LMFDB - Embedded newform 65.5.g.a.34.8

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			34.8
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.80141 + 2.80141i) q^{2} -1.58015i q^{3} +0.304183i q^{4} +(20.5382 - 14.2543i) q^{5} +(4.42666 + 4.42666i) q^{6} +(-31.3088 - 31.3088i) q^{7} +(-45.6747 - 45.6747i) q^{8} +78.5031 q^{9} +O(q^{10})$	\(q+(-2.80141 + 2.80141i) q^{2} -1.58015i q^{3} +0.304183i q^{4} +(20.5382 - 14.2543i) q^{5} +(4.42666 + 4.42666i) q^{6} +(-31.3088 - 31.3088i) q^{7} +(-45.6747 - 45.6747i) q^{8} +78.5031 q^{9} +(-17.6038 + 97.4679i) q^{10} +(28.2407 - 28.2407i) q^{11} +0.480655 q^{12} +(167.023 + 25.7740i) q^{13} +175.418 q^{14} +(-22.5239 - 32.4534i) q^{15} +251.041 q^{16} +244.539 q^{17} +(-219.920 + 219.920i) q^{18} +(230.290 + 230.290i) q^{19} +(4.33590 + 6.24735i) q^{20} +(-49.4727 + 49.4727i) q^{21} +158.228i q^{22} -225.706 q^{23} +(-72.1731 + 72.1731i) q^{24} +(218.632 - 585.513i) q^{25} +(-540.104 + 395.697i) q^{26} -252.039i q^{27} +(9.52360 - 9.52360i) q^{28} +1056.15 q^{29} +(154.014 + 27.8167i) q^{30} +(-896.324 - 896.324i) q^{31} +(27.5277 - 27.5277i) q^{32} +(-44.6246 - 44.6246i) q^{33} +(-685.054 + 685.054i) q^{34} +(-1089.31 - 196.741i) q^{35} +23.8793i q^{36} +(-303.769 - 303.769i) q^{37} -1290.28 q^{38} +(40.7269 - 263.922i) q^{39} +(-1589.13 - 287.015i) q^{40} +(-933.236 - 933.236i) q^{41} -277.187i q^{42} -1187.23 q^{43} +(8.59033 + 8.59033i) q^{44} +(1612.31 - 1119.00i) q^{45} +(632.295 - 632.295i) q^{46} +(898.587 + 898.587i) q^{47} -396.682i q^{48} -440.517i q^{49} +(1027.78 + 2252.74i) q^{50} -386.409i q^{51} +(-7.84001 + 50.8055i) q^{52} +4905.62i q^{53} +(706.066 + 706.066i) q^{54} +(177.462 - 982.562i) q^{55} +2860.04i q^{56} +(363.894 - 363.894i) q^{57} +(-2958.70 + 2958.70i) q^{58} +(4197.26 - 4197.26i) q^{59} +(9.87177 - 6.85139i) q^{60} -1193.08 q^{61} +5021.95 q^{62} +(-2457.84 - 2457.84i) q^{63} +4170.88i q^{64} +(3797.74 - 1851.44i) q^{65} +250.024 q^{66} +(1305.38 - 1305.38i) q^{67} +74.3845i q^{68} +356.650i q^{69} +(3602.76 - 2500.45i) q^{70} +(5049.40 + 5049.40i) q^{71} +(-3585.61 - 3585.61i) q^{72} +(-4890.86 - 4890.86i) q^{73} +1701.97 q^{74} +(-925.199 - 345.472i) q^{75} +(-70.0503 + 70.0503i) q^{76} -1768.36 q^{77} +(625.261 + 853.447i) q^{78} -9065.34 q^{79} +(5155.91 - 3578.40i) q^{80} +5960.49 q^{81} +5228.76 q^{82} +(-6767.93 + 6767.93i) q^{83} +(-15.0487 - 15.0487i) q^{84} +(5022.38 - 3485.72i) q^{85} +(3325.91 - 3325.91i) q^{86} -1668.87i q^{87} -2579.77 q^{88} +(-3135.82 + 3135.82i) q^{89} +(-1381.95 + 7651.53i) q^{90} +(-4422.34 - 6036.25i) q^{91} -68.6558i q^{92} +(-1416.33 + 1416.33i) q^{93} -5034.63 q^{94} +(8012.35 + 1447.12i) q^{95} +(-43.4980 - 43.4980i) q^{96} +(-2614.80 + 2614.80i) q^{97} +(1234.07 + 1234.07i) q^{98} +(2216.98 - 2216.98i) 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 $

$2$	−2.80141	+	2.80141i	−0.700353	+	0.700353i	−0.964486	−	0.264133i	$-0.914914\pi$
$2$	−2.80141	+	2.80141i	−0.700353	+	0.700353i	0.264133	+	0.964486i	$0.414914\pi$
$3$		−	1.58015i		−	0.175573i	−0.996139	−	0.0877863i	$-0.972021\pi$
$3$		−	1.58015i		−	0.175573i	0.996139	−	0.0877863i	$-0.0279793\pi$
$4$			0.304183i			0.0190114i
$5$	20.5382	−	14.2543i	0.821526	−	0.570170i
$5$	20.5382	−	14.2543i	0.821526	−	0.570170i
$6$	4.42666	+	4.42666i	0.122963	+	0.122963i
$7$	−31.3088	−	31.3088i	−0.638955	−	0.638955i	0.311343	−	0.950298i	$-0.399221\pi$
$7$	−31.3088	−	31.3088i	−0.638955	−	0.638955i	−0.950298	+	0.311343i	$0.899221\pi$
$8$	−45.6747	−	45.6747i	−0.713668	−	0.713668i
$9$	78.5031			0.969174
$10$	−17.6038	+	97.4679i	−0.176038	+	0.974679i
$11$	28.2407	−	28.2407i	0.233394	−	0.233394i	−0.580714	−	0.814108i	$-0.697226\pi$
$11$	28.2407	−	28.2407i	0.233394	−	0.233394i	0.814108	+	0.580714i	$0.197226\pi$
$12$	0.480655			0.00333788
$13$	167.023	+	25.7740i	0.988302	+	0.152509i
$13$	167.023	+	25.7740i	0.988302	+	0.152509i
$14$	175.418			0.894988
$15$	−22.5239	−	32.4534i	−0.100106	−	0.144237i
$16$	251.041			0.980627
$17$	244.539			0.846155			0.423077	−	0.906094i	$-0.360950\pi$
$17$	244.539			0.846155			0.423077	+	0.906094i	$0.360950\pi$
$18$	−219.920	+	219.920i	−0.678764	+	0.678764i
$19$	230.290	+	230.290i	0.637923	+	0.637923i	0.950043	−	0.312120i	$-0.101039\pi$
$19$	230.290	+	230.290i	0.637923	+	0.637923i	−0.312120	+	0.950043i	$0.601039\pi$
$20$	4.33590	+	6.24735i	0.0108398	+	0.0156184i
$21$	−49.4727	+	49.4727i	−0.112183	+	0.112183i
$22$			158.228i			0.326917i
$23$	−225.706			−0.426665			−0.213333	−	0.976980i	$-0.568432\pi$
$23$	−225.706			−0.426665			−0.213333	+	0.976980i	$0.568432\pi$
$24$	−72.1731	+	72.1731i	−0.125300	+	0.125300i
$25$	218.632	−	585.513i	0.349811	−	0.936820i
$26$	−540.104	+	395.697i	−0.798970	+	0.585350i
$27$		−	252.039i		−	0.345733i
$28$	9.52360	−	9.52360i	0.0121474	−	0.0121474i
$29$	1056.15			1.25582			0.627912	−	0.778285i	$-0.283910\pi$
$29$	1056.15			1.25582			0.627912	+	0.778285i	$0.283910\pi$
$30$	154.014	+	27.8167i	0.171127	+	0.0309074i
$31$	−896.324	−	896.324i	−0.932699	−	0.932699i	0.0651745	−	0.997874i	$-0.479240\pi$
$31$	−896.324	−	896.324i	−0.932699	−	0.932699i	−0.997874	+	0.0651745i	$0.979240\pi$
$32$	27.5277	−	27.5277i	0.0268825	−	0.0268825i
$33$	−44.6246	−	44.6246i	−0.0409776	−	0.0409776i
$34$	−685.054	+	685.054i	−0.592607	+	0.592607i
$35$	−1089.31	−	196.741i	−0.889232	−	0.160605i
$36$			23.8793i			0.0184254i
$37$	−303.769	−	303.769i	−0.221891	−	0.221891i	0.587403	−	0.809295i	$-0.300150\pi$
$37$	−303.769	−	303.769i	−0.221891	−	0.221891i	−0.809295	+	0.587403i	$0.800150\pi$
$38$	−1290.28			−0.893543
$39$	40.7269	−	263.922i	0.0267764	−	0.173519i
$40$	−1589.13	−	287.015i	−0.993209	−	0.179385i
$41$	−933.236	−	933.236i	−0.555167	−	0.555167i	0.372760	−	0.927928i	$-0.378411\pi$
$41$	−933.236	−	933.236i	−0.555167	−	0.555167i	−0.927928	+	0.372760i	$0.878411\pi$
$42$		−	277.187i		−	0.157135i
$43$	−1187.23			−0.642092			−0.321046	−	0.947064i	$-0.604034\pi$
$43$	−1187.23			−0.642092			−0.321046	+	0.947064i	$0.604034\pi$
$44$	8.59033	+	8.59033i	0.00443715	+	0.00443715i
$45$	1612.31	−	1119.00i	0.796202	−	0.552595i
$46$	632.295	−	632.295i	0.298816	−	0.298816i
$47$	898.587	+	898.587i	0.406785	+	0.406785i	0.880616	−	0.473831i	$-0.157129\pi$
$47$	898.587	+	898.587i	0.406785	+	0.406785i	−0.473831	+	0.880616i	$0.657129\pi$
$48$		−	396.682i		−	0.172171i
$49$		−	440.517i		−	0.183472i
$50$	1027.78	+	2252.74i	0.411113	+	0.901096i
$51$		−	386.409i		−	0.148562i
$52$	−7.84001	+	50.8055i	−0.00289941	+	0.0187890i
$53$			4905.62i			1.74639i	0.487368	+	0.873197i	$0.337957\pi$
$53$			4905.62i			1.74639i	−0.487368	+	0.873197i	$0.662043\pi$
$54$	706.066	+	706.066i	0.242135	+	0.242135i
$55$	177.462	−	982.562i	0.0586650	−	0.324814i
$56$			2860.04i			0.912003i
$57$	363.894	−	363.894i	0.112002	−	0.112002i
$58$	−2958.70	+	2958.70i	−0.879520	+	0.879520i
$59$	4197.26	−	4197.26i	1.20576	−	1.20576i	0.233376	−	0.972387i	$-0.425023\pi$
$59$	4197.26	−	4197.26i	1.20576	−	1.20576i	0.972387	−	0.233376i	$-0.0749771\pi$
$60$	9.87177	−	6.85139i	0.00274216	−	0.00190316i
$61$	−1193.08			−0.320633			−0.160317	−	0.987066i	$-0.551252\pi$
$61$	−1193.08			−0.320633			−0.160317	+	0.987066i	$0.551252\pi$
$62$	5021.95			1.30644
$63$	−2457.84	−	2457.84i	−0.619259	−	0.619259i
$64$			4170.88i			1.01828i
$65$	3797.74	−	1851.44i	0.898872	−	0.438211i
$66$	250.024			0.0573976
$67$	1305.38	−	1305.38i	0.290796	−	0.290796i	−0.546599	−	0.837395i	$-0.684078\pi$
$67$	1305.38	−	1305.38i	0.290796	−	0.290796i	0.837395	+	0.546599i	$0.184078\pi$
$68$			74.3845i			0.0160866i
$69$			356.650i			0.0749107i
$70$	3602.76	−	2500.45i	0.735257	−	0.510296i
$71$	5049.40	+	5049.40i	1.00167	+	1.00167i	0.999999	+	0.00166721i	$0.000530690\pi$
$71$	5049.40	+	5049.40i	1.00167	+	1.00167i	0.00166721	+	0.999999i	$0.499469\pi$
$72$	−3585.61	−	3585.61i	−0.691668	−	0.691668i
$73$	−4890.86	−	4890.86i	−0.917782	−	0.917782i	0.0790859	−	0.996868i	$-0.474800\pi$
$73$	−4890.86	−	4890.86i	−0.917782	−	0.917782i	−0.996868	+	0.0790859i	$0.974800\pi$
$74$	1701.97			0.310805
$75$	−925.199	−	345.472i	−0.164480	−	0.0614172i
$76$	−70.0503	+	70.0503i	−0.0121278	+	0.0121278i
$77$	−1768.36			−0.298257
$78$	625.261	+	853.447i	0.102771	+	0.140277i
