LMFDB - Embedded newform 40.5.g.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,5,Mod(11,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("40.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	40.g (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:	$4.13479852335$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 84 x^{13} + 628 x^{12} - 1392 x^{11} + 2016 x^{10} - 18048 x^{9} + \cdots + 4294967296 $ x^16 - 6x^15 + 14x^14 - 84x^13 + 628x^12 - 1392x^11 + 2016x^10 - 18048x^9 + 116992x^8 - 288768x^7 + 516096x^6 - 5701632x^5 + 41156608x^4 - 88080384x^3 + 234881024x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{25}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.15
Root			$-3.73120 + 1.44159i$ of defining polynomial
Character	$\chi$	$=$	40.11
Dual form			40.5.g.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.73120 - 1.44159i) q^{2} +7.09911 q^{3} +(11.8437 - 10.7577i) q^{4} +11.1803i q^{5} +(26.4882 - 10.2340i) q^{6} +2.59084i q^{7} +(28.6828 - 57.2127i) q^{8} -30.6027 q^{9} +(16.1174 + 41.7160i) q^{10} -7.95663 q^{11} +(84.0793 - 76.3700i) q^{12} +54.6467i q^{13} +(3.73492 + 9.66694i) q^{14} +79.3704i q^{15} +(24.5442 - 254.821i) q^{16} -28.7782 q^{17} +(-114.185 + 44.1165i) q^{18} -316.702 q^{19} +(120.275 + 132.416i) q^{20} +18.3927i q^{21} +(-29.6878 + 11.4702i) q^{22} +846.949i q^{23} +(203.623 - 406.159i) q^{24} -125.000 q^{25} +(78.7780 + 203.898i) q^{26} -792.279 q^{27} +(27.8715 + 30.6850i) q^{28} -766.738i q^{29} +(114.419 + 296.147i) q^{30} +1194.00i q^{31} +(-275.767 - 986.169i) q^{32} -56.4850 q^{33} +(-107.377 + 41.4862i) q^{34} -28.9665 q^{35} +(-362.448 + 329.214i) q^{36} -2436.16i q^{37} +(-1181.68 + 456.554i) q^{38} +387.943i q^{39} +(639.658 + 320.684i) q^{40} +2433.43 q^{41} +(26.5146 + 68.6266i) q^{42} +2338.16 q^{43} +(-94.2356 + 85.5950i) q^{44} -342.149i q^{45} +(1220.95 + 3160.13i) q^{46} -2192.51i q^{47} +(174.242 - 1809.00i) q^{48} +2394.29 q^{49} +(-466.400 + 180.198i) q^{50} -204.299 q^{51} +(587.872 + 647.216i) q^{52} -3041.70i q^{53} +(-2956.15 + 1142.14i) q^{54} -88.9578i q^{55} +(148.229 + 74.3127i) q^{56} -2248.30 q^{57} +(-1105.32 - 2860.85i) q^{58} +455.150 q^{59} +(853.842 + 940.036i) q^{60} +3920.95i q^{61} +(1721.25 + 4455.04i) q^{62} -79.2868i q^{63} +(-2450.59 - 3282.05i) q^{64} -610.969 q^{65} +(-210.756 + 81.4280i) q^{66} -4822.82 q^{67} +(-340.839 + 309.587i) q^{68} +6012.58i q^{69} +(-108.080 + 41.7577i) q^{70} +874.716i q^{71} +(-877.773 + 1750.86i) q^{72} -7682.80 q^{73} +(-3511.93 - 9089.78i) q^{74} -887.388 q^{75} +(-3750.91 + 3406.98i) q^{76} -20.6144i q^{77} +(559.253 + 1447.49i) q^{78} +1475.37i q^{79} +(2848.98 + 274.413i) q^{80} -3145.66 q^{81} +(9079.62 - 3508.01i) q^{82} +6849.50 q^{83} +(197.863 + 217.836i) q^{84} -321.750i q^{85} +(8724.14 - 3370.66i) q^{86} -5443.16i q^{87} +(-228.219 + 455.220i) q^{88} +13113.1 q^{89} +(-493.237 - 1276.62i) q^{90} -141.581 q^{91} +(9111.21 + 10031.0i) q^{92} +8476.32i q^{93} +(-3160.70 - 8180.70i) q^{94} -3540.84i q^{95} +(-1957.70 - 7000.92i) q^{96} -8603.40 q^{97} +(8933.56 - 3451.57i) q^{98} +243.494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 8 q^{4} + 84 q^{6} - 216 q^{8} + 432 q^{9} - 50 q^{10} + 192 q^{11} + 260 q^{12} + 972 q^{14} - 824 q^{16} - 806 q^{18} - 704 q^{19} - 300 q^{20} - 1100 q^{22} - 1256 q^{24} - 2000 q^{25}+ \cdots + 2624 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 8 * q^4 + 84 * q^6 - 216 * q^8 + 432 * q^9 - 50 * q^10 + 192 * q^11 + 260 * q^12 + 972 * q^14 - 824 * q^16 - 806 * q^18 - 704 * q^19 - 300 * q^20 - 1100 * q^22 - 1256 * q^24 - 2000 * q^25 + 108 * q^26 + 3648 * q^27 - 940 * q^28 - 1400 * q^30 + 4104 * q^32 - 992 * q^33 + 924 * q^34 - 2400 * q^36 - 420 * q^38 + 2200 * q^40 - 2208 * q^41 + 7820 * q^42 + 5568 * q^43 + 3816 * q^44 - 652 * q^46 + 4520 * q^48 - 2480 * q^49 + 750 * q^50 - 17792 * q^51 - 4640 * q^52 + 6488 * q^54 - 12552 * q^56 + 8608 * q^57 + 1040 * q^58 + 14016 * q^59 - 3500 * q^60 + 12480 * q^62 - 3712 * q^64 - 13312 * q^66 - 18880 * q^67 + 12360 * q^68 - 1800 * q^70 - 16456 * q^72 - 7360 * q^73 - 11508 * q^74 + 9312 * q^76 - 26760 * q^78 - 2400 * q^80 + 10384 * q^81 - 16640 * q^82 + 10560 * q^83 - 12520 * q^84 + 25764 * q^86 + 41200 * q^88 + 6816 * q^89 + 8550 * q^90 + 24576 * q^91 + 30420 * q^92 - 28388 * q^94 + 6784 * q^96 + 448 * q^97 + 23934 * q^98 + 2624 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	3.73120	−	1.44159i	0.932799	−	0.360397i
$2$	3.73120	−	1.44159i	0.932799	−	0.360397i
$3$	7.09911			0.788789			0.394395	−	0.918941i	$-0.370954\pi$
$3$	7.09911			0.788789			0.394395	+	0.918941i	$0.370954\pi$
$4$	11.8437	−	10.7577i	0.740228	−	0.672356i
$5$			11.1803i			0.447214i
$5$			11.1803i			0.447214i
$6$	26.4882	−	10.2340i	0.735782	−	0.284277i
$7$			2.59084i			0.0528743i	0.999650	+	0.0264372i	$0.00841619\pi$
$7$			2.59084i			0.0528743i	−0.999650	+	0.0264372i	$0.991584\pi$
$8$	28.6828	−	57.2127i	0.448169	−	0.893949i
$9$	−30.6027			−0.377811
$10$	16.1174	+	41.7160i	0.161174	+	0.417160i
$11$	−7.95663			−0.0657573			−0.0328786	−	0.999459i	$-0.510467\pi$
$11$	−7.95663			−0.0657573			−0.0328786	+	0.999459i	$0.510467\pi$
$12$	84.0793	−	76.3700i	0.583884	−	0.530347i
$13$			54.6467i			0.323353i	0.986844	+	0.161677i	$0.0516901\pi$
$13$			54.6467i			0.323353i	−0.986844	+	0.161677i	$0.948310\pi$
$14$	3.73492	+	9.66694i	0.0190557	+	0.0493211i
$15$			79.3704i			0.352757i
$16$	24.5442	−	254.821i	0.0958759	−	0.995393i
$17$	−28.7782			−0.0995785			−0.0497892	−	0.998760i	$-0.515855\pi$
$17$	−28.7782			−0.0995785			−0.0497892	+	0.998760i	$0.515855\pi$
$18$	−114.185	+	44.1165i	−0.352422	+	0.136162i
$19$	−316.702			−0.877291			−0.438646	−	0.898660i	$-0.644542\pi$
$19$	−316.702			−0.877291			−0.438646	+	0.898660i	$0.644542\pi$
$20$	120.275	+	132.416i	0.300687	+	0.331040i
$21$			18.3927i			0.0417067i
$22$	−29.6878	+	11.4702i	−0.0613383	+	0.0236987i
$23$			846.949i			1.60104i	0.599308	+	0.800519i	$0.295443\pi$
$23$			846.949i			1.60104i	−0.599308	+	0.800519i	$0.704557\pi$
$24$	203.623	−	406.159i	0.353511	−	0.705137i
$25$	−125.000			−0.200000
$26$	78.7780	+	203.898i	0.116535	+	0.301624i
$27$	−792.279			−1.08680
$28$	27.8715	+	30.6850i	0.0355503	+	0.0391391i
$29$		−	766.738i		−	0.911698i	−0.890057	−	0.455849i	$-0.849336\pi$
$29$		−	766.738i		−	0.911698i	0.890057	−	0.455849i	$-0.150664\pi$
$30$	114.419	+	296.147i	0.127133	+	0.329052i
$31$			1194.00i			1.24245i	0.783631	+	0.621227i	$0.213366\pi$
$31$			1194.00i			1.24245i	−0.783631	+	0.621227i	$0.786634\pi$
$32$	−275.767	−	986.169i	−0.269304	−	0.963055i
$33$	−56.4850			−0.0518686
$34$	−107.377	+	41.4862i	−0.0928867	+	0.0358878i
$35$	−28.9665			−0.0236461
$36$	−362.448	+	329.214i	−0.279666	+	0.254023i
$37$		−	2436.16i		−	1.77952i	−0.456432	−	0.889758i	$-0.650873\pi$
$37$		−	2436.16i		−	1.77952i	0.456432	−	0.889758i	$-0.349127\pi$
$38$	−1181.68	+	456.554i	−0.818336	+	0.316173i
$39$			387.943i			0.255058i
$40$	639.658	+	320.684i	0.399786	+	0.200427i
$41$	2433.43			1.44761			0.723806	−	0.690004i	$-0.242391\pi$
$41$	2433.43			1.44761			0.723806	+	0.690004i	$0.242391\pi$
$42$	26.5146	+	68.6266i	0.0150310	+	0.0389040i
$43$	2338.16			1.26455			0.632277	−	0.774742i	$-0.282120\pi$
$43$	2338.16			1.26455			0.632277	+	0.774742i	$0.282120\pi$
$44$	−94.2356	+	85.5950i	−0.0486754	+	0.0442123i
$45$		−	342.149i		−	0.168962i
$46$	1220.95	+	3160.13i	0.577009	+	1.49345i
$47$		−	2192.51i		−	0.992537i	−0.868169	−	0.496269i	$-0.834703\pi$
$47$		−	2192.51i		−	0.992537i	0.868169	−	0.496269i	$-0.165297\pi$
$48$	174.242	−	1809.00i	0.0756259	−	0.785156i
$49$	2394.29			0.997204
$50$	−466.400	+	180.198i	−0.186560	+	0.0720794i
$51$	−204.299			−0.0785464
$52$	587.872	+	647.216i	0.217408	+	0.239355i
$53$		−	3041.70i		−	1.08284i	−0.840752	−	0.541420i	$-0.817887\pi$
$53$		−	3041.70i		−	1.08284i	0.840752	−	0.541420i	$-0.182113\pi$
$54$	−2956.15	+	1142.14i	−1.01377	+	0.391680i
$55$		−	88.9578i		−	0.0294075i
$56$	148.229	+	74.3127i	0.0472669	+	0.0236967i
$57$	−2248.30			−0.691998
$58$	−1105.32	−	2860.85i	−0.328573	−	0.850431i
$59$	455.150			0.130753			0.0653764	−	0.997861i	$-0.479175\pi$
