LMFDB - Embedded newform 230.3.f.b.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,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, 3, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.1
Character	$\chi$	$=$	230.93
Dual form			230.3.f.b.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-3.78907 - 3.78907i) q^{3} -2.00000i q^{4} +(0.818077 + 4.93262i) q^{5} -7.57813 q^{6} +(-3.70466 + 3.70466i) q^{7} +(-2.00000 - 2.00000i) q^{8} +19.7140i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(-3.78907 - 3.78907i) q^{3} -2.00000i q^{4} +(0.818077 + 4.93262i) q^{5} -7.57813 q^{6} +(-3.70466 + 3.70466i) q^{7} +(-2.00000 - 2.00000i) q^{8} +19.7140i q^{9} +(5.75070 + 4.11454i) q^{10} -13.1554 q^{11} +(-7.57813 + 7.57813i) q^{12} +(6.65224 + 6.65224i) q^{13} +7.40933i q^{14} +(15.5903 - 21.7898i) q^{15} -4.00000 q^{16} +(8.90104 - 8.90104i) q^{17} +(19.7140 + 19.7140i) q^{18} +10.0119i q^{19} +(9.86524 - 1.63615i) q^{20} +28.0744 q^{21} +(-13.1554 + 13.1554i) q^{22} +(3.39116 + 3.39116i) q^{23} +15.1563i q^{24} +(-23.6615 + 8.07053i) q^{25} +13.3045 q^{26} +(40.5962 - 40.5962i) q^{27} +(7.40933 + 7.40933i) q^{28} +40.4613i q^{29} +(-6.19950 - 37.3801i) q^{30} -59.9380 q^{31} +(-4.00000 + 4.00000i) q^{32} +(49.8468 + 49.8468i) q^{33} -17.8021i q^{34} +(-21.3044 - 15.2430i) q^{35} +39.4281 q^{36} +(11.4063 - 11.4063i) q^{37} +(10.0119 + 10.0119i) q^{38} -50.4115i q^{39} +(8.22909 - 11.5014i) q^{40} -2.32786 q^{41} +(28.0744 - 28.0744i) q^{42} +(12.0618 + 12.0618i) q^{43} +26.3109i q^{44} +(-97.2419 + 16.1276i) q^{45} +6.78233 q^{46} +(-38.4537 + 38.4537i) q^{47} +(15.1563 + 15.1563i) q^{48} +21.5509i q^{49} +(-15.5910 + 31.7320i) q^{50} -67.4532 q^{51} +(13.3045 - 13.3045i) q^{52} +(-49.3600 - 49.3600i) q^{53} -81.1924i q^{54} +(-10.7622 - 64.8908i) q^{55} +14.8187 q^{56} +(37.9359 - 37.9359i) q^{57} +(40.4613 + 40.4613i) q^{58} -23.6571i q^{59} +(-43.5795 - 31.1806i) q^{60} -97.8268 q^{61} +(-59.9380 + 59.9380i) q^{62} +(-73.0339 - 73.0339i) q^{63} +8.00000i q^{64} +(-27.3709 + 38.2550i) q^{65} +99.6937 q^{66} +(63.3064 - 63.3064i) q^{67} +(-17.8021 - 17.8021i) q^{68} -25.6987i q^{69} +(-36.5474 + 6.06140i) q^{70} -42.9229 q^{71} +(39.4281 - 39.4281i) q^{72} +(-9.09857 - 9.09857i) q^{73} -22.8127i q^{74} +(120.235 + 59.0752i) q^{75} +20.0239 q^{76} +(48.7365 - 48.7365i) q^{77} +(-50.4115 - 50.4115i) q^{78} +131.359i q^{79} +(-3.27231 - 19.7305i) q^{80} -130.217 q^{81} +(-2.32786 + 2.32786i) q^{82} +(76.9382 + 76.9382i) q^{83} -56.1489i q^{84} +(51.1872 + 36.6237i) q^{85} +24.1236 q^{86} +(153.311 - 153.311i) q^{87} +(26.3109 + 26.3109i) q^{88} +16.9832i q^{89} +(-81.1143 + 113.369i) q^{90} -49.2886 q^{91} +(6.78233 - 6.78233i) q^{92} +(227.109 + 227.109i) q^{93} +76.9073i q^{94} +(-49.3851 + 8.19053i) q^{95} +30.3125 q^{96} +(-41.5485 + 41.5485i) q^{97} +(21.5509 + 21.5509i) q^{98} -259.347i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	−3.78907	−	3.78907i	−1.26302	−	1.26302i	−0.949621	−	0.313401i	$-0.898532\pi$
$3$	−3.78907	−	3.78907i	−1.26302	−	1.26302i	−0.313401	−	0.949621i	$-0.601468\pi$
$4$		−	2.00000i		−	0.500000i
$5$	0.818077	+	4.93262i	0.163615	+	0.986524i
$5$	0.818077	+	4.93262i	0.163615	+	0.986524i
$6$	−7.57813			−1.26302
$7$	−3.70466	+	3.70466i	−0.529238	+	0.529238i	−0.920345	−	0.391107i	$-0.872092\pi$
$7$	−3.70466	+	3.70466i	−0.529238	+	0.529238i	0.391107	+	0.920345i	$0.372092\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			19.7140i			2.19045i
$10$	5.75070	+	4.11454i	0.575070	+	0.411454i
$11$	−13.1554			−1.19595			−0.597975	−	0.801515i	$-0.704028\pi$
$11$	−13.1554			−1.19595			−0.597975	+	0.801515i	$0.704028\pi$
$12$	−7.57813	+	7.57813i	−0.631511	+	0.631511i
$13$	6.65224	+	6.65224i	0.511711	+	0.511711i	0.915050	−	0.403340i	$-0.132151\pi$
$13$	6.65224	+	6.65224i	0.511711	+	0.511711i	−0.403340	+	0.915050i	$0.632151\pi$
$14$			7.40933i			0.529238i
$15$	15.5903	−	21.7898i	1.03935	−	1.45265i
$16$	−4.00000			−0.250000
$17$	8.90104	−	8.90104i	0.523591	−	0.523591i	−0.395063	−	0.918654i	$-0.629277\pi$
$17$	8.90104	−	8.90104i	0.523591	−	0.523591i	0.918654	+	0.395063i	$0.129277\pi$
$18$	19.7140	+	19.7140i	1.09522	+	1.09522i
$19$			10.0119i			0.526944i	0.964667	+	0.263472i	$0.0848676\pi$
$19$			10.0119i			0.526944i	−0.964667	+	0.263472i	$0.915132\pi$
$20$	9.86524	−	1.63615i	0.493262	−	0.0818077i
$21$	28.0744			1.33688
$22$	−13.1554	+	13.1554i	−0.597975	+	0.597975i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$			15.1563i			0.631511i
$25$	−23.6615	+	8.07053i	−0.946460	+	0.322821i
$26$	13.3045			0.511711
$27$	40.5962	−	40.5962i	1.50356	−	1.50356i
$28$	7.40933	+	7.40933i	0.264619	+	0.264619i
$29$			40.4613i			1.39522i	0.716478	+	0.697609i	$0.245753\pi$
$29$			40.4613i			1.39522i	−0.716478	+	0.697609i	$0.754247\pi$
$30$	−6.19950	−	37.3801i	−0.206650	−	1.24600i
$31$	−59.9380			−1.93348			−0.966742	−	0.255753i	$-0.917677\pi$
$31$	−59.9380			−1.93348			−0.966742	+	0.255753i	$0.917677\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	49.8468	+	49.8468i	1.51051	+	1.51051i
$34$		−	17.8021i		−	0.523591i
$35$	−21.3044	−	15.2430i	−0.608697	−	0.435514i
$36$	39.4281			1.09522
$37$	11.4063	−	11.4063i	0.308280	−	0.308280i	−0.535962	−	0.844242i	$-0.680051\pi$
$37$	11.4063	−	11.4063i	0.308280	−	0.308280i	0.844242	+	0.535962i	$0.180051\pi$
$38$	10.0119	+	10.0119i	0.263472	+	0.263472i
$39$		−	50.4115i		−	1.29260i
$40$	8.22909	−	11.5014i	0.205727	−	0.287535i
$41$	−2.32786			−0.0567771			−0.0283885	−	0.999597i	$-0.509038\pi$
$41$	−2.32786			−0.0567771			−0.0283885	+	0.999597i	$0.509038\pi$
$42$	28.0744	−	28.0744i	0.668439	−	0.668439i
$43$	12.0618	+	12.0618i	0.280507	+	0.280507i	0.833311	−	0.552804i	$-0.186442\pi$
$43$	12.0618	+	12.0618i	0.280507	+	0.280507i	−0.552804	+	0.833311i	$0.686442\pi$
$44$			26.3109i			0.597975i
$45$	−97.2419	+	16.1276i	−2.16093	+	0.358391i
$46$	6.78233			0.147442
$47$	−38.4537	+	38.4537i	−0.818163	+	0.818163i	−0.985842	−	0.167679i	$-0.946373\pi$
$47$	−38.4537	+	38.4537i	−0.818163	+	0.818163i	0.167679	+	0.985842i	$0.446373\pi$
$48$	15.1563	+	15.1563i	0.315755	+	0.315755i
$49$			21.5509i			0.439815i
$50$	−15.5910	+	31.7320i	−0.311819	+	0.634641i
$51$	−67.4532			−1.32261
$52$	13.3045	−	13.3045i	0.255855	−	0.255855i
$53$	−49.3600	−	49.3600i	−0.931320	−	0.931320i	0.0664687	−	0.997789i	$-0.478827\pi$
$53$	−49.3600	−	49.3600i	−0.931320	−	0.931320i	−0.997789	+	0.0664687i	$0.978827\pi$
$54$		−	81.1924i		−	1.50356i
$55$	−10.7622	−	64.8908i	−0.195676	−	1.17983i
$56$	14.8187			0.264619
$57$	37.9359	−	37.9359i	0.665541	−	0.665541i
$58$	40.4613	+	40.4613i	0.697609	+	0.697609i
$59$		−	23.6571i		−	0.400968i	−0.979697	−	0.200484i	$-0.935748\pi$
$59$		−	23.6571i		−	0.400968i	0.979697	−	0.200484i	$-0.0642515\pi$
$60$	−43.5795	−	31.1806i	−0.726326	−	0.519676i
$61$	−97.8268			−1.60372			−0.801859	−	0.597514i	$-0.796155\pi$
$61$	−97.8268			−1.60372			−0.801859	+	0.597514i	$0.796155\pi$
$62$	−59.9380	+	59.9380i	−0.966742	+	0.966742i
$63$	−73.0339	−	73.0339i	−1.15927	−	1.15927i
$64$			8.00000i			0.125000i
$65$	−27.3709	+	38.2550i	−0.421091	+	0.588539i
$66$	99.6937			1.51051
$67$	63.3064	−	63.3064i	0.944871	−	0.944871i	−0.0536866	−	0.998558i	$-0.517097\pi$
$67$	63.3064	−	63.3064i	0.944871	−	0.944871i	0.998558	+	0.0536866i	$0.0170972\pi$
$68$	−17.8021	−	17.8021i	−0.261795	−	0.261795i
$69$		−	25.6987i		−	0.372445i
$70$	−36.5474	+	6.06140i	−0.522106	+	0.0865915i
$71$	−42.9229			−0.604547			−0.302274	−	0.953221i	$-0.597746\pi$
$71$	−42.9229			−0.604547			−0.302274	+	0.953221i	$0.597746\pi$
$72$	39.4281	−	39.4281i	0.547612	−	0.547612i
$73$	−9.09857	−	9.09857i	−0.124638	−	0.124638i	0.642036	−	0.766674i	$-0.278090\pi$
$73$	−9.09857	−	9.09857i	−0.124638	−	0.124638i	−0.766674	+	0.642036i	$0.778090\pi$
$74$		−	22.8127i		−	0.308280i
$75$	120.235	+	59.0752i	1.60313	+	0.787670i
$76$	20.0239			0.263472
$77$	48.7365	−	48.7365i	0.632942	−	0.632942i
$78$	−50.4115	−	50.4115i	−0.646302	−	0.646302i
$79$			131.359i			1.66278i	0.555692	+	0.831388i	$0.312453\pi$
