LMFDB - Embedded newform 230.5.f.b.47.2

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			47.2
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(-11.0455 + 11.0455i) q^{3} +8.00000i q^{4} +(3.15467 + 24.8002i) q^{5} -44.1818 q^{6} +(-2.46420 - 2.46420i) q^{7} +(-16.0000 + 16.0000i) q^{8} -163.004i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(-11.0455 + 11.0455i) q^{3} +8.00000i q^{4} +(3.15467 + 24.8002i) q^{5} -44.1818 q^{6} +(-2.46420 - 2.46420i) q^{7} +(-16.0000 + 16.0000i) q^{8} -163.004i q^{9} +(-43.2910 + 55.9097i) q^{10} -221.861 q^{11} +(-88.3636 - 88.3636i) q^{12} +(98.6330 - 98.6330i) q^{13} -9.85682i q^{14} +(-308.774 - 239.084i) q^{15} -64.0000 q^{16} +(17.4645 + 17.4645i) q^{17} +(326.008 - 326.008i) q^{18} +413.845i q^{19} +(-198.401 + 25.2374i) q^{20} +54.4365 q^{21} +(-443.723 - 443.723i) q^{22} +(77.9968 - 77.9968i) q^{23} -353.454i q^{24} +(-605.096 + 156.473i) q^{25} +394.532 q^{26} +(905.771 + 905.771i) q^{27} +(19.7136 - 19.7136i) q^{28} +453.332i q^{29} +(-139.379 - 1095.72i) q^{30} +1074.91 q^{31} +(-128.000 - 128.000i) q^{32} +(2450.56 - 2450.56i) q^{33} +69.8579i q^{34} +(53.3389 - 68.8864i) q^{35} +1304.03 q^{36} +(-1659.79 - 1659.79i) q^{37} +(-827.689 + 827.689i) q^{38} +2178.89i q^{39} +(-447.277 - 346.328i) q^{40} +1557.59 q^{41} +(108.873 + 108.873i) q^{42} +(-631.358 + 631.358i) q^{43} -1774.89i q^{44} +(4042.53 - 514.224i) q^{45} +311.987 q^{46} +(644.451 + 644.451i) q^{47} +(706.909 - 706.909i) q^{48} -2388.86i q^{49} +(-1523.14 - 897.246i) q^{50} -385.806 q^{51} +(789.064 + 789.064i) q^{52} +(793.116 - 793.116i) q^{53} +3623.09i q^{54} +(-699.900 - 5502.20i) q^{55} +78.8545 q^{56} +(-4571.10 - 4571.10i) q^{57} +(-906.664 + 906.664i) q^{58} +2170.20i q^{59} +(1912.67 - 2470.19i) q^{60} +4373.10 q^{61} +(2149.82 + 2149.82i) q^{62} +(-401.675 + 401.675i) q^{63} -512.000i q^{64} +(2757.27 + 2134.96i) q^{65} +9802.24 q^{66} +(1217.36 + 1217.36i) q^{67} +(-139.716 + 139.716i) q^{68} +1723.02i q^{69} +(244.451 - 31.0950i) q^{70} -8016.27 q^{71} +(2608.06 + 2608.06i) q^{72} +(-5460.32 + 5460.32i) q^{73} -6639.17i q^{74} +(4955.25 - 8411.87i) q^{75} -3310.76 q^{76} +(546.712 + 546.712i) q^{77} +(-4357.78 + 4357.78i) q^{78} -5753.66i q^{79} +(-201.899 - 1587.21i) q^{80} -6805.98 q^{81} +(3115.18 + 3115.18i) q^{82} +(-7122.53 + 7122.53i) q^{83} +435.492i q^{84} +(-378.027 + 488.217i) q^{85} -2525.43 q^{86} +(-5007.26 - 5007.26i) q^{87} +(3549.78 - 3549.78i) q^{88} -302.472i q^{89} +(9113.50 + 7056.60i) q^{90} -486.104 q^{91} +(623.974 + 623.974i) q^{92} +(-11872.9 + 11872.9i) q^{93} +2577.80i q^{94} +(-10263.4 + 1305.54i) q^{95} +2827.64 q^{96} +(-5428.70 - 5428.70i) q^{97} +(4777.71 - 4777.71i) q^{98} +36164.3i 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
$3$	−11.0455	+	11.0455i	−1.22727	+	1.22727i	−0.262281	+	0.964992i	$0.584475\pi$
$3$	−11.0455	+	11.0455i	−1.22727	+	1.22727i	−0.964992	+	0.262281i	$0.915525\pi$
$4$			8.00000i			0.500000i
$5$	3.15467	+	24.8002i	0.126187	+	0.992006i
$5$	3.15467	+	24.8002i	0.126187	+	0.992006i
$6$	−44.1818			−1.22727
$7$	−2.46420	−	2.46420i	−0.0502899	−	0.0502899i	0.681515	−	0.731805i	$-0.261322\pi$
$7$	−2.46420	−	2.46420i	−0.0502899	−	0.0502899i	−0.731805	+	0.681515i	$0.761322\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$		−	163.004i		−	2.01240i
$10$	−43.2910	+	55.9097i	−0.432910	+	0.559097i
$11$	−221.861			−1.83356			−0.916782	−	0.399387i	$-0.869223\pi$
$11$	−221.861			−1.83356			−0.916782	+	0.399387i	$0.869223\pi$
$12$	−88.3636	−	88.3636i	−0.613636	−	0.613636i
$13$	98.6330	−	98.6330i	0.583627	−	0.583627i	−0.352271	−	0.935898i	$-0.614590\pi$
$13$	98.6330	−	98.6330i	0.583627	−	0.583627i	0.935898	+	0.352271i	$0.114590\pi$
$14$		−	9.85682i		−	0.0502899i
$15$	−308.774	−	239.084i	−1.37233	−	1.06260i
$16$	−64.0000			−0.250000
$17$	17.4645	+	17.4645i	0.0604307	+	0.0604307i	0.736676	−	0.676246i	$-0.236394\pi$
$17$	17.4645	+	17.4645i	0.0604307	+	0.0604307i	−0.676246	+	0.736676i	$0.736394\pi$
$18$	326.008	−	326.008i	1.00620	−	1.00620i
$19$			413.845i			1.14638i	0.819421	+	0.573192i	$0.194295\pi$
$19$			413.845i			1.14638i	−0.819421	+	0.573192i	$0.805705\pi$
$20$	−198.401	+	25.2374i	−0.496003	+	0.0630935i
$21$	54.4365			0.123439
$22$	−443.723	−	443.723i	−0.916782	−	0.916782i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$		−	353.454i		−	0.613636i
$25$	−605.096	+	156.473i	−0.968154	+	0.250357i
$26$	394.532			0.583627
$27$	905.771	+	905.771i	1.24248	+	1.24248i
$28$	19.7136	−	19.7136i	0.0251449	−	0.0251449i
$29$			453.332i			0.539039i	0.962995	+	0.269520i	$0.0868649\pi$
$29$			453.332i			0.539039i	−0.962995	+	0.269520i	$0.913135\pi$
$30$	−139.379	−	1095.72i	−0.154866	−	1.21746i
$31$	1074.91			1.11853			0.559266	−	0.828988i	$-0.311083\pi$
$31$	1074.91			1.11853			0.559266	+	0.828988i	$0.311083\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	2450.56	−	2450.56i	2.25028	−	2.25028i
$34$			69.8579i			0.0604307i
$35$	53.3389	−	68.8864i	0.0435420	−	0.0562338i
$36$	1304.03			1.00620
$37$	−1659.79	−	1659.79i	−1.21241	−	1.21241i	−0.970231	−	0.242180i	$-0.922137\pi$
$37$	−1659.79	−	1659.79i	−1.21241	−	1.21241i	−0.242180	−	0.970231i	$-0.577863\pi$
$38$	−827.689	+	827.689i	−0.573192	+	0.573192i
$39$			2178.89i			1.43254i
$40$	−447.277	−	346.328i	−0.279548	−	0.216455i
$41$	1557.59			0.926585			0.463292	−	0.886205i	$-0.346668\pi$
$41$	1557.59			0.926585			0.463292	+	0.886205i	$0.346668\pi$
$42$	108.873	+	108.873i	0.0617194	+	0.0617194i
$43$	−631.358	+	631.358i	−0.341459	+	0.341459i	−0.856916	−	0.515457i	$-0.827622\pi$
$43$	−631.358	+	631.358i	−0.341459	+	0.341459i	0.515457	+	0.856916i	$0.327622\pi$
$44$		−	1774.89i		−	0.916782i
$45$	4042.53	−	514.224i	1.99631	−	0.253938i
$46$	311.987			0.147442
$47$	644.451	+	644.451i	0.291739	+	0.291739i	0.837767	−	0.546028i	$-0.183861\pi$
$47$	644.451	+	644.451i	0.291739	+	0.291739i	−0.546028	+	0.837767i	$0.683861\pi$
$48$	706.909	−	706.909i	0.306818	−	0.306818i
$49$		−	2388.86i		−	0.994942i
$50$	−1523.14	−	897.246i	−0.609255	−	0.358899i
$51$	−385.806			−0.148330
$52$	789.064	+	789.064i	0.291814	+	0.291814i
$53$	793.116	−	793.116i	0.282348	−	0.282348i	−0.551697	−	0.834045i	$-0.686019\pi$
$53$	793.116	−	793.116i	0.282348	−	0.282348i	0.834045	+	0.551697i	$0.186019\pi$
$54$			3623.09i			1.24248i
$55$	−699.900	−	5502.20i	−0.231372	−	1.81891i
$56$	78.8545			0.0251449
$57$	−4571.10	−	4571.10i	−1.40693	−	1.40693i
$58$	−906.664	+	906.664i	−0.269520	+	0.269520i
$59$			2170.20i			0.623442i	0.950174	+	0.311721i	$0.100905\pi$
$59$			2170.20i			0.623442i	−0.950174	+	0.311721i	$0.899095\pi$
$60$	1912.67	−	2470.19i	0.531298	−	0.686164i
$61$	4373.10			1.17525			0.587625	−	0.809133i	$-0.300063\pi$
$61$	4373.10			1.17525			0.587625	+	0.809133i	$0.300063\pi$
$62$	2149.82	+	2149.82i	0.559266	+	0.559266i
$63$	−401.675	+	401.675i	−0.101203	+	0.101203i
$64$		−	512.000i		−	0.125000i
$65$	2757.27	+	2134.96i	0.652608	+	0.505316i
$66$	9802.24			2.25028
$67$	1217.36	+	1217.36i	0.271186	+	0.271186i	0.829578	−	0.558391i	$-0.188581\pi$
$67$	1217.36	+	1217.36i	0.271186	+	0.271186i	−0.558391	+	0.829578i	$0.688581\pi$
$68$	−139.716	+	139.716i	−0.0302154	+	0.0302154i
$69$			1723.02i			0.361903i
$70$	244.451	−	31.0950i	0.0498879	−	0.00634593i
$71$	−8016.27			−1.59021			−0.795107	−	0.606469i	$-0.792585\pi$
$71$	−8016.27			−1.59021			−0.795107	+	0.606469i	$0.792585\pi$
$72$	2608.06	+	2608.06i	0.503099	+	0.503099i
$73$	−5460.32	+	5460.32i	−1.02464	+	1.02464i	−0.0249543	+	0.999689i	$0.507944\pi$
$73$	−5460.32	+	5460.32i	−1.02464	+	1.02464i	−0.999689	+	0.0249543i	$0.992056\pi$
$74$		−	6639.17i		−	1.21241i
$75$	4955.25	−	8411.87i	0.880933	−	1.49544i
$76$	−3310.76			−0.573192
$77$	546.712	+	546.712i	0.0922098	+	0.0922098i
$78$	−4357.78	+	4357.78i	−0.716269	+	0.716269i
$79$		−	5753.66i		−	0.921913i	−0.887423	−	0.460957i	$-0.847506\pi$
$79$		−	5753.66i		−	0.921913i	0.887423	−	0.460957i	$-0.152494\pi$
$80$	−201.899	−	1587.21i	−0.0315467	−	0.248002i
$81$	−6805.98			−1.03734
$82$	3115.18	+	3115.18i	0.463292	+	0.463292i
