LMFDB - Embedded newform 230.5.f.a.47.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} +(6.39678 - 6.39678i) q^{3} +8.00000i q^{4} +(22.1785 + 11.5375i) q^{5} -25.5871 q^{6} +(18.6881 + 18.6881i) q^{7} +(16.0000 - 16.0000i) q^{8} -0.837704i q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} +(6.39678 - 6.39678i) q^{3} +8.00000i q^{4} +(22.1785 + 11.5375i) q^{5} -25.5871 q^{6} +(18.6881 + 18.6881i) q^{7} +(16.0000 - 16.0000i) q^{8} -0.837704i q^{9} +(-21.2821 - 67.4320i) q^{10} +60.8714 q^{11} +(51.1743 + 51.1743i) q^{12} +(-52.7450 + 52.7450i) q^{13} -74.7526i q^{14} +(215.674 - 68.0685i) q^{15} -64.0000 q^{16} +(36.5788 + 36.5788i) q^{17} +(-1.67541 + 1.67541i) q^{18} +628.097i q^{19} +(-92.2998 + 177.428i) q^{20} +239.088 q^{21} +(-121.743 - 121.743i) q^{22} +(-77.9968 + 77.9968i) q^{23} -204.697i q^{24} +(358.773 + 511.768i) q^{25} +210.980 q^{26} +(512.781 + 512.781i) q^{27} +(-149.505 + 149.505i) q^{28} +209.990i q^{29} +(-567.485 - 295.211i) q^{30} -1454.31 q^{31} +(128.000 + 128.000i) q^{32} +(389.381 - 389.381i) q^{33} -146.315i q^{34} +(198.861 + 630.089i) q^{35} +6.70163 q^{36} +(810.354 + 810.354i) q^{37} +(1256.19 - 1256.19i) q^{38} +674.797i q^{39} +(539.456 - 170.257i) q^{40} -10.7786 q^{41} +(-478.176 - 478.176i) q^{42} +(931.031 - 931.031i) q^{43} +486.971i q^{44} +(9.66499 - 18.5790i) q^{45} +311.987 q^{46} +(-487.736 - 487.736i) q^{47} +(-409.394 + 409.394i) q^{48} -1702.51i q^{49} +(305.989 - 1741.08i) q^{50} +467.974 q^{51} +(-421.960 - 421.960i) q^{52} +(1520.46 - 1520.46i) q^{53} -2051.12i q^{54} +(1350.04 + 702.302i) q^{55} +598.021 q^{56} +(4017.80 + 4017.80i) q^{57} +(419.981 - 419.981i) q^{58} -5359.85i q^{59} +(544.548 + 1725.39i) q^{60} +3088.63 q^{61} +(2908.62 + 2908.62i) q^{62} +(15.6551 - 15.6551i) q^{63} -512.000i q^{64} +(-1778.35 + 561.262i) q^{65} -1557.52 q^{66} +(4056.65 + 4056.65i) q^{67} +(-292.631 + 292.631i) q^{68} +997.857i q^{69} +(862.456 - 1657.90i) q^{70} +1068.44 q^{71} +(-13.4033 - 13.4033i) q^{72} +(-1819.85 + 1819.85i) q^{73} -3241.41i q^{74} +(5568.67 + 978.674i) q^{75} -5024.78 q^{76} +(1137.57 + 1137.57i) q^{77} +(1349.59 - 1349.59i) q^{78} -6100.00i q^{79} +(-1419.43 - 738.398i) q^{80} +6628.15 q^{81} +(21.5573 + 21.5573i) q^{82} +(7078.81 - 7078.81i) q^{83} +1912.70i q^{84} +(389.237 + 1233.29i) q^{85} -3724.12 q^{86} +(1343.26 + 1343.26i) q^{87} +(973.942 - 973.942i) q^{88} +3669.63i q^{89} +(-56.4880 + 17.8281i) q^{90} -1971.41 q^{91} +(-623.974 - 623.974i) q^{92} +(-9302.90 + 9302.90i) q^{93} +1950.94i q^{94} +(-7246.65 + 13930.3i) q^{95} +1637.58 q^{96} +(-1703.93 - 1703.93i) q^{97} +(-3405.01 + 3405.01i) q^{98} -50.9922i 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} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * 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
$3$	6.39678	−	6.39678i	0.710754	−	0.710754i	−0.255939	−	0.966693i	$-0.582385\pi$
$3$	6.39678	−	6.39678i	0.710754	−	0.710754i	0.966693	+	0.255939i	$0.0823847\pi$
$4$			8.00000i			0.500000i
$5$	22.1785	+	11.5375i	0.887141	+	0.461499i
$5$	22.1785	+	11.5375i	0.887141	+	0.461499i
$6$	−25.5871			−0.710754
$7$	18.6881	+	18.6881i	0.381391	+	0.381391i	0.871603	−	0.490212i	$-0.163081\pi$
$7$	18.6881	+	18.6881i	0.381391	+	0.381391i	−0.490212	+	0.871603i	$0.663081\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	0.837704i		−	0.0103420i
$10$	−21.2821	−	67.4320i	−0.212821	−	0.674320i
$11$	60.8714			0.503069			0.251535	−	0.967848i	$-0.419065\pi$
$11$	60.8714			0.503069			0.251535	+	0.967848i	$0.419065\pi$
$12$	51.1743	+	51.1743i	0.355377	+	0.355377i
$13$	−52.7450	+	52.7450i	−0.312101	+	0.312101i	−0.845723	−	0.533622i	$-0.820830\pi$
$13$	−52.7450	+	52.7450i	−0.312101	+	0.312101i	0.533622	+	0.845723i	$0.320830\pi$
$14$		−	74.7526i		−	0.381391i
$15$	215.674	−	68.0685i	0.958551	−	0.302527i
$16$	−64.0000			−0.250000
$17$	36.5788	+	36.5788i	0.126570	+	0.126570i	0.767554	−	0.640984i	$-0.221473\pi$
$17$	36.5788	+	36.5788i	0.126570	+	0.126570i	−0.640984	+	0.767554i	$0.721473\pi$
$18$	−1.67541	+	1.67541i	−0.00517101	+	0.00517101i
$19$			628.097i			1.73988i	0.493156	+	0.869941i	$0.335843\pi$
$19$			628.097i			1.73988i	−0.493156	+	0.869941i	$0.664157\pi$
$20$	−92.2998	+	177.428i	−0.230749	+	0.443570i
$21$	239.088			0.542150
$22$	−121.743	−	121.743i	−0.251535	−	0.251535i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$		−	204.697i		−	0.355377i
$25$	358.773	+	511.768i	0.574037	+	0.818829i
$26$	210.980			0.312101
$27$	512.781	+	512.781i	0.703403	+	0.703403i
$28$	−149.505	+	149.505i	−0.190695	+	0.190695i
$29$			209.990i			0.249691i	0.992176	+	0.124846i	$0.0398436\pi$
$29$			209.990i			0.249691i	−0.992176	+	0.124846i	$0.960156\pi$
$30$	−567.485	−	295.211i	−0.630539	−	0.328012i
$31$	−1454.31			−1.51333			−0.756664	−	0.653804i	$-0.773172\pi$
$31$	−1454.31			−1.51333			−0.756664	+	0.653804i	$0.773172\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	389.381	−	389.381i	0.357558	−	0.357558i
$34$		−	146.315i		−	0.126570i
$35$	198.861	+	630.089i	0.162336	+	0.514359i
$36$	6.70163			0.00517101
$37$	810.354	+	810.354i	0.591931	+	0.591931i	0.938153	−	0.346222i	$-0.112535\pi$
$37$	810.354	+	810.354i	0.591931	+	0.591931i	−0.346222	+	0.938153i	$0.612535\pi$
$38$	1256.19	−	1256.19i	0.869941	−	0.869941i
$39$			674.797i			0.443653i
$40$	539.456	−	170.257i	0.337160	−	0.106410i
$41$	−10.7786			−0.00641204			−0.00320602	−	0.999995i	$-0.501021\pi$
$41$	−10.7786			−0.00641204			−0.00320602	+	0.999995i	$0.501021\pi$
$42$	−478.176	−	478.176i	−0.271075	−	0.271075i
$43$	931.031	−	931.031i	0.503532	−	0.503532i	−0.409002	−	0.912534i	$-0.634123\pi$
$43$	931.031	−	931.031i	0.503532	−	0.503532i	0.912534	+	0.409002i	$0.134123\pi$
$44$			486.971i			0.251535i
$45$	9.66499	−	18.5790i	0.00477283	−	0.00917483i
$46$	311.987			0.147442
$47$	−487.736	−	487.736i	−0.220795	−	0.220795i	0.588038	−	0.808833i	$-0.299900\pi$
$47$	−487.736	−	487.736i	−0.220795	−	0.220795i	−0.808833	+	0.588038i	$0.799900\pi$
$48$	−409.394	+	409.394i	−0.177688	+	0.177688i
$49$		−	1702.51i		−	0.709082i
$50$	305.989	−	1741.08i	0.122396	−	0.696433i
$51$	467.974			0.179921
$52$	−421.960	−	421.960i	−0.156050	−	0.156050i
$53$	1520.46	−	1520.46i	0.541281	−	0.541281i	−0.382623	−	0.923904i	$-0.624979\pi$
$53$	1520.46	−	1520.46i	0.541281	−	0.541281i	0.923904	+	0.382623i	$0.124979\pi$
$54$		−	2051.12i		−	0.703403i
$55$	1350.04	+	702.302i	0.446293	+	0.232166i
$56$	598.021			0.190695
$57$	4017.80	+	4017.80i	1.23663	+	1.23663i
$58$	419.981	−	419.981i	0.124846	−	0.124846i
$59$		−	5359.85i		−	1.53974i	−0.638198	−	0.769872i	$-0.720320\pi$
$59$		−	5359.85i		−	1.53974i	0.638198	−	0.769872i	$-0.279680\pi$
$60$	544.548	+	1725.39i	0.151263	+	0.479275i
$61$	3088.63			0.830053			0.415026	−	0.909809i	$-0.363772\pi$
$61$	3088.63			0.830053			0.415026	+	0.909809i	$0.363772\pi$
$62$	2908.62	+	2908.62i	0.756664	+	0.756664i
$63$	15.6551	−	15.6551i	0.00394435	−	0.00394435i
$64$		−	512.000i		−	0.125000i
$65$	−1778.35	+	561.262i	−0.420911	+	0.132843i
$66$	−1557.52			−0.357558
$67$	4056.65	+	4056.65i	0.903687	+	0.903687i	0.995753	−	0.0920662i	$-0.0293471\pi$
$67$	4056.65	+	4056.65i	0.903687	+	0.903687i	−0.0920662	+	0.995753i	$0.529347\pi$
$68$	−292.631	+	292.631i	−0.0632852	+	0.0632852i
$69$			997.857i			0.209590i
$70$	862.456	−	1657.90i	0.176011	−	0.338347i
$71$	1068.44			0.211949			0.105975	−	0.994369i	$-0.466204\pi$
$71$	1068.44			0.211949			0.105975	+	0.994369i	$0.466204\pi$
$72$	−13.4033	−	13.4033i	−0.00258551	−	0.00258551i
$73$	−1819.85	+	1819.85i	−0.341500	+	0.341500i	−0.856931	−	0.515431i	$-0.827632\pi$
$73$	−1819.85	+	1819.85i	−0.341500	+	0.341500i	0.515431	+	0.856931i	$0.327632\pi$
$74$		−	3241.41i		−	0.591931i
$75$	5568.67	+	978.674i	0.989985	+	0.173987i
$76$	−5024.78			−0.869941
$77$	1137.57	+	1137.57i	0.191866	+	0.191866i
$78$	1349.59	−	1349.59i	0.221827	−	0.221827i
$79$		−	6100.00i		−	0.977408i	−0.872450	−	0.488704i	$-0.837470\pi$
$79$		−	6100.00i		−	0.977408i	0.872450	−	0.488704i	$-0.162530\pi$
$80$	−1419.43	−	738.398i	−0.221785	−	0.115375i