$79$			131.359i			1.66278i	−0.555692	+	0.831388i	$0.687547\pi$
$80$	−3.27231	−	19.7305i	−0.0409039	−	0.246631i
$81$	−130.217			−1.60762
$82$	−2.32786	+	2.32786i	−0.0283885	+	0.0283885i
$83$	76.9382	+	76.9382i	0.926967	+	0.926967i	0.997509	−	0.0705423i	$-0.0224730\pi$
$83$	76.9382	+	76.9382i	0.926967	+	0.926967i	−0.0705423	+	0.997509i	$0.522473\pi$
$84$		−	56.1489i		−	0.668439i
$85$	51.1872	+	36.6237i	0.602202	+	0.430867i
$86$	24.1236			0.280507
$87$	153.311	−	153.311i	1.76219	−	1.76219i
$88$	26.3109	+	26.3109i	0.298987	+	0.298987i
$89$			16.9832i			0.190822i	0.995438	+	0.0954111i	$0.0304166\pi$
$89$			16.9832i			0.190822i	−0.995438	+	0.0954111i	$0.969583\pi$
$90$	−81.1143	+	113.369i	−0.901270	+	1.25966i
$91$	−49.2886			−0.541633
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	227.109	+	227.109i	2.44203	+	2.44203i
$94$			76.9073i			0.818163i
$95$	−49.3851	+	8.19053i	−0.519843	+	0.0862161i
$96$	30.3125			0.315755
$97$	−41.5485	+	41.5485i	−0.428335	+	0.428335i	−0.888061	−	0.459726i	$-0.847948\pi$
$97$	−41.5485	+	41.5485i	−0.428335	+	0.428335i	0.459726	+	0.888061i	$0.347948\pi$
$98$	21.5509	+	21.5509i	0.219907	+	0.219907i
$99$		−	259.347i		−	2.61967i
$100$	16.1411	+	47.3230i	0.161411	+	0.473230i
$101$	172.994			1.71281			0.856406	−	0.516303i	$-0.172692\pi$
$101$	172.994			1.71281			0.856406	+	0.516303i	$0.172692\pi$
$102$	−67.4532	+	67.4532i	−0.661306	+	0.661306i
$103$	−107.544	−	107.544i	−1.04412	−	1.04412i	−0.998981	−	0.0451357i	$-0.985628\pi$
$103$	−107.544	−	107.544i	−1.04412	−	1.04412i	−0.0451357	−	0.998981i	$-0.514372\pi$
$104$		−	26.6089i		−	0.255855i
$105$	22.9671	+	138.481i	0.218734	+	1.31886i
$106$	−98.7199			−0.931320
$107$	66.8707	−	66.8707i	0.624960	−	0.624960i	−0.321836	−	0.946796i	$-0.604300\pi$
$107$	66.8707	−	66.8707i	0.624960	−	0.624960i	0.946796	+	0.321836i	$0.104300\pi$
$108$	−81.1924	−	81.1924i	−0.751782	−	0.751782i
$109$		−	95.4040i		−	0.875266i	−0.899154	−	0.437633i	$-0.855817\pi$
$109$		−	95.4040i		−	0.875266i	0.899154	−	0.437633i	$-0.144183\pi$
$110$	−75.6530	−	54.1286i	−0.687754	−	0.492079i
$111$	−86.4388			−0.778728
$112$	14.8187	−	14.8187i	0.132309	−	0.132309i
$113$	−92.3049	−	92.3049i	−0.816858	−	0.816858i	0.168794	−	0.985651i	$-0.446013\pi$
$113$	−92.3049	−	92.3049i	−0.816858	−	0.816858i	−0.985651	+	0.168794i	$0.946013\pi$
$114$		−	75.8717i		−	0.665541i
$115$	−13.9531	+	19.5016i	−0.121331	+	0.169579i
$116$	80.9227			0.697609
$117$	−131.142	+	131.142i	−1.12088	+	1.12088i
$118$	−23.6571	−	23.6571i	−0.200484	−	0.200484i
$119$			65.9507i			0.554208i
$120$	−74.7601	+	12.3990i	−0.623001	+	0.103325i
$121$	52.0656			0.430295
$122$	−97.8268	+	97.8268i	−0.801859	+	0.801859i
$123$	8.82042	+	8.82042i	0.0717107	+	0.0717107i
$124$			119.876i			0.966742i
$125$	−59.1658	−	110.111i	−0.473326	−	0.880887i
$126$	−146.068			−1.15927
$127$	−69.3611	+	69.3611i	−0.546151	+	0.546151i	−0.925325	−	0.379174i	$-0.876208\pi$
$127$	−69.3611	+	69.3611i	−0.546151	+	0.546151i	0.379174	+	0.925325i	$0.376208\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	91.4060i		−	0.708574i
$130$	10.8841	+	65.6259i	0.0837237	+	0.504815i
$131$	219.399			1.67480			0.837401	−	0.546588i	$-0.184074\pi$
$131$	219.399			1.67480			0.837401	+	0.546588i	$0.184074\pi$
$132$	99.6937	−	99.6937i	0.755255	−	0.755255i
$133$	−37.0908	−	37.0908i	−0.278879	−	0.278879i
$134$		−	126.613i		−	0.944871i
$135$	233.457	+	167.035i	1.72931	+	1.23730i
$136$	−35.6042			−0.261795
$137$	77.1130	−	77.1130i	0.562869	−	0.562869i	−0.367252	−	0.930121i	$-0.619701\pi$
$137$	77.1130	−	77.1130i	0.562869	−	0.562869i	0.930121	+	0.367252i	$0.119701\pi$
$138$	−25.6987	−	25.6987i	−0.186222	−	0.186222i
$139$			4.27993i			0.0307908i	0.999881	+	0.0153954i	$0.00490071\pi$
$139$			4.27993i			0.0307908i	−0.999881	+	0.0153954i	$0.995099\pi$
$140$	−30.4860	+	42.6088i	−0.217757	+	0.304349i
$141$	291.407			2.06672
$142$	−42.9229	+	42.9229i	−0.302274	+	0.302274i
$143$	−87.5131	−	87.5131i	−0.611980	−	0.611980i
$144$		−	78.8562i		−	0.547612i
$145$	−199.580	+	33.1005i	−1.37642	+	0.228279i
$146$	−18.1971			−0.124638
$147$	81.6579	−	81.6579i	0.555496	−	0.555496i
$148$	−22.8127	−	22.8127i	−0.154140	−	0.154140i
$149$		−	76.1990i		−	0.511402i	−0.966756	−	0.255701i	$-0.917694\pi$
$149$		−	76.1990i		−	0.511402i	0.966756	−	0.255701i	$-0.0823063\pi$
$150$	179.310	−	61.1595i	1.19540	−	0.407730i
$151$	77.0391			0.510193			0.255096	−	0.966916i	$-0.417893\pi$
$151$	77.0391			0.510193			0.255096	+	0.966916i	$0.417893\pi$
$152$	20.0239	−	20.0239i	0.131736	−	0.131736i
$153$	175.475	+	175.475i	1.14690	+	1.14690i
$154$		−	97.4730i		−	0.632942i
$155$	−49.0339	−	295.651i	−0.316348	−	1.90743i
$156$	−100.823			−0.646302
$157$	−161.694	+	161.694i	−1.02990	+	1.02990i	−0.0303580	+	0.999539i	$0.509665\pi$
$157$	−161.694	+	161.694i	−1.02990	+	1.02990i	−0.999539	+	0.0303580i	$0.990335\pi$
$158$	131.359	+	131.359i	0.831388	+	0.831388i
$159$			374.056i			2.35255i
$160$	−23.0028	−	16.4582i	−0.143767	−	0.102864i
$161$	−25.1263			−0.156064
$162$	−130.217	+	130.217i	−0.803809	+	0.803809i
$163$	226.296	+	226.296i	1.38832	+	1.38832i	0.828849	+	0.559473i	$0.188996\pi$
$163$	226.296	+	226.296i	1.38832	+	1.38832i	0.559473	+	0.828849i	$0.311004\pi$
$164$			4.65572i			0.0283885i
$165$	−205.097	+	286.654i	−1.24301	+	1.73730i
$166$	153.876			0.926967
$167$	−129.180	+	129.180i	−0.773531	+	0.773531i	−0.978722	−	0.205191i	$-0.934218\pi$
$167$	−129.180	+	129.180i	−0.773531	+	0.773531i	0.205191	+	0.978722i	$0.434218\pi$
$168$	−56.1489	−	56.1489i	−0.334219	−	0.334219i
$169$		−	80.4955i		−	0.476305i
$170$	87.8109	−	14.5635i	0.516535	−	0.0856675i
$171$	−197.376			−1.15424
$172$	24.1236	−	24.1236i	0.140254	−	0.140254i
$173$	−102.806	−	102.806i	−0.594254	−	0.594254i	0.344524	−	0.938778i	$-0.388040\pi$
$173$	−102.806	−	102.806i	−0.594254	−	0.594254i	−0.938778	+	0.344524i	$0.888040\pi$
$174$		−	306.621i		−	1.76219i
$175$	57.7593	−	117.557i	0.330053	−	0.671752i
$176$	52.6218			0.298987
$177$	−89.6384	+	89.6384i	−0.506432	+	0.506432i
$178$	16.9832	+	16.9832i	0.0954111	+	0.0954111i
$179$		−	278.400i		−	1.55530i	−0.628694	−	0.777652i	$-0.716410\pi$
$179$		−	278.400i		−	1.55530i	0.628694	−	0.777652i	$-0.283590\pi$
$180$	32.2552	+	194.484i	0.179196	+	1.08047i
$181$	−267.758			−1.47933			−0.739663	−	0.672977i	$-0.765015\pi$
$181$	−267.758			−1.47933			−0.739663	+	0.672977i	$0.765015\pi$
$182$	−49.2886	+	49.2886i	−0.270817	+	0.270817i
$183$	370.672	+	370.672i	2.02553	+	2.02553i
$184$		−	13.5647i		−	0.0737210i
$185$	65.5944	+	46.9319i	0.354565	+	0.253686i
$186$	454.218			2.44203
$187$	−117.097	+	117.097i	−0.626188	+	0.626188i
$188$	76.9073	+	76.9073i	0.409081	+	0.409081i
$189$			300.791i			1.59148i
$190$	−41.1945	+	57.5756i	−0.216813	+	0.303029i
$191$	227.882			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$191$	227.882			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$192$	30.3125	−	30.3125i	0.157878	−	0.157878i
$193$	216.098	+	216.098i	1.11968	+	1.11968i	0.991789	+	0.127888i	$0.0408197\pi$
$193$	216.098	+	216.098i	1.11968	+	1.11968i	0.127888	+	0.991789i	$0.459180\pi$
$194$			83.0970i			0.428335i
$195$	248.661	−	41.2405i	1.27518	−	0.211490i
$196$	43.1018			0.219907
$197$	120.946	−	120.946i	0.613939	−	0.613939i	−0.330031	−	0.943970i	$-0.607059\pi$
$197$	120.946	−	120.946i	0.613939	−	0.613939i	0.943970	+	0.330031i	$0.107059\pi$
$198$	−259.347	−	259.347i	−1.30983	−	1.30983i
$199$			183.555i			0.922385i	0.887300	+	0.461193i	$0.152578\pi$
$199$			183.555i			0.922385i	−0.887300	+	0.461193i	$0.847422\pi$
$200$	63.4641	+	31.1819i	0.317320	+	0.155910i
$201$	−479.744			−2.38679
$202$	172.994	−	172.994i	0.856406	−	0.856406i
$203$	−149.896	−	149.896i	−0.738403	−	0.738403i
$204$			134.906i			0.661306i
$205$	−1.90437	−	11.4825i	−0.00928961	−	0.0560120i
$206$	−215.088			−1.04412
$207$	−66.8536	+	66.8536i	−0.322964	+	0.322964i
$208$	−26.6089	−	26.6089i	−0.127928	−	0.127928i
$209$		−	131.711i		−	0.630198i
$210$	161.448	+	115.514i	0.768798	+	0.550064i
$211$	191.123			0.905794			0.452897	−	0.891563i	$-0.350390\pi$
