LMFDB - Embedded newform 70.3.d.a.69.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,3,Mod(69,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("70.69");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.211319484596224.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} - 48x^{5} - 23x^{4} - 48x^{3} + 1226x^{2} - 7512x + 24408 $ x^8 + 2x^6 - 48x^5 - 23x^4 - 48x^3 + 1226x^2 - 7512x + 24408
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.2
Root			$1.28865 + 2.58522i$ of defining polynomial
Character	$\chi$	$=$	70.69
Dual form			70.3.d.a.69.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -2.07875 q^{3} -2.00000 q^{4} +(-4.65605 - 1.82242i) q^{5} +2.93980i q^{6} +(-3.36740 - 6.13682i) q^{7} +2.82843i q^{8} -4.67878 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -2.07875 q^{3} -2.00000 q^{4} +(-4.65605 - 1.82242i) q^{5} +2.93980i q^{6} +(-3.36740 - 6.13682i) q^{7} +2.82843i q^{8} -4.67878 q^{9} +(-2.57729 + 6.58465i) q^{10} +1.67878 q^{11} +4.15751 q^{12} +9.81063 q^{13} +(-8.67878 + 4.76222i) q^{14} +(9.67878 + 3.78837i) q^{15} +4.00000 q^{16} -0.498539 q^{17} +6.61679i q^{18} -32.2182i q^{19} +(9.31210 + 3.64484i) q^{20} +(7.00000 + 12.7570i) q^{21} -2.37415i q^{22} -3.78837i q^{23} -5.87961i q^{24} +(18.3576 + 16.9706i) q^{25} -13.8743i q^{26} +28.4348 q^{27} +(6.73480 + 12.2736i) q^{28} -39.0363 q^{29} +(5.35756 - 13.6879i) q^{30} -24.9285i q^{31} -5.65685i q^{32} -3.48977 q^{33} +0.705040i q^{34} +(4.49490 + 34.7102i) q^{35} +9.35756 q^{36} +16.0620i q^{37} -45.5634 q^{38} -20.3939 q^{39} +(5.15459 - 13.1693i) q^{40} +71.1407i q^{41} +(18.0411 - 9.89949i) q^{42} -37.7295i q^{43} -3.35756 q^{44} +(21.7846 + 8.52671i) q^{45} -5.35756 q^{46} -71.4209 q^{47} -8.31502 q^{48} +(-26.3212 + 41.3303i) q^{49} +(24.0000 - 25.9615i) q^{50} +1.03634 q^{51} -19.6213 q^{52} -83.0357i q^{53} -40.2129i q^{54} +(-7.81648 - 3.05944i) q^{55} +(17.3576 - 9.52445i) q^{56} +66.9737i q^{57} +55.2057i q^{58} -36.4484i q^{59} +(-19.3576 - 7.57673i) q^{60} -50.4424i q^{61} -35.2542 q^{62} +(15.7553 + 28.7128i) q^{63} -8.00000 q^{64} +(-45.6788 - 17.8791i) q^{65} +4.93528i q^{66} +12.2736i q^{67} +0.997077 q^{68} +7.87508i q^{69} +(49.0876 - 6.35675i) q^{70} +44.6424 q^{71} -13.2336i q^{72} +102.433 q^{73} +22.7151 q^{74} +(-38.1609 - 35.2776i) q^{75} +64.4364i q^{76} +(-5.65313 - 10.3024i) q^{77} +28.8413i q^{78} +132.394 q^{79} +(-18.6242 - 7.28969i) q^{80} -17.0000 q^{81} +100.608 q^{82} +8.72896 q^{83} +(-14.0000 - 25.5139i) q^{84} +(2.32122 + 0.908548i) q^{85} -53.3576 q^{86} +81.1470 q^{87} +4.74831i q^{88} +54.0872i q^{89} +(12.0586 - 30.8081i) q^{90} +(-33.0363 - 60.2061i) q^{91} +7.57673i q^{92} +51.8202i q^{93} +101.004i q^{94} +(-58.7151 + 150.009i) q^{95} +11.7592i q^{96} -41.7352 q^{97} +(58.4499 + 37.2238i) q^{98} -7.85464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{4} + 36 q^{9}+O(q^{10}) $ 8 * q - 16 * q^4 + 36 * q^9	$ 8 q - 16 q^{4} + 36 q^{9} - 60 q^{11} + 4 q^{14} + 4 q^{15} + 32 q^{16} + 56 q^{21} - 92 q^{29} - 104 q^{30} + 52 q^{35} - 72 q^{36} + 204 q^{39} + 120 q^{44} + 104 q^{46} - 284 q^{49} + 192 q^{50} - 212 q^{51} - 8 q^{56} - 8 q^{60} - 64 q^{64} - 292 q^{65} - 4 q^{70} + 504 q^{71} - 112 q^{74} + 692 q^{79} - 136 q^{81} - 112 q^{84} + 92 q^{85} - 280 q^{86} - 44 q^{91} - 176 q^{95} - 944 q^{99}+O(q^{100}) $ 8 * q - 16 * q^4 + 36 * q^9 - 60 * q^11 + 4 * q^14 + 4 * q^15 + 32 * q^16 + 56 * q^21 - 92 * q^29 - 104 * q^30 + 52 * q^35 - 72 * q^36 + 204 * q^39 + 120 * q^44 + 104 * q^46 - 284 * q^49 + 192 * q^50 - 212 * q^51 - 8 * q^56 - 8 * q^60 - 64 * q^64 - 292 * q^65 - 4 * q^70 + 504 * q^71 - 112 * q^74 + 692 * q^79 - 136 * q^81 - 112 * q^84 + 92 * q^85 - 280 * q^86 - 44 * q^91 - 176 * q^95 - 944 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−2.07875			−0.692918			−0.346459	−	0.938065i	$-0.612616\pi$
$3$	−2.07875			−0.692918			−0.346459	+	0.938065i	$0.612616\pi$
$4$	−2.00000			−0.500000
$5$	−4.65605	−	1.82242i	−0.931210	−	0.364484i
$5$	−4.65605	−	1.82242i	−0.931210	−	0.364484i
$6$			2.93980i			0.489967i
$7$	−3.36740	−	6.13682i	−0.481057	−	0.876689i
$7$	−3.36740	−	6.13682i	−0.481057	−	0.876689i
$8$			2.82843i			0.353553i
$9$	−4.67878			−0.519864
$10$	−2.57729	+	6.58465i	−0.257729	+	0.658465i
$11$	1.67878			0.152616			0.0763082	−	0.997084i	$-0.475687\pi$
$11$	1.67878			0.152616			0.0763082	+	0.997084i	$0.475687\pi$
$12$	4.15751			0.346459
$13$	9.81063			0.754664			0.377332	−	0.926078i	$-0.376842\pi$
$13$	9.81063			0.754664			0.377332	+	0.926078i	$0.376842\pi$
$14$	−8.67878	+	4.76222i	−0.619913	+	0.340159i
$15$	9.67878	+	3.78837i	0.645252	+	0.252558i
$16$	4.00000			0.250000
$17$	−0.498539			−0.0293258			−0.0146629	−	0.999892i	$-0.504668\pi$
$17$	−0.498539			−0.0293258			−0.0146629	+	0.999892i	$0.504668\pi$
$18$			6.61679i			0.367600i
$19$		−	32.2182i		−	1.69569i	−0.530241	−	0.847847i	$-0.677898\pi$
$19$		−	32.2182i		−	1.69569i	0.530241	−	0.847847i	$-0.322102\pi$
$20$	9.31210	+	3.64484i	0.465605	+	0.182242i
$21$	7.00000	+	12.7570i	0.333333	+	0.607474i
$22$		−	2.37415i		−	0.107916i
$23$		−	3.78837i		−	0.164712i	−0.996603	−	0.0823558i	$-0.973756\pi$
$23$		−	3.78837i		−	0.164712i	0.996603	−	0.0823558i	$-0.0262444\pi$
$24$		−	5.87961i		−	0.244984i
$25$	18.3576	+	16.9706i	0.734302	+	0.678823i
$26$		−	13.8743i		−	0.533628i
$27$	28.4348			1.05314
$28$	6.73480	+	12.2736i	0.240529	+	0.438345i
$29$	−39.0363			−1.34608			−0.673040	−	0.739606i	$-0.735012\pi$
$29$	−39.0363			−1.34608			−0.673040	+	0.739606i	$0.735012\pi$
$30$	5.35756	−	13.6879i	0.178585	−	0.456262i
$31$		−	24.9285i		−	0.804145i	−0.915608	−	0.402073i	$-0.868290\pi$
$31$		−	24.9285i		−	0.804145i	0.915608	−	0.402073i	$-0.131710\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−3.48977			−0.105751
$34$			0.705040i			0.0207365i
$35$	4.49490	+	34.7102i	0.128426	+	0.991719i
$36$	9.35756			0.259932
$37$			16.0620i			0.434109i	0.976160	+	0.217054i	$0.0696449\pi$
$37$			16.0620i			0.434109i	−0.976160	+	0.217054i	$0.930355\pi$
$38$	−45.5634			−1.19904
$39$	−20.3939			−0.522920
$40$	5.15459	−	13.1693i	0.128865	−	0.329232i
$41$			71.1407i			1.73514i	0.497317	+	0.867569i	$0.334319\pi$
$41$			71.1407i			1.73514i	−0.497317	+	0.867569i	$0.665681\pi$
$42$	18.0411	−	9.89949i	0.429549	−	0.235702i
$43$		−	37.7295i		−	0.877430i	−0.898626	−	0.438715i	$-0.855434\pi$
$43$		−	37.7295i		−	0.877430i	0.898626	−	0.438715i	$-0.144566\pi$
$44$	−3.35756			−0.0763082
$45$	21.7846	+	8.52671i	0.484103	+	0.189482i
$46$	−5.35756			−0.116469
$47$	−71.4209			−1.51959			−0.759797	−	0.650160i	$-0.774702\pi$
$47$	−71.4209			−1.51959			−0.759797	+	0.650160i	$0.774702\pi$
$48$	−8.31502			−0.173230
$49$	−26.3212	+	41.3303i	−0.537168	+	0.843475i
$50$	24.0000	−	25.9615i	0.480000	−	0.519230i
$51$	1.03634			0.0203204
$52$	−19.6213			−0.377332
$53$		−	83.0357i		−	1.56671i	−0.621574	−	0.783356i	$-0.713506\pi$
$53$		−	83.0357i		−	1.56671i	0.621574	−	0.783356i	$-0.286494\pi$
$54$		−	40.2129i		−	0.744684i
$55$	−7.81648	−	3.05944i	−0.142118	−	0.0556263i
$56$	17.3576	−	9.52445i	0.309956	−	0.170079i
$57$			66.9737i			1.17498i
$58$			55.2057i			0.951823i
$59$		−	36.4484i		−	0.617770i	−0.951099	−	0.308885i	$-0.900044\pi$
$59$		−	36.4484i		−	0.617770i	0.951099	−	0.308885i	$-0.0999558\pi$
$60$	−19.3576	−	7.57673i	−0.322626	−	0.126279i
$61$		−	50.4424i		−	0.826925i	−0.910521	−	0.413462i	$-0.864319\pi$
$61$		−	50.4424i		−	0.826925i	0.910521	−	0.413462i	$-0.135681\pi$
$62$	−35.2542			−0.568617
$63$	15.7553	+	28.7128i	0.250085	+	0.455760i
$64$	−8.00000			−0.125000
