LMFDB - Embedded newform 312.4.m.a.181.83

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			181.83
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.84

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82580 - 0.121986i) q^{2} -3.00000i q^{3} +(7.97024 - 0.689413i) q^{4} -14.7613 q^{5} +(-0.365957 - 8.47739i) q^{6} +28.6139i q^{7} +(22.4382 - 2.92040i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(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} +(66.6224 + 114.619i) 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} +(202.243 + 315.762i) 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} +(343.856 - 199.867i) 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}+O(q^{10}) $ 84 * q - 756 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.729504\pi$
$5$	−14.7613			−1.32029			−0.660143	+	0.751140i	$0.729504\pi$
$6$	−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	$-0.227979\pi$
$11$	55.0376			1.50859			0.754294	+	0.656536i	$0.227979\pi$
$12$	−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	$-0.337907\pi$
$19$	80.7496			0.975012			0.487506	+	0.873120i	$0.337907\pi$
$20$	−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
$26$	66.6224	+	114.619i	0.502528	+	0.864561i
$27$			27.0000i			0.192450i
$28$	19.7268	+	228.059i	0.133143	+	1.53926i
$29$			147.608i			0.945177i	0.881283	+	0.472588i	$0.156680\pi$
$29$			147.608i			0.945177i	−0.881283	+	0.472588i	$0.843320\pi$
$30$	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	$-0.438183\pi$
$37$	86.8675			0.385971			0.192985	+	0.981202i	$0.438183\pi$
$38$	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	$0.0776999\pi$
$43$			136.295i			0.483369i	−0.970355	+	0.241684i	$0.922300\pi$
$44$	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
$52$	202.243	+	315.762i	0.539348	+	0.842083i
$53$			124.279i			0.322096i	0.986947	+	0.161048i	$0.0514874\pi$
$53$			124.279i			0.322096i	−0.986947	+	0.161048i	$0.948513\pi$
$54$	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	$-0.625635\pi$
$59$	−348.526			−0.769054			−0.384527	+	0.923114i	$0.625635\pi$
$60$	30.5298	+	352.952i	0.0656897	+	0.759432i
$61$		−	674.715i		−	1.41620i	−0.706111	−	0.708101i	$-0.749552\pi$
$61$		−	674.715i		−	1.41620i	0.706111	−	0.708101i	$-0.250448\pi$
$62$	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	$-0.454307\pi$
$67$	156.911			0.286115			0.143057	+	0.989714i	$0.454307\pi$
$68$	−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
$78$	343.856	−	199.867i	0.499155	−	0.290135i
$79$	−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	$-0.404630\pi$
$83$	446.367			0.590302			0.295151	+	0.955451i	$0.404630\pi$
$84$	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	$-0.889361\pi$
$101$		−	691.497i		−	0.681253i	0.940199	−	0.340626i	$-0.110639\pi$
$102$	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	$0.530715\pi$
$104$	610.016	+	867.608i	0.575163	+	0.818039i
$105$	−1267.13			−1.17771
$106$	15.1603	+	351.188i	0.0138915	+	0.321796i
$107$		−	281.181i		−	0.254044i	−0.991900	−	0.127022i	$-0.959458\pi$
$107$		−	281.181i		−	0.254044i	0.991900	−	0.127022i	$-0.0405420\pi$
$108$	18.6142	+	215.196i	0.0165847	+	0.191734i
$109$	−1051.22			−0.923752			−0.461876	−	0.886945i	$-0.652823\pi$
$109$	−1051.22			−0.923752			−0.461876	+	0.886945i	$0.652823\pi$
$110$	−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
$130$	−983.430	−	1691.92i	−0.663481	−	1.14147i
$131$		−	126.112i		−	0.0841104i	−0.999115	−	0.0420552i	$-0.986609\pi$
$131$		−	126.112i		−	0.0841104i	0.999115	−	0.0420552i	$-0.0133905\pi$
$132$	−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	$-0.701913\pi$
$139$		−	2639.98i		−	1.61094i	0.592638	−	0.805469i	$-0.298087\pi$