$81$	6628.15			1.01024
$82$	21.5573	+	21.5573i	0.00320602	+	0.00320602i
$83$	7078.81	−	7078.81i	1.02755	−	1.02755i	0.0279432	−	0.999610i	$-0.491104\pi$
$83$	7078.81	−	7078.81i	1.02755	−	1.02755i	0.999610	−	0.0279432i	$-0.00889574\pi$
$84$			1912.70i			0.271075i
$85$	389.237	+	1233.29i	0.0538737	+	0.170698i
$86$	−3724.12			−0.503532
$87$	1343.26	+	1343.26i	0.177469	+	0.177469i
$88$	973.942	−	973.942i	0.125767	−	0.125767i
$89$			3669.63i			0.463278i	0.972802	+	0.231639i	$0.0744088\pi$
$89$			3669.63i			0.463278i	−0.972802	+	0.231639i	$0.925591\pi$
$90$	−56.4880	+	17.8281i	−0.00697383	+	0.00220100i
$91$	−1971.41			−0.238065
$92$	−623.974	−	623.974i	−0.0737210	−	0.0737210i
$93$	−9302.90	+	9302.90i	−1.07560	+	1.07560i
$94$			1950.94i			0.220795i
$95$	−7246.65	+	13930.3i	−0.802953	+	1.54352i
$96$	1637.58			0.177688
$97$	−1703.93	−	1703.93i	−0.181096	−	0.181096i	0.610737	−	0.791833i	$-0.290873\pi$
$97$	−1703.93	−	1703.93i	−0.181096	−	0.181096i	−0.791833	+	0.610737i	$0.790873\pi$
$98$	−3405.01	+	3405.01i	−0.354541	+	0.354541i
$99$		−	50.9922i		−	0.00520275i
$100$	−4094.15	+	2870.19i	−0.409415	+	0.287019i
$101$	8987.92			0.881082			0.440541	−	0.897732i	$-0.354787\pi$
$101$	8987.92			0.881082			0.440541	+	0.897732i	$0.354787\pi$
$102$	−935.948	−	935.948i	−0.0899604	−	0.0899604i
$103$	−2538.34	+	2538.34i	−0.239263	+	0.239263i	−0.816545	−	0.577282i	$-0.804113\pi$
$103$	−2538.34	+	2538.34i	−0.239263	+	0.239263i	0.577282	+	0.816545i	$0.304113\pi$
$104$			1687.84i			0.156050i
$105$	5302.62	+	2758.47i	0.480963	+	0.250202i
$106$	−6081.84			−0.541281
$107$	−4029.64	−	4029.64i	−0.351965	−	0.351965i	0.508876	−	0.860840i	$-0.330061\pi$
$107$	−4029.64	−	4029.64i	−0.351965	−	0.351965i	−0.860840	+	0.508876i	$0.830061\pi$
$108$	−4102.25	+	4102.25i	−0.351702	+	0.351702i
$109$		−	13870.4i		−	1.16744i	−0.811954	−	0.583722i	$-0.801596\pi$
$109$		−	13870.4i		−	1.16744i	0.811954	−	0.583722i	$-0.198404\pi$
$110$	−1295.47	−	4104.68i	−0.107064	−	0.339230i
$111$	10367.3			0.841435
$112$	−1196.04	−	1196.04i	−0.0953477	−	0.0953477i
$113$	−4622.02	+	4622.02i	−0.361972	+	0.361972i	−0.864539	−	0.502566i	$-0.832389\pi$
$113$	−4622.02	+	4622.02i	−0.361972	+	0.361972i	0.502566	+	0.864539i	$0.332389\pi$
$114$		−	16071.2i		−	1.23663i
$115$	−2629.74	+	829.967i	−0.198846	+	0.0627575i
$116$	−1679.92			−0.124846
$117$	44.1847	+	44.1847i	0.00322775	+	0.00322775i
$118$	−10719.7	+	10719.7i	−0.769872	+	0.769872i
$119$			1367.18i			0.0965456i
$120$	2361.69	−	4539.88i	0.164006	−	0.315269i
$121$	−10935.7			−0.746921
$122$	−6177.25	−	6177.25i	−0.415026	−	0.415026i
$123$	−68.9487	+	68.9487i	−0.00455738	+	0.00455738i
$124$		−	11634.5i		−	0.756664i
$125$	2052.55	+	15489.6i	0.131363	+	0.991334i
$126$	−62.6206			−0.00394435
$127$	−18374.5	−	18374.5i	−1.13922	−	1.13922i	−0.988590	−	0.150633i	$-0.951869\pi$
$127$	−18374.5	−	18374.5i	−1.13922	−	1.13922i	−0.150633	−	0.988590i	$-0.548131\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$		−	11911.2i		−	0.715775i
$130$	4679.22	+	2434.18i	0.276877	+	0.144034i
$131$	−18470.3			−1.07629			−0.538146	−	0.842851i	$-0.680875\pi$
$131$	−18470.3			−1.07629			−0.538146	+	0.842851i	$0.680875\pi$
$132$	3115.05	+	3115.05i	0.178779	+	0.178779i
$133$	−11738.0	+	11738.0i	−0.663575	+	0.663575i
$134$		−	16226.6i		−	0.903687i
$135$	5456.53	+	17288.9i	0.299398	+	0.948637i
$136$	1170.52			0.0632852
$137$	7667.30	+	7667.30i	0.408509	+	0.408509i	0.881218	−	0.472710i	$-0.156724\pi$
$137$	7667.30	+	7667.30i	0.408509	+	0.408509i	−0.472710	+	0.881218i	$0.656724\pi$
$138$	1995.71	−	1995.71i	0.104795	−	0.104795i
$139$		−	13104.8i		−	0.678268i	−0.940738	−	0.339134i	$-0.889866\pi$
$139$		−	13104.8i		−	0.678268i	0.940738	−	0.339134i	$-0.110134\pi$
$140$	−5040.72	+	1590.89i	−0.257179	+	0.0811679i
$141$	−6239.88			−0.313861
$142$	−2136.87	−	2136.87i	−0.105975	−	0.105975i
$143$	−3210.66	+	3210.66i	−0.157008	+	0.157008i
$144$			53.6131i			0.00258551i
$145$	−2422.76	+	4657.27i	−0.115232	+	0.221511i
$146$	7279.42			0.341500
$147$	−10890.6	−	10890.6i	−0.503983	−	0.503983i
$148$	−6482.83	+	6482.83i	−0.295966	+	0.295966i
$149$			9203.61i			0.414558i	0.978282	+	0.207279i	$0.0664608\pi$
$149$			9203.61i			0.414558i	−0.978282	+	0.207279i	$0.933539\pi$
$150$	−9179.99	−	13094.7i	−0.407999	−	0.581986i
$151$	−8819.15			−0.386788			−0.193394	−	0.981121i	$-0.561950\pi$
$151$	−8819.15			−0.386788			−0.193394	+	0.981121i	$0.561950\pi$
$152$	10049.6	+	10049.6i	0.434970	+	0.434970i
$153$	30.6422	−	30.6422i	0.00130899	−	0.00130899i
$154$		−	4550.29i		−	0.191866i
$155$	−32254.4	−	16779.0i	−1.34254	−	0.698400i
$156$	−5398.37			−0.221827
$157$	−2422.68	−	2422.68i	−0.0982872	−	0.0982872i	0.656253	−	0.754541i	$-0.272140\pi$
$157$	−2422.68	−	2422.68i	−0.0982872	−	0.0982872i	−0.754541	+	0.656253i	$0.772140\pi$
$158$	−12200.0	+	12200.0i	−0.488704	+	0.488704i
$159$		−	19452.1i		−	0.769435i
$160$	1362.05	+	4315.65i	0.0532052	+	0.168580i
$161$	−2915.23			−0.112466
$162$	−13256.3	−	13256.3i	−0.505118	−	0.505118i
$163$	−32255.4	+	32255.4i	−1.21402	+	1.21402i	−0.244333	+	0.969691i	$0.578569\pi$
$163$	−32255.4	+	32255.4i	−1.21402	+	1.21402i	−0.969691	+	0.244333i	$0.921431\pi$
$164$		−	86.2292i		−	0.00320602i
$165$	13128.4	−	4143.42i	0.482217	−	0.152192i
$166$	−28315.2			−1.02755
$167$	16325.6	+	16325.6i	0.585378	+	0.585378i	0.936376	−	0.350998i	$-0.114158\pi$
$167$	16325.6	+	16325.6i	0.585378	+	0.585378i	−0.350998	+	0.936376i	$0.614158\pi$
$168$	3825.41	−	3825.41i	0.135537	−	0.135537i
$169$			22996.9i			0.805186i
$170$	1688.11	−	3245.06i	0.0584121	−	0.112286i
$171$	526.160			0.0179939
$172$	7448.25	+	7448.25i	0.251766	+	0.251766i
$173$	9052.68	−	9052.68i	0.302472	−	0.302472i	−0.539508	−	0.841980i	$-0.681390\pi$
$173$	9052.68	−	9052.68i	0.302472	−	0.302472i	0.841980	+	0.539508i	$0.181390\pi$
$174$		−	5373.05i		−	0.177469i
$175$	−2859.19	+	16268.8i	−0.0933612	+	0.531226i
$176$	−3895.77			−0.125767
$177$	−34285.8	−	34285.8i	−1.09438	−	1.09438i
$178$	7339.25	−	7339.25i	0.231639	−	0.231639i
$179$			20613.7i			0.643353i	0.946850	+	0.321677i	$0.104246\pi$
$179$			20613.7i			0.643353i	−0.946850	+	0.321677i	$0.895754\pi$
$180$	148.632	+	77.3199i	0.00458742	+	0.00238642i
$181$	57425.3			1.75286			0.876428	−	0.481533i	$-0.159920\pi$
$181$	57425.3			1.75286			0.876428	+	0.481533i	$0.159920\pi$
$182$	3942.83	+	3942.83i	0.119032	+	0.119032i
$183$	19757.3	−	19757.3i	0.589963	−	0.589963i
$184$			2495.90i			0.0737210i
$185$	8623.01	+	27321.9i	0.251951	+	0.798302i
$186$	37211.6			1.07560
$187$	2226.60	+	2226.60i	0.0636737	+	0.0636737i
$188$	3901.89	−	3901.89i	0.110397	−	0.110397i
$189$			19165.9i			0.536543i
$190$	42353.8	−	13367.2i	1.17324	−	0.370283i
$191$	24897.5			0.682480			0.341240	−	0.939976i	$-0.389153\pi$
$191$	24897.5			0.682480			0.341240	+	0.939976i	$0.389153\pi$
$192$	−3275.15	−	3275.15i	−0.0888442	−	0.0888442i
$193$	3121.15	−	3121.15i	0.0837916	−	0.0837916i	−0.663969	−	0.747760i	$-0.731129\pi$
$193$	3121.15	−	3121.15i	0.0837916	−	0.0837916i	0.747760	+	0.663969i	$0.231129\pi$
$194$			6815.73i			0.181096i
$195$	−7785.45	+	14966.0i	−0.204746	+	0.393583i
$196$	13620.1			0.354541
$197$	12006.2	+	12006.2i	0.309365	+	0.309365i	0.844663	−	0.535298i	$-0.179801\pi$
$197$	12006.2	+	12006.2i	0.309365	+	0.309365i	−0.535298	+	0.844663i	$0.679801\pi$
$198$	−101.984	+	101.984i	−0.00260138	+	0.00260138i
$199$		−	47654.3i		−	1.20336i	−0.798737	−	0.601681i	$-0.794498\pi$
$199$		−	47654.3i		−	1.20336i	0.798737	−	0.601681i	$-0.205502\pi$
$200$	13928.7	+	2447.92i	0.348217	+	0.0611979i
$201$	51899.0			1.28460
$202$	−17975.8	−	17975.8i	−0.440541	−	0.440541i
$203$	−3924.33	+	3924.33i	−0.0952299	+	0.0952299i
$204$			3743.79i			0.0899604i
$205$	−239.054	−	124.358i	−0.00568839	−	0.00295915i
$206$	10153.4			0.239263
$207$	65.3382	+	65.3382i	0.00152485	+	0.00152485i
$208$	3375.68	−	3375.68i	0.0780251	−	0.0780251i
$209$			38233.1i			0.875281i
$210$	−5088.30	−	16122.2i	−0.115381	−	0.365582i
$211$	65641.7			1.47440			0.737199	−	0.675676i	$-0.236148\pi$
$211$	65641.7			1.47440			0.737199	+	0.675676i	$0.236148\pi$
