LMFDB - Embedded newform 230.5.d.a.91.5

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			91.5
Character	$\chi$	$=$	230.91
Dual form			230.5.d.a.91.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843 q^{2} -5.71864 q^{3} +8.00000 q^{4} -11.1803i q^{5} +16.1747 q^{6} -36.1607i q^{7} -22.6274 q^{8} -48.2972 q^{9} +O(q^{10})$	\(q-2.82843 q^{2} -5.71864 q^{3} +8.00000 q^{4} -11.1803i q^{5} +16.1747 q^{6} -36.1607i q^{7} -22.6274 q^{8} -48.2972 q^{9} +31.6228i q^{10} +144.561i q^{11} -45.7491 q^{12} -122.417 q^{13} +102.278i q^{14} +63.9363i q^{15} +64.0000 q^{16} -499.933i q^{17} +136.605 q^{18} -202.350i q^{19} -89.4427i q^{20} +206.790i q^{21} -408.879i q^{22} +(505.602 + 155.590i) q^{23} +129.398 q^{24} -125.000 q^{25} +346.248 q^{26} +739.404 q^{27} -289.286i q^{28} -1446.14 q^{29} -180.839i q^{30} -814.524 q^{31} -181.019 q^{32} -826.690i q^{33} +1414.02i q^{34} -404.289 q^{35} -386.378 q^{36} +2231.98i q^{37} +572.333i q^{38} +700.059 q^{39} +252.982i q^{40} +2504.62 q^{41} -584.890i q^{42} +1029.16i q^{43} +1156.48i q^{44} +539.979i q^{45} +(-1430.06 - 440.074i) q^{46} +2040.24 q^{47} -365.993 q^{48} +1093.40 q^{49} +353.553 q^{50} +2858.94i q^{51} -979.337 q^{52} +3767.63i q^{53} -2091.35 q^{54} +1616.24 q^{55} +818.223i q^{56} +1157.17i q^{57} +4090.30 q^{58} -559.916 q^{59} +511.490i q^{60} +3433.45i q^{61} +2303.82 q^{62} +1746.46i q^{63} +512.000 q^{64} +1368.67i q^{65} +2338.23i q^{66} +1899.54i q^{67} -3999.47i q^{68} +(-2891.35 - 889.760i) q^{69} +1143.50 q^{70} -8774.83 q^{71} +1092.84 q^{72} +6826.46 q^{73} -6313.00i q^{74} +714.829 q^{75} -1618.80i q^{76} +5227.41 q^{77} -1980.07 q^{78} +11777.0i q^{79} -715.542i q^{80} -316.307 q^{81} -7084.14 q^{82} -1188.75i q^{83} +1654.32i q^{84} -5589.42 q^{85} -2910.91i q^{86} +8269.94 q^{87} -3271.03i q^{88} +1226.29i q^{89} -1527.29i q^{90} +4426.69i q^{91} +(4044.81 + 1244.72i) q^{92} +4657.97 q^{93} -5770.68 q^{94} -2262.34 q^{95} +1035.18 q^{96} +7051.88i q^{97} -3092.61 q^{98} -6981.87i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.71864			−0.635404			−0.317702	−	0.948191i	$-0.602911\pi$
$3$	−5.71864			−0.635404			−0.317702	+	0.948191i	$0.602911\pi$
$4$	8.00000			0.500000
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$	16.1747			0.449298
$7$		−	36.1607i		−	0.737974i	−0.929435	−	0.368987i	$-0.879705\pi$
$7$		−	36.1607i		−	0.737974i	0.929435	−	0.368987i	$-0.120295\pi$
$8$	−22.6274			−0.353553
$9$	−48.2972			−0.596262
$10$			31.6228i			0.316228i
$11$			144.561i			1.19472i	0.801975	+	0.597358i	$0.203783\pi$
$11$			144.561i			1.19472i	−0.801975	+	0.597358i	$0.796217\pi$
$12$	−45.7491			−0.317702
$13$	−122.417			−0.724362			−0.362181	−	0.932108i	$-0.617968\pi$
$13$	−122.417			−0.724362			−0.362181	+	0.932108i	$0.617968\pi$
$14$			102.278i			0.521826i
$15$			63.9363i			0.284161i
$16$	64.0000			0.250000
$17$		−	499.933i		−	1.72987i	−0.501882	−	0.864936i	$-0.667359\pi$
$17$		−	499.933i		−	1.72987i	0.501882	−	0.864936i	$-0.332641\pi$
$18$	136.605			0.421621
$19$		−	202.350i		−	0.560527i	−0.959923	−	0.280264i	$-0.909578\pi$
$19$		−	202.350i		−	0.560527i	0.959923	−	0.280264i	$-0.0904219\pi$
$20$		−	89.4427i		−	0.223607i
$21$			206.790i			0.468911i
$22$		−	408.879i		−	0.844792i
$23$	505.602	+	155.590i	0.955768	+	0.294120i
$23$	505.602	+	155.590i	0.955768	+	0.294120i
$24$	129.398			0.224649
$25$	−125.000			−0.200000
$26$	346.248			0.512201
$27$	739.404			1.01427
$28$		−	289.286i		−	0.368987i
$29$	−1446.14			−1.71955			−0.859773	−	0.510676i	$-0.829395\pi$
$29$	−1446.14			−1.71955			−0.859773	+	0.510676i	$0.829395\pi$
$30$		−	180.839i		−	0.200932i
$31$	−814.524			−0.847580			−0.423790	−	0.905760i	$-0.639301\pi$
$31$	−814.524			−0.847580			−0.423790	+	0.905760i	$0.639301\pi$
$32$	−181.019			−0.176777
$33$		−	826.690i		−	0.759127i
$34$			1414.02i			1.22320i
$35$	−404.289			−0.330032
$36$	−386.378			−0.298131
$37$			2231.98i			1.63038i	0.579197	+	0.815188i	$0.303366\pi$
$37$			2231.98i			1.63038i	−0.579197	+	0.815188i	$0.696634\pi$
$38$			572.333i			0.396352i
$39$	700.059			0.460262
$40$			252.982i			0.158114i
$41$	2504.62			1.48996			0.744979	−	0.667088i	$-0.232459\pi$
$41$	2504.62			1.48996			0.744979	+	0.667088i	$0.232459\pi$
$42$		−	584.890i		−	0.331570i
$43$			1029.16i			0.556605i	0.960493	+	0.278303i	$0.0897718\pi$
$43$			1029.16i			0.556605i	−0.960493	+	0.278303i	$0.910228\pi$
$44$			1156.48i			0.597358i
$45$			539.979i			0.266656i
$46$	−1430.06	−	440.074i	−0.675830	−	0.207974i
$47$	2040.24			0.923605			0.461803	−	0.886983i	$-0.347203\pi$
$47$	2040.24			0.923605			0.461803	+	0.886983i	$0.347203\pi$
$48$	−365.993			−0.158851
$49$	1093.40			0.455395
$50$	353.553			0.141421
$51$			2858.94i			1.09917i
$52$	−979.337			−0.362181
$53$			3767.63i			1.34127i	0.741788	+	0.670635i	$0.233978\pi$
$53$			3767.63i			1.34127i	−0.741788	+	0.670635i	$0.766022\pi$
$54$	−2091.35			−0.717198
$55$	1616.24			0.534293
$56$			818.223i			0.260913i
$57$			1157.17i			0.356161i
$58$	4090.30			1.21590
$59$	−559.916			−0.160849			−0.0804246	−	0.996761i	$-0.525628\pi$
$59$	−559.916			−0.160849			−0.0804246	+	0.996761i	$0.525628\pi$
$60$			511.490i			0.142081i
$61$			3433.45i			0.922723i	0.887212	+	0.461362i	$0.152639\pi$
$61$			3433.45i			0.922723i	−0.887212	+	0.461362i	$0.847361\pi$
$62$	2303.82			0.599330
$63$			1746.46i			0.440025i
$64$	512.000			0.125000
$65$			1368.67i			0.323944i
$66$			2338.23i			0.536784i
$67$			1899.54i			0.423155i	0.977361	+	0.211578i	$0.0678601\pi$
$67$			1899.54i			0.423155i	−0.977361	+	0.211578i	$0.932140\pi$
$68$		−	3999.47i		−	0.864936i
$69$	−2891.35	−	889.760i	−0.607299	−	0.186885i
$70$	1143.50			0.233368
$71$	−8774.83			−1.74069			−0.870346	−	0.492441i	$-0.836105\pi$
$71$	−8774.83			−1.74069			−0.870346	+	0.492441i	$0.836105\pi$
$72$	1092.84			0.210810
$73$	6826.46			1.28100			0.640501	−	0.767957i	$-0.278727\pi$
$73$	6826.46			1.28100			0.640501	+	0.767957i	$0.278727\pi$
$74$		−	6313.00i		−	1.15285i
$75$	714.829			0.127081
$76$		−	1618.80i		−	0.280264i
$77$	5227.41			0.881669
$78$	−1980.07			−0.325455
$79$			11777.0i			1.88703i	0.331329	+	0.943515i	$0.392503\pi$
$79$			11777.0i			1.88703i	−0.331329	+	0.943515i	$0.607497\pi$
$80$		−	715.542i		−	0.111803i
$81$	−316.307			−0.0482102
$82$	−7084.14			−1.05356