$83$	−7122.53	+	7122.53i	−1.03390	+	1.03390i	−0.0344938	+	0.999405i	$0.510982\pi$
$83$	−7122.53	+	7122.53i	−1.03390	+	1.03390i	−0.999405	+	0.0344938i	$0.989018\pi$
$84$			435.492i			0.0617194i
$85$	−378.027	+	488.217i	−0.0523221	+	0.0675733i
$86$	−2525.43			−0.341459
$87$	−5007.26	−	5007.26i	−0.661548	−	0.661548i
$88$	3549.78	−	3549.78i	0.458391	−	0.458391i
$89$		−	302.472i		−	0.0381861i	−0.999818	−	0.0190931i	$-0.993922\pi$
$89$		−	302.472i		−	0.0381861i	0.999818	−	0.0190931i	$-0.00607788\pi$
$90$	9113.50	+	7056.60i	1.12512	+	0.871186i
$91$	−486.104			−0.0587011
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	−11872.9	+	11872.9i	−1.37274	+	1.37274i
$94$			2577.80i			0.291739i
$95$	−10263.4	+	1305.54i	−1.13722	+	0.144659i
$96$	2827.64			0.306818
$97$	−5428.70	−	5428.70i	−0.576969	−	0.576969i	0.357098	−	0.934067i	$-0.383766\pi$
$97$	−5428.70	−	5428.70i	−0.576969	−	0.576969i	−0.934067	+	0.357098i	$0.883766\pi$
$98$	4777.71	−	4777.71i	0.497471	−	0.497471i
$99$			36164.3i			3.68986i
$100$	−1251.78	−	4840.77i	−0.125178	−	0.484077i
$101$	−15375.2			−1.50722			−0.753611	−	0.657321i	$-0.771690\pi$
$101$	−15375.2			−1.50722			−0.753611	+	0.657321i	$0.771690\pi$
$102$	−771.612	−	771.612i	−0.0741650	−	0.0741650i
$103$	3657.22	−	3657.22i	0.344728	−	0.344728i	−0.513414	−	0.858141i	$-0.671619\pi$
$103$	3657.22	−	3657.22i	0.344728	−	0.344728i	0.858141	+	0.513414i	$0.171619\pi$
$104$			3156.26i			0.291814i
$105$	171.729	+	1350.03i	0.0155764	+	0.122452i
$106$	3172.46			0.282348
$107$	−15006.5	−	15006.5i	−1.31072	−	1.31072i	−0.920881	−	0.389843i	$-0.872529\pi$
$107$	−15006.5	−	15006.5i	−1.31072	−	1.31072i	−0.389843	−	0.920881i	$-0.627471\pi$
$108$	−7246.17	+	7246.17i	−0.621242	+	0.621242i
$109$			2503.43i			0.210708i	0.994435	+	0.105354i	$0.0335976\pi$
$109$			2503.43i			0.210708i	−0.994435	+	0.105354i	$0.966402\pi$
$110$	9604.59	−	12404.2i	0.793768	−	1.02514i
$111$	36666.3			2.97592
$112$	157.709	+	157.709i	0.0125725	+	0.0125725i
$113$	14971.3	−	14971.3i	1.17247	−	1.17247i	0.190851	−	0.981619i	$-0.438875\pi$
$113$	14971.3	−	14971.3i	1.17247	−	1.17247i	0.981619	−	0.190851i	$-0.0611247\pi$
$114$		−	18284.4i		−	1.40693i
$115$	2180.39	+	1688.28i	0.164869	+	0.127658i
$116$	−3626.66			−0.269520
$117$	−16077.6	−	16077.6i	−1.17449	−	1.17449i
$118$	−4340.40	+	4340.40i	−0.311721	+	0.311721i
$119$		−	86.0721i		−	0.00607811i
$120$	8765.73	−	1115.03i	0.608731	−	0.0774329i
$121$	34581.5			2.36196
$122$	8746.21	+	8746.21i	0.587625	+	0.587625i
$123$	−17204.3	+	17204.3i	−1.13717	+	1.13717i
$124$			8599.28i			0.559266i
$125$	−5789.43	−	14512.9i	−0.370524	−	0.928823i
$126$	−1606.70			−0.101203
$127$	−13194.4	−	13194.4i	−0.818052	−	0.818052i	0.167773	−	0.985826i	$-0.446342\pi$
$127$	−13194.4	−	13194.4i	−0.818052	−	0.818052i	−0.985826	+	0.167773i	$0.946342\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	13947.3i		−	0.838126i
$130$	1244.62	+	9784.46i	0.0736461	+	0.578962i
$131$	15448.2			0.900193			0.450097	−	0.892980i	$-0.351390\pi$
$131$	15448.2			0.900193			0.450097	+	0.892980i	$0.351390\pi$
$132$	19604.5	+	19604.5i	1.12514	+	1.12514i
$133$	1019.80	−	1019.80i	0.0576515	−	0.0576515i
$134$			4869.42i			0.271186i
$135$	−19605.9	+	25320.7i	−1.07577	+	1.38934i
$136$	−558.863			−0.0302154
$137$	−15527.6	−	15527.6i	−0.827299	−	0.827299i	0.159843	−	0.987142i	$-0.448901\pi$
$137$	−15527.6	−	15527.6i	−0.827299	−	0.827299i	−0.987142	+	0.159843i	$0.948901\pi$
$138$	−3446.04	+	3446.04i	−0.180951	+	0.180951i
$139$		−	22939.0i		−	1.18726i	−0.804738	−	0.593630i	$-0.797694\pi$
$139$		−	22939.0i		−	1.18726i	0.804738	−	0.593630i	$-0.202306\pi$
$140$	551.091	+	426.711i	0.0281169	+	0.0217710i
$141$	−14236.5			−0.716085
$142$	−16032.5	−	16032.5i	−0.795107	−	0.795107i
$143$	−21882.8	+	21882.8i	−1.07012	+	1.07012i
$144$			10432.3i			0.503099i
$145$	−11242.7	+	1430.11i	−0.534730	+	0.0680197i
$146$	−21841.3			−1.02464
$147$	26386.0	+	26386.0i	1.22106	+	1.22106i
$148$	13278.3	−	13278.3i	0.606206	−	0.606206i
$149$			16292.0i			0.733841i	0.930252	+	0.366920i	$0.119588\pi$
$149$			16292.0i			0.733841i	−0.930252	+	0.366920i	$0.880412\pi$
$150$	26734.2	−	6913.25i	1.18819	−	0.307256i
$151$	−6084.58			−0.266856			−0.133428	−	0.991059i	$-0.542598\pi$
$151$	−6084.58			−0.266856			−0.133428	+	0.991059i	$0.542598\pi$
$152$	−6621.51	−	6621.51i	−0.286596	−	0.286596i
$153$	2846.78	−	2846.78i	0.121611	−	0.121611i
$154$			2186.85i			0.0922098i
$155$	3390.99	+	26657.9i	0.141144	+	1.10959i
$156$	−17431.1			−0.716269
$157$	−16408.0	−	16408.0i	−0.665667	−	0.665667i	0.291043	−	0.956710i	$-0.405998\pi$
$157$	−16408.0	−	16408.0i	−0.665667	−	0.665667i	−0.956710	+	0.291043i	$0.905998\pi$
$158$	11507.3	−	11507.3i	0.460957	−	0.460957i
$159$			17520.6i			0.693036i
$160$	2770.62	−	3578.22i	0.108227	−	0.139774i
$161$	−384.400			−0.0148297
$162$	−13612.0	−	13612.0i	−0.518670	−	0.518670i
$163$	−12901.3	+	12901.3i	−0.485577	+	0.485577i	−0.906907	−	0.421331i	$-0.861563\pi$
$163$	−12901.3	+	12901.3i	−0.485577	+	0.485577i	0.421331	+	0.906907i	$0.361563\pi$
$164$			12460.7i			0.463292i
$165$	68505.0	+	53043.5i	2.51625	+	1.94834i
$166$	−28490.1			−1.03390
$167$	−10614.6	−	10614.6i	−0.380603	−	0.380603i	0.490716	−	0.871320i	$-0.336735\pi$
$167$	−10614.6	−	10614.6i	−0.380603	−	0.380603i	−0.871320	+	0.490716i	$0.836735\pi$
$168$	−870.984	+	870.984i	−0.0308597	+	0.0308597i
$169$			9104.07i			0.318759i
$170$	−1732.49	+	220.379i	−0.0599477	+	0.00762557i
$171$	67458.3			2.30698
$172$	−5050.86	−	5050.86i	−0.170729	−	0.170729i
$173$	267.347	−	267.347i	0.00893271	−	0.00893271i	−0.702626	−	0.711559i	$-0.747989\pi$
$173$	267.347	−	267.347i	0.00893271	−	0.00893271i	0.711559	+	0.702626i	$0.247989\pi$
$174$		−	20029.0i		−	0.661548i
$175$	1876.66	+	1105.50i	0.0612787	+	0.0360979i
$176$	14199.1			0.458391
$177$	−23970.8	−	23970.8i	−0.765133	−	0.765133i
$178$	604.945	−	604.945i	0.0190931	−	0.0190931i
$179$			41830.3i			1.30552i	0.757564	+	0.652761i	$0.226390\pi$
$179$			41830.3i			1.30552i	−0.757564	+	0.652761i	$0.773610\pi$
$180$	4113.80	+	32340.2i	0.126969	+	0.998155i
$181$	−22397.7			−0.683671			−0.341835	−	0.939760i	$-0.611048\pi$
$181$	−22397.7			−0.683671			−0.341835	+	0.939760i	$0.611048\pi$
$182$	−972.207	−	972.207i	−0.0293505	−	0.0293505i
$183$	−48302.9	+	48302.9i	−1.44235	+	1.44235i
$184$			2495.90i			0.0737210i
$185$	35927.0	−	46399.2i	1.04973	−	1.35571i
$186$	−47491.4			−1.37274
$187$	−3874.69	−	3874.69i	−0.110804	−	0.110804i
$188$	−5155.60	+	5155.60i	−0.145869	+	0.145869i
$189$		−	4464.01i		−	0.124969i
$190$	−23137.9	−	17915.7i	−0.640940	−	0.496281i
$191$	−60194.2			−1.65002			−0.825008	−	0.565121i	$-0.808829\pi$
$191$	−60194.2			−1.65002			−0.825008	+	0.565121i	$0.808829\pi$
$192$	5655.27	+	5655.27i	0.153409	+	0.153409i
$193$	21509.7	−	21509.7i	0.577458	−	0.577458i	−0.356744	−	0.934202i	$-0.616113\pi$
$193$	21509.7	−	21509.7i	0.577458	−	0.577458i	0.934202	+	0.356744i	$0.116113\pi$
$194$		−	21714.8i		−	0.576969i
$195$	−54036.9	+	6873.69i	−1.42109	+	0.180768i
$196$	19110.8			0.497471
$197$	41503.5	+	41503.5i	1.06943	+	1.06943i	0.997403	+	0.0720269i	$0.0229467\pi$
$197$	41503.5	+	41503.5i	1.06943	+	1.06943i	0.0720269	+	0.997403i	$0.477053\pi$
$198$	−72328.6	+	72328.6i	−1.84493	+	1.84493i
$199$			42904.4i			1.08342i	0.840566	+	0.541709i	$0.182222\pi$
$199$			42904.4i			1.08342i	−0.840566	+	0.541709i	$0.817778\pi$
$200$	7177.97	−	12185.1i	0.179449	−	0.304628i
$201$	−26892.5			−0.665639
$202$	−30750.3	−	30750.3i	−0.753611	−	0.753611i
$203$	1117.10	−	1117.10i	0.0271082	−	0.0271082i
$204$		−	3086.45i		−	0.0741650i
$205$	4913.68	+	38628.5i	0.116923	+	0.919178i
$206$	14628.9			0.344728
$207$	−12713.8	−	12713.8i	−0.296711	−	0.296711i
$208$	−6312.51	+	6312.51i	−0.145907	+	0.145907i
$209$		−	91816.1i		−	2.10197i
$210$	−2356.61	+	3043.53i	−0.0534379	+	0.0690142i
$211$	9818.56			0.220538			0.110269	−	0.993902i	$-0.464829\pi$
$211$	9818.56			0.220538			0.110269	+	0.993902i	$0.464829\pi$
$212$	6344.93	+	6344.93i	0.141174	+	0.141174i
$213$	88543.3	−	88543.3i	1.95163	−	1.95163i
