LMFDB - Embedded newform 230.5.f.b.47.7

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			47.7
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(-4.66373 + 4.66373i) q^{3} +8.00000i q^{4} +(-12.4209 + 21.6961i) q^{5} -18.6549 q^{6} +(-24.9944 - 24.9944i) q^{7} +(-16.0000 + 16.0000i) q^{8} +37.4993i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(-4.66373 + 4.66373i) q^{3} +8.00000i q^{4} +(-12.4209 + 21.6961i) q^{5} -18.6549 q^{6} +(-24.9944 - 24.9944i) q^{7} +(-16.0000 + 16.0000i) q^{8} +37.4993i q^{9} +(-68.2341 + 18.5503i) q^{10} +42.7740 q^{11} +(-37.3098 - 37.3098i) q^{12} +(-124.381 + 124.381i) q^{13} -99.9775i q^{14} +(-43.2568 - 159.113i) q^{15} -64.0000 q^{16} +(-82.2327 - 82.2327i) q^{17} +(-74.9986 + 74.9986i) q^{18} -142.138i q^{19} +(-173.569 - 99.3675i) q^{20} +233.134 q^{21} +(85.5480 + 85.5480i) q^{22} +(77.9968 - 77.9968i) q^{23} -149.239i q^{24} +(-316.441 - 538.971i) q^{25} -497.523 q^{26} +(-552.648 - 552.648i) q^{27} +(199.955 - 199.955i) q^{28} -448.952i q^{29} +(231.711 - 404.739i) q^{30} +1207.80 q^{31} +(-128.000 - 128.000i) q^{32} +(-199.486 + 199.486i) q^{33} -328.931i q^{34} +(852.734 - 231.827i) q^{35} -299.994 q^{36} +(1166.74 + 1166.74i) q^{37} +(284.277 - 284.277i) q^{38} -1160.16i q^{39} +(-148.403 - 545.872i) q^{40} -983.682 q^{41} +(466.268 + 466.268i) q^{42} +(1264.77 - 1264.77i) q^{43} +342.192i q^{44} +(-813.588 - 465.776i) q^{45} +311.987 q^{46} +(-1747.20 - 1747.20i) q^{47} +(298.479 - 298.479i) q^{48} -1151.56i q^{49} +(445.061 - 1710.82i) q^{50} +767.022 q^{51} +(-995.047 - 995.047i) q^{52} +(-2008.22 + 2008.22i) q^{53} -2210.59i q^{54} +(-531.293 + 928.029i) q^{55} +799.820 q^{56} +(662.894 + 662.894i) q^{57} +(897.903 - 897.903i) q^{58} +957.449i q^{59} +(1272.90 - 346.054i) q^{60} -3399.49 q^{61} +(2415.60 + 2415.60i) q^{62} +(937.271 - 937.271i) q^{63} -512.000i q^{64} +(-1153.65 - 4243.50i) q^{65} -797.945 q^{66} +(-3861.25 - 3861.25i) q^{67} +(657.862 - 657.862i) q^{68} +727.512i q^{69} +(2169.12 + 1241.81i) q^{70} +535.782 q^{71} +(-599.989 - 599.989i) q^{72} +(2478.94 - 2478.94i) q^{73} +4666.98i q^{74} +(3989.41 + 1037.82i) q^{75} +1137.11 q^{76} +(-1069.11 - 1069.11i) q^{77} +(2320.31 - 2320.31i) q^{78} +4130.99i q^{79} +(794.940 - 1388.55i) q^{80} +2117.36 q^{81} +(-1967.36 - 1967.36i) q^{82} +(-7578.13 + 7578.13i) q^{83} +1865.07i q^{84} +(2805.54 - 762.722i) q^{85} +5059.09 q^{86} +(2093.79 + 2093.79i) q^{87} +(-684.384 + 684.384i) q^{88} +8592.11i q^{89} +(-695.624 - 2558.73i) q^{90} +6217.64 q^{91} +(623.974 + 623.974i) q^{92} +(-5632.84 + 5632.84i) q^{93} -6988.80i q^{94} +(3083.85 + 1765.49i) q^{95} +1193.91 q^{96} +(-12600.5 - 12600.5i) q^{97} +(2303.13 - 2303.13i) q^{98} +1603.99i 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
$3$	−4.66373	+	4.66373i	−0.518192	+	0.518192i	−0.917024	−	0.398832i	$-0.869416\pi$
$3$	−4.66373	+	4.66373i	−0.518192	+	0.518192i	0.398832	+	0.917024i	$0.369416\pi$
$4$			8.00000i			0.500000i
$5$	−12.4209	+	21.6961i	−0.496837	+	0.867844i
$5$	−12.4209	+	21.6961i	−0.496837	+	0.867844i
$6$	−18.6549			−0.518192
$7$	−24.9944	−	24.9944i	−0.510089	−	0.510089i	0.404464	−	0.914554i	$-0.367458\pi$
$7$	−24.9944	−	24.9944i	−0.510089	−	0.510089i	−0.914554	+	0.404464i	$0.867458\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$			37.4993i			0.462954i
$10$	−68.2341	+	18.5503i	−0.682341	+	0.185503i
$11$	42.7740			0.353504			0.176752	−	0.984255i	$-0.443441\pi$
$11$	42.7740			0.353504			0.176752	+	0.984255i	$0.443441\pi$
$12$	−37.3098	−	37.3098i	−0.259096	−	0.259096i
$13$	−124.381	+	124.381i	−0.735981	+	0.735981i	−0.971798	−	0.235816i	$-0.924224\pi$
$13$	−124.381	+	124.381i	−0.735981	+	0.735981i	0.235816	+	0.971798i	$0.424224\pi$
$14$		−	99.9775i		−	0.510089i
$15$	−43.2568	−	159.113i	−0.192252	−	0.707167i
$16$	−64.0000			−0.250000
$17$	−82.2327	−	82.2327i	−0.284542	−	0.284542i	0.550375	−	0.834917i	$-0.314485\pi$
$17$	−82.2327	−	82.2327i	−0.284542	−	0.284542i	−0.834917	+	0.550375i	$0.814485\pi$
$18$	−74.9986	+	74.9986i	−0.231477	+	0.231477i
$19$		−	142.138i		−	0.393735i	−0.980430	−	0.196867i	$-0.936923\pi$
$19$		−	142.138i		−	0.393735i	0.980430	−	0.196867i	$-0.0630769\pi$
$20$	−173.569	−	99.3675i	−0.433922	−	0.248419i
$21$	233.134			0.528648
$22$	85.5480	+	85.5480i	0.176752	+	0.176752i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$		−	149.239i		−	0.259096i
$25$	−316.441	−	538.971i	−0.506305	−	0.862354i
$26$	−497.523			−0.735981
$27$	−552.648	−	552.648i	−0.758091	−	0.758091i
$28$	199.955	−	199.955i	0.255045	−	0.255045i
$29$		−	448.952i		−	0.533831i	−0.963720	−	0.266915i	$-0.913996\pi$
$29$		−	448.952i		−	0.533831i	0.963720	−	0.266915i	$-0.0860044\pi$
$30$	231.711	−	404.739i	0.257457	−	0.449710i
$31$	1207.80			1.25681			0.628407	−	0.777885i	$-0.283707\pi$
$31$	1207.80			1.25681			0.628407	+	0.777885i	$0.283707\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−199.486	+	199.486i	−0.183183	+	0.183183i
$34$		−	328.931i		−	0.284542i
$35$	852.734	−	231.827i	0.696109	−	0.189246i
$36$	−299.994			−0.231477
$37$	1166.74	+	1166.74i	0.852260	+	0.852260i	0.990411	−	0.138151i	$-0.0441159\pi$
$37$	1166.74	+	1166.74i	0.852260	+	0.852260i	−0.138151	+	0.990411i	$0.544116\pi$
$38$	284.277	−	284.277i	0.196867	−	0.196867i
$39$		−	1160.16i		−	0.762759i
$40$	−148.403	−	545.872i	−0.0927516	−	0.341170i
$41$	−983.682			−0.585177			−0.292588	−	0.956239i	$-0.594517\pi$
$41$	−983.682			−0.585177			−0.292588	+	0.956239i	$0.594517\pi$
$42$	466.268	+	466.268i	0.264324	+	0.264324i
$43$	1264.77	−	1264.77i	0.684031	−	0.684031i	−0.276875	−	0.960906i	$-0.589299\pi$
$43$	1264.77	−	1264.77i	0.684031	−	0.684031i	0.960906	+	0.276875i	$0.0892989\pi$
$44$			342.192i			0.176752i
$45$	−813.588	−	465.776i	−0.401772	−	0.230013i
$46$	311.987			0.147442
$47$	−1747.20	−	1747.20i	−0.790946	−	0.790946i	0.190702	−	0.981648i	$-0.438924\pi$
$47$	−1747.20	−	1747.20i	−0.790946	−	0.790946i	−0.981648	+	0.190702i	$0.938924\pi$
$48$	298.479	−	298.479i	0.129548	−	0.129548i
$49$		−	1151.56i		−	0.479618i
$50$	445.061	−	1710.82i	0.178025	−	0.684330i
$51$	767.022			0.294895
$52$	−995.047	−	995.047i	−0.367991	−	0.367991i
$53$	−2008.22	+	2008.22i	−0.714922	+	0.714922i	−0.967561	−	0.252639i	$-0.918702\pi$
$53$	−2008.22	+	2008.22i	−0.714922	+	0.714922i	0.252639	+	0.967561i	$0.418702\pi$
$54$		−	2210.59i		−	0.758091i
$55$	−531.293	+	928.029i	−0.175634	+	0.306786i
$56$	799.820			0.255045
$57$	662.894	+	662.894i	0.204030	+	0.204030i
$58$	897.903	−	897.903i	0.266915	−	0.266915i
$59$			957.449i			0.275050i	0.990498	+	0.137525i	$0.0439148\pi$
$59$			957.449i			0.275050i	−0.990498	+	0.137525i	$0.956085\pi$
$60$	1272.90	−	346.054i	0.353583	−	0.0961262i
$61$	−3399.49			−0.913595			−0.456797	−	0.889571i	$-0.651004\pi$
$61$	−3399.49			−0.913595			−0.456797	+	0.889571i	$0.651004\pi$
$62$	2415.60	+	2415.60i	0.628407	+	0.628407i
$63$	937.271	−	937.271i	0.236148	−	0.236148i
$64$		−	512.000i		−	0.125000i
$65$	−1153.65	−	4243.50i	−0.273054	−	1.00438i
$66$	−797.945			−0.183183
$67$	−3861.25	−	3861.25i	−0.860159	−	0.860159i	0.131198	−	0.991356i	$-0.458118\pi$
$67$	−3861.25	−	3861.25i	−0.860159	−	0.860159i	−0.991356	+	0.131198i	$0.958118\pi$
$68$	657.862	−	657.862i	0.142271	−	0.142271i
$69$			727.512i			0.152806i
$70$	2169.12	+	1241.81i	0.442678	+	0.253431i
$71$	535.782			0.106285			0.0531424	−	0.998587i	$-0.483076\pi$
$71$	535.782			0.106285			0.0531424	+	0.998587i	$0.483076\pi$
$72$	−599.989	−	599.989i	−0.115739	−	0.115739i
$73$	2478.94	−	2478.94i	0.465179	−	0.465179i	−0.435170	−	0.900348i	$-0.643312\pi$
$73$	2478.94	−	2478.94i	0.465179	−	0.465179i	0.900348	+	0.435170i	$0.143312\pi$
$74$			4666.98i			0.852260i
$75$	3989.41	+	1037.82i	0.709228	+	0.184502i
$76$	1137.11			0.196867
$77$	−1069.11	−	1069.11i	−0.180319	−	0.180319i
$78$	2320.31	−	2320.31i	0.381380	−	0.381380i
$79$			4130.99i			0.661912i	0.943646	+	0.330956i	$0.107371\pi$
$79$			4130.99i			0.661912i	−0.943646	+	0.330956i	$0.892629\pi$
$80$	794.940	−	1388.55i	0.124209	−	0.216961i
$81$	2117.36			0.322719