$211$	191.123			0.905794			0.452897	+	0.891563i	$0.350390\pi$
$212$	−98.7199	+	98.7199i	−0.465660	+	0.465660i
$213$	162.638	+	162.638i	0.763557	+	0.763557i
$214$		−	133.741i		−	0.624960i
$215$	−49.6289	+	69.3639i	−0.230832	+	0.322623i
$216$	−162.385			−0.751782
$217$	222.050	−	222.050i	1.02327	−	1.02327i
$218$	−95.4040	−	95.4040i	−0.437633	−	0.437633i
$219$			68.9502i			0.314841i
$220$	−129.782	+	21.5243i	−0.589916	+	0.0978379i
$221$	118.424			0.535854
$222$	−86.4388	+	86.4388i	−0.389364	+	0.389364i
$223$	−265.256	−	265.256i	−1.18949	−	1.18949i	−0.977209	−	0.212281i	$-0.931911\pi$
$223$	−265.256	−	265.256i	−1.18949	−	1.18949i	−0.212281	−	0.977209i	$-0.568089\pi$
$224$		−	29.6373i		−	0.132309i
$225$	−159.103	−	466.464i	−0.707123	−	2.07317i
$226$	−184.610			−0.816858
$227$	2.98007	−	2.98007i	0.0131281	−	0.0131281i	−0.700512	−	0.713640i	$-0.747045\pi$
$227$	2.98007	−	2.98007i	0.0131281	−	0.0131281i	0.713640	+	0.700512i	$0.247045\pi$
$228$	−75.8717	−	75.8717i	−0.332771	−	0.332771i
$229$			192.530i			0.840743i	0.907352	+	0.420372i	$0.138100\pi$
$229$			192.530i			0.840743i	−0.907352	+	0.420372i	$0.861900\pi$
$230$	5.54847	+	33.4547i	0.0241238	+	0.145455i
$231$	−369.332			−1.59884
$232$	80.9227	−	80.9227i	0.348805	−	0.348805i
$233$	9.84397	+	9.84397i	0.0422488	+	0.0422488i	0.727916	−	0.685667i	$-0.240489\pi$
$233$	9.84397	+	9.84397i	0.0422488	+	0.0422488i	−0.685667	+	0.727916i	$0.740489\pi$
$234$			262.285i			1.12088i
$235$	−221.135	−	158.219i	−0.941001	−	0.673273i
$236$	−47.3143			−0.200484
$237$	497.729	−	497.729i	2.10012	−	2.10012i
$238$	65.9507	+	65.9507i	0.277104	+	0.277104i
$239$			290.916i			1.21722i	0.793468	+	0.608612i	$0.208273\pi$
$239$			290.916i			1.21722i	−0.793468	+	0.608612i	$0.791727\pi$
$240$	−62.3611	+	87.1591i	−0.259838	+	0.363163i
$241$	−50.2561			−0.208531			−0.104266	−	0.994549i	$-0.533249\pi$
$241$	−50.2561			−0.208531			−0.104266	+	0.994549i	$0.533249\pi$
$242$	52.0656	−	52.0656i	0.215147	−	0.215147i
$243$	128.035	+	128.035i	0.526893	+	0.526893i
$244$			195.654i			0.801859i
$245$	−106.303	+	17.6303i	−0.433888	+	0.0719605i
$246$	17.6408			0.0717107
$247$	−66.6017	+	66.6017i	−0.269643	+	0.269643i
$248$	119.876	+	119.876i	0.483371	+	0.483371i
$249$		−	583.048i		−	2.34156i
$250$	−169.277	−	50.9451i	−0.677107	−	0.203780i
$251$	205.930			0.820439			0.410220	−	0.911987i	$-0.365452\pi$
$251$	205.930			0.820439			0.410220	+	0.911987i	$0.365452\pi$
$252$	−146.068	+	146.068i	−0.579634	+	0.579634i
$253$	−44.6123	−	44.6123i	−0.176333	−	0.176333i
$254$			138.722i			0.546151i
$255$	−55.1820	−	332.721i	−0.216400	−	1.30479i
$256$	16.0000			0.0625000
$257$	21.5059	−	21.5059i	0.0836807	−	0.0836807i	−0.664027	−	0.747708i	$-0.731154\pi$
$257$	21.5059	−	21.5059i	0.0836807	−	0.0836807i	0.747708	+	0.664027i	$0.231154\pi$
$258$	−91.4060	−	91.4060i	−0.354287	−	0.354287i
$259$			84.5134i			0.326306i
$260$	76.5100	+	54.7418i	0.294269	+	0.210546i
$261$	−797.657			−3.05616
$262$	219.399	−	219.399i	0.837401	−	0.837401i
$263$	180.933	+	180.933i	0.687958	+	0.687958i	0.961780	−	0.273822i	$-0.0882880\pi$
$263$	180.933	+	180.933i	0.687958	+	0.687958i	−0.273822	+	0.961780i	$0.588288\pi$
$264$		−	199.387i		−	0.755255i
$265$	203.094	−	283.854i	0.766391	−	1.07115i
$266$	−74.1817			−0.278879
$267$	64.3504	−	64.3504i	0.241013	−	0.241013i
$268$	−126.613	−	126.613i	−0.472436	−	0.472436i
$269$			133.881i			0.497699i	0.968542	+	0.248849i	$0.0800524\pi$
$269$			133.881i			0.497699i	−0.968542	+	0.248849i	$0.919948\pi$
$270$	400.491	−	66.4216i	1.48330	−	0.246006i
$271$	−299.275			−1.10433			−0.552167	−	0.833734i	$-0.686199\pi$
$271$	−299.275			−1.10433			−0.552167	+	0.833734i	$0.686199\pi$
$272$	−35.6042	+	35.6042i	−0.130898	+	0.130898i
$273$	186.758	+	186.758i	0.684095	+	0.684095i
$274$		−	154.226i		−	0.562869i
$275$	311.277	−	106.171i	1.13192	−	0.386078i
$276$	−51.3974			−0.186222
$277$	−221.291	+	221.291i	−0.798885	+	0.798885i	−0.982920	−	0.184035i	$-0.941084\pi$
$277$	−221.291	+	221.291i	−0.798885	+	0.798885i	0.184035	+	0.982920i	$0.441084\pi$
$278$	4.27993	+	4.27993i	0.0153954	+	0.0153954i
$279$		−	1181.62i		−	4.23520i
$280$	12.1228	+	73.0948i	0.0432957	+	0.261053i
$281$	86.9048			0.309270			0.154635	−	0.987972i	$-0.450580\pi$
$281$	86.9048			0.309270			0.154635	+	0.987972i	$0.450580\pi$
$282$	291.407	−	291.407i	1.03336	−	1.03336i
$283$	25.5811	+	25.5811i	0.0903927	+	0.0903927i	0.750857	−	0.660465i	$-0.229641\pi$
$283$	25.5811	+	25.5811i	0.0903927	+	0.0903927i	−0.660465	+	0.750857i	$0.729641\pi$
$284$			85.8457i			0.302274i
$285$	218.158	+	156.089i	0.765466	+	0.547680i
$286$	−175.026			−0.611980
$287$	8.62394	−	8.62394i	0.0300486	−	0.0300486i
$288$	−78.8562	−	78.8562i	−0.273806	−	0.273806i
$289$			130.543i			0.451706i
$290$	−166.480	+	232.681i	−0.574069	+	0.802348i
$291$	314.860			1.08199
$292$	−18.1971	+	18.1971i	−0.0623190	+	0.0623190i
$293$	−185.904	−	185.904i	−0.634484	−	0.634484i	0.314705	−	0.949189i	$-0.398094\pi$
$293$	−185.904	−	185.904i	−0.634484	−	0.634484i	−0.949189	+	0.314705i	$0.898094\pi$
$294$		−	163.316i		−	0.555496i
$295$	116.692	−	19.3534i	0.395565	−	0.0656046i
$296$	−45.6254			−0.154140
$297$	−534.061	+	534.061i	−1.79819	+	1.79819i
$298$	−76.1990	−	76.1990i	−0.255701	−	0.255701i
$299$			45.1177i			0.150895i
$300$	118.150	−	240.469i	0.393835	−	0.801565i
$301$	−89.3700			−0.296910
$302$	77.0391	−	77.0391i	0.255096	−	0.255096i
$303$	−655.485	−	655.485i	−2.16332	−	2.16332i
$304$		−	40.0477i		−	0.131736i
$305$	−80.0298	−	482.542i	−0.262393	−	1.58211i
$306$	350.951			1.14690
$307$	−165.430	+	165.430i	−0.538859	+	0.538859i	−0.923194	−	0.384335i	$-0.874431\pi$
$307$	−165.430	+	165.430i	−0.538859	+	0.538859i	0.384335	+	0.923194i	$0.374431\pi$
$308$	−97.4730	−	97.4730i	−0.316471	−	0.316471i
$309$			814.983i			2.63748i
$310$	−344.685	−	246.618i	−1.11189	−	0.795541i
$311$	−192.859			−0.620124			−0.310062	−	0.950716i	$-0.600350\pi$
$311$	−192.859			−0.620124			−0.310062	+	0.950716i	$0.600350\pi$
$312$	−100.823	+	100.823i	−0.323151	+	0.323151i
$313$	5.98024	+	5.98024i	0.0191062	+	0.0191062i	0.716595	−	0.697489i	$-0.245699\pi$
$313$	5.98024	+	5.98024i	0.0191062	+	0.0191062i	−0.697489	+	0.716595i	$0.745699\pi$
$314$			323.388i			1.02990i
$315$	300.501	−	419.996i	0.953972	−	1.33332i
$316$	262.719			0.831388
$317$	311.688	−	311.688i	0.983242	−	0.983242i	−0.0166198	−	0.999862i	$-0.505291\pi$
$317$	311.688	−	311.688i	0.983242	−	0.983242i	0.999862	+	0.0166198i	$0.00529050\pi$
$318$	374.056	+	374.056i	1.17628	+	1.17628i
$319$		−	532.287i		−	1.66861i
$320$	−39.4610	+	6.54462i	−0.123316	+	0.0204519i
$321$	−506.755			−1.57868
$322$	−25.1263	+	25.1263i	−0.0780319	+	0.0780319i
$323$	89.1166	+	89.1166i	0.275903	+	0.275903i
$324$			260.434i			0.803809i
$325$	−211.089	−	103.715i	−0.649505	−	0.319123i
$326$	452.593			1.38832
$327$	−361.492	+	361.492i	−1.10548	+	1.10548i
$328$	4.65572	+	4.65572i	0.0141943	+	0.0141943i
$329$		−	284.916i		−	0.866005i
$330$	81.5571	+	491.751i	0.247143	+	1.49015i
$331$	−103.280			−0.312023			−0.156012	−	0.987755i	$-0.549864\pi$
$331$	−103.280			−0.312023			−0.156012	+	0.987755i	$0.549864\pi$
$332$	153.876	−	153.876i	0.463483	−	0.463483i
$333$	224.865	+	224.865i	0.675271	+	0.675271i
$334$			258.359i			0.773531i
$335$	364.056	+	260.477i	1.08673	+	0.777543i
$336$	−112.298			−0.334219
$337$	−156.387	+	156.387i	−0.464055	+	0.464055i	−0.899982	−	0.435927i	$-0.856421\pi$
$337$	−156.387	+	156.387i	−0.464055	+	0.464055i	0.435927	+	0.899982i	$0.356421\pi$
$338$	−80.4955	−	80.4955i	−0.238152	−	0.238152i
$339$			699.499i			2.06342i
$340$	73.2474	−	102.374i	0.215434	−	0.301101i
$341$	788.511			2.31235
$342$	−197.376	+	197.376i	−0.577122	+	0.577122i
$343$	−261.367	−	261.367i	−0.762004	−	0.762004i
$344$		−	48.2473i		−	0.140254i
$345$	126.762	−	21.0235i	0.367426	−	0.0609377i
$346$	−205.612			−0.594254
$347$	−205.681	+	205.681i	−0.592739	+	0.592739i	−0.938370	−	0.345631i	$-0.887665\pi$
$347$	−205.681	+	205.681i	−0.592739	+	0.592739i	0.345631	+	0.938370i	$0.387665\pi$