$212$	12163.7	+	12163.7i	0.270641	+	0.270641i
$213$	6834.56	−	6834.56i	0.150644	−	0.150644i
$214$			16118.6i			0.351965i
$215$	31390.6	−	9907.14i	0.679083	−	0.214324i
$216$	16409.0			0.351702
$217$	−27178.3	−	27178.3i	−0.577170	−	0.577170i
$218$	−27740.8	+	27740.8i	−0.583722	+	0.583722i
$219$			23282.4i			0.485445i
$220$	−5618.41	+	10800.3i	−0.116083	+	0.223147i
$221$	−3858.70			−0.0790054
$222$	−20734.6	−	20734.6i	−0.420717	−	0.420717i
$223$	33094.4	−	33094.4i	0.665494	−	0.665494i	−0.291175	−	0.956670i	$-0.594046\pi$
$223$	33094.4	−	33094.4i	0.665494	−	0.665494i	0.956670	+	0.291175i	$0.0940463\pi$
$224$			4784.17i			0.0953477i
$225$	428.710	−	300.546i	0.00846835	−	0.00593671i
$226$	18488.1			0.361972
$227$	19582.0	+	19582.0i	0.380019	+	0.380019i	0.871109	−	0.491090i	$-0.163401\pi$
$227$	19582.0	+	19582.0i	0.380019	+	0.380019i	−0.491090	+	0.871109i	$0.663401\pi$
$228$	−32142.4	+	32142.4i	−0.618314	+	0.618314i
$229$		−	86628.6i		−	1.65192i	−0.563725	−	0.825962i	$-0.690632\pi$
$229$		−	86628.6i		−	1.65192i	0.563725	−	0.825962i	$-0.309368\pi$
$230$	6919.41	+	3599.54i	0.130802	+	0.0680443i
$231$	14553.6			0.272739
$232$	3359.85	+	3359.85i	0.0624228	+	0.0624228i
$233$	−52912.8	+	52912.8i	−0.974650	+	0.974650i	−0.999687	−	0.0250369i	$-0.992030\pi$
$233$	−52912.8	+	52912.8i	−0.974650	+	0.974650i	0.0250369	+	0.999687i	$0.492030\pi$
$234$		−	176.739i		−	0.00322775i
$235$	−5190.02	−	16444.5i	−0.0939795	−	0.297773i
$236$	42878.8			0.769872
$237$	−39020.4	−	39020.4i	−0.694696	−	0.694696i
$238$	2734.36	−	2734.36i	0.0482728	−	0.0482728i
$239$		−	54892.5i		−	0.960986i	−0.876998	−	0.480493i	$-0.840458\pi$
$239$		−	54892.5i		−	0.960986i	0.876998	−	0.480493i	$-0.159542\pi$
$240$	−13803.1	+	4356.38i	−0.239638	+	0.0756316i
$241$	−96850.6			−1.66751			−0.833754	−	0.552136i	$-0.813813\pi$
$241$	−96850.6			−1.66751			−0.833754	+	0.552136i	$0.813813\pi$
$242$	21871.4	+	21871.4i	0.373461	+	0.373461i
$243$	863.606	−	863.606i	0.0146252	−	0.0146252i
$244$			24709.0i			0.415026i
$245$	19642.6	−	37759.1i	0.327241	−	0.629056i
$246$	275.795			0.00455738
$247$	−33129.0	−	33129.0i	−0.543018	−	0.543018i
$248$	−23268.9	+	23268.9i	−0.378332	+	0.378332i
$249$		−	90563.2i		−	1.46067i
$250$	26874.1	−	35084.3i	0.429985	−	0.561349i
$251$	71328.2			1.13218			0.566088	−	0.824345i	$-0.308456\pi$
$251$	71328.2			1.13218			0.566088	+	0.824345i	$0.308456\pi$
$252$	125.241	+	125.241i	0.00197218	+	0.00197218i
$253$	−4747.77	+	4747.77i	−0.0741735	+	0.0741735i
$254$			73498.1i			1.13922i
$255$	10379.0	+	5399.24i	0.159615	+	0.0830332i
$256$	4096.00			0.0625000
$257$	−44409.4	−	44409.4i	−0.672370	−	0.672370i	0.285892	−	0.958262i	$-0.407710\pi$
$257$	−44409.4	−	44409.4i	−0.672370	−	0.672370i	−0.958262	+	0.285892i	$0.907710\pi$
$258$	−23822.4	+	23822.4i	−0.357887	+	0.357887i
$259$			30288.0i			0.451514i
$260$	−4490.10	−	14226.8i	−0.0664215	−	0.210456i
$261$	175.910			0.00258231
$262$	36940.5	+	36940.5i	0.538146	+	0.538146i
$263$	−19592.5	+	19592.5i	−0.283255	+	0.283255i	−0.834406	−	0.551151i	$-0.814189\pi$
$263$	−19592.5	+	19592.5i	−0.283255	+	0.283255i	0.551151	+	0.834406i	$0.314189\pi$
$264$		−	12460.2i		−	0.178779i
$265$	51263.8	−	16179.3i	0.729993	−	0.230392i
$266$	46951.9			0.663575
$267$	23473.8	+	23473.8i	0.329277	+	0.329277i
$268$	−32453.2	+	32453.2i	−0.451843	+	0.451843i
$269$			21680.1i			0.299610i	0.988716	+	0.149805i	$0.0478646\pi$
$269$			21680.1i			0.299610i	−0.988716	+	0.149805i	$0.952135\pi$
$270$	23664.8	−	45490.9i	0.324620	−	0.624018i
$271$	−81890.4			−1.11505			−0.557525	−	0.830160i	$-0.688249\pi$
$271$	−81890.4			−1.11505			−0.557525	+	0.830160i	$0.688249\pi$
$272$	−2341.05	−	2341.05i	−0.0316426	−	0.0316426i
$273$	−12610.7	+	12610.7i	−0.169205	+	0.169205i
$274$		−	30669.2i		−	0.408509i
$275$	21839.0	+	31152.0i	0.288781	+	0.411928i
$276$	−7982.86			−0.104795
$277$	18219.9	+	18219.9i	0.237457	+	0.237457i	0.815796	−	0.578339i	$-0.196299\pi$
$277$	18219.9	+	18219.9i	0.237457	+	0.237457i	−0.578339	+	0.815796i	$0.696299\pi$
$278$	−26209.6	+	26209.6i	−0.339134	+	0.339134i
$279$			1218.28i			0.0156509i
$280$	13263.2	+	6899.65i	0.169174	+	0.0880057i
$281$	−55955.1			−0.708642			−0.354321	−	0.935124i	$-0.615288\pi$
$281$	−55955.1			−0.708642			−0.354321	+	0.935124i	$0.615288\pi$
$282$	12479.8	+	12479.8i	0.156931	+	0.156931i
$283$	−7268.07	+	7268.07i	−0.0907500	+	0.0907500i	−0.751024	−	0.660274i	$-0.770440\pi$
$283$	−7268.07	+	7268.07i	−0.0907500	+	0.0907500i	0.660274	+	0.751024i	$0.270440\pi$
$284$			8547.50i			0.105975i
$285$	42753.6	+	135464.i	0.526360	+	1.66776i
$286$	12842.6			0.157008
$287$	−201.433	−	201.433i	−0.00244549	−	0.00244549i
$288$	107.226	−	107.226i	0.00129275	−	0.00129275i
$289$		−	80845.0i		−	0.967960i
$290$	14160.1	−	4469.03i	0.168372	−	0.0531395i
$291$	−21799.4			−0.257429
$292$	−14558.8	−	14558.8i	−0.170750	−	0.170750i
$293$	−97638.5	+	97638.5i	−1.13733	+	1.13733i	−0.148401	+	0.988927i	$0.547413\pi$
$293$	−97638.5	+	97638.5i	−1.13733	+	1.13733i	−0.988927	+	0.148401i	$0.952587\pi$
$294$			43562.3i			0.503983i
$295$	61839.1	−	118874.i	0.710590	−	1.36597i
$296$	25931.3			0.295966
$297$	31213.7	+	31213.7i	0.353860	+	0.353860i
$298$	18407.2	−	18407.2i	0.207279	−	0.207279i
$299$		−	8227.88i		−	0.0920334i
$300$	−7829.39	+	44549.3i	−0.0869933	+	0.494993i
$301$	34798.5			0.384085
$302$	17638.3	+	17638.3i	0.193394	+	0.193394i
$303$	57493.8	−	57493.8i	0.626233	−	0.626233i
$304$		−	40198.2i		−	0.434970i
$305$	68501.2	+	35634.9i	0.736374	+	0.383068i
$306$	−122.569			−0.00130899
$307$	−112180.	−	112180.i	−1.19025	−	1.19025i	−0.976997	−	0.213254i	$-0.931594\pi$
$307$	−112180.	−	112180.i	−1.19025	−	1.19025i	−0.213254	−	0.976997i	$-0.568406\pi$
$308$	−9100.59	+	9100.59i	−0.0959330	+	0.0959330i
$309$			32474.5i			0.340115i
$310$	30950.7	+	98066.9i	0.322068	+	1.02047i
$311$	151264.			1.56393			0.781963	−	0.623325i	$-0.214219\pi$
$311$	151264.			1.56393			0.781963	+	0.623325i	$0.214219\pi$
$312$	10796.7	+	10796.7i	0.110913	+	0.110913i
$313$	45198.6	−	45198.6i	0.461356	−	0.461356i	−0.437744	−	0.899100i	$-0.644222\pi$
$313$	45198.6	−	45198.6i	0.461356	−	0.461356i	0.899100	+	0.437744i	$0.144222\pi$
$314$			9690.72i			0.0982872i
$315$	527.829	−	166.587i	0.00531951	−	0.00167888i
$316$	48800.0			0.488704
$317$	−49569.6	−	49569.6i	−0.493284	−	0.493284i	0.416056	−	0.909339i	$-0.363412\pi$
$317$	−49569.6	−	49569.6i	−0.493284	−	0.493284i	−0.909339	+	0.416056i	$0.863412\pi$
$318$	−38904.2	+	38904.2i	−0.384718	+	0.384718i
$319$			12782.4i			0.125612i
$320$	5907.19	−	11355.4i	0.0576874	−	0.110893i
$321$	−51553.5			−0.500320
$322$	5830.46	+	5830.46i	0.0562330	+	0.0562330i
$323$	−22975.1	+	22975.1i	−0.220217	+	0.220217i
$324$			53025.2i			0.505118i
$325$	−45916.7	−	8069.71i	−0.434714	−	0.0763996i
$326$	129022.			1.21402
$327$	−88725.9	−	88725.9i	−0.829765	−	0.829765i
$328$	−172.458	+	172.458i	−0.00160301	+	0.00160301i
$329$		−	18229.8i		−	0.168418i
$330$	−34543.6	−	17969.9i	−0.317205	−	0.165013i
$331$	13035.4			0.118978			0.0594890	−	0.998229i	$-0.481053\pi$
$331$	13035.4			0.118978			0.0594890	+	0.998229i	$0.481053\pi$
$332$	56630.5	+	56630.5i	0.513776	+	0.513776i
$333$	678.837	−	678.837i	0.00612177	−	0.00612177i
$334$		−	65302.4i		−	0.585378i
$335$	43167.0	+	136774.i	0.384647	+	1.21875i
$336$	−15301.6			−0.135537
$337$	52682.6	+	52682.6i	0.463882	+	0.463882i	0.899925	−	0.436044i	$-0.143621\pi$
$337$	52682.6	+	52682.6i	0.463882	+	0.463882i	−0.436044	+	0.899925i	$0.643621\pi$
$338$	45993.9	−	45993.9i	0.402593	−	0.402593i
$339$			59132.2i			0.514546i
$340$	−9866.34	+	3113.90i	−0.0853489	+	0.0269368i
$341$	−88525.8			−0.761309
$342$	−1052.32	−	1052.32i	−0.00899695	−	0.00899695i
$343$	76686.9	−	76686.9i	0.651828	−	0.651828i
$344$		−	29793.0i		−	0.251766i
$345$	−11512.8	+	22131.0i	−0.0967255	+	0.185936i
$346$	−36210.7			−0.302472
$347$	113279.	+	113279.i	0.940785	+	0.940785i	0.998342	−	0.0575576i	$-0.0183313\pi$
$347$	113279.	+	113279.i	0.940785	+	0.940785i	−0.0575576	+	0.998342i	$0.518331\pi$
$348$	−10746.1	+	10746.1i	−0.0887345	+	0.0887345i
