LMFDB - Embedded newform 14.5.b.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,5,Mod(13,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("14.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	14.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.44717948317$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.1308672.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 72x^{2} + 1278 $ x^4 + 72*x^2 + 1278
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.3
Root			$5.63537i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.5.b.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843 q^{2} -11.2707i q^{3} +8.00000 q^{4} +43.1492i q^{5} -31.8784i q^{6} +(-44.4558 - 20.6077i) q^{7} +22.6274 q^{8} -46.0294 q^{9} +O(q^{10})$	\(q+2.82843 q^{2} -11.2707i q^{3} +8.00000 q^{4} +43.1492i q^{5} -31.8784i q^{6} +(-44.4558 - 20.6077i) q^{7} +22.6274 q^{8} -46.0294 q^{9} +122.044i q^{10} -11.8234 q^{11} -90.1659i q^{12} +20.6077i q^{13} +(-125.740 - 58.2874i) q^{14} +486.323 q^{15} +64.0000 q^{16} -289.172i q^{17} -130.191 q^{18} -104.641i q^{19} +345.193i q^{20} +(-232.264 + 501.050i) q^{21} -33.4416 q^{22} +73.5290 q^{23} -255.028i q^{24} -1236.85 q^{25} +58.2874i q^{26} -394.144i q^{27} +(-355.647 - 164.862i) q^{28} +950.881 q^{29} +1375.53 q^{30} +1385.30i q^{31} +181.019 q^{32} +133.258i q^{33} -817.901i q^{34} +(889.206 - 1918.23i) q^{35} -368.235 q^{36} -1279.47 q^{37} -295.968i q^{38} +232.264 q^{39} +976.355i q^{40} +1303.54i q^{41} +(-656.942 + 1417.18i) q^{42} -96.2338 q^{43} -94.5870 q^{44} -1986.13i q^{45} +207.971 q^{46} +186.190i q^{47} -721.327i q^{48} +(1551.64 + 1832.27i) q^{49} -3498.35 q^{50} -3259.18 q^{51} +164.862i q^{52} +4376.94 q^{53} -1114.81i q^{54} -510.169i q^{55} +(-1005.92 - 466.299i) q^{56} -1179.38 q^{57} +2689.50 q^{58} +1650.28i q^{59} +3890.58 q^{60} -5200.50i q^{61} +3918.23i q^{62} +(2046.28 + 948.562i) q^{63} +512.000 q^{64} -889.206 q^{65} +376.911i q^{66} +552.587 q^{67} -2313.37i q^{68} -828.726i q^{69} +(2515.05 - 5425.58i) q^{70} -8487.61 q^{71} -1041.53 q^{72} +317.344i q^{73} -3618.89 q^{74} +13940.2i q^{75} -837.124i q^{76} +(525.618 + 243.653i) q^{77} +656.942 q^{78} -624.377 q^{79} +2761.55i q^{80} -8170.68 q^{81} +3686.96i q^{82} -7662.33i q^{83} +(-1858.11 + 4008.40i) q^{84} +12477.5 q^{85} -272.190 q^{86} -10717.1i q^{87} -267.532 q^{88} -4190.72i q^{89} -5617.63i q^{90} +(424.678 - 916.133i) q^{91} +588.232 q^{92} +15613.4 q^{93} +526.625i q^{94} +4515.15 q^{95} -2040.22i q^{96} +12994.4i q^{97} +(4388.71 + 5182.43i) q^{98} +544.223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9}+O(q^{10}) $ 4 * q + 32 * q^4 - 76 * q^7 - 252 * q^9	$ 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9} + 360 q^{11} - 288 q^{14} + 384 q^{15} + 256 q^{16} + 192 q^{18} + 768 q^{21} - 1152 q^{22} - 792 q^{23} - 2300 q^{25} - 608 q^{28} + 1224 q^{29} + 4416 q^{30} + 4032 q^{35} - 2016 q^{36} - 3896 q^{37} - 768 q^{39} - 4800 q^{42} + 3688 q^{43} + 2880 q^{44} + 3072 q^{46} - 1532 q^{49} - 7488 q^{50} - 11136 q^{51} + 5832 q^{53} - 2304 q^{56} + 12864 q^{57} + 7296 q^{58} + 3072 q^{60} + 3060 q^{63} + 2048 q^{64} - 4032 q^{65} - 1048 q^{67} - 1344 q^{70} - 21528 q^{71} + 1536 q^{72} - 3456 q^{74} + 3528 q^{77} + 4800 q^{78} + 12776 q^{79} - 29628 q^{81} + 6144 q^{84} + 16512 q^{85} - 11520 q^{86} - 9216 q^{88} + 5568 q^{91} - 6336 q^{92} + 38016 q^{93} + 36864 q^{95} + 21888 q^{98} - 29592 q^{99}+O(q^{100}) $ 4 * q + 32 * q^4 - 76 * q^7 - 252 * q^9 + 360 * q^11 - 288 * q^14 + 384 * q^15 + 256 * q^16 + 192 * q^18 + 768 * q^21 - 1152 * q^22 - 792 * q^23 - 2300 * q^25 - 608 * q^28 + 1224 * q^29 + 4416 * q^30 + 4032 * q^35 - 2016 * q^36 - 3896 * q^37 - 768 * q^39 - 4800 * q^42 + 3688 * q^43 + 2880 * q^44 + 3072 * q^46 - 1532 * q^49 - 7488 * q^50 - 11136 * q^51 + 5832 * q^53 - 2304 * q^56 + 12864 * q^57 + 7296 * q^58 + 3072 * q^60 + 3060 * q^63 + 2048 * q^64 - 4032 * q^65 - 1048 * q^67 - 1344 * q^70 - 21528 * q^71 + 1536 * q^72 - 3456 * q^74 + 3528 * q^77 + 4800 * q^78 + 12776 * q^79 - 29628 * q^81 + 6144 * q^84 + 16512 * q^85 - 11520 * q^86 - 9216 * q^88 + 5568 * q^91 - 6336 * q^92 + 38016 * q^93 + 36864 * q^95 + 21888 * q^98 - 29592 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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
$3$		−	11.2707i		−	1.25230i	−0.779701	−	0.626152i	$-0.784629\pi$
$3$		−	11.2707i		−	1.25230i	0.779701	−	0.626152i	$-0.215371\pi$
$4$	8.00000			0.500000
$5$			43.1492i			1.72597i	0.505232	+	0.862984i	$0.331407\pi$
$5$			43.1492i			1.72597i	−0.505232	+	0.862984i	$0.668593\pi$
$6$		−	31.8784i		−	0.885512i
$7$	−44.4558	−	20.6077i	−0.907262	−	0.420566i
$7$	−44.4558	−	20.6077i	−0.907262	−	0.420566i
$8$	22.6274			0.353553
$9$	−46.0294			−0.568265
$10$			122.044i			1.22044i
$11$	−11.8234			−0.0977139			−0.0488569	−	0.998806i	$-0.515558\pi$
$11$	−11.8234			−0.0977139			−0.0488569	+	0.998806i	$0.515558\pi$
$12$		−	90.1659i		−	0.626152i
$13$			20.6077i			0.121939i	0.998140	+	0.0609696i	$0.0194193\pi$
$13$			20.6077i			0.121939i	−0.998140	+	0.0609696i	$0.980581\pi$
$14$	−125.740	−	58.2874i	−0.641531	−	0.297385i
$15$	486.323			2.16144
$16$	64.0000			0.250000
$17$		−	289.172i		−	1.00059i	−0.865854	−	0.500297i	$-0.833224\pi$
$17$		−	289.172i		−	1.00059i	0.865854	−	0.500297i	$-0.166776\pi$
$18$	−130.191			−0.401824
$19$		−	104.641i		−	0.289863i	−0.989442	−	0.144932i	$-0.953704\pi$
$19$		−	104.641i		−	0.289863i	0.989442	−	0.144932i	$-0.0462962\pi$
$20$			345.193i			0.862984i
$21$	−232.264	+	501.050i	−0.526676	+	1.13617i
$22$	−33.4416			−0.0690941
$23$	73.5290			0.138996			0.0694981	−	0.997582i	$-0.477860\pi$
$23$	73.5290			0.138996			0.0694981	+	0.997582i	$0.477860\pi$
$24$		−	255.028i		−	0.442756i
$25$	−1236.85			−1.97896
$26$			58.2874i			0.0862240i
$27$		−	394.144i		−	0.540664i
$28$	−355.647	−	164.862i	−0.453631	−	0.210283i
$29$	950.881			1.13066			0.565328	−	0.824866i	$-0.308750\pi$
$29$	950.881			1.13066			0.565328	+	0.824866i	$0.308750\pi$
$30$	1375.53			1.52837
$31$			1385.30i			1.44152i	0.693182	+	0.720762i	$0.256208\pi$
$31$			1385.30i			1.44152i	−0.693182	+	0.720762i	$0.743792\pi$
$32$	181.019			0.176777
$33$			133.258i			0.122367i
$34$		−	817.901i		−	0.707527i
$35$	889.206	−	1918.23i	0.725882	−	1.56590i
$36$	−368.235			−0.284132
$37$	−1279.47			−0.934602			−0.467301	−	0.884098i	$-0.654774\pi$
$37$	−1279.47			−0.934602			−0.467301	+	0.884098i	$0.654774\pi$
$38$		−	295.968i		−	0.204964i
$39$	232.264			0.152705
$40$			976.355i			0.610222i
$41$			1303.54i			0.775454i	0.921774	+	0.387727i	$0.126740\pi$
$41$			1303.54i			0.775454i	−0.921774	+	0.387727i	$0.873260\pi$
$42$	−656.942	+	1417.18i	−0.372416	+	0.803392i
$43$	−96.2338			−0.0520464			−0.0260232	−	0.999661i	$-0.508284\pi$
$43$	−96.2338			−0.0520464			−0.0260232	+	0.999661i	$0.508284\pi$
$44$	−94.5870			−0.0488569
$45$		−	1986.13i		−	0.980806i
$46$	207.971			0.0982852
$47$			186.190i			0.0842870i	0.999112	+	0.0421435i	$0.0134187\pi$
$47$			186.190i			0.0842870i	−0.999112	+	0.0421435i	$0.986581\pi$
$48$		−	721.327i		−	0.313076i
$49$	1551.64	+	1832.27i	0.646249	+	0.763127i
$50$	−3498.35			−1.39934
$51$	−3259.18			−1.25305
$52$			164.862i			0.0609696i