$348$	−306.621	−	306.621i	−0.881096	−	0.881096i
$349$			436.934i			1.25196i	0.779839	+	0.625980i	$0.215301\pi$
$349$			436.934i			1.25196i	−0.779839	+	0.625980i	$0.784699\pi$
$350$	−59.7972	−	175.316i	−0.170849	−	0.500902i
$351$	540.111			1.53878
$352$	52.6218	−	52.6218i	0.149494	−	0.149494i
$353$	287.500	+	287.500i	0.814447	+	0.814447i	0.985297	−	0.170850i	$-0.0546512\pi$
$353$	287.500	+	287.500i	0.814447	+	0.814447i	−0.170850	+	0.985297i	$0.554651\pi$
$354$			179.277i			0.506432i
$355$	−35.1142	−	211.722i	−0.0989133	−	0.596401i
$356$	33.9664			0.0954111
$357$	249.892	−	249.892i	0.699977	−	0.699977i
$358$	−278.400	−	278.400i	−0.777652	−	0.777652i
$359$			207.074i			0.576807i	0.957509	+	0.288403i	$0.0931244\pi$
$359$			207.074i			0.576807i	−0.957509	+	0.288403i	$0.906876\pi$
$360$	226.739	+	162.229i	0.629831	+	0.450635i
$361$	260.761			0.722330
$362$	−267.758	+	267.758i	−0.739663	+	0.739663i
$363$	−197.280	−	197.280i	−0.543472	−	0.543472i
$364$			98.5772i			0.270817i
$365$	37.4365	−	52.3231i	0.102566	−	0.143351i
$366$	741.344			2.02553
$367$	69.0145	−	69.0145i	0.188051	−	0.188051i	−0.606802	−	0.794853i	$-0.707548\pi$
$367$	69.0145	−	69.0145i	0.188051	−	0.188051i	0.794853	+	0.606802i	$0.207548\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	45.8915i		−	0.124367i
$370$	112.526	−	18.6625i	0.304125	−	0.0504393i
$371$	365.724			0.985779
$372$	454.218	−	454.218i	1.22102	−	1.22102i
$373$	257.438	+	257.438i	0.690181	+	0.690181i	0.962272	−	0.272091i	$-0.0877151\pi$
$373$	257.438	+	257.438i	0.690181	+	0.690181i	−0.272091	+	0.962272i	$0.587715\pi$
$374$			234.194i			0.626188i
$375$	−193.034	+	641.401i	−0.514758	+	1.71040i
$376$	153.815			0.409081
$377$	−269.158	+	269.158i	−0.713948	+	0.713948i
$378$	300.791	+	300.791i	0.795742	+	0.795742i
$379$			419.437i			1.10669i	0.832951	+	0.553346i	$0.186649\pi$
$379$			419.437i			1.10669i	−0.832951	+	0.553346i	$0.813351\pi$
$380$	16.3811	+	98.7701i	0.0431081	+	0.259921i
$381$	525.628			1.37960
$382$	227.882	−	227.882i	0.596550	−	0.596550i
$383$	−342.204	−	342.204i	−0.893484	−	0.893484i	0.101365	−	0.994849i	$-0.467679\pi$
$383$	−342.204	−	342.204i	−0.893484	−	0.893484i	−0.994849	+	0.101365i	$0.967679\pi$
$384$		−	60.6251i		−	0.157878i
$385$	280.269	+	200.528i	0.727971	+	0.520853i
$386$	432.195			1.11968
$387$	−237.787	+	237.787i	−0.614437	+	0.614437i
$388$	83.0970	+	83.0970i	0.214168	+	0.214168i
$389$		−	2.95987i		−	0.00760892i	−0.999993	−	0.00380446i	$-0.998789\pi$
$389$		−	2.95987i		−	0.00760892i	0.999993	−	0.00380446i	$-0.00121100\pi$
$390$	207.420	−	289.901i	0.531847	−	0.743337i
$391$	60.3698			0.154398
$392$	43.1018	−	43.1018i	0.109954	−	0.109954i
$393$	−831.318	−	831.318i	−2.11531	−	2.11531i
$394$		−	241.892i		−	0.613939i
$395$	−647.946	+	107.462i	−1.64037	+	0.272056i
$396$	−518.694			−1.30983
$397$	92.7715	−	92.7715i	0.233681	−	0.233681i	−0.580546	−	0.814227i	$-0.697161\pi$
$397$	92.7715	−	92.7715i	0.233681	−	0.233681i	0.814227	+	0.580546i	$0.197161\pi$
$398$	183.555	+	183.555i	0.461193	+	0.461193i
$399$			281.079i			0.704459i
$400$	94.6460	−	32.2821i	0.236615	−	0.0807053i
$401$	−23.9519			−0.0597303			−0.0298652	−	0.999554i	$-0.509508\pi$
$401$	−23.9519			−0.0597303			−0.0298652	+	0.999554i	$0.509508\pi$
$402$	−479.744	+	479.744i	−1.19339	+	1.19339i
$403$	−398.722	−	398.722i	−0.989384	−	0.989384i
$404$		−	345.988i		−	0.856406i
$405$	−106.528	−	642.311i	−0.263031	−	1.58595i
$406$	−299.791			−0.738403
$407$	−150.055	+	150.055i	−0.368687	+	0.368687i
$408$	134.906	+	134.906i	0.330653	+	0.330653i
$409$			659.636i			1.61280i	0.591370	+	0.806401i	$0.298587\pi$
$409$			659.636i			1.61280i	−0.591370	+	0.806401i	$0.701413\pi$
$410$	−13.3868	−	9.57808i	−0.0326508	−	0.0233612i
$411$	−584.373			−1.42183
$412$	−215.088	+	215.088i	−0.522058	+	0.522058i
$413$	87.6417	+	87.6417i	0.212208	+	0.212208i
$414$			133.707i			0.322964i
$415$	−316.566	+	442.448i	−0.762809	+	1.06614i
$416$	−53.2179			−0.127928
$417$	16.2169	−	16.2169i	0.0388895	−	0.0388895i
$418$	−131.711	−	131.711i	−0.315099	−	0.315099i
$419$			221.284i			0.528124i	0.964506	+	0.264062i	$0.0850624\pi$
$419$			221.284i			0.528124i	−0.964506	+	0.264062i	$0.914938\pi$
$420$	276.961	−	45.9341i	0.659431	−	0.109367i
$421$	−105.381			−0.250311			−0.125155	−	0.992137i	$-0.539943\pi$
$421$	−105.381			−0.250311			−0.125155	+	0.992137i	$0.539943\pi$
$422$	191.123	−	191.123i	0.452897	−	0.452897i
$423$	−758.077	−	758.077i	−1.79214	−	1.79214i
$424$			197.440i			0.465660i
$425$	−138.776	+	282.448i	−0.326531	+	0.664584i
$426$	325.275			0.763557
$427$	362.415	−	362.415i	0.848748	−	0.848748i
$428$	−133.741	−	133.741i	−0.312480	−	0.312480i
$429$			663.186i			1.54589i
$430$	19.7350	+	118.993i	0.0458953	+	0.276727i
$431$	−224.659			−0.521251			−0.260626	−	0.965440i	$-0.583929\pi$
$431$	−224.659			−0.521251			−0.260626	+	0.965440i	$0.583929\pi$
$432$	−162.385	+	162.385i	−0.375891	+	0.375891i
$433$	80.5022	+	80.5022i	0.185917	+	0.185917i	0.793928	−	0.608011i	$-0.208032\pi$
$433$	80.5022	+	80.5022i	0.185917	+	0.185917i	−0.608011	+	0.793928i	$0.708032\pi$
$434$		−	444.100i		−	1.02327i
$435$	881.644	+	630.804i	2.02677	+	1.45012i
$436$	−190.808			−0.437633
$437$	−33.9521	+	33.9521i	−0.0776936	+	0.0776936i
$438$	68.9502	+	68.9502i	0.157420	+	0.157420i
$439$			191.215i			0.435569i	0.975997	+	0.217784i	$0.0698829\pi$
$439$			191.215i			0.435569i	−0.975997	+	0.217784i	$0.930117\pi$
$440$	−108.257	+	151.306i	−0.246039	+	0.343877i
$441$	−424.856			−0.963392
$442$	118.424	−	118.424i	0.267927	−	0.267927i
$443$	393.535	+	393.535i	0.888341	+	0.888341i	0.994364	−	0.106023i	$-0.0338116\pi$
$443$	393.535	+	393.535i	0.888341	+	0.888341i	−0.106023	+	0.994364i	$0.533812\pi$
$444$			172.878i			0.389364i
$445$	−83.7716	+	13.8935i	−0.188251	+	0.0312215i
$446$	−530.512			−1.18949
$447$	−288.723	+	288.723i	−0.645912	+	0.645912i
$448$	−29.6373	−	29.6373i	−0.0661547	−	0.0661547i
$449$			6.06354i			0.0135045i	0.999977	+	0.00675227i	$0.00214933\pi$
$449$			6.06354i			0.0135045i	−0.999977	+	0.00675227i	$0.997851\pi$
$450$	−625.566	−	307.361i	−1.39015	−	0.683025i
$451$	30.6240			0.0679025
$452$	−184.610	+	184.610i	−0.408429	+	0.408429i
$453$	−291.906	−	291.906i	−0.644384	−	0.644384i
$454$		−	5.96014i		−	0.0131281i
$455$	−40.3219	−	243.122i	−0.0886195	−	0.534334i
$456$	−151.743			−0.332771
$457$	482.802	−	482.802i	1.05646	−	1.05646i	0.0581512	−	0.998308i	$-0.481479\pi$
$457$	482.802	−	482.802i	1.05646	−	1.05646i	0.998308	−	0.0581512i	$-0.0185205\pi$
$458$	192.530	+	192.530i	0.420372	+	0.420372i
$459$		−	722.697i		−	1.57450i
$460$	39.0031	+	27.9062i	0.0847894	+	0.0606656i
$461$	101.616			0.220426			0.110213	−	0.993908i	$-0.464847\pi$
$461$	101.616			0.220426			0.110213	+	0.993908i	$0.464847\pi$
$462$	−369.332	+	369.332i	−0.799419	+	0.799419i
$463$	−37.3060	−	37.3060i	−0.0805745	−	0.0805745i	0.665671	−	0.746245i	$-0.268145\pi$
$463$	−37.3060	−	37.3060i	−0.0805745	−	0.0805745i	−0.746245	+	0.665671i	$0.768145\pi$
$464$		−	161.845i		−	0.348805i
$465$	−934.450	+	1306.04i	−2.00957	+	2.80868i
$466$	19.6879			0.0422488
$467$	155.236	−	155.236i	0.332412	−	0.332412i	−0.521090	−	0.853502i	$-0.674474\pi$
$467$	155.236	−	155.236i	0.332412	−	0.332412i	0.853502	+	0.521090i	$0.174474\pi$
$468$	262.285	+	262.285i	0.560438	+	0.560438i
$469$			469.058i			1.00012i
$470$	−379.355	+	62.9161i	−0.807137	+	0.133864i
$471$	1225.34			2.60157
$472$	−47.3143	+	47.3143i	−0.100242	+	0.100242i
$473$	−158.678	−	158.678i	−0.335473	−	0.335473i
$474$		−	995.458i		−	2.10012i
$475$	−80.8016	−	236.897i	−0.170109	−	0.498731i
$476$	131.901			0.277104
$477$	973.084	−	973.084i	2.04001	−	2.04001i
$478$	290.916	+	290.916i	0.608612	+	0.608612i
$479$			166.864i			0.348358i	0.984714	+	0.174179i	$0.0557272\pi$
$479$			166.864i			0.348358i	−0.984714	+	0.174179i	$0.944273\pi$
$480$	24.7980	+	149.520i	0.0516625	+	0.311500i
$481$	151.755			0.315500
$482$	−50.2561	+	50.2561i	−0.104266	+	0.104266i
$483$	95.2050	+	95.2050i	0.197112	+	0.197112i
$484$		−	104.131i		−	0.215147i
