LMFDB - Embedded newform 65.5.g.a.34.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,5,Mod(34,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("65.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	65.g (of order $4$, degree $2$, 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:	$6.71904760045$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.5
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.80385 + 3.80385i) q^{2} +13.5404i q^{3} -12.9386i q^{4} +(-6.62279 - 24.1068i) q^{5} +(-51.5057 - 51.5057i) q^{6} +(-14.0955 - 14.0955i) q^{7} +(-11.6451 - 11.6451i) q^{8} -102.342 q^{9} +O(q^{10})$	\(q+(-3.80385 + 3.80385i) q^{2} +13.5404i q^{3} -12.9386i q^{4} +(-6.62279 - 24.1068i) q^{5} +(-51.5057 - 51.5057i) q^{6} +(-14.0955 - 14.0955i) q^{7} +(-11.6451 - 11.6451i) q^{8} -102.342 q^{9} +(116.891 + 66.5067i) q^{10} +(43.1734 - 43.1734i) q^{11} +175.194 q^{12} +(-128.450 + 109.825i) q^{13} +107.234 q^{14} +(326.416 - 89.6752i) q^{15} +295.610 q^{16} +38.4496 q^{17} +(389.295 - 389.295i) q^{18} +(-389.852 - 389.852i) q^{19} +(-311.908 + 85.6896i) q^{20} +(190.859 - 190.859i) q^{21} +328.451i q^{22} +222.149 q^{23} +(157.680 - 157.680i) q^{24} +(-537.277 + 319.309i) q^{25} +(70.8492 - 906.364i) q^{26} -288.983i q^{27} +(-182.376 + 182.376i) q^{28} +12.8546 q^{29} +(-900.526 + 1582.75i) q^{30} +(-366.001 - 366.001i) q^{31} +(-938.136 + 938.136i) q^{32} +(584.585 + 584.585i) q^{33} +(-146.257 + 146.257i) q^{34} +(-246.446 + 433.149i) q^{35} +1324.17i q^{36} +(-1518.18 - 1518.18i) q^{37} +2965.88 q^{38} +(-1487.07 - 1739.27i) q^{39} +(-203.604 + 357.851i) q^{40} +(1716.29 + 1716.29i) q^{41} +1452.00i q^{42} -1846.70 q^{43} +(-558.603 - 558.603i) q^{44} +(677.792 + 2467.15i) q^{45} +(-845.022 + 845.022i) q^{46} +(-2728.06 - 2728.06i) q^{47} +4002.68i q^{48} -2003.63i q^{49} +(829.120 - 3258.33i) q^{50} +520.623i q^{51} +(1420.98 + 1661.97i) q^{52} -2289.59i q^{53} +(1099.25 + 1099.25i) q^{54} +(-1326.70 - 754.845i) q^{55} +328.288i q^{56} +(5278.76 - 5278.76i) q^{57} +(-48.8970 + 48.8970i) q^{58} +(787.825 - 787.825i) q^{59} +(-1160.27 - 4223.36i) q^{60} +268.348 q^{61} +2784.43 q^{62} +(1442.57 + 1442.57i) q^{63} -2407.30i q^{64} +(3498.23 + 2369.18i) q^{65} -4447.35 q^{66} +(-2265.36 + 2265.36i) q^{67} -497.484i q^{68} +3007.99i q^{69} +(-710.191 - 2585.08i) q^{70} +(2144.73 + 2144.73i) q^{71} +(1191.79 + 1191.79i) q^{72} +(5934.88 + 5934.88i) q^{73} +11549.9 q^{74} +(-4323.57 - 7274.95i) q^{75} +(-5044.14 + 5044.14i) q^{76} -1217.10 q^{77} +(12272.5 + 959.326i) q^{78} -11776.0 q^{79} +(-1957.77 - 7126.22i) q^{80} -4376.78 q^{81} -13057.0 q^{82} +(4702.29 - 4702.29i) q^{83} +(-2469.44 - 2469.44i) q^{84} +(-254.644 - 926.898i) q^{85} +(7024.56 - 7024.56i) q^{86} +174.057i q^{87} -1005.52 q^{88} +(-9445.82 + 9445.82i) q^{89} +(-11962.9 - 6806.44i) q^{90} +(3358.61 + 262.538i) q^{91} -2874.30i q^{92} +(4955.80 - 4955.80i) q^{93} +20754.3 q^{94} +(-6816.19 + 11980.0i) q^{95} +(-12702.7 - 12702.7i) q^{96} +(-8426.40 + 8426.40i) q^{97} +(7621.53 + 7621.53i) q^{98} +(-4418.47 + 4418.47i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−3.80385	+	3.80385i	−0.950963	+	0.950963i	−0.998853	−	0.0478894i	$-0.984750\pi$
$2$	−3.80385	+	3.80385i	−0.950963	+	0.950963i	0.0478894	+	0.998853i	$0.484750\pi$
$3$			13.5404i			1.50449i	0.658884	+	0.752244i	$0.271029\pi$
$3$			13.5404i			1.50449i	−0.658884	+	0.752244i	$0.728971\pi$
$4$		−	12.9386i		−	0.808662i
$5$	−6.62279	−	24.1068i	−0.264912	−	0.964273i
$5$	−6.62279	−	24.1068i	−0.264912	−	0.964273i
$6$	−51.5057	−	51.5057i	−1.43071	−	1.43071i
$7$	−14.0955	−	14.0955i	−0.287663	−	0.287663i	0.548492	−	0.836156i	$-0.315202\pi$
$7$	−14.0955	−	14.0955i	−0.287663	−	0.287663i	−0.836156	+	0.548492i	$0.815202\pi$
$8$	−11.6451	−	11.6451i	−0.181955	−	0.181955i
$9$	−102.342			−1.26349
$10$	116.891	+	66.5067i	1.16891	+	0.665067i
$11$	43.1734	−	43.1734i	0.356805	−	0.356805i	−0.505829	−	0.862634i	$-0.668813\pi$
$11$	43.1734	−	43.1734i	0.356805	−	0.356805i	0.862634	+	0.505829i	$0.168813\pi$
$12$	175.194			1.21662
$13$	−128.450	+	109.825i	−0.760062	+	0.649851i
$13$	−128.450	+	109.825i	−0.760062	+	0.649851i
$14$	107.234			0.547114
$15$	326.416	−	89.6752i	1.45074	−	0.398557i
$16$	295.610			1.15473
$17$	38.4496			0.133044			0.0665218	−	0.997785i	$-0.478810\pi$
$17$	38.4496			0.133044			0.0665218	+	0.997785i	$0.478810\pi$
$18$	389.295	−	389.295i	1.20153	−	1.20153i
$19$	−389.852	−	389.852i	−1.07992	−	1.07992i	−0.996515	−	0.0834083i	$-0.973419\pi$
$19$	−389.852	−	389.852i	−1.07992	−	1.07992i	−0.0834083	−	0.996515i	$-0.526581\pi$
$20$	−311.908	+	85.6896i	−0.779771	+	0.214224i
$21$	190.859	−	190.859i	0.432786	−	0.432786i
$22$			328.451i			0.678617i
$23$	222.149			0.419941			0.209971	−	0.977708i	$-0.432663\pi$
$23$	222.149			0.419941			0.209971	+	0.977708i	$0.432663\pi$
$24$	157.680	−	157.680i	0.273750	−	0.273750i
$25$	−537.277	+	319.309i	−0.859644	+	0.510894i
$26$	70.8492	−	906.364i	0.104806	−	1.34078i
$27$		−	288.983i		−	0.396410i
$28$	−182.376	+	182.376i	−0.232622	+	0.232622i
$29$	12.8546			0.0152849			0.00764246	−	0.999971i	$-0.497567\pi$
$29$	12.8546			0.0152849			0.00764246	+	0.999971i	$0.497567\pi$
$30$	−900.526	+	1582.75i	−1.00058	+	1.75861i
$31$	−366.001	−	366.001i	−0.380854	−	0.380854i	0.490555	−	0.871410i	$-0.336794\pi$
$31$	−366.001	−	366.001i	−0.380854	−	0.380854i	−0.871410	+	0.490555i	$0.836794\pi$
$32$	−938.136	+	938.136i	−0.916148	+	0.916148i
$33$	584.585	+	584.585i	0.536809	+	0.536809i
$34$	−146.257	+	146.257i	−0.126520	+	0.126520i
$35$	−246.446	+	433.149i	−0.201180	+	0.353591i
$36$			1324.17i			1.02173i
$37$	−1518.18	−	1518.18i	−1.10897	−	1.10897i	−0.993286	−	0.115688i	$-0.963093\pi$
$37$	−1518.18	−	1518.18i	−1.10897	−	1.10897i	−0.115688	−	0.993286i	$-0.536907\pi$
$38$	2965.88			2.05394
$39$	−1487.07	−	1739.27i	−0.977693	−	1.14350i
$40$	−203.604	+	357.851i	−0.127252	+	0.223657i
$41$	1716.29	+	1716.29i	1.02099	+	1.02099i	0.999775	+	0.0212193i	$0.00675482\pi$
$41$	1716.29	+	1716.29i	1.02099	+	1.02099i	0.0212193	+	0.999775i	$0.493245\pi$
$42$			1452.00i			0.823127i
$43$	−1846.70			−0.998754			−0.499377	−	0.866385i	$-0.666438\pi$
$43$	−1846.70			−0.998754			−0.499377	+	0.866385i	$0.666438\pi$
$44$	−558.603	−	558.603i	−0.288535	−	0.288535i
$45$	677.792	+	2467.15i	0.334712	+	1.21834i
$46$	−845.022	+	845.022i	−0.399349	+	0.399349i
$47$	−2728.06	−	2728.06i	−1.23498	−	1.23498i	−0.962029	−	0.272946i	$-0.912002\pi$
$47$	−2728.06	−	2728.06i	−1.23498	−	1.23498i	−0.272946	−	0.962029i	$-0.587998\pi$
$48$			4002.68i			1.73727i
$49$		−	2003.63i		−	0.834500i
$50$	829.120	−	3258.33i	0.331648	−	1.30333i
$51$			520.623i			0.200163i
$52$	1420.98	+	1661.97i	0.525510	+	0.614633i
$53$		−	2289.59i		−	0.815092i	−0.913185	−	0.407546i	$-0.866385\pi$
$53$		−	2289.59i		−	0.815092i	0.913185	−	0.407546i	$-0.133615\pi$
$54$	1099.25	+	1099.25i	0.376972	+	0.376972i
$55$	−1326.70	−	754.845i	−0.438579	−	0.249536i
$56$			328.288i			0.104684i
$57$	5278.76	−	5278.76i	1.62473	−	1.62473i
$58$	−48.8970	+	48.8970i	−0.0145354	+	0.0145354i
$59$	787.825	−	787.825i	0.226321	−	0.226321i	−0.584833	−	0.811154i	$-0.698840\pi$
$59$	787.825	−	787.825i	0.226321	−	0.226321i	0.811154	+	0.584833i	$0.198840\pi$
$60$	−1160.27	−	4223.36i	−0.322298	−	1.17316i
$61$	268.348			0.0721171			0.0360585	−	0.999350i	$-0.488520\pi$
$61$	268.348			0.0721171			0.0360585	+	0.999350i	$0.488520\pi$
$62$	2784.43			0.724357
$63$	1442.57	+	1442.57i	0.363458	+	0.363458i
$64$		−	2407.30i		−	0.587719i
$65$	3498.23	+	2369.18i	0.827983	+	0.560754i
$66$	−4447.35			−1.02097
$67$	−2265.36	+	2265.36i	−0.504648	+	0.504648i	−0.912879	−	0.408231i	$-0.866146\pi$
$67$	−2265.36	+	2265.36i	−0.504648	+	0.504648i	0.408231	+	0.912879i	$0.366146\pi$
$68$		−	497.484i		−	0.107587i
$69$			3007.99i			0.631797i
$70$	−710.191	−	2585.08i	−0.144937	−	0.527567i
$71$	2144.73	+	2144.73i	0.425458	+	0.425458i	0.887078	−	0.461620i	$-0.152732\pi$
$71$	2144.73	+	2144.73i	0.425458	+	0.425458i	−0.461620	+	0.887078i	$0.652732\pi$
$72$	1191.79	+	1191.79i	0.229898	+	0.229898i
$73$	5934.88	+	5934.88i	1.11369	+	1.11369i	0.992647	+	0.121047i	$0.0386253\pi$
$73$	5934.88	+	5934.88i	1.11369	+	1.11369i	0.121047	+	0.992647i	$0.461375\pi$