$65$	−45.6788	−	17.8791i	−0.702750	−	0.275063i
$66$			4.93528i			0.0747770i
$67$			12.2736i			0.183189i	0.995796	+	0.0915944i	$0.0291963\pi$
$67$			12.2736i			0.183189i	−0.995796	+	0.0915944i	$0.970804\pi$
$68$	0.997077			0.0146629
$69$			7.87508i			0.114132i
$70$	49.0876	−	6.35675i	0.701251	−	0.0908107i
$71$	44.6424			0.628767			0.314383	−	0.949296i	$-0.398202\pi$
$71$	44.6424			0.628767			0.314383	+	0.949296i	$0.398202\pi$
$72$		−	13.2336i		−	0.183800i
$73$	102.433			1.40319			0.701596	−	0.712575i	$-0.252471\pi$
$73$	102.433			1.40319			0.701596	+	0.712575i	$0.252471\pi$
$74$	22.7151			0.306961
$75$	−38.1609	−	35.2776i	−0.508811	−	0.470368i
$76$			64.4364i			0.847847i
$77$	−5.65313	−	10.3024i	−0.0734172	−	0.133797i
$78$			28.8413i			0.369761i
$79$	132.394			1.67587			0.837936	−	0.545768i	$-0.183762\pi$
$79$	132.394			1.67587			0.837936	+	0.545768i	$0.183762\pi$
$80$	−18.6242	−	7.28969i	−0.232802	−	0.0911211i
$81$	−17.0000			−0.209877
$82$	100.608			1.22693
$83$	8.72896			0.105168			0.0525841	−	0.998617i	$-0.483254\pi$
$83$	8.72896			0.105168			0.0525841	+	0.998617i	$0.483254\pi$
$84$	−14.0000	−	25.5139i	−0.166667	−	0.303737i
$85$	2.32122	+	0.908548i	0.0273085	+	0.0106888i
$86$	−53.3576			−0.620437
$87$	81.1470			0.932724
$88$			4.74831i			0.0539580i
$89$			54.0872i			0.607722i	0.952716	+	0.303861i	$0.0982758\pi$
$89$			54.0872i			0.607722i	−0.952716	+	0.303861i	$0.901724\pi$
$90$	12.0586	−	30.8081i	0.133984	−	0.342312i
$91$	−33.0363	−	60.2061i	−0.363037	−	0.661606i
$92$			7.57673i			0.0823558i
$93$			51.8202i			0.557207i
$94$			101.004i			1.07452i
$95$	−58.7151	+	150.009i	−0.618054	+	1.57905i
$96$			11.7592i			0.122492i
$97$	−41.7352			−0.430260			−0.215130	−	0.976585i	$-0.569018\pi$
$97$	−41.7352			−0.430260			−0.215130	+	0.976585i	$0.569018\pi$
$98$	58.4499	+	37.2238i	0.596427	+	0.379835i
$99$	−7.85464			−0.0793398
$100$	−36.7151	−	33.9411i	−0.367151	−	0.339411i
$101$		−	103.944i		−	1.02915i	−0.857445	−	0.514576i	$-0.827950\pi$
$101$		−	103.944i		−	1.02915i	0.857445	−	0.514576i	$-0.172050\pi$
$102$		−	1.46561i		−	0.0143687i
$103$	−50.8026			−0.493229			−0.246614	−	0.969114i	$-0.579318\pi$
$103$	−50.8026			−0.493229			−0.246614	+	0.969114i	$0.579318\pi$
$104$			27.7487i			0.266814i
$105$	−9.34379	−	72.1539i	−0.0889885	−	0.687180i
$106$	−117.430			−1.10783
$107$		−	110.463i		−	1.03236i	−0.856479	−	0.516181i	$-0.827353\pi$
$107$		−	110.463i		−	1.03236i	0.856479	−	0.516181i	$-0.172647\pi$
$108$	−56.8696			−0.526571
$109$	141.182			1.29524			0.647622	−	0.761961i	$-0.275763\pi$
$109$	141.182			1.29524			0.647622	+	0.761961i	$0.275763\pi$
$110$	−4.32671	+	11.0542i	−0.0393337	+	0.100492i
$111$		−	33.3890i		−	0.300802i
$112$	−13.4696	−	24.5473i	−0.120264	−	0.219172i
$113$		−	82.1272i		−	0.726789i	−0.931635	−	0.363395i	$-0.881618\pi$
$113$		−	82.1272i		−	0.726789i	0.931635	−	0.363395i	$-0.118382\pi$
$114$	94.7151			0.830834
$115$	−6.90400	+	17.6388i	−0.0600348	+	0.153381i
$116$	78.0727			0.673040
$117$	−45.9018			−0.392323
$118$	−51.5459			−0.436829
$119$	1.67878	+	3.05944i	0.0141074	+	0.0257096i
$120$	−10.7151	+	27.3757i	−0.0892927	+	0.228131i
$121$	−118.182			−0.976708
$122$	−71.3363			−0.584724
$123$		−	147.884i		−	1.20231i
$124$			49.8570i			0.402073i
$125$	−54.5462	−	112.471i	−0.436369	−	0.899768i
$126$	40.6061	−	22.2814i	0.322271	−	0.176837i
$127$		−	78.3388i		−	0.616841i	−0.951250	−	0.308420i	$-0.900200\pi$
$127$		−	78.3388i		−	0.616841i	0.951250	−	0.308420i	$-0.0998004\pi$
$128$			11.3137i			0.0883883i
$129$			78.4304i			0.607987i
$130$	−25.2849	+	64.5996i	−0.194499	+	0.496920i
$131$			233.988i			1.78617i	0.449892	+	0.893083i	$0.351463\pi$
$131$			233.988i			1.78617i	−0.449892	+	0.893083i	$0.648537\pi$
$132$	6.97954			0.0528753
$133$	−197.717	+	108.492i	−1.48660	+	0.815726i
$134$	17.3576			0.129534
$135$	−132.394	−	51.8202i	−0.980696	−	0.383854i
$136$		−	1.41008i		−	0.0103682i
$137$			151.827i			1.10822i	0.832443	+	0.554111i	$0.186942\pi$
$137$			151.827i			1.10822i	−0.832443	+	0.554111i	$0.813058\pi$
$138$	11.1371			0.0807033
$139$		−	80.1865i		−	0.576882i	−0.957498	−	0.288441i	$-0.906863\pi$
$139$		−	80.1865i		−	0.576882i	0.957498	−	0.288441i	$-0.0931368\pi$
$140$	−8.98980	−	69.4203i	−0.0642129	−	0.495860i
$141$	148.467			1.05295
$142$		−	63.1339i		−	0.444605i
$143$	16.4699			0.115174
$144$	−18.7151			−0.129966
$145$	181.755	+	71.1407i	1.25348	+	0.490625i
$146$		−	144.862i		−	0.992207i
$147$	54.7154	−	85.9155i	0.372213	−	0.584459i
$148$		−	32.1240i		−	0.217054i
$149$	91.3576			0.613138			0.306569	−	0.951848i	$-0.400819\pi$
$149$	91.3576			0.613138			0.306569	+	0.951848i	$0.400819\pi$
$150$	−49.8901	+	53.9676i	−0.332601	+	0.359784i
$151$	−174.467			−1.15541			−0.577704	−	0.816246i	$-0.696051\pi$
$151$	−174.467			−1.15541			−0.577704	+	0.816246i	$0.696051\pi$
$152$	91.1268			0.599518
$153$	2.33255			0.0152454
$154$	−14.5698	+	7.99473i	−0.0946088	+	0.0519138i
$155$	−45.4302	+	116.068i	−0.293098	+	0.748828i
$156$	40.7878			0.261460
$157$	−38.5839			−0.245757			−0.122879	−	0.992422i	$-0.539213\pi$
$157$	−38.5839			−0.245757			−0.122879	+	0.992422i	$0.539213\pi$
$158$		−	187.233i		−	1.18502i
$159$			172.611i			1.08560i
$160$	−10.3092	+	26.3386i	−0.0644323	+	0.164616i
$161$	−23.2485	+	12.7570i	−0.144401	+	0.0792357i
$162$			24.0416i			0.148405i
$163$			291.379i			1.78760i	0.448462	+	0.893802i	$0.351972\pi$
$163$			291.379i			1.78760i	−0.448462	+	0.893802i	$0.648028\pi$
$164$		−	142.281i		−	0.867569i
$165$	16.2485	+	6.35983i	0.0984760	+	0.0385444i
$166$		−	12.3446i		−	0.0743651i
$167$	205.458			1.23029			0.615145	−	0.788414i	$-0.289098\pi$
$167$	205.458			1.23029			0.615145	+	0.788414i	$0.289098\pi$
$168$	−36.0821	+	19.7990i	−0.214774	+	0.117851i
$169$	−72.7515			−0.430482
$170$	1.28488	−	3.28270i	0.00755812	−	0.0193100i
$171$			150.742i			0.881531i
$172$			75.4590i			0.438715i
$173$	173.102			1.00059			0.500294	−	0.865856i	$-0.333225\pi$
$173$	173.102			1.00059			0.500294	+	0.865856i	$0.333225\pi$
$174$		−	114.759i		−	0.659535i
$175$	42.3281	−	169.804i	0.241875	−	0.970307i
$176$	6.71512			0.0381541
$177$			75.7673i			0.428064i
$178$	76.4909			0.429724
$179$	−14.0727			−0.0786183			−0.0393092	−	0.999227i	$-0.512516\pi$
$179$	−14.0727			−0.0786183			−0.0393092	+	0.999227i	$0.512516\pi$
$180$	−43.5692	−	17.0534i	−0.242051	−	0.0947412i
$181$		−	170.269i		−	0.940714i	−0.882476	−	0.470357i	$-0.844125\pi$
$181$		−	170.269i		−	0.940714i	0.882476	−	0.470357i	$-0.155875\pi$
$182$	−85.1443	+	46.7204i	−0.467826	+	0.256706i
$183$			104.857i			0.572991i
$184$	10.7151			0.0582343
$185$	29.2718	−	74.7855i	0.158226	−	0.404246i
$186$	73.2849			0.394005
$187$	−0.836937			−0.00447560
$188$	142.842			0.759797
$189$	−95.7515	−	174.500i	−0.506621	−	0.923278i
$190$	212.145	+	83.0357i	1.11655	+	0.437030i
$191$	151.254			0.791908			0.395954	−	0.918270i	$-0.370414\pi$
$191$	151.254			0.791908			0.395954	+	0.918270i	$0.370414\pi$
$192$	16.6300			0.0866148
$193$		−	336.686i		−	1.74449i	−0.489074	−	0.872243i	$-0.662665\pi$
$193$		−	336.686i		−	1.74449i	0.489074	−	0.872243i	$-0.337335\pi$
$194$			59.0225i			0.304240i
$195$	94.9550	+	37.1663i	0.486949	+	0.190596i
$196$	52.6424	−	82.6606i	0.268584	−	0.421738i
$197$		−	2.72564i		−	0.0138358i	−0.999976	−	0.00691788i	$-0.997798\pi$
$197$		−	2.72564i		−	0.0138358i	0.999976	−	0.00691788i	$-0.00220205\pi$
$198$			11.1081i			0.0561017i
$199$			87.4762i			0.439579i	0.975547	+	0.219790i	$0.0705371\pi$
$199$			87.4762i			0.439579i	−0.975547	+	0.219790i	$0.929463\pi$