$485$	−238.933	−	170.953i	−0.492645	−	0.352481i
$486$	256.070			0.526893
$487$	434.139	−	434.139i	0.891456	−	0.891456i	−0.103204	−	0.994660i	$-0.532910\pi$
$487$	434.139	−	434.139i	0.891456	−	0.891456i	0.994660	+	0.103204i	$0.0329095\pi$
$488$	195.654	+	195.654i	0.400929	+	0.400929i
$489$		−	1714.90i		−	3.50696i
$490$	−88.6722	+	123.933i	−0.180964	+	0.252924i
$491$	588.840			1.19927			0.599634	−	0.800275i	$-0.295313\pi$
$491$	588.840			1.19927			0.599634	+	0.800275i	$0.295313\pi$
$492$	17.6408	−	17.6408i	0.0358554	−	0.0358554i
$493$	360.148	+	360.148i	0.730523	+	0.730523i
$494$			133.203i			0.269643i
$495$	1279.26	−	212.166i	2.58436	−	0.428618i
$496$	239.752			0.483371
$497$	159.015	−	159.015i	0.319949	−	0.319949i
$498$	−583.048	−	583.048i	−1.17078	−	1.17078i
$499$		−	280.896i		−	0.562918i	−0.959573	−	0.281459i	$-0.909182\pi$
$499$		−	280.896i		−	0.562918i	0.959573	−	0.281459i	$-0.0908184\pi$
$500$	−220.222	+	118.332i	−0.440444	+	0.236663i
$501$	978.941			1.95397
$502$	205.930	−	205.930i	0.410220	−	0.410220i
$503$	−325.225	−	325.225i	−0.646571	−	0.646571i	0.305592	−	0.952163i	$-0.401146\pi$
$503$	−325.225	−	325.225i	−0.646571	−	0.646571i	−0.952163	+	0.305592i	$0.901146\pi$
$504$			292.136i			0.579634i
$505$	141.522	+	853.314i	0.280242	+	1.68973i
$506$	−89.2245			−0.176333
$507$	−305.003	+	305.003i	−0.601583	+	0.601583i
$508$	138.722	+	138.722i	0.273075	+	0.273075i
$509$			741.854i			1.45747i	0.684794	+	0.728737i	$0.259892\pi$
$509$			741.854i			1.45747i	−0.684794	+	0.728737i	$0.740108\pi$
$510$	−387.903	−	277.539i	−0.760595	−	0.544195i
$511$	67.4143			0.131926
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	406.446	+	406.446i	0.792293	+	0.792293i
$514$		−	43.0119i		−	0.0836807i
$515$	442.495	−	618.453i	0.859213	−	1.20088i
$516$	−182.812			−0.354287
$517$	505.875	−	505.875i	0.978481	−	0.978481i
$518$	84.5134	+	84.5134i	0.163153	+	0.163153i
$519$			779.077i			1.50111i
$520$	131.252	−	21.7682i	0.252407	−	0.0418619i
$521$	−361.909			−0.694643			−0.347322	−	0.937746i	$-0.612909\pi$
$521$	−361.909			−0.694643			−0.347322	+	0.937746i	$0.612909\pi$
$522$	−797.657	+	797.657i	−1.52808	+	1.52808i
$523$	160.404	+	160.404i	0.306700	+	0.306700i	0.843628	−	0.536928i	$-0.180415\pi$
$523$	160.404	+	160.404i	0.306700	+	0.306700i	−0.536928	+	0.843628i	$0.680415\pi$
$524$		−	438.798i		−	0.837401i
$525$	−664.283	+	226.576i	−1.26530	+	0.431572i
$526$	361.866			0.687958
$527$	−533.511	+	533.511i	−1.01235	+	1.01235i
$528$	−199.387	−	199.387i	−0.377628	−	0.377628i
$529$			23.0000i			0.0434783i
$530$	−80.7605	−	486.948i	−0.152378	−	0.918770i
$531$	466.378			0.878301
$532$	−74.1817	+	74.1817i	−0.139439	+	0.139439i
$533$	−15.4855	−	15.4855i	−0.0290534	−	0.0290534i
$534$		−	128.701i		−	0.241013i
$535$	384.553	+	275.143i	0.718791	+	0.514285i
$536$	−253.225			−0.472436
$537$	−1054.87	+	1054.87i	−1.96438	+	1.96438i
$538$	133.881	+	133.881i	0.248849	+	0.248849i
$539$		−	283.512i		−	0.525996i
$540$	334.070	−	466.913i	0.618648	−	0.864654i
$541$	235.297			0.434930			0.217465	−	0.976068i	$-0.430221\pi$
$541$	235.297			0.434930			0.217465	+	0.976068i	$0.430221\pi$
$542$	−299.275	+	299.275i	−0.552167	+	0.552167i
$543$	1014.55	+	1014.55i	1.86842	+	1.86842i
$544$			71.2083i			0.130898i
$545$	470.592	−	78.0478i	0.863471	−	0.143207i
$546$	373.516			0.684095
$547$	−542.478	+	542.478i	−0.991734	+	0.991734i	−0.999966	−	0.00823214i	$-0.997380\pi$
$547$	−542.478	+	542.478i	−0.991734	+	0.991734i	0.00823214	+	0.999966i	$0.497380\pi$
$548$	−154.226	−	154.226i	−0.281434	−	0.281434i
$549$		−	1928.56i		−	3.51286i
$550$	205.106	−	417.449i	0.372920	−	0.758998i
$551$	−405.096			−0.735202
$552$	−51.3974	+	51.3974i	−0.0931112	+	0.0931112i
$553$	−486.642	−	486.642i	−0.880004	−	0.880004i
$554$			442.582i			0.798885i
$555$	−70.7136	−	426.370i	−0.127412	−	0.768234i
$556$	8.55985			0.0153954
$557$	88.3077	−	88.3077i	0.158542	−	0.158542i	−0.623379	−	0.781920i	$-0.714240\pi$
$557$	88.3077	−	88.3077i	0.158542	−	0.158542i	0.781920	+	0.623379i	$0.214240\pi$
$558$	−1181.62	−	1181.62i	−2.11760	−	2.11760i
$559$			160.476i			0.287077i
$560$	85.2176	+	60.9720i	0.152174	+	0.108879i
$561$	887.377			1.58178
$562$	86.9048	−	86.9048i	0.154635	−	0.154635i
$563$	−210.944	−	210.944i	−0.374678	−	0.374678i	0.494500	−	0.869178i	$-0.335351\pi$
$563$	−210.944	−	210.944i	−0.374678	−	0.374678i	−0.869178	+	0.494500i	$0.835351\pi$
$564$		−	582.814i		−	1.03336i
$565$	379.793	−	530.818i	0.672199	−	0.939500i
$566$	51.1623			0.0903927
$567$	482.410	−	482.410i	0.850812	−	0.850812i
$568$	85.8457	+	85.8457i	0.151137	+	0.151137i
$569$			310.506i			0.545705i	0.962056	+	0.272853i	$0.0879671\pi$
$569$			310.506i			0.545705i	−0.962056	+	0.272853i	$0.912033\pi$
$570$	374.246	−	62.0689i	0.656573	−	0.108893i
$571$	−842.633			−1.47571			−0.737857	−	0.674957i	$-0.764162\pi$
$571$	−842.633			−1.47571			−0.737857	+	0.674957i	$0.764162\pi$
$572$	−175.026	+	175.026i	−0.305990	+	0.305990i
$573$	−863.460	−	863.460i	−1.50691	−	1.50691i
$574$		−	17.2479i		−	0.0300486i
$575$	−107.609	−	52.8716i	−0.187145	−	0.0919505i
$576$	−157.712			−0.273806
$577$	−140.531	+	140.531i	−0.243554	+	0.243554i	−0.818319	−	0.574765i	$-0.805094\pi$
$577$	−140.531	+	140.531i	−0.243554	+	0.243554i	0.574765	+	0.818319i	$0.305094\pi$
$578$	130.543	+	130.543i	0.225853	+	0.225853i
$579$		−	1637.62i		−	2.82835i
$580$	66.2010	+	399.161i	0.114140	+	0.688209i
$581$	−570.061			−0.981171
$582$	314.860	−	314.860i	0.540997	−	0.540997i
$583$	649.352	+	649.352i	1.11381	+	1.11381i
$584$			36.3943i			0.0623190i
$585$	−754.161	−	539.591i	−1.28916	−	0.922379i
$586$	−371.808			−0.634484
$587$	−407.264	+	407.264i	−0.693806	+	0.693806i	−0.963067	−	0.269261i	$-0.913220\pi$
$587$	−407.264	+	407.264i	−0.693806	+	0.693806i	0.269261	+	0.963067i	$0.413220\pi$
$588$	−163.316	−	163.316i	−0.277748	−	0.277748i
$589$		−	600.095i		−	1.01884i
$590$	97.3383	−	136.045i	0.164980	−	0.230585i
$591$	−916.544			−1.55084
$592$	−45.6254	+	45.6254i	−0.0770699	+	0.0770699i
$593$	67.3781	+	67.3781i	0.113623	+	0.113623i	0.761632	−	0.648010i	$-0.224398\pi$
$593$	67.3781	+	67.3781i	0.113623	+	0.113623i	−0.648010	+	0.761632i	$0.724398\pi$
$594$			1068.12i			1.79819i
$595$	−325.310	+	53.9528i	−0.546739	+	0.0906769i
$596$	−152.398			−0.255701
$597$	695.501	−	695.501i	1.16499	−	1.16499i
$598$	45.1177	+	45.1177i	0.0754476	+	0.0754476i
$599$		−	401.280i		−	0.669916i	−0.942233	−	0.334958i	$-0.891278\pi$
$599$		−	401.280i		−	0.669916i	0.942233	−	0.334958i	$-0.108722\pi$
$600$	−122.319	−	358.620i	−0.203865	−	0.597700i
$601$	−151.686			−0.252390			−0.126195	−	0.992005i	$-0.540276\pi$
$601$	−151.686			−0.252390			−0.126195	+	0.992005i	$0.540276\pi$
$602$	−89.3700	+	89.3700i	−0.148455	+	0.148455i
$603$	1248.02	+	1248.02i	2.06969	+	2.06969i
$604$		−	154.078i		−	0.255096i
$605$	42.5937	+	256.820i	0.0704028	+	0.424496i
$606$	−1310.97			−2.16332
$607$	−16.0095	+	16.0095i	−0.0263748	+	0.0263748i	−0.720171	−	0.693796i	$-0.755937\pi$
$607$	−16.0095	+	16.0095i	−0.0263748	+	0.0263748i	0.693796	+	0.720171i	$0.255937\pi$
$608$	−40.0477	−	40.0477i	−0.0658680	−	0.0658680i
$609$			1135.93i			1.86524i
$610$	−562.572	−	402.512i	−0.922249	−	0.659857i
$611$	−511.606			−0.837325
$612$	350.951	−	350.951i	0.573449	−	0.573449i
$613$	193.411	+	193.411i	0.315515	+	0.315515i	0.847042	−	0.531526i	$-0.178381\pi$
$613$	193.411	+	193.411i	0.315515	+	0.315515i	−0.531526	+	0.847042i	$0.678381\pi$
$614$			330.859i			0.538859i
$615$	−36.2920	+	50.7236i	−0.0590114	+	0.0824773i
$616$	−194.946			−0.316471
$617$	616.656	−	616.656i	0.999443	−	0.999443i	−0.000556768	−	1.00000i	$-0.500177\pi$
$617$	616.656	−	616.656i	0.999443	−	0.999443i	1.00000		0.000556768i	$0.000177225\pi$
$618$	814.983	+	814.983i	1.31874	+	1.31874i
$619$			889.291i			1.43666i	0.695703	+	0.718329i	$0.255093\pi$
$619$			889.291i			1.43666i	−0.695703	+	0.718329i	$0.744907\pi$
$620$	−591.303	+	98.0678i	−0.953714	+	0.158174i
$621$	275.337			0.443377
$622$	−192.859	+	192.859i	−0.310062	+	0.310062i
