LMFDB - Embedded newform 630.3.o.b.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(127,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.o (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:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.1
Root			$1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	630.253
Dual form			630.3.o.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.32032 + 2.51691i) q^{5} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.32032 + 2.51691i) q^{5} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.80341 - 6.83723i) q^{10} -2.92322 q^{11} +(-1.13309 - 1.13309i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-1.54506 + 1.54506i) q^{17} -3.35199i q^{19} +(5.03383 + 8.64064i) q^{20} +(2.92322 - 2.92322i) q^{22} +(-7.90681 - 7.90681i) q^{23} +(12.3303 - 21.7477i) q^{25} +2.26617 q^{26} +(-3.74166 - 3.74166i) q^{28} -13.5474i q^{29} +15.7936 q^{31} +(4.00000 - 4.00000i) q^{32} -3.09013i q^{34} +(-3.37386 + 12.7913i) q^{35} +(-16.8305 + 16.8305i) q^{37} +(3.35199 + 3.35199i) q^{38} +(-13.6745 - 3.60681i) q^{40} +72.6227 q^{41} +(20.3749 + 20.3749i) q^{43} +5.84643i q^{44} +15.8136 q^{46} +(52.3194 - 52.3194i) q^{47} -7.00000i q^{49} +(9.41742 + 34.0780i) q^{50} +(-2.26617 + 2.26617i) q^{52} +(40.5379 + 40.5379i) q^{53} +(12.6292 - 7.35748i) q^{55} +7.48331 q^{56} +(13.5474 + 13.5474i) q^{58} -117.165i q^{59} -45.4373 q^{61} +(-15.7936 + 15.7936i) q^{62} +8.00000i q^{64} +(7.74717 + 2.04341i) q^{65} +(57.7773 - 57.7773i) q^{67} +(3.09013 + 3.09013i) q^{68} +(-9.41742 - 16.1652i) q^{70} +51.7217 q^{71} +(72.3851 + 72.3851i) q^{73} -33.6610i q^{74} -6.70398 q^{76} +(-5.46884 + 5.46884i) q^{77} +37.1850i q^{79} +(17.2813 - 10.0677i) q^{80} +(-72.6227 + 72.6227i) q^{82} +(21.3331 + 21.3331i) q^{83} +(2.78638 - 10.5640i) q^{85} -40.7498 q^{86} +(-5.84643 - 5.84643i) q^{88} -100.951i q^{89} -4.23962 q^{91} +(-15.8136 + 15.8136i) q^{92} +104.639i q^{94} +(8.43666 + 14.4817i) q^{95} +(52.5887 - 52.5887i) q^{97} +(7.00000 + 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} + 8 q^{11} + 8 q^{13} - 32 q^{16} + 32 q^{17} - 8 q^{22} + 40 q^{23} - 48 q^{25} - 16 q^{26} + 144 q^{31} + 32 q^{32} + 28 q^{35} + 160 q^{37} + 320 q^{41} - 32 q^{43} - 80 q^{46} + 144 q^{47} + 112 q^{50} + 16 q^{52} + 200 q^{53} + 184 q^{55} - 64 q^{58} + 288 q^{61} - 144 q^{62} - 24 q^{65} + 80 q^{67} - 64 q^{68} - 112 q^{70} + 280 q^{71} + 312 q^{73} + 56 q^{77} - 320 q^{82} + 320 q^{83} + 80 q^{85} + 64 q^{86} + 16 q^{88} + 80 q^{92} + 472 q^{95} - 24 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 + 8 * q^11 + 8 * q^13 - 32 * q^16 + 32 * q^17 - 8 * q^22 + 40 * q^23 - 48 * q^25 - 16 * q^26 + 144 * q^31 + 32 * q^32 + 28 * q^35 + 160 * q^37 + 320 * q^41 - 32 * q^43 - 80 * q^46 + 144 * q^47 + 112 * q^50 + 16 * q^52 + 200 * q^53 + 184 * q^55 - 64 * q^58 + 288 * q^61 - 144 * q^62 - 24 * q^65 + 80 * q^67 - 64 * q^68 - 112 * q^70 + 280 * q^71 + 312 * q^73 + 56 * q^77 - 320 * q^82 + 320 * q^83 + 80 * q^85 + 64 * q^86 + 16 * q^88 + 80 * q^92 + 472 * q^95 - 24 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	−4.32032	+	2.51691i	−0.864064	+	0.503383i