$83$		−	1188.75i		−	0.172558i	−0.996271	−	0.0862791i	$-0.972502\pi$
$83$		−	1188.75i		−	0.172558i	0.996271	−	0.0862791i	$-0.0274977\pi$
$84$			1654.32i			0.234456i
$85$	−5589.42			−0.773623
$86$		−	2910.91i		−	0.393580i
$87$	8269.94			1.09261
$88$		−	3271.03i		−	0.422396i
$89$			1226.29i			0.154815i	0.997000	+	0.0774073i	$0.0246642\pi$
$89$			1226.29i			0.154815i	−0.997000	+	0.0774073i	$0.975336\pi$
$90$		−	1527.29i		−	0.188555i
$91$			4426.69i			0.534560i
$92$	4044.81	+	1244.72i	0.477884	+	0.147060i
$93$	4657.97			0.538556
$94$	−5770.68			−0.653087
$95$	−2262.34			−0.250675
$96$	1035.18			0.112325
$97$			7051.88i			0.749482i	0.927130	+	0.374741i	$0.122268\pi$
$97$			7051.88i			0.749482i	−0.927130	+	0.374741i	$0.877732\pi$
$98$	−3092.61			−0.322013
$99$		−	6981.87i		−	0.712363i
$100$	−1000.00			−0.100000
$101$	224.460			0.0220037			0.0110019	−	0.999939i	$-0.496498\pi$
$101$	224.460			0.0220037			0.0110019	+	0.999939i	$0.496498\pi$
$102$		−	8086.29i		−	0.777229i
$103$		−	11459.0i		−	1.08012i	−0.841626	−	0.540061i	$-0.818401\pi$
$103$		−	11459.0i		−	1.08012i	0.841626	−	0.540061i	$-0.181599\pi$
$104$	2769.98			0.256101
$105$	2311.98			0.209704
$106$		−	10656.5i		−	0.948421i
$107$		−	9657.02i		−	0.843482i	−0.906716	−	0.421741i	$-0.861419\pi$
$107$		−	9657.02i		−	0.843482i	0.906716	−	0.421741i	$-0.138581\pi$
$108$	5915.23			0.507136
$109$			9981.48i			0.840121i	0.907496	+	0.420061i	$0.137991\pi$
$109$			9981.48i			0.840121i	−0.907496	+	0.420061i	$0.862009\pi$
$110$	−4571.41			−0.377802
$111$		−	12763.9i		−	1.03595i
$112$		−	2314.29i		−	0.184493i
$113$			9416.99i			0.737489i	0.929531	+	0.368744i	$0.120212\pi$
$113$			9416.99i			0.737489i	−0.929531	+	0.368744i	$0.879788\pi$
$114$		−	3272.96i		−	0.251844i
$115$	1739.54	−	5652.80i	0.131534	−	0.427433i
$116$	−11569.1			−0.859773
$117$	5912.41			0.431909
$118$	1583.68			0.113738
$119$	−18077.9			−1.27660
$120$		−	1446.71i		−	0.100466i
$121$	−6256.77			−0.427346
$122$		−	9711.27i		−	0.652464i
$123$	−14323.0			−0.946726
$124$	−6516.20			−0.423790
$125$			1397.54i			0.0894427i
$126$		−	4939.74i		−	0.311145i
$127$	15075.1			0.934658			0.467329	−	0.884083i	$-0.345216\pi$
$127$	15075.1			0.934658			0.467329	+	0.884083i	$0.345216\pi$
$128$	−1448.15			−0.0883883
$129$		−	5885.41i		−	0.353669i
$130$		−	3871.17i		−	0.229063i
$131$	−14649.9			−0.853674			−0.426837	−	0.904329i	$-0.640372\pi$
$131$	−14649.9			−0.853674			−0.426837	+	0.904329i	$0.640372\pi$
$132$		−	6613.52i		−	0.379564i
$133$	−7317.13			−0.413654
$134$		−	5372.72i		−	0.299216i
$135$		−	8266.78i		−	0.453596i
$136$			11312.2i			0.611602i
$137$		−	5764.08i		−	0.307106i	−0.988140	−	0.153553i	$-0.950928\pi$
$137$		−	5764.08i		−	0.307106i	0.988140	−	0.153553i	$-0.0490716\pi$
$138$	8177.98	+	2516.62i	0.429425	+	0.132148i
$139$	30547.8			1.58107			0.790534	−	0.612418i	$-0.209803\pi$
$139$	30547.8			1.58107			0.790534	+	0.612418i	$0.209803\pi$
$140$	−3234.31			−0.165016
$141$	−11667.4			−0.586862
$142$	24819.0			1.23085
$143$		−	17696.7i		−	0.865407i
$144$	−3091.02			−0.149065
$145$			16168.3i			0.769005i
$146$	−19308.2			−0.905806
$147$	−6252.78			−0.289360
$148$			17855.9i			0.815188i
$149$			4228.94i			0.190484i	0.995454	+	0.0952422i	$0.0303626\pi$
$149$			4228.94i			0.190484i	−0.995454	+	0.0952422i	$0.969637\pi$
$150$	−2021.84			−0.0898597
$151$	44878.2			1.96826			0.984129	−	0.177455i	$-0.0567863\pi$
$151$	44878.2			1.96826			0.984129	+	0.177455i	$0.0567863\pi$
$152$			4578.66i			0.198176i
$153$			24145.4i			1.03146i
$154$	−14785.4			−0.623434
$155$			9106.66i			0.379049i
$156$	5600.47			0.230131
$157$		−	41740.1i		−	1.69338i	−0.532087	−	0.846690i	$-0.678592\pi$
$157$		−	41740.1i		−	1.69338i	0.532087	−	0.846690i	$-0.321408\pi$
$158$		−	33310.3i		−	1.33433i
$159$		−	21545.7i		−	0.852248i
$160$			2023.86i			0.0790569i
$161$	5626.23	−	18282.9i	0.217053	−	0.705332i
$162$	894.651			0.0340897
$163$	−44955.9			−1.69204			−0.846021	−	0.533150i	$-0.821008\pi$
$163$	−44955.9			−1.69204			−0.846021	+	0.533150i	$0.821008\pi$
$164$	20037.0			0.744979
$165$	−9242.67			−0.339492
$166$			3362.30i			0.122017i
$167$	20227.1			0.725273			0.362636	−	0.931931i	$-0.381877\pi$
$167$	20227.1			0.725273			0.362636	+	0.931931i	$0.381877\pi$
$168$		−	4679.12i		−	0.165785i
$169$	−13575.0			−0.475300
$170$	15809.3			0.547034
$171$			9772.95i			0.334221i
$172$			8233.31i			0.278303i
$173$	−23236.7			−0.776394			−0.388197	−	0.921576i	$-0.626902\pi$
$173$	−23236.7			−0.776394			−0.388197	+	0.921576i	$0.626902\pi$
$174$	−23390.9			−0.772590
$175$			4520.09i			0.147595i
$176$			9251.88i			0.298679i
$177$	3201.96			0.102204
$178$		−	3468.46i		−	0.109470i
$179$	−54235.3			−1.69269			−0.846343	−	0.532639i	$-0.821200\pi$
$179$	−54235.3			−1.69269			−0.846343	+	0.532639i	$0.821200\pi$
$180$			4319.83i			0.133328i
$181$			57670.3i			1.76033i	0.474665	+	0.880167i	$0.342569\pi$
$181$			57670.3i			1.76033i	−0.474665	+	0.880167i	$0.657431\pi$
$182$		−	12520.6i		−	0.377991i
$183$		−	19634.7i		−	0.586302i
$184$	−11440.5	−	3520.59i	−0.337915	−	0.103987i
$185$	24954.3			0.729126
$186$	−13174.7			−0.380816
$187$	72270.6			2.06671
$188$	16321.9			0.461803
$189$		−	26737.4i		−	0.748505i
$190$	6398.88			0.177254
$191$		−	53657.3i		−	1.47083i	−0.677618	−	0.735414i	$-0.736988\pi$
$191$		−	53657.3i		−	1.47083i	0.677618	−	0.735414i	$-0.263012\pi$
$192$	−2927.94			−0.0794255
$193$	−50150.7			−1.34636			−0.673182	−	0.739476i	$-0.735073\pi$
$193$	−50150.7			−1.34636			−0.673182	+	0.739476i	$0.735073\pi$
$194$		−	19945.7i		−	0.529964i
$195$		−	7826.90i		−	0.205836i
$196$	8747.23			0.227698
$197$	72183.0			1.85996			0.929978	−	0.367616i	$-0.119826\pi$
$197$	72183.0			1.85996			0.929978	+	0.367616i	$0.119826\pi$
$198$			19747.7i			0.503717i
$199$			23834.8i			0.601875i	0.953644	+	0.300937i	$0.0972995\pi$
$199$			23834.8i			0.601875i	−0.953644	+	0.300937i	$0.902700\pi$
$200$	2828.43			0.0707107
$201$		−	10862.8i		−	0.268874i
$202$	−634.869			−0.0155590
$203$			52293.4i			1.26898i
$204$			22871.5i			0.549584i
$205$		−	28002.5i		−	0.666330i
$206$			32411.0i			0.763762i
$207$	−24419.1	−	7514.54i	−0.569888	−	0.175373i
$208$	−7834.70			−0.181090
$209$	29251.9			0.669671
$210$	−6539.27			−0.148283
$211$	−57596.8			−1.29370			−0.646850	−	0.762617i	$-0.723914\pi$
$211$	−57596.8			−1.29370			−0.646850	+	0.762617i	$0.723914\pi$