$79$	−9065.34			−1.45255			−0.726273	−	0.687407i	$-0.758749\pi$
$79$	−9065.34			−1.45255			−0.726273	+	0.687407i	$0.758749\pi$
$80$	5155.91	−	3578.40i	0.805611	−	0.559125i
$81$	5960.49			0.908473
$82$	5228.76			0.777626
$83$	−6767.93	+	6767.93i	−0.982425	+	0.982425i	−0.999848	−	0.0174231i	$-0.994454\pi$
$83$	−6767.93	+	6767.93i	−0.982425	+	0.982425i	0.0174231	+	0.999848i	$0.494454\pi$
$84$	−15.0487	−	15.0487i	−0.00213276	−	0.00213276i
$85$	5022.38	−	3485.72i	0.695139	−	0.482453i
$86$	3325.91	−	3325.91i	0.449691	−	0.449691i
$87$		−	1668.87i		−	0.220488i
$88$	−2579.77			−0.333132
$89$	−3135.82	+	3135.82i	−0.395886	+	0.395886i	−0.876779	−	0.480893i	$-0.840313\pi$
$89$	−3135.82	+	3135.82i	−0.395886	+	0.395886i	0.480893	+	0.876779i	$0.340313\pi$
$90$	−1381.95	+	7651.53i	−0.170611	+	0.944634i
$91$	−4422.34	−	6036.25i	−0.534034	−	0.728927i
$92$		−	68.6558i		−	0.00811151i
$93$	−1416.33	+	1416.33i	−0.163756	+	0.163756i
$94$	−5034.63			−0.569786
$95$	8012.35	+	1447.12i	0.887795	+	0.160346i
$96$	−43.4980	−	43.4980i	−0.00471984	−	0.00471984i
$97$	−2614.80	+	2614.80i	−0.277904	+	0.277904i	−0.832272	−	0.554368i	$-0.812960\pi$
$97$	−2614.80	+	2614.80i	−0.277904	+	0.277904i	0.554368	+	0.832272i	$0.312960\pi$
$98$	1234.07	+	1234.07i	0.128495	+	0.128495i
$99$	2216.98	−	2216.98i	0.226200	−	0.226200i
$100$	178.103	+	66.5041i	0.0178103	+	0.00665041i
$101$			9644.41i			0.945437i	0.881213	+	0.472719i	$0.156727\pi$
$101$			9644.41i			0.945437i	−0.881213	+	0.472719i	$0.843273\pi$
$102$	1082.49	+	1082.49i	0.104046	+	0.104046i
$103$	1640.91			0.154672			0.0773360	−	0.997005i	$-0.475359\pi$
$103$	1640.91			0.154672			0.0773360	+	0.997005i	$0.475359\pi$
$104$	−6451.51	−	8805.95i	−0.596479	−	0.814160i
$105$	−310.881	+	1721.28i	−0.0281979	+	0.156125i
$106$	−13742.7	−	13742.7i	−1.22309	−	1.22309i
$107$			11516.4i			1.00589i	0.864319	+	0.502944i	$0.167750\pi$
$107$			11516.4i			1.00589i	−0.864319	+	0.502944i	$0.832250\pi$
$108$	76.6660			0.00657287
$109$	−7243.24	−	7243.24i	−0.609649	−	0.609649i	0.333205	−	0.942854i	$-0.391870\pi$
$109$	−7243.24	−	7243.24i	−0.609649	−	0.609649i	−0.942854	+	0.333205i	$0.891870\pi$
$110$	2255.42	+	3249.70i	0.186398	+	0.268571i
$111$	−480.002	+	480.002i	−0.0389581	+	0.0389581i
$112$	−7859.78	−	7859.78i	−0.626577	−	0.626577i
$113$		−	4194.26i		−	0.328472i	−0.986421	−	0.164236i	$-0.947484\pi$
$113$		−	4194.26i		−	0.328472i	0.986421	−	0.164236i	$-0.0525159\pi$
$114$			2038.83i			0.156882i
$115$	−4635.58	+	3217.27i	−0.350517	+	0.243272i
$116$			321.262i			0.0238750i
$117$	13111.8	+	2023.34i	0.957837	+	0.147808i
$118$			23516.5i			1.68892i
$119$	−7656.22	−	7656.22i	−0.540655	−	0.540655i
$120$	−453.528	+	2511.08i	−0.0314950	+	0.174380i
$121$			13045.9i			0.891054i
$122$	3342.30	−	3342.30i	0.224556	−	0.224556i
$123$	−1474.66	+	1474.66i	−0.0974721	+	0.0974721i
$124$	272.646	−	272.646i	0.0177319	−	0.0177319i
$125$	−3855.75	−	15141.8i	−0.246768	−	0.969075i
$126$	13770.8			0.867400
$127$	21059.2			1.30567			0.652836	−	0.757499i	$-0.273579\pi$
$127$	21059.2			1.30567			0.652836	+	0.757499i	$0.273579\pi$
$128$	−11243.9	−	11243.9i	−0.686274	−	0.686274i
$129$			1876.00i			0.112734i
$130$	−5452.38	+	15825.7i	−0.322626	+	0.936430i
$131$	−6794.03			−0.395899			−0.197950	−	0.980212i	$-0.563428\pi$
$131$	−6794.03			−0.395899			−0.197950	+	0.980212i	$0.563428\pi$
$132$	13.5740	−	13.5740i	0.000779042	−	0.000779042i
$133$		−	14420.2i		−	0.815208i
$134$			7313.83i			0.407320i
$135$	−3592.63	−	5176.42i	−0.197127	−	0.284029i
$136$	−11169.2	−	11169.2i	−0.603873	−	0.603873i
$137$	−16740.3	−	16740.3i	−0.891911	−	0.891911i	0.102792	−	0.994703i	$-0.467222\pi$
$137$	−16740.3	−	16740.3i	−0.891911	−	0.891911i	−0.994703	+	0.102792i	$0.967222\pi$
$138$	−999.123	−	999.123i	−0.0524639	−	0.0524639i
$139$	−9542.21			−0.493878			−0.246939	−	0.969031i	$-0.579425\pi$
$139$	−9542.21			−0.493878			−0.246939	+	0.969031i	$0.579425\pi$
$140$	59.8453	−	331.349i	0.00305333	−	0.0169056i
$141$	1419.91	−	1419.91i	0.0714202	−	0.0714202i
$142$	−28290.9			−1.40304
$143$	5444.72	−	3988.97i	0.266259	−	0.195069i
$144$	19707.5			0.950399
$145$	21691.3	−	15054.6i	1.03169	−	0.716033i
$146$	27402.6			1.28554
$147$	−696.085			−0.0322127
$148$	92.4014	−	92.4014i	0.00421847	−	0.00421847i
$149$	29579.4	+	29579.4i	1.33234	+	1.33234i	0.903269	+	0.429075i	$0.141161\pi$
$149$	29579.4	+	29579.4i	1.33234	+	1.33234i	0.429075	+	0.903269i	$0.358839\pi$
$150$	3559.67	−	1624.06i	0.158208	−	0.0721802i
$151$	−20880.0	+	20880.0i	−0.915749	+	0.915749i	−0.996717	−	0.0809675i	$-0.974199\pi$
$151$	−20880.0	+	20880.0i	−0.915749	+	0.915749i	0.0809675	+	0.996717i	$0.474199\pi$
$152$		−	21036.9i		−	0.910530i
$153$	19197.1			0.820072
$154$	4953.92	−	4953.92i	0.208885	−	0.208885i
$155$	−31185.3	−	5632.41i	−1.29803	−	0.234439i
$156$	80.2805	+	12.3884i	0.00329884	+	0.000509057i
$157$			42430.6i			1.72139i	0.509120	+	0.860696i	$0.329971\pi$
$157$			42430.6i			1.72139i	−0.509120	+	0.860696i	$0.670029\pi$
$158$	25395.7	−	25395.7i	1.01729	−	1.01729i
$159$	7751.63			0.306619
$160$	172.981	−	957.756i	0.00675709	−	0.0374123i
$161$	7066.58	+	7066.58i	0.272620	+	0.272620i
$162$	−16697.8	+	16697.8i	−0.636252	+	0.636252i
$163$	15207.6	+	15207.6i	0.572382	+	0.572382i	0.932794	−	0.360411i	$-0.117364\pi$
$163$	15207.6	+	15207.6i	0.572382	+	0.572382i	−0.360411	+	0.932794i	$0.617364\pi$
$164$	283.874	−	283.874i	0.0105545	−	0.0105545i
$165$	−1552.60	−	280.416i	−0.0570284	−	0.0103000i
$166$		−	37919.5i		−	1.37609i
$167$	2541.51	+	2541.51i	0.0911296	+	0.0911296i	0.751202	−	0.660072i	$-0.229474\pi$
$167$	2541.51	+	2541.51i	0.0911296	+	0.0911296i	−0.660072	+	0.751202i	$0.729474\pi$
$168$	4519.30			0.160123
$169$	27232.4	+	8609.71i	0.953482	+	0.301450i
$170$	−4304.81	+	23834.7i	−0.148955	+	0.824729i
$171$	18078.5	+	18078.5i	0.618259	+	0.618259i
$172$		−	361.134i		−	0.0122071i
$173$	26063.6			0.870847			0.435423	−	0.900226i	$-0.356599\pi$
$173$	26063.6			0.870847			0.435423	+	0.900226i	$0.356599\pi$
$174$	4675.20	+	4675.20i	0.154419	+	0.154419i
$175$	−25176.8	+	11486.6i	−0.822100	+	0.375072i
$176$	7089.56	−	7089.56i	0.228873	−	0.228873i
$177$	−6632.31	−	6632.31i	−0.211699	−	0.211699i
$178$		−	17569.4i		−	0.554520i
$179$			2420.16i			0.0755332i	0.999287	+	0.0377666i	$0.0120243\pi$
$179$			2420.16i			0.0755332i	−0.999287	+	0.0377666i	$0.987976\pi$
$180$	340.382	+	490.437i	0.0105056	+	0.0151369i
$181$			1222.49i			0.0373154i	0.999826	+	0.0186577i	$0.00593928\pi$
$181$			1222.49i			0.0373154i	−0.999826	+	0.0186577i	$0.994061\pi$
$182$	29298.8	+	4521.22i	0.884519	+	0.136494i
$183$			1885.24i			0.0562944i
$184$	10309.1	+	10309.1i	0.304497	+	0.304497i
$185$	−10568.9	−	1908.86i	−0.308806	−	0.0557737i
$186$		−	7935.44i		−	0.229375i
$187$	6905.94	−	6905.94i	0.197488	−	0.197488i
$188$	−273.335	+	273.335i	−0.00773356	+	0.00773356i
$189$	−7891.05	+	7891.05i	−0.220908	+	0.220908i
$190$	−26499.9	+	18391.9i	−0.734069	+	0.509472i
$191$	−29366.1			−0.804969			−0.402484	−	0.915427i	$-0.631853\pi$
$191$	−29366.1			−0.804969			−0.402484	+	0.915427i	$0.631853\pi$
$192$	6590.63			0.178782
$193$	2239.26	+	2239.26i	0.0601159	+	0.0601159i	0.736526	−	0.676410i	$-0.236465\pi$
$193$	2239.26	+	2239.26i	0.0601159	+	0.0601159i	−0.676410	+	0.736526i	$0.736465\pi$
$194$		−	14650.3i		−	0.389262i
$195$	−2925.56	−	6001.00i	−0.0769377	−	0.157817i
$196$	133.998			0.00348807
$197$	456.501	−	456.501i	0.0117628	−	0.0117628i	−0.701201	−	0.712964i	$-0.747352\pi$
$197$	456.501	−	456.501i	0.0117628	−	0.0117628i	0.712964	+	0.701201i	$0.247352\pi$
$198$			12421.4i			0.316839i
$199$		−	33420.6i		−	0.843933i	−0.906611	−	0.421967i	$-0.861340\pi$
$199$		−	33420.6i		−	0.843933i	0.906611	−	0.421967i	$-0.138660\pi$
$200$	−36729.1	+	16757.2i	−0.918227	+	0.418929i
$201$	−2062.70	−	2062.70i	−0.0510558	−	0.0510558i
$202$	−27018.0	−	27018.0i	−0.662140	−	0.662140i
$203$	−33066.7	−	33066.7i	−0.802415	−	0.802415i
$204$	117.539			0.00282437
$205$	−32469.5	−	5864.36i	−0.772624	−	0.139545i
$206$	−4596.88	+	4596.88i	−0.108325	+	0.108325i
$207$	−17718.6			−0.413513
$208$	41929.6	+	6470.32i	0.969156	+	0.149554i
$209$	13007.1			0.297775
$210$	−3951.09	−	5692.91i	−0.0895940	−	0.129091i
$211$	−86398.9			−1.94063			−0.970317	−	0.241838i	$-0.922250\pi$
