LMFDB - Embedded newform 35.5.c.c.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(34,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("35.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 6 $ x^2 + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.2
Root			$2.44949i$ of defining polynomial
Character	$\chi$	$=$	35.34
Dual form			35.5.c.c.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.44949i q^{2} -5.00000 q^{3} +10.0000 q^{4} +(-5.00000 + 24.4949i) q^{5} -12.2474i q^{6} +(-35.0000 + 34.2929i) q^{7} +63.6867i q^{8} -56.0000 q^{9} +O(q^{10})$	\(q+2.44949i q^{2} -5.00000 q^{3} +10.0000 q^{4} +(-5.00000 + 24.4949i) q^{5} -12.2474i q^{6} +(-35.0000 + 34.2929i) q^{7} +63.6867i q^{8} -56.0000 q^{9} +(-60.0000 - 12.2474i) q^{10} +89.0000 q^{11} -50.0000 q^{12} +5.00000 q^{13} +(-84.0000 - 85.7321i) q^{14} +(25.0000 - 122.474i) q^{15} +4.00000 q^{16} +485.000 q^{17} -137.171i q^{18} +220.454i q^{19} +(-50.0000 + 244.949i) q^{20} +(175.000 - 171.464i) q^{21} +218.005i q^{22} -700.554i q^{23} -318.434i q^{24} +(-575.000 - 244.949i) q^{25} +12.2474i q^{26} +685.000 q^{27} +(-350.000 + 342.929i) q^{28} +191.000 q^{29} +(300.000 + 61.2372i) q^{30} -1053.28i q^{31} +1028.79i q^{32} -445.000 q^{33} +1188.00i q^{34} +(-665.000 - 1028.79i) q^{35} -560.000 q^{36} +1631.36i q^{37} -540.000 q^{38} -25.0000 q^{39} +(-1560.00 - 318.434i) q^{40} +2914.89i q^{41} +(420.000 + 428.661i) q^{42} +377.221i q^{43} +890.000 q^{44} +(280.000 - 1371.71i) q^{45} +1716.00 q^{46} +2195.00 q^{47} -20.0000 q^{48} +(49.0000 - 2400.50i) q^{49} +(600.000 - 1408.46i) q^{50} -2425.00 q^{51} +50.0000 q^{52} -1587.27i q^{53} +1677.90i q^{54} +(-445.000 + 2180.05i) q^{55} +(-2184.00 - 2229.04i) q^{56} -1102.27i q^{57} +467.853i q^{58} -3625.24i q^{59} +(250.000 - 1224.74i) q^{60} +1935.10i q^{61} +2580.00 q^{62} +(1960.00 - 1920.40i) q^{63} -2456.00 q^{64} +(-25.0000 + 122.474i) q^{65} -1090.02i q^{66} +2047.77i q^{67} +4850.00 q^{68} +3502.77i q^{69} +(2520.00 - 1628.91i) q^{70} +4454.00 q^{71} -3566.46i q^{72} -8650.00 q^{73} -3996.00 q^{74} +(2875.00 + 1224.74i) q^{75} +2204.54i q^{76} +(-3115.00 + 3052.06i) q^{77} -61.2372i q^{78} +5561.00 q^{79} +(-20.0000 + 97.9796i) q^{80} +1111.00 q^{81} -7140.00 q^{82} -1990.00 q^{83} +(1750.00 - 1714.64i) q^{84} +(-2425.00 + 11880.0i) q^{85} -924.000 q^{86} -955.000 q^{87} +5668.12i q^{88} -808.332i q^{89} +(3360.00 + 685.857i) q^{90} +(-175.000 + 171.464i) q^{91} -7005.54i q^{92} +5266.40i q^{93} +5376.63i q^{94} +(-5400.00 - 1102.27i) q^{95} -5143.93i q^{96} -9235.00 q^{97} +(5880.00 + 120.025i) q^{98} -4984.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 10 q^{3} + 20 q^{4} - 10 q^{5} - 70 q^{7} - 112 q^{9}+O(q^{10}) $ 2 * q - 10 * q^3 + 20 * q^4 - 10 * q^5 - 70 * q^7 - 112 * q^9	$ 2 q - 10 q^{3} + 20 q^{4} - 10 q^{5} - 70 q^{7} - 112 q^{9} - 120 q^{10} + 178 q^{11} - 100 q^{12} + 10 q^{13} - 168 q^{14} + 50 q^{15} + 8 q^{16} + 970 q^{17} - 100 q^{20} + 350 q^{21} - 1150 q^{25} + 1370 q^{27} - 700 q^{28} + 382 q^{29} + 600 q^{30} - 890 q^{33} - 1330 q^{35} - 1120 q^{36} - 1080 q^{38} - 50 q^{39} - 3120 q^{40} + 840 q^{42} + 1780 q^{44} + 560 q^{45} + 3432 q^{46} + 4390 q^{47} - 40 q^{48} + 98 q^{49} + 1200 q^{50} - 4850 q^{51} + 100 q^{52} - 890 q^{55} - 4368 q^{56} + 500 q^{60} + 5160 q^{62} + 3920 q^{63} - 4912 q^{64} - 50 q^{65} + 9700 q^{68} + 5040 q^{70} + 8908 q^{71} - 17300 q^{73} - 7992 q^{74} + 5750 q^{75} - 6230 q^{77} + 11122 q^{79} - 40 q^{80} + 2222 q^{81} - 14280 q^{82} - 3980 q^{83} + 3500 q^{84} - 4850 q^{85} - 1848 q^{86} - 1910 q^{87} + 6720 q^{90} - 350 q^{91} - 10800 q^{95} - 18470 q^{97} + 11760 q^{98} - 9968 q^{99}+O(q^{100}) $ 2 * q - 10 * q^3 + 20 * q^4 - 10 * q^5 - 70 * q^7 - 112 * q^9 - 120 * q^10 + 178 * q^11 - 100 * q^12 + 10 * q^13 - 168 * q^14 + 50 * q^15 + 8 * q^16 + 970 * q^17 - 100 * q^20 + 350 * q^21 - 1150 * q^25 + 1370 * q^27 - 700 * q^28 + 382 * q^29 + 600 * q^30 - 890 * q^33 - 1330 * q^35 - 1120 * q^36 - 1080 * q^38 - 50 * q^39 - 3120 * q^40 + 840 * q^42 + 1780 * q^44 + 560 * q^45 + 3432 * q^46 + 4390 * q^47 - 40 * q^48 + 98 * q^49 + 1200 * q^50 - 4850 * q^51 + 100 * q^52 - 890 * q^55 - 4368 * q^56 + 500 * q^60 + 5160 * q^62 + 3920 * q^63 - 4912 * q^64 - 50 * q^65 + 9700 * q^68 + 5040 * q^70 + 8908 * q^71 - 17300 * q^73 - 7992 * q^74 + 5750 * q^75 - 6230 * q^77 + 11122 * q^79 - 40 * q^80 + 2222 * q^81 - 14280 * q^82 - 3980 * q^83 + 3500 * q^84 - 4850 * q^85 - 1848 * q^86 - 1910 * q^87 + 6720 * q^90 - 350 * q^91 - 10800 * q^95 - 18470 * q^97 + 11760 * q^98 - 9968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.44949i			0.612372i	0.951972	+	0.306186i	$0.0990530\pi$
$2$			2.44949i			0.612372i	−0.951972	+	0.306186i	$0.900947\pi$
$3$	−5.00000			−0.555556			−0.277778	−	0.960645i	$-0.589598\pi$
$3$	−5.00000			−0.555556			−0.277778	+	0.960645i	$0.589598\pi$
$4$	10.0000			0.625000
$5$	−5.00000	+	24.4949i	−0.200000	+	0.979796i
$5$	−5.00000	+	24.4949i	−0.200000	+	0.979796i
$6$		−	12.2474i		−	0.340207i
$7$	−35.0000	+	34.2929i	−0.714286	+	0.699854i
$7$	−35.0000	+	34.2929i	−0.714286	+	0.699854i
$8$			63.6867i			0.995105i
$9$	−56.0000			−0.691358
$10$	−60.0000	−	12.2474i	−0.600000	−	0.122474i
$11$	89.0000			0.735537			0.367769	−	0.929917i	$-0.380122\pi$
$11$	89.0000			0.735537			0.367769	+	0.929917i	$0.380122\pi$
$12$	−50.0000			−0.347222
$13$	5.00000			0.0295858			0.0147929	−	0.999891i	$-0.495291\pi$
$13$	5.00000			0.0295858			0.0147929	+	0.999891i	$0.495291\pi$
$14$	−84.0000	−	85.7321i	−0.428571	−	0.437409i
$15$	25.0000	−	122.474i	0.111111	−	0.544331i
$16$	4.00000			0.0156250
$17$	485.000			1.67820			0.839100	−	0.543977i	$-0.183082\pi$
$17$	485.000			1.67820			0.839100	+	0.543977i	$0.183082\pi$
$18$		−	137.171i		−	0.423369i
$19$			220.454i			0.610676i	0.952244	+	0.305338i	$0.0987695\pi$
$19$			220.454i			0.610676i	−0.952244	+	0.305338i	$0.901231\pi$
$20$	−50.0000	+	244.949i	−0.125000	+	0.612372i
$21$	175.000	−	171.464i	0.396825	−	0.388808i
$22$			218.005i			0.450423i
$23$		−	700.554i		−	1.32430i	−0.749372	−	0.662149i	$-0.769644\pi$
$23$		−	700.554i		−	1.32430i	0.749372	−	0.662149i	$-0.230356\pi$
$24$		−	318.434i		−	0.552836i
$25$	−575.000	−	244.949i	−0.920000	−	0.391918i
$26$			12.2474i			0.0181175i
$27$	685.000			0.939643
$28$	−350.000	+	342.929i	−0.446429	+	0.437409i
$29$	191.000			0.227111			0.113555	−	0.993532i	$-0.463776\pi$
$29$	191.000			0.227111			0.113555	+	0.993532i	$0.463776\pi$
$30$	300.000	+	61.2372i	0.333333	+	0.0680414i
$31$		−	1053.28i		−	1.09603i	−0.836470	−	0.548013i	$-0.815385\pi$
$31$		−	1053.28i		−	1.09603i	0.836470	−	0.548013i	$-0.184615\pi$
$32$			1028.79i			1.00467i
$33$	−445.000			−0.408632
$34$			1188.00i			1.02768i
$35$	−665.000	−	1028.79i	−0.542857	−	0.839825i
$36$	−560.000			−0.432099
$37$			1631.36i			1.19164i	0.803117	+	0.595822i	$0.203174\pi$
$37$			1631.36i			1.19164i	−0.803117	+	0.595822i	$0.796826\pi$
$38$	−540.000			−0.373961
$39$	−25.0000			−0.0164366
$40$	−1560.00	−	318.434i	−0.975000	−	0.199021i
$41$			2914.89i			1.73402i	0.498288	+	0.867012i	$0.333962\pi$
$41$			2914.89i			1.73402i	−0.498288	+	0.867012i	$0.666038\pi$
$42$	420.000	+	428.661i	0.238095	+	0.243005i
$43$			377.221i			0.204014i	0.994784	+	0.102007i	$0.0325264\pi$
$43$			377.221i			0.204014i	−0.994784	+	0.102007i	$0.967474\pi$
$44$	890.000			0.459711
$45$	280.000	−	1371.71i	0.138272	−	0.677390i
$46$	1716.00			0.810964
$47$	2195.00			0.993662			0.496831	−	0.867847i	$-0.334497\pi$
$47$	2195.00			0.993662			0.496831	+	0.867847i	$0.334497\pi$
$48$	−20.0000			−0.00868056
$49$	49.0000	−	2400.50i	0.0204082	−	0.999792i
$50$	600.000	−	1408.46i	0.240000	−	0.563383i
$51$	−2425.00			−0.932334
$52$	50.0000			0.0184911