$212$			30141.0i			0.670635i
$213$	50180.0			1.10604
$214$			27314.2i			0.596432i
$215$	11506.4			0.248922
$216$	−16730.8			−0.358599
$217$			29453.8i			0.625492i
$218$		−	28231.9i		−	0.594056i
$219$	−39038.1			−0.813954
$220$	12929.9			0.267147
$221$			61200.4i			1.25305i
$222$			36101.8i			0.732525i
$223$	2334.78			0.0469500			0.0234750	−	0.999724i	$-0.492527\pi$
$223$	2334.78			0.0469500			0.0234750	+	0.999724i	$0.492527\pi$
$224$			6545.79i			0.130457i
$225$	6037.15			0.119252
$226$		−	26635.3i		−	0.521483i
$227$		−	19674.3i		−	0.381809i	−0.981609	−	0.190905i	$-0.938858\pi$
$227$		−	19674.3i		−	0.381809i	0.981609	−	0.190905i	$-0.0611421\pi$
$228$			9257.34i			0.178081i
$229$			81567.7i			1.55542i	0.628625	+	0.777709i	$0.283618\pi$
$229$			81567.7i			1.55542i	−0.628625	+	0.777709i	$0.716382\pi$
$230$	−4920.17	+	15988.5i	−0.0930089	+	0.302241i
$231$	−29893.7			−0.560216
$232$	32722.4			0.607952
$233$	−54147.4			−0.997391			−0.498696	−	0.866777i	$-0.666187\pi$
$233$	−54147.4			−0.997391			−0.498696	+	0.866777i	$0.666187\pi$
$234$	−16722.8			−0.305406
$235$		−	22810.6i		−	0.413049i
$236$	−4479.33			−0.0804246
$237$		−	67348.1i		−	1.19903i
$238$	51132.1			0.902693
$239$	44657.6			0.781807			0.390903	−	0.920432i	$-0.372163\pi$
$239$	44657.6			0.781807			0.390903	+	0.920432i	$0.372163\pi$
$240$			4091.92i			0.0710403i
$241$			97384.0i			1.67669i	0.545138	+	0.838346i	$0.316477\pi$
$241$			97384.0i			1.67669i	−0.545138	+	0.838346i	$0.683523\pi$
$242$	17696.8			0.302179
$243$	−58082.9			−0.983638
$244$			27467.6i			0.461362i
$245$		−	12224.6i		−	0.203659i
$246$	40511.6			0.669436
$247$			24771.1i			0.406024i
$248$	18430.6			0.299665
$249$			6798.05i			0.109644i
$250$		−	3952.85i		−	0.0632456i
$251$		−	88261.7i		−	1.40096i	−0.713674	−	0.700478i	$-0.752970\pi$
$251$		−	88261.7i		−	1.40096i	0.713674	−	0.700478i	$-0.247030\pi$
$252$			13971.7i			0.220013i
$253$	−22492.1	+	73090.1i	−0.351390	+	1.14187i
$254$	−42638.8			−0.660903
$255$	31963.9			0.491563
$256$	4096.00			0.0625000
$257$	38259.6			0.579261			0.289630	−	0.957139i	$-0.406468\pi$
$257$	38259.6			0.579261			0.289630	+	0.957139i	$0.406468\pi$
$258$			16646.5i			0.250082i
$259$	80710.1			1.20317
$260$			10949.3i			0.161972i
$261$	69844.5			1.02530
$262$	41436.2			0.603639
$263$			117483.i			1.69849i	0.528003	+	0.849243i	$0.322941\pi$
$263$			117483.i			1.69849i	−0.528003	+	0.849243i	$0.677059\pi$
$264$			18705.8i			0.268392i
$265$	42123.4			0.599834
$266$	20696.0			0.292498
$267$		−	7012.68i		−	0.0983698i
$268$			15196.3i			0.211578i
$269$	795.933			0.0109995			0.00549974	−	0.999985i	$-0.498249\pi$
$269$	795.933			0.0109995			0.00549974	+	0.999985i	$0.498249\pi$
$270$			23382.0i			0.320741i
$271$	−28510.9			−0.388215			−0.194107	−	0.980980i	$-0.562181\pi$
$271$	−28510.9			−0.388215			−0.194107	+	0.980980i	$0.562181\pi$
$272$		−	31995.7i		−	0.432468i
$273$		−	25314.6i		−	0.339661i
$274$			16303.3i			0.217157i
$275$		−	18070.1i		−	0.238943i
$276$	−23130.8	−	7118.08i	−0.303650	−	0.0934425i
$277$	22370.5			0.291552			0.145776	−	0.989318i	$-0.453432\pi$
$277$	22370.5			0.291552			0.145776	+	0.989318i	$0.453432\pi$
$278$	−86402.3			−1.11798
$279$	39339.3			0.505380
$280$	9148.01			0.116684
$281$		−	44755.6i		−	0.566807i	−0.959001	−	0.283403i	$-0.908536\pi$
$281$		−	44755.6i		−	0.566807i	0.959001	−	0.283403i	$-0.0914635\pi$
$282$	33000.4			0.414974
$283$			86344.2i			1.07810i	0.842273	+	0.539052i	$0.181217\pi$
$283$			86344.2i			1.07810i	−0.842273	+	0.539052i	$0.818783\pi$
$284$	−70198.6			−0.870346
$285$	12937.5			0.159280
$286$			50053.8i			0.611935i
$287$		−	90568.8i		−	1.09955i
$288$	8742.73			0.105405
$289$	−166412.			−1.99246
$290$		−	45730.9i		−	0.543768i
$291$		−	40327.1i		−	0.476224i
$292$	54611.7			0.640501
$293$		−	135997.i		−	1.58414i	−0.610431	−	0.792069i	$-0.709004\pi$
$293$		−	135997.i		−	1.58414i	0.610431	−	0.792069i	$-0.290996\pi$
$294$	17685.5			0.204608
$295$			6260.05i			0.0719340i
$296$		−	50504.0i		−	0.576425i
$297$			106889.i			1.21177i
$298$		−	11961.3i		−	0.134693i
$299$	−61894.3	−	19046.8i	−0.692322	−	0.213049i
$300$	5718.64			0.0635404
$301$	37215.3			0.410760
$302$	−126935.			−1.39177
$303$	−1283.61			−0.0139813
$304$		−	12950.4i		−	0.140132i
$305$	38387.2			0.412654
$306$		−	68293.4i		−	0.729350i
$307$	−60293.2			−0.639722			−0.319861	−	0.947464i	$-0.603636\pi$
$307$	−60293.2			−0.639722			−0.319861	+	0.947464i	$0.603636\pi$
$308$	41819.3			0.440834
$309$			65530.0i			0.686314i
$310$		−	25757.5i		−	0.268028i
$311$	−129858.			−1.34261			−0.671304	−	0.741183i	$-0.734265\pi$
$311$	−129858.			−1.34261			−0.671304	+	0.741183i	$0.734265\pi$
$312$	−15840.5			−0.162727
$313$		−	119093.i		−	1.21562i	−0.794084	−	0.607808i	$-0.792049\pi$
$313$		−	119093.i		−	1.21562i	0.794084	−	0.607808i	$-0.207951\pi$
$314$			118059.i			1.19740i
$315$	19526.0			0.196785
$316$			94215.6i			0.943515i
$317$	23515.7			0.234013			0.117006	−	0.993131i	$-0.462670\pi$
$317$	23515.7			0.234013			0.117006	+	0.993131i	$0.462670\pi$
$318$			60940.4i			0.602631i
$319$		−	209055.i		−	2.05437i
$320$		−	5724.33i		−	0.0559017i
$321$			55225.0i			0.535952i
$322$	−15913.4	+	51711.9i	−0.153480	+	0.498745i
$323$	−101162.			−0.969640
$324$	−2530.45			−0.0241051
$325$	15302.1			0.144872
$326$	127154.			1.19645
$327$		−	57080.5i		−	0.533816i
$328$	−56673.1			−0.526780
$329$		−	73776.6i		−	0.681596i
$330$	26142.2			0.240057
$331$	23231.4			0.212041			0.106021	−	0.994364i	$-0.466189\pi$
$331$	23231.4			0.212041			0.106021	+	0.994364i	$0.466189\pi$
$332$		−	9510.03i		−	0.0862791i
$333$		−	107799.i		−	0.972130i
$334$	−57211.0			−0.512845
$335$	21237.5			0.189241
$336$			13234.6i			0.117228i
$337$			116385.i			1.02479i	0.858749	+	0.512396i	$0.171242\pi$
$337$			116385.i			1.02479i	−0.858749	+	0.512396i	$0.828758\pi$
$338$	38396.0			0.336088
$339$		−	53852.4i		−	0.468603i
$340$	−44715.4			−0.386811
$341$		−	117748.i		−	1.01262i
$342$		−	27642.1i		−	0.236330i
$343$		−	126360.i		−	1.07404i
$344$		−	23287.3i		−	0.196790i
$345$	−9947.82	+	32326.3i	−0.0835775	+	0.271592i
$346$	65723.3			0.548994
$347$	27828.6			0.231117			0.115559	−	0.993301i	$-0.463134\pi$
$347$	27828.6			0.231117			0.115559	+	0.993301i	$0.463134\pi$
$348$	66159.5			0.546303
$349$	−1181.38			−0.00969923			−0.00484962	−	0.999988i	$-0.501544\pi$
