912
$216$	17957.8			0.384898
$217$		−	53356.6i		−	1.13310i
$218$			35973.7i			0.756958i
$219$	−53999.6			−1.12591
$220$	−3057.95			−0.0631807
$221$			78672.1i			1.61078i
$222$			24451.0i			0.496124i
$223$	9911.25			0.199305			0.0996527	−	0.995022i	$-0.468227\pi$
$223$	9911.25			0.199305			0.0996527	+	0.995022i	$0.468227\pi$
$224$		−	13694.9i		−	0.272937i
$225$	3403.92			0.0672380
$226$			33413.4i			0.654191i
$227$			38706.5i			0.751160i	0.926790	+	0.375580i	$0.122556\pi$
$227$			38706.5i			0.751160i	−0.926790	+	0.375580i	$0.877444\pi$
$228$		−	6056.35i		−	0.116504i
$229$		−	22140.6i		−	0.422200i	−0.977464	−	0.211100i	$-0.932295\pi$
$229$		−	22140.6i		−	0.422200i	0.977464	−	0.211100i	$-0.0677046\pi$
$230$	13857.6	−	9370.65i	0.261958	−	0.177139i
$231$	18966.3			0.355433
$232$	−10580.8			−0.196581
$233$	23880.5			0.439878			0.219939	−	0.975514i	$-0.429414\pi$
$233$	23880.5			0.439878			0.219939	+	0.975514i	$0.429414\pi$
$234$	−15206.6			−0.277716
$235$			27588.4i			0.499563i
$236$	−51778.6			−0.929665
$237$			13970.0i			0.248714i
$238$	−85267.0			−1.50531
$239$	8996.17			0.157493			0.0787466	−	0.996895i	$-0.474908\pi$
$239$	8996.17			0.157493			0.0787466	+	0.996895i	$0.474908\pi$
$240$		−	5246.86i		−	0.0910913i
$241$		−	88691.7i		−	1.52703i	−0.645788	−	0.763517i	$-0.723471\pi$
$241$		−	88691.7i		−	1.52703i	0.645788	−	0.763517i	$-0.276529\pi$
$242$	−38104.9			−0.650654
$243$	37785.7			0.639904
$244$		−	52869.5i		−	0.888026i
$245$			37147.3i			0.618864i
$246$	−59504.2			−0.983280
$247$			20383.3i			0.334103i
$248$	15958.4			0.259470
$249$			19977.2i			0.322208i
$250$		−	3952.85i		−	0.0632456i
$251$		−	19277.9i		−	0.305994i	−0.988227	−	0.152997i	$-0.951108\pi$
$251$		−	19277.9i		−	0.305994i	0.988227	−	0.152997i	$-0.0488925\pi$
$252$		−	16481.3i		−	0.259532i
$253$	−14982.1	+	10131.1i	−0.234062	+	0.158276i
$254$	35195.6			0.545533
$255$	−32668.0			−0.502391
$256$	4096.00			0.0625000
$257$	76277.1			1.15486			0.577428	−	0.816442i	$-0.304056\pi$
$257$	76277.1			1.15486			0.577428	+	0.816442i	$0.304056\pi$
$258$		−	27432.3i		−	0.412118i
$259$	89190.7			1.32960
$260$			17658.9i			0.261226i
$261$	−12733.6			−0.186927
$262$	41420.5			0.603411
$263$		−	10783.2i		−	0.155897i	−0.996957	−	0.0779484i	$-0.975163\pi$
$263$		−	10783.2i		−	0.155897i	0.996957	−	0.0779484i	$-0.0248369\pi$
$264$			5672.63i			0.0813910i
$265$	−35898.3			−0.511190
$266$	−22092.0			−0.312227
$267$			31181.1i			0.437390i
$268$			41806.1i			0.582063i
$269$	138116.			1.90871			0.954353	−	0.298681i	$-0.0965465\pi$
$269$	138116.			1.90871			0.954353	+	0.298681i	$0.0965465\pi$
$270$		−	25096.8i		−	0.344263i
$271$	−13630.5			−0.185598			−0.0927991	−	0.995685i	$-0.529581\pi$
$271$	−13630.5			−0.185598			−0.0927991	+	0.995685i	$0.529581\pi$
$272$		−	25502.5i		−	0.344703i
$273$		−	109526.i		−	1.46957i
$274$		−	68714.6i		−	0.915268i
$275$			4273.61i			0.0565105i
$276$	−17383.0	−	25706.4i	−0.228195	−	0.337460i
$277$	−83154.6			−1.08374			−0.541872	−	0.840461i	$-0.682284\pi$
$277$	−83154.6			−1.08374			−0.541872	+	0.840461i	$0.682284\pi$
$278$	64157.6			0.830154
$279$	19205.5			0.246727
$280$	−19139.2			−0.244122
$281$		−	149656.i		−	1.89531i	−0.319292	−	0.947656i	$-0.603445\pi$
$281$		−	149656.i		−	1.89531i	0.319292	−	0.947656i	$-0.396555\pi$
$282$	51177.7			0.643550
$283$			110094.i			1.37465i	0.726351	+	0.687324i	$0.241215\pi$
$283$			110094.i			1.37465i	−0.726351	+	0.687324i	$0.758785\pi$
$284$	−45573.5			−0.565035
$285$	−8464.00			−0.104204
$286$		−	19091.8i		−	0.233408i
$287$			217056.i			2.63516i
$288$	4929.41			0.0594305
$289$	−75262.7			−0.901123
$290$			14787.1i			0.175827i
$291$			40203.3i			0.474762i
$292$	−58913.7			−0.690956
$293$		−	49371.6i		−	0.575098i	−0.957766	−	0.287549i	$-0.907160\pi$
$293$		−	49371.6i		−	0.575098i	0.957766	−	0.287549i	$-0.0928404\pi$
$294$	68909.9			0.797237
$295$			72362.8i			0.831518i
$296$			26676.0i			0.304465i
$297$			27133.3i			0.307602i
$298$		−	110673.i		−	1.24626i
$299$	58504.3	+	86517.6i	0.654403	+	0.967748i
$300$	−7332.71			−0.0814745
$301$	−100066.			−1.10447
$302$	−60608.5			−0.664538
$303$	145474.			1.58453
$304$		−	6607.48i		−	0.0714972i
$305$	−73887.4			−0.794274
$306$		−	30691.5i		−	0.327774i
$307$	−23380.8			−0.248075			−0.124038	−	0.992278i	$-0.539584\pi$
$307$	−23380.8			−0.248075			−0.124038	+	0.992278i	$0.539584\pi$
$308$	20692.3			0.218125
$309$			2177.96i			0.0228105i
$310$		−	22302.6i		−	0.232077i
$311$	26518.6			0.274176			0.137088	−	0.990559i	$-0.456226\pi$
$311$	26518.6			0.274176			0.137088	+	0.990559i	$0.456226\pi$
$312$	32758.0			0.336518
$313$			12279.8i			0.125343i	0.998034	+	0.0626716i	$0.0199621\pi$
$313$			12279.8i			0.125343i	−0.998034	+	0.0626716i	$0.980038\pi$
