LMFDB - Embedded newform 312.4.m.a.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.1
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82580 - 0.121986i) q^{2} +3.00000i q^{3} +(7.97024 + 0.689413i) q^{4} +14.7613 q^{5} +(0.365957 - 8.47739i) q^{6} +28.6139i q^{7} +(-22.4382 - 2.92040i) q^{8} -9.00000 q^{9} +(-41.7123 - 1.80066i) q^{10} -55.0376 q^{11} +(-2.06824 + 23.9107i) q^{12} +(-21.7849 - 41.5020i) q^{13} +(3.49048 - 80.8570i) q^{14} +44.2838i q^{15} +(63.0494 + 10.9896i) q^{16} -111.642 q^{17} +(25.4322 + 1.09787i) q^{18} -80.7496 q^{19} +(117.651 + 10.1766i) q^{20} -85.8416 q^{21} +(155.525 + 6.71381i) q^{22} +137.660 q^{23} +(8.76119 - 67.3145i) q^{24} +92.8946 q^{25} +(56.4971 + 119.934i) q^{26} -27.0000i q^{27} +(-19.7268 + 228.059i) q^{28} -147.608i q^{29} +(5.40199 - 125.137i) q^{30} +231.530i q^{31} +(-176.824 - 38.7454i) q^{32} -165.113i q^{33} +(315.477 + 13.6187i) q^{34} +422.377i q^{35} +(-71.7322 - 6.20472i) q^{36} -86.8675 q^{37} +(228.182 + 9.85030i) q^{38} +(124.506 - 65.3548i) q^{39} +(-331.215 - 43.1087i) q^{40} -122.051i q^{41} +(242.571 + 10.4715i) q^{42} -136.295i q^{43} +(-438.663 - 37.9437i) q^{44} -132.851 q^{45} +(-388.998 - 16.7925i) q^{46} -554.463i q^{47} +(-32.9687 + 189.148i) q^{48} -475.754 q^{49} +(-262.501 - 11.3318i) q^{50} -334.926i q^{51} +(-145.019 - 345.800i) q^{52} -124.279i q^{53} +(-3.29361 + 76.2965i) q^{54} -812.425 q^{55} +(83.5639 - 642.043i) q^{56} -242.249i q^{57} +(-18.0061 + 417.110i) q^{58} +348.526 q^{59} +(-30.5298 + 352.952i) q^{60} +674.715i q^{61} +(28.2433 - 654.256i) q^{62} -257.525i q^{63} +(494.943 + 131.057i) q^{64} +(-321.573 - 612.622i) q^{65} +(-20.1414 + 466.575i) q^{66} -156.911 q^{67} +(-889.812 - 76.9674i) q^{68} +412.979i q^{69} +(51.5239 - 1193.55i) q^{70} +1140.34i q^{71} +(201.943 + 26.2836i) q^{72} +775.178i q^{73} +(245.470 + 10.5966i) q^{74} +278.684i q^{75} +(-643.594 - 55.6699i) q^{76} -1574.84i q^{77} +(-359.801 + 169.491i) q^{78} -1100.02 q^{79} +(930.688 + 162.220i) q^{80} +81.0000 q^{81} +(-14.8885 + 344.892i) q^{82} -446.367 q^{83} +(-684.178 - 59.1804i) q^{84} -1647.97 q^{85} +(-16.6261 + 385.143i) q^{86} +442.824 q^{87} +(1234.94 + 160.732i) q^{88} -843.694i q^{89} +(375.411 + 16.2060i) q^{90} +(1187.53 - 623.351i) q^{91} +(1097.18 + 94.9044i) q^{92} -694.589 q^{93} +(-67.6366 + 1566.80i) q^{94} -1191.97 q^{95} +(116.236 - 530.473i) q^{96} +321.958i q^{97} +(1344.38 + 58.0352i) q^{98} +495.339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.82580	−	0.121986i	−0.999070	−	0.0431285i
$2$	−2.82580	−	0.121986i	−0.999070	−	0.0431285i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	7.97024	+	0.689413i	0.996280	+	0.0861767i
$5$	14.7613			1.32029			0.660143	−	0.751140i	$-0.270496\pi$
$5$	14.7613			1.32029			0.660143	+	0.751140i	$0.270496\pi$
$6$	0.365957	−	8.47739i	0.0249002	−	0.576813i
$7$			28.6139i			1.54500i	0.635012	+	0.772502i	$0.280995\pi$
$7$			28.6139i			1.54500i	−0.635012	+	0.772502i	$0.719005\pi$
$8$	−22.4382	−	2.92040i	−0.991636	−	0.129065i
$9$	−9.00000			−0.333333
$10$	−41.7123	−	1.80066i	−1.31906	−	0.0569419i
$11$	−55.0376			−1.50859			−0.754294	−	0.656536i	$-0.772021\pi$
$11$	−55.0376			−1.50859			−0.754294	+	0.656536i	$0.772021\pi$
$12$	−2.06824	+	23.9107i	−0.0497541	+	0.575202i
$13$	−21.7849	−	41.5020i	−0.464773	−	0.885430i
$13$	−21.7849	−	41.5020i	−0.464773	−	0.885430i
$14$	3.49048	−	80.8570i	0.0666337	−	1.54357i
$15$			44.2838i			0.762268i
$16$	63.0494	+	10.9896i	0.985147	+	0.171712i
$17$	−111.642			−1.59277			−0.796386	−	0.604788i	$-0.793258\pi$
$17$	−111.642			−1.59277			−0.796386	+	0.604788i	$0.793258\pi$
$18$	25.4322	+	1.09787i	0.333023	+	0.0143762i
$19$	−80.7496			−0.975012			−0.487506	−	0.873120i	$-0.662093\pi$
$19$	−80.7496			−0.975012			−0.487506	+	0.873120i	$0.662093\pi$
$20$	117.651	+	10.1766i	1.31538	+	0.113778i
$21$	−85.8416			−0.892009
$22$	155.525	+	6.71381i	1.50718	+	0.0650631i
$23$	137.660			1.24800			0.624000	−	0.781424i	$-0.285506\pi$
$23$	137.660			1.24800			0.624000	+	0.781424i	$0.285506\pi$
$24$	8.76119	−	67.3145i	0.0745154	−	0.572521i
$25$	92.8946			0.743157
$26$	56.4971	+	119.934i	0.426153	+	0.904651i
$27$		−	27.0000i		−	0.192450i
$28$	−19.7268	+	228.059i	−0.133143	+	1.53926i
$29$		−	147.608i		−	0.945177i	−0.881283	−	0.472588i	$-0.843320\pi$
$29$		−	147.608i		−	0.945177i	0.881283	−	0.472588i	$-0.156680\pi$
$30$	5.40199	−	125.137i	0.0328754	−	0.761559i
$31$			231.530i			1.34142i	0.741720	+	0.670709i	$0.234010\pi$
$31$			231.530i			1.34142i	−0.741720	+	0.670709i	$0.765990\pi$
$32$	−176.824	−	38.7454i	−0.976825	−	0.214040i
$33$		−	165.113i		−	0.870984i
$34$	315.477	+	13.6187i	1.59129	+	0.0686938i
$35$			422.377i			2.03985i
$36$	−71.7322	−	6.20472i	−0.332093	−	0.0287256i
$37$	−86.8675			−0.385971			−0.192985	−	0.981202i	$-0.561817\pi$
$37$	−86.8675			−0.385971			−0.192985	+	0.981202i	$0.561817\pi$
$38$	228.182	+	9.85030i	0.974105	+	0.0420508i
$39$	124.506	−	65.3548i	0.511203	−	0.268337i
$40$	−331.215	−	43.1087i	−1.30924	−	0.170402i
$41$		−	122.051i		−	0.464908i	−0.972607	−	0.232454i	$-0.925324\pi$
$41$		−	122.051i		−	0.464908i	0.972607	−	0.232454i	$-0.0746755\pi$
$42$	242.571	+	10.4715i	0.891179	+	0.0384710i
$43$		−	136.295i		−	0.483369i	−0.970355	−	0.241684i	$-0.922300\pi$
$43$		−	136.295i		−	0.483369i	0.970355	−	0.241684i	$-0.0776999\pi$
$44$	−438.663	−	37.9437i	−1.50298	−	0.130005i
$45$	−132.851			−0.440096
$46$	−388.998	−	16.7925i	−1.24684	−	0.0538243i
$47$		−	554.463i		−	1.72078i	−0.509634	−	0.860391i	$-0.670219\pi$
$47$		−	554.463i		−	1.72078i	0.509634	−	0.860391i	$-0.329781\pi$
$48$	−32.9687	+	189.148i	−0.0991381	+	0.568775i
$49$	−475.754			−1.38704
$50$	−262.501	−	11.3318i	−0.742465	−	0.0320512i
$51$		−	334.926i		−	0.919588i
$52$	−145.019	−	345.800i	−0.386741	−	0.922188i
$53$		−	124.279i		−	0.322096i	−0.986947	−	0.161048i	$-0.948513\pi$
$53$		−	124.279i		−	0.322096i	0.986947	−	0.161048i	$-0.0514874\pi$
$54$	−3.29361	+	76.2965i	−0.00830008	+	0.192271i
$55$	−812.425			−1.99177
$56$	83.5639	−	642.043i	0.199405	−	1.53208i
$57$		−	242.249i		−	0.562924i
$58$	−18.0061	+	417.110i	−0.0407640	+	0.944297i
