LMFDB - Embedded newform 230.5.f.b.47.19

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			47.19
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(7.61108 - 7.61108i) q^{3} +8.00000i q^{4} +(-1.36901 + 24.9625i) q^{5} +30.4443 q^{6} +(45.0835 + 45.0835i) q^{7} +(-16.0000 + 16.0000i) q^{8} -34.8570i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(7.61108 - 7.61108i) q^{3} +8.00000i q^{4} +(-1.36901 + 24.9625i) q^{5} +30.4443 q^{6} +(45.0835 + 45.0835i) q^{7} +(-16.0000 + 16.0000i) q^{8} -34.8570i q^{9} +(-52.6630 + 47.1870i) q^{10} -201.176 q^{11} +(60.8886 + 60.8886i) q^{12} +(-180.082 + 180.082i) q^{13} +180.334i q^{14} +(179.572 + 200.411i) q^{15} -64.0000 q^{16} +(66.9876 + 66.9876i) q^{17} +(69.7141 - 69.7141i) q^{18} -264.492i q^{19} +(-199.700 - 10.9521i) q^{20} +686.268 q^{21} +(-402.352 - 402.352i) q^{22} +(-77.9968 + 77.9968i) q^{23} +243.555i q^{24} +(-621.252 - 68.3477i) q^{25} -720.329 q^{26} +(351.198 + 351.198i) q^{27} +(-360.668 + 360.668i) q^{28} -1180.35i q^{29} +(-41.6785 + 759.966i) q^{30} +123.184 q^{31} +(-128.000 - 128.000i) q^{32} +(-1531.17 + 1531.17i) q^{33} +267.951i q^{34} +(-1187.12 + 1063.68i) q^{35} +278.856 q^{36} +(1627.01 + 1627.01i) q^{37} +(528.984 - 528.984i) q^{38} +2741.24i q^{39} +(-377.496 - 421.304i) q^{40} +1575.51 q^{41} +(1372.54 + 1372.54i) q^{42} +(237.179 - 237.179i) q^{43} -1609.41i q^{44} +(870.118 + 47.7196i) q^{45} -311.987 q^{46} +(375.623 + 375.623i) q^{47} +(-487.109 + 487.109i) q^{48} +1664.05i q^{49} +(-1105.81 - 1379.20i) q^{50} +1019.70 q^{51} +(-1440.66 - 1440.66i) q^{52} +(-781.757 + 781.757i) q^{53} +1404.79i q^{54} +(275.411 - 5021.85i) q^{55} -1442.67 q^{56} +(-2013.07 - 2013.07i) q^{57} +(2360.69 - 2360.69i) q^{58} +6256.03i q^{59} +(-1603.29 + 1436.57i) q^{60} +6728.12 q^{61} +(246.369 + 246.369i) q^{62} +(1571.48 - 1571.48i) q^{63} -512.000i q^{64} +(-4248.77 - 4741.84i) q^{65} -6124.66 q^{66} +(4269.51 + 4269.51i) q^{67} +(-535.901 + 535.901i) q^{68} +1187.28i q^{69} +(-4501.59 - 246.879i) q^{70} +2275.71 q^{71} +(557.712 + 557.712i) q^{72} +(-1767.29 + 1767.29i) q^{73} +6508.02i q^{74} +(-5248.59 + 4208.20i) q^{75} +2115.94 q^{76} +(-9069.71 - 9069.71i) q^{77} +(-5482.48 + 5482.48i) q^{78} -3549.25i q^{79} +(87.6165 - 1597.60i) q^{80} +8169.41 q^{81} +(3151.02 + 3151.02i) q^{82} +(-1012.47 + 1012.47i) q^{83} +5490.15i q^{84} +(-1763.88 + 1580.47i) q^{85} +948.716 q^{86} +(-8983.71 - 8983.71i) q^{87} +(3218.81 - 3218.81i) q^{88} -10341.1i q^{89} +(1644.80 + 1835.68i) q^{90} -16237.5 q^{91} +(-623.974 - 623.974i) q^{92} +(937.566 - 937.566i) q^{93} +1502.49i q^{94} +(6602.38 + 362.092i) q^{95} -1948.44 q^{96} +(3957.47 + 3957.47i) q^{97} +(-3328.09 + 3328.09i) q^{98} +7012.39i 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
$3$	7.61108	−	7.61108i	0.845675	−	0.845675i	−0.143915	−	0.989590i	$-0.545969\pi$
$3$	7.61108	−	7.61108i	0.845675	−	0.845675i	0.989590	+	0.143915i	$0.0459691\pi$
$4$			8.00000i			0.500000i
$5$	−1.36901	+	24.9625i	−0.0547603	+	0.998500i
$5$	−1.36901	+	24.9625i	−0.0547603	+	0.998500i
$6$	30.4443			0.845675
$7$	45.0835	+	45.0835i	0.920072	+	0.920072i	0.997034	−	0.0769623i	$-0.0245221\pi$
$7$	45.0835	+	45.0835i	0.920072	+	0.920072i	−0.0769623	+	0.997034i	$0.524522\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$		−	34.8570i		−	0.430334i
$10$	−52.6630	+	47.1870i	−0.526630	+	0.471870i
$11$	−201.176			−1.66261			−0.831305	−	0.555816i	$-0.812406\pi$
$11$	−201.176			−1.66261			−0.831305	+	0.555816i	$0.812406\pi$
$12$	60.8886	+	60.8886i	0.422838	+	0.422838i
$13$	−180.082	+	180.082i	−1.06558	+	1.06558i	−0.0678826	+	0.997693i	$0.521624\pi$
$13$	−180.082	+	180.082i	−1.06558	+	1.06558i	−0.997693	+	0.0678826i	$0.978376\pi$
$14$			180.334i			0.920072i
$15$	179.572	+	200.411i	0.798097	+	0.890716i
$16$	−64.0000			−0.250000
$17$	66.9876	+	66.9876i	0.231791	+	0.231791i	0.813440	−	0.581649i	$-0.197592\pi$
$17$	66.9876	+	66.9876i	0.231791	+	0.231791i	−0.581649	+	0.813440i	$0.697592\pi$
$18$	69.7141	−	69.7141i	0.215167	−	0.215167i
$19$		−	264.492i		−	0.732665i	−0.930484	−	0.366332i	$-0.880613\pi$
$19$		−	264.492i		−	0.732665i	0.930484	−	0.366332i	$-0.119387\pi$
$20$	−199.700	−	10.9521i	−0.499250	−	0.0273802i
$21$	686.268			1.55616
$22$	−402.352	−	402.352i	−0.831305	−	0.831305i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$			243.555i			0.422838i
$25$	−621.252	−	68.3477i	−0.994003	−	0.109356i
$26$	−720.329			−1.06558
$27$	351.198	+	351.198i	0.481753	+	0.481753i
$28$	−360.668	+	360.668i	−0.460036	+	0.460036i
$29$		−	1180.35i		−	1.40350i	−0.712422	−	0.701752i	$-0.752402\pi$
$29$		−	1180.35i		−	1.40350i	0.712422	−	0.701752i	$-0.247598\pi$
$30$	−41.6785	+	759.966i	−0.0463095	+	0.844406i
$31$	123.184			0.128184			0.0640918	−	0.997944i	$-0.479585\pi$
$31$	123.184			0.128184			0.0640918	+	0.997944i	$0.479585\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−1531.17	+	1531.17i	−1.40603	+	1.40603i
$34$			267.951i			0.231791i
$35$	−1187.12	+	1063.68i	−0.969075	+	0.868308i
$36$	278.856			0.215167
$37$	1627.01	+	1627.01i	1.18846	+	1.18846i	0.977493	+	0.210970i	$0.0676622\pi$
$37$	1627.01	+	1627.01i	1.18846	+	1.18846i	0.210970	+	0.977493i	$0.432338\pi$
$38$	528.984	−	528.984i	0.366332	−	0.366332i
$39$			2741.24i			1.80226i
$40$	−377.496	−	421.304i	−0.235935	−	0.263315i
$41$	1575.51			0.937245			0.468623	−	0.883398i	$-0.344750\pi$
$41$	1575.51			0.937245			0.468623	+	0.883398i	$0.344750\pi$
$42$	1372.54	+	1372.54i	0.778082	+	0.778082i
$43$	237.179	−	237.179i	0.128274	−	0.128274i	−0.640055	−	0.768329i	$-0.721088\pi$
$43$	237.179	−	237.179i	0.128274	−	0.128274i	0.768329	+	0.640055i	$0.221088\pi$
$44$		−	1609.41i		−	0.831305i
$45$	870.118	+	47.7196i	0.429688	+	0.0235652i
$46$	−311.987			−0.147442
$47$	375.623	+	375.623i	0.170042	+	0.170042i	0.786998	−	0.616956i	$-0.211634\pi$
$47$	375.623	+	375.623i	0.170042	+	0.170042i	−0.616956	+	0.786998i	$0.711634\pi$
$48$	−487.109	+	487.109i	−0.211419	+	0.211419i
$49$			1664.05i			0.693064i
$50$	−1105.81	−	1379.20i	−0.442323	−	0.551679i
$51$	1019.70			0.392040
$52$	−1440.66	−	1440.66i	−0.532788	−	0.532788i
$53$	−781.757	+	781.757i	−0.278304	+	0.278304i	−0.832432	−	0.554127i	$-0.813052\pi$
$53$	−781.757	+	781.757i	−0.278304	+	0.278304i	0.554127	+	0.832432i	$0.313052\pi$
$54$			1404.79i			0.481753i
$55$	275.411	−	5021.85i	0.0910451	−	1.66012i
$56$	−1442.67			−0.460036
$57$	−2013.07	−	2013.07i	−0.619597	−	0.619597i
$58$	2360.69	−	2360.69i	0.701752	−	0.701752i
$59$			6256.03i			1.79719i	0.438775	+	0.898597i	$0.355412\pi$
$59$			6256.03i			1.79719i	−0.438775	+	0.898597i	$0.644588\pi$
$60$	−1603.29	+	1436.57i	−0.445358	+	0.399049i
$61$	6728.12			1.80815			0.904075	−	0.427374i	$-0.140561\pi$
$61$	6728.12			1.80815			0.904075	+	0.427374i	$0.140561\pi$
$62$	246.369	+	246.369i	0.0640918	+	0.0640918i
$63$	1571.48	−	1571.48i	0.395938	−	0.395938i
$64$		−	512.000i		−	0.125000i
$65$	−4248.77	−	4741.84i	−1.00563	−	1.12233i
$66$	−6124.66			−1.40603
$67$	4269.51	+	4269.51i	0.951104	+	0.951104i	0.998859	−	0.0477547i	$-0.0152066\pi$
$67$	4269.51	+	4269.51i	0.951104	+	0.951104i	−0.0477547	+	0.998859i	$0.515207\pi$
$68$	−535.901	+	535.901i	−0.115896	+	0.115896i
$69$			1187.28i			0.249376i
$70$	−4501.59	−	246.879i	−0.918691	−	0.0503834i
$71$	2275.71			0.451441			0.225720	−	0.974192i	$-0.427526\pi$
$71$	2275.71			0.451441			0.225720	+	0.974192i	$0.427526\pi$
$72$	557.712	+	557.712i	0.107583	+	0.107583i
$73$	−1767.29	+	1767.29i	−0.331637	+	0.331637i	−0.853208	−	0.521571i	$-0.825346\pi$
$73$	−1767.29	+	1767.29i	−0.331637	+	0.331637i	0.521571	+	0.853208i	$0.325346\pi$
$74$			6508.02i			1.18846i
$75$	−5248.59	+	4208.20i	−0.933084	+	0.748124i
$76$	2115.94			0.366332
$77$	−9069.71	−	9069.71i	−1.52972	−	1.52972i
$78$	−5482.48	+	5482.48i	−0.901131	+	0.901131i
$79$		−	3549.25i		−	0.568698i	−0.958721	−	0.284349i	$-0.908223\pi$
$79$		−	3549.25i		−	0.568698i	0.958721	−	0.284349i	$-0.0917775\pi$
$80$	87.6165	−	1597.60i	0.0136901	−	0.249625i
$81$	8169.41			1.24515