$314$		−	32990.0i		−	0.334598i
$315$	−23033.4			−0.232133
$316$			15241.3i			0.152633i
$317$	87667.0			0.872404			0.436202	−	0.899849i	$-0.356323\pi$
$317$	87667.0			0.872404			0.436202	+	0.899849i	$0.356323\pi$
$318$			66593.0i			0.658529i
$319$		−	15987.0i		−	0.157103i
$320$		−	5724.33i		−	0.0559017i
$321$			90674.2i			0.879982i
$322$	−93770.2	+	63408.6i	−0.904384	+	0.611556i
$323$	−41139.5			−0.394325
$324$	−28909.7			−0.275393
$325$	24679.0			0.233648
$326$	−91429.1			−0.860298
$327$		−	93261.9i		−	0.872185i
$328$	−64919.2			−0.603428
$329$		−	186683.i		−	1.72470i
$330$	7927.74			0.0727983
$331$	−91366.6			−0.833933			−0.416967	−	0.908922i	$-0.636907\pi$
$331$	−91366.6			−0.833933			−0.416967	+	0.908922i	$0.636907\pi$
$332$			21795.2i			0.197735i
$333$			32103.8i			0.289513i
$334$	48246.2			0.432484
$335$	58425.8			0.520613
$336$			35504.0i			0.314484i
$337$			29057.7i			0.255859i	0.991783	+	0.127930i	$0.0408332\pi$
$337$			29057.7i			0.255859i	−0.991783	+	0.127930i	$0.959167\pi$
$338$	−29467.9			−0.257938
$339$		−	86624.5i		−	0.753774i
$340$	−35640.8			−0.308312
$341$			24112.4i			0.207363i
$342$		−	7951.90i		−	0.0679859i
$343$		−	69719.7i		−	0.592608i
$344$		−	29928.6i		−	0.252912i
$345$	−35925.8	+	24293.5i	−0.301834	+	0.204104i
$346$	126518.			1.05682
$347$	−45410.6			−0.377136			−0.188568	−	0.982060i	$-0.560385\pi$
$347$	−45410.6			−0.377136			−0.188568	+	0.982060i	$0.560385\pi$
$348$	27430.7			0.226505
$349$	−118826.			−0.975573			−0.487787	−	0.872963i	$-0.662196\pi$
$349$	−118826.			−0.975573			−0.487787	+	0.872963i	$0.662196\pi$
$350$			26747.8i			0.218349i
$351$	156688.			1.27181
$352$			6188.85i			0.0499487i
$353$	−20670.1			−0.165880			−0.0829398	−	0.996555i	$-0.526431\pi$
$353$	−20670.1			−0.165880			−0.0829398	+	0.996555i	$0.526431\pi$
$354$	134236.			1.07118
$355$			63690.9i			0.505383i
$356$			34018.7i			0.268421i
$357$	221055.			1.73446
$358$	−119440.			−0.931932
$359$		−	77971.9i		−	0.604991i	−0.953151	−	0.302496i	$-0.902180\pi$
$359$		−	77971.9i		−	0.604991i	0.953151	−	0.302496i	$-0.0978198\pi$
$360$		−	6889.05i		−	0.0531563i
$361$	119662.			0.918210
$362$		−	86821.3i		−	0.662535i
$363$	98787.1			0.749699
$364$		−	119493.i		−	0.901858i
$365$			82334.3i			0.618010i
$366$			137064.i			1.02320i
$367$		−	45694.0i		−	0.339255i	−0.985508	−	0.169628i	$-0.945743\pi$
$367$		−	45694.0i		−	0.339255i	0.985508	−	0.169628i	$-0.0542565\pi$
$368$	−18964.9	−	28045.7i	−0.140041	−	0.207096i
$369$	−78128.2			−0.573793
$370$	37280.9			0.272322
$371$	242914.			1.76484
$372$	−41372.3			−0.298967
$373$		−	152588.i		−	1.09674i	−0.836236	−	0.548370i	$-0.815249\pi$
$373$		−	152588.i		−	1.09674i	0.836236	−	0.548370i	$-0.184751\pi$
$374$	38533.0			0.275480
$375$			10247.8i			0.0728730i
$376$	55834.9			0.394939
$377$	−92320.9			−0.649557
$378$			169823.i			1.18854i
$379$			145616.i			1.01375i	0.862020	+	0.506874i	$0.169199\pi$
$379$			145616.i			1.01375i	−0.862020	+	0.506874i	$0.830801\pi$
$380$	−9234.24			−0.0639490
$381$	−91244.8			−0.628577
$382$			139168.i			0.953700i
$383$		−	115611.i		−	0.788134i	−0.919082	−	0.394067i	$-0.871068\pi$
$383$		−	115611.i		−	0.788134i	0.919082	−	0.394067i	$-0.128932\pi$
$384$	−10618.9			−0.0720140
$385$		−	28918.3i		−	0.195097i
$386$	−21625.3			−0.145140
$387$		−	36018.2i		−	0.240492i
$388$			43861.9i			0.291356i
$389$			131120.i			0.866506i	0.901272	+	0.433253i	$0.142634\pi$
$389$			131120.i			0.866506i	−0.901272	+	0.433253i	$0.857366\pi$
$390$		−	45780.7i		−	0.300991i
$391$	−174618.	+	118079.i	−1.14218	+	0.772359i
$392$	75180.9			0.489255
$393$	−107383.			−0.695265
$394$	69789.1			0.449568
$395$	21300.4			0.136519
$396$			7448.08i			0.0474957i
$397$	−233526.			−1.48168			−0.740838	−	0.671684i	$-0.765571\pi$
$397$	−233526.			−1.48168			−0.740838	+	0.671684i	$0.765571\pi$
$398$			142239.i			0.897951i
$399$	57273.5			0.359756
$400$	−8000.00			−0.0500000
$401$			139878.i			0.869885i	0.900458	+	0.434942i	$0.143231\pi$
$401$			139878.i			0.869885i	−0.900458	+	0.434942i	$0.856769\pi$
$402$		−	108382.i		−	0.670667i
$403$	139243.			0.857359
$404$	158712.			0.972406
$405$			40402.5i			0.246319i
$406$		−	100060.i		−	0.607027i
$407$	−40306.1			−0.243323
$408$			66115.4i			0.397175i
$409$	−161738.			−0.966863			−0.483431	−	0.875382i	$-0.660610\pi$
$409$	−161738.			−0.966863			−0.483431	+	0.875382i	$0.660610\pi$
$410$			90727.3i			0.539722i
$411$			178143.i			1.05459i
$412$			2376.16i			0.0139985i
$413$		−	489659.i		−	2.87074i
$414$	−22823.6	−	33752.1i	−0.133163	−	0.196925i
$415$	30459.7			0.176860
$416$	35739.0			0.206517
$417$	−166329.			−0.956524
$418$	9983.57			0.0571391
$419$			74698.9i			0.425487i	0.977108	+	0.212744i	$0.0682399\pi$