$214$		−	60025.9i		−	1.31072i
$215$	−17649.5	−	13666.0i	−0.381817	−	0.295642i
$216$	−28984.7			−0.621242
$217$	−2648.80	−	2648.80i	−0.0562509	−	0.0562509i
$218$	−5006.85	+	5006.85i	−0.105354	+	0.105354i
$219$		−	120623.i		−	2.51503i
$220$	44017.6	−	5599.20i	0.909454	−	0.115686i
$221$	3445.15			0.0705380
$222$	73332.6	+	73332.6i	1.48796	+	1.48796i
$223$	33948.1	−	33948.1i	0.682662	−	0.682662i	−0.277937	−	0.960599i	$-0.589651\pi$
$223$	33948.1	−	33948.1i	0.682662	−	0.682662i	0.960599	+	0.277937i	$0.0896507\pi$
$224$			630.836i			0.0125725i
$225$	25505.7	+	98633.1i	0.503816	+	1.94831i
$226$	59885.1			1.17247
$227$	−22450.2	−	22450.2i	−0.435680	−	0.435680i	0.454875	−	0.890555i	$-0.349684\pi$
$227$	−22450.2	−	22450.2i	−0.435680	−	0.435680i	−0.890555	+	0.454875i	$0.849684\pi$
$228$	36568.8	−	36568.8i	0.703463	−	0.703463i
$229$		−	32247.2i		−	0.614924i	−0.951560	−	0.307462i	$-0.900520\pi$
$229$		−	32247.2i		−	0.614924i	0.951560	−	0.307462i	$-0.0994796\pi$
$230$	984.218	+	7737.33i	0.0186052	+	0.146263i
$231$	−12077.4			−0.226333
$232$	−7253.31	−	7253.31i	−0.134760	−	0.134760i
$233$	35508.5	−	35508.5i	0.654064	−	0.654064i	−0.299905	−	0.953969i	$-0.596955\pi$
$233$	35508.5	−	35508.5i	0.654064	−	0.654064i	0.953969	+	0.299905i	$0.0969551\pi$
$234$		−	64310.3i		−	1.17449i
$235$	−13949.4	+	18015.5i	−0.252593	+	0.326220i
$236$	−17361.6			−0.311721
$237$	63551.8	+	63551.8i	1.13144	+	1.13144i
$238$	172.144	−	172.144i	0.00303906	−	0.00303906i
$239$			108591.i			1.90107i	0.310614	+	0.950536i	$0.399465\pi$
$239$			108591.i			1.90107i	−0.310614	+	0.950536i	$0.600535\pi$
$240$	19761.5	+	15301.4i	0.343082	+	0.265649i
$241$	−10263.2			−0.176706			−0.0883529	−	0.996089i	$-0.528160\pi$
$241$	−10263.2			−0.176706			−0.0883529	+	0.996089i	$0.528160\pi$
$242$	69162.9	+	69162.9i	1.18098	+	1.18098i
$243$	1807.66	−	1807.66i	0.0306130	−	0.0306130i
$244$			34984.8i			0.587625i
$245$	59244.0	−	7536.06i	0.986989	−	0.125549i
$246$	−68817.1			−1.13717
$247$	40818.7	+	40818.7i	0.669061	+	0.669061i
$248$	−17198.6	+	17198.6i	−0.279633	+	0.279633i
$249$		−	157343.i		−	2.53775i
$250$	17446.9	−	40604.6i	0.279150	−	0.649673i
$251$	63367.1			1.00581			0.502906	−	0.864341i	$-0.332264\pi$
$251$	63367.1			1.00581			0.502906	+	0.864341i	$0.332264\pi$
$252$	−3213.40	−	3213.40i	−0.0506016	−	0.0506016i
$253$	−17304.5	+	17304.5i	−0.270344	+	0.270344i
$254$		−	52777.5i		−	0.818052i
$255$	−1217.09	−	9568.06i	−0.0187173	−	0.147144i
$256$	4096.00			0.0625000
$257$	−28959.7	−	28959.7i	−0.438457	−	0.438457i	0.453035	−	0.891493i	$-0.350341\pi$
$257$	−28959.7	−	28959.7i	−0.438457	−	0.438457i	−0.891493	+	0.453035i	$0.850341\pi$
$258$	27894.5	−	27894.5i	0.419063	−	0.419063i
$259$			8180.13i			0.121944i
$260$	−17079.7	+	22058.1i	−0.252658	+	0.326304i
$261$	73894.9			1.08476
$262$	30896.4	+	30896.4i	0.450097	+	0.450097i
$263$	5963.14	−	5963.14i	0.0862111	−	0.0862111i	−0.662686	−	0.748897i	$-0.730584\pi$
$263$	5963.14	−	5963.14i	0.0862111	−	0.0862111i	0.748897	+	0.662686i	$0.230584\pi$
$264$			78417.9i			1.12514i
$265$	22171.4	+	17167.4i	0.315720	+	0.244463i
$266$	4079.19			0.0576515
$267$	3340.94	+	3340.94i	0.0468648	+	0.0468648i
$268$	−9738.84	+	9738.84i	−0.135593	+	0.135593i
$269$			69672.7i			0.962848i	0.876488	+	0.481424i	$0.159880\pi$
$269$			69672.7i			0.962848i	−0.876488	+	0.481424i	$0.840120\pi$
$270$	−89853.1	+	11429.7i	−1.23255	+	0.156785i
$271$	−46298.7			−0.630420			−0.315210	−	0.949022i	$-0.602075\pi$
$271$	−46298.7			−0.630420			−0.315210	+	0.949022i	$0.602075\pi$
$272$	−1117.73	−	1117.73i	−0.0151077	−	0.0151077i
$273$	5369.23	−	5369.23i	0.0720422	−	0.0720422i
$274$		−	62110.3i		−	0.827299i
$275$	134247.	−	34715.3i	1.77517	−	0.459045i
$276$	−13784.2			−0.180951
$277$	−33047.6	−	33047.6i	−0.430705	−	0.430705i	0.458163	−	0.888868i	$-0.348508\pi$
$277$	−33047.6	−	33047.6i	−0.430705	−	0.430705i	−0.888868	+	0.458163i	$0.848508\pi$
$278$	45878.1	−	45878.1i	0.593630	−	0.593630i
$279$		−	175215.i		−	2.25093i
$280$	248.760	+	1955.61i	0.00317296	+	0.0249439i
$281$	−61082.5			−0.773578			−0.386789	−	0.922168i	$-0.626416\pi$
$281$	−61082.5			−0.773578			−0.386789	+	0.922168i	$0.626416\pi$
$282$	−28473.0	−	28473.0i	−0.358043	−	0.358043i
$283$	−9609.41	+	9609.41i	−0.119984	+	0.119984i	−0.764549	−	0.644565i	$-0.777038\pi$
$283$	−9609.41	+	9609.41i	−0.119984	+	0.119984i	0.644565	+	0.764549i	$0.277038\pi$
$284$		−	64130.2i		−	0.795107i
$285$	98943.7	−	127784.i	1.21814	−	1.57321i
$286$	−87531.4			−1.07012
$287$	−3838.22	−	3838.22i	−0.0465978	−	0.0465978i
$288$	−20864.5	+	20864.5i	−0.251549	+	0.251549i
$289$		−	82911.0i		−	0.992696i
$290$	−25345.6	−	19625.2i	−0.301375	−	0.233355i
$291$	119925.			1.41620
$292$	−43682.6	−	43682.6i	−0.512321	−	0.512321i
$293$	−107587.	+	107587.i	−1.25321	+	1.25321i	−0.298943	+	0.954271i	$0.596634\pi$
$293$	−107587.	+	107587.i	−1.25321	+	1.25321i	−0.954271	+	0.298943i	$0.903366\pi$
$294$			105544.i			1.22106i
$295$	−53821.3	+	6846.27i	−0.618458	+	0.0786702i
$296$	53113.3			0.606206
$297$	−200956.	−	200956.i	−2.27818	−	2.27818i
$298$	−32584.0	+	32584.0i	−0.366920	+	0.366920i
$299$		−	15386.1i		−	0.172102i
$300$	67295.0	+	39642.0i	0.747722	+	0.440466i
$301$	3111.59			0.0343439
$302$	−12169.2	−	12169.2i	−0.133428	−	0.133428i
$303$	169826.	−	169826.i	1.84977	−	1.84977i
$304$		−	26486.1i		−	0.286596i
$305$	13795.7	+	108454.i	0.148301	+	1.16586i
$306$	11387.1			0.121611
$307$	16354.3	+	16354.3i	0.173522	+	0.173522i	0.788525	−	0.615003i	$-0.210845\pi$
$307$	16354.3	+	16354.3i	0.173522	+	0.173522i	−0.615003	+	0.788525i	$0.710845\pi$
$308$	−4373.69	+	4373.69i	−0.0461049	+	0.0461049i
$309$			80791.2i			0.846149i
$310$	−46533.9	+	60097.8i	−0.484224	+	0.625368i
$311$	−56871.4			−0.587994			−0.293997	−	0.955806i	$-0.594986\pi$
$311$	−56871.4			−0.587994			−0.293997	+	0.955806i	$0.594986\pi$
$312$	−34862.3	−	34862.3i	−0.358135	−	0.358135i
$313$	−33482.2	+	33482.2i	−0.341763	+	0.341763i	−0.857030	−	0.515267i	$-0.827693\pi$
$313$	−33482.2	+	33482.2i	−0.341763	+	0.341763i	0.515267	+	0.857030i	$0.327693\pi$
$314$		−	65632.1i		−	0.665667i
$315$	−11228.8	−	8694.46i	−0.113165	−	0.0876236i
$316$	46029.3			0.460957
$317$	−49802.1	−	49802.1i	−0.495598	−	0.495598i	0.414467	−	0.910064i	$-0.363968\pi$
$317$	−49802.1	−	49802.1i	−0.495598	−	0.495598i	−0.910064	+	0.414467i	$0.863968\pi$
$318$	−35041.3	+	35041.3i	−0.346518	+	0.346518i
$319$		−	100577.i		−	0.988364i
$320$	12697.7	−	1615.19i	0.124001	−	0.0157734i
$321$	331507.			3.21723
$322$	−768.800	−	768.800i	−0.00741484	−	0.00741484i
$323$	−7227.58	+	7227.58i	−0.0692768	+	0.0692768i
$324$		−	54447.9i		−	0.518670i
$325$	−44249.0	+	75115.8i	−0.418926	+	0.711156i
$326$	−51605.1			−0.485577
$327$	−27651.5	−	27651.5i	−0.258597	−	0.258597i
$328$	−24921.4	+	24921.4i	−0.231646	+	0.231646i
$329$		−	3176.12i		−	0.0293430i
$330$	30922.9	+	243097.i	0.283956	+	2.23230i
$331$	196859.			1.79679			0.898397	−	0.439184i	$-0.144732\pi$
$331$	196859.			1.79679			0.898397	+	0.439184i	$0.144732\pi$
$332$	−56980.2	−	56980.2i	−0.516949	−	0.516949i
$333$	−270553.	+	270553.i	−2.43985	+	2.43985i
$334$		−	42458.6i		−	0.380603i
$335$	−26350.2	+	34031.0i	−0.234798	+	0.303239i
$336$	−3483.94			−0.0308597
$337$	−87645.9	−	87645.9i	−0.771741	−	0.771741i	0.206669	−	0.978411i	$-0.433738\pi$
$337$	−87645.9	−	87645.9i	−0.771741	−	0.771741i	−0.978411	+	0.206669i	$0.933738\pi$
$338$	−18208.1	+	18208.1i	−0.159379	+	0.159379i
$339$			330729.i			2.87788i
$340$	−3905.73	−	3024.22i	−0.0337866	−	0.0261611i
$341$	−238481.			−2.05090
$342$	134917.	+	134917.i	1.15349	+	1.15349i
$343$	−11803.2	+	11803.2i	−0.100325	+	0.100325i
$344$		−	20203.4i		−	0.170729i
$345$	−42731.2	+	5435.56i	−0.359010	+	0.0456674i
$346$	1069.39			0.00893271
$347$	97932.0	+	97932.0i	0.813328	+	0.813328i	0.985131	−	0.171803i	$-0.0549593\pi$
$347$	97932.0	+	97932.0i	0.813328	+	0.813328i	−0.171803	+	0.985131i	$0.554959\pi$
$348$	40058.1	−	40058.1i	0.330774	−	0.330774i
$349$		−	46806.2i		−	0.384284i	−0.981367	−	0.192142i	$-0.938457\pi$
$349$		−	46806.2i		−	0.384284i	0.981367	−	0.192142i	$-0.0615434\pi$