$59$	348.526			0.769054			0.384527	−	0.923114i	$-0.374365\pi$
$59$	348.526			0.769054			0.384527	+	0.923114i	$0.374365\pi$
$60$	−30.5298	+	352.952i	−0.0656897	+	0.759432i
$61$			674.715i			1.41620i	0.706111	+	0.708101i	$0.250448\pi$
$61$			674.715i			1.41620i	−0.706111	+	0.708101i	$0.749552\pi$
$62$	28.2433	−	654.256i	0.0578533	−	1.34017i
$63$		−	257.525i		−	0.515001i
$64$	494.943	+	131.057i	0.966685	+	0.255970i
$65$	−321.573	−	612.622i	−0.613634	−	1.16902i
$66$	−20.1414	+	466.575i	−0.0375642	+	0.870174i
$67$	−156.911			−0.286115			−0.143057	−	0.989714i	$-0.545693\pi$
$67$	−156.911			−0.286115			−0.143057	+	0.989714i	$0.545693\pi$
$68$	−889.812	−	76.9674i	−1.58685	−	0.137260i
$69$			412.979i			0.720533i
$70$	51.5239	−	1193.55i	0.0879755	−	2.03795i
$71$			1140.34i			1.90611i	0.302798	+	0.953055i	$0.402079\pi$
$71$			1140.34i			1.90611i	−0.302798	+	0.953055i	$0.597921\pi$
$72$	201.943	+	26.2836i	0.330545	+	0.0430215i
$73$			775.178i			1.24285i	0.783476	+	0.621423i	$0.213445\pi$
$73$			775.178i			1.24285i	−0.783476	+	0.621423i	$0.786555\pi$
$74$	245.470	+	10.5966i	0.385612	+	0.0166463i
$75$			278.684i			0.429062i
$76$	−643.594	−	55.6699i	−0.971385	−	0.0840233i
$77$		−	1574.84i		−	2.33078i
$78$	−359.801	+	169.491i	−0.522300	+	0.246040i
$79$	−1100.02			−1.56661			−0.783307	−	0.621635i	$-0.786469\pi$
$79$	−1100.02			−1.56661			−0.783307	+	0.621635i	$0.786469\pi$
$80$	930.688	+	162.220i	1.30068	+	0.226709i
$81$	81.0000			0.111111
$82$	−14.8885	+	344.892i	−0.0200508	+	0.464475i
$83$	−446.367			−0.590302			−0.295151	−	0.955451i	$-0.595370\pi$
$83$	−446.367			−0.590302			−0.295151	+	0.955451i	$0.595370\pi$
$84$	−684.178	−	59.1804i	−0.888690	−	0.0768703i
$85$	−1647.97			−2.10292
$86$	−16.6261	+	385.143i	−0.0208470	+	0.482919i
$87$	442.824			0.545698
$88$	1234.94	+	160.732i	1.49597	+	0.194705i
$89$		−	843.694i		−	1.00485i	−0.864622	−	0.502424i	$-0.832442\pi$
$89$		−	843.694i		−	1.00485i	0.864622	−	0.502424i	$-0.167558\pi$
$90$	375.411	+	16.2060i	0.439686	+	0.0189806i
$91$	1187.53	−	623.351i	1.36799	−	0.718076i
$92$	1097.18	+	94.9044i	1.24336	+	0.107549i
$93$	−694.589			−0.774468
$94$	−67.6366	+	1566.80i	−0.0742147	+	1.71918i
$95$	−1191.97			−1.28730
$96$	116.236	−	530.473i	0.123576	−	0.563970i
$97$			321.958i			0.337009i	0.985701	+	0.168505i	$0.0538938\pi$
$97$			321.958i			0.337009i	−0.985701	+	0.168505i	$0.946106\pi$
$98$	1344.38	+	58.0352i	1.38575	+	0.0598208i
$99$	495.339			0.502863
$100$	740.392	+	64.0428i	0.740392	+	0.0640428i
$101$			691.497i			0.681253i	0.940199	+	0.340626i	$0.110639\pi$
$101$			691.497i			0.681253i	−0.940199	+	0.340626i	$0.889361\pi$
$102$	−40.8561	+	946.431i	−0.0396604	+	0.918732i
$103$	−201.424			−0.192689			−0.0963443	−	0.995348i	$-0.530715\pi$
$103$	−201.424			−0.192689			−0.0963443	+	0.995348i	$0.530715\pi$
$104$	367.611	+	994.850i	0.346608	+	0.938010i
$105$	−1267.13			−1.17771
$106$	−15.1603	+	351.188i	−0.0138915	+	0.321796i
$107$			281.181i			0.254044i	0.991900	+	0.127022i	$0.0405420\pi$
$107$			281.181i			0.254044i	−0.991900	+	0.127022i	$0.959458\pi$
$108$	18.6142	−	215.196i	0.0165847	−	0.191734i
$109$	1051.22			0.923752			0.461876	−	0.886945i	$-0.347177\pi$
$109$	1051.22			0.923752			0.461876	+	0.886945i	$0.347177\pi$
$110$	2295.75	+	99.1042i	1.98992	+	0.0859020i
$111$		−	260.602i		−	0.222840i
$112$	−314.454	+	1804.09i	−0.265296	+	1.52206i
$113$	−478.806			−0.398604			−0.199302	−	0.979938i	$-0.563867\pi$
$113$	−478.806			−0.398604			−0.199302	+	0.979938i	$0.563867\pi$
$114$	−29.5509	+	684.546i	−0.0242780	+	0.562400i
$115$	2032.03			1.64772
$116$	101.763	−	1176.47i	0.0814522	−	0.941660i
$117$	196.064	+	373.518i	0.154924	+	0.295143i
$118$	−984.863	−	42.5152i	−0.768339	−	0.0331681i
$119$		−	3194.51i		−	2.46084i
$120$	129.326	−	993.646i	0.0983817	−	0.755892i
$121$	1698.14			1.27584
$122$	82.3055	−	1906.61i	0.0610786	−	1.41488i
$123$	366.154			0.268415
$124$	−159.620	+	1845.35i	−0.115599	+	1.33643i
$125$	−473.916			−0.339107
$126$	−31.4144	+	727.713i	−0.0222112	+	0.514522i
$127$	−365.896			−0.255654			−0.127827	−	0.991796i	$-0.540800\pi$
$127$	−365.896			−0.255654			−0.127827	+	0.991796i	$0.540800\pi$
$128$	−1382.62	−	430.715i	−0.954746	−	0.297424i
$129$	408.886			0.279073
$130$	833.968	+	1770.37i	0.562645	+	1.19440i
$131$			126.112i			0.0841104i	0.999115	+	0.0420552i	$0.0133905\pi$
$131$			126.112i			0.0841104i	−0.999115	+	0.0420552i	$0.986609\pi$
$132$	113.831	−	1315.99i	0.0750585	−	0.867744i
$133$		−	2310.56i		−	1.50640i
$134$	443.397	+	19.1409i	0.285849	+	0.0123397i
$135$		−	398.554i		−	0.254089i
$136$	2505.04	+	326.039i	1.57945	+	0.205570i
$137$		−	6.22945i		−	0.00388480i	−0.999998	−	0.00194240i	$-0.999382\pi$
$137$		−	6.22945i		−	0.00388480i	0.999998	−	0.00194240i	$-0.000618285\pi$
$138$	50.3775	−	1166.99i	0.0310755	−	0.719863i
$139$			2639.98i			1.61094i	0.592638	+	0.805469i	$0.298087\pi$
$139$			2639.98i			1.61094i	−0.592638	+	0.805469i	$0.701913\pi$
$140$	−291.192	+	3366.44i	−0.175787	+	2.03226i
$141$	1663.39			0.993494
$142$	139.106	−	3222.38i	0.0822076	−	1.90434i
$143$	1198.99	+	2284.17i	0.701151	+	1.33575i
$144$	−567.445	−	98.9062i	−0.328382	−	0.0572374i
$145$		−	2178.88i		−	1.24790i
$146$	94.5606	−	2190.49i	0.0536020	−	1.24169i
$147$		−	1427.26i		−	0.800807i
$148$	−692.354	−	59.8876i	−0.384535	−	0.0332617i
$149$	−2423.27			−1.33236			−0.666181	−	0.745790i	$-0.732072\pi$
$149$	−2423.27			−1.33236			−0.666181	+	0.745790i	$0.732072\pi$
$150$	33.9954	−	787.503i	0.0185048	−	0.428663i
$151$		−	1708.00i		−	0.920497i	−0.887790	−	0.460249i	$-0.847760\pi$
$151$		−	1708.00i		−	0.920497i	0.887790	−	0.460249i	$-0.152240\pi$
$152$	1811.87	+	235.821i	0.966858	+	0.125840i
$153$	1004.78			0.530924
$154$	−192.108	+	4450.18i	−0.100523	+	2.32861i
$155$			3417.67i			1.77106i
$156$	1037.40	−	435.057i	0.532426	−	0.223285i
$157$			442.408i			0.224892i	0.993658	+	0.112446i	$0.0358685\pi$
$157$			442.408i			0.224892i	−0.993658	+	0.112446i	$0.964131\pi$
$158$	3108.45	+	134.187i	1.56516	+	0.0675656i
$159$	372.838			0.185962
$160$	−2610.15	−	571.931i	−1.28969	−	0.282595i
$161$			3938.97i			1.92817i