$53$	4376.94			1.55818			0.779092	−	0.626910i	$-0.215681\pi$
$53$	4376.94			1.55818			0.779092	+	0.626910i	$0.215681\pi$
$54$		−	1114.81i		−	0.382307i
$55$		−	510.169i		−	0.168651i
$56$	−1005.92	−	466.299i	−0.320766	−	0.148692i
$57$	−1179.38			−0.362997
$58$	2689.50			0.799494
$59$			1650.28i			0.474081i	0.971500	+	0.237041i	$0.0761774\pi$
$59$			1650.28i			0.474081i	−0.971500	+	0.237041i	$0.923823\pi$
$60$	3890.58			1.08072
$61$		−	5200.50i		−	1.39761i	−0.715313	−	0.698804i	$-0.753716\pi$
$61$		−	5200.50i		−	1.39761i	0.715313	−	0.698804i	$-0.246284\pi$
$62$			3918.23i			1.01931i
$63$	2046.28	+	948.562i	0.515565	+	0.238993i
$64$	512.000			0.125000
$65$	−889.206			−0.210463
$66$			376.911i			0.0865268i
$67$	552.587			0.123098			0.0615490	−	0.998104i	$-0.480396\pi$
$67$	552.587			0.123098			0.0615490	+	0.998104i	$0.480396\pi$
$68$		−	2313.37i		−	0.500297i
$69$		−	828.726i		−	0.174065i
$70$	2515.05	−	5425.58i	0.513276	−	1.10726i
$71$	−8487.61			−1.68372			−0.841858	−	0.539699i	$-0.818538\pi$
$71$	−8487.61			−1.68372			−0.841858	+	0.539699i	$0.818538\pi$
$72$	−1041.53			−0.200912
$73$			317.344i			0.0595503i	0.999557	+	0.0297751i	$0.00947912\pi$
$73$			317.344i			0.0595503i	−0.999557	+	0.0297751i	$0.990521\pi$
$74$	−3618.89			−0.660863
$75$			13940.2i			2.47826i
$76$		−	837.124i		−	0.144932i
$77$	525.618	+	243.653i	0.0886521	+	0.0410951i
$78$	656.942			0.107979
$79$	−624.377			−0.100044			−0.0500222	−	0.998748i	$-0.515929\pi$
$79$	−624.377			−0.100044			−0.0500222	+	0.998748i	$0.515929\pi$
$80$			2761.55i			0.431492i
$81$	−8170.68			−1.24534
$82$			3686.96i			0.548329i
$83$		−	7662.33i		−	1.11226i	−0.831097	−	0.556128i	$-0.812287\pi$
$83$		−	7662.33i		−	1.11226i	0.831097	−	0.556128i	$-0.187713\pi$
$84$	−1858.11	+	4008.40i	−0.263338	+	0.568084i
$85$	12477.5			1.72699
$86$	−272.190			−0.0368024
$87$		−	10717.1i		−	1.41592i
$88$	−267.532			−0.0345471
$89$		−	4190.72i		−	0.529065i	−0.964377	−	0.264532i	$-0.914782\pi$
$89$		−	4190.72i		−	0.529065i	0.964377	−	0.264532i	$-0.0852176\pi$
$90$		−	5617.63i		−	0.693535i
$91$	424.678	−	916.133i	0.0512834	−	0.110631i
$92$	588.232			0.0694981
$93$	15613.4			1.80523
$94$			526.625i			0.0595999i
$95$	4515.15			0.500294
$96$		−	2040.22i		−	0.221378i
$97$			12994.4i			1.38106i	0.723305	+	0.690529i	$0.242622\pi$
$97$			12994.4i			1.38106i	−0.723305	+	0.690529i	$0.757378\pi$
$98$	4388.71	+	5182.43i	0.456967	+	0.539612i
$99$	544.223			0.0555273
$100$	−9894.82			−0.989482
$101$			13694.8i			1.34249i	0.741234	+	0.671246i	$0.234241\pi$
$101$			13694.8i			1.34249i	−0.741234	+	0.671246i	$0.765759\pi$
$102$	−9218.34			−0.886038
$103$		−	15146.7i		−	1.42773i	−0.700285	−	0.713863i	$-0.746944\pi$
$103$		−	15146.7i		−	1.42773i	0.700285	−	0.713863i	$-0.253056\pi$
$104$			466.299i			0.0431120i
$105$	−21619.9	−	10022.0i	−1.96099	−	0.909025i
$106$	12379.8			1.10180
$107$	7137.28			0.623398			0.311699	−	0.950181i	$-0.399102\pi$
$107$	7137.28			0.623398			0.311699	+	0.950181i	$0.399102\pi$
$108$		−	3153.15i		−	0.270332i
$109$	−13556.3			−1.14101			−0.570505	−	0.821294i	$-0.693252\pi$
$109$	−13556.3			−1.14101			−0.570505	+	0.821294i	$0.693252\pi$
$110$		−	1442.98i		−	0.119254i
$111$			14420.6i			1.17041i
$112$	−2845.17	−	1318.89i	−0.226816	−	0.105141i
$113$	768.202			0.0601615			0.0300807	−	0.999547i	$-0.490424\pi$
$113$	768.202			0.0601615			0.0300807	+	0.999547i	$0.490424\pi$
$114$	−3335.78			−0.256677
$115$			3172.72i			0.239903i
$116$	7607.05			0.565328
$117$		−	948.562i		−	0.0692937i
$118$			4667.69i			0.335226i
$119$	−5959.17	+	12855.4i	−0.420815	+	0.907801i
$120$	11004.2			0.764183
$121$	−14501.2			−0.990452
$122$		−	14709.2i		−	0.988258i
$123$	14691.8			0.971104
$124$			11082.4i			0.720762i
$125$		−	26400.9i		−	1.68966i
$126$	5787.75	+	2682.94i	0.364560	+	0.168993i
$127$	948.919			0.0588331			0.0294166	−	0.999567i	$-0.490635\pi$
$127$	948.919			0.0588331			0.0294166	+	0.999567i	$0.490635\pi$
$128$	1448.15			0.0883883
$129$			1084.63i			0.0651779i
$130$	−2515.05			−0.148820
$131$			5443.08i			0.317177i	0.987345	+	0.158589i	$0.0506944\pi$
$131$			5443.08i			0.317177i	−0.987345	+	0.158589i	$0.949306\pi$
$132$			1066.07i			0.0611837i
$133$	−2156.40	+	4651.88i	−0.121906	+	0.262982i
$134$	1562.95			0.0870434
$135$	17007.0			0.933168
$136$		−	6543.21i		−	0.353763i
$137$	453.997			0.0241886			0.0120943	−	0.999927i	$-0.496150\pi$
$137$	453.997			0.0241886			0.0120943	+	0.999927i	$0.496150\pi$
$138$		−	2343.99i		−	0.123083i
$139$		−	18530.3i		−	0.959074i	−0.877522	−	0.479537i	$-0.840805\pi$
$139$		−	18530.3i		−	0.959074i	0.877522	−	0.479537i	$-0.159195\pi$
$140$	7113.65	−	15345.9i	0.362941	−	0.782952i
$141$	2098.50			0.105553
$142$	−24006.6			−1.19057
$143$		−	243.653i		−	0.0119151i
$144$	−2945.88			−0.142066
$145$			41029.8i			1.95147i
$146$			897.583i			0.0421084i
$147$	20651.0	−	17488.2i	0.955666	−	0.809300i
$148$	−10235.8			−0.467301
$149$	18132.6			0.816746			0.408373	−	0.912815i	$-0.366096\pi$
$149$	18132.6			0.816746			0.408373	+	0.912815i	$0.366096\pi$
$150$			39428.9i			1.75240i
$151$	8838.45			0.387634			0.193817	−	0.981038i	$-0.437913\pi$
$151$	8838.45			0.387634			0.193817	+	0.981038i	$0.437913\pi$
$152$		−	2367.75i		−	0.102482i
$153$			13310.4i			0.568602i
$154$	1486.67	+	689.154i	0.0626865	+	0.0290586i
$155$	−59774.8			−2.48802
$156$	1858.11			0.0763524
$157$		−	20618.3i		−	0.836475i	−0.908338	−	0.418238i	$-0.862648\pi$
$157$		−	20618.3i		−	0.836475i	0.908338	−	0.418238i	$-0.137352\pi$
$158$	−1766.00			−0.0707420
$159$		−	49331.3i		−	1.95132i
$160$			7810.84i			0.305111i
$161$	−3268.79	−	1515.26i	−0.126106	−	0.0584570i
$162$	−23110.2			−0.880588
$163$	−30626.0			−1.15270			−0.576348	−	0.817204i	$-0.695523\pi$
$163$	−30626.0			−1.15270			−0.576348	+	0.817204i	$0.695523\pi$
$164$			10428.3i			0.387727i
$165$	−5749.98			−0.211202
$166$		−	21672.3i		−	0.786483i
$167$			52757.1i			1.89168i	0.324629	+	0.945841i	$0.394760\pi$
$167$			52757.1i			1.89168i	−0.324629	+	0.945841i	$0.605240\pi$
$168$	−5255.54	+	11337.5i	−0.186208	+	0.401696i
$169$	28136.3			0.985131
$170$	35291.7			1.22117
$171$			4816.55i			0.164719i
$172$	−769.870			−0.0260232
$173$			17169.1i			0.573663i	0.957981	+	0.286831i	$0.0926019\pi$
$173$			17169.1i			0.573663i	−0.957981	+	0.286831i	$0.907398\pi$
$174$		−	30312.6i		−	1.00121i
$175$	54985.3	+	25488.7i	1.79544	+	0.832284i
$176$	−756.696			−0.0244285
$177$	18599.8			0.593693
$178$		−	11853.2i		−	0.374105i
$179$	30421.3			0.949451			0.474725	−	0.880134i	$-0.342547\pi$
$179$	30421.3			0.949451			0.474725	+	0.880134i	$0.342547\pi$
$180$		−	15889.1i		−	0.490403i
$181$		−	41530.0i		−	1.26766i	−0.773471	−	0.633832i	$-0.781481\pi$
$181$		−	41530.0i		−	1.26766i	0.773471	−	0.633832i	$-0.218519\pi$
$182$	1201.17	−	2591.22i	0.0362628	−	0.0782278i
$183$	−58613.5			−1.75023
$184$	1663.77			0.0491426
$185$		−	55208.1i		−	1.61309i
$186$	44161.4			1.27649
$187$			3418.98i			0.0977719i
$188$			1489.52i			0.0421435i
$189$	−8122.41	+	17522.0i	−0.227385	+	0.490524i
$190$	12770.8			0.353761
$191$	−51530.4			−1.41253			−0.706263	−	0.707949i	$-0.749621\pi$
$191$	−51530.4			−1.41253			−0.706263	+	0.707949i	$0.749621\pi$
$192$		−	5770.62i		−	0.156538i
$193$	−23547.7			−0.632169			−0.316084	−	0.948731i	$-0.602368\pi$