$140$	−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	$-0.267928\pi$
$149$	2423.27			1.33236			0.666181	+	0.745790i	$0.267928\pi$
$150$	−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
$156$	947.286	−	606.729i	0.486177	−	0.311392i
$157$		−	442.408i		−	0.224892i	−0.993658	−	0.112446i	$-0.964131\pi$
$157$		−	442.408i		−	0.224892i	0.993658	−	0.112446i	$-0.0358685\pi$
$158$	−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	$-0.309194\pi$
$163$	2348.15			1.12835			0.564176	+	0.825654i	$0.309194\pi$
$164$	−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	$-0.842411\pi$
$173$		−	2162.16i		−	0.950207i	0.879930	−	0.475103i	$-0.157589\pi$
$174$	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	$-0.719125\pi$
$179$		−	3698.91i		−	1.54452i	0.635304	−	0.772262i	$-0.280875\pi$
$180$	1058.86	−	91.5895i	0.438458	−	0.0379260i
$181$			1667.31i			0.684698i	0.939573	+	0.342349i	$0.111222\pi$
$181$			1667.31i			0.684698i	−0.939573	+	0.342349i	$0.888778\pi$
$182$	−3279.69	+	1906.32i	−1.33575	+	0.776408i
$183$	−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	$-0.357251\pi$
$197$	2397.70			0.867154			0.433577	+	0.901117i	$0.357251\pi$
$198$	−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
$208$	1829.62	+	2377.27i	0.609909	+	0.792471i
$209$	4444.27			1.47089
$210$	−3580.65	+	154.572i	−1.17661	+	0.0507927i
$211$		−	2966.19i		−	0.967777i	−0.875130	−	0.483888i	$-0.839224\pi$
$211$		−	2966.19i		−	0.967777i	0.875130	−	0.483888i	$-0.160776\pi$
$212$	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	$-0.464927\pi$
$227$	752.153			0.219921			0.109961	+	0.993936i	$0.464927\pi$
$228$	−167.010	−	1930.78i	−0.0485109	−	0.560830i
$229$	566.263			0.163405			0.0817024	−	0.996657i	$-0.473964\pi$
$229$	566.263			0.163405			0.0817024	+	0.996657i	$0.473964\pi$
$230$	−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	$0.556936\pi$
$234$	−599.601	−	1031.57i	−0.167509	−	0.288187i
$235$			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	$-0.872280\pi$
$251$		−	3106.22i		−	0.781128i	0.920576	−	0.390564i	$-0.127720\pi$
$252$	−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
$260$	−2985.36	−	4661.05i	−0.712093	−	1.11179i
$261$		−	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	$0.00837728\pi$
$269$			232.200i			0.0526299i	−0.999654	+	0.0263150i	$0.991623\pi$
$270$	−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	$0.00244295\pi$
$277$			70.7636i			0.0153494i	−0.999971	+	0.00767469i	$0.997557\pi$
$278$	−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	$0.140891\pi$
$283$			4078.19i			0.856620i	−0.903632	+	0.428310i	$0.859109\pi$
$284$	786.168	+	9088.80i	0.164262	+	1.89902i
$285$			3575.90i			0.743221i
$286$	3666.74	+	6308.35i	0.758108	+	1.30427i
$287$	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	$-0.387852\pi$
$293$	3461.38			0.690157			0.345078	+	0.938574i	$0.387852\pi$
$294$	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	$-0.414204\pi$
$307$	2864.72			0.532567			0.266284	+	0.963895i	$0.414204\pi$
$308$	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	$0.870513\pi$
$312$	2602.83	−	1830.05i	0.472295	−	0.332071i
$313$	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	$-0.547558\pi$
$317$	−1680.26			−0.297707			−0.148853	+	0.988859i	$0.547558\pi$
$318$	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	$-0.431333\pi$
$331$	2578.08			0.428109			0.214055	+	0.976822i	$0.431333\pi$
$332$	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	$0.175200\pi$
$338$	−3305.55	+	5261.92i	−0.531947	+	0.846778i
$339$			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	$-0.755291\pi$
$347$		−	8988.12i		−	1.39051i	0.718762	−	0.695256i	$-0.244709\pi$