$350$	1542.32	+	5964.32i	0.0125904	+	0.0486883i
$351$	178678.			1.45030
$352$	28398.3	+	28398.3i	0.229196	+	0.229196i
$353$	−121615.	+	121615.i	−0.975973	+	0.975973i	−0.999718	−	0.0237455i	$-0.992441\pi$
$353$	−121615.	+	121615.i	−0.975973	+	0.975973i	0.0237455	+	0.999718i	$0.492441\pi$
$354$		−	95883.4i		−	0.765133i
$355$	−25288.7	−	198805.i	−0.200664	−	1.57750i
$356$	2419.78			0.0190931
$357$	950.705	+	950.705i	0.00745950	+	0.00745950i
$358$	−83660.5	+	83660.5i	−0.652761	+	0.652761i
$359$			2232.42i			0.0173215i	0.999962	+	0.00866077i	$0.00275684\pi$
$359$			2232.42i			0.0173215i	−0.999962	+	0.00866077i	$0.997243\pi$
$360$	−56452.8	+	72908.0i	−0.435593	+	0.562562i
$361$	−40946.4			−0.314196
$362$	−44795.5	−	44795.5i	−0.341835	−	0.341835i
$363$	−381968.	+	381968.i	−2.89877	+	2.89877i
$364$		−	3888.83i		−	0.0293505i
$365$	−152642.	−	118191.i	−1.14575	−	0.887156i
$366$	−193212.			−1.44235
$367$	−13563.6	−	13563.6i	−0.100703	−	0.100703i	0.654960	−	0.755663i	$-0.272685\pi$
$367$	−13563.6	−	13563.6i	−0.100703	−	0.100703i	−0.755663	+	0.654960i	$0.772685\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$		−	253893.i		−	1.86465i
$370$	164652.	−	20944.4i	1.20272	−	0.152990i
$371$	−3908.80			−0.0283985
$372$	−94982.9	−	94982.9i	−0.686372	−	0.686372i
$373$	47968.0	−	47968.0i	0.344774	−	0.344774i	−0.513385	−	0.858158i	$-0.671609\pi$
$373$	47968.0	−	47968.0i	0.344774	−	0.344774i	0.858158	+	0.513385i	$0.171609\pi$
$374$		−	15498.8i		−	0.110804i
$375$	224248.	+	96354.2i	1.59465	+	0.685185i
$376$	−20622.4			−0.145869
$377$	44713.5	+	44713.5i	0.314598	+	0.314598i
$378$	8928.02	−	8928.02i	0.0624844	−	0.0624844i
$379$			92411.7i			0.643352i	0.946850	+	0.321676i	$0.104246\pi$
$379$			92411.7i			0.643352i	−0.946850	+	0.321676i	$0.895754\pi$
$380$	−10444.4	−	82107.3i	−0.0723293	−	0.568610i
$381$	291476.			2.00795
$382$	−120388.	−	120388.i	−0.825008	−	0.825008i
$383$	−151988.	+	151988.i	−1.03613	+	1.03613i	−0.0368031	+	0.999323i	$0.511717\pi$
$383$	−151988.	+	151988.i	−1.03613	+	1.03613i	−0.999323	+	0.0368031i	$0.988283\pi$
$384$			22621.1i			0.153409i
$385$	−11833.8	+	15283.2i	−0.0798370	+	0.103108i
$386$	86039.0			0.577458
$387$	102914.	+	102914.i	0.687150	+	0.687150i
$388$	43429.6	−	43429.6i	0.288485	−	0.288485i
$389$			230556.i			1.52362i	0.647798	+	0.761812i	$0.275690\pi$
$389$			230556.i			1.52362i	−0.647798	+	0.761812i	$0.724310\pi$
$390$	−121821.	−	94326.3i	−0.800928	−	0.620160i
$391$	2724.35			0.0178201
$392$	38221.7	+	38221.7i	0.248735	+	0.248735i
$393$	−170632.	+	170632.i	−1.10478	+	1.10478i
$394$			166014.i			1.06943i
$395$	142692.	−	18150.9i	0.914544	−	0.116333i
$396$	−289314.			−1.84493
$397$	−32617.4	−	32617.4i	−0.206951	−	0.206951i	0.596019	−	0.802970i	$-0.296748\pi$
$397$	−32617.4	−	32617.4i	−0.206951	−	0.206951i	−0.802970	+	0.596019i	$0.796748\pi$
$398$	−85808.9	+	85808.9i	−0.541709	+	0.541709i
$399$			22528.3i			0.141508i
$400$	38726.1	−	10014.3i	0.242038	−	0.0625891i
$401$	312315.			1.94225			0.971123	−	0.238581i	$-0.0766822\pi$
$401$	312315.			1.94225			0.971123	+	0.238581i	$0.0766822\pi$
$402$	−53784.9	−	53784.9i	−0.332819	−	0.332819i
$403$	106022.	−	106022.i	0.652806	−	0.652806i
$404$		−	123001.i		−	0.753611i
$405$	−21470.6	−	168789.i	−0.130899	−	1.02905i
$406$	4468.41			0.0271082
$407$	368244.	+	368244.i	2.22304	+	2.22304i
$408$	6172.90	−	6172.90i	0.0370825	−	0.0370825i
$409$			154948.i			0.926276i	0.886286	+	0.463138i	$0.153277\pi$
$409$			154948.i			0.926276i	−0.886286	+	0.463138i	$0.846723\pi$
$410$	−67429.6	+	87084.3i	−0.401128	+	0.518051i
$411$	343018.			2.03064
$412$	29257.7	+	29257.7i	0.172364	+	0.172364i
$413$	5347.82	−	5347.82i	0.0313528	−	0.0313528i
$414$		−	50855.2i		−	0.296711i
$415$	−199109.	−	154171.i	−1.15610	−	0.895170i
$416$	−25250.0			−0.145907
$417$	253372.	+	253372.i	1.45709	+	1.45709i
$418$	183632.	−	183632.i	1.05098	−	1.05098i
$419$			235071.i			1.33897i	0.742825	+	0.669485i	$0.233485\pi$
$419$			235071.i			1.33897i	−0.742825	+	0.669485i	$0.766515\pi$
$420$	−10800.3	+	1373.84i	−0.0612260	+	0.00778818i
$421$	−311993.			−1.76028			−0.880138	−	0.474718i	$-0.842550\pi$
$421$	−311993.			−1.76028			−0.880138	+	0.474718i	$0.842550\pi$
$422$	19637.1	+	19637.1i	0.110269	+	0.110269i
$423$	105048.	−	105048.i	0.587093	−	0.587093i
$424$			25379.7i			0.141174i
$425$	−13300.4	−	7834.97i	−0.0736355	−	0.0433770i
$426$	354173.			1.95163
$427$	−10776.2	−	10776.2i	−0.0591032	−	0.0591032i
$428$	120052.	−	120052.i	0.655362	−	0.655362i
$429$		−	483412.i		−	2.62665i
$430$	−7966.91	−	62631.1i	−0.0430877	−	0.338729i
$431$	−309966.			−1.66863			−0.834314	−	0.551289i	$-0.814136\pi$
$431$	−309966.			−1.66863			−0.834314	+	0.551289i	$0.814136\pi$
$432$	−57969.4	−	57969.4i	−0.310621	−	0.310621i
$433$	−167123.	+	167123.i	−0.891377	+	0.891377i	−0.994653	−	0.103276i	$-0.967067\pi$
$433$	−167123.	+	167123.i	−0.891377	+	0.891377i	0.103276	+	0.994653i	$0.467067\pi$
$434$		−	10595.2i		−	0.0562509i
$435$	108385.	−	139977.i	0.572781	−	0.739739i
$436$	−20027.4			−0.105354
$437$	32278.6	+	32278.6i	0.169025	+	0.169025i
$438$	241247.	−	241247.i	1.25752	−	1.25752i
$439$		−	107885.i		−	0.559798i	−0.960029	−	0.279899i	$-0.909699\pi$
$439$		−	107885.i		−	0.559798i	0.960029	−	0.279899i	$-0.0903010\pi$
$440$	99233.6	+	76836.8i	0.512570	+	0.396884i
$441$	−389393.			−2.00222
$442$	6890.30	+	6890.30i	0.0352690	+	0.0352690i
$443$	−36567.6	+	36567.6i	−0.186333	+	0.186333i	−0.794109	−	0.607776i	$-0.792062\pi$
$443$	−36567.6	+	36567.6i	−0.186333	+	0.186333i	0.607776	+	0.794109i	$0.292062\pi$
$444$			293330.i			1.48796i
$445$	7501.36	−	954.202i	0.0378809	−	0.00481859i
$446$	135792.			0.682662
$447$	−179952.	−	179952.i	−0.900623	−	0.900623i
$448$	−1261.67	+	1261.67i	−0.00628624	+	0.00628624i
$449$			320790.i			1.59121i	0.605813	+	0.795607i	$0.292848\pi$
$449$			320790.i			1.59121i	−0.605813	+	0.795607i	$0.707152\pi$
$450$	−146255.	+	248278.i	−0.722246	+	1.22606i
$451$	−345569.			−1.69895
$452$	119770.	+	119770.i	0.586235	+	0.586235i
$453$	67207.0	−	67207.0i	0.327505	−	0.327505i
$454$		−	89800.6i		−	0.435680i
$455$	−1533.50	−	12055.4i	−0.00740731	−	0.0582319i
$456$	146275.			0.703463
$457$	24319.3	+	24319.3i	0.116445	+	0.116445i	0.762928	−	0.646483i	$-0.223761\pi$
$457$	24319.3	+	24319.3i	0.116445	+	0.116445i	−0.646483	+	0.762928i	$0.723761\pi$
$458$	64494.4	−	64494.4i	0.307462	−	0.307462i
$459$			31637.7i			0.150169i
$460$	−13506.2	+	17443.1i	−0.0638291	+	0.0824343i
$461$	314836.			1.48143			0.740716	−	0.671818i	$-0.234486\pi$
$461$	314836.			1.48143			0.740716	+	0.671818i	$0.234486\pi$
$462$	−24154.7	−	24154.7i	−0.113167	−	0.113167i
$463$	−153033.	+	153033.i	−0.713875	+	0.713875i	−0.967344	−	0.253468i	$-0.918429\pi$
$463$	−153033.	+	153033.i	−0.713875	+	0.713875i	0.253468	+	0.967344i	$0.418429\pi$
$464$		−	29013.3i		−	0.134760i
$465$	−331904.	−	256994.i	−1.53499	−	1.18855i
$466$	142034.			0.654064
$467$	−84366.9	−	84366.9i	−0.386846	−	0.386846i	0.486715	−	0.873561i	$-0.338195\pi$
$467$	−84366.9	−	84366.9i	−0.386846	−	0.386846i	−0.873561	+	0.486715i	$0.838195\pi$
$468$	128621.	−	128621.i	0.587244	−	0.587244i
$469$		−	5999.62i		−	0.0272759i
$470$	−63929.9	+	8132.12i	−0.289407	+	0.0368136i
$471$	362468.			1.63391
$472$	−34723.2	−	34723.2i	−0.155860	−	0.155860i
$473$	140074.	−	140074.i	0.626087	−	0.626087i
$474$			254207.i			1.13144i
$475$	−64755.4	−	250416.i	−0.287005	−	1.10988i
$476$	688.577			0.00303906
$477$	−129281.	−	129281.i	−0.568196	−	0.568196i
$478$	−217182.	+	217182.i	−0.950536	+	0.950536i
$479$		−	162768.i		−	0.709411i	−0.934978	−	0.354706i	$-0.884581\pi$
$479$		−	162768.i		−	0.709411i	0.934978	−	0.354706i	$-0.115419\pi$
$480$	8920.27	+	70125.8i	0.0387164	+	0.304366i
$481$	−327420.			−1.41519
$482$	−20526.5	−	20526.5i	−0.0883529	−	0.0883529i
$483$	4245.87	−	4245.87i	0.0182001	−	0.0182001i
$484$			276652.i			1.18098i
$485$	117507.	−	151758.i	0.499551	−	0.645163i
$486$	7230.66			0.0306130
$487$	−46866.5	−	46866.5i	−0.197608	−	0.197608i	0.601366	−	0.798974i	$-0.294623\pi$
