LMFDB - Embedded newform 230.5.f.b.47.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.16
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(5.56222 - 5.56222i) q^{3} +8.00000i q^{4} +(-17.4021 + 17.9490i) q^{5} +22.2489 q^{6} +(-33.3744 - 33.3744i) q^{7} +(-16.0000 + 16.0000i) q^{8} +19.1234i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(5.56222 - 5.56222i) q^{3} +8.00000i q^{4} +(-17.4021 + 17.9490i) q^{5} +22.2489 q^{6} +(-33.3744 - 33.3744i) q^{7} +(-16.0000 + 16.0000i) q^{8} +19.1234i q^{9} +(-70.7022 + 1.09393i) q^{10} -105.285 q^{11} +(44.4978 + 44.4978i) q^{12} +(219.096 - 219.096i) q^{13} -133.498i q^{14} +(3.04235 + 196.631i) q^{15} -64.0000 q^{16} +(-179.703 - 179.703i) q^{17} +(-38.2468 + 38.2468i) q^{18} -700.031i q^{19} +(-143.592 - 139.217i) q^{20} -371.272 q^{21} +(-210.571 - 210.571i) q^{22} +(77.9968 - 77.9968i) q^{23} +177.991i q^{24} +(-19.3358 - 624.701i) q^{25} +876.385 q^{26} +(556.908 + 556.908i) q^{27} +(266.995 - 266.995i) q^{28} -149.999i q^{29} +(-387.177 + 399.346i) q^{30} -1297.64 q^{31} +(-128.000 - 128.000i) q^{32} +(-585.620 + 585.620i) q^{33} -718.813i q^{34} +(1179.82 - 18.2547i) q^{35} -152.987 q^{36} +(-877.703 - 877.703i) q^{37} +(1400.06 - 1400.06i) q^{38} -2437.32i q^{39} +(-8.75145 - 565.618i) q^{40} -414.765 q^{41} +(-742.544 - 742.544i) q^{42} +(-1787.11 + 1787.11i) q^{43} -842.283i q^{44} +(-343.247 - 332.787i) q^{45} +311.987 q^{46} +(1515.30 + 1515.30i) q^{47} +(-355.982 + 355.982i) q^{48} -173.295i q^{49} +(1210.73 - 1288.07i) q^{50} -1999.10 q^{51} +(1752.77 + 1752.77i) q^{52} +(-3835.06 + 3835.06i) q^{53} +2227.63i q^{54} +(1832.18 - 1889.77i) q^{55} +1067.98 q^{56} +(-3893.73 - 3893.73i) q^{57} +(299.999 - 299.999i) q^{58} -1876.67i q^{59} +(-1573.05 + 24.3388i) q^{60} +451.446 q^{61} +(-2595.28 - 2595.28i) q^{62} +(638.232 - 638.232i) q^{63} -512.000i q^{64} +(119.838 + 7745.29i) q^{65} -2342.48 q^{66} +(687.703 + 687.703i) q^{67} +(1437.63 - 1437.63i) q^{68} -867.671i q^{69} +(2396.16 + 2323.14i) q^{70} +1109.02 q^{71} +(-305.974 - 305.974i) q^{72} +(3219.26 - 3219.26i) q^{73} -3510.81i q^{74} +(-3582.27 - 3367.17i) q^{75} +5600.25 q^{76} +(3513.84 + 3513.84i) q^{77} +(4874.65 - 4874.65i) q^{78} -9800.26i q^{79} +(1113.73 - 1148.74i) q^{80} +4646.30 q^{81} +(-829.530 - 829.530i) q^{82} +(8322.18 - 8322.18i) q^{83} -2970.18i q^{84} +(6352.70 - 98.2915i) q^{85} -7148.45 q^{86} +(-834.330 - 834.330i) q^{87} +(1684.57 - 1684.57i) q^{88} +12026.5i q^{89} +(-20.9197 - 1352.07i) q^{90} -14624.4 q^{91} +(623.974 + 623.974i) q^{92} +(-7217.75 + 7217.75i) q^{93} +6061.21i q^{94} +(12564.9 + 12182.0i) q^{95} -1423.93 q^{96} +(4596.94 + 4596.94i) q^{97} +(346.590 - 346.590i) q^{98} -2013.41i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	5.56222	−	5.56222i	0.618025	−	0.618025i	−0.327000	−	0.945024i	$-0.606038\pi$
$3$	5.56222	−	5.56222i	0.618025	−	0.618025i	0.945024	+	0.327000i	$0.106038\pi$
$4$			8.00000i			0.500000i
$5$	−17.4021	+	17.9490i	−0.696083	+	0.717961i
$5$	−17.4021	+	17.9490i	−0.696083	+	0.717961i
$6$	22.2489			0.618025
$7$	−33.3744	−	33.3744i	−0.681111	−	0.681111i	0.279140	−	0.960250i	$-0.409951\pi$
$7$	−33.3744	−	33.3744i	−0.681111	−	0.681111i	−0.960250	+	0.279140i	$0.909951\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$			19.1234i			0.236091i
$10$	−70.7022	+	1.09393i	−0.707022	+	0.0109393i
$11$	−105.285			−0.870127			−0.435063	−	0.900400i	$-0.643274\pi$
$11$	−105.285			−0.870127			−0.435063	+	0.900400i	$0.643274\pi$
$12$	44.4978	+	44.4978i	0.309012	+	0.309012i
$13$	219.096	−	219.096i	1.29643	−	1.29643i	0.365691	−	0.930736i	$-0.380833\pi$
$13$	219.096	−	219.096i	1.29643	−	1.29643i	0.930736	−	0.365691i	$-0.119167\pi$
$14$		−	133.498i		−	0.681111i
$15$	3.04235	+	196.631i	0.0135215	+	0.873914i
$16$	−64.0000			−0.250000
$17$	−179.703	−	179.703i	−0.621810	−	0.621810i	0.324184	−	0.945994i	$-0.394910\pi$
$17$	−179.703	−	179.703i	−0.621810	−	0.621810i	−0.945994	+	0.324184i	$0.894910\pi$
$18$	−38.2468	+	38.2468i	−0.118046	+	0.118046i
$19$		−	700.031i		−	1.93914i	−0.244805	−	0.969572i	$-0.578724\pi$
$19$		−	700.031i		−	1.93914i	0.244805	−	0.969572i	$-0.421276\pi$
$20$	−143.592	−	139.217i	−0.358981	−	0.348041i
$21$	−371.272			−0.841886
$22$	−210.571	−	210.571i	−0.435063	−	0.435063i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$			177.991i			0.309012i
$25$	−19.3358	−	624.701i	−0.0309374	−	0.999521i
$26$	876.385			1.29643
$27$	556.908	+	556.908i	0.763935	+	0.763935i
$28$	266.995	−	266.995i	0.340555	−	0.340555i
$29$		−	149.999i		−	0.178358i	−0.996016	−	0.0891792i	$-0.971576\pi$
$29$		−	149.999i		−	0.178358i	0.996016	−	0.0891792i	$-0.0284244\pi$
$30$	−387.177	+	399.346i	−0.430196	+	0.443718i
$31$	−1297.64			−1.35030			−0.675150	−	0.737680i	$-0.735921\pi$
$31$	−1297.64			−1.35030			−0.675150	+	0.737680i	$0.735921\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−585.620	+	585.620i	−0.537760	+	0.537760i
$34$		−	718.813i		−	0.621810i
$35$	1179.82	−	18.2547i	0.963121	−	0.0149018i
$36$	−152.987			−0.118046
$37$	−877.703	−	877.703i	−0.641127	−	0.641127i	0.309705	−	0.950833i	$-0.399770\pi$
$37$	−877.703	−	877.703i	−0.641127	−	0.641127i	−0.950833	+	0.309705i	$0.899770\pi$
$38$	1400.06	−	1400.06i	0.969572	−	0.969572i
$39$		−	2437.32i		−	1.60245i
$40$	−8.75145	−	565.618i	−0.00546966	−	0.353511i
$41$	−414.765			−0.246737			−0.123369	−	0.992361i	$-0.539370\pi$
$41$	−414.765			−0.246737			−0.123369	+	0.992361i	$0.539370\pi$
$42$	−742.544	−	742.544i	−0.420943	−	0.420943i
$43$	−1787.11	+	1787.11i	−0.966530	+	0.966530i	−0.999458	−	0.0329279i	$-0.989517\pi$
$43$	−1787.11	+	1787.11i	−0.966530	+	0.966530i	0.0329279	+	0.999458i	$0.489517\pi$
$44$		−	842.283i		−	0.435063i
$45$	−343.247	−	332.787i	−0.169504	−	0.164339i
$46$	311.987			0.147442
$47$	1515.30	+	1515.30i	0.685968	+	0.685968i	0.961338	−	0.275370i	$-0.0888005\pi$
$47$	1515.30	+	1515.30i	0.685968	+	0.685968i	−0.275370	+	0.961338i	$0.588800\pi$
$48$	−355.982	+	355.982i	−0.154506	+	0.154506i
$49$		−	173.295i		−	0.0721763i
$50$	1210.73	−	1288.07i	0.484292	−	0.515229i
$51$	−1999.10			−0.768588
$52$	1752.77	+	1752.77i	0.648214	+	0.648214i
$53$	−3835.06	+	3835.06i	−1.36528	+	1.36528i	−0.498232	+	0.867044i	$0.666017\pi$
$53$	−3835.06	+	3835.06i	−1.36528	+	1.36528i	−0.867044	+	0.498232i	$0.833983\pi$
$54$			2227.63i			0.763935i
$55$	1832.18	−	1889.77i	0.605680	−	0.624718i
$56$	1067.98			0.340555
$57$	−3893.73	−	3893.73i	−1.19844	−	1.19844i
$58$	299.999	−	299.999i	0.0891792	−	0.0891792i
$59$		−	1876.67i		−	0.539119i	−0.962984	−	0.269559i	$-0.913122\pi$
$59$		−	1876.67i		−	0.539119i	0.962984	−	0.269559i	$-0.0868781\pi$
$60$	−1573.05	+	24.3388i	−0.436957	+	0.00676077i
$61$	451.446			0.121324			0.0606620	−	0.998158i	$-0.480679\pi$
$61$	451.446			0.121324			0.0606620	+	0.998158i	$0.480679\pi$
$62$	−2595.28	−	2595.28i	−0.675150	−	0.675150i
$63$	638.232	−	638.232i	0.160804	−	0.160804i
$64$		−	512.000i		−	0.125000i
$65$	119.838	+	7745.29i	0.0283641	+	1.83321i
$66$	−2342.48			−0.537760
$67$	687.703	+	687.703i	0.153197	+	0.153197i	0.779544	−	0.626347i	$-0.215451\pi$
$67$	687.703	+	687.703i	0.153197	+	0.153197i	−0.626347	+	0.779544i	$0.715451\pi$
$68$	1437.63	−	1437.63i	0.310905	−	0.310905i
$69$		−	867.671i		−	0.182245i
$70$	2396.16	+	2323.14i	0.489011	+	0.474110i
$71$	1109.02			0.219999			0.110000	−	0.993932i	$-0.464915\pi$
$71$	1109.02			0.219999			0.110000	+	0.993932i	$0.464915\pi$
$72$	−305.974	−	305.974i	−0.0590228	−	0.0590228i
$73$	3219.26	−	3219.26i	0.604102	−	0.604102i	−0.337297	−	0.941398i	$-0.609512\pi$
$73$	3219.26	−	3219.26i	0.604102	−	0.604102i	0.941398	+	0.337297i	$0.109512\pi$
$74$		−	3510.81i		−	0.641127i
$75$	−3582.27	−	3367.17i	−0.636849	−	0.598609i
$76$	5600.25			0.969572
$77$	3513.84	+	3513.84i	0.592653	+	0.592653i
$78$	4874.65	−	4874.65i	0.801224	−	0.801224i
$79$		−	9800.26i		−	1.57030i	−0.619304	−	0.785152i	$-0.712585\pi$
$79$		−	9800.26i		−	1.57030i	0.619304	−	0.785152i	$-0.287415\pi$
$80$	1113.73	−	1148.74i	0.174021	−	0.179490i
$81$	4646.30			0.708170