$211$	−86398.9			−1.94063			−0.970317	+	0.241838i	$0.922250\pi$
$212$	−1492.20			−0.0332014
$213$	7978.82	−	7978.82i	0.175865	−	0.175865i
$214$	−32262.2	−	32262.2i	−0.704476	−	0.704476i
$215$	−24383.5	+	16923.1i	−0.527495	+	0.366102i
$216$	−11511.8	+	11511.8i	−0.246738	+	0.246738i
$217$			56125.7i			1.19191i
$218$	40582.6			0.853939
$219$	−7728.31	+	7728.31i	−0.161137	+	0.161137i
$220$	298.878	+	53.9807i	0.00617517	+	0.00111530i
$221$	40843.6	+	6302.74i	0.836257	+	0.129046i
$222$		−	2689.37i		−	0.0545688i
$223$	53297.1	−	53297.1i	1.07175	−	1.07175i	0.0745328	−	0.997219i	$-0.476253\pi$
$223$	53297.1	−	53297.1i	1.07175	−	1.07175i	0.997219	−	0.0745328i	$-0.0237465\pi$
$224$	−1723.72			−0.0343535
$225$	17163.3	−	45964.6i	0.339028	−	0.907942i
$226$	11749.8	+	11749.8i	0.230046	+	0.230046i
$227$	−26798.5	+	26798.5i	−0.520067	+	0.520067i	−0.917591	−	0.397525i	$-0.869869\pi$
$227$	−26798.5	+	26798.5i	−0.520067	+	0.520067i	0.397525	+	0.917591i	$0.369869\pi$
$228$	110.690	+	110.690i	0.00212931	+	0.00212931i
$229$	8256.91	−	8256.91i	0.157452	−	0.157452i	−0.623985	−	0.781436i	$-0.714487\pi$
$229$	8256.91	−	8256.91i	0.157452	−	0.157452i	0.781436	+	0.623985i	$0.214487\pi$
$230$	3973.28	−	21999.1i	0.0751092	−	0.415862i
$231$			2794.29i			0.0523657i
$232$	−48239.2	−	48239.2i	−0.896240	−	0.896240i
$233$	−61369.8			−1.13043			−0.565214	−	0.824945i	$-0.691206\pi$
$233$	−61369.8			−1.13043			−0.565214	+	0.824945i	$0.691206\pi$
$234$	−42399.8	+	31063.4i	−0.774342	+	0.567306i
$235$	31264.0	+	5646.63i	0.566121	+	0.102248i
$236$	1276.73	+	1276.73i	0.0229233	+	0.0229233i
$237$			14324.6i			0.255027i
$238$	42896.4			0.757299
$239$	−31009.5	−	31009.5i	−0.542875	−	0.542875i	0.381496	−	0.924371i	$-0.375409\pi$
$239$	−31009.5	−	31009.5i	−0.542875	−	0.542875i	−0.924371	+	0.381496i	$0.875409\pi$
$240$	−5654.42	−	8147.13i	−0.0981669	−	0.141443i
$241$	−21471.4	+	21471.4i	−0.369680	+	0.369680i	−0.867360	−	0.497680i	$-0.834185\pi$
$241$	−21471.4	+	21471.4i	−0.369680	+	0.369680i	0.497680	+	0.867360i	$0.334185\pi$
$242$	−36547.0	−	36547.0i	−0.624053	−	0.624053i
$243$		−	29833.7i		−	0.505236i
$244$		−	362.913i		−	0.00609569i
$245$	−6279.25	−	9047.42i	−0.104611	−	0.150727i
$246$		−	8262.23i		−	0.136530i
$247$	32528.3	+	44399.3i	0.533172	+	0.727750i
$248$			81878.7i			1.33127i
$249$	10694.4	+	10694.4i	0.172487	+	0.172487i
$250$	53219.9	+	31616.8i	0.851519	+	0.505870i
$251$		−	76061.4i		−	1.20730i	−0.797248	−	0.603652i	$-0.793712\pi$
$251$		−	76061.4i		−	1.20730i	0.797248	−	0.603652i	$-0.206288\pi$
$252$	747.632	−	747.632i	0.0117730	−	0.0117730i
$253$	−6374.09	+	6374.09i	−0.0995811	+	0.0995811i
$254$	−58995.5	+	58995.5i	−0.914431	+	0.914431i
$255$	−5507.97	−	7936.12i	−0.0847054	−	0.122047i
$256$	−3736.44			−0.0570135
$257$	72747.0			1.10141			0.550705	−	0.834700i	$-0.314359\pi$
$257$	72747.0			1.10141			0.550705	+	0.834700i	$0.314359\pi$
$258$	−5255.45	−	5255.45i	−0.0789534	−	0.0789534i
$259$			19021.3i			0.283557i
$260$	563.176	+	1155.21i	0.00833101	+	0.0170888i
$261$	82910.9			1.21711
$262$	19032.9	−	19032.9i	0.277269	−	0.277269i
$263$			38370.1i			0.554730i	0.960765	+	0.277365i	$0.0894611\pi$
$263$			38370.1i			0.554730i	−0.960765	+	0.277365i	$0.910539\pi$
$264$			4076.43i			0.0584888i
$265$	69926.0	+	100752.i	0.995742	+	1.43471i
$266$	40397.0	+	40397.0i	0.570934	+	0.570934i
$267$	4955.07	+	4955.07i	0.0695068	+	0.0695068i
$268$	397.075	+	397.075i	0.00552844	+	0.00552844i
$269$	32862.5			0.454146			0.227073	−	0.973878i	$-0.427084\pi$
$269$	32862.5			0.454146			0.227073	+	0.973878i	$0.427084\pi$
$270$	24565.7	+	4436.85i	0.336979	+	0.0608621i
$271$	22620.0	−	22620.0i	0.308003	−	0.308003i	−0.536132	−	0.844134i	$-0.680115\pi$
$271$	22620.0	−	22620.0i	0.308003	−	0.308003i	0.844134	+	0.536132i	$0.180115\pi$
$272$	61389.1			0.829762
$273$	−9538.19	+	6987.97i	−0.127980	+	0.0937618i
$274$	93792.8			1.24930
$275$	−10361.0	−	22709.6i	−0.137004	−	0.300292i
$276$	−108.487			−0.00142416
$277$	−52062.1			−0.678519			−0.339260	−	0.940693i	$-0.610177\pi$
$277$	−52062.1			−0.678519			−0.339260	+	0.940693i	$0.610177\pi$
$278$	26731.7	−	26731.7i	0.345889	−	0.345889i
$279$	−70364.2	−	70364.2i	−0.903948	−	0.903948i
$280$	40767.8	+	58740.0i	0.519997	+	0.749235i
$281$	82293.7	−	82293.7i	1.04221	−	1.04221i	0.0431376	−	0.999069i	$-0.486265\pi$
$281$	82293.7	−	82293.7i	1.04221	−	1.04221i	0.999069	−	0.0431376i	$-0.0137354\pi$
$282$			7955.48i			0.100039i
$283$	−27261.2			−0.340386			−0.170193	−	0.985411i	$-0.554439\pi$
$283$	−27261.2			−0.340386			−0.170193	+	0.985411i	$0.554439\pi$
$284$	−1535.94	+	1535.94i	−0.0190431	+	0.0190431i
$285$	2286.67	−	12660.7i	0.0281523	−	0.155873i
$286$	−4078.16	+	26427.7i	−0.0498577	+	0.323092i
$287$			58437.0i			0.709454i
$288$	2161.01	−	2161.01i	0.0260539	−	0.0260539i
$289$	−23721.8			−0.284022
$290$	−18592.2	+	102940.i	−0.221072	+	1.22402i
$291$	4131.79	+	4131.79i	0.0487924	+	0.0487924i
$292$	1487.71	−	1487.71i	0.0174483	−	0.0174483i
$293$	−23808.6	−	23808.6i	−0.277331	−	0.277331i	0.554712	−	0.832043i	$-0.312829\pi$
$293$	−23808.6	−	23808.6i	−0.277331	−	0.277331i	−0.832043	+	0.554712i	$0.812829\pi$
$294$	1950.02	−	1950.02i	0.0225603	−	0.0225603i
$295$	26375.1	−	146033.i	0.303075	−	1.67806i
$296$			27749.2i			0.316714i
$297$	−7117.76	−	7117.76i	−0.0806920	−	0.0806920i
$298$	−165728.			−1.86622
$299$	−37698.1	−	5817.34i	−0.421674	−	0.0650702i
$300$	105.087	−	281.430i	0.00116763	−	0.00312700i
$301$	37170.7	+	37170.7i	0.410268	+	0.410268i
$302$		−	116987.i		−	1.28270i
$303$	15239.6			0.165993
$304$	57812.2	+	57812.2i	0.625565	+	0.625565i
$305$	−24503.6	+	17006.4i	−0.263409	+	0.182816i
$306$	−53778.9	+	53778.9i	−0.574340	+	0.574340i
$307$	−25349.8	−	25349.8i	−0.268966	−	0.268966i	0.559717	−	0.828684i	$-0.310910\pi$
$307$	−25349.8	−	25349.8i	−0.268966	−	0.268966i	−0.828684	+	0.559717i	$0.810910\pi$
$308$		−	537.906i		−	0.00567028i
$309$		−	2592.90i		−	0.0271561i
$310$	103142.	−	71584.1i	1.07327	−	0.744892i
$311$			86195.1i			0.891173i	0.895239	+	0.445586i	$0.147005\pi$
$311$			86195.1i			0.891173i	−0.895239	+	0.445586i	$0.852995\pi$
$312$	−13914.8	+	10194.4i	−0.142944	+	0.104725i
$313$		−	98374.5i		−	1.00414i	−0.864827	−	0.502069i	$-0.832572\pi$
$313$		−	98374.5i		−	1.00414i	0.864827	−	0.502069i	$-0.167428\pi$
$314$	−118866.	−	118866.i	−1.20558	−	1.20558i
$315$	−85514.2	−	15444.8i	−0.861821	−	0.155654i
$316$		−	2757.52i		−	0.0276150i
$317$	93303.3	−	93303.3i	0.928493	−	0.928493i	−0.0691159	−	0.997609i	$-0.522018\pi$
$317$	93303.3	−	93303.3i	0.928493	−	0.928493i	0.997609	+	0.0691159i	$0.0220178\pi$
$318$	−21715.5	+	21715.5i	−0.214741	+	0.214741i
$319$	29826.3	−	29826.3i	0.293102	−	0.293102i
$320$	59452.8	+	85662.2i	0.580594	+	0.836545i
$321$	18197.7			0.176606
$322$	−39592.8			−0.381860
$323$	56314.9	+	56314.9i	0.539782	+	0.539782i
$324$			1813.08i			0.0172714i
$325$	51607.6	−	92159.1i	0.488593	−	0.872512i
$326$	−85205.7			−0.801739
$327$	−11445.4	+	11445.4i	−0.107038	+	0.107038i
$328$			85250.6i			0.792410i
$329$		−	56267.4i		−	0.519834i
$330$	5135.03	−	3563.90i	0.0471536	−	0.0327264i
$331$	−82070.2	−	82070.2i	−0.749082	−	0.749082i	0.225225	−	0.974307i	$-0.427688\pi$
$331$	−82070.2	−	82070.2i	−0.749082	−	0.749082i	−0.974307	+	0.225225i	$0.927688\pi$
$332$	−2058.69	−	2058.69i	−0.0186773	−	0.0186773i
$333$	−23846.8	−	23846.8i	−0.215052	−	0.215052i
$334$	−14239.7			−0.127646
$335$	8202.89	−	45417.4i	0.0730933	−	0.404700i
$336$	−12419.7	+	12419.7i	−0.110010	+	0.110010i
$337$	172922.			1.52262			0.761310	−	0.648388i	$-0.224556\pi$
$337$	172922.			1.52262			0.761310	+	0.648388i	$0.224556\pi$
$338$	−100409.	+	52169.8i	−0.878895	+	0.456653i
$339$	−6627.57			−0.0576707
$340$	1060.30	+	1527.72i	0.00917211	+	0.0132156i
$341$	−50625.6			−0.435373
$342$	−101291.			−0.865998
$343$	−88964.5	+	88964.5i	−0.756186	+	0.756186i
$344$	54226.3	+	54226.3i	0.458240	+	0.458240i
$345$	5083.78	+	7324.93i	0.0427119	+	0.0615411i
$346$	−73014.8	+	73014.8i	−0.609900	+	0.609900i
$347$			227287.i			1.88762i	0.330483	+	0.943812i	$0.392788\pi$
$347$			227287.i			1.88762i	−0.330483	+	0.943812i	$0.607212\pi$
$348$	507.643			0.00419179
$349$	−29999.9	+	29999.9i	−0.246303	+	0.246303i	−0.819452	−	0.573149i	$-0.805722\pi$