$419$			74698.9i			0.425487i	−0.977108	+	0.212744i	$0.931760\pi$
$420$	49618.4			0.281283
$421$		−	256989.i		−	1.44994i	−0.688781	−	0.724970i	$-0.741854\pi$
$421$		−	256989.i		−	1.44994i	0.688781	−	0.724970i	$-0.258146\pi$
$422$	7961.19			0.0447047
$423$	67195.6			0.375543
$424$			72653.1i			0.404131i
$425$			49809.6i			0.275762i
$426$	118149.			0.651047
$427$	499975.			2.74216
$428$			98925.8i			0.540035i
$429$			49495.7i			0.268938i
$430$	−41826.6			−0.226212
$431$			82265.7i			0.442858i	0.975177	+	0.221429i	$0.0710720\pi$
$431$			82265.7i			0.442858i	−0.975177	+	0.221429i	$0.928928\pi$
$432$	−50792.3			−0.272164
$433$			204218.i			1.08923i	0.838687	+	0.544614i	$0.183324\pi$
$433$			204218.i			1.08923i	−0.838687	+	0.544614i	$0.816676\pi$
$434$			150915.i			0.801223i
$435$		−	38335.5i		−	0.202592i
$436$		−	101749.i		−	0.535250i
$437$	−45242.1	+	30593.3i	−0.236908	+	0.160200i
$438$	152734.			0.796136
$439$	−120041.			−0.622875			−0.311437	−	0.950267i	$-0.600810\pi$
$439$	−120041.			−0.622875			−0.311437	+	0.950267i	$0.600810\pi$
$440$	8649.18			0.0446755
$441$	90477.8			0.465227
$442$		−	222518.i		−	1.13899i
$443$	210137.			1.07077			0.535383	−	0.844610i	$-0.320167\pi$
$443$	210137.			1.07077			0.535383	+	0.844610i	$0.320167\pi$
$444$		−	69157.7i		−	0.350812i
$445$	47542.5			0.240083
$446$	−28033.3			−0.140930
$447$			286921.i			1.43597i
$448$			38734.9i			0.192995i
$449$	110489.			0.548059			0.274029	−	0.961721i	$-0.411643\pi$
$449$	110489.			0.548059			0.274029	+	0.961721i	$0.411643\pi$
$450$	−9627.75			−0.0475444
$451$		−	98089.6i		−	0.482247i
$452$		−	94507.5i		−	0.462583i
$453$	157128.			0.765696
$454$		−	109479.i		−	0.531150i
$455$	−166996.			−0.806646
$456$			17129.9i			0.0823808i
$457$		−	137632.i		−	0.659000i	−0.944156	−	0.329500i	$-0.893120\pi$
$457$		−	137632.i		−	0.659000i	0.944156	−	0.329500i	$-0.106880\pi$
$458$			62623.1i			0.298541i
$459$			316243.i			1.50105i
$460$	−39195.1	+	26504.2i	−0.185232	+	0.125256i
$461$	−97031.1			−0.456572			−0.228286	−	0.973594i	$-0.573312\pi$
$461$	−97031.1			−0.456572			−0.228286	+	0.973594i	$0.573312\pi$
$462$	−53644.8			−0.251329
$463$	−21338.9			−0.0995427			−0.0497713	−	0.998761i	$-0.515849\pi$
$463$	−21338.9			−0.0995427			−0.0497713	+	0.998761i	$0.515849\pi$
$464$	29926.9			0.139004
$465$			57819.5i			0.267404i
$466$	−67544.4			−0.311041
$467$		−	236374.i		−	1.08384i	−0.840430	−	0.541920i	$-0.817698\pi$
$467$		−	236374.i		−	1.08384i	0.840430	−	0.541920i	$-0.182302\pi$
$468$	43010.8			0.196375
$469$	−395351.			−1.79737
$470$		−	78031.7i		−	0.353244i
$471$			85526.7i			0.385532i
$472$	146452.			0.657372
$473$	45220.7			0.202122
$474$		−	39513.1i		−	0.175867i
$475$			12905.2i			0.0571978i
$476$	241171.			1.06442
$477$			87435.8i			0.384284i
$478$	−25445.0			−0.111365
$479$			323857.i			1.41150i	0.708459	+	0.705752i	$0.249391\pi$
$479$			323857.i			1.41150i	−0.708459	+	0.705752i	$0.750609\pi$
$480$			14840.4i			0.0644113i
$481$			232758.i			1.00604i
$482$			250858.i			1.07978i
$483$	243100.	−	164387.i	1.04205	−	0.704650i
$484$	107777.			0.460082
$485$	61298.9			0.260597
$486$	−106874.			−0.452480
$487$	−62892.8			−0.265181			−0.132591	−	0.991171i	$-0.542330\pi$
$487$	−62892.8			−0.265181			−0.132591	+	0.991171i	$0.542330\pi$
$488$			149538.i			0.627929i
$489$	237030.			0.991256
$490$		−	105068.i		−	0.437603i
$491$	−289126.			−1.19929			−0.599644	−	0.800267i	$-0.704691\pi$
$491$	−289126.			−1.19929			−0.599644	+	0.800267i	$0.704691\pi$
$492$	168303.			0.695284
$493$		−	186331.i		−	0.766640i
$494$		−	57652.6i		−	0.236246i
$495$	10409.0			0.0424814
$496$	−45137.2			−0.183473
$497$		−	430978.i		−	1.74479i
$498$		−	56504.1i		−	0.227835i
$499$	65916.0			0.264722			0.132361	−	0.991202i	$-0.457744\pi$
$499$	65916.0			0.264722			0.132361	+	0.991202i	$0.457744\pi$
$500$			11180.3i			0.0447214i
$501$	−125078.			−0.498318
$502$			54526.2i			0.216370i
$503$		−	361875.i		−	1.43028i	−0.698979	−	0.715142i	$-0.746362\pi$
$503$		−	361875.i		−	1.43028i	0.698979	−	0.715142i	$-0.253638\pi$
$504$			46616.3i			0.183517i
$505$		−	221807.i		−	0.869746i
$506$	42375.7	−	28655.0i	0.165507	−	0.111918i
$507$	76395.6			0.297203
$508$	−99548.3			−0.385750
$509$	−254033.			−0.980518			−0.490259	−	0.871577i	$-0.663098\pi$
$509$	−254033.			−0.980518			−0.490259	+	0.871577i	$0.663098\pi$
$510$	92399.0			0.355244
$511$		−	557133.i		−	2.13362i
$512$	−11585.2			−0.0441942
$513$			81935.8i			0.311343i
$514$	−215744.			−0.816606
$515$	3320.79			0.0125207
$516$			77590.1i			0.291412i
$517$			84363.8i			0.315627i
$518$	−252269.			−0.940167
$519$	−328000.			−1.21770
$520$		−	49946.8i		−	0.184715i
$521$		−	101656.i		−	0.374503i	−0.982312	−	0.187252i	$-0.940042\pi$