$74$	11549.9			2.10919
$75$	−4323.57	−	7274.95i	−0.768634	−	1.29332i
$76$	−5044.14	+	5044.14i	−0.873293	+	0.873293i
$77$	−1217.10			−0.205279
$78$	12272.5	+	959.326i	2.01718	+	0.157680i
$79$	−11776.0			−1.88688			−0.943440	−	0.331544i	$-0.892430\pi$
$79$	−11776.0			−1.88688			−0.943440	+	0.331544i	$0.892430\pi$
$80$	−1957.77	−	7126.22i	−0.305901	−	1.11347i
$81$	−4376.78			−0.667091
$82$	−13057.0			−1.94186
$83$	4702.29	−	4702.29i	0.682579	−	0.682579i	−0.278001	−	0.960581i	$-0.589672\pi$
$83$	4702.29	−	4702.29i	0.682579	−	0.682579i	0.960581	+	0.278001i	$0.0896720\pi$
$84$	−2469.44	−	2469.44i	−0.349978	−	0.349978i
$85$	−254.644	−	926.898i	−0.0352448	−	0.128290i
$86$	7024.56	−	7024.56i	0.949779	−	0.949779i
$87$			174.057i			0.0229960i
$88$	−1005.52			−0.129845
$89$	−9445.82	+	9445.82i	−1.19250	+	1.19250i	−0.216141	+	0.976362i	$0.569347\pi$
$89$	−9445.82	+	9445.82i	−1.19250	+	1.19250i	−0.976362	+	0.216141i	$0.930653\pi$
$90$	−11962.9	−	6806.44i	−1.47690	−	0.840302i
$91$	3358.61	+	262.538i	0.405580	+	0.0317036i
$92$		−	2874.30i		−	0.339591i
$93$	4955.80	−	4955.80i	0.572991	−	0.572991i
$94$	20754.3			2.34883
$95$	−6816.19	+	11980.0i	−0.755257	+	1.32743i
$96$	−12702.7	−	12702.7i	−1.37833	−	1.37833i
$97$	−8426.40	+	8426.40i	−0.895568	+	0.895568i	−0.995040	−	0.0994724i	$-0.968285\pi$
$97$	−8426.40	+	8426.40i	−0.895568	+	0.895568i	0.0994724	+	0.995040i	$0.468285\pi$
$98$	7621.53	+	7621.53i	0.793579	+	0.793579i
$99$	−4418.47	+	4418.47i	−0.450818	+	0.450818i
$100$	4131.41	+	6951.61i	0.413141	+	0.695161i
$101$		−	2254.00i		−	0.220959i	−0.993878	−	0.110480i	$-0.964761\pi$
$101$		−	2254.00i		−	0.220959i	0.993878	−	0.110480i	$-0.0352387\pi$
$102$	−1980.37	−	1980.37i	−0.190347	−	0.190347i
$103$	−3617.22			−0.340958			−0.170479	−	0.985361i	$-0.554531\pi$
$103$	−3617.22			−0.340958			−0.170479	+	0.985361i	$0.554531\pi$
$104$	2774.75	+	216.898i	0.256541	+	0.0200534i
$105$	−5865.01	−	3336.98i	−0.531974	−	0.302674i
$106$	8709.27	+	8709.27i	0.775122	+	0.775122i
$107$			10340.0i			0.903136i	0.892237	+	0.451568i	$0.149135\pi$
$107$			10340.0i			0.903136i	−0.892237	+	0.451568i	$0.850865\pi$
$108$	−3739.03			−0.320562
$109$	12305.2	+	12305.2i	1.03570	+	1.03570i	0.999339	+	0.0363657i	$0.0115781\pi$
$109$	12305.2	+	12305.2i	1.03570	+	1.03570i	0.0363657	+	0.999339i	$0.488422\pi$
$110$	7917.90	−	2175.26i	0.654372	−	0.179774i
$111$	20556.8	−	20556.8i	1.66844	−	1.66844i
$112$	−4166.77	−	4166.77i	−0.332173	−	0.332173i
$113$		−	14720.2i		−	1.15281i	−0.817164	−	0.576405i	$-0.804455\pi$
$113$		−	14720.2i		−	1.15281i	0.817164	−	0.576405i	$-0.195545\pi$
$114$			40159.2i			3.09012i
$115$	−1471.25	−	5355.31i	−0.111247	−	0.404938i
$116$		−	166.321i		−	0.0123603i
$117$	13145.9	−	11239.7i	0.960327	−	0.821077i
$118$			5993.54i			0.430447i
$119$	−541.967	−	541.967i	−0.0382718	−	0.0382718i
$120$	−4845.44	−	2756.88i	−0.336489	−	0.191450i
$121$			10913.1i			0.745380i
$122$	−1020.76	+	1020.76i	−0.0685807	+	0.0685807i
$123$	−23239.3	+	23239.3i	−1.53607	+	1.53607i
$124$	−4735.54	+	4735.54i	−0.307983	+	0.307983i
$125$	11255.8	+	10837.3i	0.720371	+	0.693589i
$126$	−10974.6			−0.691271
$127$	8494.34			0.526650			0.263325	−	0.964707i	$-0.415181\pi$
$127$	8494.34			0.526650			0.263325	+	0.964707i	$0.415181\pi$
$128$	−5853.17	−	5853.17i	−0.357249	−	0.357249i
$129$		−	25005.0i		−	1.50261i
$130$	−22318.8	+	4294.71i	−1.32064	+	0.254125i
$131$	−2226.89			−0.129764			−0.0648822	−	0.997893i	$-0.520667\pi$
$131$	−2226.89			−0.129764			−0.0648822	+	0.997893i	$0.520667\pi$
$132$	7563.71	−	7563.71i	0.434097	−	0.434097i
$133$			10990.3i			0.621309i
$134$		−	17234.2i		−	0.959803i
$135$	−6966.46	+	1913.87i	−0.382248	+	0.105014i
$136$	−447.751	−	447.751i	−0.0242080	−	0.0242080i
$137$	−2334.35	−	2334.35i	−0.124373	−	0.124373i	0.642181	−	0.766553i	$-0.278030\pi$
$137$	−2334.35	−	2334.35i	−0.124373	−	0.124373i	−0.766553	+	0.642181i	$0.778030\pi$
$138$	−11441.9	−	11441.9i	−0.600816	−	0.600816i
$139$	−5325.35			−0.275625			−0.137813	−	0.990458i	$-0.544007\pi$
$139$	−5325.35			−0.275625			−0.137813	+	0.990458i	$0.544007\pi$
$140$	5604.34	+	3188.67i	0.285936	+	0.162687i
$141$	36939.0	−	36939.0i	1.85801	−	1.85801i
$142$	−16316.5			−0.809190
$143$	−804.132	+	10287.2i	−0.0393238	+	0.503064i
$144$	−30253.4			−1.45898
$145$	−85.1334	−	309.884i	−0.00404915	−	0.0147388i
$146$	−45150.8			−2.11816
$147$	27130.0			1.25550
$148$	−19643.2	+	19643.2i	−0.896785	+	0.896785i
$149$	−29158.9	−	29158.9i	−1.31340	−	1.31340i	−0.918890	−	0.394514i	$-0.870913\pi$
$149$	−29158.9	−	29158.9i	−1.31340	−	1.31340i	−0.394514	−	0.918890i	$-0.629087\pi$
$150$	44119.0	+	11226.6i	1.96085	+	0.498960i
$151$	6142.77	−	6142.77i	0.269408	−	0.269408i	−0.559454	−	0.828862i	$-0.688989\pi$
$151$	6142.77	−	6142.77i	0.269408	−	0.269408i	0.828862	+	0.559454i	$0.188989\pi$
$152$			9079.77i			0.392996i
$153$	−3935.02			−0.168099
$154$	4629.68	−	4629.68i	0.195213	−	0.195213i
$155$	−6399.17	+	11247.1i	−0.266355	+	0.468140i
$156$	−22503.7	+	19240.6i	−0.924708	+	0.790623i
$157$		−	12362.2i		−	0.501530i	−0.968048	−	0.250765i	$-0.919318\pi$
$157$		−	12362.2i		−	0.501530i	0.968048	−	0.250765i	$-0.0806821\pi$
$158$	44794.2	−	44794.2i	1.79435	−	1.79435i
$159$	31002.0			1.22630
$160$	28828.5	+	16402.4i	1.12612	+	0.640718i
$161$	−3131.30	−	3131.30i	−0.120802	−	0.120802i
$162$	16648.6	−	16648.6i	0.634379	−	0.634379i
$163$	−15708.8	−	15708.8i	−0.591247	−	0.591247i	0.346721	−	0.937968i	$-0.387295\pi$
$163$	−15708.8	−	15708.8i	−0.591247	−	0.591247i	−0.937968	+	0.346721i	$0.887295\pi$
$164$	22206.4	−	22206.4i	0.825639	−	0.825639i
$165$	10220.9	−	17964.1i	0.375423	−	0.659837i
$166$			35773.6i			1.29822i
$167$	−6505.80	−	6505.80i	−0.233275	−	0.233275i	0.580783	−	0.814058i	$-0.302746\pi$
$167$	−6505.80	−	6505.80i	−0.233275	−	0.233275i	−0.814058	+	0.580783i	$0.802746\pi$
$168$	−4445.15			−0.157495
$169$	4438.03	−	28214.1i	0.155388	−	0.987854i
$170$	4494.41	+	2557.16i	0.155516	+	0.0884829i
$171$	39898.4	+	39898.4i	1.36447	+	1.36447i
$172$			23893.7i			0.807655i
$173$	31729.2			1.06015			0.530075	−	0.847951i	$-0.322164\pi$
$173$	31729.2			1.06015			0.530075	+	0.847951i	$0.322164\pi$
$174$	−662.085	−	662.085i	−0.0218683	−	0.0218683i
$175$	12074.0	+	3072.37i	0.394253	+	0.100322i
$176$	12762.5	−	12762.5i	0.412013	−	0.412013i
$177$	10667.5	+	10667.5i	0.340498	+	0.340498i
$178$		−	71861.0i		−	2.26805i
$179$			26701.7i			0.833361i	0.909053	+	0.416681i	$0.136807\pi$
$179$			26701.7i			0.833361i	−0.909053	+	0.416681i	$0.863193\pi$
$180$	31921.4	−	8769.67i	0.985229	−	0.270669i
$181$			46293.0i			1.41305i	0.707687	+	0.706526i	$0.249739\pi$
$181$			46293.0i			1.41305i	−0.707687	+	0.706526i	$0.750261\pi$
$182$	−13774.3	+	11777.0i	−0.415841	+	0.355543i
$183$			3633.53i			0.108499i
$184$	−2586.96	−	2586.96i	−0.0764106	−	0.0764106i
$185$	−26544.0	+	46653.2i	−0.775573	+	1.36313i
$186$			37702.3i			1.08979i
$187$	1660.00	−	1660.00i	0.0474707	−	0.0474707i
$188$	−35297.3	+	35297.3i	−0.998678	+	0.998678i
$189$	−4073.36	+	4073.36i	−0.114033	+	0.114033i
$190$	−19642.4	−	71498.0i	−0.544112	−	1.98055i
$191$	−34497.1			−0.945617			−0.472809	−	0.881165i	$-0.656760\pi$
$191$	−34497.1			−0.945617			−0.472809	+	0.881165i	$0.656760\pi$
$192$	32595.7			0.884216
$193$	−2943.96	−	2943.96i	−0.0790347	−	0.0790347i	0.666484	−	0.745519i	$-0.267798\pi$
$193$	−2943.96	−	2943.96i	−0.0790347	−	0.0790347i	−0.745519	+	0.666484i	$0.767798\pi$
$194$		−	64105.6i		−	1.70330i
$195$	−32079.7	+	47367.4i	−0.843647	+	1.24569i
$196$	−25924.2			−0.674828
$197$	−15995.4	+	15995.4i	−0.412158	+	0.412158i	−0.882490	−	0.470332i	$-0.844134\pi$
$197$	−15995.4	+	15995.4i	−0.412158	+	0.412158i	0.470332	+	0.882490i	$0.344134\pi$
$198$		−	33614.4i		−	0.857423i
$199$		−	24087.1i		−	0.608244i	−0.952633	−	0.304122i	$-0.901637\pi$
$199$		−	24087.1i		−	0.608244i	0.952633	−	0.304122i	$-0.0983630\pi$
$200$	9975.07	+	2538.27i	0.249377	+	0.0634568i
$201$	−30673.9	−	30673.9i	−0.759237	−	0.759237i
$202$	8573.90	+	8573.90i	0.210124	+	0.210124i
$203$	−181.192	−	181.192i	−0.00439691	−	0.00439691i
$204$	6736.13			0.161864
$205$	30007.7	−	52741.0i	0.714043	−	1.25499i
$206$	13759.4	−	13759.4i	0.324238	−	0.324238i