$59$	455.150			0.130753			0.0653764	+	0.997861i	$0.479175\pi$
$60$	853.842	+	940.036i	0.237178	+	0.261121i
$61$			3920.95i			1.05374i	0.849947	+	0.526868i	$0.176634\pi$
$61$			3920.95i			1.05374i	−0.849947	+	0.526868i	$0.823366\pi$
$62$	1721.25	+	4455.04i	0.447776	+	1.15896i
$63$		−	79.2868i		−	0.0199765i
$64$	−2450.59	−	3282.05i	−0.598288	−	0.801281i
$65$	−610.969			−0.144608
$66$	−210.756	+	81.4280i	−0.0483830	+	0.0186933i
$67$	−4822.82			−1.07436			−0.537182	−	0.843466i	$-0.680511\pi$
$67$	−4822.82			−1.07436			−0.537182	+	0.843466i	$0.680511\pi$
$68$	−340.839	+	309.587i	−0.0737108	+	0.0669521i
$69$			6012.58i			1.26288i
$70$	−108.080	+	41.7577i	−0.0220571	+	0.00852198i
$71$			874.716i			0.173520i	0.996229	+	0.0867602i	$0.0276514\pi$
$71$			874.716i			0.173520i	−0.996229	+	0.0867602i	$0.972349\pi$
$72$	−877.773	+	1750.86i	−0.169323	+	0.337744i
$73$	−7682.80			−1.44170			−0.720848	−	0.693093i	$-0.756248\pi$
$73$	−7682.80			−1.44170			−0.720848	+	0.693093i	$0.756248\pi$
$74$	−3511.93	−	9089.78i	−0.641332	−	1.65993i
$75$	−887.388			−0.157758
$76$	−3750.91	+	3406.98i	−0.649396	+	0.589852i
$77$		−	20.6144i		−	0.00347687i
$78$	559.253	+	1447.49i	0.0919220	+	0.237918i
$79$			1475.37i			0.236400i	0.992990	+	0.118200i	$0.0377123\pi$
$79$			1475.37i			0.236400i	−0.992990	+	0.118200i	$0.962288\pi$
$80$	2848.98	+	274.413i	0.445153	+	0.0428770i
$81$	−3145.66			−0.479448
$82$	9079.62	−	3508.01i	1.35033	−	0.521714i
$83$	6849.50			0.994266			0.497133	−	0.867674i	$-0.334386\pi$
$83$	6849.50			0.994266			0.497133	+	0.867674i	$0.334386\pi$
$84$	197.863	+	217.836i	0.0280417	+	0.0308725i
$85$		−	321.750i		−	0.0445328i
$86$	8724.14	−	3370.66i	1.17957	−	0.455741i
$87$		−	5443.16i		−	0.719138i
$88$	−228.219	+	455.220i	−0.0294704	+	0.0587836i
$89$	13113.1			1.65548			0.827740	−	0.561111i	$-0.189626\pi$
$89$	13113.1			1.65548			0.827740	+	0.561111i	$0.189626\pi$
$90$	−493.237	−	1276.62i	−0.0608935	−	0.157608i
$91$	−141.581			−0.0170971
$92$	9111.21	+	10031.0i	1.07647	+	1.18513i
$93$			8476.32i			0.980035i
$94$	−3160.70	−	8180.70i	−0.357707	−	0.925838i
$95$		−	3540.84i		−	0.392337i
$96$	−1957.70	−	7000.92i	−0.212424	−	0.759648i
$97$	−8603.40			−0.914380			−0.457190	−	0.889369i	$-0.651144\pi$
$97$	−8603.40			−0.914380			−0.457190	+	0.889369i	$0.651144\pi$
$98$	8933.56	−	3451.57i	0.930191	−	0.359389i
$99$	243.494			0.0248438
$100$	−1480.46	+	1344.71i	−0.148046	+	0.134471i
$101$		−	7164.77i		−	0.702360i	−0.936308	−	0.351180i	$-0.885781\pi$
$101$		−	7164.77i		−	0.702360i	0.936308	−	0.351180i	$-0.114219\pi$
$102$	−762.281	+	294.515i	−0.0732680	+	0.0283079i
$103$			8010.36i			0.755053i	0.925999	+	0.377527i	$0.123225\pi$
$103$			8010.36i			0.755053i	−0.925999	+	0.377527i	$0.876775\pi$
$104$	3126.49	+	1567.42i	0.289061	+	0.144917i
$105$	−205.636			−0.0186518
$106$	−4384.88	−	11349.2i	−0.390252	−	1.01007i
$107$	−2003.50			−0.174994			−0.0874969	−	0.996165i	$-0.527887\pi$
$107$	−2003.50			−0.174994			−0.0874969	+	0.996165i	$0.527887\pi$
$108$	−9383.48	+	8523.10i	−0.804482	+	0.730718i
$109$			20282.4i			1.70713i	0.520985	+	0.853566i	$0.325565\pi$
$109$			20282.4i			1.70713i	−0.520985	+	0.853566i	$0.674435\pi$
$110$	−128.240	−	331.919i	−0.0105984	−	0.0274313i
$111$		−	17294.5i		−	1.40366i
$112$	660.200	+	63.5902i	0.0526307	+	0.00506937i
$113$	−570.501			−0.0446786			−0.0223393	−	0.999750i	$-0.507111\pi$
$113$	−570.501			−0.0446786			−0.0223393	+	0.999750i	$0.507111\pi$
$114$	−8388.85	+	3241.12i	−0.645495	+	0.249394i
$115$	−9469.18			−0.716006
$116$	−8248.33	−	9080.98i	−0.612985	−	0.674865i
$117$		−	1672.34i		−	0.122166i
$118$	1698.25	−	656.139i	0.121966	−	0.0471229i
$119$		−	74.5597i		−	0.00526514i
$120$	4541.00	+	2276.57i	0.315347	+	0.158095i
$121$	−14577.7			−0.995676
$122$	5652.39	+	14629.8i	0.379763	+	0.982923i
$123$	17275.2			1.14186
$124$	12844.7	+	14141.3i	0.835371	+	0.919700i
$125$		−	1397.54i		−	0.0894427i
$126$	−114.299	−	295.834i	−0.00719947	−	0.0186341i
$127$		−	6367.53i		−	0.394788i	−0.980324	−	0.197394i	$-0.936752\pi$
$127$		−	6367.53i		−	0.394788i	0.980324	−	0.197394i	$-0.0632478\pi$
$128$	−13875.0	−	8713.22i	−0.846862	−	0.531813i
$129$	16598.8			0.997467
$130$	−2279.64	+	880.765i	−0.134890	+	0.0521162i
$131$	17348.8			1.01094			0.505472	−	0.862843i	$-0.331319\pi$
$131$	17348.8			1.01094			0.505472	+	0.862843i	$0.331319\pi$
$132$	−668.988	+	607.648i	−0.0383946	+	0.0348742i
$133$		−	820.525i		−	0.0463862i
$134$	−17994.9	+	6952.52i	−1.00217	+	0.387198i
$135$		−	8857.95i		−	0.486033i
$136$	−825.440	+	1646.48i	−0.0446280	+	0.0890180i
$137$	−425.657			−0.0226787			−0.0113394	−	0.999936i	$-0.503610\pi$
$137$	−425.657			−0.0226787			−0.0113394	+	0.999936i	$0.503610\pi$
$138$	8667.66	+	22434.1i	0.455138	+	1.17801i
$139$	−21843.4			−1.13055			−0.565276	−	0.824902i	$-0.691230\pi$
$139$	−21843.4			−1.13055			−0.565276	+	0.824902i	$0.691230\pi$
$140$	−343.069	+	311.613i	−0.0175035	+	0.0158986i
$141$		−	15564.9i		−	0.782903i
$142$	1260.98	+	3263.74i	0.0625362	+	0.161860i
$143$		−	434.804i		−	0.0212628i
$144$	−751.119	+	7798.20i	−0.0362230	+	0.376071i
$145$	8572.39			0.407724
$146$	−28666.0	+	11075.4i	−1.34481	+	0.519583i
$147$	16997.3			0.786584
$148$	−26207.4	−	28853.0i	−1.19647	−	1.31725i
$149$		−	19745.1i		−	0.889381i	−0.895684	−	0.444690i	$-0.853314\pi$
$149$		−	19745.1i		−	0.889381i	0.895684	−	0.444690i	$-0.146686\pi$
$150$	−3311.02	+	1279.25i	−0.147156	+	0.0568554i
$151$			28379.1i			1.24464i	0.782761	+	0.622322i	$0.213811\pi$
$151$			28379.1i			1.24464i	−0.782761	+	0.622322i	$0.786189\pi$
$152$	−9083.92	+	18119.4i	−0.393175	+	0.784253i
$153$	880.690			0.0376218
$154$	−29.7174	−	76.9163i	−0.00125305	−	0.00324322i
$155$	−13349.3			−0.555642
$156$	4173.37	+	4594.66i	0.171489	+	0.188801i
$157$		−	4457.00i		−	0.180819i	−0.995905	−	0.0904094i	$-0.971182\pi$
$157$		−	4457.00i		−	0.180819i	0.995905	−	0.0904094i	$-0.0288176\pi$
$158$	2126.87	+	5504.90i	0.0851977	+	0.220513i
$159$		−	21593.3i		−	0.854133i
$160$	11025.7	−	3083.17i	0.430691	−	0.120436i
$161$	−2194.31			−0.0846538
$162$	−11737.1	+	4534.74i	−0.447228	+	0.172791i
$163$	−1910.59			−0.0719107			−0.0359553	−	0.999353i	$-0.511447\pi$
$163$	−1910.59			−0.0719107			−0.0359553	+	0.999353i	$0.511447\pi$
$164$	28820.8	−	26178.1i	1.07156	−	0.973310i
$165$		−	631.521i		−	0.0231964i
$166$	25556.8	−	9874.15i	0.927451	−	0.358330i
$167$			50764.6i			1.82024i	0.414347	+	0.910119i	$0.364010\pi$
$167$			50764.6i			1.82024i	−0.414347	+	0.910119i	$0.635990\pi$
$168$	1052.29	+	527.554i	0.0372837	+	0.0186917i
$169$	25574.7			0.895443
$170$	−463.830	−	1200.51i	−0.0160495	−	0.0415402i
$171$	9691.94			0.331450
$172$	27692.4	−	25153.2i	0.936059	−	0.850230i
$173$		−	42367.9i		−	1.41561i	−0.706407	−	0.707806i	$-0.749685\pi$
$173$		−	42367.9i		−	1.41561i	0.706407	−	0.707806i	$-0.250315\pi$
$174$	−7846.78	−	20309.5i	−0.259175	−	0.670811i
$175$		−	323.855i		−	0.0105749i
$176$	−195.289	+	2027.51i	−0.00630454	+	0.0654544i
$177$	3231.16			0.103136
$178$	48927.4	−	18903.6i	1.54423	−	0.596630i
$179$	−51902.2			−1.61987			−0.809934	−	0.586521i	$-0.800497\pi$
$179$	−51902.2			−1.61987			−0.809934	+	0.586521i	$0.800497\pi$
$180$	−3680.73	−	4052.29i	−0.113603	−	0.125071i
$181$			8176.63i			0.249584i	0.992183	+	0.124792i	$0.0398264\pi$
$181$			8176.63i			0.249584i	−0.992183	+	0.124792i	$0.960174\pi$
$182$	−528.266	+	204.101i	−0.0159481	+	0.00616173i
$183$			27835.2i			0.831175i
$184$	48456.2	+	24292.9i	1.43125	+	0.717536i
$185$	27237.1			0.795824
$186$	12219.4	+	31626.8i	0.353201	+	0.914175i
$187$	228.977			0.00654801
$188$	−23586.4	−	25967.4i	−0.667338	−	0.734704i
$189$		−	2052.67i		−	0.0574640i
$190$	−5104.43	−	13211.6i	−0.141397	−	0.365971i
$191$			38144.4i			1.04560i	0.852456	+	0.522799i	$0.175112\pi$
$191$			38144.4i			1.04560i	−0.852456	+	0.522799i	$0.824888\pi$
$192$	−17397.0	−	23299.6i	−0.471923	−	0.632042i
$193$	−35295.2			−0.947547			−0.473774	−	0.880647i	$-0.657109\pi$
$193$	−35295.2			−0.947547			−0.473774	+	0.880647i	$0.657109\pi$
$194$	−32101.0	+	12402.5i	−0.852932	+	0.329539i
$195$	−4337.33			−0.114065
$196$	28357.1	−	25757.0i	0.738159	−	0.670476i
$197$		−	6283.20i		−	0.161901i	−0.996718	−	0.0809503i	$-0.974204\pi$