$53$		−	1587.27i		−	0.565066i	−0.959258	−	0.282533i	$-0.908825\pi$
$53$		−	1587.27i		−	0.565066i	0.959258	−	0.282533i	$-0.0911746\pi$
$54$			1677.90i			0.575412i
$55$	−445.000	+	2180.05i	−0.147107	+	0.720676i
$56$	−2184.00	−	2229.04i	−0.696429	−	0.710789i
$57$		−	1102.27i		−	0.339265i
$58$			467.853i			0.139076i
$59$		−	3625.24i		−	1.04144i	−0.853728	−	0.520719i	$-0.825664\pi$
$59$		−	3625.24i		−	1.04144i	0.853728	−	0.520719i	$-0.174336\pi$
$60$	250.000	−	1224.74i	0.0694444	−	0.340207i
$61$			1935.10i			0.520048i	0.965602	+	0.260024i	$0.0837304\pi$
$61$			1935.10i			0.520048i	−0.965602	+	0.260024i	$0.916270\pi$
$62$	2580.00			0.671176
$63$	1960.00	−	1920.40i	0.493827	−	0.483850i
$64$	−2456.00			−0.599609
$65$	−25.0000	+	122.474i	−0.00591716	+	0.0289880i
$66$		−	1090.02i		−	0.250235i
$67$			2047.77i			0.456176i	0.973641	+	0.228088i	$0.0732474\pi$
$67$			2047.77i			0.456176i	−0.973641	+	0.228088i	$0.926753\pi$
$68$	4850.00			1.04888
$69$			3502.77i			0.735722i
$70$	2520.00	−	1628.91i	0.514286	−	0.332431i
$71$	4454.00			0.883555			0.441777	−	0.897125i	$-0.354348\pi$
$71$	4454.00			0.883555			0.441777	+	0.897125i	$0.354348\pi$
$72$		−	3566.46i		−	0.687974i
$73$	−8650.00			−1.62319			−0.811597	−	0.584218i	$-0.801401\pi$
$73$	−8650.00			−1.62319			−0.811597	+	0.584218i	$0.801401\pi$
$74$	−3996.00			−0.729730
$75$	2875.00	+	1224.74i	0.511111	+	0.217732i
$76$			2204.54i			0.381673i
$77$	−3115.00	+	3052.06i	−0.525384	+	0.514769i
$78$		−	61.2372i		−	0.0100653i
$79$	5561.00			0.891043			0.445522	−	0.895271i	$-0.353018\pi$
$79$	5561.00			0.891043			0.445522	+	0.895271i	$0.353018\pi$
$80$	−20.0000	+	97.9796i	−0.00312500	+	0.0153093i
$81$	1111.00			0.169334
$82$	−7140.00			−1.06187
$83$	−1990.00			−0.288866			−0.144433	−	0.989515i	$-0.546136\pi$
$83$	−1990.00			−0.288866			−0.144433	+	0.989515i	$0.546136\pi$
$84$	1750.00	−	1714.64i	0.248016	−	0.243005i
$85$	−2425.00	+	11880.0i	−0.335640	+	1.64429i
$86$	−924.000			−0.124932
$87$	−955.000			−0.126173
$88$			5668.12i			0.731937i
$89$		−	808.332i		−	0.102049i	−0.998697	−	0.0510246i	$-0.983751\pi$
$89$		−	808.332i		−	0.102049i	0.998697	−	0.0510246i	$-0.0162487\pi$
$90$	3360.00	+	685.857i	0.414815	+	0.0846737i
$91$	−175.000	+	171.464i	−0.0211327	+	0.0207057i
$92$		−	7005.54i		−	0.827687i
$93$			5266.40i			0.608903i
$94$			5376.63i			0.608491i
$95$	−5400.00	−	1102.27i	−0.598338	−	0.122135i
$96$		−	5143.93i		−	0.558152i
$97$	−9235.00			−0.981507			−0.490754	−	0.871298i	$-0.663278\pi$
$97$	−9235.00			−0.981507			−0.490754	+	0.871298i	$0.663278\pi$
$98$	5880.00	+	120.025i	0.612245	+	0.0124974i
$99$	−4984.00			−0.508520
$100$	−5750.00	−	2449.49i	−0.575000	−	0.244949i
$101$		−	4825.49i		−	0.473041i	−0.971626	−	0.236521i	$-0.923993\pi$
$101$		−	4825.49i		−	0.473041i	0.971626	−	0.236521i	$-0.0760071\pi$
$102$		−	5940.01i		−	0.570935i
$103$	4715.00			0.444434			0.222217	−	0.974997i	$-0.428671\pi$
$103$	4715.00			0.444434			0.222217	+	0.974997i	$0.428671\pi$
$104$			318.434i			0.0294410i
$105$	3325.00	+	5143.93i	0.301587	+	0.466569i
$106$	3888.00			0.346031
$107$		−	12668.8i		−	1.10654i	−0.833002	−	0.553269i	$-0.813380\pi$
$107$		−	12668.8i		−	1.10654i	0.833002	−	0.553269i	$-0.186620\pi$
$108$	6850.00			0.587277
$109$	12311.0			1.03619			0.518096	−	0.855322i	$-0.326641\pi$
$109$	12311.0			1.03619			0.518096	+	0.855322i	$0.326641\pi$
$110$	−5340.00	−	1090.02i	−0.441322	−	0.0900845i
$111$		−	8156.80i		−	0.662024i
$112$	−140.000	+	137.171i	−0.0111607	+	0.0109352i
$113$			3120.65i			0.244393i	0.992506	+	0.122196i	$0.0389938\pi$
$113$			3120.65i			0.244393i	−0.992506	+	0.122196i	$0.961006\pi$
$114$	2700.00			0.207756
$115$	17160.0	+	3502.77i	1.29754	+	0.264860i
$116$	1910.00			0.141944
$117$	−280.000			−0.0204544
$118$	8880.00			0.637748
$119$	−16975.0	+	16632.0i	−1.19871	+	1.17450i
$120$	7800.00	+	1592.17i	0.541667	+	0.110567i
$121$	−6720.00			−0.458985
$122$	−4740.00			−0.318463
$123$		−	14574.5i		−	0.963346i
$124$		−	10532.8i		−	0.685016i
$125$	8875.00	−	12859.8i	0.568000	−	0.823029i
$126$	4704.00	+	4801.00i	0.296296	+	0.302406i
$127$		−	23867.8i		−	1.47981i	−0.672712	−	0.739904i	$-0.734871\pi$
$127$		−	23867.8i		−	1.47981i	0.672712	−	0.739904i	$-0.265129\pi$
$128$			10444.6i			0.637489i
$129$		−	1886.11i		−	0.113341i
$130$	−300.000	−	61.2372i	−0.0177515	−	0.00362351i
$131$			6736.10i			0.392524i	0.980552	+	0.196262i	$0.0628802\pi$
$131$			6736.10i			0.392524i	−0.980552	+	0.196262i	$0.937120\pi$
$132$	−4450.00			−0.255395
$133$	−7560.00	−	7715.89i	−0.427384	−	0.436197i
$134$	−5016.00			−0.279350
$135$	−3425.00	+	16779.0i	−0.187929	+	0.920659i
$136$			30888.1i			1.66999i
$137$			23069.3i			1.22912i	0.788871	+	0.614558i	$0.210666\pi$
$137$			23069.3i			1.22912i	−0.788871	+	0.614558i	$0.789334\pi$
$138$	−8580.00			−0.450536
$139$		−	29491.9i		−	1.52641i	−0.646154	−	0.763207i	$-0.723624\pi$
$139$		−	29491.9i		−	1.52641i	0.646154	−	0.763207i	$-0.276376\pi$
$140$	−6650.00	−	10287.9i	−0.339286	−	0.524891i
$141$	−10975.0			−0.552035
$142$			10910.0i			0.541065i
$143$	445.000			0.0217615
$144$	−224.000			−0.0108025
$145$	−955.000	+	4678.53i	−0.0454221	+	0.222522i
$146$		−	21188.1i		−	0.993999i
$147$	−245.000	+	12002.5i	−0.0113379	+	0.555440i
$148$			16313.6i			0.744777i
$149$	28346.0			1.27679			0.638395	−	0.769709i	$-0.279599\pi$
$149$	28346.0			1.27679			0.638395	+	0.769709i	$0.279599\pi$
$150$	−3000.00	+	7042.28i	−0.133333	+	0.312990i
$151$	−17551.0			−0.769747			−0.384873	−	0.922969i	$-0.625755\pi$
$151$	−17551.0			−0.769747			−0.384873	+	0.922969i	$0.625755\pi$
$152$	−14040.0			−0.607687
$153$	−27160.0			−1.16024
$154$	−7476.00	−	7630.16i	−0.315230	−	0.321731i
$155$	25800.0	+	5266.40i	1.07388	+	0.219205i
$156$	−250.000			−0.0102728
$157$	25790.0			1.04629			0.523145	−	0.852244i	$-0.324759\pi$
$157$	25790.0			1.04629			0.523145	+	0.852244i	$0.324759\pi$
$158$			13621.6i			0.545650i
$159$			7936.35i			0.313925i
$160$	−25200.0	−	5143.93i	−0.984375	−	0.200935i
$161$	24024.0	+	24519.4i	0.926816	+	0.945928i
$162$			2721.38i			0.103695i
$163$		−	37153.9i		−	1.39839i	−0.714930	−	0.699196i	$-0.753542\pi$
$163$		−	37153.9i		−	1.39839i	0.714930	−	0.699196i	$-0.246458\pi$
$164$			29148.9i			1.08376i
$165$	2225.00	−	10900.2i	0.0817264	−	0.400376i
$166$		−	4874.48i		−	0.176894i
$167$	20795.0			0.745634			0.372817	−	0.927905i	$-0.378392\pi$
$167$	20795.0			0.745634			0.372817	+	0.927905i	$0.378392\pi$
$168$	10920.0	+	11145.2i	0.386905	+	0.394883i
$169$	−28536.0			−0.999125
$170$	−29100.0	−	5940.01i	−1.00692	−	0.205537i
$171$		−	12345.4i		−	0.422196i
$172$			3772.21i			0.127509i
$173$	−115.000			−0.00384243			−0.00192121	−	0.999998i	$-0.500612\pi$
$173$	−115.000			−0.00384243			−0.00192121	+	0.999998i	$0.500612\pi$
$174$		−	2339.26i		−	0.0772646i
$175$	28525.0	−	11145.2i	0.931429	−	0.363924i
$176$	356.000			0.0114928
$177$			18126.2i			0.578577i
$178$	1980.00			0.0624921
$179$	5318.00			0.165975			0.0829874	−	0.996551i	$-0.473554\pi$
$179$	5318.00			0.165975			0.0829874	+	0.996551i	$0.473554\pi$
$180$	2800.00	−	13717.1i	0.0864198	−	0.423369i
$181$		−	12345.4i		−	0.376833i	−0.982089	−	0.188417i	$-0.939665\pi$
$181$		−	12345.4i		−	0.376833i	0.982089	−	0.188417i	$-0.0603355\pi$
$182$	−420.000	−	428.661i	−0.0126796	−	0.0129411i
$183$		−	9675.48i		−	0.288915i
$184$	44616.0			1.31782
$185$	−39960.0	−	8156.80i	−1.16757	−	0.238329i
$186$	−12900.0			−0.372875
$187$	43165.0			1.23438
$188$	21950.0			0.621039
$189$	−23975.0	+	23490.6i	−0.671174	+	0.657613i
$190$	2700.00	−	13227.2i	0.0747922	−	0.366406i
$191$	−14263.0			−0.390971			−0.195485	−	0.980707i	$-0.562628\pi$
$191$	−14263.0			−0.390971			−0.195485	+	0.980707i	$0.562628\pi$
$192$	12280.0			0.333116