$349$	−29999.9	+	29999.9i	−0.246303	+	0.246303i	0.573149	+	0.819452i	$0.305722\pi$
$350$	38351.9	−	102709.i	0.313077	−	0.838443i
$351$	6496.06	−	42096.4i	0.0527274	−	0.341689i
$352$		−	1554.80i		−	0.0125485i
$353$	−113770.	+	113770.i	−0.913017	+	0.913017i	−0.996508	−	0.0834915i	$-0.973393\pi$
$353$	−113770.	+	113770.i	−0.913017	+	0.913017i	0.0834915	+	0.996508i	$0.473393\pi$
$354$	37159.7			0.296528
$355$	175681.	+	31729.9i	1.39402	+	0.251775i
$356$	−953.861	−	953.861i	−0.00752636	−	0.00752636i
$357$	−12098.0	+	12098.0i	−0.0949242	+	0.0949242i
$358$	−6779.86	−	6779.86i	−0.0528999	−	0.0528999i
$359$	−42823.9	+	42823.9i	−0.332275	+	0.332275i	−0.853450	−	0.521175i	$-0.825494\pi$
$359$	−42823.9	+	42823.9i	−0.332275	+	0.332275i	0.521175	+	0.853450i	$0.325494\pi$
$360$	−124752.	−	22531.6i	−0.962593	−	0.173855i
$361$		−	24253.8i		−	0.186108i
$362$	−3424.70	−	3424.70i	−0.0261340	−	0.0261340i
$363$	20614.6			0.156445
$364$	1836.12	−	1345.20i	0.0138579	−	0.0101528i
$365$	−170165.	−	30733.7i	−1.27727	−	0.230690i
$366$	−5281.34	−	5281.34i	−0.0394259	−	0.0394259i
$367$		−	61251.0i		−	0.454759i	−0.973806	−	0.227379i	$-0.926984\pi$
$367$		−	61251.0i		−	0.454759i	0.973806	−	0.227379i	$-0.0730157\pi$
$368$	−56661.3			−0.418399
$369$	−73261.9	−	73261.9i	−0.538054	−	0.538054i
$370$	34955.3	−	24260.3i	0.255334	−	0.177212i
$371$	153589.	−	153589.i	1.11587	−	1.11587i
$372$	−430.823	−	430.823i	−0.00311324	−	0.00311324i
$373$			66992.3i			0.481512i	0.970586	+	0.240756i	$0.0773954\pi$
$373$			66992.3i			0.481512i	−0.970586	+	0.240756i	$0.922605\pi$
$374$			38692.8i			0.276622i
$375$	−23926.3	+	6092.68i	−0.170143	+	0.0433257i
$376$		−	82085.5i		−	0.580618i
$377$	176401.	+	27221.1i	1.24113	+	0.191524i
$378$		−	44212.2i		−	0.309427i
$379$	162680.	+	162680.i	1.13254	+	1.13254i	0.989753	+	0.142791i	$0.0456075\pi$
$379$	162680.	+	162680.i	1.13254	+	1.13254i	0.142791	+	0.989753i	$0.454392\pi$
$380$	−440.189	+	2437.22i	−0.00304840	+	0.0168783i
$381$		−	33276.7i		−	0.229240i
$382$	82266.4	−	82266.4i	0.563762	−	0.563762i
$383$	26325.5	−	26325.5i	0.179464	−	0.179464i	−0.611658	−	0.791122i	$-0.709497\pi$
$383$	26325.5	−	26325.5i	0.179464	−	0.179464i	0.791122	+	0.611658i	$0.209497\pi$
$384$	−17767.1	+	17767.1i	−0.120491	+	0.120491i
$385$	−36318.9	+	25206.7i	−0.245026	+	0.170057i
$386$	−12546.2			−0.0842046
$387$	−93201.0			−0.622299
$388$	−795.378	−	795.378i	−0.00528336	−	0.00528336i
$389$			4429.52i			0.0292724i	0.999893	+	0.0146362i	$0.00465901\pi$
$389$			4429.52i			0.0292724i	−0.999893	+	0.0146362i	$0.995341\pi$
$390$	25007.0	+	8615.59i	0.164411	+	0.0566442i
$391$	−55193.8			−0.361025
$392$	−20120.5	+	20120.5i	−0.130938	+	0.130938i
$393$			10735.6i			0.0695090i
$394$			2557.69i			0.0164762i
$395$	−186185.	+	129220.i	−1.19330	+	0.828199i
$396$	674.368	+	674.368i	0.00430037	+	0.00430037i
$397$	−77134.6	−	77134.6i	−0.489405	−	0.489405i	0.418713	−	0.908118i	$-0.362481\pi$
$397$	−77134.6	−	77134.6i	−0.489405	−	0.489405i	−0.908118	+	0.418713i	$0.862481\pi$
$398$	93624.9	+	93624.9i	0.591051	+	0.591051i
$399$	−22786.2			−0.143128
$400$	54885.5	−	146987.i	0.343034	−	0.918671i
$401$	−144460.	+	144460.i	−0.898377	+	0.898377i	−0.995293	−	0.0969157i	$-0.969102\pi$
$401$	−144460.	+	144460.i	−0.898377	+	0.898377i	0.0969157	+	0.995293i	$0.469102\pi$
$402$	11557.0			0.0715141
$403$	−126605.	−	172809.i	−0.779544	−	1.06403i
$404$	−2933.66			−0.0179741
$405$	122418.	−	84962.4i	0.746335	−	0.517985i
$406$	185267.			1.12395
$407$	−17157.3			−0.103576
$408$	−17649.1	+	17649.1i	−0.106024	+	0.106024i
$409$	217207.	+	217207.i	1.29846	+	1.29846i	0.929412	+	0.369043i	$0.120314\pi$
$409$	217207.	+	217207.i	1.29846	+	1.29846i	0.369043	+	0.929412i	$0.379686\pi$
$410$	107389.	−	74532.1i	0.638840	−	0.443379i
$411$	−26452.2	+	26452.2i	−0.156595	+	0.156595i
$412$			499.138i			0.00294053i
$413$	−262822.			−1.54086
$414$	49637.1	−	49637.1i	0.289605	−	0.289605i
$415$	−42529.0	+	235473.i	−0.246938	+	1.36724i
$416$	5307.26	−	3888.26i	0.0306679	−	0.0224682i
$417$			15078.2i			0.0867114i
$418$	−36438.3	+	36438.3i	−0.208548	+	0.208548i
$419$	188017.			1.07095			0.535474	−	0.844552i	$-0.320133\pi$
$419$	188017.			1.07095			0.535474	+	0.844552i	$0.320133\pi$
$420$	−523.582	−	94.5647i	−0.00296815	−	0.000536081i
$421$	−57303.2	−	57303.2i	−0.323306	−	0.323306i	0.526728	−	0.850034i	$-0.323419\pi$
$421$	−57303.2	−	57303.2i	−0.323306	−	0.323306i	−0.850034	+	0.526728i	$0.823419\pi$
$422$	242039.	−	242039.i	1.35913	−	1.35913i
$423$	70541.9	+	70541.9i	0.394245	+	0.394245i
$424$	224063.	−	224063.i	1.24634	−	1.24634i
$425$	53464.0	−	143181.i	0.295994	−	0.792695i
$426$			44703.9i			0.246335i
$427$	37353.8	+	37353.8i	0.204870	+	0.204870i
$428$	−3503.09			−0.0191233
$429$	−6303.18	−	8603.49i	−0.0342488	−	0.0467477i
$430$	20899.7	−	115717.i	0.113032	−	0.625833i
$431$	18374.3	+	18374.3i	0.0989138	+	0.0989138i	0.754832	−	0.655918i	$-0.227718\pi$
$431$	18374.3	+	18374.3i	0.0989138	+	0.0989138i	−0.655918	+	0.754832i	$0.727718\pi$
$432$		−	63272.1i		−	0.339035i
$433$	14413.5			0.0768763			0.0384381	−	0.999261i	$-0.487762\pi$
$433$	14413.5			0.0768763			0.0384381	+	0.999261i	$0.487762\pi$
$434$	−157231.	−	157231.i	−0.834755	−	0.834755i
$435$	−23788.6	−	34275.6i	−0.125716	−	0.181137i
$436$	2203.27	−	2203.27i	0.0115903	−	0.0115903i
$437$	−51977.8	−	51977.8i	−0.272179	−	0.272179i
$438$		−	43300.3i		−	0.225706i
$439$			350950.i			1.82103i	0.413481	+	0.910513i	$0.364313\pi$
$439$			350950.i			1.82103i	−0.413481	+	0.910513i	$0.635687\pi$
$440$	−52983.8	+	36772.7i	−0.273676	+	0.189942i
$441$		−	34582.0i		−	0.177817i
$442$	−132076.	+	96763.2i	−0.676053	+	0.495297i
$443$		−	269427.i		−	1.37288i	−0.727185	−	0.686441i	$-0.759172\pi$
$443$		−	269427.i		−	1.37288i	0.727185	−	0.686441i	$-0.240828\pi$
$444$	−146.008	−	146.008i	−0.000740648	−	0.000740648i
$445$	−19705.1	+	109103.i	−0.0995084	+	0.550954i
$446$			298614.i			1.50121i
$447$	46739.9	−	46739.9i	0.233923	−	0.233923i
$448$	130585.	−	130585.i	0.650636	−	0.650636i
$449$	110523.	−	110523.i	0.548227	−	0.548227i	−0.377701	−	0.925928i	$-0.623285\pi$
$449$	110523.	−	110523.i	0.548227	−	0.548227i	0.925928	+	0.377701i	$0.123285\pi$
$450$	80684.2	+	176847.i	0.398441	+	0.873319i
$451$	−52710.4			−0.259145
$452$	1275.82			0.00624472
$453$	32993.6	+	32993.6i	0.160780	+	0.160780i
$454$		−	150147.i		−	0.728460i
$455$	−176869.	−	60936.2i	−0.854336	−	0.294342i
$456$	−33241.5			−0.159864
$457$	−257075.	+	257075.i	−1.23091	+	1.23091i	−0.267302	+	0.963613i	$0.586132\pi$
$457$	−257075.	+	257075.i	−1.23091	+	1.23091i	−0.963613	+	0.267302i	$0.913868\pi$
$458$			46262.0i			0.220543i
$459$		−	61633.4i		−	0.292544i
$460$	−978.638	−	1410.06i	−0.00462494	−	0.00666382i
$461$	133877.	+	133877.i	0.629948	+	0.629948i	0.948055	−	0.318107i	$-0.103047\pi$
$461$	133877.	+	133877.i	0.629948	+	0.629948i	−0.318107	+	0.948055i	$0.603047\pi$
$462$	−7827.95	−	7827.95i	−0.0366745	−	0.0366745i
$463$	216280.	+	216280.i	1.00891	+	1.00891i	0.999960	+	0.00895337i	$0.00284998\pi$
$463$	216280.	+	216280.i	1.00891	+	1.00891i	0.00895337	+	0.999960i	$0.497150\pi$
$464$	265136.			1.23149
$465$	−8900.07	+	49277.5i	−0.0411611	+	0.227899i
$466$	171922.	−	171922.i	0.791698	−	0.791698i
$467$	346548.			1.58902			0.794511	−	0.607250i	$-0.207727\pi$
$467$	346548.			1.58902			0.794511	+	0.607250i	$0.207727\pi$
$468$	−615.465	+	3988.39i	−0.00281003	+	0.0182098i
$469$	−81740.0			−0.371611
$470$	−103402.	+	71764.9i	−0.468094	+	0.324875i
$471$	67046.8			0.302229
$472$	−383417.			−1.72103
$473$	−33528.1	+	33528.1i	−0.149860	+	0.149860i
$474$	−40129.2	−	40129.2i	−0.178609	−	0.178609i
$475$	185187.	−	84489.0i	0.820772	−	0.374467i
$476$	2328.89	−	2328.89i	0.0102786	−	0.0102786i
$477$			385106.i			1.69256i
$478$	173741.			0.760408
$479$	−290259.	+	290259.i	−1.26507	+	1.26507i	−0.316470	+	0.948603i	$0.602498\pi$
$479$	−290259.	+	290259.i	−1.26507	+	1.26507i	−0.948603	+	0.316470i	$0.897502\pi$
$480$	−1513.40	−	273.337i	−0.00656858	−	0.00118636i
$481$	−42907.1	−	58565.9i	−0.185455	−	0.253136i
$482$		−	120300.i		−	0.517813i
$483$	11166.3	−	11166.3i	0.0478646	−	0.0478646i
$484$	−3968.35			−0.0169402
$485$	−16431.1	+	90975.3i	−0.0698529	+	0.386759i