$82$	−1967.36	−	1967.36i	−0.292588	−	0.292588i
$83$	−7578.13	+	7578.13i	−1.10003	+	1.10003i	−0.105628	+	0.994406i	$0.533685\pi$
$83$	−7578.13	+	7578.13i	−1.10003	+	1.10003i	−0.994406	+	0.105628i	$0.966315\pi$
$84$			1865.07i			0.264324i
$85$	2805.54	−	762.722i	0.388310	−	0.105567i
$86$	5059.09			0.684031
$87$	2093.79	+	2093.79i	0.276627	+	0.276627i
$88$	−684.384	+	684.384i	−0.0883761	+	0.0883761i
$89$			8592.11i			1.08473i	0.840145	+	0.542363i	$0.182470\pi$
$89$			8592.11i			1.08473i	−0.840145	+	0.542363i	$0.817530\pi$
$90$	−695.624	−	2558.73i	−0.0858795	−	0.315892i
$91$	6217.64			0.750832
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	−5632.84	+	5632.84i	−0.651271	+	0.651271i
$94$		−	6988.80i		−	0.790946i
$95$	3083.85	+	1765.49i	0.341700	+	0.195622i
$96$	1193.91			0.129548
$97$	−12600.5	−	12600.5i	−1.33920	−	1.33920i	−0.896836	−	0.442363i	$-0.854140\pi$
$97$	−12600.5	−	12600.5i	−1.33920	−	1.33920i	−0.442363	−	0.896836i	$-0.645860\pi$
$98$	2303.13	−	2303.13i	0.239809	−	0.239809i
$99$			1603.99i			0.163656i
$100$	4311.77	−	2531.53i	0.431177	−	0.253153i
$101$	5054.13			0.495455			0.247727	−	0.968830i	$-0.420316\pi$
$101$	5054.13			0.495455			0.247727	+	0.968830i	$0.420316\pi$
$102$	1534.04	+	1534.04i	0.147448	+	0.147448i
$103$	−9510.99	+	9510.99i	−0.896502	+	0.896502i	−0.995125	−	0.0986228i	$-0.968556\pi$
$103$	−9510.99	+	9510.99i	−0.896502	+	0.896502i	0.0986228	+	0.995125i	$0.468556\pi$
$104$		−	3980.19i		−	0.367991i
$105$	−2895.74	+	5058.09i	−0.262652	+	0.458784i
$106$	−8032.86			−0.714922
$107$	6390.68	+	6390.68i	0.558186	+	0.558186i	0.928791	−	0.370604i	$-0.120849\pi$
$107$	6390.68	+	6390.68i	0.558186	+	0.558186i	−0.370604	+	0.928791i	$0.620849\pi$
$108$	4421.19	−	4421.19i	0.379046	−	0.379046i
$109$		−	145.625i		−	0.0122569i	−0.999981	−	0.00612847i	$-0.998049\pi$
$109$		−	145.625i		−	0.0122569i	0.999981	−	0.00612847i	$-0.00195076\pi$
$110$	−2918.64	+	793.471i	−0.241210	+	0.0655761i
$111$	−10882.8			−0.883269
$112$	1599.64	+	1599.64i	0.127522	+	0.127522i
$113$	−10026.1	+	10026.1i	−0.785191	+	0.785191i	−0.980702	−	0.195511i	$-0.937364\pi$
$113$	−10026.1	+	10026.1i	−0.785191	+	0.785191i	0.195511	+	0.980702i	$0.437364\pi$
$114$			2651.58i			0.204030i
$115$	723.433	+	2661.02i	0.0547019	+	0.201211i
$116$	3591.61			0.266915
$117$	−4664.19	−	4664.19i	−0.340726	−	0.340726i
$118$	−1914.90	+	1914.90i	−0.137525	+	0.137525i
$119$			4110.71i			0.290284i
$120$	3237.91	+	1853.69i	0.224855	+	0.128729i
$121$	−12811.4			−0.875035
$122$	−6798.97	−	6798.97i	−0.456797	−	0.456797i
$123$	4587.62	−	4587.62i	0.303234	−	0.303234i
$124$			9662.39i			0.628407i
$125$	15624.1	−	171.000i	0.999940	−	0.0109440i
$126$	3749.08			0.236148
$127$	−12405.3	−	12405.3i	−0.769127	−	0.769127i	0.208825	−	0.977953i	$-0.433036\pi$
$127$	−12405.3	−	12405.3i	−0.769127	−	0.769127i	−0.977953	+	0.208825i	$0.933036\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$			11797.1i			0.708918i
$130$	6179.70	−	10794.3i	0.365663	−	0.638717i
$131$	−15991.0			−0.931821			−0.465910	−	0.884832i	$-0.654273\pi$
$131$	−15991.0			−0.931821			−0.465910	+	0.884832i	$0.654273\pi$
$132$	−1595.89	−	1595.89i	−0.0915915	−	0.0915915i
$133$	−3552.66	+	3552.66i	−0.200840	+	0.200840i
$134$		−	15445.0i		−	0.860159i
$135$	18854.7	−	5125.90i	1.03455	−	0.281257i
$136$	2631.45			0.142271
$137$	−7572.59	−	7572.59i	−0.403463	−	0.403463i	0.475989	−	0.879451i	$-0.342090\pi$
$137$	−7572.59	−	7572.59i	−0.403463	−	0.403463i	−0.879451	+	0.475989i	$0.842090\pi$
$138$	−1455.02	+	1455.02i	−0.0764032	+	0.0764032i
$139$			20076.9i			1.03912i	0.854433	+	0.519561i	$0.173905\pi$
$139$			20076.9i			1.03912i	−0.854433	+	0.519561i	$0.826095\pi$
$140$	1854.61	+	6821.87i	0.0946232	+	0.348055i
$141$	16296.9			0.819724
$142$	1071.56	+	1071.56i	0.0531424	+	0.0531424i
$143$	−5320.27	+	5320.27i	−0.260172	+	0.260172i
$144$		−	2399.95i		−	0.115739i
$145$	9740.49	+	5576.40i	0.463282	+	0.265227i
$146$	9915.75			0.465179
$147$	5370.57	+	5370.57i	0.248534	+	0.248534i
$148$	−9333.95	+	9333.95i	−0.426130	+	0.426130i
$149$		−	5570.13i		−	0.250896i	−0.992100	−	0.125448i	$-0.959963\pi$
$149$		−	5570.13i		−	0.250896i	0.992100	−	0.125448i	$-0.0400368\pi$
$150$	5903.17	+	10054.5i	0.262363	+	0.446865i
$151$	25453.1			1.11631			0.558156	−	0.829736i	$-0.311509\pi$
$151$	25453.1			1.11631			0.558156	+	0.829736i	$0.311509\pi$
$152$	2274.21	+	2274.21i	0.0984337	+	0.0984337i
$153$	3083.67	−	3083.67i	0.131730	−	0.131730i
$154$		−	4276.44i		−	0.180319i
$155$	−15002.0	+	26204.5i	−0.624432	+	1.09072i
$156$	9281.25			0.381380
$157$	4542.67	+	4542.67i	0.184294	+	0.184294i	0.793224	−	0.608930i	$-0.208401\pi$
$157$	4542.67	+	4542.67i	0.184294	+	0.184294i	−0.608930	+	0.793224i	$0.708401\pi$
$158$	−8261.98	+	8261.98i	−0.330956	+	0.330956i
$159$		−	18731.5i		−	0.740934i
$160$	4366.98	−	1187.22i	0.170585	−	0.0463758i
$161$	−3898.96			−0.150417
$162$	4234.72	+	4234.72i	0.161360	+	0.161360i
$163$	−27110.2	+	27110.2i	−1.02037	+	1.02037i	−0.0205802	+	0.999788i	$0.506551\pi$
$163$	−27110.2	+	27110.2i	−1.02037	+	1.02037i	−0.999788	+	0.0205802i	$0.993449\pi$
$164$		−	7869.46i		−	0.292588i
$165$	−1850.27	−	6805.88i	−0.0679621	−	0.249986i
$166$	−30312.5			−1.10003
$167$	−12748.7	−	12748.7i	−0.457125	−	0.457125i	0.440586	−	0.897710i	$-0.354771\pi$
$167$	−12748.7	−	12748.7i	−0.457125	−	0.457125i	−0.897710	+	0.440586i	$0.854771\pi$
$168$	−3730.14	+	3730.14i	−0.132162	+	0.132162i
$169$		−	2380.18i		−	0.0833366i
$170$	7136.52	+	4085.63i	0.246938	+	0.141371i
$171$	5330.09			0.182281
$172$	10118.2	+	10118.2i	0.342015	+	0.342015i
$173$	18097.1	−	18097.1i	0.604668	−	0.604668i	−0.336880	−	0.941548i	$-0.609372\pi$
$173$	18097.1	−	18097.1i	0.604668	−	0.604668i	0.941548	+	0.336880i	$0.109372\pi$
$174$			8375.15i			0.276627i
$175$	−5562.01	+	21380.5i	−0.181617	+	0.698139i
$176$	−2737.54			−0.0883761
$177$	−4465.28	−	4465.28i	−0.142529	−	0.142529i
$178$	−17184.2	+	17184.2i	−0.542363	+	0.542363i
$179$			45446.0i			1.41837i	0.705023	+	0.709185i	$0.250937\pi$
$179$			45446.0i			1.41837i	−0.705023	+	0.709185i	$0.749063\pi$
$180$	3726.21	−	6508.70i	0.115006	−	0.200886i
$181$	−3679.25			−0.112306			−0.0561529	−	0.998422i	$-0.517883\pi$
$181$	−3679.25			−0.112306			−0.0561529	+	0.998422i	$0.517883\pi$
$182$	12435.3	+	12435.3i	0.375416	+	0.375416i
$183$	15854.3	−	15854.3i	0.473418	−	0.473418i
$184$			2495.90i			0.0737210i
$185$	−39805.8	+	10821.7i	−1.16306	+	0.316194i
$186$	−22531.4			−0.651271
$187$	−3517.42	−	3517.42i	−0.100587	−	0.100587i
$188$	13977.6	−	13977.6i	0.395473	−	0.395473i
$189$			27626.2i			0.773388i
$190$	2636.71	+	9698.67i	0.0730391	+	0.268661i
$191$	5569.88			0.152679			0.0763395	−	0.997082i	$-0.475677\pi$
$191$	5569.88			0.152679			0.0763395	+	0.997082i	$0.475677\pi$
$192$	2387.83	+	2387.83i	0.0647740	+	0.0647740i
$193$	14063.7	−	14063.7i	0.377560	−	0.377560i	−0.492661	−	0.870221i	$-0.663976\pi$
$193$	14063.7	−	14063.7i	0.377560	−	0.377560i	0.870221	+	0.492661i	$0.163976\pi$
$194$		−	50402.1i		−	1.33920i
$195$	25170.9	+	14410.2i	0.661956	+	0.378967i
$196$	9212.50			0.239809
$197$	−15522.4	−	15522.4i	−0.399968	−	0.399968i	0.478253	−	0.878222i	$-0.341270\pi$
$197$	−15522.4	−	15522.4i	−0.399968	−	0.399968i	−0.878222	+	0.478253i	$0.841270\pi$
$198$	−3207.99	+	3207.99i	−0.0818281	+	0.0818281i
$199$		−	23916.6i		−	0.603940i	−0.953317	−	0.301970i	$-0.902356\pi$
$199$		−	23916.6i		−	0.603940i	0.953317	−	0.301970i	$-0.0976442\pi$
$200$	13686.6	+	3560.49i	0.342165	+	0.0890123i
$201$	36015.7			0.891455
$202$	10108.3	+	10108.3i	0.247727	+	0.247727i
$203$	−11221.3	+	11221.3i	−0.272301	+	0.272301i
$204$			6136.18i			0.147448i
$205$	12218.2	−	21342.1i	0.290738	−	0.507842i
$206$	−38044.0			−0.896502
$207$	2924.82	+	2924.82i	0.0682589	+	0.0682589i
$208$	7960.37	−	7960.37i	0.183995	−	0.183995i
$209$		−	6079.83i		−	0.139187i
$210$	−15907.7	+	4324.71i	−0.360718	+	0.0980659i
$211$	52595.9			1.18137			0.590686	−	0.806902i	$-0.298857\pi$
$211$	52595.9			1.18137			0.590686	+	0.806902i	$0.298857\pi$
$212$	−16065.7	−	16065.7i	−0.357461	−	0.357461i