$193$		−	32005.0i		−	0.859219i	−0.903015	−	0.429609i	$-0.858651\pi$
$193$		−	32005.0i		−	0.859219i	0.903015	−	0.429609i	$-0.141349\pi$
$194$		−	22621.0i		−	0.601048i
$195$	125.000	−	612.372i	0.00328731	−	0.0161045i
$196$	490.000	−	24005.0i	0.0127551	−	0.624870i
$197$			3394.99i			0.0874795i	0.999043	+	0.0437398i	$0.0139272\pi$
$197$			3394.99i			0.0874795i	−0.999043	+	0.0437398i	$0.986073\pi$
$198$		−	12208.3i		−	0.311403i
$199$		−	19400.0i		−	0.489886i	−0.969538	−	0.244943i	$-0.921231\pi$
$199$		−	19400.0i		−	0.489886i	0.969538	−	0.244943i	$-0.0787692\pi$
$200$	15600.0	−	36619.9i	0.390000	−	0.915497i
$201$		−	10238.9i		−	0.253431i
$202$	11820.0			0.289677
$203$	−6685.00	+	6549.94i	−0.162222	+	0.158944i
$204$	−24250.0			−0.582709
$205$	−71400.0	−	14574.5i	−1.69899	−	0.346805i
$206$			11549.3i			0.272159i
$207$			39231.0i			0.915565i
$208$	20.0000			0.000462278
$209$			19620.4i			0.449175i
$210$	−12600.0	+	8144.55i	−0.285714	+	0.184684i
$211$	52817.0			1.18634			0.593170	−	0.805078i	$-0.297876\pi$
$211$	52817.0			1.18634			0.593170	+	0.805078i	$0.297876\pi$
$212$		−	15872.7i		−	0.353166i
$213$	−22270.0			−0.490864
$214$	31032.0			0.677614
$215$	−9240.00	−	1886.11i	−0.199892	−	0.0408027i
$216$			43625.4i			0.935044i
$217$	36120.0	+	36864.8i	0.767058	+	0.782875i
$218$			30155.7i			0.634536i
$219$	43250.0			0.901774
$220$	−4450.00	+	21800.5i	−0.0919421	+	0.450423i
$221$	2425.00			0.0496509
$222$	19980.0			0.405405
$223$	−13645.0			−0.274387			−0.137194	−	0.990544i	$-0.543808\pi$
$223$	−13645.0			−0.274387			−0.137194	+	0.990544i	$0.543808\pi$
$224$	−35280.0	−	36007.5i	−0.703125	−	0.717624i
$225$	32200.0	+	13717.1i	0.636049	+	0.270956i
$226$	−7644.00			−0.149659
$227$	−74485.0			−1.44550			−0.722748	−	0.691111i	$-0.757121\pi$
$227$	−74485.0			−1.44550			−0.722748	+	0.691111i	$0.757121\pi$
$228$		−	11022.7i		−	0.212040i
$229$			68463.2i			1.30553i	0.757561	+	0.652764i	$0.226391\pi$
$229$			68463.2i			1.30553i	−0.757561	+	0.652764i	$0.773609\pi$
$230$	−8580.00	+	42033.2i	−0.162193	+	0.794579i
$231$	15575.0	−	15260.3i	0.291880	−	0.285983i
$232$			12164.2i			0.225999i
$233$			60169.3i			1.10831i	0.832412	+	0.554157i	$0.186959\pi$
$233$			60169.3i			1.10831i	−0.832412	+	0.554157i	$0.813041\pi$
$234$		−	685.857i		−	0.0125257i
$235$	−10975.0	+	53766.3i	−0.198732	+	0.973586i
$236$		−	36252.4i		−	0.650899i
$237$	−27805.0			−0.495024
$238$	−40740.0	−	41580.1i	−0.719229	−	0.734060i
$239$	−75367.0			−1.31943			−0.659714	−	0.751517i	$-0.729322\pi$
$239$	−75367.0			−1.31943			−0.659714	+	0.751517i	$0.729322\pi$
$240$	100.000	−	489.898i	0.00173611	−	0.00850517i
$241$		−	77869.3i		−	1.34070i	−0.742044	−	0.670351i	$-0.766144\pi$
$241$		−	77869.3i		−	1.34070i	0.742044	−	0.670351i	$-0.233856\pi$
$242$		−	16460.6i		−	0.281070i
$243$	−61040.0			−1.03372
$244$			19351.0i			0.325030i
$245$	58555.0	+	13202.7i	0.975510	+	0.219954i
$246$	35700.0			0.589927
$247$			1102.27i			0.0180673i
$248$	67080.0			1.09066
$249$	9950.00			0.160481
$250$	31500.0	+	21739.2i	0.504000	+	0.347828i
$251$			50410.5i			0.800154i	0.916482	+	0.400077i	$0.131017\pi$
$251$			50410.5i			0.800154i	−0.916482	+	0.400077i	$0.868983\pi$
$252$	19600.0	−	19204.0i	0.308642	−	0.302406i
$253$		−	62349.3i		−	0.974071i
$254$	58464.0			0.906194
$255$	12125.0	−	59400.1i	0.186467	−	0.913497i
$256$	−64880.0			−0.989990
$257$	−3370.00			−0.0510227			−0.0255114	−	0.999675i	$-0.508121\pi$
$257$	−3370.00			−0.0510227			−0.0255114	+	0.999675i	$0.508121\pi$
$258$	4620.00			0.0694069
$259$	−55944.0	−	57097.6i	−0.833977	−	0.851174i
$260$	−250.000	+	1224.74i	−0.00369822	+	0.0181175i
$261$	−10696.0			−0.157015
$262$	−16500.0			−0.240371
$263$			59385.4i			0.858556i	0.903173	+	0.429278i	$0.141232\pi$
$263$			59385.4i			0.858556i	−0.903173	+	0.429278i	$0.858768\pi$
$264$		−	28340.6i		−	0.406632i
$265$	38880.0	+	7936.35i	0.553649	+	0.113013i
$266$	18900.0	−	18518.1i	0.267115	−	0.261718i
$267$			4041.66i			0.0566940i
$268$			20477.7i			0.285110i
$269$		−	77012.0i		−	1.06427i	−0.846658	−	0.532137i	$-0.821389\pi$
$269$		−	77012.0i		−	1.06427i	0.846658	−	0.532137i	$-0.178611\pi$
$270$	−41100.0	−	8389.50i	−0.563786	−	0.115082i
$271$			143222.i			1.95016i	0.221855	+	0.975080i	$0.428789\pi$
$271$			143222.i			1.95016i	−0.221855	+	0.975080i	$0.571211\pi$
$272$	1940.00			0.0262219
$273$	875.000	−	857.321i	0.0117404	−	0.0115032i
$274$	−56508.0			−0.752677
$275$	−51175.0	−	21800.5i	−0.676694	−	0.288271i
$276$			35027.7i			0.459826i
$277$		−	101928.i		−	1.32842i	−0.747547	−	0.664209i	$-0.768769\pi$
$277$		−	101928.i		−	1.32842i	0.747547	−	0.664209i	$-0.231231\pi$
$278$	72240.0			0.934734
$279$			58983.7i			0.757746i
$280$	65520.0	−	42351.7i	0.835714	−	0.540200i
$281$	−47521.0			−0.601829			−0.300914	−	0.953651i	$-0.597292\pi$
$281$	−47521.0			−0.601829			−0.300914	+	0.953651i	$0.597292\pi$
$282$		−	26883.1i		−	0.338051i
$283$	43115.0			0.538339			0.269169	−	0.963093i	$-0.413251\pi$
$283$	43115.0			0.538339			0.269169	+	0.963093i	$0.413251\pi$
$284$	44540.0			0.552222
$285$	27000.0	+	5511.35i	0.332410	+	0.0678529i
$286$			1090.02i			0.0133261i
$287$	−99960.0	−	102021.i	−1.21356	−	1.23859i
$288$		−	57612.0i		−	0.694589i
$289$	151704.			1.81636
$290$	−11460.0	−	2339.26i	−0.136266	−	0.0278153i
$291$	46175.0			0.545282
$292$	−86500.0			−1.01450
$293$	162125.			1.88849			0.944245	−	0.329243i	$-0.106794\pi$
$293$	162125.			1.88849			0.944245	+	0.329243i	$0.106794\pi$
$294$	−29400.0	−	600.125i	−0.340136	−	0.00694300i
$295$	88800.0	+	18126.2i	1.02040	+	0.208288i
$296$	−103896.			−1.18581
$297$	60965.0			0.691143
$298$			69433.2i			0.781871i
$299$		−	3502.77i		−	0.0391804i
$300$	28750.0	+	12247.4i	0.319444	+	0.136083i
$301$	−12936.0	−	13202.7i	−0.142780	−	0.145724i
$302$		−	42991.0i		−	0.471372i
$303$			24127.5i			0.262801i
$304$			881.816i			0.00954181i
$305$	−47400.0	−	9675.48i	−0.509540	−	0.104010i
$306$		−	66528.1i		−	0.710497i
$307$	−33805.0			−0.358678			−0.179339	−	0.983787i	$-0.557396\pi$
$307$	−33805.0			−0.358678			−0.179339	+	0.983787i	$0.557396\pi$
$308$	−31150.0	+	30520.6i	−0.328365	+	0.321731i
$309$	−23575.0			−0.246908
$310$	−12900.0	+	63196.8i	−0.134235	+	0.657615i
$311$		−	50435.0i		−	0.521448i	−0.965413	−	0.260724i	$-0.916039\pi$
$311$		−	50435.0i		−	0.521448i	0.965413	−	0.260724i	$-0.0839613\pi$
$312$		−	1592.17i		−	0.0163561i
$313$	−68155.0			−0.695679			−0.347840	−	0.937554i	$-0.613085\pi$
$313$	−68155.0			−0.695679			−0.347840	+	0.937554i	$0.613085\pi$
$314$			63172.3i			0.640719i
$315$	37240.0	+	57612.0i	0.375309	+	0.580620i
$316$	55610.0			0.556902
$317$		−	42435.0i		−	0.422285i	−0.977455	−	0.211142i	$-0.932282\pi$
$317$		−	42435.0i		−	0.422285i	0.977455	−	0.211142i	$-0.0677184\pi$
$318$	−19440.0			−0.192239
$319$	16999.0			0.167048
$320$	12280.0	−	60159.5i	0.119922	−	0.587495i
$321$			63343.8i			0.614744i
$322$	−60060.0	+	58846.5i	−0.579260	+	0.567557i
$323$			106920.i			1.02484i
$324$	11110.0			0.105834
$325$	−2875.00	−	1224.74i	−0.0272189	−	0.0115952i
$326$	91008.0			0.856336
$327$	−61555.0			−0.575662
$328$	−185640.			−1.72554
$329$	−76825.0	+	75272.8i	−0.709759	+	0.695419i
$330$	26700.0	+	5450.11i	0.245179	+	0.0500470i
$331$	−114706.			−1.04696			−0.523480	−	0.852038i	$-0.675367\pi$
$331$	−114706.			−1.04696			−0.523480	+	0.852038i	$0.675367\pi$
$332$	−19900.0			−0.180541
$333$		−	91356.2i		−	0.823852i
$334$			50937.1i			0.456606i
$335$	−50160.0	−	10238.9i	−0.446959	−	0.0912352i
$336$	700.000	−	685.857i	0.00620040	−	0.00607512i
$337$			117007.i			1.03027i	0.857108	+	0.515137i	$0.172259\pi$
$337$			117007.i			1.03027i	−0.857108	+	0.515137i	$0.827741\pi$
$338$		−	69898.6i		−	0.611836i
$339$		−	15603.2i		−	0.135774i
$340$	−24250.0	+	118800.i	−0.209775	+	1.02768i