$200$	−48.0000	+	51.9230i	−0.240000	+	0.259615i
$201$		−	25.5139i		−	0.126935i
$202$	−146.999			−0.727720
$203$	131.451	+	239.559i	0.647542	+	1.18009i
$204$	−2.07268			−0.0101602
$205$	129.648	−	331.234i	0.632431	−	1.61578i
$206$			71.8457i			0.348766i
$207$			17.7249i			0.0856277i
$208$	39.2425			0.188666
$209$		−	54.0872i		−	0.258791i
$210$	−102.041	+	13.2141i	−0.485910	+	0.0629244i
$211$	−14.6119			−0.0692509			−0.0346254	−	0.999400i	$-0.511024\pi$
$211$	−14.6119			−0.0692509			−0.0346254	+	0.999400i	$0.511024\pi$
$212$			166.071i			0.783356i
$213$	−92.8007			−0.435684
$214$	−156.218			−0.729991
$215$	−68.7590	+	175.670i	−0.319809	+	0.817071i
$216$			80.4258i			0.372342i
$217$	−152.982	+	83.9443i	−0.704985	+	0.386840i
$218$		−	199.661i		−	0.915876i
$219$	−212.933			−0.972298
$220$	15.6330	+	6.11889i	0.0710589	+	0.0278131i
$221$	−4.89098			−0.0221311
$222$	−47.2192			−0.212699
$223$	−129.964			−0.582800			−0.291400	−	0.956601i	$-0.594121\pi$
$223$	−129.964			−0.582800			−0.291400	+	0.956601i	$0.594121\pi$
$224$	−34.7151	+	19.0489i	−0.154978	+	0.0850397i
$225$	−85.8910	−	79.4015i	−0.381738	−	0.352896i
$226$	−116.145			−0.513918
$227$	−133.276			−0.587119			−0.293559	−	0.955941i	$-0.594840\pi$
$227$	−133.276			−0.587119			−0.293559	+	0.955941i	$0.594840\pi$
$228$		−	133.947i		−	0.587489i
$229$		−	220.579i		−	0.963228i	−0.876383	−	0.481614i	$-0.840051\pi$
$229$		−	220.579i		−	0.963228i	0.876383	−	0.481614i	$-0.159949\pi$
$230$	24.9451	+	9.76373i	0.108457	+	0.0424510i
$231$	11.7515	+	21.4161i	0.0508721	+	0.0927104i
$232$		−	110.411i		−	0.475911i
$233$			216.983i			0.931258i	0.884980	+	0.465629i	$0.154172\pi$
$233$			216.983i			0.931258i	−0.884980	+	0.465629i	$0.845828\pi$
$234$			64.9149i			0.277414i
$235$	332.539	+	130.159i	1.41506	+	0.553868i
$236$			72.8969i			0.308885i
$237$	−275.214			−1.16124
$238$	4.32671	−	2.37415i	0.0181794	−	0.00997543i
$239$	−315.897			−1.32174			−0.660872	−	0.750499i	$-0.729813\pi$
$239$	−315.897			−1.32174			−0.660872	+	0.750499i	$0.729813\pi$
$240$	38.7151	+	15.1535i	0.161313	+	0.0631394i
$241$			228.001i			0.946064i	0.881045	+	0.473032i	$0.156840\pi$
$241$			228.001i			0.946064i	−0.881045	+	0.473032i	$0.843160\pi$
$242$			167.134i			0.690637i
$243$	−220.575			−0.907714
$244$			100.885i			0.413462i
$245$	197.874	−	144.467i	0.807649	−	0.589663i
$246$	−209.140			−0.850161
$247$		−	316.081i		−	1.27968i
$248$	70.5085			0.284308
$249$	−18.1454			−0.0728729
$250$	−159.058	+	77.1399i	−0.636232	+	0.308560i
$251$		−	83.9638i		−	0.334517i	−0.985913	−	0.167259i	$-0.946509\pi$
$251$		−	83.9638i		−	0.334517i	0.985913	−	0.167259i	$-0.0534915\pi$
$252$	−31.5107	−	57.4257i	−0.125042	−	0.227880i
$253$		−	6.35983i		−	0.0251377i
$254$	−110.788			−0.436172
$255$	−4.82525	−	1.88865i	−0.0189225	−	0.00740646i
$256$	16.0000			0.0625000
$257$	174.597			0.679367			0.339683	−	0.940540i	$-0.389680\pi$
$257$	174.597			0.679367			0.339683	+	0.940540i	$0.389680\pi$
$258$	110.917			0.429912
$259$	98.5698	−	54.0872i	0.380578	−	0.208831i
$260$	91.3576	+	35.7582i	0.351375	+	0.137532i
$261$	182.642			0.699779
$262$	330.909			1.26301
$263$		−	151.672i		−	0.576701i	−0.957525	−	0.288350i	$-0.906893\pi$
$263$		−	151.672i		−	0.576701i	0.957525	−	0.288350i	$-0.0931068\pi$
$264$		−	9.87056i		−	0.0373885i
$265$	−151.326	+	386.618i	−0.571042	+	1.45894i
$266$	153.430	+	279.615i	0.576805	+	1.05118i
$267$		−	112.434i		−	0.421102i
$268$		−	24.5473i		−	0.0915944i
$269$		−	440.120i		−	1.63613i	−0.575123	−	0.818067i	$-0.695046\pi$
$269$		−	440.120i		−	1.63613i	0.575123	−	0.818067i	$-0.304954\pi$
$270$	−73.2849	+	187.233i	−0.271425	+	0.693456i
$271$		−	376.269i		−	1.38845i	−0.719760	−	0.694223i	$-0.755748\pi$
$271$		−	376.269i		−	1.38845i	0.719760	−	0.694223i	$-0.244252\pi$
$272$	−1.99415			−0.00733145
$273$	68.6744	+	125.154i	0.251555	+	0.458439i
$274$	214.715			0.783632
$275$	30.8183	+	28.4898i	0.112067	+	0.103599i
$276$		−	15.7502i		−	0.0570658i
$277$			333.960i			1.20563i	0.797880	+	0.602816i	$0.205955\pi$
$277$			333.960i			1.20563i	−0.797880	+	0.602816i	$0.794045\pi$
$278$	−113.401			−0.407917
$279$			116.635i			0.418047i
$280$	−98.1752	+	12.7135i	−0.350626	+	0.0454053i
$281$	378.612			1.34737			0.673687	−	0.739017i	$-0.264710\pi$
$281$	378.612			1.34737			0.673687	+	0.739017i	$0.264710\pi$
$282$		−	209.963i		−	0.744551i
$283$	−279.447			−0.987447			−0.493723	−	0.869619i	$-0.664364\pi$
$283$	−279.447			−0.987447			−0.493723	+	0.869619i	$0.664364\pi$
$284$	−89.2849			−0.314383
$285$	122.054	−	311.833i	0.428261	−	1.09415i
$286$		−	23.2919i		−	0.0814404i
$287$	436.578	−	239.559i	1.52118	−	0.834701i
$288$			26.4672i			0.0918999i
$289$	−288.751			−0.999140
$290$	100.608	−	257.040i	0.346924	−	0.886346i
$291$	86.7573			0.298135
$292$	−204.866			−0.701596
$293$	−235.954			−0.805303			−0.402651	−	0.915353i	$-0.631911\pi$
$293$	−235.954			−0.805303			−0.402651	+	0.915353i	$0.631911\pi$
$294$	−121.503	−	77.3792i	−0.413275	−	0.263195i
$295$	−66.4244	+	169.706i	−0.225167	+	0.575273i
$296$	−45.4302			−0.153481
$297$	47.7358			0.160727
$298$		−	129.199i		−	0.433554i
$299$		−	37.1663i		−	0.124302i
$300$	76.3217	+	70.5553i	0.254406	+	0.235184i
$301$	−231.539	+	127.050i	−0.769233	+	0.422094i
$302$			246.733i			0.816997i
$303$			216.075i			0.713117i
$304$		−	128.873i		−	0.423924i
$305$	−91.9273	+	234.862i	−0.301401	+	0.770040i
$306$		−	3.29873i		−	0.0107802i
$307$	425.450			1.38583			0.692915	−	0.721019i	$-0.256326\pi$
$307$	425.450			1.38583			0.692915	+	0.721019i	$0.256326\pi$
$308$	11.3063	+	20.6048i	0.0367086	+	0.0668986i
$309$	105.606			0.341767
$310$	164.145	+	64.2481i	0.529501	+	0.207252i
$311$		−	199.881i		−	0.642704i	−0.946960	−	0.321352i	$-0.895863\pi$
$311$		−	199.881i		−	0.642704i	0.946960	−	0.321352i	$-0.104137\pi$
$312$		−	57.6827i		−	0.184880i
$313$	412.243			1.31707			0.658535	−	0.752550i	$-0.271176\pi$
$313$	412.243			1.31707			0.658535	+	0.752550i	$0.271176\pi$
$314$			54.5658i			0.173776i
$315$	−21.0306	−	162.401i	−0.0667640	−	0.515560i
$316$	−264.788			−0.837936
$317$		−	107.891i		−	0.340351i	−0.985414	−	0.170176i	$-0.945566\pi$
$317$		−	107.891i		−	0.340351i	0.985414	−	0.170176i	$-0.0544335\pi$
$318$	244.109			0.767637
$319$	−65.5334			−0.205434
$320$	37.2484	+	14.5794i	0.116401	+	0.0455605i
$321$			229.625i			0.715343i
$322$	18.0411	+	32.8784i	0.0560281	+	0.102107i
$323$			16.0620i			0.0497276i
$324$	34.0000			0.104938
$325$	180.099	+	166.492i	0.554152	+	0.512283i
$326$	412.073			1.26403
$327$	−293.482			−0.897499
$328$	−201.216			−0.613464
$329$	240.503	+	438.298i	0.731012	+	1.33221i
$330$	8.99416	−	22.9789i	0.0272550	−	0.0696331i
$331$	−38.0727			−0.115023			−0.0575116	−	0.998345i	$-0.518317\pi$
$331$	−38.0727			−0.115023			−0.0575116	+	0.998345i	$0.518317\pi$
$332$	−17.4579			−0.0525841
$333$		−	75.1506i		−	0.225678i
$334$		−	290.562i		−	0.869946i
$335$	22.3678	−	57.1467i	0.0667694	−	0.170587i
$336$	28.0000	+	51.0278i	0.0833333	+	0.151868i
$337$			260.626i			0.773372i	0.922211	+	0.386686i	$0.126380\pi$
$337$			260.626i			0.773372i	−0.922211	+	0.386686i	$0.873620\pi$
$338$			102.886i			0.304397i
$339$			170.722i			0.503605i
$340$	−4.64244	−	1.81710i	−0.0136542	−	0.00534440i
$341$		−	41.8495i		−	0.122726i
$342$	213.181			0.623337
$343$	342.271	+	22.3530i	0.997874	+	0.0651691i
$344$	106.715			0.310218
$345$	14.3517	−	36.6668i	0.0415992	−	0.106280i
$346$		−	244.803i		−	0.707522i
$347$		−	390.785i		−	1.12618i	−0.826395	−	0.563091i	$-0.809612\pi$
$347$		−	390.785i		−	1.12618i	0.826395	−	0.563091i	$-0.190388\pi$