$162$	−228.889	−	9.88084i	−0.111008	−	0.00479205i
$163$	−2348.15			−1.12835			−0.564176	−	0.825654i	$-0.690806\pi$
$163$	−2348.15			−1.12835			−0.564176	+	0.825654i	$0.690806\pi$
$164$	84.1439	−	972.779i	0.0400642	−	0.463179i
$165$		−	2437.27i		−	1.14995i
$166$	1261.34	+	54.4503i	0.589753	+	0.0254588i
$167$		−	1882.37i		−	0.872228i	−0.899891	−	0.436114i	$-0.856354\pi$
$167$		−	1882.37i		−	0.872228i	0.899891	−	0.436114i	$-0.143646\pi$
$168$	1926.13	+	250.692i	0.884548	+	0.115127i
$169$	−1247.83	+	1808.24i	−0.567972	+	0.823048i
$170$	4656.84	+	201.029i	2.10096	+	0.0906956i
$171$	726.747			0.325004
$172$	93.9639	−	1086.31i	0.0416551	−	0.481571i
$173$			2162.16i			0.950207i	0.879930	+	0.475103i	$0.157589\pi$
$173$			2162.16i			0.950207i	−0.879930	+	0.475103i	$0.842411\pi$
$174$	−1251.33	−	54.0182i	−0.545190	−	0.0235351i
$175$			2658.07i			1.14818i
$176$	−3470.09	−	604.841i	−1.48618	−	0.259043i
$177$			1045.58i			0.444014i
$178$	−102.919	+	2384.11i	−0.0433375	+	1.00391i
$179$			3698.91i			1.54452i	0.635304	+	0.772262i	$0.280875\pi$
$179$			3698.91i			1.54452i	−0.635304	+	0.772262i	$0.719125\pi$
$180$	−1058.86	−	91.5895i	−0.438458	−	0.0379260i
$181$		−	1667.31i		−	0.684698i	−0.939573	−	0.342349i	$-0.888778\pi$
$181$		−	1667.31i		−	0.684698i	0.939573	−	0.342349i	$-0.111222\pi$
$182$	−3431.77	+	1616.60i	−1.39769	+	0.658409i
$183$	−2024.14			−0.817645
$184$	−3088.83	−	402.021i	−1.23756	−	0.161073i
$185$	−1282.27			−0.509592
$186$	1962.77	+	84.7300i	0.773748	+	0.0334016i
$187$	6144.51			2.40284
$188$	382.254	−	4419.20i	0.148291	−	1.71438i
$189$	772.575			0.297336
$190$	3368.25	+	145.403i	1.28610	+	0.0555191i
$191$	1529.96			0.579604			0.289802	−	0.957087i	$-0.406411\pi$
$191$	1529.96			0.579604			0.289802	+	0.957087i	$0.406411\pi$
$192$	−393.170	+	1484.83i	−0.147784	+	0.558116i
$193$		−	2760.18i		−	1.02944i	−0.857358	−	0.514721i	$-0.827895\pi$
$193$		−	2760.18i		−	1.02944i	0.857358	−	0.514721i	$-0.172105\pi$
$194$	39.2743	−	909.788i	0.0145347	−	0.336696i
$195$	1837.87	−	964.718i	0.674935	−	0.354282i
$196$	−3791.87	−	327.991i	−1.38188	−	0.119530i
$197$	−2397.70			−0.867154			−0.433577	−	0.901117i	$-0.642749\pi$
$197$	−2397.70			−0.867154			−0.433577	+	0.901117i	$0.642749\pi$
$198$	−1399.73	−	60.4243i	−0.502395	−	0.0216877i
$199$	1900.64			0.677050			0.338525	−	0.940957i	$-0.390072\pi$
$199$	1900.64			0.677050			0.338525	+	0.940957i	$0.390072\pi$
$200$	−2084.38	−	271.289i	−0.736941	−	0.0959152i
$201$		−	470.732i		−	0.165188i
$202$	84.3528	−	1954.03i	0.0293814	−	0.680619i
$203$	4223.64			1.46030
$204$	230.902	−	2669.44i	0.0792470	−	0.916167i
$205$		−	1801.63i		−	0.613812i
$206$	569.184	+	24.5709i	0.192509	+	0.00831036i
$207$	−1238.94			−0.416000
$208$	−917.437	−	2856.08i	−0.305831	−	0.952086i
$209$	4444.27			1.47089
$210$	3580.65	+	154.572i	1.17661	+	0.0507927i
$211$			2966.19i			0.967777i	0.875130	+	0.483888i	$0.160776\pi$
$211$			2966.19i			0.967777i	−0.875130	+	0.483888i	$0.839224\pi$
$212$	85.6799	−	990.536i	0.0277572	−	0.320898i
$213$	−3421.03			−1.10049
$214$	34.3000	−	794.559i	0.0109565	−	0.253808i
$215$		−	2011.89i		−	0.638185i
$216$	−78.8507	+	605.830i	−0.0248385	+	0.190840i
$217$	−6624.96			−2.07250
$218$	−2970.54	−	128.234i	−0.922892	−	0.0398400i
$219$	−2325.53			−0.717557
$220$	−6475.22	−	560.096i	−1.98436	−	0.171644i
$221$	2432.11	+	4633.36i	0.740278	+	1.41029i
$222$	−31.7898	+	736.409i	−0.00961076	+	0.222633i
$223$			4484.95i			1.34679i	0.739282	+	0.673395i	$0.235165\pi$
$223$			4484.95i			1.34679i	−0.739282	+	0.673395i	$0.764835\pi$
$224$	1108.66	−	5059.63i	0.330693	−	1.50920i
$225$	−836.051			−0.247719
$226$	1353.01	+	58.4075i	0.398233	+	0.0171912i
$227$	−752.153			−0.219921			−0.109961	−	0.993936i	$-0.535073\pi$
$227$	−752.153			−0.219921			−0.109961	+	0.993936i	$0.535073\pi$
$228$	167.010	−	1930.78i	0.0485109	−	0.560830i
$229$	−566.263			−0.163405			−0.0817024	−	0.996657i	$-0.526036\pi$
$229$	−566.263			−0.163405			−0.0817024	+	0.996657i	$0.526036\pi$
$230$	−5742.10	−	247.878i	−1.64619	−	0.0710636i
$231$	4724.52			1.34567
$232$	−431.074	+	3312.05i	−0.121989	+	0.937271i
$233$	−1265.57			−0.355837			−0.177919	−	0.984045i	$-0.556936\pi$
$233$	−1265.57			−0.355837			−0.177919	+	0.984045i	$0.556936\pi$
$234$	−508.474	−	1079.40i	−0.142051	−	0.301550i
$235$		−	8184.57i		−	2.27193i
$236$	2777.83	+	240.278i	0.766193	+	0.0662745i
$237$		−	3300.07i		−	0.904485i
$238$	−389.684	+	9027.02i	−0.106132	+	2.45855i
$239$			1229.17i			0.332672i	0.986069	+	0.166336i	$0.0531936\pi$
$239$			1229.17i			0.332672i	−0.986069	+	0.166336i	$0.946806\pi$
$240$	−486.660	+	2792.07i	−0.130891	+	0.750946i
$241$			1452.65i			0.388272i	0.980975	+	0.194136i	$0.0621903\pi$
$241$			1452.65i			0.388272i	−0.980975	+	0.194136i	$0.937810\pi$
$242$	−4798.60	−	207.149i	−1.27465	−	0.0550250i
$243$			243.000i			0.0641500i
$244$	−465.157	+	5377.64i	−0.122044	+	1.41093i
$245$	−7022.72			−1.83129
$246$	−1034.68	−	44.6656i	−0.268165	−	0.0115763i
$247$	1759.12	+	3351.27i	0.453160	+	0.863305i
$248$	676.159	−	5195.10i	0.173130	−	1.33020i
$249$		−	1339.10i		−	0.340811i
$250$	1339.19	+	57.8110i	0.338791	+	0.0146251i
$251$			3106.22i			0.781128i	0.920576	+	0.390564i	$0.127720\pi$
$251$			3106.22i			0.781128i	−0.920576	+	0.390564i	$0.872280\pi$
$252$	177.541	−	2052.53i	0.0443811	−	0.513085i
$253$	−7576.46			−1.88272
$254$	1033.95	+	44.6341i	0.255416	+	0.0110260i
$255$		−	4943.92i		−	1.21412i
$256$	3854.46	+	1385.77i	0.941030	+	0.338324i
$257$	−2214.32			−0.537452			−0.268726	−	0.963217i	$-0.586603\pi$
$257$	−2214.32			−0.537452			−0.268726	+	0.963217i	$0.586603\pi$
$258$	−1155.43	−	49.8783i	−0.278813	−	0.0120360i
$259$		−	2485.61i		−	0.596327i
$260$	−2140.66	−	5104.44i	−0.510609	−	1.21755i
$261$			1328.47i			0.315059i
$262$	15.3839	−	356.367i	0.00362755	−	0.0840321i
$263$	6539.84			1.53332			0.766662	−	0.642051i	$-0.221916\pi$
$263$	6539.84			1.53332			0.766662	+	0.642051i	$0.221916\pi$
$264$	−482.195	+	3704.83i	−0.112413	+	0.863699i
$265$		−	1834.52i		−	0.425259i
$266$	−281.855	+	6529.17i	−0.0649686	+	1.50500i
$267$	2531.08			0.580149
$268$	−1250.62	−	108.176i	−0.285050	−	0.0246564i