$82$	3151.02	+	3151.02i	0.468623	+	0.468623i
$83$	−1012.47	+	1012.47i	−0.146970	+	0.146970i	−0.776763	−	0.629793i	$-0.783140\pi$
$83$	−1012.47	+	1012.47i	−0.146970	+	0.146970i	0.629793	+	0.776763i	$0.283140\pi$
$84$			5490.15i			0.778082i
$85$	−1763.88	+	1580.47i	−0.244136	+	0.218750i
$86$	948.716			0.128274
$87$	−8983.71	−	8983.71i	−1.18691	−	1.18691i
$88$	3218.81	−	3218.81i	0.415653	−	0.415653i
$89$		−	10341.1i		−	1.30553i	−0.757562	−	0.652763i	$-0.773610\pi$
$89$		−	10341.1i		−	1.30553i	0.757562	−	0.652763i	$-0.226390\pi$
$90$	1644.80	+	1835.68i	0.203061	+	0.226627i
$91$	−16237.5			−1.96081
$92$	−623.974	−	623.974i	−0.0737210	−	0.0737210i
$93$	937.566	−	937.566i	0.108402	−	0.108402i
$94$			1502.49i			0.170042i
$95$	6602.38	+	362.092i	0.731565	+	0.0401210i
$96$	−1948.44			−0.211419
$97$	3957.47	+	3957.47i	0.420605	+	0.420605i	0.885412	−	0.464807i	$-0.153876\pi$
$97$	3957.47	+	3957.47i	0.420605	+	0.420605i	−0.464807	+	0.885412i	$0.653876\pi$
$98$	−3328.09	+	3328.09i	−0.346532	+	0.346532i
$99$			7012.39i			0.715477i
$100$	546.782	−	4970.01i	0.0546782	−	0.497001i
$101$	3274.61			0.321009			0.160505	−	0.987035i	$-0.448688\pi$
$101$	3274.61			0.321009			0.160505	+	0.987035i	$0.448688\pi$
$102$	2039.39	+	2039.39i	0.196020	+	0.196020i
$103$	−7556.89	+	7556.89i	−0.712309	+	0.712309i	−0.967018	−	0.254709i	$-0.918020\pi$
$103$	−7556.89	+	7556.89i	−0.712309	+	0.712309i	0.254709	+	0.967018i	$0.418020\pi$
$104$		−	5762.63i		−	0.532788i
$105$	−939.507	+	17131.0i	−0.0852161	+	1.55383i
$106$	−3127.03			−0.278304
$107$	−7574.45	−	7574.45i	−0.661582	−	0.661582i	0.294171	−	0.955753i	$-0.404957\pi$
$107$	−7574.45	−	7574.45i	−0.661582	−	0.661582i	−0.955753	+	0.294171i	$0.904957\pi$
$108$	−2809.58	+	2809.58i	−0.240876	+	0.240876i
$109$		−	17815.8i		−	1.49952i	−0.661708	−	0.749761i	$-0.730168\pi$
$109$		−	17815.8i		−	1.49952i	0.661708	−	0.749761i	$-0.269832\pi$
$110$	10594.5	−	9492.88i	0.875580	−	0.784535i
$111$	24766.5			2.01011
$112$	−2885.34	−	2885.34i	−0.230018	−	0.230018i
$113$	10930.8	−	10930.8i	0.856043	−	0.856043i	−0.134826	−	0.990869i	$-0.543048\pi$
$113$	10930.8	−	10930.8i	0.856043	−	0.856043i	0.990869	+	0.134826i	$0.0430475\pi$
$114$		−	8052.28i		−	0.619597i
$115$	−1840.22	−	2053.77i	−0.139147	−	0.155295i
$116$	9442.77			0.701752
$117$	6277.14	+	6277.14i	0.458553	+	0.458553i
$118$	−12512.1	+	12512.1i	−0.898597	+	0.898597i
$119$			6040.08i			0.426529i
$120$	−6079.73	−	333.428i	−0.422203	−	0.0231547i
$121$	25830.7			1.76427
$122$	13456.2	+	13456.2i	0.904075	+	0.904075i
$123$	11991.3	−	11991.3i	0.792605	−	0.792605i
$124$			985.475i			0.0640918i
$125$	2556.63	−	15414.4i	0.163624	−	0.986523i
$126$	6285.91			0.395938
$127$	−2697.69	−	2697.69i	−0.167257	−	0.167257i	0.618516	−	0.785773i	$-0.287734\pi$
$127$	−2697.69	−	2697.69i	−0.167257	−	0.167257i	−0.785773	+	0.618516i	$0.787734\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	3610.38i		−	0.216957i
$130$	986.137	−	17981.2i	0.0583513	−	1.06398i
$131$	−5147.02			−0.299926			−0.149963	−	0.988692i	$-0.547915\pi$
$131$	−5147.02			−0.299926			−0.149963	+	0.988692i	$0.547915\pi$
$132$	−12249.3	−	12249.3i	−0.703014	−	0.703014i
$133$	11924.2	−	11924.2i	0.674104	−	0.674104i
$134$			17078.0i			0.951104i
$135$	−9247.56	+	8285.98i	−0.507411	+	0.454649i
$136$	−2143.60			−0.115896
$137$	17697.0	+	17697.0i	0.942883	+	0.942883i	0.998455	−	0.0555716i	$-0.0176981\pi$
$137$	17697.0	+	17697.0i	0.942883	+	0.942883i	−0.0555716	+	0.998455i	$0.517698\pi$
$138$	−2374.56	+	2374.56i	−0.124688	+	0.124688i
$139$			27204.7i			1.40804i	0.710182	+	0.704018i	$0.248613\pi$
$139$			27204.7i			1.40804i	−0.710182	+	0.704018i	$0.751387\pi$
$140$	−8509.42	−	9496.93i	−0.434154	−	0.484537i
$141$	5717.79			0.287601
$142$	4551.43	+	4551.43i	0.225720	+	0.225720i
$143$	36228.2	−	36228.2i	1.77164	−	1.77164i
$144$			2230.85i			0.107583i
$145$	29464.4	+	1615.90i	1.40140	+	0.0768563i
$146$	−7069.17			−0.331637
$147$	12665.2	+	12665.2i	0.586107	+	0.586107i
$148$	−13016.0	+	13016.0i	−0.594231	+	0.594231i
$149$		−	37868.4i		−	1.70571i	−0.522149	−	0.852854i	$-0.674870\pi$
$149$		−	37868.4i		−	1.70571i	0.522149	−	0.852854i	$-0.325130\pi$
$150$	−18913.6	−	2080.80i	−0.840604	−	0.0924800i
$151$	−4783.83			−0.209808			−0.104904	−	0.994482i	$-0.533454\pi$
$151$	−4783.83			−0.209808			−0.104904	+	0.994482i	$0.533454\pi$
$152$	4231.87	+	4231.87i	0.183166	+	0.183166i
$153$	2334.99	−	2334.99i	0.0997475	−	0.0997475i
$154$		−	36278.9i		−	1.52972i
$155$	−168.640	+	3074.99i	−0.00701937	+	0.127991i
$156$	−21929.9			−0.901131
$157$	15642.0	+	15642.0i	0.634591	+	0.634591i	0.949216	−	0.314625i	$-0.101879\pi$
$157$	15642.0	+	15642.0i	0.634591	+	0.634591i	−0.314625	+	0.949216i	$0.601879\pi$
$158$	7098.49	−	7098.49i	0.284349	−	0.284349i
$159$			11900.0i			0.470710i
$160$	3370.43	−	3019.97i	0.131657	−	0.117967i
$161$	−7032.74			−0.271314
$162$	16338.8	+	16338.8i	0.622573	+	0.622573i
$163$	−33570.4	+	33570.4i	−1.26352	+	1.26352i	−0.314142	+	0.949376i	$0.601717\pi$
$163$	−33570.4	+	33570.4i	−1.26352	+	1.26352i	−0.949376	+	0.314142i	$0.898283\pi$
$164$			12604.1i			0.468623i
$165$	−36125.5	−	40317.9i	−1.32692	−	1.48091i
$166$	−4049.90			−0.146970
$167$	−5825.16	−	5825.16i	−0.208870	−	0.208870i	0.594917	−	0.803787i	$-0.297185\pi$
$167$	−5825.16	−	5825.16i	−0.208870	−	0.208870i	−0.803787	+	0.594917i	$0.797185\pi$
$168$	−10980.3	+	10980.3i	−0.389041	+	0.389041i
$169$		−	36298.3i		−	1.27090i
$170$	−6688.71	−	366.827i	−0.231443	−	0.0126930i
$171$	−9219.40			−0.315290
$172$	1897.43	+	1897.43i	0.0641371	+	0.0641371i
$173$	−11972.9	+	11972.9i	−0.400044	+	0.400044i	−0.878248	−	0.478205i	$-0.841288\pi$
$173$	−11972.9	+	11972.9i	−0.400044	+	0.400044i	0.478205	+	0.878248i	$0.341288\pi$
$174$		−	35934.8i		−	1.18691i
$175$	−24926.9	−	31089.6i	−0.813938	−	1.01517i
$176$	12875.3			0.415653
$177$	47615.1	+	47615.1i	1.51984	+	1.51984i
$178$	20682.2	−	20682.2i	0.652763	−	0.652763i
$179$			22932.0i			0.715707i	0.933778	+	0.357854i	$0.116491\pi$
$179$			22932.0i			0.715707i	−0.933778	+	0.357854i	$0.883509\pi$
$180$	−381.757	+	6960.95i	−0.0117826	+	0.214844i
$181$	−62446.9			−1.90614			−0.953068	−	0.302758i	$-0.902093\pi$
$181$	−62446.9			−1.90614			−0.953068	+	0.302758i	$0.902093\pi$
$182$	−32475.0	−	32475.0i	−0.980406	−	0.980406i
$183$	51208.3	−	51208.3i	1.52911	−	1.52911i
$184$		−	2495.90i		−	0.0737210i
$185$	−42841.5	+	38386.7i	−1.25176	+	1.12160i
$186$	3750.26			0.108402
$187$	−13476.3	−	13476.3i	−0.385378	−	0.385378i
$188$	−3004.98	+	3004.98i	−0.0850210	+	0.0850210i
$189$			31666.5i			0.886494i
$190$	12480.6	+	13928.9i	0.345722	+	0.385843i
$191$	8279.61			0.226957			0.113478	−	0.993540i	$-0.463801\pi$
$191$	8279.61			0.226957			0.113478	+	0.993540i	$0.463801\pi$
$192$	−3896.87	−	3896.87i	−0.105709	−	0.105709i
$193$	8084.47	−	8084.47i	0.217039	−	0.217039i	−0.590211	−	0.807249i	$-0.700955\pi$
$193$	8084.47	−	8084.47i	0.217039	−	0.217039i	0.807249	+	0.590211i	$0.200955\pi$
$194$			15829.9i			0.420605i
$195$	−68428.2	−	3752.78i	−1.79956	−	0.0986925i
$196$	−13312.4			−0.346532
$197$	3461.78	+	3461.78i	0.0892004	+	0.0892004i	0.750299	−	0.661099i	$-0.229910\pi$
$197$	3461.78	+	3461.78i	0.0892004	+	0.0892004i	−0.661099	+	0.750299i	$0.729910\pi$
$198$	−14024.8	+	14024.8i	−0.357739	+	0.357739i
$199$		−	66429.4i		−	1.67747i	−0.544542	−	0.838734i	$-0.683296\pi$
$199$		−	66429.4i		−	1.67747i	0.544542	−	0.838734i	$-0.316704\pi$
$200$	11033.6	−	8846.46i	0.275840	−	0.221162i
$201$	64991.1			1.60865
$202$	6549.23	+	6549.23i	0.160505	+	0.160505i
$203$	53214.1	−	53214.1i	1.29132	−	1.29132i
$204$			8157.57i			0.196020i
$205$	−2156.89	+	39328.6i	−0.0513239	+	0.935839i
$206$	−30227.6			−0.712309
$207$	2718.74	+	2718.74i	0.0634492	+	0.0634492i
$208$	11525.3	−	11525.3i	0.266394	−	0.266394i
$209$			53209.4i			1.21814i
$210$	−36140.9	+	32382.9i	−0.819523	+	0.734306i
$211$	−30071.2			−0.675438			−0.337719	−	0.941247i	$-0.609655\pi$
$211$	−30071.2			−0.675438			−0.337719	+	0.941247i	$0.609655\pi$
$212$	−6254.05	−	6254.05i	−0.139152	−	0.139152i
$213$	17320.6	−	17320.6i	0.381773	−	0.381773i