$348$	−162.294			−0.466362
$349$			561.118i			1.60779i	0.594773	+	0.803894i	$0.297242\pi$
$349$			561.118i			1.60779i	−0.594773	+	0.803894i	$0.702758\pi$
$350$	−240.139	−	59.8610i	−0.686111	−	0.171031i
$351$	278.964			0.794768
$352$		−	9.49661i		−	0.0269790i
$353$	−254.916			−0.722143			−0.361071	−	0.932538i	$-0.617589\pi$
$353$	−254.916			−0.722143			−0.361071	+	0.932538i	$0.617589\pi$
$354$	107.151			0.302687
$355$	−207.857	−	81.3573i	−0.585514	−	0.229176i
$356$		−	108.174i		−	0.303861i
$357$	−3.48977	−	6.35983i	−0.00977527	−	0.0178147i
$358$			19.9018i			0.0555915i
$359$	36.9332			0.102878			0.0514389	−	0.998676i	$-0.483619\pi$
$359$	36.9332			0.102878			0.0514389	+	0.998676i	$0.483619\pi$
$360$	−24.1172	+	61.6162i	−0.0669922	+	0.171156i
$361$	−677.012			−1.87538
$362$	−240.797			−0.665185
$363$	245.671			0.676779
$364$	66.0727	+	120.412i	0.181518	+	0.330803i
$365$	−476.933	−	186.676i	−1.30667	−	0.511442i
$366$	148.291			0.405166
$367$	−267.483			−0.728835			−0.364418	−	0.931236i	$-0.618732\pi$
$367$	−267.483			−0.728835			−0.364418	+	0.931236i	$0.618732\pi$
$368$		−	15.1535i		−	0.0411779i
$369$		−	332.852i		−	0.902037i
$370$	−105.763	−	41.3965i	−0.285845	−	0.111882i
$371$	−509.576	+	279.615i	−1.37352	+	0.753678i
$372$		−	103.640i		−	0.278603i
$373$			126.971i			0.340404i	0.985409	+	0.170202i	$0.0544421\pi$
$373$			126.971i			0.340404i	−0.985409	+	0.170202i	$0.945558\pi$
$374$			1.18361i			0.00316473i
$375$	113.388	+	233.800i	0.302368	+	0.623465i
$376$		−	202.009i		−	0.537258i
$377$	−382.971			−1.01584
$378$	−246.780	+	135.413i	−0.652856	+	0.358235i
$379$	519.939			1.37187			0.685935	−	0.727662i	$-0.259393\pi$
$379$	519.939			1.37187			0.685935	+	0.727662i	$0.259393\pi$
$380$	117.430	−	300.019i	0.309027	−	0.789523i
$381$			162.847i			0.427420i
$382$		−	213.906i		−	0.559963i
$383$	−393.703			−1.02795			−0.513973	−	0.857806i	$-0.671827\pi$
$383$	−393.703			−1.02795			−0.513973	+	0.857806i	$0.671827\pi$
$384$		−	23.5184i		−	0.0612459i
$385$	7.54595	+	58.2707i	0.0195999	+	0.151353i
$386$	−476.145			−1.23354
$387$			176.528i			0.456145i
$388$	83.4705			0.215130
$389$	106.031			0.272572			0.136286	−	0.990670i	$-0.456483\pi$
$389$	106.031			0.272572			0.136286	+	0.990670i	$0.456483\pi$
$390$	52.5611	−	134.287i	0.134772	−	0.344325i
$391$			1.88865i			0.00483030i
$392$	−116.900	−	74.4477i	−0.298214	−	0.189917i
$393$		−	486.403i		−	1.23767i
$394$	−3.85464			−0.00978335
$395$	−616.432	−	241.277i	−1.56059	−	0.610829i
$396$	15.7093			0.0396699
$397$	391.625			0.986460			0.493230	−	0.869899i	$-0.335816\pi$
$397$	391.625			0.986460			0.493230	+	0.869899i	$0.335816\pi$
$398$	123.710			0.310829
$399$	411.006	−	225.527i	1.03009	−	0.565231i
$400$	73.4302	+	67.8823i	0.183576	+	0.169706i
$401$	41.1090			0.102516			0.0512581	−	0.998685i	$-0.483677\pi$
$401$	41.1090			0.102516			0.0512581	+	0.998685i	$0.483677\pi$
$402$	−36.0821			−0.0897565
$403$		−	244.564i		−	0.606860i
$404$			207.889i			0.514576i
$405$	79.1528	+	30.9812i	0.195439	+	0.0764967i
$406$	338.788	−	185.900i	0.834453	−	0.457881i
$407$			26.9646i			0.0662521i
$408$			2.93121i			0.00718434i
$409$			511.846i			1.25146i	0.780041	+	0.625729i	$0.215198\pi$
$409$			511.846i			1.25146i	−0.780041	+	0.625729i	$0.784802\pi$
$410$	−468.436	−	183.350i	−1.14253	−	0.447196i
$411$		−	315.610i		−	0.767908i
$412$	101.605			0.246614
$413$	−223.678	+	122.736i	−0.541592	+	0.297183i
$414$	25.0668			0.0605479
$415$	−40.6424	−	15.9078i	−0.0979336	−	0.0383321i
$416$		−	55.4973i		−	0.133407i
$417$			166.688i			0.399732i
$418$	−76.4909			−0.182993
$419$		−	82.5281i		−	0.196965i	−0.995139	−	0.0984823i	$-0.968601\pi$
$419$		−	82.5281i		−	0.196965i	0.995139	−	0.0984823i	$-0.0313988\pi$
$420$	18.6876	+	144.308i	0.0444943	+	0.343590i
$421$	−227.400			−0.540142			−0.270071	−	0.962840i	$-0.587047\pi$
$421$	−227.400			−0.540142			−0.270071	+	0.962840i	$0.587047\pi$
$422$			20.6644i			0.0489678i
$423$	334.163			0.789983
$424$	234.860			0.553916
$425$	−9.15195	−	8.46048i	−0.0215340	−	0.0199070i
$426$			131.240i			0.308075i
$427$	−309.556	+	169.860i	−0.724956	+	0.397798i
$428$			220.926i			0.516181i
$429$	−34.2369			−0.0798062
$430$	248.435	+	97.2400i	0.577757	+	0.226139i
$431$	254.964			0.591563			0.295782	−	0.955256i	$-0.404420\pi$
$431$	254.964			0.591563			0.295782	+	0.955256i	$0.404420\pi$
$432$	113.739			0.263285
$433$	675.154			1.55925			0.779624	−	0.626248i	$-0.215410\pi$
$433$	675.154			1.55925			0.779624	+	0.626248i	$0.215410\pi$
$434$	118.715	+	216.349i	0.273537	+	0.498500i
$435$	−377.824	−	147.884i	−0.868561	−	0.339963i
$436$	−282.363			−0.647622
$437$	−122.054			−0.279300
$438$			301.133i			0.687518i
$439$		−	3.77730i		−	0.00860432i	−0.999991	−	0.00430216i	$-0.998631\pi$
$439$		−	3.77730i		−	0.00860432i	0.999991	−	0.00430216i	$-0.00136942\pi$
$440$	8.65342	−	22.1083i	0.0196669	−	0.0502462i
$441$	123.151	−	193.375i	0.279254	−	0.438493i
$442$			6.91689i			0.0156491i
$443$		−	273.500i		−	0.617382i	−0.951162	−	0.308691i	$-0.900109\pi$
$443$		−	273.500i		−	0.617382i	0.951162	−	0.308691i	$-0.0998909\pi$
$444$			66.7780i			0.150401i
$445$	98.5698	−	251.833i	0.221505	−	0.565916i
$446$			183.797i			0.412102i
$447$	−189.910			−0.424854
$448$	26.9392	+	49.0946i	0.0601322	+	0.109586i
$449$	232.042			0.516798			0.258399	−	0.966038i	$-0.416805\pi$
$449$	232.042			0.516798			0.258399	+	0.966038i	$0.416805\pi$
$450$	−112.291	+	121.468i	−0.249535	+	0.269929i
$451$			119.430i			0.264810i
$452$			164.254i			0.363395i
$453$	362.673			0.800603
$454$			188.481i			0.415156i
$455$	44.0978	+	340.529i	0.0969183	+	0.748415i
$456$	−189.430			−0.415417
$457$			371.243i			0.812349i	0.913796	+	0.406174i	$0.133137\pi$
$457$			371.243i			0.812349i	−0.913796	+	0.406174i	$0.866863\pi$
$458$	−311.946			−0.681105
$459$	−14.1759			−0.0308842
$460$	13.8080	−	35.2776i	0.0300174	−	0.0766905i
$461$			12.2378i			0.0265462i	0.999912	+	0.0132731i	$0.00422508\pi$
$461$			12.2378i			0.0265462i	−0.999912	+	0.0132731i	$0.995775\pi$
$462$	30.2870	−	16.6191i	0.0655562	−	0.0359720i
$463$		−	266.232i		−	0.575015i	−0.957778	−	0.287507i	$-0.907173\pi$
$463$		−	266.232i		−	0.575015i	0.957778	−	0.287507i	$-0.0928266\pi$
$464$	−156.145			−0.336520
$465$	94.4383	−	241.277i	0.203093	−	0.518876i
$466$	306.860			0.658499
$467$	287.932			0.616556			0.308278	−	0.951296i	$-0.400247\pi$
$467$	287.932			0.616556			0.308278	+	0.951296i	$0.400247\pi$
$468$	91.8036			0.196162
$469$	75.3212	−	41.3303i	0.160600	−	0.0881243i
$470$	184.073	−	470.282i	0.391644	−	1.00060i
$471$	80.2064			0.170290
$472$	103.092			0.218415
$473$		−	63.3395i		−	0.133910i
$474$			389.212i			0.821122i
$475$	546.761	−	591.447i	1.15108	−	1.24515i
$476$	−3.35756	−	6.11889i	−0.00705370	−	0.0128548i
$477$			388.506i			0.814478i
$478$			446.746i			0.934614i
$479$		−	235.159i		−	0.490937i	−0.969405	−	0.245468i	$-0.921058\pi$
$479$		−	235.159i		−	0.490937i	0.969405	−	0.245468i	$-0.0789417\pi$
$480$	21.4302	−	54.7514i	0.0446463	−	0.114066i
$481$			157.579i			0.327606i
$482$	322.443			0.668968
$483$	48.3280	−	26.5186i	0.100058	−	0.0549039i
$484$	236.363			0.488354
$485$	194.321	+	76.0592i	0.400662	+	0.156823i
$486$			311.940i			0.641851i
$487$			291.379i			0.598315i	0.954204	+	0.299157i	$0.0967056\pi$
$487$			291.379i			0.598315i	−0.954204	+	0.299157i	$0.903294\pi$
$488$	142.673			0.292362
$489$		−	605.706i		−	1.23866i
$490$	−204.308	−	279.836i	−0.416955	−	0.571094i
$491$	610.260			1.24289			0.621446	−	0.783457i	$-0.286545\pi$
$491$	610.260			1.24289			0.621446	+	0.783457i	$0.286545\pi$