$349$	−1181.38			−0.00969923			−0.00484962	+	0.999988i	$0.501544\pi$
$350$		−	12784.7i		−	0.104365i
$351$	−90515.7			−0.734699
$352$		−	26168.3i		−	0.211198i
$353$	−104506.			−0.838672			−0.419336	−	0.907831i	$-0.637737\pi$
$353$	−104506.			−0.838672			−0.419336	+	0.907831i	$0.637737\pi$
$354$	−9056.50			−0.0722693
$355$			98105.5i			0.778461i
$356$			9810.29i			0.0774073i
$357$	103381.			0.811157
$358$	153401.			1.19691
$359$			115023.i			0.892475i	0.894915	+	0.446238i	$0.147236\pi$
$359$			115023.i			0.892475i	−0.894915	+	0.446238i	$0.852764\pi$
$360$		−	12218.3i		−	0.0942773i
$361$	89375.4			0.685809
$362$		−	163116.i		−	1.24474i
$363$	35780.2			0.271537
$364$			35413.5i			0.267280i
$365$		−	76322.2i		−	0.572882i
$366$			55535.2i			0.414578i
$367$			38982.4i			0.289425i	0.989474	+	0.144713i	$0.0462258\pi$
$367$			38982.4i			0.289425i	−0.989474	+	0.144713i	$0.953774\pi$
$368$	32358.5	+	9957.73i	0.238942	+	0.0735300i
$369$	−120966.			−0.888405
$370$	−70581.5			−0.515570
$371$	136240.			0.989822
$372$	37263.8			0.269278
$373$			194728.i			1.39962i	0.714329	+	0.699810i	$0.246732\pi$
$373$			194728.i			1.39962i	−0.714329	+	0.699810i	$0.753268\pi$
$374$	−204412.			−1.46138
$375$		−	7992.04i		−	0.0568323i
$376$	−46165.4			−0.326544
$377$	177032.			1.24557
$378$			75624.7i			0.529273i
$379$		−	47511.4i		−	0.330765i	−0.986230	−	0.165383i	$-0.947114\pi$
$379$		−	47511.4i		−	0.330765i	0.986230	−	0.165383i	$-0.0528859\pi$
$380$	−18098.8			−0.125338
$381$	−86209.0			−0.593886
$382$			151766.i			1.04003i
$383$		−	119372.i		−	0.813774i	−0.913479	−	0.406887i	$-0.866614\pi$
$383$		−	119372.i		−	0.813774i	0.913479	−	0.406887i	$-0.133386\pi$
$384$	8281.47			0.0561623
$385$		−	58444.3i		−	0.394294i
$386$	141848.			0.952024
$387$		−	49705.7i		−	0.331883i
$388$			56415.0i			0.374741i
$389$			125616.i			0.830126i	0.909793	+	0.415063i	$0.136240\pi$
$389$			125616.i			0.830126i	−0.909793	+	0.415063i	$0.863760\pi$
$390$			22137.8i			0.145548i
$391$	77784.4	−	252767.i	0.508790	−	1.65336i
$392$	−24740.9			−0.161006
$393$	83777.4			0.542428
$394$	−204164.			−1.31519
$395$	131670.			0.843906
$396$		−	55855.0i		−	0.356182i
$397$	−149926.			−0.951255			−0.475627	−	0.879647i	$-0.657779\pi$
$397$	−149926.			−0.951255			−0.475627	+	0.879647i	$0.657779\pi$
$398$		−	67415.1i		−	0.425590i
$399$	41844.0			0.262837
$400$	−8000.00			−0.0500000
$401$			81187.0i			0.504891i	0.967611	+	0.252445i	$0.0812348\pi$
$401$			81187.0i			0.504891i	−0.967611	+	0.252445i	$0.918765\pi$
$402$			30724.6i			0.190123i
$403$	99711.8			0.613955
$404$	1795.68			0.0110019
$405$			3536.42i			0.0215602i
$406$		−	147908.i		−	0.897304i
$407$	−322657.			−1.94784
$408$		−	64690.3i		−	0.388615i
$409$	−11773.7			−0.0703828			−0.0351914	−	0.999381i	$-0.511204\pi$
$409$	−11773.7			−0.0703828			−0.0351914	+	0.999381i	$0.511204\pi$
$410$			79203.1i			0.471166i
$411$			32962.7i			0.195136i
$412$		−	91672.2i		−	0.540061i
$413$			20247.0i			0.118703i
$414$	69067.8	+	21254.3i	0.402972	+	0.124007i
$415$	−13290.7			−0.0771704
$416$	22159.9			0.128050
$417$	−174692.			−1.00462
$418$	−82736.8			−0.473529
$419$			120401.i			0.685807i	0.939371	+	0.342903i	$0.111410\pi$
$419$			120401.i			0.685807i	−0.939371	+	0.342903i	$0.888590\pi$
$420$	18495.9			0.104852
$421$			195390.i			1.10240i	0.834374	+	0.551198i	$0.185829\pi$
$421$			195390.i			1.10240i	−0.834374	+	0.551198i	$0.814171\pi$
$422$	162908.			0.914784
$423$	−98538.1			−0.550710
$424$		−	85251.7i		−	0.474211i
$425$			62491.6i			0.345975i
$426$	−141931.			−0.782090
$427$	124156.			0.680945
$428$		−	77256.2i		−	0.421741i
$429$			101201.i			0.549883i
$430$	−32545.0			−0.176014
$431$		−	134910.i		−	0.726254i	−0.931740	−	0.363127i	$-0.881709\pi$
$431$		−	134910.i		−	0.726254i	0.931740	−	0.363127i	$-0.118291\pi$
$432$	47321.8			0.253568
$433$			59064.8i			0.315031i	0.987517	+	0.157515i	$0.0503484\pi$
$433$			59064.8i			0.315031i	−0.987517	+	0.157515i	$0.949652\pi$
$434$		−	83307.9i		−	0.442289i
$435$		−	92460.8i		−	0.488629i
$436$			79851.9i			0.420061i
$437$	31483.6	−	102309.i	0.164862	−	0.535734i
$438$	110416.			0.575553
$439$	−113608.			−0.589494			−0.294747	−	0.955575i	$-0.595235\pi$
$439$	−113608.			−0.589494			−0.294747	+	0.955575i	$0.595235\pi$
$440$	−36571.3			−0.188901
$441$	−52808.3			−0.271535
$442$		−	173101.i		−	0.886043i
$443$	−8455.98			−0.0430880			−0.0215440	−	0.999768i	$-0.506858\pi$
$443$	−8455.98			−0.0430880			−0.0215440	+	0.999768i	$0.506858\pi$
$444$		−	102111.i		−	0.517973i
$445$	13710.3			0.0692352
$446$	−6603.75			−0.0331987
$447$		−	24183.8i		−	0.121035i
$448$		−	18514.3i		−	0.0922467i
$449$	17689.1			0.0877430			0.0438715	−	0.999037i	$-0.486031\pi$
$449$	17689.1			0.0877430			0.0438715	+	0.999037i	$0.486031\pi$
$450$	−17075.6			−0.0843241
$451$			362069.i			1.78008i
$452$			75335.9i			0.368744i
$453$	−256642.			−1.25064
$454$			55647.2i			0.269980i
$455$	49491.9			0.239062
$456$		−	26183.7i		−	0.125922i
$457$		−	86592.4i		−	0.414617i	−0.978276	−	0.207309i	$-0.933530\pi$
$457$		−	86592.4i		−	0.414617i	0.978276	−	0.207309i	$-0.0664704\pi$
$458$		−	230708.i		−	1.09985i
$459$		−	369652.i		−	1.75456i
$460$	13916.3	−	45222.4i	0.0657672	−	0.213716i
$461$	−69562.4			−0.327320			−0.163660	−	0.986517i	$-0.552330\pi$
$461$	−69562.4			−0.327320			−0.163660	+	0.986517i	$0.552330\pi$
$462$	84552.1			0.396132
$463$	278222.			1.29786			0.648931	−	0.760847i	$-0.275216\pi$
$463$	278222.			1.29786			0.648931	+	0.760847i	$0.275216\pi$
$464$	−92552.9			−0.429887
$465$		−	52077.7i		−	0.240849i
$466$	153152.			0.705262
$467$		−	312915.i		−	1.43481i	−0.696659	−	0.717403i	$-0.745331\pi$
$467$		−	312915.i		−	1.43481i	0.696659	−	0.717403i	$-0.254669\pi$
$468$	47299.2			0.215955
$469$	68688.8			0.312277
$470$			64518.2i			0.292070i
$471$			238697.i			1.07598i
$472$	12669.5			0.0568688
$473$	−148777.			−0.664985
$474$			190489.i			0.847840i
$475$			25293.8i			0.112105i
$476$	−144623.			−0.638300
$477$		−	181966.i		−	0.799748i
$478$	−126311.			−0.552821
$479$			20091.3i			0.0875664i	0.999041	+	0.0437832i	$0.0139411\pi$
$479$			20091.3i			0.0875664i	−0.999041	+	0.0437832i	$0.986059\pi$
$480$		−	11573.7i		−	0.0502331i
$481$		−	273233.i		−	1.18098i
$482$		−	275443.i		−	1.18560i
$483$	−32174.3	+	104553.i	−0.137916	+	0.448171i