$269$		−	232.200i		−	0.0526299i	−0.999654	−	0.0263150i	$-0.991623\pi$
$269$		−	232.200i		−	0.0526299i	0.999654	−	0.0263150i	$-0.00837728\pi$
$270$	−48.6179	+	1126.23i	−0.0109585	+	0.253853i
$271$			911.832i			0.204391i	0.994764	+	0.102195i	$0.0325867\pi$
$271$			911.832i			0.204391i	−0.994764	+	0.102195i	$0.967413\pi$
$272$	−7038.96	−	1226.90i	−1.56912	−	0.273498i
$273$	1870.05	+	3562.60i	0.414582	+	0.789811i
$274$	−0.759903	+	17.6031i	−0.000167545	+	0.00388118i
$275$	−5112.70			−1.12112
$276$	−284.713	+	3291.54i	−0.0620932	+	0.717853i
$277$		−	70.7636i		−	0.0153494i	−0.999971	−	0.00767469i	$-0.997557\pi$
$277$		−	70.7636i		−	0.0153494i	0.999971	−	0.00767469i	$-0.00244295\pi$
$278$	322.040	−	7460.05i	0.0694773	−	1.60944i
$279$		−	2083.77i		−	0.447139i
$280$	1233.51	−	9477.36i	0.263272	−	2.02279i
$281$		−	5851.66i		−	1.24228i	−0.783700	−	0.621140i	$-0.786670\pi$
$281$		−	5851.66i		−	1.24228i	0.783700	−	0.621140i	$-0.213330\pi$
$282$	−4700.40	−	202.910i	−0.992570	−	0.0428479i
$283$		−	4078.19i		−	0.856620i	−0.903632	−	0.428310i	$-0.859109\pi$
$283$		−	4078.19i		−	0.856620i	0.903632	−	0.428310i	$-0.140891\pi$
$284$	−786.168	+	9088.80i	−0.164262	+	1.89902i
$285$		−	3575.90i		−	0.743221i
$286$	−3109.47	−	6600.87i	−0.642890	−	1.36475i
$287$	3492.36			0.718285
$288$	1591.42	+	348.709i	0.325608	+	0.0713468i
$289$	7550.91			1.53692
$290$	−265.792	+	6157.07i	−0.0538202	+	1.24674i
$291$	−965.875			−0.194572
$292$	−534.418	+	6178.35i	−0.107104	+	1.23822i
$293$	−3461.38			−0.690157			−0.345078	−	0.938574i	$-0.612148\pi$
$293$	−3461.38			−0.690157			−0.345078	+	0.938574i	$0.612148\pi$
$294$	−174.106	+	4033.15i	−0.0345376	+	0.800061i
$295$	5144.68			1.01537
$296$	1949.15	+	253.687i	0.382743	+	0.0498151i
$297$			1486.02i			0.290328i
$298$	6847.66	+	295.604i	1.33112	+	0.0574627i
$299$	−2998.90	−	5713.15i	−0.580037	−	1.10502i
$300$	−192.128	+	2221.18i	−0.0369751	+	0.427466i
$301$	3899.94			0.746807
$302$	−208.352	+	4826.46i	−0.0396996	+	0.919641i
$303$	−2074.49			−0.393321
$304$	−5091.22	−	887.405i	−0.960531	−	0.167422i
$305$			9959.63i			1.86979i
$306$	−2839.29	−	122.568i	−0.530430	−	0.0228979i
$307$	−2864.72			−0.532567			−0.266284	−	0.963895i	$-0.585796\pi$
$307$	−2864.72			−0.532567			−0.266284	+	0.963895i	$0.585796\pi$
$308$	1085.72	−	12551.9i	0.200858	−	2.32210i
$309$		−	604.273i		−	0.111249i
$310$	416.907	−	9657.63i	0.0763830	−	1.76941i
$311$	−10073.9			−1.83679			−0.918394	−	0.395667i	$-0.870513\pi$
$311$	−10073.9			−1.83679			−0.918394	+	0.395667i	$0.870513\pi$
$312$	−2984.55	+	1102.83i	−0.541560	+	0.200114i
$313$	2224.17			0.401653			0.200826	−	0.979627i	$-0.435637\pi$
$313$	2224.17			0.401653			0.200826	+	0.979627i	$0.435637\pi$
$314$	53.9675	−	1250.15i	0.00969924	−	0.224683i
$315$		−	3801.39i		−	0.679949i
$316$	−8767.46	−	758.372i	−1.56079	−	0.135006i
$317$	1680.26			0.297707			0.148853	−	0.988859i	$-0.452442\pi$
$317$	1680.26			0.297707			0.148853	+	0.988859i	$0.452442\pi$
$318$	−1053.56	−	45.4809i	−0.185789	−	0.00802026i
$319$			8124.00i			1.42588i
$320$	7305.97	+	1934.56i	1.27630	+	0.337954i
$321$	−843.542			−0.146673
$322$	480.499	−	11130.7i	0.0831588	−	1.92637i
$323$	9015.04			1.55297
$324$	645.589	+	55.8425i	0.110698	+	0.00957519i
$325$	−2023.70	−	3855.31i	−0.345399	−	0.658013i
$326$	6635.40	+	286.441i	1.12730	+	0.0486641i
$327$			3153.67i			0.533328i
$328$	−356.439	+	2738.61i	−0.0600031	+	0.461020i
$329$	15865.3			2.65862
$330$	−297.313	+	6887.24i	−0.0495955	+	1.14888i
$331$	−2578.08			−0.428109			−0.214055	−	0.976822i	$-0.568667\pi$
$331$	−2578.08			−0.428109			−0.214055	+	0.976822i	$0.568667\pi$
$332$	−3557.65	−	307.731i	−0.588106	−	0.0508703i
$333$	781.807			0.128657
$334$	−229.622	+	5319.19i	−0.0376179	+	0.871417i
$335$	−2316.20			−0.377754
$336$	−5412.26	−	943.363i	−0.878760	−	0.153169i
$337$	10545.7			1.70462			0.852312	−	0.523033i	$-0.175200\pi$
$337$	10545.7			1.70462			0.852312	+	0.523033i	$0.175200\pi$
$338$	3746.70	−	4957.49i	0.602940	−	0.797786i
$339$		−	1436.42i		−	0.230134i
$340$	−13134.7	−	1136.14i	−2.09509	−	0.181222i
$341$		−	12742.9i		−	2.02365i
$342$	−2053.64	−	88.6527i	−0.324702	−	0.0140169i
$343$		−	3798.60i		−	0.597975i
$344$	−398.037	+	3058.22i	−0.0623858	+	0.479326i
$345$			6096.08i			0.951311i
$346$	263.752	−	6109.81i	0.0409810	−	0.949323i
$347$			8988.12i			1.39051i	0.718762	+	0.695256i	$0.244709\pi$
$347$			8988.12i			1.39051i	−0.718762	+	0.695256i	$0.755291\pi$
$348$	3529.41	+	305.289i	0.543668	+	0.0470264i
$349$	7103.89			1.08958			0.544789	−	0.838573i	$-0.316610\pi$
$349$	7103.89			1.08958			0.544789	+	0.838573i	$0.316610\pi$
$350$	324.247	−	7511.18i	0.0495193	−	1.14711i
$351$	−1120.55	+	588.193i	−0.170401	+	0.0894456i
$352$	9731.99	+	2132.46i	1.47363	+	0.322899i
$353$			3516.18i			0.530163i	0.964226	+	0.265081i	$0.0853988\pi$
$353$			3516.18i			0.530163i	−0.964226	+	0.265081i	$0.914601\pi$
$354$	127.546	−	2954.59i	0.0191496	−	0.443600i
$355$			16832.9i			2.51661i
$356$	581.654	−	6724.45i	0.0865944	−	1.00111i
$357$	9583.52			1.42077
$358$	451.215	−	10452.4i	0.0666130	−	1.54309i
$359$		−	250.400i		−	0.0368123i	−0.999831	−	0.0184061i	$-0.994141\pi$
$359$		−	250.400i		−	0.0368123i	0.999831	−	0.0184061i	$-0.00585918\pi$
$360$	2980.94	+	387.978i	0.436415	+	0.0568007i
$361$	−338.496			−0.0493507
$362$	−203.388	+	4711.48i	−0.0295300	+	0.684060i
$363$			5094.43i			0.736606i
$364$	9894.67	−	4149.56i	1.42478	−	0.597516i
$365$			11442.6i			1.64091i
$366$	5719.82	+	246.917i	0.816884	+	0.0352638i
$367$	−5349.22			−0.760837			−0.380418	−	0.924814i	$-0.624220\pi$
$367$	−5349.22			−0.760837			−0.380418	+	0.924814i	$0.624220\pi$
$368$	8679.36	+	1512.82i	1.22946	+	0.214297i
$369$			1098.46i			0.154969i
$370$	3623.44	+	156.419i	0.509118	+	0.0219779i
$371$	3556.11			0.497640
$372$	−5536.04	−	478.859i	−0.771587	−	0.0667411i
$373$		−	4243.43i		−	0.589052i	−0.955643	−	0.294526i	$-0.904838\pi$
$373$		−	4243.43i		−	0.589052i	0.955643	−	0.294526i	$-0.0951617\pi$
$374$	−17363.1	−	749.542i	−2.40060	−	0.103631i
$375$		−	1421.75i		−	0.195783i
$376$	−1619.25	+	12441.1i	−0.222092	+	1.70639i
$377$	−6126.03	+	3215.63i	−0.836888	+	0.439293i