$214$		−	30297.8i		−	0.661582i
$215$	5595.88	+	6245.28i	0.121057	+	0.135106i
$216$	−11238.3			−0.240876
$217$	5553.58	+	5553.58i	0.117938	+	0.117938i
$218$	35631.7	−	35631.7i	0.749761	−	0.749761i
$219$			26902.0i			0.560914i
$220$	40174.8	+	2203.29i	0.830058	+	0.0455226i
$221$	−24126.6			−0.493982
$222$	49533.1	+	49533.1i	1.00505	+	1.00505i
$223$	2611.70	−	2611.70i	0.0525186	−	0.0525186i	−0.680360	−	0.732878i	$-0.738176\pi$
$223$	2611.70	−	2611.70i	0.0525186	−	0.0525186i	0.732878	+	0.680360i	$0.238176\pi$
$224$		−	11541.4i		−	0.230018i
$225$	−2382.40	+	21655.0i	−0.0470597	+	0.427753i
$226$	43723.3			0.856043
$227$	10039.5	+	10039.5i	0.194832	+	0.194832i	0.797780	−	0.602948i	$-0.206007\pi$
$227$	10039.5	+	10039.5i	0.194832	+	0.194832i	−0.602948	+	0.797780i	$0.706007\pi$
$228$	16104.6	−	16104.6i	0.309798	−	0.309798i
$229$			101415.i			1.93388i	0.254999	+	0.966941i	$0.417925\pi$
$229$			101415.i			1.93388i	−0.254999	+	0.966941i	$0.582075\pi$
$230$	427.113	−	7787.98i	0.00807397	−	0.147221i
$231$	−138061.			−2.58729
$232$	18885.5	+	18885.5i	0.350876	+	0.350876i
$233$	−2918.14	+	2918.14i	−0.0537520	+	0.0537520i	−0.733472	−	0.679720i	$-0.762101\pi$
$233$	−2918.14	+	2918.14i	−0.0537520	+	0.0537520i	0.679720	+	0.733472i	$0.262101\pi$
$234$			25108.5i			0.458553i
$235$	−9890.70	+	8862.24i	−0.179098	+	0.160475i
$236$	−50048.3			−0.898597
$237$	−27013.6	−	27013.6i	−0.480934	−	0.480934i
$238$	−12080.2	+	12080.2i	−0.213264	+	0.213264i
$239$		−	37665.8i		−	0.659403i	−0.944085	−	0.329702i	$-0.893052\pi$
$239$		−	37665.8i		−	0.659403i	0.944085	−	0.329702i	$-0.106948\pi$
$240$	−11492.6	−	12826.3i	−0.199524	−	0.222679i
$241$	−70744.7			−1.21804			−0.609018	−	0.793157i	$-0.708436\pi$
$241$	−70744.7			−1.21804			−0.609018	+	0.793157i	$0.708436\pi$
$242$	51661.5	+	51661.5i	0.882137	+	0.882137i
$243$	33731.0	−	33731.0i	0.571237	−	0.571237i
$244$			53825.0i			0.904075i
$245$	−41538.7	−	2278.09i	−0.692024	−	0.0379524i
$246$	47965.3			0.792605
$247$	47630.3	+	47630.3i	0.780710	+	0.780710i
$248$	−1970.95	+	1970.95i	−0.0320459	+	0.0320459i
$249$			15412.1i			0.248577i
$250$	35942.1	−	25715.6i	0.575073	−	0.411449i
$251$	−86310.7			−1.36999			−0.684995	−	0.728548i	$-0.740196\pi$
$251$	−86310.7			−1.36999			−0.684995	+	0.728548i	$0.740196\pi$
$252$	12571.8	+	12571.8i	0.197969	+	0.197969i
$253$	15691.1	−	15691.1i	0.245139	−	0.245139i
$254$		−	10790.8i		−	0.167257i
$255$	−1395.97	+	25454.2i	−0.0214682	+	0.391452i
$256$	4096.00			0.0625000
$257$	−15117.0	−	15117.0i	−0.228876	−	0.228876i	0.583347	−	0.812223i	$-0.301743\pi$
$257$	−15117.0	−	15117.0i	−0.228876	−	0.228876i	−0.812223	+	0.583347i	$0.801743\pi$
$258$	7220.75	−	7220.75i	0.108478	−	0.108478i
$259$			146702.i			2.18694i
$260$	37934.7	−	33990.2i	0.561164	−	0.502813i
$261$	−41143.4			−0.603975
$262$	−10294.0	−	10294.0i	−0.149963	−	0.149963i
$263$	21659.6	−	21659.6i	0.313140	−	0.313140i	−0.532985	−	0.846125i	$-0.678930\pi$
$263$	21659.6	−	21659.6i	0.313140	−	0.313140i	0.846125	+	0.532985i	$0.178930\pi$
$264$		−	48997.3i		−	0.703014i
$265$	−18444.4	−	20584.8i	−0.262647	−	0.293127i
$266$	47696.9			0.674104
$267$	−78706.8	−	78706.8i	−1.10405	−	1.10405i
$268$	−34156.1	+	34156.1i	−0.475552	+	0.475552i
$269$		−	42936.1i		−	0.593359i	−0.954977	−	0.296680i	$-0.904121\pi$
$269$		−	42936.1i		−	0.593359i	0.954977	−	0.296680i	$-0.0958793\pi$
$270$	−35067.1	−	1923.17i	−0.481030	−	0.0263809i
$271$	79383.3			1.08091			0.540457	−	0.841372i	$-0.318252\pi$
$271$	79383.3			1.08091			0.540457	+	0.841372i	$0.318252\pi$
$272$	−4287.21	−	4287.21i	−0.0579478	−	0.0579478i
$273$	−123585.	+	123585.i	−1.65821	+	1.65821i
$274$			70787.9i			0.942883i
$275$	124981.	+	13749.9i	1.65264	+	0.181817i
$276$	−9498.24			−0.124688
$277$	50169.0	+	50169.0i	0.653847	+	0.653847i	0.953917	−	0.300070i	$-0.0970101\pi$
$277$	50169.0	+	50169.0i	0.653847	+	0.653847i	−0.300070	+	0.953917i	$0.597010\pi$
$278$	−54409.3	+	54409.3i	−0.704018	+	0.704018i
$279$		−	4293.84i		−	0.0551617i
$280$	1975.03	−	36012.7i	0.0251917	−	0.459346i
$281$	−58351.2			−0.738988			−0.369494	−	0.929233i	$-0.620469\pi$
$281$	−58351.2			−0.738988			−0.369494	+	0.929233i	$0.620469\pi$
$282$	11435.6	+	11435.6i	0.143800	+	0.143800i
$283$	95048.7	−	95048.7i	1.18679	−	1.18679i	0.208839	−	0.977950i	$-0.433032\pi$
$283$	95048.7	−	95048.7i	1.18679	−	1.18679i	0.977950	−	0.208839i	$-0.0669684\pi$
$284$			18205.7i			0.225720i
$285$	53007.1	−	47495.3i	0.652596	−	0.584738i
$286$	144913.			1.77164
$287$	71029.5	+	71029.5i	0.862333	+	0.862333i
$288$	−4461.70	+	4461.70i	−0.0537917	+	0.0537917i
$289$		−	74546.3i		−	0.892546i
$290$	55696.9	+	62160.6i	0.662270	+	0.739127i
$291$	60241.3			0.711391
$292$	−14138.3	−	14138.3i	−0.165818	−	0.165818i
$293$	−58996.9	+	58996.9i	−0.687217	+	0.687217i	−0.961616	−	0.274399i	$-0.911521\pi$
$293$	−58996.9	+	58996.9i	−0.687217	+	0.687217i	0.274399	+	0.961616i	$0.411521\pi$
$294$			50660.7i			0.586107i
$295$	−156166.	−	8564.56i	−1.79450	−	0.0984149i
$296$	−52064.2			−0.594231
$297$	−70652.5	−	70652.5i	−0.800967	−	0.800967i
$298$	75736.8	−	75736.8i	0.852854	−	0.852854i
$299$		−	28091.7i		−	0.314221i
$300$	−33665.6	−	41988.8i	−0.374062	−	0.466542i
$301$	21385.7			0.236043
$302$	−9567.66	−	9567.66i	−0.104904	−	0.104904i
$303$	24923.3	−	24923.3i	0.271470	−	0.271470i
$304$			16927.5i			0.183166i
$305$	−9210.86	+	167951.i	−0.0990149	+	1.80544i
$306$	9339.96			0.0997475
$307$	58817.9	+	58817.9i	0.624069	+	0.624069i	0.946569	−	0.322500i	$-0.104523\pi$
$307$	58817.9	+	58817.9i	0.624069	+	0.624069i	−0.322500	+	0.946569i	$0.604523\pi$
$308$	72557.7	−	72557.7i	0.764860	−	0.764860i
$309$			115032.i			1.20476i
$310$	−6487.26	+	5812.70i	−0.0675053	+	0.0604859i
$311$	19415.2			0.200734			0.100367	−	0.994950i	$-0.467998\pi$
$311$	19415.2			0.200734			0.100367	+	0.994950i	$0.467998\pi$
$312$	−43859.9	−	43859.9i	−0.450566	−	0.450566i
$313$	−88288.6	+	88288.6i	−0.901189	+	0.901189i	−0.995539	−	0.0943497i	$-0.969923\pi$
$313$	−88288.6	+	88288.6i	−0.901189	+	0.901189i	0.0943497	+	0.995539i	$0.469923\pi$
$314$			62568.1i			0.634591i
$315$	37076.6	+	41379.4i	0.373662	+	0.417025i
$316$	28394.0			0.284349
$317$	−54089.2	−	54089.2i	−0.538260	−	0.538260i	0.384758	−	0.923018i	$-0.374285\pi$
$317$	−54089.2	−	54089.2i	−0.538260	−	0.538260i	−0.923018	+	0.384758i	$0.874285\pi$
$318$	−23800.0	+	23800.0i	−0.235355	+	0.235355i
$319$			237457.i			2.33348i
$320$	12780.8	+	700.932i	0.124812	+	0.00684504i
$321$	−115300.			−1.11897
$322$	−14065.5	−	14065.5i	−0.135657	−	0.135657i
$323$	17717.7	−	17717.7i	0.169825	−	0.169825i
$324$			65355.3i			0.622573i
$325$	124185.	−	99568.2i	1.17571	−	0.942658i
$326$	−134282.			−1.26352
$327$	−135598.	−	135598.i	−1.26811	−	1.26811i
$328$	−25208.2	+	25208.2i	−0.234311	+	0.234311i
$329$			33868.8i			0.312901i
$330$	8384.71	−	152887.i	0.0769946	−	1.40392i
$331$	−121731.			−1.11108			−0.555539	−	0.831491i	$-0.687488\pi$
$331$	−121731.			−1.11108			−0.555539	+	0.831491i	$0.687488\pi$
$332$	−8099.80	−	8099.80i	−0.0734849	−	0.0734849i
$333$	56712.6	−	56712.6i	0.511435	−	0.511435i
$334$		−	23300.7i		−	0.208870i
$335$	−112423.	+	100733.i	−1.00176	+	0.897595i
$336$	−43921.2			−0.389041
$337$	47528.3	+	47528.3i	0.418497	+	0.418497i	0.884686	−	0.466188i	$-0.154373\pi$
$337$	47528.3	+	47528.3i	0.418497	+	0.418497i	−0.466188	+	0.884686i	$0.654373\pi$
$338$	72596.6	−	72596.6i	0.635452	−	0.635452i
$339$		−	166391.i		−	1.44787i
$340$	−12643.8	−	14111.1i	−0.109375	−	0.122068i
$341$	−24781.7			−0.213119
$342$	−18438.8	−	18438.8i	−0.157645	−	0.157645i
$343$	33224.5	−	33224.5i	0.282403	−	0.282403i
$344$			7589.73i			0.0641371i
$345$	−29637.4	−	1625.40i	−0.249002	−	0.0136559i
$346$	−47891.6			−0.400044
$347$	−13032.5	−	13032.5i	−0.108236	−	0.108236i	0.650915	−	0.759151i	$-0.274385\pi$
$347$	−13032.5	−	13032.5i	−0.108236	−	0.108236i	−0.759151	+	0.650915i	$0.774385\pi$
$348$	71869.7	−	71869.7i	0.593454	−	0.593454i
$349$			152486.i			1.25193i	0.779852	+	0.625964i	$0.215294\pi$
$349$			152486.i			1.25193i	−0.779852	+	0.625964i	$0.784706\pi$