$5$	−4.32032	+	2.51691i	−0.864064	+	0.503383i
$6$		0			0
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	1.80341	−	6.83723i	0.180341	−	0.683723i
$11$	−2.92322			−0.265747			−0.132873	−	0.991133i	$-0.542420\pi$
$11$	−2.92322			−0.265747			−0.132873	+	0.991133i	$0.542420\pi$
$12$		0			0
$13$	−1.13309	−	1.13309i	−0.0871605	−	0.0871605i	0.662182	−	0.749343i	$-0.269630\pi$
$13$	−1.13309	−	1.13309i	−0.0871605	−	0.0871605i	−0.749343	+	0.662182i	$0.769630\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−1.54506	+	1.54506i	−0.0908861	+	0.0908861i	−0.751088	−	0.660202i	$-0.770471\pi$
$17$	−1.54506	+	1.54506i	−0.0908861	+	0.0908861i	0.660202	+	0.751088i	$0.270471\pi$
$18$		0			0
$19$		−	3.35199i		−	0.176420i	−0.996102	−	0.0882102i	$-0.971885\pi$
$19$		−	3.35199i		−	0.176420i	0.996102	−	0.0882102i	$-0.0281147\pi$
$20$	5.03383	+	8.64064i	0.251691	+	0.432032i
$21$		0			0
$22$	2.92322	−	2.92322i	0.132873	−	0.132873i
$23$	−7.90681	−	7.90681i	−0.343774	−	0.343774i	0.514010	−	0.857784i	$-0.328159\pi$
$23$	−7.90681	−	7.90681i	−0.343774	−	0.343774i	−0.857784	+	0.514010i	$0.828159\pi$
$24$		0			0
$25$	12.3303	−	21.7477i	0.493212	−	0.869909i
$26$	2.26617			0.0871605
$27$		0			0
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	13.5474i		−	0.467153i	−0.972338	−	0.233577i	$-0.924957\pi$
$29$		−	13.5474i		−	0.467153i	0.972338	−	0.233577i	$-0.0750430\pi$
$30$		0			0
$31$	15.7936			0.509473			0.254736	−	0.967011i	$-0.418011\pi$
$31$	15.7936			0.509473			0.254736	+	0.967011i	$0.418011\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$		0			0
$34$		−	3.09013i		−	0.0908861i
$35$	−3.37386	+	12.7913i	−0.0963961	+	0.365465i
$36$		0			0
$37$	−16.8305	+	16.8305i	−0.454878	+	0.454878i	−0.896970	−	0.442092i	$-0.854236\pi$
$37$	−16.8305	+	16.8305i	−0.454878	+	0.454878i	0.442092	+	0.896970i	$0.354236\pi$
$38$	3.35199	+	3.35199i	0.0882102	+	0.0882102i
$39$		0			0
$40$	−13.6745	−	3.60681i	−0.341862	−	0.0901703i
$41$	72.6227			1.77129			0.885643	−	0.464367i	$-0.153718\pi$
$41$	72.6227			1.77129			0.885643	+	0.464367i	$0.153718\pi$
$42$		0			0
$43$	20.3749	+	20.3749i	0.473835	+	0.473835i	0.903153	−	0.429318i	$-0.141246\pi$
$43$	20.3749	+	20.3749i	0.473835	+	0.473835i	−0.429318	+	0.903153i	$0.641246\pi$
$44$			5.84643i			0.132873i
$45$		0			0
$46$	15.8136			0.343774
$47$	52.3194	−	52.3194i	1.11318	−	1.11318i	0.120461	−	0.992718i	$-0.461563\pi$
$47$	52.3194	−	52.3194i	1.11318	−	1.11318i	0.992718	−	0.120461i	$-0.0384372\pi$
$48$		0			0
$49$		−	7.00000i		−	0.142857i
$50$	9.41742	+	34.0780i	0.188348	+	0.681561i
$51$		0			0