$197$		−	6283.20i		−	0.161901i	0.996718	−	0.0809503i	$-0.0257955\pi$
$198$	908.525	−	351.018i	0.0231743	−	0.00895364i
$199$			20814.6i			0.525609i	0.964849	+	0.262805i	$0.0846474\pi$
$199$			20814.6i			0.525609i	−0.964849	+	0.262805i	$0.915353\pi$
$200$	−3585.36	+	7151.59i	−0.0896339	+	0.178790i
$201$	−34237.7			−0.847448
$202$	−10328.6	−	26733.2i	−0.253128	−	0.655161i
$203$	1986.50			0.0482054
$204$	−2419.65	+	2197.79i	−0.0581423	+	0.0528111i
$205$			27206.6i			0.647391i
$206$	11547.6	+	29888.2i	0.272119	+	0.704313i
$207$		−	25918.9i		−	0.604890i
$208$	13925.1	+	1341.26i	0.321864	+	0.0310018i
$209$	2519.88			0.0576883
$210$	−767.269	+	296.442i	−0.0173984	+	0.00672205i
$211$	21192.8			0.476017			0.238009	−	0.971263i	$-0.423505\pi$
$211$	21192.8			0.476017			0.238009	+	0.971263i	$0.423505\pi$
$212$	−32721.7	−	36024.8i	−0.728054	−	0.801549i
$213$			6209.70i			0.136871i
$214$	−7475.47	+	2888.23i	−0.163234	+	0.0630672i
$215$			26141.4i			0.565526i
$216$	−22724.8	+	45328.4i	−0.487072	+	0.971546i
$217$	−3093.46			−0.0656939
$218$	29238.9	+	75677.7i	0.615245	+	1.59241i
$219$	−54541.0			−1.13720
$220$	−956.981	−	1053.59i	−0.0197723	−	0.0217683i
$221$		−	1572.63i		−	0.0321990i
$222$	−24931.6	−	64529.3i	−0.505876	−	1.30934i
$223$		−	46813.2i		−	0.941365i	−0.882303	−	0.470683i	$-0.844008\pi$
$223$		−	46813.2i		−	0.941365i	0.882303	−	0.470683i	$-0.155992\pi$
$224$	2555.01	−	714.468i	0.0509209	−	0.0142392i
$225$	3825.34			0.0755622
$226$	−2128.65	+	822.427i	−0.0416762	+	0.0161020i
$227$	1993.76			0.0386920			0.0193460	−	0.999813i	$-0.493842\pi$
$227$	1993.76			0.0386920			0.0193460	+	0.999813i	$0.493842\pi$
$228$	−26628.1	+	24186.5i	−0.512237	+	0.465269i
$229$			45591.9i			0.869394i	0.900577	+	0.434697i	$0.143144\pi$
$229$			45591.9i			0.869394i	−0.900577	+	0.434697i	$0.856856\pi$
$230$	−35331.4	+	13650.6i	−0.667890	+	0.258046i
$231$		−	146.344i		−	0.00274252i
$232$	−43867.2	−	21992.2i	−0.815011	−	0.408595i
$233$	−82293.2			−1.51584			−0.757918	−	0.652350i	$-0.773783\pi$
$233$	−82293.2			−1.51584			−0.757918	+	0.652350i	$0.773783\pi$
$234$	−2410.82	−	6239.82i	−0.0440284	−	0.113957i
$235$	24513.1			0.443876
$236$	5390.64	−	4896.36i	0.0967869	−	0.0879123i
$237$			10473.8i			0.186470i
$238$	−107.484	−	278.197i	−0.00189754	−	0.00491132i
$239$		−	104832.i		−	1.83527i	−0.397426	−	0.917634i	$-0.630097\pi$
$239$		−	104832.i		−	1.83527i	0.397426	−	0.917634i	$-0.369903\pi$
$240$	20225.2	+	1948.08i	0.351132	+	0.0338209i
$241$	10146.4			0.174693			0.0873467	−	0.996178i	$-0.472161\pi$
$241$	10146.4			0.174693			0.0873467	+	0.996178i	$0.472161\pi$
$242$	−54392.2	+	21015.0i	−0.928766	+	0.358838i
$243$	41843.3			0.708620
$244$	42180.3	+	46438.4i	0.708485	+	0.780005i
$245$			26768.9i			0.445963i
$246$	64457.2	−	24903.7i	1.06513	−	0.411523i
$247$		−	17306.7i		−	0.283675i
$248$	68311.9	+	34247.3i	1.11069	+	0.556830i
$249$	48625.3			0.784267
$250$	−2014.68	−	5214.51i	−0.0322349	−	0.0834321i
$251$	14884.6			0.236260			0.118130	−	0.992998i	$-0.462310\pi$
$251$	14884.6			0.236260			0.118130	+	0.992998i	$0.462310\pi$
$252$	−852.942	−	939.045i	−0.0134313	−	0.0147872i
$253$		−	6738.86i		−	0.105280i
$254$	−9179.35	−	23758.5i	−0.142280	−	0.368257i
$255$		−	2284.14i		−	0.0351270i
$256$	−64331.2	−	12508.8i	−0.981616	−	0.190868i
$257$	63894.6			0.967382			0.483691	−	0.875239i	$-0.339296\pi$
$257$	63894.6			0.967382			0.483691	+	0.875239i	$0.339296\pi$
$258$	61933.6	−	23928.7i	0.930436	−	0.359484i
$259$	6311.70			0.0940907
$260$	−7236.10	+	6572.61i	−0.107043	+	0.0972280i
$261$			23464.3i			0.344450i
$262$	64731.8	−	25009.8i	0.943007	−	0.364341i
$263$			46265.3i			0.668874i	0.942418	+	0.334437i	$0.108546\pi$
$263$			46265.3i			0.668874i	−0.942418	+	0.334437i	$0.891454\pi$
$264$	−1620.15	+	3231.66i	−0.0232459	+	0.0463679i
$265$	34007.2			0.484261
$266$	−1182.86	−	3061.54i	−0.0167174	−	0.0432690i
$267$	93091.0			1.30583
$268$	−57119.9	+	51882.4i	−0.795275	+	0.722355i
$269$		−	87276.9i		−	1.20613i	−0.797691	−	0.603066i	$-0.793946\pi$
$269$		−	87276.9i		−	1.20613i	0.797691	−	0.603066i	$-0.206054\pi$
$270$	−12769.5	−	33050.8i	−0.175165	−	0.453371i
$271$		−	142380.i		−	1.93869i	−0.245696	−	0.969347i	$-0.579016\pi$
$271$		−	142380.i		−	1.93869i	0.245696	−	0.969347i	$-0.420984\pi$
$272$	−706.338	+	7333.27i	−0.00954717	+	0.0991197i
$273$	−1005.10			−0.0134860
$274$	−1588.21	+	613.622i	−0.0211547	+	0.00817334i
$275$	994.579			0.0131515
$276$	64681.5	+	71210.9i	0.849106	+	0.934821i
$277$			75663.5i			0.986114i	0.869997	+	0.493057i	$0.164121\pi$
$277$			75663.5i			0.986114i	−0.869997	+	0.493057i	$0.835879\pi$
$278$	−81501.9	+	31489.1i	−1.05458	+	0.407447i
$279$		−	36539.6i		−	0.469413i
$280$	−830.841	+	1657.25i	−0.0105975	+	0.0211384i
$281$	43571.0			0.551804			0.275902	−	0.961186i	$-0.411023\pi$
$281$	43571.0			0.551804			0.275902	+	0.961186i	$0.411023\pi$
$282$	−22438.2	−	58075.7i	−0.282156	−	0.730291i
$283$	67132.6			0.838225			0.419112	−	0.907934i	$-0.362341\pi$
$283$	67132.6			0.838225			0.419112	+	0.907934i	$0.362341\pi$
$284$	9409.93	+	10359.8i	0.116667	+	0.128445i
$285$		−	25136.8i		−	0.309471i
$286$	−626.807	−	1622.34i	−0.00766305	−	0.0198339i
$287$			6304.64i			0.0765415i
$288$	8439.21	+	30179.4i	0.101746	+	0.363853i
$289$	−82692.8			−0.990084
$290$	31985.3	−	12357.9i	0.380324	−	0.146942i
$291$	−61076.4			−0.721253
$292$	−90992.4	+	82649.2i	−1.06718	+	0.969333i
$293$		−	42456.8i		−	0.494552i	−0.968945	−	0.247276i	$-0.920465\pi$
$293$		−	42456.8i		−	0.494552i	0.968945	−	0.247276i	$-0.0795355\pi$
$294$	63420.3	−	24503.1i	0.733725	−	0.283482i
$295$			5088.73i			0.0584744i
$296$	−139379.	−	69876.0i	−1.59080	−	0.797525i
$297$	6303.87			0.0714652
$298$	−28464.3	−	73673.0i	−0.320530	−	0.829614i
$299$	−46283.0			−0.517701
$300$	−10509.9	+	9546.25i	−0.116777	+	0.106069i
$301$			6057.80i			0.0668624i
$302$	40911.0	+	105888.i	0.448566	+	1.16100i
$303$		−	50863.5i		−	0.554014i
$304$	−7773.21	+	80702.2i	−0.0841110	+	0.873250i
$305$	−43837.5			−0.471245
$306$	3286.03	−	1269.59i	0.0350936	−	0.0135588i
$307$	−22580.4			−0.239582			−0.119791	−	0.992799i	$-0.538223\pi$
$307$	−22580.4			−0.239582			−0.119791	+	0.992799i	$0.538223\pi$
$308$	−221.763	−	244.149i	−0.00233769	−	0.00257368i
$309$			56866.4i			0.595578i
$310$	−49808.9	+	19244.2i	−0.518303	+	0.200252i
$311$			104096.i			1.07625i	0.842865	+	0.538125i	$0.180867\pi$
$311$			104096.i			1.07625i	−0.842865	+	0.538125i	$0.819133\pi$
$312$	22195.3	+	11127.3i	0.228008	+	0.114309i
$313$	−84004.7			−0.857462			−0.428731	−	0.903432i	$-0.641039\pi$
$313$	−84004.7			−0.857462			−0.428731	+	0.903432i	$0.641039\pi$
$314$	−6425.16	−	16629.9i	−0.0651665	−	0.168668i
$315$	886.453			0.00893377
$316$	15871.6	+	17473.8i	0.158945	+	0.174990i
$317$			52955.1i			0.526974i	0.964663	+	0.263487i	$0.0848726\pi$
$317$			52955.1i			0.526974i	−0.964663	+	0.263487i	$0.915127\pi$
$318$	−31128.7	−	80569.0i	−0.307827	−	0.796735i
$319$			6100.65i			0.0599508i
$320$	36694.4	−	27398.4i	0.358344	−	0.267563i
$321$	−14223.1			−0.138033
$322$	−8187.40	+	3163.29i	−0.0789650	+	0.0305089i
$323$	9114.11			0.0873593
$324$	−37256.1	+	33840.0i	−0.354901	+	0.322359i
$325$		−	6830.84i		−	0.0646706i
$326$	−7128.80	+	2754.29i	−0.0670782	+	0.0259164i
$327$			143987.i			1.34657i
$328$	69797.8	−	139223.i	0.648775	−	1.29409i
$329$	5680.46			0.0524797
$330$	−910.393	−	2356.33i	−0.00835990	−	0.0216375i
$331$	−61731.5			−0.563444			−0.281722	−	0.959496i	$-0.590906\pi$
$331$	−61731.5			−0.563444			−0.281722	+	0.959496i	$0.590906\pi$
$332$	81123.1	−	73684.8i	0.735984	−	0.668501i
$333$			74553.0i			0.672321i
$334$	73181.6	+	189413.i	0.656008	+	1.69792i
$335$		−	53920.8i		−	0.480471i
$336$	4686.83	+	451.433i	0.0415146	+	0.00399867i
$337$	−15465.0			−0.136173			−0.0680865	−	0.997679i	$-0.521689\pi$
$337$	−15465.0			−0.136173			−0.0680865	+	0.997679i	$0.521689\pi$
$338$	95424.4	−	36868.2i	0.835268	−	0.322715i
$339$	−4050.05			−0.0352420
$340$	−3461.28	−	3810.69i	−0.0299419	−	0.0329645i
$341$		−	9500.20i		−	0.0817004i
$342$	36162.5	−	13971.8i	0.309177	−	0.119454i
$343$			12423.8i			0.105601i
$344$	67065.1	−	133773.i	0.566735	−	1.13045i