$350$	12325.4	−	112033.i	0.100616	−	0.914554i
$351$	−126489.			−1.02669
$352$	25750.5	+	25750.5i	0.207826	+	0.207826i
$353$	114100.	−	114100.i	0.915661	−	0.915661i	−0.0810487	−	0.996710i	$-0.525827\pi$
$353$	114100.	−	114100.i	0.915661	−	0.915661i	0.996710	+	0.0810487i	$0.0258269\pi$
$354$			190461.i			1.51984i
$355$	−3115.47	+	56807.5i	−0.0247211	+	0.450764i
$356$	82728.6			0.652763
$357$	45971.5	+	45971.5i	0.360705	+	0.360705i
$358$	−45863.9	+	45863.9i	−0.357854	+	0.357854i
$359$		−	203221.i		−	1.57681i	−0.615156	−	0.788405i	$-0.710907\pi$
$359$		−	203221.i		−	1.57681i	0.615156	−	0.788405i	$-0.289093\pi$
$360$	−14685.4	+	13158.4i	−0.113313	+	0.101531i
$361$	60365.0			0.463202
$362$	−124894.	−	124894.i	−0.953068	−	0.953068i
$363$	196600.	−	196600.i	1.49200	−	1.49200i
$364$		−	129900.i		−	0.980406i
$365$	−41696.6	−	46535.5i	−0.312979	−	0.349300i
$366$	204833.			1.52911
$367$	−96382.0	−	96382.0i	−0.715590	−	0.715590i	0.252109	−	0.967699i	$-0.418876\pi$
$367$	−96382.0	−	96382.0i	−0.715590	−	0.715590i	−0.967699	+	0.252109i	$0.918876\pi$
$368$	4991.79	−	4991.79i	0.0368605	−	0.0368605i
$369$		−	54917.6i		−	0.403328i
$370$	−162456.	−	8909.53i	−1.18668	−	0.0650806i
$371$	−70488.7			−0.512120
$372$	7500.53	+	7500.53i	0.0542008	+	0.0542008i
$373$	129843.	−	129843.i	0.933254	−	0.933254i	−0.0646538	−	0.997908i	$-0.520594\pi$
$373$	129843.	−	129843.i	0.933254	−	0.933254i	0.997908	+	0.0646538i	$0.0205943\pi$
$374$		−	53905.2i		−	0.385378i
$375$	−97861.7	−	136779.i	−0.695905	−	0.972651i
$376$	−12019.9			−0.0850210
$377$	212559.	+	212559.i	1.49554	+	1.49554i
$378$	−63332.9	+	63332.9i	−0.443247	+	0.443247i
$379$		−	79191.3i		−	0.551314i	−0.961256	−	0.275657i	$-0.911105\pi$
$379$		−	79191.3i		−	0.551314i	0.961256	−	0.275657i	$-0.0888954\pi$
$380$	−2896.73	+	52819.0i	−0.0200605	+	0.365783i
$381$	−41064.6			−0.282890
$382$	16559.2	+	16559.2i	0.113478	+	0.113478i
$383$	27806.2	−	27806.2i	0.189559	−	0.189559i	−0.605947	−	0.795505i	$-0.707205\pi$
$383$	27806.2	−	27806.2i	0.189559	−	0.189559i	0.795505	+	0.605947i	$0.207205\pi$
$384$		−	15587.5i		−	0.105709i
$385$	238819.	−	213986.i	1.61119	−	1.44366i
$386$	32337.9			0.217039
$387$	−8267.36	−	8267.36i	−0.0552007	−	0.0552007i
$388$	−31659.8	+	31659.8i	−0.210303	+	0.210303i
$389$			54915.3i			0.362906i	0.983400	+	0.181453i	$0.0580800\pi$
$389$			54915.3i			0.362906i	−0.983400	+	0.181453i	$0.941920\pi$
$390$	−129351.	−	144362.i	−0.850433	−	0.949125i
$391$	−10449.6			−0.0683515
$392$	−26624.7	−	26624.7i	−0.173266	−	0.173266i
$393$	−39174.4	+	39174.4i	−0.253640	+	0.253640i
$394$			13847.1i			0.0892004i
$395$	88598.0	+	4858.95i	0.567845	+	0.0311421i
$396$	−56099.1			−0.357739
$397$	82703.5	+	82703.5i	0.524738	+	0.524738i	0.918999	−	0.394260i	$-0.128999\pi$
$397$	82703.5	+	82703.5i	0.524738	+	0.524738i	−0.394260	+	0.918999i	$0.628999\pi$
$398$	132859.	−	132859.i	0.838734	−	0.838734i
$399$		−	181512.i		−	1.14015i
$400$	39760.1	+	4374.25i	0.248501	+	0.0273391i
$401$	124788.			0.776037			0.388018	−	0.921652i	$-0.373160\pi$
$401$	124788.			0.776037			0.388018	+	0.921652i	$0.373160\pi$
$402$	129982.	+	129982.i	0.804326	+	0.804326i
$403$	−22183.3	+	22183.3i	−0.136589	+	0.136589i
$404$			26196.9i			0.160505i
$405$	−11184.0	+	203929.i	−0.0681846	+	1.24328i
$406$	212857.			1.29132
$407$	−327314.	−	327314.i	−1.97595	−	1.97595i
$408$	−16315.1	+	16315.1i	−0.0980100	+	0.0980100i
$409$			332802.i			1.98948i	0.102432	+	0.994740i	$0.467338\pi$
$409$			332802.i			1.98948i	−0.102432	+	0.994740i	$0.532662\pi$
$410$	−82971.0	+	74343.5i	−0.493581	+	0.442258i
$411$	269386.			1.59475
$412$	−60455.1	−	60455.1i	−0.356155	−	0.356155i
$413$	−282044.	+	282044.i	−1.65355	+	1.65355i
$414$			10874.9i			0.0634492i
$415$	−23887.8	−	26660.0i	−0.138701	−	0.154797i
$416$	46101.1			0.266394
$417$	207057.	+	207057.i	1.19074	+	1.19074i
$418$	−106419.	+	106419.i	−0.609068	+	0.609068i
$419$		−	192951.i		−	1.09905i	−0.835477	−	0.549526i	$-0.814808\pi$
$419$		−	192951.i		−	1.09905i	0.835477	−	0.549526i	$-0.185192\pi$
$420$	−137048.	−	7516.06i	−0.776914	−	0.0426080i
$421$	179583.			1.01321			0.506606	−	0.862178i	$-0.330900\pi$
$421$	179583.			1.01321			0.506606	+	0.862178i	$0.330900\pi$
$422$	−60142.3	−	60142.3i	−0.337719	−	0.337719i
$423$	13093.1	−	13093.1i	0.0731748	−	0.0731748i
$424$		−	25016.2i		−	0.139152i
$425$	−37037.7	−	46194.6i	−0.205053	−	0.255749i
$426$	69282.6			0.381773
$427$	303327.	+	303327.i	1.66363	+	1.66363i
$428$	60595.6	−	60595.6i	0.330791	−	0.330791i
$429$		−	551472.i		−	2.99646i
$430$	−1298.80	+	23682.3i	−0.00702434	+	0.128082i
$431$	65268.3			0.351356			0.175678	−	0.984448i	$-0.443788\pi$
$431$	65268.3			0.351356			0.175678	+	0.984448i	$0.443788\pi$
$432$	−22476.7	−	22476.7i	−0.120438	−	0.120438i
$433$	110158.	−	110158.i	0.587544	−	0.587544i	−0.349422	−	0.936965i	$-0.613622\pi$
$433$	110158.	−	110158.i	0.587544	−	0.587544i	0.936965	+	0.349422i	$0.113622\pi$
$434$			22214.3i			0.117938i
$435$	236554.	−	211957.i	1.25012	−	1.12013i
$436$	142527.			0.749761
$437$	20629.5	+	20629.5i	0.108026	+	0.108026i
$438$	−53804.0	+	53804.0i	−0.280457	+	0.280457i
$439$		−	280360.i		−	1.45474i	−0.686243	−	0.727372i	$-0.740741\pi$
$439$		−	280360.i		−	1.45474i	0.686243	−	0.727372i	$-0.259259\pi$
$440$	75943.0	+	84756.2i	0.392268	+	0.437790i
$441$	58003.7			0.298249
$442$	−48253.2	−	48253.2i	−0.246991	−	0.246991i
$443$	5637.57	−	5637.57i	0.0287266	−	0.0287266i	−0.692598	−	0.721324i	$-0.743534\pi$
$443$	5637.57	−	5637.57i	0.0287266	−	0.0287266i	0.721324	+	0.692598i	$0.243534\pi$
$444$			198132.i			1.00505i
$445$	258139.	+	14157.0i	1.30357	+	0.0714911i
$446$	10446.8			0.0525186
$447$	−288220.	−	288220.i	−1.44248	−	1.44248i
$448$	23082.8	−	23082.8i	0.115009	−	0.115009i
$449$		−	227090.i		−	1.12643i	−0.826309	−	0.563217i	$-0.809563\pi$
$449$		−	227090.i		−	1.12643i	0.826309	−	0.563217i	$-0.190437\pi$
$450$	−48074.8	+	38545.2i	−0.237406	+	0.190347i
$451$	−316954.			−1.55827
$452$	87446.5	+	87446.5i	0.428022	+	0.428022i
$453$	−36410.1	+	36410.1i	−0.177429	+	0.177429i
$454$			40158.0i			0.194832i
$455$	22229.3	−	405328.i	0.107375	−	1.95787i
$456$	64418.2			0.309798
$457$	118992.	+	118992.i	0.569750	+	0.569750i	0.932058	−	0.362308i	$-0.118011\pi$
$457$	118992.	+	118992.i	0.569750	+	0.569750i	−0.362308	+	0.932058i	$0.618011\pi$
$458$	−202829.	+	202829.i	−0.966941	+	0.966941i
$459$			47051.8i			0.223332i
$460$	16430.2	−	14721.7i	0.0776473	−	0.0695734i
$461$	109297.			0.514286			0.257143	−	0.966373i	$-0.417219\pi$
$461$	109297.			0.514286			0.257143	+	0.966373i	$0.417219\pi$
$462$	−276121.	−	276121.i	−1.29365	−	1.29365i
$463$	−1019.98	+	1019.98i	−0.00475804	+	0.00475804i	−0.709482	−	0.704724i	$-0.751071\pi$
$463$	−1019.98	+	1019.98i	−0.00475804	+	0.00475804i	0.704724	+	0.709482i	$0.251071\pi$
$464$			75542.2i			0.350876i
$465$	22120.4	+	24687.5i	0.102303	+	0.114175i
$466$	−11672.6			−0.0537520
$467$	26718.5	+	26718.5i	0.122512	+	0.122512i	0.765704	−	0.643193i	$-0.222391\pi$
$467$	26718.5	+	26718.5i	0.122512	+	0.122512i	−0.643193	+	0.765704i	$0.722391\pi$
$468$	−50217.1	+	50217.1i	−0.229277	+	0.229277i
$469$			384969.i			1.75017i
$470$	−37505.9	−	2056.92i	−0.169787	−	0.00931155i
$471$	238105.			1.07332
$472$	−100097.	−	100097.i	−0.449298	−	0.449298i
$473$	−47714.7	+	47714.7i	−0.213270	+	0.213270i
$474$		−	108054.i		−	0.480934i
$475$	−18077.4	+	164316.i	−0.0801215	+	0.728271i
$476$	−48320.6			−0.213264
$477$	27249.7	+	27249.7i	0.119764	+	0.119764i
$478$	75331.6	−	75331.6i	0.329702	−	0.329702i
$479$			213069.i			0.928645i	0.885666	+	0.464323i	$0.153702\pi$
$479$			213069.i			0.928645i	−0.885666	+	0.464323i	$0.846298\pi$
$480$	2667.43	−	48637.8i	0.0115774	−	0.211102i
$481$	−585990.			−2.53279
$482$	−141489.	−	141489.i	−0.609018	−	0.609018i
$483$	−53526.7	+	53526.7i	−0.229444	+	0.229444i
$484$			206646.i			0.882137i
$485$	−104206.	+	93370.6i	−0.443006	+	0.396942i
$486$	134924.			0.571237
$487$	273271.	+	273271.i	1.15222	+	1.15222i	0.986107	+	0.166112i	$0.0531214\pi$