$193$	−23547.7			−0.632169			−0.316084	+	0.948731i	$0.602368\pi$
$194$			36753.6i			0.976555i
$195$			10022.0i			0.263564i
$196$	12413.2	+	14658.1i	0.323125	+	0.381563i
$197$	53661.4			1.38270			0.691352	−	0.722518i	$-0.257015\pi$
$197$	53661.4			1.38270			0.691352	+	0.722518i	$0.257015\pi$
$198$	1539.30			0.0392638
$199$			48660.6i			1.22877i	0.789006	+	0.614386i	$0.210596\pi$
$199$			48660.6i			1.22877i	−0.789006	+	0.614386i	$0.789404\pi$
$200$	−27986.8			−0.699669
$201$		−	6228.06i		−	0.154156i
$202$			38734.6i			0.949286i
$203$	−42272.2	−	19595.5i	−1.02580	−	0.475515i
$204$	−26073.4			−0.626524
$205$	−56246.6			−1.33841
$206$		−	42841.5i		−	1.00955i
$207$	−3384.50			−0.0789866
$208$			1318.89i			0.0304848i
$209$			1237.20i			0.0283236i
$210$	−61150.3	−	28346.5i	−1.38663	−	0.642778i
$211$	56724.4			1.27410			0.637052	−	0.770821i	$-0.280154\pi$
$211$	56724.4			1.27410			0.637052	+	0.770821i	$0.280154\pi$
$212$	35015.5			0.779092
$213$			95661.6i			2.10852i
$214$	20187.3			0.440809
$215$		−	4152.41i		−	0.0898304i
$216$		−	8918.46i		−	0.191154i
$217$	28548.0	−	61584.9i	0.606256	−	1.30784i
$218$	−38343.1			−0.806816
$219$	3576.69			0.0745751
$220$		−	4081.35i		−	0.0843255i
$221$	5959.17			0.122012
$222$			40787.5i			0.827602i
$223$		−	63263.2i		−	1.27216i	−0.771623	−	0.636080i	$-0.780555\pi$
$223$		−	63263.2i		−	1.27216i	0.771623	−	0.636080i	$-0.219445\pi$
$224$	−8047.37	−	3730.39i	−0.160383	−	0.0743462i
$225$	56931.6			1.12457
$226$	2172.80			0.0425406
$227$			17.6038i			0.000341630i	1.00000		0.000170815i	$5.43721e-5\pi$
$227$			17.6038i			0.000341630i	−1.00000		0.000170815i	$0.999946\pi$
$228$	−9435.01			−0.181498
$229$		−	31463.8i		−	0.599984i	−0.953942	−	0.299992i	$-0.903016\pi$
$229$		−	31463.8i		−	0.599984i	0.953942	−	0.299992i	$-0.0969841\pi$
$230$			8973.80i			0.169637i
$231$	2746.15	−	5924.10i	0.0514635	−	0.111019i
$232$	21516.0			0.399747
$233$	58746.9			1.08211			0.541057	−	0.840986i	$-0.318024\pi$
$233$	58746.9			1.08211			0.541057	+	0.840986i	$0.318024\pi$
$234$		−	2682.94i		−	0.0489980i
$235$	−8033.94			−0.145477
$236$			13202.2i			0.237041i
$237$			7037.18i			0.125286i
$238$	−16855.1	+	36360.5i	−0.297561	+	0.641912i
$239$	48468.5			0.848524			0.424262	−	0.905539i	$-0.360534\pi$
$239$	48468.5			0.848524			0.424262	+	0.905539i	$0.360534\pi$
$240$	31124.7			0.540359
$241$		−	35732.8i		−	0.615223i	−0.951512	−	0.307612i	$-0.900470\pi$
$241$		−	35732.8i		−	0.615223i	0.951512	−	0.307612i	$-0.0995297\pi$
$242$	−41015.6			−0.700355
$243$			60163.8i			1.01888i
$244$		−	41604.0i		−	0.698804i
$245$	−79060.8	+	66952.2i	−1.31713	+	1.11540i
$246$	41554.8			0.686674
$247$	2156.40			0.0353456
$248$			31345.9i			0.509656i
$249$	−86360.0			−1.39288
$250$		−	74673.1i		−	1.19477i
$251$			15060.5i			0.239052i	0.992831	+	0.119526i	$0.0381375\pi$
$251$			15060.5i			0.239052i	−0.992831	+	0.119526i	$0.961863\pi$
$252$	16370.2	+	7588.49i	0.257783	+	0.119496i
$253$	−869.361			−0.0135819
$254$	2683.95			0.0416013
$255$		−	140631.i		−	2.16272i
$256$	4096.00			0.0625000
$257$		−	75600.7i		−	1.14461i	−0.820039	−	0.572307i	$-0.806048\pi$
$257$		−	75600.7i		−	1.14461i	0.820039	−	0.572307i	$-0.193952\pi$
$258$			3067.78i			0.0460877i
$259$	56879.9	+	26367.0i	0.847929	+	0.393061i
$260$	−7113.65			−0.105231
$261$	−43768.5			−0.642512
$262$			15395.4i			0.224278i
$263$	−37721.9			−0.545358			−0.272679	−	0.962105i	$-0.587910\pi$
$263$	−37721.9			−0.545358			−0.272679	+	0.962105i	$0.587910\pi$
$264$			3015.29i			0.0432634i
$265$			188861.i			2.68937i
$266$	−6099.23	+	13157.5i	−0.0862009	+	0.185956i
$267$	−47232.5			−0.662550
$268$	4420.70			0.0615490
$269$			53660.8i			0.741571i	0.928719	+	0.370785i	$0.120911\pi$
$269$			53660.8i			0.741571i	−0.928719	+	0.370785i	$0.879089\pi$
$270$	48103.0			0.659849
$271$			90791.9i			1.23626i	0.786077	+	0.618128i	$0.212109\pi$
$271$			90791.9i			1.23626i	−0.786077	+	0.618128i	$0.787891\pi$
$272$		−	18507.0i		−	0.250148i
$273$	−10325.5	−	4786.43i	−0.138543	−	0.0642224i
$274$	1284.10			0.0171039
$275$	14623.8			0.193372
$276$		−	6629.81i		−	0.0870327i
$277$	−112687.			−1.46863			−0.734317	−	0.678806i	$-0.762498\pi$
$277$	−112687.			−1.46863			−0.734317	+	0.678806i	$0.762498\pi$
$278$		−	52411.5i		−	0.678168i
$279$		−	63764.8i		−	0.819167i
$280$	20120.4	−	43404.7i	0.256638	−	0.553631i
$281$	48637.8			0.615972			0.307986	−	0.951391i	$-0.400345\pi$
$281$	48637.8			0.615972			0.307986	+	0.951391i	$0.400345\pi$
$282$	5935.45			0.0746372
$283$		−	8280.01i		−	0.103385i	−0.998663	−	0.0516925i	$-0.983538\pi$
$283$		−	8280.01i		−	0.103385i	0.998663	−	0.0516925i	$-0.0164616\pi$
$284$	−67900.9			−0.841858
$285$		−	50889.1i		−	0.626520i
$286$		−	689.154i		−	0.00842528i
$287$	26862.9	−	57949.9i	0.326129	−	0.703540i
$288$	−8332.22			−0.100456
$289$	−99.1974			−0.00118769
$290$			116050.i			1.37990i
$291$	146456.			1.72950
$292$			2538.75i			0.0297751i
$293$		−	109853.i		−	1.27961i	−0.768538	−	0.639805i	$-0.779015\pi$
$293$		−	109853.i		−	1.27961i	0.768538	−	0.639805i	$-0.220985\pi$
$294$	58409.8	−	49464.0i	0.675758	−	0.572262i
$295$	−71208.1			−0.818248
$296$	−28951.1			−0.330432
$297$			4660.11i			0.0528303i
$298$	51286.7			0.577526
$299$			1515.26i			0.0169491i
$300$			111522.i			1.23913i
$301$	4278.15	+	1983.16i	0.0472197	+	0.0218889i
$302$	24998.9			0.274099
$303$	154350.			1.68121
$304$		−	6697.00i		−	0.0724658i
$305$	224397.			2.41223
$306$			37647.5i			0.402062i
$307$		−	76154.3i		−	0.808011i	−0.914756	−	0.404006i	$-0.867618\pi$
$307$		−	76154.3i		−	0.808011i	0.914756	−	0.404006i	$-0.132382\pi$
$308$	4204.95	+	1949.22i	0.0443260	+	0.0205475i
$309$	−170715.			−1.78795
$310$	−169069.			−1.75930
$311$			81972.5i			0.847515i	0.905776	+	0.423758i	$0.139289\pi$
$311$			81972.5i			0.847515i	−0.905776	+	0.423758i	$0.860711\pi$
$312$	5255.54			0.0539893
$313$			31765.5i			0.324240i	0.986771	+	0.162120i	$0.0518332\pi$
$313$			31765.5i			0.324240i	−0.986771	+	0.162120i	$0.948167\pi$
$314$		−	58317.3i		−	0.591477i
$315$	−40929.7	+	88295.2i	−0.412493	+	0.889848i
$316$	−4995.01			−0.0500222
$317$	−1127.92			−0.0112243			−0.00561214	−	0.999984i	$-0.501786\pi$
$317$	−1127.92			−0.0112243			−0.00561214	+	0.999984i	$0.501786\pi$
$318$		−	139530.i		−	1.37979i
$319$	−11242.6			−0.110481
$320$			22092.4i			0.215746i
$321$		−	80442.4i		−	0.780683i
$322$	−9245.55	−	4285.82i	−0.0891704	−	0.0413354i
$323$	−30259.1			−0.290035
$324$	−65365.4			−0.622670
$325$		−	25488.7i		−	0.241313i
$326$	−86623.4			−0.815080
$327$			152790.i			1.42889i
$328$			29495.7i			0.274164i
$329$	3836.95	−	8277.23i	0.0354482	−	0.0764704i
$330$	−16263.4			−0.149342
$331$	−136973.			−1.25019			−0.625097	−	0.780547i	$-0.714941\pi$
$331$	−136973.			−1.25019			−0.625097	+	0.780547i	$0.714941\pi$
$332$		−	61298.6i		−	0.556128i
$333$	58893.3			0.531101
$334$			149220.i			1.33762i
$335$			23843.7i			0.212463i
$336$	−14864.9	+	32067.2i	−0.131669	+	0.284042i
$337$	−150838.			−1.32816			−0.664082	−	0.747660i	$-0.731177\pi$
$337$	−150838.			−1.32816			−0.664082	+	0.747660i	$0.731177\pi$
$338$	79581.5			0.696593
$339$		−	8658.20i		−	0.0753404i
$340$	99820.1			0.863496
$341$		−	16379.0i		−	0.140857i
$342$			13623.2i			0.116474i