$492$			295.768i			0.601154i
$493$	19.4611			0.0394749
$494$	−447.006			−0.904870
$495$	36.5716	+	14.3145i	0.0738820	+	0.0289181i
$496$		−	99.7140i		−	0.201036i
$497$	−150.329	−	273.963i	−0.302473	−	0.551233i
$498$			25.6614i			0.0515289i
$499$	49.6788			0.0995567			0.0497783	−	0.998760i	$-0.484149\pi$
$499$	49.6788			0.0995567			0.0497783	+	0.998760i	$0.484149\pi$
$500$	109.092	+	224.942i	0.218185	+	0.449884i
$501$	−427.097			−0.852490
$502$	−118.743			−0.236539
$503$	−441.083			−0.876904			−0.438452	−	0.898755i	$-0.644473\pi$
$503$	−441.083			−0.876904			−0.438452	+	0.898755i	$0.644473\pi$
$504$	−81.2122	+	44.5628i	−0.161135	+	0.0884183i
$505$	−189.430	+	483.969i	−0.375109	+	0.958355i
$506$	−8.99416			−0.0177750
$507$	151.232			0.298289
$508$			156.678i			0.308420i
$509$			420.460i			0.826051i	0.910719	+	0.413026i	$0.135528\pi$
$509$			420.460i			0.826051i	−0.910719	+	0.413026i	$0.864472\pi$
$510$	−2.67095	+	6.82393i	−0.00523716	+	0.0133803i
$511$	−344.933	−	628.614i	−0.675016	−	1.23016i
$512$		−	22.6274i		−	0.0441942i
$513$		−	916.119i		−	1.78581i
$514$		−	246.918i		−	0.480385i
$515$	236.539	+	92.5837i	0.459300	+	0.179774i
$516$		−	156.861i		−	0.303994i
$517$	−119.900			−0.231915
$518$	−76.4909	−	139.399i	−0.147666	−	0.269109i
$519$	−359.836			−0.693325
$520$	50.5698	−	129.199i	0.0972495	−	0.248460i
$521$		−	698.451i		−	1.34060i	−0.742092	−	0.670298i	$-0.766166\pi$
$521$		−	698.451i		−	1.34060i	0.742092	−	0.670298i	$-0.233834\pi$
$522$		−	258.295i		−	0.494819i
$523$	−434.940			−0.831625			−0.415813	−	0.909450i	$-0.636503\pi$
$523$	−434.940			−0.831625			−0.415813	+	0.909450i	$0.636503\pi$
$524$		−	467.976i		−	0.893083i
$525$	−87.9897	+	352.980i	−0.167599	+	0.672344i
$526$	−214.497			−0.407789
$527$			12.4278i			0.0235822i
$528$	−13.9591			−0.0264377
$529$	514.648			0.972870
$530$	546.761	+	214.007i	1.03162	+	0.403788i
$531$			170.534i			0.321157i
$532$	395.435	−	216.983i	0.743298	−	0.407863i
$533$			697.935i			1.30945i
$534$	−159.006			−0.297764
$535$	−201.310	+	514.320i	−0.376280	+	0.961346i
$536$	−34.7151			−0.0647670
$537$	29.2536			0.0544761
$538$	−622.424			−1.15692
$539$	−44.1875	+	69.3845i	−0.0819806	+	0.128728i
$540$	264.788	+	103.640i	0.490348	+	0.191927i
$541$	769.254			1.42191			0.710956	−	0.703237i	$-0.248262\pi$
$541$	769.254			1.42191			0.710956	+	0.703237i	$0.248262\pi$
$542$	−532.125			−0.981780
$543$			353.948i			0.651838i
$544$			2.82016i			0.00518412i
$545$	−657.349	−	257.293i	−1.20614	−	0.472096i
$546$	176.994	−	97.1203i	0.324165	−	0.177876i
$547$		−	242.885i		−	0.444031i	−0.975043	−	0.222016i	$-0.928736\pi$
$547$		−	242.885i		−	0.444031i	0.975043	−	0.222016i	$-0.0712636\pi$
$548$		−	303.653i		−	0.554111i
$549$			236.009i			0.429889i
$550$	40.2907	−	43.5837i	0.0732558	−	0.0792430i
$551$			1257.68i			2.28254i
$552$	−22.2741			−0.0403516
$553$	−445.823	−	812.478i	−0.806191	−	1.46922i
$554$	472.291			0.852510
$555$	−60.8488	+	155.461i	−0.109637	+	0.280109i
$556$			160.373i			0.288441i
$557$		−	766.109i		−	1.37542i	−0.725985	−	0.687710i	$-0.758616\pi$
$557$		−	766.109i		−	1.37542i	0.725985	−	0.687710i	$-0.241384\pi$
$558$	164.947			0.295604
$559$		−	370.150i		−	0.662165i
$560$	17.9796	+	138.841i	0.0321064	+	0.247930i
$561$	1.73979			0.00310122
$562$		−	535.438i		−	0.952737i
$563$	586.605			1.04193			0.520963	−	0.853579i	$-0.325573\pi$
$563$	586.605			1.04193			0.520963	+	0.853579i	$0.325573\pi$
$564$	−296.933			−0.526477
$565$	−149.670	+	382.388i	−0.264903	+	0.676793i
$566$			395.198i			0.698230i
$567$	57.2458	+	104.326i	0.100963	+	0.183996i
$568$			126.268i			0.222303i
$569$	−744.375			−1.30822			−0.654108	−	0.756401i	$-0.726956\pi$
$569$	−744.375			−1.30822			−0.654108	+	0.756401i	$0.726956\pi$
$570$	−440.998	−	172.611i	−0.773681	−	0.302826i
$571$	−323.503			−0.566555			−0.283278	−	0.959038i	$-0.591422\pi$
$571$	−323.503			−0.566555			−0.283278	+	0.959038i	$0.591422\pi$
$572$	−32.9398			−0.0575870
$573$	−314.421			−0.548727
$574$	−338.788	−	617.414i	−0.590223	−	1.07563i
$575$	64.2907	−	69.5452i	0.111810	−	0.120948i
$576$	37.4302			0.0649831
$577$	394.936			0.684465			0.342232	−	0.939615i	$-0.388817\pi$
$577$	394.936			0.684465			0.342232	+	0.939615i	$0.388817\pi$
$578$			408.356i			0.706499i
$579$			699.887i			1.20879i
$580$	−363.510	−	142.281i	−0.626742	−	0.245313i
$581$	−29.3939	−	53.5681i	−0.0505919	−	0.0921998i
$582$		−	122.693i		−	0.210813i
$583$		−	139.399i		−	0.239106i
$584$			289.724i			0.496103i
$585$	213.721	+	83.6524i	0.365335	+	0.142996i
$586$			333.689i			0.569435i
$587$	63.9610			0.108962			0.0544812	−	0.998515i	$-0.482649\pi$
$587$	63.9610			0.108962			0.0544812	+	0.998515i	$0.482649\pi$
$588$	−109.431	+	171.831i	−0.186107	+	0.292230i
$589$	−803.151			−1.36358
$590$	240.000	+	93.9383i	0.406780	+	0.159217i
$591$			5.66594i			0.00958704i
$592$			64.2481i			0.108527i
$593$	310.432			0.523495			0.261747	−	0.965136i	$-0.415701\pi$
$593$	310.432			0.523495			0.261747	+	0.965136i	$0.415701\pi$
$594$		−	67.5086i		−	0.113651i
$595$	−2.24088	−	17.3044i	−0.00376619	−	0.0290830i
$596$	−182.715			−0.306569
$597$		−	181.842i		−	0.304592i
$598$	−52.5611			−0.0878947
$599$	−429.885			−0.717671			−0.358836	−	0.933401i	$-0.616826\pi$
$599$	−429.885			−0.717671			−0.358836	+	0.933401i	$0.616826\pi$
$600$	99.7802	−	107.935i	0.166300	−	0.179892i
$601$		−	67.8163i		−	0.112839i	−0.998407	−	0.0564196i	$-0.982032\pi$
$601$		−	67.8163i		−	0.112839i	0.998407	−	0.0564196i	$-0.0179684\pi$
$602$	179.676	+	327.446i	0.298466	+	0.543930i
$603$		−	57.4257i		−	0.0952333i
$604$	348.933			0.577704
$605$	550.260	+	215.377i	0.909520	+	0.355995i
$606$	305.576			0.504250
$607$	−389.350			−0.641433			−0.320716	−	0.947175i	$-0.603924\pi$
$607$	−389.350			−0.641433			−0.320716	+	0.947175i	$0.603924\pi$
$608$	−182.254			−0.299759
$609$	−273.254	−	497.985i	−0.448694	−	0.817709i
$610$	332.145	+	130.005i	0.544501	+	0.213123i
$611$	−700.685			−1.14678
$612$	−4.66511			−0.00762272
$613$			822.472i			1.34172i	0.741586	+	0.670858i	$0.234074\pi$
$613$			822.472i			1.34172i	−0.741586	+	0.670858i	$0.765926\pi$
$614$		−	601.677i		−	0.979930i
$615$	−269.507	+	688.555i	−0.438223	+	1.11960i
$616$	29.1395	−	15.9895i	0.0473044	−	0.0259569i
$617$		−	507.916i		−	0.823203i	−0.911364	−	0.411602i	$-0.864969\pi$
$617$		−	507.916i		−	0.823203i	0.911364	−	0.411602i	$-0.135031\pi$
$618$		−	149.350i		−	0.241666i
$619$		−	167.210i		−	0.270129i	−0.990837	−	0.135064i	$-0.956876\pi$
$619$		−	167.210i		−	0.270129i	0.990837	−	0.135064i	$-0.0431242\pi$
$620$	90.8605	−	232.137i	0.146549	−	0.374414i
$621$		−	107.722i		−	0.173465i
$622$	−282.674			−0.454460
$623$	331.924	−	182.133i	0.532783	−	0.292349i
$624$	−81.5756			−0.130730
$625$	49.0000	+	623.076i	0.0784000	+	0.996922i
$626$		−	583.000i		−	0.931309i
$627$			112.434i			0.179321i
$628$	77.1677			0.122879
$629$		−	8.00754i		−	0.0127306i
$630$	−229.670	+	29.7418i	−0.364556	+	0.0472092i
$631$	538.696			0.853718			0.426859	−	0.904318i	$-0.359620\pi$
$631$	538.696			0.853718			0.426859	+	0.904318i	$0.359620\pi$
$632$			374.466i			0.592510i
$633$	30.3746			0.0479852
$634$	−152.581			−0.240665
$635$	−142.766	+	364.749i	−0.224829	+	0.574408i
$636$		−	345.222i		−	0.542801i
$637$	−258.228	+	405.476i	−0.405381	+	0.636541i
$638$			92.6783i			0.145264i
$639$	−208.872			−0.326873
$640$	20.6183	−	52.6772i	0.0322162	−	0.0823081i
$641$	520.788			0.812461			0.406231	−	0.913771i	$-0.366843\pi$
$641$	520.788			0.812461			0.406231	+	0.913771i	$0.366843\pi$
$642$	324.739			0.505824
