LMFDB - Embedded newform 230.5.f.b.47.13

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			47.13
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(2.64936 - 2.64936i) q^{3} +8.00000i q^{4} +(22.4224 + 11.0560i) q^{5} +10.5974 q^{6} +(-62.5314 - 62.5314i) q^{7} +(-16.0000 + 16.0000i) q^{8} +66.9618i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(2.64936 - 2.64936i) q^{3} +8.00000i q^{4} +(22.4224 + 11.0560i) q^{5} +10.5974 q^{6} +(-62.5314 - 62.5314i) q^{7} +(-16.0000 + 16.0000i) q^{8} +66.9618i q^{9} +(22.7329 + 66.9568i) q^{10} -187.806 q^{11} +(21.1949 + 21.1949i) q^{12} +(-63.2613 + 63.2613i) q^{13} -250.126i q^{14} +(88.6964 - 30.1138i) q^{15} -64.0000 q^{16} +(-295.445 - 295.445i) q^{17} +(-133.924 + 133.924i) q^{18} +514.491i q^{19} +(-88.4480 + 179.379i) q^{20} -331.336 q^{21} +(-375.612 - 375.612i) q^{22} +(-77.9968 + 77.9968i) q^{23} +84.7795i q^{24} +(380.530 + 495.804i) q^{25} -253.045 q^{26} +(392.004 + 392.004i) q^{27} +(500.251 - 500.251i) q^{28} +672.295i q^{29} +(237.620 + 117.165i) q^{30} -333.091 q^{31} +(-128.000 - 128.000i) q^{32} +(-497.565 + 497.565i) q^{33} -1181.78i q^{34} +(-710.758 - 2093.45i) q^{35} -535.694 q^{36} +(-724.203 - 724.203i) q^{37} +(-1028.98 + 1028.98i) q^{38} +335.204i q^{39} +(-535.655 + 181.863i) q^{40} +556.503 q^{41} +(-662.672 - 662.672i) q^{42} +(2229.79 - 2229.79i) q^{43} -1502.45i q^{44} +(-740.329 + 1501.45i) q^{45} -311.987 q^{46} +(-1759.12 - 1759.12i) q^{47} +(-169.559 + 169.559i) q^{48} +5419.35i q^{49} +(-230.549 + 1752.67i) q^{50} -1565.48 q^{51} +(-506.090 - 506.090i) q^{52} +(-2261.92 + 2261.92i) q^{53} +1568.02i q^{54} +(-4211.06 - 2076.38i) q^{55} +2001.00 q^{56} +(1363.07 + 1363.07i) q^{57} +(-1344.59 + 1344.59i) q^{58} +2968.34i q^{59} +(240.910 + 709.571i) q^{60} -2243.48 q^{61} +(-666.183 - 666.183i) q^{62} +(4187.21 - 4187.21i) q^{63} -512.000i q^{64} +(-2117.89 + 719.055i) q^{65} -1990.26 q^{66} +(-5381.94 - 5381.94i) q^{67} +(2363.56 - 2363.56i) q^{68} +413.283i q^{69} +(2765.39 - 5608.42i) q^{70} +4785.83 q^{71} +(-1071.39 - 1071.39i) q^{72} +(-2032.14 + 2032.14i) q^{73} -2896.81i q^{74} +(2321.72 + 305.403i) q^{75} -4115.93 q^{76} +(11743.8 + 11743.8i) q^{77} +(-670.407 + 670.407i) q^{78} -4856.02i q^{79} +(-1435.03 - 707.584i) q^{80} -3346.79 q^{81} +(1113.01 + 1113.01i) q^{82} +(4032.62 - 4032.62i) q^{83} -2650.69i q^{84} +(-3358.16 - 9891.04i) q^{85} +8919.14 q^{86} +(1781.15 + 1781.15i) q^{87} +(3004.89 - 3004.89i) q^{88} -7296.60i q^{89} +(-4483.55 + 1522.23i) q^{90} +7911.63 q^{91} +(-623.974 - 623.974i) q^{92} +(-882.479 + 882.479i) q^{93} -7036.47i q^{94} +(-5688.21 + 11536.1i) q^{95} -678.236 q^{96} +(4629.56 + 4629.56i) q^{97} +(-10838.7 + 10838.7i) q^{98} -12575.8i 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
$3$	2.64936	−	2.64936i	0.294373	−	0.294373i	−0.544432	−	0.838805i	$-0.683255\pi$
$3$	2.64936	−	2.64936i	0.294373	−	0.294373i	0.838805	+	0.544432i	$0.183255\pi$
$4$			8.00000i			0.500000i
$5$	22.4224	+	11.0560i	0.896897	+	0.442240i
$5$	22.4224	+	11.0560i	0.896897	+	0.442240i
$6$	10.5974			0.294373
$7$	−62.5314	−	62.5314i	−1.27615	−	1.27615i	−0.942805	−	0.333346i	$-0.891822\pi$
$7$	−62.5314	−	62.5314i	−1.27615	−	1.27615i	−0.333346	−	0.942805i	$-0.608178\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$			66.9618i			0.826689i
$10$	22.7329	+	66.9568i	0.227329	+	0.669568i
$11$	−187.806			−1.55211			−0.776057	−	0.630663i	$-0.782783\pi$
$11$	−187.806			−1.55211			−0.776057	+	0.630663i	$0.782783\pi$
$12$	21.1949	+	21.1949i	0.147187	+	0.147187i
$13$	−63.2613	+	63.2613i	−0.374327	+	0.374327i	−0.869050	−	0.494723i	$-0.835269\pi$
$13$	−63.2613	+	63.2613i	−0.374327	+	0.374327i	0.494723	+	0.869050i	$0.335269\pi$
$14$		−	250.126i		−	1.27615i
$15$	88.6964	−	30.1138i	0.394206	−	0.133839i
$16$	−64.0000			−0.250000
$17$	−295.445	−	295.445i	−1.02230	−	1.02230i	−0.999746	−	0.0225560i	$-0.992820\pi$
$17$	−295.445	−	295.445i	−1.02230	−	1.02230i	−0.0225560	−	0.999746i	$-0.507180\pi$
$18$	−133.924	+	133.924i	−0.413344	+	0.413344i
$19$			514.491i			1.42518i	0.701579	+	0.712592i	$0.252479\pi$
$19$			514.491i			1.42518i	−0.701579	+	0.712592i	$0.747521\pi$
$20$	−88.4480	+	179.379i	−0.221120	+	0.448448i
$21$	−331.336			−0.751329
$22$	−375.612	−	375.612i	−0.776057	−	0.776057i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$			84.7795i			0.147187i
$25$	380.530	+	495.804i	0.608848	+	0.793287i
$26$	−253.045			−0.374327
$27$	392.004	+	392.004i	0.537728	+	0.537728i
$28$	500.251	−	500.251i	0.638075	−	0.638075i
$29$			672.295i			0.799399i	0.916646	+	0.399699i	$0.130886\pi$
$29$			672.295i			0.799399i	−0.916646	+	0.399699i	$0.869114\pi$
$30$	237.620	+	117.165i	0.264022	+	0.130184i
$31$	−333.091			−0.346609			−0.173305	−	0.984868i	$-0.555445\pi$
$31$	−333.091			−0.346609			−0.173305	+	0.984868i	$0.555445\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−497.565	+	497.565i	−0.456901	+	0.456901i
$34$		−	1181.78i		−	1.02230i
$35$	−710.758	−	2093.45i	−0.580211	−	1.70894i
$36$	−535.694			−0.413344
$37$	−724.203	−	724.203i	−0.529002	−	0.529002i	0.391273	−	0.920275i	$-0.372035\pi$
$37$	−724.203	−	724.203i	−0.529002	−	0.529002i	−0.920275	+	0.391273i	$0.872035\pi$
$38$	−1028.98	+	1028.98i	−0.712592	+	0.712592i
$39$			335.204i			0.220384i
$40$	−535.655	+	181.863i	−0.334784	+	0.113664i
$41$	556.503			0.331055			0.165527	−	0.986205i	$-0.447067\pi$
$41$	556.503			0.331055			0.165527	+	0.986205i	$0.447067\pi$
$42$	−662.672	−	662.672i	−0.375665	−	0.375665i
$43$	2229.79	−	2229.79i	1.20594	−	1.20594i	0.233612	−	0.972330i	$-0.424946\pi$
$43$	2229.79	−	2229.79i	1.20594	−	1.20594i	0.972330	−	0.233612i	$-0.0750544\pi$
$44$		−	1502.45i		−	0.776057i
$45$	−740.329	+	1501.45i	−0.365595	+	0.741455i
$46$	−311.987			−0.147442
$47$	−1759.12	−	1759.12i	−0.796341	−	0.796341i	0.186175	−	0.982517i	$-0.440391\pi$
$47$	−1759.12	−	1759.12i	−0.796341	−	0.796341i	−0.982517	+	0.186175i	$0.940391\pi$
$48$	−169.559	+	169.559i	−0.0735933	+	0.0735933i
$49$			5419.35i			2.25712i
$50$	−230.549	+	1752.67i	−0.0922195	+	0.701067i
$51$	−1565.48			−0.601877
$52$	−506.090	−	506.090i	−0.187164	−	0.187164i
$53$	−2261.92	+	2261.92i	−0.805239	+	0.805239i	−0.983909	−	0.178670i	$-0.942821\pi$
$53$	−2261.92	+	2261.92i	−0.805239	+	0.805239i	0.178670	+	0.983909i	$0.442821\pi$
$54$			1568.02i			0.537728i
$55$	−4211.06	−	2076.38i	−1.39209	−	0.686406i
$56$	2001.00			0.638075
$57$	1363.07	+	1363.07i	0.419536	+	0.419536i
$58$	−1344.59	+	1344.59i	−0.399699	+	0.399699i
$59$			2968.34i			0.852725i	0.904552	+	0.426362i	$0.140205\pi$
$59$			2968.34i			0.852725i	−0.904552	+	0.426362i	$0.859795\pi$
$60$	240.910	+	709.571i	0.0669195	+	0.197103i
$61$	−2243.48			−0.602925			−0.301462	−	0.953478i	$-0.597475\pi$
$61$	−2243.48			−0.602925			−0.301462	+	0.953478i	$0.597475\pi$
$62$	−666.183	−	666.183i	−0.173305	−	0.173305i
$63$	4187.21	−	4187.21i	1.05498	−	1.05498i
$64$		−	512.000i		−	0.125000i
$65$	−2117.89	+	719.055i	−0.501275	+	0.170190i
$66$	−1990.26			−0.456901
$67$	−5381.94	−	5381.94i	−1.19892	−	1.19892i	−0.974491	−	0.224427i	$-0.927949\pi$
$67$	−5381.94	−	5381.94i	−1.19892	−	1.19892i	−0.224427	−	0.974491i	$-0.572051\pi$
$68$	2363.56	−	2363.56i	0.511151	−	0.511151i
$69$			413.283i			0.0868059i
$70$	2765.39	−	5608.42i	0.564365	−	1.14458i
$71$	4785.83			0.949382			0.474691	−	0.880153i	$-0.342560\pi$
$71$	4785.83			0.949382			0.474691	+	0.880153i	$0.342560\pi$
$72$	−1071.39	−	1071.39i	−0.206672	−	0.206672i
$73$	−2032.14	+	2032.14i	−0.381335	+	0.381335i	−0.871583	−	0.490248i	$-0.836906\pi$
$73$	−2032.14	+	2032.14i	−0.381335	+	0.381335i	0.490248	+	0.871583i	$0.336906\pi$
$74$		−	2896.81i		−	0.529002i
$75$	2321.72	+	305.403i	0.412751	+	0.0542939i
$76$	−4115.93			−0.712592
$77$	11743.8	+	11743.8i	1.98073	+	1.98073i
$78$	−670.407	+	670.407i	−0.110192	+	0.110192i
$79$		−	4856.02i		−	0.778083i	−0.921220	−	0.389042i	$-0.872806\pi$
$79$		−	4856.02i		−	0.778083i	0.921220	−	0.389042i	$-0.127194\pi$
$80$	−1435.03	−	707.584i	−0.224224	−	0.110560i
$81$	−3346.79			−0.510103