$207$	−22735.2			−0.530590
$208$	−37971.3	+	32465.3i	−0.877664	+	0.750401i
$209$	−33662.5			−0.770645
$210$	35003.0	−	9616.27i	0.793719	−	0.218056i
$211$	39243.0			0.881450			0.440725	−	0.897642i	$-0.354721\pi$
$211$	39243.0			0.881450			0.440725	+	0.897642i	$0.354721\pi$
$212$	−29624.1			−0.659134
$213$	−29040.5	+	29040.5i	−0.640097	+	0.640097i
$214$	−39331.8	−	39331.8i	−0.858849	−	0.858849i
$215$	12230.3	+	44518.0i	0.264582	+	0.963072i
$216$	−3365.25	+	3365.25i	−0.0721290	+	0.0721290i
$217$			10317.9i			0.219116i
$218$	−93614.4			−1.96983
$219$	−80360.6	+	80360.6i	−1.67554	+	1.67554i
$220$	−9766.63	+	17165.7i	−0.201790	+	0.354662i
$221$	−4938.87	+	4222.72i	−0.101121	+	0.0864586i
$222$			156390.i			3.17325i
$223$	−60995.3	+	60995.3i	−1.22655	+	1.22655i	−0.261295	+	0.965259i	$0.584149\pi$
$223$	−60995.3	+	60995.3i	−1.22655	+	1.22655i	−0.965259	+	0.261295i	$0.915851\pi$
$224$	26447.0			0.527084
$225$	54986.2	−	32678.8i	1.08615	−	0.645507i
$226$	55993.6	+	55993.6i	1.09628	+	1.09628i
$227$	10083.5	−	10083.5i	0.195685	−	0.195685i	−0.602462	−	0.798147i	$-0.705814\pi$
$227$	10083.5	−	10083.5i	0.195685	−	0.195685i	0.798147	+	0.602462i	$0.205814\pi$
$228$	−68299.7	−	68299.7i	−1.31386	−	1.31386i
$229$	68077.3	−	68077.3i	1.29817	−	1.29817i	0.368570	−	0.929600i	$-0.379847\pi$
$229$	68077.3	−	68077.3i	1.29817	−	1.29817i	0.929600	−	0.368570i	$-0.120153\pi$
$230$	25967.2	+	14774.4i	0.490873	+	0.279289i
$231$		−	16480.0i		−	0.308841i
$232$	−149.694	−	149.694i	−0.00278117	−	0.00278117i
$233$	44659.0			0.822616			0.411308	−	0.911496i	$-0.365072\pi$
$233$	44659.0			0.822616			0.411308	+	0.911496i	$0.365072\pi$
$234$	−7250.87	+	92759.4i	−0.132421	+	1.69405i
$235$	−47697.5	+	83832.2i	−0.863694	+	1.51801i
$236$	−10193.3	−	10193.3i	−0.183018	−	0.183018i
$237$		−	159452.i		−	2.83879i
$238$	4123.12			0.0727901
$239$	53602.9	+	53602.9i	0.938410	+	0.938410i	0.998210	−	0.0598001i	$-0.0190463\pi$
$239$	53602.9	+	53602.9i	0.938410	+	0.938410i	−0.0598001	+	0.998210i	$0.519046\pi$
$240$	96491.9	−	26508.9i	1.67521	−	0.460224i
$241$	−69056.7	+	69056.7i	−1.18897	+	1.18897i	−0.211621	+	0.977352i	$0.567874\pi$
$241$	−69056.7	+	69056.7i	−1.18897	+	1.18897i	−0.977352	+	0.211621i	$0.932126\pi$
$242$	−41511.9	−	41511.9i	−0.708829	−	0.708829i
$243$		−	82671.0i		−	1.40004i
$244$		−	3472.04i		−	0.0583184i
$245$	−48301.2	+	13269.7i	−0.804685	+	0.221069i
$246$		−	176797.i		−	2.92150i
$247$	92892.2	+	7261.25i	1.52260	+	0.119019i
$248$			8524.27i			0.138597i
$249$	63670.9	+	63670.9i	1.02693	+	1.02693i
$250$	−84039.0	+	1591.79i	−1.34462	+	0.0254687i
$251$		−	46259.0i		−	0.734257i	−0.930170	−	0.367129i	$-0.880341\pi$
$251$		−	46259.0i		−	0.734257i	0.930170	−	0.367129i	$-0.119659\pi$
$252$	18664.8	−	18664.8i	0.293915	−	0.293915i
$253$	9590.93	−	9590.93i	0.149837	−	0.149837i
$254$	−32311.2	+	32311.2i	−0.500825	+	0.500825i
$255$	12550.6	−	3447.98i	0.193011	−	0.0530254i
$256$	83045.9			1.26718
$257$	71560.9			1.08345			0.541726	−	0.840555i	$-0.317771\pi$
$257$	71560.9			1.08345			0.541726	+	0.840555i	$0.317771\pi$
$258$	95115.4	+	95115.4i	1.42893	+	1.42893i
$259$			42799.1i			0.638022i
$260$	30653.9	−	45262.1i	0.453460	−	0.669558i
$261$	−1315.57			−0.0193123
$262$	8470.75	−	8470.75i	0.123401	−	0.123401i
$263$		−	13881.9i		−	0.200696i	−0.994952	−	0.100348i	$-0.968004\pi$
$263$		−	13881.9i		−	0.200696i	0.994952	−	0.100348i	$-0.0319955\pi$
$264$		−	13615.2i		−	0.195351i
$265$	−55194.8	+	15163.5i	−0.785971	+	0.215927i
$266$	−41805.6	−	41805.6i	−0.590842	−	0.590842i
$267$	−127900.	−	127900.i	−1.79411	−	1.79411i
$268$	29310.6	+	29310.6i	0.408089	+	0.408089i
$269$	77012.2			1.06428			0.532139	−	0.846657i	$-0.321388\pi$
$269$	77012.2			1.06428			0.532139	+	0.846657i	$0.321388\pi$
$270$	19219.3	−	33779.5i	0.263639	−	0.463368i
$271$	72717.2	−	72717.2i	0.990144	−	0.990144i	−0.00980798	−	0.999952i	$-0.503122\pi$
$271$	72717.2	−	72717.2i	0.990144	−	0.990144i	0.999952	+	0.00980798i	$0.00312203\pi$
$272$	11366.1			0.153629
$273$	−3554.86	+	45476.9i	−0.0476977	+	0.610190i
$274$	17759.1			0.236548
$275$	−9410.44	+	36981.8i	−0.124436	+	0.489015i
$276$	38919.1			0.510910
$277$	39112.1			0.509744			0.254872	−	0.966975i	$-0.417967\pi$
$277$	39112.1			0.509744			0.254872	+	0.966975i	$0.417967\pi$
$278$	20256.9	−	20256.9i	0.262109	−	0.262109i
$279$	37457.4	+	37457.4i	0.481204	+	0.481204i
$280$	7913.98	−	2174.18i	0.100944	−	0.0277319i
$281$	7688.19	−	7688.19i	0.0973669	−	0.0973669i	−0.656745	−	0.754112i	$-0.728067\pi$
$281$	7688.19	−	7688.19i	0.0973669	−	0.0973669i	0.754112	+	0.656745i	$0.228067\pi$
$282$			281021.i			3.53379i
$283$	4674.66			0.0583683			0.0291842	−	0.999574i	$-0.490709\pi$
$283$	4674.66			0.0583683			0.0291842	+	0.999574i	$0.490709\pi$
$284$	27749.8	−	27749.8i	0.344052	−	0.344052i
$285$	−162214.	−	92293.9i	−1.99710	−	1.13627i
$286$	−36072.0	−	42189.6i	−0.441000	−	0.515791i
$287$		−	48384.0i		−	0.587405i
$288$	96011.0	−	96011.0i	1.15754	−	1.15754i
$289$	−82042.6			−0.982299
$290$	1502.59	+	854.917i	0.0178667	+	0.0101655i
$291$	−114097.	−	114097.i	−1.34737	−	1.34737i
$292$	76788.9	−	76788.9i	0.900602	−	0.900602i
$293$	−41691.3	−	41691.3i	−0.485635	−	0.485635i	0.421291	−	0.906926i	$-0.361577\pi$
$293$	−41691.3	−	41691.3i	−0.485635	−	0.485635i	−0.906926	+	0.421291i	$0.861577\pi$
$294$	−103199.	+	103199.i	−1.19393	+	1.19393i
$295$	−24209.6	−	13774.4i	−0.278191	−	0.158280i
$296$			35358.9i			0.403567i
$297$	−12476.4	−	12476.4i	−0.141441	−	0.141441i
$298$	221832.			2.49800
$299$	−28535.1	+	24397.5i	−0.319181	+	0.272899i
$300$	−94127.6	+	55940.9i	−1.04586	+	0.621565i
$301$	26030.1	+	26030.1i	0.287305	+	0.287305i
$302$			46732.4i			0.512394i
$303$	30520.1			0.332431
$304$	−115244.	−	115244.i	−1.24702	−	1.24702i
$305$	−1777.21	−	6469.01i	−0.0191047	−	0.0695405i
$306$	14968.2	−	14968.2i	0.159856	−	0.159856i
$307$	−93150.5	−	93150.5i	−0.988345	−	0.988345i	0.0115878	−	0.999933i	$-0.496311\pi$
$307$	−93150.5	−	93150.5i	−0.988345	−	0.988345i	−0.999933	+	0.0115878i	$0.996311\pi$
$308$			15747.6i			0.166002i
$309$		−	48978.6i		−	0.512967i
$310$	−18440.7	−	67123.7i	−0.191891	−	0.698478i
$311$			39978.2i			0.413336i	0.978411	+	0.206668i	$0.0662619\pi$
$311$			39978.2i			0.413336i	−0.978411	+	0.206668i	$0.933738\pi$
$312$	−2936.89	+	37571.2i	−0.0301702	+	0.385963i
$313$		−	52319.4i		−	0.534040i	−0.963691	−	0.267020i	$-0.913961\pi$
$313$		−	52319.4i		−	0.534040i	0.963691	−	0.267020i	$-0.0860391\pi$
$314$	47024.0	+	47024.0i	0.476937	+	0.476937i
$315$	25221.9	−	44329.5i	0.254188	−	0.446757i
$316$			152365.i			1.52585i
$317$	92287.6	−	92287.6i	0.918385	−	0.918385i	−0.0785268	−	0.996912i	$-0.525022\pi$
$317$	92287.6	−	92287.6i	0.918385	−	0.918385i	0.996912	+	0.0785268i	$0.0250216\pi$
$318$	−117927.	+	117927.i	−1.16616	+	1.16616i
$319$	554.978	−	554.978i	0.00545373	−	0.00545373i
$320$	−58032.3	+	15943.0i	−0.566721	+	0.155694i
$321$	−140008.			−1.35876
$322$	23822.0			0.229756
$323$	−14989.7	−	14989.7i	−0.143677	−	0.143677i
$324$			56629.4i			0.539451i
$325$	33945.5	−	100022.i	0.321377	−	0.946951i
$326$	119508.			1.12451
$327$	−166617.	+	166617.i	−1.55820	+	1.55820i
$328$		−	39972.9i		−	0.371551i
$329$			76906.7i			0.710514i
$330$	29453.9	+	107211.i	0.270467	+	0.984495i
$331$	−32743.2	−	32743.2i	−0.298858	−	0.298858i	0.541708	−	0.840567i	$-0.317778\pi$
$331$	−32743.2	−	32743.2i	−0.298858	−	0.298858i	−0.840567	+	0.541708i	$0.817778\pi$
$332$	−60841.0	−	60841.0i	−0.551976	−	0.551976i
$333$	155374.	+	155374.i	1.40117	+	1.40117i
$334$	49494.2			0.443671
$335$	69613.7	+	39607.7i	0.620305	+	0.352931i
$336$	56419.8	−	56419.8i	0.499750	−	0.499750i
$337$	124397.			1.09535			0.547673	−	0.836692i	$-0.315514\pi$
$337$	124397.			1.09535			0.547673	+	0.836692i	$0.315514\pi$
$338$	90440.6	+	124204.i	0.791644	+	1.08718i
$339$	199318.			1.73439
$340$	−11992.8	+	3294.73i	−0.103744	+	0.0285012i
$341$	−31603.0			−0.271782
$342$	−303535.			−2.59512
$343$	−62085.5	+	62085.5i	−0.527718	+	0.527718i
$344$	21505.0	+	21505.0i	0.181729	+	0.181729i
$345$	72513.0	−	19921.3i	0.609225	−	0.167370i
$346$	−120693.	+	120693.i	−1.00816	+	1.00816i
$347$			106129.i			0.881402i	0.897654	+	0.440701i	$0.145270\pi$