$343$	−31220.8	−	113431.i	−0.265373	−	0.964146i
$344$	−2177.52			−0.0184012
$345$	35758.8			0.300431
$346$			48561.7i			0.405641i
$347$	12987.5			0.107861			0.0539306	−	0.998545i	$-0.482825\pi$
$347$	12987.5			0.107861			0.0539306	+	0.998545i	$0.482825\pi$
$348$		−	85737.0i		−	0.707962i
$349$			184152.i			1.51191i	0.654623	+	0.755955i	$0.272827\pi$
$349$			184152.i			1.51191i	−0.654623	+	0.755955i	$0.727173\pi$
$350$	155522.	+	72092.9i	1.26957	+	0.588514i
$351$	8122.41			0.0659281
$352$	−2140.26			−0.0172735
$353$		−	61196.5i		−	0.491108i	−0.969383	−	0.245554i	$-0.921030\pi$
$353$		−	61196.5i		−	0.491108i	0.969383	−	0.245554i	$-0.0789698\pi$
$354$	52608.2			0.419805
$355$		−	366234.i		−	2.90604i
$356$		−	33525.8i		−	0.264532i
$357$	144889.	+	67164.2i	1.13684	+	0.526989i
$358$	86044.6			0.671363
$359$	−6045.92			−0.0469109			−0.0234555	−	0.999725i	$-0.507467\pi$
$359$	−6045.92			−0.0469109			−0.0234555	+	0.999725i	$0.507467\pi$
$360$		−	44941.1i		−	0.346767i
$361$	119371.			0.915979
$362$		−	117464.i		−	0.896374i
$363$			163439.i			1.24035i
$364$	3397.42	−	7329.07i	0.0256417	−	0.0553154i
$365$	−13693.1			−0.102782
$366$	−165784.			−1.23760
$367$			214788.i			1.59470i	0.603518	+	0.797349i	$0.293765\pi$
$367$			214788.i			1.59470i	−0.603518	+	0.797349i	$0.706235\pi$
$368$	4705.86			0.0347491
$369$		−	60001.1i		−	0.440663i
$370$		−	156152.i		−	1.14063i
$371$	−194580.	−	90198.7i	−1.41368	−	0.655318i
$372$	124907.			0.902613
$373$	231029.			1.66053			0.830267	−	0.557365i	$-0.188188\pi$
$373$	231029.			1.66053			0.830267	+	0.557365i	$0.188188\pi$
$374$			9670.35i			0.0691351i
$375$	−297558.			−2.11597
$376$			4213.00i			0.0297999i
$377$			19595.5i			0.137871i
$378$	−22973.6	+	49559.7i	−0.160785	+	0.346853i
$379$	91543.4			0.637307			0.318654	−	0.947871i	$-0.396769\pi$
$379$	91543.4			0.637307			0.318654	+	0.947871i	$0.396769\pi$
$380$	36121.2			0.250147
$381$		−	10695.0i		−	0.0736769i
$382$	−145750.			−0.998807
$383$			84780.4i			0.577960i	0.957335	+	0.288980i	$0.0933162\pi$
$383$			84780.4i			0.577960i	−0.957335	+	0.288980i	$0.906684\pi$
$384$		−	16321.8i		−	0.110689i
$385$	−10513.4	+	22680.0i	−0.0709288	+	0.153011i
$386$	−66602.8			−0.447011
$387$	4429.59			0.0295761
$388$			103955.i			0.690529i
$389$	−55678.0			−0.367946			−0.183973	−	0.982931i	$-0.558896\pi$
$389$	−55678.0			−0.367946			−0.183973	+	0.982931i	$0.558896\pi$
$390$			28346.5i			0.186368i
$391$		−	21262.5i		−	0.139079i
$392$	35109.7	+	41459.5i	0.228484	+	0.269806i
$393$	61347.5			0.397202
$394$	151777.			0.977719
$395$		−	26941.3i		−	0.172673i
$396$	4353.79			0.0277637
$397$			194941.i			1.23687i	0.785837	+	0.618434i	$0.212232\pi$
$397$			194941.i			1.23687i	−0.785837	+	0.618434i	$0.787768\pi$
$398$			137633.i			0.868873i
$399$	52430.1	+	24304.2i	0.329333	+	0.152664i
$400$	−79158.5			−0.494741
$401$	−198450.			−1.23413			−0.617066	−	0.786912i	$-0.711679\pi$
$401$	−198450.			−1.23413			−0.617066	+	0.786912i	$0.711679\pi$
$402$		−	17615.6i		−	0.109005i
$403$	−28548.0			−0.175778
$404$			109558.i			0.671246i
$405$		−	352558.i		−	2.14942i
$406$	−119564.	−	55424.4i	−0.725351	−	0.336240i
$407$	15127.7			0.0913236
$408$	−73746.7			−0.443019
$409$		−	272739.i		−	1.63042i	−0.579163	−	0.815212i	$-0.696620\pi$
$409$		−	272739.i		−	1.63042i	0.579163	−	0.815212i	$-0.303380\pi$
$410$	−159089.			−0.946397
$411$		−	5116.87i		−	0.0302915i
$412$		−	121174.i		−	0.713863i
$413$	34008.4	−	73364.4i	0.199382	−	0.430116i
$414$	−9572.81			−0.0558520
$415$	330623.			1.91972
$416$			3730.39i			0.0215560i
$417$	−208850.			−1.20105
$418$			3499.34i			0.0200278i
$419$			187423.i			1.06756i	0.845622	+	0.533782i	$0.179230\pi$
$419$			187423.i			1.06756i	−0.845622	+	0.533782i	$0.820770\pi$
$420$	−172959.	−	80176.0i	−0.980494	−	0.454513i
$421$	167675.			0.946030			0.473015	−	0.881054i	$-0.343166\pi$
$421$	167675.			0.946030			0.473015	+	0.881054i	$0.343166\pi$
$422$	160441.			0.900927
$423$		−	8570.22i		−	0.0478973i
$424$	99038.8			0.550901
$425$			357662.i			1.98014i
$426$			270572.i			1.49095i
$427$	−107170.	+	231193.i	−0.587786	+	1.26800i
$428$	57098.2			0.311699
$429$	−2746.15			−0.0149214
$430$		−	11744.8i		−	0.0635197i
$431$	49932.1			0.268798			0.134399	−	0.990927i	$-0.457090\pi$
$431$	49932.1			0.268798			0.134399	+	0.990927i	$0.457090\pi$
$432$		−	25225.2i		−	0.135166i
$433$		−	209375.i		−	1.11673i	−0.829595	−	0.558365i	$-0.811429\pi$
$433$		−	209375.i		−	1.11673i	0.829595	−	0.558365i	$-0.188571\pi$
$434$	80745.8	−	174188.i	0.428687	−	0.924783i
$435$	462435.			2.44384
$436$	−108451.			−0.570505
$437$		−	7694.12i		−	0.0402899i
$438$	10116.4			0.0527325
$439$		−	146706.i		−	0.761233i	−0.924733	−	0.380617i	$-0.875712\pi$
$439$		−	146706.i		−	0.761233i	0.924733	−	0.380617i	$-0.124288\pi$
$440$		−	11543.8i		−	0.0596271i
$441$	−71421.3	−	84338.2i	−0.367241	−	0.433658i
$442$	16855.1			0.0862752
$443$	−295799.			−1.50726			−0.753632	−	0.657297i	$-0.771700\pi$
$443$	−295799.			−1.50726			−0.753632	+	0.657297i	$0.771700\pi$
$444$			115365.i			0.585203i
$445$	180826.			0.913149
$446$		−	178935.i		−	0.899553i
$447$		−	204367.i		−	1.02281i
$448$	−22761.4	−	10551.2i	−0.113408	−	0.0525707i
$449$	−141239.			−0.700585			−0.350292	−	0.936640i	$-0.613918\pi$
$449$	−141239.			−0.700585			−0.350292	+	0.936640i	$0.613918\pi$
$450$	161027.			0.795194
$451$		−	15412.2i		−	0.0757726i
$452$	6145.61			0.0300807
$453$		−	99615.8i		−	0.485436i
$454$			49.7912i			0.000241569i
$455$	39530.4	+	18324.5i	0.190945	+	0.0885135i
$456$	−26686.2			−0.128339
$457$	−58499.5			−0.280104			−0.140052	−	0.990144i	$-0.544727\pi$
$457$	−58499.5			−0.280104			−0.140052	+	0.990144i	$0.544727\pi$
$458$		−	88993.0i		−	0.424253i
$459$	−113975.			−0.540985
$460$			25381.7i			0.119951i
$461$			203637.i			0.958195i	0.877762	+	0.479098i	$0.159036\pi$
$461$			203637.i			0.958195i	−0.877762	+	0.479098i	$0.840964\pi$
$462$	7767.27	−	16755.9i	0.0363902	−	0.0785025i
$463$	137727.			0.642474			0.321237	−	0.946999i	$-0.395901\pi$
$463$	137727.			0.642474			0.321237	+	0.946999i	$0.395901\pi$
$464$	60856.4			0.282664
$465$			673706.i			3.11576i
$466$	166161.			0.765170
$467$		−	243217.i		−	1.11522i	−0.830103	−	0.557610i	$-0.811718\pi$
$467$		−	243217.i		−	1.11522i	0.830103	−	0.557610i	$-0.188282\pi$
$468$		−	7588.49i		−	0.0346469i
$469$	−24565.7	−	11387.6i	−0.111682	−	0.0517708i
$470$	−22723.4			−0.102867
$471$	−232383.			−1.04752
$472$			37341.5i			0.167613i
$473$	1137.81			0.00508565
$474$			19904.2i			0.0885905i
$475$			129425.i			0.573628i
$476$	−47673.3	+	102843.i	−0.210408	+	0.453900i
$477$	−201468.			−0.885460
$478$	137090.			0.599997
$479$		−	363910.i		−	1.58607i	−0.609174	−	0.793036i	$-0.708499\pi$
$479$		−	363910.i		−	1.58607i	0.609174	−	0.793036i	$-0.291501\pi$
$480$	88033.9			0.382091
$481$		−	26367.0i		−	0.113965i
$482$		−	101068.i		−	0.435028i
$483$	−17078.1	+	36841.7i	−0.0732060	+	0.157923i
$484$	−116010.			−0.495226
$485$	−560696.			−2.38366
$486$			170169.i			0.720457i
$487$	−441526.			−1.86165			−0.930825	−	0.365466i	$-0.880910\pi$
$487$	−441526.			−1.86165			−0.930825	+	0.365466i	$0.880910\pi$
$488$		−	117674.i		−	0.494129i
$489$			345178.i			1.44353i
$490$	−223618.	+	189369.i	−0.931353	+	0.788710i