$341$		−	93742.0i		−	0.806168i
$342$	30240.0			0.258541
$343$	80605.0	+	85697.8i	0.685131	+	0.728420i
$344$	−24024.0			−0.203015
$345$	−85800.0	−	17513.9i	−0.720857	−	0.147144i
$346$		−	281.691i		−	0.00235300i
$347$		−	70481.6i		−	0.585352i	−0.956212	−	0.292676i	$-0.905454\pi$
$347$		−	70481.6i		−	0.585352i	0.956212	−	0.292676i	$-0.0945457\pi$
$348$	−9550.00			−0.0788578
$349$		−	91390.5i		−	0.750326i	−0.926959	−	0.375163i	$-0.877587\pi$
$349$		−	91390.5i		−	0.750326i	0.926959	−	0.375163i	$-0.122413\pi$
$350$	27300.0	+	69871.7i	0.222857	+	0.570381i
$351$	3425.00			0.0278001
$352$			91561.9i			0.738975i
$353$	11405.0			0.0915263			0.0457631	−	0.998952i	$-0.485428\pi$
$353$	11405.0			0.0915263			0.0457631	+	0.998952i	$0.485428\pi$
$354$	−44400.0			−0.354304
$355$	−22270.0	+	109100.i	−0.176711	+	0.865703i
$356$		−	8083.32i		−	0.0637807i
$357$	84875.0	−	83160.2i	0.665953	−	0.652498i
$358$			13026.4i			0.101638i
$359$	230366.			1.78743			0.893716	−	0.448633i	$-0.148089\pi$
$359$	230366.			1.78743			0.893716	+	0.448633i	$0.148089\pi$
$360$	87360.0	+	17832.3i	0.674074	+	0.137595i
$361$	81721.0			0.627075
$362$	30240.0			0.230762
$363$	33600.0			0.254992
$364$	−1750.00	+	1714.64i	−0.0132079	+	0.0129411i
$365$	43250.0	−	211881.i	0.324639	−	1.59040i
$366$	23700.0			0.176924
$367$	−74485.0			−0.553015			−0.276507	−	0.961012i	$-0.589177\pi$
$367$	−74485.0			−0.553015			−0.276507	+	0.961012i	$0.589177\pi$
$368$		−	2802.22i		−	0.0206922i
$369$		−	163234.i		−	1.19883i
$370$	19980.0	−	97881.6i	0.145946	−	0.714986i
$371$	54432.0	+	55554.4i	0.395464	+	0.403618i
$372$			52664.0i			0.380564i
$373$		−	102550.i		−	0.737088i	−0.929610	−	0.368544i	$-0.879856\pi$
$373$		−	102550.i		−	0.737088i	0.929610	−	0.368544i	$-0.120144\pi$
$374$			105732.i			0.755900i
$375$	−44375.0	+	64299.1i	−0.315556	+	0.457238i
$376$			139792.i			0.988799i
$377$	955.000			0.00671925
$378$	−57540.0	−	58726.5i	−0.402704	−	0.411008i
$379$	−172954.			−1.20407			−0.602036	−	0.798469i	$-0.705643\pi$
$379$	−172954.			−1.20407			−0.602036	+	0.798469i	$0.705643\pi$
$380$	−54000.0	−	11022.7i	−0.373961	−	0.0763345i
$381$			119339.i			0.822116i
$382$		−	34937.1i		−	0.239420i
$383$	144050.			0.982010			0.491005	−	0.871157i	$-0.336630\pi$
$383$	144050.			0.982010			0.491005	+	0.871157i	$0.336630\pi$
$384$		−	52223.1i		−	0.354161i
$385$	−59185.0	−	91561.9i	−0.399292	−	0.617723i
$386$	78396.0			0.526162
$387$		−	21124.4i		−	0.141047i
$388$	−92350.0			−0.613442
$389$	−148969.			−0.984457			−0.492228	−	0.870466i	$-0.663818\pi$
$389$	−148969.			−0.984457			−0.492228	+	0.870466i	$0.663818\pi$
$390$	1500.00	+	306.186i	0.00986193	+	0.00201306i
$391$		−	339769.i		−	2.22244i
$392$	152880.	+	3120.65i	0.994898	+	0.0203083i
$393$		−	33680.5i		−	0.218069i
$394$	−8316.00			−0.0535700
$395$	−27805.0	+	136216.i	−0.178209	+	0.873040i
$396$	−49840.0			−0.317825
$397$	256925.			1.63014			0.815071	−	0.579361i	$-0.196698\pi$
$397$	256925.			1.63014			0.815071	+	0.579361i	$0.196698\pi$
$398$	47520.0			0.299992
$399$	37800.0	+	38579.5i	0.237436	+	0.242332i
$400$	−2300.00	−	979.796i	−0.0143750	−	0.00612372i
$401$	−35641.0			−0.221647			−0.110823	−	0.993840i	$-0.535349\pi$
$401$	−35641.0			−0.221647			−0.110823	+	0.993840i	$0.535349\pi$
$402$	25080.0			0.155194
$403$		−	5266.40i		−	0.0324268i
$404$		−	48254.9i		−	0.295651i
$405$	−5555.00	+	27213.8i	−0.0338668	+	0.165913i
$406$	−16044.0	−	16374.8i	−0.0973331	−	0.0993402i
$407$			145191.i			0.876498i
$408$		−	154440.i		−	0.927770i
$409$			151721.i			0.906985i	0.891260	+	0.453493i	$0.149822\pi$
$409$			151721.i			0.906985i	−0.891260	+	0.453493i	$0.850178\pi$
$410$	35700.0	−	174894.i	0.212374	−	1.04041i
$411$		−	115346.i		−	0.682843i
$412$	47150.0			0.277771
$413$	124320.	+	126884.i	0.728855	+	0.743884i
$414$	−96096.0			−0.560667
$415$	9950.00	−	48744.8i	0.0577733	−	0.283030i
$416$			5143.93i			0.0297241i
$417$			147459.i			0.848008i
$418$	−48060.0			−0.275062
$419$		−	150889.i		−	0.859465i	−0.902956	−	0.429733i	$-0.858608\pi$
$419$		−	150889.i		−	0.859465i	0.902956	−	0.429733i	$-0.141392\pi$
$420$	33250.0	+	51439.3i	0.188492	+	0.291606i
$421$	−4681.00			−0.0264104			−0.0132052	−	0.999913i	$-0.504203\pi$
$421$	−4681.00			−0.0264104			−0.0132052	+	0.999913i	$0.504203\pi$
$422$			129375.i			0.726481i
$423$	−122920.			−0.686976
$424$	101088.			0.562300
$425$	−278875.	−	118800.i	−1.54394	−	0.657718i
$426$		−	54550.1i		−	0.300591i
$427$	−66360.0	−	67728.4i	−0.363957	−	0.371463i
$428$		−	126688.i		−	0.691587i
$429$	−2225.00			−0.0120897
$430$	4620.00	−	22633.3i	0.0249865	−	0.122408i
$431$	−87103.0			−0.468898			−0.234449	−	0.972128i	$-0.575329\pi$
$431$	−87103.0			−0.468898			−0.234449	+	0.972128i	$0.575329\pi$
$432$	2740.00			0.0146819
$433$	−231730.			−1.23597			−0.617983	−	0.786192i	$-0.712050\pi$
$433$	−231730.			−1.23597			−0.617983	+	0.786192i	$0.712050\pi$
$434$	−90300.0	+	88475.6i	−0.479411	+	0.469725i
$435$	4775.00	−	23392.6i	0.0252345	−	0.123623i
$436$	123110.			0.647620
$437$	154440.			0.808718
$438$			105940.i			0.552222i
$439$			246272.i			1.27787i	0.769262	+	0.638933i	$0.220624\pi$
$439$			246272.i			1.27787i	−0.769262	+	0.638933i	$0.779376\pi$
$440$	−138840.	−	28340.6i	−0.717149	−	0.146387i
$441$	−2744.00	+	134428.i	−0.0141093	+	0.691214i
$442$			5940.01i			0.0304048i
$443$			349841.i			1.78264i	0.453376	+	0.891319i	$0.350219\pi$
$443$			349841.i			1.78264i	−0.453376	+	0.891319i	$0.649781\pi$
$444$		−	81568.0i		−	0.413765i
$445$	19800.0	+	4041.66i	0.0999874	+	0.0204098i
$446$		−	33423.3i		−	0.168027i
$447$	−141730.			−0.709327
$448$	85960.0	−	84223.3i	0.428292	−	0.419639i
$449$	254711.			1.26344			0.631721	−	0.775196i	$-0.282349\pi$
$449$	254711.			1.26344			0.631721	+	0.775196i	$0.282349\pi$
$450$	−33600.0	+	78873.6i	−0.165926	+	0.389499i
$451$			259425.i			1.27544i
$452$			31206.5i			0.152745i
$453$	87755.0			0.427637
$454$		−	182450.i		−	0.885182i
$455$	−3325.00	−	5143.93i	−0.0160609	−	0.0248469i
$456$	70200.0			0.337604
$457$			263629.i			1.26229i	0.775663	+	0.631147i	$0.217415\pi$
$457$			263629.i			1.26229i	−0.775663	+	0.631147i	$0.782585\pi$
$458$	−167700.			−0.799470
$459$	332225.			1.57691
$460$	171600.	+	35027.7i	0.810964	+	0.165537i
$461$			128255.i			0.603495i	0.953388	+	0.301747i	$0.0975699\pi$
$461$			128255.i			0.603495i	−0.953388	+	0.301747i	$0.902430\pi$
$462$	37380.0	+	38150.8i	0.175128	+	0.178739i
$463$		−	81857.0i		−	0.381851i	−0.981605	−	0.190926i	$-0.938851\pi$
$463$		−	81857.0i		−	0.381851i	0.981605	−	0.190926i	$-0.0611489\pi$
$464$	764.000			0.00354860
$465$	−129000.	−	26332.0i	−0.596601	−	0.121781i
$466$	−147384.			−0.678701
$467$	−204445.			−0.937438			−0.468719	−	0.883347i	$-0.655284\pi$
$467$	−204445.			−0.937438			−0.468719	+	0.883347i	$0.655284\pi$
$468$	−2800.00			−0.0127840
$469$	−70224.0	−	71672.1i	−0.319257	−	0.325840i
$470$	−131700.	−	26883.1i	−0.596197	−	0.121698i
$471$	−128950.			−0.581272
$472$	230880.			1.03634
$473$			33572.7i			0.150060i
$474$		−	68108.1i		−	0.303139i
$475$	54000.0	−	126761.i	0.239335	−	0.561822i
$476$	−169750.	+	166320.i	−0.749197	+	0.734060i
$477$			88887.1i			0.390663i
$478$		−	184611.i		−	0.807981i
$479$			79534.9i			0.346647i	0.984865	+	0.173323i	$0.0554505\pi$
$479$			79534.9i			0.346647i	−0.984865	+	0.173323i	$0.944549\pi$
$480$	126000.	+	25719.6i	0.546875	+	0.111630i
$481$			8156.80i			0.0352557i
$482$	190740.			0.821009
$483$	−120120.	−	122597.i	−0.514898	−	0.525515i
$484$	−67200.0			−0.286866
$485$	46175.0	−	226210.i	0.196301	−	0.961677i
$486$		−	149517.i		−	0.633020i
$487$		−	164958.i		−	0.695531i	−0.937582	−	0.347766i	$-0.886941\pi$
$487$		−	164958.i		−	0.695531i	0.937582	−	0.347766i	$-0.113059\pi$
$488$	−123240.			−0.517502
$489$			185769.i			0.776884i