$347$			106129.i			0.881402i	−0.897654	+	0.440701i	$0.854730\pi$
$348$	2252.05			0.0185960
$349$	49889.9	−	49889.9i	0.409602	−	0.409602i	−0.471998	−	0.881600i	$-0.656467\pi$
$349$	49889.9	−	49889.9i	0.409602	−	0.409602i	0.881600	+	0.471998i	$0.156467\pi$
$350$	−57614.6	+	34240.9i	−0.470323	+	0.279518i
$351$	31737.5	+	37120.0i	0.257608	+	0.301296i
$352$			81005.1i			0.653773i
$353$	24939.9	−	24939.9i	0.200145	−	0.200145i	−0.599917	−	0.800062i	$-0.704800\pi$
$353$	24939.9	−	24939.9i	0.200145	−	0.200145i	0.800062	+	0.599917i	$0.204800\pi$
$354$	−81154.9			−0.647602
$355$	37498.6	−	65906.8i	0.297549	−	0.522966i
$356$	122216.	+	122216.i	0.964332	+	0.964332i
$357$	7338.44	−	7338.44i	0.0575794	−	0.0575794i
$358$	−101569.	−	101569.i	−0.792496	−	0.792496i
$359$	136392.	−	136392.i	1.05828	−	1.05828i	0.0600873	−	0.998193i	$-0.480862\pi$
$359$	136392.	−	136392.i	1.05828	−	1.05828i	0.998193	−	0.0600873i	$-0.0191379\pi$
$360$	20837.3	−	36623.3i	0.160782	−	0.282587i
$361$			173649.i			1.33247i
$362$	−176092.	−	176092.i	−1.34376	−	1.34376i
$363$	−147768.			−1.12142
$364$	3396.87	−	43455.7i	0.0256375	−	0.327977i
$365$	103766.	−	182376.i	0.778874	−	1.36894i
$366$	−13821.4	−	13821.4i	−0.103179	−	0.103179i
$367$			64468.3i			0.478645i	0.970940	+	0.239323i	$0.0769254\pi$
$367$			64468.3i			0.478645i	−0.970940	+	0.239323i	$0.923075\pi$
$368$	65669.5			0.484918
$369$	−175649.	−	175649.i	−1.29001	−	1.29001i
$370$	−76492.6	−	278431.i	−0.558748	−	2.03383i
$371$	−32272.9	+	32272.9i	−0.234472	+	0.234472i
$372$	−64121.1	−	64121.1i	−0.463356	−	0.463356i
$373$		−	66758.9i		−	0.479835i	−0.970793	−	0.239917i	$-0.922880\pi$
$373$		−	66758.9i		−	0.479835i	0.970793	−	0.239917i	$-0.0771204\pi$
$374$			12628.8i			0.0902857i
$375$	−146742.	+	152408.i	−1.04350	+	1.08379i
$376$			63537.3i			0.449421i
$377$	−1651.18	+	1411.76i	−0.0116175	+	0.00993291i
$378$		−	30988.9i		−	0.216882i
$379$	−149550.	−	149550.i	−1.04114	−	1.04114i	−0.999117	−	0.0420221i	$-0.986620\pi$
$379$	−149550.	−	149550.i	−1.04114	−	1.04114i	−0.0420221	−	0.999117i	$-0.513380\pi$
$380$	155005.	+	88191.9i	1.07344	+	0.610747i
$381$			115017.i			0.792339i
$382$	131222.	−	131222.i	0.899247	−	0.899247i
$383$	−126409.	+	126409.i	−0.861748	+	0.861748i	−0.991541	−	0.129793i	$-0.958569\pi$
$383$	−126409.	+	126409.i	−0.861748	+	0.861748i	0.129793	+	0.991541i	$0.458569\pi$
$384$	79254.2	−	79254.2i	0.537477	−	0.537477i
$385$	8060.61	+	29340.4i	0.0543809	+	0.197945i
$386$	22396.8			0.150318
$387$	188995.			1.26191
$388$	109026.	+	109026.i	0.724212	+	0.724212i
$389$			13710.1i			0.0906027i	0.998973	+	0.0453014i	$0.0144248\pi$
$389$			13710.1i			0.0906027i	−0.998973	+	0.0453014i	$0.985575\pi$
$390$	−58152.1	−	302205.i	−0.382328	−	1.98688i
$391$	8541.55			0.0558706
$392$	−23332.6	+	23332.6i	−0.151842	+	0.151842i
$393$		−	30152.9i		−	0.195229i
$394$		−	121689.i		−	0.783894i
$395$	77990.1	+	283882.i	0.499856	+	1.81947i
$396$	57168.7	+	57168.7i	0.364559	+	0.364559i
$397$	126920.	+	126920.i	0.805286	+	0.805286i	0.983916	−	0.178630i	$-0.0571665\pi$
$397$	126920.	+	126920.i	0.805286	+	0.805286i	−0.178630	+	0.983916i	$0.557167\pi$
$398$	91623.6	+	91623.6i	0.578417	+	0.578417i
$399$	−148813.			−0.934752
$400$	−158825.	+	94391.0i	−0.992654	+	0.589944i
$401$	−145212.	+	145212.i	−0.903056	+	0.903056i	−0.995699	−	0.0926431i	$-0.970468\pi$
$401$	−145212.	+	145212.i	−0.903056	+	0.903056i	0.0926431	+	0.995699i	$0.470468\pi$
$402$	233358.			1.44401
$403$	87209.0	+	6817.00i	0.536972	+	0.0419743i
$404$	−29163.7			−0.178681
$405$	28986.5	+	105510.i	0.176720	+	0.643257i
$406$	1378.46			0.00836259
$407$	−131090.			−0.791375
$408$	6062.73	−	6062.73i	0.0364207	−	0.0364207i
$409$	156739.	+	156739.i	0.936978	+	0.936978i	0.998129	−	0.0611506i	$-0.0194770\pi$
$409$	156739.	+	156739.i	0.936978	+	0.936978i	−0.0611506	+	0.998129i	$0.519477\pi$
$410$	86474.0	+	314764.i	0.514420	+	1.87248i
$411$	31608.1	−	31608.1i	0.187117	−	0.187117i
$412$			46801.7i			0.275719i
$413$	−22209.6			−0.130209
$414$	86481.5	−	86481.5i	0.504571	−	0.504571i
$415$	−144500.	−	82214.9i	−0.839016	−	0.477369i
$416$	17473.4	−	223535.i	0.100969	−	1.29169i
$417$		−	72107.4i		−	0.414675i
$418$	128047.	−	128047.i	0.732855	−	0.732855i
$419$	−202105.			−1.15120			−0.575599	−	0.817732i	$-0.695231\pi$
$419$	−202105.			−1.15120			−0.575599	+	0.817732i	$0.695231\pi$
$420$	−43175.8	+	75885.0i	−0.244761	+	0.430187i
$421$	−82635.7	−	82635.7i	−0.466233	−	0.466233i	0.434458	−	0.900692i	$-0.356940\pi$
$421$	−82635.7	−	82635.7i	−0.466233	−	0.466233i	−0.900692	+	0.434458i	$0.856940\pi$
$422$	−149275.	+	149275.i	−0.838227	+	0.838227i
$423$	279196.	+	279196.i	1.56037	+	1.56037i
$424$	−26662.6	+	26662.6i	−0.148310	+	0.148310i
$425$	−20658.1	+	12277.3i	−0.114370	+	0.0679713i
$426$		−	220932.i		−	1.21742i
$427$	−3782.49	−	3782.49i	−0.0207454	−	0.0207454i
$428$	133785.			0.730332
$429$	−139292.	−	10888.3i	−0.756854	−	0.0591622i
$430$	−215862.	−	122818.i	−1.16745	−	0.664238i
$431$	−93662.1	−	93662.1i	−0.504207	−	0.504207i	0.408535	−	0.912743i	$-0.366040\pi$
$431$	−93662.1	−	93662.1i	−0.504207	−	0.504207i	−0.912743	+	0.408535i	$0.866040\pi$
$432$		−	85426.4i		−	0.457746i
$433$	188158.			1.00357			0.501785	−	0.864992i	$-0.332677\pi$
$433$	188158.			1.00357			0.501785	+	0.864992i	$0.332677\pi$
$434$	−39247.9	−	39247.9i	−0.208371	−	0.208371i
$435$	4195.95	−	1152.74i	0.0221744	−	0.00609190i
$436$	159212.	−	159212.i	0.837535	−	0.837535i
$437$	−86605.3	−	86605.3i	−0.453505	−	0.453505i
$438$		−	611359.i		−	3.18675i
$439$		−	39194.4i		−	0.203374i	−0.994816	−	0.101687i	$-0.967576\pi$
$439$		−	39194.4i		−	0.203374i	0.994816	−	0.101687i	$-0.0324240\pi$
$440$	6659.36	+	24239.9i	0.0343975	+	0.125206i
$441$			205056.i			1.05438i
$442$	2724.12	−	34849.4i	0.0139438	−	0.178382i
$443$		−	206599.i		−	1.05274i	−0.850255	−	0.526370i	$-0.823553\pi$
$443$		−	206599.i		−	1.05274i	0.850255	−	0.526370i	$-0.176447\pi$
$444$	−265976.	−	265976.i	−1.34920	−	1.34920i
$445$	290266.	+	165151.i	1.46581	+	0.833990i
$446$		−	464034.i		−	2.33282i
$447$	394823.	−	394823.i	1.97600	−	1.97600i
$448$	−33932.0	+	33932.0i	−0.169065	+	0.169065i
$449$	40427.5	−	40427.5i	0.200532	−	0.200532i	−0.599696	−	0.800228i	$-0.704712\pi$
$449$	40427.5	−	40427.5i	0.200532	−	0.200532i	0.800228	+	0.599696i	$0.204712\pi$
$450$	−84854.0	+	333465.i	−0.419032	+	1.64674i
$451$	148196.			0.728592
$452$	−190459.			−0.932234
$453$	83175.5	+	83175.5i	0.405321	+	0.405321i
$454$			76712.1i			0.372179i
$455$	−15914.4	−	82704.1i	−0.0768720	−	0.399488i
$456$	−122944.			−0.591257
$457$	−193322.	+	193322.i	−0.925656	+	0.925656i	−0.997422	−	0.0717652i	$-0.977137\pi$
$457$	−193322.	+	193322.i	−0.925656	+	0.925656i	0.0717652	+	0.997422i	$0.477137\pi$
$458$			517912.i			2.46902i
$459$		−	11111.3i		−	0.0527399i
$460$	−69290.1	+	19035.9i	−0.327458	+	0.0899615i
$461$	54969.9	+	54969.9i	0.258656	+	0.258656i	0.824507	−	0.565851i	$-0.191452\pi$
$461$	54969.9	+	54969.9i	0.258656	+	0.258656i	−0.565851	+	0.824507i	$0.691452\pi$
$462$	62687.6	+	62687.6i	0.293696	+	0.293696i
$463$	−97628.2	−	97628.2i	−0.455421	−	0.455421i	0.441728	−	0.897149i	$-0.354366\pi$
$463$	−97628.2	−	97628.2i	−0.455421	−	0.455421i	−0.897149	+	0.441728i	$0.854366\pi$
$464$	3799.96			0.0176499
$465$	−152290.	−	86647.3i	−0.704312	−	0.400728i
$466$	−169876.	+	169876.i	−0.782277	+	0.782277i
$467$	−225559.			−1.03425			−0.517126	−	0.855909i	$-0.672998\pi$
$467$	−225559.			−1.03425			−0.517126	+	0.855909i	$0.672998\pi$
$468$	−145426.	−	170090.i	−0.663974	−	0.776580i
$469$	63862.9			0.290337
$470$	−137451.	−	500320.i	−0.622233	−	2.26491i
$471$	167389.			0.754546
$472$	−18348.7			−0.0823608
$473$	−79728.2	+	79728.2i	−0.356361	+	0.356361i
$474$	606532.	+	606532.i	2.69958	+	2.69958i
$475$	333942.	+	84975.5i	1.48008	+	0.376623i
$476$	−7012.29	+	7012.29i	−0.0309489	+	0.0309489i
$477$			234322.i			1.02986i
$478$	−407795.			−1.78479
$479$	−72614.3	+	72614.3i	−0.316484	+	0.316484i	−0.847415	−	0.530931i	$-0.821842\pi$
$479$	−72614.3	+	72614.3i	−0.316484	+	0.316484i	0.530931	+	0.847415i	$0.321842\pi$
$480$	−222095.	+	390350.i	−0.963953	+	1.69423i
$481$	361746.	+	28277.1i	1.56356	+	0.122221i
$482$		−	525363.i		−	2.26134i