$487$	273271.	+	273271.i	1.15222	+	1.15222i	0.166112	+	0.986107i	$0.446879\pi$
$488$	−107650.	+	107650.i	−0.452037	+	0.452037i
$489$			511014.i			2.13705i
$490$	−78521.3	−	87633.7i	−0.327036	−	0.364988i
$491$	99655.8			0.413371			0.206685	−	0.978407i	$-0.433732\pi$
$491$	99655.8			0.413371			0.206685	+	0.978407i	$0.433732\pi$
$492$	95930.6	+	95930.6i	0.396303	+	0.396303i
$493$	79068.6	−	79068.6i	0.325320	−	0.325320i
$494$			190521.i			0.780710i
$495$	−175047.	−	9600.03i	−0.714404	−	0.0391798i
$496$	−7883.80			−0.0320459
$497$	102597.	+	102597.i	0.415358	+	0.415358i
$498$	−30824.1	+	30824.1i	−0.124289	+	0.124289i
$499$			394400.i			1.58393i	0.610566	+	0.791965i	$0.290942\pi$
$499$			394400.i			1.58393i	−0.610566	+	0.791965i	$0.709058\pi$
$500$	123315.	+	20453.0i	0.493261	+	0.0818121i
$501$	−88671.5			−0.353272
$502$	−172621.	−	172621.i	−0.684995	−	0.684995i
$503$	−214140.	+	214140.i	−0.846373	+	0.846373i	−0.989679	−	0.143305i	$-0.954227\pi$
$503$	−214140.	+	214140.i	−0.846373	+	0.846373i	0.143305	+	0.989679i	$0.454227\pi$
$504$			50287.3i			0.197969i
$505$	−4482.97	+	81742.5i	−0.0175786	+	0.320528i
$506$	62764.3			0.245139
$507$	−276269.	−	276269.i	−1.07477	−	1.07477i
$508$	21581.5	−	21581.5i	0.0836285	−	0.0836285i
$509$		−	166763.i		−	0.643673i	−0.946795	−	0.321837i	$-0.895700\pi$
$509$		−	166763.i		−	0.643673i	0.946795	−	0.321837i	$-0.104300\pi$
$510$	−53700.3	+	48116.4i	−0.206460	+	0.184992i
$511$	−159352.			−0.610259
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	92889.0	−	92889.0i	0.352963	−	0.352963i
$514$		−	60468.1i		−	0.228876i
$515$	−178293.	−	198984.i	−0.672234	−	0.750247i
$516$	28883.0			0.108478
$517$	−75566.2	−	75566.2i	−0.282713	−	0.282713i
$518$	−293404.	+	293404.i	−1.09347	+	1.09347i
$519$			182253.i			0.676614i
$520$	143850.	+	7889.10i	0.531989	+	0.0291756i
$521$	−482673.			−1.77819			−0.889094	−	0.457725i	$-0.848665\pi$
$521$	−482673.			−1.77819			−0.889094	+	0.457725i	$0.848665\pi$
$522$	−82286.7	−	82286.7i	−0.301987	−	0.301987i
$523$	148477.	−	148477.i	0.542822	−	0.542822i	−0.381534	−	0.924355i	$-0.624604\pi$
$523$	148477.	−	148477.i	0.542822	−	0.542822i	0.924355	+	0.381534i	$0.124604\pi$
$524$		−	41176.2i		−	0.149963i
$525$	−426345.	−	46904.9i	−1.54683	−	0.170176i
$526$	86638.3			0.313140
$527$	8251.83	+	8251.83i	0.0297118	+	0.0297118i
$528$	97994.6	−	97994.6i	0.351507	−	0.351507i
$529$		−	12167.0i		−	0.0434783i
$530$	4280.93	−	78058.4i	0.0152400	−	0.277887i
$531$	218067.			0.773393
$532$	95393.8	+	95393.8i	0.337052	+	0.337052i
$533$	−283721.	+	283721.i	−0.998706	+	0.998706i
$534$		−	314827.i		−	1.10405i
$535$	199447.	−	178708.i	0.696818	−	0.624361i
$536$	−136624.			−0.475552
$537$	174537.	+	174537.i	0.605256	+	0.605256i
$538$	85872.1	−	85872.1i	0.296680	−	0.296680i
$539$		−	334766.i		−	1.15230i
$540$	−66287.8	−	73980.5i	−0.227324	−	0.253705i
$541$	307157.			1.04946			0.524731	−	0.851268i	$-0.324166\pi$
$541$	307157.			1.04946			0.524731	+	0.851268i	$0.324166\pi$
$542$	158767.	+	158767.i	0.540457	+	0.540457i
$543$	−475288.	+	475288.i	−1.61197	+	1.61197i
$544$		−	17148.8i		−	0.0579478i
$545$	444727.	+	24390.0i	1.49727	+	0.0821144i
$546$	−494339.			−1.65821
$547$	314454.	+	314454.i	1.05095	+	1.05095i	0.998630	+	0.0523219i	$0.0166622\pi$
$547$	314454.	+	314454.i	1.05095	+	1.05095i	0.0523219	+	0.998630i	$0.483338\pi$
$548$	−141576.	+	141576.i	−0.471442	+	0.471442i
$549$		−	234522.i		−	0.778108i
$550$	222462.	+	277461.i	0.735411	+	0.917228i
$551$	−312192.			−1.02830
$552$	−18996.5	−	18996.5i	−0.0623440	−	0.0623440i
$553$	160012.	−	160012.i	0.523243	−	0.523243i
$554$			200676.i			0.653847i
$555$	−33905.6	+	618234.i	−0.110074	+	2.00709i
$556$	−217637.			−0.704018
$557$	−171433.	−	171433.i	−0.552565	−	0.552565i	0.374615	−	0.927180i	$-0.377775\pi$
$557$	−171433.	−	171433.i	−0.552565	−	0.552565i	−0.927180	+	0.374615i	$0.877775\pi$
$558$	8587.68	−	8587.68i	0.0275808	−	0.0275808i
$559$			85423.5i			0.273372i
$560$	75975.4	−	68075.3i	0.242269	−	0.217077i
$561$	−205138.			−0.651810
$562$	−116702.	−	116702.i	−0.369494	−	0.369494i
$563$	172614.	−	172614.i	0.544578	−	0.544578i	−0.380290	−	0.924867i	$-0.624176\pi$
$563$	172614.	−	172614.i	0.544578	−	0.544578i	0.924867	+	0.380290i	$0.124176\pi$
$564$			45742.3i			0.143800i
$565$	257896.	+	287825.i	0.807882	+	0.901636i
$566$	380195.			1.18679
$567$	368306.	+	368306.i	1.14562	+	1.14562i
$568$	−36411.4	+	36411.4i	−0.112860	+	0.112860i
$569$		−	41862.2i		−	0.129300i	−0.997908	−	0.0646499i	$-0.979407\pi$
$569$		−	41862.2i		−	0.129300i	0.997908	−	0.0646499i	$-0.0205931\pi$
$570$	201005.	+	11023.6i	0.618667	+	0.0339293i
$571$	−10276.1			−0.0315178			−0.0157589	−	0.999876i	$-0.505016\pi$
$571$	−10276.1			−0.0315178			−0.0157589	+	0.999876i	$0.505016\pi$
$572$	289826.	+	289826.i	0.885819	+	0.885819i
$573$	63016.8	−	63016.8i	0.191932	−	0.191932i
$574$			284118.i			0.862333i
$575$	53786.5	−	43124.7i	0.162681	−	0.130434i
$576$	−17846.8			−0.0537917
$577$	−31842.2	−	31842.2i	−0.0956425	−	0.0956425i	0.657667	−	0.753309i	$-0.271544\pi$
$577$	−31842.2	−	31842.2i	−0.0956425	−	0.0956425i	−0.753309	+	0.657667i	$0.771544\pi$
$578$	149093.	−	149093.i	0.446273	−	0.446273i
$579$		−	123063.i		−	0.367089i
$580$	−12927.2	+	235715.i	−0.0384282	+	0.700699i
$581$	−91291.8			−0.270445
$582$	120483.	+	120483.i	0.355695	+	0.355695i
$583$	157271.	−	157271.i	0.462712	−	0.462712i
$584$		−	56553.4i		−	0.165818i
$585$	−165286.	+	148099.i	−0.482976	+	0.432755i
$586$	−235987.			−0.687217
$587$	−20975.0	−	20975.0i	−0.0608732	−	0.0608732i	0.676015	−	0.736888i	$-0.263706\pi$
$587$	−20975.0	−	20975.0i	−0.0608732	−	0.0608732i	−0.736888	+	0.676015i	$0.763706\pi$
$588$	−101321.	+	101321.i	−0.293053	+	0.293053i
$589$		−	32581.3i		−	0.0939155i
$590$	−295203.	−	329461.i	−0.848041	−	0.946456i
$591$	52695.7			0.150869
$592$	−104128.	−	104128.i	−0.297116	−	0.297116i
$593$	382625.	−	382625.i	1.08809	−	1.08809i	0.0923639	−	0.995725i	$-0.470558\pi$
$593$	382625.	−	382625.i	1.08809	−	1.08809i	0.995725	−	0.0923639i	$-0.0294423\pi$
$594$		−	282610.i		−	0.800967i
$595$	−150775.	−	8268.91i	−0.425889	−	0.0233569i
$596$	302947.			0.852854
$597$	−505599.	−	505599.i	−1.41859	−	1.41859i
$598$	56183.4	−	56183.4i	0.157111	−	0.157111i
$599$		−	14440.3i		−	0.0402461i	−0.999798	−	0.0201231i	$-0.993594\pi$
$599$		−	14440.3i		−	0.0402461i	0.999798	−	0.0201231i	$-0.00640580\pi$
$600$	16646.4	−	151309.i	0.0462400	−	0.420302i
$601$	612293.			1.69516			0.847579	−	0.530669i	$-0.178059\pi$
$601$	612293.			1.69516			0.847579	+	0.530669i	$0.178059\pi$
$602$	42771.5	+	42771.5i	0.118021	+	0.118021i
$603$	148822.	−	148822.i	0.409292	−	0.409292i
$604$		−	38270.6i		−	0.104904i
$605$	−35362.5	+	644799.i	−0.0966122	+	1.76163i
$606$	99693.4			0.271470
$607$	−67049.5	−	67049.5i	−0.181978	−	0.181978i	0.610239	−	0.792217i	$-0.291073\pi$
$607$	−67049.5	−	67049.5i	−0.181978	−	0.181978i	−0.792217	+	0.610239i	$0.791073\pi$
$608$	−33855.0	+	33855.0i	−0.0915831	+	0.0915831i
$609$		−	810034.i		−	2.18408i
$610$	−354323.	+	317480.i	−0.952226	+	0.853211i
$611$	−135286.			−0.362385
$612$	18679.9	+	18679.9i	0.0498738	+	0.0498738i
$613$	−475989.	+	475989.i	−1.26671	+	1.26671i	−0.318927	+	0.947779i	$0.603322\pi$
$613$	−475989.	+	475989.i	−1.26671	+	1.26671i	−0.947779	+	0.318927i	$0.896678\pi$
$614$			235272.i			0.624069i
$615$	282917.	+	315750.i	0.748013	+	0.834819i
$616$	290231.			0.764860
$617$	−104485.	−	104485.i	−0.274464	−	0.274464i	0.556431	−	0.830894i	$-0.312171\pi$
$617$	−104485.	−	104485.i	−0.274464	−	0.274464i	−0.830894	+	0.556431i	$0.812171\pi$
$618$	−230064.	+	230064.i	−0.602382	+	0.602382i
$619$		−	462668.i		−	1.20750i	−0.797173	−	0.603751i	$-0.793672\pi$
$619$		−	462668.i		−	1.20750i	0.797173	−	0.603751i	$-0.206328\pi$
$620$	−24599.9	−	1349.12i	−0.0639956	−	0.00350969i
$621$	−54784.6			−0.142061
$622$	38830.4	+	38830.4i	0.100367	+	0.100367i
$623$	466212.	−	466212.i	1.20118	−	1.20118i
$624$		−	175439.i		−	0.450566i
$625$	381282.	+	84922.3i	0.976082	+	0.217401i
$626$	−353155.			−0.901189
$627$	404981.	+	404981.i	1.03015	+	1.03015i