$82$	1113.01	+	1113.01i	0.165527	+	0.165527i
$83$	4032.62	−	4032.62i	0.585371	−	0.585371i	−0.351003	−	0.936374i	$-0.614159\pi$
$83$	4032.62	−	4032.62i	0.585371	−	0.585371i	0.936374	+	0.351003i	$0.114159\pi$
$84$		−	2650.69i		−	0.375665i
$85$	−3358.16	−	9891.04i	−0.464797	−	1.36900i
$86$	8919.14			1.20594
$87$	1781.15	+	1781.15i	0.235322	+	0.235322i
$88$	3004.89	−	3004.89i	0.388028	−	0.388028i
$89$		−	7296.60i		−	0.921172i	−0.887615	−	0.460586i	$-0.847639\pi$
$89$		−	7296.60i		−	0.921172i	0.887615	−	0.460586i	$-0.152361\pi$
$90$	−4483.55	+	1522.23i	−0.553525	+	0.187930i
$91$	7911.63			0.955395
$92$	−623.974	−	623.974i	−0.0737210	−	0.0737210i
$93$	−882.479	+	882.479i	−0.102032	+	0.102032i
$94$		−	7036.47i		−	0.796341i
$95$	−5688.21	+	11536.1i	−0.630273	+	1.27824i
$96$	−678.236			−0.0735933
$97$	4629.56	+	4629.56i	0.492035	+	0.492035i	0.908947	−	0.416912i	$-0.136888\pi$
$97$	4629.56	+	4629.56i	0.492035	+	0.492035i	−0.416912	+	0.908947i	$0.636888\pi$
$98$	−10838.7	+	10838.7i	−1.12856	+	1.12856i
$99$		−	12575.8i		−	1.28312i
$100$	−3966.43	+	3044.24i	−0.396643	+	0.304424i
$101$	14772.8			1.44818			0.724088	−	0.689708i	$-0.242261\pi$
$101$	14772.8			1.44818			0.724088	+	0.689708i	$0.242261\pi$
$102$	−3130.96	−	3130.96i	−0.300938	−	0.300938i
$103$	−9059.21	+	9059.21i	−0.853917	+	0.853917i	−0.990613	−	0.136696i	$-0.956352\pi$
$103$	−9059.21	+	9059.21i	−0.853917	+	0.853917i	0.136696	+	0.990613i	$0.456352\pi$
$104$		−	2024.36i		−	0.187164i
$105$	−7429.36	−	3663.25i	−0.673865	−	0.332268i
$106$	−9047.67			−0.805239
$107$	8096.27	+	8096.27i	0.707160	+	0.707160i	0.965937	−	0.258777i	$-0.0833196\pi$
$107$	8096.27	+	8096.27i	0.707160	+	0.707160i	−0.258777	+	0.965937i	$0.583320\pi$
$108$	−3136.03	+	3136.03i	−0.268864	+	0.268864i
$109$		−	270.236i		−	0.0227452i	−0.999935	−	0.0113726i	$-0.996380\pi$
$109$		−	270.236i		−	0.0227452i	0.999935	−	0.0113726i	$-0.00362009\pi$
$110$	−4269.36	−	12574.9i	−0.352840	−	1.03925i
$111$	−3837.35			−0.311448
$112$	4002.01	+	4002.01i	0.319038	+	0.319038i
$113$	−9024.98	+	9024.98i	−0.706788	+	0.706788i	−0.965858	−	0.259070i	$-0.916584\pi$
$113$	−9024.98	+	9024.98i	−0.706788	+	0.706788i	0.259070	+	0.965858i	$0.416584\pi$
$114$			5452.29i			0.419536i
$115$	−2611.21	+	886.545i	−0.197445	+	0.0670355i
$116$	−5378.36			−0.399699
$117$	−4236.09	−	4236.09i	−0.309452	−	0.309452i
$118$	−5936.67	+	5936.67i	−0.426362	+	0.426362i
$119$			36949.2i			2.60922i
$120$	−937.322	+	1900.96i	−0.0650918	+	0.132011i
$121$	20630.0			1.40906
$122$	−4486.97	−	4486.97i	−0.301462	−	0.301462i
$123$	1474.38	−	1474.38i	0.0974537	−	0.0974537i
$124$		−	2664.73i		−	0.173305i
$125$	3050.79	+	15324.3i	0.195251	+	0.980753i
$126$	16748.9			1.05498
$127$	20555.4	+	20555.4i	1.27444	+	1.27444i	0.943734	+	0.330705i	$0.107286\pi$
$127$	20555.4	+	20555.4i	1.27444	+	1.27444i	0.330705	+	0.943734i	$0.392714\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	11815.0i		−	0.709994i
$130$	−5673.88	−	2797.66i	−0.335733	−	0.165542i
$131$	15147.2			0.882653			0.441326	−	0.897347i	$-0.354508\pi$
$131$	15147.2			0.882653			0.441326	+	0.897347i	$0.354508\pi$
$132$	−3980.52	−	3980.52i	−0.228450	−	0.228450i
$133$	32171.8	−	32171.8i	1.81875	−	1.81875i
$134$		−	21527.8i		−	1.19892i
$135$	4455.68	+	13123.7i	0.244482	+	0.720092i
$136$	9454.25			0.511151
$137$	−427.023	−	427.023i	−0.0227515	−	0.0227515i	0.695640	−	0.718391i	$-0.255121\pi$
$137$	−427.023	−	427.023i	−0.0227515	−	0.0227515i	−0.718391	+	0.695640i	$0.755121\pi$
$138$	−826.566	+	826.566i	−0.0434030	+	0.0434030i
$139$		−	25178.9i		−	1.30319i	−0.758567	−	0.651595i	$-0.774100\pi$
$139$		−	25178.9i		−	1.30319i	0.758567	−	0.651595i	$-0.225900\pi$
$140$	16747.6	−	5686.07i	0.854470	−	0.290105i
$141$	−9321.07			−0.468843
$142$	9571.67	+	9571.67i	0.474691	+	0.474691i
$143$	11880.8	−	11880.8i	0.580998	−	0.580998i
$144$		−	4285.55i		−	0.206672i
$145$	−7432.88	+	15074.5i	−0.353526	+	0.716978i
$146$	−8128.54			−0.381335
$147$	14357.8	+	14357.8i	0.664436	+	0.664436i
$148$	5793.63	−	5793.63i	0.264501	−	0.264501i
$149$			34573.5i			1.55730i	0.627461	+	0.778648i	$0.284094\pi$
$149$			34573.5i			1.55730i	−0.627461	+	0.778648i	$0.715906\pi$
$150$	4032.64	+	5254.26i	0.179229	+	0.233522i
$151$	−13228.9			−0.580191			−0.290095	−	0.956998i	$-0.593687\pi$
$151$	−13228.9			−0.580191			−0.290095	+	0.956998i	$0.593687\pi$
$152$	−8231.86	−	8231.86i	−0.356296	−	0.356296i
$153$	19783.5	−	19783.5i	0.845125	−	0.845125i
$154$			46975.0i			1.98073i
$155$	−7468.72	−	3682.66i	−0.310873	−	0.153284i
$156$	−2681.63			−0.110192
$157$	1589.21	+	1589.21i	0.0644736	+	0.0644736i	0.738608	−	0.674135i	$-0.235483\pi$
$157$	1589.21	+	1589.21i	0.0644736	+	0.0644736i	−0.674135	+	0.738608i	$0.735483\pi$
$158$	9712.04	−	9712.04i	0.389042	−	0.389042i
$159$			11985.3i			0.474082i
$160$	−1454.90	−	4285.24i	−0.0568321	−	0.167392i
$161$	9754.49			0.376316
$162$	−6693.57	−	6693.57i	−0.255052	−	0.255052i
$163$	9385.42	−	9385.42i	0.353247	−	0.353247i	−0.508069	−	0.861316i	$-0.669641\pi$
$163$	9385.42	−	9385.42i	0.353247	−	0.353247i	0.861316	+	0.508069i	$0.169641\pi$
$164$			4452.02i			0.165527i
$165$	−16657.7	+	5655.54i	−0.611853	+	0.207733i
$166$	16130.5			0.585371
$167$	−37505.7	−	37505.7i	−1.34482	−	1.34482i	−0.891190	−	0.453631i	$-0.850129\pi$
$167$	−37505.7	−	37505.7i	−1.34482	−	1.34482i	−0.453631	−	0.891190i	$-0.649871\pi$
$168$	5301.38	−	5301.38i	0.187832	−	0.187832i
$169$			20557.0i			0.719759i
$170$	13065.8	−	26498.4i	0.452102	−	0.916899i
$171$	−34451.3			−1.17818
$172$	17838.3	+	17838.3i	0.602971	+	0.602971i
$173$	−22820.9	+	22820.9i	−0.762500	+	0.762500i	−0.976774	−	0.214273i	$-0.931262\pi$
$173$	−22820.9	+	22820.9i	−0.762500	+	0.762500i	0.214273	+	0.976774i	$0.431262\pi$
$174$			7124.60i			0.235322i
$175$	7208.26	−	54798.4i	0.235372	−	1.78934i
$176$	12019.6			0.388028
$177$	7864.19	+	7864.19i	0.251019	+	0.251019i
$178$	14593.2	−	14593.2i	0.460586	−	0.460586i
$179$			14516.9i			0.453073i	0.974003	+	0.226536i	$0.0727402\pi$
$179$			14516.9i			0.453073i	−0.974003	+	0.226536i	$0.927260\pi$
$180$	−12011.6	−	5922.63i	−0.370727	−	0.182797i
$181$	−13484.6			−0.411605			−0.205803	−	0.978594i	$-0.565980\pi$
$181$	−13484.6			−0.411605			−0.205803	+	0.978594i	$0.565980\pi$
$182$	15823.3	+	15823.3i	0.477698	+	0.477698i
$183$	−5943.79	+	5943.79i	−0.177485	+	0.177485i
$184$		−	2495.90i		−	0.0737210i
$185$	−8231.61	−	24245.2i	−0.240514	−	0.708406i
$186$	−3529.92			−0.102032
$187$	55486.3	+	55486.3i	1.58673	+	1.58673i
$188$	14072.9	−	14072.9i	0.398171	−	0.398171i
$189$		−	49025.1i		−	1.37244i
$190$	−34448.7	+	11695.9i	−0.954258	+	0.323985i
$191$	−25051.5			−0.686700			−0.343350	−	0.939208i	$-0.611562\pi$
$191$	−25051.5			−0.686700			−0.343350	+	0.939208i	$0.611562\pi$
$192$	−1356.47	−	1356.47i	−0.0367967	−	0.0367967i
$193$	−13272.2	+	13272.2i	−0.356310	+	0.356310i	−0.862451	−	0.506141i	$-0.831072\pi$
$193$	−13272.2	+	13272.2i	−0.356310	+	0.356310i	0.506141	+	0.862451i	$0.331072\pi$
$194$			18518.2i			0.492035i
$195$	−3706.01	+	7516.08i	−0.0974625	+	0.197662i
$196$	−43354.8			−1.12856
$197$	4027.70	+	4027.70i	0.103783	+	0.103783i	0.757092	−	0.653309i	$-0.226620\pi$
$197$	4027.70	+	4027.70i	0.103783	+	0.103783i	−0.653309	+	0.757092i	$0.726620\pi$
$198$	25151.6	−	25151.6i	0.641558	−	0.641558i
$199$			16870.5i			0.426013i	0.977051	+	0.213006i	$0.0683255\pi$
$199$			16870.5i			0.426013i	−0.977051	+	0.213006i	$0.931674\pi$
$200$	−14021.3	−	1844.39i	−0.350534	−	0.0461097i
$201$	−28517.4			−0.705859
$202$	29545.7	+	29545.7i	0.724088	+	0.724088i
$203$	42039.5	−	42039.5i	1.02015	−	1.02015i
$204$		−	12523.8i		−	0.300938i
$205$	12478.1	+	6152.69i	0.296922	+	0.146406i
$206$	−36236.8			−0.853917
$207$	−5222.80	−	5222.80i	−0.121889	−	0.121889i
$208$	4048.72	−	4048.72i	0.0935818	−	0.0935818i
$209$		−	96624.4i		−	2.21205i
$210$	−7532.22	−	22185.2i	−0.170799	−	0.503066i
$211$	−48372.9			−1.08652			−0.543259	−	0.839565i	$-0.682810\pi$
$211$	−48372.9			−1.08652			−0.543259	+	0.839565i	$0.682810\pi$
$212$	−18095.3	−	18095.3i	−0.402620	−	0.402620i