$82$	−829.530	−	829.530i	−0.123369	−	0.123369i
$83$	8322.18	−	8322.18i	1.20804	−	1.20804i	0.236378	−	0.971661i	$-0.424040\pi$
$83$	8322.18	−	8322.18i	1.20804	−	1.20804i	0.971661	−	0.236378i	$-0.0759602\pi$
$84$		−	2970.18i		−	0.420943i
$85$	6352.70	−	98.2915i	0.879267	−	0.0136044i
$86$	−7148.45			−0.966530
$87$	−834.330	−	834.330i	−0.110230	−	0.110230i
$88$	1684.57	−	1684.57i	0.217532	−	0.217532i
$89$			12026.5i			1.51830i	0.650915	+	0.759151i	$0.274386\pi$
$89$			12026.5i			1.51830i	−0.650915	+	0.759151i	$0.725614\pi$
$90$	−20.9197	−	1352.07i	−0.00258268	−	0.166922i
$91$	−14624.4			−1.76602
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	−7217.75	+	7217.75i	−0.834519	+	0.834519i
$94$			6061.21i			0.685968i
$95$	12564.9	+	12182.0i	1.39223	+	1.34981i
$96$	−1423.93			−0.154506
$97$	4596.94	+	4596.94i	0.488568	+	0.488568i	0.907854	−	0.419286i	$-0.137720\pi$
$97$	4596.94	+	4596.94i	0.488568	+	0.488568i	−0.419286	+	0.907854i	$0.637720\pi$
$98$	346.590	−	346.590i	0.0360881	−	0.0360881i
$99$		−	2013.41i		−	0.205429i
$100$	4997.61	−	154.687i	0.499761	−	0.0154687i
$101$	−9439.68			−0.925368			−0.462684	−	0.886523i	$-0.653114\pi$
$101$	−9439.68			−0.925368			−0.462684	+	0.886523i	$0.653114\pi$
$102$	−3998.19	−	3998.19i	−0.384294	−	0.384294i
$103$	7992.57	−	7992.57i	0.753376	−	0.753376i	−0.221731	−	0.975108i	$-0.571171\pi$
$103$	7992.57	−	7992.57i	0.753376	−	0.753376i	0.975108	+	0.221731i	$0.0711708\pi$
$104$			7011.08i			0.648214i
$105$	6460.90	−	6663.97i	0.586023	−	0.604442i
$106$	−15340.2			−1.36528
$107$	−11683.5	−	11683.5i	−1.02048	−	1.02048i	−0.999786	−	0.0206951i	$-0.993412\pi$
$107$	−11683.5	−	11683.5i	−1.02048	−	1.02048i	−0.0206951	−	0.999786i	$-0.506588\pi$
$108$	−4455.27	+	4455.27i	−0.381967	+	0.381967i
$109$			13476.3i			1.13427i	0.823624	+	0.567137i	$0.191949\pi$
$109$			13476.3i			1.13427i	−0.823624	+	0.567137i	$0.808051\pi$
$110$	7443.91	−	115.175i	0.615199	−	0.00951859i
$111$	−9763.96			−0.792465
$112$	2135.96	+	2135.96i	0.170278	+	0.170278i
$113$	−3582.04	+	3582.04i	−0.280526	+	0.280526i	−0.833319	−	0.552793i	$-0.813562\pi$
$113$	−3582.04	+	3582.04i	−0.280526	+	0.280526i	0.552793	+	0.833319i	$0.313562\pi$
$114$		−	15574.9i		−	1.19844i
$115$	42.6616	+	2757.27i	0.00322583	+	0.208489i
$116$	1200.00			0.0891792
$117$	4189.86	+	4189.86i	0.306075	+	0.306075i
$118$	3753.35	−	3753.35i	0.269559	−	0.269559i
$119$			11995.0i			0.847043i
$120$	−3194.77	−	3097.41i	−0.221859	−	0.215098i
$121$	−3555.99			−0.242879
$122$	902.893	+	902.893i	0.0606620	+	0.0606620i
$123$	−2307.01	+	2307.01i	−0.152490	+	0.152490i
$124$		−	10381.1i		−	0.675150i
$125$	11549.3	+	10524.0i	0.739153	+	0.673538i
$126$	2552.93			0.160804
$127$	11307.2	+	11307.2i	0.701046	+	0.701046i	0.964635	−	0.263589i	$-0.0849063\pi$
$127$	11307.2	+	11307.2i	0.701046	+	0.701046i	−0.263589	+	0.964635i	$0.584906\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$			19880.6i			1.19468i
$130$	−15250.9	+	15730.3i	−0.902421	+	0.930785i
$131$	−6049.92			−0.352539			−0.176270	−	0.984342i	$-0.556403\pi$
$131$	−6049.92			−0.352539			−0.176270	+	0.984342i	$0.556403\pi$
$132$	−4684.96	−	4684.96i	−0.268880	−	0.268880i
$133$	−23363.1	+	23363.1i	−1.32077	+	1.32077i
$134$			2750.81i			0.153197i
$135$	−19687.3	+	304.610i	−1.08024	+	0.0167139i
$136$	5750.50			0.310905
$137$	−6626.04	−	6626.04i	−0.353031	−	0.353031i	0.508205	−	0.861236i	$-0.330309\pi$
$137$	−6626.04	−	6626.04i	−0.353031	−	0.353031i	−0.861236	+	0.508205i	$0.830309\pi$
$138$	1735.34	−	1735.34i	0.0911227	−	0.0911227i
$139$			22921.8i			1.18637i	0.805068	+	0.593183i	$0.202129\pi$
$139$			22921.8i			1.18637i	−0.805068	+	0.593183i	$0.797871\pi$
$140$	146.037	+	9438.58i	0.00745089	+	0.481560i
$141$	16856.9			0.847890
$142$	2218.03	+	2218.03i	0.110000	+	0.110000i
$143$	−23067.6	+	23067.6i	−1.12806	+	1.12806i
$144$		−	1223.90i		−	0.0590228i
$145$	2692.34	+	2610.30i	0.128054	+	0.124152i
$146$	12877.0			0.604102
$147$	−963.906	−	963.906i	−0.0446067	−	0.0446067i
$148$	7021.63	−	7021.63i	0.320564	−	0.320564i
$149$		−	5219.37i		−	0.235096i	−0.993067	−	0.117548i	$-0.962497\pi$
$149$		−	5219.37i		−	0.235096i	0.993067	−	0.117548i	$-0.0375035\pi$
$150$	−430.201	−	13898.9i	−0.0191200	−	0.617729i
$151$	10490.9			0.460106			0.230053	−	0.973178i	$-0.426110\pi$
$151$	10490.9			0.460106			0.230053	+	0.973178i	$0.426110\pi$
$152$	11200.5	+	11200.5i	0.484786	+	0.484786i
$153$	3436.53	−	3436.53i	0.146804	−	0.146804i
$154$			14055.4i			0.592653i
$155$	22581.6	−	23291.4i	0.939921	−	0.969463i
$156$	19498.6			0.801224
$157$	−33955.4	−	33955.4i	−1.37756	−	1.37756i	−0.848730	−	0.528827i	$-0.822632\pi$
$157$	−33955.4	−	33955.4i	−1.37756	−	1.37756i	−0.528827	−	0.848730i	$-0.677368\pi$
$158$	19600.5	−	19600.5i	0.785152	−	0.785152i
$159$			42662.9i			1.68755i
$160$	4524.94	−	70.0116i	0.176756	−	0.00273483i
$161$	−5206.20			−0.200849
$162$	9292.60	+	9292.60i	0.354085	+	0.354085i
$163$	−18819.7	+	18819.7i	−0.708333	+	0.708333i	−0.966185	−	0.257851i	$-0.916986\pi$
$163$	−18819.7	+	18819.7i	−0.708333	+	0.708333i	0.257851	+	0.966185i	$0.416986\pi$
$164$		−	3318.12i		−	0.123369i
$165$	−320.314	−	20702.3i	−0.0117655	−	0.760416i
$166$	33288.7			1.20804
$167$	−2463.14	−	2463.14i	−0.0883193	−	0.0883193i	0.661567	−	0.749886i	$-0.269892\pi$
$167$	−2463.14	−	2463.14i	−0.0883193	−	0.0883193i	−0.749886	+	0.661567i	$0.769892\pi$
$168$	5940.35	−	5940.35i	0.210472	−	0.210472i
$169$		−	67445.3i		−	2.36145i
$170$	12902.0	+	12508.8i	0.446436	+	0.432831i
$171$	13387.0			0.457815
$172$	−14296.9	−	14296.9i	−0.483265	−	0.483265i
$173$	−13429.3	+	13429.3i	−0.448706	+	0.448706i	−0.894924	−	0.446218i	$-0.852771\pi$
$173$	−13429.3	+	13429.3i	−0.448706	+	0.448706i	0.446218	+	0.894924i	$0.352771\pi$
$174$		−	3337.32i		−	0.110230i
$175$	−20203.7	+	21494.4i	−0.659713	+	0.701856i
$176$	6738.26			0.217532
$177$	−10438.5	−	10438.5i	−0.333189	−	0.333189i
$178$	−24052.9	+	24052.9i	−0.759151	+	0.759151i
$179$		−	31708.2i		−	0.989614i	−0.869003	−	0.494807i	$-0.835239\pi$
$179$		−	31708.2i		−	0.989614i	0.869003	−	0.494807i	$-0.164761\pi$
$180$	2662.29	−	2745.97i	0.0821696	−	0.0847522i
$181$	35072.7			1.07056			0.535281	−	0.844674i	$-0.320206\pi$
$181$	35072.7			1.07056			0.535281	+	0.844674i	$0.320206\pi$
$182$	−29248.8	−	29248.8i	−0.883010	−	0.883010i
$183$	2511.04	−	2511.04i	0.0749812	−	0.0749812i
$184$			2495.90i			0.0737210i
$185$	31027.8	−	480.074i	0.906582	−	0.0140270i
$186$	−28871.0			−0.834519
$187$	18920.1	+	18920.1i	0.541054	+	0.541054i
$188$	−12122.4	+	12122.4i	−0.342984	+	0.342984i
$189$		−	37173.0i		−	1.04065i
$190$	765.786	+	49493.8i	0.0212129	+	1.37102i
$191$	7524.95			0.206270			0.103135	−	0.994667i	$-0.467113\pi$
$191$	7524.95			0.206270			0.103135	+	0.994667i	$0.467113\pi$
$192$	−2847.86	−	2847.86i	−0.0772531	−	0.0772531i
$193$	−40841.8	+	40841.8i	−1.09645	+	1.09645i	−0.101632	+	0.994822i	$0.532407\pi$
$193$	−40841.8	+	40841.8i	−1.09645	+	1.09645i	−0.994822	+	0.101632i	$0.967593\pi$
$194$			18387.8i			0.488568i
$195$	43747.6	+	42414.5i	1.15050	+	1.11544i
$196$	1386.36			0.0360881
$197$	17905.0	+	17905.0i	0.461362	+	0.461362i	0.899102	−	0.437740i	$-0.144221\pi$
$197$	17905.0	+	17905.0i	0.461362	+	0.461362i	−0.437740	+	0.899102i	$0.644221\pi$
$198$	4026.83	−	4026.83i	0.102715	−	0.102715i
$199$		−	26906.5i		−	0.679439i	−0.940527	−	0.339719i	$-0.889668\pi$
$199$		−	26906.5i		−	0.679439i	0.940527	−	0.339719i	$-0.110332\pi$
$200$	10304.6	+	9685.84i	0.257615	+	0.242146i
$201$	7650.31			0.189359
$202$	−18879.4	−	18879.4i	−0.462684	−	0.462684i
$203$	−5006.14	+	5006.14i	−0.121482	+	0.121482i
$204$		−	15992.8i		−	0.384294i
$205$	7217.77	−	7444.63i	0.171749	−	0.177148i
$206$	31970.3			0.753376
$207$	1491.56	+	1491.56i	0.0348098	+	0.0348098i
$208$	−14022.2	+	14022.2i	−0.324107	+	0.324107i
$209$			73703.0i			1.68730i
$210$	26249.7	−	406.146i	0.595232	−	0.00920966i
$211$	59440.4			1.33511			0.667554	−	0.744561i	$-0.267341\pi$
$211$	59440.4			1.33511			0.667554	+	0.744561i	$0.267341\pi$
$212$	−30680.5	−	30680.5i	−0.682638	−	0.682638i