$628$	−125136.	+	125136.i	−0.317295	+	0.317295i
$629$			217978.i			0.550950i
$630$	−8605.46	+	156912.i	−0.0216817	+	0.395344i
$631$	−122681.			−0.308119			−0.154059	−	0.988062i	$-0.549235\pi$
$631$	−122681.			−0.308119			−0.154059	+	0.988062i	$0.549235\pi$
$632$	56787.9	+	56787.9i	0.142175	+	0.142175i
$633$	−228874.	+	228874.i	−0.571201	+	0.571201i
$634$		−	216357.i		−	0.538260i
$635$	71034.2	−	63647.9i	0.176165	−	0.157847i
$636$	−95200.2			−0.235355
$637$	−299665.	−	299665.i	−0.738512	−	0.738512i
$638$	−474914.	+	474914.i	−1.16674	+	1.16674i
$639$		−	79324.6i		−	0.194270i
$640$	24159.7	+	26963.5i	0.0589837	+	0.0658287i
$641$	193986.			0.472121			0.236061	−	0.971738i	$-0.424144\pi$
$641$	193986.			0.472121			0.236061	+	0.971738i	$0.424144\pi$
$642$	−230599.	−	230599.i	−0.559484	−	0.559484i
$643$	18524.6	−	18524.6i	0.0448051	−	0.0448051i	−0.684349	−	0.729154i	$-0.739914\pi$
$643$	18524.6	−	18524.6i	0.0448051	−	0.0448051i	0.729154	+	0.684349i	$0.239914\pi$
$644$		−	56261.9i		−	0.135657i
$645$	90124.0	+	4942.64i	0.216631	+	0.0118806i
$646$	70870.8			0.169825
$647$	−149567.	−	149567.i	−0.357294	−	0.357294i	0.505520	−	0.862815i	$-0.331301\pi$
$647$	−149567.	−	149567.i	−0.357294	−	0.357294i	−0.862815	+	0.505520i	$0.831301\pi$
$648$	−130711.	+	130711.i	−0.311287	+	0.311287i
$649$		−	1.25856e6i		−	2.98803i
$650$	447506.	+	49232.9i	1.05919	+	0.116527i
$651$	84537.5			0.199475
$652$	−268563.	−	268563.i	−0.631759	−	0.631759i
$653$	−307008.	+	307008.i	−0.719985	+	0.719985i	−0.968602	−	0.248617i	$-0.920024\pi$
$653$	−307008.	+	307008.i	−0.719985	+	0.719985i	0.248617	+	0.968602i	$0.420024\pi$
$654$		−	542391.i		−	1.26811i
$655$	7046.32	−	128482.i	0.0164240	−	0.299476i
$656$	−100833.			−0.234311
$657$	61602.6	+	61602.6i	0.142715	+	0.142715i
$658$	−67737.5	+	67737.5i	−0.156451	+	0.156451i
$659$		−	467391.i		−	1.07624i	−0.842868	−	0.538121i	$-0.819134\pi$
$659$		−	467391.i		−	1.07624i	0.842868	−	0.538121i	$-0.180866\pi$
$660$	322543.	−	289004.i	0.740457	−	0.663462i
$661$	861924.			1.97272			0.986362	−	0.164591i	$-0.0526305\pi$
$661$	861924.			1.97272			0.986362	+	0.164591i	$0.0526305\pi$
$662$	−243461.	−	243461.i	−0.555539	−	0.555539i
$663$	−183629.	+	183629.i	−0.417748	+	0.417748i
$664$		−	32399.2i		−	0.0734849i
$665$	281334.	+	313983.i	0.636178	+	0.710007i
$666$	226850.			0.511435
$667$	92063.2	+	92063.2i	0.206935	+	0.206935i
$668$	46601.3	−	46601.3i	0.104435	−	0.104435i
$669$		−	39755.7i		−	0.0888275i
$670$	−426310.	−	23380.0i	−0.949677	−	0.0520828i
$671$	−1.35354e6			−3.00625
$672$	−87842.3	−	87842.3i	−0.194520	−	0.194520i
$673$	215645.	−	215645.i	0.476112	−	0.476112i	−0.427774	−	0.903886i	$-0.640702\pi$
$673$	215645.	−	215645.i	0.476112	−	0.476112i	0.903886	+	0.427774i	$0.140702\pi$
$674$			190113.i			0.418497i
$675$	−194179.	−	242186.i	−0.426181	−	0.531546i
$676$	290386.			0.635452
$677$	26576.1	+	26576.1i	0.0579848	+	0.0579848i	0.735505	−	0.677520i	$-0.236945\pi$
$677$	26576.1	+	26576.1i	0.0579848	+	0.0579848i	−0.677520	+	0.735505i	$0.736945\pi$
$678$	332781.	−	332781.i	0.723935	−	0.723935i
$679$			356834.i			0.773974i
$680$	2934.61	−	53509.7i	0.00634648	−	0.115722i
$681$	152823.			0.329529
$682$	−49563.4	−	49563.4i	−0.106560	−	0.106560i
$683$	−420032.	+	420032.i	−0.900412	+	0.900412i	−0.995472	−	0.0950596i	$-0.969696\pi$
$683$	−420032.	+	420032.i	−0.900412	+	0.900412i	0.0950596	+	0.995472i	$0.469696\pi$
$684$		−	73755.2i		−	0.157645i
$685$	−465988.	+	417533.i	−0.993101	+	0.889836i
$686$	132898.			0.282403
$687$	771876.	+	771876.i	1.63544	+	1.63544i
$688$	−15179.5	+	15179.5i	−0.0320686	+	0.0320686i
$689$		−	281561.i		−	0.593109i
$690$	−56024.1	−	62525.7i	−0.117673	−	0.131329i
$691$	−300047.			−0.628395			−0.314197	−	0.949358i	$-0.601735\pi$
$691$	−300047.			−0.628395			−0.314197	+	0.949358i	$0.601735\pi$
$692$	−95783.3	−	95783.3i	−0.200022	−	0.200022i
$693$	−316143.	+	316143.i	−0.658290	+	0.658290i
$694$		−	52130.1i		−	0.108236i
$695$	−679096.	−	37243.4i	−1.40592	−	0.0771045i
$696$	287479.			0.593454
$697$	105540.	+	105540.i	0.217245	+	0.217245i
$698$	−304972.	+	304972.i	−0.625964	+	0.625964i
$699$			44420.4i			0.0909135i
$700$	248716.	−	199415.i	0.507585	−	0.406969i
$701$	69229.8			0.140882			0.0704412	−	0.997516i	$-0.477559\pi$
$701$	69229.8			0.140882			0.0704412	+	0.997516i	$0.477559\pi$
$702$	−252978.	−	252978.i	−0.513344	−	0.513344i
$703$	430330.	−	430330.i	0.870745	−	0.870745i
$704$			103002.i			0.207826i
$705$	−7827.70	+	142730.i	−0.0157491	+	0.287169i
$706$	456399.			0.915661
$707$	147631.	+	147631.i	0.295351	+	0.295351i
$708$	−380921.	+	380921.i	−0.759921	+	0.759921i
$709$		−	533339.i		−	1.06099i	−0.847688	−	0.530495i	$-0.822006\pi$
$709$		−	533339.i		−	1.06099i	0.847688	−	0.530495i	$-0.177994\pi$
$710$	−119846.	+	107384.i	−0.237742	+	0.213021i
$711$	−123716.			−0.244730
$712$	165457.	+	165457.i	0.326382	+	0.326382i
$713$	−9607.98	+	9607.98i	−0.0188996	+	0.0188996i
$714$			183886.i			0.360705i
$715$	854750.	+	953943.i	1.67196	+	1.86599i
$716$	−183456.			−0.357854
$717$	−286677.	−	286677.i	−0.557641	−	0.557641i
$718$	406442.	−	406442.i	0.788405	−	0.788405i
$719$			419665.i			0.811792i	0.913919	+	0.405896i	$0.133041\pi$
$719$			419665.i			0.811792i	−0.913919	+	0.405896i	$0.866959\pi$
$720$	−55687.6	−	3054.05i	−0.107422	−	0.00589130i
$721$	−681382.			−1.31075
$722$	120730.	+	120730.i	0.231601	+	0.231601i
$723$	−538444.	+	538444.i	−1.03006	+	1.03006i
$724$		−	499575.i		−	0.953068i
$725$	−80674.0	+	733292.i	−0.153482	+	1.39509i
$726$	786399.			1.49200
$727$	−127073.	−	127073.i	−0.240428	−	0.240428i	0.576599	−	0.817027i	$-0.304379\pi$
$727$	−127073.	−	127073.i	−0.240428	−	0.240428i	−0.817027	+	0.576599i	$0.804379\pi$
$728$	259800.	−	259800.i	0.490203	−	0.490203i
$729$			148264.i			0.278984i
$730$	9677.76	−	176464.i	0.0181605	−	0.331139i
$731$	31776.1			0.0594656
$732$	409666.	+	409666.i	0.764554	+	0.764554i
$733$	343654.	−	343654.i	0.639608	−	0.639608i	−0.310851	−	0.950459i	$-0.600614\pi$
$733$	343654.	−	343654.i	0.639608	−	0.639608i	0.950459	+	0.310851i	$0.100614\pi$
$734$		−	385528.i		−	0.715590i
$735$	−333493.	+	298816.i	−0.617323	+	0.553132i
$736$	19967.2			0.0368605
$737$	−858922.	−	858922.i	−1.58132	−	1.58132i
$738$	109835.	−	109835.i	0.201664	−	0.201664i
$739$		−	304082.i		−	0.556804i	−0.960465	−	0.278402i	$-0.910195\pi$
$739$		−	304082.i		−	0.556804i	0.960465	−	0.278402i	$-0.0898047\pi$
$740$	−307094.	−	342732.i	−0.560799	−	0.625880i
$741$	725036.			1.32045
$742$	−140977.	−	140977.i	−0.256060	−	0.256060i
$743$	−215584.	+	215584.i	−0.390517	+	0.390517i	−0.874872	−	0.484355i	$-0.839054\pi$
$743$	−215584.	+	215584.i	−0.390517	+	0.390517i	0.484355	+	0.874872i	$0.339054\pi$
$744$			30002.1i			0.0542008i
$745$	945290.	+	51842.2i	1.70315	+	0.0934051i
$746$	519371.			0.933254
$747$	35291.9	+	35291.9i	0.0632461	+	0.0632461i
$748$	107810.	−	107810.i	0.192689	−	0.192689i
$749$		−	682966.i		−	1.21741i
$750$	77834.8	−	469281.i	0.138373	−	0.834278i
$751$	563914.			0.999846			0.499923	−	0.866070i	$-0.333362\pi$
$751$	563914.			0.999846			0.499923	+	0.866070i	$0.333362\pi$
$752$	−24039.8	−	24039.8i	−0.0425105	−	0.0425105i
$753$	−656918.	+	656918.i	−1.15857	+	1.15857i
$754$			850238.i			1.49554i
$755$	6549.10	−	119416.i	0.0114892	−	0.209493i
$756$	−253332.			−0.443247
$757$	−429702.	−	429702.i	−0.749852	−	0.749852i	0.224599	−	0.974451i	$-0.427893\pi$
$757$	−429702.	−	429702.i	−0.749852	−	0.749852i	−0.974451	+	0.224599i	$0.927893\pi$
$758$	158383.	−	158383.i	0.275657	−	0.275657i
$759$		−	238852.i		−	0.414615i
$760$	−111432.	+	99844.6i	−0.192922	+	0.172861i
$761$	913386.			1.57719			0.788597	−	0.614911i	$-0.210808\pi$
$761$	913386.			1.57719			0.788597	+	0.614911i	$0.210808\pi$
$762$	−82129.3	−	82129.3i	−0.141445	−	0.141445i
$763$	803200.	−	803200.i	1.37967	−	1.37967i
$764$			66236.9i			0.113478i
$765$	55090.5	+	61483.8i	0.0941357	+	0.105060i
$766$	111225.			0.189559
$767$	−1.12660e6	−	1.12660e6i	−1.91505	−	1.91505i
$768$	31175.0	−	31175.0i	0.0528547	−	0.0528547i