$348$	3529.41	−	305.289i	0.543668	−	0.0470264i
$349$	−7103.89			−1.08958			−0.544789	−	0.838573i	$-0.683390\pi$
$349$	−7103.89			−1.08958			−0.544789	+	0.838573i	$0.683390\pi$
$350$	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
$364$	−9035.18	+	5786.96i	−1.30102	+	0.833294i
$365$		−	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	$0.0951617\pi$
$373$			4243.43i			0.589052i	−0.955643	+	0.294526i	$0.904838\pi$
$374$	−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	$-0.817976\pi$
$379$	−12409.0			−1.68181			−0.840904	+	0.541184i	$0.817976\pi$
$380$	−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	$-0.751006\pi$
$389$		−	10815.9i		−	1.40974i	0.709337	−	0.704869i	$-0.248994\pi$
$390$	−5075.75	+	2950.29i	−0.659027	+	0.383061i
$391$	−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	$-0.454968\pi$
$397$	2230.69			0.282003			0.141002	+	0.990009i	$0.454968\pi$
$398$	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
$416$	5460.11	+	6494.49i	0.643520	+	0.765430i
$417$	−7919.95			−0.930076
$418$	12558.6	−	542.138i	1.46952	−	0.0634373i
$419$			2466.87i			0.287624i	0.989605	+	0.143812i	$0.0459360\pi$
$419$			2466.87i			0.287624i	−0.989605	+	0.143812i	$0.954064\pi$
$420$	−10099.3	+	873.576i	−1.17333	+	0.101491i
$421$	−13264.4			−1.53555			−0.767773	−	0.640721i	$-0.778635\pi$
$421$	−13264.4			−1.53555			−0.767773	+	0.640721i	$0.778635\pi$
$422$	−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
$442$	−7437.85	−	12796.3i	−0.800413	−	1.37705i
$443$			15712.9i			1.68520i	0.538542	+	0.842599i	$0.318975\pi$
$443$			15712.9i			1.68520i	−0.538542	+	0.842599i	$0.681025\pi$
$444$	−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	$-0.831128\pi$
$461$	−17075.0			−1.72508			−0.862540	+	0.505989i	$0.831128\pi$
$462$	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	$0.0181589\pi$
$467$			1150.82i			0.114034i	−0.998373	+	0.0570168i	$0.981841\pi$
$468$	−1820.19	−	2841.86i	−0.179783	−	0.280694i
$469$			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	$0.0920003\pi$
$491$			6201.94i			0.570040i	−0.958522	+	0.285020i	$0.908000\pi$
$492$	−2918.34	+	252.432i	−0.267416	+	0.0231311i
$493$		−	16479.2i		−	1.50545i
$494$	5379.73	+	9255.42i	0.489971	+	0.842958i
$495$	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	$-0.404536\pi$
$499$	6586.27			0.590866			0.295433	+	0.955363i	$0.404536\pi$
$500$	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	$-0.726677\pi$
$509$	−15007.7			−1.30689			−0.653444	+	0.756975i	$0.726677\pi$
$510$	−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
$520$	−9004.60	−	12807.0i	−0.759381	−	1.08005i
$521$	−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	$0.218597\pi$
$523$			15166.5i			1.26804i	−0.773316	+	0.634021i	$0.781403\pi$
$524$	−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	$-0.442641\pi$
$541$	4510.52			0.358452			0.179226	+	0.983808i	$0.442641\pi$
$542$	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
$546$	5718.97	+	9839.06i	0.448259	+	0.771196i
$547$		−	19668.3i		−	1.53740i	−0.639611	−	0.768698i	$-0.720905\pi$
$547$		−	19668.3i		−	1.53740i	0.639611	−	0.768698i	$-0.279095\pi$
$548$	−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	$-0.497947\pi$
$557$	169.552			0.0128980			0.00644898	+	0.999979i	$0.497947\pi$
$558$	−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	$0.0179862\pi$
$563$			1508.87i			0.112951i	−0.998404	+	0.0564753i	$0.982014\pi$
$564$	−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	$0.0462626\pi$
$571$			3952.16i			0.289655i	−0.989457	+	0.144827i	$0.953737\pi$
$572$	11131.0	+	17378.8i	0.813653	+	1.27036i