$213$	6168.59	−	6168.59i	0.135965	−	0.135965i
$214$		−	46733.9i		−	1.02048i
$215$	−977.490	−	63176.4i	−0.0211464	−	1.36672i
$216$	−17821.1			−0.381967
$217$	43307.9	+	43307.9i	0.919704	+	0.919704i
$218$	−26952.6	+	26952.6i	−0.567137	+	0.567137i
$219$		−	35812.5i		−	0.746700i
$220$	15118.2	+	14657.5i	0.312359	+	0.302840i
$221$	−78744.5			−1.61226
$222$	−19527.9	−	19527.9i	−0.396232	−	0.396232i
$223$	59890.3	−	59890.3i	1.20433	−	1.20433i	0.231497	−	0.972836i	$-0.425638\pi$
$223$	59890.3	−	59890.3i	1.20433	−	1.20433i	0.972836	−	0.231497i	$-0.0743623\pi$
$224$			8543.85i			0.170278i
$225$	11946.4	−	369.767i	0.235978	−	0.00730404i
$226$	−14328.2			−0.280526
$227$	43421.0	+	43421.0i	0.842651	+	0.842651i	0.989203	−	0.146552i	$-0.0468176\pi$
$227$	43421.0	+	43421.0i	0.842651	+	0.842651i	−0.146552	+	0.989203i	$0.546818\pi$
$228$	31149.8	−	31149.8i	0.599219	−	0.599219i
$229$		−	1509.87i		−	0.0287917i	−0.999896	−	0.0143959i	$-0.995417\pi$
$229$		−	1509.87i		−	0.0287917i	0.999896	−	0.0143959i	$-0.00458251\pi$
$230$	−5429.22	+	5599.87i	−0.102632	+	0.105858i
$231$	39089.5			0.732548
$232$	2399.99	+	2399.99i	0.0445896	+	0.0445896i
$233$	−3275.08	+	3275.08i	−0.0603267	+	0.0603267i	−0.736627	−	0.676300i	$-0.763582\pi$
$233$	−3275.08	+	3275.08i	−0.0603267	+	0.0603267i	0.676300	+	0.736627i	$0.263582\pi$
$234$			16759.5i			0.306075i
$235$	−53567.6	+	828.819i	−0.969989	+	0.0150080i
$236$	15013.4			0.269559
$237$	−54511.2	−	54511.2i	−0.970486	−	0.970486i
$238$	−23990.0	+	23990.0i	−0.423522	+	0.423522i
$239$		−	55644.3i		−	0.974149i	−0.873361	−	0.487074i	$-0.838064\pi$
$239$		−	55644.3i		−	0.974149i	0.873361	−	0.487074i	$-0.161936\pi$
$240$	−194.710	−	12584.4i	−0.00338038	−	0.218479i
$241$	−8860.99			−0.152563			−0.0762813	−	0.997086i	$-0.524305\pi$
$241$	−8860.99			−0.152563			−0.0762813	+	0.997086i	$0.524305\pi$
$242$	−7111.99	−	7111.99i	−0.121440	−	0.121440i
$243$	−19265.8	+	19265.8i	−0.326269	+	0.326269i
$244$			3611.57i			0.0606620i
$245$	3110.48	+	3015.70i	0.0518198	+	0.0502407i
$246$	−9228.06			−0.152490
$247$	−153374.	−	153374.i	−2.51396	−	2.51396i
$248$	20762.2	−	20762.2i	0.337575	−	0.337575i
$249$		−	92579.6i		−	1.49320i
$250$	2050.47	+	44146.6i	0.0328075	+	0.706345i
$251$	6272.37			0.0995598			0.0497799	−	0.998760i	$-0.484148\pi$
$251$	6272.37			0.0995598			0.0497799	+	0.998760i	$0.484148\pi$
$252$	5105.86	+	5105.86i	0.0804022	+	0.0804022i
$253$	−8211.92	+	8211.92i	−0.128293	+	0.128293i
$254$			45228.7i			0.701046i
$255$	34788.4	−	35881.9i	0.535001	−	0.551816i
$256$	4096.00			0.0625000
$257$	−55297.5	−	55297.5i	−0.837219	−	0.837219i	0.151273	−	0.988492i	$-0.451663\pi$
$257$	−55297.5	−	55297.5i	−0.837219	−	0.837219i	−0.988492	+	0.151273i	$0.951663\pi$
$258$	−39761.3	+	39761.3i	−0.597339	+	0.597339i
$259$			58585.7i			0.873357i
$260$	−61962.3	+	958.705i	−0.916603	+	0.0141820i
$261$	2868.50			0.0421089
$262$	−12099.8	−	12099.8i	−0.176270	−	0.176270i
$263$	14613.4	−	14613.4i	0.211271	−	0.211271i	−0.593536	−	0.804807i	$-0.702269\pi$
$263$	14613.4	−	14613.4i	0.211271	−	0.211271i	0.804807	+	0.593536i	$0.202269\pi$
$264$		−	18739.9i		−	0.268880i
$265$	−2097.65	−	135574.i	−0.0298704	−	1.93056i
$266$	−93452.6			−1.32077
$267$	66893.9	+	66893.9i	0.938348	+	0.938348i
$268$	−5501.62	+	5501.62i	−0.0765987	+	0.0765987i
$269$		−	26690.3i		−	0.368849i	−0.982847	−	0.184425i	$-0.940958\pi$
$269$		−	26690.3i		−	0.368849i	0.982847	−	0.184425i	$-0.0590421\pi$
$270$	−39983.9	−	38765.4i	−0.548476	−	0.531762i
$271$	131451.			1.78989			0.894943	−	0.446181i	$-0.147216\pi$
$271$	131451.			1.78989			0.894943	+	0.446181i	$0.147216\pi$
$272$	11501.0	+	11501.0i	0.155453	+	0.155453i
$273$	−81344.3	+	81344.3i	−1.09144	+	1.09144i
$274$		−	26504.2i		−	0.353031i
$275$	2035.78	+	65771.8i	0.0269194	+	0.869710i
$276$	6941.37			0.0911227
$277$	−75180.9	−	75180.9i	−0.979824	−	0.979824i	0.0199766	−	0.999800i	$-0.493641\pi$
$277$	−75180.9	−	75180.9i	−0.979824	−	0.979824i	−0.999800	+	0.0199766i	$0.993641\pi$
$278$	−45843.5	+	45843.5i	−0.593183	+	0.593183i
$279$		−	24815.3i		−	0.318794i
$280$	−18585.1	+	19169.2i	−0.237055	+	0.244506i
$281$	−54454.2			−0.689634			−0.344817	−	0.938670i	$-0.612059\pi$
$281$	−54454.2			−0.689634			−0.344817	+	0.938670i	$0.612059\pi$
$282$	33713.8	+	33713.8i	0.423945	+	0.423945i
$283$	−25427.8	+	25427.8i	−0.317495	+	0.317495i	−0.847804	−	0.530309i	$-0.822076\pi$
$283$	−25427.8	+	25427.8i	−0.317495	+	0.317495i	0.530309	+	0.847804i	$0.322076\pi$
$284$			8872.13i			0.110000i
$285$	137648.	−	2129.74i	1.69465	−	0.0262202i
$286$	−92270.5			−1.12806
$287$	13842.5	+	13842.5i	0.168055	+	0.168055i
$288$	2447.79	−	2447.79i	0.0295114	−	0.0295114i
$289$		−	18934.6i		−	0.226704i
$290$	164.089	+	10605.3i	0.00195112	+	0.126103i
$291$	51138.4			0.603894
$292$	25754.1	+	25754.1i	0.302051	+	0.302051i
$293$	106170.	−	106170.i	1.23671	−	1.23671i	0.275371	−	0.961338i	$-0.411199\pi$
$293$	106170.	−	106170.i	1.23671	−	1.23671i	0.961338	−	0.275371i	$-0.0888007\pi$
$294$		−	3855.63i		−	0.0446067i
$295$	33684.5	+	32658.0i	0.387067	+	0.375271i
$296$	28086.5			0.320564
$297$	−58634.3	−	58634.3i	−0.664720	−	0.664720i
$298$	10438.7	−	10438.7i	0.117548	−	0.117548i
$299$		−	34177.6i		−	0.382296i
$300$	26937.4	−	28658.2i	0.299304	−	0.318424i
$301$	119288.			1.31663
$302$	20981.8	+	20981.8i	0.230053	+	0.230053i
$303$	−52505.6	+	52505.6i	−0.571900	+	0.571900i
$304$			44802.0i			0.484786i
$305$	−7856.10	+	8103.03i	−0.0844515	+	0.0871059i
$306$	13746.1			0.146804
$307$	−90064.8	−	90064.8i	−0.955604	−	0.955604i	0.0434512	−	0.999056i	$-0.486165\pi$
$307$	−90064.8	−	90064.8i	−0.955604	−	0.955604i	−0.999056	+	0.0434512i	$0.986165\pi$
$308$	−28110.7	+	28110.7i	−0.296326	+	0.296326i
$309$		−	88912.9i		−	0.931210i
$310$	91745.9	−	1419.53i	0.954692	−	0.0147714i
$311$	15199.6			0.157149			0.0785744	−	0.996908i	$-0.474963\pi$
$311$	15199.6			0.157149			0.0785744	+	0.996908i	$0.474963\pi$
$312$	38997.2	+	38997.2i	0.400612	+	0.400612i
$313$	−71098.5	+	71098.5i	−0.725724	+	0.725724i	−0.969765	−	0.244041i	$-0.921527\pi$
$313$	−71098.5	+	71098.5i	−0.725724	+	0.725724i	0.244041	+	0.969765i	$0.421527\pi$
$314$		−	135822.i		−	1.37756i
$315$	349.091	+	22562.2i	0.00351818	+	0.227384i
$316$	78402.1			0.785152
$317$	39739.1	+	39739.1i	0.395457	+	0.395457i	0.876627	−	0.481170i	$-0.159788\pi$
$317$	39739.1	+	39739.1i	0.395457	+	0.395457i	−0.481170	+	0.876627i	$0.659788\pi$
$318$	−85325.8	+	85325.8i	−0.843774	+	0.843774i
$319$			15792.7i			0.155194i
$320$	9189.91	+	8909.86i	0.0897452	+	0.0870104i
$321$	−129972.			−1.26136
$322$	−10412.4	−	10412.4i	−0.100424	−	0.100424i
$323$	−125798.	+	125798.i	−1.20578	+	1.20578i
$324$			37170.4i			0.354085i
$325$	−141106.	−	132633.i	−1.33591	−	1.25570i
$326$	−75278.8			−0.708333
$327$	74958.2	+	74958.2i	0.701009	+	0.701009i
$328$	6636.24	−	6636.24i	0.0616843	−	0.0616843i
$329$		−	101145.i		−	0.934440i
$330$	40764.0	−	42045.3i	0.374325	−	0.386091i
$331$	101921.			0.930265			0.465132	−	0.885241i	$-0.346007\pi$
$331$	101921.			0.930265			0.465132	+	0.885241i	$0.346007\pi$
$332$	66577.4	+	66577.4i	0.604019	+	0.604019i
$333$	16784.7	−	16784.7i	0.151365	−	0.151365i
$334$		−	9852.55i		−	0.0883193i
$335$	−24311.1	+	376.150i	−0.216628	+	0.00335175i
$336$	23761.4			0.210472
$337$	49946.0	+	49946.0i	0.439786	+	0.439786i	0.891940	−	0.452154i	$-0.149344\pi$
$337$	49946.0	+	49946.0i	0.439786	+	0.439786i	−0.452154	+	0.891940i	$0.649344\pi$
$338$	134891.	−	134891.i	1.18072	−	1.18072i
$339$			39848.2i			0.346744i
$340$	786.332	+	50821.6i	0.00680218	+	0.439634i
$341$	136622.			1.17493
$342$	26773.9	+	26773.9i	0.228908	+	0.228908i
$343$	−85915.6	+	85915.6i	−0.730271	+	0.730271i
$344$		−	57187.6i		−	0.483265i
$345$	15573.9	+	15099.3i	0.130845	+	0.126858i
$346$	−53717.3			−0.448706
$347$	36408.9	+	36408.9i	0.302377	+	0.302377i	0.841943	−	0.539566i	$-0.181412\pi$
$347$	36408.9	+	36408.9i	0.302377	+	0.302377i	−0.539566	+	0.841943i	$0.681412\pi$
$348$	6674.64	−	6674.64i	0.0551149	−	0.0551149i
$349$			19753.3i			0.162177i	0.996707	+	0.0810885i	$0.0258396\pi$