$52$	−2.26617	+	2.26617i	−0.0435802	+	0.0435802i
$53$	40.5379	+	40.5379i	0.764865	+	0.764865i	0.977198	−	0.212332i	$-0.0681059\pi$
$53$	40.5379	+	40.5379i	0.764865	+	0.764865i	−0.212332	+	0.977198i	$0.568106\pi$
$54$		0			0
$55$	12.6292	−	7.35748i	0.229622	−	0.133772i
$56$	7.48331			0.133631
$57$		0			0
$58$	13.5474	+	13.5474i	0.233577	+	0.233577i
$59$		−	117.165i		−	1.98585i	−0.118752	−	0.992924i	$-0.537889\pi$
$59$		−	117.165i		−	1.98585i	0.118752	−	0.992924i	$-0.462111\pi$
$60$		0			0
$61$	−45.4373			−0.744874			−0.372437	−	0.928057i	$-0.621478\pi$
$61$	−45.4373			−0.744874			−0.372437	+	0.928057i	$0.621478\pi$
$62$	−15.7936	+	15.7936i	−0.254736	+	0.254736i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	7.74717	+	2.04341i	0.119187	+	0.0314371i
$66$		0			0
$67$	57.7773	−	57.7773i	0.862348	−	0.862348i	−0.129263	−	0.991610i	$-0.541261\pi$
$67$	57.7773	−	57.7773i	0.862348	−	0.862348i	0.991610	+	0.129263i	$0.0412611\pi$
$68$	3.09013	+	3.09013i	0.0454430	+	0.0454430i
$69$		0			0
$70$	−9.41742	−	16.1652i	−0.134535	−	0.230931i
$71$	51.7217			0.728475			0.364238	−	0.931306i	$-0.381330\pi$
$71$	51.7217			0.728475			0.364238	+	0.931306i	$0.381330\pi$
$72$		0			0
$73$	72.3851	+	72.3851i	0.991576	+	0.991576i	0.999965	−	0.00838858i	$-0.00267020\pi$
$73$	72.3851	+	72.3851i	0.991576	+	0.991576i	−0.00838858	+	0.999965i	$0.502670\pi$
$74$		−	33.6610i		−	0.454878i
$75$		0			0
$76$	−6.70398			−0.0882102
$77$	−5.46884	+	5.46884i	−0.0710238	+	0.0710238i
$78$		0			0
$79$			37.1850i			0.470696i	0.971911	+	0.235348i	$0.0756230\pi$
$79$			37.1850i			0.470696i	−0.971911	+	0.235348i	$0.924377\pi$
$80$	17.2813	−	10.0677i	0.216016	−	0.125846i
$81$		0			0
$82$	−72.6227	+	72.6227i	−0.885643	+	0.885643i
$83$	21.3331	+	21.3331i	0.257026	+	0.257026i	0.823843	−	0.566818i	$-0.191826\pi$
$83$	21.3331	+	21.3331i	0.257026	+	0.257026i	−0.566818	+	0.823843i	$0.691826\pi$
$84$		0			0
$85$	2.78638	−	10.5640i	0.0327809	−	0.124282i
$86$	−40.7498			−0.473835
$87$		0			0
$88$	−5.84643	−	5.84643i	−0.0664367	−	0.0664367i
$89$		−	100.951i		−	1.13428i	−0.823620	−	0.567141i	$-0.808049\pi$
$89$		−	100.951i		−	1.13428i	0.823620	−	0.567141i	$-0.191951\pi$
$90$		0			0
$91$	−4.23962			−0.0465892
$92$	−15.8136	+	15.8136i	−0.171887	+	0.171887i
$93$		0			0
$94$			104.639i			1.11318i
$95$	8.43666	+	14.4817i	0.0888070	+	0.152438i
$96$		0			0
$97$	52.5887	−	52.5887i	0.542151	−	0.542151i	−0.382008	−	0.924159i	$-0.624767\pi$
$97$	52.5887	−	52.5887i	0.542151	−	0.542151i	0.924159	+	0.382008i	$0.124767\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$		0			0
$100$	−43.4955	−	24.6606i	−0.434955	−	0.246606i
$101$	129.417			1.28136			0.640679	−	0.767808i	$-0.278653\pi$
$101$	129.417			1.28136			0.640679	+	0.767808i	$0.278653\pi$
$102$		0			0
$103$	31.0447	+	31.0447i	0.301405	+	0.301405i	0.841563	−	0.540158i	$-0.181636\pi$