$486$	83576.4	+	83576.4i	0.353843	+	0.353843i
$487$	−138475.	+	138475.i	−0.583867	+	0.583867i	−0.935964	−	0.352097i	$-0.885469\pi$
$487$	−138475.	+	138475.i	−0.583867	+	0.583867i	0.352097	+	0.935964i	$0.385469\pi$
$488$	54493.4	+	54493.4i	0.228826	+	0.228826i
$489$	24030.4	−	24030.4i	0.100495	−	0.100495i
$490$	42936.3	+	7754.77i	0.178827	+	0.0322981i
$491$		−	268395.i		−	1.11330i	−0.830748	−	0.556649i	$-0.812087\pi$
$491$		−	268395.i		−	1.11330i	0.830748	−	0.556649i	$-0.187913\pi$
$492$	−448.565	−	448.565i	−0.00185308	−	0.00185308i
$493$	258269.			1.06262
$494$	−215506.	−	33255.6i	−0.883090	−	0.136273i
$495$	13931.3	−	77134.2i	0.0568566	−	0.314801i
$496$	−225014.	−	225014.i	−0.914630	−	0.914630i
$497$		−	316181.i		−	1.28004i
$498$	−59918.6			−0.241603
$499$	−272555.	−	272555.i	−1.09460	−	1.09460i	−0.995031	−	0.0995639i	$-0.968255\pi$
$499$	−272555.	−	272555.i	−1.09460	−	1.09460i	−0.0995639	−	0.995031i	$-0.531745\pi$
$500$	4605.87	−	1172.85i	0.0184235	−	0.00469141i
$501$	4015.98	−	4015.98i	0.0159999	−	0.0159999i
$502$	213079.	+	213079.i	0.845539	+	0.845539i
$503$		−	2947.95i		−	0.0116516i	−0.999983	−	0.00582579i	$-0.998146\pi$
$503$		−	2947.95i		−	0.0116516i	0.999983	−	0.00582579i	$-0.00185442\pi$
$504$			224522.i			0.883890i
$505$	137474.	+	198078.i	0.539060	+	0.776702i
$506$		−	35712.9i		−	0.139484i
$507$	13604.7	−	43031.4i	0.0529263	−	0.167405i
$508$			6405.84i			0.0248227i
$509$	−160741.	−	160741.i	−0.620428	−	0.620428i	0.325213	−	0.945641i	$-0.394564\pi$
$509$	−160741.	−	160741.i	−0.620428	−	0.620428i	−0.945641	+	0.325213i	$0.894564\pi$
$510$	37662.4	+	6802.25i	0.144800	+	0.0261525i
$511$			306254.i			1.17284i
$512$	190370.	−	190370.i	0.726204	−	0.726204i
$513$	58042.2	−	58042.2i	0.220551	−	0.220551i
$514$	−203794.	+	203794.i	−0.771375	+	0.771375i
$515$	33701.4	−	23390.0i	0.127067	−	0.0881894i
$516$	−570.647			−0.00214323
$517$	50753.5			0.189882
$518$	−53286.5	−	53286.5i	−0.198590	−	0.198590i
$519$		−	41184.4i		−	0.152897i
$520$	−258025.	−	88896.5i	−0.954233	−	0.328759i
$521$	−410680.			−1.51296			−0.756481	−	0.654016i	$-0.773083\pi$
$521$	−410680.			−1.51296			−0.756481	+	0.654016i	$0.773083\pi$
$522$	−232267.	+	232267.i	−0.852408	+	0.852408i
$523$		−	349117.i		−	1.27634i	−0.769894	−	0.638172i	$-0.779691\pi$
$523$		−	349117.i		−	1.27634i	0.769894	−	0.638172i	$-0.220309\pi$
$524$		−	2066.63i		−	0.00752661i
$525$	18150.6	+	39783.2i	0.0658524	+	0.144338i
$526$	−107490.	−	107490.i	−0.388507	−	0.388507i
$527$	−219186.	−	219186.i	−0.789208	−	0.789208i
$528$	−11202.6	−	11202.6i	−0.0401837	−	0.0401837i
$529$	−228898.			−0.817957
$530$	−478140.	−	86357.5i	−1.70217	−	0.307431i
$531$	329498.	−	329498.i	1.16859	−	1.16859i
$532$	4386.38			0.0154983
$533$	−131819.	−	179925.i	−0.464005	−	0.633341i
$534$	−27762.4			−0.0973585
$535$	164158.	+	236526.i	0.573527	+	0.826363i
$536$	−119246.			−0.415063
$537$	3824.22			0.0132616
$538$	−92061.3	+	92061.3i	−0.318063	+	0.318063i
$539$	−12440.5	−	12440.5i	−0.0428214	−	0.0428214i
$540$	1574.58	−	1092.82i	0.00539979	−	0.00374766i
$541$	−99242.2	+	99242.2i	−0.339080	+	0.339080i	−0.856021	−	0.516941i	$-0.827071\pi$
$541$	−99242.2	+	99242.2i	−0.339080	+	0.339080i	0.516941	+	0.856021i	$0.327071\pi$
$542$			126736.i			0.431421i
$543$	1931.72			0.00655157
$544$	6731.59	−	6731.59i	0.0227468	−	0.0227468i
$545$	−252010.	−	45515.8i	−0.848447	−	0.153239i
$546$	7144.21	−	46296.6i	0.0239645	−	0.155297i
$547$		−	441464.i		−	1.47544i	−0.675108	−	0.737719i	$-0.735903\pi$
$547$		−	441464.i		−	1.47544i	0.675108	−	0.737719i	$-0.264097\pi$
$548$	5092.10	−	5092.10i	0.0169565	−	0.0169565i
$549$	−93660.2			−0.310749
$550$	92644.3	+	34593.6i	0.306262	+	0.114359i
$551$	243220.	+	243220.i	0.801119	+	0.801119i
$552$	16289.9	−	16289.9i	0.0534613	−	0.0534613i
$553$	283825.	+	283825.i	0.928112	+	0.928112i
$554$	145847.	−	145847.i	0.475203	−	0.475203i
$555$	−3016.28	+	16700.4i	−0.00979234	+	0.0542178i
$556$		−	2902.58i		−	0.00938932i
$557$	107555.	+	107555.i	0.346672	+	0.346672i	0.858868	−	0.512196i	$-0.171168\pi$
$557$	107555.	+	107555.i	0.346672	+	0.346672i	−0.512196	+	0.858868i	$0.671168\pi$
$558$	394238.			1.26617
$559$	−198294.	−	30599.6i	−0.634580	−	0.0979247i
$560$	−273461.	−	49390.1i	−0.872005	−	0.157494i
$561$	−10912.4	−	10912.4i	−0.0346734	−	0.0346734i
$562$			461077.i			1.45983i
$563$	308136.			0.972134			0.486067	−	0.873922i	$-0.338431\pi$
$563$	308136.			0.972134			0.486067	+	0.873922i	$0.338431\pi$
$564$	431.911	+	431.911i	0.00135780	+	0.00135780i
$565$	−59786.1	−	86142.4i	−0.187285	−	0.269848i
$566$	76369.8	−	76369.8i	0.238390	−	0.238390i
$567$	−186616.	−	186616.i	−0.580474	−	0.580474i
$568$		−	461260.i		−	1.42971i
$569$		−	151305.i		−	0.467337i	−0.972316	−	0.233668i	$-0.924927\pi$
$569$		−	151305.i		−	0.467337i	0.972316	−	0.233668i	$-0.0750730\pi$
$570$	29062.1	+	41873.9i	0.0894492	+	0.128882i
$571$			111312.i			0.341405i	0.985323	+	0.170702i	$0.0546037\pi$
$571$			111312.i			0.341405i	−0.985323	+	0.170702i	$0.945396\pi$
$572$	1213.38	+	1656.19i	0.00370854	+	0.00506195i
$573$			46402.9i			0.141330i
$574$	−163706.	−	163706.i	−0.496868	−	0.496868i
$575$	−49346.5	+	132154.i	−0.149252	+	0.399708i
$576$			327427.i			0.986892i
$577$	33656.5	−	33656.5i	0.101092	−	0.101092i	−0.654752	−	0.755844i	$-0.727227\pi$
$577$	33656.5	−	33656.5i	0.101092	−	0.101092i	0.755844	+	0.654752i	$0.227227\pi$
$578$	66454.5	−	66454.5i	0.198916	−	0.198916i
$579$	3538.37	−	3538.37i	0.0105547	−	0.0105547i
$580$	4579.35	+	6598.13i	0.0136128	+	0.0196139i
$581$	423791.			1.25545
$582$	−23149.7			−0.0683438
$583$	138538.	+	138538.i	0.407598	+	0.407598i
$584$			446777.i			1.30998i
$585$	298134.	−	145344.i	0.871164	−	0.424702i
$586$	133395.			0.388459
$587$	−180184.	+	180184.i	−0.522927	+	0.522927i	−0.918454	−	0.395527i	$-0.870562\pi$
$587$	−180184.	+	180184.i	−0.522927	+	0.522927i	0.395527	+	0.918454i	$0.370562\pi$
$588$		−	211.737i		−	0.000612410i
$589$		−	412829.i		−	1.18998i
$590$	335210.	+	482986.i	0.962971	+	1.38749i
$591$	−721.341	−	721.341i	−0.00206522	−	0.00206522i
$592$	−76258.5	−	76258.5i	−0.217593	−	0.217593i
$593$	−113829.	−	113829.i	−0.323702	−	0.323702i	0.526483	−	0.850185i	$-0.323510\pi$
$593$	−113829.	−	113829.i	−0.323702	−	0.323702i	−0.850185	+	0.526483i	$0.823510\pi$
$594$	39879.6			0.113026
$595$	−266378.	−	48110.9i	−0.752428	−	0.135897i
$596$	−8997.53	+	8997.53i	−0.0253298	+	0.0253298i
$597$	−52809.7			−0.148172
$598$	121905.	−	89311.1i	0.340893	−	0.249749i
$599$	548580.			1.52893			0.764463	−	0.644668i	$-0.223004\pi$
$599$	548580.			1.52893			0.764463	+	0.644668i	$0.223004\pi$
$600$	26478.9	+	58037.6i	0.0735525	+	0.161215i
$601$	−228479.			−0.632553			−0.316276	−	0.948667i	$-0.602433\pi$
$601$	−228479.			−0.632553			−0.316276	+	0.948667i	$0.602433\pi$
$602$	−208261.			−0.574665
$603$	102477.	−	102477.i	0.281832	−	0.281832i
$604$	−6351.33	−	6351.33i	−0.0174097	−	0.0174097i
$605$	185960.	+	267939.i	0.508053	+	0.732025i
$606$	−42692.5	+	42692.5i	−0.116254	+	0.116254i
$607$			412092.i			1.11845i	0.829016	+	0.559225i	$0.188901\pi$
$607$			412092.i			1.11845i	−0.829016	+	0.559225i	$0.811099\pi$
$608$	12678.7			0.0342980
$609$	−52250.5	+	52250.5i	−0.140882	+	0.140882i
$610$	21002.7	−	116287.i	0.0564436	−	0.312514i
$611$	126925.	+	173245.i	0.339988	+	0.464064i
$612$			5839.41i			0.0155907i
$613$	28178.5	−	28178.5i	0.0749889	−	0.0749889i	−0.668618	−	0.743606i	$-0.733114\pi$
$613$	28178.5	−	28178.5i	0.0749889	−	0.0749889i	0.743606	+	0.668618i	$0.233114\pi$
$614$	142031.			0.376743
$615$	−9266.58	+	51306.8i	−0.0245002	+	0.135652i
$616$	80769.6	+	80769.6i	0.212856	+	0.212856i
$617$	34002.1	−	34002.1i	0.0893173	−	0.0893173i	−0.661036	−	0.750354i	$-0.729883\pi$
$617$	34002.1	−	34002.1i	0.0893173	−	0.0893173i	0.750354	+	0.661036i	$0.229883\pi$
$618$	7263.77	+	7263.77i	0.0190189	+	0.0190189i
$619$	253173.	−	253173.i	0.660749	−	0.660749i	−0.294808	−	0.955557i	$-0.595256\pi$
$619$	253173.	−	253173.i	0.660749	−	0.660749i	0.955557	+	0.294808i	$0.0952556\pi$
$620$	1713.28	−	9486.03i	0.00445703	−	0.0246775i
$621$			56886.7i			0.147512i
$622$	−241468.	−	241468.i	−0.624135	−	0.624135i
$623$	196357.			0.505907
$624$	10224.1	−	66255.1i	0.0262576	−	0.170157i
$625$	−295025.	−	256024.i	−0.755264	−	0.655420i