$349$			19753.3i			0.162177i	−0.996707	+	0.0810885i	$0.974160\pi$
$350$	−83396.1	+	2581.29i	−0.680785	+	0.0210718i
$351$	244033.			1.98077
$352$	13476.5	+	13476.5i	0.108766	+	0.108766i
$353$	−18614.5	+	18614.5i	−0.149383	+	0.149383i	−0.777842	−	0.628459i	$-0.783686\pi$
$353$	−18614.5	+	18614.5i	−0.149383	+	0.149383i	0.628459	+	0.777842i	$0.283686\pi$
$354$		−	41753.9i		−	0.333189i
$355$	−19299.2	+	19905.8i	−0.153138	+	0.157951i
$356$	−96211.8			−0.759151
$357$	66718.7	+	66718.7i	0.523493	+	0.523493i
$358$	63416.5	−	63416.5i	0.494807	−	0.494807i
$359$			88111.1i			0.683663i	0.939761	+	0.341831i	$0.111047\pi$
$359$			88111.1i			0.683663i	−0.939761	+	0.341831i	$0.888953\pi$
$360$	10816.5	−	167.358i	0.0834609	−	0.00129134i
$361$	−359723.			−2.76028
$362$	70145.4	+	70145.4i	0.535281	+	0.535281i
$363$	−19779.2	+	19779.2i	−0.150105	+	0.150105i
$364$		−	116995.i		−	0.883010i
$365$	1760.82	+	113804.i	0.0132169	+	0.854227i
$366$	10044.2			0.0749812
$367$	−28383.6	−	28383.6i	−0.210734	−	0.210734i	0.593845	−	0.804579i	$-0.297609\pi$
$367$	−28383.6	−	28383.6i	−0.210734	−	0.210734i	−0.804579	+	0.593845i	$0.797609\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$		−	7931.71i		−	0.0582525i
$370$	63015.7	+	61095.4i	0.460305	+	0.446278i
$371$	255986.			1.85981
$372$	−57742.0	−	57742.0i	−0.417259	−	0.417259i
$373$	109265.	−	109265.i	0.785353	−	0.785353i	−0.195376	−	0.980728i	$-0.562593\pi$
$373$	109265.	−	109265.i	0.785353	−	0.785353i	0.980728	+	0.195376i	$0.0625927\pi$
$374$			75680.4i			0.541054i
$375$	122777.	−	5702.58i	0.873077	−	0.0405517i
$376$	−48489.7			−0.342984
$377$	−32864.3	−	32864.3i	−0.231229	−	0.231229i
$378$	74346.0	−	74346.0i	0.520324	−	0.520324i
$379$		−	158001.i		−	1.09997i	−0.835174	−	0.549985i	$-0.814633\pi$
$379$		−	158001.i		−	1.09997i	0.835174	−	0.549985i	$-0.185367\pi$
$380$	−97455.9	+	100519.i	−0.674903	+	0.696116i
$381$	125786.			0.866527
$382$	15049.9	+	15049.9i	0.103135	+	0.103135i
$383$	133417.	−	133417.i	0.909521	−	0.909521i	−0.0867125	−	0.996233i	$-0.527636\pi$
$383$	133417.	−	133417.i	0.909521	−	0.909521i	0.996233	+	0.0867125i	$0.0276361\pi$
$384$		−	11391.4i		−	0.0772531i
$385$	−124218.	+	1921.95i	−0.838037	+	0.0129664i
$386$	−163367.			−1.09645
$387$	−34175.7	−	34175.7i	−0.228189	−	0.228189i
$388$	−36775.5	+	36775.5i	−0.244284	+	0.244284i
$389$			60085.0i			0.397070i	0.980094	+	0.198535i	$0.0636183\pi$
$389$			60085.0i			0.397070i	−0.980094	+	0.198535i	$0.936382\pi$
$390$	2666.26	+	172324.i	0.0175297	+	1.13297i
$391$	−28032.5			−0.183362
$392$	2772.72	+	2772.72i	0.0180441	+	0.0180441i
$393$	−33651.0	+	33651.0i	−0.217878	+	0.217878i
$394$			71619.9i			0.461362i
$395$	175905.	+	170545.i	1.12742	+	1.09306i
$396$	16107.3			0.102715
$397$	−38390.7	−	38390.7i	−0.243582	−	0.243582i	0.574748	−	0.818330i	$-0.305100\pi$
$397$	−38390.7	−	38390.7i	−0.243582	−	0.243582i	−0.818330	+	0.574748i	$0.805100\pi$
$398$	53812.9	−	53812.9i	0.339719	−	0.339719i
$399$			259902.i			1.63254i
$400$	1237.49	+	39980.9i	0.00773434	+	0.249880i
$401$	−155596.			−0.967628			−0.483814	−	0.875171i	$-0.660749\pi$
$401$	−155596.			−0.967628			−0.483814	+	0.875171i	$0.660749\pi$
$402$	15300.6	+	15300.6i	0.0946797	+	0.0946797i
$403$	−284308.	+	284308.i	−1.75057	+	1.75057i
$404$		−	75517.4i		−	0.462684i
$405$	−80855.3	+	83396.6i	−0.492945	+	0.508438i
$406$	−20024.6			−0.121482
$407$	92409.3	+	92409.3i	0.557862	+	0.557862i
$408$	31985.6	−	31985.6i	0.192147	−	0.192147i
$409$		−	92430.5i		−	0.552547i	−0.961079	−	0.276273i	$-0.910901\pi$
$409$		−	92430.5i		−	0.552547i	0.961079	−	0.276273i	$-0.0890995\pi$
$410$	29324.8	−	453.725i	0.174449	−	0.00269913i
$411$	−73711.0			−0.436364
$412$	63940.6	+	63940.6i	0.376688	+	0.376688i
$413$	−62632.9	+	62632.9i	−0.367200	+	0.367200i
$414$			5966.25i			0.0348098i
$415$	4551.95	+	294198.i	0.0264302	+	1.70822i
$416$	−56088.6			−0.324107
$417$	127496.	+	127496.i	0.733203	+	0.733203i
$418$	−147406.	+	147406.i	−0.843651	+	0.843651i
$419$		−	177539.i		−	1.01127i	−0.862749	−	0.505633i	$-0.831259\pi$
$419$		−	177539.i		−	1.01127i	0.862749	−	0.505633i	$-0.168741\pi$
$420$	53311.8	+	51687.2i	0.302221	+	0.293011i
$421$	123013.			0.694043			0.347022	−	0.937857i	$-0.387193\pi$
$421$	123013.			0.694043			0.347022	+	0.937857i	$0.387193\pi$
$422$	118881.	+	118881.i	0.667554	+	0.667554i
$423$	−28977.7	+	28977.7i	−0.161951	+	0.161951i
$424$		−	122722.i		−	0.682638i
$425$	−108786.	+	115735.i	−0.602275	+	0.640750i
$426$	24674.4			0.135965
$427$	−15066.8	−	15066.8i	−0.0826350	−	0.0826350i
$428$	93467.9	−	93467.9i	0.510240	−	0.510240i
$429$			256614.i			1.39433i
$430$	124398.	−	128308.i	0.672785	−	0.693931i
$431$	294422.			1.58495			0.792475	−	0.609904i	$-0.208792\pi$
$431$	294422.			1.58495			0.792475	+	0.609904i	$0.208792\pi$
$432$	−35642.1	−	35642.1i	−0.190984	−	0.190984i
$433$	−160926.	+	160926.i	−0.858325	+	0.858325i	−0.991141	−	0.132816i	$-0.957598\pi$
$433$	−160926.	+	160926.i	−0.858325	+	0.858325i	0.132816	+	0.991141i	$0.457598\pi$
$434$			173232.i			0.919704i
$435$	29494.5	−	456.350i	0.155870	−	0.00241168i
$436$	−107810.			−0.567137
$437$	−54600.2	−	54600.2i	−0.285911	−	0.285911i
$438$	71624.9	−	71624.9i	0.373350	−	0.373350i
$439$		−	116502.i		−	0.604511i	−0.953227	−	0.302255i	$-0.902260\pi$
$439$		−	116502.i		−	0.604511i	0.953227	−	0.302255i	$-0.0977396\pi$
$440$	921.400	+	59551.3i	0.00475930	+	0.307599i
$441$	3313.99			0.0170402
$442$	−157489.	−	157489.i	−0.806132	−	0.806132i
$443$	−51538.3	+	51538.3i	−0.262617	+	0.262617i	−0.826116	−	0.563500i	$-0.809455\pi$
$443$	−51538.3	+	51538.3i	−0.262617	+	0.262617i	0.563500	+	0.826116i	$0.309455\pi$
$444$		−	78111.7i		−	0.396232i
$445$	−215864.	−	209285.i	−1.09008	−	1.05686i
$446$	239561.			1.20433
$447$	−29031.3	−	29031.3i	−0.145295	−	0.145295i
$448$	−17087.7	+	17087.7i	−0.0851388	+	0.0851388i
$449$			256873.i			1.27417i	0.770795	+	0.637083i	$0.219859\pi$
$449$			256873.i			1.27417i	−0.770795	+	0.637083i	$0.780141\pi$
$450$	24632.3	+	23153.3i	0.121641	+	0.114337i
$451$	43668.7			0.214693
$452$	−28656.3	−	28656.3i	−0.140263	−	0.140263i
$453$	58352.6	−	58352.6i	0.284357	−	0.284357i
$454$			173684.i			0.842651i
$455$	254495.	−	262494.i	1.22930	−	1.26793i
$456$	124599.			0.599219
$457$	232921.	+	232921.i	1.11526	+	1.11526i	0.992428	+	0.122830i	$0.0391971\pi$
$457$	232921.	+	232921.i	1.11526	+	1.11526i	0.122830	+	0.992428i	$0.460803\pi$
$458$	3019.74	−	3019.74i	0.0143959	−	0.0143959i
$459$		−	200156.i		−	0.950045i
$460$	−22058.2	+	341.293i	−0.104245	+	0.00161291i
$461$	160200.			0.753806			0.376903	−	0.926253i	$-0.376989\pi$
$461$	160200.			0.753806			0.376903	+	0.926253i	$0.376989\pi$
$462$	78179.0	+	78179.0i	0.366274	+	0.366274i
$463$	−138515.	+	138515.i	−0.646150	+	0.646150i	−0.952060	−	0.305910i	$-0.901039\pi$
$463$	−138515.	+	138515.i	−0.646150	+	0.646150i	0.305910	+	0.952060i	$0.401039\pi$
$464$			9599.96i			0.0445896i
$465$	−3947.86	−	255156.i	−0.0182581	−	1.18005i
$466$	−13100.3			−0.0603267
$467$	−23885.2	−	23885.2i	−0.109521	−	0.109521i	0.650223	−	0.759744i	$-0.274676\pi$
$467$	−23885.2	−	23885.2i	−0.109521	−	0.109521i	−0.759744	+	0.650223i	$0.774676\pi$
$468$	−33518.9	+	33518.9i	−0.153038	+	0.153038i
$469$		−	45903.4i		−	0.208689i
$470$	−108793.	−	105478.i	−0.492499	−	0.477490i
$471$	−377735.			−1.70273
$472$	30026.8	+	30026.8i	0.134780	+	0.134780i
$473$	188157.	−	188157.i	0.841004	−	0.841004i
$474$		−	218045.i		−	0.970486i
$475$	−437310.	+	13535.7i	−1.93822	+	0.0599920i
$476$	−95959.8			−0.423522
$477$	−73339.4	−	73339.4i	−0.322330	−	0.322330i
$478$	111289.	−	111289.i	0.487074	−	0.487074i
$479$		−	2788.41i		−	0.0121531i	−0.999982	−	0.00607653i	$-0.998066\pi$
$479$		−	2788.41i		−	0.0121531i	0.999982	−	0.00607653i	$-0.00193423\pi$
$480$	24779.3	−	25558.1i	0.107549	−	0.110929i
$481$	−384603.			−1.66235
$482$	−17722.0	−	17722.0i	−0.0762813	−	0.0762813i
$483$	−28958.0	+	28958.0i	−0.124129	+	0.124129i
$484$		−	28448.0i		−	0.121440i
$485$	−162507.	+	2514.37i	−0.690857	+	0.0106892i
$486$	−77063.3			−0.326269
$487$	40229.1	+	40229.1i	0.169622	+	0.169622i	0.786813	−	0.617191i	$-0.211729\pi$