$349$		−	64976.5i		−	0.533465i	−0.963771	−	0.266732i	$-0.914056\pi$
$349$		−	64976.5i		−	0.533465i	0.963771	−	0.266732i	$-0.0859440\pi$
$350$	38256.0	−	26819.2i	0.312294	−	0.218933i
$351$	−54093.3			−0.439065
$352$	7791.54	+	7791.54i	0.0628836	+	0.0628836i
$353$	−166393.	+	166393.i	−1.33532	+	1.33532i	−0.434784	+	0.900535i	$0.643175\pi$
$353$	−166393.	+	166393.i	−1.33532	+	1.33532i	−0.900535	+	0.434784i	$0.856825\pi$
$354$			137143.i			1.09438i
$355$	23696.4	+	12327.1i	0.188029	+	0.0978144i
$356$	−29357.0			−0.231639
$357$	8745.57	+	8745.57i	0.0686201	+	0.0686201i
$358$	41227.4	−	41227.4i	0.321677	−	0.321677i
$359$		−	137875.i		−	1.06978i	−0.844920	−	0.534892i	$-0.820352\pi$
$359$		−	137875.i		−	1.06978i	0.844920	−	0.534892i	$-0.179648\pi$
$360$	−142.625	−	451.904i	−0.00110050	−	0.00348692i
$361$	−264185.			−2.02719
$362$	−114851.	−	114851.i	−0.876428	−	0.876428i
$363$	−69953.2	+	69953.2i	−0.530877	+	0.530877i
$364$		−	15771.3i		−	0.119032i
$365$	−61358.2	+	19365.2i	−0.460561	+	0.145357i
$366$	−79029.1			−0.589963
$367$	−132324.	−	132324.i	−0.982440	−	0.982440i	0.0174089	−	0.999848i	$-0.494458\pi$
$367$	−132324.	−	132324.i	−0.982440	−	0.982440i	−0.999848	+	0.0174089i	$0.994458\pi$
$368$	4991.79	−	4991.79i	0.0368605	−	0.0368605i
$369$			9.02932i			6.63135e-5i
$370$	37397.7	−	71889.8i	0.273176	−	0.525126i
$371$	56829.1			0.412879
$372$	−74423.2	−	74423.2i	−0.537802	−	0.537802i
$373$	−71789.4	+	71789.4i	−0.515992	+	0.515992i	−0.916356	−	0.400364i	$-0.868884\pi$
$373$	−71789.4	+	71789.4i	−0.515992	+	0.515992i	0.400364	+	0.916356i	$0.368884\pi$
$374$		−	8906.42i		−	0.0636737i
$375$	112213.	+	85953.9i	0.797962	+	0.611228i
$376$	−15607.5			−0.110397
$377$	−11075.9	−	11075.9i	−0.0779288	−	0.0779288i
$378$	38331.7	−	38331.7i	0.268271	−	0.268271i
$379$		−	217361.i		−	1.51323i	−0.653863	−	0.756613i	$-0.726853\pi$
$379$		−	217361.i		−	1.51323i	0.653863	−	0.756613i	$-0.273147\pi$
$380$	−111442.	−	57973.2i	−0.771760	−	0.401477i
$381$	−235076.			−1.61941
$382$	−49795.1	−	49795.1i	−0.341240	−	0.341240i
$383$	114245.	−	114245.i	0.778828	−	0.778828i	−0.200804	−	0.979632i	$-0.564355\pi$
$383$	114245.	−	114245.i	0.778828	−	0.778828i	0.979632	+	0.200804i	$0.0643553\pi$
$384$			13100.6i			0.0888442i
$385$	12105.0	+	38354.4i	0.0816662	+	0.258758i
$386$	−12484.6			−0.0837916
$387$	−779.928	−	779.928i	−0.00520754	−	0.00520754i
$388$	13631.5	−	13631.5i	0.0905480	−	0.0905480i
$389$			141974.i			0.938232i	0.883137	+	0.469116i	$0.155427\pi$
$389$			141974.i			0.938232i	−0.883137	+	0.469116i	$0.844573\pi$
$390$	45502.9	−	14361.1i	0.299164	−	0.0944187i
$391$	−5706.07			−0.0373236
$392$	−27240.1	−	27240.1i	−0.177271	−	0.177271i
$393$	−118150.	+	118150.i	−0.764979	+	0.764979i
$394$		−	48024.6i		−	0.309365i
$395$	70378.6	−	135289.i	0.451073	−	0.867098i
$396$	407.938			0.00260138
$397$	98851.0	+	98851.0i	0.627191	+	0.627191i	0.947360	−	0.320169i	$-0.103740\pi$
$397$	98851.0	+	98851.0i	0.627191	+	0.627191i	−0.320169	+	0.947360i	$0.603740\pi$
$398$	−95308.7	+	95308.7i	−0.601681	+	0.601681i
$399$			150171.i			0.943277i
$400$	−22961.5	−	32753.2i	−0.143509	−	0.204707i
$401$	−89563.2			−0.556982			−0.278491	−	0.960439i	$-0.589834\pi$
$401$	−89563.2			−0.556982			−0.278491	+	0.960439i	$0.589834\pi$
$402$	−103798.	−	103798.i	−0.642299	−	0.642299i
$403$	76707.5	−	76707.5i	0.472311	−	0.472311i
$404$			71903.4i			0.440541i
$405$	147003.	+	76472.1i	0.896221	+	0.466222i
$406$	15697.3			0.0952299
$407$	49327.3	+	49327.3i	0.297782	+	0.297782i
$408$	7487.58	−	7487.58i	0.0449802	−	0.0449802i
$409$		−	193227.i		−	1.15511i	−0.816353	−	0.577553i	$-0.804008\pi$
$409$		−	193227.i		−	1.15511i	0.816353	−	0.577553i	$-0.195992\pi$
$410$	229.392	+	726.825i	0.00136462	+	0.00432377i
$411$	98092.1			0.580698
$412$	−20306.8	−	20306.8i	−0.119632	−	0.119632i
$413$	100166.	−	100166.i	0.587244	−	0.587244i
$414$		−	261.353i		−	0.00152485i
$415$	238669.	−	75325.9i	1.38580	−	0.437369i
$416$	−13502.7			−0.0780251
$417$	−83828.7	−	83828.7i	−0.482082	−	0.482082i
$418$	76466.3	−	76466.3i	0.437640	−	0.437640i
$419$		−	148384.i		−	0.845199i	−0.906317	−	0.422600i	$-0.861118\pi$
$419$		−	148384.i		−	0.845199i	0.906317	−	0.422600i	$-0.138882\pi$
$420$	−22067.8	+	42421.0i	−0.125101	+	0.240482i
$421$	−121966.			−0.688138			−0.344069	−	0.938944i	$-0.611805\pi$
$421$	−121966.			−0.688138			−0.344069	+	0.938944i	$0.611805\pi$
$422$	−131283.	−	131283.i	−0.737199	−	0.737199i
$423$	−408.578	+	408.578i	−0.00228347	+	0.00228347i
$424$		−	48654.7i		−	0.270641i
$425$	−5596.37	+	31843.4i	−0.0309834	+	0.176296i
$426$	−27338.2			−0.150644
$427$	57720.7	+	57720.7i	0.316574	+	0.316574i
$428$	32237.1	−	32237.1i	0.175982	−	0.175982i
$429$			41075.8i			0.223188i
$430$	−82595.5	−	42967.0i	−0.446704	−	0.232379i
$431$	−337225.			−1.81537			−0.907685	−	0.419652i	$-0.862152\pi$
$431$	−337225.			−1.81537			−0.907685	+	0.419652i	$0.862152\pi$
$432$	−32818.0	−	32818.0i	−0.175851	−	0.175851i
$433$	−83334.0	+	83334.0i	−0.444474	+	0.444474i	−0.893512	−	0.449038i	$-0.851767\pi$
$433$	−83334.0	+	83334.0i	−0.444474	+	0.444474i	0.449038	+	0.893512i	$0.351767\pi$
$434$			108713.i			0.577170i
$435$	14293.7	+	45289.4i	0.0755382	+	0.239342i
$436$	110963.			0.583722
$437$	−48989.6	−	48989.6i	−0.256532	−	0.256532i
$438$	46564.9	−	46564.9i	0.242723	−	0.242723i
$439$			96328.1i			0.499832i	0.968268	+	0.249916i	$0.0804030\pi$
$439$			96328.1i			0.499832i	−0.968268	+	0.249916i	$0.919597\pi$
$440$	32837.4	−	10363.8i	0.169615	−	0.0535318i
$441$	−1426.20			−0.00733335
$442$	7717.40	+	7717.40i	0.0395027	+	0.0395027i
$443$	209948.	−	209948.i	1.06981	−	1.06981i	0.0724323	−	0.997373i	$-0.476924\pi$
$443$	209948.	−	209948.i	1.06981	−	1.06981i	0.997373	−	0.0724323i	$-0.0230761\pi$
$444$			82938.5i			0.420717i
$445$	−42338.2	+	81386.9i	−0.213802	+	0.410993i
$446$	−132377.			−0.665494
$447$	58873.5	+	58873.5i	0.294649	+	0.294649i
$448$	9568.33	−	9568.33i	0.0476738	−	0.0476738i
$449$		−	244816.i		−	1.21436i	−0.794564	−	0.607180i	$-0.792301\pi$
$449$		−	244816.i		−	1.21436i	0.794564	−	0.607180i	$-0.207699\pi$
$450$	−1458.51	−	256.329i	−0.00720253	−	0.00126582i
$451$	−656.111			−0.00322570
$452$	−36976.2	−	36976.2i	−0.180986	−	0.180986i
$453$	−56414.2	+	56414.2i	−0.274911	+	0.274911i
$454$		−	78328.1i		−	0.380019i
$455$	−43723.0	−	22745.1i	−0.211197	−	0.109867i
$456$	128570.			0.618314
$457$	144717.	+	144717.i	0.692925	+	0.692925i	0.962875	−	0.269949i	$-0.0870069\pi$
$457$	144717.	+	144717.i	0.692925	+	0.692925i	−0.269949	+	0.962875i	$0.587007\pi$
$458$	−173257.	+	173257.i	−0.825962	+	0.825962i
$459$			37513.9i			0.178060i
$460$	−6639.74	−	21037.9i	−0.0313787	−	0.0994230i
$461$	9727.58			0.0457723			0.0228862	−	0.999738i	$-0.492714\pi$
$461$	9727.58			0.0457723			0.0228862	+	0.999738i	$0.492714\pi$
$462$	−29107.2	−	29107.2i	−0.136369	−	0.136369i
$463$	269866.	−	269866.i	1.25889	−	1.25889i	0.307261	−	0.951625i	$-0.400588\pi$
$463$	269866.	−	269866.i	1.25889	−	1.25889i	0.951625	−	0.307261i	$-0.0994124\pi$
$464$		−	13439.4i		−	0.0624228i
$465$	−313657.	+	98992.6i	−1.45060	+	0.457822i
$466$	211651.			0.974650
$467$	162266.	+	162266.i	0.744038	+	0.744038i	0.973352	−	0.229315i	$-0.0736485\pi$
$467$	162266.	+	162266.i	0.744038	+	0.744038i	−0.229315	+	0.973352i	$0.573648\pi$
$468$	−353.478	+	353.478i	−0.00161388	+	0.00161388i
$469$			151623.i			0.689316i
$470$	−22508.9	+	43269.0i	−0.101897	+	0.195876i
$471$	−30994.7			−0.139716
$472$	−85757.6	−	85757.6i	−0.384936	−	0.384936i
$473$	56673.1	−	56673.1i	0.253311	−	0.253311i
$474$			156082.i			0.694696i
$475$	−321440.	+	225345.i	−1.42467	+	0.998757i
$476$	−10937.5			−0.0482728
$477$	−1273.69	−	1273.69i	−0.00559794	−	0.00559794i
$478$	−109785.	+	109785.i	−0.480493	+	0.480493i
$479$			153202.i			0.667719i	0.942623	+	0.333859i	$0.108351\pi$
$479$			153202.i			0.667719i	−0.942623	+	0.333859i	$0.891649\pi$
$480$	36319.0	+	18893.5i	0.157635	+	0.0820030i
$481$	−85484.2			−0.369484
$482$	193701.	+	193701.i	0.833754	+	0.833754i
$483$	−18648.1	+	18648.1i	−0.0799356	+	0.0799356i
$484$		−	87485.4i		−	0.373461i