$483$	42399.1	−	42399.1i	0.181745	−	0.181745i
$484$	141200.			0.602761
$485$	258940.	+	147327.i	1.10082	+	0.626325i
$486$	314468.	+	314468.i	1.33139	+	1.33139i
$487$	170734.	−	170734.i	0.719883	−	0.719883i	−0.248698	−	0.968581i	$-0.580003\pi$
$487$	170734.	−	170734.i	0.719883	−	0.719883i	0.968581	+	0.248698i	$0.0800026\pi$
$488$	−3124.95	−	3124.95i	−0.0131221	−	0.0131221i
$489$	212704.	−	212704.i	0.889524	−	0.889524i
$490$	133255.	−	234207.i	0.554998	−	0.975454i
$491$		−	394604.i		−	1.63681i	−0.574641	−	0.818406i	$-0.694858\pi$
$491$		−	394604.i		−	1.63681i	0.574641	−	0.818406i	$-0.305142\pi$
$492$	300683.	+	300683.i	1.24216	+	1.24216i
$493$	494.255			0.00203356
$494$	−380969.	+	325727.i	−1.56112	+	1.33475i
$495$	135778.	+	77252.6i	0.554138	+	0.315284i
$496$	−108194.	−	108194.i	−0.439783	−	0.439783i
$497$		−	60462.2i		−	0.244777i
$498$	−484389.			−1.95315
$499$	3359.03	+	3359.03i	0.0134900	+	0.0134900i	0.713820	−	0.700330i	$-0.246964\pi$
$499$	3359.03	+	3359.03i	0.0134900	+	0.0134900i	−0.700330	+	0.713820i	$0.746964\pi$
$500$	140220.	−	145634.i	0.560879	−	0.582537i
$501$	88091.1	−	88091.1i	0.350959	−	0.350959i
$502$	175962.	+	175962.i	0.698252	+	0.698252i
$503$			96974.7i			0.383286i	0.981465	+	0.191643i	$0.0613815\pi$
$503$			96974.7i			0.383286i	−0.981465	+	0.191643i	$0.938618\pi$
$504$		−	33597.8i		−	0.132266i
$505$	−54336.9	+	14927.8i	−0.213065	+	0.0585347i
$506$			72965.0i			0.284979i
$507$	382030.	+	60092.6i	1.48621	+	0.233779i
$508$		−	109905.i		−	0.425882i
$509$	23372.8	+	23372.8i	0.0902144	+	0.0902144i	0.750774	−	0.660559i	$-0.229681\pi$
$509$	23372.8	+	23372.8i	0.0902144	+	0.0902144i	−0.660559	+	0.750774i	$0.729681\pi$
$510$	−34624.9	+	60856.1i	−0.133122	+	0.233972i
$511$		−	167310.i		−	0.640738i
$512$	−222244.	+	222244.i	−0.847793	+	0.847793i
$513$	−112661.	+	112661.i	−0.428093	+	0.428093i
$514$	−272207.	+	272207.i	−1.03032	+	1.03032i
$515$	23956.1	+	87199.6i	0.0903236	+	0.328776i
$516$	−323530.			−1.21511
$517$	−235559.			−0.881291
$518$	−162802.	−	162802.i	−0.606735	−	0.606735i
$519$			429627.i			1.59498i
$520$	−13147.9	−	68326.8i	−0.0486237	−	0.252688i
$521$	−393235.			−1.44870			−0.724348	−	0.689435i	$-0.757859\pi$
$521$	−393235.			−1.44870			−0.724348	+	0.689435i	$0.757859\pi$
$522$	5004.24	−	5004.24i	0.0183652	−	0.0183652i
$523$		−	330104.i		−	1.20683i	−0.797426	−	0.603416i	$-0.793806\pi$
$523$		−	330104.i		−	1.20683i	0.797426	−	0.603416i	$-0.206194\pi$
$524$			28812.8i			0.104936i
$525$	−41601.1	+	163487.i	−0.150934	+	0.593150i
$526$	52804.8	+	52804.8i	0.190854	+	0.190854i
$527$	−14072.6	−	14072.6i	−0.0506703	−	0.0506703i
$528$	172809.	+	172809.i	0.619868	+	0.619868i
$529$	−230491.			−0.823649
$530$	152273.	−	267633.i	0.542090	−	0.952768i
$531$	−80627.8	+	80627.8i	−0.285954	+	0.285954i
$532$	142199.			0.502429
$533$	−408950.	−	31967.0i	−1.43951	−	0.112525i
$534$	973026.			3.41226
$535$	249265.	−	68479.7i	0.870869	−	0.239251i
$536$	52761.0			0.183647
$537$	−361552.			−1.25378
$538$	−292943.	+	292943.i	−1.01209	+	1.01209i
$539$	−86503.7	−	86503.7i	−0.297754	−	0.297754i
$540$	24762.8	+	90136.2i	0.0849206	+	0.309109i
$541$	−155484.	+	155484.i	−0.531239	+	0.531239i	−0.920941	−	0.389702i	$-0.872578\pi$
$541$	−155484.	+	155484.i	−0.531239	+	0.531239i	0.389702	+	0.920941i	$0.372578\pi$
$542$			553211.i			1.88318i
$543$	−626825.			−2.12592
$544$	−36071.0	+	36071.0i	−0.121888	+	0.121888i
$545$	215144.	−	378134.i	0.724331	−	1.27307i
$546$	−159465.	−	186510.i	−0.534910	−	0.625627i
$547$			441985.i			1.47718i	0.674156	+	0.738589i	$0.264508\pi$
$547$			441985.i			1.47718i	−0.674156	+	0.738589i	$0.735492\pi$
$548$	−30203.2	+	30203.2i	−0.100576	+	0.100576i
$549$	−27463.3			−0.0911189
$550$	−104877.	−	176469.i	−0.346702	−	0.583369i
$551$	−5011.40	−	5011.40i	−0.0165065	−	0.0165065i
$552$	35028.4	−	35028.4i	0.114959	−	0.114959i
$553$	165989.	+	165989.i	0.542786	+	0.542786i
$554$	−148777.	+	148777.i	−0.484748	+	0.484748i
$555$	−631703.	−	359416.i	−2.05082	−	1.16684i
$556$			68902.6i			0.222888i
$557$	−413308.	−	413308.i	−1.33218	−	1.33218i	−0.903416	−	0.428766i	$-0.858949\pi$
$557$	−413308.	−	413308.i	−1.33218	−	1.33218i	−0.428766	−	0.903416i	$-0.641051\pi$
$558$	−284965.			−0.915215
$559$	237209.	−	202813.i	0.759115	−	0.649041i
$560$	−72852.0	+	128043.i	−0.232309	+	0.408301i
$561$	22477.1	+	22477.1i	0.0714191	+	0.0714191i
$562$			58489.5i			0.185185i
$563$	195674.			0.617330			0.308665	−	0.951171i	$-0.400118\pi$
$563$	195674.			0.617330			0.308665	+	0.951171i	$0.400118\pi$
$564$	−477939.	−	477939.i	−1.50250	−	1.50250i
$565$	−354858.	+	97489.0i	−1.11162	+	0.305393i
$566$	−17781.7	+	17781.7i	−0.0555061	+	0.0555061i
$567$	61692.9	+	61692.9i	0.191897	+	0.191897i
$568$		−	49951.4i		−	0.154829i
$569$			123681.i			0.382015i	0.981589	+	0.191007i	$0.0611754\pi$
$569$			123681.i			0.382015i	−0.981589	+	0.191007i	$0.938825\pi$
$570$	968111.	−	265966.i	2.97972	−	0.818609i
$571$			216358.i			0.663593i	0.943351	+	0.331796i	$0.107655\pi$
$571$			216358.i			0.663593i	−0.943351	+	0.331796i	$0.892345\pi$
$572$	133101.	+	10404.3i	0.406809	+	0.0317997i
$573$		−	467104.i		−	1.42267i
$574$	184045.	+	184045.i	0.558600	+	0.558600i
$575$	−119356.	+	70934.2i	−0.361000	+	0.214546i
$576$			246368.i			0.742574i
$577$	−80872.0	+	80872.0i	−0.242911	+	0.242911i	−0.818053	−	0.575143i	$-0.804947\pi$
$577$	−80872.0	+	80872.0i	−0.242911	+	0.242911i	0.575143	+	0.818053i	$0.304947\pi$
$578$	312078.	−	312078.i	0.934131	−	0.934131i
$579$	39862.4	−	39862.4i	0.118907	−	0.118907i
$580$	−4009.46	+	1101.51i	−0.0119187	+	0.00327440i
$581$	−132562.			−0.392706
$582$	868015.			2.56260
$583$	−98849.5	−	98849.5i	−0.290829	−	0.290829i
$584$		−	138225.i		−	0.405285i
$585$	−358017.	−	242468.i	−1.04614	−	0.708504i
$586$	317175.			0.923642
$587$	141882.	−	141882.i	0.411765	−	0.411765i	−0.470588	−	0.882353i	$-0.655958\pi$
$587$	141882.	−	141882.i	0.411765	−	0.411765i	0.882353	+	0.470588i	$0.155958\pi$
$588$		−	351024.i		−	1.01527i
$589$			285373.i			0.822588i
$590$	144485.	−	39694.0i	0.415068	−	0.114030i
$591$	−216585.	−	216585.i	−0.620087	−	0.620087i
$592$	−448791.	−	448791.i	−1.28056	−	1.28056i
$593$	176288.	+	176288.i	0.501318	+	0.501318i	0.911847	−	0.410529i	$-0.134656\pi$
$593$	176288.	+	176288.i	0.501318	+	0.501318i	−0.410529	+	0.911847i	$0.634656\pi$
$594$	94916.7			0.269011
$595$	−9475.76	+	16654.4i	−0.0267658	+	0.0470431i
$596$	−377275.	+	377275.i	−1.06210	+	1.06210i
$597$	326148.			0.915096
$598$	15739.1	−	201348.i	0.0440126	−	0.563047i
$599$	173188.			0.482686			0.241343	−	0.970440i	$-0.422412\pi$
$599$	173188.			0.482686			0.241343	+	0.970440i	$0.422412\pi$
$600$	−34369.2	+	135066.i	−0.0954700	+	0.375184i
$601$	163895.			0.453749			0.226874	−	0.973924i	$-0.427149\pi$
$601$	163895.			0.453749			0.226874	+	0.973924i	$0.427149\pi$
$602$	−198029.			−0.546433
$603$	231842.	−	231842.i	0.637615	−	0.637615i
$604$	−79478.8	−	79478.8i	−0.217860	−	0.217860i
$605$	263080.	−	72275.3i	0.718750	−	0.197460i
$606$	−116094.	+	116094.i	−0.316129	+	0.316129i
$607$			114069.i			0.309593i	0.987946	+	0.154796i	$0.0494722\pi$
$607$			114069.i			0.309593i	−0.987946	+	0.154796i	$0.950528\pi$
$608$	731469.			1.97874
$609$	2453.41	−	2453.41i	0.00661510	−	0.00661510i
$610$	31367.4	+	17846.9i	0.0842983	+	0.0479627i
$611$	650029.	+	50811.9i	1.74121	+	0.136108i
$612$			50913.7i			0.135935i
$613$	−144005.	+	144005.i	−0.383227	+	0.383227i	−0.872264	−	0.489036i	$-0.837349\pi$
$613$	−144005.	+	144005.i	−0.383227	+	0.383227i	0.489036	+	0.872264i	$0.337349\pi$
$614$	708662.			1.87976
$615$	714133.	+	406316.i	1.88812	+	1.07427i
$616$	14173.3	+	14173.3i	0.0373517	+	0.0373517i
$617$	−39559.3	+	39559.3i	−0.103915	+	0.103915i	−0.757153	−	0.653238i	$-0.773410\pi$
$617$	−39559.3	+	39559.3i	−0.103915	+	0.103915i	0.653238	+	0.757153i	$0.273410\pi$
$618$	186307.	+	186307.i	0.487812	+	0.487812i
$619$	−196003.	+	196003.i	−0.511542	+	0.511542i	−0.914999	−	0.403457i	$-0.867809\pi$
$619$	−196003.	+	196003.i	−0.511542	+	0.511542i	0.403457	+	0.914999i	$0.367809\pi$
$620$	145521.	+	82796.3i	0.378567	+	0.215391i
$621$		−	64197.3i		−	0.166469i
$622$	−152071.	−	152071.i	−0.393067	−	0.393067i
$623$	266287.			0.686079