$487$	40229.1	+	40229.1i	0.169622	+	0.169622i	−0.617191	+	0.786813i	$0.711729\pi$
$488$	−7223.14	+	7223.14i	−0.0303310	+	0.0303310i
$489$			209359.i			0.875535i
$490$	189.573	+	12252.4i	0.000789559	+	0.0510302i
$491$	−109390.			−0.453750			−0.226875	−	0.973924i	$-0.572851\pi$
$491$	−109390.			−0.453750			−0.226875	+	0.973924i	$0.572851\pi$
$492$	−18456.1	−	18456.1i	−0.0762448	−	0.0762448i
$493$	−26955.4	+	26955.4i	−0.110905	+	0.110905i
$494$		−	613497.i		−	2.51396i
$495$	36138.8	+	35037.6i	0.147490	+	0.142996i
$496$	83048.9			0.337575
$497$	−37012.8	−	37012.8i	−0.149844	−	0.149844i
$498$	185159.	−	185159.i	0.746598	−	0.746598i
$499$			389489.i			1.56421i	0.623150	+	0.782103i	$0.285853\pi$
$499$			389489.i			1.56421i	−0.623150	+	0.782103i	$0.714147\pi$
$500$	−84192.2	+	92394.1i	−0.336769	+	0.369576i
$501$	−27401.0			−0.109167
$502$	12544.7	+	12544.7i	0.0497799	+	0.0497799i
$503$	340016.	−	340016.i	1.34389	−	1.34389i	0.451740	−	0.892150i	$-0.350804\pi$
$503$	340016.	−	340016.i	1.34389	−	1.34389i	0.892150	−	0.451740i	$-0.149196\pi$
$504$			20423.4i			0.0804022i
$505$	164270.	−	169433.i	0.644133	−	0.664379i
$506$	−32847.7			−0.128293
$507$	−375146.	−	375146.i	−1.45943	−	1.45943i
$508$	−90457.4	+	90457.4i	−0.350523	+	0.350523i
$509$		−	399280.i		−	1.54114i	−0.637355	−	0.770570i	$-0.719972\pi$
$509$		−	399280.i		−	1.54114i	0.637355	−	0.770570i	$-0.280028\pi$
$510$	141341.	−	2186.88i	0.543409	−	0.00840783i
$511$	−214882.			−0.822921
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	389853.	−	389853.i	1.48138	−	1.48138i
$514$		−	221190.i		−	0.837219i
$515$	4371.66	+	282546.i	0.0164828	+	1.06531i
$516$	−159045.			−0.597339
$517$	−159539.	−	159539.i	−0.596879	−	0.596879i
$518$	−117171.	+	117171.i	−0.436679	+	0.436679i
$519$			149394.i			0.554623i
$520$	−125842.	−	122007.i	−0.465392	−	0.451210i
$521$	424869.			1.56523			0.782617	−	0.622503i	$-0.213884\pi$
$521$	424869.			1.56523			0.782617	+	0.622503i	$0.213884\pi$
$522$	5737.00	+	5737.00i	0.0210544	+	0.0210544i
$523$	209720.	−	209720.i	0.766718	−	0.766718i	−0.210809	−	0.977527i	$-0.567610\pi$
$523$	209720.	−	209720.i	0.766718	−	0.766718i	0.977527	+	0.210809i	$0.0676099\pi$
$524$		−	48399.4i		−	0.176270i
$525$	7178.86	+	231934.i	0.0260457	+	0.841483i
$526$	58453.5			0.211271
$527$	233190.	+	233190.i	0.839630	+	0.839630i
$528$	37479.7	−	37479.7i	0.134440	−	0.134440i
$529$		−	12167.0i		−	0.0434783i
$530$	266952.	−	275343.i	0.950345	−	0.980215i
$531$	35888.4			0.127281
$532$	−186905.	−	186905.i	−0.660386	−	0.660386i
$533$	−90873.4	+	90873.4i	−0.319877	+	0.319877i
$534$			267576.i			0.938348i
$535$	413024.	−	6390.47i	1.44301	−	0.0223267i
$536$	−22006.5			−0.0765987
$537$	−176368.	−	176368.i	−0.611606	−	0.611606i
$538$	53380.6	−	53380.6i	0.184425	−	0.184425i
$539$			18245.5i			0.0628025i
$540$	−2436.88	−	157499.i	−0.00835693	−	0.540119i
$541$	320743.			1.09588			0.547940	−	0.836517i	$-0.315412\pi$
$541$	320743.			1.09588			0.547940	+	0.836517i	$0.315412\pi$
$542$	262902.	+	262902.i	0.894943	+	0.894943i
$543$	195082.	−	195082.i	0.661634	−	0.661634i
$544$			46004.0i			0.155453i
$545$	−241887.	−	234516.i	−0.814365	−	0.789548i
$546$	−325377.			−1.09144
$547$	−200618.	−	200618.i	−0.670493	−	0.670493i	0.287337	−	0.957830i	$-0.407230\pi$
$547$	−200618.	−	200618.i	−0.670493	−	0.670493i	−0.957830	+	0.287337i	$0.907230\pi$
$548$	53008.3	−	53008.3i	0.176516	−	0.176516i
$549$			8633.19i			0.0286435i
$550$	−127472.	+	135615.i	−0.421395	+	0.448315i
$551$	−105004.			−0.345863
$552$	13882.7	+	13882.7i	0.0455614	+	0.0455614i
$553$	−327078.	+	327078.i	−1.06955	+	1.06955i
$554$		−	300724.i		−	0.979824i
$555$	169913.	−	175254.i	0.551621	−	0.568959i
$556$	−183374.			−0.593183
$557$	−352525.	−	352525.i	−1.13627	−	1.13627i	−0.989114	−	0.147151i	$-0.952990\pi$
$557$	−352525.	−	352525.i	−1.13627	−	1.13627i	−0.147151	−	0.989114i	$-0.547010\pi$
$558$	49630.5	−	49630.5i	0.159397	−	0.159397i
$559$			783100.i			2.50607i
$560$	−75508.7	+	1168.30i	−0.240780	+	0.00372544i
$561$	210476.			0.668769
$562$	−108908.	−	108908.i	−0.344817	−	0.344817i
$563$	−263615.	+	263615.i	−0.831674	+	0.831674i	−0.987746	−	0.156072i	$-0.950117\pi$
$563$	−263615.	+	263615.i	−0.831674	+	0.831674i	0.156072	+	0.987746i	$0.450117\pi$
$564$			134855.i			0.423945i
$565$	−1959.25	−	126629.i	−0.00613753	−	0.396677i
$566$	−101711.			−0.317495
$567$	−155068.	−	155068.i	−0.482342	−	0.482342i
$568$	−17744.3	+	17744.3i	−0.0549998	+	0.0549998i
$569$		−	194382.i		−	0.600387i	−0.953878	−	0.300194i	$-0.902949\pi$
$569$		−	194382.i		−	0.600387i	0.953878	−	0.300194i	$-0.0970513\pi$
$570$	279555.	+	271036.i	0.860433	+	0.834213i
$571$	−69628.5			−0.213557			−0.106779	−	0.994283i	$-0.534054\pi$
$571$	−69628.5			−0.213557			−0.106779	+	0.994283i	$0.534054\pi$
$572$	−184541.	−	184541.i	−0.564028	−	0.564028i
$573$	41855.4	−	41855.4i	0.127480	−	0.127480i
$574$			55370.2i			0.168055i
$575$	−50232.8	−	47216.5i	−0.151933	−	0.142810i
$576$	9791.18			0.0295114
$577$	46726.3	+	46726.3i	0.140349	+	0.140349i	0.773791	−	0.633442i	$-0.218358\pi$
$577$	46726.3	+	46726.3i	0.140349	+	0.140349i	−0.633442	+	0.773791i	$0.718358\pi$
$578$	37869.1	−	37869.1i	0.113352	−	0.113352i
$579$			454343.i			1.35527i
$580$	−20882.4	+	21538.8i	−0.0620761	+	0.0640272i
$581$	−555496.			−1.64562
$582$	102277.	+	102277.i	0.301947	+	0.301947i
$583$	403776.	−	403776.i	1.18796	−	1.18796i
$584$			103016.i			0.302051i
$585$	−148116.	+	2291.71i	−0.432804	+	0.00669651i
$586$	424681.			1.23671
$587$	−182007.	−	182007.i	−0.528217	−	0.528217i	0.391824	−	0.920040i	$-0.371844\pi$
$587$	−182007.	−	182007.i	−0.528217	−	0.528217i	−0.920040	+	0.391824i	$0.871844\pi$
$588$	7711.25	−	7711.25i	0.0223034	−	0.0223034i
$589$			908387.i			2.61843i
$590$	2052.95	+	132685.i	0.00589759	+	0.381169i
$591$	199183.			0.570266
$592$	56173.0	+	56173.0i	0.160282	+	0.160282i
$593$	−29100.7	+	29100.7i	−0.0827548	+	0.0827548i	−0.747273	−	0.664518i	$-0.768637\pi$
$593$	−29100.7	+	29100.7i	−0.0827548	+	0.0827548i	0.664518	+	0.747273i	$0.268637\pi$
$594$		−	234537.i		−	0.664720i
$595$	−215298.	−	208737.i	−0.608144	−	0.589612i
$596$	41755.0			0.117548
$597$	−149660.	−	149660.i	−0.419910	−	0.419910i
$598$	68355.2	−	68355.2i	0.191148	−	0.191148i
$599$		−	207258.i		−	0.577639i	−0.957384	−	0.288820i	$-0.906737\pi$
$599$		−	207258.i		−	0.577639i	0.957384	−	0.288820i	$-0.0932628\pi$
$600$	111191.	−	3441.61i	0.308864	−	0.00956002i
$601$	−258391.			−0.715366			−0.357683	−	0.933843i	$-0.616433\pi$
$601$	−258391.			−0.715366			−0.357683	+	0.933843i	$0.616433\pi$
$602$	238576.	+	238576.i	0.658314	+	0.658314i
$603$	−13151.2	+	13151.2i	−0.0361686	+	0.0361686i
$604$			83927.0i			0.230053i
$605$	61881.7	−	63826.7i	0.169064	−	0.174378i
$606$	−210022.			−0.571900
$607$	224876.	+	224876.i	0.610331	+	0.610331i	0.943032	−	0.332701i	$-0.107960\pi$
$607$	224876.	+	224876.i	0.610331	+	0.610331i	−0.332701	+	0.943032i	$0.607960\pi$
$608$	−89604.0	+	89604.0i	−0.242393	+	0.242393i
$609$			55690.6i			0.150157i
$610$	−31918.3	+	493.852i	−0.0857787	+	0.00132720i
$611$	663994.			1.77861
$612$	27492.3	+	27492.3i	0.0734020	+	0.0734020i
$613$	−355705.	+	355705.i	−0.946606	+	0.946606i	−0.998645	−	0.0520389i	$-0.983428\pi$
$613$	−355705.	+	355705.i	−0.946606	+	0.946606i	0.0520389	+	0.998645i	$0.483428\pi$
$614$		−	360259.i		−	0.955604i
$615$	−1261.86	−	81555.5i	−0.00333626	−	0.215627i
$616$	−112443.			−0.296326
$617$	26367.4	+	26367.4i	0.0692623	+	0.0692623i	0.740889	−	0.671627i	$-0.234404\pi$
$617$	26367.4	+	26367.4i	0.0692623	+	0.0692623i	−0.671627	+	0.740889i	$0.734404\pi$
$618$	177826.	−	177826.i	0.465605	−	0.465605i
$619$		−	246750.i		−	0.643984i	−0.946742	−	0.321992i	$-0.895648\pi$
$619$		−	246750.i		−	0.643984i	0.946742	−	0.321992i	$-0.104352\pi$
$620$	186331.	+	180653.i	0.484732	+	0.469960i
$621$	86874.1			0.225272
$622$	30399.2	+	30399.2i	0.0785744	+	0.0785744i
$623$	401377.	−	401377.i	1.03413	−	1.03413i
$624$			155989.i			0.400612i
$625$	−389877.	+	24158.2i	−0.998086	+	0.0618451i