$485$	−18131.6	−	57449.8i	−0.0770820	−	0.244233i
$486$	−3454.43			−0.0146252
$487$	104612.	+	104612.i	0.441084	+	0.441084i	0.892376	−	0.451292i	$-0.149037\pi$
$487$	104612.	+	104612.i	0.441084	+	0.441084i	−0.451292	+	0.892376i	$0.649037\pi$
$488$	49418.0	−	49418.0i	0.207513	−	0.207513i
$489$			412662.i			1.72575i
$490$	−114803.	+	36232.9i	−0.478148	+	0.150908i
$491$	−218784.			−0.907514			−0.453757	−	0.891125i	$-0.649917\pi$
$491$	−218784.			−0.907514			−0.453757	+	0.891125i	$0.649917\pi$
$492$	−551.589	−	551.589i	−0.00227869	−	0.00227869i
$493$	−7681.20	+	7681.20i	−0.0316035	+	0.0316035i
$494$			132516.i			0.543018i
$495$	588.321	−	1130.93i	0.00240107	−	0.00461558i
$496$	93075.8			0.378332
$497$	19967.1	+	19967.1i	0.0808356	+	0.0808356i
$498$	−181126.	+	181126.i	−0.730337	+	0.730337i
$499$		−	205585.i		−	0.825637i	−0.910813	−	0.412819i	$-0.864544\pi$
$499$		−	205585.i		−	0.825637i	0.910813	−	0.412819i	$-0.135456\pi$
$500$	−123917.	+	16420.4i	−0.495667	+	0.0656817i
$501$	208863.			0.832119
$502$	−142656.	−	142656.i	−0.566088	−	0.566088i
$503$	143390.	−	143390.i	0.566741	−	0.566741i	−0.364473	−	0.931214i	$-0.618751\pi$
$503$	143390.	−	143390.i	0.566741	−	0.566741i	0.931214	+	0.364473i	$0.118751\pi$
$504$		−	500.964i		−	0.00197218i
$505$	199339.	+	103698.i	0.781644	+	0.406618i
$506$	18991.1			0.0741735
$507$	147106.	+	147106.i	0.572289	+	0.572289i
$508$	146996.	−	146996.i	0.569611	−	0.569611i
$509$			39772.9i			0.153515i	0.997050	+	0.0767577i	$0.0244568\pi$
$509$			39772.9i			0.153515i	−0.997050	+	0.0767577i	$0.975543\pi$
$510$	−9959.46	−	31556.4i	−0.0382909	−	0.121324i
$511$	−68019.4			−0.260490
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−322076.	+	322076.i	−1.22384	+	1.22384i
$514$			177637.i			0.672370i
$515$	−85582.8	+	27010.6i	−0.322680	+	0.101840i
$516$	95289.6			0.357887
$517$	−29689.1	−	29689.1i	−0.111075	−	0.111075i
$518$	60576.0	−	60576.0i	0.225757	−	0.225757i
$519$		−	115816.i		−	0.429966i
$520$	−19473.4	+	37433.8i	−0.0720170	+	0.138439i
$521$	169375.			0.623983			0.311992	−	0.950085i	$-0.399004\pi$
$521$	169375.			0.623983			0.311992	+	0.950085i	$0.399004\pi$
$522$	−351.820	−	351.820i	−0.00129116	−	0.00129116i
$523$	80165.0	−	80165.0i	0.293077	−	0.293077i	−0.545218	−	0.838294i	$-0.683553\pi$
$523$	80165.0	−	80165.0i	0.293077	−	0.293077i	0.838294	+	0.545218i	$0.183553\pi$
$524$		−	147762.i		−	0.538146i
$525$	85778.5	+	122358.i	0.311214	+	0.443928i
$526$	78369.9			0.283255
$527$	−53196.9	−	53196.9i	−0.191543	−	0.191543i
$528$	−24920.4	+	24920.4i	−0.0893896	+	0.0893896i
$529$		−	12167.0i		−	0.0434783i
$530$	−134886.	−	70169.0i	−0.480193	−	0.249801i
$531$	−4489.97			−0.0159241
$532$	−93903.8	−	93903.8i	−0.331787	−	0.331787i
$533$	568.520	−	568.520i	0.00200120	−	0.00200120i
$534$		−	93895.2i		−	0.329277i
$535$	−42879.6	−	135863.i	−0.149811	−	0.474673i
$536$	129813.			0.451843
$537$	131861.	+	131861.i	0.457266	+	0.457266i
$538$	43360.1	−	43360.1i	0.149805	−	0.149805i
$539$		−	103634.i		−	0.356717i
$540$	−138311.	+	43652.2i	−0.474319	+	0.149699i
$541$	179715.			0.614029			0.307014	−	0.951705i	$-0.400670\pi$
$541$	179715.			0.614029			0.307014	+	0.951705i	$0.400670\pi$
$542$	163781.	+	163781.i	0.557525	+	0.557525i
$543$	367337.	−	367337.i	1.24585	−	1.24585i
$544$			9364.18i			0.0316426i
$545$	160029.	−	307625.i	0.538774	−	1.03569i
$546$	50442.8			0.169205
$547$	41863.4	+	41863.4i	0.139914	+	0.139914i	0.773595	−	0.633681i	$-0.218457\pi$
$547$	41863.4	+	41863.4i	0.139914	+	0.139914i	−0.633681	+	0.773595i	$0.718457\pi$
$548$	−61338.4	+	61338.4i	−0.204254	+	0.204254i
$549$		−	2587.35i		−	0.00858443i
$550$	18626.0	−	105982.i	0.0615735	−	0.350354i
$551$	−131894.			−0.434433
$552$	15965.7	+	15965.7i	0.0523975	+	0.0523975i
$553$	113998.	−	113998.i	0.372774	−	0.372774i
$554$		−	72879.5i		−	0.237457i
$555$	229932.	+	119613.i	0.746471	+	0.388321i
$556$	104839.			0.339134
$557$	179470.	+	179470.i	0.578470	+	0.578470i	0.934482	−	0.356011i	$-0.115864\pi$
$557$	179470.	+	179470.i	0.578470	+	0.578470i	−0.356011	+	0.934482i	$0.615864\pi$
$558$	2436.56	−	2436.56i	0.00782544	−	0.00782544i
$559$			98214.4i			0.314305i
$560$	−12727.1	−	40325.7i	−0.0405840	−	0.128590i
$561$	28486.2			0.0905126
$562$	111910.	+	111910.i	0.354321	+	0.354321i
$563$	−101006.	+	101006.i	−0.318664	+	0.318664i	−0.848254	−	0.529590i	$-0.822346\pi$
$563$	−101006.	+	101006.i	−0.318664	+	0.318664i	0.529590	+	0.848254i	$0.322346\pi$
$564$		−	49919.0i		−	0.156931i
$565$	−155836.	+	49183.2i	−0.488170	+	0.154071i
$566$	29072.3			0.0907500
$567$	123868.	+	123868.i	0.385294	+	0.385294i
$568$	17095.0	−	17095.0i	0.0529874	−	0.0529874i
$569$			350949.i			1.08398i	0.840386	+	0.541988i	$0.182328\pi$
$569$			350949.i			1.08398i	−0.840386	+	0.541988i	$0.817672\pi$
$570$	185421.	−	356436.i	0.570702	−	1.09706i
$571$	235661.			0.722796			0.361398	−	0.932412i	$-0.382300\pi$
$571$	235661.			0.722796			0.361398	+	0.932412i	$0.382300\pi$
$572$	−25685.3	−	25685.3i	−0.0785041	−	0.0785041i
$573$	159264.	−	159264.i	0.485075	−	0.485075i
$574$			805.732i			0.00244549i
$575$	−67899.5	−	11933.1i	−0.205367	−	0.0360925i
$576$	−428.904			−0.00129275
$577$	218333.	+	218333.i	0.655796	+	0.655796i	0.954383	−	0.298587i	$-0.0965152\pi$
$577$	218333.	+	218333.i	0.655796	+	0.655796i	−0.298587	+	0.954383i	$0.596515\pi$
$578$	−161690.	+	161690.i	−0.483980	+	0.483980i
$579$		−	39930.7i		−	0.119110i
$580$	−37258.2	−	19382.1i	−0.110756	−	0.0576161i
$581$	264580.			0.783798
$582$	43598.7	+	43598.7i	0.128715	+	0.128715i
$583$	92552.4	−	92552.4i	0.272302	−	0.272302i
$584$			58235.4i			0.170750i
$585$	470.171	+	1489.73i	0.00137387	+	0.00435307i
$586$	390554.			1.13733
$587$	270860.	+	270860.i	0.786082	+	0.786082i	0.980849	−	0.194767i	$-0.0623951\pi$
$587$	270860.	+	270860.i	0.786082	+	0.786082i	−0.194767	+	0.980849i	$0.562395\pi$
$588$	87124.5	−	87124.5i	0.251991	−	0.251991i
$589$		−	913447.i		−	2.63301i
$590$	−361425.	+	114069.i	−1.03828	+	0.327690i
$591$	153602.			0.439765
$592$	−51862.6	−	51862.6i	−0.147983	−	0.147983i
$593$	288022.	−	288022.i	0.819062	−	0.819062i	−0.166910	−	0.985972i	$-0.553379\pi$
$593$	288022.	−	288022.i	0.819062	−	0.819062i	0.985972	+	0.166910i	$0.0533789\pi$
$594$		−	124855.i		−	0.353860i
$595$	−15773.8	+	30322.1i	−0.0445557	+	0.0856495i
$596$	−73628.8			−0.207279
$597$	−304834.	−	304834.i	−0.855294	−	0.855294i
$598$	−16455.8	+	16455.8i	−0.0460167	+	0.0460167i
$599$		−	201380.i		−	0.561259i	−0.959816	−	0.280630i	$-0.909457\pi$
$599$		−	201380.i		−	0.561259i	0.959816	−	0.280630i	$-0.0905433\pi$
$600$	104757.	−	73439.9i	0.290993	−	0.204000i
$601$	190697.			0.527951			0.263976	−	0.964529i	$-0.414966\pi$
$601$	190697.			0.527951			0.263976	+	0.964529i	$0.414966\pi$
$602$	−69597.0	−	69597.0i	−0.192042	−	0.192042i
$603$	3398.27	−	3398.27i	0.00934595	−	0.00934595i
$604$		−	70553.2i		−	0.193394i
$605$	−242537.	−	126170.i	−0.662624	−	0.344703i
$606$	−229975.			−0.626233
$607$	168969.	+	168969.i	0.458596	+	0.458596i	0.898194	−	0.439599i	$-0.144879\pi$
$607$	168969.	+	168969.i	0.458596	+	0.458596i	−0.439599	+	0.898194i	$0.644879\pi$
$608$	−80396.4	+	80396.4i	−0.217485	+	0.217485i
$609$			50206.2i			0.135370i
$610$	−65732.4	−	208272.i	−0.176653	−	0.559721i
$611$	51451.2			0.137820
$612$	245.138	+	245.138i	0.000654497	+	0.000654497i
$613$	−184117.	+	184117.i	−0.489973	+	0.489973i	−0.908298	−	0.418325i	$-0.862617\pi$
$613$	−184117.	+	184117.i	−0.489973	+	0.489973i	0.418325	+	0.908298i	$0.362617\pi$
$614$			448720.i			1.19025i
$615$	−2324.67	+	733.686i	−0.00614627	+	0.00193981i
$616$	36402.3			0.0959330
$617$	44529.3	+	44529.3i	0.116970	+	0.116970i	0.763169	−	0.646199i	$-0.223642\pi$
$617$	44529.3	+	44529.3i	0.116970	+	0.116970i	−0.646199	+	0.763169i	$0.723642\pi$
$618$	64949.0	−	64949.0i	0.170057	−	0.170057i
$619$			605161.i			1.57939i	0.613499	+	0.789696i	$0.289762\pi$
$619$			605161.i			1.57939i	−0.613499	+	0.789696i	$0.710238\pi$
$620$	134232.	−	258035.i	0.349200	−	0.671268i
$621$	−79990.5			−0.207422
$622$	−302529.	−	302529.i	−0.781963	−	0.781963i