$213$	−2498.74	+	2498.74i	−0.0550759	+	0.0550759i
$214$			25562.7i			0.558186i
$215$	11731.0	+	43150.3i	0.253780	+	0.933484i
$216$	17684.7			0.379046
$217$	−30188.2	−	30188.2i	−0.641088	−	0.641088i
$218$	291.249	−	291.249i	0.00612847	−	0.00612847i
$219$			23122.2i			0.482104i
$220$	−7424.23	−	4250.35i	−0.153393	−	0.0878171i
$221$	20456.4			0.418836
$222$	−21765.5	−	21765.5i	−0.441634	−	0.441634i
$223$	−29029.2	+	29029.2i	−0.583748	+	0.583748i	−0.935931	−	0.352183i	$-0.885439\pi$
$223$	−29029.2	+	29029.2i	−0.583748	+	0.583748i	0.352183	+	0.935931i	$0.385439\pi$
$224$			6398.56i			0.127522i
$225$	20211.0	−	11866.3i	0.399231	−	0.234396i
$226$	−40104.4			−0.785191
$227$	−3673.75	−	3673.75i	−0.0712948	−	0.0712948i	0.670560	−	0.741855i	$-0.266054\pi$
$227$	−3673.75	−	3673.75i	−0.0712948	−	0.0712948i	−0.741855	+	0.670560i	$0.766054\pi$
$228$	−5303.16	+	5303.16i	−0.102015	+	0.102015i
$229$		−	101280.i		−	1.93131i	−0.259820	−	0.965657i	$-0.583663\pi$
$229$		−	101280.i		−	1.93131i	0.259820	−	0.965657i	$-0.416337\pi$
$230$	−3875.17	+	6768.90i	−0.0732547	+	0.127957i
$231$	9972.07			0.186879
$232$	7183.22	+	7183.22i	0.133458	+	0.133458i
$233$	−1199.03	+	1199.03i	−0.0220860	+	0.0220860i	−0.718064	−	0.695978i	$-0.754971\pi$
$233$	−1199.03	+	1199.03i	−0.0220860	+	0.0220860i	0.695978	+	0.718064i	$0.254971\pi$
$234$		−	18656.8i		−	0.340726i
$235$	59609.3	−	16205.6i	1.07939	−	0.293446i
$236$	−7659.60			−0.137525
$237$	−19265.8	−	19265.8i	−0.342997	−	0.342997i
$238$	−8221.42	+	8221.42i	−0.145142	+	0.145142i
$239$		−	54134.6i		−	0.947717i	−0.880601	−	0.473859i	$-0.842861\pi$
$239$		−	54134.6i		−	0.947717i	0.880601	−	0.473859i	$-0.157139\pi$
$240$	2768.44	+	10183.2i	0.0480631	+	0.176792i
$241$	−7291.94			−0.125548			−0.0627739	−	0.998028i	$-0.519995\pi$
$241$	−7291.94			−0.125548			−0.0627739	+	0.998028i	$0.519995\pi$
$242$	−25622.8	−	25622.8i	−0.437517	−	0.437517i
$243$	34889.7	−	34889.7i	0.590861	−	0.590861i
$244$		−	27195.9i		−	0.456797i
$245$	24984.4	+	14303.5i	0.416233	+	0.238292i
$246$	18350.5			0.303234
$247$	17679.3	+	17679.3i	0.289781	+	0.289781i
$248$	−19324.8	+	19324.8i	−0.314204	+	0.314204i
$249$		−	70684.7i		−	1.14006i
$250$	31590.1	+	30906.1i	0.505442	+	0.494498i
$251$	10648.0			0.169013			0.0845066	−	0.996423i	$-0.473069\pi$
$251$	10648.0			0.169013			0.0845066	+	0.996423i	$0.473069\pi$
$252$	7498.17	+	7498.17i	0.118074	+	0.118074i
$253$	3336.24	−	3336.24i	0.0521214	−	0.0521214i
$254$		−	49621.0i		−	0.769127i
$255$	−9527.13	+	16641.4i	−0.146515	+	0.255923i
$256$	4096.00			0.0625000
$257$	−8601.08	−	8601.08i	−0.130223	−	0.130223i	0.638991	−	0.769214i	$-0.279352\pi$
$257$	−8601.08	−	8601.08i	−0.130223	−	0.130223i	−0.769214	+	0.638991i	$0.779352\pi$
$258$	−23594.2	+	23594.2i	−0.354459	+	0.354459i
$259$		−	58324.1i		−	0.869458i
$260$	33948.0	−	9229.21i	0.502190	−	0.136527i
$261$	16835.4			0.247139
$262$	−31982.0	−	31982.0i	−0.465910	−	0.465910i
$263$	60665.1	−	60665.1i	0.877057	−	0.877057i	−0.116172	−	0.993229i	$-0.537063\pi$
$263$	60665.1	−	60665.1i	0.877057	−	0.877057i	0.993229	+	0.116172i	$0.0370625\pi$
$264$		−	6383.56i		−	0.0915915i
$265$	−18626.5	−	68514.3i	−0.265241	−	0.975640i
$266$	−14210.6			−0.200840
$267$	−40071.3	−	40071.3i	−0.562096	−	0.562096i
$268$	30890.0	−	30890.0i	0.430079	−	0.430079i
$269$		−	100241.i		−	1.38528i	−0.721281	−	0.692642i	$-0.756447\pi$
$269$		−	100241.i		−	1.38528i	0.721281	−	0.692642i	$-0.243553\pi$
$270$	47961.2	+	27457.6i	0.657905	+	0.376648i
$271$	−73657.3			−1.00294			−0.501472	−	0.865174i	$-0.667208\pi$
$271$	−73657.3			−1.00294			−0.501472	+	0.865174i	$0.667208\pi$
$272$	5262.90	+	5262.90i	0.0711356	+	0.0711356i
$273$	−28997.4	+	28997.4i	−0.389075	+	0.389075i
$274$		−	30290.4i		−	0.403463i
$275$	−13535.4	−	23054.0i	−0.178981	−	0.304846i
$276$	−5820.09			−0.0764032
$277$	−60519.8	−	60519.8i	−0.788747	−	0.788747i	0.192541	−	0.981289i	$-0.438327\pi$
$277$	−60519.8	−	60519.8i	−0.788747	−	0.788747i	−0.981289	+	0.192541i	$0.938327\pi$
$278$	−40153.8	+	40153.8i	−0.519561	+	0.519561i
$279$			45291.6i			0.581847i
$280$	−9934.51	+	17353.0i	−0.126716	+	0.221339i
$281$	−17421.0			−0.220628			−0.110314	−	0.993897i	$-0.535186\pi$
$281$	−17421.0			−0.220628			−0.110314	+	0.993897i	$0.535186\pi$
$282$	32593.9	+	32593.9i	0.409862	+	0.409862i
$283$	5222.91	−	5222.91i	0.0652139	−	0.0652139i	−0.673748	−	0.738962i	$-0.735317\pi$
$283$	5222.91	−	5222.91i	0.0652139	−	0.0652139i	0.738962	+	0.673748i	$0.235317\pi$
$284$			4286.25i			0.0531424i
$285$	−22616.0	+	6148.45i	−0.278436	+	0.0756965i
$286$	−21281.1			−0.260172
$287$	24586.5	+	24586.5i	0.298492	+	0.298492i
$288$	4799.91	−	4799.91i	0.0578693	−	0.0578693i
$289$		−	69996.6i		−	0.838071i
$290$	8328.19	+	30633.8i	0.0990273	+	0.364254i
$291$	117531.			1.38792
$292$	19831.5	+	19831.5i	0.232589	+	0.232589i
$293$	−61084.0	+	61084.0i	−0.711529	+	0.711529i	−0.966855	−	0.255326i	$-0.917817\pi$
$293$	−61084.0	+	61084.0i	−0.711529	+	0.711529i	0.255326	+	0.966855i	$0.417817\pi$
$294$			21482.3i			0.248534i
$295$	−20772.9	−	11892.4i	−0.238700	−	0.136655i
$296$	−37335.8			−0.426130
$297$	−23639.0	−	23639.0i	−0.267988	−	0.267988i
$298$	11140.3	−	11140.3i	0.125448	−	0.125448i
$299$			19402.6i			0.217029i
$300$	−8302.58	+	31915.3i	−0.0922509	+	0.354614i
$301$	−63224.4			−0.697833
$302$	50906.1	+	50906.1i	0.558156	+	0.558156i
$303$	−23571.1	+	23571.1i	−0.256741	+	0.256741i
$304$			9096.85i			0.0984337i
$305$	42224.8	−	73755.6i	0.453908	−	0.792858i
$306$	12334.7			0.131730
$307$	−43241.8	−	43241.8i	−0.458804	−	0.458804i	0.439459	−	0.898263i	$-0.355170\pi$
$307$	−43241.8	−	43241.8i	−0.458804	−	0.458804i	−0.898263	+	0.439459i	$0.855170\pi$
$308$	8552.88	−	8552.88i	0.0901594	−	0.0901594i
$309$		−	88713.3i		−	0.929120i
$310$	−82413.0	+	22405.0i	−0.857575	+	0.233143i
$311$	13366.9			0.138201			0.0691005	−	0.997610i	$-0.477987\pi$
$311$	13366.9			0.138201			0.0691005	+	0.997610i	$0.477987\pi$
$312$	18562.5	+	18562.5i	0.190690	+	0.190690i
$313$	−120302.	+	120302.i	−1.22796	+	1.22796i	−0.263224	+	0.964735i	$0.584786\pi$
$313$	−120302.	+	120302.i	−1.22796	+	1.22796i	−0.964735	+	0.263224i	$0.915214\pi$
$314$			18170.7i			0.184294i
$315$	8693.34	+	31976.9i	0.0876124	+	0.322267i
$316$	−33047.9			−0.330956
$317$	106460.	+	106460.i	1.05942	+	1.05942i	0.998119	+	0.0613025i	$0.0195254\pi$
$317$	106460.	+	106460.i	1.05942	+	1.05942i	0.0613025	+	0.998119i	$0.480475\pi$
$318$	37463.1	−	37463.1i	0.370467	−	0.370467i
$319$		−	19203.5i		−	0.188711i
$320$	11108.4	+	6359.52i	0.108480	+	0.0621047i
$321$	−59608.7			−0.578495
$322$	−7797.92	−	7797.92i	−0.0752086	−	0.0752086i
$323$	−11688.4	+	11688.4i	−0.112034	+	0.112034i
$324$			16938.9i			0.161360i
$325$	106397.	+	27678.5i	1.00731	+	0.262045i
$326$	−108441.			−1.02037
$327$	679.153	+	679.153i	0.00635144	+	0.00635144i
$328$	15738.9	−	15738.9i	0.146294	−	0.146294i
$329$			87340.3i			0.806906i
$330$	9911.23	−	17312.3i	0.0910122	−	0.158974i
$331$	134180.			1.22471			0.612355	−	0.790583i	$-0.290222\pi$
$331$	134180.			1.22471			0.612355	+	0.790583i	$0.290222\pi$
$332$	−60625.1	−	60625.1i	−0.550017	−	0.550017i
$333$	−43752.1	+	43752.1i	−0.394557	+	0.394557i
$334$		−	50995.0i		−	0.457125i
$335$	131734.	−	35813.7i	1.17384	−	0.319124i
$336$	−14920.6			−0.132162
$337$	−35691.1	−	35691.1i	−0.314268	−	0.314268i	0.532293	−	0.846560i	$-0.321331\pi$
$337$	−35691.1	−	35691.1i	−0.314268	−	0.314268i	−0.846560	+	0.532293i	$0.821331\pi$
$338$	4760.35	−	4760.35i	0.0416683	−	0.0416683i
$339$		−	93518.0i		−	0.813759i
$340$	6101.77	+	22444.3i	0.0527835	+	0.194155i
$341$	51662.4			0.444289
$342$	10660.2	+	10660.2i	0.0911406	+	0.0911406i
$343$	−88794.1	+	88794.1i	−0.754737	+	0.754737i
$344$			40472.7i			0.342015i
$345$	−15784.2	−	9036.37i	−0.132612	−	0.0759200i
$346$	72388.4			0.604668
$347$	82239.1	+	82239.1i	0.682998	+	0.682998i	0.960675	−	0.277677i	$-0.0895644\pi$
$347$	82239.1	+	82239.1i	0.682998	+	0.682998i	−0.277677	+	0.960675i	$0.589564\pi$
$348$	−16750.3	+	16750.3i	−0.138313	+	0.138313i
$349$		−	63602.5i		−	0.522184i	−0.965314	−	0.261092i	$-0.915917\pi$