$643$	547.317			0.851192			0.425596	−	0.904913i	$-0.360064\pi$
$643$	547.317			0.851192			0.425596	+	0.904913i	$0.360064\pi$
$644$	46.4971	−	25.5139i	0.0722004	−	0.0396179i
$645$	142.933	−	365.175i	0.221602	−	0.566163i
$646$	22.7151			0.0351627
$647$	639.806			0.988881			0.494441	−	0.869211i	$-0.335373\pi$
$647$	639.806			0.988881			0.494441	+	0.869211i	$0.335373\pi$
$648$		−	48.0833i		−	0.0742026i
$649$		−	61.1889i		−	0.0942818i
$650$	235.455	−	254.699i	0.362239	−	0.391844i
$651$	318.012	−	174.500i	0.488497	−	0.268048i
$652$		−	582.759i		−	0.893802i
$653$			386.397i			0.591726i	0.955230	+	0.295863i	$0.0956071\pi$
$653$			386.397i			0.591726i	−0.955230	+	0.295863i	$0.904393\pi$
$654$			415.046i			0.634627i
$655$	426.424	−	1089.46i	0.651030	−	1.66330i
$656$			284.563i			0.433785i
$657$	−479.262			−0.729470
$658$	619.847	−	340.122i	0.942016	−	0.516903i
$659$	−684.042			−1.03800			−0.519000	−	0.854774i	$-0.673696\pi$
$659$	−684.042			−1.03800			−0.519000	+	0.854774i	$0.673696\pi$
$660$	−32.4971	−	12.7197i	−0.0492380	−	0.0192722i
$661$			36.5809i			0.0553417i	0.999617	+	0.0276709i	$0.00880903\pi$
$661$			36.5809i			0.0553417i	−0.999617	+	0.0276709i	$0.991191\pi$
$662$			53.8429i			0.0813337i
$663$	10.1671			0.0153351
$664$			24.6892i			0.0371826i
$665$	1118.30	−	144.818i	1.68165	−	0.217771i
$666$	−106.279			−0.159578
$667$			147.884i			0.221715i
$668$	−410.917			−0.615145
$669$	270.164			0.403833
$670$	−80.8176	−	31.6328i	−0.120623	−	0.0472131i
$671$		−	84.6817i		−	0.126202i
$672$	72.1642	−	39.5980i	0.107387	−	0.0589256i
$673$			85.1447i			0.126515i	0.997997	+	0.0632575i	$0.0201490\pi$
$673$			85.1447i			0.126515i	−0.997997	+	0.0632575i	$0.979851\pi$
$674$	368.581			0.546857
$675$	521.994	+	482.555i	0.773324	+	0.714896i
$676$	145.503			0.215241
$677$	623.768			0.921371			0.460686	−	0.887563i	$-0.347604\pi$
$677$	623.768			0.921371			0.460686	+	0.887563i	$0.347604\pi$
$678$	241.438			0.356103
$679$	140.539	+	256.122i	0.206980	+	0.377204i
$680$	−2.56976	+	6.56540i	−0.00377906	+	0.00965500i
$681$	277.048			0.406825
$682$	−59.1841			−0.0867802
$683$			898.085i			1.31491i	0.753493	+	0.657456i	$0.228368\pi$
$683$			898.085i			1.31491i	−0.753493	+	0.657456i	$0.771632\pi$
$684$		−	301.484i		−	0.440766i
$685$	276.692	−	706.912i	0.403930	−	1.03199i
$686$	31.6119	−	484.044i	0.0460815	−	0.705604i
$687$			458.530i			0.667438i
$688$		−	150.918i		−	0.219358i
$689$		−	814.633i		−	1.18234i
$690$	−51.8546	−	20.2964i	−0.0751517	−	0.0294151i
$691$			487.503i			0.705504i	0.935717	+	0.352752i	$0.114754\pi$
$691$			487.503i			0.705504i	−0.935717	+	0.352752i	$0.885246\pi$
$692$	−346.203			−0.500294
$693$	26.4497	+	48.2026i	0.0381670	+	0.0695564i
$694$	−552.654			−0.796332
$695$	−146.134	+	373.352i	−0.210264	+	0.537198i
$696$			229.518i			0.329768i
$697$		−	35.4664i		−	0.0508843i
$698$	793.540			1.13688
$699$		−	451.055i		−	0.645286i
$700$	−84.6562	+	339.608i	−0.120937	+	0.485154i
$701$	399.170			0.569429			0.284715	−	0.958612i	$-0.408101\pi$
$701$	399.170			0.569429			0.284715	+	0.958612i	$0.408101\pi$
$702$		−	394.514i		−	0.561986i
$703$	517.489			0.736115
$704$	−13.4302			−0.0190770
$705$	−691.267	−	270.569i	−0.980521	−	0.383785i
$706$			360.506i			0.510632i
$707$	−637.888	+	350.022i	−0.902246	+	0.495081i
$708$		−	151.535i		−	0.214032i
$709$	−241.751			−0.340975			−0.170488	−	0.985360i	$-0.554534\pi$
$709$	−241.751			−0.340975			−0.170488	+	0.985360i	$0.554534\pi$
$710$	−115.057	+	293.955i	−0.162052	+	0.414021i
$711$	−619.442			−0.871226
$712$	−152.982			−0.214862
$713$	−94.4383			−0.132452
$714$	−8.99416	+	4.93528i	−0.0125969	+	0.00691216i
$715$	−76.6846	−	30.0151i	−0.107251	−	0.0419791i
$716$	28.1454			0.0393092
$717$	656.672			0.915860
$718$		−	52.2314i		−	0.0727456i
$719$		−	544.197i		−	0.756880i	−0.925626	−	0.378440i	$-0.876461\pi$
$719$		−	544.197i		−	0.756880i	0.925626	−	0.378440i	$-0.123539\pi$
$720$	87.1385	+	34.1068i	0.121026	+	0.0473706i
$721$	171.073	+	311.767i	0.237271	+	0.432409i
$722$			957.439i			1.32609i
$723$		−	473.959i		−	0.655545i
$724$			340.539i			0.470357i
$725$	−716.612	−	662.469i	−0.988430	−	0.913750i
$726$		−	347.431i		−	0.478555i
$727$	211.414			0.290803			0.145401	−	0.989373i	$-0.453553\pi$
$727$	211.414			0.290803			0.145401	+	0.989373i	$0.453553\pi$
$728$	170.289	−	93.4409i	0.233913	−	0.128353i
$729$	611.520			0.838848
$730$	−264.000	+	674.485i	−0.361644	+	0.923953i
$731$			18.8096i			0.0257313i
$732$		−	209.715i		−	0.286496i
$733$	−1085.37			−1.48072			−0.740359	−	0.672211i	$-0.765345\pi$
$733$	−1085.37			−1.48072			−0.740359	+	0.672211i	$0.765345\pi$
$734$			378.277i			0.515364i
$735$	−411.332	+	300.312i	−0.559635	+	0.408588i
$736$	−21.4302			−0.0291172
$737$			20.6048i			0.0279576i
$738$	−470.723			−0.637836
$739$	−671.193			−0.908245			−0.454123	−	0.890939i	$-0.650047\pi$
$739$	−671.193			−0.908245			−0.454123	+	0.890939i	$0.650047\pi$
$740$	−58.5435	+	149.571i	−0.0791129	+	0.202123i
$741$			657.054i			0.886713i
$742$	395.435	+	720.649i	0.532931	+	0.971225i
$743$			194.699i			0.262044i	0.991379	+	0.131022i	$0.0418259\pi$
$743$			194.699i			0.262044i	−0.991379	+	0.131022i	$0.958174\pi$
$744$	−146.570			−0.197002
$745$	−425.365	−	166.492i	−0.570960	−	0.223479i
$746$	179.564			0.240702
$747$	−40.8409			−0.0546732
$748$	1.67387			0.00223780
$749$	−677.891	+	371.973i	−0.905061	+	0.496626i
$750$	330.642	−	160.355i	0.440857	−	0.213807i
$751$	218.115			0.290433			0.145216	−	0.989400i	$-0.453612\pi$
$751$	218.115			0.290433			0.145216	+	0.989400i	$0.453612\pi$
$752$	−285.684			−0.379899
$753$			174.540i			0.231793i
$754$			541.603i			0.718307i
$755$	812.325	+	317.952i	1.07593	+	0.421128i
$756$	191.503	+	348.999i	0.253311	+	0.461639i
$757$		−	1248.55i		−	1.64934i	−0.565611	−	0.824672i	$-0.691360\pi$
$757$		−	1248.55i		−	1.64934i	0.565611	−	0.824672i	$-0.308640\pi$
$758$		−	735.305i		−	0.970059i
$759$			13.2205i			0.0174184i
$760$	−424.291	−	166.071i	−0.558277	−	0.218515i
$761$		−	947.736i		−	1.24538i	−0.782468	−	0.622691i	$-0.786039\pi$
$761$		−	947.736i		−	1.24538i	0.782468	−	0.622691i	$-0.213961\pi$
$762$	230.301			0.302232
$763$	−475.415	−	866.407i	−0.623087	−	1.13553i
$764$	−302.509			−0.395954
$765$	−10.8605	−	4.25089i	−0.0141967	−	0.00555673i
$766$			556.781i			0.726868i
$767$		−	357.582i		−	0.466209i
$768$	−33.2601			−0.0433074
$769$			127.967i			0.166407i	0.996533	+	0.0832034i	$0.0265151\pi$
$769$			127.967i			0.166407i	−0.996533	+	0.0832034i	$0.973485\pi$
$770$	82.4073	−	10.6716i	0.107022	−	0.0138592i
$771$	−362.945			−0.470746
$772$			673.371i			0.872243i
$773$	−698.585			−0.903733			−0.451866	−	0.892086i	$-0.649242\pi$
$773$	−698.585			−0.903733			−0.451866	+	0.892086i	$0.649242\pi$
$774$	249.648			0.322543
$775$	423.051	−	457.626i	0.545872	−	0.590486i
$776$		−	118.045i		−	0.152120i
$777$	−204.902	+	112.434i	−0.263710	+	0.144703i
$778$		−	149.950i		−	0.192738i
$779$	2292.02			2.94226
$780$	−189.910	−	74.3326i	−0.243474	−	0.0952982i
$781$	74.9448			0.0959601
$782$	2.67095			0.00341554
$783$	−1109.99			−1.41761
$784$	−105.285	+	165.321i	−0.134292	+	0.210869i
$785$	179.648	+	70.3161i	0.228851	+	0.0895746i
$786$	−687.878			−0.875163
$787$	−1450.29			−1.84281			−0.921403	−	0.388609i	$-0.872956\pi$
$787$	−1450.29			−1.84281			−0.921403	+	0.388609i	$0.872956\pi$
$788$			5.45129i			0.00691788i
$789$			315.290i			0.399607i
$790$	−341.218	+	871.767i	−0.431921	+	1.10350i
$791$	−504.000	+	276.555i	−0.637168	+	0.349627i
$792$		−	22.2163i		−	0.0280509i
$793$		−	494.872i		−	0.624050i