$345$	−67222.7			−0.564778
$346$	−61077.0	−	158083.i	−0.510182	−	1.32048i
$347$	−74344.2			−0.617431			−0.308715	−	0.951154i	$-0.599899\pi$
$347$	−74344.2			−0.617431			−0.308715	+	0.951154i	$0.599899\pi$
$348$	−58555.8	−	64466.8i	−0.483516	−	0.532326i
$349$			82400.1i			0.676514i	0.941054	+	0.338257i	$0.109837\pi$
$349$			82400.1i			0.676514i	−0.941054	+	0.338257i	$0.890163\pi$
$350$	−466.866	−	1208.37i	−0.00381115	−	0.00986422i
$351$		−	43295.4i		−	0.351421i
$352$	2194.18	+	7846.58i	0.0177087	+	0.0633279i
$353$	153677.			1.23327			0.616635	−	0.787249i	$-0.288495\pi$
$353$	153677.			1.23327			0.616635	+	0.787249i	$0.288495\pi$
$354$	12056.1	−	4658.00i	0.0962055	−	0.0371700i
$355$	−9779.62			−0.0776007
$356$	155307.	−	141066.i	1.22543	−	1.11307i
$357$		−	529.307i		−	0.00415309i
$358$	−193657.	+	74821.5i	−1.51101	+	0.583795i
$359$			235554.i			1.82768i	0.406072	+	0.913841i	$0.366898\pi$
$359$			235554.i			1.82768i	−0.406072	+	0.913841i	$0.633102\pi$
$360$	−19575.2	−	9813.80i	−0.151044	−	0.0757237i
$361$	−30020.8			−0.230360
$362$	11787.3	+	30508.6i	0.0899493	+	0.232812i
$363$	−103489.			−0.785379
$364$	−1676.84	+	1523.08i	−0.0126557	+	0.0114953i
$365$		−	85896.3i		−	0.644746i
$366$	40126.9	+	103859.i	0.299553	+	0.775319i
$367$		−	112718.i		−	0.836878i	−0.908245	−	0.418439i	$-0.862577\pi$
$367$		−	112718.i		−	0.836878i	0.908245	−	0.418439i	$-0.137423\pi$
$368$	215820.	+	20787.7i	1.59366	+	0.153501i
$369$	−74469.7			−0.546924
$370$	101627.	−	39264.6i	0.742344	−	0.286812i
$371$	7880.56			0.0572545
$372$	91185.6	+	100391.i	0.658932	+	0.725449i
$373$		−	16080.3i		−	0.115578i	−0.998329	−	0.0577892i	$-0.981595\pi$
$373$		−	16080.3i		−	0.115578i	0.998329	−	0.0577892i	$-0.0184051\pi$
$374$	854.359	−	330.091i	0.00610798	−	0.00235988i
$375$		−	9921.30i		−	0.0705515i
$376$	−125440.	−	62887.6i	−0.887277	−	0.444825i
$377$	41899.7			0.294801
$378$	−2959.10	−	7658.92i	−0.0207098	−	0.0536023i
$379$	208815.			1.45373			0.726864	−	0.686781i	$-0.240977\pi$
$379$	208815.			1.45373			0.726864	+	0.686781i	$0.240977\pi$
$380$	−38091.2	−	41936.4i	−0.263790	−	0.290419i
$381$		−	45203.8i		−	0.311404i
$382$	54988.5	+	142324.i	0.376830	+	0.975332i
$383$			96057.8i			0.654840i	0.944879	+	0.327420i	$0.106179\pi$
$383$			96057.8i			0.654840i	−0.944879	+	0.327420i	$0.893821\pi$
$384$	−98500.0	−	61856.1i	−0.667996	−	0.419488i
$385$	230.476			0.00155490
$386$	−131693.	+	50881.1i	−0.883871	+	0.341493i
$387$	−71554.0			−0.477763
$388$	−101896.	+	92552.7i	−0.676850	+	0.614788i
$389$		−	168851.i		−	1.11584i	−0.829893	−	0.557922i	$-0.811599\pi$
$389$		−	168851.i		−	1.11584i	0.829893	−	0.557922i	$-0.188401\pi$
$390$	−16183.4	+	6252.64i	−0.106400	+	0.0411087i
$391$		−	24373.6i		−	0.159429i
$392$	68675.0	−	136984.i	0.446917	−	0.891449i
$393$	123161.			0.797422
$394$	−9057.78	−	23443.9i	−0.0583485	−	0.151021i
$395$	−16495.1			−0.105721
$396$	2883.86	−	2619.44i	0.0183901	−	0.0167039i
$397$		−	189472.i		−	1.20216i	−0.799188	−	0.601081i	$-0.794737\pi$
$397$		−	189472.i		−	1.20216i	0.799188	−	0.601081i	$-0.205263\pi$
$398$	30006.1	+	77663.5i	0.189428	+	0.490288i
$399$		−	5824.99i		−	0.0365889i
$400$	−3068.03	+	31852.6i	−0.0191752	+	0.199079i
$401$	120359.			0.748494			0.374247	−	0.927329i	$-0.377901\pi$
$401$	120359.			0.748494			0.374247	+	0.927329i	$0.377901\pi$
$402$	−127748.	+	49356.7i	−0.790499	+	0.305417i
$403$	−65248.1			−0.401751
$404$	−77076.4	−	84857.1i	−0.472236	−	0.519907i
$405$		−	35169.5i		−	0.214415i
$406$	7412.01	−	2863.71i	0.0449660	−	0.0173731i
$407$			19383.6i			0.117016i
$408$	−5859.88	+	11688.5i	−0.0352021	+	0.0702165i
$409$	150488.			0.899615			0.449807	−	0.893126i	$-0.351493\pi$
$409$	150488.			0.899615			0.449807	+	0.893126i	$0.351493\pi$
$410$	39220.7	+	101513.i	0.233318	+	0.603886i
$411$	−3021.79			−0.0178887
$412$	86173.0	+	94871.9i	0.507664	+	0.558912i
$413$			1179.22i			0.00691346i
$414$	−37364.4	−	96708.6i	−0.218000	−	0.564241i
$415$			76579.7i			0.444649i
$416$	53890.9	−	15069.8i	0.311407	−	0.0870802i
$417$	−155068.			−0.891767
$418$	9402.17	−	3632.63i	0.0538116	−	0.0207907i
$419$	288889.			1.64552			0.822761	−	0.568388i	$-0.192433\pi$
$419$	288889.			1.64552			0.822761	+	0.568388i	$0.192433\pi$
$420$	−2435.48	+	2212.17i	−0.0138066	+	0.0125406i
$421$		−	182304.i		−	1.02857i	−0.857620	−	0.514284i	$-0.828058\pi$
$421$		−	182304.i		−	1.02857i	0.857620	−	0.514284i	$-0.171942\pi$
$422$	79074.4	−	30551.2i	0.444029	−	0.171555i
$423$			67096.9i			0.374992i
$424$	−174024.	−	87244.6i	−0.968004	−	0.485296i
$425$	3597.27			0.0199157
$426$	8951.83	+	23169.6i	0.0493279	+	0.127673i
$427$	−10158.6			−0.0557155
$428$	−23728.8	+	21553.1i	−0.129535	+	0.117658i
$429$		−	3086.72i		−	0.0167719i
$430$	37685.2	+	97538.8i	0.203814	+	0.527522i
$431$			100495.i			0.540992i	0.962721	+	0.270496i	$0.0871877\pi$
$431$			100495.i			0.540992i	−0.962721	+	0.270496i	$0.912812\pi$
$432$	−19445.9	+	201889.i	−0.104198	+	1.08180i
$433$	328152.			1.75025			0.875124	−	0.483898i	$-0.160779\pi$
$433$	328152.			1.75025			0.875124	+	0.483898i	$0.160779\pi$
$434$	−11542.3	+	4459.49i	−0.0612792	+	0.0236759i
$435$	60856.3			0.321608
$436$	218192.	+	240218.i	1.14780	+	1.26367i
$437$		−	268230.i		−	1.40458i
$438$	−203503.	+	78625.6i	−1.06077	+	0.409842i
$439$			155253.i			0.805582i	0.915292	+	0.402791i	$0.131960\pi$
$439$			155253.i			0.805582i	−0.915292	+	0.402791i	$0.868040\pi$
$440$	−5089.52	−	2551.56i	−0.0262888	−	0.0131796i
$441$	−73271.7			−0.376755
$442$	−2267.09	−	5867.80i	−0.0116044	−	0.0300352i
$443$	−337851.			−1.72154			−0.860772	−	0.508991i	$-0.830019\pi$
$443$	−337851.			−1.72154			−0.860772	+	0.508991i	$0.830019\pi$
$444$	−186049.	−	204831.i	−0.943761	−	1.03903i
$445$			146608.i			0.740353i
$446$	−67485.2	−	174669.i	−0.339265	−	0.878105i
$447$		−	140173.i		−	0.701534i
$448$	8503.26	−	6349.09i	0.0423672	−	0.0316341i
$449$	−245472.			−1.21761			−0.608806	−	0.793319i	$-0.708351\pi$
$449$	−245472.			−1.21761			−0.608806	+	0.793319i	$0.708351\pi$
$450$	14273.1	−	5514.56i	0.0704844	−	0.0272324i
$451$	−19361.9			−0.0951910
$452$	−6756.82	+	6137.28i	−0.0330724	+	0.0300399i
$453$			201466.i			0.981762i
$454$	7439.12	−	2874.18i	0.0360919	−	0.0139445i
$455$		−	1582.92i		−	0.00764605i
$456$	−64487.7	+	128631.i	−0.310132	+	0.618611i
$457$	−115007.			−0.550671			−0.275336	−	0.961348i	$-0.588789\pi$
$457$	−115007.			−0.550671			−0.275336	+	0.961348i	$0.588789\pi$
$458$	65724.7	+	170112.i	0.313327	+	0.810970i
$459$	22800.4			0.108222
$460$	−112150.	+	101866.i	−0.530008	+	0.481410i
$461$			115456.i			0.543270i	0.962400	+	0.271635i	$0.0875644\pi$
$461$			115456.i			0.543270i	−0.962400	+	0.271635i	$0.912436\pi$
$462$	−210.967	−	546.037i	−0.000988395	−	0.00255822i
$463$		−	308334.i		−	1.43833i	−0.694837	−	0.719167i	$-0.744524\pi$
$463$		−	308334.i		−	1.43833i	0.694837	−	0.719167i	$-0.255476\pi$
$464$	−195381.	−	18819.0i	−0.907498	−	0.0874099i
$465$	−94768.1			−0.438285
$466$	−307052.	+	118633.i	−1.41397	+	0.546302i
$467$	−234153.			−1.07366			−0.536829	−	0.843691i	$-0.680378\pi$
$467$	−234153.			−1.07366			−0.536829	+	0.843691i	$0.680378\pi$
$468$	−17990.5	−	19806.6i	−0.0821393	−	0.0904311i
$469$		−	12495.2i		−	0.0568063i
$470$	91463.0	−	35337.7i	0.414047	−	0.159972i
$471$		−	31640.7i		−	0.142628i
$472$	13055.0	−	26040.4i	0.0585994	−	0.116886i
$473$	−18603.9			−0.0831536
$474$	15098.9	+	39079.8i	0.0672030	+	0.173939i
$475$	39587.8			0.175458
$476$	−802.090	−	883.059i	−0.00354005	−	0.00389741i
$477$			93084.2i			0.409109i
$478$	−151125.	−	391150.i	−0.661425	−	1.71194i
$479$			175880.i			0.766558i	0.923633	+	0.383279i	$0.125205\pi$
$479$			175880.i			0.766558i	−0.923633	+	0.383279i	$0.874795\pi$
$480$	78272.6	−	21887.7i	0.339725	−	0.0949988i
$481$	133128.			0.575412
$482$	37858.1	−	14626.9i	0.162954	−	0.0629589i
$483$	−15577.6			−0.0667740
$484$	−172653.	+	156822.i	−0.737028	+	0.669448i
$485$		−	96188.9i		−	0.408923i
$486$	156126.	−	60320.7i	0.661000	−	0.255384i
$487$		−	289085.i		−	1.21890i	−0.792826	−	0.609449i	$-0.791391\pi$
$487$		−	289085.i		−	1.21890i	0.792826	−	0.609449i	$-0.208609\pi$
$488$	224328.	+	112464.i	0.941985	+	0.472252i