$349$		−	63602.5i		−	0.522184i	0.965314	−	0.261092i	$-0.0840825\pi$
$350$	−53885.0	+	31637.0i	−0.439878	+	0.258261i
$351$	137478.			1.11588
$352$	−5475.07	−	5475.07i	−0.0441880	−	0.0441880i
$353$	−126451.	+	126451.i	−1.01478	+	1.01478i	−0.0148933	+	0.999889i	$0.504741\pi$
$353$	−126451.	+	126451.i	−1.01478	+	1.01478i	−0.999889	+	0.0148933i	$0.995259\pi$
$354$		−	17861.1i		−	0.142529i
$355$	−6654.91	+	11624.4i	−0.0528063	+	0.0922386i
$356$	−68736.9			−0.542363
$357$	−19171.2	−	19171.2i	−0.150423	−	0.150423i
$358$	−90891.9	+	90891.9i	−0.709185	+	0.709185i
$359$			93543.3i			0.725812i	0.931826	+	0.362906i	$0.118215\pi$
$359$			93543.3i			0.725812i	−0.931826	+	0.362906i	$0.881785\pi$
$360$	20469.8	−	5564.99i	0.157946	−	0.0429397i
$361$	110118.			0.844973
$362$	−7358.50	−	7358.50i	−0.0561529	−	0.0561529i
$363$	59748.8	−	59748.8i	0.453436	−	0.453436i
$364$			49741.1i			0.375416i
$365$	22992.5	+	84574.0i	0.172584	+	0.634821i
$366$	63417.1			0.473418
$367$	−62615.3	−	62615.3i	−0.464888	−	0.464888i	0.435366	−	0.900254i	$-0.356619\pi$
$367$	−62615.3	−	62615.3i	−0.464888	−	0.464888i	−0.900254	+	0.435366i	$0.856619\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$		−	36887.4i		−	0.270910i
$370$	−101255.	−	57968.2i	−0.739629	−	0.423435i
$371$	100388.			0.729348
$372$	−45062.8	−	45062.8i	−0.325636	−	0.325636i
$373$	−184074.	+	184074.i	−1.32305	+	1.32305i	−0.411753	+	0.911295i	$0.635083\pi$
$373$	−184074.	+	184074.i	−1.32305	+	1.32305i	−0.911295	+	0.411753i	$0.864917\pi$
$374$		−	14069.7i		−	0.100587i
$375$	−72068.9	+	73663.9i	−0.512490	+	0.523832i
$376$	55910.4			0.395473
$377$	55841.0	+	55841.0i	0.392889	+	0.392889i
$378$	−55252.4	+	55252.4i	−0.386694	+	0.386694i
$379$			227889.i			1.58651i	0.608886	+	0.793257i	$0.291617\pi$
$379$			227889.i			1.58651i	−0.608886	+	0.793257i	$0.708383\pi$
$380$	−14123.9	+	24670.8i	−0.0978111	+	0.170850i
$381$	115709.			0.797111
$382$	11139.8	+	11139.8i	0.0763395	+	0.0763395i
$383$	−18342.5	+	18342.5i	−0.125044	+	0.125044i	−0.766859	−	0.641815i	$-0.778182\pi$
$383$	−18342.5	+	18342.5i	−0.125044	+	0.125044i	0.641815	+	0.766859i	$0.278182\pi$
$384$			9551.31i			0.0647740i
$385$	36474.8	−	9916.16i	0.246078	−	0.0668994i
$386$	56254.9			0.377560
$387$	47428.1	+	47428.1i	0.316675	+	0.316675i
$388$	100804.	−	100804.i	0.669599	−	0.669599i
$389$			1991.67i			0.0131619i	0.999978	+	0.00658096i	$0.00209480\pi$
$389$			1991.67i			0.0131619i	−0.999978	+	0.00658096i	$0.997905\pi$
$390$	21521.3	+	79162.2i	0.141494	+	0.520461i
$391$	−12827.8			−0.0839070
$392$	18425.0	+	18425.0i	0.119904	+	0.119904i
$393$	74577.6	−	74577.6i	0.482862	−	0.482862i
$394$		−	62089.5i		−	0.399968i
$395$	−89626.4	−	51310.8i	−0.574436	−	0.328863i
$396$	−12832.0			−0.0818281
$397$	98644.9	+	98644.9i	0.625884	+	0.625884i	0.947030	−	0.321146i	$-0.104068\pi$
$397$	98644.9	+	98644.9i	0.625884	+	0.625884i	−0.321146	+	0.947030i	$0.604068\pi$
$398$	47833.3	−	47833.3i	0.301970	−	0.301970i
$399$		−	33137.3i		−	0.208147i
$400$	20252.2	+	34494.2i	0.126576	+	0.215589i
$401$	−15128.5			−0.0940820			−0.0470410	−	0.998893i	$-0.514979\pi$
$401$	−15128.5			−0.0940820			−0.0470410	+	0.998893i	$0.514979\pi$
$402$	72031.3	+	72031.3i	0.445727	+	0.445727i
$403$	−150227.	+	150227.i	−0.924992	+	0.924992i
$404$			40433.1i			0.247727i
$405$	−26299.6	+	45938.5i	−0.160339	+	0.280070i
$406$	−44885.1			−0.272301
$407$	49906.3	+	49906.3i	0.301278	+	0.301278i
$408$	−12272.4	+	12272.4i	−0.0737238	+	0.0737238i
$409$			207979.i			1.24329i	0.783298	+	0.621646i	$0.213536\pi$
$409$			207979.i			1.24329i	−0.783298	+	0.621646i	$0.786464\pi$
$410$	67120.6	−	18247.6i	0.399290	−	0.108552i
$411$	70633.0			0.418142
$412$	−76087.9	−	76087.9i	−0.448251	−	0.448251i
$413$	23930.8	−	23930.8i	0.140300	−	0.140300i
$414$			11699.3i			0.0682589i
$415$	−70288.4	−	258543.i	−0.408119	−	1.50120i
$416$	31841.5			0.183995
$417$	−93633.1	−	93633.1i	−0.538465	−	0.538465i
$418$	12159.7	−	12159.7i	0.0695935	−	0.0695935i
$419$		−	108509.i		−	0.618071i	−0.951050	−	0.309036i	$-0.899994\pi$
$419$		−	108509.i		−	0.618071i	0.951050	−	0.309036i	$-0.100006\pi$
$420$	−40464.8	−	23165.9i	−0.229392	−	0.131326i
$421$	152462.			0.860194			0.430097	−	0.902783i	$-0.358479\pi$
$421$	152462.			0.860194			0.430097	+	0.902783i	$0.358479\pi$
$422$	105192.	+	105192.i	0.590686	+	0.590686i
$423$	65518.7	−	65518.7i	0.366172	−	0.366172i
$424$		−	64262.9i		−	0.357461i
$425$	−18299.3	+	70342.9i	−0.101311	+	0.389442i
$426$	−9994.96			−0.0550759
$427$	84968.0	+	84968.0i	0.466015	+	0.466015i
$428$	−51125.4	+	51125.4i	−0.279093	+	0.279093i
$429$		−	49624.5i		−	0.269639i
$430$	−62838.6	+	109762.i	−0.339852	+	0.593632i
$431$	235938.			1.27012			0.635059	−	0.772464i	$-0.280976\pi$
$431$	235938.			1.27012			0.635059	+	0.772464i	$0.280976\pi$
$432$	35369.5	+	35369.5i	0.189523	+	0.189523i
$433$	−37855.5	+	37855.5i	−0.201908	+	0.201908i	−0.800817	−	0.598909i	$-0.795601\pi$
$433$	−37855.5	+	37855.5i	−0.201908	+	0.201908i	0.598909	+	0.800817i	$0.295601\pi$
$434$		−	120753.i		−	0.641088i
$435$	−71433.8	+	19420.2i	−0.377507	+	0.102630i
$436$	1165.00			0.00612847
$437$	−11086.3	−	11086.3i	−0.0580530	−	0.0580530i
$438$	−46244.4	+	46244.4i	−0.241052	+	0.241052i
$439$			37764.4i			0.195954i	0.995189	+	0.0979768i	$0.0312371\pi$
$439$			37764.4i			0.195954i	−0.995189	+	0.0979768i	$0.968763\pi$
$440$	−6347.77	−	23349.2i	−0.0327881	−	0.120605i
$441$	43182.8			0.222041
$442$	40912.7	+	40912.7i	0.209418	+	0.209418i
$443$	80557.2	−	80557.2i	0.410485	−	0.410485i	−0.471423	−	0.881907i	$-0.656259\pi$
$443$	80557.2	−	80557.2i	0.410485	−	0.410485i	0.881907	+	0.471423i	$0.156259\pi$
$444$		−	87062.0i		−	0.441634i
$445$	−186415.	−	106722.i	−0.941372	−	0.538932i
$446$	−116117.			−0.583748
$447$	25977.6	+	25977.6i	0.130012	+	0.130012i
$448$	−12797.1	+	12797.1i	−0.0637612	+	0.0637612i
$449$			97935.5i			0.485789i	0.970053	+	0.242894i	$0.0780968\pi$
$449$			97935.5i			0.485789i	−0.970053	+	0.242894i	$0.921903\pi$
$450$	64154.7	+	16689.5i	0.316813	+	0.0824172i
$451$	−42076.0			−0.206862
$452$	−80208.8	−	80208.8i	−0.392595	−	0.392595i
$453$	−118706.	+	118706.i	−0.578464	+	0.578464i
$454$		−	14695.0i		−	0.0712948i
$455$	−77228.9	+	134899.i	−0.373041	+	0.651605i
$456$	−21212.6			−0.102015
$457$	−278458.	−	278458.i	−1.33330	−	1.33330i	−0.902402	−	0.430895i	$-0.858198\pi$
$457$	−278458.	−	278458.i	−1.33330	−	1.33330i	−0.430895	−	0.902402i	$-0.641802\pi$
$458$	202560.	−	202560.i	0.965657	−	0.965657i
$459$			90891.6i			0.431418i
$460$	−21288.1	+	5787.46i	−0.100606	+	0.0273509i
$461$	−220655.			−1.03828			−0.519138	−	0.854691i	$-0.673747\pi$
$461$	−220655.			−1.03828			−0.519138	+	0.854691i	$0.673747\pi$
$462$	19944.1	+	19944.1i	0.0934397	+	0.0934397i
$463$	−170047.	+	170047.i	−0.793245	+	0.793245i	−0.982020	−	0.188775i	$-0.939548\pi$
$463$	−170047.	+	170047.i	−0.793245	+	0.793245i	0.188775	+	0.982020i	$0.439548\pi$
$464$			28732.9i			0.133458i
$465$	−52245.5	−	192176.i	−0.241626	−	0.888777i
$466$	−4796.11			−0.0220860
$467$	232244.	+	232244.i	1.06491	+	1.06491i	0.997742	+	0.0671643i	$0.0213952\pi$
$467$	232244.	+	232244.i	1.06491	+	1.06491i	0.0671643	+	0.997742i	$0.478605\pi$
$468$	37313.5	−	37313.5i	0.170363	−	0.170363i
$469$			193019.i			0.877515i
$470$	151630.	+	86807.4i	0.686417	+	0.392972i
$471$	−42371.6			−0.191000
$472$	−15319.2	−	15319.2i	−0.0687625	−	0.0687625i
$473$	54099.4	−	54099.4i	0.241808	−	0.241808i
$474$		−	77063.3i		−	0.342997i
$475$	−76608.5	+	44978.4i	−0.339539	+	0.199350i
$476$	−32885.7			−0.145142
$477$	−75306.7	−	75306.7i	−0.330976	−	0.330976i
$478$	108269.	−	108269.i	0.473859	−	0.473859i
$479$			215924.i			0.941086i	0.882377	+	0.470543i	$0.155942\pi$
$479$			215924.i			0.941086i	−0.882377	+	0.470543i	$0.844058\pi$
$480$	−14829.5	+	25903.3i	−0.0643643	+	0.112427i
$481$	−290241.			−1.25450
$482$	−14583.9	−	14583.9i	−0.0627739	−	0.0627739i
$483$	18183.7	−	18183.7i	0.0779449	−	0.0779449i
$484$		−	102491.i		−	0.437517i
$485$	429892.	−	116872.i	1.82758	−	0.496851i
$486$	139559.			0.590861
$487$	−244390.	−	244390.i	−1.03045	−	1.03045i	−0.999522	−	0.0309271i	$-0.990154\pi$