$626$	−284394.			−0.725724
$627$	409953.	+	409953.i	1.04279	+	1.04279i
$628$	271643.	−	271643.i	0.688778	−	0.688778i
$629$			315452.i			0.797319i
$630$	−44426.3	+	45822.6i	−0.111933	+	0.115451i
$631$	−490980.			−1.23312			−0.616560	−	0.787308i	$-0.711474\pi$
$631$	−490980.			−1.23312			−0.616560	+	0.787308i	$0.711474\pi$
$632$	156804.	+	156804.i	0.392576	+	0.392576i
$633$	330620.	−	330620.i	0.825130	−	0.825130i
$634$			158956.i			0.395457i
$635$	−399721.	+	6184.64i	−0.991310	+	0.0153379i
$636$	−341303.			−0.843774
$637$	−37968.3	−	37968.3i	−0.0935713	−	0.0935713i
$638$	−31585.5	+	31585.5i	−0.0775972	+	0.0775972i
$639$			21208.2i			0.0519399i
$640$	560.093	+	36199.5i	0.00136741	+	0.0883778i
$641$	−191815.			−0.466839			−0.233420	−	0.972376i	$-0.574992\pi$
$641$	−191815.			−0.466839			−0.233420	+	0.972376i	$0.574992\pi$
$642$	−259945.	−	259945.i	−0.630682	−	0.630682i
$643$	−482600.	+	482600.i	−1.16725	+	1.16725i	−0.184402	+	0.982851i	$0.559035\pi$
$643$	−482600.	+	482600.i	−1.16725	+	1.16725i	−0.982851	+	0.184402i	$0.940965\pi$
$644$		−	41649.6i		−	0.100424i
$645$	−356838.	−	345964.i	−0.857733	−	0.831595i
$646$	−503191.			−1.20578
$647$	517782.	+	517782.i	1.23691	+	1.23691i	0.961257	+	0.275654i	$0.0888945\pi$
$647$	517782.	+	517782.i	1.23691	+	1.23691i	0.275654	+	0.961257i	$0.411105\pi$
$648$	−74340.8	+	74340.8i	−0.177042	+	0.177042i
$649$			197586.i			0.469102i
$650$	−16945.6	−	547478.i	−0.0401080	−	1.29581i
$651$	481777.			1.13680
$652$	−150558.	−	150558.i	−0.354167	−	0.354167i
$653$	327407.	−	327407.i	0.767825	−	0.767825i	−0.209899	−	0.977723i	$-0.567313\pi$
$653$	327407.	−	327407.i	0.767825	−	0.767825i	0.977723	+	0.209899i	$0.0673134\pi$
$654$			299833.i			0.701009i
$655$	105281.	−	108590.i	0.245396	−	0.253110i
$656$	26545.0			0.0616843
$657$	61563.2	+	61563.2i	0.142623	+	0.142623i
$658$	202289.	−	202289.i	0.467220	−	0.467220i
$659$		−	523053.i		−	1.20441i	−0.798341	−	0.602206i	$-0.794289\pi$
$659$		−	523053.i		−	1.20441i	0.798341	−	0.602206i	$-0.205711\pi$
$660$	165619.	−	2562.52i	0.380208	−	0.00588273i
$661$	218213.			0.499432			0.249716	−	0.968319i	$-0.419663\pi$
$661$	218213.			0.499432			0.249716	+	0.968319i	$0.419663\pi$
$662$	203841.	+	203841.i	0.465132	+	0.465132i
$663$	−437995.	+	437995.i	−0.996418	+	0.996418i
$664$			266310.i			0.604019i
$665$	−12778.8	−	825913.i	−0.0288967	−	1.86763i
$666$	67138.7			0.151365
$667$	−11699.5	−	11699.5i	−0.0262975	−	0.0262975i
$668$	19705.1	−	19705.1i	0.0441596	−	0.0441596i
$669$		−	666246.i		−	1.48861i
$670$	−49374.4	−	47869.8i	−0.109990	−	0.106638i
$671$	−47530.7			−0.105567
$672$	47522.8	+	47522.8i	0.105236	+	0.105236i
$673$	555628.	−	555628.i	1.22674	−	1.22674i	0.261555	−	0.965188i	$-0.415765\pi$
$673$	555628.	−	555628.i	1.22674	−	1.22674i	0.965188	−	0.261555i	$-0.0842354\pi$
$674$			199784.i			0.439786i
$675$	337133.	−	358669.i	0.739935	−	0.787203i
$676$	539562.			1.18072
$677$	444331.	+	444331.i	0.969460	+	0.969460i	0.999547	−	0.0300877i	$-0.00957864\pi$
$677$	444331.	+	444331.i	0.969460	+	0.969460i	−0.0300877	+	0.999547i	$0.509579\pi$
$678$	−79696.4	+	79696.4i	−0.173372	+	0.173372i
$679$		−	306840.i		−	0.665538i
$680$	−100071.	+	103216.i	−0.216416	+	0.223218i
$681$	483034.			1.04156
$682$	273245.	+	273245.i	0.587466	+	0.587466i
$683$	177168.	−	177168.i	0.379790	−	0.379790i	−0.491237	−	0.871026i	$-0.663455\pi$
$683$	177168.	−	177168.i	0.379790	−	0.379790i	0.871026	+	0.491237i	$0.163455\pi$
$684$			107096.i			0.228908i
$685$	234238.	−	3624.22i	0.499202	−	0.00772384i
$686$	−343663.			−0.730271
$687$	−8398.22	−	8398.22i	−0.0177940	−	0.0177940i
$688$	114375.	−	114375.i	0.241632	−	0.241632i
$689$			1.68049e6i			3.53996i
$690$	949.173	+	61346.2i	0.00199364	+	0.128852i
$691$	−93955.5			−0.196773			−0.0983867	−	0.995148i	$-0.531368\pi$
$691$	−93955.5			−0.196773			−0.0983867	+	0.995148i	$0.531368\pi$
$692$	−107435.	−	107435.i	−0.224353	−	0.224353i
$693$	−67196.5	+	67196.5i	−0.139920	+	0.139920i
$694$			145636.i			0.302377i
$695$	−411424.	−	398886.i	−0.851765	−	0.825809i
$696$	26698.6			0.0551149
$697$	74534.6	+	74534.6i	0.153424	+	0.153424i
$698$	−39506.6	+	39506.6i	−0.0810885	+	0.0810885i
$699$			36433.4i			0.0745668i
$700$	−171955.	−	161630.i	−0.350928	−	0.329856i
$701$	645636.			1.31387			0.656934	−	0.753948i	$-0.271853\pi$
$701$	645636.			1.31387			0.656934	+	0.753948i	$0.271853\pi$
$702$	488066.	+	488066.i	0.990386	+	0.990386i
$703$	−614420.	+	614420.i	−1.24324	+	1.24324i
$704$			53906.1i			0.108766i
$705$	−293345.	+	302565.i	−0.590202	+	0.608752i
$706$	−74457.9			−0.149383
$707$	315044.	+	315044.i	0.630278	+	0.630278i
$708$	83507.8	−	83507.8i	0.166594	−	0.166594i
$709$		−	191834.i		−	0.381621i	−0.981627	−	0.190811i	$-0.938888\pi$
$709$		−	191834.i		−	0.381621i	0.981627	−	0.190811i	$-0.0611117\pi$
$710$	−78409.9	+	1213.19i	−0.155544	+	0.00240664i
$711$	187414.			0.370735
$712$	−192424.	−	192424.i	−0.379575	−	0.379575i
$713$	−101212.	+	101212.i	−0.199091	+	0.199091i
$714$			266875.i			0.523493i
$715$	−12617.2	−	815466.i	−0.0246803	−	1.59512i
$716$	253666.			0.494807
$717$	−309506.	−	309506.i	−0.602048	−	0.602048i
$718$	−176222.	+	176222.i	−0.341831	+	0.341831i
$719$			191597.i			0.370622i	0.982680	+	0.185311i	$0.0593293\pi$
$719$			191597.i			0.370622i	−0.982680	+	0.185311i	$0.940671\pi$
$720$	21967.8	+	21298.3i	0.0423761	+	0.0410848i
$721$	−533495.			−1.02627
$722$	−719445.	−	719445.i	−1.38014	−	1.38014i
$723$	−49286.8	+	49286.8i	−0.0942874	+	0.0942874i
$724$			280581.i			0.535281i
$725$	−93704.8	+	2900.37i	−0.178273	+	0.00551794i
$726$	−79116.9			−0.150105
$727$	35305.3	+	35305.3i	0.0667992	+	0.0667992i	0.739717	−	0.672918i	$-0.234959\pi$
$727$	35305.3	+	35305.3i	0.0667992	+	0.0667992i	−0.672918	+	0.739717i	$0.734959\pi$
$728$	233991.	−	233991.i	0.441505	−	0.441505i
$729$			590672.i			1.11145i
$730$	−224087.	+	231130.i	−0.420505	+	0.433722i
$731$	642300.			1.20200
$732$	20088.4	+	20088.4i	0.0374906	+	0.0374906i
$733$	326011.	−	326011.i	0.606770	−	0.606770i	−0.335331	−	0.942100i	$-0.608848\pi$
$733$	326011.	−	326011.i	0.606770	−	0.606770i	0.942100	+	0.335331i	$0.108848\pi$
$734$		−	113534.i		−	0.210734i
$735$	34075.2	−	527.224i	0.0630759	−	0.000975934i
$736$	−19967.2			−0.0368605
$737$	−72405.0	−	72405.0i	−0.133301	−	0.133301i
$738$	15863.4	−	15863.4i	0.0291262	−	0.0291262i
$739$		−	287660.i		−	0.526734i	−0.964696	−	0.263367i	$-0.915167\pi$
$739$		−	287660.i		−	0.526734i	0.964696	−	0.263367i	$-0.0848330\pi$
$740$	3840.59	+	248222.i	0.00701350	+	0.453291i
$741$	−1.70620e6			−3.10738
$742$	511972.	+	511972.i	0.929904	+	0.929904i
$743$	−323250.	+	323250.i	−0.585545	+	0.585545i	−0.936422	−	0.350877i	$-0.885884\pi$
$743$	−323250.	+	323250.i	−0.585545	+	0.585545i	0.350877	+	0.936422i	$0.385884\pi$
$744$		−	230968.i		−	0.417259i
$745$	93682.7	+	90827.9i	0.168790	+	0.163647i
$746$	437061.			0.785353
$747$	159148.	+	159148.i	0.285207	+	0.285207i
$748$	−151361.	+	151361.i	−0.270527	+	0.270527i
$749$			779859.i			1.39012i
$750$	256958.	+	234148.i	0.456815	+	0.416263i
$751$	123210.			0.218458			0.109229	−	0.994017i	$-0.465162\pi$
$751$	123210.			0.218458			0.109229	+	0.994017i	$0.465162\pi$
$752$	−96979.4	−	96979.4i	−0.171492	−	0.171492i
$753$	34888.3	−	34888.3i	0.0615304	−	0.0615304i
$754$		−	131457.i		−	0.231229i
$755$	−182563.	+	188301.i	−0.320272	+	0.330338i
$756$	297384.			0.520324
$757$	−586215.	−	586215.i	−1.02298	−	1.02298i	−0.999730	−	0.0232462i	$-0.992600\pi$
$757$	−586215.	−	586215.i	−1.02298	−	1.02298i	−0.0232462	−	0.999730i	$-0.507400\pi$
$758$	316002.	−	316002.i	0.549985	−	0.549985i
$759$			91353.0i			0.158577i
$760$	−395950.	+	6126.29i	−0.685509	+	0.0106065i
$761$	−267065.			−0.461156			−0.230578	−	0.973054i	$-0.574062\pi$
$761$	−267065.			−0.461156			−0.230578	+	0.973054i	$0.574062\pi$
$762$	251572.	+	251572.i	0.433264	+	0.433264i
$763$	449764.	−	449764.i	0.772566	−	0.772566i
$764$			60199.6i			0.103135i
$765$	1879.67	+	121485.i	0.00321187	+	0.207587i
$766$	533667.			0.909521
$767$	−411172.	−	411172.i	−0.698928	−	0.698928i