$490$	−32340.0	+	143430.i	−0.134694	+	0.597376i
$491$	−74191.0			−0.307743			−0.153872	−	0.988091i	$-0.549174\pi$
$491$	−74191.0			−0.307743			−0.153872	+	0.988091i	$0.549174\pi$
$492$		−	145745.i		−	0.602091i
$493$	92635.0			0.381137
$494$	−2700.00			−0.0110639
$495$	24920.0	−	122083.i	0.101704	−	0.498245i
$496$		−	4213.12i		−	0.0171254i
$497$	−155890.	+	152740.i	−0.631111	+	0.618360i
$498$			24372.4i			0.0982743i
$499$	−278527.			−1.11858			−0.559289	−	0.828973i	$-0.688926\pi$
$499$	−278527.			−1.11858			−0.559289	+	0.828973i	$0.688926\pi$
$500$	88750.0	−	128598.i	0.355000	−	0.514393i
$501$	−103975.			−0.414241
$502$	−123480.			−0.489992
$503$	60275.0			0.238233			0.119116	−	0.992880i	$-0.461994\pi$
$503$	60275.0			0.238233			0.119116	+	0.992880i	$0.461994\pi$
$504$	122304.	+	124826.i	0.481481	+	0.491410i
$505$	118200.	+	24127.5i	0.463484	+	0.0946083i
$506$	152724.			0.596494
$507$	142680.			0.555069
$508$		−	238678.i		−	0.924880i
$509$		−	348709.i		−	1.34595i	−0.739666	−	0.672974i	$-0.765017\pi$
$509$		−	348709.i		−	1.34595i	0.739666	−	0.672974i	$-0.234983\pi$
$510$	145500.	+	29700.1i	0.559400	+	0.114187i
$511$	302750.	−	296633.i	1.15942	−	1.13600i
$512$			8191.09i			0.0312465i
$513$			151011.i			0.573818i
$514$		−	8254.78i		−	0.0312449i
$515$	−23575.0	+	115493.i	−0.0888868	+	0.435455i
$516$		−	18861.1i		−	0.0708381i
$517$	195355.			0.730876
$518$	139860.	−	137034.i	0.521236	−	0.510704i
$519$	575.000			0.00213468
$520$	−7800.00	−	1592.17i	−0.0288462	−	0.00588820i
$521$		−	84727.9i		−	0.312141i	−0.987746	−	0.156070i	$-0.950117\pi$
$521$		−	84727.9i		−	0.312141i	0.987746	−	0.156070i	$-0.0498827\pi$
$522$		−	26199.7i		−	0.0961515i
$523$	235610.			0.861371			0.430686	−	0.902502i	$-0.358272\pi$
$523$	235610.			0.861371			0.430686	+	0.902502i	$0.358272\pi$
$524$			67361.0i			0.245327i
$525$	−142625.	+	55725.9i	−0.517460	+	0.202180i
$526$	−145464.			−0.525756
$527$		−	510841.i		−	1.83935i
$528$	−1780.00			−0.00638487
$529$	−210935.			−0.753767
$530$	−19440.0	+	95236.2i	−0.0692061	+	0.339039i
$531$			203014.i			0.720006i
$532$	−75600.0	−	77158.9i	−0.267115	−	0.272623i
$533$			14574.5i			0.0513025i
$534$	−9900.00			−0.0347178
$535$	310320.	+	63343.8i	1.08418	+	0.221308i
$536$	−130416.			−0.453943
$537$	−26590.0			−0.0922082
$538$	188640.			0.651732
$539$	4361.00	−	213644.i	0.0150110	−	0.735384i
$540$	−34250.0	+	167790.i	−0.117455	+	0.575412i
$541$	259199.			0.885602			0.442801	−	0.896620i	$-0.353985\pi$
$541$	259199.			0.885602			0.442801	+	0.896620i	$0.353985\pi$
$542$	−350820.			−1.19422
$543$			61727.1i			0.209352i
$544$			498961.i			1.68604i
$545$	−61555.0	+	301557.i	−0.207238	+	1.01526i
$546$	2100.00	+	2143.30i	0.00704424	+	0.00718950i
$547$		−	423894.i		−	1.41672i	−0.705854	−	0.708358i	$-0.749436\pi$
$547$		−	423894.i		−	1.41672i	0.705854	−	0.708358i	$-0.250564\pi$
$548$			230693.i			0.768198i
$549$		−	108365.i		−	0.359539i
$550$	53400.0	−	125353.i	0.176529	−	0.414389i
$551$			42106.7i			0.138691i
$552$	−223080.			−0.732120
$553$	−194635.	+	190703.i	−0.636459	+	0.623600i
$554$	249672.			0.813486
$555$	199800.	+	40784.0i	0.648649	+	0.132405i
$556$		−	294919.i		−	0.954009i
$557$			133389.i			0.429943i	0.976620	+	0.214972i	$0.0689659\pi$
$557$			133389.i			0.429943i	−0.976620	+	0.214972i	$0.931034\pi$
$558$	−144480.			−0.464023
$559$			1886.11i			0.00603591i
$560$	−2660.00	−	4115.14i	−0.00848214	−	0.0131223i
$561$	−215825.			−0.685766
$562$		−	116402.i		−	0.368543i
$563$	369770.			1.16658			0.583290	−	0.812264i	$-0.301765\pi$
$563$	369770.			1.16658			0.583290	+	0.812264i	$0.301765\pi$
$564$	−109750.			−0.345022
$565$	−76440.0	−	15603.2i	−0.239455	−	0.0488785i
$566$			105610.i			0.329664i
$567$	−38885.0	+	38099.4i	−0.120953	+	0.118509i
$568$			283661.i			0.879230i
$569$	−326134.			−1.00733			−0.503665	−	0.863899i	$-0.668015\pi$
$569$	−326134.			−1.00733			−0.503665	+	0.863899i	$0.668015\pi$
$570$	−13500.0	+	66136.2i	−0.0415512	+	0.203559i
$571$	306374.			0.939679			0.469840	−	0.882752i	$-0.344312\pi$
$571$	306374.			0.939679			0.469840	+	0.882752i	$0.344312\pi$
$572$	4450.00			0.0136009
$573$	71315.0			0.217206
$574$	249900.	−	244851.i	0.758477	−	0.743153i
$575$	−171600.	+	402819.i	−0.519017	+	1.21835i
$576$	137536.			0.414545
$577$	−387595.			−1.16420			−0.582099	−	0.813118i	$-0.697768\pi$
$577$	−387595.			−1.16420			−0.582099	+	0.813118i	$0.697768\pi$
$578$			371597.i			1.11229i
$579$			160025.i			0.477344i
$580$	−9550.00	+	46785.3i	−0.0283888	+	0.139076i
$581$	69650.0	−	68242.8i	0.206333	−	0.202164i
$582$			113105.i			0.333915i
$583$		−	141267.i		−	0.415627i
$584$		−	550890.i		−	1.61525i
$585$	1400.00	−	6858.57i	0.00409088	−	0.0200411i
$586$			397124.i			1.15646i
$587$	−467350.			−1.35633			−0.678166	−	0.734909i	$-0.737225\pi$
$587$	−467350.			−1.35633			−0.678166	+	0.734909i	$0.737225\pi$
$588$	−2450.00	+	120025.i	−0.00708617	+	0.347150i
$589$	232200.			0.669317
$590$	−44400.0	+	217515.i	−0.127550	+	0.624863i
$591$		−	16975.0i		−	0.0485997i
$592$			6525.44i			0.0186194i
$593$	−214315.			−0.609457			−0.304729	−	0.952439i	$-0.598566\pi$
$593$	−214315.			−0.609457			−0.304729	+	0.952439i	$0.598566\pi$
$594$			149333.i			0.423237i
$595$	−322525.	−	498961.i	−0.911023	−	1.40939i
$596$	283460.			0.797993
$597$			96999.8i			0.272159i
$598$	8580.00			0.0239930
$599$	−283999.			−0.791522			−0.395761	−	0.918353i	$-0.629519\pi$
$599$	−283999.			−0.791522			−0.395761	+	0.918353i	$0.629519\pi$
$600$	−78000.0	+	183099.i	−0.216667	+	0.508609i
$601$			91219.0i			0.252544i	0.991996	+	0.126272i	$0.0403011\pi$
$601$			91219.0i			0.252544i	−0.991996	+	0.126272i	$0.959699\pi$
$602$	32340.0	−	31686.6i	0.0892374	−	0.0874345i
$603$		−	114675.i		−	0.315381i
$604$	−175510.			−0.481092
$605$	33600.0	−	164606.i	0.0917970	−	0.449712i
$606$	−59100.0			−0.160932
$607$	193715.			0.525758			0.262879	−	0.964829i	$-0.415328\pi$
$607$	193715.			0.525758			0.262879	+	0.964829i	$0.415328\pi$
$608$	−226800.			−0.613530
$609$	33425.0	−	32749.7i	0.0901232	−	0.0883024i
$610$	23700.0	−	116106.i	0.0636926	−	0.312029i
$611$	10975.0			0.0293983
$612$	−271600.			−0.725148
$613$		−	296231.i		−	0.788334i	−0.919039	−	0.394167i	$-0.871033\pi$
$613$		−	296231.i		−	0.788334i	0.919039	−	0.394167i	$-0.128967\pi$
$614$		−	82805.0i		−	0.219644i
$615$	357000.	+	72872.3i	0.943883	+	0.192669i
$616$	−194376.	−	198384.i	−0.512249	−	0.522812i
$617$		−	424751.i		−	1.11574i	−0.829927	−	0.557872i	$-0.811618\pi$
$617$		−	424751.i		−	1.11574i	0.829927	−	0.557872i	$-0.188382\pi$
$618$		−	57746.7i		−	0.151200i
$619$			375825.i			0.980855i	0.871482	+	0.490427i	$0.163159\pi$
$619$			375825.i			0.980855i	−0.871482	+	0.490427i	$0.836841\pi$
$620$	258000.	+	52664.0i	0.671176	+	0.137003i
$621$		−	479880.i		−	1.24437i
$622$	123540.			0.319321
$623$	27720.0	+	28291.6i	0.0714196	+	0.0728923i
$624$	−100.000			−0.000256821
$625$	270625.	+	281691.i	0.692800	+	0.721130i
$626$		−	166945.i		−	0.426015i
$627$		−	98102.1i		−	0.249542i
$628$	257900.			0.653931
$629$			791210.i			1.99982i
$630$	−141120.	+	91219.0i	−0.355556	+	0.229829i
$631$	−471511.			−1.18422			−0.592111	−	0.805856i	$-0.701705\pi$
$631$	−471511.			−1.18422			−0.592111	+	0.805856i	$0.701705\pi$
$632$			354162.i			0.886682i
$633$	−264085.			−0.659077
$634$	103944.			0.258595
$635$	584640.	+	119339.i	1.44991	+	0.295962i
$636$			79363.5i			0.196203i
$637$	245.000	−	12002.5i	0.000603792	−	0.0295796i
$638$			41638.9i			0.102296i
$639$	−249424.			−0.610853
$640$	−255840.	−	52223.1i	−0.624609	−	0.127498i
$641$	558794.			1.35999			0.679995	−	0.733217i	$-0.261982\pi$
$641$	558794.			1.35999			0.679995	+	0.733217i	$0.261982\pi$
$642$	−155160.			−0.376452
$643$	454235.			1.09865			0.549324	−	0.835609i	$-0.314885\pi$