$484$	−50054.2			−0.213673
$485$	78842.4			0.335179
$486$	164283.			0.695537
$487$	−90270.3			−0.380616			−0.190308	−	0.981724i	$-0.560949\pi$
$487$	−90270.3			−0.380616			−0.190308	+	0.981724i	$0.560949\pi$
$488$		−	77690.2i		−	0.326232i
$489$	257086.			1.07513
$490$			34576.5i			0.144009i
$491$	69594.4			0.288677			0.144338	−	0.989528i	$-0.453895\pi$
$491$	69594.4			0.288677			0.144338	+	0.989528i	$0.453895\pi$
$492$	−114584.			−0.473363
$493$			722973.i			2.97460i
$494$		−	70063.4i		−	0.287103i
$495$	−78059.7			−0.318579
$496$	−52129.6			−0.211895
$497$			317304.i			1.28458i
$498$		−	19227.8i		−	0.0775302i
$499$	343899.			1.38111			0.690557	−	0.723278i	$-0.257365\pi$
$499$	343899.			1.38111			0.690557	+	0.723278i	$0.257365\pi$
$500$			11180.3i			0.0447214i
$501$	−115672.			−0.460841
$502$			249642.i			0.990626i
$503$		−	173030.i		−	0.683890i	−0.939720	−	0.341945i	$-0.888914\pi$
$503$		−	173030.i		−	0.683890i	0.939720	−	0.341945i	$-0.111086\pi$
$504$		−	39517.9i		−	0.155572i
$505$		−	2509.54i		−	0.00984038i
$506$	63617.3	−	206730.i	0.248470	−	0.807425i
$507$	77630.7			0.302007
$508$	120601.			0.467329
$509$	64774.3			0.250016			0.125008	−	0.992156i	$-0.460104\pi$
$509$	64774.3			0.250016			0.125008	+	0.992156i	$0.460104\pi$
$510$	−90407.5			−0.347587
$511$		−	246850.i		−	0.945346i
$512$	−11585.2			−0.0441942
$513$		−	149619.i		−	0.568526i
$514$	−108214.			−0.409599
$515$	−128116.			−0.483045
$516$		−	47083.3i		−	0.176835i
$517$			294939.i			1.10345i
$518$	−228283.			−0.850772
$519$	132882.			0.493324
$520$		−	30969.4i		−	0.114532i
$521$			101470.i			0.373820i	0.982377	+	0.186910i	$0.0598472\pi$
$521$			101470.i			0.373820i	−0.982377	+	0.186910i	$0.940153\pi$
$522$	−197550.			−0.724997
$523$		−	24840.6i		−	0.0908153i	−0.998969	−	0.0454076i	$-0.985541\pi$
$523$		−	24840.6i		−	0.0908153i	0.998969	−	0.0454076i	$-0.0144587\pi$
$524$	−117199.			−0.426837
$525$		−	25848.7i		−	0.0937823i
$526$		−	332291.i		−	1.20101i
$527$			407208.i			1.46621i
$528$		−	52908.1i		−	0.189782i
$529$	231425.	+	157333.i	0.826987	+	0.562221i
$530$	−119143.			−0.424147
$531$	27042.4			0.0959083
$532$	−58537.0			−0.206827
$533$	−306609.			−1.07927
$534$			19834.9i			0.0695579i
$535$	−107969.			−0.377217
$536$		−	42981.8i		−	0.149608i
$537$	310152.			1.07554
$538$	−2251.24			−0.00777780
$539$			158063.i			0.544068i
$540$		−	66134.3i		−	0.226798i
$541$	438463.			1.49809			0.749046	−	0.662518i	$-0.230512\pi$
$541$	438463.			1.49809			0.749046	+	0.662518i	$0.230512\pi$
$542$	80640.9			0.274509
$543$		−	329795.i		−	1.11852i
$544$			90497.6i			0.305801i
$545$	111596.			0.375714
$546$			71600.6i			0.240177i
$547$	78673.1			0.262937			0.131468	−	0.991320i	$-0.458031\pi$
$547$	78673.1			0.262937			0.131468	+	0.991320i	$0.458031\pi$
$548$		−	46112.6i		−	0.153553i
$549$		−	165826.i		−	0.550185i
$550$			51109.9i			0.168958i
$551$			292627.i			0.963853i
$552$	65423.8	+	20133.0i	0.214713	+	0.0660739i
$553$	425863.			1.39258
$554$	−63273.4			−0.206159
$555$	−142705.			−0.463290
$556$	244383.			0.790534
$557$			565989.i			1.82431i	0.409850	+	0.912153i	$0.365581\pi$
$557$			565989.i			1.82431i	−0.409850	+	0.912153i	$0.634419\pi$
$558$	−111268.			−0.357357
$559$		−	125987.i		−	0.403184i
$560$	−25874.5			−0.0825080
$561$	−413290.			−1.31319
$562$			126588.i			0.400793i
$563$			374472.i			1.18142i	0.806886	+	0.590708i	$0.201151\pi$
$563$			374472.i			1.18142i	−0.806886	+	0.590708i	$0.798849\pi$
$564$	−93339.3			−0.293431
$565$	105285.			0.329815
$566$		−	244218.i		−	0.762334i
$567$			11437.9i			0.0355778i
$568$	198552.			0.615427
$569$			130238.i			0.402265i	0.979564	+	0.201133i	$0.0644622\pi$
$569$			130238.i			0.402265i	−0.979564	+	0.201133i	$0.935538\pi$
$570$	−36592.8			−0.112628
$571$			166694.i			0.511267i	0.966774	+	0.255633i	$0.0822840\pi$
$571$			166694.i			0.511267i	−0.966774	+	0.255633i	$0.917716\pi$
$572$		−	141574.i		−	0.432703i
$573$			306846.i			0.934570i
$574$			256167.i			0.777499i
$575$	−63200.2	−	19448.7i	−0.191154	−	0.0588240i
$576$	−24728.2			−0.0745327
$577$	9991.79			0.0300118			0.0150059	−	0.999887i	$-0.495223\pi$
$577$	9991.79			0.0300118			0.0150059	+	0.999887i	$0.495223\pi$
$578$	470685.			1.40888
$579$	286794.			0.855486
$580$			129347.i			0.384502i
$581$	−42986.2			−0.127343
$582$			114062.i			0.336741i
$583$	−544650.			−1.60244
$584$	−154465.			−0.452903
$585$		−	66102.7i		−	0.193156i
$586$			384657.i			1.12016i
$587$	−443800.			−1.28798			−0.643992	−	0.765032i	$-0.722723\pi$
$587$	−443800.			−1.28798			−0.643992	+	0.765032i	$0.722723\pi$
$588$	−50022.2			−0.144680
$589$			164819.i			0.475092i
$590$		−	17706.1i		−	0.0508650i
$591$	−412788.			−1.18182
$592$			142847.i			0.407594i
$593$	335864.			0.955113			0.477556	−	0.878601i	$-0.341523\pi$
$593$	335864.			0.955113			0.477556	+	0.878601i	$0.341523\pi$
$594$		−	302327.i		−	0.856848i
$595$			202117.i			0.570913i
$596$			33831.6i			0.0952422i
$597$		−	136303.i		−	0.382434i
$598$	175064.	+	53872.6i	0.489546	+	0.150649i
$599$	163368.			0.455315			0.227658	−	0.973741i	$-0.426893\pi$
$599$	163368.			0.455315			0.227658	+	0.973741i	$0.426893\pi$
$600$	−16174.7			−0.0449298
$601$	−498851.			−1.38109			−0.690544	−	0.723290i	$-0.742629\pi$
$601$	−498851.			−1.38109			−0.690544	+	0.723290i	$0.742629\pi$
$602$	−105261.			−0.290451
$603$		−	91742.6i		−	0.252311i
$604$	359026.			0.984129
$605$			69952.8i			0.191115i
$606$	3630.59			0.00988625
$607$	−70558.8			−0.191502			−0.0957511	−	0.995405i	$-0.530525\pi$
$607$	−70558.8			−0.191502			−0.0957511	+	0.995405i	$0.530525\pi$
$608$			36629.3i			0.0990881i
$609$		−	299047.i		−	0.806315i
$610$	−108575.			−0.291791
$611$	−249761.			−0.669024
$612$			193163.i			0.515728i
$613$			194211.i			0.516836i	0.966033	+	0.258418i	$0.0832012\pi$
$613$			194211.i			0.516836i	−0.966033	+	0.258418i	$0.916799\pi$
$614$	170535.			0.452352
$615$			160136.i			0.423389i
$616$	−118283.			−0.311717
$617$			370058.i			0.972073i	0.873938	+	0.486037i	$0.161558\pi$
$617$			370058.i			0.972073i	−0.873938	+	0.486037i	$0.838442\pi$
$618$		−	185347.i		−	0.485297i
$619$			250478.i			0.653715i	0.945074	+	0.326858i	$0.105990\pi$
$619$			250478.i			0.653715i	−0.945074	+	0.326858i	$0.894010\pi$
$620$			72853.3i			0.189525i
$621$	373844.	+	115043.i	0.969408	+	0.298317i
$622$	367295.			0.949367