$769$			213013.i			0.360208i	0.983648	+	0.180104i	$0.0576434\pi$
$769$			213013.i			0.360208i	−0.983648	+	0.180104i	$0.942357\pi$
$770$	905611.	+	49666.1i	1.52743	+	0.0837680i
$771$	−230114.			−0.387109
$772$	64675.8	+	64675.8i	0.108519	+	0.108519i
$773$	206963.	−	206963.i	0.346365	−	0.346365i	−0.512388	−	0.858754i	$-0.671239\pi$
$773$	206963.	−	206963.i	0.346365	−	0.346365i	0.858754	+	0.512388i	$0.171239\pi$
$774$		−	33069.4i		−	0.0552007i
$775$	−76528.5	−	8419.37i	−0.127415	−	0.0140177i
$776$	−126639.			−0.210303
$777$	1.11656e6	+	1.11656e6i	1.84944	+	1.84944i
$778$	−109831.	+	109831.i	−0.181453	+	0.181453i
$779$		−	416710.i		−	0.686687i
$780$	30022.3	−	547426.i	0.0493463	−	0.899779i
$781$	−457819.			−0.750570
$782$	−20899.3	−	20899.3i	−0.0341757	−	0.0341757i
$783$	414535.	−	414535.i	0.676141	−	0.676141i
$784$		−	106499.i		−	0.173266i
$785$	−411878.	+	369050.i	−0.668389	+	0.598888i
$786$	−156698.			−0.253640
$787$	270489.	+	270489.i	0.436717	+	0.436717i	0.890905	−	0.454189i	$-0.150071\pi$
$787$	270489.	+	270489.i	0.436717	+	0.436717i	−0.454189	+	0.890905i	$0.650071\pi$
$788$	−27694.2	+	27694.2i	−0.0446002	+	0.0446002i
$789$		−	329706.i		−	0.529630i
$790$	167478.	+	186914.i	0.268351	+	0.299494i
$791$	985599.			1.57524
$792$	−112198.	−	112198.i	−0.178869	−	0.178869i
$793$	−1.21162e6	+	1.21162e6i	−1.92672	+	1.92672i
$794$			330814.i			0.524738i
$795$	−297054.	−	16291.2i	−0.470004	−	0.0257762i
$796$	531435.			0.838734
$797$	−344099.	−	344099.i	−0.541710	−	0.541710i	0.382320	−	0.924030i	$-0.375125\pi$
$797$	−344099.	−	344099.i	−0.541710	−	0.541710i	−0.924030	+	0.382320i	$0.875125\pi$
$798$	363025.	−	363025.i	0.570073	−	0.570073i
$799$			50324.1i			0.0788284i
$800$	70771.7	+	88268.7i	0.110581	+	0.137920i
$801$	−360459.			−0.561812
$802$	249575.	+	249575.i	0.388018	+	0.388018i
$803$	355537.	−	355537.i	0.551383	−	0.551383i
$804$			519929.i			0.804326i
$805$	9627.88	−	175555.i	0.0148573	−	0.270907i
$806$	−88733.3			−0.136589
$807$	−326790.	−	326790.i	−0.501789	−	0.501789i
$808$	−52393.8	+	52393.8i	−0.0802523	+	0.0802523i
$809$			853033.i			1.30337i	0.758489	+	0.651686i	$0.225938\pi$
$809$			853033.i			1.30337i	−0.758489	+	0.651686i	$0.774062\pi$
$810$	−430225.	+	385489.i	−0.655731	+	0.587547i
$811$	82390.2			0.125266			0.0626331	−	0.998037i	$-0.480050\pi$
$811$	82390.2			0.125266			0.0626331	+	0.998037i	$0.480050\pi$
$812$	425713.	+	425713.i	0.645662	+	0.645662i
$813$	604193.	−	604193.i	0.914102	−	0.914102i
$814$		−	1.30926e6i		−	1.97595i
$815$	−792043.	−	883959.i	−1.19243	−	1.33081i
$816$	−65260.6			−0.0980100
$817$	−62731.9	−	62731.9i	−0.0939820	−	0.0939820i
$818$	−665604.	+	665604.i	−0.994740	+	0.994740i
$819$			565991.i			0.843804i
$820$	−314629.	−	17255.1i	−0.467920	−	0.0256619i
$821$	−1.12927e6			−1.67537			−0.837685	−	0.546154i	$-0.816091\pi$
$821$	−1.12927e6			−1.67537			−0.837685	+	0.546154i	$0.816091\pi$
$822$	538772.	+	538772.i	0.797373	+	0.797373i
$823$	−311111.	+	311111.i	−0.459321	+	0.459321i	−0.898433	−	0.439111i	$-0.855293\pi$
$823$	−311111.	+	311111.i	−0.459321	+	0.459321i	0.439111	+	0.898433i	$0.355293\pi$
$824$		−	241820.i		−	0.356155i
$825$	1.05589e6	−	846587.i	1.55135	−	1.24384i
$826$	−1.12818e6			−1.65355
$827$	−298230.	−	298230.i	−0.436054	−	0.436054i	0.454627	−	0.890682i	$-0.349772\pi$
$827$	−298230.	−	298230.i	−0.436054	−	0.436054i	−0.890682	+	0.454627i	$0.849772\pi$
$828$	−21749.9	+	21749.9i	−0.0317246	+	0.0317246i
$829$			334398.i			0.486580i	0.969954	+	0.243290i	$0.0782268\pi$
$829$			334398.i			0.486580i	−0.969954	+	0.243290i	$0.921773\pi$
$830$	5544.35	−	101096.i	0.00804812	−	0.146749i
$831$	763681.			1.10588
$832$	92202.2	+	92202.2i	0.133197	+	0.133197i
$833$	−111471.	+	111471.i	−0.160646	+	0.160646i
$834$			828227.i			1.19074i
$835$	153385.	−	137436.i	0.219994	−	0.197118i
$836$	−425675.			−0.609068
$837$	43262.1	+	43262.1i	0.0617528	+	0.0617528i
$838$	385901.	−	385901.i	0.549526	−	0.549526i
$839$			1.32404e6i			1.88095i	0.339860	+	0.940476i	$0.389620\pi$
$839$			1.32404e6i			1.88095i	−0.339860	+	0.940476i	$0.610380\pi$
$840$	−259063.	−	289128.i	−0.367153	−	0.409761i
$841$	−685936.			−0.969821
$842$	359165.	+	359165.i	0.506606	+	0.506606i
$843$	−444116.	+	444116.i	−0.624944	+	0.624944i
$844$		−	240569.i		−	0.337719i
$845$	906096.	+	49692.7i	1.26900	+	0.0695951i
$846$	52372.4			0.0731748
$847$	1.16454e6	+	1.16454e6i	1.62326	+	1.62326i
$848$	50032.4	−	50032.4i	0.0695761	−	0.0695761i
$849$		−	1.44685e6i		−	2.00728i
$850$	18313.8	−	166465.i	0.0253478	−	0.230401i
$851$	−253802.			−0.350458
$852$	138565.	+	138565.i	0.190886	+	0.190886i
$853$	119799.	−	119799.i	0.164647	−	0.164647i	−0.619975	−	0.784622i	$-0.712857\pi$
$853$	119799.	−	119799.i	0.164647	−	0.164647i	0.784622	+	0.619975i	$0.212857\pi$
$854$			1.21331e6i			1.66363i
$855$	12621.4	−	230139.i	0.0172654	−	0.314817i
$856$	242383.			0.330791
$857$	−929827.	−	929827.i	−1.26602	−	1.26602i	−0.948127	−	0.317893i	$-0.897025\pi$
$857$	−929827.	−	929827.i	−1.26602	−	1.26602i	−0.317893	−	0.948127i	$-0.602975\pi$
$858$	1.10294e6	−	1.10294e6i	1.49823	−	1.49823i
$859$		−	682166.i		−	0.924493i	−0.886751	−	0.462247i	$-0.847043\pi$
$859$		−	682166.i		−	0.924493i	0.886751	−	0.462247i	$-0.152957\pi$
$860$	−49962.2	+	44767.0i	−0.0675530	+	0.0605287i
$861$	1.08122e6			1.45851
$862$	130537.	+	130537.i	0.175678	+	0.175678i
$863$	873351.	−	873351.i	1.17265	−	1.17265i	0.191070	−	0.981576i	$-0.438804\pi$
$863$	873351.	−	873351.i	1.17265	−	1.17265i	0.981576	−	0.191070i	$-0.0611958\pi$
$864$		−	89906.6i		−	0.120438i
$865$	−282483.	−	315265.i	−0.377537	−	0.421350i
$866$	440632.			0.587544
$867$	−567378.	−	567378.i	−0.754804	−	0.754804i
$868$	−44428.7	+	44428.7i	−0.0589690	+	0.0589690i
$869$			714023.i			0.945524i
$870$	897023.	+	49195.1i	1.18513	+	0.0649955i
$871$	−1.53773e6			−2.02695
$872$	285053.	+	285053.i	0.374881	+	0.374881i
$873$	137946.	−	137946.i	0.181001	−	0.181001i
$874$			82518.1i			0.108026i
$875$	810198.	−	579674.i	1.05822	−	0.757126i
$876$	−215216.			−0.280457
$877$	−196825.	−	196825.i	−0.255906	−	0.255906i	0.567481	−	0.823387i	$-0.307918\pi$
$877$	−196825.	−	196825.i	−0.255906	−	0.255906i	−0.823387	+	0.567481i	$0.807918\pi$
$878$	560720.	−	560720.i	0.727372	−	0.727372i
$879$			898060.i			1.16232i
$880$	−17626.3	+	321398.i	−0.0227613	+	0.415029i
$881$	1.25166e6			1.61263			0.806314	−	0.591488i	$-0.201459\pi$
$881$	1.25166e6			1.61263			0.806314	+	0.591488i	$0.201459\pi$
$882$	116007.	+	116007.i	0.149124	+	0.149124i
$883$	−852234.	+	852234.i	−1.09304	+	1.09304i	−0.0978409	+	0.995202i	$0.531194\pi$
$883$	−852234.	+	852234.i	−1.09304	+	1.09304i	−0.995202	+	0.0978409i	$0.968806\pi$
$884$		−	193013.i		−	0.246991i
$885$	−1.25378e6	+	1.12341e6i	−1.60079	+	1.43433i
$886$	22550.3			0.0287266
$887$	−513820.	−	513820.i	−0.653077	−	0.653077i	0.300656	−	0.953733i	$-0.402794\pi$
$887$	−513820.	−	513820.i	−0.653077	−	0.653077i	−0.953733	+	0.300656i	$0.902794\pi$
$888$	−396264.	+	396264.i	−0.502527	+	0.502527i
$889$		−	243243.i		−	0.307777i
$890$	487964.	+	544592.i	0.616038	+	0.687529i
$891$	−1.64349e6			−2.07019
$892$	20893.6	+	20893.6i	0.0262593	+	0.0262593i
$893$	99349.2	−	99349.2i	0.124584	−	0.124584i
$894$		−	1.15288e6i		−	1.44248i
$895$	−572439.	−	31394.1i	−0.714633	−	0.0391924i
$896$	92331.0			0.115009
$897$	−213808.	−	213808.i	−0.265729	−	0.265729i
$898$	454181.	−	454181.i	0.563217	−	0.563217i
$899$		−	145400.i		−	0.179906i
$900$	−173240.	−	19059.2i	−0.213876	−	0.0235299i
$901$	−104736.			−0.129017
$902$	−633909.	−	633909.i	−0.779137	−	0.779137i
$903$	162768.	−	162768.i	0.199616	−	0.199616i
$904$			349786.i			0.428022i
$905$	85490.3	−	1.55883e6i	0.104381	−	1.90328i
$906$	−145640.			−0.177429
$907$	−665799.	−	665799.i	−0.809335	−	0.809335i	0.175198	−	0.984533i	$-0.443943\pi$
$907$	−665799.	−	665799.i	−0.809335	−	0.809335i	−0.984533	+	0.175198i	$0.943943\pi$
$908$	−80316.0	+	80316.0i	−0.0974160	+	0.0974160i
$909$		−	114143.i		−	0.138141i
$910$	855115.	−	766198.i	1.03262	−	0.925248i
$911$	263504.			0.317505			0.158753	−	0.987318i	$-0.449253\pi$