$768$	22782.9	−	22782.9i	0.0386265	−	0.0386265i
$769$			66443.0i			0.112356i	0.998421	+	0.0561781i	$0.0178915\pi$
$769$			66443.0i			0.112356i	−0.998421	+	0.0561781i	$0.982109\pi$
$770$	−252280.	−	244592.i	−0.425502	−	0.412535i
$771$	−615153.			−1.03484
$772$	−326735.	−	326735.i	−0.548227	−	0.548227i
$773$	−316867.	+	316867.i	−0.530296	+	0.530296i	−0.920660	−	0.390364i	$-0.872349\pi$
$773$	−316867.	+	316867.i	−0.530296	+	0.530296i	0.390364	+	0.920660i	$0.372349\pi$
$774$		−	136703.i		−	0.228189i
$775$	25090.9	+	810636.i	0.0417747	+	1.34965i
$776$	−147102.			−0.244284
$777$	325867.	+	325867.i	0.539756	+	0.539756i
$778$	−120170.	+	120170.i	−0.198535	+	0.198535i
$779$			290348.i			0.478459i
$780$	−339316.	+	349981.i	−0.557718	+	0.575248i
$781$	−116763.			−0.191427
$782$	−56065.1	−	56065.1i	−0.0916809	−	0.0916809i
$783$	83535.9	−	83535.9i	0.136254	−	0.136254i
$784$			11090.9i			0.0180441i
$785$	1.20036e6	−	18572.4i	1.94793	−	0.0301391i
$786$	−134604.			−0.217878
$787$	109912.	+	109912.i	0.177458	+	0.177458i	0.790247	−	0.612789i	$-0.209952\pi$
$787$	109912.	+	109912.i	0.177458	+	0.177458i	−0.612789	+	0.790247i	$0.709952\pi$
$788$	−143240.	+	143240.i	−0.230681	+	0.230681i
$789$		−	162566.i		−	0.261141i
$790$	10720.8	+	692900.i	0.0171780	+	1.11024i
$791$	239097.			0.382139
$792$	32214.6	+	32214.6i	0.0513573	+	0.0513573i
$793$	98910.2	−	98910.2i	0.157288	−	0.157288i
$794$		−	153563.i		−	0.243582i
$795$	−765758.	−	742423.i	−1.21159	−	1.17467i
$796$	215252.			0.339719
$797$	335450.	+	335450.i	0.528094	+	0.528094i	0.920004	−	0.391909i	$-0.128185\pi$
$797$	335450.	+	335450.i	0.528094	+	0.528094i	−0.391909	+	0.920004i	$0.628185\pi$
$798$	−519804.	+	519804.i	−0.816270	+	0.816270i
$799$		−	544609.i		−	0.853084i
$800$	−77486.7	+	82436.7i	−0.121073	+	0.128807i
$801$	−229987.			−0.358458
$802$	−311191.	−	311191.i	−0.483814	−	0.483814i
$803$	−338941.	+	338941.i	−0.525645	+	0.525645i
$804$			61202.5i			0.0946797i
$805$	90598.6	−	93446.2i	0.139807	−	0.144202i
$806$	−1.13723e6			−1.75057
$807$	−148457.	−	148457.i	−0.227958	−	0.227958i
$808$	151035.	−	151035.i	0.231342	−	0.231342i
$809$		−	618753.i		−	0.945410i	−0.881221	−	0.472705i	$-0.843278\pi$
$809$		−	618753.i		−	0.945410i	0.881221	−	0.472705i	$-0.156722\pi$
$810$	−328504.	+	5082.74i	−0.500692	+	0.00774689i
$811$	502963.			0.764706			0.382353	−	0.924016i	$-0.375114\pi$
$811$	502963.			0.764706			0.382353	+	0.924016i	$0.375114\pi$
$812$	−40049.2	−	40049.2i	−0.0607409	−	0.0607409i
$813$	731159.	−	731159.i	1.10619	−	1.10619i
$814$			369637.i			0.557862i
$815$	−10293.7	−	665298.i	−0.0154974	−	1.00161i
$816$	127942.			0.192147
$817$	1.25104e6	+	1.25104e6i	1.87424	+	1.87424i
$818$	184861.	−	184861.i	0.276273	−	0.276273i
$819$		−	279669.i		−	0.416942i
$820$	59557.0	+	57742.1i	0.0885738	+	0.0858747i
$821$	868509.			1.28851			0.644255	−	0.764811i	$-0.277168\pi$
$821$	868509.			1.28851			0.644255	+	0.764811i	$0.277168\pi$
$822$	−147422.	−	147422.i	−0.218182	−	0.218182i
$823$	−205216.	+	205216.i	−0.302979	+	0.302979i	−0.842178	−	0.539199i	$-0.818727\pi$
$823$	−205216.	+	205216.i	−0.302979	+	0.302979i	0.539199	+	0.842178i	$0.318727\pi$
$824$			255762.i			0.376688i
$825$	377161.	+	354514.i	0.554139	+	0.520866i
$826$	−250532.			−0.367200
$827$	429031.	+	429031.i	0.627303	+	0.627303i	0.947389	−	0.320085i	$-0.103712\pi$
$827$	429031.	+	429031.i	0.627303	+	0.627303i	−0.320085	+	0.947389i	$0.603712\pi$
$828$	−11932.5	+	11932.5i	−0.0174049	+	0.0174049i
$829$		−	878260.i		−	1.27795i	−0.769227	−	0.638975i	$-0.779359\pi$
$829$		−	878260.i		−	1.27795i	0.769227	−	0.638975i	$-0.220641\pi$
$830$	−579293.	+	597500.i	−0.840895	+	0.867325i
$831$	−836346.			−1.21111
$832$	−112177.	−	112177.i	−0.162053	−	0.162053i
$833$	−31141.7	+	31141.7i	−0.0448799	+	0.0448799i
$834$			509984.i			0.733203i
$835$	87074.6	−	1347.25i	0.124887	−	0.00193231i
$836$	−589624.			−0.843651
$837$	−722666.	−	722666.i	−1.03154	−	1.03154i
$838$	355078.	−	355078.i	0.505633	−	0.505633i
$839$		−	259361.i		−	0.368451i	−0.982884	−	0.184226i	$-0.941022\pi$
$839$		−	259361.i		−	0.368451i	0.982884	−	0.184226i	$-0.0589777\pi$
$840$	3249.17	+	209998.i	0.00460483	+	0.297616i
$841$	684781.			0.968188
$842$	246026.	+	246026.i	0.347022	+	0.347022i
$843$	−302886.	+	302886.i	−0.426211	+	0.426211i
$844$			475523.i			0.667554i
$845$	1.21058e6	+	1.17369e6i	1.69543	+	1.64376i
$846$	−115911.			−0.161951
$847$	118679.	+	118679.i	0.165428	+	0.165428i
$848$	245444.	−	245444.i	0.341319	−	0.341319i
$849$			282871.i			0.392439i
$850$	−449043.	+	13898.9i	−0.621512	+	0.0192372i
$851$	−136916.			−0.189058
$852$	49348.7	+	49348.7i	0.0679825	+	0.0679825i
$853$	66878.2	−	66878.2i	0.0919150	−	0.0919150i	−0.659654	−	0.751569i	$-0.729297\pi$
$853$	66878.2	−	66878.2i	0.0919150	−	0.0919150i	0.751569	+	0.659654i	$0.229297\pi$
$854$		−	60267.1i		−	0.0826350i
$855$	−232961.	+	240283.i	−0.318677	+	0.328694i
$856$	373872.			0.510240
$857$	88762.9	+	88762.9i	0.120856	+	0.120856i	0.764948	−	0.644092i	$-0.222765\pi$
$857$	88762.9	+	88762.9i	0.120856	+	0.120856i	−0.644092	+	0.764948i	$0.722765\pi$
$858$	−513229.	+	513229.i	−0.697166	+	0.697166i
$859$		−	162025.i		−	0.219582i	−0.993955	−	0.109791i	$-0.964982\pi$
$859$		−	162025.i		−	0.219582i	0.993955	−	0.109791i	$-0.0350181\pi$
$860$	505412.	−	7819.92i	0.683358	−	0.0105732i
$861$	153991.			0.207725
$862$	588844.	+	588844.i	0.792475	+	0.792475i
$863$	535627.	−	535627.i	0.719186	−	0.719186i	−0.249253	−	0.968439i	$-0.580185\pi$
$863$	535627.	−	535627.i	0.719186	−	0.719186i	0.968439	+	0.249253i	$0.0801849\pi$
$864$		−	142569.i		−	0.190984i
$865$	−7345.39	−	474742.i	−0.00981709	−	0.634491i
$866$	−643706.			−0.858325
$867$	−105318.	−	105318.i	−0.140109	−	0.140109i
$868$	−346464.	+	346464.i	−0.459852	+	0.459852i
$869$			1.03182e6i			1.36636i
$870$	59901.7	+	58076.3i	0.0791408	+	0.0767291i
$871$	301346.			0.397218
$872$	−215621.	−	215621.i	−0.283568	−	0.283568i
$873$	−87909.1	+	87909.1i	−0.115347	+	0.115347i
$874$		−	218401.i		−	0.285911i
$875$	−34216.6	−	736683.i	−0.0446911	−	0.962199i
$876$	286500.			0.373350
$877$	924999.	+	924999.i	1.20266	+	1.20266i	0.973355	+	0.229302i	$0.0736445\pi$
$877$	924999.	+	924999.i	1.20266	+	1.20266i	0.229302	+	0.973355i	$0.426356\pi$
$878$	233004.	−	233004.i	0.302255	−	0.302255i
$879$		−	1.18108e6i		−	1.52863i
$880$	−117260.	+	120945.i	−0.151420	+	0.156179i
$881$	−649631.			−0.836979			−0.418490	−	0.908222i	$-0.637440\pi$
$881$	−649631.			−0.836979			−0.418490	+	0.908222i	$0.637440\pi$
$882$	6627.99	+	6627.99i	0.00852010	+	0.00852010i
$883$	−358681.	+	358681.i	−0.460031	+	0.460031i	−0.898666	−	0.438634i	$-0.855462\pi$
$883$	−358681.	+	358681.i	−0.460031	+	0.460031i	0.438634	+	0.898666i	$0.355462\pi$
$884$		−	629956.i		−	0.806132i
$885$	369011.	−	5709.49i	0.471144	−	0.00728971i
$886$	−206153.			−0.262617
$887$	−300250.	−	300250.i	−0.381624	−	0.381624i	0.490063	−	0.871687i	$-0.336974\pi$
$887$	−300250.	−	300250.i	−0.381624	−	0.381624i	−0.871687	+	0.490063i	$0.836974\pi$
$888$	156223.	−	156223.i	0.198116	−	0.198116i
$889$		−	754741.i		−	0.954980i
$890$	−13156.1	−	850298.i	−0.0166092	−	1.07347i
$891$	−489187.			−0.616197
$892$	479122.	+	479122.i	0.602166	+	0.602166i
$893$	1.06076e6	−	1.06076e6i	1.33019	−	1.33019i
$894$		−	116125.i		−	0.145295i
$895$	569132.	+	551789.i	0.710505	+	0.688853i
$896$	−68350.8			−0.0851388
$897$	−190103.	−	190103.i	−0.236268	−	0.236268i
$898$	−513747.	+	513747.i	−0.637083	+	0.637083i
$899$			194645.i			0.240837i
$900$	2958.14	+	95571.2i	0.00365202	+	0.117989i
$901$	1.37834e6			1.69788
$902$	87337.3	+	87337.3i	0.107346	+	0.107346i
$903$	663505.	−	663505.i	0.813708	−	0.813708i
$904$		−	114625.i		−	0.140263i
$905$	−610337.	+	629521.i	−0.745200	+	0.768622i
$906$	233410.			0.284357
$907$	−603367.	−	603367.i	−0.733444	−	0.733444i	0.237857	−	0.971300i	$-0.423555\pi$
$907$	−603367.	−	603367.i	−0.733444	−	0.733444i	−0.971300	+	0.237857i	$0.923555\pi$
$908$	−347368.	+	347368.i	−0.421325	+	0.421325i
$909$		−	180519.i		−	0.218471i
$910$	1.03398e6	−	15998.1i	1.24862	−	0.0193191i