$521$		−	101656.i		−	0.374503i	0.982312	−	0.187252i	$-0.0599580\pi$
$522$	36016.1			0.132177
$523$		−	236479.i		−	0.864547i	−0.901742	−	0.432274i	$-0.857711\pi$
$523$		−	236479.i		−	0.864547i	0.901742	−	0.432274i	$-0.142289\pi$
$524$	−117155.			−0.426676
$525$		−	69343.8i		−	0.251587i
$526$			30499.6i			0.110236i
$527$			281033.i			1.01190i
$528$		−	16044.6i		−	0.0575521i
$529$	−104223.	+	259709.i	−0.372435	+	0.928058i
$530$	101536.			0.361466
$531$	176250.			0.625088
$532$	62485.5			0.220778
$533$	−566443.			−1.99389
$534$		−	88193.5i		−	0.309282i
$535$	138253.			0.483022
$536$		−	118245.i		−	0.411580i
$537$	309649.			1.07379
$538$	−390651.			−1.34966
$539$			113595.i			0.391003i
$540$			70984.4i			0.243431i
$541$	−9888.56			−0.0337861			−0.0168931	−	0.999857i	$-0.505377\pi$
$541$	−9888.56			−0.0337861			−0.0168931	+	0.999857i	$0.505377\pi$
$542$	38552.9			0.131238
$543$			225084.i			0.763389i
$544$			72132.0i			0.243742i
$545$	−142198.			−0.478742
$546$			309785.i			1.03914i
$547$	−507649.			−1.69664			−0.848319	−	0.529486i	$-0.822385\pi$
$547$	−507649.			−1.69664			−0.848319	+	0.529486i	$0.822385\pi$
$548$			194354.i			0.647192i
$549$			179964.i			0.597090i
$550$		−	12087.6i		−	0.0399590i
$551$		−	48276.8i		−	0.159014i
$552$	49166.5	+	72708.6i	0.161358	+	0.238621i
$553$	−144133.			−0.471319
$554$	235197.			0.766323
$555$	−96650.9			−0.313776
$556$	−181465.			−0.587008
$557$		−	218863.i		−	0.705444i	−0.935728	−	0.352722i	$-0.885256\pi$
$557$		−	218863.i		−	0.705444i	0.935728	−	0.352722i	$-0.114744\pi$
$558$	−54321.2			−0.174462
$559$		−	261138.i		−	0.835692i
$560$	54133.7			0.172620
$561$	−99896.9			−0.317414
$562$			423290.i			1.34019i
$563$			559390.i			1.76481i	0.470492	+	0.882404i	$0.344077\pi$
$563$			559390.i			1.76481i	−0.470492	+	0.882404i	$0.655923\pi$
$564$	−144752.			−0.455059
$565$	−132078.			−0.413747
$566$		−	311394.i		−	0.972023i
$567$		−	273392.i		−	0.850394i
$568$	128901.			0.399540
$569$			25361.1i			0.0783327i	0.999233	+	0.0391663i	$0.0124702\pi$
$569$			25361.1i			0.0783327i	−0.999233	+	0.0391663i	$0.987530\pi$
$570$	23939.8			0.0736836
$571$		−	527124.i		−	1.61674i	−0.588675	−	0.808370i	$-0.700350\pi$
$571$		−	527124.i		−	1.61674i	0.588675	−	0.808370i	$-0.299650\pi$
$572$			53999.9i			0.165044i
$573$		−	360793.i		−	1.09888i
$574$		−	613926.i		−	1.86334i
$575$	37040.8	+	54776.8i	0.112033	+	0.165677i
$576$	−13942.5			−0.0420237
$577$	−283742.			−0.852261			−0.426130	−	0.904662i	$-0.640124\pi$
$577$	−283742.			−0.852261			−0.426130	+	0.904662i	$0.640124\pi$
$578$	212875.			0.637190
$579$	56063.8			0.167234
$580$		−	41824.2i		−	0.124329i
$581$	−206112.			−0.610592
$582$		−	113712.i		−	0.335707i
$583$	−109775.			−0.322974
$584$	166633.			0.488580
$585$		−	60109.4i		−	0.175643i
$586$			139644.i			0.406656i
$587$	−181654.			−0.527193			−0.263596	−	0.964633i	$-0.584909\pi$
$587$	−181654.			−0.527193			−0.263596	+	0.964633i	$0.584909\pi$
$588$	−194907.			−0.563731
$589$			72813.4i			0.209885i
$590$		−	204673.i		−	0.587972i
$591$	−180929.			−0.518003
$592$		−	75451.2i		−	0.215290i
$593$	431300.			1.22651			0.613253	−	0.789886i	$-0.289860\pi$
$593$	431300.			1.22651			0.613253	+	0.789886i	$0.289860\pi$
$594$		−	76744.5i		−	0.217508i
$595$		−	337047.i		−	0.952044i
$596$			313031.i			0.881241i
$597$		−	368755.i		−	1.03464i
$598$	−165475.	−	244709.i	−0.462733	−	0.684301i
$599$	139346.			0.388365			0.194182	−	0.980965i	$-0.437795\pi$
$599$	139346.			0.388365			0.194182	+	0.980965i	$0.437795\pi$
$600$	20740.0			0.0576112
$601$	−142142.			−0.393526			−0.196763	−	0.980451i	$-0.563043\pi$
$601$	−142142.			−0.393526			−0.196763	+	0.980451i	$0.563043\pi$
$602$	283028.			0.780975
$603$		−	142305.i		−	0.391367i
$604$	171427.			0.469899
$605$		−	150623.i		−	0.411510i
$606$	−411462.			−1.12043
$607$	−68766.9			−0.186639			−0.0933195	−	0.995636i	$-0.529748\pi$
$607$	−68766.9			−0.186639			−0.0933195	+	0.995636i	$0.529748\pi$
$608$			18688.8i			0.0505561i
$609$			259406.i			0.699431i
$610$	208985.			0.561637
$611$	487180.			1.30499
$612$			86808.6i			0.231771i
$613$			319435.i			0.850083i	0.905174	+	0.425042i	$0.139741\pi$
$613$			319435.i			0.850083i	−0.905174	+	0.425042i	$0.860259\pi$
$614$	66131.0			0.175416
$615$		−	235211.i		−	0.621881i
$616$	−58526.5			−0.154238
$617$			31986.3i			0.0840221i	0.999117	+	0.0420111i	$0.0133765\pi$
$617$			31986.3i			0.0840221i	−0.999117	+	0.0420111i	$0.986624\pi$
$618$		−	6160.21i		−	0.0161294i
$619$		−	178467.i		−	0.465776i	−0.972504	−	0.232888i	$-0.925182\pi$
$619$		−	178467.i		−	0.465776i	0.972504	−	0.232888i	$-0.0748175\pi$
$620$			63081.2i			0.164103i
$621$	235173.	+	347780.i	0.609824	+	0.901822i
$622$	−75006.0			−0.193872