$487$	−46866.5	−	46866.5i	−0.197608	−	0.197608i	−0.798974	+	0.601366i	$0.794623\pi$
$488$	−69969.7	+	69969.7i	−0.293812	+	0.293812i
$489$		−	285001.i		−	1.19187i
$490$	133560.	+	103416.i	0.556269	+	0.430720i
$491$	−433811.			−1.79944			−0.899721	−	0.436466i	$-0.856230\pi$
$491$	−433811.			−1.79944			−0.899721	+	0.436466i	$0.856230\pi$
$492$	−137634.	−	137634.i	−0.568586	−	0.568586i
$493$	−7917.21	+	7917.21i	−0.0325745	+	0.0325745i
$494$			163275.i			0.669061i
$495$	−896880.	+	114087.i	−3.66036	+	0.465612i
$496$	−68794.2			−0.279633
$497$	19753.7	+	19753.7i	0.0799717	+	0.0799717i
$498$	314686.	−	314686.i	1.26888	−	1.26888i
$499$			202219.i			0.812120i	0.913847	+	0.406060i	$0.133098\pi$
$499$			202219.i			0.812120i	−0.913847	+	0.406060i	$0.866902\pi$
$500$	116103.	−	46315.5i	0.464412	−	0.185262i
$501$	234487.			0.934208
$502$	126734.	+	126734.i	0.502906	+	0.502906i
$503$	213210.	−	213210.i	0.842697	−	0.842697i	−0.146512	−	0.989209i	$-0.546805\pi$
$503$	213210.	−	213210.i	0.842697	−	0.842697i	0.989209	+	0.146512i	$0.0468048\pi$
$504$		−	12853.6i		−	0.0506016i
$505$	−48503.6	−	381307.i	−0.190192	−	1.49517i
$506$	−69217.9			−0.270344
$507$	−100559.	−	100559.i	−0.391204	−	0.391204i
$508$	105555.	−	105555.i	0.409026	−	0.409026i
$509$			186362.i			0.719320i	0.933083	+	0.359660i	$0.117107\pi$
$509$			186362.i			0.719320i	−0.933083	+	0.359660i	$0.882893\pi$
$510$	16701.9	−	21570.3i	0.0642135	−	0.0829308i
$511$	26910.7			0.103058
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−374849.	+	374849.i	−1.42436	+	1.42436i
$514$		−	115839.i		−	0.438457i
$515$	102237.	+	79162.2i	0.385472	+	0.298472i
$516$	111578.			0.419063
$517$	−142979.	−	142979.i	−0.534922	−	0.534922i
$518$	−16360.3	+	16360.3i	−0.0609720	+	0.0609720i
$519$			5905.94i			0.0219257i
$520$	−78275.6	+	9956.95i	−0.289481	+	0.0368231i
$521$	322397.			1.18772			0.593862	−	0.804567i	$-0.297602\pi$
$521$	322397.			1.18772			0.593862	+	0.804567i	$0.297602\pi$
$522$	147790.	+	147790.i	0.542380	+	0.542380i
$523$	−87472.6	+	87472.6i	−0.319793	+	0.319793i	−0.848687	−	0.528895i	$-0.822607\pi$
$523$	−87472.6	+	87472.6i	−0.319793	+	0.319793i	0.528895	+	0.848687i	$0.322607\pi$
$524$			123586.i			0.450097i
$525$	−32939.3	+	8517.83i	−0.119508	+	0.0309037i
$526$	23852.5			0.0862111
$527$	18772.7	+	18772.7i	0.0675937	+	0.0675937i
$528$	−156836.	+	156836.i	−0.562571	+	0.562571i
$529$		−	12167.0i		−	0.0434783i
$530$	10008.1	+	78677.6i	0.0356286	+	0.280091i
$531$	353751.			1.25461
$532$	8158.38	+	8158.38i	0.0288258	+	0.0288258i
$533$	153630.	−	153630.i	0.540780	−	0.540780i
$534$			13363.8i			0.0468648i
$535$	324823.	−	419504.i	1.13485	−	1.46564i
$536$	−38955.4			−0.135593
$537$	−462034.	−	462034.i	−1.60223	−	1.60223i
$538$	−139345.	+	139345.i	−0.481424	+	0.481424i
$539$			529995.i			1.82429i
$540$	−202565.	−	156847.i	−0.694669	−	0.537884i
$541$	−104054.			−0.355520			−0.177760	−	0.984074i	$-0.556885\pi$
$541$	−104054.			−0.355520			−0.177760	+	0.984074i	$0.556885\pi$
$542$	−92597.4	−	92597.4i	−0.315210	−	0.315210i
$543$	247393.	−	247393.i	0.839050	−	0.839050i
$544$		−	4470.91i		−	0.0151077i
$545$	−62085.4	+	7897.49i	−0.209024	+	0.0265886i
$546$	21476.9			0.0720422
$547$	−37822.5	−	37822.5i	−0.126408	−	0.126408i	0.641072	−	0.767481i	$-0.278490\pi$
$547$	−37822.5	−	37822.5i	−0.126408	−	0.126408i	−0.767481	+	0.641072i	$0.778490\pi$
$548$	124221.	−	124221.i	0.413650	−	0.413650i
$549$		−	712834.i		−	2.36507i
$550$	337925.	+	199064.i	1.11711	+	0.658064i
$551$	−187609.			−0.617946
$552$	−27568.3	−	27568.3i	−0.0904757	−	0.0904757i
$553$	−14178.2	+	14178.2i	−0.0463629	+	0.0463629i
$554$		−	132190.i		−	0.430705i
$555$	115670.	+	909330.i	0.375522	+	2.95213i
$556$	183512.			0.593630
$557$	−28448.0	−	28448.0i	−0.0916940	−	0.0916940i	0.659772	−	0.751466i	$-0.270653\pi$
$557$	−28448.0	−	28448.0i	−0.0916940	−	0.0916940i	−0.751466	+	0.659772i	$0.770653\pi$
$558$	350429.	−	350429.i	1.12546	−	1.12546i
$559$			124545.i			0.398569i
$560$	−3413.69	+	4408.73i	−0.0108855	+	0.0140585i
$561$	85595.5			0.271973
$562$	−122165.	−	122165.i	−0.386789	−	0.386789i
$563$	342691.	−	342691.i	1.08115	−	1.08115i	0.0847477	−	0.996402i	$-0.472992\pi$
$563$	342691.	−	342691.i	1.08115	−	1.08115i	0.996402	−	0.0847477i	$-0.0270084\pi$
$564$		−	113892.i		−	0.358043i
$565$	418519.	+	324060.i	1.31105	+	1.01515i
$566$	−38437.7			−0.119984
$567$	16771.3	+	16771.3i	0.0521677	+	0.0521677i
$568$	128260.	−	128260.i	0.397553	−	0.397553i
$569$		−	38464.5i		−	0.118805i	−0.998234	−	0.0594026i	$-0.981080\pi$
$569$		−	38464.5i		−	0.118805i	0.998234	−	0.0594026i	$-0.0189196\pi$
$570$	453456.	−	57681.3i	1.39568	−	0.177536i
$571$	−280712.			−0.860971			−0.430485	−	0.902598i	$-0.641658\pi$
$571$	−280712.			−0.860971			−0.430485	+	0.902598i	$0.641658\pi$
$572$	−175063.	−	175063.i	−0.535059	−	0.535059i
$573$	664872.	−	664872.i	2.02502	−	2.02502i
$574$		−	15352.9i		−	0.0465978i
$575$	−34991.2	+	59399.9i	−0.105833	+	0.179660i
$576$	−83458.1			−0.251549
$577$	313659.	+	313659.i	0.942120	+	0.942120i	0.998414	−	0.0562940i	$-0.0179284\pi$
$577$	313659.	+	313659.i	0.942120	+	0.942120i	−0.0562940	+	0.998414i	$0.517928\pi$
$578$	165822.	−	165822.i	0.496348	−	0.496348i
$579$			475170.i			1.41740i
$580$	−11440.9	−	89941.7i	−0.0340099	−	0.267365i
$581$	35102.7			0.103989
$582$	239850.	+	239850.i	0.708098	+	0.708098i
$583$	−175962.	+	175962.i	−0.517704	+	0.517704i
$584$		−	174730.i		−	0.512321i
$585$	348007.	−	449446.i	1.01689	−	1.31331i
$586$	−430349.			−1.25321
$587$	10615.3	+	10615.3i	0.0308076	+	0.0308076i	0.722343	−	0.691535i	$-0.243065\pi$
$587$	10615.3	+	10615.3i	0.0308076	+	0.0308076i	−0.691535	+	0.722343i	$0.743065\pi$
$588$	−211088.	+	211088.i	−0.610532	+	0.610532i
$589$			444846.i			1.28227i
$590$	−121335.	−	93950.1i	−0.348564	−	0.269894i
$591$	−916850.			−2.62496
$592$	106227.	+	106227.i	0.303103	+	0.303103i
$593$	147787.	−	147787.i	0.420269	−	0.420269i	−0.465027	−	0.885296i	$-0.653955\pi$
$593$	147787.	−	147787.i	0.420269	−	0.420269i	0.885296	+	0.465027i	$0.153955\pi$
$594$		−	803823.i		−	2.27818i
$595$	2134.60	−	271.529i	0.00602952	−	0.000766978i
$596$	−130336.			−0.366920
$597$	−473899.	−	473899.i	−1.32965	−	1.32965i
$598$	30772.2	−	30772.2i	0.0860511	−	0.0860511i
$599$		−	549407.i		−	1.53123i	−0.643298	−	0.765616i	$-0.722434\pi$
$599$		−	549407.i		−	1.53123i	0.643298	−	0.765616i	$-0.277566\pi$
$600$	55306.0	+	213874.i	0.153628	+	0.594094i
$601$	−460349.			−1.27449			−0.637247	−	0.770660i	$-0.719927\pi$
$601$	−460349.			−1.27449			−0.637247	+	0.770660i	$0.719927\pi$
$602$	6223.18	+	6223.18i	0.0171719	+	0.0171719i
$603$	198434.	−	198434.i	0.545734	−	0.545734i
$604$		−	48676.7i		−	0.133428i
$605$	109093.	+	857626.i	0.298049	+	2.34308i
$606$	679303.			1.84977
$607$	−451049.	−	451049.i	−1.22418	−	1.22418i	−0.966131	−	0.258051i	$-0.916920\pi$
$607$	−451049.	−	451049.i	−1.22418	−	1.22418i	−0.258051	−	0.966131i	$-0.583080\pi$
$608$	52972.1	−	52972.1i	0.143298	−	0.143298i
$609$			24677.8i			0.0665384i
$610$	−189316.	+	244499.i	−0.508777	+	0.657078i
$611$	127128.			0.340533
$612$	22774.2	+	22774.2i	0.0608053	+	0.0608053i
$613$	−202120.	+	202120.i	−0.537883	+	0.537883i	−0.922907	−	0.385024i	$-0.874193\pi$
$613$	−202120.	+	202120.i	−0.537883	+	0.537883i	0.385024	+	0.922907i	$0.374193\pi$
$614$			65417.1i			0.173522i
$615$	−480943.	−	372395.i	−1.27158	−	0.984586i
$616$	−17494.8			−0.0461049
$617$	365182.	+	365182.i	0.959266	+	0.959266i	0.999202	−	0.0399362i	$-0.0127155\pi$
$617$	365182.	+	365182.i	0.959266	+	0.959266i	−0.0399362	+	0.999202i	$0.512715\pi$
$618$	−161582.	+	161582.i	−0.423075	+	0.423075i
$619$		−	469510.i		−	1.22536i	−0.790331	−	0.612680i	$-0.790092\pi$
$619$		−	469510.i		−	1.22536i	0.790331	−	0.612680i	$-0.209908\pi$
$620$	−213263.	+	27127.9i	−0.554796	+	0.0705721i
$621$	141295.			0.366389
$622$	−113743.	−	113743.i	−0.293997	−	0.293997i
$623$	−745.354	+	745.354i	−0.00192038	+	0.00192038i
$624$		−	139449.i		−	0.358135i
$625$	341658.	−	189362.i	0.874643	−	0.484767i
$626$	−133929.			−0.341763