$626$	275587.	+	275587.i	0.703251	+	0.703251i
$627$		−	20553.2i		−	0.0522811i
$628$	−12906.6			−0.0327261
$629$	−74283.4	−	74283.4i	−0.187755	−	0.187755i
$630$	282828.	−	196293.i	0.712592	−	0.494566i
$631$	−2133.44	+	2133.44i	−0.00535824	+	0.00535824i	−0.709781	−	0.704423i	$-0.751206\pi$
$631$	−2133.44	+	2133.44i	−0.00535824	+	0.00535824i	0.704423	+	0.709781i	$0.251206\pi$
$632$	414057.	+	414057.i	1.03663	+	1.03663i
$633$			136524.i			0.340722i
$634$			522762.i			1.30055i
$635$	432517.	−	300183.i	1.07264	−	0.744456i
$636$			2357.91i			0.00582926i
$637$	11353.9	−	73576.6i	0.0279812	−	0.181326i
$638$			167112.i			0.410549i
$639$	396393.	+	396393.i	0.970789	+	0.970789i
$640$	−391203.	−	70655.6i	−0.955085	−	0.172499i
$641$		−	526216.i		−	1.28070i	−0.768083	−	0.640350i	$-0.778789\pi$
$641$		−	526216.i		−	1.28070i	0.768083	−	0.640350i	$-0.221211\pi$
$642$	−50979.2	+	50979.2i	−0.123687	+	0.123687i
$643$	41559.7	−	41559.7i	0.100519	−	0.100519i	−0.655059	−	0.755578i	$-0.727356\pi$
$643$	41559.7	−	41559.7i	0.100519	−	0.100519i	0.755578	+	0.655059i	$0.227356\pi$
$644$	−2149.53	+	2149.53i	−0.00518289	+	0.00518289i
$645$	26741.0	+	38529.6i	0.0642774	+	0.0926137i
$646$	−315522.			−0.756075
$647$	453014.			1.08219			0.541095	−	0.840962i	$-0.318010\pi$
$647$	453014.			1.08219			0.541095	+	0.840962i	$0.318010\pi$
$648$	−272244.	−	272244.i	−0.648348	−	0.648348i
$649$		−	237067.i		−	0.562836i
$650$	113601.	+	402750.i	0.268879	+	0.953254i
$651$	88687.1			0.209266
$652$	−4625.90	+	4625.90i	−0.0108818	+	0.0108818i
$653$			191158.i			0.448296i	0.974555	+	0.224148i	$0.0719600\pi$
$653$			191158.i			0.448296i	−0.974555	+	0.224148i	$0.928040\pi$
$654$		−	64126.7i		−	0.149928i
$655$	−139537.	+	96843.8i	−0.325242	+	0.225730i
$656$	−234280.	−	234280.i	−0.544412	−	0.544412i
$657$	−383948.	−	383948.i	−0.889491	−	0.889491i
$658$	157628.	+	157628.i	0.364068	+	0.364068i
$659$	418759.			0.964258			0.482129	−	0.876100i	$-0.339864\pi$
$659$	418759.			0.964258			0.482129	+	0.876100i	$0.339864\pi$
$660$	85.2978	−	472.273i	0.000195817	−	0.00108419i
$661$	−191867.	+	191867.i	−0.439135	+	0.439135i	−0.891721	−	0.452586i	$-0.850502\pi$
$661$	−191867.	+	191867.i	−0.439135	+	0.439135i	0.452586	+	0.891721i	$0.350502\pi$
$662$	459825.			1.04924
$663$	9959.30	−	64539.1i	0.0226570	−	0.146824i
$664$	618246.			1.40225
$665$	−205550.	−	296165.i	−0.464808	−	0.669715i
$666$	133610.			0.301224
$667$	−238379.			−0.535816
$668$	−773.084	+	773.084i	−0.00173250	+	0.00173250i
$669$	−84217.6	−	84217.6i	−0.188170	−	0.188170i
$670$	104253.	+	150213.i	0.232242	+	0.334624i
$671$	−33693.3	+	33693.3i	−0.0748339	+	0.0748339i
$672$			2723.74i			0.00603153i
$673$	−704470.			−1.55537			−0.777683	−	0.628657i	$-0.783605\pi$
$673$	−704470.			−1.55537			−0.777683	+	0.628657i	$0.783605\pi$
$674$	−484427.	+	484427.i	−1.06637	+	1.06637i
$675$	−147572.	−	55103.9i	−0.323890	−	0.120941i
$676$	−2618.92	+	8283.63i	−0.00573099	+	0.0181270i
$677$		−	369668.i		−	0.806556i	−0.915078	−	0.403278i	$-0.867871\pi$
$677$		−	369668.i		−	0.806556i	0.915078	−	0.403278i	$-0.132129\pi$
$678$	18566.6	−	18566.6i	0.0403898	−	0.0403898i
$679$	163733.			0.355137
$680$	−388605.	−	70186.4i	−0.840409	−	0.151787i
$681$	42345.7	+	42345.7i	0.0913094	+	0.0913094i
$682$	141823.	−	141823.i	0.304915	−	0.304915i
$683$	33460.7	+	33460.7i	0.0717288	+	0.0717288i	0.742061	−	0.670332i	$-0.233848\pi$
$683$	33460.7	+	33460.7i	0.0717288	+	0.0717288i	−0.670332	+	0.742061i	$0.733848\pi$
$684$	−5499.17	+	5499.17i	−0.0117540	+	0.0117540i
$685$	−582435.	−	105194.i	−1.24127	−	0.224187i
$686$		−	498453.i		−	1.05919i
$687$	−13047.2	−	13047.2i	−0.0276442	−	0.0276442i
$688$	−298042.			−0.629652
$689$	−126437.	+	819351.i	−0.266341	+	1.72596i
$690$	−34761.9	−	6278.39i	−0.0730139	−	0.0131871i
$691$	125638.	+	125638.i	0.263126	+	0.263126i	0.826323	−	0.563197i	$-0.190429\pi$
$691$	125638.	+	125638.i	0.263126	+	0.263126i	−0.563197	+	0.826323i	$0.690429\pi$
$692$			7928.09i			0.0165560i
$693$	−138822.			−0.289063
$694$	−636724.	−	636724.i	−1.32200	−	1.32200i
$695$	−195980.	+	136017.i	−0.405734	+	0.281595i
$696$	−76225.4	+	76225.4i	−0.157355	+	0.157355i
$697$	−228212.	−	228212.i	−0.469757	−	0.469757i
$698$		−	168084.i		−	0.344998i
$699$			96973.6i			0.198472i
$700$	−3494.02	−	7658.35i	−0.00713066	−	0.0156293i
$701$		−	415754.i		−	0.846058i	−0.906116	−	0.423029i	$-0.860967\pi$
$701$		−	415754.i		−	0.846058i	0.906116	−	0.423029i	$-0.139033\pi$
$702$	99731.1	+	136127.i	0.202375	+	0.276230i
$703$		−	139910.i		−	0.283099i
$704$	117789.	+	117789.i	0.237661	+	0.237661i
$705$	8922.54	−	49402.0i	0.0179519	−	0.0993953i
$706$		−	637434.i		−	1.27887i
$707$	301955.	−	301955.i	0.604092	−	0.604092i
$708$	2017.43	−	2017.43i	0.00402469	−	0.00402469i
$709$	−529347.	+	529347.i	−1.05305	+	1.05305i	−0.0545352	+	0.998512i	$0.517368\pi$
$709$	−529347.	+	529347.i	−1.05305	+	1.05305i	−0.998512	+	0.0545352i	$0.982632\pi$
$710$	−581043.	+	403266.i	−1.15263	+	0.799972i
$711$	−711657.			−1.40777
$712$	286455.			0.565063
$713$	202306.	+	202306.i	0.397950	+	0.397950i
$714$		−	67782.9i		−	0.132961i
$715$	54964.7	−	159537.i	0.107516	−	0.312067i
$716$	−736.171			−0.00143599
$717$	−48999.8	+	48999.8i	−0.0953139	+	0.0953139i
$718$		−	239935.i		−	0.465419i
$719$		−	460771.i		−	0.891307i	−0.895206	−	0.445653i	$-0.852971\pi$
$719$		−	460771.i		−	0.891307i	0.895206	−	0.445653i	$-0.147029\pi$
$720$	404755.	−	280915.i	0.780778	−	0.541889i
$721$	−51375.1	−	51375.1i	−0.0988285	−	0.0988285i
$722$	67945.0	+	67945.0i	0.130342	+	0.130342i
$723$	33928.1	+	33928.1i	0.0649056	+	0.0649056i
$724$	−371.861			−0.000709419
$725$	230908.	−	618388.i	0.439301	−	1.17648i
$726$	−57749.9	+	57749.9i	−0.109566	+	0.109566i
$727$	−631233.			−1.19432			−0.597161	−	0.802122i	$-0.703705\pi$
$727$	−631233.			−1.19432			−0.597161	+	0.802122i	$0.703705\pi$
$728$	−73714.8	+	477693.i	−0.139089	+	0.901335i
$729$	435658.			0.819768
$730$	562799.	−	390604.i	1.05611	−	0.732978i
$731$	−290323.			−0.543309
$732$	−573.458			−0.00107024
$733$	−524330.	+	524330.i	−0.975881	+	0.975881i	−0.999716	−	0.0238345i	$-0.992413\pi$
$733$	−524330.	+	524330.i	−0.975881	+	0.975881i	0.0238345	+	0.999716i	$0.492413\pi$
$734$	171589.	+	171589.i	0.318492	+	0.318492i
$735$	−14296.3	+	9922.18i	−0.0264636	+	0.0183667i
$736$	−6213.17	+	6213.17i	−0.0114698	+	0.0114698i
$737$		−	73729.8i		−	0.135740i
$738$	410474.			0.753655
$739$	442272.	−	442272.i	0.809843	−	0.809843i	−0.174767	−	0.984610i	$-0.555917\pi$
$739$	442272.	−	442272.i	0.809843	−	0.809843i	0.984610	+	0.174767i	$0.0559171\pi$
$740$	580.641	−	3214.87i	0.00106034	−	0.00587084i
$741$	70157.6	−	51399.6i	0.127773	−	0.0936103i
$742$			860533.i			1.56300i
$743$	−74177.7	+	74177.7i	−0.134368	+	0.134368i	−0.771092	−	0.636724i	$-0.780289\pi$
$743$	−74177.7	+	74177.7i	−0.134368	+	0.134368i	0.636724	+	0.771092i	$0.280289\pi$
$744$	129381.			0.233735
$745$	1.02914e6	+	185874.i	1.85422	+	0.334893i
$746$	−187673.	−	187673.i	−0.337229	−	0.337229i
$747$	−531303.	+	531303.i	−0.952141	+	0.952141i
$748$	2100.67	+	2100.67i	0.00375452	+	0.00375452i
$749$	360565.	−	360565.i	0.642717	−	0.642717i
$750$	49959.4	−	84095.6i	0.0888168	−	0.149503i
$751$			650953.i			1.15417i	0.816684	+	0.577085i	$0.195810\pi$
$751$			650953.i			1.15417i	−0.816684	+	0.577085i	$0.804190\pi$
$752$	225582.	+	225582.i	0.398904	+	0.398904i
$753$	−120189.			−0.211969
$754$	−570429.	+	417914.i	−1.00337	+	0.735096i
$755$	−131208.	+	726466.i	−0.230179	+	1.27445i
$756$	−2400.32	−	2400.32i	−0.00419977	−	0.00419977i
$757$			27667.8i			0.0482817i	0.999709	+	0.0241408i	$0.00768501\pi$
$757$			27667.8i			0.0482817i	−0.999709	+	0.0241408i	$0.992315\pi$
$758$	−911466.			−1.58636
$759$	10072.0	+	10072.0i	0.0174837	+	0.0174837i
$760$	−299865.	−	432059.i	−0.519157	−	0.748024i
$761$	−619802.	+	619802.i	−1.07025	+	1.07025i	−0.0729082	+	0.997339i	$0.523228\pi$
$761$	−619802.	+	619802.i	−1.07025	+	1.07025i	−0.997339	+	0.0729082i	$0.976772\pi$
$762$	93221.8	+	93221.8i	0.160549	+	0.160549i
$763$			453554.i			0.779077i
$764$		−	8932.65i		−	0.0153036i
$765$	394272.	−	273640.i	0.673710	−	0.467581i
$766$			147497.i			0.251377i
$767$	809219.	−	592859.i	1.37555	−	1.00777i