$213$	12679.4	−	12679.4i	0.279473	−	0.279473i
$214$			32385.1i			0.707160i
$215$	74649.7	−	25344.7i	1.61492	−	0.548290i
$216$	−12544.1			−0.268864
$217$	20828.7	+	20828.7i	0.442326	+	0.442326i
$218$	540.471	−	540.471i	0.0113726	−	0.0113726i
$219$			10767.7i			0.224510i
$220$	16611.0	−	33688.5i	0.343203	−	0.696043i
$221$	37380.5			0.765350
$222$	−7674.70	−	7674.70i	−0.155724	−	0.155724i
$223$	28045.0	−	28045.0i	0.563957	−	0.563957i	−0.366472	−	0.930429i	$-0.619435\pi$
$223$	28045.0	−	28045.0i	0.563957	−	0.563957i	0.930429	+	0.366472i	$0.119435\pi$
$224$			16008.0i			0.319038i
$225$	−33199.9	+	25481.0i	−0.655801	+	0.503328i
$226$	−36099.9			−0.706788
$227$	6346.89	+	6346.89i	0.123171	+	0.123171i	0.766005	−	0.642834i	$-0.222242\pi$
$227$	6346.89	+	6346.89i	0.123171	+	0.123171i	−0.642834	+	0.766005i	$0.722242\pi$
$228$	−10904.6	+	10904.6i	−0.209768	+	0.209768i
$229$			51421.4i			0.980556i	0.871566	+	0.490278i	$0.163105\pi$
$229$			51421.4i			0.980556i	−0.871566	+	0.490278i	$0.836895\pi$
$230$	−6995.51	−	3449.33i	−0.132240	−	0.0652047i
$231$	62226.9			1.16615
$232$	−10756.7	−	10756.7i	−0.199850	−	0.199850i
$233$	2960.00	−	2960.00i	0.0545230	−	0.0545230i	−0.679320	−	0.733843i	$-0.737725\pi$
$233$	2960.00	−	2960.00i	0.0545230	−	0.0545230i	0.733843	+	0.679320i	$0.237725\pi$
$234$		−	16944.4i		−	0.309452i
$235$	−19994.9	−	58892.5i	−0.362062	−	1.06641i
$236$	−23746.7			−0.426362
$237$	−12865.3	−	12865.3i	−0.229047	−	0.229047i
$238$	−73898.4	+	73898.4i	−1.30461	+	1.30461i
$239$		−	29413.5i		−	0.514933i	−0.966287	−	0.257467i	$-0.917112\pi$
$239$		−	29413.5i		−	0.514933i	0.966287	−	0.257467i	$-0.0828877\pi$
$240$	−5676.57	+	1927.28i	−0.0985515	+	0.0334597i
$241$	−34542.7			−0.594734			−0.297367	−	0.954763i	$-0.596108\pi$
$241$	−34542.7			−0.594734			−0.297367	+	0.954763i	$0.596108\pi$
$242$	41260.0	+	41260.0i	0.704529	+	0.704529i
$243$	−40619.2	+	40619.2i	−0.687889	+	0.687889i
$244$		−	17947.9i		−	0.301462i
$245$	−59916.3	+	121515.i	−0.998189	+	2.02440i
$246$	5897.51			0.0974537
$247$	−32547.4	−	32547.4i	−0.533485	−	0.533485i
$248$	5329.46	−	5329.46i	0.0866523	−	0.0866523i
$249$		−	21367.7i		−	0.344635i
$250$	−24547.0	+	36750.1i	−0.392751	+	0.588002i
$251$	−16025.4			−0.254367			−0.127184	−	0.991879i	$-0.540594\pi$
$251$	−16025.4			−0.254367			−0.127184	+	0.991879i	$0.540594\pi$
$252$	33497.7	+	33497.7i	0.527490	+	0.527490i
$253$	14648.2	−	14648.2i	0.228847	−	0.228847i
$254$			82221.7i			1.27444i
$255$	−35101.9	−	17307.9i	−0.539821	−	0.266174i
$256$	4096.00			0.0625000
$257$	−54118.7	−	54118.7i	−0.819372	−	0.819372i	0.166645	−	0.986017i	$-0.446707\pi$
$257$	−54118.7	−	54118.7i	−0.819372	−	0.819372i	−0.986017	+	0.166645i	$0.946707\pi$
$258$	23630.0	−	23630.0i	0.354997	−	0.354997i
$259$			90570.9i			1.35017i
$260$	−5752.44	−	16943.1i	−0.0850952	−	0.250638i
$261$	−45018.0			−0.660854
$262$	30294.4	+	30294.4i	0.441326	+	0.441326i
$263$	−87481.5	+	87481.5i	−1.26475	+	1.26475i	−0.315986	+	0.948764i	$0.602335\pi$
$263$	−87481.5	+	87481.5i	−1.26475	+	1.26475i	−0.948764	+	0.315986i	$0.897665\pi$
$264$		−	15922.1i		−	0.228450i
$265$	−75725.4	+	25709.9i	−1.07833	+	0.366108i
$266$	128687.			1.81875
$267$	−19331.3	−	19331.3i	−0.271168	−	0.271168i
$268$	43055.6	−	43055.6i	0.599459	−	0.599459i
$269$		−	45485.1i		−	0.628585i	−0.949326	−	0.314293i	$-0.898233\pi$
$269$		−	45485.1i		−	0.628585i	0.949326	−	0.314293i	$-0.101767\pi$
$270$	−17336.0	+	35158.7i	−0.237805	+	0.482287i
$271$	−83706.2			−1.13977			−0.569887	−	0.821723i	$-0.693013\pi$
$271$	−83706.2			−1.13977			−0.569887	+	0.821723i	$0.693013\pi$
$272$	18908.5	+	18908.5i	0.255575	+	0.255575i
$273$	20960.8	−	20960.8i	0.281243	−	0.281243i
$274$		−	1708.09i		−	0.0227515i
$275$	−71465.7	−	93114.9i	−0.945001	−	1.23127i
$276$	−3306.26			−0.0434030
$277$	−37432.4	−	37432.4i	−0.487851	−	0.487851i	0.419776	−	0.907628i	$-0.362109\pi$
$277$	−37432.4	−	37432.4i	−0.487851	−	0.487851i	−0.907628	+	0.419776i	$0.862109\pi$
$278$	50357.9	−	50357.9i	0.651595	−	0.651595i
$279$		−	22304.4i		−	0.286538i
$280$	44867.4	+	22123.1i	0.572288	+	0.282182i
$281$	55811.9			0.706829			0.353415	−	0.935467i	$-0.385020\pi$
$281$	55811.9			0.706829			0.353415	+	0.935467i	$0.385020\pi$
$282$	−18642.1	−	18642.1i	−0.234422	−	0.234422i
$283$	57203.3	−	57203.3i	0.714246	−	0.714246i	−0.253174	−	0.967421i	$-0.581475\pi$
$283$	57203.3	−	57203.3i	0.714246	−	0.714246i	0.967421	+	0.253174i	$0.0814746\pi$
$284$			38286.7i			0.474691i
$285$	15493.3	+	45633.5i	0.190745	+	0.561816i
$286$	47523.3			0.580998
$287$	−34798.9	−	34798.9i	−0.422476	−	0.422476i
$288$	8571.11	−	8571.11i	0.103336	−	0.103336i
$289$			91054.7i			1.09020i
$290$	−45014.7	+	15283.2i	−0.535252	+	0.181726i
$291$	24530.7			0.289684
$292$	−16257.1	−	16257.1i	−0.190668	−	0.190668i
$293$	51133.0	−	51133.0i	0.595616	−	0.595616i	−0.343527	−	0.939143i	$-0.611622\pi$
$293$	51133.0	−	51133.0i	0.595616	−	0.595616i	0.939143	+	0.343527i	$0.111622\pi$
$294$			57431.2i			0.664436i
$295$	−32817.9	+	66557.3i	−0.377109	+	0.764806i
$296$	23174.5			0.264501
$297$	−73620.6	−	73620.6i	−0.834616	−	0.834616i
$298$	−69147.0	+	69147.0i	−0.778648	+	0.778648i
$299$		−	9868.35i		−	0.110383i
$300$	−2443.23	+	18573.8i	−0.0271469	+	0.206376i
$301$	−278863.			−3.07793
$302$	−26457.9	−	26457.9i	−0.290095	−	0.290095i
$303$	39138.6	−	39138.6i	0.426304	−	0.426304i
$304$		−	32927.4i		−	0.356296i
$305$	−50304.3	−	24803.9i	−0.540761	−	0.266637i
$306$	79134.1			0.845125
$307$	72960.7	+	72960.7i	0.774127	+	0.774127i	0.978825	−	0.204698i	$-0.0656213\pi$
$307$	72960.7	+	72960.7i	0.774127	+	0.774127i	−0.204698	+	0.978825i	$0.565621\pi$
$308$	−93950.0	+	93950.0i	−0.990366	+	0.990366i
$309$			48002.2i			0.502741i
$310$	−7572.12	−	22302.7i	−0.0787942	−	0.232079i
$311$	−142994.			−1.47842			−0.739209	−	0.673476i	$-0.764801\pi$
$311$	−142994.			−1.47842			−0.739209	+	0.673476i	$0.764801\pi$
$312$	−5363.26	−	5363.26i	−0.0550959	−	0.0550959i
$313$	−19009.5	+	19009.5i	−0.194036	+	0.194036i	−0.797438	−	0.603401i	$-0.793812\pi$
$313$	−19009.5	+	19009.5i	−0.194036	+	0.194036i	0.603401	+	0.797438i	$0.293812\pi$
$314$			6356.84i			0.0644736i
$315$	140181.	−	47593.7i	1.41276	−	0.479654i
$316$	38848.2			0.389042
$317$	47621.8	+	47621.8i	0.473901	+	0.473901i	0.903175	−	0.429274i	$-0.141230\pi$
$317$	47621.8	+	47621.8i	0.473901	+	0.473901i	−0.429274	+	0.903175i	$0.641230\pi$
$318$	−23970.5	+	23970.5i	−0.237041	+	0.237041i
$319$		−	126261.i		−	1.24076i
$320$	5660.67	−	11480.3i	0.0552800	−	0.112112i
$321$	42899.9			0.416338
$322$	19509.0	+	19509.0i	0.188158	+	0.188158i
$323$	152004.	−	152004.i	1.45697	−	1.45697i
$324$		−	26774.3i		−	0.255052i
$325$	−55438.0	−	7292.40i	−0.524857	−	0.0690405i
$326$	37541.7			0.353247
$327$	−715.951	−	715.951i	−0.00669557	−	0.00669557i
$328$	−8904.05	+	8904.05i	−0.0827637	+	0.0827637i
$329$			220000.i			2.03250i
$330$	−44626.5	−	22004.3i	−0.409793	−	0.202060i
$331$	−91697.4			−0.836953			−0.418476	−	0.908228i	$-0.637436\pi$
$331$	−91697.4			−0.836953			−0.418476	+	0.908228i	$0.637436\pi$
$332$	32261.0	+	32261.0i	0.292686	+	0.292686i
$333$	48494.0	−	48494.0i	0.437320	−	0.437320i
$334$		−	150023.i		−	1.34482i
$335$	−61173.5	−	180179.i	−0.545097	−	1.60552i
$336$	21205.5			0.187832
$337$	446.494	+	446.494i	0.00393148	+	0.00393148i	0.709070	−	0.705138i	$-0.249115\pi$
$337$	446.494	+	446.494i	0.00393148	+	0.00393148i	−0.705138	+	0.709070i	$0.749115\pi$
$338$	−41114.0	+	41114.0i	−0.359879	+	0.359879i
$339$			47820.8i			0.416119i
$340$	79128.3	−	26865.2i	0.684501	−	0.232398i
$341$	62556.5			0.537977
$342$	−68902.5	−	68902.5i	−0.589092	−	0.589092i
$343$	188741.	−	188741.i	1.60428	−	1.60428i
$344$			71353.1i			0.602971i
$345$	−4569.26	+	9266.81i	−0.0383890	+	0.0778560i
$346$	−91283.5			−0.762500
$347$	157424.	+	157424.i	1.30741	+	1.30741i	0.923279	+	0.384131i	$0.125499\pi$
$347$	157424.	+	157424.i	1.30741	+	1.30741i	0.384131	+	0.923279i	$0.374501\pi$
$348$	−14249.2	+	14249.2i	−0.117661	+	0.117661i
$349$			46900.5i			0.385058i	0.981291	+	0.192529i	$0.0616690\pi$