$623$	44343.4			0.114249
$624$	44803.8			0.115066
$625$	15625.0			0.0400000
$626$			336845.i			0.859570i
$627$	−167281.			−0.425511
$628$		−	333921.i		−	0.846690i
$629$	1.11584e6			2.82034
$630$	−55227.9			−0.139148
$631$			669366.i			1.68114i	0.541700	+	0.840572i	$0.317781\pi$
$631$			669366.i			1.68114i	−0.541700	+	0.840572i	$0.682219\pi$
$632$		−	266482.i		−	0.667166i
$633$	329375.			0.822022
$634$	−66512.4			−0.165472
$635$		−	168545.i		−	0.417992i
$636$		−	172366.i		−	0.426124i
$637$	−133851.			−0.329871
$638$			591296.i			1.45266i
$639$	423800.			1.03791
$640$			16190.9i			0.0395285i
$641$		−	97539.2i		−	0.237390i	−0.992931	−	0.118695i	$-0.962129\pi$
$641$		−	97539.2i		−	0.237390i	0.992931	−	0.118695i	$-0.0378711\pi$
$642$		−	156200.i		−	0.378975i
$643$		−	33151.4i		−	0.0801825i	−0.999196	−	0.0400912i	$-0.987235\pi$
$643$		−	33151.4i		−	0.0801825i	0.999196	−	0.0400912i	$-0.0127649\pi$
$644$	45009.8	−	146263.i	0.108526	−	0.352666i
$645$	−65800.9			−0.158166
$646$	286128.			0.685639
$647$	114599.			0.273763			0.136881	−	0.990587i	$-0.456292\pi$
$647$	114599.			0.273763			0.136881	+	0.990587i	$0.456292\pi$
$648$	7157.21			0.0170449
$649$		−	80941.8i		−	0.192169i
$650$	−43281.0			−0.102440
$651$		−	168435.i		−	0.397440i
$652$	−359647.			−0.846021
$653$	377785.			0.885970			0.442985	−	0.896529i	$-0.353920\pi$
$653$	377785.			0.885970			0.442985	+	0.896529i	$0.353920\pi$
$654$			161448.i			0.377465i
$655$			163791.i			0.381775i
$656$	160296.			0.372490
$657$	−329699.			−0.763813
$658$			208672.i			0.481961i
$659$		−	662097.i		−	1.52458i	−0.647234	−	0.762291i	$-0.724074\pi$
$659$		−	662097.i		−	1.52458i	0.647234	−	0.762291i	$-0.275926\pi$
$660$	−73941.4			−0.169746
$661$		−	459787.i		−	1.05234i	−0.850381	−	0.526168i	$-0.823628\pi$
$661$		−	459787.i		−	1.05234i	0.850381	−	0.526168i	$-0.176372\pi$
$662$	−65708.4			−0.149936
$663$		−	349983.i		−	0.796195i
$664$			26898.4i			0.0610086i
$665$			81808.0i			0.184992i
$666$			304900.i			0.687400i
$667$	−731170.	−	225004.i	−1.64349	−	0.505753i
$668$	161817.			0.362636
$669$	−13351.7			−0.0298322
$670$	−60068.8			−0.133813
$671$	−496342.			−1.10239
$672$		−	37433.0i		−	0.0828926i
$673$	−680753.			−1.50300			−0.751500	−	0.659733i	$-0.770669\pi$
$673$	−680753.			−1.50300			−0.751500	+	0.659733i	$0.770669\pi$
$674$		−	329185.i		−	0.724638i
$675$	−92425.5			−0.202854
$676$	−108600.			−0.237650
$677$			47364.1i			0.103341i	0.998664	+	0.0516705i	$0.0164545\pi$
$677$			47364.1i			0.103341i	−0.998664	+	0.0516705i	$0.983545\pi$
$678$			152317.i			0.331353i
$679$	255001.			0.553098
$680$	126474.			0.273517
$681$			112510.i			0.242603i
$682$			333042.i			0.716029i
$683$	122890.			0.263436			0.131718	−	0.991287i	$-0.457951\pi$
$683$	122890.			0.263436			0.131718	+	0.991287i	$0.457951\pi$
$684$			78183.6i			0.167110i
$685$	−64444.3			−0.137342
$686$			357400.i			0.759463i
$687$		−	466456.i		−	0.988319i
$688$			65866.5i			0.139151i
$689$		−	461222.i		−	0.971565i
$690$	28136.7	−	91432.5i	0.0590982	−	0.192045i
$691$	−146788.			−0.307421			−0.153711	−	0.988116i	$-0.549122\pi$
$691$	−146788.			−0.307421			−0.153711	+	0.988116i	$0.549122\pi$
$692$	−185894.			−0.388197
$693$	−252469.			−0.525705
$694$	−78711.2			−0.163425
$695$		−	341535.i		−	0.707075i
$696$	−187127.			−0.386295
$697$		−	1.25214e6i		−	2.57744i
$698$	3341.44			0.00685839
$699$	309649.			0.633746
$700$			36160.7i			0.0737974i
$701$			899856.i			1.83121i	0.402084	+	0.915603i	$0.368286\pi$
$701$			899856.i			1.83121i	−0.402084	+	0.915603i	$0.631714\pi$
$702$	256017.			0.519511
$703$	451642.			0.913869
$704$			74015.0i			0.149339i
$705$			130446.i			0.262453i
$706$	295588.			0.593031
$707$		−	8116.64i		−	0.0162382i
$708$	25615.7			0.0511021
$709$			495343.i			0.985402i	0.870199	+	0.492701i	$0.163990\pi$
$709$			495343.i			0.985402i	−0.870199	+	0.492701i	$0.836010\pi$
$710$		−	277484.i		−	0.550455i
$711$		−	568794.i		−	1.12516i
$712$		−	27747.7i		−	0.0547352i
$713$	−411825.	−	126731.i	−0.810090	−	0.249290i
$714$	−292406.			−0.573575
$715$	−197855.			−0.387022
$716$	−433883.			−0.846343
$717$	−255380.			−0.496763
$718$		−	325334.i		−	0.631075i
$719$	421943.			0.816200			0.408100	−	0.912937i	$-0.366192\pi$
$719$	421943.			0.816200			0.408100	+	0.912937i	$0.366192\pi$
$720$			34558.7i			0.0666641i
$721$	−414366.			−0.797102
$722$	−252792.			−0.484940
$723$		−	556904.i		−	1.06538i
$724$			461362.i			0.880167i
$725$	180767.			0.343909
$726$	−101202.			−0.192006
$727$			17004.3i			0.0321729i	0.999871	+	0.0160864i	$0.00512069\pi$
$727$			17004.3i			0.0321729i	−0.999871	+	0.0160864i	$0.994879\pi$
$728$		−	100165.i		−	0.188995i
$729$	357776.			0.673218
$730$			215872.i			0.405089i
$731$	514513.			0.962857
$732$		−	157077.i		−	0.293151i
$733$		−	584429.i		−	1.08774i	−0.839170	−	0.543869i	$-0.816959\pi$
$733$		−	584429.i		−	1.08774i	0.839170	−	0.543869i	$-0.183041\pi$
$734$		−	110259.i		−	0.204655i
$735$			69908.2i			0.129406i
$736$	−91523.7	−	28164.7i	−0.168958	−	0.0519936i
$737$	−274599.			−0.505550
$738$	342144.			0.628197
$739$	203324.			0.372306			0.186153	−	0.982521i	$-0.440398\pi$
$739$	203324.			0.372306			0.186153	+	0.982521i	$0.440398\pi$
$740$	199635.			0.364563
$741$		−	141657.i		−	0.257990i
$742$	−385345.			−0.699910
$743$		−	948126.i		−	1.71747i	−0.512422	−	0.858734i	$-0.671252\pi$
$743$		−	948126.i		−	1.71747i	0.512422	−	0.858734i	$-0.328748\pi$
$744$	−105398.			−0.190408
$745$	47281.0			0.0851872
$746$		−	550773.i		−	0.989680i
$747$			57413.5i			0.102890i
$748$	578165.			1.03335
$749$	−349205.			−0.622467
$750$			22604.9i			0.0401865i
$751$		−	834331.i		−	1.47931i	−0.672988	−	0.739654i	$-0.734989\pi$
$751$		−	834331.i		−	1.47931i	0.672988	−	0.739654i	$-0.265011\pi$
$752$	130576.			0.230901
$753$			504736.i			0.890173i
$754$	−500723.			−0.880754
$755$		−	501754.i		−	0.880232i
$756$		−	213899.i		−	0.374253i
$757$			102601.i			0.179045i	0.995985	+	0.0895223i	$0.0285340\pi$
$757$			102601.i			0.179045i	−0.995985	+	0.0895223i	$0.971466\pi$
$758$			134383.i			0.233886i
$759$	128624.	−	417975.i	0.223275	−	0.725550i
$760$	51191.0			0.0886271
$761$	−537205.			−0.927622			−0.463811	−	0.885934i	$-0.653518\pi$
$761$	−537205.			−0.927622			−0.463811	+	0.885934i	$0.653518\pi$
$762$	243836.			0.419941
$763$	360937.			0.619987