$489$	−13563.5			−0.0567224
$490$	38589.8	+	99880.2i	0.160724	+	0.415994i
$491$	182813.			0.758304			0.379152	−	0.925334i	$-0.376216\pi$
$491$	182813.			0.758304			0.379152	+	0.925334i	$0.376216\pi$
$492$	204602.	−	185841.i	0.845237	−	0.767736i
$493$			22065.3i			0.0907855i
$494$	−24949.2	−	64574.8i	−0.102236	−	0.264612i
$495$			2722.35i			0.0111105i
$496$	304255.	+	29305.8i	1.23673	+	0.119121i
$497$	−2266.25			−0.00917477
$498$	181431.	−	70097.7i	0.731563	−	0.282647i
$499$	463712.			1.86229			0.931145	−	0.364650i	$-0.118811\pi$
$499$	463712.			1.86229			0.931145	+	0.364650i	$0.118811\pi$
$500$	−15034.3	−	16552.0i	−0.0601373	−	0.0662080i
$501$			360383.i			1.43578i
$502$	55537.3	−	21457.4i	0.220383	−	0.0851472i
$503$		−	173588.i		−	0.686094i	−0.939318	−	0.343047i	$-0.888541\pi$
$503$		−	173588.i		−	0.686094i	0.939318	−	0.343047i	$-0.111459\pi$
$504$	−4536.21	−	2274.17i	−0.0178580	−	0.00895286i
$505$	80104.6			0.314105
$506$	−9714.65	−	25144.0i	−0.0379425	−	0.0982050i
$507$	181558.			0.706316
$508$	−68499.9	−	75414.8i	−0.265438	−	0.292233i
$509$			231066.i			0.891867i	0.895066	+	0.445934i	$0.147128\pi$
$509$			231066.i			0.891867i	−0.895066	+	0.445934i	$0.852872\pi$
$510$	−3292.78	−	8522.56i	−0.0126597	−	0.0327665i
$511$		−	19904.9i		−	0.0762287i
$512$	−258065.	+	46066.4i	−0.984439	+	0.175729i
$513$	250917.			0.953443
$514$	238403.	−	92109.7i	0.902373	−	0.348641i
$515$	−89558.5			−0.337670
$516$	196591.	−	178565.i	0.738353	−	0.670653i
$517$			17445.0i			0.0652665i
$518$	23550.2	−	9098.87i	0.0877678	−	0.0339100i
$519$		−	300774.i		−	1.11662i
$520$	−17524.3	+	34955.2i	−0.0648089	+	0.129272i
$521$	39770.4			0.146516			0.0732578	−	0.997313i	$-0.476660\pi$
$521$	39770.4			0.146516			0.0732578	+	0.997313i	$0.476660\pi$
$522$	33825.8	+	87549.8i	0.124139	+	0.321302i
$523$	−71651.8			−0.261953			−0.130977	−	0.991385i	$-0.541811\pi$
$523$	−71651.8			−0.261953			−0.130977	+	0.991385i	$0.541811\pi$
$524$	205473.	−	186633.i	0.748329	−	0.679713i
$525$		−	2299.08i		−	0.00834134i
$526$	66695.5	+	172625.i	0.241060	+	0.623925i
$527$		−	34361.1i		−	0.123722i
$528$	−1386.38	+	14393.5i	−0.00497295	+	0.0516297i
$529$	−437481.			−1.56332
$530$	126888.	−	49024.4i	0.451718	−	0.174526i
$531$	−13928.8			−0.0493998
$532$	−8826.95	−	9718.01i	−0.0311880	−	0.0343364i
$533$			132979.i			0.468090i
$534$	347341.	−	134199.i	1.21807	−	0.470615i
$535$		−	22399.9i		−	0.0782596i
$536$	−138332.	+	275927.i	−0.481498	+	0.960427i
$537$	−368459.			−1.27774
$538$	−125817.	−	325647.i	−0.434686	−	1.12508i
$539$	−19050.5			−0.0655734
$540$	−95291.1	−	104911.i	−0.326787	−	0.359775i
$541$			335147.i			1.14509i	0.819873	+	0.572546i	$0.194044\pi$
$541$			335147.i			1.14509i	−0.819873	+	0.572546i	$0.805956\pi$
$542$	−205253.	−	531246.i	−0.698699	−	1.80841i
$543$			58046.7i			0.196869i
$544$	7936.07	+	28380.1i	0.0268168	+	0.0958996i
$545$	−226764.			−0.763452
$546$	−3750.22	+	1448.94i	−0.0125797	+	0.00486031i
$547$	−174207.			−0.582225			−0.291112	−	0.956689i	$-0.594025\pi$
$547$	−174207.			−0.582225			−0.291112	+	0.956689i	$0.594025\pi$
$548$	−5041.34	+	4579.09i	−0.0167874	+	0.0152482i
$549$		−	119992.i		−	0.398113i
$550$	3710.97	−	1433.77i	0.0122677	−	0.00473974i
$551$			242828.i			0.799825i
$552$	343996.	+	172458.i	1.12895	+	0.565985i
$553$	−3822.45			−0.0124995
$554$	109076.	+	282315.i	0.355392	+	0.919846i
$555$	193359.			0.627738
$556$	−258705.	+	234984.i	−0.836866	+	0.760132i
$557$			179035.i			0.577069i	0.957470	+	0.288534i	$0.0931680\pi$
$557$			179035.i			0.577069i	−0.957470	+	0.288534i	$0.906832\pi$
$558$	−52675.0	−	136336.i	−0.169175	−	0.437868i
$559$			127773.i			0.408898i
$560$	−710.960	+	7381.26i	−0.00226709	+	0.0235372i
$561$	1625.53			0.00516500
$562$	162572.	−	62811.4i	0.514722	−	0.198868i
$563$	−126413.			−0.398819			−0.199410	−	0.979916i	$-0.563902\pi$
$563$	−126413.			−0.398819			−0.199410	+	0.979916i	$0.563902\pi$
$564$	−167442.	−	184345.i	−0.526389	−	0.579527i
$565$		−	6378.40i		−	0.0199809i
$566$	250485.	−	96777.5i	0.781895	−	0.302094i
$567$		−	8149.90i		−	0.0253505i
$568$	50044.9	+	25089.4i	0.155118	+	0.0777665i
$569$	−160597.			−0.496035			−0.248017	−	0.968756i	$-0.579779\pi$
$569$	−160597.			−0.496035			−0.248017	+	0.968756i	$0.579779\pi$
$570$	−36236.9	−	93790.3i	−0.111532	−	0.288674i
$571$	−372210.			−1.14160			−0.570802	−	0.821088i	$-0.693367\pi$
$571$	−372210.			−1.14160			−0.570802	+	0.821088i	$0.693367\pi$
$572$	−4677.48	−	5149.66i	−0.0142962	−	0.0157393i
$573$			270791.i			0.824756i
$574$	9088.69	+	23523.9i	0.0275853	+	0.0713978i
$575$		−	105869.i		−	0.320208i
$576$	74994.6	+	100440.i	0.226040	+	0.302733i
$577$	328066.			0.985393			0.492696	−	0.870201i	$-0.336011\pi$
$577$	328066.			0.985393			0.492696	+	0.870201i	$0.336011\pi$
$578$	−308543.	+	119209.i	−0.923550	+	0.356823i
$579$	−250564.			−0.747415
$580$	101528.	−	92219.2i	0.301809	−	0.274135i
$581$			17746.0i			0.0525712i
$582$	−227888.	+	88047.0i	−0.672784	+	0.259937i
$583$			24201.7i			0.0712047i
$584$	−220365.	+	439554.i	−0.646125	+	1.28880i
$585$	18697.3			0.0546345
$586$	−61205.2	−	158415.i	−0.178235	−	0.461318i
$587$	128807.			0.373822			0.186911	−	0.982377i	$-0.440152\pi$
$587$	128807.			0.373822			0.186911	+	0.982377i	$0.440152\pi$
$588$	201310.	−	182852.i	0.582252	−	0.528864i
$589$		−	378142.i		−	1.08999i
$590$	7335.85	+	18987.1i	0.0210740	+	0.0545449i
$591$		−	44605.1i		−	0.127706i
$592$	−620784.	−	59793.6i	−1.77132	−	0.170613i
$593$	−210780.			−0.599405			−0.299703	−	0.954033i	$-0.596887\pi$
$593$	−210780.			−0.599405			−0.299703	+	0.954033i	$0.596887\pi$
$594$	23521.0	−	9087.58i	0.0666627	−	0.0257558i
$595$	833.603			0.00235464
$596$	−212412.	−	233855.i	−0.597980	−	0.658345i
$597$			147765.i			0.414595i
$598$	−172691.	+	66720.9i	−0.482911	+	0.186578i
$599$		−	187457.i		−	0.522453i	−0.965278	−	0.261226i	$-0.915873\pi$
$599$		−	187457.i		−	0.522453i	0.965278	−	0.261226i	$-0.0841269\pi$
$600$	−25452.8	+	50769.9i	−0.0707023	+	0.141027i
$601$	14463.8			0.0400436			0.0200218	−	0.999800i	$-0.493626\pi$
$601$	14463.8			0.0400436			0.0200218	+	0.999800i	$0.493626\pi$
$602$	8732.85	+	22602.9i	0.0240970	+	0.0623692i
$603$	147591.			0.405907
$604$	305294.	+	336113.i	0.836843	+	0.921321i
$605$		−	162984.i		−	0.445280i
$606$	−73324.1	−	189782.i	−0.199665	−	0.516784i
$607$			579553.i			1.57295i	0.617620	+	0.786477i	$0.288097\pi$
$607$			579553.i			1.57295i	−0.617620	+	0.786477i	$0.711903\pi$
$608$	87336.0	+	312322.i	0.236258	+	0.844880i
$609$	14102.4			0.0380239
$610$	−163566.	+	63195.6i	−0.439577	+	0.169835i
$611$	119814.			0.320940
$612$	10430.6	−	9474.19i	0.0278488	−	0.0252953i
$613$		−	377775.i		−	1.00534i	−0.864479	−	0.502669i	$-0.832352\pi$
$613$		−	377775.i		−	1.00534i	0.864479	−	0.502669i	$-0.167648\pi$
$614$	−84251.9	+	32551.6i	−0.223482	+	0.0863448i
$615$			193143.i			0.510656i
$616$	−1179.40	−	591.279i	−0.00310814	−	0.00155823i
$617$	699981.			1.83872			0.919361	−	0.393414i	$-0.128706\pi$
$617$	699981.			1.83872			0.919361	+	0.393414i	$0.128706\pi$
$618$	81977.9	+	212180.i	0.214644	+	0.555555i
$619$	−117981.			−0.307915			−0.153957	−	0.988077i	$-0.549202\pi$
$619$	−117981.			−0.307915			−0.153957	+	0.988077i	$0.549202\pi$
$620$	−158105.	+	143608.i	−0.411302	+	0.373589i
$621$		−	671020.i		−	1.74001i
$622$	150064.	+	388403.i	0.387877	+	1.00393i
$623$			33973.9i			0.0875324i
$624$	98855.8	+	9521.75i	0.253883	+	0.0244539i
$625$	15625.0			0.0400000
$626$	−313438.	+	121100.i	−0.799840	+	0.309027i
$627$	17888.9			0.0455039
$628$	−47947.0	−	52787.2i	−0.121575	−	0.133847i
$629$			70108.2i			0.177202i
$630$	3307.53	−	1277.90i	0.00833341	−	0.00321970i
$631$		−	749113.i		−	1.88143i	−0.339193	−	0.940717i	$-0.610154\pi$
$631$		−	749113.i		−	1.88143i	0.339193	−	0.940717i	$-0.389846\pi$
$632$	84409.9	+	42317.8i	0.211329	+	0.105947i
$633$	150450.			0.375478
$634$	76339.3	+	197586.i	0.189920	+	0.491561i
$635$	71191.1			0.176554
$636$	−232295.	−	255744.i	−0.574281	−	0.632254i
$637$			130840.i			0.322449i
$638$	8794.62	+	22762.7i	0.0216061	+	0.0559220i
$639$		−	26768.7i		−	0.0655579i
$640$	97416.8	−	155127.i	0.237834	−	0.378728i
$641$	190520.			0.463686			0.231843	−	0.972753i	$-0.425525\pi$