$349$			46900.5i			0.385058i	−0.981291	+	0.192529i	$0.938331\pi$
$350$	124013.	−	95180.3i	1.01235	−	0.776982i
$351$	−49597.3			−0.402573
$352$	24039.1	+	24039.1i	0.194014	+	0.194014i
$353$	166556.	−	166556.i	1.33663	−	1.33663i	0.437332	−	0.899300i	$-0.355923\pi$
$353$	166556.	−	166556.i	1.33663	−	1.33663i	0.899300	−	0.437332i	$-0.144077\pi$
$354$			31456.8i			0.251019i
$355$	107310.	+	52912.1i	0.851498	+	0.419854i
$356$	58372.8			0.460586
$357$	97891.7	+	97891.7i	0.768085	+	0.768085i
$358$	−29033.8	+	29033.8i	−0.226536	+	0.226536i
$359$			79935.1i			0.620224i	0.950700	+	0.310112i	$0.100367\pi$
$359$			79935.1i			0.620224i	−0.950700	+	0.310112i	$0.899633\pi$
$360$	−12177.9	−	35868.4i	−0.0939650	−	0.276762i
$361$	−134380.			−1.03115
$362$	−26969.2	−	26969.2i	−0.205803	−	0.205803i
$363$	54656.3	−	54656.3i	0.414789	−	0.414789i
$364$			63293.0i			0.477698i
$365$	−68032.7	+	23098.1i	−0.510660	+	0.173377i
$366$	−23775.2			−0.177485
$367$	−104574.	−	104574.i	−0.776412	−	0.776412i	0.202807	−	0.979219i	$-0.434994\pi$
$367$	−104574.	−	104574.i	−0.776412	−	0.776412i	−0.979219	+	0.202807i	$0.934994\pi$
$368$	4991.79	−	4991.79i	0.0368605	−	0.0368605i
$369$			37264.4i			0.273679i
$370$	32027.2	−	64953.6i	0.233946	−	0.474460i
$371$	282882.			2.05521
$372$	−7059.83	−	7059.83i	−0.0510162	−	0.0510162i
$373$	−114906.	+	114906.i	−0.825895	+	0.825895i	−0.986946	−	0.161051i	$-0.948512\pi$
$373$	−114906.	+	114906.i	−0.825895	+	0.825895i	0.161051	+	0.986946i	$0.448512\pi$
$374$			221945.i			1.58673i
$375$	48682.2	+	32516.9i	0.346184	+	0.231231i
$376$	56291.8			0.398171
$377$	−42530.2	−	42530.2i	−0.299237	−	0.299237i
$378$	98050.2	−	98050.2i	0.686222	−	0.686222i
$379$		−	103196.i		−	0.718431i	−0.933255	−	0.359216i	$-0.883044\pi$
$379$		−	103196.i		−	0.718431i	0.933255	−	0.359216i	$-0.116956\pi$
$380$	−92289.1	−	45505.7i	−0.639121	−	0.315136i
$381$	108917.			0.750322
$382$	−50103.0	−	50103.0i	−0.343350	−	0.343350i
$383$	−60795.1	+	60795.1i	−0.414449	+	0.414449i	−0.883285	−	0.468836i	$-0.844673\pi$
$383$	−60795.1	+	60795.1i	−0.414449	+	0.414449i	0.468836	+	0.883285i	$0.344673\pi$
$384$		−	5425.89i		−	0.0367967i
$385$	133485.	+	393162.i	0.900553	+	2.65247i
$386$	−53088.7			−0.356310
$387$	149310.	+	149310.i	0.996938	+	0.996938i
$388$	−37036.4	+	37036.4i	−0.246017	+	0.246017i
$389$			18753.4i			0.123931i	0.998078	+	0.0619655i	$0.0197369\pi$
$389$			18753.4i			0.123931i	−0.998078	+	0.0619655i	$0.980263\pi$
$390$	−22444.2	+	7620.14i	−0.147562	+	0.0500995i
$391$	46087.6			0.301460
$392$	−86709.6	−	86709.6i	−0.564280	−	0.564280i
$393$	40130.4	−	40130.4i	0.259829	−	0.259829i
$394$			16110.8i			0.103783i
$395$	53688.1	−	108884.i	0.344099	−	0.697861i
$396$	100606.			0.641558
$397$	67578.1	+	67578.1i	0.428771	+	0.428771i	0.888210	−	0.459439i	$-0.151949\pi$
$397$	67578.1	+	67578.1i	0.428771	+	0.428771i	−0.459439	+	0.888210i	$0.651949\pi$
$398$	−33741.1	+	33741.1i	−0.213006	+	0.213006i
$399$		−	170470.i		−	1.07078i
$400$	−24353.9	−	31731.5i	−0.152212	−	0.198322i
$401$	−241559.			−1.50223			−0.751113	−	0.660174i	$-0.770483\pi$
$401$	−241559.			−1.50223			−0.751113	+	0.660174i	$0.770483\pi$
$402$	−57034.8	−	57034.8i	−0.352929	−	0.352929i
$403$	21071.8	−	21071.8i	0.129745	−	0.129745i
$404$			118183.i			0.724088i
$405$	−75043.0	−	37002.0i	−0.457510	−	0.225588i
$406$	168158.			1.02015
$407$	136010.	+	136010.i	0.821071	+	0.821071i
$408$	25047.7	−	25047.7i	0.150469	−	0.150469i
$409$			70334.1i			0.420455i	0.977653	+	0.210227i	$0.0674204\pi$
$409$			70334.1i			0.420455i	−0.977653	+	0.210227i	$0.932580\pi$
$410$	12650.9	+	37261.7i	0.0752582	+	0.221664i
$411$	−2262.67			−0.0133949
$412$	−72473.7	−	72473.7i	−0.426959	−	0.426959i
$413$	185614.	−	185614.i	1.08821	−	1.08821i
$414$		−	20891.2i		−	0.121889i
$415$	135006.	−	45836.5i	0.783892	−	0.266143i
$416$	16194.9			0.0935818
$417$	−66708.1	−	66708.1i	−0.383624	−	0.383624i
$418$	193249.	−	193249.i	1.10602	−	1.10602i
$419$			144125.i			0.820937i	0.911875	+	0.410468i	$0.134635\pi$
$419$			144125.i			0.820937i	−0.911875	+	0.410468i	$0.865365\pi$
$420$	29306.0	−	59434.9i	0.166134	−	0.336932i
$421$	−91923.5			−0.518635			−0.259318	−	0.965792i	$-0.583498\pi$
$421$	−91923.5			−0.518635			−0.259318	+	0.965792i	$0.583498\pi$
$422$	−96745.7	−	96745.7i	−0.543259	−	0.543259i
$423$	117794.	−	117794.i	0.658326	−	0.658326i
$424$		−	72381.4i		−	0.402620i
$425$	34057.2	−	258909.i	0.188552	−	1.43340i
$426$	50717.6			0.279473
$427$	140288.	+	140288.i	0.769423	+	0.769423i
$428$	−64770.2	+	64770.2i	−0.353580	+	0.353580i
$429$		−	62953.2i		−	0.342061i
$430$	199989.	+	98610.0i	1.08161	+	0.533315i
$431$	283378.			1.52550			0.762748	−	0.646696i	$-0.223850\pi$
$431$	283378.			1.52550			0.762748	+	0.646696i	$0.223850\pi$
$432$	−25088.3	−	25088.3i	−0.134432	−	0.134432i
$433$	−135750.	+	135750.i	−0.724040	+	0.724040i	−0.969426	−	0.245385i	$-0.921086\pi$
$433$	−135750.	+	135750.i	−0.724040	+	0.724040i	0.245385	+	0.969426i	$0.421086\pi$
$434$			83314.7i			0.442326i
$435$	20245.3	+	59630.1i	0.106991	+	0.315128i
$436$	2161.88			0.0113726
$437$	−40128.7	−	40128.7i	−0.210132	−	0.210132i
$438$	−21535.4	+	21535.4i	−0.112255	+	0.112255i
$439$			165670.i			0.859635i	0.902916	+	0.429817i	$0.141422\pi$
$439$			165670.i			0.859635i	−0.902916	+	0.429817i	$0.858578\pi$
$440$	100599.	−	34154.9i	0.519623	−	0.176420i
$441$	−362889.			−1.86594
$442$	74760.9	+	74760.9i	0.382675	+	0.382675i
$443$	−33291.1	+	33291.1i	−0.169637	+	0.169637i	−0.786820	−	0.617183i	$-0.788274\pi$
$443$	−33291.1	+	33291.1i	−0.169637	+	0.169637i	0.617183	+	0.786820i	$0.288274\pi$
$444$		−	30698.8i		−	0.155724i
$445$	80671.2	−	163608.i	0.407379	−	0.826196i
$446$	112180.			0.563957
$447$	91597.7	+	91597.7i	0.458426	+	0.458426i
$448$	−32016.1	+	32016.1i	−0.159519	+	0.159519i
$449$		−	179056.i		−	0.888170i	−0.895985	−	0.444085i	$-0.853529\pi$
$449$		−	179056.i		−	0.888170i	0.895985	−	0.444085i	$-0.146471\pi$
$450$	−117362.	−	15437.9i	−0.579565	−	0.0762368i
$451$	−104514.			−0.513835
$452$	−72199.8	−	72199.8i	−0.353394	−	0.353394i
$453$	−35048.2	+	35048.2i	−0.170793	+	0.170793i
$454$			25387.6i			0.123171i
$455$	177398.	+	87470.9i	0.856891	+	0.422514i
$456$	−43618.3			−0.209768
$457$	40120.7	+	40120.7i	0.192104	+	0.192104i	0.796605	−	0.604501i	$-0.206627\pi$
$457$	40120.7	+	40120.7i	0.192104	+	0.192104i	−0.604501	+	0.796605i	$0.706627\pi$
$458$	−102843.	+	102843.i	−0.490278	+	0.490278i
$459$		−	231631.i		−	1.09944i
$460$	−7092.36	−	20889.7i	−0.0335178	−	0.0987225i
$461$	203856.			0.959229			0.479614	−	0.877479i	$-0.340777\pi$
$461$	203856.			0.959229			0.479614	+	0.877479i	$0.340777\pi$
$462$	124454.	+	124454.i	0.583074	+	0.583074i
$463$	−286555.	+	286555.i	−1.33674	+	1.33674i	−0.437540	+	0.899199i	$0.644150\pi$
$463$	−286555.	+	286555.i	−1.33674	+	1.33674i	−0.899199	+	0.437540i	$0.855850\pi$
$464$		−	43026.9i		−	0.199850i
$465$	−29544.0	+	10030.6i	−0.136635	+	0.0463898i
$466$	11840.0			0.0545230
$467$	−24773.4	−	24773.4i	−0.113593	−	0.113593i	0.648026	−	0.761619i	$-0.275595\pi$
$467$	−24773.4	−	24773.4i	−0.113593	−	0.113593i	−0.761619	+	0.648026i	$0.775595\pi$
$468$	33888.7	−	33888.7i	0.154726	−	0.154726i
$469$			673081.i			3.06000i
$470$	77795.2	−	157775.i	0.352174	−	0.714236i
$471$	8420.78			0.0379586
$472$	−47493.4	−	47493.4i	−0.213181	−	0.213181i
$473$	−418767.	+	418767.i	−1.87176	+	1.87176i
$474$		−	51461.4i		−	0.229047i
$475$	−255087.	+	195779.i	−1.13058	+	0.867720i
$476$	−295594.			−1.30461
$477$	−151462.	−	151462.i	−0.665682	−	0.665682i
$478$	58827.0	−	58827.0i	0.257467	−	0.257467i
$479$		−	327934.i		−	1.42927i	−0.699495	−	0.714637i	$-0.746592\pi$
$479$		−	327934.i		−	1.42927i	0.699495	−	0.714637i	$-0.253408\pi$
$480$	−15207.7	−	7498.57i	−0.0660056	−	0.0325459i
$481$	91628.1			0.396039
$482$	−69085.5	−	69085.5i	−0.297367	−	0.297367i
$483$	25843.2	−	25843.2i	0.110777	−	0.110777i
$484$			165040.i			0.704529i
$485$	52621.5	+	154990.i	0.223707	+	0.658902i
$486$	−162477.			−0.687889
$487$	−222550.	−	222550.i	−0.938360	−	0.938360i	0.0598475	−	0.998208i	$-0.480939\pi$