$623$	−62.9170	−	62.9170i	−0.100990	−	0.100990i
$624$			201.646i			0.323151i
$625$	494.733	−	381.922i	0.791573	−	0.611075i
$626$	11.9605			0.0191062
$627$	−499.063	+	499.063i	−0.795954	+	0.795954i
$628$	323.388	+	323.388i	0.514949	+	0.514949i
$629$		−	203.057i		−	0.322825i
$630$	−119.495	−	720.497i	−0.189674	−	1.14365i
$631$	−907.148			−1.43764			−0.718818	−	0.695199i	$-0.755316\pi$
$631$	−907.148			−1.43764			−0.718818	+	0.695199i	$0.755316\pi$
$632$	262.719	−	262.719i	0.415694	−	0.415694i
$633$	−724.176	−	724.176i	−1.14404	−	1.14404i
$634$		−	623.375i		−	0.983242i
$635$	−398.875	−	285.389i	−0.628150	−	0.449432i
$636$	748.112			1.17628
$637$	−143.362	+	143.362i	−0.225058	+	0.225058i
$638$	−532.287	−	532.287i	−0.834305	−	0.834305i
$639$		−	846.183i		−	1.32423i
$640$	−32.9164	+	46.0056i	−0.0514318	+	0.0718837i
$641$	−820.680			−1.28031			−0.640156	−	0.768245i	$-0.721130\pi$
$641$	−820.680			−1.28031			−0.640156	+	0.768245i	$0.721130\pi$
$642$	−506.755	+	506.755i	−0.789338	+	0.789338i
$643$	−224.861	−	224.861i	−0.349707	−	0.349707i	0.510294	−	0.860000i	$-0.329537\pi$
$643$	−224.861	−	224.861i	−0.349707	−	0.349707i	−0.860000	+	0.510294i	$0.829537\pi$
$644$			50.2525i			0.0780319i
$645$	450.871	−	74.7772i	0.699025	−	0.115934i
$646$	178.233			0.275903
$647$	−236.065	+	236.065i	−0.364860	+	0.364860i	−0.865599	−	0.500738i	$-0.833062\pi$
$647$	−236.065	+	236.065i	−0.364860	+	0.364860i	0.500738	+	0.865599i	$0.333062\pi$
$648$	260.434	+	260.434i	0.401904	+	0.401904i
$649$			311.220i			0.479538i
$650$	−314.804	+	107.374i	−0.484314	+	0.165191i
$651$	−1682.73			−2.58483
$652$	452.593	−	452.593i	0.694161	−	0.694161i
$653$	−574.018	−	574.018i	−0.879048	−	0.879048i	0.114388	−	0.993436i	$-0.463509\pi$
$653$	−574.018	−	574.018i	−0.879048	−	0.879048i	−0.993436	+	0.114388i	$0.963509\pi$
$654$			722.984i			1.10548i
$655$	179.485	+	1082.21i	0.274024	+	1.65223i
$656$	9.31144			0.0141943
$657$	179.370	−	179.370i	0.273013	−	0.273013i
$658$	−284.916	−	284.916i	−0.433003	−	0.433003i
$659$		−	123.517i		−	0.187430i	−0.995599	−	0.0937152i	$-0.970126\pi$
$659$		−	123.517i		−	0.187430i	0.995599	−	0.0937152i	$-0.0298743\pi$
$660$	573.308	+	410.194i	0.868649	+	0.621506i
$661$	698.871			1.05729			0.528646	−	0.848842i	$-0.322700\pi$
$661$	698.871			1.05729			0.528646	+	0.848842i	$0.322700\pi$
$662$	−103.280	+	103.280i	−0.156012	+	0.156012i
$663$	−448.715	−	448.715i	−0.676795	−	0.676795i
$664$		−	307.753i		−	0.463483i
$665$	152.612	−	213.298i	0.229492	−	0.320749i
$666$	449.730			0.675271
$667$	−137.211	+	137.211i	−0.205714	+	0.205714i
$668$	258.359	+	258.359i	0.386766	+	0.386766i
$669$			2010.15i			3.00470i
$670$	624.533	−	103.579i	0.932138	−	0.154595i
$671$	1286.95			1.91796
$672$	−112.298	+	112.298i	−0.167110	+	0.167110i
$673$	−763.682	−	763.682i	−1.13474	−	1.13474i	−0.989378	−	0.145365i	$-0.953565\pi$
$673$	−763.682	−	763.682i	−1.13474	−	1.13474i	−0.145365	−	0.989378i	$-0.546435\pi$
$674$			312.773i			0.464055i
$675$	−632.934	+	1288.20i	−0.937680	+	1.90844i
$676$	−160.991			−0.238152
$677$	18.4824	−	18.4824i	0.0273005	−	0.0273005i	−0.693325	−	0.720625i	$-0.743855\pi$
$677$	18.4824	−	18.4824i	0.0273005	−	0.0273005i	0.720625	+	0.693325i	$0.243855\pi$
$678$	699.499	+	699.499i	1.03171	+	1.03171i
$679$		−	307.847i		−	0.453382i
$680$	−29.1269	−	175.622i	−0.0428337	−	0.258267i
$681$	−22.5834			−0.0331620
$682$	788.511	−	788.511i	1.15617	−	1.15617i
$683$	416.193	+	416.193i	0.609360	+	0.609360i	0.942779	−	0.333419i	$-0.108202\pi$
$683$	416.193	+	416.193i	0.609360	+	0.609360i	−0.333419	+	0.942779i	$0.608202\pi$
$684$			394.751i			0.577122i
$685$	443.454	+	317.285i	0.647378	+	0.463190i
$686$	−522.735			−0.762004
$687$	729.510	−	729.510i	1.06188	−	1.06188i
$688$	−48.2473	−	48.2473i	−0.0701268	−	0.0701268i
$689$		−	656.708i		−	0.953132i
$690$	105.738	−	147.785i	0.153244	−	0.214182i
$691$	−187.344			−0.271120			−0.135560	−	0.990769i	$-0.543283\pi$
$691$	−187.344			−0.271120			−0.135560	+	0.990769i	$0.543283\pi$
$692$	−205.612	+	205.612i	−0.297127	+	0.297127i
$693$	960.793	+	960.793i	1.38643	+	1.38643i
$694$			411.361i			0.592739i
$695$	−21.1113	+	3.50131i	−0.0303759	+	0.00503785i
$696$	−613.243			−0.881096
$697$	−20.7204	+	20.7204i	−0.0297279	+	0.0297279i
$698$	436.934	+	436.934i	0.625980	+	0.625980i
$699$		−	74.5989i		−	0.106722i
$700$	−235.113	−	115.519i	−0.335876	−	0.165027i
$701$	533.465			0.761006			0.380503	−	0.924780i	$-0.375751\pi$
$701$	533.465			0.761006			0.380503	+	0.924780i	$0.375751\pi$
$702$	540.111	−	540.111i	0.769389	−	0.769389i
$703$	114.200	+	114.200i	0.162446	+	0.162446i
$704$		−	105.244i		−	0.149494i
$705$	238.393	+	1437.40i	0.338146	+	2.03886i
$706$	575.000			0.814447
$707$	−640.885	+	640.885i	−0.906485	+	0.906485i
$708$	179.277	+	179.277i	0.253216	+	0.253216i
$709$		−	1343.63i		−	1.89510i	−0.319600	−	0.947552i	$-0.603549\pi$
$709$		−	1343.63i		−	1.89510i	0.319600	−	0.947552i	$-0.396451\pi$
$710$	−246.836	−	176.608i	−0.347657	−	0.248744i
$711$	−2589.62			−3.64223
$712$	33.9664	−	33.9664i	0.0477056	−	0.0477056i
$713$	−203.260	−	203.260i	−0.285077	−	0.285077i
$714$		−	499.783i		−	0.699977i
$715$	360.077	−	503.262i	0.503604	−	0.703862i
$716$	−556.799			−0.777652
$717$	1102.30	−	1102.30i	1.53738	−	1.53738i
$718$	207.074	+	207.074i	0.288403	+	0.288403i
$719$			86.6051i			0.120452i	0.998185	+	0.0602261i	$0.0191822\pi$
$719$			86.6051i			0.120452i	−0.998185	+	0.0602261i	$0.980818\pi$
$720$	388.968	−	64.5104i	0.540233	−	0.0895978i
$721$	796.829			1.10517
$722$	260.761	−	260.761i	0.361165	−	0.361165i
$723$	190.423	+	190.423i	0.263380	+	0.263380i
$724$			535.516i			0.739663i
$725$	−326.544	−	957.376i	−0.450406	−	1.32052i
$726$	−394.560			−0.543472
$727$	776.915	−	776.915i	1.06866	−	1.06866i	0.0711972	−	0.997462i	$-0.477318\pi$
$727$	776.915	−	776.915i	1.06866	−	1.06866i	0.997462	−	0.0711972i	$-0.0226820\pi$
$728$	98.5772	+	98.5772i	0.135408	+	0.135408i
$729$			201.687i			0.276662i
$730$	−14.8867	−	89.7596i	−0.0203927	−	0.122958i
$731$	214.725			0.293742
$732$	741.344	−	741.344i	1.01277	−	1.01277i
$733$	221.110	+	221.110i	0.301651	+	0.301651i	0.841660	−	0.540008i	$-0.181579\pi$
$733$	221.110	+	221.110i	0.301651	+	0.301651i	−0.540008	+	0.841660i	$0.681579\pi$
$734$		−	138.029i		−	0.188051i
$735$	469.590	+	335.985i	0.638898	+	0.457122i
$736$	−27.1293			−0.0368605
$737$	−832.823	+	832.823i	−1.13002	+	1.13002i
$738$	−45.8915	−	45.8915i	−0.0621837	−	0.0621837i
$739$			793.629i			1.07392i	0.843607	+	0.536962i	$0.180428\pi$
$739$			793.629i			1.07392i	−0.843607	+	0.536962i	$0.819572\pi$
$740$	93.8638	−	131.189i	0.126843	−	0.177282i
$741$	504.717			0.681129
$742$	365.724	−	365.724i	0.492890	−	0.492890i
$743$	821.820	+	821.820i	1.10608	+	1.10608i	0.993660	+	0.112423i	$0.0358613\pi$
$743$	821.820	+	821.820i	1.10608	+	1.10608i	0.112423	+	0.993660i	$0.464139\pi$
$744$		−	908.436i		−	1.22102i
$745$	375.861	−	62.3366i	0.504511	−	0.0836733i
$746$	514.875			0.690181
$747$	−1516.76	+	1516.76i	−2.03047	+	2.03047i
$748$	234.194	+	234.194i	0.313094	+	0.313094i
$749$			495.467i			0.661505i
$750$	448.366	+	834.435i	0.597822	+	1.11258i
$751$	−1321.54			−1.75970			−0.879851	−	0.475250i	$-0.842358\pi$
$751$	−1321.54			−1.75970			−0.879851	+	0.475250i	$0.842358\pi$
$752$	153.815	−	153.815i	0.204541	−	0.204541i
$753$	−780.283	−	780.283i	−1.03623	−	1.03623i
$754$			538.317i			0.713948i
$755$	63.0239	+	380.005i	0.0834754	+	0.503317i
$756$	601.581			0.795742
$757$	874.570	−	874.570i	1.15531	−	1.15531i	0.169839	−	0.985472i	$-0.445675\pi$
$757$	874.570	−	874.570i	1.15531	−	1.15531i	0.985472	−	0.169839i	$-0.0543247\pi$
$758$	419.437	+	419.437i	0.553346	+	0.553346i
$759$			338.078i			0.445425i
$760$	115.151	+	82.3890i	0.151515	+	0.108407i
$761$	1233.20			1.62050			0.810252	−	0.586082i	$-0.199330\pi$
$761$	1233.20			1.62050			0.810252	+	0.586082i	$0.199330\pi$
$762$	525.628	−	525.628i	0.689800	−	0.689800i
$763$	353.440	+	353.440i	0.463224	+	0.463224i
$764$		−	455.764i		−	0.596550i
$765$	−722.001	+	1009.11i	−0.943793	+	1.31909i