$487$	−244390.	−	244390.i	−1.03045	−	1.03045i	−0.0309271	−	0.999522i	$-0.509846\pi$
$488$	54391.8	−	54391.8i	0.228399	−	0.228399i
$489$		−	252869.i		−	1.05749i
$490$	21361.8	+	78575.8i	0.0889706	+	0.327263i
$491$	−76961.6			−0.319235			−0.159618	−	0.987179i	$-0.551026\pi$
$491$	−76961.6			−0.319235			−0.159618	+	0.987179i	$0.551026\pi$
$492$	36701.0	+	36701.0i	0.151617	+	0.151617i
$493$	−36918.5	+	36918.5i	−0.151897	+	0.151897i
$494$			70717.1i			0.289781i
$495$	−34800.4	−	19923.1i	−0.142028	−	0.0813105i
$496$	−77299.1			−0.314204
$497$	−13391.5	−	13391.5i	−0.0542147	−	0.0542147i
$498$	141369.	−	141369.i	0.570029	−	0.570029i
$499$		−	14490.0i		−	0.0581926i	−0.999577	−	0.0290963i	$-0.990737\pi$
$499$		−	14490.0i		−	0.0581926i	0.999577	−	0.0290963i	$-0.00926294\pi$
$500$	1368.00	+	124993.i	0.00547199	+	0.499970i
$501$	118913.			0.473757
$502$	21296.0	+	21296.0i	0.0845066	+	0.0845066i
$503$	82880.3	−	82880.3i	0.327578	−	0.327578i	−0.524087	−	0.851665i	$-0.675593\pi$
$503$	82880.3	−	82880.3i	0.327578	−	0.327578i	0.851665	+	0.524087i	$0.175593\pi$
$504$			29992.7i			0.118074i
$505$	−62777.0	+	109655.i	−0.246160	+	0.429977i
$506$	13344.9			0.0521214
$507$	11100.5	+	11100.5i	0.0431844	+	0.0431844i
$508$	99242.1	−	99242.1i	0.384564	−	0.384564i
$509$			179121.i			0.691370i	0.938351	+	0.345685i	$0.112353\pi$
$509$			179121.i			0.691370i	−0.938351	+	0.345685i	$0.887647\pi$
$510$	−52337.0	+	14228.5i	−0.201219	+	0.0547040i
$511$	−123919.			−0.474566
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−78552.5	+	78552.5i	−0.298487	+	0.298487i
$514$		−	34404.3i		−	0.130223i
$515$	−88215.9	−	324487.i	−0.332608	−	1.22344i
$516$	−94376.9			−0.354459
$517$	−74734.7	−	74734.7i	−0.279603	−	0.279603i
$518$	116648.	−	116648.i	0.434729	−	0.434729i
$519$			168800.i			0.626668i
$520$	86354.5	+	49437.6i	0.319358	+	0.182831i
$521$	−277840.			−1.02358			−0.511788	−	0.859112i	$-0.671017\pi$
$521$	−277840.			−1.02358			−0.511788	+	0.859112i	$0.671017\pi$
$522$	33670.7	+	33670.7i	0.123570	+	0.123570i
$523$	4303.41	−	4303.41i	0.0157329	−	0.0157329i	−0.699197	−	0.714929i	$-0.746459\pi$
$523$	4303.41	−	4303.41i	0.0157329	−	0.0157329i	0.714929	+	0.699197i	$0.246459\pi$
$524$		−	127928.i		−	0.465910i
$525$	−73773.1	−	125653.i	−0.267657	−	0.455882i
$526$	242661.			0.877057
$527$	−99320.6	−	99320.6i	−0.357617	−	0.357617i
$528$	12767.1	−	12767.1i	0.0457958	−	0.0457958i
$529$		−	12167.0i		−	0.0434783i
$530$	99775.7	−	174282.i	0.355200	−	0.620440i
$531$	−35903.7			−0.127336
$532$	−28421.3	−	28421.3i	−0.100420	−	0.100420i
$533$	122351.	−	122351.i	0.430679	−	0.430679i
$534$		−	160285.i		−	0.562096i
$535$	−218031.	+	59274.5i	−0.761746	+	0.207091i
$536$	123560.			0.430079
$537$	−211948.	−	211948.i	−0.734988	−	0.734988i
$538$	200481.	−	200481.i	0.692642	−	0.692642i
$539$		−	49256.9i		−	0.169547i
$540$	41007.2	+	150838.i	0.140628	+	0.517276i
$541$	−287938.			−0.983794			−0.491897	−	0.870653i	$-0.663696\pi$
$541$	−287938.			−0.983794			−0.491897	+	0.870653i	$0.663696\pi$
$542$	−147315.	−	147315.i	−0.501472	−	0.501472i
$543$	17159.0	−	17159.0i	0.0581959	−	0.0581959i
$544$			21051.6i			0.0711356i
$545$	3159.48	+	1808.79i	0.0106371	+	0.00608970i
$546$	−115990.			−0.389075
$547$	313350.	+	313350.i	1.04726	+	1.04726i	0.998826	+	0.0484353i	$0.0154235\pi$
$547$	313350.	+	313350.i	1.04726	+	1.04726i	0.0484353	+	0.998826i	$0.484577\pi$
$548$	60580.7	−	60580.7i	0.201731	−	0.201731i
$549$		−	127478.i		−	0.422953i
$550$	19037.1	−	73178.8i	0.0629324	−	0.241913i
$551$	−63813.2			−0.210188
$552$	−11640.2	−	11640.2i	−0.0382016	−	0.0382016i
$553$	103252.	−	103252.i	0.337634	−	0.337634i
$554$		−	242079.i		−	0.788747i
$555$	135174.	−	236113.i	0.438841	−	0.766539i
$556$	−160615.			−0.519561
$557$	−159935.	−	159935.i	−0.515505	−	0.515505i	0.400703	−	0.916208i	$-0.368766\pi$
$557$	−159935.	−	159935.i	−0.515505	−	0.515505i	−0.916208	+	0.400703i	$0.868766\pi$
$558$	−90583.2	+	90583.2i	−0.290924	+	0.290924i
$559$			314627.i			1.00687i
$560$	−54575.0	+	14836.9i	−0.174027	+	0.0473116i
$561$	32808.6			0.104247
$562$	−34842.0	−	34842.0i	−0.110314	−	0.110314i
$563$	243163.	−	243163.i	0.767149	−	0.767149i	−0.210454	−	0.977604i	$-0.567494\pi$
$563$	243163.	−	243163.i	0.767149	−	0.767149i	0.977604	+	0.210454i	$0.0674943\pi$
$564$			130375.i			0.409862i
$565$	−92993.7	−	342061.i	−0.291311	−	1.07153i
$566$	20891.6			0.0652139
$567$	−52922.1	−	52922.1i	−0.164616	−	0.164616i
$568$	−8572.51	+	8572.51i	−0.0265712	+	0.0265712i
$569$			576729.i			1.78134i	0.454647	+	0.890672i	$0.349765\pi$
$569$			576729.i			1.78134i	−0.454647	+	0.890672i	$0.650235\pi$
$570$	−57528.9	−	32935.1i	−0.177066	−	0.101370i
$571$	−287622.			−0.882164			−0.441082	−	0.897467i	$-0.645405\pi$
$571$	−287622.			−0.882164			−0.441082	+	0.897467i	$0.645405\pi$
$572$	−42562.1	−	42562.1i	−0.130086	−	0.130086i
$573$	−25976.4	+	25976.4i	−0.0791170	+	0.0791170i
$574$			98346.1i			0.298492i
$575$	−66719.4	−	17356.7i	−0.201798	−	0.0524966i
$576$	19199.6			0.0578693
$577$	−223235.	−	223235.i	−0.670517	−	0.670517i	0.287318	−	0.957835i	$-0.407236\pi$
$577$	−223235.	−	223235.i	−0.670517	−	0.670517i	−0.957835	+	0.287318i	$0.907236\pi$
$578$	139993.	−	139993.i	0.419036	−	0.419036i
$579$			131179.i			0.391297i
$580$	−44611.2	+	77924.0i	−0.132613	+	0.231641i
$581$	378821.			1.12223
$582$	235062.	+	235062.i	0.693962	+	0.693962i
$583$	−85899.4	+	85899.4i	−0.252728	+	0.252728i
$584$			79326.0i			0.232589i
$585$	159128.	−	43261.1i	0.464982	−	0.126411i
$586$	−244336.			−0.711529
$587$	396735.	+	396735.i	1.15139	+	1.15139i	0.986273	+	0.165120i	$0.0528012\pi$
$587$	396735.	+	396735.i	1.15139	+	1.15139i	0.165120	+	0.986273i	$0.447199\pi$
$588$	−42964.6	+	42964.6i	−0.124267	+	0.124267i
$589$		−	171674.i		−	0.494852i
$590$	−17761.0	−	65330.7i	−0.0510227	−	0.187678i
$591$	144784.			0.414521
$592$	−74671.6	−	74671.6i	−0.213065	−	0.213065i
$593$	−31678.1	+	31678.1i	−0.0900843	+	0.0900843i	−0.750713	−	0.660629i	$-0.770290\pi$
$593$	−31678.1	+	31678.1i	−0.0900843	+	0.0900843i	0.660629	+	0.750713i	$0.270290\pi$
$594$		−	94556.0i		−	0.267988i
$595$	−89186.4	−	51058.9i	−0.251921	−	0.144224i
$596$	44561.1			0.125448
$597$	111541.	+	111541.i	0.312957	+	0.312957i
$598$	−38805.2	+	38805.2i	−0.108515	+	0.108515i
$599$			25172.7i			0.0701578i	0.999385	+	0.0350789i	$0.0111683\pi$
$599$			25172.7i			0.0701578i	−0.999385	+	0.0350789i	$0.988832\pi$
$600$	−80435.7	+	47225.4i	−0.223433	+	0.131182i
$601$	146403.			0.405324			0.202662	−	0.979249i	$-0.435041\pi$
$601$	146403.			0.405324			0.202662	+	0.979249i	$0.435041\pi$
$602$	−126449.	−	126449.i	−0.348917	−	0.348917i
$603$	144794.	−	144794.i	0.398214	−	0.398214i
$604$			203624.i			0.558156i
$605$	159129.	−	277957.i	0.434750	−	0.759393i
$606$	−94284.4			−0.256741
$607$	94409.0	+	94409.0i	0.256234	+	0.256234i	0.823520	−	0.567287i	$-0.192007\pi$
$607$	94409.0	+	94409.0i	0.256234	+	0.256234i	−0.567287	+	0.823520i	$0.692007\pi$
$608$	−18193.7	+	18193.7i	−0.0492169	+	0.0492169i
$609$		−	104666.i		−	0.282209i
$610$	231961.	−	63061.6i	0.623383	−	0.169475i
$611$	434636.			1.16424
$612$	24669.4	+	24669.4i	0.0658650	+	0.0658650i
$613$	377419.	−	377419.i	1.00439	−	1.00439i	0.00440021	−	0.999990i	$-0.498599\pi$
$613$	377419.	−	377419.i	1.00439	−	1.00439i	0.999990	−	0.00440021i	$-0.00140064\pi$
$614$		−	172967.i		−	0.458804i
$615$	42550.9	+	156516.i	0.112502	+	0.413817i
$616$	34211.5			0.0901594
$617$	−258016.	−	258016.i	−0.677759	−	0.677759i	0.281733	−	0.959493i	$-0.409091\pi$
$617$	−258016.	−	258016.i	−0.677759	−	0.677759i	−0.959493	+	0.281733i	$0.909091\pi$
$618$	177427.	−	177427.i	0.464560	−	0.464560i
$619$		−	142371.i		−	0.371569i	−0.982591	−	0.185784i	$-0.940517\pi$
$619$		−	142371.i		−	0.371569i	0.982591	−	0.185784i	$-0.0594826\pi$
$620$	−209636.	−	120016.i	−0.545359	−	0.312216i
$621$	−86209.6			−0.223549
$622$	26733.9	+	26733.9i	0.0691005	+	0.0691005i
$623$	214754.	−	214754.i	0.553307	−	0.553307i
$624$			74250.0i			0.190690i
$625$	−190355.	+	341105.i	−0.487310	+	0.873229i