$378$	−2183.14	−	94.2431i	−0.297060	−	0.0128237i
$379$	12409.0			1.68181			0.840904	−	0.541184i	$-0.182024\pi$
$379$	12409.0			1.68181			0.840904	+	0.541184i	$0.182024\pi$
$380$	−9500.25	−	821.757i	−1.28251	−	0.110935i
$381$		−	1097.69i		−	0.147602i
$382$	−4323.37	−	186.634i	−0.579065	−	0.0249974i
$383$			1993.05i			0.265900i	0.991123	+	0.132950i	$0.0424450\pi$
$383$			1993.05i			0.265900i	−0.991123	+	0.132950i	$0.957555\pi$
$384$	1292.15	−	4147.86i	0.171718	−	0.551223i
$385$		−	23246.6i		−	3.07729i
$386$	−336.703	+	7799.71i	−0.0443983	+	1.02848i
$387$			1226.66i			0.161123i
$388$	−221.962	+	2566.08i	−0.0290423	+	0.335756i
$389$			10815.9i			1.40974i	0.709337	+	0.704869i	$0.248994\pi$
$389$			10815.9i			1.40974i	−0.709337	+	0.704869i	$0.751006\pi$
$390$	−5311.11	+	2501.90i	−0.689586	+	0.324843i
$391$	−15368.6			−1.98778
$392$	10675.0	+	1389.39i	1.37544	+	0.179017i
$393$	−378.336			−0.0485612
$394$	6775.42	+	292.486i	0.866347	+	0.0373990i
$395$	−16237.7			−2.06838
$396$	3947.97	+	341.493i	0.500992	+	0.0433351i
$397$	−2230.69			−0.282003			−0.141002	−	0.990009i	$-0.545032\pi$
$397$	−2230.69			−0.282003			−0.141002	+	0.990009i	$0.545032\pi$
$398$	−5370.83	−	231.851i	−0.676420	−	0.0292001i
$399$	6931.68			0.869719
$400$	5856.95	+	1020.87i	0.732119	+	0.127609i
$401$			6529.51i			0.813137i	0.913620	+	0.406569i	$0.133275\pi$
$401$			6529.51i			0.813137i	−0.913620	+	0.406569i	$0.866725\pi$
$402$	−57.4226	+	1330.19i	−0.00712432	+	0.165035i
$403$	9608.95	−	5043.86i	1.18773	−	0.623455i
$404$	−476.727	+	5511.40i	−0.0587081	+	0.678718i
$405$	1195.66			0.146699
$406$	−11935.1	−	515.224i	−1.45894	−	0.0629806i
$407$	4780.98			0.582271
$408$	−978.116	+	7515.12i	−0.118686	+	0.911896i
$409$		−	4392.09i		−	0.530990i	−0.964112	−	0.265495i	$-0.914465\pi$
$409$		−	4392.09i		−	0.530990i	0.964112	−	0.265495i	$-0.0855354\pi$
$410$	−219.773	+	5091.04i	−0.0264728	+	0.613241i
$411$	18.6883			0.00224289
$412$	−1605.40	−	138.865i	−0.191972	−	0.0166053i
$413$			9972.67i			1.18819i
$414$	3500.98	+	151.133i	0.415613	+	0.0179414i
$415$	−6588.93			−0.779368
$416$	2244.09	+	8182.63i	0.264484	+	0.964390i
$417$	−7919.95			−0.930076
$418$	−12558.6	−	542.138i	−1.46952	−	0.0634373i
$419$		−	2466.87i		−	0.287624i	−0.989605	−	0.143812i	$-0.954064\pi$
$419$		−	2466.87i		−	0.287624i	0.989605	−	0.143812i	$-0.0459360\pi$
$420$	−10099.3	−	873.576i	−1.17333	−	0.101491i
$421$	13264.4			1.53555			0.767773	−	0.640721i	$-0.221365\pi$
$421$	13264.4			1.53555			0.767773	+	0.640721i	$0.221365\pi$
$422$	361.833	−	8381.85i	0.0417387	−	0.966876i
$423$			4990.17i			0.573594i
$424$	−362.945	+	2788.60i	−0.0415712	+	0.319402i
$425$	−10370.9			−1.18368
$426$	9667.13	+	417.317i	1.09947	+	0.0474626i
$427$	−19306.2			−2.18804
$428$	−193.850	+	2241.08i	−0.0218927	+	0.253099i
$429$	−6852.52	+	3596.97i	−0.771195	+	0.404810i
$430$	−245.422	+	5685.19i	−0.0275240	+	0.637592i
$431$			3549.54i			0.396695i	0.980132	+	0.198347i	$0.0635574\pi$
$431$			3549.54i			0.396695i	−0.980132	+	0.198347i	$0.936443\pi$
$432$	296.719	−	1702.33i	0.0330460	−	0.189592i
$433$	6541.59			0.726025			0.363012	−	0.931784i	$-0.381748\pi$
$433$	6541.59			0.726025			0.363012	+	0.931784i	$0.381748\pi$
$434$	18720.8	+	808.151i	2.07057	+	0.0893836i
$435$	6536.64			0.720478
$436$	8378.50	+	724.727i	0.920315	+	0.0796058i
$437$	−11116.0			−1.21682
$438$	6571.48	+	283.682i	0.716889	+	0.0309471i
$439$	12339.3			1.34151			0.670754	−	0.741680i	$-0.265971\pi$
$439$	12339.3			1.34151			0.670754	+	0.741680i	$0.265971\pi$
$440$	18229.3	+	2372.60i	1.97511	+	0.257067i
$441$	4281.79			0.462346
$442$	−6307.44	−	13389.6i	−0.678765	−	1.44090i
$443$		−	15712.9i		−	1.68520i	−0.538542	−	0.842599i	$-0.681025\pi$
$443$		−	15712.9i		−	1.68520i	0.538542	−	0.842599i	$-0.318975\pi$
$444$	179.663	−	2077.06i	0.0192036	−	0.222011i
$445$		−	12454.0i		−	1.32669i
$446$	547.100	−	12673.5i	0.0580850	−	1.34554i
$447$		−	7269.81i		−	0.769240i
$448$	−3750.04	+	14162.2i	−0.395475	+	1.49353i
$449$		−	17297.9i		−	1.81813i	−0.416660	−	0.909063i	$-0.636799\pi$
$449$		−	17297.9i		−	1.81813i	0.416660	−	0.909063i	$-0.363201\pi$
$450$	2362.51	+	101.986i	0.247488	+	0.0106837i
$451$			6717.42i			0.701355i
$452$	−3816.20	−	330.095i	−0.397121	−	0.0343504i
$453$	5124.00			0.531449
$454$	2125.43	+	91.7520i	0.219717	+	0.00948488i
$455$	17529.5	−	9201.44i	1.80614	−	0.948067i
$456$	−707.463	+	5435.62i	−0.0726535	+	0.558216i
$457$		−	2827.39i		−	0.289408i	−0.989475	−	0.144704i	$-0.953777\pi$
$457$		−	2827.39i		−	0.289408i	0.989475	−	0.144704i	$-0.0462230\pi$
$458$	1600.14	+	69.0760i	0.163253	+	0.00704740i
$459$			3014.33i			0.306529i
$460$	16195.7	+	1400.91i	1.64159	+	0.141995i
$461$	17075.0			1.72508			0.862540	−	0.505989i	$-0.168872\pi$
$461$	17075.0			1.72508			0.862540	+	0.505989i	$0.168872\pi$
$462$	−13350.5	−	576.324i	−1.34442	−	0.0580369i
$463$		−	5646.99i		−	0.566820i	−0.958999	−	0.283410i	$-0.908534\pi$
$463$		−	5646.99i		−	0.566820i	0.958999	−	0.283410i	$-0.0914658\pi$
$464$	1622.15	−	9306.60i	0.162298	−	0.931138i
$465$	−10253.0			−1.02252
$466$	3576.23	+	154.381i	0.355506	+	0.0153467i
$467$		−	1150.82i		−	0.114034i	−0.998373	−	0.0570168i	$-0.981841\pi$
$467$		−	1150.82i		−	0.114034i	0.998373	−	0.0570168i	$-0.0181589\pi$
$468$	1305.17	+	3112.20i	0.128914	+	0.307396i
$469$		−	4489.82i		−	0.442049i
$470$	−998.401	+	23127.9i	−0.0979847	+	2.26981i
$471$	−1327.22			−0.129841
$472$	−7820.28	−	1017.83i	−0.762622	−	0.0992576i
$473$			7501.38i			0.729205i
$474$	−402.562	+	9325.34i	−0.0390090	+	0.903643i
$475$	−7501.21			−0.724587
$476$	2202.34	−	25461.0i	0.212067	−	2.45169i
$477$			1118.51i			0.107365i
$478$	149.942	−	3473.39i	0.0143476	−	0.332362i
$479$			4098.99i			0.390997i	0.980704	+	0.195498i	$0.0626325\pi$
$479$			4098.99i			0.390997i	−0.980704	+	0.195498i	$0.937368\pi$
$480$	1715.79	−	7830.44i	0.163156	−	0.744602i
$481$	1892.40	+	3605.17i	0.179389	+	0.341750i
$482$	177.203	−	4104.90i	0.0167456	−	0.387911i
$483$	−11816.9			−1.11323
$484$	13534.6	+	1170.72i	1.27109	+	0.109948i
$485$			4752.51i			0.444949i
$486$	29.6425	−	686.668i	0.00276669	−	0.0640903i