$764$		−	429258.i		−	0.735414i
$765$	269953.			0.461282
$766$			337634.i			0.575425i
$767$	68543.4			0.116513
$768$	−23423.5			−0.0397127
$769$			245882.i			0.415790i	0.978151	+	0.207895i	$0.0666612\pi$
$769$			245882.i			0.415790i	−0.978151	+	0.207895i	$0.933339\pi$
$770$			165305.i			0.278808i
$771$	−218793.			−0.368065
$772$	−401206.			−0.673182
$773$			568513.i			0.951440i	0.879597	+	0.475720i	$0.157812\pi$
$773$			568513.i			0.951440i	−0.879597	+	0.475720i	$0.842188\pi$
$774$			140589.i			0.234676i
$775$	101816.			0.169516
$776$		−	159566.i		−	0.264982i
$777$	−461552.			−0.764501
$778$		−	355294.i		−	0.586988i
$779$		−	506811.i		−	0.835162i
$780$		−	62615.2i		−	0.102918i
$781$		−	1.26849e6i		−	2.07963i
$782$	−220007.	+	714933.i	−0.359769	+	1.16910i
$783$	−1.06928e6			−1.74409
$784$	69977.8			0.113849
$785$	−466669.			−0.757303
$786$	−236958.			−0.383554
$787$			1.03348e6i			1.66860i	0.551307	+	0.834302i	$0.314129\pi$
$787$			1.03348e6i			1.66860i	−0.551307	+	0.834302i	$0.685871\pi$
$788$	577464.			0.929978
$789$		−	671840.i		−	1.07922i
$790$	−372420.			−0.596731
$791$	340525.			0.544247
$792$			157982.i			0.251858i
$793$		−	420314.i		−	0.668386i
$794$	424056.			0.672639
$795$	−240888.			−0.381137
$796$			190679.i			0.300937i
$797$		−	887425.i		−	1.39706i	−0.715581	−	0.698530i	$-0.753838\pi$
$797$		−	887425.i		−	1.39706i	0.715581	−	0.698530i	$-0.246162\pi$
$798$	−118353.			−0.185854
$799$		−	1.01999e6i		−	1.59772i
$800$	22627.4			0.0353553
$801$		−	59226.2i		−	0.0923100i
$802$		−	229631.i		−	0.357012i
$803$			986838.i			1.53043i
$804$		−	86902.4i		−	0.134437i
$805$	−204409.	−	62903.1i	−0.315434	−	0.0970690i
$806$	−282027.			−0.434132
$807$	−4551.65			−0.00698911
$808$	−5078.96			−0.00777950
$809$	−56308.1			−0.0860347			−0.0430174	−	0.999074i	$-0.513697\pi$
$809$	−56308.1			−0.0860347			−0.0430174	+	0.999074i	$0.513697\pi$
$810$		−	10002.5i		−	0.0152454i
$811$	−50714.6			−0.0771065			−0.0385533	−	0.999257i	$-0.512275\pi$
$811$	−50714.6			−0.0771065			−0.0385533	+	0.999257i	$0.512275\pi$
$812$			418347.i			0.634490i
$813$	163043.			0.246673
$814$	912612.			1.37733
$815$			502622.i			0.756704i
$816$			182972.i			0.274792i
$817$	208252.			0.311992
$818$	33301.1			0.0497681
$819$		−	213797.i		−	0.318738i
$820$		−	224020.i		−	0.333165i
$821$	861904.			1.27871			0.639355	−	0.768911i	$-0.279201\pi$
$821$	861904.			1.27871			0.639355	+	0.768911i	$0.279201\pi$
$822$		−	93232.5i		−	0.137982i
$823$	−83544.0			−0.123343			−0.0616716	−	0.998096i	$-0.519643\pi$
$823$	−83544.0			−0.123343			−0.0616716	+	0.998096i	$0.519643\pi$
$824$			259288.i			0.381881i
$825$			103336.i			0.151825i
$826$		−	57267.1i		−	0.0839353i
$827$			380181.i			0.555877i	0.960599	+	0.277939i	$0.0896512\pi$
$827$			380181.i			0.555877i	−0.960599	+	0.277939i	$0.910349\pi$
$828$	−195353.	−	60116.3i	−0.284944	−	0.0876863i
$829$	165977.			0.241511			0.120756	−	0.992682i	$-0.461468\pi$
$829$	165977.			0.241511			0.120756	+	0.992682i	$0.461468\pi$
$830$	37591.7			0.0545677
$831$	−127929.			−0.185253
$832$	−62677.6			−0.0905452
$833$		−	546629.i		−	0.787775i
$834$	494103.			0.710372
$835$		−	226146.i		−	0.324352i
$836$	234015.			0.334835
$837$	−602262.			−0.859676
$838$		−	340545.i		−	0.484939i
$839$			1.07186e6i			1.52270i	0.648342	+	0.761349i	$0.275463\pi$
$839$			1.07186e6i			1.52270i	−0.648342	+	0.761349i	$0.724537\pi$
$840$	−52314.2			−0.0741414
$841$	1.38404e6			1.95684
$842$		−	552646.i		−	0.779512i
$843$			255941.i			0.360151i
$844$	−460774.			−0.646850
$845$			151774.i			0.212561i
$846$	278708.			0.389411
$847$			226249.i			0.315370i
$848$			241128.i			0.335317i
$849$		−	493771.i		−	0.685031i
$850$		−	176753.i		−	0.244641i
$851$	−347273.	+	1.12849e6i	−0.479526	+	1.55826i
$852$	401440.			0.553021
$853$	−1.15091e6			−1.58177			−0.790885	−	0.611964i	$-0.790380\pi$
$853$	−1.15091e6			−1.58177			−0.790885	+	0.611964i	$0.790380\pi$
$854$	−351166.			−0.481501
$855$	109265.			0.149468
$856$			218513.i			0.298216i
$857$	853624.			1.16226			0.581132	−	0.813809i	$-0.302610\pi$
$857$	853624.			1.16226			0.581132	+	0.813809i	$0.302610\pi$
$858$		−	286240.i		−	0.388826i
$859$	−925091.			−1.25371			−0.626856	−	0.779135i	$-0.715659\pi$
$859$	−925091.			−1.25371			−0.626856	+	0.779135i	$0.715659\pi$
$860$	92051.2			0.124461
$861$			517930.i			0.698659i
$862$			381582.i			0.513539i
$863$	−373391.			−0.501351			−0.250676	−	0.968071i	$-0.580653\pi$
$863$	−373391.			−0.501351			−0.250676	+	0.968071i	$0.580653\pi$
$864$	−133846.			−0.179299
$865$			259794.i			0.347214i
$866$		−	167061.i		−	0.222761i
$867$	951651.			1.26602
$868$			235630.i			0.312746i
$869$	−1.70248e6			−2.25446
$870$			261519.i			0.345513i
$871$		−	232537.i		−	0.306517i
$872$		−	225855.i		−	0.297028i
$873$		−	340586.i		−	0.446887i
$874$	−89049.0	+	289372.i	−0.116575	+	0.378821i
$875$	50536.1			0.0660064
$876$	−312305.			−0.406977
$877$	−1.31205e6			−1.70589			−0.852943	−	0.522004i	$-0.825185\pi$
$877$	−1.31205e6			−1.70589			−0.852943	+	0.522004i	$0.825185\pi$
$878$	321332.			0.416835
$879$			777716.i			1.00657i
$880$	103439.			0.133573
$881$		−	502151.i		−	0.646967i	−0.946234	−	0.323484i	$-0.895146\pi$
$881$		−	502151.i		−	0.646967i	0.946234	−	0.323484i	$-0.104854\pi$
$882$	149365.			0.192004
$883$	288451.			0.369956			0.184978	−	0.982743i	$-0.440779\pi$
$883$	288451.			0.369956			0.184978	+	0.982743i	$0.440779\pi$
$884$			489603.i			0.626527i
$885$		−	35799.0i		−	0.0457071i
$886$	23917.1			0.0304678
$887$	−374154.			−0.475558			−0.237779	−	0.971319i	$-0.576419\pi$
$887$	−374154.			−0.475558			−0.237779	+	0.971319i	$0.576419\pi$
$888$			288814.i			0.366263i
$889$		−	545126.i		−	0.689753i
$890$	−38778.6			−0.0489566
$891$		−	45725.5i		−	0.0575974i
$892$	18678.2			0.0234750
$893$		−	412844.i		−	0.517706i
$894$			68402.1i			0.0855844i
$895$			606369.i			0.756992i
$896$			52366.3i			0.0652283i
$897$	353951.	+	108922.i	0.439904	+	0.135372i
$898$	−50032.3			−0.0620437
$899$	1.17792e6			1.45745
$900$	48297.2			0.0596262
$901$	1.88356e6			2.32023
$902$		−	1.02409e6i		−	1.25870i
$903$	−212821.			−0.260999
$904$		−	213082.i		−	0.260742i
$905$	644773.			0.787245
$906$	725894.			0.884335
$907$			331129.i			0.402515i	0.979538	+	0.201258i	$0.0645028\pi$
$907$			331129.i			0.402515i	−0.979538	+	0.201258i	$0.935497\pi$