$641$	190520.			0.463686			0.231843	+	0.972753i	$0.425525\pi$
$642$	−53069.1	+	20503.8i	−0.128757	+	0.0497467i
$643$	272152.			0.658248			0.329124	−	0.944287i	$-0.393247\pi$
$643$	272152.			0.658248			0.329124	+	0.944287i	$0.393247\pi$
$644$	−25988.7	+	23605.7i	−0.0626631	+	0.0569174i
$645$			185581.i			0.446081i
$646$	34006.5	−	13138.8i	0.0814887	−	0.0314840i
$647$		−	26959.8i		−	0.0644034i	−0.999481	−	0.0322017i	$-0.989748\pi$
$647$		−	26959.8i		−	0.0644034i	0.999481	−	0.0322017i	$-0.0102519\pi$
$648$	−90226.4	+	179971.i	−0.214874	+	0.428602i
$649$	−3621.46			−0.00859794
$650$	−9847.25	−	25487.2i	−0.0233071	−	0.0603247i
$651$	−21960.8			−0.0518187
$652$	−22628.4	+	20553.6i	−0.0532303	+	0.0483495i
$653$		−	497282.i		−	1.16621i	−0.812397	−	0.583104i	$-0.801838\pi$
$653$		−	497282.i		−	1.16621i	0.812397	−	0.583104i	$-0.198162\pi$
$654$	207570.	+	537244.i	0.485299	+	1.25608i
$655$			193965.i			0.452108i
$656$	59726.8	−	620089.i	0.138791	−	1.44094i
$657$	235115.			0.544689
$658$	21194.9	−	8188.88i	0.0489530	−	0.0189135i
$659$	150938.			0.347558			0.173779	−	0.984785i	$-0.444402\pi$
$659$	150938.			0.347558			0.173779	+	0.984785i	$0.444402\pi$
$660$	−6793.71	−	7479.52i	−0.0155962	−	0.0171706i
$661$		−	535544.i		−	1.22572i	−0.790191	−	0.612861i	$-0.790018\pi$
$661$		−	535544.i		−	1.22572i	0.790191	−	0.612861i	$-0.209982\pi$
$662$	−230332.	+	88991.3i	−0.525580	+	0.203063i
$663$		−	11164.3i		−	0.0253982i
$664$	196463.	−	391879.i	0.445600	−	0.888823i
$665$	9173.75			0.0207445
$666$	107475.	+	278172.i	0.242302	+	0.627141i
$667$	649388.			1.45966
$668$	546110.	+	601239.i	1.22385	+	1.34739i
$669$		−	332332.i		−	0.742539i
$670$	−77731.6	−	201189.i	−0.173160	−	0.448183i
$671$		−	31197.5i		−	0.0692908i
$672$	18138.3	−	5072.09i	0.0401659	−	0.0112318i
$673$	−189265.			−0.417868			−0.208934	−	0.977930i	$-0.566999\pi$
$673$	−189265.			−0.417868			−0.208934	+	0.977930i	$0.566999\pi$
$674$	−57703.1	+	22294.2i	−0.127022	+	0.0490763i
$675$	99034.9			0.217361
$676$	302898.	−	275125.i	0.662832	−	0.602056i
$677$			464037.i			1.01245i	0.862400	+	0.506227i	$0.168960\pi$
$677$			464037.i			1.01245i	−0.862400	+	0.506227i	$0.831040\pi$
$678$	−15111.5	+	5838.50i	−0.0328737	+	0.0127011i
$679$		−	22290.0i		−	0.0483472i
$680$	−18408.2	−	9228.70i	−0.0398101	−	0.0199583i
$681$	14153.9			0.0305199
$682$	−13695.4	−	35447.1i	−0.0294446	−	0.0762100i
$683$	−42942.9			−0.0920556			−0.0460278	−	0.998940i	$-0.514656\pi$
$683$	−42942.9			−0.0920556			−0.0460278	+	0.998940i	$0.514656\pi$
$684$	114788.	−	104263.i	0.245349	−	0.222853i
$685$		−	4758.99i		−	0.0101422i
$686$	17910.0	+	46355.8i	0.0380582	+	0.0985044i
$687$			323661.i			0.685769i
$688$	57388.3	−	595812.i	0.121240	−	1.25873i
$689$	166219.			0.350140
$690$	−250821.	+	96907.4i	−0.526824	+	0.203544i
$691$	−695800.			−1.45723			−0.728615	−	0.684924i	$-0.759836\pi$
$691$	−695800.			−1.45723			−0.728615	+	0.684924i	$0.759836\pi$
$692$	−455780.	−	501790.i	−0.951795	−	1.04788i
$693$			630.855i			0.00131360i
$694$	−277393.	+	107174.i	−0.575939	+	0.222520i
$695$		−	244216.i		−	0.505598i
$696$	−311418.	−	156125.i	−0.642872	−	0.322296i
$697$	−70029.8			−0.144151
$698$	118787.	+	307451.i	0.243814	+	0.631052i
$699$	−584208.			−1.19568
$700$	−3483.93	−	3835.63i	−0.00711007	−	0.00782781i
$701$			243528.i			0.495580i	0.968814	+	0.247790i	$0.0797043\pi$
$701$			243528.i			0.495580i	−0.968814	+	0.247790i	$0.920296\pi$
$702$	−62414.2	−	161544.i	−0.126651	−	0.327805i
$703$			771536.i			1.56115i
$704$	19498.4	+	26114.0i	0.0393418	+	0.0526901i
$705$	174021.			0.350125
$706$	573397.	−	221538.i	1.15039	−	0.444467i
$707$	18562.8			0.0371368
$708$	38268.7	−	34759.8i	0.0763445	−	0.0693443i
$709$			210565.i			0.418883i	0.977821	+	0.209442i	$0.0671646\pi$
$709$			210565.i			0.418883i	−0.977821	+	0.209442i	$0.932835\pi$
$710$	−36489.7	+	14098.2i	−0.0723858	+	0.0279670i
$711$		−	45150.3i		−	0.0893144i
$712$	376120.	−	750234.i	0.741936	−	1.47991i
$713$	−1.01126e6			−1.98922
$714$	−763.042	−	1974.95i	−0.00149676	−	0.00387400i
$715$	4861.25			0.00950903
$716$	−614712.	+	558348.i	−1.19907	+	1.08913i
$717$		−	744216.i		−	1.44764i
$718$	339571.	+	878897.i	0.658691	+	1.70486i
$719$			174495.i			0.337539i	0.985656	+	0.168770i	$0.0539794\pi$
$719$			174495.i			0.337539i	−0.985656	+	0.168770i	$0.946021\pi$
$720$	−87186.5	−	8397.77i	−0.168184	−	0.0161994i
$721$	−20753.6			−0.0399229
$722$	−112013.	+	43277.6i	−0.214880	+	0.0830211i
$723$	72030.1			0.137796
$724$	87961.6	+	96841.1i	0.167809	+	0.184749i
$725$			95842.3i			0.182340i
$726$	−386136.	+	149188.i	−0.732601	+	0.283048i
$727$			511384.i			0.967561i	0.875189	+	0.483781i	$0.160737\pi$
$727$			511384.i			0.967561i	−0.875189	+	0.483781i	$0.839263\pi$
$728$	−4060.94	+	8100.23i	−0.00766239	+	0.0152839i
$729$	551848.			1.03840
$730$	−123827.	−	320496.i	−0.232365	−	0.601419i
$731$	−67288.0			−0.125922
$732$	299443.	+	329671.i	0.558845	+	0.615259i
$733$			384728.i			0.716055i	0.933711	+	0.358027i	$0.116551\pi$
$733$			384728.i			0.716055i	−0.933711	+	0.358027i	$0.883449\pi$
$734$	−162493.	−	420574.i	−0.301608	−	0.780639i
$735$			190036.i			0.351771i
$736$	835234.	−	233560.i	1.54189	−	0.431165i
$737$	38373.4			0.0706473
$738$	−277861.	+	107355.i	−0.510170	+	0.197110i
$739$	−66307.5			−0.121415			−0.0607077	−	0.998156i	$-0.519336\pi$
$739$	−66307.5			−0.121415			−0.0607077	+	0.998156i	$0.519336\pi$
$740$	322586.	−	293008.i	0.589091	−	0.535077i
$741$		−	122862.i		−	0.223760i
$742$	29403.9	−	11360.5i	0.0534069	−	0.0206343i
$743$		−	786533.i		−	1.42475i	−0.701798	−	0.712376i	$-0.747619\pi$
$743$		−	786533.i		−	1.42475i	0.701798	−	0.712376i	$-0.252381\pi$
$744$	484953.	+	243125.i	0.876101	+	0.439222i
$745$	220757.			0.397743
$746$	−23181.2	−	59998.8i	−0.0416541	−	0.107811i
$747$	−209613.			−0.375645
$748$	2711.93	−	2463.27i	0.00484702	−	0.00440259i
$749$		−	5190.76i		−	0.00925268i
$750$	−14302.4	−	37018.3i	−0.0254265	−	0.0658104i
$751$			743780.i			1.31876i	0.751811	+	0.659379i	$0.229181\pi$
$751$			743780.i			1.31876i	−0.751811	+	0.659379i	$0.770819\pi$
$752$	−558698.	−	53813.6i	−0.987965	−	0.0951604i
$753$	105667.			0.186359
$754$	156336.	−	60402.1i	0.274990	−	0.106245i
$755$	−317288.			−0.556622
$756$	−22082.0	−	24311.1i	−0.0386362	−	0.0425365i
$757$			378393.i			0.660315i	0.943926	+	0.330158i	$0.107102\pi$
$757$			378393.i			0.660315i	−0.943926	+	0.330158i	$0.892898\pi$
$758$	779130.	−	301025.i	1.35604	−	0.523919i
$759$		−	47839.9i		−	0.0830437i
$760$	−202581.	−	101561.i	−0.350729	−	0.175833i
$761$	−487660.			−0.842070			−0.421035	−	0.907044i	$-0.638333\pi$
$761$	−487660.			−0.842070			−0.421035	+	0.907044i	$0.638333\pi$
$762$	−65165.2	−	168664.i	−0.112229	−	0.290478i
$763$	−52548.6			−0.0902634
$764$	410346.	+	451770.i	0.703013	+	0.773981i
$765$			9846.41i			0.0168250i
$766$	138476.	+	358410.i	0.236002	+	0.610834i
$767$			24872.5i			0.0422793i
$768$	−456694.	−	88800.9i	−0.774288	−	0.150555i
$769$	−264950.			−0.448034			−0.224017	−	0.974585i	$-0.571917\pi$
$769$	−264950.			−0.448034			−0.224017	+	0.974585i	$0.571917\pi$
$770$	859.950	−	332.251i	0.00145041	−	0.000560382i
$771$	453595.			0.763061
$772$	−418024.	+	379695.i	−0.701401	+	0.637089i
$773$		−	515794.i		−	0.863212i	−0.902062	−	0.431606i	$-0.857947\pi$
$773$		−	515794.i		−	0.863212i	0.902062	−	0.431606i	$-0.142053\pi$
$774$	−266982.	+	103151.i	−0.445657	+	0.172184i
$775$		−	149250.i		−	0.248491i
$776$	−246770.	+	492224.i	−0.409797	+	0.817408i
$777$	44807.4			0.0742178
$778$	−243413.	−	630015.i	−0.402147	−	1.04086i
$779$	−770674.			−1.26998
$780$	−51369.8	+	46659.7i	−0.0844343	+	0.0766924i
$781$		−	6959.79i		−	0.0114102i
$782$	−35136.7	−	90942.8i	−0.0574576	−	0.148715i
$783$			607471.i			0.990836i
$784$	58765.9	−	610114.i	0.0956078	−	0.992610i
$785$	49830.8			0.0808646
$786$	459538.	−	177547.i	0.743834	−	0.287388i
$787$	−537891.			−0.868449			−0.434225	−	0.900805i	$-0.642978\pi$
$787$	−537891.			−0.868449			−0.434225	+	0.900805i	$0.642978\pi$
$788$	−67592.7	−	74416.1i	−0.108855	−	0.119843i
$789$			328443.i			0.527601i
$790$	−61546.6	+	23779.2i	−0.0986166	+	0.0381016i
$791$		−	1478.08i		−	0.00236235i