$626$	−481208.			−1.22796
$627$	28354.7	+	28354.7i	0.0721256	+	0.0721256i
$628$	−36341.4	+	36341.4i	−0.0921472	+	0.0921472i
$629$		−	191889.i		−	0.485008i
$630$	−46567.1	+	81340.5i	−0.117327	+	0.204939i
$631$	−164037.			−0.411988			−0.205994	−	0.978553i	$-0.566043\pi$
$631$	−164037.			−0.411988			−0.205994	+	0.978553i	$0.566043\pi$
$632$	−66095.9	−	66095.9i	−0.165478	−	0.165478i
$633$	−245293.	+	245293.i	−0.612177	+	0.612177i
$634$			425841.i			1.05942i
$635$	423230.	−	115061.i	1.04961	−	0.285351i
$636$	149852.			0.370467
$637$	143232.	+	143232.i	0.352990	+	0.352990i
$638$	38406.9	−	38406.9i	0.0943557	−	0.0943557i
$639$			20091.4i			0.0492050i
$640$	9497.76	+	34935.8i	0.0231879	+	0.0852926i
$641$	1611.31			0.00392160			0.00196080	−	0.999998i	$-0.499376\pi$
$641$	1611.31			0.00392160			0.00196080	+	0.999998i	$0.499376\pi$
$642$	−119217.	−	119217.i	−0.289248	−	0.289248i
$643$	−340836.	+	340836.i	−0.824372	+	0.824372i	−0.986732	−	0.162360i	$-0.948090\pi$
$643$	−340836.	+	340836.i	−0.824372	+	0.824372i	0.162360	+	0.986732i	$0.448090\pi$
$644$		−	31191.7i		−	0.0752086i
$645$	−255951.	−	146531.i	−0.615230	−	0.352217i
$646$	−46753.7			−0.112034
$647$	427266.	+	427266.i	1.02068	+	1.02068i	0.999782	+	0.0208983i	$0.00665262\pi$
$647$	427266.	+	427266.i	1.02068	+	1.02068i	0.0208983	+	0.999782i	$0.493347\pi$
$648$	−33877.8	+	33877.8i	−0.0806798	+	0.0806798i
$649$			40954.0i			0.0972314i
$650$	157437.	+	268151.i	0.372631	+	0.634677i
$651$	281579.			0.664413
$652$	−216881.	−	216881.i	−0.510184	−	0.510184i
$653$	404699.	−	404699.i	0.949086	−	0.949086i	−0.0496792	−	0.998765i	$-0.515820\pi$
$653$	404699.	−	404699.i	0.949086	−	0.949086i	0.998765	+	0.0496792i	$0.0158199\pi$
$654$			2716.61i			0.00635144i
$655$	198623.	−	346942.i	0.462963	−	0.808675i
$656$	62955.6			0.146294
$657$	92958.4	+	92958.4i	0.215356	+	0.215356i
$658$	−174681.	+	174681.i	−0.403453	+	0.403453i
$659$			158812.i			0.365690i	0.983142	+	0.182845i	$0.0585306\pi$
$659$			158812.i			0.365690i	−0.983142	+	0.182845i	$0.941469\pi$
$660$	54447.0	−	14802.1i	0.124993	−	0.0339810i
$661$	−245185.			−0.561164			−0.280582	−	0.959830i	$-0.590528\pi$
$661$	−245185.			−0.561164			−0.280582	+	0.959830i	$0.590528\pi$
$662$	268361.	+	268361.i	0.612355	+	0.612355i
$663$	−95402.9	+	95402.9i	−0.217037	+	0.217037i
$664$		−	242500.i		−	0.550017i
$665$	−32951.5	−	121206.i	−0.0745129	−	0.274082i
$666$	−175008.			−0.394557
$667$	−35016.8	−	35016.8i	−0.0787090	−	0.0787090i
$668$	101990.	−	101990.i	0.228562	−	0.228562i
$669$		−	270768.i		−	0.604987i
$670$	335096.	+	191841.i	0.746483	+	0.427359i
$671$	−145410.			−0.322960
$672$	−29841.1	−	29841.1i	−0.0660810	−	0.0660810i
$673$	370502.	−	370502.i	0.818013	−	0.818013i	−0.167807	−	0.985820i	$-0.553669\pi$
$673$	370502.	−	370502.i	0.818013	−	0.818013i	0.985820	+	0.167807i	$0.0536686\pi$
$674$		−	142764.i		−	0.314268i
$675$	−122981.	+	472742.i	−0.269918	+	1.03757i
$676$	19041.4			0.0416683
$677$	101209.	+	101209.i	0.220821	+	0.220821i	0.808844	−	0.588023i	$-0.200094\pi$
$677$	101209.	+	101209.i	0.220821	+	0.220821i	−0.588023	+	0.808844i	$0.700094\pi$
$678$	187036.	−	187036.i	0.406880	−	0.406880i
$679$			629884.i			1.36622i
$680$	−32685.0	+	57092.1i	−0.0706856	+	0.123469i
$681$	34266.8			0.0738888
$682$	103325.	+	103325.i	0.222145	+	0.222145i
$683$	116405.	−	116405.i	0.249534	−	0.249534i	−0.571245	−	0.820779i	$-0.693539\pi$
$683$	116405.	−	116405.i	0.249534	−	0.249534i	0.820779	+	0.571245i	$0.193539\pi$
$684$			42640.7i			0.0911406i
$685$	258354.	−	70237.0i	0.550598	−	0.149687i
$686$	−355176.			−0.754737
$687$	472343.	+	472343.i	1.00079	+	1.00079i
$688$	−80945.5	+	80945.5i	−0.171008	+	0.171008i
$689$		−	499567.i		−	1.05234i
$690$	−13495.6	−	49641.1i	−0.0283461	−	0.104266i
$691$	−323661.			−0.677852			−0.338926	−	0.940813i	$-0.610064\pi$
$691$	−323661.			−0.677852			−0.338926	+	0.940813i	$0.610064\pi$
$692$	144777.	+	144777.i	0.302334	+	0.302334i
$693$	40090.8	−	40090.8i	0.0834793	−	0.0834793i
$694$			328956.i			0.682998i
$695$	−435590.	−	249374.i	−0.901796	−	0.516275i
$696$	−67001.2			−0.138313
$697$	80890.9	+	80890.9i	0.166508	+	0.166508i
$698$	127205.	−	127205.i	0.261092	−	0.261092i
$699$		−	11183.9i		−	0.0228896i
$700$	−171044.	−	44496.1i	−0.349069	−	0.0908084i
$701$	233087.			0.474332			0.237166	−	0.971469i	$-0.423782\pi$
$701$	233087.			0.474332			0.237166	+	0.971469i	$0.423782\pi$
$702$	274955.	+	274955.i	0.557941	+	0.557941i
$703$	165839.	−	165839.i	0.335565	−	0.335565i
$704$		−	21900.3i		−	0.0441880i
$705$	−202423.	+	353580.i	−0.407269	+	0.711392i
$706$	−505804.			−1.01478
$707$	−126325.	−	126325.i	−0.252726	−	0.252726i
$708$	35722.3	−	35722.3i	0.0712644	−	0.0712644i
$709$			557827.i			1.10970i	0.831949	+	0.554852i	$0.187225\pi$
$709$			557827.i			1.10970i	−0.831949	+	0.554852i	$0.812775\pi$
$710$	−36558.6	+	9938.92i	−0.0725224	+	0.0197162i
$711$	−154909.			−0.306435
$712$	−137474.	−	137474.i	−0.271181	−	0.271181i
$713$	94204.4	−	94204.4i	0.185307	−	0.185307i
$714$		−	76685.0i		−	0.150423i
$715$	−49346.3	−	181512.i	−0.0965256	−	0.355052i
$716$	−363568.			−0.709185
$717$	252469.	+	252469.i	0.491099	+	0.491099i
$718$	−187087.	+	187087.i	−0.362906	+	0.362906i
$719$			509896.i			0.986333i	0.869935	+	0.493166i	$0.164161\pi$
$719$			509896.i			0.986333i	−0.869935	+	0.493166i	$0.835839\pi$
$720$	52069.6	+	29809.7i	0.100443	+	0.0575032i
$721$	475443.			0.914592
$722$	220235.	+	220235.i	0.422486	+	0.422486i
$723$	34007.6	−	34007.6i	0.0650578	−	0.0650578i
$724$		−	29434.0i		−	0.0561529i
$725$	−241972.	+	142067.i	−0.460351	+	0.270281i
$726$	238995.			0.453436
$727$	−230319.	−	230319.i	−0.435774	−	0.435774i	0.454813	−	0.890587i	$-0.349706\pi$
$727$	−230319.	−	230319.i	−0.435774	−	0.435774i	−0.890587	+	0.454813i	$0.849706\pi$
$728$	−99482.3	+	99482.3i	−0.187708	+	0.187708i
$729$			496939.i			0.935078i
$730$	−123163.	+	215133.i	−0.231118	+	0.403703i
$731$	−208011.			−0.389271
$732$	126834.	+	126834.i	0.236709	+	0.236709i
$733$	−220700.	+	220700.i	−0.410766	+	0.410766i	−0.882005	−	0.471240i	$-0.843807\pi$
$733$	−220700.	+	220700.i	−0.410766	+	0.410766i	0.471240	+	0.882005i	$0.343807\pi$
$734$		−	250461.i		−	0.464888i
$735$	−183228.	+	49812.9i	−0.339170	+	0.0922077i
$736$	−19967.2			−0.0368605
$737$	−165161.	−	165161.i	−0.304070	−	0.304070i
$738$	73774.7	−	73774.7i	0.135455	−	0.135455i
$739$		−	118916.i		−	0.217746i	−0.994056	−	0.108873i	$-0.965276\pi$
$739$		−	118916.i		−	0.217746i	0.994056	−	0.108873i	$-0.0347242\pi$
$740$	−86573.9	−	318447.i	−0.158097	−	0.581532i
$741$	−164903.			−0.300325
$742$	200776.	+	200776.i	0.364674	+	0.364674i
$743$	−246622.	+	246622.i	−0.446739	+	0.446739i	−0.894269	−	0.447530i	$-0.852304\pi$
$743$	−246622.	+	246622.i	−0.446739	+	0.446739i	0.447530	+	0.894269i	$0.352304\pi$
$744$		−	180251.i		−	0.325636i
$745$	120850.	+	69186.3i	0.217738	+	0.124654i
$746$	−736298.			−1.32305
$747$	−284175.	−	284175.i	−0.509265	−	0.509265i
$748$	28139.4	−	28139.4i	0.0502935	−	0.0502935i
$749$		−	319462.i		−	0.569450i
$750$	−291466.	+	3189.99i	−0.518161	+	0.00567109i
$751$	−785884.			−1.39341			−0.696704	−	0.717358i	$-0.745351\pi$
$751$	−785884.			−1.39341			−0.696704	+	0.717358i	$0.745351\pi$
$752$	111821.	+	111821.i	0.197736	+	0.197736i
$753$	−49659.4	+	49659.4i	−0.0875813	+	0.0875813i
$754$			223364.i			0.392889i
$755$	−316151.	+	552232.i	−0.554626	+	0.968785i
$756$	−221010.			−0.386694
$757$	10653.9	+	10653.9i	0.0185916	+	0.0185916i	0.716341	−	0.697750i	$-0.245815\pi$
$757$	10653.9	+	10653.9i	0.0185916	+	0.0185916i	−0.697750	+	0.716341i	$0.745815\pi$
$758$	−455777.	+	455777.i	−0.793257	+	0.793257i
$759$			31118.6i			0.0540177i
$760$	−77589.4	+	21093.7i	−0.134331	+	0.0365195i
$761$	−394139.			−0.680581			−0.340290	−	0.940320i	$-0.610525\pi$
$761$	−394139.			−0.680581			−0.340290	+	0.940320i	$0.610525\pi$
$762$	231419.	+	231419.i	0.398556	+	0.398556i
$763$	−3639.80	+	3639.80i	−0.00625213	+	0.00625213i
$764$			44559.0i			0.0763395i
$765$	28601.5	+	105206.i	0.0488727	+	0.179770i
$766$	−73370.1			−0.125044