$794$		−	553.841i		−	0.697533i
$795$	314.570	−	803.684i	0.395685	−	1.01092i
$796$		−	174.952i		−	0.219790i
$797$	742.137			0.931163			0.465581	−	0.885005i	$-0.345845\pi$
$797$	742.137			0.931163			0.465581	+	0.885005i	$0.345845\pi$
$798$	−318.944	−	581.250i	−0.399679	−	0.728383i
$799$	35.6061			0.0445633
$800$	96.0000	−	103.846i	0.120000	−	0.129808i
$801$		−	253.062i		−	0.315933i
$802$		−	58.1369i		−	0.0724899i
$803$	171.963			0.214150
$804$			51.0278i			0.0634674i
$805$	131.495	−	17.0283i	0.163348	−	0.0211532i
$806$	−345.866			−0.429115
$807$			914.902i			1.13371i
$808$	293.999			0.363860
$809$	884.551			1.09339			0.546694	−	0.837332i	$-0.315886\pi$
$809$	884.551			1.09339			0.546694	+	0.837332i	$0.315886\pi$
$810$	43.8140	−	111.939i	0.0540913	−	0.138196i
$811$		−	472.924i		−	0.583136i	−0.956550	−	0.291568i	$-0.905823\pi$
$811$		−	472.924i		−	0.583136i	0.956550	−	0.291568i	$-0.0941770\pi$
$812$	−262.902	−	479.118i	−0.323771	−	0.590047i
$813$			782.171i			0.962080i
$814$	38.1337			0.0468473
$815$	531.016	−	1356.68i	0.651553	−	1.66463i
$816$	4.14536			0.00508010
$817$	−1215.58			−1.48785
$818$	723.860			0.884914
$819$	154.570	+	281.691i	0.188730	+	0.343945i
$820$	−259.297	+	662.469i	−0.316215	+	0.807889i
$821$	−1091.40			−1.32935			−0.664677	−	0.747131i	$-0.731431\pi$
$821$	−1091.40			−1.32935			−0.664677	+	0.747131i	$0.731431\pi$
$822$	−446.340			−0.542993
$823$			749.909i			0.911190i	0.890187	+	0.455595i	$0.150573\pi$
$823$			749.909i			0.911190i	−0.890187	+	0.455595i	$0.849427\pi$
$824$		−	143.691i		−	0.174383i
$825$	−64.0637	−	59.2234i	−0.0776529	−	0.0717859i
$826$	173.576	+	316.328i	0.210140	+	0.382964i
$827$			511.380i			0.618355i	0.951004	+	0.309178i	$0.100054\pi$
$827$			511.380i			0.618355i	−0.951004	+	0.309178i	$0.899946\pi$
$828$		−	35.4499i		−	0.0428139i
$829$			200.919i			0.242363i	0.992630	+	0.121182i	$0.0386684\pi$
$829$			200.919i			0.242363i	−0.992630	+	0.121182i	$0.961332\pi$
$830$	−22.4971	+	57.4771i	−0.0271049	+	0.0692495i
$831$		−	694.221i		−	0.835404i
$832$	−78.4851			−0.0943330
$833$	13.1221	−	20.6048i	0.0157529	−	0.0247356i
$834$	235.733			0.282653
$835$	−956.624	−	374.432i	−1.14566	−	0.448421i
$836$			108.174i			0.129395i
$837$		−	708.838i		−	0.846879i
$838$	−116.712			−0.139275
$839$			1403.47i			1.67279i	0.548124	+	0.836397i	$0.315342\pi$
$839$			1403.47i			1.67279i	−0.548124	+	0.836397i	$0.684658\pi$
$840$	204.082	−	26.4282i	0.242955	−	0.0314622i
$841$	682.836			0.811933
$842$			321.592i			0.381938i
$843$	−787.041			−0.933620
$844$	29.2239			0.0346254
$845$	338.734	+	132.584i	0.400869	+	0.156904i
$846$		−	472.578i		−	0.558602i
$847$	397.965	+	725.260i	0.469853	+	0.856270i
$848$		−	332.143i		−	0.391678i
$849$	580.903			0.684220
$850$	−11.9649	+	12.9428i	−0.0140764	+	0.0152268i
$851$	60.8488			0.0715027
$852$	185.601			0.217842
$853$	1221.54			1.43205			0.716026	−	0.698074i	$-0.245959\pi$
$853$	1221.54			1.43205			0.716026	+	0.698074i	$0.245959\pi$
$854$	240.218	+	437.779i	0.281286	+	0.512621i
$855$	274.715	−	701.861i	0.321304	−	0.820890i
$856$	312.436			0.364995
$857$	541.135			0.631429			0.315715	−	0.948854i	$-0.397756\pi$
$857$	541.135			0.631429			0.315715	+	0.948854i	$0.397756\pi$
$858$			48.4182i			0.0564315i
$859$		−	1175.60i		−	1.36857i	−0.729213	−	0.684287i	$-0.760114\pi$
$859$		−	1175.60i		−	1.36857i	0.729213	−	0.684287i	$-0.239886\pi$
$860$	137.518	−	351.341i	0.159905	−	0.408536i
$861$	−907.538	+	497.985i	−1.05405	+	0.578379i
$862$		−	360.573i		−	0.418298i
$863$		−	1155.08i		−	1.33844i	−0.743062	−	0.669222i	$-0.766627\pi$
$863$		−	1155.08i		−	1.33844i	0.743062	−	0.669222i	$-0.233373\pi$
$864$		−	160.852i		−	0.186171i
$865$	−805.969	−	315.464i	−0.931757	−	0.364698i
$866$		−	954.812i		−	1.10255i
$867$	600.243			0.692322
$868$	305.964	−	167.889i	0.352493	−	0.193420i
$869$	222.260			0.255765
$870$	−209.140	+	534.324i	−0.240390	+	0.614166i
$871$			120.412i			0.138246i
$872$			399.322i			0.457938i
$873$	195.270			0.223677
$874$			172.611i			0.197495i
$875$	−506.536	+	713.475i	−0.578898	+	0.815400i
$876$	425.866			0.486149
$877$		−	993.086i		−	1.13237i	−0.824279	−	0.566184i	$-0.808419\pi$
$877$		−	993.086i		−	1.13237i	0.824279	−	0.566184i	$-0.191581\pi$
$878$	−5.34190			−0.00608417
$879$	490.490			0.558009
$880$	−31.2659	−	12.2378i	−0.0355295	−	0.0139066i
$881$		−	431.925i		−	0.490266i	−0.969489	−	0.245133i	$-0.921168\pi$
$881$		−	431.925i		−	0.490266i	0.969489	−	0.245133i	$-0.0788317\pi$
$882$	−273.474	−	174.162i	−0.310061	−	0.197463i
$883$			1064.16i			1.20516i	0.798058	+	0.602580i	$0.205861\pi$
$883$			1064.16i			1.20516i	−0.798058	+	0.602580i	$0.794139\pi$
$884$	9.78196			0.0110656
$885$	138.080	−	352.776i	0.156023	−	0.398617i
$886$	−386.788			−0.436555
$887$	−367.743			−0.414592			−0.207296	−	0.978278i	$-0.566466\pi$
$887$	−367.743			−0.414592			−0.207296	+	0.978278i	$0.566466\pi$
$888$	94.4383			0.106349
$889$	−480.751	+	263.798i	−0.540778	+	0.296736i
$890$	−356.145	−	139.399i	−0.400163	−	0.156628i
$891$	−28.5393			−0.0320306
$892$	259.929			0.291400
$893$			2301.05i			2.57677i
$894$			268.573i			0.300417i
$895$	65.5231	+	25.6464i	0.0732101	+	0.0286551i
$896$	69.4302	−	38.0978i	0.0774891	−	0.0425199i
$897$			77.2596i			0.0861311i
$898$		−	328.157i		−	0.365431i
$899$			973.117i			1.08244i
$900$	171.782	+	158.803i	0.190869	+	0.176448i
$901$			41.3965i			0.0459451i
$902$	168.899			0.187249
$903$	481.313	−	264.106i	0.533016	−	0.292477i
$904$	232.291			0.256959
$905$	−310.302	+	792.782i	−0.342876	+	0.876002i
$906$		−	512.897i		−	0.566112i
$907$			872.646i			0.962123i	0.876687	+	0.481062i	$0.159749\pi$
$907$			872.646i			0.962123i	−0.876687	+	0.481062i	$0.840251\pi$
$908$	266.552			0.293559
$909$			486.332i			0.535019i
$910$	481.580	−	62.3637i	0.529209	−	0.0685316i
$911$	−467.939			−0.513654			−0.256827	−	0.966457i	$-0.582677\pi$
$911$	−467.939			−0.513654			−0.256827	+	0.966457i	$0.582677\pi$
$912$			267.895i			0.293744i
$913$	14.6540			0.0160504
$914$	525.018			0.574417
$915$	191.094	−	488.221i	0.208846	−	0.533575i
$916$			441.158i			0.481614i
$917$	1435.94	−	787.931i	1.56591	−	0.859248i
$918$			20.0477i			0.0218384i
$919$	254.964			0.277436			0.138718	−	0.990332i	$-0.455702\pi$
$919$	254.964			0.277436			0.138718	+	0.990332i	$0.455702\pi$
$920$	−49.8901	−	19.5275i	−0.0542284	−	0.0212255i
$921$	−884.406			−0.960267
$922$	17.3068			0.0187710
$923$	437.971			0.474508
$924$	−23.5029	−	42.8322i	−0.0254361	−	0.0463552i
$925$	−272.581	+	294.859i	−0.294683	+	0.318767i
$926$	−376.509			−0.406597
$927$	237.694			0.256412
$928$			220.823i			0.237956i
$929$		−	21.7366i		−	0.0233979i	−0.999932	−	0.0116989i	$-0.996276\pi$
$929$		−	21.7366i		−	0.0233979i	0.999932	−	0.0116989i	$-0.00372397\pi$
$930$	−341.218	−	133.556i	−0.366901	−	0.143609i
$931$	1331.59	+	848.022i	1.43028	+	0.910872i
$932$		−	433.966i		−	0.465629i
$933$			415.503i			0.445341i
$934$		−	407.197i		−	0.435971i
$935$	3.89682	+	1.52525i	0.00416772	+	0.00163129i
$936$		−	129.830i		−	0.138707i
$937$	1089.71			1.16298			0.581490	−	0.813554i	$-0.302470\pi$
$937$	1089.71			1.16298			0.581490	+	0.813554i	$0.302470\pi$
$938$	−58.4499	−	106.520i	−0.0623133	−	0.113561i
$939$	−856.952			−0.912622
$940$	−665.079	−	260.318i	−0.707530	−	0.276934i
$941$			1017.39i			1.08117i	0.841288	+	0.540587i	$0.181798\pi$
$941$			1017.39i			1.08117i	−0.841288	+	0.540587i	$0.818202\pi$
$942$		−	113.429i		−	0.120413i
$943$	269.507			0.285797
$944$		−	145.794i		−	0.154443i
$945$	127.812	+	986.978i	0.135250	+	1.04442i
$946$	−89.5756			−0.0946888