$103$	31.0447	+	31.0447i	0.301405	+	0.301405i	−0.540158	+	0.841563i	$0.681636\pi$
$104$		−	4.53234i		−	0.0435802i
$105$		0			0
$106$	−81.0757			−0.764865
$107$	−109.421	+	109.421i	−1.02263	+	1.02263i	−0.0228904	+	0.999738i	$0.507287\pi$
$107$	−109.421	+	109.421i	−1.02263	+	1.02263i	−0.999738	+	0.0228904i	$0.992713\pi$
$108$		0			0
$109$		−	68.6170i		−	0.629514i	−0.949172	−	0.314757i	$-0.898077\pi$
$109$		−	68.6170i		−	0.629514i	0.949172	−	0.314757i	$-0.101923\pi$
$110$	−5.27174	+	19.9867i	−0.0479249	+	0.181697i
$111$		0			0
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	68.0366	+	68.0366i	0.602094	+	0.602094i	0.940868	−	0.338774i	$-0.110012\pi$
$113$	68.0366	+	68.0366i	0.602094	+	0.602094i	−0.338774	+	0.940868i	$0.610012\pi$
$114$		0			0
$115$	54.0607	+	14.2592i	0.470093	+	0.123993i
$116$	−27.0949			−0.233577
$117$		0			0
$118$	117.165	+	117.165i	0.992924	+	0.992924i
$119$			5.78110i			0.0485807i
$120$		0			0
$121$	−112.455			−0.929379
$122$	45.4373	−	45.4373i	0.372437	−	0.372437i
$123$		0			0
$124$		−	31.5873i		−	0.254736i
$125$	1.46629	+	124.991i	0.0117303	+	0.999931i
$126$		0			0
$127$	142.963	−	142.963i	1.12569	−	1.12569i	0.134824	−	0.990870i	$-0.456953\pi$
$127$	142.963	−	142.963i	1.12569	−	1.12569i	0.990870	−	0.134824i	$-0.0430470\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−9.79058	+	5.70376i	−0.0753122	+	0.0438750i
$131$	−3.55384			−0.0271285			−0.0135643	−	0.999908i	$-0.504318\pi$
$131$	−3.55384			−0.0271285			−0.0135643	+	0.999908i	$0.504318\pi$
$132$		0			0
$133$	−6.27100	−	6.27100i	−0.0471503	−	0.0471503i
$134$			115.555i			0.862348i
$135$		0			0
$136$	−6.18025			−0.0454430
$137$	−75.1054	+	75.1054i	−0.548214	+	0.548214i	−0.925924	−	0.377710i	$-0.876712\pi$
$137$	−75.1054	+	75.1054i	−0.548214	+	0.548214i	0.377710	+	0.925924i	$0.376712\pi$
$138$		0			0
$139$		−	192.352i		−	1.38383i	−0.721980	−	0.691914i	$-0.756768\pi$
$139$		−	192.352i		−	1.38383i	0.721980	−	0.691914i	$-0.243232\pi$
$140$	25.5826	+	6.74773i	0.182733	+	0.0481981i
$141$		0			0
$142$	−51.7217	+	51.7217i	−0.364238	+	0.364238i
$143$	3.31225	+	3.31225i	0.0231626	+	0.0231626i
$144$		0			0
$145$	34.0977	+	58.5293i	0.235157	+	0.403650i
$146$	−144.770			−0.991576
$147$		0			0
$148$	33.6610	+	33.6610i	0.227439	+	0.227439i
$149$		−	77.5005i		−	0.520138i	−0.965590	−	0.260069i	$-0.916255\pi$
$149$		−	77.5005i		−	0.520138i	0.965590	−	0.260069i	$-0.0837453\pi$
$150$		0			0
$151$	36.8195			0.243837			0.121919	−	0.992540i	$-0.461095\pi$
$151$	36.8195			0.243837			0.121919	+	0.992540i	$0.461095\pi$
$152$	6.70398	−	6.70398i	0.0441051	−	0.0441051i
$153$		0			0
$154$		−	10.9377i		−	0.0710238i
$155$	−68.2336	+	39.7512i	−0.440217	+	0.256460i
$156$		0			0
$157$	75.7654	−	75.7654i	0.482582	−	0.482582i	−0.423373	−	0.905955i	$-0.639154\pi$
$157$	75.7654	−	75.7654i	0.482582	−	0.482582i	0.905955	+	0.423373i	$0.139154\pi$
$158$	−37.1850	−	37.1850i	−0.235348	−	0.235348i