$491$	219482.			0.910409			0.455204	−	0.890387i	$-0.349566\pi$
$491$	219482.			0.910409			0.455204	+	0.890387i	$0.349566\pi$
$492$	117535.			0.485552
$493$		−	274968.i		−	1.13133i
$494$	6099.23			0.0249931
$495$			23482.8i			0.0958384i
$496$			88659.5i			0.360381i
$497$	377324.	+	174910.i	1.52757	+	0.708113i
$498$	−244263.			−0.984916
$499$	322884.			1.29672			0.648360	−	0.761334i	$-0.275455\pi$
$499$	322884.			1.29672			0.648360	+	0.761334i	$0.275455\pi$
$500$		−	211207.i		−	0.844829i
$501$	594612.			2.36896
$502$			42597.6i			0.169035i
$503$			28222.0i			0.111546i	0.998443	+	0.0557728i	$0.0177622\pi$
$503$			28222.0i			0.111546i	−0.998443	+	0.0557728i	$0.982238\pi$
$504$	46302.0	+	21463.5i	0.182280	+	0.0844966i
$505$	−590918.			−2.31710
$506$	−2458.92			−0.00960382
$507$		−	317117.i		−	1.23368i
$508$	7591.36			0.0294166
$509$		−	47084.6i		−	0.181737i	−0.995863	−	0.0908685i	$-0.971036\pi$
$509$		−	47084.6i		−	0.181737i	0.995863	−	0.0908685i	$-0.0289643\pi$
$510$		−	397764.i		−	1.52927i
$511$	6539.72	−	14107.8i	0.0250448	−	0.0540277i
$512$	11585.2			0.0441942
$513$	−41243.4			−0.156718
$514$		−	213831.i		−	0.809365i
$515$	653570.			2.46421
$516$			8677.00i			0.0325889i
$517$		−	2201.39i		−	0.00823600i
$518$	160881.	+	74577.0i	0.599576	+	0.277936i
$519$	193509.			0.718400
$520$	−20120.4			−0.0744099
$521$			146513.i			0.539760i	0.962894	+	0.269880i	$0.0869840\pi$
$521$			146513.i			0.539760i	−0.962894	+	0.269880i	$0.913016\pi$
$522$	−123796.			−0.454324
$523$			462892.i			1.69229i	0.532949	+	0.846147i	$0.321084\pi$
$523$			462892.i			1.69229i	−0.532949	+	0.846147i	$0.678916\pi$
$524$			43544.7i			0.158589i
$525$	287276.	−	619725.i	1.04227	−	2.24843i
$526$	−106694.			−0.385626
$527$	400591.			1.44238
$528$			8528.52i			0.0305919i
$529$	−274434.			−0.980680
$530$			534180.i			1.90167i
$531$		−	75961.3i		−	0.269404i
$532$	−17251.2	+	37215.1i	−0.0609532	+	0.131491i
$533$	−26862.9			−0.0945582
$534$	−133594.			−0.468493
$535$			307968.i			1.07596i
$536$	12503.6			0.0435217
$537$		−	342871.i		−	1.18900i
$538$			151776.i			0.524370i
$539$	−18345.7	−	21663.6i	−0.0631475	−	0.0745680i
$540$	136056.			0.466584
$541$	272724.			0.931814			0.465907	−	0.884834i	$-0.345728\pi$
$541$	272724.			0.931814			0.465907	+	0.884834i	$0.345728\pi$
$542$			256798.i			0.874166i
$543$	−468073.			−1.58750
$544$		−	52345.6i		−	0.176882i
$545$		−	584945.i		−	1.96935i
$546$	−29204.9	−	13538.1i	−0.0979649	−	0.0454121i
$547$	−494466.			−1.65258			−0.826288	−	0.563248i	$-0.809552\pi$
$547$	−494466.			−1.65258			−0.826288	+	0.563248i	$0.809552\pi$
$548$	3631.97			0.0120943
$549$			239376.i			0.794211i
$550$	41362.3			0.136735
$551$		−	99500.7i		−	0.327735i
$552$		−	18751.9i		−	0.0615414i
$553$	27757.2	+	12867.0i	0.0907664	+	0.0420752i
$554$	−318727.			−1.03848
$555$	−622236.			−2.02008
$556$		−	148242.i		−	0.479537i
$557$	−65156.0			−0.210012			−0.105006	−	0.994472i	$-0.533486\pi$
$557$	−65156.0			−0.210012			−0.105006	+	0.994472i	$0.533486\pi$
$558$		−	180354.i		−	0.579239i
$559$		−	1983.16i		−	0.00634649i
$560$	56909.2	−	122767.i	0.181471	−	0.391476i
$561$	38534.5			0.122440
$562$	137568.			0.435558
$563$			478300.i			1.50898i	0.656311	+	0.754491i	$0.272116\pi$
$563$			478300.i			1.50898i	−0.656311	+	0.754491i	$0.727884\pi$
$564$	16788.0			0.0527764
$565$			33147.3i			0.103837i
$566$		−	23419.4i		−	0.0731043i
$567$	363234.	+	168379.i	1.12985	+	0.523747i
$568$	−192053.			−0.595284
$569$	−132853.			−0.410343			−0.205172	−	0.978726i	$-0.565775\pi$
$569$	−132853.			−0.410343			−0.205172	+	0.978726i	$0.565775\pi$
$570$		−	143936.i		−	0.443017i
$571$	304216.			0.933060			0.466530	−	0.884505i	$-0.345504\pi$
$571$	304216.			0.933060			0.466530	+	0.884505i	$0.345504\pi$
$572$		−	1949.22i		−	0.00595757i
$573$			580785.i			1.76891i
$574$	75979.8	−	163907.i	0.230608	−	0.497478i
$575$	−90944.5			−0.275068
$576$	−23567.1			−0.0710331
$577$			211529.i			0.635357i	0.948199	+	0.317678i	$0.102903\pi$
$577$			211529.i			0.635357i	−0.948199	+	0.317678i	$0.897097\pi$
$578$	−280.573			−0.000839826
$579$			265399.i			0.791667i
$580$			328238.i			0.975737i
$581$	−157903.	+	340635.i	−0.467776	+	1.00911i
$582$	414240.			1.22294
$583$	−51750.2			−0.152256
$584$			7180.66i			0.0210542i
$585$	40929.7			0.119599
$586$		−	310712.i		−	0.904820i
$587$		−	544796.i		−	1.58109i	−0.612401	−	0.790547i	$-0.709796\pi$
$587$		−	544796.i		−	1.58109i	0.612401	−	0.790547i	$-0.290204\pi$
$588$	165208.	−	139905.i	0.477833	−	0.404650i
$589$	144959.			0.417845
$590$	−201407.			−0.578589
$591$		−	604803.i		−	1.73157i
$592$	−81886.1			−0.233650
$593$		−	189340.i		−	0.538435i	−0.963079	−	0.269218i	$-0.913235\pi$
$593$		−	189340.i		−	0.538435i	0.963079	−	0.269218i	$-0.0867651\pi$
$594$			13180.8i			0.0373567i
$595$	−554699.	−	257133.i	−1.56683	−	0.726313i
$596$	145061.			0.408373
$597$	548440.			1.53880
$598$			4285.82i			0.0119848i
$599$	−281405.			−0.784292			−0.392146	−	0.919903i	$-0.628267\pi$
$599$	−281405.			−0.784292			−0.392146	+	0.919903i	$0.628267\pi$
$600$			315431.i			0.876198i
$601$		−	261703.i		−	0.724534i	−0.932074	−	0.362267i	$-0.882003\pi$
$601$		−	261703.i		−	0.724534i	0.932074	−	0.362267i	$-0.117997\pi$
$602$	12100.4	+	5609.22i	0.0333894	+	0.0154778i
$603$	−25435.3			−0.0699523
$604$	70707.6			0.193817
$605$		−	625715.i		−	1.70949i
$606$	436568.			1.18879
$607$			49166.7i			0.133442i	0.997772	+	0.0667212i	$0.0212538\pi$
$607$			49166.7i			0.133442i	−0.997772	+	0.0667212i	$0.978746\pi$
$608$		−	18942.0i		−	0.0512410i
$609$	−220856.	+	476439.i	−0.595489	+	1.28461i
$610$	634692.			1.70570
$611$	−3836.95			−0.0102779
$612$			106483.i			0.284301i
$613$	143767.			0.382594			0.191297	−	0.981532i	$-0.438731\pi$
$613$	143767.			0.382594			0.191297	+	0.981532i	$0.438731\pi$
$614$		−	215397.i		−	0.571350i
$615$			633940.i			1.67609i
$616$	11893.4	+	5513.23i	0.0313432	+	0.0145293i
$617$	270776.			0.711280			0.355640	−	0.934623i	$-0.384263\pi$
$617$	270776.			0.711280			0.355640	+	0.934623i	$0.384263\pi$
$618$	−482855.			−1.26427
$619$		−	94786.2i		−	0.247379i	−0.992321	−	0.123690i	$-0.960527\pi$
$619$		−	94786.2i		−	0.247379i	0.992321	−	0.123690i	$-0.0394728\pi$
$620$	−478198.			−1.24401
$621$		−	28981.0i		−	0.0751502i
$622$			231853.i			0.599284i
$623$	−86361.2	+	186302.i	−0.222506	+	0.480000i
$624$	14864.9			0.0381762
$625$	366145.			0.937332
$626$			89846.3i			0.229272i
$627$	13944.2			0.0354698
$628$		−	164946.i		−	0.418238i
$629$			369986.i			0.935157i
$630$	−115767.	+	249737.i	−0.291677	+	0.629218i
$631$	−71201.8			−0.178827			−0.0894133	−	0.995995i	$-0.528499\pi$
$631$	−71201.8			−0.178827			−0.0894133	+	0.995995i	$0.528499\pi$
$632$	−14128.0			−0.0353710
$633$		−	639325.i		−	1.59557i
$634$	−3190.23			−0.00793677
$635$			40945.1i			0.101544i
$636$		−	394650.i		−	0.975659i
$637$	−37758.8	+	31975.8i	−0.0930550	+	0.0788031i
$638$	−31799.0			−0.0781217
$639$	390680.			0.956796
$640$			62486.7i			0.152555i
$641$	471662.			1.14793			0.573964	−	0.818880i	$-0.305405\pi$
$641$	471662.			1.14793			0.573964	+	0.818880i	$0.305405\pi$
$642$		−	227525.i		−	0.552026i
$643$		−	279296.i		−	0.675526i	−0.941231	−	0.337763i	$-0.890330\pi$
$643$		−	279296.i		−	0.675526i	0.941231	−	0.337763i	$-0.109670\pi$