$908$		−	157394.i		−	0.190905i
$909$	−10840.8			−0.0131200
$910$	−139984.			−0.169043
$911$		−	354311.i		−	0.426921i	−0.976952	−	0.213461i	$-0.931527\pi$
$911$		−	354311.i		−	0.426921i	0.976952	−	0.213461i	$-0.0684735\pi$
$912$			74058.7i			0.0890403i
$913$	171847.			0.206158
$914$			244920.i			0.293179i
$915$	−219522.			−0.262202
$916$			652541.i			0.777709i
$917$			529751.i			0.629989i
$918$			1.04553e6i			1.24066i
$919$		−	126428.i		−	0.149697i	−0.997195	−	0.0748486i	$-0.976153\pi$
$919$		−	126428.i		−	0.149697i	0.997195	−	0.0748486i	$-0.0238473\pi$
$920$	−39361.4	+	127908.i	−0.0465045	+	0.151120i
$921$	344795.			0.406482
$922$	196752.			0.231450
$923$	1.07419e6			1.26089
$924$	−239149.			−0.280108
$925$		−	278998.i		−	0.326075i
$926$	−786929.			−0.917728
$927$			553439.i			0.644036i
$928$	261779.			0.303976
$929$	−456058.			−0.528432			−0.264216	−	0.964464i	$-0.585113\pi$
$929$	−456058.			−0.528432			−0.264216	+	0.964464i	$0.585113\pi$
$930$			147298.i			0.170306i
$931$		−	221250.i		−	0.255261i
$932$	−433179.			−0.498696
$933$	742612.			0.853098
$934$			885058.i			1.01456i
$935$		−	808010.i		−	0.924259i
$936$	−133782.			−0.152703
$937$			277761.i			0.316368i	0.987410	+	0.158184i	$0.0505639\pi$
$937$			277761.i			0.316368i	−0.987410	+	0.158184i	$0.949436\pi$
$938$	−194281.			−0.220813
$939$			681048.i			0.772407i
$940$		−	182485.i		−	0.206524i
$941$			16601.4i			0.0187485i	0.999956	+	0.00937423i	$0.00298395\pi$
$941$			16601.4i			0.0187485i	−0.999956	+	0.00937423i	$0.997016\pi$
$942$		−	675136.i		−	0.760833i
$943$	1.26634e6	+	389693.i	1.42406	+	0.438227i
$944$	−35834.6			−0.0402123
$945$	−298933.			−0.334742
$946$	420804.			0.470216
$947$	−729272.			−0.813185			−0.406592	−	0.913610i	$-0.633283\pi$
$947$	−729272.			−0.813185			−0.406592	+	0.913610i	$0.633283\pi$
$948$		−	538785.i		−	0.599513i
$949$	−835676.			−0.927910
$950$		−	71541.6i		−	0.0792705i
$951$	−134478.			−0.148693
$952$	409057.			0.451346
$953$			1.57446e6i			1.73358i	0.498671	+	0.866791i	$0.333822\pi$
$953$			1.57446e6i			1.73358i	−0.498671	+	0.866791i	$0.666178\pi$
$954$			514677.i			0.565507i
$955$	−599906.			−0.657774
$956$	357261.			0.390903
$957$			1.19551e6i			1.30535i
$958$		−	56826.9i		−	0.0619188i
$959$	−208433.			−0.226636
$960$			32735.4i			0.0355202i
$961$	−260071.			−0.281608
$962$			772820.i			0.835080i
$963$			466407.i			0.502936i
$964$			779072.i			0.838346i
$965$			560702.i			0.602113i
$966$	91002.8	−	295721.i	0.0975215	−	0.316905i
$967$	1.00919e6			1.07924			0.539620	−	0.841909i	$-0.318568\pi$
$967$	1.00919e6			1.07924			0.539620	+	0.841909i	$0.318568\pi$
$968$	141575.			0.151090
$969$	578506.			0.616113
$970$	−223000.			−0.237007
$971$			448208.i			0.475381i	0.971341	+	0.237690i	$0.0763904\pi$
$971$			448208.i			0.475381i	−0.971341	+	0.237690i	$0.923610\pi$
$972$	−464663.			−0.491819
$973$		−	1.10463e6i		−	1.16679i
$974$	255323.			0.269136
$975$	−87507.4			−0.0920525
$976$			219741.i			0.230681i
$977$		−	315215.i		−	0.330231i	−0.986274	−	0.165116i	$-0.947200\pi$
$977$		−	315215.i		−	0.330231i	0.986274	−	0.165116i	$-0.0527997\pi$
$978$	−727150.			−0.760232
$979$	−177273.			−0.184959
$980$		−	97797.0i		−	0.101829i
$981$		−	482078.i		−	0.500932i
$982$	−196843.			−0.204125
$983$			1.27633e6i			1.32085i	0.750890	+	0.660427i	$0.229625\pi$
$983$			1.27633e6i			1.32085i	−0.750890	+	0.660427i	$0.770375\pi$
$984$	324093.			0.334718
$985$		−	807031.i		−	0.831797i
$986$		−	2.04488e6i		−	2.10336i
$987$			421902.i			0.433089i
$988$			198169.i			0.203012i
$989$	−160127.	+	520347.i	−0.163709	+	0.531986i
$990$	220786.			0.225269
$991$	542128.			0.552020			0.276010	−	0.961155i	$-0.410988\pi$
$991$	542128.			0.552020			0.276010	+	0.961155i	$0.410988\pi$
$992$	147445.			0.149832
$993$	−132852.			−0.134732
$994$		−	897471.i		−	0.908338i
$995$	266482.			0.269167
$996$			54384.4i			0.0548221i
$997$	−1.50138e6			−1.51043			−0.755216	−	0.655476i	$-0.772468\pi$
$997$	−1.50138e6			−1.51043			−0.755216	+	0.655476i	$0.772468\pi$
$998$	−972693.			−0.976595
$999$			1.65034e6i			1.65364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.d.a.91.5	✓	32
23.22	odd	2	inner	230.5.d.a.91.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.d.a.91.5	✓	32	1.1	even	1	trivial
230.5.d.a.91.12	yes	32	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.82843 q^{2} -5.71864 q^{3} +8.00000 q^{4} -11.1803i q^{5} +16.1747 q^{6} -36.1607i q^{7} -22.6274 q^{8} -48.2972 q^{9} +O(q^{10})\)	\(q-2.82843 q^{2} -5.71864 q^{3} +8.00000 q^{4} -11.1803i q^{5} +16.1747 q^{6} -36.1607i q^{7} -22.6274 q^{8} -48.2972 q^{9} +31.6228i q^{10} +144.561i q^{11} -45.7491 q^{12} -122.417 q^{13} +102.278i q^{14} +63.9363i q^{15} +64.0000 q^{16} -499.933i q^{17} +136.605 q^{18} -202.350i q^{19} -89.4427i q^{20} +206.790i q^{21} -408.879i q^{22} +(505.602 + 155.590i) q^{23} +129.398 q^{24} -125.000 q^{25} +346.248 q^{26} +739.404 q^{27} -289.286i q^{28} -1446.14 q^{29} -180.839i q^{30} -814.524 q^{31} -181.019 q^{32} -826.690i q^{33} +1414.02i q^{34} -404.289 q^{35} -386.378 q^{36} +2231.98i q^{37} +572.333i q^{38} +700.059 q^{39} +252.982i q^{40} +2504.62 q^{41} -584.890i q^{42} +1029.16i q^{43} +1156.48i q^{44} +539.979i q^{45} +(-1430.06 - 440.074i) q^{46} +2040.24 q^{47} -365.993 q^{48} +1093.40 q^{49} +353.553 q^{50} +2858.94i q^{51} -979.337 q^{52} +3767.63i q^{53} -2091.35 q^{54} +1616.24 q^{55} +818.223i q^{56} +1157.17i q^{57} +4090.30 q^{58} -559.916 q^{59} +511.490i q^{60} +3433.45i q^{61} +2303.82 q^{62} +1746.46i q^{63} +512.000 q^{64} +1368.67i q^{65} +2338.23i q^{66} +1899.54i q^{67} -3999.47i q^{68} +(-2891.35 - 889.760i) q^{69} +1143.50 q^{70} -8774.83 q^{71} +1092.84 q^{72} +6826.46 q^{73} -6313.00i q^{74} +714.829 q^{75} -1618.80i q^{76} +5227.41 q^{77} -1980.07 q^{78} +11777.0i q^{79} -715.542i q^{80} -316.307 q^{81} -7084.14 q^{82} -1188.75i q^{83} +1654.32i q^{84} -5589.42 q^{85} -2910.91i q^{86} +8269.94 q^{87} -3271.03i q^{88} +1226.29i q^{89} -1527.29i q^{90} +4426.69i q^{91} +(4044.81 + 1244.72i) q^{92} +4657.97 q^{93} -5770.68 q^{94} -2262.34 q^{95} +1035.18 q^{96} +7051.88i q^{97} -3092.61 q^{98} -6981.87i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) 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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