$623$	−321707.			−0.828866
$624$	−92653.6			−0.237954
$625$	15625.0			0.0400000
$626$		−	34732.4i		−	0.0886311i
$627$	−25882.5			−0.0658371
$628$			93309.8i			0.236596i
$629$	−469774.			−1.18738
$630$	65148.2			0.164143
$631$			531111.i			1.33391i	0.745097	+	0.666956i	$0.232403\pi$
$631$			531111.i			1.33391i	−0.745097	+	0.666956i	$0.767597\pi$
$632$		−	43108.9i		−	0.107928i
$633$	−20639.4			−0.0515098
$634$	−247960.			−0.616882
$635$			139123.i			0.345026i
$636$		−	188354.i		−	0.465650i
$637$	655980.			1.61663
$638$			45218.1i			0.111089i
$639$	155129.			0.379918
$640$			16190.9i			0.0395285i
$641$		−	763524.i		−	1.85826i	−0.369754	−	0.929130i	$-0.620558\pi$
$641$		−	763524.i		−	1.85826i	0.369754	−	0.929130i	$-0.379442\pi$
$642$		−	256465.i		−	0.622241i
$643$			591043.i			1.42954i	0.699358	+	0.714771i	$0.253469\pi$
$643$			591043.i			1.42954i	−0.699358	+	0.714771i	$0.746531\pi$
$644$	265222.	−	179347.i	0.639496	−	0.432435i
$645$	108436.			0.260647
$646$	116360.			0.278830
$647$	−305043.			−0.728707			−0.364354	−	0.931261i	$-0.618710\pi$
$647$	−305043.			−0.728707			−0.364354	+	0.931261i	$0.618710\pi$
$648$	81768.9			0.194732
$649$			221282.i			0.525359i
$650$	−69802.8			−0.165214
$651$		−	391248.i		−	0.923188i
$652$	258600.			0.608323
$653$	211550.			0.496119			0.248060	−	0.968745i	$-0.420207\pi$
$653$	211550.			0.496119			0.248060	+	0.968745i	$0.420207\pi$
$654$			263784.i			0.616728i
$655$			163729.i			0.381631i
$656$	183619.			0.426688
$657$	200538.			0.464585
$658$			528018.i			1.21954i
$659$		−	235761.i		−	0.542876i	−0.962456	−	0.271438i	$-0.912501\pi$
$659$		−	235761.i		−	0.542876i	0.962456	−	0.271438i	$-0.0874991\pi$
$660$	−22423.0			−0.0514762
$661$			158962.i			0.363824i	0.983315	+	0.181912i	$0.0582285\pi$
$661$			158962.i			0.363824i	−0.983315	+	0.181912i	$0.941771\pi$
$662$	258424.			0.589680
$663$			576880.i			1.31238i
$664$		−	61646.0i		−	0.139820i
$665$		−	87326.1i		−	0.197470i
$666$		−	90803.2i		−	0.204716i
$667$	−138565.	−	204913.i	−0.311459	−	0.460593i
$668$	−136461.			−0.305812
$669$	72676.3			0.162383
$670$	−165253.			−0.368129
$671$	−225944.			−0.501828
$672$		−	100421.i		−	0.222374i
$673$	47211.8			0.104237			0.0521183	−	0.998641i	$-0.483403\pi$
$673$	47211.8			0.104237			0.0521183	+	0.998641i	$0.483403\pi$
$674$		−	82187.5i		−	0.180920i
$675$	99203.7			0.217731
$676$	83347.8			0.182390
$677$			10943.8i			0.0238776i	0.999929	+	0.0119388i	$0.00380032\pi$
$677$			10943.8i			0.0238776i	−0.999929	+	0.0119388i	$0.996200\pi$
$678$			245011.i			0.532999i
$679$	−414792.			−0.899686
$680$	100808.			0.218009
$681$			283823.i			0.612004i
$682$		−	68200.0i		−	0.146628i
$683$	−878085.			−1.88233			−0.941164	−	0.337951i	$-0.890266\pi$
$683$	−878085.			−1.88233			−0.941164	+	0.337951i	$0.890266\pi$
$684$			22491.4i			0.0480733i
$685$	271618.			0.578866
$686$			197197.i			0.419037i
$687$		−	162351.i		−	0.343986i
$688$			84651.0i			0.178836i
$689$			633924.i			1.33536i
$690$	101613.	−	68712.3i	0.213429	−	0.144323i
$691$	620279.			1.29907			0.649533	−	0.760334i	$-0.274965\pi$
$691$	620279.			1.29907			0.649533	+	0.760334i	$0.274965\pi$
$692$	−357848.			−0.747286
$693$	−70434.8			−0.146663
$694$	128440.			0.266675
$695$			253605.i			0.525036i
$696$	−77585.7			−0.160163
$697$		−	1.14325e6i		−	2.35329i
$698$	336090.			0.689835
$699$	175109.			0.358389
$700$		−	75654.2i		−	0.154396i
$701$		−	646194.i		−	1.31500i	−0.753453	−	0.657501i	$-0.771613\pi$
$701$		−	646194.i		−	1.31500i	0.753453	−	0.657501i	$-0.228387\pi$
$702$	−443180.			−0.899304
$703$	−121715.			−0.246282
$704$		−	17504.7i		−	0.0353191i
$705$			202298.i			0.407017i
$706$	58463.8			0.117295
$707$			1.50091e6i			3.00272i
$708$	−379678.			−0.757440
$709$			250757.i			0.498839i	0.968396	+	0.249419i	$0.0802398\pi$
$709$			250757.i			0.498839i	−0.968396	+	0.249419i	$0.919760\pi$
$710$		−	180145.i		−	0.357360i
$711$		−	51880.2i		−	0.102627i
$712$		−	96219.3i		−	0.189803i
$713$	208990.	+	309059.i	0.411098	+	0.607942i
$714$	−625238.			−1.22645
$715$	75467.1			0.147620
$716$	337828.			0.658975
$717$	65966.3			0.128317
$718$			220538.i			0.427794i
$719$	−723829.			−1.40016			−0.700081	−	0.714064i	$-0.746853\pi$
$719$	−723829.			−1.40016			−0.700081	+	0.714064i	$0.746853\pi$
$720$			19485.2i			0.0375872i
$721$	−22470.8			−0.0432264
$722$	−338456.			−0.649273
$723$		−	650350.i		−	1.24414i
$724$			245568.i			0.468483i
$725$	−58451.0			−0.111203
$726$	−279412.			−0.530118
$727$		−	148801.i		−	0.281537i	−0.990043	−	0.140769i	$-0.955043\pi$
$727$		−	148801.i		−	0.281537i	0.990043	−	0.140769i	$-0.0449573\pi$
$728$			337976.i			0.637710i
$729$	569782.			1.07215
$730$		−	232877.i		−	0.436999i
$731$	527054.			0.986326
$732$		−	387677.i		−	0.723515i