$627$	1.01415e6	+	1.01415e6i	2.57969	+	2.57969i
$628$	131264.	−	131264.i	0.332833	−	0.332833i
$629$		−	57974.8i		−	0.146534i
$630$	−5068.62	−	39846.4i	−0.0127705	−	0.100394i
$631$	394781.			0.991512			0.495756	−	0.868462i	$-0.334891\pi$
$631$	394781.			0.991512			0.495756	+	0.868462i	$0.334891\pi$
$632$	92058.6	+	92058.6i	0.230478	+	0.230478i
$633$	−108450.	+	108450.i	−0.270660	+	0.270660i
$634$		−	199208.i		−	0.495598i
$635$	285599.	−	368846.i	0.708286	−	0.914741i
$636$	−140165.			−0.346518
$637$	−235620.	−	235620.i	−0.580675	−	0.580675i
$638$	201154.	−	201154.i	0.494182	−	0.494182i
$639$			1.30668e6i			3.20014i
$640$	28625.8	+	22165.0i	0.0698871	+	0.0541137i
$641$	596066.			1.45070			0.725351	−	0.688379i	$-0.241677\pi$
$641$	596066.			1.45070			0.725351	+	0.688379i	$0.241677\pi$
$642$	663014.	+	663014.i	1.60862	+	1.60862i
$643$	−18476.3	+	18476.3i	−0.0446883	+	0.0446883i	−0.729098	−	0.684410i	$-0.760060\pi$
$643$	−18476.3	+	18476.3i	−0.0446883	+	0.0446883i	0.684410	+	0.729098i	$0.260060\pi$
$644$		−	3075.20i		−	0.00741484i
$645$	345894.	−	43999.0i	0.831427	−	0.105761i
$646$	−28910.3			−0.0692768
$647$	194733.	+	194733.i	0.465191	+	0.465191i	0.900352	−	0.435162i	$-0.143309\pi$
$647$	194733.	+	194733.i	0.465191	+	0.465191i	−0.435162	+	0.900352i	$0.643309\pi$
$648$	108896.	−	108896.i	0.259335	−	0.259335i
$649$		−	481484.i		−	1.14312i
$650$	−238730.	+	61733.5i	−0.565041	+	0.146115i
$651$	58514.3			0.138070
$652$	−103210.	−	103210.i	−0.242788	−	0.242788i
$653$	216648.	−	216648.i	0.508075	−	0.508075i	−0.405860	−	0.913935i	$-0.633028\pi$
$653$	216648.	−	216648.i	0.508075	−	0.508075i	0.913935	+	0.405860i	$0.133028\pi$
$654$		−	110606.i		−	0.258597i
$655$	48734.1	+	383118.i	0.113593	+	0.892997i
$656$	−99685.7			−0.231646
$657$	890054.	+	890054.i	2.06199	+	2.06199i
$658$	6352.23	−	6352.23i	0.0146715	−	0.0146715i
$659$			592164.i			1.36355i	0.731562	+	0.681775i	$0.238792\pi$
$659$			592164.i			1.36355i	−0.731562	+	0.681775i	$0.761208\pi$
$660$	−424348.	+	548040.i	−0.974170	+	1.25813i
$661$	587584.			1.34483			0.672414	−	0.740175i	$-0.265257\pi$
$661$	587584.			1.34483			0.672414	+	0.740175i	$0.265257\pi$
$662$	393717.	+	393717.i	0.898397	+	0.898397i
$663$	−38053.2	+	38053.2i	−0.0865694	+	0.0865694i
$664$		−	227921.i		−	0.516949i
$665$	28508.3	+	22074.0i	0.0644656	+	0.0499158i
$666$	−1.08221e6			−2.43985
$667$	35358.4	+	35358.4i	0.0794770	+	0.0794770i
$668$	84917.2	−	84917.2i	0.190302	−	0.190302i
$669$			749944.i			1.67562i
$670$	−120762.	+	15361.4i	−0.269019	+	0.0342202i
$671$	−970223.			−2.15490
$672$	−6967.87	−	6967.87i	−0.0154298	−	0.0154298i
$673$	−426701.	+	426701.i	−0.942093	+	0.942093i	−0.998413	−	0.0563193i	$-0.982064\pi$
$673$	−426701.	+	426701.i	−0.942093	+	0.942093i	0.0563193	+	0.998413i	$0.482064\pi$
$674$		−	350584.i		−	0.771741i
$675$	−689807.	−	406350.i	−1.51398	−	0.891852i
$676$	−72832.6			−0.159379
$677$	−281905.	−	281905.i	−0.615071	−	0.615071i	0.329192	−	0.944263i	$-0.393224\pi$
$677$	−281905.	−	281905.i	−0.615071	−	0.615071i	−0.944263	+	0.329192i	$0.893224\pi$
$678$	−661458.	+	661458.i	−1.43894	+	1.43894i
$679$			26754.9i			0.0580314i
$680$	−1763.03	−	13859.9i	−0.00381278	−	0.0299738i
$681$	495944.			1.06940
$682$	−476962.	−	476962.i	−1.02545	−	1.02545i
$683$	99849.8	−	99849.8i	0.214045	−	0.214045i	−0.591938	−	0.805983i	$-0.701637\pi$
$683$	99849.8	−	99849.8i	0.214045	−	0.214045i	0.805983	+	0.591938i	$0.201637\pi$
$684$			539667.i			1.15349i
$685$	336102.	−	434071.i	0.716292	−	0.925081i
$686$	−47212.7			−0.100325
$687$	356185.	+	356185.i	0.754679	+	0.754679i
$688$	40406.9	−	40406.9i	0.0853647	−	0.0853647i
$689$		−	156455.i		−	0.329572i
$690$	−96333.5	−	74591.2i	−0.202339	−	0.156671i
$691$	−259183.			−0.542814			−0.271407	−	0.962465i	$-0.587489\pi$
$691$	−259183.			−0.542814			−0.271407	+	0.962465i	$0.587489\pi$
$692$	2138.78	+	2138.78i	0.00446636	+	0.00446636i
$693$	89116.2	−	89116.2i	0.185563	−	0.185563i
$694$			391728.i			0.813328i
$695$	568892.	−	72365.2i	1.17777	−	0.149817i
$696$	160232.			0.330774
$697$	27202.5	+	27202.5i	0.0559942	+	0.0559942i
$698$	93612.3	−	93612.3i	0.192142	−	0.192142i
$699$			784414.i			1.60543i
$700$	−8844.00	+	15013.3i	−0.0180490	+	0.0306394i
$701$	54131.4			0.110157			0.0550787	−	0.998482i	$-0.482459\pi$
$701$	54131.4			0.110157			0.0550787	+	0.998482i	$0.482459\pi$
$702$	357356.	+	357356.i	0.725148	+	0.725148i
$703$	686896.	−	686896.i	1.38989	−	1.38989i
$704$			113593.i			0.229196i
$705$	−44911.5	−	353067.i	−0.0903606	−	0.710361i
$706$	−486460.			−0.975973
$707$	37887.6	+	37887.6i	0.0757980	+	0.0757980i
$708$	191767.	−	191767.i	0.382566	−	0.382566i
$709$		−	182784.i		−	0.363619i	−0.983334	−	0.181809i	$-0.941805\pi$
$709$		−	182784.i		−	0.363619i	0.983334	−	0.181809i	$-0.0581953\pi$
$710$	347032.	−	448187.i	0.688419	−	0.889083i
$711$	−937870.			−1.85525
$712$	4839.56	+	4839.56i	0.00954653	+	0.00954653i
$713$	83839.5	−	83839.5i	0.164919	−	0.164919i
$714$			3802.82i			0.00745950i
$715$	−611731.	−	473665.i	−1.19660	−	0.926529i
$716$	−334642.			−0.652761
$717$	−1.19944e6	−	1.19944e6i	−2.33313	−	2.33313i
$718$	−4464.83	+	4464.83i	−0.00866077	+	0.00866077i
$719$			306679.i			0.593234i	0.954997	+	0.296617i	$0.0958584\pi$
$719$			306679.i			0.593234i	−0.954997	+	0.296617i	$0.904142\pi$
$720$	−258722.	+	32910.4i	−0.499077	+	0.0634845i
$721$	−18024.3			−0.0346726
$722$	−81892.8	−	81892.8i	−0.157098	−	0.157098i
$723$	113362.	−	113362.i	0.216866	−	0.216866i
$724$		−	179182.i		−	0.341835i
$725$	−70934.1	−	274309.i	−0.134952	−	0.521873i
$726$	−1.52787e6			−2.89877
$727$	178962.	+	178962.i	0.338604	+	0.338604i	0.855842	−	0.517238i	$-0.173040\pi$
$727$	178962.	+	178962.i	0.338604	+	0.338604i	−0.517238	+	0.855842i	$0.673040\pi$
$728$	7777.66	−	7777.66i	0.0146753	−	0.0146753i
$729$		−	511352.i		−	0.962198i
$730$	−68902.1	−	541667.i	−0.129297	−	1.01645i
$731$	−22052.7			−0.0412692
$732$	−386423.	−	386423.i	−0.721176	−	0.721176i
$733$	−302713.	+	302713.i	−0.563409	+	0.563409i	−0.930274	−	0.366865i	$-0.880431\pi$
$733$	−302713.	+	302713.i	−0.563409	+	0.563409i	0.366865	+	0.930274i	$0.380431\pi$
$734$		−	54254.5i		−	0.100703i
$735$	−571138.	+	737616.i	−1.05722	+	1.36539i
$736$	−19967.2			−0.0368605
$737$	−270084.	−	270084.i	−0.497238	−	0.497238i
$738$	507787.	−	507787.i	0.932327	−	0.932327i
$739$		−	119522.i		−	0.218857i	−0.993995	−	0.109429i	$-0.965098\pi$
$739$		−	119522.i		−	0.218857i	0.993995	−	0.109429i	$-0.0349021\pi$
$740$	371194.	+	287416.i	0.677855	+	0.524865i
$741$	−901723.			−1.64224
$742$	−7817.60	−	7817.60i	−0.0141993	−	0.0141993i
$743$	662097.	−	662097.i	1.19934	−	1.19934i	0.224982	−	0.974363i	$-0.427768\pi$
$743$	662097.	−	662097.i	1.19934	−	1.19934i	0.974363	−	0.224982i	$-0.0722322\pi$
$744$		−	379932.i		−	0.686372i
$745$	−404044.	+	51395.9i	−0.727975	+	0.0926011i
$746$	191872.			0.344774
$747$	1.16100e6	+	1.16100e6i	2.08061	+	2.08061i
$748$	30997.6	−	30997.6i	0.0554018	−	0.0554018i
$749$			73958.1i			0.131832i
$750$	255788.	+	641204.i	0.454733	+	1.13992i
$751$	−977158.			−1.73255			−0.866274	−	0.499570i	$-0.833491\pi$
$751$	−977158.			−1.73255			−0.866274	+	0.499570i	$0.833491\pi$
$752$	−41244.8	−	41244.8i	−0.0729346	−	0.0729346i
$753$	−699919.	+	699919.i	−1.23440	+	1.23440i
$754$			178854.i			0.314598i
$755$	−19194.9	−	150899.i	−0.0336737	−	0.264723i
$756$	35712.1			0.0624844
$757$	−610743.	−	610743.i	−1.06578	−	1.06578i	−0.997679	−	0.0680996i	$-0.978306\pi$
$757$	−610743.	−	610743.i	−1.06578	−	1.06578i	−0.0680996	−	0.997679i	$-0.521694\pi$
$758$	−184823.	+	184823.i	−0.321676	+	0.321676i
$759$		−	382271.i		−	0.663572i
$760$	143326.	−	185103.i	0.248140	−	0.320470i
$761$	−833754.			−1.43969			−0.719844	−	0.694135i	$-0.755787\pi$
$761$	−833754.			−1.43969			−0.719844	+	0.694135i	$0.755787\pi$
$762$	582951.	+	582951.i	1.00397	+	1.00397i
$763$	6168.95	−	6168.95i	0.0105965	−	0.0105965i
$764$		−	481554.i		−	0.825008i
$765$	79581.3	+	61620.0i	0.135984	+	0.105293i
$766$	−607953.			−1.03613
$767$	214053.	+	214053.i	0.363857	+	0.363857i
$768$	−45242.2	+	45242.2i	−0.0767045	+	0.0767045i