$643$	454235.			1.09865			0.549324	+	0.835609i	$0.314885\pi$
$644$	240240.	+	245194.i	0.579260	+	0.591205i
$645$	46200.0	+	9430.54i	0.111051	+	0.0226682i
$646$	−261900.			−0.627582
$647$	129530.			0.309430			0.154715	−	0.987959i	$-0.450554\pi$
$647$	129530.			0.309430			0.154715	+	0.987959i	$0.450554\pi$
$648$			70756.0i			0.168505i
$649$		−	322647.i		−	0.766016i
$650$	3000.00	−	7042.28i	0.00710059	−	0.0166681i
$651$	−180600.	−	184324.i	−0.426143	−	0.434931i
$652$		−	371539.i		−	0.873995i
$653$		−	343903.i		−	0.806511i	−0.915087	−	0.403255i	$-0.867879\pi$
$653$		−	343903.i		−	0.806511i	0.915087	−	0.403255i	$-0.132121\pi$
$654$		−	150778.i		−	0.352520i
$655$	−165000.	−	33680.5i	−0.384593	−	0.0785047i
$656$			11659.6i			0.0270941i
$657$	484400.			1.12221
$658$	−184380.	−	188182.i	−0.425855	−	0.434637i
$659$	526913.			1.21330			0.606650	−	0.794969i	$-0.292513\pi$
$659$	526913.			1.21330			0.606650	+	0.794969i	$0.292513\pi$
$660$	22250.0	−	109002.i	0.0510790	−	0.250235i
$661$			191844.i			0.439082i	0.975603	+	0.219541i	$0.0704559\pi$
$661$			191844.i			0.439082i	−0.975603	+	0.219541i	$0.929544\pi$
$662$		−	280971.i		−	0.641130i
$663$	−12125.0			−0.0275838
$664$		−	126737.i		−	0.287452i
$665$	226800.	−	146602.i	0.512861	−	0.331510i
$666$	223776.			0.504505
$667$		−	133806.i		−	0.300762i
$668$	207950.			0.466022
$669$	68225.0			0.152437
$670$	25080.0	−	122866.i	0.0558699	−	0.273706i
$671$			172224.i			0.382514i
$672$	176400.	+	180037.i	0.390625	+	0.398680i
$673$			429792.i			0.948918i	0.880278	+	0.474459i	$0.157356\pi$
$673$			429792.i			0.948918i	−0.880278	+	0.474459i	$0.842644\pi$
$674$	−286608.			−0.630912
$675$	−393875.	−	167790.i	−0.864472	−	0.368263i
$676$	−285360.			−0.624453
$677$	79685.0			0.173860			0.0869299	−	0.996214i	$-0.472294\pi$
$677$	79685.0			0.173860			0.0869299	+	0.996214i	$0.472294\pi$
$678$	38220.0			0.0831441
$679$	323225.	−	316695.i	0.701076	−	0.686912i
$680$	−756600.	−	154440.i	−1.63625	−	0.333997i
$681$	372425.			0.803054
$682$	229620.			0.493675
$683$		−	719577.i		−	1.54254i	−0.636510	−	0.771269i	$-0.719622\pi$
$683$		−	719577.i		−	1.54254i	0.636510	−	0.771269i	$-0.280378\pi$
$684$		−	123454.i		−	0.263872i
$685$	−565080.	−	115346.i	−1.20428	−	0.245823i
$686$	−209916.	+	197441.i	−0.446064	+	0.419555i
$687$		−	342316.i		−	0.725294i
$688$			1508.89i			0.00318771i
$689$		−	7936.35i		−	0.0167179i
$690$	42900.0	−	210166.i	0.0901071	−	0.441433i
$691$			398532.i			0.834655i	0.908756	+	0.417328i	$0.137033\pi$
$691$			398532.i			0.834655i	−0.908756	+	0.417328i	$0.862967\pi$
$692$	−1150.00			−0.00240152
$693$	174440.	−	170916.i	0.363228	−	0.355890i
$694$	172644.			0.358453
$695$	722400.	+	147459.i	1.49557	+	0.305283i
$696$		−	60820.8i		−	0.125555i
$697$			1.41372e6i			2.91004i
$698$	223860.			0.459479
$699$		−	300846.i		−	0.615730i
$700$	285250.	−	111452.i	0.582143	−	0.227453i
$701$	−658873.			−1.34081			−0.670403	−	0.741998i	$-0.733879\pi$
$701$	−658873.			−1.34081			−0.670403	+	0.741998i	$0.733879\pi$
$702$			8389.50i			0.0170240i
$703$	−359640.			−0.727708
$704$	−218584.			−0.441035
$705$	54875.0	−	268831.i	0.110407	−	0.540881i
$706$			27936.4i			0.0560482i
$707$	165480.	+	168892.i	0.331060	+	0.337887i
$708$			181262.i			0.361610i
$709$	−593737.			−1.18114			−0.590570	−	0.806986i	$-0.701097\pi$
$709$	−593737.			−1.18114			−0.590570	+	0.806986i	$0.701097\pi$
$710$	−267240.	−	54550.1i	−0.530133	−	0.108213i
$711$	−311416.			−0.616030
$712$	51480.0			0.101550
$713$	−737880.			−1.45147
$714$	203700.	+	207900.i	0.399572	+	0.407811i
$715$	−2225.00	+	10900.2i	−0.00435229	+	0.0213218i
$716$	53180.0			0.103734
$717$	376835.			0.733015
$718$			564279.i			1.09457i
$719$			75321.8i			0.145701i	0.997343	+	0.0728506i	$0.0232096\pi$
$719$			75321.8i			0.145701i	−0.997343	+	0.0728506i	$0.976790\pi$
$720$	1120.00	−	5486.86i	0.00216049	−	0.0105842i
$721$	−165025.	+	161691.i	−0.317453	+	0.311039i
$722$			200175.i			0.384003i
$723$			389346.i			0.744834i
$724$		−	123454.i		−	0.235521i
$725$	−109825.	−	46785.3i	−0.208942	−	0.0890088i
$726$			82302.9i			0.156150i
$727$	−342190.			−0.647438			−0.323719	−	0.946153i	$-0.604933\pi$
$727$	−342190.			−0.647438			−0.323719	+	0.946153i	$0.604933\pi$
$728$	−10920.0	−	11145.2i	−0.0206044	−	0.0210293i
$729$	215209.			0.404954
$730$	519000.	+	105940.i	0.973916	+	0.198800i
$731$			182952.i			0.342376i
$732$		−	96754.8i		−	0.180572i
$733$	−958555.			−1.78406			−0.892029	−	0.451978i	$-0.850719\pi$
$733$	−958555.			−1.78406			−0.892029	+	0.451978i	$0.850719\pi$
$734$		−	182450.i		−	0.338651i
$735$	−292775.	−	66013.7i	−0.541950	−	0.122197i
$736$	720720.			1.33049
$737$			182252.i			0.335534i
$738$	399840.			0.734131
$739$	−229399.			−0.420052			−0.210026	−	0.977696i	$-0.567355\pi$
$739$	−229399.			−0.420052			−0.210026	+	0.977696i	$0.567355\pi$
$740$	−399600.	−	81568.0i	−0.729730	−	0.148955i
$741$		−	5511.35i		−	0.0100374i
$742$	−136080.	+	133331.i	−0.247165	+	0.242171i
$743$		−	97803.2i		−	0.177164i	−0.996069	−	0.0885820i	$-0.971766\pi$
$743$		−	97803.2i		−	0.177164i	0.996069	−	0.0885820i	$-0.0282335\pi$
$744$	−335400.			−0.605923
$745$	−141730.	+	694332.i	−0.255358	+	1.25099i
$746$	251196.			0.451372
$747$	111440.			0.199710
$748$	431650.			0.771487
$749$	434448.	+	443407.i	0.774416	+	0.790385i
$750$	−157500.	−	108696.i	−0.280000	−	0.193238i
$751$	246977.			0.437902			0.218951	−	0.975736i	$-0.429737\pi$
$751$	246977.			0.437902			0.218951	+	0.975736i	$0.429737\pi$
$752$	8780.00			0.0155260
$753$		−	252052.i		−	0.444530i
$754$			2339.26i			0.00411468i
$755$	87755.0	−	429910.i	0.153949	−	0.754195i
$756$	−239750.	+	234906.i	−0.419484	+	0.411008i
$757$			1.05636e6i			1.84340i	0.387906	+	0.921699i	$0.373198\pi$
$757$			1.05636e6i			1.84340i	−0.387906	+	0.921699i	$0.626802\pi$
$758$		−	423649.i		−	0.737340i
$759$			311747.i			0.541151i
$760$	70200.0	−	343908.i	0.121537	−	0.595409i
$761$		−	406836.i		−	0.702506i	−0.936281	−	0.351253i	$-0.885756\pi$
$761$		−	406836.i		−	0.702506i	0.936281	−	0.351253i	$-0.114244\pi$
$762$	−292320.			−0.503441
$763$	−430885.	+	422179.i	−0.740137	+	0.725184i
$764$	−142630.			−0.244357
$765$	135800.	−	665281.i	0.232048	−	1.13680i
$766$			352849.i			0.601356i
$767$		−	18126.2i		−	0.0308118i
$768$	324400.			0.549995
$769$		−	592238.i		−	1.00148i	−0.865597	−	0.500741i	$-0.833061\pi$
$769$		−	592238.i		−	1.00148i	0.865597	−	0.500741i	$-0.166939\pi$
$770$	224280.	−	144973.i	0.378276	−	0.244515i
$771$	16850.0			0.0283460
$772$		−	320050.i		−	0.537012i
$773$	401165.			0.671373			0.335687	−	0.941974i	$-0.391032\pi$
$773$	401165.			0.671373			0.335687	+	0.941974i	$0.391032\pi$
$774$	51744.0			0.0863730
$775$	−258000.	+	605636.i	−0.429553	+	1.00834i
$776$		−	588147.i		−	0.976703i
$777$	279720.	+	285488.i	0.463320	+	0.472874i
$778$		−	364898.i		−	0.602854i
$779$	−642600.			−1.05893
$780$	1250.00	−	6123.72i	0.00205457	−	0.0100653i
$781$	396406.			0.649887
$782$	832260.			1.36096
$783$	130835.			0.213403
$784$	196.000	−	9602.00i	0.000318878	−	0.0156217i
$785$	−128950.	+	631723.i	−0.209258	+	1.02515i
$786$	82500.0			0.133539
$787$	−357565.			−0.577305			−0.288653	−	0.957434i	$-0.593207\pi$
$787$	−357565.			−0.577305			−0.288653	+	0.957434i	$0.593207\pi$
$788$			33949.9i			0.0546747i
$789$		−	296927.i		−	0.476975i
$790$	−333660.	−	68108.1i	−0.534626	−	0.109130i
$791$	−107016.	−	109223.i	−0.171039	−	0.174566i
$792$		−	317415.i		−	0.506030i
$793$			9675.48i			0.0153860i
$794$			629335.i			0.998254i
$795$	−194400.	−	39681.7i	−0.307583	−	0.0627851i
$796$		−	194000.i		−	0.306178i
$797$	1.18188e6			1.86062			0.930312	−	0.366769i	$-0.119536\pi$
$797$	1.18188e6			1.86062			0.930312	+	0.366769i	$0.119536\pi$