$733$		−	265248.i		−	0.493679i	−0.969056	−	0.246840i	$-0.920608\pi$
$733$		−	265248.i		−	0.493679i	0.969056	−	0.246840i	$-0.0793921\pi$
$734$			129242.i			0.239890i
$735$			272390.i			0.504217i
$736$	53640.8	+	79325.3i	0.0990237	+	0.146439i
$737$	178663.			0.328927
$738$	220980.			0.405733
$739$	465115.			0.851669			0.425835	−	0.904801i	$-0.359981\pi$
$739$	465115.			0.851669			0.425835	+	0.904801i	$0.359981\pi$
$740$	−105446.			−0.192561
$741$			149465.i			0.272209i
$742$	−687064.			−1.24793
$743$		−	1.04306e6i		−	1.88943i	−0.327892	−	0.944715i	$-0.606338\pi$
$743$		−	1.04306e6i		−	1.88943i	0.327892	−	0.944715i	$-0.393662\pi$
$744$	117018.			0.211402
$745$	437474.			0.788206
$746$			431585.i			0.775512i
$747$		−	74189.1i		−	0.132953i
$748$	−108988.			−0.194794
$749$	−935519.			−1.66759
$750$		−	28985.1i		−	0.0515290i
$751$			828260.i			1.46854i	0.678856	+	0.734272i	$0.262476\pi$
$751$			828260.i			1.46854i	−0.678856	+	0.734272i	$0.737524\pi$
$752$	−157925.			−0.279264
$753$		−	141359.i		−	0.249307i
$754$	261123.			0.459306
$755$		−	239576.i		−	0.420291i
$756$		−	480331.i		−	0.840421i
$757$		−	55911.9i		−	0.0975692i	−0.998809	−	0.0487846i	$-0.984465\pi$
$757$		−	55911.9i		−	0.0975692i	0.998809	−	0.0487846i	$-0.0155348\pi$
$758$		−	411864.i		−	0.716828i
$759$	−109859.	+	74288.1i	−0.190701	+	0.128954i
$760$	26118.4			0.0452188
$761$	1.14940e6			1.98472			0.992362	−	0.123357i	$-0.0393660\pi$
$761$	1.14940e6			1.98472			0.992362	+	0.123357i	$0.0393660\pi$
$762$	258079.			0.444471
$763$	962216.			1.65281
$764$		−	393626.i		−	0.674368i
$765$	121319.			0.207303
$766$			326996.i			0.557295i
$767$	1.27785e6			2.17214
$768$	30034.8			0.0509216
$769$			709531.i			1.19983i	0.800065	+	0.599914i	$0.204798\pi$
$769$			709531.i			1.19983i	−0.800065	+	0.599914i	$0.795202\pi$
$770$			81793.3i			0.137955i
$771$	559318.			0.940913
$772$	61165.7			0.102630
$773$			1.08765e6i			1.82025i	0.414337	+	0.910124i	$0.364014\pi$
$773$			1.08765e6i			1.82025i	−0.414337	+	0.910124i	$0.635986\pi$
$774$			101875.i			0.170053i
$775$	88158.6			0.146778
$776$		−	124060.i		−	0.206020i
$777$	654009.			1.08328
$778$		−	370865.i		−	0.612712i
$779$		−	296206.i		−	0.488112i
$780$			129487.i			0.212833i
$781$			194763.i			0.319305i
$782$	493895.	−	333978.i	0.807646	−	0.546140i
$783$	−371108.			−0.605308
$784$	−212644.			−0.345956
$785$	130404.			0.211618
$786$	303725.			0.491626
$787$			5203.80i			0.00840178i	0.999991	+	0.00420089i	$0.00133719\pi$
$787$			5203.80i			0.00840178i	−0.999991	+	0.00420089i	$0.998663\pi$
$788$	−197393.			−0.317892
$789$		−	79070.2i		−	0.127016i
$790$	−60246.5			−0.0965334
$791$	893736.			1.42842
$792$		−	21066.4i		−	0.0335845i
$793$			1.30477e6i			2.07485i
$794$	660510.			1.04770
$795$	−263232.			−0.416490
$796$		−	402313.i		−	0.634947i
$797$		−	884029.i		−	1.39171i	−0.718181	−	0.695857i	$-0.755025\pi$
$797$		−	884029.i		−	1.39171i	0.718181	−	0.695857i	$-0.244975\pi$
$798$	−161994.			−0.254386
$799$			983273.i			1.54021i
$800$	22627.4			0.0353553
$801$		−	115797.i		−	0.180481i
$802$		−	395636.i		−	0.615101i
$803$			251774.i			0.390463i
$804$			306552.i			0.474233i
$805$	−250644.	−	370659.i	−0.386782	−	0.571983i
$806$	−393838.			−0.606244
$807$	1.01276e6			1.55511
$808$	−448906.			−0.687595
$809$	−57648.7			−0.0880831			−0.0440415	−	0.999030i	$-0.514023\pi$
$809$	−57648.7			−0.0880831			−0.0440415	+	0.999030i	$0.514023\pi$
$810$		−	114276.i		−	0.174174i
$811$	−114560.			−0.174177			−0.0870885	−	0.996201i	$-0.527756\pi$
$811$	−114560.			−0.174177			−0.0870885	+	0.996201i	$0.527756\pi$
$812$			283012.i			0.429233i
$813$	−99948.6			−0.151215
$814$	114003.			0.172055
$815$		−	361405.i		−	0.544100i
$816$		−	187002.i		−	0.280845i
$817$	136555.			0.204580
$818$	457463.			0.683675
$819$			406744.i			0.606391i
$820$		−	256616.i		−	0.381641i
$821$	−1.04781e6			−1.55452			−0.777260	−	0.629180i	$-0.783391\pi$
$821$	−1.04781e6			−1.55452			−0.777260	+	0.629180i	$0.783391\pi$
$822$		−	503864.i		−	0.745710i
$823$	−335862.			−0.495862			−0.247931	−	0.968778i	$-0.579751\pi$
$823$	−335862.			−0.495862			−0.247931	+	0.968778i	$0.579751\pi$
$824$		−	6720.81i		−	0.00989844i
$825$			31337.1i			0.0460417i
$826$			1.38496e6i			2.02992i
$827$		−	528594.i		−	0.772878i	−0.922315	−	0.386439i	$-0.873705\pi$
$827$		−	528594.i		−	0.772878i	0.922315	−	0.386439i	$-0.126295\pi$
$828$	64555.0	+	95465.5i	0.0941605	+	0.139247i
$829$	120599.			0.175483			0.0877413	−	0.996143i	$-0.472035\pi$
$829$	120599.			0.175483			0.0877413	+	0.996143i	$0.472035\pi$
$830$	−86153.0			−0.125059
$831$	−609748.			−0.882976
$832$	−101085.			−0.146030
$833$			1.32396e6i			1.90803i
$834$	470449.			0.676364
$835$			190710.i			0.273527i