$767$	−119088.	−	119088.i	−0.202432	−	0.202432i
$768$	−19102.6	+	19102.6i	−0.0323870	+	0.0323870i
$769$		−	119699.i		−	0.202412i	−0.994865	−	0.101206i	$-0.967730\pi$
$769$		−	119699.i		−	0.202412i	0.994865	−	0.101206i	$-0.0322701\pi$
$770$	92782.0	+	53117.4i	0.156488	+	0.0895891i
$771$	80226.2			0.134961
$772$	112510.	+	112510.i	0.188780	+	0.188780i
$773$	229621.	−	229621.i	0.384285	−	0.384285i	−0.488358	−	0.872643i	$-0.662404\pi$
$773$	229621.	−	229621.i	0.384285	−	0.384285i	0.872643	+	0.488358i	$0.162404\pi$
$774$			189712.i			0.316675i
$775$	−382197.	−	650969.i	−0.636332	−	1.08382i
$776$	403217.			0.669599
$777$	272008.	+	272008.i	0.450546	+	0.450546i
$778$	−3983.35	+	3983.35i	−0.00658096	+	0.00658096i
$779$			139819.i			0.230404i
$780$	−115282.	+	201367.i	−0.189484	+	0.330978i
$781$	22917.5			0.0375721
$782$	−25655.6	−	25655.6i	−0.0419535	−	0.0419535i
$783$	−248112.	+	248112.i	−0.404692	+	0.404692i
$784$			73700.0i			0.119904i
$785$	−154982.	+	42134.0i	−0.251503	+	0.0683744i
$786$	298310.			0.482862
$787$	−855733.	−	855733.i	−1.38162	−	1.38162i	−0.841745	−	0.539875i	$-0.818471\pi$
$787$	−855733.	−	855733.i	−1.38162	−	1.38162i	−0.539875	−	0.841745i	$-0.681529\pi$
$788$	124179.	−	124179.i	0.199984	−	0.199984i
$789$			565851.i			0.908967i
$790$	−76631.2	−	281874.i	−0.122787	−	0.451649i
$791$	501192.			0.801035
$792$	−25663.9	−	25663.9i	−0.0409141	−	0.0409141i
$793$	422831.	−	422831.i	0.672389	−	0.672389i
$794$			394580.i			0.625884i
$795$	406401.	+	232663.i	0.643015	+	0.368123i
$796$	191333.			0.301970
$797$	−553344.	−	553344.i	−0.871122	−	0.871122i	0.121473	−	0.992595i	$-0.461238\pi$
$797$	−553344.	−	553344.i	−0.871122	−	0.871122i	−0.992595	+	0.121473i	$0.961238\pi$
$798$	66274.5	−	66274.5i	0.104074	−	0.104074i
$799$			287354.i			0.450115i
$800$	−28483.9	+	109493.i	−0.0445061	+	0.171082i
$801$	−322198.			−0.502178
$802$	−30257.0	−	30257.0i	−0.0470410	−	0.0470410i
$803$	106034.	−	106034.i	0.164443	−	0.164443i
$804$			288125.i			0.445727i
$805$	48428.8	−	84592.2i	0.0747328	−	0.130539i
$806$	−600908.			−0.924992
$807$	467495.	+	467495.i	0.717843	+	0.717843i
$808$	−80866.1	+	80866.1i	−0.123864	+	0.123864i
$809$			872153.i			1.33259i	0.745690	+	0.666293i	$0.232120\pi$
$809$			872153.i			1.33259i	−0.745690	+	0.666293i	$0.767880\pi$
$810$	−144476.	+	39277.7i	−0.220204	+	0.0598655i
$811$	471012.			0.716128			0.358064	−	0.933697i	$-0.383437\pi$
$811$	471012.			0.716128			0.358064	+	0.933697i	$0.383437\pi$
$812$	−89770.1	−	89770.1i	−0.136151	−	0.136151i
$813$	343517.	−	343517.i	0.519718	−	0.519718i
$814$			199625.i			0.301278i
$815$	−251451.	−	924918.i	−0.378563	−	1.39248i
$816$	−49089.4			−0.0737238
$817$	−179773.	−	179773.i	−0.269327	−	0.269327i
$818$	−415958.	+	415958.i	−0.621646	+	0.621646i
$819$			233157.i			0.347601i
$820$	170736.	+	97746.0i	0.253921	+	0.145369i
$821$	−382604.			−0.567628			−0.283814	−	0.958879i	$-0.591600\pi$
$821$	−382604.			−0.567628			−0.283814	+	0.958879i	$0.591600\pi$
$822$	141266.	+	141266.i	0.209071	+	0.209071i
$823$	372527.	−	372527.i	0.549994	−	0.549994i	−0.376445	−	0.926439i	$-0.622854\pi$
$823$	372527.	−	372527.i	0.549994	−	0.549994i	0.926439	+	0.376445i	$0.122854\pi$
$824$		−	304352.i		−	0.448251i
$825$	170643.	+	44391.8i	0.250715	+	0.0652222i
$826$	95723.4			0.140300
$827$	807954.	+	807954.i	1.18134	+	1.18134i	0.979397	+	0.201945i	$0.0647263\pi$
$827$	807954.	+	807954.i	1.18134	+	1.18134i	0.201945	+	0.979397i	$0.435274\pi$
$828$	−23398.6	+	23398.6i	−0.0341294	+	0.0341294i
$829$		−	634241.i		−	0.922880i	−0.887172	−	0.461440i	$-0.847333\pi$
$829$		−	634241.i		−	0.922880i	0.887172	−	0.461440i	$-0.152667\pi$
$830$	376510.	−	657663.i	0.546538	−	0.954657i
$831$	564496.			0.817445
$832$	63683.0	+	63683.0i	0.0919976	+	0.0919976i
$833$	−94696.1	+	94696.1i	−0.136472	+	0.136472i
$834$		−	374532.i		−	0.538465i
$835$	434949.	−	118247.i	0.623829	−	0.169596i
$836$	48638.6			0.0695935
$837$	−667488.	−	667488.i	−0.952780	−	0.952780i
$838$	217018.	−	217018.i	0.309036	−	0.309036i
$839$			454249.i			0.645313i	0.946516	+	0.322656i	$0.104576\pi$
$839$			454249.i			0.645313i	−0.946516	+	0.322656i	$0.895424\pi$
$840$	−34597.7	−	127261.i	−0.0490330	−	0.180359i
$841$	505724.			0.715025
$842$	304923.	+	304923.i	0.430097	+	0.430097i
$843$	81246.7	−	81246.7i	0.114327	−	0.114327i
$844$			420767.i			0.590686i
$845$	51640.5	+	29564.0i	0.0723231	+	0.0414047i
$846$	262075.			0.366172
$847$	320213.	+	320213.i	0.446346	+	0.446346i
$848$	128526.	−	128526.i	0.178730	−	0.178730i
$849$			48716.5i			0.0675866i
$850$	−177284.	+	104087.i	−0.245376	+	0.144065i
$851$	182005.			0.251318
$852$	−19989.9	−	19989.9i	−0.0275380	−	0.0275380i
$853$	−468758.	+	468758.i	−0.644244	+	0.644244i	−0.951596	−	0.307352i	$-0.900557\pi$
$853$	−468758.	+	468758.i	−0.644244	+	0.644244i	0.307352	+	0.951596i	$0.400557\pi$
$854$			339872.i			0.466015i
$855$	−66204.6	+	115642.i	−0.0905641	+	0.158192i
$856$	−204502.			−0.279093
$857$	749030.	+	749030.i	1.01985	+	1.01985i	0.999799	+	0.0200546i	$0.00638402\pi$
$857$	749030.	+	749030.i	1.01985	+	1.01985i	0.0200546	+	0.999799i	$0.493616\pi$
$858$	99249.1	−	99249.1i	0.134819	−	0.134819i
$859$		−	1.01362e6i		−	1.37370i	−0.726801	−	0.686848i	$-0.758994\pi$
$859$		−	1.01362e6i		−	1.37370i	0.726801	−	0.686848i	$-0.241006\pi$
$860$	−345202.	+	93847.7i	−0.466742	+	0.126890i
$861$	−229330.			−0.309353
$862$	471877.	+	471877.i	0.635059	+	0.635059i
$863$	504686.	−	504686.i	0.677641	−	0.677641i	−0.281825	−	0.959466i	$-0.590940\pi$
$863$	504686.	−	504686.i	0.677641	−	0.677641i	0.959466	+	0.281825i	$0.0909398\pi$
$864$			141478.i			0.189523i
$865$	167853.	+	617419.i	0.224336	+	0.825179i
$866$	−151422.			−0.201908
$867$	326445.	+	326445.i	0.434282	+	0.434282i
$868$	241505.	−	241505.i	0.320544	−	0.320544i
$869$			176699.i			0.233989i
$870$	−181708.	−	104027.i	−0.240069	−	0.137439i
$871$	960531.			1.26612
$872$	2329.99	+	2329.99i	0.00306423	+	0.00306423i
$873$	472511.	−	472511.i	0.619988	−	0.619988i
$874$		−	44345.3i		−	0.0580530i
$875$	−394788.	−	386240.i	−0.515641	−	0.504476i
$876$	−184977.			−0.241052
$877$	744464.	+	744464.i	0.967932	+	0.967932i	0.999502	−	0.0315697i	$-0.0100506\pi$
$877$	744464.	+	744464.i	0.967932	+	0.967932i	−0.0315697	+	0.999502i	$0.510051\pi$
$878$	−75528.8	+	75528.8i	−0.0979768	+	0.0979768i
$879$		−	569758.i		−	0.737417i
$880$	34002.8	−	59393.8i	0.0439085	−	0.0766966i
$881$	702725.			0.905386			0.452693	−	0.891666i	$-0.350463\pi$
$881$	702725.			0.905386			0.452693	+	0.891666i	$0.350463\pi$
$882$	86365.5	+	86365.5i	0.111021	+	0.111021i
$883$	−166088.	+	166088.i	−0.213018	+	0.213018i	−0.805548	−	0.592530i	$-0.798129\pi$
$883$	−166088.	+	166088.i	−0.213018	+	0.213018i	0.592530	+	0.805548i	$0.298129\pi$
$884$			163651.i			0.209418i
$885$	152342.	−	41416.2i	0.194506	−	0.0528791i
$886$	322229.			0.410485
$887$	−576103.	−	576103.i	−0.732238	−	0.732238i	0.238824	−	0.971063i	$-0.423238\pi$
$887$	−576103.	−	576103.i	−0.732238	−	0.732238i	−0.971063	+	0.238824i	$0.923238\pi$
$888$	174124.	−	174124.i	0.220817	−	0.220817i
$889$			620123.i			0.784647i
$890$	−159386.	−	586274.i	−0.201220	−	0.740152i
$891$	90568.0			0.114083
$892$	−232234.	−	232234.i	−0.291874	−	0.291874i
$893$	−248344.	+	248344.i	−0.311423	+	0.311423i
$894$			103910.i			0.130012i
$895$	−986000.	−	564481.i	−1.23092	−	0.704699i
$896$	−51188.5			−0.0637612
$897$	−90488.5	−	90488.5i	−0.112463	−	0.112463i
$898$	−195871.	+	195871.i	−0.242894	+	0.242894i
$899$		−	542243.i		−	0.670926i
$900$	94930.4	+	161688.i	0.117198	+	0.199615i
$901$	330282.			0.406851
$902$	−84152.0	−	84152.0i	−0.103431	−	0.103431i
$903$	294861.	−	294861.i	0.361612	−	0.361612i
$904$		−	320835.i		−	0.392595i
$905$	45699.7	−	79825.3i	0.0557977	−	0.0974638i
$906$	−474824.			−0.578464
$907$	−947695.	−	947695.i	−1.15200	−	1.15200i	−0.986150	−	0.165853i	$-0.946962\pi$
$907$	−947695.	−	947695.i	−1.15200	−	1.15200i	−0.165853	−	0.986150i	$-0.553038\pi$
$908$	29390.0	−	29390.0i	0.0356474	−	0.0356474i
$909$			189526.i			0.229373i
$910$	−424255.	+	115339.i	−0.512323	+	0.139282i