$623$	−68578.5	+	68578.5i	−0.176690	+	0.176690i
$624$		−	43187.0i		−	0.110913i
$625$	−133188.	+	367218.i	−0.340962	+	0.940077i
$626$	−180794.			−0.461356
$627$	244569.	+	244569.i	0.622109	+	0.622109i
$628$	19381.4	−	19381.4i	0.0491436	−	0.0491436i
$629$			59283.6i			0.149842i
$630$	−1388.83	−	722.483i	−0.00349920	−	0.00182031i
$631$	−589948.			−1.48168			−0.740841	−	0.671681i	$-0.765573\pi$
$631$	−589948.			−1.48168			−0.740841	+	0.671681i	$0.765573\pi$
$632$	−97600.0	−	97600.0i	−0.244352	−	0.244352i
$633$	419896.	−	419896.i	1.04793	−	1.04793i
$634$			198278.i			0.493284i
$635$	−195524.	−	619515.i	−0.484901	−	1.53640i
$636$	155617.			0.384718
$637$	89798.7	+	89798.7i	0.221305	+	0.221305i
$638$	25564.8	−	25564.8i	0.0628060	−	0.0628060i
$639$		−	895.034i		−	0.00219199i
$640$	−34525.2	+	10896.4i	−0.0842900	+	0.0266026i
$641$	468222.			1.13956			0.569778	−	0.821799i	$-0.307029\pi$
$641$	468222.			1.13956			0.569778	+	0.821799i	$0.307029\pi$
$642$	103107.	+	103107.i	0.250160	+	0.250160i
$643$	73845.3	−	73845.3i	0.178608	−	0.178608i	−0.612141	−	0.790749i	$-0.709691\pi$
$643$	73845.3	−	73845.3i	0.178608	−	0.178608i	0.790749	+	0.612141i	$0.209691\pi$
$644$		−	23321.8i		−	0.0562330i
$645$	137425.	−	264173.i	0.330329	−	0.634993i
$646$	91900.3			0.220217
$647$	153536.	+	153536.i	0.366776	+	0.366776i	0.866300	−	0.499524i	$-0.166492\pi$
$647$	153536.	+	153536.i	0.366776	+	0.366776i	−0.499524	+	0.866300i	$0.666492\pi$
$648$	106050.	−	106050.i	0.252559	−	0.252559i
$649$		−	326261.i		−	0.774598i
$650$	75694.0	+	107973.i	0.179157	+	0.255557i
$651$	−347708.			−0.820451
$652$	−258043.	−	258043.i	−0.607012	−	0.607012i
$653$	−386795.	+	386795.i	−0.907099	+	0.907099i	−0.996037	−	0.0889377i	$-0.971653\pi$
$653$	−386795.	+	386795.i	−0.907099	+	0.907099i	0.0889377	+	0.996037i	$0.471653\pi$
$654$			354904.i			0.829765i
$655$	−409643.	−	213100.i	−0.954823	−	0.496708i
$656$	689.833			0.00160301
$657$	1524.50	+	1524.50i	0.00353180	+	0.00353180i
$658$	−36459.5	+	36459.5i	−0.0842091	+	0.0842091i
$659$			610898.i			1.40669i	0.710850	+	0.703344i	$0.248311\pi$
$659$			610898.i			1.40669i	−0.710850	+	0.703344i	$0.751689\pi$
$660$	33147.4	+	105027.i	0.0760959	+	0.241109i
$661$	−24176.3			−0.0553333			−0.0276666	−	0.999617i	$-0.508808\pi$
$661$	−24176.3			−0.0553333			−0.0276666	+	0.999617i	$0.508808\pi$
$662$	−26070.7	−	26070.7i	−0.0594890	−	0.0594890i
$663$	−24683.3	+	24683.3i	−0.0561534	+	0.0561534i
$664$		−	226522.i		−	0.513776i
$665$	−395757.	+	124904.i	−0.894923	+	0.282445i
$666$	−2715.35			−0.00612177
$667$	−16378.6	−	16378.6i	−0.0368150	−	0.0368150i
$668$	−130605.	+	130605.i	−0.292689	+	0.292689i
$669$		−	423395.i		−	0.946005i
$670$	187214.	−	359882.i	0.417050	−	0.801697i
$671$	188009.			0.417574
$672$	30603.3	+	30603.3i	0.0677687	+	0.0677687i
$673$	−153584.	+	153584.i	−0.339090	+	0.339090i	−0.856025	−	0.516935i	$-0.827073\pi$
$673$	−153584.	+	153584.i	−0.339090	+	0.339090i	0.516935	+	0.856025i	$0.327073\pi$
$674$		−	210730.i		−	0.463882i
$675$	−78452.8	+	446397.i	−0.172187	+	0.979747i
$676$	−183975.			−0.402593
$677$	23302.8	+	23302.8i	0.0508430	+	0.0508430i	0.732071	−	0.681228i	$-0.238554\pi$
$677$	23302.8	+	23302.8i	0.0508430	+	0.0508430i	−0.681228	+	0.732071i	$0.738554\pi$
$678$	118264.	−	118264.i	0.257273	−	0.257273i
$679$		−	63686.7i		−	0.138137i
$680$	25960.5	+	13504.9i	0.0561429	+	0.0292061i
$681$	250524.			0.540200
$682$	177052.	+	177052.i	0.380654	+	0.380654i
$683$	299958.	−	299958.i	0.643012	−	0.643012i	−0.308282	−	0.951295i	$-0.599754\pi$
$683$	299958.	−	299958.i	0.643012	−	0.643012i	0.951295	+	0.308282i	$0.0997542\pi$
$684$			4209.28i			0.00899695i
$685$	81588.1	+	258511.i	0.173878	+	0.550931i
$686$	−306748.			−0.651828
$687$	−554144.	−	554144.i	−1.17411	−	1.17411i
$688$	−59586.0	+	59586.0i	−0.125883	+	0.125883i
$689$			160393.i			0.337868i
$690$	67287.5	−	21236.5i	0.141331	−	0.0446051i
$691$	−435880.			−0.912874			−0.456437	−	0.889756i	$-0.650875\pi$
$691$	−435880.			−0.912874			−0.456437	+	0.889756i	$0.650875\pi$
$692$	72421.4	+	72421.4i	0.151236	+	0.151236i
$693$	952.950	−	952.950i	0.00198428	−	0.00198428i
$694$		−	453116.i		−	0.940785i
$695$	151196.	−	290645.i	0.313020	−	0.601719i
$696$	42984.4			0.0887345
$697$	−394.270	−	394.270i	−0.000811575	−	0.000811575i
$698$	−129953.	+	129953.i	−0.266732	+	0.266732i
$699$			676943.i			1.38547i
$700$	−130150.	−	22873.5i	−0.265613	−	0.0466806i
$701$	4389.77			0.00893317			0.00446659	−	0.999990i	$-0.498578\pi$
$701$	4389.77			0.00893317			0.00446659	+	0.999990i	$0.498578\pi$
$702$	108187.	+	108187.i	0.219533	+	0.219533i
$703$	−508981.	+	508981.i	−1.02989	+	1.02989i
$704$		−	31166.1i		−	0.0628836i
$705$	−138391.	−	71992.4i	−0.278439	−	0.144847i
$706$	665571.			1.33532
$707$	167968.	+	167968.i	0.336037	+	0.336037i
$708$	274286.	−	274286.i	0.547189	−	0.547189i
$709$		−	347450.i		−	0.691194i	−0.938383	−	0.345597i	$-0.887676\pi$
$709$		−	347450.i		−	0.691194i	0.938383	−	0.345597i	$-0.112324\pi$
$710$	−22738.6	−	72046.8i	−0.0451073	−	0.142922i
$711$	−5110.00			−0.0101084
$712$	58714.0	+	58714.0i	0.115820	+	0.115820i
$713$	113431.	−	113431.i	0.223128	−	0.223128i
$714$		−	34982.3i		−	0.0686201i
$715$	−108251.	+	34164.8i	−0.211747	+	0.0668292i
$716$	−164909.			−0.321677
$717$	−351136.	−	351136.i	−0.683025	−	0.683025i
$718$	−275750.	+	275750.i	−0.534892	+	0.534892i
$719$			60112.0i			0.116280i	0.998308	+	0.0581398i	$0.0185169\pi$
$719$			60112.0i			0.116280i	−0.998308	+	0.0581398i	$0.981483\pi$
$720$	−618.559	+	1189.06i	−0.00119321	+	0.00229371i
$721$	−94873.9			−0.182506
$722$	528370.	+	528370.i	1.01359	+	1.01359i
$723$	−619532.	+	619532.i	−1.18519	+	1.18519i
$724$			459402.i			0.876428i
$725$	−107466.	+	75338.9i	−0.204454	+	0.143332i
$726$	279813.			0.530877
$727$	−413052.	−	413052.i	−0.781512	−	0.781512i	0.198574	−	0.980086i	$-0.436369\pi$
$727$	−413052.	−	413052.i	−0.781512	−	0.781512i	−0.980086	+	0.198574i	$0.936369\pi$
$728$	−31542.6	+	31542.6i	−0.0595161	+	0.0595161i
$729$			525832.i			0.989445i
$730$	161447.	+	83986.1i	0.302959	+	0.157602i
$731$	68112.1			0.127464
$732$	158058.	+	158058.i	0.294982	+	0.294982i
$733$	59277.0	−	59277.0i	0.110326	−	0.110326i	−0.649789	−	0.760115i	$-0.725143\pi$
$733$	59277.0	−	59277.0i	0.110326	−	0.110326i	0.760115	+	0.649789i	$0.225143\pi$
$734$			529295.i			0.982440i
$735$	−115887.	−	367186.i	−0.214516	−	0.679691i
$736$	−19967.2			−0.0368605
$737$	246934.	+	246934.i	0.454617	+	0.454617i
$738$	18.0586	−	18.0586i	3.31568e−5	−	3.31568e-5i
$739$		−	371650.i		−	0.680526i	−0.940330	−	0.340263i	$-0.889484\pi$
$739$		−	371650.i		−	0.680526i	0.940330	−	0.340263i	$-0.110516\pi$
$740$	−218575.	+	68984.1i	−0.399151	+	0.125975i
$741$	−423838.			−0.771904
$742$	−113658.	−	113658.i	−0.206440	−	0.206440i
$743$	430744.	−	430744.i	0.780263	−	0.780263i	−0.199612	−	0.979875i	$-0.563968\pi$
$743$	430744.	−	430744.i	0.780263	−	0.780263i	0.979875	+	0.199612i	$0.0639681\pi$
$744$			297693.i			0.537802i
$745$	−106186.	+	204122.i	−0.191318	+	0.367771i
$746$	287158.			0.515992
$747$	−5929.95	−	5929.95i	−0.0106270	−	0.0106270i
$748$	−17812.8	+	17812.8i	−0.0318368	+	0.0318368i
$749$		−	150613.i		−	0.268472i
$750$	−52518.9	−	396334.i	−0.0933670	−	0.704595i
$751$	−410041.			−0.727022			−0.363511	−	0.931590i	$-0.618422\pi$
$751$	−410041.			−0.727022			−0.363511	+	0.931590i	$0.618422\pi$
$752$	31215.1	+	31215.1i	0.0551987	+	0.0551987i
$753$	456271.	−	456271.i	0.804698	−	0.804698i
$754$			44303.8i			0.0779288i
$755$	−195596.	−	101751.i	−0.343135	−	0.178502i
$756$	−153327.			−0.268271
$757$	−283358.	−	283358.i	−0.494474	−	0.494474i	0.415239	−	0.909712i	$-0.363698\pi$
$757$	−283358.	−	283358.i	−0.494474	−	0.494474i	−0.909712	+	0.415239i	$0.863698\pi$
$758$	−434723.	+	434723.i	−0.756613	+	0.756613i
$759$			60740.9i			0.105438i
$760$	106938.	+	338831.i	0.185142	+	0.586618i
$761$	−851842.			−1.47092			−0.735461	−	0.677567i	$-0.763034\pi$
$761$	−851842.			−1.47092			−0.735461	+	0.677567i	$0.763034\pi$
$762$	470152.	+	470152.i	0.809707	+	0.809707i
$763$	259212.	−	259212.i	0.445252	−	0.445252i