$487$	−222550.	−	222550.i	−0.938360	−	0.938360i	−0.998208	+	0.0598475i	$0.980939\pi$
$488$	35895.7	−	35895.7i	0.150731	−	0.150731i
$489$		−	49730.7i		−	0.207973i
$490$	−362862.	+	123197.i	−1.51130	+	0.513108i
$491$	−159235.			−0.660505			−0.330252	−	0.943893i	$-0.607134\pi$
$491$	−159235.			−0.660505			−0.330252	+	0.943893i	$0.607134\pi$
$492$	11795.0	+	11795.0i	0.0487268	+	0.0487268i
$493$	198626.	−	198626.i	0.817227	−	0.817227i
$494$		−	130189.i		−	0.533485i
$495$	139038.	−	281980.i	0.567444	−	1.15082i
$496$	21317.9			0.0866523
$497$	−299265.	−	299265.i	−1.21155	−	1.21155i
$498$	42735.5	−	42735.5i	0.172318	−	0.172318i
$499$			44585.7i			0.179058i	0.995984	+	0.0895291i	$0.0285362\pi$
$499$			44585.7i			0.179058i	−0.995984	+	0.0895291i	$0.971464\pi$
$500$	−122594.	+	24406.4i	−0.490377	+	0.0976254i
$501$	−198732.			−0.791758
$502$	−32050.8	−	32050.8i	−0.127184	−	0.127184i
$503$	127131.	−	127131.i	0.502478	−	0.502478i	−0.409729	−	0.912207i	$-0.634377\pi$
$503$	127131.	−	127131.i	0.502478	−	0.502478i	0.912207	+	0.409729i	$0.134377\pi$
$504$			133991.i			0.527490i
$505$	331243.	+	163328.i	1.29886	+	0.640441i
$506$	58593.0			0.228847
$507$	54462.9	+	54462.9i	0.211878	+	0.211878i
$508$	−164443.	+	164443.i	−0.637220	+	0.637220i
$509$		−	317112.i		−	1.22399i	−0.790862	−	0.611994i	$-0.790368\pi$
$509$		−	317112.i		−	1.22399i	0.790862	−	0.611994i	$-0.209632\pi$
$510$	−35587.9	−	104820.i	−0.136824	−	0.402997i
$511$	254144.			0.973282
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−201683.	+	201683.i	−0.766362	+	0.766362i
$514$		−	216475.i		−	0.819372i
$515$	−303288.	+	102971.i	−1.14351	+	0.388240i
$516$	94520.1			0.354997
$517$	330373.	+	330373.i	1.23601	+	1.23601i
$518$	−181142.	+	181142.i	−0.675086	+	0.675086i
$519$			120921.i			0.448919i
$520$	22381.3	−	45391.1i	0.0827711	−	0.167866i
$521$	422177.			1.55532			0.777659	−	0.628686i	$-0.216407\pi$
$521$	422177.			1.55532			0.777659	+	0.628686i	$0.216407\pi$
$522$	−90036.1	−	90036.1i	−0.330427	−	0.330427i
$523$	−139172.	+	139172.i	−0.508801	+	0.508801i	−0.914158	−	0.405357i	$-0.867147\pi$
$523$	−139172.	+	139172.i	−0.508801	+	0.508801i	0.405357	+	0.914158i	$0.367147\pi$
$524$			121178.i			0.441326i
$525$	−126083.	−	164278.i	−0.457445	−	0.596020i
$526$	−349926.			−1.26475
$527$	98410.2	+	98410.2i	0.354339	+	0.354339i
$528$	31844.2	−	31844.2i	0.114225	−	0.114225i
$529$		−	12167.0i		−	0.0434783i
$530$	−202871.	−	100031.i	−0.722217	−	0.356109i
$531$	−198765.			−0.704938
$532$	257375.	+	257375.i	0.909374	+	0.909374i
$533$	−35205.1	+	35205.1i	−0.123923	+	0.123923i
$534$		−	77325.3i		−	0.271168i
$535$	92025.7	+	271050.i	0.321515	+	0.946983i
$536$	172222.			0.599459
$537$	38460.5	+	38460.5i	0.133373	+	0.133373i
$538$	90970.1	−	90970.1i	0.314293	−	0.314293i
$539$		−	1.01778e6i		−	3.50331i
$540$	−104989.	+	35645.5i	−0.360046	+	0.122241i
$541$	417393.			1.42610			0.713051	−	0.701112i	$-0.247313\pi$
$541$	417393.			1.42610			0.713051	+	0.701112i	$0.247313\pi$
$542$	−167412.	−	167412.i	−0.569887	−	0.569887i
$543$	−35725.6	+	35725.6i	−0.121166	+	0.121166i
$544$			75634.0i			0.255575i
$545$	2987.72	−	6059.33i	0.0100588	−	0.0204001i
$546$	83843.0			0.281243
$547$	206403.	+	206403.i	0.689828	+	0.689828i	0.962194	−	0.272366i	$-0.0878060\pi$
$547$	206403.	+	206403.i	0.689828	+	0.689828i	−0.272366	+	0.962194i	$0.587806\pi$
$548$	3416.18	−	3416.18i	0.0113757	−	0.0113757i
$549$		−	150228.i		−	0.498431i
$550$	43298.4	−	329161.i	0.143135	−	1.08814i
$551$	−345890.			−1.13929
$552$	−6612.53	−	6612.53i	−0.0217015	−	0.0217015i
$553$	−303654.	+	303654.i	−0.992952	+	0.992952i
$554$		−	149729.i		−	0.487851i
$555$	−86042.7	−	42425.7i	−0.279337	−	0.137735i
$556$	201432.			0.651595
$557$	−146771.	−	146771.i	−0.473076	−	0.473076i	0.429833	−	0.902909i	$-0.358573\pi$
$557$	−146771.	−	146771.i	−0.473076	−	0.473076i	−0.902909	+	0.429833i	$0.858573\pi$
$558$	44608.8	−	44608.8i	0.143269	−	0.143269i
$559$			282118.i			0.902833i
$560$	45488.5	+	133981.i	0.145053	+	0.427235i
$561$	294006.			0.934181
$562$	111624.	+	111624.i	0.353415	+	0.353415i
$563$	−185392.	+	185392.i	−0.584890	+	0.584890i	−0.936243	−	0.351353i	$-0.885722\pi$
$563$	−185392.	+	185392.i	−0.584890	+	0.584890i	0.351353	+	0.936243i	$0.385722\pi$
$564$		−	74568.6i		−	0.234422i
$565$	−302142.	+	102582.i	−0.946486	+	0.321346i
$566$	228813.			0.714246
$567$	209279.	+	209279.i	0.650968	+	0.650968i
$568$	−76573.3	+	76573.3i	−0.237345	+	0.237345i
$569$		−	91453.7i		−	0.282473i	−0.989976	−	0.141236i	$-0.954892\pi$
$569$		−	91453.7i		−	0.282473i	0.989976	−	0.141236i	$-0.0451078\pi$
$570$	−60280.5	+	122254.i	−0.185535	+	0.376280i
$571$	−342959.			−1.05189			−0.525945	−	0.850519i	$-0.676288\pi$
$571$	−342959.			−1.05189			−0.525945	+	0.850519i	$0.676288\pi$
$572$	95046.7	+	95046.7i	0.290499	+	0.290499i
$573$	−66370.4	+	66370.4i	−0.202146	+	0.202146i
$574$		−	139196.i		−	0.422476i
$575$	−68351.3	−	8991.03i	−0.206734	−	0.0271940i
$576$	34284.4			0.103336
$577$	232825.	+	232825.i	0.699323	+	0.699323i	0.964264	−	0.264942i	$-0.0853527\pi$
$577$	232825.	+	232825.i	0.699323	+	0.699323i	−0.264942	+	0.964264i	$0.585353\pi$
$578$	−182109.	+	182109.i	−0.545101	+	0.545101i
$579$			70325.6i			0.209776i
$580$	−120596.	−	59463.1i	−0.358489	−	0.176763i
$581$	−504331.			−1.49404
$582$	49061.4	+	49061.4i	0.144842	+	0.144842i
$583$	424801.	−	424801.i	1.24982	−	1.24982i
$584$		−	65028.3i		−	0.190668i
$585$	−48149.2	−	141818.i	−0.140695	−	0.414398i
$586$	204532.			0.595616
$587$	−259360.	−	259360.i	−0.752709	−	0.752709i	0.222275	−	0.974984i	$-0.428652\pi$
$587$	−259360.	−	259360.i	−0.752709	−	0.752709i	−0.974984	+	0.222275i	$0.928652\pi$
$588$	−114862.	+	114862.i	−0.332218	+	0.332218i
$589$		−	171373.i		−	0.493982i
$590$	−198750.	+	67478.7i	−0.570958	+	0.193849i
$591$	21341.7			0.0611017
$592$	46349.0	+	46349.0i	0.132250	+	0.132250i
$593$	−271151.	+	271151.i	−0.771084	+	0.771084i	−0.978296	−	0.207212i	$-0.933561\pi$
$593$	−271151.	+	271151.i	−0.771084	+	0.771084i	0.207212	+	0.978296i	$0.433561\pi$
$594$		−	294482.i		−	0.834616i
$595$	−408510.	+	828490.i	−1.15390	+	2.34020i
$596$	−276588.			−0.778648
$597$	44696.1	+	44696.1i	0.125407	+	0.125407i
$598$	19736.7	−	19736.7i	0.0551915	−	0.0551915i
$599$		−	429073.i		−	1.19585i	−0.801551	−	0.597927i	$-0.795991\pi$
$599$		−	429073.i		−	1.19585i	0.801551	−	0.597927i	$-0.204009\pi$
$600$	−42034.0	+	32261.1i	−0.116761	+	0.0896143i
$601$	−407826.			−1.12908			−0.564541	−	0.825405i	$-0.690947\pi$
$601$	−407826.			−1.12908			−0.564541	+	0.825405i	$0.690947\pi$
$602$	−557726.	−	557726.i	−1.53896	−	1.53896i
$603$	360385.	−	360385.i	0.991132	−	0.991132i
$604$		−	105831.i		−	0.290095i
$605$	462575.	+	228085.i	1.26378	+	0.623141i
$606$	156554.			0.426304
$607$	−417980.	−	417980.i	−1.13443	−	1.13443i	−0.989432	−	0.144998i	$-0.953682\pi$
$607$	−417980.	−	417980.i	−1.13443	−	1.13443i	−0.144998	−	0.989432i	$-0.546318\pi$
$608$	65854.9	−	65854.9i	0.178148	−	0.178148i
$609$		−	222756.i		−	0.600612i
$610$	−51000.8	−	150216.i	−0.137062	−	0.403699i
$611$	222568.			0.596184
$612$	158268.	+	158268.i	0.422563	+	0.422563i
$613$	387841.	−	387841.i	1.03213	−	1.03213i	0.0326601	−	0.999467i	$-0.489602\pi$
$613$	387841.	−	387841.i	1.03213	−	1.03213i	0.999467	−	0.0326601i	$-0.0103979\pi$
$614$			291843.i			0.774127i
$615$	49359.8	−	16758.4i	0.130504	−	0.0443080i
$616$	−375800.			−0.990366
$617$	302216.	+	302216.i	0.793867	+	0.793867i	0.982120	−	0.188254i	$-0.0602827\pi$
$617$	302216.	+	302216.i	0.793867	+	0.793867i	−0.188254	+	0.982120i	$0.560283\pi$
$618$	−96004.4	+	96004.4i	−0.251370	+	0.251370i
$619$			117940.i			0.307809i	0.988086	+	0.153905i	$0.0491848\pi$
$619$			117940.i			0.307809i	−0.988086	+	0.153905i	$0.950815\pi$
$620$	29461.3	−	59749.7i	0.0766422	−	0.155436i
$621$	−61150.1			−0.158567
$622$	−285988.	−	285988.i	−0.739209	−	0.739209i
$623$	−456267.	+	456267.i	−1.17555	+	1.17555i
$624$		−	21453.0i		−	0.0550959i
$625$	−101019.	+	377337.i	−0.258608	+	0.965982i
$626$	−76038.1			−0.194036