$644$	−26150.4	−	12122.1i	−0.0630530	−	0.0292285i
$645$	−46800.7			−0.112495
$646$	−85585.6			−0.205086
$647$			652466.i			1.55865i	0.626618	+	0.779326i	$0.284439\pi$
$647$			652466.i			1.55865i	−0.626618	+	0.779326i	$0.715561\pi$
$648$	−184881.			−0.440294
$649$		−	19511.8i		−	0.0463243i
$650$		−	72092.9i		−	0.170634i
$651$	−694107.	−	321757.i	−1.63781	−	0.759216i
$652$	−245008.			−0.576348
$653$	−329674.			−0.773141			−0.386570	−	0.922260i	$-0.626340\pi$
$653$	−329674.			−0.773141			−0.386570	+	0.922260i	$0.626340\pi$
$654$			432155.i			1.01038i
$655$	−234865.			−0.547438
$656$			83426.4i			0.193863i
$657$		−	14607.1i		−	0.0338403i
$658$	10852.5	−	23411.5i	0.0250657	−	0.0540727i
$659$	714693.			1.64569			0.822847	−	0.568264i	$-0.192385\pi$
$659$	714693.			1.64569			0.822847	+	0.568264i	$0.192385\pi$
$660$	−45999.8			−0.105601
$661$		−	6632.86i		−	0.0151809i	−0.999971	−	0.00759046i	$-0.997584\pi$
$661$		−	6632.86i		−	0.0151809i	0.999971	−	0.00759046i	$-0.00241614\pi$
$662$	−387417.			−0.884021
$663$		−	67164.2i		−	0.152796i
$664$		−	173379.i		−	0.393242i
$665$	−200725.	−	93047.0i	−0.453898	−	0.210406i
$666$	166575.			0.375545
$667$	69917.4			0.157157
$668$			422057.i			0.945841i
$669$	−713023.			−1.59313
$670$			67440.1i			0.150234i
$671$			61487.5i			0.136566i
$672$	−42044.3	+	90699.7i	−0.0931040	+	0.200848i
$673$	324015.			0.715377			0.357688	−	0.933841i	$-0.383565\pi$
$673$	324015.			0.715377			0.357688	+	0.933841i	$0.383565\pi$
$674$	−426635.			−0.939154
$675$			487498.i			1.06995i
$676$	225091.			0.492565
$677$			129070.i			0.281609i	0.990037	+	0.140805i	$0.0449690\pi$
$677$			129070.i			0.281609i	−0.990037	+	0.140805i	$0.955031\pi$
$678$		−	24489.1i		−	0.0532737i
$679$	267784.	−	577676.i	0.580825	−	1.25298i
$680$	282334.			0.610584
$681$	198.408			0.000427824
$682$		−	46326.8i		−	0.0996009i
$683$	−63841.7			−0.136856			−0.0684279	−	0.997656i	$-0.521798\pi$
$683$	−63841.7			−0.136856			−0.0684279	+	0.997656i	$0.521798\pi$
$684$			38532.4i			0.0823595i
$685$			19589.6i			0.0417488i
$686$	−88305.8	−	320831.i	−0.187647	−	0.681754i
$687$	−354620.			−0.751363
$688$	−6158.96			−0.0130116
$689$			90198.7i			0.190004i
$690$	101141.			0.212437
$691$			411380.i			0.861563i	0.902456	+	0.430781i	$0.141762\pi$
$691$			411380.i			0.861563i	−0.902456	+	0.430781i	$0.858238\pi$
$692$			137353.i			0.286831i
$693$	−24193.9	−	11215.2i	−0.0503778	−	0.0233529i
$694$	36734.1			0.0762693
$695$	799566.			1.65533
$696$		−	242501.i		−	0.500605i
$697$	376946.			0.775914
$698$			520861.i			1.06908i
$699$		−	662120.i		−	1.35513i
$700$	439882.	+	203910.i	0.897719	+	0.416142i
$701$	−203545.			−0.414213			−0.207106	−	0.978318i	$-0.566405\pi$
$701$	−203545.			−0.414213			−0.207106	+	0.978318i	$0.566405\pi$
$702$	22973.6			0.0466182
$703$			133884.i			0.270907i
$704$	−6053.57			−0.0122142
$705$			90548.4i			0.182181i
$706$		−	173090.i		−	0.347266i
$707$	282218.	−	608812.i	0.564606	−	1.21799i
$708$	148799.			0.296847
$709$	271184.			0.539475			0.269738	−	0.962934i	$-0.413063\pi$
$709$	271184.			0.539475			0.269738	+	0.962934i	$0.413063\pi$
$710$		−	1.03586e6i		−	2.05488i
$711$	28739.7			0.0568517
$712$		−	94825.2i		−	0.187053i
$713$			101860.i			0.200366i
$714$	409809.	+	189969.i	0.803869	+	0.372637i
$715$	10513.4			0.0205651
$716$	243371.			0.474725
$717$		−	546276.i		−	1.06261i
$718$	−17100.5			−0.0331710
$719$		−	457951.i		−	0.885853i	−0.896558	−	0.442927i	$-0.853940\pi$
$719$		−	457951.i		−	0.885853i	0.896558	−	0.442927i	$-0.146060\pi$
$720$		−	127112.i		−	0.245202i
$721$	−312140.	+	673361.i	−0.600453	+	1.29532i
$722$	337633.			0.647695
$723$	−402735.			−0.770446
$724$		−	332240.i		−	0.633832i
$725$	−1.17610e6			−2.23753
$726$			462276.i			0.877058i
$727$			331283.i			0.626802i	0.949621	+	0.313401i	$0.101468\pi$
$727$			331283.i			0.626802i	−0.949621	+	0.313401i	$0.898532\pi$
$728$	9609.36	−	20729.7i	0.0181314	−	0.0391139i
$729$	16266.0			0.0306074
$730$	−38730.0			−0.0726778
$731$			27828.1i			0.0520773i
$732$	−468908.			−0.875115
$733$		−	179732.i		−	0.334516i	−0.985913	−	0.167258i	$-0.946509\pi$
$733$		−	179732.i		−	0.334516i	0.985913	−	0.167258i	$-0.0534914\pi$
$734$			607513.i			1.12762i
$735$	754600.	+	891073.i	1.39683	+	1.64945i
$736$	13310.2			0.0245713
$737$	−6533.44			−0.0120284
$738$		−	169709.i		−	0.311596i
$739$	735946.			1.34759			0.673794	−	0.738920i	$-0.264664\pi$
$739$	735946.			1.34759			0.673794	+	0.738920i	$0.264664\pi$
$740$		−	441665.i		−	0.806546i
$741$		−	24304.2i		−	0.0442635i
$742$	−550357.	−	255120.i	−0.999623	−	0.463380i
$743$	−705656.			−1.27825			−0.639125	−	0.769103i	$-0.720703\pi$
$743$	−705656.			−1.27825			−0.639125	+	0.769103i	$0.720703\pi$
$744$	353291.			0.638244
$745$			782406.i			1.40968i
$746$	653447.			1.17418
$747$			352693.i			0.632055i
$748$			27351.9i			0.0488859i
$749$	−317294.	−	147083.i	−0.565585	−	0.262180i
$750$	−841620.			−1.49621
$751$	−662604.			−1.17483			−0.587414	−	0.809287i	$-0.699854\pi$
$751$	−662604.			−1.17483			−0.587414	+	0.809287i	$0.699854\pi$
$752$			11916.2i			0.0210717i
$753$	169743.			0.299366
$754$			55424.4i			0.0974896i
$755$			381372.i			0.669044i
$756$	−64979.2	+	140176.i	−0.113692	+	0.245262i
$757$	−628368.			−1.09653			−0.548267	−	0.836303i	$-0.684712\pi$
$757$	−628368.			−1.09653			−0.548267	+	0.836303i	$0.684712\pi$
$758$	258924.			0.450644
$759$			9798.34i			0.0170086i
$760$	102166.			0.176881
$761$		−	118942.i		−	0.205384i	−0.994713	−	0.102692i	$-0.967254\pi$
$761$		−	118942.i		−	0.205384i	0.994713	−	0.102692i	$-0.0327456\pi$
$762$		−	30250.1i		−	0.0520975i
$763$	602658.	+	279365.i	1.03519	+	0.479869i
$764$	−412243.			−0.706263
$765$	−574333.			−0.981388
$766$			239795.i			0.408680i
$767$	−34008.4			−0.0578090
$768$		−	46164.9i		−	0.0782690i
$769$		−	814229.i		−	1.37687i	−0.725297	−	0.688436i	$-0.758297\pi$
$769$		−	814229.i		−	1.37687i	0.725297	−	0.688436i	$-0.241703\pi$
$770$	−29736.4	+	64148.7i	−0.0501542	+	0.108195i
$771$	−852075.			−1.43341
$772$	−188381.			−0.316084
$773$			547344.i			0.916012i	0.888949	+	0.458006i	$0.151436\pi$
$773$			547344.i			0.916012i	−0.888949	+	0.458006i	$0.848564\pi$
$774$	12528.8			0.0209135
$775$		−	1.71342e6i		−	2.85272i
$776$			294029.i			0.488278i
$777$	297175.	−	641078.i	0.492232	−	1.06186i
$778$	−157481.			−0.260177
$779$	136403.			0.224775
$780$			80176.0i			0.131782i
$781$	100352.			0.164522
$782$		−	60139.4i		−	0.0983435i
$783$		−	374784.i		−	0.611305i
$784$	99305.2	+	117265.i	0.161562	+	0.190782i
$785$	889662.			1.44373
$786$	173517.			0.280865
$787$		−	493397.i		−	0.796612i	−0.917253	−	0.398306i	$-0.869598\pi$
$787$		−	493397.i		−	0.796612i	0.917253	−	0.398306i	$-0.130402\pi$
$788$	429291.			0.691352
$789$			425153.i			0.682954i
$790$		−	76201.6i		−	0.122098i
$791$	−34151.1	−	15830.9i	−0.0545822	−	0.0253018i
$792$	12314.4			0.0196319
$793$	107170.			0.170423
$794$			551378.i			0.874597i
$795$	2.12860e6			3.36791
$796$			389285.i			0.614386i
$797$			1.12201e6i			1.76637i	0.469028	+	0.883183i	$0.344604\pi$
$797$			1.12201e6i			1.76637i	−0.469028	+	0.883183i	$0.655396\pi$
$798$	148295.	+	68742.8i	0.232874	+	0.107950i
$799$	53840.8			0.0843370
$800$	−223894.			−0.349835