$911$	263504.			0.317505			0.158753	+	0.987318i	$0.449253\pi$
$912$	128836.	+	128836.i	0.154899	+	0.154899i
$913$	203686.	−	203686.i	0.244354	−	0.244354i
$914$			475967.i			0.569750i
$915$	1.20818e6	+	1.34839e6i	1.44308	+	1.61055i
$916$	−811318.			−0.966941
$917$	−232046.	−	232046.i	−0.275953	−	0.275953i
$918$	−94103.6	+	94103.6i	−0.111666	+	0.111666i
$919$			1.21110e6i			1.43400i	0.697071	+	0.717002i	$0.254486\pi$
$919$			1.21110e6i			1.43400i	−0.697071	+	0.717002i	$0.745514\pi$
$920$	62303.8	+	3416.90i	0.0736104	+	0.00403699i
$921$	895336.			1.05552
$922$	218593.	+	218593.i	0.257143	+	0.257143i
$923$	−409816.	+	409816.i	−0.481045	+	0.481045i
$924$		−	1.10448e6i		−	1.29365i
$925$	−899577.	−	1.12198e6i	−1.05137	−	1.31130i
$926$	−4079.91			−0.00475804
$927$	263411.	+	263411.i	0.306531	+	0.306531i
$928$	−151084.	+	151084.i	−0.175438	+	0.175438i
$929$		−	636412.i		−	0.737407i	−0.929547	−	0.368703i	$-0.879802\pi$
$929$		−	636412.i		−	0.737407i	0.929547	−	0.368703i	$-0.120198\pi$
$930$	−5134.14	+	93615.9i	−0.00593611	+	0.108239i
$931$	440127.			0.507783
$932$	−23345.2	−	23345.2i	−0.0268760	−	0.0268760i
$933$	147771.	−	147771.i	0.169756	−	0.169756i
$934$			106874.i			0.122512i
$935$	354851.	−	317953.i	0.405904	−	0.363697i
$936$	−200868.			−0.229277
$937$	−438956.	−	438956.i	−0.499968	−	0.499968i	0.411460	−	0.911428i	$-0.365019\pi$
$937$	−438956.	−	438956.i	−0.499968	−	0.499968i	−0.911428	+	0.411460i	$0.865019\pi$
$938$	−769938.	+	769938.i	−0.875084	+	0.875084i
$939$			1.34394e6i			1.52423i
$940$	−70897.9	−	79125.6i	−0.0802376	−	0.0895492i
$941$	1.57866e6			1.78283			0.891415	−	0.453188i	$-0.149713\pi$
$941$	1.57866e6			1.78283			0.891415	+	0.453188i	$0.149713\pi$
$942$	476211.	+	476211.i	0.536658	+	0.536658i
$943$	−122885.	+	122885.i	−0.138189	+	0.138189i
$944$		−	400386.i		−	0.449298i
$945$	−790474.	−	43351.6i	−0.885164	−	0.0485447i
$946$	−190859.			−0.213270
$947$	−180147.	−	180147.i	−0.200876	−	0.200876i	0.599499	−	0.800375i	$-0.295366\pi$
$947$	−180147.	−	180147.i	−0.200876	−	0.200876i	−0.800375	+	0.599499i	$0.795366\pi$
$948$	216109.	−	216109.i	0.240467	−	0.240467i
$949$		−	636516.i		−	0.706769i
$950$	−364787.	+	292477.i	−0.404196	+	0.324075i
$951$	−823354.			−0.910386
$952$	−96641.2	−	96641.2i	−0.106632	−	0.106632i
$953$	359259.	−	359259.i	0.395569	−	0.395569i	−0.481098	−	0.876667i	$-0.659762\pi$
$953$	359259.	−	359259.i	0.395569	−	0.395569i	0.876667	+	0.481098i	$0.159762\pi$
$954$			108999.i			0.119764i
$955$	−11334.9	+	206680.i	−0.0124282	+	0.226616i
$956$	301326.			0.329702
$957$	1.80730e6	+	1.80730e6i	1.97337	+	1.97337i
$958$	−426139.	+	426139.i	−0.464323	+	0.464323i
$959$			1.59568e6i			1.73504i
$960$	102610.	−	91940.8i	0.111339	−	0.0997621i
$961$	−908347.			−0.983569
$962$	−1.17198e6	−	1.17198e6i	−1.26640	−	1.26640i
$963$	−264023.	+	264023.i	−0.284701	+	0.284701i
$964$		−	565958.i		−	0.609018i
$965$	190741.	+	212876.i	0.204828	+	0.228598i
$966$	−214107.			−0.229444
$967$	−1.18763e6	−	1.18763e6i	−1.27007	−	1.27007i	−0.946050	−	0.324019i	$-0.894966\pi$
$967$	−1.18763e6	−	1.18763e6i	−1.27007	−	1.27007i	−0.324019	−	0.946050i	$-0.605034\pi$
$968$	−413292.	+	413292.i	−0.441068	+	0.441068i
$969$		−	269701.i		−	0.287234i
$970$	−395154.	−	21671.3i	−0.419974	−	0.0230325i
$971$	−501387.			−0.531783			−0.265892	−	0.964003i	$-0.585666\pi$
$971$	−501387.			−0.531783			−0.265892	+	0.964003i	$0.585666\pi$
$972$	269848.	+	269848.i	0.285619	+	0.285619i
$973$	−1.22648e6	+	1.22648e6i	−1.29549	+	1.29549i
$974$			1.09308e6i			1.15222i
$975$	187358.	−	1.70300e6i	0.197089	−	1.79145i
$976$	−430600.			−0.452037
$977$	−826900.	−	826900.i	−0.866291	−	0.866291i	0.125769	−	0.992060i	$-0.459860\pi$
$977$	−826900.	−	826900.i	−0.866291	−	0.866291i	−0.992060	+	0.125769i	$0.959860\pi$
$978$	−1.02203e6	+	1.02203e6i	−1.06853	+	1.06853i
$979$			2.08038e6i			2.17058i
$980$	18224.7	−	332310.i	0.0189762	−	0.346012i
$981$	−621007.			−0.645295
$982$	199312.	+	199312.i	0.206685	+	0.206685i
$983$	−533658.	+	533658.i	−0.552275	+	0.552275i	−0.927097	−	0.374822i	$-0.877704\pi$
$983$	−533658.	+	533658.i	−0.552275	+	0.552275i	0.374822	+	0.927097i	$0.377704\pi$
$984$			383722.i			0.396303i
$985$	−91153.8	+	81675.4i	−0.0939512	+	0.0841819i
$986$	316274.			0.325320
$987$	257778.	+	257778.i	0.264613	+	0.264613i
$988$	−381043.	+	381043.i	−0.390355	+	0.390355i
$989$			36998.4i			0.0378260i
$990$	−330894.	−	369294.i	−0.337612	−	0.376792i
$991$	535215.			0.544980			0.272490	−	0.962159i	$-0.412153\pi$
$991$	535215.			0.544980			0.272490	+	0.962159i	$0.412153\pi$
$992$	−15767.6	−	15767.6i	−0.0160229	−	0.0160229i
$993$	−926502.	+	926502.i	−0.939611	+	0.939611i
$994$			410389.i			0.415358i
$995$	1.65824e6	+	90942.4i	1.67495	+	0.0918587i
$996$	−123296.			−0.124289
$997$	569006.	+	569006.i	0.572435	+	0.572435i	0.932808	−	0.360373i	$-0.117351\pi$
$997$	569006.	+	569006.i	0.572435	+	0.572435i	−0.360373	+	0.932808i	$0.617351\pi$
$998$	−788800.	+	788800.i	−0.791965	+	0.791965i
$999$			1.14280e6i			1.14509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.19	✓	44
5.3	odd	4	inner	230.5.f.b.93.19	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.19	✓	44	1.1	even	1	trivial
230.5.f.b.93.19	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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(7.61108 - 7.61108i) q^{3} +8.00000i q^{4} +(-1.36901 + 24.9625i) q^{5} +30.4443 q^{6} +(45.0835 + 45.0835i) q^{7} +(-16.0000 + 16.0000i) q^{8} -34.8570i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(7.61108 - 7.61108i) q^{3} +8.00000i q^{4} +(-1.36901 + 24.9625i) q^{5} +30.4443 q^{6} +(45.0835 + 45.0835i) q^{7} +(-16.0000 + 16.0000i) q^{8} -34.8570i q^{9} +(-52.6630 + 47.1870i) q^{10} -201.176 q^{11} +(60.8886 + 60.8886i) q^{12} +(-180.082 + 180.082i) q^{13} +180.334i q^{14} +(179.572 + 200.411i) q^{15} -64.0000 q^{16} +(66.9876 + 66.9876i) q^{17} +(69.7141 - 69.7141i) q^{18} -264.492i q^{19} +(-199.700 - 10.9521i) q^{20} +686.268 q^{21} +(-402.352 - 402.352i) q^{22} +(-77.9968 + 77.9968i) q^{23} +243.555i q^{24} +(-621.252 - 68.3477i) q^{25} -720.329 q^{26} +(351.198 + 351.198i) q^{27} +(-360.668 + 360.668i) q^{28} -1180.35i q^{29} +(-41.6785 + 759.966i) q^{30} +123.184 q^{31} +(-128.000 - 128.000i) q^{32} +(-1531.17 + 1531.17i) q^{33} +267.951i q^{34} +(-1187.12 + 1063.68i) q^{35} +278.856 q^{36} +(1627.01 + 1627.01i) q^{37} +(528.984 - 528.984i) q^{38} +2741.24i q^{39} +(-377.496 - 421.304i) q^{40} +1575.51 q^{41} +(1372.54 + 1372.54i) q^{42} +(237.179 - 237.179i) q^{43} -1609.41i q^{44} +(870.118 + 47.7196i) q^{45} -311.987 q^{46} +(375.623 + 375.623i) q^{47} +(-487.109 + 487.109i) q^{48} +1664.05i q^{49} +(-1105.81 - 1379.20i) q^{50} +1019.70 q^{51} +(-1440.66 - 1440.66i) q^{52} +(-781.757 + 781.757i) q^{53} +1404.79i q^{54} +(275.411 - 5021.85i) q^{55} -1442.67 q^{56} +(-2013.07 - 2013.07i) q^{57} +(2360.69 - 2360.69i) q^{58} +6256.03i q^{59} +(-1603.29 + 1436.57i) q^{60} +6728.12 q^{61} +(246.369 + 246.369i) q^{62} +(1571.48 - 1571.48i) q^{63} -512.000i q^{64} +(-4248.77 - 4741.84i) q^{65} -6124.66 q^{66} +(4269.51 + 4269.51i) q^{67} +(-535.901 + 535.901i) q^{68} +1187.28i q^{69} +(-4501.59 - 246.879i) q^{70} +2275.71 q^{71} +(557.712 + 557.712i) q^{72} +(-1767.29 + 1767.29i) q^{73} +6508.02i q^{74} +(-5248.59 + 4208.20i) q^{75} +2115.94 q^{76} +(-9069.71 - 9069.71i) q^{77} +(-5482.48 + 5482.48i) q^{78} -3549.25i q^{79} +(87.6165 - 1597.60i) q^{80} +8169.41 q^{81} +(3151.02 + 3151.02i) q^{82} +(-1012.47 + 1012.47i) q^{83} +5490.15i q^{84} +(-1763.88 + 1580.47i) q^{85} +948.716 q^{86} +(-8983.71 - 8983.71i) q^{87} +(3218.81 - 3218.81i) q^{88} -10341.1i q^{89} +(1644.80 + 1835.68i) q^{90} -16237.5 q^{91} +(-623.974 - 623.974i) q^{92} +(937.566 - 937.566i) q^{93} +1502.49i q^{94} +(6602.38 + 362.092i) q^{95} -1948.44 q^{96} +(3957.47 + 3957.47i) q^{97} +(-3328.09 + 3328.09i) q^{98} +7012.39i 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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