$764$			199180.i			0.341240i
$765$	1033.13	−	326.066i	0.00176536	−	0.000557163i
$766$	−456982.			−0.778828
$767$	282705.	+	282705.i	0.480555	+	0.480555i
$768$	26201.2	−	26201.2i	0.0444221	−	0.0444221i
$769$			52108.6i			0.0881164i	0.999029	+	0.0440582i	$0.0140287\pi$
$769$			52108.6i			0.0881164i	−0.999029	+	0.0440582i	$0.985971\pi$
$770$	52498.9	−	100919.i	0.0885459	−	0.170212i
$771$	−568154.			−0.955779
$772$	24969.2	+	24969.2i	0.0418958	+	0.0418958i
$773$	242697.	−	242697.i	0.406168	−	0.406168i	−0.474232	−	0.880400i	$-0.657274\pi$
$773$	242697.	−	242697.i	0.406168	−	0.406168i	0.880400	+	0.474232i	$0.157274\pi$
$774$			3119.71i			0.00520754i
$775$	−521767.	−	744269.i	−0.868707	−	1.23916i
$776$	−54525.8			−0.0905480
$777$	193746.	+	193746.i	0.320915	+	0.320915i
$778$	283948.	−	283948.i	0.469116	−	0.469116i
$779$		−	6770.04i		−	0.0111562i
$780$	−119728.	−	62283.6i	−0.196791	−	0.102373i
$781$	65037.2			0.106625
$782$	11412.1	+	11412.1i	0.0186618	+	0.0186618i
$783$	−107679.	+	107679.i	−0.175634	+	0.175634i
$784$			108960.i			0.177271i
$785$	−25779.9	−	81683.1i	−0.0418351	−	0.132554i
$786$	472601.			0.764979
$787$	−173159.	−	173159.i	−0.279574	−	0.279574i	0.553365	−	0.832939i	$-0.313343\pi$
$787$	−173159.	−	173159.i	−0.279574	−	0.279574i	−0.832939	+	0.553365i	$0.813343\pi$
$788$	−96049.2	+	96049.2i	−0.154683	+	0.154683i
$789$			250658.i			0.402649i
$790$	−411335.	+	129821.i	−0.659085	+	0.208013i
$791$	−172754.			−0.276106
$792$	−815.875	−	815.875i	−0.00130069	−	0.00130069i
$793$	−162910.	+	162910.i	−0.259060	+	0.259060i
$794$		−	395404.i		−	0.627191i
$795$	224428.	−	431419.i	0.355094	−	0.682598i
$796$	381235.			0.601681
$797$	49515.7	+	49515.7i	0.0779518	+	0.0779518i	0.745008	−	0.667056i	$-0.232446\pi$
$797$	49515.7	+	49515.7i	0.0779518	+	0.0779518i	−0.667056	+	0.745008i	$0.732446\pi$
$798$	300341.	−	300341.i	0.471638	−	0.471638i
$799$		−	35681.6i		−	0.0558922i
$800$	−19583.3	+	111429.i	−0.0305989	+	0.174108i
$801$	3074.06			0.00479123
$802$	179126.	+	179126.i	0.278491	+	0.278491i
$803$	−110777.	+	110777.i	−0.171798	+	0.171798i
$804$			415192.i			0.642299i
$805$	−64655.5	−	33634.4i	−0.0997732	−	0.0519029i
$806$	−306830.			−0.472311
$807$	138683.	+	138683.i	0.212949	+	0.212949i
$808$	143807.	−	143807.i	0.220271	−	0.220271i
$809$		−	592645.i		−	0.905519i	−0.891633	−	0.452760i	$-0.850440\pi$
$809$		−	592645.i		−	0.905519i	0.891633	−	0.452760i	$-0.149560\pi$
$810$	−141061.	−	446949.i	−0.214999	−	0.681222i
$811$	−755772.			−1.14908			−0.574538	−	0.818478i	$-0.694818\pi$
$811$	−755772.			−1.14908			−0.574538	+	0.818478i	$0.694818\pi$
$812$	−31394.6	−	31394.6i	−0.0476150	−	0.0476150i
$813$	−523835.	+	523835.i	−0.792526	+	0.792526i
$814$		−	197309.i		−	0.297782i
$815$	−1.08752e6	+	343231.i	−1.63728	+	0.516740i
$816$	−29950.3			−0.0449802
$817$	584778.	+	584778.i	0.876086	+	0.876086i
$818$	−386455.	+	386455.i	−0.577553	+	0.577553i
$819$			1651.46i			0.00246207i
$820$	994.867	−	1912.44i	0.00147958	−	0.00284419i
$821$	−872843.			−1.29494			−0.647471	−	0.762090i	$-0.724173\pi$
$821$	−872843.			−1.29494			−0.647471	+	0.762090i	$0.724173\pi$
$822$	−196184.	−	196184.i	−0.290349	−	0.290349i
$823$	890612.	−	890612.i	1.31489	−	1.31489i	0.397123	−	0.917765i	$-0.370009\pi$
$823$	890612.	−	890612.i	1.31489	−	1.31489i	0.917765	−	0.397123i	$-0.129991\pi$
$824$			81227.0i			0.119632i
$825$	338972.	+	59573.2i	0.498031	+	0.0875273i
$826$	−400663.			−0.587244
$827$	−693632.	−	693632.i	−1.01419	−	1.01419i	−0.999898	−	0.0142887i	$-0.995452\pi$
$827$	−693632.	−	693632.i	−1.01419	−	1.01419i	−0.0142887	−	0.999898i	$-0.504548\pi$
$828$	−522.706	+	522.706i	−0.000762424	+	0.000762424i
$829$		−	18687.0i		−	0.0271914i	−0.999908	−	0.0135957i	$-0.995672\pi$
$829$		−	18687.0i		−	0.0271914i	0.999908	−	0.0135957i	$-0.00432777\pi$
$830$	−627990.	−	326686.i	−0.911584	−	0.474214i
$831$	233097.			0.337547
$832$	27005.4	+	27005.4i	0.0390126	+	0.0390126i
$833$	62275.7	−	62275.7i	0.0897488	−	0.0897488i
$834$			335315.i			0.482082i
$835$	173721.	+	550434.i	0.249161	+	0.789464i
$836$	−305865.			−0.437640
$837$	−745742.	−	745742.i	−1.06448	−	1.06448i
$838$	−296768.	+	296768.i	−0.422600	+	0.422600i
$839$		−	404766.i		−	0.575016i	−0.957778	−	0.287508i	$-0.907173\pi$
$839$		−	404766.i		−	0.575016i	0.957778	−	0.287508i	$-0.0928268\pi$
$840$	128977.	−	40706.4i	0.182791	−	0.0576904i
$841$	663185.			0.937654
$842$	243932.	+	243932.i	0.344069	+	0.344069i
$843$	−357933.	+	357933.i	−0.503670	+	0.503670i
$844$			525133.i			0.737199i
$845$	−265326.	+	510038.i	−0.371593	+	0.714314i
$846$	1634.31			0.00228347
$847$	−204368.	−	204368.i	−0.284869	−	0.284869i
$848$	−97309.4	+	97309.4i	−0.135320	+	0.135320i
$849$			92984.6i			0.129002i
$850$	74879.5	−	52494.1i	0.103640	−	0.0726561i
$851$	−126410.			−0.174551
$852$	54676.5	+	54676.5i	0.0753219	+	0.0753219i
$853$	42003.6	−	42003.6i	0.0577283	−	0.0577283i	−0.677653	−	0.735382i	$-0.737003\pi$
$853$	42003.6	−	42003.6i	0.0577283	−	0.0577283i	0.735382	+	0.677653i	$0.237003\pi$
$854$		−	230883.i		−	0.316574i
$855$	11669.4	+	6070.55i	0.0159631	+	0.00830416i
$856$	−128949.			−0.175982
$857$	−767593.	−	767593.i	−1.04513	−	1.04513i	−0.998932	−	0.0461953i	$-0.985290\pi$
$857$	−767593.	−	767593.i	−1.04513	−	1.04513i	−0.0461953	−	0.998932i	$-0.514710\pi$
$858$	82151.6	−	82151.6i	0.111594	−	0.111594i
$859$			887341.i			1.20255i	0.799041	+	0.601276i	$0.205341\pi$
$859$			887341.i			1.20255i	−0.799041	+	0.601276i	$0.794659\pi$
$860$	79257.1	+	251125.i	0.107162	+	0.339542i
$861$	−2577.05			−0.00347629
$862$	674450.	+	674450.i	0.907685	+	0.907685i
$863$	671948.	−	671948.i	0.902223	−	0.902223i	−0.0934054	−	0.995628i	$-0.529775\pi$
$863$	671948.	−	671948.i	0.902223	−	0.902223i	0.995628	+	0.0934054i	$0.0297753\pi$
$864$			131272.i			0.175851i
$865$	305220.	−	96330.0i	0.407925	−	0.128745i
$866$	333336.			0.444474
$867$	−517148.	−	517148.i	−0.687981	−	0.687981i
$868$	217427.	−	217427.i	0.288585	−	0.288585i
$869$		−	371315.i		−	0.491704i
$870$	61991.4	−	119166.i	0.0819018	−	0.157440i
$871$	−427936.			−0.564082
$872$	−221926.	−	221926.i	−0.291861	−	0.291861i
$873$	−1427.39	+	1427.39i	−0.00187290	+	0.00187290i
$874$			195958.i			0.256532i
$875$	−251114.	+	327830.i	−0.327985	+	0.428187i
$876$	−186259.			−0.242723
$877$	569701.	+	569701.i	0.740709	+	0.740709i	0.972715	−	0.232005i	$-0.0745286\pi$
$877$	569701.	+	569701.i	0.740709	+	0.740709i	−0.232005	+	0.972715i	$0.574529\pi$
$878$	192656.	−	192656.i	0.249916	−	0.249916i
$879$			1.24914e6i			1.61672i
$880$	−86402.4	−	44947.3i	−0.111573	−	0.0580415i
$881$	1.17290e6			1.51115			0.755577	−	0.655060i	$-0.227357\pi$
$881$	1.17290e6			1.51115			0.755577	+	0.655060i	$0.227357\pi$
$882$	2852.39	+	2852.39i	0.00366667	+	0.00366667i
$883$	923979.	−	923979.i	1.18506	−	1.18506i	0.206645	−	0.978416i	$-0.433745\pi$
$883$	923979.	−	923979.i	1.18506	−	1.18506i	0.978416	−	0.206645i	$-0.0662546\pi$
$884$		−	30869.6i		−	0.0395027i
$885$	−364837.	−	1.15598e6i	−0.465813	−	1.47592i
$886$	−839793.			−1.06981
$887$	99804.1	+	99804.1i	0.126853	+	0.126853i	0.767683	−	0.640830i	$-0.221410\pi$
$887$	99804.1	+	99804.1i	0.126853	+	0.126853i	−0.640830	+	0.767683i	$0.721410\pi$
$888$	165877.	−	165877.i	0.210359	−	0.210359i
$889$		−	686772.i		−	0.868978i
$890$	247450.	−	78097.3i	0.312398	−	0.0985953i
$891$	403465.			0.508218
$892$	264755.	+	264755.i	0.332747	+	0.332747i
$893$	306345.	−	306345.i	0.384157	−	0.384157i
$894$		−	235494.i		−	0.294649i
$895$	−237830.	+	457181.i	−0.296907	+	0.570745i
$896$	−38273.3			−0.0476738
$897$	−52632.0	−	52632.0i	−0.0654131	−	0.0654131i
$898$	−489632.	+	489632.i	−0.607180	+	0.607180i
$899$		−	305391.i		−	0.377865i
$900$	2404.37	+	3429.68i	0.00296836	+	0.00423418i
$901$	111233.			0.137020
$902$	1312.22	+	1312.22i	0.00161285	+	0.00161285i
$903$	222598.	−	222598.i	0.272990	−	0.272990i
$904$			147905.i			0.180986i
$905$	1.27361e6	+	662543.i	1.55503	+	0.808941i
$906$	225657.			0.274911
$907$	377498.	+	377498.i	0.458881	+	0.458881i	0.898288	−	0.439407i	$-0.144811\pi$