$801$			192897.i			0.300649i
$802$	−561300.			−0.872663
$803$		−	3752.07i		−	0.00581889i
$804$		−	49824.5i		−	0.0770781i
$805$	65382.4	−	141046.i	0.100895	−	0.217655i
$806$	−80745.8			−0.124294
$807$	604797.			0.928672
$808$			309877.i			0.474643i
$809$	−417208.			−0.637464			−0.318732	−	0.947845i	$-0.603257\pi$
$809$	−417208.			−0.637464			−0.318732	+	0.947845i	$0.603257\pi$
$810$		−	997184.i		−	1.51987i
$811$			919516.i			1.39803i	0.715105	+	0.699017i	$0.246379\pi$
$811$			919516.i			1.39803i	−0.715105	+	0.699017i	$0.753621\pi$
$812$	−338178.	−	156764.i	−0.512901	−	0.237757i
$813$	1.02329e6			1.54817
$814$	42787.5			0.0645755
$815$		−	1.32149e6i		−	1.98952i
$816$	−208587.			−0.313262
$817$			10070.0i			0.0150863i
$818$		−	771422.i		−	1.15288i
$819$	−19547.7	+	42169.1i	−0.0291425	+	0.0628676i
$820$	−449973.			−0.669204
$821$	−339844.			−0.504189			−0.252095	−	0.967703i	$-0.581119\pi$
$821$	−339844.			−0.504189			−0.252095	+	0.967703i	$0.581119\pi$
$822$		−	14472.7i		−	0.0214193i
$823$	−428314.			−0.632357			−0.316179	−	0.948700i	$-0.602400\pi$
$823$	−428314.			−0.632357			−0.316179	+	0.948700i	$0.602400\pi$
$824$		−	342732.i		−	0.504777i
$825$		−	164821.i		−	0.242161i
$826$	96190.3	−	207506.i	0.140984	−	0.304138i
$827$	−641009.			−0.937245			−0.468623	−	0.883398i	$-0.655250\pi$
$827$	−641009.			−0.937245			−0.468623	+	0.883398i	$0.655250\pi$
$828$	−27076.0			−0.0394933
$829$			109753.i			0.159701i	0.996807	+	0.0798504i	$0.0254443\pi$
$829$			109753.i			0.159701i	−0.996807	+	0.0798504i	$0.974556\pi$
$830$	935143.			1.35744
$831$			1.27006e6i			1.83918i
$832$			10551.2i			0.0152424i
$833$	529839.	−	448691.i	0.763580	−	0.646633i
$834$	−590716.			−0.849272
$835$	−2.27643e6			−3.26498
$836$			9897.64i			0.0141618i
$837$	546009.			0.779380
$838$			530111.i			0.754882i
$839$		−	882140.i		−	1.25318i	−0.779349	−	0.626591i	$-0.784450\pi$
$839$		−	882140.i		−	1.25318i	0.779349	−	0.626591i	$-0.215550\pi$
$840$	−489202.	−	226772.i	−0.693314	−	0.321389i
$841$	196894.			0.278382
$842$	474257.			0.668944
$843$		−	548184.i		−	0.771385i
$844$	453795.			0.637052
$845$			1.21406e6i			1.70030i
$846$		−	24240.2i		−	0.0338685i
$847$	644663.	+	298837.i	0.898600	+	0.416550i
$848$	280124.			0.389546
$849$	−93321.8			−0.129470
$850$			1.01162e6i			1.40017i
$851$	−94078.2			−0.129906
$852$			765293.i			1.05426i
$853$		−	699021.i		−	0.960709i	−0.877074	−	0.480355i	$-0.840508\pi$
$853$		−	699021.i		−	0.960709i	0.877074	−	0.480355i	$-0.159492\pi$
$854$	−303124.	+	653912.i	−0.415627	+	0.896609i
$855$	−207830.			−0.284299
$856$	161498.			0.220404
$857$		−	776746.i		−	1.05759i	−0.848750	−	0.528795i	$-0.822644\pi$
$857$		−	776746.i		−	1.05759i	0.848750	−	0.528795i	$-0.177356\pi$
$858$	−7767.27			−0.0105510
$859$			1.10160e6i			1.49292i	0.665429	+	0.746461i	$0.268249\pi$
$859$			1.10160e6i			1.49292i	−0.665429	+	0.746461i	$0.731751\pi$
$860$		−	33219.3i		−	0.0449152i
$861$	−653137.	−	302765.i	−0.881045	−	0.408413i
$862$	141229.			0.190069
$863$	−27628.8			−0.0370971			−0.0185486	−	0.999828i	$-0.505905\pi$
$863$	−27628.8			−0.0370971			−0.0185486	+	0.999828i	$0.505905\pi$
$864$		−	71347.7i		−	0.0955768i
$865$	−740835.			−0.990123
$866$		−	592201.i		−	0.789648i
$867$			1118.03i			0.00148735i
$868$	228384.	−	492679.i	0.303128	−	0.653920i
$869$	7382.24			0.00977572
$870$	1.30796e6			1.72806
$871$			11387.6i			0.0150105i
$872$	−306745.			−0.403408
$873$		−	598123.i		−	0.784806i
$874$		−	21762.2i		−	0.0284892i
$875$	−544062.	+	1.17367e6i	−0.710612	+	1.53296i
$876$	28613.6			0.0372875
$877$	−546244.			−0.710211			−0.355105	−	0.934826i	$-0.615555\pi$
$877$	−546244.			−0.710211			−0.355105	+	0.934826i	$0.615555\pi$
$878$		−	414946.i		−	0.538273i
$879$	−1.23813e6			−1.60246
$880$		−	32650.8i		−	0.0421627i
$881$		−	516904.i		−	0.665975i	−0.942931	−	0.332988i	$-0.891943\pi$
$881$		−	516904.i		−	0.665975i	0.942931	−	0.332988i	$-0.108057\pi$
$882$	−202010.	−	238544.i	−0.259678	−	0.306642i
$883$	1.24811e6			1.60078			0.800388	−	0.599482i	$-0.204627\pi$
$883$	1.24811e6			1.60078			0.800388	+	0.599482i	$0.204627\pi$
$884$	47673.3			0.0610058
$885$			802567.i			1.02470i
$886$	−836646.			−1.06580
$887$			229954.i			0.292276i	0.989264	+	0.146138i	$0.0466844\pi$
$887$			229954.i			0.292276i	−0.989264	+	0.146138i	$0.953316\pi$
$888$			326300.i			0.413801i
$889$	−42185.0	−	19555.1i	−0.0533771	−	0.0247432i
$890$	511454.			0.645694
$891$	96605.0			0.121687
$892$		−	506106.i		−	0.636080i
$893$	19483.0			0.0244317
$894$		−	578038.i		−	0.723238i
$895$			1.31266e6i			1.63872i
$896$	−64378.9	−	29843.2i	−0.0801914	−	0.0371731i
$897$	17078.1			0.0212254
$898$	−399483.			−0.495388
$899$			1.31726e6i			1.62987i
$900$	455453.			0.562287
$901$		−	1.26569e6i		−	1.55911i
$902$		−	43592.3i		−	0.0535793i
$903$	22351.6	−	48217.9i	0.0274116	−	0.0591334i
$904$	17382.4			0.0212703
$905$	1.79198e6			2.18795
$906$		−	281756.i		−	0.343255i
$907$	−66711.4			−0.0810933			−0.0405467	−	0.999178i	$-0.512910\pi$
$907$	−66711.4			−0.0810933			−0.0405467	+	0.999178i	$0.512910\pi$
$908$			140.831i			0.000170815i
$909$		−	630362.i		−	0.762891i
$910$	111809.	+	51829.5i	0.135019	+	0.0625885i
$911$	−681437.			−0.821086			−0.410543	−	0.911841i	$-0.634661\pi$
$911$	−681437.			−0.821086			−0.410543	+	0.911841i	$0.634661\pi$
$912$	−75480.0			−0.0907491
$913$			90594.6i			0.108683i
$914$	−165462.			−0.198064
$915$		−	2.52912e6i		−	3.02084i
$916$		−	251710.i		−	0.299992i
$917$	112169.	−	241977.i	0.133394	−	0.287763i
$918$	−322371.			−0.382534
$919$	659165.			0.780483			0.390241	−	0.920713i	$-0.372392\pi$
$919$	659165.			0.780483			0.390241	+	0.920713i	$0.372392\pi$
$920$			71790.4i			0.0848185i
$921$	−858314.			−1.01188
$922$			575971.i			0.677546i
$923$		−	174910.i		−	0.205311i
$924$	21969.2	−	47392.8i	0.0257318	−	0.0555097i
$925$	1.58252e6			1.84954
$926$	389549.			0.454298
$927$			697196.i			0.811326i
$928$	172128.			0.199874
$929$			146974.i			0.170298i	0.996368	+	0.0851491i	$0.0271367\pi$
$929$			146974.i			0.170298i	−0.996368	+	0.0851491i	$0.972863\pi$
$930$			1.90553e6i			2.20318i
$931$	191729.	−	162365.i	0.221202	−	0.187324i
$932$	469975.			0.541057
$933$	923891.			1.06135
$934$		−	687922.i		−	0.788580i
$935$	−147526.			−0.168751
$936$		−	21463.5i		−	0.0244990i
$937$			1.11634e6i			1.27150i	0.771894	+	0.635751i	$0.219309\pi$
$937$			1.11634e6i			1.27150i	−0.771894	+	0.635751i	$0.780691\pi$
$938$	−69482.4	−	32208.9i	−0.0789712	−	0.0366075i
$939$	358020.			0.406047
$940$	−64271.5			−0.0727383
$941$			569425.i			0.643068i	0.946898	+	0.321534i	$0.104199\pi$
$941$			569425.i			0.643068i	−0.946898	+	0.321534i	$0.895801\pi$
$942$	−657279.			−0.740709
$943$			95847.8i			0.107785i
$944$			105618.i			0.118520i
$945$	−756060.	−	350475.i	−0.846628	−	0.392458i
$946$	3218.21			0.00359610
$947$	−165748.			−0.184820			−0.0924099	−	0.995721i	$-0.529457\pi$
$947$	−165748.			−0.184820			−0.0924099	+	0.995721i	$0.529457\pi$
$948$			56297.5i			0.0626429i
$949$	−6539.72			−0.00726151
$950$			366069.i			0.405616i
$951$			12712.5i			0.0140562i
$952$	−134841.	+	290884.i	−0.148781	+	0.320956i
$953$	1.21791e6			1.34100			0.670501	−	0.741909i	$-0.266079\pi$
$953$	1.21791e6			1.34100			0.670501	+	0.741909i	$0.266079\pi$