$627$	−255993.	−	255993.i	−0.651168	−	0.651168i
$628$	−12713.7	+	12713.7i	−0.0322368	+	0.0322368i
$629$			427925.i			1.08160i
$630$	375550.	+	185175.i	0.946208	+	0.466554i
$631$	31094.8			0.0780960			0.0390480	−	0.999237i	$-0.487567\pi$
$631$	31094.8			0.0780960			0.0390480	+	0.999237i	$0.487567\pi$
$632$	77696.3	+	77696.3i	0.194521	+	0.194521i
$633$	−128157.	+	128157.i	−0.319842	+	0.319842i
$634$			190487.i			0.473901i
$635$	233642.	+	688163.i	0.579433	+	1.70665i
$636$	−95882.1			−0.237041
$637$	−342835.	−	342835.i	−0.844901	−	0.844901i
$638$	252522.	−	252522.i	0.620379	−	0.620379i
$639$			320468.i			0.784843i
$640$	34281.9	−	11639.2i	0.0836960	−	0.0284161i
$641$	89149.0			0.216970			0.108485	−	0.994098i	$-0.465400\pi$
$641$	89149.0			0.216970			0.108485	+	0.994098i	$0.465400\pi$
$642$	85799.7	+	85799.7i	0.208169	+	0.208169i
$643$	370437.	−	370437.i	0.895967	−	0.895967i	−0.0991097	−	0.995077i	$-0.531599\pi$
$643$	370437.	−	370437.i	0.895967	−	0.895967i	0.995077	+	0.0991097i	$0.0315995\pi$
$644$			78036.0i			0.188158i
$645$	130627.	−	264921.i	0.313988	−	0.636791i
$646$	608016.			1.45697
$647$	306107.	+	306107.i	0.731248	+	0.731248i	0.970867	−	0.239619i	$-0.0770225\pi$
$647$	306107.	+	306107.i	0.731248	+	0.731248i	−0.239619	+	0.970867i	$0.577022\pi$
$648$	53548.6	−	53548.6i	0.127526	−	0.127526i
$649$		−	557471.i		−	1.32353i
$650$	−96291.2	−	125461.i	−0.227908	−	0.296949i
$651$	110365.			0.260418
$652$	75083.4	+	75083.4i	0.176624	+	0.176624i
$653$	18110.4	−	18110.4i	0.0424718	−	0.0424718i	−0.685552	−	0.728024i	$-0.740439\pi$
$653$	18110.4	−	18110.4i	0.0424718	−	0.0424718i	0.728024	+	0.685552i	$0.240439\pi$
$654$		−	2863.80i		−	0.00669557i
$655$	339637.	+	167467.i	0.791648	+	0.390344i
$656$	−35616.2			−0.0827637
$657$	−136075.	−	136075.i	−0.315246	−	0.315246i
$658$	−440000.	+	440000.i	−1.01625	+	1.01625i
$659$		−	535210.i		−	1.23240i	−0.787588	−	0.616202i	$-0.788670\pi$
$659$		−	535210.i		−	1.23240i	0.787588	−	0.616202i	$-0.211330\pi$
$660$	−45244.3	−	133262.i	−0.103867	−	0.305926i
$661$	−202209.			−0.462804			−0.231402	−	0.972858i	$-0.574331\pi$
$661$	−202209.			−0.462804			−0.231402	+	0.972858i	$0.574331\pi$
$662$	−183395.	−	183395.i	−0.418476	−	0.418476i
$663$	99034.3	−	99034.3i	0.225299	−	0.225299i
$664$			129044.i			0.292686i
$665$	1.07706e6	−	365679.i	2.43555	−	0.826907i
$666$	193976.			0.437320
$667$	−52436.8	−	52436.8i	−0.117865	−	0.117865i
$668$	300046.	−	300046.i	0.672410	−	0.672410i
$669$		−	148603.i		−	0.332028i
$670$	238011.	−	482705.i	0.530209	−	1.07531i
$671$	421339.			0.935808
$672$	42411.0	+	42411.0i	0.0939162	+	0.0939162i
$673$	−398998.	+	398998.i	−0.880928	+	0.880928i	−0.993629	−	0.112701i	$-0.964050\pi$
$673$	−398998.	+	398998.i	−0.880928	+	0.880928i	0.112701	+	0.993629i	$0.464050\pi$
$674$			1785.98i			0.00393148i
$675$	−45188.0	+	343527.i	−0.0991780	+	0.753968i
$676$	−164456.			−0.359879
$677$	196805.	+	196805.i	0.429397	+	0.429397i	0.888423	−	0.459026i	$-0.151802\pi$
$677$	196805.	+	196805.i	0.429397	+	0.429397i	−0.459026	+	0.888423i	$0.651802\pi$
$678$	−95641.6	+	95641.6i	−0.208060	+	0.208060i
$679$		−	578985.i		−	1.25582i
$680$	211987.	+	104526.i	0.458450	+	0.226051i
$681$	33630.4			0.0725166
$682$	125113.	+	125113.i	0.268988	+	0.268988i
$683$	159121.	−	159121.i	0.341103	−	0.341103i	−0.515679	−	0.856782i	$-0.672460\pi$
$683$	159121.	−	159121.i	0.341103	−	0.341103i	0.856782	+	0.515679i	$0.172460\pi$
$684$		−	275610.i		−	0.589092i
$685$	−4853.72	−	14296.0i	−0.0103441	−	0.0304673i
$686$	754966.			1.60428
$687$	136234.	+	136234.i	0.288650	+	0.288650i
$688$	−142706.	+	142706.i	−0.301485	+	0.301485i
$689$		−	286184.i		−	0.602846i
$690$	−27672.1	+	9395.11i	−0.0581225	+	0.0197335i
$691$	−165759.			−0.347154			−0.173577	−	0.984820i	$-0.555533\pi$
$691$	−165759.			−0.347154			−0.173577	+	0.984820i	$0.555533\pi$
$692$	−182567.	−	182567.i	−0.381250	−	0.381250i
$693$	−786383.	+	786383.i	−1.63745	+	1.63745i
$694$			629695.i			1.30741i
$695$	278378.	−	564573.i	0.576323	−	1.16883i
$696$	−56996.8			−0.117661
$697$	−164416.	−	164416.i	−0.338438	−	0.338438i
$698$	−93801.0	+	93801.0i	−0.192529	+	0.192529i
$699$		−	15684.2i		−	0.0321002i
$700$	438387.	+	57666.1i	0.894668	+	0.117686i
$701$	−108545.			−0.220889			−0.110444	−	0.993882i	$-0.535227\pi$
$701$	−108545.			−0.220889			−0.110444	+	0.993882i	$0.535227\pi$
$702$	−99194.7	−	99194.7i	−0.201286	−	0.201286i
$703$	372596.	−	372596.i	0.753925	−	0.753925i
$704$			96156.6i			0.194014i
$705$	−209001.	−	103054.i	−0.420504	−	0.207341i
$706$	666226.			1.33663
$707$	−923766.	−	923766.i	−1.84809	−	1.84809i
$708$	−62913.5	+	62913.5i	−0.125510	+	0.125510i
$709$		−	575985.i		−	1.14583i	−0.819616	−	0.572913i	$-0.805813\pi$
$709$		−	575985.i		−	1.14583i	0.819616	−	0.572913i	$-0.194187\pi$
$710$	108796.	+	320444.i	0.215822	+	0.635676i
$711$	325168.			0.643233
$712$	116746.	+	116746.i	0.230293	+	0.230293i
$713$	25980.1	−	25980.1i	0.0511047	−	0.0511047i
$714$			391567.i			0.768085i
$715$	397751.	−	135043.i	0.778036	−	0.264155i
$716$	−116135.			−0.226536
$717$	−77926.9	−	77926.9i	−0.151583	−	0.151583i
$718$	−159870.	+	159870.i	−0.310112	+	0.310112i
$719$			505202.i			0.977253i	0.872493	+	0.488626i	$0.162502\pi$
$719$			505202.i			0.977253i	−0.872493	+	0.488626i	$0.837498\pi$
$720$	47381.1	−	96092.5i	0.0913987	−	0.185364i
$721$	1.13297e6			2.17945
$722$	−268760.	−	268760.i	−0.515574	−	0.515574i
$723$	−91516.1	+	91516.1i	−0.175074	+	0.175074i
$724$		−	107877.i		−	0.205803i
$725$	−333327.	+	255828.i	−0.634153	+	0.486712i
$726$	218625.			0.414789
$727$	−321022.	−	321022.i	−0.607388	−	0.607388i	0.334875	−	0.942263i	$-0.391306\pi$
$727$	−321022.	−	321022.i	−0.607388	−	0.607388i	−0.942263	+	0.334875i	$0.891306\pi$
$728$	−126586.	+	126586.i	−0.238849	+	0.238849i
$729$		−	55860.1i		−	0.105111i
$730$	−182262.	−	89869.1i	−0.342018	−	0.168642i
$731$	−1.31756e6			−2.46567
$732$	−47550.3	−	47550.3i	−0.0887425	−	0.0887425i
$733$	−256340.	+	256340.i	−0.477100	+	0.477100i	−0.904203	−	0.427103i	$-0.859534\pi$
$733$	−256340.	+	256340.i	−0.477100	+	0.477100i	0.427103	+	0.904203i	$0.359534\pi$
$734$		−	418297.i		−	0.776412i
$735$	163197.	+	480676.i	0.302091	+	0.889771i
$736$	19967.2			0.0368605
$737$	1.01076e6	+	1.01076e6i	1.86086	+	1.86086i
$738$	−74528.9	+	74528.9i	−0.136840	+	0.136840i
$739$			757098.i			1.38632i	0.720785	+	0.693159i	$0.243782\pi$
$739$			757098.i			1.38632i	−0.720785	+	0.693159i	$0.756218\pi$
$740$	193961.	−	65852.8i	0.354203	−	0.120257i
$741$	−172459.			−0.314087
$742$	565763.	+	565763.i	1.02761	+	1.02761i
$743$	138870.	−	138870.i	0.251554	−	0.251554i	−0.570054	−	0.821607i	$-0.693078\pi$
$743$	138870.	−	138870.i	0.251554	−	0.251554i	0.821607	+	0.570054i	$0.193078\pi$
$744$		−	28239.3i		−	0.0510162i
$745$	−382245.	+	775222.i	−0.688698	+	1.39673i
$746$	−459624.			−0.825895
$747$	270032.	+	270032.i	0.483920	+	0.483920i
$748$	−443890.	+	443890.i	−0.793364	+	0.793364i
$749$		−	1.01254e6i		−	1.80488i
$750$	32330.6	+	162398.i	0.0574766	+	0.288708i
$751$	584538.			1.03641			0.518207	−	0.855255i	$-0.326600\pi$
$751$	584538.			1.03641			0.518207	+	0.855255i	$0.326600\pi$
$752$	112584.	+	112584.i	0.199085	+	0.199085i
$753$	−42457.0	+	42457.0i	−0.0748790	+	0.0748790i
$754$		−	170121.i		−	0.299237i
$755$	−296625.	−	146259.i	−0.520371	−	0.256583i
$756$	392201.			0.686222
$757$	−633906.	−	633906.i	−1.10620	−	1.10620i	−0.993646	−	0.112553i	$-0.964097\pi$
$757$	−633906.	−	633906.i	−1.10620	−	1.10620i	−0.112553	−	0.993646i	$-0.535903\pi$
$758$	206392.	−	206392.i	0.359216	−	0.359216i
$759$		−	77617.0i		−	0.134733i
$760$	−93566.8	−	275590.i	−0.161992	−	0.477129i
$761$	−27969.8			−0.0482969			−0.0241485	−	0.999708i	$-0.507687\pi$
$761$	−27969.8			−0.0482969			−0.0241485	+	0.999708i	$0.507687\pi$
$762$	217835.	+	217835.i	0.375161	+	0.375161i
$763$	−16898.2	+	16898.2i	−0.0290263	+	0.0290263i
$764$		−	200412.i		−	0.343350i
$765$	662321.	−	224868.i	1.13174	−	0.384242i
$766$	−243180.			−0.414449
$767$	−187781.	−	187781.i	−0.319198	−	0.319198i
$768$	10851.8	−	10851.8i	0.0183983	−	0.0183983i