$766$	−684.409			−0.893484
$767$	157.373	−	157.373i	0.205180	−	0.205180i
$768$	−60.6251	−	60.6251i	−0.0789389	−	0.0789389i
$769$		−	691.258i		−	0.898905i	−0.893304	−	0.449452i	$-0.851619\pi$
$769$		−	691.258i		−	0.898905i	0.893304	−	0.449452i	$-0.148381\pi$
$770$	480.797	−	79.7404i	0.624412	−	0.103559i
$771$	−162.975			−0.211381
$772$	432.195	−	432.195i	0.559838	−	0.559838i
$773$	311.187	+	311.187i	0.402571	+	0.402571i	0.879138	−	0.476567i	$-0.158119\pi$
$773$	311.187	+	311.187i	0.402571	+	0.402571i	−0.476567	+	0.879138i	$0.658119\pi$
$774$			475.574i			0.614437i
$775$	1418.22	−	483.731i	1.82997	−	0.624170i
$776$	166.194			0.214168
$777$	320.227	−	320.227i	0.412132	−	0.412132i
$778$	−2.95987	−	2.95987i	−0.00380446	−	0.00380446i
$779$		−	23.3064i		−	0.0299183i
$780$	−82.4810	−	497.322i	−0.105745	−	0.637592i
$781$	564.669			0.723008
$782$	60.3698	−	60.3698i	0.0771992	−	0.0771992i
$783$	1642.58	+	1642.58i	2.09780	+	2.09780i
$784$		−	86.2037i		−	0.109954i
$785$	−929.852	−	665.296i	−1.18453	−	0.847511i
$786$	−1662.64			−2.11531
$787$	666.914	−	666.914i	0.847412	−	0.847412i	−0.142397	−	0.989810i	$-0.545481\pi$
$787$	666.914	−	666.914i	0.847412	−	0.847412i	0.989810	+	0.142397i	$0.0454810\pi$
$788$	−241.892	−	241.892i	−0.306969	−	0.306969i
$789$		−	1371.13i		−	1.73781i
$790$	−540.484	+	755.408i	−0.684157	+	0.956213i
$791$	683.918			0.864624
$792$	−518.694	+	518.694i	−0.654916	+	0.654916i
$793$	−650.767	−	650.767i	−0.820639	−	0.820639i
$794$		−	185.543i		−	0.233681i
$795$	−1845.08	+	306.007i	−2.32085	+	0.384914i
$796$	367.109			0.461193
$797$	−961.969	+	961.969i	−1.20699	+	1.20699i	−0.234989	+	0.971998i	$0.575506\pi$
$797$	−961.969	+	961.969i	−1.20699	+	1.20699i	−0.971998	+	0.234989i	$0.924494\pi$
$798$	281.079	+	281.079i	0.352230	+	0.352230i
$799$			684.555i			0.856765i
$800$	62.3639	−	126.928i	0.0779549	−	0.158660i
$801$	−334.807			−0.417986
$802$	−23.9519	+	23.9519i	−0.0298652	+	0.0298652i
$803$	119.696	+	119.696i	0.149061	+	0.149061i
$804$			959.488i			1.19339i
$805$	−20.5552	−	123.938i	−0.0255344	−	0.153961i
$806$	−797.444			−0.989384
$807$	507.284	−	507.284i	0.628604	−	0.628604i
$808$	−345.988	−	345.988i	−0.428203	−	0.428203i
$809$			18.2564i			0.0225666i	0.999936	+	0.0112833i	$0.00359167\pi$
$809$			18.2564i			0.0225666i	−0.999936	+	0.0112833i	$0.996408\pi$
$810$	−748.839	−	535.784i	−0.924492	−	0.661461i
$811$	57.4191			0.0708004			0.0354002	−	0.999373i	$-0.488729\pi$
$811$	57.4191			0.0708004			0.0354002	+	0.999373i	$0.488729\pi$
$812$	−299.791	+	299.791i	−0.369201	+	0.369201i
$813$	1133.97	+	1133.97i	1.39480	+	1.39480i
$814$			300.111i			0.368687i
$815$	−931.107	+	1301.36i	−1.14246	+	1.59676i
$816$	269.813			0.330653
$817$	−120.762	+	120.762i	−0.147812	+	0.147812i
$818$	659.636	+	659.636i	0.806401	+	0.806401i
$819$		−	971.678i		−	1.18642i
$820$	−22.9649	+	3.80874i	−0.0280060	+	0.00464480i
$821$	−245.011			−0.298430			−0.149215	−	0.988805i	$-0.547675\pi$
$821$	−245.011			−0.298430			−0.149215	+	0.988805i	$0.547675\pi$
$822$	−584.373	+	584.373i	−0.710916	+	0.710916i
$823$	418.436	+	418.436i	0.508428	+	0.508428i	0.914044	−	0.405616i	$-0.132943\pi$
$823$	418.436	+	418.436i	0.508428	+	0.508428i	−0.405616	+	0.914044i	$0.632943\pi$
$824$			430.176i			0.522058i
$825$	−1581.74	−	777.161i	−1.91726	−	0.942013i
$826$	175.283			0.212208
$827$	−168.274	+	168.274i	−0.203475	+	0.203475i	−0.801487	−	0.598012i	$-0.795957\pi$
$827$	−168.274	+	168.274i	−0.203475	+	0.203475i	0.598012	+	0.801487i	$0.295957\pi$
$828$	133.707	+	133.707i	0.161482	+	0.161482i
$829$			11.0678i			0.0133508i	0.999978	+	0.00667540i	$0.00212486\pi$
$829$			11.0678i			0.0133508i	−0.999978	+	0.00667540i	$0.997875\pi$
$830$	125.883	+	759.014i	0.151666	+	0.914475i
$831$	1676.97			2.01802
$832$	−53.2179	+	53.2179i	−0.0639638	+	0.0639638i
$833$	191.826	+	191.826i	0.230283	+	0.230283i
$834$		−	32.4338i		−	0.0388895i
$835$	−742.873	−	531.516i	−0.889669	−	0.636546i
$836$	−263.423			−0.315099
$837$	−2433.26	+	2433.26i	−2.90712	+	2.90712i
$838$	221.284	+	221.284i	0.264062	+	0.264062i
$839$		−	794.606i		−	0.947087i	−0.880770	−	0.473544i	$-0.842975\pi$
$839$		−	794.606i		−	0.947087i	0.880770	−	0.473544i	$-0.157025\pi$
$840$	231.027	−	322.895i	0.275032	−	0.384399i
$841$	−796.120			−0.946635
$842$	−105.381	+	105.381i	−0.125155	+	0.125155i
$843$	−329.288	−	329.288i	−0.390615	−	0.390615i
$844$		−	382.245i		−	0.452897i
$845$	397.054	−	65.8515i	0.469886	−	0.0779308i
$846$	−1516.15			−1.79214
$847$	−192.886	+	192.886i	−0.227728	+	0.227728i
$848$	197.440	+	197.440i	0.232830	+	0.232830i
$849$		−	193.857i		−	0.228336i
$850$	143.672	+	421.224i	0.169026	+	0.495558i
$851$	77.3616			0.0909067
$852$	325.275	−	325.275i	0.381778	−	0.381778i
$853$	−69.4575	−	69.4575i	−0.0814273	−	0.0814273i	0.665220	−	0.746647i	$-0.268338\pi$
$853$	−69.4575	−	69.4575i	−0.0814273	−	0.0814273i	−0.746647	+	0.665220i	$0.768338\pi$
$854$		−	724.831i		−	0.848748i
$855$	−161.468	−	973.579i	−0.188852	−	1.13869i
$856$	−267.483			−0.312480
$857$	860.302	−	860.302i	1.00385	−	1.00385i	0.00385990	−	0.999993i	$-0.498771\pi$
$857$	860.302	−	860.302i	1.00385	−	1.00385i	0.999993	−	0.00385990i	$-0.00122865\pi$
$858$	663.186	+	663.186i	0.772944	+	0.772944i
$859$		−	895.628i		−	1.04264i	−0.853361	−	0.521320i	$-0.825440\pi$
$859$		−	895.628i		−	1.04264i	0.853361	−	0.521320i	$-0.174560\pi$
$860$	138.728	+	99.2577i	0.161311	+	0.115416i
$861$	−65.3534			−0.0759040
$862$	−224.659	+	224.659i	−0.260626	+	0.260626i
$863$	−230.452	−	230.452i	−0.267036	−	0.267036i	0.560869	−	0.827905i	$-0.310467\pi$
$863$	−230.452	−	230.452i	−0.267036	−	0.267036i	−0.827905	+	0.560869i	$0.810467\pi$
$864$			324.770i			0.375891i
$865$	423.000	−	591.206i	0.489017	−	0.683475i
$866$	161.004			0.185917
$867$	494.636	−	494.636i	0.570514	−	0.570514i
$868$	−444.100	−	444.100i	−0.511636	−	0.511636i
$869$		−	1728.09i		−	1.98860i
$870$	1512.45	−	250.840i	1.73844	−	0.288322i
$871$	842.258			0.967001
$872$	−190.808	+	190.808i	−0.218816	+	0.218816i
$873$	−819.089	−	819.089i	−0.938246	−	0.938246i
$874$			67.9042i			0.0776936i
$875$	627.113	+	188.735i	0.716701	+	0.215697i
$876$	137.900			0.157420
$877$	−92.5345	+	92.5345i	−0.105513	+	0.105513i	−0.757892	−	0.652380i	$-0.773771\pi$
$877$	−92.5345	+	92.5345i	−0.105513	+	0.105513i	0.652380	+	0.757892i	$0.273771\pi$
$878$	191.215	+	191.215i	0.217784	+	0.217784i
$879$			1408.80i			1.60273i
$880$	43.0487	+	259.563i	0.0489189	+	0.294958i
$881$	−1323.21			−1.50194			−0.750970	−	0.660336i	$-0.770414\pi$
$881$	−1323.21			−1.50194			−0.750970	+	0.660336i	$0.770414\pi$
$882$	−424.856	+	424.856i	−0.481696	+	0.481696i
$883$	−426.837	−	426.837i	−0.483394	−	0.483394i	0.422820	−	0.906214i	$-0.361040\pi$
$883$	−426.837	−	426.837i	−0.483394	−	0.483394i	−0.906214	+	0.422820i	$0.861040\pi$
$884$		−	236.847i		−	0.267927i
$885$	−515.484	−	368.821i	−0.582467	−	0.416747i
$886$	787.070			0.888341
$887$	608.858	−	608.858i	0.686424	−	0.686424i	−0.275016	−	0.961440i	$-0.588683\pi$
$887$	608.858	−	608.858i	0.686424	−	0.686424i	0.961440	+	0.275016i	$0.0886832\pi$
$888$	172.878	+	172.878i	0.194682	+	0.194682i
$889$		−	513.920i		−	0.578087i
$890$	−69.8780	+	97.6651i	−0.0785146	+	0.109736i
$891$	1713.06			1.92263
$892$	−530.512	+	530.512i	−0.594745	+	0.594745i
$893$	−384.995	−	384.995i	−0.431126	−	0.431126i
$894$			577.446i			0.645912i
$895$	1373.24	−	227.752i	1.53435	−	0.254472i
$896$	−59.2746			−0.0661547
$897$	170.954	−	170.954i	0.190584	−	0.190584i
$898$	6.06354	+	6.06354i	0.00675227	+	0.00675227i
$899$		−	2425.17i		−	2.69763i
$900$	−932.928	+	318.205i	−1.03659	+	0.353562i
$901$	−878.710			−0.975261
$902$	30.6240	−	30.6240i	0.0339513	−	0.0339513i
$903$	338.629	+	338.629i	0.375004	+	0.375004i
$904$			369.220i			0.408429i
$905$	−219.047	−	1320.75i	−0.242041	−	1.45939i
$906$	−583.812			−0.644384
$907$	445.689	−	445.689i	0.491388	−	0.491388i	−0.417356	−	0.908743i	$-0.637043\pi$
$907$	445.689	−	445.689i	0.491388	−	0.491388i	0.908743	+	0.417356i	$0.137043\pi$
$908$	−5.96014	−	5.96014i	−0.00656403	−	0.00656403i