$836$	−28237.8			−0.0404034
$837$	559722.			0.798954
$838$		−	211280.i		−	0.300865i
$839$			372806.i			0.529613i	0.964302	+	0.264806i	$0.0853080\pi$
$839$			372806.i			0.529613i	−0.964302	+	0.264806i	$0.914692\pi$
$840$	−140342.			−0.198897
$841$	−488623.			−0.690848
$842$			726874.i			1.02526i
$843$		−	1.09738e6i		−	1.54420i
$844$	−22517.7			−0.0316110
$845$		−	116482.i		−	0.163134i
$846$	−190058.			−0.265549
$847$			1.01922e6i			1.42070i
$848$		−	205494.i		−	0.285764i
$849$			807289.i			1.11999i
$850$		−	140883.i		−	0.194993i
$851$	−516622.	+	349346.i	−0.713368	+	0.482389i
$852$	−334177.			−0.460360
$853$	1.43436e6			1.97133			0.985664	−	0.168720i	$-0.0539635\pi$
$853$	1.43436e6			1.97133			0.985664	+	0.168720i	$0.0539635\pi$
$854$	−1.41414e6			−1.93900
$855$	31432.6			0.0429980
$856$		−	279804.i		−	0.381862i
$857$	−20657.6			−0.0281267			−0.0140633	−	0.999901i	$-0.504477\pi$
$857$	−20657.6			−0.0281267			−0.0140633	+	0.999901i	$0.504477\pi$
$858$		−	139995.i		−	0.190168i
$859$	975464.			1.32198			0.660990	−	0.750395i	$-0.270136\pi$
$859$	975464.			1.32198			0.660990	+	0.750395i	$0.270136\pi$
$860$	118303.			0.159956
$861$			1.59161e6i			2.14699i
$862$		−	232682.i		−	0.313148i
$863$	433391.			0.581913			0.290956	−	0.956736i	$-0.406027\pi$
$863$	433391.			0.581913			0.290956	+	0.956736i	$0.406027\pi$
$864$	143662.			0.192449
$865$			500108.i			0.668393i
$866$		−	577616.i		−	0.770200i
$867$	−551879.			−0.734186
$868$		−	426853.i		−	0.566550i
$869$	65135.3			0.0862536
$870$			108429.i			0.143254i
$871$		−	1.03173e6i		−	1.35998i
$872$			287789.i			0.378479i
$873$		−	149302.i		−	0.195902i
$874$	127964.	−	86530.9i	0.167519	−	0.113279i
$875$	−105730.			−0.138096
$876$	−431997.			−0.562953
$877$	1.24995e6			1.62516			0.812578	−	0.582853i	$-0.198063\pi$
$877$	1.24995e6			1.62516			0.812578	+	0.582853i	$0.198063\pi$
$878$	339527.			0.440439
$879$		−	362027.i		−	0.468558i
$880$	−24463.6			−0.0315904
$881$		−	471278.i		−	0.607191i	−0.952801	−	0.303595i	$-0.901813\pi$
$881$		−	471278.i		−	0.607191i	0.952801	−	0.303595i	$-0.0981871\pi$
$882$	−255910.			−0.328965
$883$	−686292.			−0.880213			−0.440106	−	0.897946i	$-0.645059\pi$
$883$	−686292.			−0.880213			−0.440106	+	0.897946i	$0.645059\pi$
$884$			629377.i			0.805390i
$885$			530615.i			0.677475i
$886$	−594356.			−0.757145
$887$	−51577.0			−0.0655554			−0.0327777	−	0.999463i	$-0.510435\pi$
$887$	−51577.0			−0.0655554			−0.0327777	+	0.999463i	$0.510435\pi$
$888$			195608.i			0.248062i
$889$		−	941406.i		−	1.19117i
$890$	−134471.			−0.169765
$891$			123549.i			0.155626i
$892$	79290.0			0.0996527
$893$			254758.i			0.319466i
$894$		−	811534.i		−	1.01539i
$895$		−	472128.i		−	0.589405i
$896$		−	109559.i		−	0.136468i
$897$	428995.	+	634409.i	0.533172	+	0.788468i
$898$	−312511.			−0.387536
$899$	−329790.			−0.408054
$900$	27231.4			0.0336190
$901$	−1.27945e6			−1.57606
$902$			277439.i			0.341000i
$903$	−733752.			−0.899858
$904$			267308.i			0.327095i
$905$	343191.			0.419024
$906$	−444424.			−0.541429
$907$			601451.i			0.731115i	0.930789	+	0.365558i	$0.119122\pi$
$907$			601451.i			0.731115i	−0.930789	+	0.365558i	$0.880878\pi$
$908$			309652.i			0.375580i
$909$	−540244.			−0.653826
$910$	472336.			0.570385
$911$		−	1.65516e6i		−	1.99436i	−0.0750576	−	0.997179i	$-0.523914\pi$
$911$		−	1.65516e6i		−	1.99436i	0.0750576	−	0.997179i	$-0.476086\pi$
$912$		−	48450.8i		−	0.0582520i
$913$	93144.0			0.111741
$914$			389281.i			0.465983i
$915$	−541795.			−0.647131
$916$		−	177125.i		−	0.211100i
$917$		−	1.10791e6i		−	1.31754i
$918$		−	894470.i		−	1.06140i
$919$		−	1.22836e6i		−	1.45444i	−0.686404	−	0.727220i	$-0.740812\pi$
$919$		−	1.22836e6i		−	1.45444i	0.686404	−	0.727220i	$-0.259188\pi$
$920$	110860.	−	74965.2i	0.130979	−	0.0885695i
$921$	−171445.			−0.202118
$922$	274445.			0.322845
$923$	1.12471e6			1.32019
$924$	151730.			0.177717
$925$			147366.i			0.172232i
$926$	60355.4			0.0703873
$927$		−	8088.28i		−	0.00941232i
$928$	−84646.2			−0.0982904
$929$	−1.14384e6			−1.32536			−0.662678	−	0.748904i	$-0.730580\pi$
$929$	−1.14384e6			−1.32536			−0.662678	+	0.748904i	$0.730580\pi$
$930$		−	163538.i		−	0.189083i
$931$			343027.i			0.395758i
$932$	191044.			0.219939
$933$	194453.			0.223384
$934$			668566.i			0.766391i
$935$			152315.i			0.174229i
$936$	−121653.			−0.138858
$937$		−	932474.i		−	1.06208i	−0.847347	−	0.531040i	$-0.821801\pi$
$937$		−	932474.i		−	1.06208i	0.847347	−	0.531040i	$-0.178199\pi$
$938$	1.11822e6			1.27093
$939$			90043.9i			0.102123i
$940$			220707.i			0.249782i
$941$		−	669645.i		−	0.756249i	−0.925755	−	0.378125i	$-0.876569\pi$
$941$		−	669645.i		−	0.756249i	0.925755	−	0.378125i	$-0.123431\pi$
$942$		−	241906.i		−	0.272612i