$769$			616447.i			1.04242i	0.853428	+	0.521210i	$0.174519\pi$
$769$			616447.i			1.04242i	−0.853428	+	0.521210i	$0.825481\pi$
$770$	−54234.2	+	6898.79i	−0.0914727	+	0.0116357i
$771$	639745.			1.07621
$772$	172078.	+	172078.i	0.288729	+	0.288729i
$773$	−703024.	+	703024.i	−1.17655	+	1.17655i	−0.195935	+	0.980617i	$0.562774\pi$
$773$	−703024.	+	703024.i	−1.17655	+	1.17655i	−0.980617	+	0.195935i	$0.937226\pi$
$774$			411655.i			0.687150i
$775$	−650423.	+	168194.i	−1.08291	+	0.280032i
$776$	173718.			0.288485
$777$	−90353.2	−	90353.2i	−0.149659	−	0.149659i
$778$	−461112.	+	461112.i	−0.761812	+	0.761812i
$779$			644600.i			1.06222i
$780$	−54989.5	−	432295.i	−0.0903838	−	0.710544i
$781$	1.77850e6			2.91576
$782$	5448.69	+	5448.69i	0.00891003	+	0.00891003i
$783$	−410615.	+	410615.i	−0.669748	+	0.669748i
$784$			152887.i			0.248735i
$785$	355160.	−	458684.i	0.576347	−	0.744344i
$786$	−682530.			−1.10478
$787$	−239219.	−	239219.i	−0.386231	−	0.386231i	0.487110	−	0.873341i	$-0.338051\pi$
$787$	−239219.	−	239219.i	−0.386231	−	0.386231i	−0.873341	+	0.487110i	$0.838051\pi$
$788$	−332028.	+	332028.i	−0.534715	+	0.534715i
$789$			131731.i			0.211609i
$790$	321685.	+	249082.i	0.515439	+	0.399105i
$791$	−73784.5			−0.117927
$792$	−578629.	−	578629.i	−0.922464	−	0.922464i
$793$	431332.	−	431332.i	0.685908	−	0.685908i
$794$		−	130470.i		−	0.206951i
$795$	−434515.	+	55271.9i	−0.687496	+	0.0874521i
$796$	−343235.			−0.541709
$797$	295869.	+	295869.i	0.465782	+	0.465782i	0.900545	−	0.434763i	$-0.143168\pi$
$797$	295869.	+	295869.i	0.465782	+	0.465782i	−0.434763	+	0.900545i	$0.643168\pi$
$798$	−45056.5	+	45056.5i	−0.0707541	+	0.0707541i
$799$			22510.0i			0.0352600i
$800$	97480.8	+	57423.8i	0.152314	+	0.0897246i
$801$	−49304.2			−0.0768456
$802$	624630.	+	624630.i	0.971123	+	0.971123i
$803$	1.21143e6	−	1.21143e6i	1.87875	−	1.87875i
$804$		−	215140.i		−	0.332819i
$805$	−1212.66	−	9533.19i	−0.00187131	−	0.0147111i
$806$	424086.			0.652806
$807$	−769566.	−	769566.i	−1.18168	−	1.18168i
$808$	246003.	−	246003.i	0.376805	−	0.376805i
$809$		−	44204.1i		−	0.0675407i	−0.999430	−	0.0337703i	$-0.989249\pi$
$809$		−	44204.1i		−	0.0675407i	0.999430	−	0.0337703i	$-0.0107515\pi$
$810$	294638.	−	380520.i	0.449074	−	0.579973i
$811$	358334.			0.544811			0.272406	−	0.962183i	$-0.412181\pi$
$811$	358334.			0.544811			0.272406	+	0.962183i	$0.412181\pi$
$812$	8936.82	+	8936.82i	0.0135541	+	0.0135541i
$813$	511390.	−	511390.i	0.773698	−	0.773698i
$814$			1.47297e6i			2.22304i
$815$	−360653.	−	279255.i	−0.542968	−	0.420422i
$816$	24691.6			0.0370825
$817$	−261284.	−	261284.i	−0.391443	−	0.391443i
$818$	−309897.	+	309897.i	−0.463138	+	0.463138i
$819$			79236.8i			0.118130i
$820$	−309028.	+	39309.5i	−0.459589	+	0.0584614i
$821$	874303.			1.29711			0.648553	−	0.761170i	$-0.275375\pi$
$821$	874303.			1.29711			0.648553	+	0.761170i	$0.275375\pi$
$822$	686037.	+	686037.i	1.01532	+	1.01532i
$823$	−66183.2	+	66183.2i	−0.0977121	+	0.0977121i	−0.754273	−	0.656561i	$-0.772010\pi$
$823$	−66183.2	+	66183.2i	−0.0977121	+	0.0977121i	0.656561	+	0.754273i	$0.272010\pi$
$824$			117031.i			0.172364i
$825$	−1.09938e6	+	1.86627e6i	−1.61525	+	2.74199i
$826$	21391.3			0.0313528
$827$	−226372.	−	226372.i	−0.330987	−	0.330987i	0.521974	−	0.852961i	$-0.325196\pi$
$827$	−226372.	−	226372.i	−0.330987	−	0.330987i	−0.852961	+	0.521974i	$0.825196\pi$
$828$	101710.	−	101710.i	0.148356	−	0.148356i
$829$		−	244313.i		−	0.355499i	−0.984076	−	0.177749i	$-0.943118\pi$
$829$		−	244313.i		−	0.355499i	0.984076	−	0.177749i	$-0.0568816\pi$
$830$	−89877.0	−	706559.i	−0.130465	−	1.02563i
$831$	730051.			1.05718
$832$	−50500.1	−	50500.1i	−0.0729534	−	0.0729534i
$833$	41720.1	−	41720.1i	0.0601251	−	0.0601251i
$834$			1.01349e6i			1.45709i
$835$	229759.	−	296731.i	0.329534	−	0.425588i
$836$	734529.			1.05098
$837$	973622.	+	973622.i	1.38976	+	1.38976i
$838$	−470142.	+	470142.i	−0.669485	+	0.669485i
$839$		−	725293.i		−	1.03036i	−0.857081	−	0.515181i	$-0.827725\pi$
$839$		−	725293.i		−	1.03036i	0.857081	−	0.515181i	$-0.172275\pi$
$840$	−24348.2	−	18852.9i	−0.0345071	−	0.0267189i
$841$	501771.			0.709437
$842$	−623986.	−	623986.i	−0.880138	−	0.880138i
$843$	674684.	−	674684.i	0.949391	−	0.949391i
$844$			78548.5i			0.110269i
$845$	−225782.	+	28720.4i	−0.316211	+	0.0402232i
$846$	420192.			0.587093
$847$	−85215.8	−	85215.8i	−0.118783	−	0.118783i
$848$	−50759.4	+	50759.4i	−0.0705870	+	0.0705870i
$849$		−	212281.i		−	0.294507i
$850$	−10930.9	−	42270.8i	−0.0151292	−	0.0585062i
$851$	−258917.			−0.357521
$852$	708346.	+	708346.i	0.975813	+	0.975813i
$853$	766992.	−	766992.i	1.05413	−	1.05413i	0.0556779	−	0.998449i	$-0.482268\pi$
$853$	766992.	−	766992.i	1.05413	−	1.05413i	0.998449	−	0.0556779i	$-0.0177320\pi$
$854$		−	43104.9i		−	0.0591032i
$855$	212809.	+	1.67298e6i	0.291110	+	2.28854i
$856$	480208.			0.655362
$857$	−16137.9	−	16137.9i	−0.0219728	−	0.0219728i	0.696035	−	0.718008i	$-0.254946\pi$
$857$	−16137.9	−	16137.9i	−0.0219728	−	0.0219728i	−0.718008	+	0.696035i	$0.754946\pi$
$858$	966824.	−	966824.i	1.31333	−	1.31333i
$859$		−	598457.i		−	0.811048i	−0.914084	−	0.405524i	$-0.867089\pi$
$859$		−	598457.i		−	0.811048i	0.914084	−	0.405524i	$-0.132911\pi$
$860$	109328.	−	141196.i	0.147821	−	0.190909i
$861$	84789.7			0.114377
$862$	−619932.	−	619932.i	−0.834314	−	0.834314i
$863$	−941938.	+	941938.i	−1.26474	+	1.26474i	−0.315968	+	0.948770i	$0.602329\pi$
$863$	−941938.	+	941938.i	−1.26474	+	1.26474i	−0.948770	+	0.315968i	$0.897671\pi$
$864$		−	231877.i		−	0.310621i
$865$	7473.65	+	5786.86i	0.00998850	+	0.00773412i
$866$	−668493.			−0.891377
$867$	915789.	+	915789.i	1.21831	+	1.21831i
$868$	21190.4	−	21190.4i	0.0281254	−	0.0281254i
$869$			1.27652e6i			1.69039i
$870$	496723.	−	63185.0i	0.656260	−	0.0834787i
$871$	240143.			0.316543
$872$	−40054.8	−	40054.8i	−0.0526771	−	0.0526771i
$873$	−884900.	+	884900.i	−1.16109	+	1.16109i
$874$			129114.i			0.169025i
$875$	−21496.3	+	50029.0i	−0.0280768	+	0.0653440i
$876$	964988.			1.25752
$877$	−655248.	−	655248.i	−0.851935	−	0.851935i	0.138436	−	0.990371i	$-0.455792\pi$
$877$	−655248.	−	655248.i	−0.851935	−	0.851935i	−0.990371	+	0.138436i	$0.955792\pi$
$878$	215770.	−	215770.i	0.279899	−	0.279899i
$879$		−	2.37670e6i		−	3.07607i
$880$	44793.6	+	352141.i	0.0578430	+	0.454727i
$881$	−171718.			−0.221241			−0.110620	−	0.993863i	$-0.535284\pi$
$881$	−171718.			−0.221241			−0.110620	+	0.993863i	$0.535284\pi$
$882$	−778786.	−	778786.i	−1.00111	−	1.00111i
$883$	879404.	−	879404.i	1.12789	−	1.12789i	0.137371	−	0.990520i	$-0.456135\pi$
$883$	879404.	−	879404.i	1.12789	−	1.12789i	0.990520	−	0.137371i	$-0.0438652\pi$
$884$			27561.2i			0.0352690i
$885$	518861.	−	670101.i	0.662467	−	0.855566i
$886$	−146270.			−0.186333
$887$	314558.	+	314558.i	0.399810	+	0.399810i	0.878166	−	0.478356i	$-0.158767\pi$
$887$	314558.	+	314558.i	0.399810	+	0.399810i	−0.478356	+	0.878166i	$0.658767\pi$
$888$	−586661.	+	586661.i	−0.743980	+	0.743980i
$889$			65027.2i			0.0822795i
$890$	16911.1	+	13094.3i	0.0213497	+	0.0165312i
$891$	1.50998e6			1.90203
$892$	271585.	+	271585.i	0.341331	+	0.341331i
$893$	−266702.	+	266702.i	−0.334444	+	0.334444i
$894$		−	719810.i		−	0.900623i
$895$	−1.03740e6	+	131961.i	−1.29509	+	0.164740i
$896$	−5046.69			−0.00628624
$897$	169947.	+	169947.i	0.211216	+	0.211216i
$898$	−641581.	+	641581.i	−0.795607	+	0.795607i
$899$			487291.i			0.602933i
$900$	−789065.	+	204046.i	−0.974154	+	0.251908i
$901$	27702.7			0.0341250
$902$	−691138.	−	691138.i	−0.849477	−	0.849477i
$903$	−34368.9	+	34368.9i	−0.0421493	+	0.0421493i
$904$			479081.i			0.586235i
$905$	−70657.5	−	555467.i	−0.0862703	−	0.678206i
$906$	268828.			0.327505
$907$	−634552.	−	634552.i	−0.771352	−	0.771352i	0.206991	−	0.978343i	$-0.433633\pi$
$907$	−634552.	−	634552.i	−0.771352	−	0.771352i	−0.978343	+	0.206991i	$0.933633\pi$
$908$	179601.	−	179601.i	0.217840	−	0.217840i
$909$			2.50621e6i			3.03313i
$910$	21043.9	−	27177.9i	0.0254123	−	0.0328196i