$911$	774755.			0.933529			0.466764	−	0.884382i	$-0.345420\pi$
$911$	774755.			0.933529			0.466764	+	0.884382i	$0.345420\pi$
$912$	−42425.2	−	42425.2i	−0.0510076	−	0.0510076i
$913$	−324147.	+	324147.i	−0.388867	+	0.388867i
$914$		−	1.11383e6i		−	1.33330i
$915$	147051.	+	540901.i	0.175641	+	0.646064i
$916$	810240.			0.965657
$917$	399685.	+	399685.i	0.475312	+	0.475312i
$918$	−181783.	+	181783.i	−0.215709	+	0.215709i
$919$		−	1.02993e6i		−	1.21949i	−0.792598	−	0.609745i	$-0.791272\pi$
$919$		−	1.02993e6i		−	1.21949i	0.792598	−	0.609745i	$-0.208728\pi$
$920$	−54151.2	−	31001.4i	−0.0639783	−	0.0366273i
$921$	403336.			0.475497
$922$	−441311.	−	441311.i	−0.519138	−	0.519138i
$923$	−66641.0	+	66641.0i	−0.0782236	+	0.0782236i
$924$			79776.6i			0.0934397i
$925$	259636.	−	998047.i	0.303446	−	1.16645i
$926$	−680189.			−0.793245
$927$	−356655.	−	356655.i	−0.415039	−	0.415039i
$928$	−57465.8	+	57465.8i	−0.0667288	+	0.0667288i
$929$			534769.i			0.619634i	0.950796	+	0.309817i	$0.100268\pi$
$929$			534769.i			0.619634i	−0.950796	+	0.309817i	$0.899732\pi$
$930$	279861.	−	488843.i	0.323576	−	0.565202i
$931$	−163681.			−0.188842
$932$	−9592.22	−	9592.22i	−0.0110430	−	0.0110430i
$933$	−62339.8	+	62339.8i	−0.0716147	+	0.0716147i
$934$			928977.i			1.06491i
$935$	120004.	−	32624.7i	0.137269	−	0.0373184i
$936$	149254.			0.170363
$937$	175076.	+	175076.i	0.199410	+	0.199410i	0.799747	−	0.600337i	$-0.204967\pi$
$937$	175076.	+	175076.i	0.199410	+	0.199410i	−0.600337	+	0.799747i	$0.704967\pi$
$938$	−386038.	+	386038.i	−0.438758	+	0.438758i
$939$		−	1.12211e6i		−	1.27264i
$940$	129644.	+	476874.i	0.146723	+	0.539694i
$941$	197693.			0.223261			0.111630	−	0.993750i	$-0.464393\pi$
$941$	197693.			0.223261			0.111630	+	0.993750i	$0.464393\pi$
$942$	−84743.1	−	84743.1i	−0.0954999	−	0.0954999i
$943$	−76724.0	+	76724.0i	−0.0862796	+	0.0862796i
$944$		−	61276.8i		−	0.0687625i
$945$	−599381.	−	343143.i	−0.671180	−	0.384248i
$946$	216398.			0.241808
$947$	−185844.	−	185844.i	−0.207228	−	0.207228i	0.595860	−	0.803088i	$-0.296811\pi$
$947$	−185844.	−	185844.i	−0.207228	−	0.207228i	−0.803088	+	0.595860i	$0.796811\pi$
$948$	154127.	−	154127.i	0.171499	−	0.171499i
$949$			616665.i			0.684726i
$950$	−243174.	−	63260.3i	−0.269445	−	0.0700945i
$951$	−993003.			−1.09797
$952$	−65771.4	−	65771.4i	−0.0725710	−	0.0725710i
$953$	−938606.	+	938606.i	−1.03347	+	1.03347i	−0.0340494	+	0.999420i	$0.510840\pi$
$953$	−938606.	+	938606.i	−1.03347	+	1.03347i	−0.999420	+	0.0340494i	$0.989160\pi$
$954$		−	301227.i		−	0.330976i
$955$	−69183.1	+	120845.i	−0.0758566	+	0.132501i
$956$	433076.			0.473859
$957$	89559.7	+	89559.7i	0.0977887	+	0.0977887i
$958$	−431847.	+	431847.i	−0.470543	+	0.470543i
$959$			378544.i			0.411604i
$960$	−81465.6	+	22147.5i	−0.0883958	+	0.0240316i
$961$	535256.			0.579582
$962$	−580482.	−	580482.i	−0.627248	−	0.627248i
$963$	−239646.	+	239646.i	−0.258415	+	0.258415i
$964$		−	58335.5i		−	0.0627739i
$965$	130443.	+	479812.i	0.140077	+	0.515249i
$966$	72734.8			0.0779449
$967$	−109058.	−	109058.i	−0.116629	−	0.116629i	0.646384	−	0.763012i	$-0.276281\pi$
$967$	−109058.	−	109058.i	−0.116629	−	0.116629i	−0.763012	+	0.646384i	$0.776281\pi$
$968$	204982.	−	204982.i	0.218759	−	0.218759i
$969$		−	109023.i		−	0.116111i
$970$	1.09353e6	+	626041.i	1.16222	+	0.665364i
$971$	−1.67376e6			−1.77523			−0.887613	−	0.460590i	$-0.847638\pi$
$971$	−1.67376e6			−1.77523			−0.887613	+	0.460590i	$0.847638\pi$
$972$	279118.	+	279118.i	0.295430	+	0.295430i
$973$	501809.	−	501809.i	0.530045	−	0.530045i
$974$		−	977562.i		−	1.03045i
$975$	−625291.	+	367121.i	−0.657769	+	0.386189i
$976$	217567.			0.228399
$977$	761307.	+	761307.i	0.797573	+	0.797573i	0.982712	−	0.185139i	$-0.0592736\pi$
$977$	761307.	+	761307.i	0.797573	+	0.797573i	−0.185139	+	0.982712i	$0.559274\pi$
$978$	505738.	−	505738.i	0.528747	−	0.528747i
$979$			367519.i			0.383455i
$980$	−114428.	+	199875.i	−0.119146	+	0.208117i
$981$	5460.82			0.00567440
$982$	−153923.	−	153923.i	−0.159618	−	0.159618i
$983$	549265.	−	549265.i	0.568427	−	0.568427i	−0.363260	−	0.931688i	$-0.618336\pi$
$983$	549265.	−	549265.i	0.568427	−	0.568427i	0.931688	+	0.363260i	$0.118336\pi$
$984$			146804.i			0.151617i
$985$	529577.	−	143972.i	0.545829	−	0.148391i
$986$	−147674.			−0.151897
$987$	−407332.	−	407332.i	−0.418132	−	0.418132i
$988$	−141434.	+	141434.i	−0.144891	+	0.144891i
$989$		−	197296.i		−	0.201710i
$990$	−29754.6	−	109447.i	−0.0303588	−	0.111669i
$991$	−1.39416e6			−1.41960			−0.709800	−	0.704403i	$-0.751215\pi$
$991$	−1.39416e6			−1.41960			−0.709800	+	0.704403i	$0.751215\pi$
$992$	−154598.	−	154598.i	−0.157102	−	0.157102i
$993$	−625781.	+	625781.i	−0.634635	+	0.634635i
$994$		−	53566.1i		−	0.0542147i
$995$	518897.	+	297067.i	0.524125	+	0.300060i
$996$	565478.			0.570029
$997$	−1.38856e6	−	1.38856e6i	−1.39692	−	1.39692i	−0.808691	−	0.588234i	$-0.799823\pi$
$997$	−1.38856e6	−	1.38856e6i	−1.39692	−	1.39692i	−0.588234	−	0.808691i	$-0.700177\pi$
$998$	28980.0	−	28980.0i	0.0290963	−	0.0290963i
$999$		−	1.28960e6i		−	1.29218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.7	✓	44
5.3	odd	4	inner	230.5.f.b.93.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.7	✓	44	1.1	even	1	trivial
230.5.f.b.93.7	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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(-4.66373 + 4.66373i) q^{3} +8.00000i q^{4} +(-12.4209 + 21.6961i) q^{5} -18.6549 q^{6} +(-24.9944 - 24.9944i) q^{7} +(-16.0000 + 16.0000i) q^{8} +37.4993i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(-4.66373 + 4.66373i) q^{3} +8.00000i q^{4} +(-12.4209 + 21.6961i) q^{5} -18.6549 q^{6} +(-24.9944 - 24.9944i) q^{7} +(-16.0000 + 16.0000i) q^{8} +37.4993i q^{9} +(-68.2341 + 18.5503i) q^{10} +42.7740 q^{11} +(-37.3098 - 37.3098i) q^{12} +(-124.381 + 124.381i) q^{13} -99.9775i q^{14} +(-43.2568 - 159.113i) q^{15} -64.0000 q^{16} +(-82.2327 - 82.2327i) q^{17} +(-74.9986 + 74.9986i) q^{18} -142.138i q^{19} +(-173.569 - 99.3675i) q^{20} +233.134 q^{21} +(85.5480 + 85.5480i) q^{22} +(77.9968 - 77.9968i) q^{23} -149.239i q^{24} +(-316.441 - 538.971i) q^{25} -497.523 q^{26} +(-552.648 - 552.648i) q^{27} +(199.955 - 199.955i) q^{28} -448.952i q^{29} +(231.711 - 404.739i) q^{30} +1207.80 q^{31} +(-128.000 - 128.000i) q^{32} +(-199.486 + 199.486i) q^{33} -328.931i q^{34} +(852.734 - 231.827i) q^{35} -299.994 q^{36} +(1166.74 + 1166.74i) q^{37} +(284.277 - 284.277i) q^{38} -1160.16i q^{39} +(-148.403 - 545.872i) q^{40} -983.682 q^{41} +(466.268 + 466.268i) q^{42} +(1264.77 - 1264.77i) q^{43} +342.192i q^{44} +(-813.588 - 465.776i) q^{45} +311.987 q^{46} +(-1747.20 - 1747.20i) q^{47} +(298.479 - 298.479i) q^{48} -1151.56i q^{49} +(445.061 - 1710.82i) q^{50} +767.022 q^{51} +(-995.047 - 995.047i) q^{52} +(-2008.22 + 2008.22i) q^{53} -2210.59i q^{54} +(-531.293 + 928.029i) q^{55} +799.820 q^{56} +(662.894 + 662.894i) q^{57} +(897.903 - 897.903i) q^{58} +957.449i q^{59} +(1272.90 - 346.054i) q^{60} -3399.49 q^{61} +(2415.60 + 2415.60i) q^{62} +(937.271 - 937.271i) q^{63} -512.000i q^{64} +(-1153.65 - 4243.50i) q^{65} -797.945 q^{66} +(-3861.25 - 3861.25i) q^{67} +(657.862 - 657.862i) q^{68} +727.512i q^{69} +(2169.12 + 1241.81i) q^{70} +535.782 q^{71} +(-599.989 - 599.989i) q^{72} +(2478.94 - 2478.94i) q^{73} +4666.98i q^{74} +(3989.41 + 1037.82i) q^{75} +1137.11 q^{76} +(-1069.11 - 1069.11i) q^{77} +(2320.31 - 2320.31i) q^{78} +4130.99i q^{79} +(794.940 - 1388.55i) q^{80} +2117.36 q^{81} +(-1967.36 - 1967.36i) q^{82} +(-7578.13 + 7578.13i) q^{83} +1865.07i q^{84} +(2805.54 - 762.722i) q^{85} +5059.09 q^{86} +(2093.79 + 2093.79i) q^{87} +(-684.384 + 684.384i) q^{88} +8592.11i q^{89} +(-695.624 - 2558.73i) q^{90} +6217.64 q^{91} +(623.974 + 623.974i) q^{92} +(-5632.84 + 5632.84i) q^{93} -6988.80i q^{94} +(3083.85 + 1765.49i) q^{95} +1193.91 q^{96} +(-12600.5 - 12600.5i) q^{97} +(2303.13 - 2303.13i) q^{98} +1603.99i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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