$624$	−439594.	−	514146.i	−1.12897	−	1.32044i
$625$	186709.	−	343115.i	0.477974	−	0.878374i
$626$	199015.	+	199015.i	0.507853	+	0.507853i
$627$		−	455804.i		−	1.15943i
$628$	−159950.			−0.405568
$629$	−58373.6	−	58373.6i	−0.147542	−	0.147542i
$630$	72682.6	+	264563.i	0.183126	+	0.666573i
$631$	−273562.	+	273562.i	−0.687065	+	0.687065i	−0.961582	−	0.274517i	$-0.911482\pi$
$631$	−273562.	+	273562.i	−0.687065	+	0.687065i	0.274517	+	0.961582i	$0.411482\pi$
$632$	137133.	+	137133.i	0.343328	+	0.343328i
$633$			531366.i			1.32613i
$634$			702097.i			1.74670i
$635$	−56256.2	−	204772.i	−0.139516	−	0.507834i
$636$		−	401122.i		−	0.991659i
$637$	220049.	+	257368.i	0.542300	+	0.634271i
$638$			4222.11i			0.0103726i
$639$	−219497.	−	219497.i	−0.537560	−	0.537560i
$640$	−102337.	+	179866.i	−0.249846	+	0.439125i
$641$		−	198202.i		−	0.482384i	−0.970477	−	0.241192i	$-0.922462\pi$
$641$		−	198202.i		−	0.482384i	0.970477	−	0.241192i	$-0.0775383\pi$
$642$	532569.	−	532569.i	1.29213	−	1.29213i
$643$	226576.	−	226576.i	0.548013	−	0.548013i	−0.377852	−	0.925866i	$-0.623337\pi$
$643$	226576.	−	226576.i	0.548013	−	0.548013i	0.925866	+	0.377852i	$0.123337\pi$
$644$	−40514.6	+	40514.6i	−0.0976878	+	0.0976878i
$645$	−602791.	+	165603.i	−1.44893	+	0.398060i
$646$	114037.			0.273263
$647$	−146466.			−0.349888			−0.174944	−	0.984578i	$-0.555975\pi$
$647$	−146466.			−0.349888			−0.174944	+	0.984578i	$0.555975\pi$
$648$	50968.2	+	50968.2i	0.121381	+	0.121381i
$649$		−	68026.2i		−	0.161505i
$650$	251344.	+	509591.i	0.594898	+	1.20613i
$651$	−139709.			−0.329657
$652$	−203250.	+	203250.i	−0.478119	+	0.478119i
$653$		−	125114.i		−	0.293414i	−0.989180	−	0.146707i	$-0.953133\pi$
$653$		−	125114.i		−	0.293414i	0.989180	−	0.146707i	$-0.0468674\pi$
$654$		−	1.26758e6i		−	2.96359i
$655$	14748.2	+	53683.2i	0.0343761	+	0.125128i
$656$	507353.	+	507353.i	1.17897	+	1.17897i
$657$	−607389.	−	607389.i	−1.40714	−	1.40714i
$658$	−292542.	−	292542.i	−0.675673	−	0.675673i
$659$	188068.			0.433055			0.216528	−	0.976276i	$-0.430527\pi$
$659$	188068.			0.433055			0.216528	+	0.976276i	$0.430527\pi$
$660$	−232430.	−	132244.i	−0.533585	−	0.303591i
$661$	426969.	−	426969.i	0.977224	−	0.977224i	−0.0225228	−	0.999746i	$-0.507170\pi$
$661$	426969.	−	426969.i	0.977224	−	0.977224i	0.999746	+	0.0225228i	$0.00716984\pi$
$662$	249101.			0.568406
$663$	−57177.3	−	66874.3i	−0.130076	−	0.152136i
$664$	−109518.			−0.248398
$665$	264942.	−	72786.7i	0.599111	−	0.164592i
$666$	−1.18204e6			−2.66492
$667$	2855.64			0.00641877
$668$	−84175.9	+	84175.9i	−0.188640	+	0.188640i
$669$	−825900.	−	825900.i	−1.84534	−	1.84534i
$670$	−415462.	+	114139.i	−0.925512	+	0.254263i
$671$	11585.5	−	11585.5i	0.0257318	−	0.0257318i
$672$			358103.i			0.792992i
$673$	−137308.			−0.303156			−0.151578	−	0.988445i	$-0.548435\pi$
$673$	−137308.			−0.303156			−0.151578	+	0.988445i	$0.548435\pi$
$674$	−473189.	+	473189.i	−1.04163	+	1.04163i
$675$	92274.9	+	155264.i	0.202524	+	0.340772i
$676$	−365051.	−	57421.8i	−0.798840	−	0.125656i
$677$			46329.0i			0.101082i	0.998722	+	0.0505412i	$0.0160946\pi$
$677$			46329.0i			0.101082i	−0.998722	+	0.0505412i	$0.983905\pi$
$678$	−758175.	+	758175.i	−1.64934	+	1.64934i
$679$	237549.			0.515244
$680$	−7828.50	+	13759.2i	−0.0169301	+	0.0297561i
$681$	136534.	+	136534.i	0.294406	+	0.294406i
$682$	120213.	−	120213.i	0.258454	−	0.258454i
$683$	−473398.	−	473398.i	−1.01481	−	1.01481i	−0.999889	−	0.0149210i	$-0.995250\pi$
$683$	−473398.	−	473398.i	−1.01481	−	1.01481i	−0.0149210	−	0.999889i	$-0.504750\pi$
$684$	516229.	−	516229.i	1.10339	−	1.10339i
$685$	−40813.9	+	71733.8i	−0.0869815	+	0.152877i
$686$		−	472328.i		−	1.00368i
$687$	921794.	+	921794.i	1.95308	+	1.95308i
$688$	−545903.			−1.15329
$689$	251454.	+	294099.i	0.529688	+	0.619520i
$690$	−200051.	+	351606.i	−0.420187	+	0.738513i
$691$	−481994.	−	481994.i	−1.00945	−	1.00945i	−0.999955	−	0.00949745i	$-0.996977\pi$
$691$	−481994.	−	481994.i	−1.00945	−	1.00945i	−0.00949745	−	0.999955i	$-0.503023\pi$
$692$		−	410532.i		−	0.857304i
$693$	124561.			0.259367
$694$	−403698.	−	403698.i	−0.838181	−	0.838181i
$695$	35268.7	+	128377.i	0.0730163	+	0.265778i
$696$	2026.91	−	2026.91i	0.00418424	−	0.00418424i
$697$	65990.8	+	65990.8i	0.135837	+	0.135837i
$698$			379548.i			0.779032i
$699$			604700.i			1.23762i
$700$	39752.2	−	156221.i	0.0811269	−	0.318818i
$701$			168793.i			0.343493i	0.985141	+	0.171747i	$0.0549411\pi$
$701$			168793.i			0.343493i	−0.985141	+	0.171747i	$0.945059\pi$
$702$	−261924.	−	20474.2i	−0.531497	−	0.0415464i
$703$			1.18374e6i			2.39521i
$704$	−103931.	−	103931.i	−0.209701	−	0.209701i
$705$	−1.13512e6	−	645843.i	−2.28383	−	1.29942i
$706$			189735.i			0.380661i
$707$	−31771.3	+	31771.3i	−0.0635618	+	0.0635618i
$708$	138022.	−	138022.i	0.275348	−	0.275348i
$709$	−369244.	+	369244.i	−0.734550	+	0.734550i	−0.971518	−	0.236968i	$-0.923846\pi$
$709$	−369244.	+	369244.i	−0.734550	+	0.734550i	0.236968	+	0.971518i	$0.423846\pi$
$710$	108061.	+	393339.i	0.214364	+	0.780280i
$711$	1.20518e6			2.38404
$712$	219996.			0.433965
$713$	−81306.8	−	81306.8i	−0.159937	−	0.159937i
$714$			55828.7i			0.109512i
$715$	253316.	−	48744.6i	0.495508	−	0.0953487i
$716$	345483.			0.673908
$717$	−725805.	+	725805.i	−1.41183	+	1.41183i
$718$			1.03763e6i			2.01277i
$719$		−	266353.i		−	0.515228i	−0.966248	−	0.257614i	$-0.917064\pi$
$719$		−	266353.i		−	0.515228i	0.966248	−	0.257614i	$-0.0829363\pi$
$720$	200362.	+	729314.i	0.386501	+	1.40686i
$721$	50986.5	+	50986.5i	0.0980809	+	0.0980809i
$722$	−660535.	−	660535.i	−1.26713	−	1.26713i
$723$	−935056.	−	935056.i	−1.78880	−	1.78880i
$724$	598966.			1.14268
$725$	−6906.49	+	4104.59i	−0.0131396	+	0.00780897i
$726$	562087.	−	562087.i	1.06643	−	1.06643i
$727$	308605.			0.583895			0.291947	−	0.956434i	$-0.405697\pi$
$727$	308605.			0.583895			0.291947	+	0.956434i	$0.405697\pi$
$728$	−36054.2	−	42168.7i	−0.0680288	−	0.0795661i
$729$	764878.			1.43925
$730$	299024.	+	1.08844e6i	0.561126	+	2.04249i
$731$	−71004.8			−0.132878
$732$	47012.8			0.0877393
$733$	80351.6	−	80351.6i	0.149550	−	0.149550i	−0.628367	−	0.777917i	$-0.716276\pi$
$733$	80351.6	−	80351.6i	0.149550	−	0.149550i	0.777917	+	0.628367i	$0.216276\pi$
$734$	−245228.	−	245228.i	−0.455174	−	0.455174i
$735$	−179676.	−	654018.i	−0.332595	−	1.21064i
$736$	−208406.	+	208406.i	−0.384729	+	0.384729i
$737$			195607.i			0.360122i
$738$	1.33629e6			2.45351
$739$	−632147.	+	632147.i	−1.15752	+	1.15752i	−0.172514	+	0.985007i	$0.555189\pi$
$739$	−632147.	+	632147.i	−1.15752	+	1.15752i	−0.985007	+	0.172514i	$0.944811\pi$
$740$	603627.	+	343442.i	1.10231	+	0.627176i
$741$	−98320.2	+	1.25780e6i	−0.179063	+	2.29073i
$742$		−	245523.i		−	0.445948i
$743$	537527.	−	537527.i	0.973695	−	0.973695i	−0.0259677	−	0.999663i	$-0.508267\pi$
$743$	537527.	−	537527.i	0.973695	−	0.973695i	0.999663	+	0.0259677i	$0.00826671\pi$
$744$	−115422.			−0.208518
$745$	−509815.	+	896041.i	−0.918543	+	1.61442i
$746$	253941.	+	253941.i	0.456305	+	0.456305i
$747$	−481243.	+	481243.i	−0.862429	+	0.862429i
$748$	−21478.1	−	21478.1i	−0.0383877	−	0.0383877i
$749$	145747.	−	145747.i	0.259799	−	0.259799i
$750$	−21553.5	−	1.13792e6i	−0.0383173	−	2.02297i
$751$		−	1.07389e6i		−	1.90405i	−0.306018	−	0.952026i	$-0.598997\pi$
$751$		−	1.07389e6i		−	1.90405i	0.306018	−	0.952026i	$-0.401003\pi$
$752$	−806443.	−	806443.i	−1.42606	−	1.42606i
$753$	626364.			1.10468
$754$	910.738	−	11651.0i	0.00160196	−	0.0204936i
$755$	−188765.	−	107400.i	−0.331152	−	0.188413i
$756$	52703.6	+	52703.6i	0.0922139	+	0.0922139i
$757$			165538.i			0.288873i	0.989514	+	0.144436i	$0.0461369\pi$
$757$			165538.i			0.288873i	−0.989514	+	0.144436i	$0.953863\pi$
$758$	1.13773e6			1.98017
$759$	129865.	+	129865.i	0.225428	+	0.225428i
$760$	218884.	−	60133.5i	0.378955	−	0.104109i
$761$	66178.9	−	66178.9i	0.114275	−	0.114275i	−0.647657	−	0.761932i	$-0.724251\pi$
$761$	66178.9	−	66178.9i	0.114275	−	0.114275i	0.761932	+	0.647657i	$0.224251\pi$
$762$	−437507.	−	437507.i	−0.753485	−	0.753485i
$763$		−	346896.i		−	0.595868i
$764$			446343.i			0.764685i
$765$	26060.8	+	94860.9i	0.0445313	+	0.162093i
$766$		−	961682.i		−	1.63898i
$767$	−14673.7	+	187719.i	−0.0249431	+	0.319093i