$792$	6984.11	−	13931.0i	0.0111342	−	0.0222091i
$793$	−214267.			−0.340729
$794$	−273140.	−	706955.i	−0.433255	−	1.12138i
$795$	241421.			0.381980
$796$	223917.	+	246521.i	0.353396	+	0.389071i
$797$			839237.i			1.32120i	0.750739	+	0.660599i	$0.229698\pi$
$797$			839237.i			1.32120i	−0.750739	+	0.660599i	$0.770302\pi$
$798$	−8397.24	−	21734.2i	−0.0131865	−	0.0341301i
$799$			63096.6i			0.0988353i
$800$	34470.9	+	123271.i	0.0538607	+	0.192611i
$801$	−401295.			−0.625459
$802$	449081.	−	173507.i	0.698194	−	0.269755i
$803$	61129.2			0.0948021
$804$	−405500.	+	368319.i	−0.627305	+	0.569786i
$805$		−	24533.1i		−	0.0378583i
$806$	−243453.	+	94060.8i	−0.374753	+	0.144790i
$807$		−	619588.i		−	0.951384i
$808$	−409916.	−	205506.i	−0.627874	−	0.314776i
$809$	514568.			0.786223			0.393111	−	0.919491i	$-0.371399\pi$
$809$	514568.			0.786223			0.393111	+	0.919491i	$0.371399\pi$
$810$	−50699.9	−	131224.i	−0.0772747	−	0.200007i
$811$	174798.			0.265763			0.132881	−	0.991132i	$-0.457577\pi$
$811$	174798.			0.265763			0.132881	+	0.991132i	$0.457577\pi$
$812$	23527.4	−	21370.1i	0.0356830	−	0.0324112i
$813$		−	1.01077e6i		−	1.52922i
$814$	27943.2	+	72324.1i	0.0421723	+	0.109153i
$815$		−	21361.1i		−	0.0321594i
$816$	−5014.37	+	52059.7i	−0.00753071	+	0.0781846i
$817$	−740500.			−1.10938
$818$	561502.	−	216942.i	0.839160	−	0.324218i
$819$	4332.76			0.00645947
$820$	292680.	+	322226.i	0.435277	+	0.479217i
$821$			1.02886e6i			1.52641i	0.646159	+	0.763203i	$0.276374\pi$
$821$			1.02886e6i			1.52641i	−0.646159	+	0.763203i	$0.723626\pi$
$822$	−11274.9	+	4356.17i	−0.0166866	+	0.00644705i
$823$		−	54452.4i		−	0.0803928i	−0.999192	−	0.0401964i	$-0.987202\pi$
$823$		−	54452.4i		−	0.0803928i	0.999192	−	0.0401964i	$-0.0127984\pi$
$824$	458294.	+	229760.i	0.674979	+	0.338392i
$825$	7060.62			0.0103737
$826$	1699.95	+	4399.91i	0.00249159	+	0.00644887i
$827$	1.20898e6			1.76770			0.883848	−	0.467773i	$-0.154944\pi$
$827$	1.20898e6			1.76770			0.883848	+	0.467773i	$0.154944\pi$
$828$	−278828.	−	306975.i	−0.406701	−	0.447757i
$829$			366682.i			0.533556i	0.963758	+	0.266778i	$0.0859591\pi$
$829$			366682.i			0.533556i	−0.963758	+	0.266778i	$0.914041\pi$
$830$	110396.	+	285734.i	0.160250	+	0.414769i
$831$			537143.i			0.777836i
$832$	179353.	−	133917.i	0.259097	−	0.193458i
$833$	−68903.2			−0.0993001
$834$	−578591.	+	223545.i	−0.831839	+	0.321390i
$835$	−567566.			−0.814035
$836$	29844.6	−	27108.1i	0.0427025	−	0.0387870i
$837$		−	945980.i		−	1.35030i
$838$	1.07790e6	−	416459.i	1.53494	−	0.593041i
$839$		−	1.27074e6i		−	1.80523i	−0.430444	−	0.902617i	$-0.641643\pi$
$839$		−	1.27074e6i		−	1.80523i	0.430444	−	0.902617i	$-0.358357\pi$
$840$	−5898.23	+	11765.0i	−0.00835917	+	0.0166738i
$841$	119393.			0.168806
$842$	−262808.	−	680214.i	−0.370693	−	0.959448i
$843$	309315.			0.435257
$844$	251000.	−	227985.i	0.352362	−	0.320053i
$845$			285934.i			0.400454i
$846$	96726.0	+	250352.i	0.135146	+	0.349792i
$847$		−	37768.5i		−	0.0526457i
$848$	−775088.	−	74656.2i	−1.07785	−	0.103818i
$849$	476581.			0.661183
$850$	13422.1	−	5185.78i	0.0185773	−	0.00717755i
$851$	2.06330e6			2.84907
$852$	66802.1	+	73545.6i	0.0920260	+	0.101316i
$853$			927864.i			1.27522i	0.770358	+	0.637612i	$0.220077\pi$
$853$			927864.i			1.27522i	−0.770358	+	0.637612i	$0.779923\pi$
$854$	−37903.6	+	14644.4i	−0.0519714	+	0.0200797i
$855$			108359.i			0.148229i
$856$	−57466.2	+	114626.i	−0.0784269	+	0.156435i
$857$	155651.			0.211928			0.105964	−	0.994370i	$-0.466207\pi$
$857$	155651.			0.211928			0.105964	+	0.994370i	$0.466207\pi$
$858$	−4449.77	−	11517.1i	−0.00604454	−	0.0156448i
$859$	−1.04127e6			−1.41116			−0.705578	−	0.708632i	$-0.749313\pi$
$859$	−1.04127e6			−1.41116			−0.705578	+	0.708632i	$0.749313\pi$
$860$	281221.	+	309610.i	0.380234	+	0.418618i
$861$			44757.3i			0.0603751i
$862$	144873.	+	374967.i	0.194972	+	0.504637i
$863$		−	1.42220e6i		−	1.90959i	−0.297264	−	0.954795i	$-0.596074\pi$
$863$		−	1.42220e6i		−	1.90959i	0.297264	−	0.954795i	$-0.403926\pi$
$864$	218484.	+	781321.i	0.292680	+	1.04665i
$865$	473687.			0.633081
$866$	1.22440e6	−	473060.i	1.63263	−	0.630784i
$867$	−587045.			−0.780968
$868$	−36637.9	+	33278.5i	−0.0486285	+	0.0441697i
$869$		−	11739.0i		−	0.0155450i
$870$	227067.	−	87729.7i	0.299996	−	0.115907i
$871$		−	263551.i		−	0.347399i
$872$	1.16041e6	+	581758.i	1.52609	+	0.765084i
$873$	263287.			0.345463
$874$	−386678.	−	1.00082e6i	−0.506205	−	1.31019i
$875$	3620.81			0.00472922
$876$	−645965.	+	586735.i	−0.841784	+	0.764600i
$877$		−	577824.i		−	0.751271i	−0.926768	−	0.375635i	$-0.877424\pi$
$877$		−	577824.i		−	0.751271i	0.926768	−	0.375635i	$-0.122576\pi$
$878$	223810.	+	579278.i	0.290329	+	0.751446i
$879$		−	301405.i		−	0.390098i
$880$	−22668.3	−	2183.40i	−0.0292721	−	0.00281947i
$881$	−95874.2			−0.123524			−0.0617618	−	0.998091i	$-0.519672\pi$
$881$	−95874.2			−0.123524			−0.0617618	+	0.998091i	$0.519672\pi$
$882$	−273391.	+	105627.i	−0.351437	+	0.135781i
$883$	1.28768e6			1.65153			0.825765	−	0.564014i	$-0.190744\pi$
$883$	1.28768e6			1.65153			0.825765	+	0.564014i	$0.190744\pi$
$884$	−16917.9	−	18625.7i	−0.0216492	−	0.0238346i
$885$			36125.5i			0.0461240i
$886$	−1.26059e6	+	487042.i	−1.60585	+	0.620439i
$887$		−	1.17289e6i		−	1.49077i	−0.666633	−	0.745386i	$-0.732265\pi$
$887$		−	1.17289e6i		−	1.49077i	0.666633	−	0.745386i	$-0.267735\pi$
$888$	−989468.	−	496057.i	−1.25480	−	0.629079i
$889$	16497.3			0.0208741
$890$	211349.	+	547025.i	0.266821	+	0.690601i
$891$	25028.8			0.0315272
$892$	−503601.	−	554439.i	−0.632932	−	0.696825i
$893$			694374.i			0.870744i
$894$	−202071.	−	523012.i	−0.252831	−	0.654390i
$895$		−	580284.i		−	0.724427i
$896$	22574.6	−	35947.9i	0.0281193	−	0.0447772i
$897$	−328568.			−0.408357
$898$	−915903.	+	353869.i	−1.13579	+	0.438823i
$899$	915484.			1.13274
$900$	45306.0	−	41151.8i	0.0559333	−	0.0508047i
$901$			87534.6i			0.107828i
$902$	−72243.2	+	27911.9i	−0.0887940	+	0.0343065i
$903$			43005.0i			0.0527404i
$904$	−16363.6	+	32639.9i	−0.0200236	+	0.0399404i
$905$	−91417.5			−0.111617
$906$	290431.	+	751711.i	0.353824	+	0.915787i
$907$	410980.			0.499581			0.249791	−	0.968300i	$-0.419638\pi$
$907$	410980.			0.499581			0.249791	+	0.968300i	$0.419638\pi$
$908$	23613.4	−	21448.3i	0.0286409	−	0.0260148i
$909$			219261.i			0.265359i
$910$	−2281.92	−	5906.20i	−0.00275561	−	0.00713223i
$911$		−	67611.8i		−	0.0814678i	−0.999170	−	0.0407339i	$-0.987030\pi$
$911$		−	67611.8i		−	0.0814678i	0.999170	−	0.0407339i	$-0.0129696\pi$
$912$	−55182.8	+	572914.i	−0.0663459	+	0.688810i
$913$	−54498.9			−0.0653802
$914$	−429114.	+	165793.i	−0.513666	+	0.198460i
$915$	−311207.			−0.371713
$916$	490463.	+	539974.i	0.584542	+	0.643550i
$917$			44948.0i			0.0534529i
$918$	85072.6	−	32868.7i	0.100950	−	0.0390029i
$919$		−	423513.i		−	0.501459i	−0.968057	−	0.250729i	$-0.919330\pi$
$919$		−	423513.i		−	0.501459i	0.968057	−	0.250729i	$-0.0806705\pi$
$920$	−271603.	+	541757.i	−0.320892	+	0.640072i
$921$	−160301.			−0.188980
$922$	166440.	+	430790.i	0.195793	+	0.506762i
$923$	−47800.4			−0.0561084
$924$	−1574.32	−	1733.24i	−0.00184395	−	0.00203009i
$925$			304520.i			0.355903i
$926$	−444491.	−	1.15046e6i	−0.518371	−	1.34168i
$927$		−	245139.i		−	0.285268i
$928$	−756133.	+	211441.i	−0.878016	+	0.245524i
$929$	963117.			1.11596			0.557979	−	0.829855i	$-0.311577\pi$
$929$	963117.			1.11596			0.557979	+	0.829855i	$0.311577\pi$
$930$	−353599.	+	136617.i	−0.408832	+	0.157956i
$931$	−758276.			−0.874839
$932$	−974652.	+	885285.i	−1.12206	+	1.01918i
$933$			738989.i			0.848935i
$934$	−873671.	+	337552.i	−1.00151	+	0.386943i
$935$			2560.04i			0.00292836i
$936$	−95678.9	−	47967.4i	−0.109211	−	0.0547513i
$937$	−1.35035e6			−1.53804			−0.769019	−	0.639226i	$-0.779255\pi$
$937$	−1.35035e6			−1.53804			−0.769019	+	0.639226i	$0.779255\pi$
$938$	−18012.9	−	46621.9i	−0.0204728	−	0.0529889i
$939$	−596358.			−0.676357
$940$	290324.	−	263704.i	0.328570	−	0.298443i
$941$		−	651491.i		−	0.735748i	−0.929876	−	0.367874i	$-0.880086\pi$
$941$		−	651491.i		−	0.735748i	0.929876	−	0.367874i	$-0.119914\pi$
$942$	−45612.9	−	118058.i	−0.0514027	−	0.133043i