$943$	−850175.	−	1.25726e6i	−0.956059	−	1.41384i
$944$	−414229.			−0.464832
$945$	−671283.			−0.751696
$946$	−127903.			−0.142922
$947$	−1.17286e6			−1.30781			−0.653905	−	0.756577i	$-0.726870\pi$
$947$	−1.17286e6			−1.30781			−0.653905	+	0.756577i	$0.726870\pi$
$948$			111760.i			0.124357i
$949$	1.45393e6			1.61440
$950$		−	36501.5i		−	0.0404449i
$951$	642836.			0.710787
$952$	−682136.			−0.752657
$953$		−	259053.i		−	0.285235i	−0.989778	−	0.142618i	$-0.954448\pi$
$953$		−	259053.i		−	0.285235i	0.989778	−	0.142618i	$-0.0455519\pi$
$954$		−	247306.i		−	0.271730i
$955$	−550109.			−0.603173
$956$	71969.4			0.0787466
$957$		−	117228.i		−	0.127999i
$958$		−	916006.i		−	0.998085i
$959$	−1.83797e6			−1.99848
$960$		−	41974.9i		−	0.0455457i
$961$	−426117.			−0.461404
$962$		−	658339.i		−	0.711376i
$963$		−	336736.i		−	0.363109i
$964$		−	709533.i		−	0.763517i
$965$		−	85481.7i		−	0.0917948i
$966$	−687589.	+	464957.i	−0.736843	+	0.498262i
$967$	−1.16404e6			−1.24485			−0.622423	−	0.782681i	$-0.713852\pi$
$967$	−1.16404e6			−1.24485			−0.622423	+	0.782681i	$0.713852\pi$
$968$	−304839.			−0.325327
$969$	−301664.			−0.321274
$970$	−173379.			−0.184270
$971$			835673.i			0.886335i	0.896439	+	0.443167i	$0.146145\pi$
$971$			835673.i			0.886335i	−0.896439	+	0.443167i	$0.853855\pi$
$972$	302285.			0.319952
$973$		−	1.71608e6i		−	1.81264i
$974$	177888.			0.187511
$975$	180964.			0.190363
$976$		−	422956.i		−	0.444013i
$977$		−	486657.i		−	0.509840i	−0.966962	−	0.254920i	$-0.917951\pi$
$977$		−	486657.i		−	0.509840i	0.966962	−	0.254920i	$-0.0820492\pi$
$978$	−670423.			−0.700924
$979$	145382.			0.151686
$980$			297179.i			0.309432i
$981$			346345.i			0.359891i
$982$	817770.			0.848025
$983$		−	1.61922e6i		−	1.67571i	−0.545893	−	0.837855i	$-0.683809\pi$
$983$		−	1.61922e6i		−	1.67571i	0.545893	−	0.837855i	$-0.316191\pi$
$984$	−476034.			−0.491640
$985$			275866.i			0.284332i
$986$			527024.i			0.542096i
$987$		−	1.36889e6i		−	1.40519i
$988$			163066.i			0.167051i
$989$	579614.	−	391942.i	0.592579	−	0.400709i
$990$	−29441.1			−0.0300389
$991$	−263930.			−0.268745			−0.134373	−	0.990931i	$-0.542902\pi$
$991$	−263930.			−0.268745			−0.134373	+	0.990931i	$0.542902\pi$
$992$	127667.			0.129735
$993$	−669964.			−0.679443
$994$			1.21899e6i			1.23375i
$995$	−562249.			−0.567914
$996$			159818.i			0.161104i
$997$	−848999.			−0.854116			−0.427058	−	0.904224i	$-0.640450\pi$
$997$	−848999.			−0.854116			−0.427058	+	0.904224i	$0.640450\pi$
$998$	−186439.			−0.187187
$999$			935630.i			0.937504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.d.a.91.14	yes	32
23.22	odd	2	inner	230.5.d.a.91.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.d.a.91.3	✓	32	23.22	odd	2	inner
230.5.d.a.91.14	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} +7.33271 q^{3} +8.00000 q^{4} -11.1803i q^{5} -20.7400 q^{6} +75.6542i q^{7} -22.6274 q^{8} -27.2314 q^{9} +O(q^{10})\)	\(q-2.82843 q^{2} +7.33271 q^{3} +8.00000 q^{4} -11.1803i q^{5} -20.7400 q^{6} +75.6542i q^{7} -22.6274 q^{8} -27.2314 q^{9} +31.6228i q^{10} -34.1889i q^{11} +58.6617 q^{12} -197.432 q^{13} -213.982i q^{14} -81.9822i q^{15} +64.0000 q^{16} -398.477i q^{17} +77.0220 q^{18} -103.242i q^{19} -89.4427i q^{20} +554.750i q^{21} +96.7007i q^{22} +(-296.326 - 438.214i) q^{23} -165.920 q^{24} -125.000 q^{25} +558.423 q^{26} -793.629 q^{27} +605.234i q^{28} +467.608 q^{29} +231.881i q^{30} -705.269 q^{31} -181.019 q^{32} -250.697i q^{33} +1127.06i q^{34} +845.840 q^{35} -217.851 q^{36} -1178.93i q^{37} +292.012i q^{38} -1447.71 q^{39} +252.982i q^{40} +2869.05 q^{41} -1569.07i q^{42} +1322.67i q^{43} -273.511i q^{44} +304.456i q^{45} +(838.137 + 1239.46i) q^{46} -2467.58 q^{47} +469.293 q^{48} -3322.56 q^{49} +353.553 q^{50} -2921.91i q^{51} -1579.46 q^{52} -3210.85i q^{53} +2244.72 q^{54} -382.243 q^{55} -1711.86i q^{56} -757.043i q^{57} -1322.60 q^{58} -6472.33 q^{59} -655.857i q^{60} -6608.69i q^{61} +1994.80 q^{62} -2060.17i q^{63} +512.000 q^{64} +2207.36i q^{65} +709.078i q^{66} +5225.76i q^{67} -3187.81i q^{68} +(-2172.87 - 3213.30i) q^{69} -2392.40 q^{70} -5696.69 q^{71} +616.176 q^{72} -7364.21 q^{73} +3334.51i q^{74} -916.589 q^{75} -825.936i q^{76} +2586.53 q^{77} +4094.75 q^{78} +1905.16i q^{79} -715.542i q^{80} -3613.71 q^{81} -8114.90 q^{82} +2724.40i q^{83} +4438.00i q^{84} -4455.11 q^{85} -3741.08i q^{86} +3428.84 q^{87} +773.606i q^{88} +4252.33i q^{89} -861.132i q^{90} -14936.6i q^{91} +(-2370.61 - 3505.71i) q^{92} -5171.53 q^{93} +6979.37 q^{94} -1154.28 q^{95} -1327.36 q^{96} +5482.74i q^{97} +9397.61 q^{98} +931.010i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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