$907$	377498.	+	377498.i	0.458881	+	0.458881i	−0.439407	+	0.898288i	$0.644811\pi$
$908$	−156656.	+	156656.i	−0.190010	+	0.190010i
$909$		−	7529.22i		−	0.00911217i
$910$	41955.8	+	132936.i	0.0506651	+	0.160532i
$911$	1.17653e6			1.41765			0.708823	−	0.705386i	$-0.249226\pi$
$911$	1.17653e6			1.41765			0.708823	+	0.705386i	$0.249226\pi$
$912$	−257139.	−	257139.i	−0.309157	−	0.309157i
$913$	430897.	−	430897.i	0.516930	−	0.516930i
$914$		−	578867.i		−	0.692925i
$915$	666136.	−	210238.i	0.795648	−	0.251113i
$916$	693029.			0.825962
$917$	−345175.	−	345175.i	−0.410488	−	0.410488i
$918$	75027.7	−	75027.7i	0.0890300	−	0.0890300i
$919$			145677.i			0.172488i	0.996274	+	0.0862442i	$0.0274865\pi$
$919$			145677.i			0.172488i	−0.996274	+	0.0862442i	$0.972513\pi$
$920$	−28796.3	+	55355.3i	−0.0340222	+	0.0654009i
$921$	−1.43518e6			−1.69195
$922$	−19455.2	−	19455.2i	−0.0228862	−	0.0228862i
$923$	−56354.7	+	56354.7i	−0.0661495	+	0.0661495i
$924$			116429.i			0.136369i
$925$	−123980.	+	705447.i	−0.144900	+	0.824481i
$926$	−1.07946e6			−1.25889
$927$	2126.38	+	2126.38i	0.00247447	+	0.00247447i
$928$	−26878.8	+	26878.8i	−0.0312114	+	0.0312114i
$929$		−	154033.i		−	0.178477i	−0.996010	−	0.0892383i	$-0.971557\pi$
$929$		−	154033.i		−	0.178477i	0.996010	−	0.0892383i	$-0.0284433\pi$
$930$	825298.	+	429328.i	0.954212	+	0.496390i
$931$	1.06934e6			1.23372
$932$	−423302.	−	423302.i	−0.487325	−	0.487325i
$933$	967606.	−	967606.i	1.11157	−	1.11157i
$934$		−	649066.i		−	0.744038i
$935$	23693.4	+	75072.2i	0.0271022	+	0.0858728i
$936$	1413.91			0.00161388
$937$	621763.	+	621763.i	0.708183	+	0.708183i	0.966153	−	0.257970i	$-0.0830535\pi$
$937$	621763.	+	621763.i	0.708183	+	0.708183i	−0.257970	+	0.966153i	$0.583053\pi$
$938$	303245.	−	303245.i	0.344658	−	0.344658i
$939$		−	578251.i		−	0.655821i
$940$	131556.	−	41520.1i	0.148886	−	0.0469897i
$941$	−649101.			−0.733049			−0.366525	−	0.930408i	$-0.619452\pi$
$941$	−649101.			−0.733049			−0.366525	+	0.930408i	$0.619452\pi$
$942$	61989.5	+	61989.5i	0.0698580	+	0.0698580i
$943$	840.700	−	840.700i	0.000945404	−	0.000945404i
$944$			343030.i			0.384936i
$945$	−221125.	+	425070.i	−0.247614	+	0.475989i
$946$	−226692.			−0.253311
$947$	338512.	+	338512.i	0.377463	+	0.377463i	0.870186	−	0.492723i	$-0.163999\pi$
$947$	338512.	+	338512.i	0.377463	+	0.377463i	−0.492723	+	0.870186i	$0.663999\pi$
$948$	312163.	−	312163.i	0.347348	−	0.347348i
$949$		−	191976.i		−	0.213165i
$950$	1.09357e6	+	192191.i	1.21171	+	0.212954i
$951$	−634172.			−0.701206
$952$	21874.9	+	21874.9i	0.0241364	+	0.0241364i
$953$	−966832.	+	966832.i	−1.06455	+	1.06455i	−0.0667797	+	0.997768i	$0.521272\pi$
$953$	−966832.	+	966832.i	−1.06455	+	1.06455i	−0.997768	+	0.0667797i	$0.978728\pi$
$954$			5094.78i			0.00559794i
$955$	552191.	+	287255.i	0.605456	+	0.314964i
$956$	439140.			0.480493
$957$	81766.3	+	81766.3i	0.0892792	+	0.0892792i
$958$	306404.	−	306404.i	0.333859	−	0.333859i
$959$			286575.i			0.311603i
$960$	−34851.1	−	110425.i	−0.0378158	−	0.119819i
$961$	1.19149e6			1.29016
$962$	170968.	+	170968.i	0.184742	+	0.184742i
$963$	−3375.65	+	3375.65i	−0.00364003	+	0.00364003i
$964$		−	774805.i		−	0.833754i
$965$	105233.	−	33212.3i	0.113005	−	0.0356652i
$966$	74592.4			0.0799356
$967$	240966.	+	240966.i	0.257693	+	0.257693i	0.824115	−	0.566422i	$-0.191673\pi$
$967$	240966.	+	240966.i	0.257693	+	0.257693i	−0.566422	+	0.824115i	$0.691673\pi$
$968$	−174971.	+	174971.i	−0.186730	+	0.186730i
$969$			293933.i			0.313041i
$970$	−78636.3	+	151163.i	−0.0835756	+	0.160658i
$971$	619216.			0.656755			0.328378	−	0.944546i	$-0.393498\pi$
$971$	619216.			0.656755			0.328378	+	0.944546i	$0.393498\pi$
$972$	6908.85	+	6908.85i	0.00731262	+	0.00731262i
$973$	244905.	−	244905.i	0.258685	−	0.258685i
$974$		−	418446.i		−	0.441084i
$975$	−345339.	+	242099.i	−0.363276	+	0.254674i
$976$	−197672.			−0.207513
$977$	203480.	+	203480.i	0.213173	+	0.213173i	0.805614	−	0.592441i	$-0.201836\pi$
$977$	203480.	+	203480.i	0.213173	+	0.213173i	−0.592441	+	0.805614i	$0.701836\pi$
$978$	825324.	−	825324.i	0.862873	−	0.862873i
$979$			223375.i			0.233061i
$980$	302073.	+	157141.i	0.314528	+	0.163620i
$981$	−11619.3			−0.0120737
$982$	437569.	+	437569.i	0.453757	+	0.453757i
$983$	927844.	−	927844.i	0.960214	−	0.960214i	−0.0390240	−	0.999238i	$-0.512425\pi$
$983$	927844.	−	927844.i	0.960214	−	0.960214i	0.999238	+	0.0390240i	$0.0124249\pi$
$984$			2206.36i			0.00227869i
$985$	127758.	+	404799.i	0.131679	+	0.417222i
$986$	30724.8			0.0316035
$987$	−116612.	−	116612.i	−0.119704	−	0.119704i
$988$	265032.	−	265032.i	0.271509	−	0.271509i
$989$			145235.i			0.148483i
$990$	−3438.50	+	1085.22i	−0.00350832	+	0.00110725i
$991$	−1.42126e6			−1.44719			−0.723596	−	0.690224i	$-0.757512\pi$
$991$	−1.42126e6			−1.44719			−0.723596	+	0.690224i	$0.757512\pi$
$992$	−186152.	−	186152.i	−0.189166	−	0.189166i
$993$	83384.4	−	83384.4i	0.0845641	−	0.0845641i
$994$		−	79868.4i		−	0.0808356i
$995$	549811.	−	1.05690e6i	0.555350	−	1.06755i
$996$	724506.			0.730337
$997$	−510899.	−	510899.i	−0.513978	−	0.513978i	0.401765	−	0.915743i	$-0.368397\pi$
$997$	−510899.	−	510899.i	−0.513978	−	0.513978i	−0.915743	+	0.401765i	$0.868397\pi$
$998$	−411169.	+	411169.i	−0.412819	+	0.412819i
$999$			831068.i			0.832732i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(6.39678 - 6.39678i) q^{3} +8.00000i q^{4} +(22.1785 + 11.5375i) q^{5} -25.5871 q^{6} +(18.6881 + 18.6881i) q^{7} +(16.0000 - 16.0000i) q^{8} -0.837704i q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} +(6.39678 - 6.39678i) q^{3} +8.00000i q^{4} +(22.1785 + 11.5375i) q^{5} -25.5871 q^{6} +(18.6881 + 18.6881i) q^{7} +(16.0000 - 16.0000i) q^{8} -0.837704i q^{9} +(-21.2821 - 67.4320i) q^{10} +60.8714 q^{11} +(51.1743 + 51.1743i) q^{12} +(-52.7450 + 52.7450i) q^{13} -74.7526i q^{14} +(215.674 - 68.0685i) q^{15} -64.0000 q^{16} +(36.5788 + 36.5788i) q^{17} +(-1.67541 + 1.67541i) q^{18} +628.097i q^{19} +(-92.2998 + 177.428i) q^{20} +239.088 q^{21} +(-121.743 - 121.743i) q^{22} +(-77.9968 + 77.9968i) q^{23} -204.697i q^{24} +(358.773 + 511.768i) q^{25} +210.980 q^{26} +(512.781 + 512.781i) q^{27} +(-149.505 + 149.505i) q^{28} +209.990i q^{29} +(-567.485 - 295.211i) q^{30} -1454.31 q^{31} +(128.000 + 128.000i) q^{32} +(389.381 - 389.381i) q^{33} -146.315i q^{34} +(198.861 + 630.089i) q^{35} +6.70163 q^{36} +(810.354 + 810.354i) q^{37} +(1256.19 - 1256.19i) q^{38} +674.797i q^{39} +(539.456 - 170.257i) q^{40} -10.7786 q^{41} +(-478.176 - 478.176i) q^{42} +(931.031 - 931.031i) q^{43} +486.971i q^{44} +(9.66499 - 18.5790i) q^{45} +311.987 q^{46} +(-487.736 - 487.736i) q^{47} +(-409.394 + 409.394i) q^{48} -1702.51i q^{49} +(305.989 - 1741.08i) q^{50} +467.974 q^{51} +(-421.960 - 421.960i) q^{52} +(1520.46 - 1520.46i) q^{53} -2051.12i q^{54} +(1350.04 + 702.302i) q^{55} +598.021 q^{56} +(4017.80 + 4017.80i) q^{57} +(419.981 - 419.981i) q^{58} -5359.85i q^{59} +(544.548 + 1725.39i) q^{60} +3088.63 q^{61} +(2908.62 + 2908.62i) q^{62} +(15.6551 - 15.6551i) q^{63} -512.000i q^{64} +(-1778.35 + 561.262i) q^{65} -1557.52 q^{66} +(4056.65 + 4056.65i) q^{67} +(-292.631 + 292.631i) q^{68} +997.857i q^{69} +(862.456 - 1657.90i) q^{70} +1068.44 q^{71} +(-13.4033 - 13.4033i) q^{72} +(-1819.85 + 1819.85i) q^{73} -3241.41i q^{74} +(5568.67 + 978.674i) q^{75} -5024.78 q^{76} +(1137.57 + 1137.57i) q^{77} +(1349.59 - 1349.59i) q^{78} -6100.00i q^{79} +(-1419.43 - 738.398i) q^{80} +6628.15 q^{81} +(21.5573 + 21.5573i) q^{82} +(7078.81 - 7078.81i) q^{83} +1912.70i q^{84} +(389.237 + 1233.29i) q^{85} -3724.12 q^{86} +(1343.26 + 1343.26i) q^{87} +(973.942 - 973.942i) q^{88} +3669.63i q^{89} +(-56.4880 + 17.8281i) q^{90} -1971.41 q^{91} +(-623.974 - 623.974i) q^{92} +(-9302.90 + 9302.90i) q^{93} +1950.94i q^{94} +(-7246.65 + 13930.3i) q^{95} +1637.58 q^{96} +(-1703.93 - 1703.93i) q^{97} +(-3405.01 + 3405.01i) q^{98} -50.9922i 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	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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