$768$			5904.14i			0.0100100i
$769$	−337148.	−	337148.i	−0.570122	−	0.570122i	0.362040	−	0.932162i	$-0.382080\pi$
$769$	−337148.	−	337148.i	−0.570122	−	0.570122i	−0.932162	+	0.362040i	$0.882080\pi$
$770$	31129.9	−	172359.i	0.0525045	−	0.290705i
$771$		−	114951.i		−	0.193377i
$772$	−681.143	+	681.143i	−0.00114289	+	0.00114289i
$773$	−533394.	+	533394.i	−0.892665	+	0.892665i	−0.994773	−	0.102108i	$-0.967441\pi$
$773$	−533394.	+	533394.i	−0.892665	+	0.892665i	0.102108	+	0.994773i	$0.467441\pi$
$774$	261095.	−	261095.i	0.435829	−	0.435829i
$775$	−720774.	+	328844.i	−1.20004	+	0.547503i
$776$	238861.			0.396663
$777$	30056.6			0.0497849
$778$	−12408.9	−	12408.9i	−0.0205010	−	0.0205010i
$779$		−	429830.i		−	0.708308i
$780$	1825.40	−	889.904i	0.00300033	−	0.00146270i
$781$	285197.			0.467566
$782$	154621.	−	154621.i	0.252845	−	0.252845i
$783$		−	266191.i		−	0.434179i
$784$		−	110588.i		−	0.179918i
$785$	604816.	+	871446.i	0.981486	+	1.41417i
$786$	−30074.8	−	30074.8i	−0.0486809	−	0.0486809i
$787$	164118.	+	164118.i	0.264976	+	0.264976i	0.827072	−	0.562096i	$-0.190005\pi$
$787$	164118.	+	164118.i	0.264976	+	0.264976i	−0.562096	+	0.827072i	$0.690005\pi$
$788$	138.860	+	138.860i	0.000223627	+	0.000223627i
$789$	60630.6			0.0973953
$790$	159584.	−	883579.i	0.255703	−	1.41577i
$791$	−131317.	+	131317.i	−0.209879	+	0.209879i
$792$	−202520.			−0.322863
$793$	−199271.	−	30750.4i	−0.316882	−	0.0488994i
$794$	432172.			0.685512
$795$	159204.	−	110494.i	0.251895	−	0.174825i
$796$	10166.0			0.0160444
$797$	867268.			1.36533			0.682664	−	0.730733i	$-0.260821\pi$
$797$	867268.			1.36533			0.682664	+	0.730733i	$0.260821\pi$
$798$	63833.4	−	63833.4i	0.100240	−	0.100240i
$799$	219739.	+	219739.i	0.344203	+	0.344203i
$800$	−10099.4	−	22136.3i	−0.0157803	−	0.0345879i
$801$	−246171.	+	246171.i	−0.383683	+	0.383683i
$802$		−	809383.i		−	1.25836i
$803$	−276242.			−0.428410
$804$	627.439	−	627.439i	0.000970643	−	0.000970643i
$805$	245863.	+	44405.7i	0.379404	+	0.0685246i
$806$	838781.	+	129436.i	1.29115	+	0.199243i
$807$		−	51927.7i		−	0.0797356i
$808$	440506.	−	440506.i	0.674728	−	0.674728i
$809$	−98828.6			−0.151003			−0.0755015	−	0.997146i	$-0.524056\pi$
$809$	−98828.6			−0.151003			−0.0755015	+	0.997146i	$0.524056\pi$
$810$	−104927.	+	580957.i	−0.159926	+	0.885470i
$811$	539581.	+	539581.i	0.820380	+	0.820380i	0.986162	−	0.165782i	$-0.0530149\pi$
$811$	539581.	+	539581.i	0.820380	+	0.820380i	−0.165782	+	0.986162i	$0.553015\pi$
$812$	10058.3	−	10058.3i	0.0152550	−	0.0152550i
$813$	−35743.1	−	35743.1i	−0.0540768	−	0.0540768i
$814$	48064.7	−	48064.7i	0.0725400	−	0.0725400i
$815$	529110.	+	95563.2i	0.796583	+	0.143872i
$816$		−	97004.2i		−	0.145683i
$817$	−273407.	−	273407.i	−0.409605	−	0.409605i
$818$	−1.21697e6			−1.81875
$819$	−347167.	−	473864.i	−0.517572	−	0.706457i
$820$	1783.84	−	9876.67i	0.00265294	−	0.0146887i
$821$	−120183.	−	120183.i	−0.178302	−	0.178302i	0.612313	−	0.790615i	$-0.290239\pi$
$821$	−120183.	−	120183.i	−0.178302	−	0.178302i	−0.790615	+	0.612313i	$0.790239\pi$
$822$		−	148207.i		−	0.219344i
$823$	1.02441e6			1.51242			0.756210	−	0.654329i	$-0.227049\pi$
$823$	1.02441e6			1.51242			0.756210	+	0.654329i	$0.227049\pi$
$824$	−74948.3	−	74948.3i	−0.110384	−	0.110384i
$825$	−35884.6	+	16371.9i	−0.0527231	+	0.0240542i
$826$	736273.	−	736273.i	1.07914	−	1.07914i
$827$	−744353.	−	744353.i	−1.08835	−	1.08835i	−0.995699	−	0.0926494i	$-0.970466\pi$
$827$	−744353.	−	744353.i	−1.08835	−	1.08835i	−0.0926494	−	0.995699i	$-0.529534\pi$
$828$		−	5389.70i		−	0.00786147i
$829$			902014.i			1.31252i	0.754537	+	0.656258i	$0.227862\pi$
$829$			902014.i			1.31252i	−0.754537	+	0.656258i	$0.772138\pi$
$830$	−540514.	−	778797.i	−0.784605	−	1.13049i
$831$			82266.1i			0.119129i
$832$	−107500.	+	696633.i	−0.155297	+	1.00637i
$833$		−	107724.i		−	0.155246i
$834$	−42240.1	−	42240.1i	−0.0607286	−	0.0607286i
$835$	88425.4	+	15970.6i	0.126825	+	0.0229060i
$836$			3956.54i			0.00566112i
$837$	−225909.	+	225909.i	−0.322465	+	0.322465i
$838$	−526712.	+	526712.i	−0.750041	+	0.750041i
$839$	−904151.	+	904151.i	−1.28445	+	1.28445i	−0.346340	+	0.938109i	$0.612576\pi$
$839$	−904151.	+	904151.i	−1.28445	+	1.28445i	−0.938109	+	0.346340i	$0.887424\pi$
$840$	92818.2	−	64419.4i	0.131545	−	0.0912973i
$841$	408166.			0.577092
$842$	321059.			0.452857
$843$	−130037.	−	130037.i	−0.182983	−	0.182983i
$844$		−	26281.1i		−	0.0368942i
$845$	682028.	−	211350.i	0.955188	−	0.295998i
$846$	−395234.			−0.552222
$847$	408452.	−	408452.i	0.569344	−	0.569344i
$848$			1.23151e6i			1.71256i
$849$			43076.8i			0.0597624i
$850$	251333.	+	550882.i	0.347866	+	0.762467i
$851$	68562.5	+	68562.5i	0.0946734	+	0.0946734i
$852$	2427.02	+	2427.02i	0.00334344	+	0.00334344i
$853$	−701518.	−	701518.i	−0.964141	−	0.964141i	0.0352378	−	0.999379i	$-0.488781\pi$
$853$	−701518.	−	701518.i	−0.964141	−	0.964141i	−0.999379	+	0.0352378i	$0.988781\pi$
$854$	−209287.			−0.286963
$855$	628995.	+	113603.i	0.860429	+	0.155403i
$856$	526009.	−	526009.i	0.717869	−	0.717869i
$857$	264489.			0.360119			0.180060	−	0.983656i	$-0.442371\pi$
$857$	264489.			0.360119			0.180060	+	0.983656i	$0.442371\pi$
$858$	41759.7	+	6444.11i	0.0567261	+	0.00875364i
$859$	485346.			0.657757			0.328879	−	0.944372i	$-0.393329\pi$
$859$	485346.			0.657757			0.328879	+	0.944372i	$0.393329\pi$
$860$	−5147.70	−	7417.03i	−0.00696011	−	0.0100284i
$861$	92339.4			0.124561
$862$	−102948.			−0.138549
$863$	640174.	−	640174.i	0.859561	−	0.859561i	−0.131726	−	0.991286i	$-0.542052\pi$
$863$	640174.	−	640174.i	0.859561	−	0.859561i	0.991286	+	0.131726i	$0.0420518\pi$
$864$	−6938.07	−	6938.07i	−0.00929418	−	0.00929418i
$865$	535298.	−	371517.i	0.715423	−	0.496531i
$866$	−40378.0	+	40378.0i	−0.0538405	+	0.0538405i
$867$			37484.1i			0.0498665i
$868$	−17072.5			−0.0226598
$869$	−256011.	+	256011.i	−0.339016	+	0.339016i
$870$	162662.	+	29378.5i	0.214905	+	0.0388142i
$871$	251674.	−	184384.i	0.331743	−	0.243045i
$872$			661666.i			0.870174i
$873$	−205270.	+	205270.i	−0.269338	+	0.269338i
$874$	291223.			0.381243
$875$	−353352.	+	594790.i	−0.461522	+	0.776869i
$876$	−2350.82	−	2350.82i	−0.00306345	−	0.00306345i
$877$	576979.	−	576979.i	0.750172	−	0.750172i	−0.224339	−	0.974511i	$-0.572022\pi$
$877$	576979.	−	576979.i	0.750172	−	0.750172i	0.974511	+	0.224339i	$0.0720224\pi$
$878$	−983155.	−	983155.i	−1.27536	−	1.27536i
$879$	−37621.2	+	37621.2i	−0.0486917	+	0.0486917i
$880$	44550.1	−	246663.i	0.0575285	−	0.318521i
$881$		−	1.28317e6i		−	1.65322i	−0.562773	−	0.826612i	$-0.690265\pi$
$881$		−	1.28317e6i		−	1.65322i	0.562773	−	0.826612i	$-0.309735\pi$
$882$	96878.4	+	96878.4i	0.124535	+	0.124535i
$883$	93617.0			0.120070			0.0600348	−	0.998196i	$-0.480879\pi$
$883$	93617.0			0.120070			0.0600348	+	0.998196i	$0.480879\pi$
$884$	−1917.19	+	12423.9i	−0.00245335	+	0.0158984i
$885$	−230754.	−	41676.8i	−0.294620	−	0.0532117i
$886$	754775.	+	754775.i	0.961502	+	0.961502i
$887$		−	248307.i		−	0.315603i	−0.987471	−	0.157802i	$-0.949559\pi$
$887$		−	248307.i		−	0.315603i	0.987471	−	0.157802i	$-0.0504406\pi$
$888$	43847.9			0.0556062
$889$	−659338.	−	659338.i	−0.834266	−	0.834266i
$890$	−250439.	−	360844.i	−0.316171	−	0.455553i
$891$	168328.	−	168328.i	0.212032	−	0.212032i
$892$	16212.1	+	16212.1i	0.0203755	+	0.0203755i
$893$			413872.i			0.518995i
$894$			261876.i			0.327657i
$895$	34497.6	+	49705.6i	0.0430668	+	0.0620525i
$896$			704067.i			0.876997i
$897$	−9192.29	+	59568.7i	−0.0114245	+	0.0740344i
$898$			619241.i			0.767904i
$899$	−946650.	−	946650.i	−1.17131	−	1.17131i
$900$	13981.6	+	5220.78i	0.0172613	+	0.00644540i
$901$			1.19961e6i			1.47772i
$902$	147664.	−	147664.i	0.181493	−	0.181493i
$903$	58735.3	−	58735.3i	0.0720318	−	0.0720318i
$904$	−191572.	+	191572.i	−0.234420	+	0.234420i
$905$	17425.7	+	25107.7i	0.0212762	+	0.0306556i
$906$	−184857.			−0.225206
$907$	−497882.			−0.605218			−0.302609	−	0.953115i	$-0.597858\pi$
$907$	−497882.			−0.605218			−0.302609	+	0.953115i	$0.597858\pi$
$908$	−8151.64	−	8151.64i	−0.00988720	−	0.00988720i
$909$			757116.i			0.916294i
$910$	666190.	−	324775.i	0.804480	−	0.392193i
$911$	−634324.			−0.764319			−0.382159	−	0.924096i	$-0.624819\pi$