$947$			260.781i			0.275376i	0.990476	+	0.137688i	$0.0439670\pi$
$947$			260.781i			0.275376i	−0.990476	+	0.137688i	$0.956033\pi$
$948$	550.429			0.580621
$949$	1004.93			1.05894
$950$	−836.433	−	773.237i	−0.880456	−	0.813933i
$951$			224.280i			0.235836i
$952$	−8.65342	+	4.74831i	−0.00908972	+	0.00498772i
$953$		−	862.773i		−	0.905323i	−0.891682	−	0.452662i	$-0.850475\pi$
$953$		−	862.773i		−	0.905323i	0.891682	−	0.452662i	$-0.149525\pi$
$954$	549.430			0.575923
$955$	−704.248	−	275.649i	−0.737432	−	0.288638i
$956$	631.794			0.660872
$957$	136.228			0.142349
$958$	−332.564			−0.347145
$959$	931.733	−	511.261i	0.971567	−	0.533119i
$960$	−77.4302	−	30.3069i	−0.0806565	−	0.0315697i
$961$	339.570			0.353350
$962$	222.850			0.231653
$963$			516.831i			0.536689i
$964$		−	456.003i		−	0.473032i
$965$	−613.583	+	1567.62i	−0.635837	+	1.62448i
$966$	−37.5029	−	68.3461i	−0.0388229	−	0.0707517i
$967$		−	948.088i		−	0.980443i	−0.871598	−	0.490222i	$-0.836916\pi$
$967$		−	948.088i		−	0.980443i	0.871598	−	0.490222i	$-0.163084\pi$
$968$		−	334.268i		−	0.345319i
$969$		−	33.3890i		−	0.0344572i
$970$	107.564	−	274.812i	0.110891	−	0.283311i
$971$		−	1415.45i		−	1.45772i	−0.684662	−	0.728860i	$-0.740050\pi$
$971$		−	1415.45i		−	1.45772i	0.684662	−	0.728860i	$-0.259950\pi$
$972$	441.149			0.453857
$973$	−492.091	+	270.020i	−0.505746	+	0.277513i
$974$	412.073			0.423073
$975$	−374.382	−	346.096i	−0.383982	−	0.354970i
$976$		−	201.770i		−	0.206731i
$977$		−	925.821i		−	0.947616i	−0.880628	−	0.473808i	$-0.842879\pi$
$977$		−	925.821i		−	0.947616i	0.880628	−	0.473808i	$-0.157121\pi$
$978$	−856.598			−0.875867
$979$			90.8006i			0.0927483i
$980$	−395.748	+	288.935i	−0.403825	+	0.294832i
$981$	−660.558			−0.673352
$982$		−	863.038i		−	0.878858i
$983$	1048.06			1.06619			0.533093	−	0.846057i	$-0.321030\pi$
$983$	1048.06			1.06619			0.533093	+	0.846057i	$0.321030\pi$
$984$	418.279			0.425080
$985$	−4.96727	+	12.6907i	−0.00504291	+	0.0128840i
$986$		−	27.5222i		−	0.0279130i
$987$	−499.947	−	911.113i	−0.506531	−	0.923114i
$988$			632.162i			0.639840i
$989$	−142.933			−0.144523
$990$	20.2437	−	51.7200i	0.0204482	−	0.0522425i
$991$	1014.10			1.02331			0.511653	−	0.859192i	$-0.329033\pi$
$991$	1014.10			1.02331			0.511653	+	0.859192i	$0.329033\pi$
$992$	−141.017			−0.142154
$993$	79.1438			0.0797017
$994$	−387.442	+	212.597i	−0.389781	+	0.213881i
$995$	159.419	−	407.294i	0.160220	−	0.409340i
$996$	36.2907			0.0364365
$997$	−459.819			−0.461202			−0.230601	−	0.973048i	$-0.574069\pi$
$997$	−459.819			−0.461202			−0.230601	+	0.973048i	$0.574069\pi$
$998$		−	70.2564i		−	0.0703972i
$999$			456.721i			0.457178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.d.a.69.2	✓	8
3.2	odd	2		630.3.h.d.559.8		8
4.3	odd	2		560.3.p.g.209.5		8
5.2	odd	4		350.3.b.c.251.7		8
5.3	odd	4		350.3.b.c.251.2		8
5.4	even	2	inner	70.3.d.a.69.7	yes	8
7.2	even	3		490.3.h.a.129.3		16
7.3	odd	6		490.3.h.a.19.6		16
7.4	even	3		490.3.h.a.19.7		16
7.5	odd	6		490.3.h.a.129.2		16
7.6	odd	2	inner	70.3.d.a.69.3	yes	8
15.14	odd	2		630.3.h.d.559.1		8
20.19	odd	2		560.3.p.g.209.3		8
21.20	even	2		630.3.h.d.559.5		8
28.27	even	2		560.3.p.g.209.4		8
35.4	even	6		490.3.h.a.19.2		16
35.9	even	6		490.3.h.a.129.6		16
35.13	even	4		350.3.b.c.251.3		8
35.19	odd	6		490.3.h.a.129.7		16
35.24	odd	6		490.3.h.a.19.3		16
35.27	even	4		350.3.b.c.251.6		8
35.34	odd	2	inner	70.3.d.a.69.6	yes	8
105.104	even	2		630.3.h.d.559.4		8
140.139	even	2		560.3.p.g.209.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.d.a.69.2	✓	8	1.1	even	1	trivial
70.3.d.a.69.3	yes	8	7.6	odd	2	inner
70.3.d.a.69.6	yes	8	35.34	odd	2	inner
70.3.d.a.69.7	yes	8	5.4	even	2	inner
350.3.b.c.251.2		8	5.3	odd	4
350.3.b.c.251.3		8	35.13	even	4
350.3.b.c.251.6		8	35.27	even	4
350.3.b.c.251.7		8	5.2	odd	4
490.3.h.a.19.2		16	35.4	even	6
490.3.h.a.19.3		16	35.24	odd	6
490.3.h.a.19.6		16	7.3	odd	6
490.3.h.a.19.7		16	7.4	even	3
490.3.h.a.129.2		16	7.5	odd	6
490.3.h.a.129.3		16	7.2	even	3
490.3.h.a.129.6		16	35.9	even	6
490.3.h.a.129.7		16	35.19	odd	6
560.3.p.g.209.3		8	20.19	odd	2
560.3.p.g.209.4		8	28.27	even	2
560.3.p.g.209.5		8	4.3	odd	2
560.3.p.g.209.6		8	140.139	even	2
630.3.h.d.559.1		8	15.14	odd	2
630.3.h.d.559.4		8	105.104	even	2
630.3.h.d.559.5		8	21.20	even	2
630.3.h.d.559.8		8	3.2	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.07875 q^{3} -2.00000 q^{4} +(-4.65605 - 1.82242i) q^{5} +2.93980i q^{6} +(-3.36740 - 6.13682i) q^{7} +2.82843i q^{8} -4.67878 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -2.07875 q^{3} -2.00000 q^{4} +(-4.65605 - 1.82242i) q^{5} +2.93980i q^{6} +(-3.36740 - 6.13682i) q^{7} +2.82843i q^{8} -4.67878 q^{9} +(-2.57729 + 6.58465i) q^{10} +1.67878 q^{11} +4.15751 q^{12} +9.81063 q^{13} +(-8.67878 + 4.76222i) q^{14} +(9.67878 + 3.78837i) q^{15} +4.00000 q^{16} -0.498539 q^{17} +6.61679i q^{18} -32.2182i q^{19} +(9.31210 + 3.64484i) q^{20} +(7.00000 + 12.7570i) q^{21} -2.37415i q^{22} -3.78837i q^{23} -5.87961i q^{24} +(18.3576 + 16.9706i) q^{25} -13.8743i q^{26} +28.4348 q^{27} +(6.73480 + 12.2736i) q^{28} -39.0363 q^{29} +(5.35756 - 13.6879i) q^{30} -24.9285i q^{31} -5.65685i q^{32} -3.48977 q^{33} +0.705040i q^{34} +(4.49490 + 34.7102i) q^{35} +9.35756 q^{36} +16.0620i q^{37} -45.5634 q^{38} -20.3939 q^{39} +(5.15459 - 13.1693i) q^{40} +71.1407i q^{41} +(18.0411 - 9.89949i) q^{42} -37.7295i q^{43} -3.35756 q^{44} +(21.7846 + 8.52671i) q^{45} -5.35756 q^{46} -71.4209 q^{47} -8.31502 q^{48} +(-26.3212 + 41.3303i) q^{49} +(24.0000 - 25.9615i) q^{50} +1.03634 q^{51} -19.6213 q^{52} -83.0357i q^{53} -40.2129i q^{54} +(-7.81648 - 3.05944i) q^{55} +(17.3576 - 9.52445i) q^{56} +66.9737i q^{57} +55.2057i q^{58} -36.4484i q^{59} +(-19.3576 - 7.57673i) q^{60} -50.4424i q^{61} -35.2542 q^{62} +(15.7553 + 28.7128i) q^{63} -8.00000 q^{64} +(-45.6788 - 17.8791i) q^{65} +4.93528i q^{66} +12.2736i q^{67} +0.997077 q^{68} +7.87508i q^{69} +(49.0876 - 6.35675i) q^{70} +44.6424 q^{71} -13.2336i q^{72} +102.433 q^{73} +22.7151 q^{74} +(-38.1609 - 35.2776i) q^{75} +64.4364i q^{76} +(-5.65313 - 10.3024i) q^{77} +28.8413i q^{78} +132.394 q^{79} +(-18.6242 - 7.28969i) q^{80} -17.0000 q^{81} +100.608 q^{82} +8.72896 q^{83} +(-14.0000 - 25.5139i) q^{84} +(2.32122 + 0.908548i) q^{85} -53.3576 q^{86} +81.1470 q^{87} +4.74831i q^{88} +54.0872i q^{89} +(12.0586 - 30.8081i) q^{90} +(-33.0363 - 60.2061i) q^{91} +7.57673i q^{92} +51.8202i q^{93} +101.004i q^{94} +(-58.7151 + 150.009i) q^{95} +11.7592i q^{96} -41.7352 q^{97} +(58.4499 + 37.2238i) q^{98} -7.85464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{4} + 36 q^{9}+O(q^{10}) \) 8 * q - 16 * q^4 + 36 * q^9	\( 8 q - 16 q^{4} + 36 q^{9} - 60 q^{11} + 4 q^{14} + 4 q^{15} + 32 q^{16} + 56 q^{21} - 92 q^{29} - 104 q^{30} + 52 q^{35} - 72 q^{36} + 204 q^{39} + 120 q^{44} + 104 q^{46} - 284 q^{49} + 192 q^{50} - 212 q^{51} - 8 q^{56} - 8 q^{60} - 64 q^{64} - 292 q^{65} - 4 q^{70} + 504 q^{71} - 112 q^{74} + 692 q^{79} - 136 q^{81} - 112 q^{84} + 92 q^{85} - 280 q^{86} - 44 q^{91} - 176 q^{95} - 944 q^{99}+O(q^{100}) \) 8 * q - 16 * q^4 + 36 * q^9 - 60 * q^11 + 4 * q^14 + 4 * q^15 + 32 * q^16 + 56 * q^21 - 92 * q^29 - 104 * q^30 + 52 * q^35 - 72 * q^36 + 204 * q^39 + 120 * q^44 + 104 * q^46 - 284 * q^49 + 192 * q^50 - 212 * q^51 - 8 * q^56 - 8 * q^60 - 64 * q^64 - 292 * q^65 - 4 * q^70 + 504 * q^71 - 112 * q^74 + 692 * q^79 - 136 * q^81 - 112 * q^84 + 92 * q^85 - 280 * q^86 - 44 * q^91 - 176 * q^95 - 944 * q^99

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