$954$	−569837.			−0.626115
$955$		−	2.22349e6i		−	2.43797i
$956$	387748.			0.424262
$957$			126713.i			0.138355i
$958$		−	1.02929e6i		−	1.12152i
$959$	−20182.8	−	9355.83i	−0.0219454	−	0.0101729i
$960$	248997.			0.270179
$961$	−995549.			−1.07799
$962$		−	74577.0i		−	0.0805851i
$963$	−328525.			−0.354255
$964$		−	285862.i		−	0.307612i
$965$		−	1.01606e6i		−	1.09110i
$966$	−48304.3	+	104204.i	−0.0517644	+	0.111668i
$967$	−473000.			−0.505834			−0.252917	−	0.967488i	$-0.581390\pi$
$967$	−473000.			−0.505834			−0.252917	+	0.967488i	$0.581390\pi$
$968$	−328125.			−0.350178
$969$			341042.i			0.363212i
$970$	−1.58589e6			−1.68550
$971$		−	823487.i		−	0.873410i	−0.899605	−	0.436705i	$-0.856145\pi$
$971$		−	823487.i		−	0.873410i	0.899605	−	0.436705i	$-0.143855\pi$
$972$			481311.i			0.509440i
$973$	−381867.	+	823779.i	−0.403354	+	0.870132i
$974$	−1.24882e6			−1.31639
$975$	−287276.			−0.302197
$976$		−	332832.i		−	0.349402i
$977$	−513003.			−0.537441			−0.268721	−	0.963218i	$-0.586601\pi$
$977$	−513003.			−0.537441			−0.268721	+	0.963218i	$0.586601\pi$
$978$			976310.i			1.02073i
$979$			49548.5i			0.0516970i
$980$	−632486.	+	535617.i	−0.658566	+	0.557702i
$981$	623991.			0.648396
$982$	620790.			0.643756
$983$			672941.i			0.696418i	0.937417	+	0.348209i	$0.113210\pi$
$983$			672941.i			0.696418i	−0.937417	+	0.348209i	$0.886790\pi$
$984$	332438.			0.343337
$985$			2.31544e6i			2.38650i
$986$		−	777727.i		−	0.799969i
$987$	−93290.5	−	43245.2i	−0.0957641	−	0.0443919i
$988$	17251.2			0.0176728
$989$	−7075.97			−0.00723425
$990$			66419.4i			0.0677680i
$991$	496654.			0.505716			0.252858	−	0.967503i	$-0.418629\pi$
$991$	496654.			0.505716			0.252858	+	0.967503i	$0.418629\pi$
$992$			250767.i			0.254828i
$993$			1.54378e6i			1.56562i
$994$	1.06723e6	+	494721.i	1.08016	+	0.500712i
$995$	−2.09966e6			−2.12082
$996$	−690880.			−0.696441
$997$		−	972300.i		−	0.978160i	−0.872239	−	0.489080i	$-0.837333\pi$
$997$		−	972300.i		−	0.978160i	0.872239	−	0.489080i	$-0.162667\pi$
$998$	913255.			0.916919
$999$			504295.i			0.505305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.5.b.a.13.3	✓	4
3.2	odd	2		126.5.c.a.55.1		4
4.3	odd	2		112.5.c.c.97.3		4
5.2	odd	4		350.5.d.a.349.6		8
5.3	odd	4		350.5.d.a.349.3		8
5.4	even	2		350.5.b.a.251.2		4
7.2	even	3		98.5.d.d.31.2		8
7.3	odd	6		98.5.d.d.19.2		8
7.4	even	3		98.5.d.d.19.1		8
7.5	odd	6		98.5.d.d.31.1		8
7.6	odd	2	inner	14.5.b.a.13.4	yes	4
8.3	odd	2		448.5.c.f.321.2		4
8.5	even	2		448.5.c.e.321.3		4
12.11	even	2		1008.5.f.h.433.1		4
21.20	even	2		126.5.c.a.55.2		4
28.27	even	2		112.5.c.c.97.2		4
35.13	even	4		350.5.d.a.349.2		8
35.27	even	4		350.5.d.a.349.7		8
35.34	odd	2		350.5.b.a.251.1		4
56.13	odd	2		448.5.c.e.321.2		4
56.27	even	2		448.5.c.f.321.3		4
84.83	odd	2		1008.5.f.h.433.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.b.a.13.3	✓	4	1.1	even	1	trivial
14.5.b.a.13.4	yes	4	7.6	odd	2	inner
98.5.d.d.19.1		8	7.4	even	3
98.5.d.d.19.2		8	7.3	odd	6
98.5.d.d.31.1		8	7.5	odd	6
98.5.d.d.31.2		8	7.2	even	3
112.5.c.c.97.2		4	28.27	even	2
112.5.c.c.97.3		4	4.3	odd	2
126.5.c.a.55.1		4	3.2	odd	2
126.5.c.a.55.2		4	21.20	even	2
350.5.b.a.251.1		4	35.34	odd	2
350.5.b.a.251.2		4	5.4	even	2
350.5.d.a.349.2		8	35.13	even	4
350.5.d.a.349.3		8	5.3	odd	4
350.5.d.a.349.6		8	5.2	odd	4
350.5.d.a.349.7		8	35.27	even	4
448.5.c.e.321.2		4	56.13	odd	2
448.5.c.e.321.3		4	8.5	even	2
448.5.c.f.321.2		4	8.3	odd	2
448.5.c.f.321.3		4	56.27	even	2
1008.5.f.h.433.1		4	12.11	even	2
1008.5.f.h.433.4		4	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} -11.2707i q^{3} +8.00000 q^{4} +43.1492i q^{5} -31.8784i q^{6} +(-44.4558 - 20.6077i) q^{7} +22.6274 q^{8} -46.0294 q^{9} +O(q^{10})\)	\(q+2.82843 q^{2} -11.2707i q^{3} +8.00000 q^{4} +43.1492i q^{5} -31.8784i q^{6} +(-44.4558 - 20.6077i) q^{7} +22.6274 q^{8} -46.0294 q^{9} +122.044i q^{10} -11.8234 q^{11} -90.1659i q^{12} +20.6077i q^{13} +(-125.740 - 58.2874i) q^{14} +486.323 q^{15} +64.0000 q^{16} -289.172i q^{17} -130.191 q^{18} -104.641i q^{19} +345.193i q^{20} +(-232.264 + 501.050i) q^{21} -33.4416 q^{22} +73.5290 q^{23} -255.028i q^{24} -1236.85 q^{25} +58.2874i q^{26} -394.144i q^{27} +(-355.647 - 164.862i) q^{28} +950.881 q^{29} +1375.53 q^{30} +1385.30i q^{31} +181.019 q^{32} +133.258i q^{33} -817.901i q^{34} +(889.206 - 1918.23i) q^{35} -368.235 q^{36} -1279.47 q^{37} -295.968i q^{38} +232.264 q^{39} +976.355i q^{40} +1303.54i q^{41} +(-656.942 + 1417.18i) q^{42} -96.2338 q^{43} -94.5870 q^{44} -1986.13i q^{45} +207.971 q^{46} +186.190i q^{47} -721.327i q^{48} +(1551.64 + 1832.27i) q^{49} -3498.35 q^{50} -3259.18 q^{51} +164.862i q^{52} +4376.94 q^{53} -1114.81i q^{54} -510.169i q^{55} +(-1005.92 - 466.299i) q^{56} -1179.38 q^{57} +2689.50 q^{58} +1650.28i q^{59} +3890.58 q^{60} -5200.50i q^{61} +3918.23i q^{62} +(2046.28 + 948.562i) q^{63} +512.000 q^{64} -889.206 q^{65} +376.911i q^{66} +552.587 q^{67} -2313.37i q^{68} -828.726i q^{69} +(2515.05 - 5425.58i) q^{70} -8487.61 q^{71} -1041.53 q^{72} +317.344i q^{73} -3618.89 q^{74} +13940.2i q^{75} -837.124i q^{76} +(525.618 + 243.653i) q^{77} +656.942 q^{78} -624.377 q^{79} +2761.55i q^{80} -8170.68 q^{81} +3686.96i q^{82} -7662.33i q^{83} +(-1858.11 + 4008.40i) q^{84} +12477.5 q^{85} -272.190 q^{86} -10717.1i q^{87} -267.532 q^{88} -4190.72i q^{89} -5617.63i q^{90} +(424.678 - 916.133i) q^{91} +588.232 q^{92} +15613.4 q^{93} +526.625i q^{94} +4515.15 q^{95} -2040.22i q^{96} +12994.4i q^{97} +(4388.71 + 5182.43i) q^{98} +544.223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9}+O(q^{10}) \) 4 * q + 32 * q^4 - 76 * q^7 - 252 * q^9	\( 4 q + 32 q^{4} - 76 q^{7} - 252 q^{9} + 360 q^{11} - 288 q^{14} + 384 q^{15} + 256 q^{16} + 192 q^{18} + 768 q^{21} - 1152 q^{22} - 792 q^{23} - 2300 q^{25} - 608 q^{28} + 1224 q^{29} + 4416 q^{30} + 4032 q^{35} - 2016 q^{36} - 3896 q^{37} - 768 q^{39} - 4800 q^{42} + 3688 q^{43} + 2880 q^{44} + 3072 q^{46} - 1532 q^{49} - 7488 q^{50} - 11136 q^{51} + 5832 q^{53} - 2304 q^{56} + 12864 q^{57} + 7296 q^{58} + 3072 q^{60} + 3060 q^{63} + 2048 q^{64} - 4032 q^{65} - 1048 q^{67} - 1344 q^{70} - 21528 q^{71} + 1536 q^{72} - 3456 q^{74} + 3528 q^{77} + 4800 q^{78} + 12776 q^{79} - 29628 q^{81} + 6144 q^{84} + 16512 q^{85} - 11520 q^{86} - 9216 q^{88} + 5568 q^{91} - 6336 q^{92} + 38016 q^{93} + 36864 q^{95} + 21888 q^{98} - 29592 q^{99}+O(q^{100}) \) 4 * q + 32 * q^4 - 76 * q^7 - 252 * q^9 + 360 * q^11 - 288 * q^14 + 384 * q^15 + 256 * q^16 + 192 * q^18 + 768 * q^21 - 1152 * q^22 - 792 * q^23 - 2300 * q^25 - 608 * q^28 + 1224 * q^29 + 4416 * q^30 + 4032 * q^35 - 2016 * q^36 - 3896 * q^37 - 768 * q^39 - 4800 * q^42 + 3688 * q^43 + 2880 * q^44 + 3072 * q^46 - 1532 * q^49 - 7488 * q^50 - 11136 * q^51 + 5832 * q^53 - 2304 * q^56 + 12864 * q^57 + 7296 * q^58 + 3072 * q^60 + 3060 * q^63 + 2048 * q^64 - 4032 * q^65 - 1048 * q^67 - 1344 * q^70 - 21528 * q^71 + 1536 * q^72 - 3456 * q^74 + 3528 * q^77 + 4800 * q^78 + 12776 * q^79 - 29628 * q^81 + 6144 * q^84 + 16512 * q^85 - 11520 * q^86 - 9216 * q^88 + 5568 * q^91 - 6336 * q^92 + 38016 * q^93 + 36864 * q^95 + 21888 * q^98 - 29592 * q^99

Introduction

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