$487$			4666.70i			0.434226i	0.976146	+	0.217113i	$0.0696641\pi$
$487$			4666.70i			0.434226i	−0.976146	+	0.217113i	$0.930336\pi$
$488$	1970.43	−	15139.4i	0.182781	−	1.40436i
$489$		−	7044.46i		−	0.651455i
$490$	19844.8	+	856.672i	1.82958	+	0.0789806i
$491$		−	6201.94i		−	0.570040i	−0.958522	−	0.285020i	$-0.908000\pi$
$491$		−	6201.94i		−	0.570040i	0.958522	−	0.285020i	$-0.0920003\pi$
$492$	2918.34	+	252.432i	0.267416	+	0.0231311i
$493$			16479.2i			1.50545i
$494$	−4562.12	−	9684.60i	−0.415505	−	0.882046i
$495$	7311.82			0.663923
$496$	−2544.41	+	14597.8i	−0.230338	+	1.32149i
$497$	−32629.6			−2.94495
$498$	−163.351	+	3784.02i	−0.0146987	+	0.340494i
$499$	−6586.27			−0.590866			−0.295433	−	0.955363i	$-0.595464\pi$
$499$	−6586.27			−0.590866			−0.295433	+	0.955363i	$0.595464\pi$
$500$	−3777.22	−	326.724i	−0.337845	−	0.0292231i
$501$	5647.11			0.503581
$502$	378.915	−	8777.55i	0.0336888	−	0.780401i
$503$	−21802.5			−1.93265			−0.966327	−	0.257316i	$-0.917162\pi$
$503$	−21802.5			−1.93265			−0.966327	+	0.257316i	$0.917162\pi$
$504$	−752.075	+	5778.39i	−0.0664684	+	0.510694i
$505$			10207.4i			0.899449i
$506$	21409.5	+	924.220i	1.88097	+	0.0811988i
$507$	−5424.71	−	3743.50i	−0.475187	−	0.327919i
$508$	−2916.28	−	252.254i	−0.254703	−	0.0220314i
$509$	15007.7			1.30689			0.653444	−	0.756975i	$-0.273323\pi$
$509$	15007.7			1.30689			0.653444	+	0.756975i	$0.273323\pi$
$510$	−603.088	+	13970.5i	−0.0523631	+	1.21299i
$511$	−22180.8			−1.92020
$512$	−10722.9	−	4386.10i	−0.925563	−	0.378594i
$513$			2180.24i			0.187641i
$514$	6257.21	+	270.115i	0.536952	+	0.0231795i
$515$	−2973.27			−0.254404
$516$	3258.92	+	281.892i	0.278035	+	0.0240496i
$517$			30516.4i			2.59595i
$518$	−303.210	+	7023.84i	−0.0257187	+	0.595772i
$519$	−6486.47			−0.548602
$520$	5426.40	+	14685.2i	0.457622	+	1.23844i
$521$	−6194.23			−0.520872			−0.260436	−	0.965491i	$-0.583866\pi$
$521$	−6194.23			−0.520872			−0.260436	+	0.965491i	$0.583866\pi$
$522$	162.055	−	3753.99i	0.0135880	−	0.314766i
$523$		−	15166.5i		−	1.26804i	−0.773316	−	0.634021i	$-0.781403\pi$
$523$		−	15166.5i		−	1.26804i	0.773316	−	0.634021i	$-0.218597\pi$
$524$	−86.9433	+	1005.14i	−0.00724835	+	0.0837975i
$525$	−7974.22			−0.662902
$526$	−18480.3	−	797.768i	−1.53190	−	0.0661299i
$527$		−	25848.4i		−	2.13657i
$528$	1814.52	−	10410.3i	0.149559	−	0.858047i
$529$	6783.16			0.557505
$530$	−223.785	+	5183.98i	−0.0183408	+	0.424863i
$531$	−3136.73			−0.256351
$532$	1592.93	−	18415.7i	0.129816	−	1.50079i
$533$	−5065.38	+	2658.88i	−0.411643	+	0.216077i
$534$	−7152.32	−	308.756i	−0.579609	−	0.0250209i
$535$			4150.58i			0.335412i
$536$	3520.79	+	458.241i	0.283722	+	0.0369273i
$537$	−11096.7			−0.891731
$538$	−28.3250	+	656.148i	−0.00226985	+	0.0525810i
$539$	26184.4			2.09247
$540$	274.768	−	3176.57i	0.0218966	−	0.253144i
$541$	−4510.52			−0.358452			−0.179226	−	0.983808i	$-0.557359\pi$
$541$	−4510.52			−0.358452			−0.179226	+	0.983808i	$0.557359\pi$
$542$	111.230	−	2576.65i	0.00881505	−	0.204200i
$543$	5001.93			0.395310
$544$	19741.0	+	4325.61i	1.55586	+	0.340917i
$545$	15517.4			1.21962
$546$	−4849.80	−	10295.3i	−0.380132	−	0.806956i
$547$			19668.3i			1.53740i	0.639611	+	0.768698i	$0.279095\pi$
$547$			19668.3i			1.53740i	−0.639611	+	0.768698i	$0.720905\pi$
$548$	4.29466	−	49.6502i	0.000334779	−	0.00387035i
$549$		−	6072.43i		−	0.472067i
$550$	14447.4	+	623.676i	1.12007	+	0.0483521i
$551$			11919.3i			0.921559i
$552$	1206.06	−	9266.49i	0.0929953	−	0.714507i
$553$		−	31476.0i		−	2.42042i
$554$	−8.63216	+	199.964i	−0.000661995	+	0.0153351i
$555$		−	3846.82i		−	0.294213i
$556$	−1820.04	+	21041.3i	−0.138825	+	1.60495i
$557$	−169.552			−0.0128980			−0.00644898	−	0.999979i	$-0.502053\pi$
$557$	−169.552			−0.0128980			−0.00644898	+	0.999979i	$0.502053\pi$
$558$	−254.190	+	5888.30i	−0.0192844	+	0.446723i
$559$	−5656.53	+	2969.19i	−0.427989	+	0.224657i
$560$	−4641.74	+	26630.6i	−0.350267	+	2.00955i
$561$			18433.5i			1.38728i
$562$	−713.819	+	16535.6i	−0.0535776	+	1.24112i
$563$		−	1508.87i		−	0.112951i	−0.998404	−	0.0564753i	$-0.982014\pi$
$563$		−	1508.87i		−	0.112951i	0.998404	−	0.0564753i	$-0.0179862\pi$
$564$	13257.6	+	1146.76i	0.989798	+	0.0856160i
$565$	−7067.77			−0.526272
$566$	−497.481	+	11524.1i	−0.0369447	+	0.855823i
$567$			2317.72i			0.171667i
$568$	3330.25	−	25587.2i	0.246011	−	1.89017i
$569$	−11553.8			−0.851247			−0.425624	−	0.904900i	$-0.639945\pi$
$569$	−11553.8			−0.851247			−0.425624	+	0.904900i	$0.639945\pi$
$570$	−436.208	+	10104.8i	−0.0320540	+	0.742529i
$571$		−	3952.16i		−	0.289655i	−0.989457	−	0.144827i	$-0.953737\pi$
$571$		−	3952.16i		−	0.289655i	0.989457	−	0.144827i	$-0.0462626\pi$
$572$	7981.50	+	19032.0i	0.583433	+	1.39120i
$573$			4589.89i			0.334634i
$574$	−9868.71	−	426.019i	−0.717617	−	0.0309785i
$575$	12787.8			0.927460
$576$	−4454.48	−	1179.51i	−0.322228	−	0.0853234i
$577$		−	23411.7i		−	1.68915i	−0.535437	−	0.844575i	$-0.679853\pi$
$577$		−	23411.7i		−	1.68915i	0.535437	−	0.844575i	$-0.320147\pi$
$578$	−21337.3	−	921.103i	−1.53549	−	0.0662852i
$579$	8280.55			0.594349
$580$	1502.15	−	17366.2i	0.107540	−	1.24326i
$581$		−	12772.3i		−	0.912019i
$582$	2729.36	+	117.823i	0.194391	+	0.00839161i
$583$			6840.04i			0.485910i
$584$	2263.83	−	17393.6i	0.160407	−	1.23245i
$585$	2894.15	+	5513.60i	0.204545	+	0.389674i
$586$	9781.15	+	422.239i	0.689515	+	0.0297654i
$587$	−12824.9			−0.901771			−0.450886	−	0.892582i	$-0.648892\pi$
$587$	−12824.9			−0.901771			−0.450886	+	0.892582i	$0.648892\pi$
$588$	983.973	−	11375.6i	0.0690108	−	0.797827i
$589$		−	18695.9i		−	1.30790i
$590$	−14537.8	−	627.577i	−1.01443	−	0.0437914i
$591$		−	7193.11i		−	0.500651i
$592$	−5476.94	−	954.637i	−0.380238	−	0.0662759i
$593$			22496.5i			1.55788i	0.627100	+	0.778939i	$0.284242\pi$
$593$			22496.5i			1.55788i	−0.627100	+	0.778939i	$0.715758\pi$
$594$	181.273	−	4199.18i	0.0125214	−	0.290058i
$595$		−	47154.9i		−	3.24901i
$596$	−19314.0	−	1670.63i	−1.32741	−	0.114819i
$597$			5701.93i			0.390895i
$598$	7777.37	+	16510.0i	0.531840	+	1.12900i
$599$	−14283.0			−0.974268			−0.487134	−	0.873327i	$-0.661958\pi$