$911$	873451.			1.05245			0.526225	−	0.850345i	$-0.323607\pi$
$911$	873451.			1.05245			0.526225	+	0.850345i	$0.323607\pi$
$912$	292550.	+	292550.i	0.351731	+	0.351731i
$913$	1.58021e6	−	1.58021e6i	1.89572	−	1.89572i
$914$			97277.3i			0.116445i
$915$	−1.35030e6	−	1.04554e6i	−1.61283	−	1.24882i
$916$	257978.			0.307462
$917$	−38067.6	−	38067.6i	−0.0452706	−	0.0452706i
$918$	−63275.3	+	63275.3i	−0.0750843	+	0.0750843i
$919$			557457.i			0.660055i	0.943971	+	0.330028i	$0.107058\pi$
$919$			557457.i			0.660055i	−0.943971	+	0.330028i	$0.892942\pi$
$920$	−61898.7	+	7873.74i	−0.0731317	+	0.00930262i
$921$	−361281.			−0.425918
$922$	629671.	+	629671.i	0.740716	+	0.740716i
$923$	−790668.	+	790668.i	−0.928092	+	0.928092i
$924$		−	96618.9i		−	0.113167i
$925$	1.26405e6	+	744621.i	1.47734	+	0.870266i
$926$	−612131.			−0.713875
$927$	−596141.	−	596141.i	−0.693728	−	0.693728i
$928$	58026.5	−	58026.5i	0.0673799	−	0.0673799i
$929$		−	251389.i		−	0.291283i	−0.989337	−	0.145642i	$-0.953475\pi$
$929$		−	251389.i		−	0.291283i	0.989337	−	0.145642i	$-0.0465246\pi$
$930$	−149820.	−	1.17780e6i	−0.173222	−	1.36177i
$931$	988615.			1.14059
$932$	284068.	+	284068.i	0.327032	+	0.327032i
$933$	628170.	−	628170.i	0.721629	−	0.721629i
$934$		−	337468.i		−	0.386846i
$935$	83869.6	−	108316.i	0.0959360	−	0.123900i
$936$	514482.			0.587244
$937$	−19408.5	−	19408.5i	−0.0221061	−	0.0221061i	0.695967	−	0.718073i	$-0.254976\pi$
$937$	−19408.5	−	19408.5i	−0.0221061	−	0.0221061i	−0.718073	+	0.695967i	$0.754976\pi$
$938$	11999.2	−	11999.2i	0.0136379	−	0.0136379i
$939$		−	739652.i		−	0.838873i
$940$	−144124.	−	111596.i	−0.163110	−	0.126296i
$941$	−708458.			−0.800083			−0.400041	−	0.916497i	$-0.631004\pi$
$941$	−708458.			−0.800083			−0.400041	+	0.916497i	$0.631004\pi$
$942$	724936.	+	724936.i	0.816955	+	0.816955i
$943$	121487.	−	121487.i	0.136617	−	0.136617i
$944$		−	138893.i		−	0.155860i
$945$	110708.	−	14082.5i	0.123970	−	0.0157694i
$946$	560295.			0.626087
$947$	−224002.	−	224002.i	−0.249776	−	0.249776i	0.571102	−	0.820879i	$-0.306516\pi$
$947$	−224002.	−	224002.i	−0.249776	−	0.249776i	−0.820879	+	0.571102i	$0.806516\pi$
$948$	−508414.	+	508414.i	−0.565719	+	0.565719i
$949$			1.07714e6i			1.19602i
$950$	371321.	−	630342.i	0.411436	−	0.698440i
$951$	1.10017e6			1.21647
$952$	1377.15	+	1377.15i	0.00151953	+	0.00151953i
$953$	−227287.	+	227287.i	−0.250258	+	0.250258i	−0.821076	−	0.570818i	$-0.806626\pi$
$953$	−227287.	+	227287.i	−0.250258	+	0.250258i	0.570818	+	0.821076i	$0.306626\pi$
$954$		−	517124.i		−	0.568196i
$955$	−189893.	−	1.49283e6i	−0.208210	−	1.63683i
$956$	−868729.			−0.950536
$957$	1.11092e6	+	1.11092e6i	1.21299	+	1.21299i
$958$	325536.	−	325536.i	0.354706	−	0.354706i
$959$			76526.3i			0.0832096i
$960$	−122411.	+	158092.i	−0.132825	+	0.171541i
$961$	231909.			0.251114
$962$	−654841.	−	654841.i	−0.707596	−	0.707596i
$963$	−2.44612e6	+	2.44612e6i	−2.63770	+	2.63770i
$964$		−	82106.0i		−	0.0883529i
$965$	601301.	+	465589.i	0.645710	+	0.499975i
$966$	16983.5			0.0182001
$967$	−474258.	−	474258.i	−0.507180	−	0.507180i	0.406480	−	0.913660i	$-0.366756\pi$
$967$	−474258.	−	474258.i	−0.507180	−	0.507180i	−0.913660	+	0.406480i	$0.866756\pi$
$968$	−553303.	+	553303.i	−0.590490	+	0.590490i
$969$		−	159664.i		−	0.170043i
$970$	538531.	−	68503.1i	0.572357	−	0.0728060i
$971$	11716.1			0.0124264			0.00621320	−	0.999981i	$-0.498022\pi$
$971$	11716.1			0.0124264			0.00621320	+	0.999981i	$0.498022\pi$
$972$	14461.3	+	14461.3i	0.0153065	+	0.0153065i
$973$	−56526.5	+	56526.5i	−0.0597072	+	0.0597072i
$974$		−	187466.i		−	0.197608i
$975$	−340937.	−	1.31844e6i	−0.358645	−	1.38692i
$976$	−279879.			−0.293812
$977$	−1.25559e6	−	1.25559e6i	−1.31540	−	1.31540i	−0.917376	−	0.398022i	$-0.869697\pi$
$977$	−1.25559e6	−	1.25559e6i	−1.31540	−	1.31540i	−0.398022	−	0.917376i	$-0.630303\pi$
$978$	570002.	−	570002.i	0.595935	−	0.595935i
$979$			67106.9i			0.0700168i
$980$	60288.5	+	473952.i	0.0627743	+	0.493494i
$981$	408069.			0.424029
$982$	−867622.	−	867622.i	−0.899721	−	0.899721i
$983$	−657305.	+	657305.i	−0.680237	+	0.680237i	−0.960053	−	0.279817i	$-0.909726\pi$
$983$	−657305.	+	657305.i	−0.680237	+	0.680237i	0.279817	+	0.960053i	$0.409726\pi$
$984$		−	550537.i		−	0.568586i
$985$	−898363.	+	1.16022e6i	−0.925933	+	1.19583i
$986$	−31668.8			−0.0325745
$987$	35081.6	+	35081.6i	0.0360119	+	0.0360119i
$988$	−326550.	+	326550.i	−0.334530	+	0.334530i
$989$			98487.7i			0.100691i
$990$	−2.02193e6	−	1.56559e6i	−2.06299	−	1.59738i
$991$	746529.			0.760150			0.380075	−	0.924956i	$-0.375898\pi$
$991$	746529.			0.760150			0.380075	+	0.924956i	$0.375898\pi$
$992$	−137588.	−	137588.i	−0.139817	−	0.139817i
$993$	−2.17439e6	+	2.17439e6i	−2.20516	+	2.20516i
$994$			79014.9i			0.0799717i
$995$	−1.06404e6	+	135349.i	−1.07476	+	0.136713i
$996$	1.25874e6			1.26888
$997$	853388.	+	853388.i	0.858531	+	0.858531i	0.991165	−	0.132634i	$-0.0423434\pi$
$997$	853388.	+	853388.i	0.858531	+	0.858531i	−0.132634	+	0.991165i	$0.542343\pi$
$998$	−404437.	+	404437.i	−0.406060	+	0.406060i
$999$		−	3.00678e6i		−	3.01281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.2	✓	44
5.3	odd	4	inner	230.5.f.b.93.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.2	✓	44	1.1	even	1	trivial
230.5.f.b.93.2	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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(-11.0455 + 11.0455i) q^{3} +8.00000i q^{4} +(3.15467 + 24.8002i) q^{5} -44.1818 q^{6} +(-2.46420 - 2.46420i) q^{7} +(-16.0000 + 16.0000i) q^{8} -163.004i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(-11.0455 + 11.0455i) q^{3} +8.00000i q^{4} +(3.15467 + 24.8002i) q^{5} -44.1818 q^{6} +(-2.46420 - 2.46420i) q^{7} +(-16.0000 + 16.0000i) q^{8} -163.004i q^{9} +(-43.2910 + 55.9097i) q^{10} -221.861 q^{11} +(-88.3636 - 88.3636i) q^{12} +(98.6330 - 98.6330i) q^{13} -9.85682i q^{14} +(-308.774 - 239.084i) q^{15} -64.0000 q^{16} +(17.4645 + 17.4645i) q^{17} +(326.008 - 326.008i) q^{18} +413.845i q^{19} +(-198.401 + 25.2374i) q^{20} +54.4365 q^{21} +(-443.723 - 443.723i) q^{22} +(77.9968 - 77.9968i) q^{23} -353.454i q^{24} +(-605.096 + 156.473i) q^{25} +394.532 q^{26} +(905.771 + 905.771i) q^{27} +(19.7136 - 19.7136i) q^{28} +453.332i q^{29} +(-139.379 - 1095.72i) q^{30} +1074.91 q^{31} +(-128.000 - 128.000i) q^{32} +(2450.56 - 2450.56i) q^{33} +69.8579i q^{34} +(53.3389 - 68.8864i) q^{35} +1304.03 q^{36} +(-1659.79 - 1659.79i) q^{37} +(-827.689 + 827.689i) q^{38} +2178.89i q^{39} +(-447.277 - 346.328i) q^{40} +1557.59 q^{41} +(108.873 + 108.873i) q^{42} +(-631.358 + 631.358i) q^{43} -1774.89i q^{44} +(4042.53 - 514.224i) q^{45} +311.987 q^{46} +(644.451 + 644.451i) q^{47} +(706.909 - 706.909i) q^{48} -2388.86i q^{49} +(-1523.14 - 897.246i) q^{50} -385.806 q^{51} +(789.064 + 789.064i) q^{52} +(793.116 - 793.116i) q^{53} +3623.09i q^{54} +(-699.900 - 5502.20i) q^{55} +78.8545 q^{56} +(-4571.10 - 4571.10i) q^{57} +(-906.664 + 906.664i) q^{58} +2170.20i q^{59} +(1912.67 - 2470.19i) q^{60} +4373.10 q^{61} +(2149.82 + 2149.82i) q^{62} +(-401.675 + 401.675i) q^{63} -512.000i q^{64} +(2757.27 + 2134.96i) q^{65} +9802.24 q^{66} +(1217.36 + 1217.36i) q^{67} +(-139.716 + 139.716i) q^{68} +1723.02i q^{69} +(244.451 - 31.0950i) q^{70} -8016.27 q^{71} +(2608.06 + 2608.06i) q^{72} +(-5460.32 + 5460.32i) q^{73} -6639.17i q^{74} +(4955.25 - 8411.87i) q^{75} -3310.76 q^{76} +(546.712 + 546.712i) q^{77} +(-4357.78 + 4357.78i) q^{78} -5753.66i q^{79} +(-201.899 - 1587.21i) q^{80} -6805.98 q^{81} +(3115.18 + 3115.18i) q^{82} +(-7122.53 + 7122.53i) q^{83} +435.492i q^{84} +(-378.027 + 488.217i) q^{85} -2525.43 q^{86} +(-5007.26 - 5007.26i) q^{87} +(3549.78 - 3549.78i) q^{88} -302.472i q^{89} +(9113.50 + 7056.60i) q^{90} -486.104 q^{91} +(623.974 + 623.974i) q^{92} +(-11872.9 + 11872.9i) q^{93} +2577.80i q^{94} +(-10263.4 + 1305.54i) q^{95} +2827.64 q^{96} +(-5428.70 - 5428.70i) q^{97} +(4777.71 - 4777.71i) q^{98} +36164.3i 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

Related objects

Downloads

Learn more