$909$			3410.41i			3.75183i
$910$	−283.444	−	202.800i	−0.311477	−	0.222857i
$911$	398.727			0.437681			0.218840	−	0.975761i	$-0.429773\pi$
$911$	398.727			0.437681			0.218840	+	0.975761i	$0.429773\pi$
$912$	−151.743	+	151.743i	−0.166385	+	0.166385i
$913$	−1012.16	−	1012.16i	−1.10860	−	1.10860i
$914$		−	965.603i		−	1.05646i
$915$	−1525.15	+	2131.62i	−1.66683	+	2.32964i
$916$	385.060			0.420372
$917$	−812.800	+	812.800i	−0.886369	+	0.886369i
$918$	−722.697	−	722.697i	−0.787251	−	0.787251i
$919$		−	1270.23i		−	1.38219i	−0.722766	−	0.691093i	$-0.757129\pi$
$919$		−	1270.23i		−	1.38219i	0.722766	−	0.691093i	$-0.242871\pi$
$920$	66.9093	−	11.0969i	0.0727275	−	0.0120619i
$921$	1253.65			1.36118
$922$	101.616	−	101.616i	0.110213	−	0.110213i
$923$	−285.533	−	285.533i	−0.309353	−	0.309353i
$924$			738.663i			0.799419i
$925$	−177.836	+	361.946i	−0.192255	+	0.391293i
$926$	−74.6120			−0.0805745
$927$	2120.13	−	2120.13i	2.28708	−	2.28708i
$928$	−161.845	−	161.845i	−0.174402	−	0.174402i
$929$			864.036i			0.930071i	0.885292	+	0.465035i	$0.153958\pi$
$929$			864.036i			0.930071i	−0.885292	+	0.465035i	$0.846042\pi$
$930$	371.585	+	2240.49i	0.399554	+	2.40912i
$931$	−215.766			−0.231758
$932$	19.6879	−	19.6879i	0.0211244	−	0.0211244i
$933$	730.754	+	730.754i	0.783230	+	0.783230i
$934$		−	310.472i		−	0.332412i
$935$	−673.390	−	481.801i	−0.720203	−	0.515295i
$936$	524.570			0.560438
$937$	324.809	−	324.809i	0.346647	−	0.346647i	−0.512212	−	0.858859i	$-0.671174\pi$
$937$	324.809	−	324.809i	0.346647	−	0.346647i	0.858859	+	0.512212i	$0.171174\pi$
$938$	469.058	+	469.058i	0.500062	+	0.500062i
$939$		−	45.3191i		−	0.0482631i
$940$	−316.438	+	442.271i	−0.336637	+	0.470501i
$941$	704.098			0.748245			0.374122	−	0.927379i	$-0.377944\pi$
$941$	704.098			0.748245			0.374122	+	0.927379i	$0.377944\pi$
$942$	1225.34	−	1225.34i	1.30078	−	1.30078i
$943$	−7.89416	−	7.89416i	−0.00837132	−	0.00837132i
$944$			94.6285i			0.100242i
$945$	−1483.69	+	246.070i	−1.57004	+	0.260391i
$946$	−317.357			−0.335473
$947$	−984.377	+	984.377i	−1.03947	+	1.03947i	−0.0402800	+	0.999188i	$0.512825\pi$
$947$	−984.377	+	984.377i	−1.03947	+	1.03947i	−0.999188	+	0.0402800i	$0.987175\pi$
$948$	−995.458	−	995.458i	−1.05006	−	1.05006i
$949$		−	121.052i		−	0.127557i
$950$	−317.699	−	156.096i	−0.334420	−	0.164311i
$951$	−2362.01			−2.48371
$952$	131.901	−	131.901i	0.138552	−	0.138552i
$953$	−1167.75	−	1167.75i	−1.22535	−	1.22535i	−0.965706	−	0.259640i	$-0.916396\pi$
$953$	−1167.75	−	1167.75i	−1.22535	−	1.22535i	−0.259640	−	0.965706i	$-0.583604\pi$
$954$		−	1946.17i		−	2.04001i
$955$	186.425	+	1124.06i	0.195210	+	1.17702i
$956$	581.833			0.608612
$957$	−2016.87	+	2016.87i	−2.10749	+	2.10749i
$958$	166.864	+	166.864i	0.174179	+	0.174179i
$959$			571.356i			0.595783i
$960$	174.318	+	124.722i	0.181581	+	0.129919i
$961$	2631.57			2.73836
$962$	151.755	−	151.755i	0.157750	−	0.157750i
$963$	1318.29	+	1318.29i	1.36894	+	1.36894i
$964$			100.512i			0.104266i
$965$	−889.143	+	1242.71i	−0.921392	+	1.28778i
$966$	190.410			0.197112
$967$	−1010.45	+	1010.45i	−1.04493	+	1.04493i	−0.0459902	+	0.998942i	$0.514644\pi$
$967$	−1010.45	+	1010.45i	−1.04493	+	1.04493i	−0.998942	+	0.0459902i	$0.985356\pi$
$968$	−104.131	−	104.131i	−0.107574	−	0.107574i
$969$		−	675.337i		−	0.696942i
$970$	−409.886	+	67.9798i	−0.422563	+	0.0700822i
$971$	114.386			0.117802			0.0589012	−	0.998264i	$-0.481240\pi$
$971$	114.386			0.117802			0.0589012	+	0.998264i	$0.481240\pi$
$972$	256.070	−	256.070i	0.263447	−	0.263447i
$973$	−15.8557	−	15.8557i	−0.0162957	−	0.0162957i
$974$		−	868.278i		−	0.891456i
$975$	406.848	+	1192.81i	0.417280	+	1.22340i
$976$	391.307			0.400929
$977$	−772.174	+	772.174i	−0.790352	+	0.790352i	−0.981551	−	0.191199i	$-0.938762\pi$
$977$	−772.174	+	772.174i	−0.790352	+	0.790352i	0.191199	+	0.981551i	$0.438762\pi$
$978$	−1714.90	−	1714.90i	−1.75348	−	1.75348i
$979$		−	223.421i		−	0.228214i
$980$	35.2606	+	212.605i	0.0359802	+	0.216944i
$981$	1880.80			1.91722
$982$	588.840	−	588.840i	0.599634	−	0.599634i
$983$	491.094	+	491.094i	0.499587	+	0.499587i	0.911309	−	0.411722i	$-0.135073\pi$
$983$	491.094	+	491.094i	0.499587	+	0.499587i	−0.411722	+	0.911309i	$0.635073\pi$
$984$		−	35.2817i		−	0.0358554i
$985$	695.524	+	497.637i	0.706115	+	0.505216i
$986$	720.296			0.730523
$987$	−1079.56	+	1079.56i	−1.09378	+	1.09378i
$988$	133.203	+	133.203i	0.134821	+	0.134821i
$989$			81.8072i			0.0827171i
$990$	1067.09	−	1491.43i	1.07787	−	1.50649i
$991$	−676.497			−0.682640			−0.341320	−	0.939947i	$-0.610874\pi$
$991$	−676.497			−0.682640			−0.341320	+	0.939947i	$0.610874\pi$
$992$	239.752	−	239.752i	0.241686	−	0.241686i
$993$	391.334	+	391.334i	0.394092	+	0.394092i
$994$		−	318.030i		−	0.319949i
$995$	−905.406	+	150.162i	−0.909956	+	0.150916i
$996$	−1166.10			−1.17078
$997$	193.493	−	193.493i	0.194075	−	0.194075i	−0.603379	−	0.797454i	$-0.706179\pi$
$997$	193.493	−	193.493i	0.194075	−	0.194075i	0.797454	+	0.603379i	$0.206179\pi$
$998$	−280.896	−	280.896i	−0.281459	−	0.281459i
$999$		−	926.109i		−	0.927036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.93.1	yes	24
5.2	odd	4	inner	230.3.f.b.47.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.1	✓	24	5.2	odd	4	inner
230.3.f.b.93.1	yes	24	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-3.78907 - 3.78907i) q^{3} -2.00000i q^{4} +(0.818077 + 4.93262i) q^{5} -7.57813 q^{6} +(-3.70466 + 3.70466i) q^{7} +(-2.00000 - 2.00000i) q^{8} +19.7140i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(-3.78907 - 3.78907i) q^{3} -2.00000i q^{4} +(0.818077 + 4.93262i) q^{5} -7.57813 q^{6} +(-3.70466 + 3.70466i) q^{7} +(-2.00000 - 2.00000i) q^{8} +19.7140i q^{9} +(5.75070 + 4.11454i) q^{10} -13.1554 q^{11} +(-7.57813 + 7.57813i) q^{12} +(6.65224 + 6.65224i) q^{13} +7.40933i q^{14} +(15.5903 - 21.7898i) q^{15} -4.00000 q^{16} +(8.90104 - 8.90104i) q^{17} +(19.7140 + 19.7140i) q^{18} +10.0119i q^{19} +(9.86524 - 1.63615i) q^{20} +28.0744 q^{21} +(-13.1554 + 13.1554i) q^{22} +(3.39116 + 3.39116i) q^{23} +15.1563i q^{24} +(-23.6615 + 8.07053i) q^{25} +13.3045 q^{26} +(40.5962 - 40.5962i) q^{27} +(7.40933 + 7.40933i) q^{28} +40.4613i q^{29} +(-6.19950 - 37.3801i) q^{30} -59.9380 q^{31} +(-4.00000 + 4.00000i) q^{32} +(49.8468 + 49.8468i) q^{33} -17.8021i q^{34} +(-21.3044 - 15.2430i) q^{35} +39.4281 q^{36} +(11.4063 - 11.4063i) q^{37} +(10.0119 + 10.0119i) q^{38} -50.4115i q^{39} +(8.22909 - 11.5014i) q^{40} -2.32786 q^{41} +(28.0744 - 28.0744i) q^{42} +(12.0618 + 12.0618i) q^{43} +26.3109i q^{44} +(-97.2419 + 16.1276i) q^{45} +6.78233 q^{46} +(-38.4537 + 38.4537i) q^{47} +(15.1563 + 15.1563i) q^{48} +21.5509i q^{49} +(-15.5910 + 31.7320i) q^{50} -67.4532 q^{51} +(13.3045 - 13.3045i) q^{52} +(-49.3600 - 49.3600i) q^{53} -81.1924i q^{54} +(-10.7622 - 64.8908i) q^{55} +14.8187 q^{56} +(37.9359 - 37.9359i) q^{57} +(40.4613 + 40.4613i) q^{58} -23.6571i q^{59} +(-43.5795 - 31.1806i) q^{60} -97.8268 q^{61} +(-59.9380 + 59.9380i) q^{62} +(-73.0339 - 73.0339i) q^{63} +8.00000i q^{64} +(-27.3709 + 38.2550i) q^{65} +99.6937 q^{66} +(63.3064 - 63.3064i) q^{67} +(-17.8021 - 17.8021i) q^{68} -25.6987i q^{69} +(-36.5474 + 6.06140i) q^{70} -42.9229 q^{71} +(39.4281 - 39.4281i) q^{72} +(-9.09857 - 9.09857i) q^{73} -22.8127i q^{74} +(120.235 + 59.0752i) q^{75} +20.0239 q^{76} +(48.7365 - 48.7365i) q^{77} +(-50.4115 - 50.4115i) q^{78} +131.359i q^{79} +(-3.27231 - 19.7305i) q^{80} -130.217 q^{81} +(-2.32786 + 2.32786i) q^{82} +(76.9382 + 76.9382i) q^{83} -56.1489i q^{84} +(51.1872 + 36.6237i) q^{85} +24.1236 q^{86} +(153.311 - 153.311i) q^{87} +(26.3109 + 26.3109i) q^{88} +16.9832i q^{89} +(-81.1143 + 113.369i) q^{90} -49.2886 q^{91} +(6.78233 - 6.78233i) q^{92} +(227.109 + 227.109i) q^{93} +76.9073i q^{94} +(-49.3851 + 8.19053i) q^{95} +30.3125 q^{96} +(-41.5485 + 41.5485i) q^{97} +(21.5509 + 21.5509i) q^{98} -259.347i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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