$599$	−14283.0			−0.974268			−0.487134	+	0.873327i	$0.661958\pi$
$600$	813.867	−	6253.15i	0.0553767	−	0.425473i
$601$	14705.3			0.998075			0.499038	−	0.866580i	$-0.333687\pi$
$601$	14705.3			0.998075			0.499038	+	0.866580i	$0.333687\pi$
$602$	−11020.4	−	475.737i	−0.746112	−	0.0322086i
$603$	1412.20			0.0953716
$604$	1177.52	−	13613.2i	0.0793254	−	0.917073i
$605$	25066.7			1.68447
$606$	5862.09	+	253.058i	0.392955	+	0.0169633i
$607$	16346.3			1.09304			0.546519	−	0.837447i	$-0.315953\pi$
$607$	16346.3			1.09304			0.546519	+	0.837447i	$0.315953\pi$
$608$	14278.5	+	3128.68i	0.952416	+	0.208692i
$609$			12670.9i			0.843106i
$610$	1214.93	−	28143.9i	0.0806413	−	1.86805i
$611$	−23011.3	+	12078.9i	−1.52363	+	0.799773i
$612$	8008.31	+	692.707i	0.528949	+	0.0457533i
$613$	24742.1			1.63022			0.815111	−	0.579305i	$-0.196676\pi$
$613$	24742.1			1.63022			0.815111	+	0.579305i	$0.196676\pi$
$614$	8095.11	+	349.455i	0.532072	+	0.0229688i
$615$	5404.90			0.354384
$616$	−4599.16	+	35336.5i	−0.300820	+	2.31128i
$617$			10891.4i			0.710650i	0.934743	+	0.355325i	$0.115630\pi$
$617$			10891.4i			0.710650i	−0.934743	+	0.355325i	$0.884370\pi$
$618$	−73.7126	+	1707.55i	−0.00479799	+	0.111145i
$619$	−291.372			−0.0189196			−0.00945981	−	0.999955i	$-0.503011\pi$
$619$	−291.372			−0.0189196			−0.00945981	+	0.999955i	$0.503011\pi$
$620$	−2356.19	+	27239.6i	−0.152624	+	1.76447i
$621$		−	3716.81i		−	0.240178i
$622$	28466.9	+	1228.88i	1.83508	+	0.0792179i
$623$	24141.4			1.55249
$624$	8568.25	−	2752.31i	0.549687	−	0.176572i
$625$	−18607.4			−1.19087
$626$	−6285.04	−	271.317i	−0.401279	−	0.0173227i
$627$			13332.8i			0.849220i
$628$	−305.002	+	3526.10i	−0.0193804	+	0.224055i
$629$	9698.05			0.614764
$630$	−463.715	+	10742.0i	−0.0293252	+	0.679317i
$631$		−	3616.73i		−	0.228177i	−0.993471	−	0.114088i	$-0.963605\pi$
$631$		−	3616.73i		−	0.228177i	0.993471	−	0.114088i	$-0.0363947\pi$
$632$	24682.5	+	3212.51i	1.55351	+	0.202194i
$633$	−8898.57			−0.558746
$634$	−4748.08	−	204.968i	−0.297430	−	0.0128396i
$635$	−5401.09			−0.337537
$636$	2971.61	+	257.040i	0.185270	+	0.0160256i
$637$	10364.3	+	19744.7i	0.644658	+	1.22812i
$638$	991.012	−	22956.8i	0.0614961	−	1.42456i
$639$		−	10263.1i		−	0.635370i
$640$	−20409.2	−	6357.90i	−1.26054	−	0.392684i
$641$	14015.0			0.863586			0.431793	−	0.901973i	$-0.357881\pi$
$641$	14015.0			0.863586			0.431793	+	0.901973i	$0.357881\pi$
$642$	2383.68	+	102.900i	0.146536	+	0.00632577i
$643$	−15384.8			−0.943573			−0.471787	−	0.881713i	$-0.656391\pi$
$643$	−15384.8			−0.943573			−0.471787	+	0.881713i	$0.656391\pi$
$644$	−2715.58	+	31394.6i	−0.166163	+	1.92099i
$645$	6035.67			0.368456
$646$	−25474.7	−	1099.71i	−1.55153	−	0.0669773i
$647$	−22195.7			−1.34869			−0.674346	−	0.738415i	$-0.735575\pi$
$647$	−22195.7			−1.34869			−0.674346	+	0.738415i	$0.735575\pi$
$648$	−1817.49	−	236.552i	−0.110182	−	0.0143405i
$649$	−19182.0			−1.16019
$650$	5248.27	+	11141.2i	0.316699	+	0.672297i
$651$		−	19874.9i		−	1.19656i
$652$	−18715.3	−	1618.85i	−1.12416	−	0.0972377i
$653$		−	1942.96i		−	0.116438i	−0.998304	−	0.0582190i	$-0.981458\pi$
$653$		−	1942.96i		−	0.116438i	0.998304	−	0.0582190i	$-0.0185422\pi$
$654$	384.703	−	8911.62i	0.0230016	−	0.532832i
$655$			1861.57i			0.111050i
$656$	1341.29	−	7695.27i	0.0798304	−	0.458003i
$657$		−	6976.60i		−	0.414282i
$658$	−44832.2	−	1935.35i	−2.65614	−	0.114662i
$659$			27887.3i			1.64846i	0.566253	+	0.824231i	$0.308392\pi$
$659$			27887.3i			1.64846i	−0.566253	+	0.824231i	$0.691608\pi$
$660$	1680.29	−	19425.7i	0.0990987	−	1.14567i
$661$	−9000.63			−0.529628			−0.264814	−	0.964300i	$-0.585311\pi$
$661$	−9000.63			−0.529628			−0.264814	+	0.964300i	$0.585311\pi$
$662$	7285.13	+	314.489i	0.427711	+	0.0184637i
$663$	−13900.1	+	7296.33i	−0.814230	+	0.427400i
$664$	10015.6	+	1303.57i	0.585365	+	0.0761871i
$665$		−	34106.8i		−	1.98888i
$666$	−2209.23	−	95.3693i	−0.128537	−	0.00554878i
$667$		−	20319.7i		−	1.17958i
$668$	1297.73	−	15002.9i	0.0751658	−	0.868984i
$669$	−13454.8			−0.777570
$670$	6545.10	+	282.543i	0.377402	+	0.0162919i
$671$		−	37134.7i		−	2.13647i
$672$	15178.9	+	3325.97i	0.871336	+	0.190926i
$673$	22407.7			1.28344			0.641718	−	0.766940i	$-0.278222\pi$
$673$	22407.7			1.28344			0.641718	+	0.766940i	$0.278222\pi$
$674$	−29799.9	−	1286.42i	−1.70304	−	0.0735178i
$675$		−	2508.15i		−	0.143021i
$676$	−11192.2	+	13551.8i	−0.636787	+	0.771040i
$677$		−	21060.3i		−	1.19559i	−0.801651	−	0.597793i	$-0.796045\pi$
$677$		−	21060.3i		−	1.19559i	0.801651	−	0.597793i	$-0.203955\pi$
$678$	−175.222	+	4059.02i	−0.00992533	+	0.229920i
$679$	−9212.47			−0.520681
$680$	36977.5	+	4812.74i	2.08533	+	0.271412i
$681$		−	2256.46i		−	0.126972i
$682$	−1554.45	+	36008.7i	−0.0872769	+	2.02177i
$683$	−17468.5			−0.978642			−0.489321	−	0.872104i	$-0.662755\pi$
$683$	−17468.5			−0.978642			−0.489321	+	0.872104i	$0.662755\pi$
$684$	5792.35	+	501.029i	0.323795	+	0.0280078i
$685$		−	91.9544i		−	0.00512905i
$686$	−463.375	+	10734.1i	−0.0257897	+	0.597418i
$687$		−	1698.79i		−	0.0943419i
$688$	1497.83	−	8593.35i	0.0830003	−	0.476189i
$689$	−5157.84	+	2707.42i	−0.285193	+	0.149702i
$690$	743.635	−	17226.3i	0.0410286	−	0.950425i
$691$	−24317.9			−1.33878			−0.669389	−	0.742912i	$-0.733444\pi$
$691$	−24317.9			−1.33878			−0.669389	+	0.742912i	$0.733444\pi$
$692$	−1490.62	+	17232.9i	−0.0818857	+	0.946672i
$693$			14173.6i			0.776925i
$694$	1096.42	−	25398.6i	0.0599707	−	1.38922i
$695$			38969.5i			2.12690i
$696$	−9936.16	−	1293.22i	−0.541134	−	0.0704302i
$697$			13626.0i			0.740493i
$698$	−20074.1	−	866.574i	−1.08856	−	0.0469918i
$699$		−	3796.70i		−	0.205443i
$700$	−1832.51	+	21185.5i	−0.0989464	+	1.14391i
$701$		−	13793.0i		−	0.743159i	−0.928401	−	0.371579i	$-0.878816\pi$
$701$		−	13793.0i		−	0.743159i	0.928401	−	0.371579i	$-0.121184\pi$
$702$	3238.21	−	1525.42i	0.174100	−	0.0820133i
$703$	7014.52			0.376326
$704$	−27240.5	−	7213.05i	−1.45833	−	0.386154i
$705$	24553.7			1.31170
$706$	428.924	−	9936.01i	0.0228651	−	0.529669i
$707$	−19786.4			−1.05254
$708$	−720.835	+	8333.50i	−0.0382636	+	0.442362i
$709$	−11081.2			−0.586970			−0.293485	−	0.955964i	$-0.594815\pi$