$911$	51542.2			0.0621050			0.0310525	−	0.999518i	$-0.490114\pi$
$911$	51542.2			0.0621050			0.0310525	+	0.999518i	$0.490114\pi$
$912$	249199.	+	249199.i	0.299610	+	0.299610i
$913$	−876204.	+	876204.i	−1.05115	+	1.05115i
$914$			931682.i			1.11526i
$915$	1373.46	+	88768.2i	0.00164049	+	0.106027i
$916$	12078.9			0.0143959
$917$	201913.	+	201913.i	0.240118	+	0.240118i
$918$	400313.	−	400313.i	0.475022	−	0.475022i
$919$			139574.i			0.165262i	0.996580	+	0.0826309i	$0.0263323\pi$
$919$			139574.i			0.165262i	−0.996580	+	0.0826309i	$0.973668\pi$
$920$	−44799.0	−	43433.8i	−0.0529288	−	0.0513159i
$921$	−1.00192e6			−1.18117
$922$	320399.	+	320399.i	0.376903	+	0.376903i
$923$	242981.	−	242981.i	0.285213	−	0.285213i
$924$			312716.i			0.366274i
$925$	−531331.	+	565273.i	−0.620986	+	0.660655i
$926$	−554058.			−0.646150
$927$	152845.	+	152845.i	0.177866	+	0.177866i
$928$	−19199.9	+	19199.9i	−0.0222948	+	0.0222948i
$929$		−	287603.i		−	0.333244i	−0.986021	−	0.166622i	$-0.946714\pi$
$929$		−	287603.i		−	0.333244i	0.986021	−	0.166622i	$-0.0532860\pi$
$930$	502415.	−	518207.i	0.580894	−	0.599152i
$931$	−121312.			−0.139960
$932$	−26200.6	−	26200.6i	−0.0301634	−	0.0301634i
$933$	84543.5	−	84543.5i	0.0971218	−	0.0971218i
$934$		−	95541.0i		−	0.109521i
$935$	−668847.	+	10348.7i	−0.765074	+	0.0118375i
$936$	−134076.			−0.153038
$937$	−1.07010e6	−	1.07010e6i	−1.21883	−	1.21883i	−0.968041	−	0.250791i	$-0.919309\pi$
$937$	−1.07010e6	−	1.07010e6i	−1.21883	−	1.21883i	−0.250791	−	0.968041i	$-0.580691\pi$
$938$	91806.8	−	91806.8i	0.104344	−	0.104344i
$939$			790931.i			0.897031i
$940$	−6630.55	−	428541.i	−0.00750402	−	0.484995i
$941$	−1.20341e6			−1.35904			−0.679522	−	0.733655i	$-0.737813\pi$
$941$	−1.20341e6			−1.35904			−0.679522	+	0.733655i	$0.737813\pi$
$942$	−755470.	−	755470.i	−0.851364	−	0.851364i
$943$	−32350.3	+	32350.3i	−0.0363794	+	0.0363794i
$944$			120107.i			0.134780i
$945$	667220.	+	646887.i	0.747145	+	0.724377i
$946$	752628.			0.841004
$947$	105817.	+	105817.i	0.117992	+	0.117992i	0.763638	−	0.645645i	$-0.223411\pi$
$947$	105817.	+	105817.i	0.117992	+	0.117992i	−0.645645	+	0.763638i	$0.723411\pi$
$948$	436090.	−	436090.i	0.485243	−	0.485243i
$949$		−	1.41065e6i		−	1.56635i
$950$	−901692.	−	847549.i	−0.999104	−	0.939112i
$951$	442076.			0.488805
$952$	−191920.	−	191920.i	−0.211761	−	0.211761i
$953$	−723858.	+	723858.i	−0.797016	+	0.797016i	−0.982624	−	0.185607i	$-0.940575\pi$
$953$	−723858.	+	723858.i	−0.797016	+	0.797016i	0.185607	+	0.982624i	$0.440575\pi$
$954$		−	293357.i		−	0.322330i
$955$	−130950.	+	135066.i	−0.143581	+	0.148094i
$956$	445155.			0.487074
$957$	87842.7	+	87842.7i	0.0959140	+	0.0959140i
$958$	5576.82	−	5576.82i	0.00607653	−	0.00607653i
$959$			442281.i			0.480906i
$960$	100675.	−	1557.68i	0.109239	−	0.00169019i
$961$	760344.			0.823310
$962$	−769206.	−	769206.i	−0.831175	−	0.831175i
$963$	223428.	−	223428.i	0.240927	−	0.240927i
$964$		−	70887.9i		−	0.0762813i
$965$	−22339.1	−	1.44380e6i	−0.0239889	−	1.55043i
$966$	−115832.			−0.124129
$967$	232094.	+	232094.i	0.248205	+	0.248205i	0.820234	−	0.572028i	$-0.193843\pi$
$967$	232094.	+	232094.i	0.248205	+	0.248205i	−0.572028	+	0.820234i	$0.693843\pi$
$968$	56895.9	−	56895.9i	0.0607198	−	0.0607198i
$969$			1.39943e6i			1.49040i
$970$	−330042.	−	319985.i	−0.350773	−	0.340084i
$971$	−872338.			−0.925222			−0.462611	−	0.886561i	$-0.653087\pi$
$971$	−872338.			−0.925222			−0.462611	+	0.886561i	$0.653087\pi$
$972$	−154127.	−	154127.i	−0.163134	−	0.163134i
$973$	765001.	−	765001.i	0.808047	−	0.808047i
$974$			160916.i			0.169622i
$975$	−1.52260e6	+	47127.7i	−1.60168	+	0.0495755i
$976$	−28892.6			−0.0303310
$977$	392919.	+	392919.i	0.411636	+	0.411636i	0.882308	−	0.470672i	$-0.155988\pi$
$977$	392919.	+	392919.i	0.411636	+	0.411636i	−0.470672	+	0.882308i	$0.655988\pi$
$978$	−418718.	+	418718.i	−0.437767	+	0.437767i
$979$		−	1.26621e6i		−	1.32112i
$980$	−24125.6	+	24883.9i	−0.0251203	+	0.0259099i
$981$	−257713.			−0.267792
$982$	−218781.	−	218781.i	−0.226875	−	0.226875i
$983$	−234958.	+	234958.i	−0.243155	+	0.243155i	−0.818154	−	0.574999i	$-0.805002\pi$
$983$	−234958.	+	234958.i	−0.243155	+	0.243155i	0.574999	+	0.818154i	$0.305002\pi$
$984$		−	73824.5i		−	0.0762448i
$985$	−632961.	+	9793.42i	−0.652386	+	0.0100940i
$986$	−107821.			−0.110905
$987$	−562589.	−	562589.i	−0.577507	−	0.577507i
$988$	1.22699e6	−	1.22699e6i	1.25698	−	1.25698i
$989$			278778.i			0.285014i
$990$	2202.54	+	142353.i	0.00224726	+	0.145243i
$991$	−382431.			−0.389409			−0.194705	−	0.980862i	$-0.562375\pi$
$991$	−382431.			−0.389409			−0.194705	+	0.980862i	$0.562375\pi$
$992$	166098.	+	166098.i	0.168788	+	0.168788i
$993$	566906.	−	566906.i	0.574926	−	0.574926i
$994$		−	148051.i		−	0.149844i
$995$	482945.	+	468228.i	0.487811	+	0.472946i
$996$	740637.			0.746598
$997$	−881022.	−	881022.i	−0.886332	−	0.886332i	0.107837	−	0.994169i	$-0.465608\pi$
$997$	−881022.	−	881022.i	−0.886332	−	0.886332i	−0.994169	+	0.107837i	$0.965608\pi$
$998$	−778977.	+	778977.i	−0.782103	+	0.782103i
$999$		−	977601.i		−	0.979559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.16	✓	44
5.3	odd	4	inner	230.5.f.b.93.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.16	✓	44	1.1	even	1	trivial
230.5.f.b.93.16	yes	44	5.3	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(5.56222 - 5.56222i) q^{3} +8.00000i q^{4} +(-17.4021 + 17.9490i) q^{5} +22.2489 q^{6} +(-33.3744 - 33.3744i) q^{7} +(-16.0000 + 16.0000i) q^{8} +19.1234i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(5.56222 - 5.56222i) q^{3} +8.00000i q^{4} +(-17.4021 + 17.9490i) q^{5} +22.2489 q^{6} +(-33.3744 - 33.3744i) q^{7} +(-16.0000 + 16.0000i) q^{8} +19.1234i q^{9} +(-70.7022 + 1.09393i) q^{10} -105.285 q^{11} +(44.4978 + 44.4978i) q^{12} +(219.096 - 219.096i) q^{13} -133.498i q^{14} +(3.04235 + 196.631i) q^{15} -64.0000 q^{16} +(-179.703 - 179.703i) q^{17} +(-38.2468 + 38.2468i) q^{18} -700.031i q^{19} +(-143.592 - 139.217i) q^{20} -371.272 q^{21} +(-210.571 - 210.571i) q^{22} +(77.9968 - 77.9968i) q^{23} +177.991i q^{24} +(-19.3358 - 624.701i) q^{25} +876.385 q^{26} +(556.908 + 556.908i) q^{27} +(266.995 - 266.995i) q^{28} -149.999i q^{29} +(-387.177 + 399.346i) q^{30} -1297.64 q^{31} +(-128.000 - 128.000i) q^{32} +(-585.620 + 585.620i) q^{33} -718.813i q^{34} +(1179.82 - 18.2547i) q^{35} -152.987 q^{36} +(-877.703 - 877.703i) q^{37} +(1400.06 - 1400.06i) q^{38} -2437.32i q^{39} +(-8.75145 - 565.618i) q^{40} -414.765 q^{41} +(-742.544 - 742.544i) q^{42} +(-1787.11 + 1787.11i) q^{43} -842.283i q^{44} +(-343.247 - 332.787i) q^{45} +311.987 q^{46} +(1515.30 + 1515.30i) q^{47} +(-355.982 + 355.982i) q^{48} -173.295i q^{49} +(1210.73 - 1288.07i) q^{50} -1999.10 q^{51} +(1752.77 + 1752.77i) q^{52} +(-3835.06 + 3835.06i) q^{53} +2227.63i q^{54} +(1832.18 - 1889.77i) q^{55} +1067.98 q^{56} +(-3893.73 - 3893.73i) q^{57} +(299.999 - 299.999i) q^{58} -1876.67i q^{59} +(-1573.05 + 24.3388i) q^{60} +451.446 q^{61} +(-2595.28 - 2595.28i) q^{62} +(638.232 - 638.232i) q^{63} -512.000i q^{64} +(119.838 + 7745.29i) q^{65} -2342.48 q^{66} +(687.703 + 687.703i) q^{67} +(1437.63 - 1437.63i) q^{68} -867.671i q^{69} +(2396.16 + 2323.14i) q^{70} +1109.02 q^{71} +(-305.974 - 305.974i) q^{72} +(3219.26 - 3219.26i) q^{73} -3510.81i q^{74} +(-3582.27 - 3367.17i) q^{75} +5600.25 q^{76} +(3513.84 + 3513.84i) q^{77} +(4874.65 - 4874.65i) q^{78} -9800.26i q^{79} +(1113.73 - 1148.74i) q^{80} +4646.30 q^{81} +(-829.530 - 829.530i) q^{82} +(8322.18 - 8322.18i) q^{83} -2970.18i q^{84} +(6352.70 - 98.2915i) q^{85} -7148.45 q^{86} +(-834.330 - 834.330i) q^{87} +(1684.57 - 1684.57i) q^{88} +12026.5i q^{89} +(-20.9197 - 1352.07i) q^{90} -14624.4 q^{91} +(623.974 + 623.974i) q^{92} +(-7217.75 + 7217.75i) q^{93} +6061.21i q^{94} +(12564.9 + 12182.0i) q^{95} -1423.93 q^{96} +(4596.94 + 4596.94i) q^{97} +(346.590 - 346.590i) q^{98} -2013.41i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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