$769$			323335.i			0.546764i	0.961906	+	0.273382i	$0.0881423\pi$
$769$			323335.i			0.546764i	−0.961906	+	0.273382i	$0.911858\pi$
$770$	−519356.	+	1.05329e6i	−0.875958	+	1.77651i
$771$	−286760.			−0.482403
$772$	−106177.	−	106177.i	−0.178155	−	0.178155i
$773$	172710.	−	172710.i	0.289040	−	0.289040i	−0.547661	−	0.836700i	$-0.684482\pi$
$773$	172710.	−	172710.i	0.289040	−	0.289040i	0.836700	+	0.547661i	$0.184482\pi$
$774$			597242.i			0.996938i
$775$	−126751.	−	165148.i	−0.211032	−	0.274961i
$776$	−148146.			−0.246017
$777$	239955.	+	239955.i	0.397455	+	0.397455i
$778$	−37506.7	+	37506.7i	−0.0619655	+	0.0619655i
$779$			286316.i			0.471814i
$780$	−60128.6	−	29648.1i	−0.0988308	−	0.0487312i
$781$	−898807.			−1.47355
$782$	92175.1	+	92175.1i	0.150730	+	0.150730i
$783$	−263542.	+	263542.i	−0.429860	+	0.429860i
$784$		−	346838.i		−	0.564280i
$785$	18063.6	+	53204.2i	0.0293134	+	0.0863390i
$786$	160522.			0.259829
$787$	568086.	+	568086.i	0.917202	+	0.917202i	0.996825	−	0.0796231i	$-0.0253717\pi$
$787$	568086.	+	568086.i	0.917202	+	0.917202i	−0.0796231	+	0.996825i	$0.525372\pi$
$788$	−32221.6	+	32221.6i	−0.0518914	+	0.0518914i
$789$			463540.i			0.744617i
$790$	325144.	−	110391.i	0.520980	−	0.176881i
$791$	1.12869e6			1.80394
$792$	201213.	+	201213.i	0.320779	+	0.320779i
$793$	141926.	−	141926.i	0.225691	−	0.225691i
$794$			270313.i			0.428771i
$795$	−132509.	+	268739.i	−0.209658	+	0.425203i
$796$	−134964.			−0.213006
$797$	−738865.	−	738865.i	−1.16318	−	1.16318i	−0.983774	−	0.179410i	$-0.942581\pi$
$797$	−738865.	−	738865.i	−1.16318	−	1.16318i	−0.179410	−	0.983774i	$-0.557419\pi$
$798$	340939.	−	340939.i	0.535391	−	0.535391i
$799$			1.03945e6i			1.62820i
$800$	14755.1	−	112171.i	0.0230549	−	0.175267i
$801$	488594.			0.761522
$802$	−483119.	−	483119.i	−0.751113	−	0.751113i
$803$	381647.	−	381647.i	0.591876	−	0.591876i
$804$		−	228139.i		−	0.352929i
$805$	218719.	+	107846.i	0.337517	+	0.166422i
$806$	84287.1			0.129745
$807$	−120506.	−	120506.i	−0.185039	−	0.185039i
$808$	−236365.	+	236365.i	−0.362044	+	0.362044i
$809$		−	635486.i		−	0.970977i	−0.874243	−	0.485489i	$-0.838642\pi$
$809$		−	635486.i		−	0.970977i	0.874243	−	0.485489i	$-0.161358\pi$
$810$	−76082.0	−	224090.i	−0.115961	−	0.341549i
$811$	−511659.			−0.777928			−0.388964	−	0.921253i	$-0.627167\pi$
$811$	−511659.			−0.777928			−0.388964	+	0.921253i	$0.627167\pi$
$812$	336316.	+	336316.i	0.510077	+	0.510077i
$813$	−221768.	+	221768.i	−0.335519	+	0.335519i
$814$			544038.i			0.821071i
$815$	314209.	−	106679.i	0.473046	−	0.160606i
$816$	100191.			0.150469
$817$	1.14721e6	+	1.14721e6i	1.71869	+	1.71869i
$818$	−140668.	+	140668.i	−0.210227	+	0.210227i
$819$			529777.i			0.789815i
$820$	−49221.5	+	99825.1i	−0.0732028	+	0.148461i
$821$	−1.19029e6			−1.76590			−0.882951	−	0.469465i	$-0.844447\pi$
$821$	−1.19029e6			−1.76590			−0.882951	+	0.469465i	$0.844447\pi$
$822$	−4525.35	−	4525.35i	−0.00669743	−	0.00669743i
$823$	−407230.	+	407230.i	−0.601229	+	0.601229i	−0.940639	−	0.339410i	$-0.889773\pi$
$823$	−407230.	+	407230.i	−0.601229	+	0.601229i	0.339410	+	0.940639i	$0.389773\pi$
$824$		−	289895.i		−	0.426959i
$825$	−436033.	−	57356.5i	−0.640637	−	0.0842703i
$826$	742457.			1.08821
$827$	−736630.	−	736630.i	−1.07706	−	1.07706i	−0.996772	−	0.0802846i	$-0.974417\pi$
$827$	−736630.	−	736630.i	−1.07706	−	1.07706i	−0.0802846	−	0.996772i	$-0.525583\pi$
$828$	41782.4	−	41782.4i	0.0609443	−	0.0609443i
$829$		−	1.35902e6i		−	1.97750i	−0.149588	−	0.988748i	$-0.547795\pi$
$829$		−	1.35902e6i		−	1.97750i	0.149588	−	0.988748i	$-0.452205\pi$
$830$	361685.	+	178339.i	0.525017	+	0.258874i
$831$	−198344.			−0.287221
$832$	32389.8	+	32389.8i	0.0467909	+	0.0467909i
$833$	1.60112e6	−	1.60112e6i	2.30746	−	2.30746i
$834$		−	266832.i		−	0.383624i
$835$	−426306.	−	1.25563e6i	−0.611432	−	1.80090i
$836$	772995.			1.10602
$837$	−130573.	−	130573.i	−0.186382	−	0.186382i
$838$	−288249.	+	288249.i	−0.410468	+	0.410468i
$839$			131066.i			0.186194i	0.995657	+	0.0930971i	$0.0296767\pi$
$839$			131066.i			0.186194i	−0.995657	+	0.0930971i	$0.970323\pi$
$840$	177482.	−	60257.7i	0.251533	−	0.0853993i
$841$	255301.			0.360961
$842$	−183847.	−	183847.i	−0.259318	−	0.259318i
$843$	147866.	−	147866.i	0.208072	−	0.208072i
$844$		−	386983.i		−	0.543259i
$845$	−227278.	+	460938.i	−0.318306	+	0.645549i
$846$	471175.			0.658326
$847$	−1.29002e6	−	1.29002e6i	−1.79817	−	1.79817i
$848$	144763.	−	144763.i	0.201310	−	0.201310i
$849$		−	303104.i		−	0.420510i
$850$	585932.	−	449703.i	0.810978	−	0.622426i
$851$	112971.			0.155994
$852$	101435.	+	101435.i	0.139736	+	0.139736i
$853$	617422.	−	617422.i	0.848562	−	0.848562i	−0.141391	−	0.989954i	$-0.545158\pi$
$853$	617422.	−	617422.i	0.848562	−	0.848562i	0.989954	+	0.141391i	$0.0451576\pi$
$854$			561152.i			0.769423i
$855$	−772481.	−	380893.i	−1.05671	−	0.521039i
$856$	−259081.			−0.353580
$857$	919585.	+	919585.i	1.25207	+	1.25207i	0.954789	+	0.297286i	$0.0960815\pi$
$857$	919585.	+	919585.i	1.25207	+	1.25207i	0.297286	+	0.954789i	$0.403919\pi$
$858$	125906.	−	125906.i	0.171030	−	0.171030i
$859$			1.10683e6i			1.50002i	0.661428	+	0.750008i	$0.269951\pi$
$859$			1.10683e6i			1.50002i	−0.661428	+	0.750008i	$0.730049\pi$
$860$	202758.	+	597198.i	0.274145	+	0.807460i
$861$	−184390.			−0.248731
$862$	566755.	+	566755.i	0.762748	+	0.762748i
$863$	−478311.	+	478311.i	−0.642227	+	0.642227i	−0.951102	−	0.308876i	$-0.900047\pi$
$863$	−478311.	+	478311.i	−0.642227	+	0.642227i	0.308876	+	0.951102i	$0.400047\pi$
$864$		−	100353.i		−	0.134432i
$865$	−764007.	+	259392.i	−1.02109	+	0.346676i
$866$	−542998.			−0.724040
$867$	241237.	+	241237.i	0.320926	+	0.320926i
$868$	−166629.	+	166629.i	−0.221163	+	0.221163i
$869$			911988.i			1.20767i
$870$	−78769.5	+	159751.i	−0.104069	+	0.211059i
$871$	680937.			0.897575
$872$	4323.77	+	4323.77i	0.00568630	+	0.00568630i
$873$	−310003.	+	310003.i	−0.406760	+	0.406760i
$874$		−	160515.i		−	0.210132i
$875$	767477.	−	1.14902e6i	1.00242	−	1.50076i
$876$	−86141.7			−0.112255
$877$	47275.1	+	47275.1i	0.0614657	+	0.0614657i	0.737171	−	0.675706i	$-0.236161\pi$
$877$	47275.1	+	47275.1i	0.0614657	+	0.0614657i	−0.675706	+	0.737171i	$0.736161\pi$
$878$	−331339.	+	331339.i	−0.429817	+	0.429817i
$879$		−	270940.i		−	0.350667i
$880$	269508.	+	132888.i	0.348022	+	0.171602i
$881$	1.21254e6			1.56223			0.781115	−	0.624387i	$-0.214651\pi$
$881$	1.21254e6			1.56223			0.781115	+	0.624387i	$0.214651\pi$
$882$	−725778.	−	725778.i	−0.932968	−	0.932968i
$883$	765785.	−	765785.i	0.982168	−	0.982168i	−0.0176761	−	0.999844i	$-0.505627\pi$
$883$	765785.	−	765785.i	0.982168	−	0.982168i	0.999844	+	0.0176761i	$0.00562679\pi$
$884$			299044.i			0.382675i
$885$	89387.7	+	263281.i	0.114128	+	0.336149i
$886$	−133164.			−0.169637
$887$	341331.	+	341331.i	0.433839	+	0.433839i	0.889932	−	0.456093i	$-0.150752\pi$
$887$	341331.	+	341331.i	0.433839	+	0.433839i	−0.456093	+	0.889932i	$0.650752\pi$
$888$	61397.6	−	61397.6i	0.0778620	−	0.0778620i
$889$		−	2.57072e6i		−	3.25275i
$890$	488557.	−	165873.i	0.616788	−	0.209409i
$891$	628546.			0.791738
$892$	224360.	+	224360.i	0.281978	+	0.281978i
$893$	905051.	−	905051.i	1.13493	−	1.13493i
$894$			366391.i			0.458426i
$895$	−160499.	+	325504.i	−0.200367	+	0.406360i
$896$	−128064.			−0.159519
$897$	−26144.8	−	26144.8i	−0.0324938	−	0.0324938i
$898$	358112.	−	358112.i	0.444085	−	0.444085i
$899$		−	223936.i		−	0.277079i
$900$	−203848.	−	265600.i	−0.251664	−	0.327901i
$901$	1.33655e6			1.64639
$902$	−209029.	−	209029.i	−0.256917	−	0.256917i
$903$	−738809.	+	738809.i	−0.906059	+	0.906059i
$904$		−	288799.i		−	0.353394i
$905$	−302357.	−	149086.i	−0.369167	−	0.182028i
$906$	−140193.			−0.170793
$907$	851857.	+	851857.i	1.03550	+	1.03550i	0.999346	+	0.0361587i	$0.0115122\pi$
$907$	851857.	+	851857.i	1.03550	+	1.03550i	0.0361587	+	0.999346i	$0.488488\pi$
$908$	−50775.1	+	50775.1i	−0.0615856	+	0.0615856i
$909$			989216.i			1.19719i
$910$	179854.	+	529738.i	0.217189	+	0.639702i