$798$	−94500.0	+	92590.7i	−0.148397	+	0.145399i
$799$	1.06458e6			1.66756
$800$	252000.	−	591552.i	0.393750	−	0.924300i
$801$			45266.6i			0.0705525i
$802$		−	87302.3i		−	0.135730i
$803$	−769850.			−1.19392
$804$		−	102389.i		−	0.158394i
$805$	−720720.	+	465868.i	−1.11218	+	0.718905i
$806$	12900.0			0.0198573
$807$			385060.i			0.591264i
$808$	307320.			0.470726
$809$	−272449.			−0.416283			−0.208141	−	0.978099i	$-0.566741\pi$
$809$	−272449.			−0.416283			−0.208141	+	0.978099i	$0.566741\pi$
$810$	−66660.0	−	13606.9i	−0.101600	−	0.0207391i
$811$		−	1.22117e6i		−	1.85667i	−0.371749	−	0.928333i	$-0.621242\pi$
$811$		−	1.22117e6i		−	1.85667i	0.371749	−	0.928333i	$-0.378758\pi$
$812$	−66850.0	+	65499.4i	−0.101389	+	0.0993402i
$813$		−	716108.i		−	1.08342i
$814$	−355644.			−0.536743
$815$	910080.	+	185769.i	1.37014	+	0.279678i
$816$	−9700.00			−0.0145677
$817$	−83160.0			−0.124586
$818$	−371640.			−0.555413
$819$	9800.00	−	9602.00i	0.0146103	−	0.0143151i
$820$	−714000.	−	145745.i	−1.06187	−	0.216753i
$821$	−621793.			−0.922485			−0.461243	−	0.887274i	$-0.652596\pi$
$821$	−621793.			−0.922485			−0.461243	+	0.887274i	$0.652596\pi$
$822$	282540.			0.418154
$823$		−	117394.i		−	0.173319i	−0.996238	−	0.0866597i	$-0.972381\pi$
$823$		−	117394.i		−	0.173319i	0.996238	−	0.0866597i	$-0.0276193\pi$
$824$			300283.i			0.442259i
$825$	255875.	+	109002.i	0.375941	+	0.160150i
$826$	−310800.	+	304521.i	−0.455534	+	0.446330i
$827$		−	199790.i		−	0.292121i	−0.989276	−	0.146061i	$-0.953341\pi$
$827$		−	199790.i		−	0.292121i	0.989276	−	0.146061i	$-0.0466595\pi$
$828$			392310.i			0.572228i
$829$		−	197894.i		−	0.287955i	−0.989581	−	0.143977i	$-0.954011\pi$
$829$		−	197894.i		−	0.287955i	0.989581	−	0.143977i	$-0.0459892\pi$
$830$	119400.	+	24372.4i	0.173320	+	0.0353788i
$831$			509641.i			0.738010i
$832$	−12280.0			−0.0177399
$833$	23765.0	−	1.16424e6i	0.0342490	−	1.67785i
$834$	−361200.			−0.519297
$835$	−103975.	+	509371.i	−0.149127	+	0.730570i
$836$			196204.i			0.280734i
$837$		−	721497.i		−	1.02987i
$838$	369600.			0.526313
$839$		−	826972.i		−	1.17481i	−0.809294	−	0.587404i	$-0.800150\pi$
$839$		−	826972.i		−	1.17481i	0.809294	−	0.587404i	$-0.199850\pi$
$840$	−327600.	+	211758.i	−0.464286	+	0.300111i
$841$	−670800.			−0.948421
$842$		−	11466.1i		−	0.0161730i
$843$	237605.			0.334349
$844$	528170.			0.741462
$845$	142680.	−	698986.i	0.199825	−	0.978938i
$846$		−	301091.i		−	0.420685i
$847$	235200.	−	230448.i	0.327846	−	0.321223i
$848$		−	6349.08i		−	0.00882915i
$849$	−215575.			−0.299077
$850$	291000.	−	683101.i	0.402768	−	0.945469i
$851$	1.14286e6			1.57809
$852$	−222700.			−0.306790
$853$	−385450.			−0.529749			−0.264874	−	0.964283i	$-0.585330\pi$
$853$	−385450.			−0.529749			−0.264874	+	0.964283i	$0.585330\pi$
$854$	165900.	−	162548.i	0.227473	−	0.222878i
$855$	302400.	+	61727.1i	0.413666	+	0.0844392i
$856$	806832.			1.10112
$857$	356750.			0.485738			0.242869	−	0.970059i	$-0.421911\pi$
$857$	356750.			0.485738			0.242869	+	0.970059i	$0.421911\pi$
$858$		−	5450.11i		−	0.00740340i
$859$			578227.i			0.783631i	0.920044	+	0.391816i	$0.128153\pi$
$859$			578227.i			0.783631i	−0.920044	+	0.391816i	$0.871847\pi$
$860$	−92400.0	−	18861.1i	−0.124932	−	0.0255017i
$861$	499800.	+	510106.i	0.674202	+	0.688104i
$862$		−	213358.i		−	0.287140i
$863$			151217.i			0.203039i	0.994834	+	0.101519i	$0.0323704\pi$
$863$			151217.i			0.203039i	−0.994834	+	0.101519i	$0.967630\pi$
$864$			704718.i			0.944035i
$865$	575.000	−	2816.91i	0.000768485	−	0.00376479i
$866$		−	567620.i		−	0.756871i
$867$	−758520.			−1.00909
$868$	361200.	+	368648.i	0.479411	+	0.489297i
$869$	494929.			0.655395
$870$	57300.0	+	11696.3i	0.0757035	+	0.0154529i
$871$			10238.9i			0.0134963i
$872$			784047.i			1.03112i
$873$	517160.			0.678573
$874$			378299.i			0.495236i
$875$	130375.	+	754443.i	0.170286	+	0.985395i
$876$	432500.			0.563609
$877$		−	553981.i		−	0.720271i	−0.932900	−	0.360136i	$-0.882730\pi$
$877$		−	553981.i		−	0.720271i	0.932900	−	0.360136i	$-0.117270\pi$
$878$	−603240.			−0.782530
$879$	−810625.			−1.04916
$880$	−1780.00	+	8720.18i	−0.00229855	+	0.0112606i
$881$			531882.i			0.685273i	0.939468	+	0.342637i	$0.111320\pi$
$881$			531882.i			0.685273i	−0.939468	+	0.342637i	$0.888680\pi$
$882$	−329280.	−	6721.40i	−0.423280	−	0.00864018i
$883$			606675.i			0.778099i	0.921217	+	0.389049i	$0.127196\pi$
$883$			606675.i			0.778099i	−0.921217	+	0.389049i	$0.872804\pi$
$884$	24250.0			0.0310318
$885$	−444000.	−	90631.1i	−0.566887	−	0.115715i
$886$	−856932.			−1.09164
$887$	−1.35703e6			−1.72481			−0.862407	−	0.506216i	$-0.831044\pi$
$887$	−1.35703e6			−1.72481			−0.862407	+	0.506216i	$0.831044\pi$
$888$	519480.			0.658784
$889$	818496.	+	835374.i	1.03565	+	1.05701i
$890$	−9900.00	+	48499.9i	−0.0124984	+	0.0612295i
$891$	98879.0			0.124551
$892$	−136450.			−0.171492
$893$			483897.i			0.606806i
$894$		−	347166.i		−	0.434373i
$895$	−26590.0	+	130264.i	−0.0331950	+	0.162621i
$896$	−358176.	−	365562.i	−0.446150	−	0.455349i
$897$			17513.9i			0.0217669i
$898$			623912.i			0.773697i
$899$		−	201177.i		−	0.248919i
$900$	322000.	+	137171.i	0.397531	+	0.169347i
$901$		−	769826.i		−	0.948294i
$902$	−635460.			−0.781043
$903$	64680.0	+	66013.7i	0.0793222	+	0.0809578i
$904$	−198744.			−0.243196
$905$	302400.	+	61727.1i	0.369219	+	0.0753666i
$906$			214955.i			0.261873i
$907$		−	452230.i		−	0.549724i	−0.961484	−	0.274862i	$-0.911368\pi$
$907$		−	452230.i		−	0.549724i	0.961484	−	0.274862i	$-0.0886321\pi$
$908$	−744850.			−0.903435
$909$			270228.i			0.327041i
$910$	12600.0	−	8144.55i	0.0152156	−	0.00983523i
$911$	−948106.			−1.14241			−0.571203	−	0.820809i	$-0.693523\pi$
$911$	−948106.			−1.14241			−0.571203	+	0.820809i	$0.693523\pi$
$912$		−	4409.08i		−	0.00530101i
$913$	−177110.			−0.212472
$914$	−645756.			−0.772994
$915$	237000.	+	48377.4i	0.283078	+	0.0577831i
$916$			684632.i			0.815956i
$917$	−231000.	−	235763.i	−0.274709	−	0.280374i
$918$			813782.i			0.965656i
$919$	394481.			0.467084			0.233542	−	0.972347i	$-0.424968\pi$
$919$	394481.			0.467084			0.233542	+	0.972347i	$0.424968\pi$
$920$	−223080.	+	1.09286e6i	−0.263563	+	1.29119i
$921$	169025.			0.199265
$922$	−314160.			−0.369563
$923$	22270.0			0.0261407
$924$	155750.	−	152603.i	0.182425	−	0.178739i
$925$	399600.	−	938032.i	0.467027	−	1.09631i
$926$	200508.			0.233835
$927$	−264040.			−0.307263
$928$			196498.i			0.228172i
$929$		−	139523.i		−	0.161664i	−0.996728	−	0.0808322i	$-0.974242\pi$
$929$		−	139523.i		−	0.161664i	0.996728	−	0.0808322i	$-0.0257578\pi$
$930$	64500.0	−	315984.i	0.0745751	−	0.365342i
$931$	529200.	+	10802.2i	0.610549	+	0.0124628i
$932$			601693.i			0.692696i
$933$			252175.i			0.289693i
$934$		−	500786.i		−	0.574061i
$935$	−215825.	+	1.05732e6i	−0.246876	+	1.20944i
$936$		−	17832.3i		−	0.0203543i
$937$	434285.			0.494647			0.247324	−	0.968933i	$-0.420449\pi$
$937$	434285.			0.494647			0.247324	+	0.968933i	$0.420449\pi$
$938$	175560.	−	172013.i	0.199535	−	0.195504i
$939$	340775.			0.386488
$940$	−109750.	+	537663.i	−0.124208	+	0.608491i
$941$		−	539108.i		−	0.608831i	−0.952539	−	0.304415i	$-0.901539\pi$
$941$		−	539108.i		−	0.608831i	0.952539	−	0.304415i	$-0.0984611\pi$
$942$		−	315862.i		−	0.355955i
$943$	2.04204e6			2.29636
$944$		−	14501.0i		−	0.0162725i
$945$	−455525.	−	704718.i	−0.510092	−	0.789136i
$946$	−82236.0			−0.0918924
$947$			167540.i			0.186818i	0.995628	+	0.0934091i	$0.0297764\pi$
$947$			167540.i			0.186818i	−0.995628	+	0.0934091i	$0.970224\pi$
$948$	−278050.			−0.309390
$949$	−43250.0			−0.0480235
$950$	310500.	+	132272.i	0.344044	+	0.146562i
$951$			212175.i			0.234603i
$952$	−1.05924e6	−	1.08108e6i	−1.16875	−	1.19285i