$911$	−634324.			−0.764319			−0.382159	+	0.924096i	$0.624819\pi$
$912$	91352.1	−	91352.1i	0.109832	−	0.109832i
$913$			382262.i			0.458584i
$914$		−	1.44035e6i		−	1.72415i
$915$	26872.7	+	38719.4i	0.0320974	+	0.0462473i
$916$	2511.61	+	2511.61i	0.00299338	+	0.00299338i
$917$	212713.	+	212713.i	0.252962	+	0.252962i
$918$	172660.	+	172660.i	0.204884	+	0.204884i
$919$	−25624.4			−0.0303404			−0.0151702	−	0.999885i	$-0.504829\pi$
$919$	−25624.4			−0.0303404			−0.0151702	+	0.999885i	$0.504829\pi$
$920$	358677.	+	64781.0i	0.423768	+	0.0765371i
$921$	−40056.6	+	40056.6i	−0.0472231	+	0.0472231i
$922$	−750091.			−0.882372
$923$	713223.	+	973509.i	0.837185	+	1.14271i
$924$	−849.973			−0.000995546
$925$	−244275.	+	111447.i	−0.285493	+	0.130252i
$926$	−1.21178e6			−1.41319
$927$	128817.			0.149904
$928$	29073.3	−	29073.3i	0.0337597	−	0.0337597i
$929$	576995.	+	576995.i	0.668561	+	0.668561i	0.957383	−	0.288822i	$-0.0932636\pi$
$929$	576995.	+	576995.i	0.668561	+	0.668561i	−0.288822	+	0.957383i	$0.593264\pi$
$930$	−113114.	−	162979.i	−0.130783	−	0.188437i
$931$	101447.	−	101447.i	0.117041	−	0.117041i
$932$		−	18667.6i		−	0.0214910i
$933$	136201.			0.156465
$934$	−970824.	+	970824.i	−1.11288	+	1.11288i
$935$	43396.2	−	240274.i	0.0496397	−	0.274843i
$936$	−506464.	−	691295.i	−0.578092	−	0.789063i
$937$			1.07202e6i			1.22102i	0.792009	+	0.610509i	$0.209035\pi$
$937$			1.07202e6i			1.22102i	−0.792009	+	0.610509i	$0.790965\pi$
$938$	228987.	−	228987.i	0.260259	−	0.260259i
$939$	−155447.			−0.176299
$940$	−1717.61	+	9509.98i	−0.00194387	+	0.0107628i
$941$	393193.	+	393193.i	0.444045	+	0.444045i	0.893369	−	0.449324i	$-0.148335\pi$
$941$	393193.	+	393193.i	0.444045	+	0.444045i	−0.449324	+	0.893369i	$0.648335\pi$
$942$	−187826.	+	187826.i	−0.211667	+	0.211667i
$943$	210637.	+	210637.i	0.236870	+	0.236870i
$944$	1.05368e6	−	1.05368e6i	1.18240	−	1.18240i
$945$	−49586.5	+	274549.i	−0.0555265	+	0.307437i
$946$		−	187852.i		−	0.209910i
$947$	−401562.	−	401562.i	−0.447768	−	0.447768i	0.446844	−	0.894612i	$-0.352548\pi$
$947$	−401562.	−	401562.i	−0.447768	−	0.447768i	−0.894612	+	0.446844i	$0.852548\pi$
$948$	−4357.30			−0.00484843
$949$	−690829.	−	942943.i	−0.767076	−	1.04702i
$950$	−282096.	+	755473.i	−0.312571	+	0.837089i
$951$	−147433.	−	147433.i	−0.163018	−	0.163018i
$952$			699391.i			0.771696i
$953$	225433.			0.248217			0.124109	−	0.992269i	$-0.460393\pi$
$953$	225433.			0.248217			0.124109	+	0.992269i	$0.460393\pi$
$954$	−1.07884e6	−	1.07884e6i	−1.18539	−	1.18539i
$955$	−603125.	+	418592.i	−0.661303	+	0.458969i
$956$	9432.57	−	9432.57i	0.0103208	−	0.0103208i
$957$	−47130.2	−	47130.2i	−0.0514606	−	0.0514606i
$958$		−	1.62627e6i		−	1.77199i
$959$			1.04824e6i			1.13978i
$960$	135359.	−	93944.6i	0.146874	−	0.101936i
$961$			683273.i			0.739856i
$962$	284268.	+	43866.5i	0.307169	+	0.0474005i
$963$			904073.i			0.974880i
$964$	−6531.22	−	6531.22i	−0.00702814	−	0.00702814i
$965$	77909.1	+	14071.3i	0.0836630	+	0.0151105i
$966$			62562.7i			0.0670442i
$967$	−838362.	+	838362.i	−0.896559	+	0.896559i	−0.995130	−	0.0985711i	$-0.968573\pi$
$967$	−838362.	+	838362.i	−0.896559	+	0.896559i	0.0985711	+	0.995130i	$0.468573\pi$
$968$	595869.	−	595869.i	0.635917	−	0.635917i
$969$	88986.1	−	88986.1i	0.0947708	−	0.0947708i
$970$	−208829.	−	300890.i	−0.221946	−	0.319789i
$971$	−184036.			−0.195193			−0.0975965	−	0.995226i	$-0.531115\pi$
$971$	−184036.			−0.195193			−0.0975965	+	0.995226i	$0.531115\pi$
$972$	9074.89			0.00960525
$973$	298755.	+	298755.i	0.315566	+	0.315566i
$974$		−	775851.i		−	0.817825i
$975$	−145625.	−	81547.9i	−0.153189	−	0.0857834i
$976$	−299510.			−0.314422
$977$	744817.	−	744817.i	0.780298	−	0.780298i	−0.199583	−	0.979881i	$-0.563959\pi$
$977$	744817.	−	744817.i	0.780298	−	0.780298i	0.979881	+	0.199583i	$0.0639587\pi$
$978$			134638.i			0.140763i
$979$			177115.i			0.184795i
$980$	2752.07	−	1910.04i	0.00286554	−	0.00198880i
$981$	−568617.	−	568617.i	−0.590856	−	0.590856i
$982$	751885.	+	751885.i	0.779702	+	0.779702i
$983$	−780178.	−	780178.i	−0.807397	−	0.807397i	0.176843	−	0.984239i	$-0.443412\pi$
$983$	−780178.	−	780178.i	−0.807397	−	0.807397i	−0.984239	+	0.176843i	$0.943412\pi$
$984$	134709.			0.139125
$985$	2868.61	−	15882.8i	0.00295664	−	0.0163702i
$986$	−723518.	+	723518.i	−0.744210	+	0.744210i
$987$	−88911.1			−0.0912687
$988$	−13505.5	+	9894.54i	−0.0138356	+	0.0101364i
$989$	267964.			0.273958
$990$	177057.	+	255112.i	0.180652	+	0.260292i
$991$	425232.			0.432991			0.216496	−	0.976284i	$-0.430537\pi$
$991$	425232.			0.432991			0.216496	+	0.976284i	$0.430537\pi$
$992$	−49347.5			−0.0501467
$993$	−129683.	+	129683.i	−0.131518	+	0.131518i
$994$	885754.	+	885754.i	0.896479	+	0.896479i
$995$	−476386.	−	686398.i	−0.481186	−	0.693314i
$996$	−3253.04	+	3253.04i	−0.00327922	+	0.00327922i
$997$		−	1.83417e6i		−	1.84522i	−0.385732	−	0.922611i	$-0.626051\pi$
$997$		−	1.83417e6i		−	1.84522i	0.385732	−	0.922611i	$-0.373949\pi$
$998$	1.52708e6			1.53321
$999$	−76561.8	+	76561.8i	−0.0767152	+	0.0767152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.8	✓	52
5.4	even	2	inner	65.5.g.a.34.19	yes	52
13.5	odd	4	inner	65.5.g.a.44.19	yes	52
65.44	odd	4	inner	65.5.g.a.44.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.8	✓	52	1.1	even	1	trivial
65.5.g.a.34.19	yes	52	5.4	even	2	inner
65.5.g.a.44.8	yes	52	65.44	odd	4	inner
65.5.g.a.44.19	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)

\(f(q)\)	\(=\)	\(q+(-2.80141 + 2.80141i) q^{2} -1.58015i q^{3} +0.304183i q^{4} +(20.5382 - 14.2543i) q^{5} +(4.42666 + 4.42666i) q^{6} +(-31.3088 - 31.3088i) q^{7} +(-45.6747 - 45.6747i) q^{8} +78.5031 q^{9} +O(q^{10})\)	\(q+(-2.80141 + 2.80141i) q^{2} -1.58015i q^{3} +0.304183i q^{4} +(20.5382 - 14.2543i) q^{5} +(4.42666 + 4.42666i) q^{6} +(-31.3088 - 31.3088i) q^{7} +(-45.6747 - 45.6747i) q^{8} +78.5031 q^{9} +(-17.6038 + 97.4679i) q^{10} +(28.2407 - 28.2407i) q^{11} +0.480655 q^{12} +(167.023 + 25.7740i) q^{13} +175.418 q^{14} +(-22.5239 - 32.4534i) q^{15} +251.041 q^{16} +244.539 q^{17} +(-219.920 + 219.920i) q^{18} +(230.290 + 230.290i) q^{19} +(4.33590 + 6.24735i) q^{20} +(-49.4727 + 49.4727i) q^{21} +158.228i q^{22} -225.706 q^{23} +(-72.1731 + 72.1731i) q^{24} +(218.632 - 585.513i) q^{25} +(-540.104 + 395.697i) q^{26} -252.039i q^{27} +(9.52360 - 9.52360i) q^{28} +1056.15 q^{29} +(154.014 + 27.8167i) q^{30} +(-896.324 - 896.324i) q^{31} +(27.5277 - 27.5277i) q^{32} +(-44.6246 - 44.6246i) q^{33} +(-685.054 + 685.054i) q^{34} +(-1089.31 - 196.741i) q^{35} +23.8793i q^{36} +(-303.769 - 303.769i) q^{37} -1290.28 q^{38} +(40.7269 - 263.922i) q^{39} +(-1589.13 - 287.015i) q^{40} +(-933.236 - 933.236i) q^{41} -277.187i q^{42} -1187.23 q^{43} +(8.59033 + 8.59033i) q^{44} +(1612.31 - 1119.00i) q^{45} +(632.295 - 632.295i) q^{46} +(898.587 + 898.587i) q^{47} -396.682i q^{48} -440.517i q^{49} +(1027.78 + 2252.74i) q^{50} -386.409i q^{51} +(-7.84001 + 50.8055i) q^{52} +4905.62i q^{53} +(706.066 + 706.066i) q^{54} +(177.462 - 982.562i) q^{55} +2860.04i q^{56} +(363.894 - 363.894i) q^{57} +(-2958.70 + 2958.70i) q^{58} +(4197.26 - 4197.26i) q^{59} +(9.87177 - 6.85139i) q^{60} -1193.08 q^{61} +5021.95 q^{62} +(-2457.84 - 2457.84i) q^{63} +4170.88i q^{64} +(3797.74 - 1851.44i) q^{65} +250.024 q^{66} +(1305.38 - 1305.38i) q^{67} +74.3845i q^{68} +356.650i q^{69} +(3602.76 - 2500.45i) q^{70} +(5049.40 + 5049.40i) q^{71} +(-3585.61 - 3585.61i) q^{72} +(-4890.86 - 4890.86i) q^{73} +1701.97 q^{74} +(-925.199 - 345.472i) q^{75} +(-70.0503 + 70.0503i) q^{76} -1768.36 q^{77} +(625.261 + 853.447i) q^{78} -9065.34 q^{79} +(5155.91 - 3578.40i) q^{80} +5960.49 q^{81} +5228.76 q^{82} +(-6767.93 + 6767.93i) q^{83} +(-15.0487 - 15.0487i) q^{84} +(5022.38 - 3485.72i) q^{85} +(3325.91 - 3325.91i) q^{86} -1668.87i q^{87} -2579.77 q^{88} +(-3135.82 + 3135.82i) q^{89} +(-1381.95 + 7651.53i) q^{90} +(-4422.34 - 6036.25i) q^{91} -68.6558i q^{92} +(-1416.33 + 1416.33i) q^{93} -5034.63 q^{94} +(8012.35 + 1447.12i) q^{95} +(-43.4980 - 43.4980i) q^{96} +(-2614.80 + 2614.80i) q^{97} +(1234.07 + 1234.07i) q^{98} +(2216.98 - 2216.98i) 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

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