$911$	−315643.			−0.380329			−0.190164	−	0.981752i	$-0.560902\pi$
$911$	−315643.			−0.380329			−0.190164	+	0.981752i	$0.560902\pi$
$912$	−87236.6	−	87236.6i	−0.104884	−	0.104884i
$913$	−757350.	+	757350.i	−0.908563	+	0.908563i
$914$			160483.i			0.192104i
$915$	−198989.	+	67559.7i	−0.237677	+	0.0806948i
$916$	−411371.			−0.490278
$917$	−947176.	−	947176.i	−1.12640	−	1.12640i
$918$	463263.	−	463263.i	0.549721	−	0.549721i
$919$		−	307918.i		−	0.364590i	−0.983244	−	0.182295i	$-0.941647\pi$
$919$		−	307918.i		−	0.364590i	0.983244	−	0.182295i	$-0.0583526\pi$
$920$	27594.6	−	55964.1i	0.0326023	−	0.0661201i
$921$	386598.			0.455765
$922$	407713.	+	407713.i	0.479614	+	0.479614i
$923$	−302758.	+	302758.i	−0.355379	+	0.355379i
$924$			497815.i			0.583074i
$925$	83482.1	−	634644.i	0.0975685	−	0.741732i
$926$	−1.14622e6			−1.33674
$927$	−606621.	−	606621.i	−0.705924	−	0.705924i
$928$	86053.7	−	86053.7i	0.0999249	−	0.0999249i
$929$			300402.i			0.348073i	0.984739	+	0.174037i	$0.0556811\pi$
$929$			300402.i			0.348073i	−0.984739	+	0.174037i	$0.944319\pi$
$930$	−79149.3	−	39026.7i	−0.0915126	−	0.0451228i
$931$	−2.78821e6			−3.21681
$932$	23680.0	+	23680.0i	0.0272615	+	0.0272615i
$933$	−378843.	+	378843.i	−0.435207	+	0.435207i
$934$		−	99093.4i		−	0.113593i
$935$	630681.	+	1.85759e6i	0.721417	+	2.12485i
$936$	135555.			0.154726
$937$	572402.	+	572402.i	0.651962	+	0.651962i	0.953465	−	0.301503i	$-0.0974885\pi$
$937$	572402.	+	572402.i	0.651962	+	0.651962i	−0.301503	+	0.953465i	$0.597488\pi$
$938$	−1.34616e6	+	1.34616e6i	−1.53000	+	1.53000i
$939$			100726.i			0.114238i
$940$	471140.	−	159959.i	0.533205	−	0.181031i
$941$	971061.			1.09665			0.548324	−	0.836266i	$-0.315266\pi$
$941$	971061.			1.09665			0.548324	+	0.836266i	$0.315266\pi$
$942$	16841.6	+	16841.6i	0.0189793	+	0.0189793i
$943$	−43405.4	+	43405.4i	−0.0488113	+	0.0488113i
$944$		−	189973.i		−	0.213181i
$945$	542021.	−	1.09926e6i	0.606950	−	1.23094i
$946$	−1.67507e6			−1.87176
$947$	399219.	+	399219.i	0.445155	+	0.445155i	0.893740	−	0.448585i	$-0.148072\pi$
$947$	399219.	+	399219.i	0.445155	+	0.445155i	−0.448585	+	0.893740i	$0.648072\pi$
$948$	102923.	−	102923.i	0.114523	−	0.114523i
$949$		−	257111.i		−	0.285488i
$950$	−901733.	−	118615.i	−0.999150	−	0.131430i
$951$	252335.			0.279008
$952$	−591187.	−	591187.i	−0.652305	−	0.652305i
$953$	−244919.	+	244919.i	−0.269673	+	0.269673i	−0.828968	−	0.559296i	$-0.811072\pi$
$953$	−244919.	+	244919.i	−0.269673	+	0.269673i	0.559296	+	0.828968i	$0.311072\pi$
$954$		−	605848.i		−	0.665682i
$955$	−561715.	−	276969.i	−0.615899	−	0.303686i
$956$	235308.			0.257467
$957$	−334510.	−	334510.i	−0.365246	−	0.365246i
$958$	655868.	−	655868.i	0.714637	−	0.714637i
$959$			53404.6i			0.0580686i
$960$	−15418.2	−	45412.5i	−0.0167299	−	0.0492758i
$961$	−812571.			−0.879862
$962$	183256.	+	183256.i	0.198020	+	0.198020i
$963$	−542141.	+	542141.i	−0.584601	+	0.584601i
$964$		−	276342.i		−	0.297367i
$965$	−444332.	+	150857.i	−0.477148	+	0.161999i
$966$	103373.			0.110777
$967$	−840897.	−	840897.i	−0.899269	−	0.899269i	0.0961024	−	0.995371i	$-0.469362\pi$
$967$	−840897.	−	840897.i	−0.899269	−	0.899269i	−0.995371	+	0.0961024i	$0.969362\pi$
$968$	−330080.	+	330080.i	−0.352264	+	0.352264i
$969$		−	805426.i		−	0.857785i
$970$	−204737.	+	415223.i	−0.217597	+	0.441304i
$971$	257432.			0.273038			0.136519	−	0.990637i	$-0.456409\pi$
$971$	257432.			0.273038			0.136519	+	0.990637i	$0.456409\pi$
$972$	−324953.	−	324953.i	−0.343945	−	0.343945i
$973$	−1.57447e6	+	1.57447e6i	−1.66307	+	1.66307i
$974$		−	890200.i		−	0.938360i
$975$	−166195.	+	127555.i	−0.174828	+	0.134180i
$976$	143583.			0.150731
$977$	33565.3	+	33565.3i	0.0351643	+	0.0351643i	0.724470	−	0.689306i	$-0.242084\pi$
$977$	33565.3	+	33565.3i	0.0351643	+	0.0351643i	−0.689306	+	0.724470i	$0.742084\pi$
$978$	99461.4	−	99461.4i	0.103986	−	0.103986i
$979$			1.37034e6i			1.42976i
$980$	−972119.	−	479330.i	−1.01220	−	0.499094i
$981$	18095.5			0.0188032
$982$	−318470.	−	318470.i	−0.330252	−	0.330252i
$983$	−678853.	+	678853.i	−0.702537	+	0.702537i	−0.964954	−	0.262418i	$-0.915480\pi$
$983$	−678853.	+	678853.i	−0.702537	+	0.702537i	0.262418	+	0.964954i	$0.415480\pi$
$984$			47180.0i			0.0487268i
$985$	45780.6	+	134841.i	0.0471856	+	0.138979i
$986$	794505.			0.817227
$987$	582860.	+	582860.i	0.598315	+	0.598315i
$988$	260379.	−	260379.i	0.266742	−	0.266742i
$989$			347832.i			0.355613i
$990$	842036.	−	285884.i	0.859133	−	0.291689i
$991$	290146.			0.295440			0.147720	−	0.989029i	$-0.452807\pi$
$991$	290146.			0.295440			0.147720	+	0.989029i	$0.452807\pi$
$992$	42635.7	+	42635.7i	0.0433261	+	0.0433261i
$993$	−242939.	+	242939.i	−0.246377	+	0.246377i
$994$		−	1.19706e6i		−	1.21155i
$995$	−186521.	+	378278.i	−0.188400	+	0.382090i
$996$	170942.			0.172318
$997$	−1.07895e6	−	1.07895e6i	−1.08546	−	1.08546i	−0.995990	−	0.0894671i	$-0.971484\pi$
$997$	−1.07895e6	−	1.07895e6i	−1.08546	−	1.08546i	−0.0894671	−	0.995990i	$-0.528516\pi$
$998$	−89171.3	+	89171.3i	−0.0895291	+	0.0895291i
$999$		−	567781.i		−	0.568918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.13	✓	44
5.3	odd	4	inner	230.5.f.b.93.13	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.13	✓	44	1.1	even	1	trivial
230.5.f.b.93.13	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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(2.64936 - 2.64936i) q^{3} +8.00000i q^{4} +(22.4224 + 11.0560i) q^{5} +10.5974 q^{6} +(-62.5314 - 62.5314i) q^{7} +(-16.0000 + 16.0000i) q^{8} +66.9618i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(2.64936 - 2.64936i) q^{3} +8.00000i q^{4} +(22.4224 + 11.0560i) q^{5} +10.5974 q^{6} +(-62.5314 - 62.5314i) q^{7} +(-16.0000 + 16.0000i) q^{8} +66.9618i q^{9} +(22.7329 + 66.9568i) q^{10} -187.806 q^{11} +(21.1949 + 21.1949i) q^{12} +(-63.2613 + 63.2613i) q^{13} -250.126i q^{14} +(88.6964 - 30.1138i) q^{15} -64.0000 q^{16} +(-295.445 - 295.445i) q^{17} +(-133.924 + 133.924i) q^{18} +514.491i q^{19} +(-88.4480 + 179.379i) q^{20} -331.336 q^{21} +(-375.612 - 375.612i) q^{22} +(-77.9968 + 77.9968i) q^{23} +84.7795i q^{24} +(380.530 + 495.804i) q^{25} -253.045 q^{26} +(392.004 + 392.004i) q^{27} +(500.251 - 500.251i) q^{28} +672.295i q^{29} +(237.620 + 117.165i) q^{30} -333.091 q^{31} +(-128.000 - 128.000i) q^{32} +(-497.565 + 497.565i) q^{33} -1181.78i q^{34} +(-710.758 - 2093.45i) q^{35} -535.694 q^{36} +(-724.203 - 724.203i) q^{37} +(-1028.98 + 1028.98i) q^{38} +335.204i q^{39} +(-535.655 + 181.863i) q^{40} +556.503 q^{41} +(-662.672 - 662.672i) q^{42} +(2229.79 - 2229.79i) q^{43} -1502.45i q^{44} +(-740.329 + 1501.45i) q^{45} -311.987 q^{46} +(-1759.12 - 1759.12i) q^{47} +(-169.559 + 169.559i) q^{48} +5419.35i q^{49} +(-230.549 + 1752.67i) q^{50} -1565.48 q^{51} +(-506.090 - 506.090i) q^{52} +(-2261.92 + 2261.92i) q^{53} +1568.02i q^{54} +(-4211.06 - 2076.38i) q^{55} +2001.00 q^{56} +(1363.07 + 1363.07i) q^{57} +(-1344.59 + 1344.59i) q^{58} +2968.34i q^{59} +(240.910 + 709.571i) q^{60} -2243.48 q^{61} +(-666.183 - 666.183i) q^{62} +(4187.21 - 4187.21i) q^{63} -512.000i q^{64} +(-2117.89 + 719.055i) q^{65} -1990.26 q^{66} +(-5381.94 - 5381.94i) q^{67} +(2363.56 - 2363.56i) q^{68} +413.283i q^{69} +(2765.39 - 5608.42i) q^{70} +4785.83 q^{71} +(-1071.39 - 1071.39i) q^{72} +(-2032.14 + 2032.14i) q^{73} -2896.81i q^{74} +(2321.72 + 305.403i) q^{75} -4115.93 q^{76} +(11743.8 + 11743.8i) q^{77} +(-670.407 + 670.407i) q^{78} -4856.02i q^{79} +(-1435.03 - 707.584i) q^{80} -3346.79 q^{81} +(1113.01 + 1113.01i) q^{82} +(4032.62 - 4032.62i) q^{83} -2650.69i q^{84} +(-3358.16 - 9891.04i) q^{85} +8919.14 q^{86} +(1781.15 + 1781.15i) q^{87} +(3004.89 - 3004.89i) q^{88} -7296.60i q^{89} +(-4483.55 + 1522.23i) q^{90} +7911.63 q^{91} +(-623.974 - 623.974i) q^{92} +(-882.479 + 882.479i) q^{93} -7036.47i q^{94} +(-5688.21 + 11536.1i) q^{95} -678.236 q^{96} +(4629.56 + 4629.56i) q^{97} +(-10838.7 + 10838.7i) q^{98} -12575.8i 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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