$768$			1.12447e6i			1.90646i
$769$	483494.	+	483494.i	0.817595	+	0.817595i	0.985759	−	0.168164i	$-0.0537840\pi$
$769$	483494.	+	483494.i	0.817595	+	0.817595i	−0.168164	+	0.985759i	$0.553784\pi$
$770$	−142268.	−	80945.4i	−0.239953	−	0.136524i
$771$			968963.i			1.63004i
$772$	−38090.7	+	38090.7i	−0.0639123	+	0.0639123i
$773$	643422.	−	643422.i	1.07681	−	1.07681i	0.0800115	−	0.996794i	$-0.474504\pi$
$773$	643422.	−	643422.i	1.07681	−	1.07681i	0.996794	−	0.0800115i	$-0.0254957\pi$
$774$	−718910.	+	718910.i	−1.20003	+	1.20003i
$775$	313512.	+	79776.7i	0.521975	+	0.132823i
$776$	196253.			0.325907
$777$	−579517.			−0.959896
$778$	−52151.2	−	52151.2i	−0.0861599	−	0.0861599i
$779$		−	1.33820e6i		−	2.20519i
$780$	612867.	+	415066.i	1.00734	+	0.682226i
$781$	185191.			0.303611
$782$	−32490.8	+	32490.8i	−0.0531308	+	0.0531308i
$783$		−	3714.76i		−	0.00605910i
$784$		−	592295.i		−	0.963620i
$785$	−298014.	+	81872.4i	−0.483612	+	0.132861i
$786$	114697.	+	114697.i	0.185656	+	0.185656i
$787$	276257.	+	276257.i	0.446029	+	0.446029i	0.894032	−	0.448003i	$-0.147865\pi$
$787$	276257.	+	276257.i	0.446029	+	0.446029i	−0.448003	+	0.894032i	$0.647865\pi$
$788$	206959.	+	206959.i	0.333297	+	0.333297i
$789$	187967.			0.301944
$790$	−1.37651e6	−	783183.i	−2.20559	−	1.25490i
$791$	−207489.	+	207489.i	−0.331621	+	0.331621i
$792$	102907.			0.164057
$793$	−34469.4	+	29471.2i	−0.0548134	+	0.0468654i
$794$	−965573.			−1.53160
$795$	−205320.	−	747359.i	−0.324860	−	1.18248i
$796$	−311653.			−0.491864
$797$	−98830.2			−0.155587			−0.0777935	−	0.996969i	$-0.524787\pi$
$797$	−98830.2			−0.155587			−0.0777935	+	0.996969i	$0.524787\pi$
$798$	566064.	−	566064.i	0.888914	−	0.888914i
$799$	−104893.	−	104893.i	−0.164306	−	0.164306i
$800$	204484.	−	803594.i	0.319506	−	1.25562i
$801$	966707.	−	966707.i	1.50671	−	1.50671i
$802$		−	1.10473e6i		−	1.71755i
$803$	512458.			0.794743
$804$	−396877.	+	396877.i	−0.613966	+	0.613966i
$805$	−54747.7	+	96223.7i	−0.0844840	+	0.148488i
$806$	−357661.	+	305799.i	−0.550556	+	0.470724i
$807$			1.04278e6i			1.60119i
$808$	−26248.2	+	26248.2i	−0.0402047	+	0.0402047i
$809$	838450.			1.28109			0.640546	−	0.767920i	$-0.278708\pi$
$809$	838450.			1.28109			0.640546	+	0.767920i	$0.278708\pi$
$810$	−511606.	−	291085.i	−0.779768	−	0.443660i
$811$	−541529.	−	541529.i	−0.823342	−	0.823342i	0.163244	−	0.986586i	$-0.447804\pi$
$811$	−541529.	−	541529.i	−0.823342	−	0.823342i	−0.986586	+	0.163244i	$0.947804\pi$
$812$	−2344.37	+	2344.37i	−0.00355561	+	0.00355561i
$813$	984619.	+	984619.i	1.48966	+	1.48966i
$814$	498649.	−	498649.i	0.752568	−	0.752568i
$815$	−274654.	+	482726.i	−0.413495	+	0.726751i
$816$			153902.i			0.231133i
$817$	719939.	+	719939.i	1.07858	+	1.07858i
$818$	−1.19242e6			−1.78206
$819$	−343728.	−	26868.7i	−0.512444	−	0.0400570i
$820$	−682394.	−	388257.i	−1.01486	−	0.577420i
$821$	−609022.	−	609022.i	−0.903538	−	0.903538i	0.0922020	−	0.995740i	$-0.470609\pi$
$821$	−609022.	−	609022.i	−0.903538	−	0.903538i	−0.995740	+	0.0922020i	$0.970609\pi$
$822$			240465.i			0.355884i
$823$	341665.			0.504430			0.252215	−	0.967671i	$-0.418841\pi$
$823$	341665.			0.504430			0.252215	+	0.967671i	$0.418841\pi$
$824$	42123.0	+	42123.0i	0.0620390	+	0.0620390i
$825$	−500748.	−	127421.i	−0.735717	−	0.187212i
$826$	84481.9	−	84481.9i	0.123824	−	0.123824i
$827$	−683254.	−	683254.i	−0.999013	−	0.999013i	0.000986779	−	1.00000i	$-0.499686\pi$
$827$	−683254.	−	683254.i	−0.999013	−	0.999013i	−1.00000		0.000986779i	$0.999686\pi$
$828$			294162.i			0.429068i
$829$			641983.i			0.934146i	0.884219	+	0.467073i	$0.154691\pi$
$829$			641983.i			0.934146i	−0.884219	+	0.467073i	$0.845309\pi$
$830$	862388.	−	236921.i	1.25183	−	0.343913i
$831$			529594.i			0.766903i
$832$	264381.	+	309218.i	0.381930	+	0.446703i
$833$		−	77039.0i		−	0.111025i
$834$	274286.	+	274286.i	0.394340	+	0.394340i
$835$	−113748.	+	199921.i	−0.163143	+	0.286738i
$836$			435546.i			0.623191i
$837$	−105768.	+	105768.i	−0.150975	+	0.150975i
$838$	768779.	−	768779.i	1.09475	−	1.09475i
$839$	112909.	−	112909.i	0.160400	−	0.160400i	−0.622344	−	0.782744i	$-0.713819\pi$
$839$	112909.	−	112909.i	0.160400	−	0.160400i	0.782744	+	0.622344i	$0.213819\pi$
$840$	29439.3	+	107158.i	0.0417224	+	0.151869i
$841$	−707116.			−0.999766
$842$	628668.			0.886742
$843$	104101.	+	104101.i	0.146487	+	0.146487i
$844$		−	507750.i		−	0.712795i
$845$	−709544.	+	79869.3i	−0.993724	+	0.111858i
$846$	−2.12404e6			−2.96771
$847$	153826.	−	153826.i	0.214418	−	0.214418i
$848$		−	676827.i		−	0.941209i
$849$			63296.8i			0.0878145i
$850$	31879.3	−	125281.i	0.0441237	−	0.173400i
$851$	−337263.	−	337263.i	−0.465704	−	0.465704i
$852$	375744.	+	375744.i	0.517622	+	0.517622i
$853$	248000.	+	248000.i	0.340842	+	0.340842i	0.856684	−	0.515842i	$-0.172521\pi$
$853$	248000.	+	248000.i	0.340842	+	0.340842i	−0.515842	+	0.856684i	$0.672521\pi$
$854$	28776.1			0.0394563
$855$	697585.	−	1.22606e6i	0.954255	−	1.67718i
$856$	120411.	−	120411.i	0.164330	−	0.164330i
$857$	219984.			0.299523			0.149761	−	0.988722i	$-0.452149\pi$
$857$	219984.			0.299523			0.149761	+	0.988722i	$0.452149\pi$
$858$	571264.	−	488430.i	0.776001	−	0.663479i
$859$	735303.			0.996506			0.498253	−	0.867032i	$-0.333975\pi$
$859$	735303.			0.996506			0.498253	+	0.867032i	$0.333975\pi$
$860$	576000.	−	158243.i	0.778799	−	0.213957i
$861$	655138.			0.883744
$862$	712553.			0.958965
$863$	−933811.	+	933811.i	−1.25383	+	1.25383i	−0.299834	+	0.953991i	$0.596931\pi$
$863$	−933811.	+	933811.i	−1.25383	+	1.25383i	−0.953991	+	0.299834i	$0.903069\pi$
$864$	271105.	+	271105.i	0.363171	+	0.363171i
$865$	−210136.	−	764891.i	−0.280846	−	1.02227i
$866$	−715727.	+	715727.i	−0.954358	+	0.954358i
$867$		−	1.11089e6i		−	1.47786i
$868$	133500.			0.177191
$869$	−508411.	+	508411.i	−0.673248	+	0.673248i
$870$	−11575.9	+	20345.6i	−0.0152939	+	0.0268802i
$871$	42193.8	−	539780.i	0.0556176	−	0.711509i
$872$		−	286592.i		−	0.376904i
$873$	862377.	−	862377.i	1.13154	−	1.13154i
$874$	658868.			0.862533
$875$	−5898.52	−	311414.i	−0.00770419	−	0.406744i
$876$	1.03975e6	+	1.03975e6i	1.35495	+	1.35495i
$877$	69714.1	−	69714.1i	0.0906403	−	0.0906403i	−0.660333	−	0.750973i	$-0.729585\pi$
$877$	69714.1	−	69714.1i	0.0906403	−	0.0906403i	0.750973	+	0.660333i	$0.229585\pi$
$878$	149090.	+	149090.i	0.193401	+	0.193401i
$879$	564516.	−	564516.i	0.730632	−	0.730632i
$880$	−392187.	−	223140.i	−0.506440	−	0.288146i
$881$			788257.i			1.01558i	0.861480	+	0.507792i	$0.169538\pi$
$881$			788257.i			1.01558i	−0.861480	+	0.507792i	$0.830462\pi$
$882$	−780005.	−	780005.i	−1.00267	−	1.00267i
$883$	−1.43460e6			−1.83996			−0.919981	−	0.391963i	$-0.871796\pi$
$883$	−1.43460e6			−1.83996			−0.919981	+	0.391963i	$0.871796\pi$
$884$	54636.1	+	63902.0i	0.0699158	+	0.0817731i
$885$	186510.	−	327807.i	0.238131	−	0.418535i
$886$	785873.	+	785873.i	1.00112	+	1.00112i
$887$			300346.i			0.381746i	0.981615	+	0.190873i	$0.0611319\pi$
$887$			300346.i			0.381746i	−0.981615	+	0.190873i	$0.938868\pi$
$888$	−478774.			−0.607162
$889$	−119732.	−	119732.i	−0.151498	−	0.151498i
$890$	−1.73234e6	+	475920.i	−2.18702	+	0.600834i
$891$	−188961.	+	188961.i	−0.238021	+	0.238021i
$892$	789193.	+	789193.i	0.991868	+	0.991868i
$893$			2.12708e6i			2.66736i
$894$			3.00369e6i			3.75821i
$895$	643694.	−	176840.i	0.803588	−	0.220767i
$896$			165007.i			0.205535i
$897$	−330351.	−	386377.i	−0.410574	−	0.480205i
$898$			307560.i			0.381397i
$899$	−4704.80	−	4704.80i	−0.00582133	−	0.00582133i
$900$	−422818.	−	711444.i	−0.521997	−	0.878326i
$901$		−	88034.0i		−	0.108443i
$902$	−563717.	+	563717.i	−0.692864	+	0.692864i
$903$	−352458.	+	352458.i	−0.432247	+	0.432247i
$904$	−171419.	+	171419.i	−0.209760	+	0.209760i
$905$	1.11598e6	−	306589.i	1.36257	−	0.374334i
$906$	−632775.			−0.770891
$907$	−825898.			−1.00395			−0.501975	−	0.864882i	$-0.667393\pi$
$907$	−825898.			−1.00395			−0.501975	+	0.864882i	$0.667393\pi$
$908$	−130466.	−	130466.i	−0.158243	−	0.158243i
$909$			230680.i			0.279179i
$910$	375130.	+	254058.i	0.453001	+	0.306796i
$911$	160295.			0.193145			0.0965723	−	0.995326i	$-0.469212\pi$
$911$	160295.			0.193145			0.0965723	+	0.995326i	$0.469212\pi$