$953$		−	1.31304e6i		−	1.44575i	−0.690981	−	0.722873i	$-0.742821\pi$
$953$		−	1.31304e6i		−	1.44575i	0.690981	−	0.722873i	$-0.257179\pi$
$954$	−217728.			−0.239231
$955$	71315.0	−	349371.i	0.0781941	−	0.383071i
$956$	−753670.			−0.824642
$957$	−84995.0			−0.0928046
$958$	−194820.			−0.212277
$959$	−791112.	−	807425.i	−0.860203	−	0.877941i
$960$	−61400.0	+	300797.i	−0.0666233	+	0.326386i
$961$	−185879.			−0.201272
$962$	−19980.0			−0.0215896
$963$			709451.i			0.765014i
$964$		−	778693.i		−	0.837938i
$965$	783960.	+	160025.i	0.841859	+	0.171844i
$966$	300300.	−	294233.i	0.321811	−	0.315309i
$967$		−	338745.i		−	0.362259i	−0.983459	−	0.181130i	$-0.942025\pi$
$967$		−	338745.i		−	0.362259i	0.983459	−	0.181130i	$-0.0579754\pi$
$968$		−	427975.i		−	0.456738i
$969$		−	534601.i		−	0.569354i
$970$	554100.	+	113105.i	0.588904	+	0.120210i
$971$			1.60718e6i			1.70462i	0.523039	+	0.852309i	$0.324798\pi$
$971$			1.60718e6i			1.70462i	−0.523039	+	0.852309i	$0.675202\pi$
$972$	−610400.			−0.646074
$973$	1.01136e6	+	1.03221e6i	1.06827	+	1.09030i
$974$	404064.			0.425924
$975$	14375.0	+	6123.72i	0.0151216	+	0.00644179i
$976$			7740.39i			0.00812574i
$977$		−	1.40070e6i		−	1.46743i	−0.679459	−	0.733713i	$-0.737785\pi$
$977$		−	1.40070e6i		−	1.46743i	0.679459	−	0.733713i	$-0.262215\pi$
$978$	−455040.			−0.475742
$979$		−	71941.5i		−	0.0750610i
$980$	585550.	+	132027.i	0.609694	+	0.137471i
$981$	−689416.			−0.716380
$982$		−	181730.i		−	0.188453i
$983$	−1.73768e6			−1.79831			−0.899154	−	0.437633i	$-0.855817\pi$
$983$	−1.73768e6			−1.79831			−0.899154	+	0.437633i	$0.855817\pi$
$984$	928200.			0.958631
$985$	−83160.0	−	16975.0i	−0.0857121	−	0.0174959i
$986$			226908.i			0.233398i
$987$	384125.	−	376364.i	0.394310	−	0.386344i
$988$			11022.7i			0.0112921i
$989$	264264.			0.270175
$990$	299040.	+	61041.3i	0.305112	+	0.0622807i
$991$	−423586.			−0.431315			−0.215657	−	0.976469i	$-0.569189\pi$
$991$	−423586.			−0.431315			−0.215657	+	0.976469i	$0.569189\pi$
$992$	1.08360e6			1.10115
$993$	573530.			0.581645
$994$	−374136.	−	381851.i	−0.378666	−	0.386475i
$995$	475200.	+	96999.8i	0.479988	+	0.0979771i
$996$	99500.0			0.100301
$997$	−548035.			−0.551338			−0.275669	−	0.961253i	$-0.588899\pi$
$997$	−548035.			−0.551338			−0.275669	+	0.961253i	$0.588899\pi$
$998$		−	682249.i		−	0.684986i
$999$			1.11748e6i			1.11972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.c.c.34.2	yes	2
3.2	odd	2		315.5.e.d.244.1		2
4.3	odd	2		560.5.p.e.209.2		2
5.2	odd	4		175.5.d.e.76.2		4
5.3	odd	4		175.5.d.e.76.3		4
5.4	even	2		35.5.c.d.34.1	yes	2
7.6	odd	2		35.5.c.d.34.2	yes	2
15.14	odd	2		315.5.e.c.244.2		2
20.19	odd	2		560.5.p.d.209.2		2
21.20	even	2		315.5.e.c.244.1		2
28.27	even	2		560.5.p.d.209.1		2
35.13	even	4		175.5.d.e.76.4		4
35.27	even	4		175.5.d.e.76.1		4
35.34	odd	2	inner	35.5.c.c.34.1	✓	2
105.104	even	2		315.5.e.d.244.2		2
140.139	even	2		560.5.p.e.209.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.c.c.34.1	✓	2	35.34	odd	2	inner
35.5.c.c.34.2	yes	2	1.1	even	1	trivial
35.5.c.d.34.1	yes	2	5.4	even	2
35.5.c.d.34.2	yes	2	7.6	odd	2
175.5.d.e.76.1		4	35.27	even	4
175.5.d.e.76.2		4	5.2	odd	4
175.5.d.e.76.3		4	5.3	odd	4
175.5.d.e.76.4		4	35.13	even	4
315.5.e.c.244.1		2	21.20	even	2
315.5.e.c.244.2		2	15.14	odd	2
315.5.e.d.244.1		2	3.2	odd	2
315.5.e.d.244.2		2	105.104	even	2
560.5.p.d.209.1		2	28.27	even	2
560.5.p.d.209.2		2	20.19	odd	2
560.5.p.e.209.1		2	140.139	even	2
560.5.p.e.209.2		2	4.3	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.44949i q^{2} -5.00000 q^{3} +10.0000 q^{4} +(-5.00000 + 24.4949i) q^{5} -12.2474i q^{6} +(-35.0000 + 34.2929i) q^{7} +63.6867i q^{8} -56.0000 q^{9} +O(q^{10})\)	\(q+2.44949i q^{2} -5.00000 q^{3} +10.0000 q^{4} +(-5.00000 + 24.4949i) q^{5} -12.2474i q^{6} +(-35.0000 + 34.2929i) q^{7} +63.6867i q^{8} -56.0000 q^{9} +(-60.0000 - 12.2474i) q^{10} +89.0000 q^{11} -50.0000 q^{12} +5.00000 q^{13} +(-84.0000 - 85.7321i) q^{14} +(25.0000 - 122.474i) q^{15} +4.00000 q^{16} +485.000 q^{17} -137.171i q^{18} +220.454i q^{19} +(-50.0000 + 244.949i) q^{20} +(175.000 - 171.464i) q^{21} +218.005i q^{22} -700.554i q^{23} -318.434i q^{24} +(-575.000 - 244.949i) q^{25} +12.2474i q^{26} +685.000 q^{27} +(-350.000 + 342.929i) q^{28} +191.000 q^{29} +(300.000 + 61.2372i) q^{30} -1053.28i q^{31} +1028.79i q^{32} -445.000 q^{33} +1188.00i q^{34} +(-665.000 - 1028.79i) q^{35} -560.000 q^{36} +1631.36i q^{37} -540.000 q^{38} -25.0000 q^{39} +(-1560.00 - 318.434i) q^{40} +2914.89i q^{41} +(420.000 + 428.661i) q^{42} +377.221i q^{43} +890.000 q^{44} +(280.000 - 1371.71i) q^{45} +1716.00 q^{46} +2195.00 q^{47} -20.0000 q^{48} +(49.0000 - 2400.50i) q^{49} +(600.000 - 1408.46i) q^{50} -2425.00 q^{51} +50.0000 q^{52} -1587.27i q^{53} +1677.90i q^{54} +(-445.000 + 2180.05i) q^{55} +(-2184.00 - 2229.04i) q^{56} -1102.27i q^{57} +467.853i q^{58} -3625.24i q^{59} +(250.000 - 1224.74i) q^{60} +1935.10i q^{61} +2580.00 q^{62} +(1960.00 - 1920.40i) q^{63} -2456.00 q^{64} +(-25.0000 + 122.474i) q^{65} -1090.02i q^{66} +2047.77i q^{67} +4850.00 q^{68} +3502.77i q^{69} +(2520.00 - 1628.91i) q^{70} +4454.00 q^{71} -3566.46i q^{72} -8650.00 q^{73} -3996.00 q^{74} +(2875.00 + 1224.74i) q^{75} +2204.54i q^{76} +(-3115.00 + 3052.06i) q^{77} -61.2372i q^{78} +5561.00 q^{79} +(-20.0000 + 97.9796i) q^{80} +1111.00 q^{81} -7140.00 q^{82} -1990.00 q^{83} +(1750.00 - 1714.64i) q^{84} +(-2425.00 + 11880.0i) q^{85} -924.000 q^{86} -955.000 q^{87} +5668.12i q^{88} -808.332i q^{89} +(3360.00 + 685.857i) q^{90} +(-175.000 + 171.464i) q^{91} -7005.54i q^{92} +5266.40i q^{93} +5376.63i q^{94} +(-5400.00 - 1102.27i) q^{95} -5143.93i q^{96} -9235.00 q^{97} +(5880.00 + 120.025i) q^{98} -4984.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 10 q^{3} + 20 q^{4} - 10 q^{5} - 70 q^{7} - 112 q^{9}+O(q^{10}) \) 2 * q - 10 * q^3 + 20 * q^4 - 10 * q^5 - 70 * q^7 - 112 * q^9	\( 2 q - 10 q^{3} + 20 q^{4} - 10 q^{5} - 70 q^{7} - 112 q^{9} - 120 q^{10} + 178 q^{11} - 100 q^{12} + 10 q^{13} - 168 q^{14} + 50 q^{15} + 8 q^{16} + 970 q^{17} - 100 q^{20} + 350 q^{21} - 1150 q^{25} + 1370 q^{27} - 700 q^{28} + 382 q^{29} + 600 q^{30} - 890 q^{33} - 1330 q^{35} - 1120 q^{36} - 1080 q^{38} - 50 q^{39} - 3120 q^{40} + 840 q^{42} + 1780 q^{44} + 560 q^{45} + 3432 q^{46} + 4390 q^{47} - 40 q^{48} + 98 q^{49} + 1200 q^{50} - 4850 q^{51} + 100 q^{52} - 890 q^{55} - 4368 q^{56} + 500 q^{60} + 5160 q^{62} + 3920 q^{63} - 4912 q^{64} - 50 q^{65} + 9700 q^{68} + 5040 q^{70} + 8908 q^{71} - 17300 q^{73} - 7992 q^{74} + 5750 q^{75} - 6230 q^{77} + 11122 q^{79} - 40 q^{80} + 2222 q^{81} - 14280 q^{82} - 3980 q^{83} + 3500 q^{84} - 4850 q^{85} - 1848 q^{86} - 1910 q^{87} + 6720 q^{90} - 350 q^{91} - 10800 q^{95} - 18470 q^{97} + 11760 q^{98} - 9968 q^{99}+O(q^{100}) \) 2 * q - 10 * q^3 + 20 * q^4 - 10 * q^5 - 70 * q^7 - 112 * q^9 - 120 * q^10 + 178 * q^11 - 100 * q^12 + 10 * q^13 - 168 * q^14 + 50 * q^15 + 8 * q^16 + 970 * q^17 - 100 * q^20 + 350 * q^21 - 1150 * q^25 + 1370 * q^27 - 700 * q^28 + 382 * q^29 + 600 * q^30 - 890 * q^33 - 1330 * q^35 - 1120 * q^36 - 1080 * q^38 - 50 * q^39 - 3120 * q^40 + 840 * q^42 + 1780 * q^44 + 560 * q^45 + 3432 * q^46 + 4390 * q^47 - 40 * q^48 + 98 * q^49 + 1200 * q^50 - 4850 * q^51 + 100 * q^52 - 890 * q^55 - 4368 * q^56 + 500 * q^60 + 5160 * q^62 + 3920 * q^63 - 4912 * q^64 - 50 * q^65 + 9700 * q^68 + 5040 * q^70 + 8908 * q^71 - 17300 * q^73 - 7992 * q^74 + 5750 * q^75 - 6230 * q^77 + 11122 * q^79 - 40 * q^80 + 2222 * q^81 - 14280 * q^82 - 3980 * q^83 + 3500 * q^84 - 4850 * q^85 - 1848 * q^86 - 1910 * q^87 + 6720 * q^90 - 350 * q^91 - 10800 * q^95 - 18470 * q^97 + 11760 * q^98 - 9968 * q^99

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