$943$			2.06099e6i			2.31768i
$944$	11171.3	−	115982.i	0.0125360	−	0.130150i
$945$	22949.6			0.0256987
$946$	−69414.7	+	26819.1i	−0.0775656	+	0.0299683i
$947$	−1.31859e6			−1.47032			−0.735158	−	0.677896i	$-0.762892\pi$
$947$	−1.31859e6			−1.47032			−0.735158	+	0.677896i	$0.762892\pi$
$948$	112674.	+	124048.i	0.125374	+	0.138030i
$949$		−	419840.i		−	0.466177i
$950$	147710.	−	57069.2i	0.163667	−	0.0632346i
$951$			375934.i			0.415671i
$952$	−4265.76	−	2138.58i	−0.00470677	−	0.00235968i
$953$	−76396.5			−0.0841178			−0.0420589	−	0.999115i	$-0.513392\pi$
$953$	−76396.5			−0.0841178			−0.0420589	+	0.999115i	$0.513392\pi$
$954$	134189.	+	347316.i	0.147442	+	0.381617i
$955$	−426468.			−0.467605
$956$	−1.12775e6	−	1.24160e6i	−1.23395	−	1.35852i
$957$			43309.2i			0.0472886i
$958$	253546.	+	656242.i	0.276265	+	0.715044i
$959$		−	1102.81i		−	0.00119912i
$960$	260497.	−	194504.i	0.282658	−	0.211051i
$961$	−502111.			−0.543692
$962$	496727.	−	191916.i	0.536744	−	0.207377i
$963$	61312.6			0.0661146
$964$	120170.	−	109151.i	0.129313	−	0.117456i
$965$		−	394612.i		−	0.423756i
$966$	−58123.2	+	22456.5i	−0.0622867	+	0.0240651i
$967$		−	462106.i		−	0.494184i	−0.968992	−	0.247092i	$-0.920525\pi$
$967$		−	462106.i		−	0.494184i	0.968992	−	0.247092i	$-0.0794749\pi$
$968$	−418130.	+	834029.i	−0.446232	+	0.890083i
$969$	64702.0			0.0689081
$970$	−138665.	−	358900.i	−0.147375	−	0.381443i
$971$	901828.			0.956501			0.478250	−	0.878223i	$-0.341271\pi$
$971$	901828.			0.956501			0.478250	+	0.878223i	$0.341271\pi$
$972$	495577.	−	450137.i	0.524540	−	0.476444i
$973$		−	56592.7i		−	0.0597771i
$974$	−416741.	−	1.07863e6i	−0.439287	−	1.13699i
$975$		−	48492.8i		−	0.0510115i
$976$	999139.	+	96236.6i	1.04888	+	0.101028i
$977$	46500.7			0.0487159			0.0243580	−	0.999703i	$-0.492246\pi$
$977$	46500.7			0.0487159			0.0243580	+	0.999703i	$0.492246\pi$
$978$	−50608.1	+	19553.0i	−0.0529106	+	0.0204426i
$979$	−104336.			−0.108860
$980$	287972.	+	317042.i	0.299846	+	0.330115i
$981$		−	620697.i		−	0.644973i
$982$	682110.	−	263540.i	0.707345	−	0.273290i
$983$			649309.i			0.671961i	0.941869	+	0.335981i	$0.109068\pi$
$983$			649309.i			0.671961i	−0.941869	+	0.335981i	$0.890932\pi$
$984$	495502.	−	988361.i	0.511747	−	1.02076i
$985$	70248.3			0.0724042
$986$	31809.1	+	82330.1i	0.0327188	+	0.0846846i
$987$	40326.2			0.0413955
$988$	−186180.	−	204975.i	−0.190730	−	0.209984i
$989$			1.98030e6i			2.02460i
$990$	3924.50	+	10157.6i	0.00400419	+	0.0103639i
$991$		−	194704.i		−	0.198257i	−0.995075	−	0.0991285i	$-0.968395\pi$
$991$		−	194704.i		−	0.198257i	0.995075	−	0.0991285i	$-0.0316055\pi$
$992$	1.17748e6	−	329265.i	1.19655	−	0.334597i
$993$	−438238.			−0.444439
$994$	−8455.83	+	3267.00i	−0.00855822	+	0.00330656i
$995$	−232715.			−0.235060
$996$	575902.	−	523096.i	0.580537	−	0.527306i
$997$		−	1.72172e6i		−	1.73210i	−0.499959	−	0.866049i	$-0.666652\pi$
$997$		−	1.72172e6i		−	1.73210i	0.499959	−	0.866049i	$-0.333348\pi$
$998$	1.73020e6	−	668481.i	1.73714	−	0.671163i
$999$			1.93012e6i			1.93398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.5.g.a.11.15	✓	16
3.2	odd	2		360.5.g.a.91.2		16
4.3	odd	2		160.5.g.a.111.6		16
5.2	odd	4		200.5.e.e.99.20		32
5.3	odd	4		200.5.e.e.99.13		32
5.4	even	2		200.5.g.h.51.2		16
8.3	odd	2	inner	40.5.g.a.11.16	yes	16
8.5	even	2		160.5.g.a.111.5		16
12.11	even	2		1440.5.g.a.271.5		16
20.3	even	4		800.5.e.e.399.17		32
20.7	even	4		800.5.e.e.399.16		32
20.19	odd	2		800.5.g.h.751.12		16
24.5	odd	2		1440.5.g.a.271.12		16
24.11	even	2		360.5.g.a.91.1		16
40.3	even	4		200.5.e.e.99.19		32
40.13	odd	4		800.5.e.e.399.15		32
40.19	odd	2		200.5.g.h.51.1		16
40.27	even	4		200.5.e.e.99.14		32
40.29	even	2		800.5.g.h.751.11		16
40.37	odd	4		800.5.e.e.399.18		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.5.g.a.11.15	✓	16	1.1	even	1	trivial
40.5.g.a.11.16	yes	16	8.3	odd	2	inner
160.5.g.a.111.5		16	8.5	even	2
160.5.g.a.111.6		16	4.3	odd	2
200.5.e.e.99.13		32	5.3	odd	4
200.5.e.e.99.14		32	40.27	even	4
200.5.e.e.99.19		32	40.3	even	4
200.5.e.e.99.20		32	5.2	odd	4
200.5.g.h.51.1		16	40.19	odd	2
200.5.g.h.51.2		16	5.4	even	2
360.5.g.a.91.1		16	24.11	even	2
360.5.g.a.91.2		16	3.2	odd	2
800.5.e.e.399.15		32	40.13	odd	4
800.5.e.e.399.16		32	20.7	even	4
800.5.e.e.399.17		32	20.3	even	4
800.5.e.e.399.18		32	40.37	odd	4
800.5.g.h.751.11		16	40.29	even	2
800.5.g.h.751.12		16	20.19	odd	2
1440.5.g.a.271.5		16	12.11	even	2
1440.5.g.a.271.12		16	24.5	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	40.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.73120 - 1.44159i) q^{2} +7.09911 q^{3} +(11.8437 - 10.7577i) q^{4} +11.1803i q^{5} +(26.4882 - 10.2340i) q^{6} +2.59084i q^{7} +(28.6828 - 57.2127i) q^{8} -30.6027 q^{9} +(16.1174 + 41.7160i) q^{10} -7.95663 q^{11} +(84.0793 - 76.3700i) q^{12} +54.6467i q^{13} +(3.73492 + 9.66694i) q^{14} +79.3704i q^{15} +(24.5442 - 254.821i) q^{16} -28.7782 q^{17} +(-114.185 + 44.1165i) q^{18} -316.702 q^{19} +(120.275 + 132.416i) q^{20} +18.3927i q^{21} +(-29.6878 + 11.4702i) q^{22} +846.949i q^{23} +(203.623 - 406.159i) q^{24} -125.000 q^{25} +(78.7780 + 203.898i) q^{26} -792.279 q^{27} +(27.8715 + 30.6850i) q^{28} -766.738i q^{29} +(114.419 + 296.147i) q^{30} +1194.00i q^{31} +(-275.767 - 986.169i) q^{32} -56.4850 q^{33} +(-107.377 + 41.4862i) q^{34} -28.9665 q^{35} +(-362.448 + 329.214i) q^{36} -2436.16i q^{37} +(-1181.68 + 456.554i) q^{38} +387.943i q^{39} +(639.658 + 320.684i) q^{40} +2433.43 q^{41} +(26.5146 + 68.6266i) q^{42} +2338.16 q^{43} +(-94.2356 + 85.5950i) q^{44} -342.149i q^{45} +(1220.95 + 3160.13i) q^{46} -2192.51i q^{47} +(174.242 - 1809.00i) q^{48} +2394.29 q^{49} +(-466.400 + 180.198i) q^{50} -204.299 q^{51} +(587.872 + 647.216i) q^{52} -3041.70i q^{53} +(-2956.15 + 1142.14i) q^{54} -88.9578i q^{55} +(148.229 + 74.3127i) q^{56} -2248.30 q^{57} +(-1105.32 - 2860.85i) q^{58} +455.150 q^{59} +(853.842 + 940.036i) q^{60} +3920.95i q^{61} +(1721.25 + 4455.04i) q^{62} -79.2868i q^{63} +(-2450.59 - 3282.05i) q^{64} -610.969 q^{65} +(-210.756 + 81.4280i) q^{66} -4822.82 q^{67} +(-340.839 + 309.587i) q^{68} +6012.58i q^{69} +(-108.080 + 41.7577i) q^{70} +874.716i q^{71} +(-877.773 + 1750.86i) q^{72} -7682.80 q^{73} +(-3511.93 - 9089.78i) q^{74} -887.388 q^{75} +(-3750.91 + 3406.98i) q^{76} -20.6144i q^{77} +(559.253 + 1447.49i) q^{78} +1475.37i q^{79} +(2848.98 + 274.413i) q^{80} -3145.66 q^{81} +(9079.62 - 3508.01i) q^{82} +6849.50 q^{83} +(197.863 + 217.836i) q^{84} -321.750i q^{85} +(8724.14 - 3370.66i) q^{86} -5443.16i q^{87} +(-228.219 + 455.220i) q^{88} +13113.1 q^{89} +(-493.237 - 1276.62i) q^{90} -141.581 q^{91} +(9111.21 + 10031.0i) q^{92} +8476.32i q^{93} +(-3160.70 - 8180.70i) q^{94} -3540.84i q^{95} +(-1957.70 - 7000.92i) q^{96} -8603.40 q^{97} +(8933.56 - 3451.57i) q^{98} +243.494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 8 q^{4} + 84 q^{6} - 216 q^{8} + 432 q^{9} - 50 q^{10} + 192 q^{11} + 260 q^{12} + 972 q^{14} - 824 q^{16} - 806 q^{18} - 704 q^{19} - 300 q^{20} - 1100 q^{22} - 1256 q^{24} - 2000 q^{25}+ \cdots + 2624 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 8 * q^4 + 84 * q^6 - 216 * q^8 + 432 * q^9 - 50 * q^10 + 192 * q^11 + 260 * q^12 + 972 * q^14 - 824 * q^16 - 806 * q^18 - 704 * q^19 - 300 * q^20 - 1100 * q^22 - 1256 * q^24 - 2000 * q^25 + 108 * q^26 + 3648 * q^27 - 940 * q^28 - 1400 * q^30 + 4104 * q^32 - 992 * q^33 + 924 * q^34 - 2400 * q^36 - 420 * q^38 + 2200 * q^40 - 2208 * q^41 + 7820 * q^42 + 5568 * q^43 + 3816 * q^44 - 652 * q^46 + 4520 * q^48 - 2480 * q^49 + 750 * q^50 - 17792 * q^51 - 4640 * q^52 + 6488 * q^54 - 12552 * q^56 + 8608 * q^57 + 1040 * q^58 + 14016 * q^59 - 3500 * q^60 + 12480 * q^62 - 3712 * q^64 - 13312 * q^66 - 18880 * q^67 + 12360 * q^68 - 1800 * q^70 - 16456 * q^72 - 7360 * q^73 - 11508 * q^74 + 9312 * q^76 - 26760 * q^78 - 2400 * q^80 + 10384 * q^81 - 16640 * q^82 + 10560 * q^83 - 12520 * q^84 + 25764 * q^86 + 41200 * q^88 + 6816 * q^89 + 8550 * q^90 + 24576 * q^91 + 30420 * q^92 - 28388 * q^94 + 6784 * q^96 + 448 * q^97 + 23934 * q^98 + 2624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more