$912$	1.56045e6	−	1.56045e6i	1.87612	−	1.87612i
$913$		−	406028.i		−	0.487096i
$914$		−	1.47074e6i		−	1.76053i
$915$	87592.9	−	24064.1i	0.104623	−	0.0287427i
$916$	−880825.	−	880825.i	−1.04978	−	1.04978i
$917$	31389.1	+	31389.1i	0.0373285	+	0.0373285i
$918$	42265.7	+	42265.7i	0.0501537	+	0.0501537i
$919$	−883157.			−1.04570			−0.522849	−	0.852425i	$-0.675131\pi$
$919$	−883157.			−1.04570			−0.522849	+	0.852425i	$0.675131\pi$
$920$	−45230.4	+	79496.2i	−0.0534386	+	0.0939227i
$921$	1.26129e6	−	1.26129e6i	1.48695	−	1.48695i
$922$	−418195.			−0.491946
$923$	−511037.	−	39947.0i	−0.599859	−	0.0468901i
$924$	−213229.			−0.249748
$925$	1.30046e6	+	330916.i	1.51989	+	0.386754i
$926$	742727.			0.866178
$927$	370194.			0.430795
$928$	−12059.4	+	12059.4i	−0.0140032	+	0.0140032i
$929$	927720.	+	927720.i	1.07494	+	1.07494i	0.996954	+	0.0779887i	$0.0248498\pi$
$929$	927720.	+	927720.i	1.07494	+	1.07494i	0.0779887	+	0.996954i	$0.475150\pi$
$930$	908882.	−	249694.i	1.05085	−	0.288697i
$931$	−781122.	+	781122.i	−0.901196	+	0.901196i
$932$		−	577825.i		−	0.665218i
$933$	−541321.			−0.621859
$934$	857993.	−	857993.i	0.983535	−	0.983535i
$935$	−51011.2	−	29023.5i	−0.0583502	−	0.0331991i
$936$	−283974.	−	22197.8i	−0.324136	−	0.0253372i
$937$		−	1.32455e6i		−	1.50866i	−0.656497	−	0.754329i	$-0.727963\pi$
$937$		−	1.32455e6i		−	1.50866i	0.656497	−	0.754329i	$-0.272037\pi$
$938$	−242925.	+	242925.i	−0.276100	+	0.276100i
$939$	708426.			0.803458
$940$	1.08467e6	+	617138.i	1.22756	+	0.698436i
$941$	239441.	+	239441.i	0.270408	+	0.270408i	0.829264	−	0.558857i	$-0.188760\pi$
$941$	239441.	+	239441.i	0.270408	+	0.270408i	−0.558857	+	0.829264i	$0.688760\pi$
$942$	−636724.	+	636724.i	−0.717546	+	0.717546i
$943$	381272.	+	381272.i	0.428758	+	0.428758i
$944$	232889.	−	232889.i	0.261340	−	0.261340i
$945$	125173.	+	71218.7i	0.140167	+	0.0797500i
$946$		−	606549.i		−	0.677772i
$947$	45631.3	+	45631.3i	0.0508818	+	0.0508818i	0.732090	−	0.681208i	$-0.238545\pi$
$947$	45631.3	+	45631.3i	0.0508818	+	0.0508818i	−0.681208	+	0.732090i	$0.738545\pi$
$948$	−2.06308e6			−2.29562
$949$	−1.41413e6	−	110541.i	−1.57021	−	0.122741i
$950$	−1.59350e6	+	947033.i	−1.76565	+	1.04934i
$951$	1.24961e6	+	1.24961e6i	1.38170	+	1.38170i
$952$			12622.6i			0.0139275i
$953$	−250545.			−0.275867			−0.137933	−	0.990442i	$-0.544046\pi$
$953$	−250545.			−0.275867			−0.137933	+	0.990442i	$0.544046\pi$
$954$	−891327.	−	891327.i	−0.979355	−	0.979355i
$955$	228467.	+	831614.i	0.250505	+	0.911833i
$956$	693547.	−	693547.i	0.758857	−	0.758857i
$957$	7514.61	+	7514.61i	0.00820508	+	0.00820508i
$958$		−	552428.i		−	0.601928i
$959$			65807.7i			0.0715550i
$960$	−215875.	−	785780.i	−0.234239	−	0.852626i
$961$		−	655607.i		−	0.709900i
$962$	−1.48359e6	+	1.26847e6i	−1.60311	+	1.37066i
$963$		−	1.05822e6i		−	1.14110i
$964$	893497.	+	893497.i	0.961478	+	0.961478i
$965$	−51472.3	+	90466.8i	−0.0552738	+	0.0971482i
$966$			322560.i			0.345665i
$967$	−205444.	+	205444.i	−0.219706	+	0.219706i	−0.808374	−	0.588669i	$-0.799652\pi$
$967$	−205444.	+	205444.i	−0.219706	+	0.219706i	0.588669	+	0.808374i	$0.299652\pi$
$968$	127085.	−	127085.i	0.135626	−	0.135626i
$969$	202966.	−	202966.i	0.216160	−	0.216160i
$970$	−1.54538e6	+	424558.i	−1.64245	+	0.451225i
$971$	−717908.			−0.761431			−0.380716	−	0.924692i	$-0.624322\pi$
$971$	−717908.			−0.761431			−0.380716	+	0.924692i	$0.624322\pi$
$972$	−1.06965e6			−1.13216
$973$	75063.5	+	75063.5i	0.0792872	+	0.0792872i
$974$			1.29889e6i			1.36917i
$975$	1.35433e6	+	459635.i	1.42468	+	0.483508i
$976$	79326.4			0.0832756
$977$	172482.	−	172482.i	0.180698	−	0.180698i	−0.610962	−	0.791660i	$-0.709217\pi$
$977$	172482.	−	172482.i	0.180698	−	0.180698i	0.791660	+	0.610962i	$0.209217\pi$
$978$			1.61819e6i			1.69181i
$979$			815617.i			0.850983i
$980$	171691.	+	624950.i	0.178770	+	0.650718i
$981$	−1.25934e6	−	1.25934e6i	−1.30860	−	1.30860i
$982$	1.50102e6	+	1.50102e6i	1.55655	+	1.55655i
$983$	−764797.	−	764797.i	−0.791478	−	0.791478i	0.190256	−	0.981734i	$-0.439068\pi$
$983$	−764797.	−	764797.i	−0.791478	−	0.791478i	−0.981734	+	0.190256i	$0.939068\pi$
$984$	541249.			0.558994
$985$	491534.	+	279665.i	0.506618	+	0.288247i
$986$	−1880.07	+	1880.07i	−0.00193384	+	0.00193384i
$987$	−1.04135e6			−1.06896
$988$	93950.3	−	1.20189e6i	0.0962464	−	1.23127i
$989$	−410242.			−0.419418
$990$	−810336.	+	222621.i	−0.826789	+	0.227141i
$991$	527478.			0.537103			0.268551	−	0.963265i	$-0.413455\pi$
$991$	527478.			0.537103			0.268551	+	0.963265i	$0.413455\pi$
$992$	686718.			0.697838
$993$	443356.	−	443356.i	0.449629	−	0.449629i
$994$	229989.	+	229989.i	0.232774	+	0.232774i
$995$	−580662.	+	159524.i	−0.586513	+	0.161131i
$996$	823811.	−	823811.i	0.830442	−	0.830442i
$997$		−	553444.i		−	0.556780i	−0.960468	−	0.278390i	$-0.910199\pi$
$997$		−	553444.i		−	0.556780i	0.960468	−	0.278390i	$-0.0898007\pi$
$998$	−25554.5			−0.0256571
$999$	−438730.	+	438730.i	−0.439608	+	0.439608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.5	✓	52
5.4	even	2	inner	65.5.g.a.34.22	yes	52
13.5	odd	4	inner	65.5.g.a.44.22	yes	52
65.44	odd	4	inner	65.5.g.a.44.5	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.5	✓	52	1.1	even	1	trivial
65.5.g.a.34.22	yes	52	5.4	even	2	inner
65.5.g.a.44.5	yes	52	65.44	odd	4	inner
65.5.g.a.44.22	yes	52	13.5	odd	4	inner

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	65.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.80385 + 3.80385i) q^{2} +13.5404i q^{3} -12.9386i q^{4} +(-6.62279 - 24.1068i) q^{5} +(-51.5057 - 51.5057i) q^{6} +(-14.0955 - 14.0955i) q^{7} +(-11.6451 - 11.6451i) q^{8} -102.342 q^{9} +O(q^{10})\)	\(q+(-3.80385 + 3.80385i) q^{2} +13.5404i q^{3} -12.9386i q^{4} +(-6.62279 - 24.1068i) q^{5} +(-51.5057 - 51.5057i) q^{6} +(-14.0955 - 14.0955i) q^{7} +(-11.6451 - 11.6451i) q^{8} -102.342 q^{9} +(116.891 + 66.5067i) q^{10} +(43.1734 - 43.1734i) q^{11} +175.194 q^{12} +(-128.450 + 109.825i) q^{13} +107.234 q^{14} +(326.416 - 89.6752i) q^{15} +295.610 q^{16} +38.4496 q^{17} +(389.295 - 389.295i) q^{18} +(-389.852 - 389.852i) q^{19} +(-311.908 + 85.6896i) q^{20} +(190.859 - 190.859i) q^{21} +328.451i q^{22} +222.149 q^{23} +(157.680 - 157.680i) q^{24} +(-537.277 + 319.309i) q^{25} +(70.8492 - 906.364i) q^{26} -288.983i q^{27} +(-182.376 + 182.376i) q^{28} +12.8546 q^{29} +(-900.526 + 1582.75i) q^{30} +(-366.001 - 366.001i) q^{31} +(-938.136 + 938.136i) q^{32} +(584.585 + 584.585i) q^{33} +(-146.257 + 146.257i) q^{34} +(-246.446 + 433.149i) q^{35} +1324.17i q^{36} +(-1518.18 - 1518.18i) q^{37} +2965.88 q^{38} +(-1487.07 - 1739.27i) q^{39} +(-203.604 + 357.851i) q^{40} +(1716.29 + 1716.29i) q^{41} +1452.00i q^{42} -1846.70 q^{43} +(-558.603 - 558.603i) q^{44} +(677.792 + 2467.15i) q^{45} +(-845.022 + 845.022i) q^{46} +(-2728.06 - 2728.06i) q^{47} +4002.68i q^{48} -2003.63i q^{49} +(829.120 - 3258.33i) q^{50} +520.623i q^{51} +(1420.98 + 1661.97i) q^{52} -2289.59i q^{53} +(1099.25 + 1099.25i) q^{54} +(-1326.70 - 754.845i) q^{55} +328.288i q^{56} +(5278.76 - 5278.76i) q^{57} +(-48.8970 + 48.8970i) q^{58} +(787.825 - 787.825i) q^{59} +(-1160.27 - 4223.36i) q^{60} +268.348 q^{61} +2784.43 q^{62} +(1442.57 + 1442.57i) q^{63} -2407.30i q^{64} +(3498.23 + 2369.18i) q^{65} -4447.35 q^{66} +(-2265.36 + 2265.36i) q^{67} -497.484i q^{68} +3007.99i q^{69} +(-710.191 - 2585.08i) q^{70} +(2144.73 + 2144.73i) q^{71} +(1191.79 + 1191.79i) q^{72} +(5934.88 + 5934.88i) q^{73} +11549.9 q^{74} +(-4323.57 - 7274.95i) q^{75} +(-5044.14 + 5044.14i) q^{76} -1217.10 q^{77} +(12272.5 + 959.326i) q^{78} -11776.0 q^{79} +(-1957.77 - 7126.22i) q^{80} -4376.78 q^{81} -13057.0 q^{82} +(4702.29 - 4702.29i) q^{83} +(-2469.44 - 2469.44i) q^{84} +(-254.644 - 926.898i) q^{85} +(7024.56 - 7024.56i) q^{86} +174.057i q^{87} -1005.52 q^{88} +(-9445.82 + 9445.82i) q^{89} +(-11962.9 - 6806.44i) q^{90} +(3358.61 + 262.538i) q^{91} -2874.30i q^{92} +(4955.80 - 4955.80i) q^{93} +20754.3 q^{94} +(-6816.19 + 11980.0i) q^{95} +(-12702.7 - 12702.7i) q^{96} +(-8426.40 + 8426.40i) q^{97} +(7621.53 + 7621.53i) q^{98} +(-4418.47 + 4418.47i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more