$573$		−	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	$-0.351108\pi$
$587$	12824.9			0.901771			0.450886	+	0.892582i	$0.351108\pi$
$588$	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
$598$	9171.21	+	15778.4i	0.627155	+	1.07897i
$599$	−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	$-0.803324\pi$
$613$	−24742.1			−1.63022			−0.815111	+	0.579305i	$0.803324\pi$
$614$	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	$-0.496989\pi$
$619$	291.372			0.0189196			0.00945981	+	0.999955i	$0.496989\pi$
$620$	−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
$624$	7131.81	−	5488.85i	0.457534	−	0.352131i
$625$	−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	$-0.343609\pi$
$643$	15384.8			0.943573			0.471787	+	0.881713i	$0.343609\pi$
$644$	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
$650$	6188.86	+	10647.5i	0.373457	+	0.642504i
$651$			19874.9i			1.19656i
$652$	18715.3	−	1618.85i	1.12416	−	0.0972377i
$653$			1942.96i			0.116438i	0.998304	+	0.0582190i	$0.0185422\pi$
$653$			1942.96i			0.116438i	−0.998304	+	0.0582190i	$0.981458\pi$
$654$	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	$-0.691608\pi$
$659$		−	27887.3i		−	1.64846i	0.566253	−	0.824231i	$-0.308392\pi$
$660$	1680.29	+	19425.7i	0.0990987	+	1.14567i
$661$	9000.63			0.529628			0.264814	−	0.964300i	$-0.414689\pi$
$661$	9000.63			0.529628			0.264814	+	0.964300i	$0.414689\pi$
$662$	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
$676$	−8698.91	+	15272.3i	−0.494931	+	0.868932i
$677$			21060.3i			1.19559i	0.801651	+	0.597793i	$0.203955\pi$
$677$			21060.3i			1.19559i	−0.801651	+	0.597793i	$0.796045\pi$
$678$	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	$-0.337245\pi$
$683$	17468.5			0.978642			0.489321	+	0.872104i	$0.337245\pi$
$684$	−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	$-0.266556\pi$
$691$	24317.9			1.33878			0.669389	+	0.742912i	$0.266556\pi$
$692$	−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	$0.121184\pi$
$701$			13793.0i			0.743159i	−0.928401	+	0.371579i	$0.878816\pi$
$702$	−3094.71	+	1798.80i	−0.166385	+	0.0967115i
$703$	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	$-0.405185\pi$
$709$	11081.2			0.586970			0.293485	+	0.955964i	$0.405185\pi$
$710$	−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	$0.735656\pi$
$728$	−24825.6	+	17454.9i	−1.26387	+	0.888630i
$729$	−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	$-0.392935\pi$
$733$	13099.8			0.660097			0.330049	+	0.943964i	$0.392935\pi$
$734$	−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	$-0.465974\pi$
$739$	4286.73			0.213383			0.106691	+	0.994292i	$0.465974\pi$
$740$	−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
$754$	−16918.6	+	9834.00i	−0.817163	+	0.474978i
$755$			25212.2i			1.21532i
$756$	−6157.60	+	532.623i	−0.296230	+	0.0256234i
$757$		−	6559.08i		−	0.314919i	−0.987525	−	0.157460i	$-0.949670\pi$
$757$		−	6559.08i		−	0.314919i	0.987525	−	0.157460i	$-0.0503304\pi$
$758$	−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

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)

\(f(q)\)	\(=\)	\(q+(2.82580 - 0.121986i) q^{2} -3.00000i q^{3} +(7.97024 - 0.689413i) q^{4} -14.7613 q^{5} +(-0.365957 - 8.47739i) q^{6} +28.6139i q^{7} +(22.4382 - 2.92040i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(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} +(66.6224 + 114.619i) 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} +(202.243 + 315.762i) 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} +(343.856 - 199.867i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 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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