$709$	−11081.2			−0.586970			−0.293485	+	0.955964i	$0.594815\pi$
$710$	2053.37	−	47566.3i	0.108538	−	2.51427i
$711$	9900.22			0.522205
$712$	−2463.92	+	18931.0i	−0.129690	+	0.996443i
$713$			31872.3i			1.67409i
$714$	−27081.1	−	1169.05i	−1.41944	−	0.0612755i
$715$	17698.6	+	33717.3i	0.925721	+	1.76357i
$716$	−2550.08	+	29481.2i	−0.133102	+	1.53878i
$717$	−3687.52			−0.192068
$718$	−30.5452	+	707.579i	−0.00158766	+	0.0367780i
$719$	17777.0			0.922070			0.461035	−	0.887382i	$-0.347478\pi$
$719$	17777.0			0.922070			0.461035	+	0.887382i	$0.347478\pi$
$720$	−8376.20	−	1459.98i	−0.433559	−	0.0755698i
$721$		−	5763.53i		−	0.297705i
$722$	956.521	+	41.2917i	0.0493047	+	0.00212842i
$723$	−4357.96			−0.224169
$724$	1149.47	−	13288.9i	0.0590050	−	0.682150i
$725$		−	13712.0i		−	0.702414i
$726$	621.447	−	14395.8i	0.0317687	−	0.735921i
$727$	−26444.6			−1.34907			−0.674535	−	0.738242i	$-0.735656\pi$
$727$	−26444.6			−1.34907			−0.674535	+	0.738242i	$0.735656\pi$
$728$	−28466.5	+	10518.8i	−1.44923	+	0.535511i
$729$	−729.000			−0.0370370
$730$	1395.83	−	32334.4i	0.0707700	−	1.63938i
$731$			15216.3i			0.769896i
$732$	−16132.9	−	1395.47i	−0.814603	−	0.0704619i
$733$	−13099.8			−0.660097			−0.330049	−	0.943964i	$-0.607065\pi$
$733$	−13099.8			−0.660097			−0.330049	+	0.943964i	$0.607065\pi$
$734$	15115.8	+	652.529i	0.760129	+	0.0328137i
$735$		−	21068.2i		−	1.05729i
$736$	−24341.5	−	5333.68i	−1.21908	−	0.267122i
$737$	8635.99			0.431630
$738$	133.997	−	3104.03i	0.00668359	−	0.154825i
$739$	−4286.73			−0.213383			−0.106691	−	0.994292i	$-0.534026\pi$
$739$	−4286.73			−0.213383			−0.106691	+	0.994292i	$0.534026\pi$
$740$	−10220.0	−	884.016i	−0.507696	−	0.0439150i
$741$	−10053.8	+	5277.37i	−0.498429	+	0.261632i
$742$	−10048.9	−	433.795i	−0.497177	−	0.0214624i
$743$		−	5226.63i		−	0.258071i	−0.991640	−	0.129035i	$-0.958812\pi$
$743$		−	5226.63i		−	0.258071i	0.991640	−	0.129035i	$-0.0411881\pi$
$744$	15585.3	+	2028.48i	0.767991	+	0.0999564i
$745$	−35770.5			−1.75910
$746$	−517.638	+	11991.1i	−0.0254049	+	0.588504i
$747$	4017.30			0.196767
$748$	48973.2	+	4236.10i	2.39390	+	0.207069i
$749$	−8045.67			−0.392500
$750$	−173.433	+	4017.57i	−0.00844383	+	0.195601i
$751$	−9695.17			−0.471081			−0.235540	−	0.971865i	$-0.575686\pi$
$751$	−9695.17			−0.471081			−0.235540	+	0.971865i	$0.575686\pi$
$752$	6093.32	−	34958.6i	0.295479	−	1.69522i
$753$	−9318.67			−0.450984
$754$	17703.2	−	8339.42i	0.855055	−	0.402790i
$755$		−	25212.2i		−	1.21532i
$756$	6157.60	+	532.623i	0.296230	+	0.0256234i
$757$			6559.08i			0.314919i	0.987525	+	0.157460i	$0.0503304\pi$
$757$			6559.08i			0.314919i	−0.987525	+	0.157460i	$0.949670\pi$
$758$	−35065.2	−	1513.72i	−1.68024	−	0.0725338i
$759$		−	22729.4i		−	1.08699i
$760$	26745.5	+	3481.01i	1.27653	+	0.166144i
$761$		−	14168.8i		−	0.674924i	−0.941339	−	0.337462i	$-0.890431\pi$
$761$		−	14168.8i		−	0.674924i	0.941339	−	0.337462i	$-0.109569\pi$
$762$	−133.902	+	3101.85i	−0.00636584	+	0.147465i
$763$			30079.6i			1.42720i
$764$	12194.2	+	1054.78i	0.577448	+	0.0499483i
$765$	14831.8			0.700972
$766$	243.123	−	5631.94i	0.0114679	−	0.265653i
$767$	−7592.61	−	14464.5i	−0.357436	−	0.680943i
$768$	−4157.32	+	11563.4i	−0.195331	+	0.543304i
$769$			12392.6i			0.581130i	0.956855	+	0.290565i	$0.0938433\pi$
$769$			12392.6i			0.581130i	−0.956855	+	0.290565i	$0.906157\pi$
$770$	−2835.76	+	65690.2i	−0.132719	+	3.07443i
$771$		−	6642.95i		−	0.310298i
$772$	1902.91	−	21999.3i	0.0887139	−	1.02561i
$773$	3097.37			0.144120			0.0720598	−	0.997400i	$-0.477043\pi$
$773$	3097.37			0.144120			0.0720598	+	0.997400i	$0.477043\pi$
$774$	149.635	−	3466.29i	0.00694899

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82580 - 0.121986i) q^{2} +3.00000i q^{3} +(7.97024 + 0.689413i) q^{4} +14.7613 q^{5} +(0.365957 - 8.47739i) q^{6} +28.6139i q^{7} +(-22.4382 - 2.92040i) q^{8} -9.00000 q^{9} +(-41.7123 - 1.80066i) q^{10} -55.0376 q^{11} +(-2.06824 + 23.9107i) q^{12} +(-21.7849 - 41.5020i) q^{13} +(3.49048 - 80.8570i) q^{14} +44.2838i q^{15} +(63.0494 + 10.9896i) q^{16} -111.642 q^{17} +(25.4322 + 1.09787i) q^{18} -80.7496 q^{19} +(117.651 + 10.1766i) q^{20} -85.8416 q^{21} +(155.525 + 6.71381i) q^{22} +137.660 q^{23} +(8.76119 - 67.3145i) q^{24} +92.8946 q^{25} +(56.4971 + 119.934i) q^{26} -27.0000i q^{27} +(-19.7268 + 228.059i) q^{28} -147.608i q^{29} +(5.40199 - 125.137i) q^{30} +231.530i q^{31} +(-176.824 - 38.7454i) q^{32} -165.113i q^{33} +(315.477 + 13.6187i) q^{34} +422.377i q^{35} +(-71.7322 - 6.20472i) q^{36} -86.8675 q^{37} +(228.182 + 9.85030i) q^{38} +(124.506 - 65.3548i) q^{39} +(-331.215 - 43.1087i) q^{40} -122.051i q^{41} +(242.571 + 10.4715i) q^{42} -136.295i q^{43} +(-438.663 - 37.9437i) q^{44} -132.851 q^{45} +(-388.998 - 16.7925i) q^{46} -554.463i q^{47} +(-32.9687 + 189.148i) q^{48} -475.754 q^{49} +(-262.501 - 11.3318i) q^{50} -334.926i q^{51} +(-145.019 - 345.800i) q^{52} -124.279i q^{53} +(-3.29361 + 76.2965i) q^{54} -812.425 q^{55} +(83.5639 - 642.043i) q^{56} -242.249i q^{57} +(-18.0061 + 417.110i) q^{58} +348.526 q^{59} +(-30.5298 + 352.952i) q^{60} +674.715i q^{61} +(28.2433 - 654.256i) q^{62} -257.525i q^{63} +(494.943 + 131.057i) q^{64} +(-321.573 - 612.622i) q^{65} +(-20.1414 + 466.575i) q^{66} -156.911 q^{67} +(-889.812 - 76.9674i) q^{68} +412.979i q^{69} +(51.5239 - 1193.55i) q^{70} +1140.34i q^{71} +(201.943 + 26.2836i) q^{72} +775.178i q^{73} +(245.470 + 10.5966i) q^{74} +278.684i q^{75} +(-643.594 - 55.6699i) q^{76} -1574.84i q^{77} +(-359.801 + 169.491i) q^{78} -1100.02 q^{79} +(930.688 + 162.220i) q^{80} +81.0000 q^{81} +(-14.8885 + 344.892i) q^{82} -446.367 q^{83} +(-684.178 - 59.1804i) q^{84} -1647.97 q^{85} +(-16.6261 + 385.143i) q^{86} +442.824 q^{87} +(1234.94 + 160.732i) q^{88} -843.694i q^{89} +(375.411 + 16.2060i) q^{90} +(1187.53 - 623.351i) q^{91} +(1097.18 + 94.9044i) q^{92} -694.589 q^{93} +(-67.6366 + 1566.80i) q^{94} -1191.97 q^{95} +(116.236 - 530.473i) q^{96} +321.958i q^{97} +(1344.38 + 58.0352i) q^{98} +495.339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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