$159$		0			0
$160$	−7.21362	+	27.3489i	−0.0450851	+	0.170931i
$161$	−29.5846			−0.183755
$162$		0			0
$163$	174.453	+	174.453i	1.07026	+	1.07026i	0.997338	+	0.0729236i	$0.0232329\pi$
$163$	174.453	+	174.453i	1.07026	+	1.07026i	0.0729236	+	0.997338i	$0.476767\pi$
$164$		−	145.245i		−	0.885643i
$165$		0			0
$166$	−42.6663			−0.257026
$167$	−119.275	+	119.275i	−0.714222	+	0.714222i	−0.967416	−	0.253194i	$-0.918519\pi$
$167$	−119.275	+	119.275i	−0.714222	+	0.714222i	0.253194	+	0.967416i	$0.418519\pi$
$168$		0			0
$169$		−	166.432i		−	0.984806i
$170$	7.77758	+	13.3503i	0.0457505	+	0.0785314i
$171$		0			0
$172$	40.7498	−	40.7498i	0.236918	−	0.236918i
$173$	−110.021	−	110.021i	−0.635957	−	0.635957i	0.313599	−	0.949556i	$-0.398465\pi$
$173$	−110.021	−	110.021i	−0.635957	−	0.635957i	−0.949556	+	0.313599i	$0.898465\pi$
$174$		0			0
$175$	−17.6184	−	63.7542i	−0.100677	−	0.364309i
$176$	11.6929			0.0664367
$177$		0			0
$178$	100.951	+	100.951i	0.567141	+	0.567141i
$179$		−	49.0357i		−	0.273943i	−0.990575	−	0.136971i	$-0.956263\pi$
$179$		−	49.0357i		−	0.273943i	0.990575	−	0.136971i	$-0.0437368\pi$
$180$		0			0
$181$	−327.143			−1.80742			−0.903709	−	0.428148i	$-0.859166\pi$
$181$	−327.143			−1.80742			−0.903709	+	0.428148i	$0.859166\pi$
$182$	4.23962	−	4.23962i	0.0232946	−	0.0232946i
$183$		0			0
$184$		−	31.6272i		−	0.171887i
$185$	30.3522	−	115.074i	0.164066	−	0.622021i
$186$		0			0
$187$	4.51655	−	4.51655i	0.0241527	−	0.0241527i
$188$	−104.639	−	104.639i	−0.556589	−	0.556589i
$189$		0			0
$190$	−22.9183	−	6.04500i	−0.120623	−	0.0318158i
$191$	−289.078			−1.51350			−0.756749	−	0.653705i	$-0.773214\pi$
$191$	−289.078			−1.51350			−0.756749	+	0.653705i	$0.773214\pi$
$192$		0			0
$193$	−131.213	−	131.213i	−0.679858	−	0.679858i	0.280110	−	0.959968i	$-0.409629\pi$
$193$	−131.213	−	131.213i	−0.679858	−	0.679858i	−0.959968	+	0.280110i	$0.909629\pi$
$194$			105.177i			0.542151i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−111.798	+	111.798i	−0.567504	+	0.567504i	−0.931429	−	0.363924i	$-0.881437\pi$
$197$	−111.798	+	111.798i	−0.567504	+	0.567504i	0.363924	+	0.931429i	$0.381437\pi$
$198$		0			0
$199$			58.3715i			0.293324i	0.989187	+	0.146662i	$0.0468530\pi$
$199$			58.3715i			0.293324i	−0.989187	+	0.146662i	$0.953147\pi$
$200$	68.1561	−	18.8348i	0.340780	−	0.0941742i
$201$		0			0
$202$	−129.417	+	129.417i	−0.640679	+	0.640679i
$203$	−25.3450	−	25.3450i	−0.124852	−	0.124852i
$204$		0			0
$205$	−313.753	+	182.785i	−1.53050	+	0.891634i
$206$	−62.0894			−0.301405
$207$		0			0
$208$	4.53234	+	4.53234i	0.0217901	+	0.0217901i
$209$			9.79858i			0.0468832i
$210$		0			0
$211$	55.0602			0.260949			0.130474	−	0.991452i	$-0.458350\pi$
$211$	55.0602			0.260949			0.130474	+	0.991452i	$0.458350\pi$
$212$	81.0757	−	81.0757i	0.382433	−	0.382433i
$213$		0			0
$214$		−	218.842i		−	1.02263i
$215$	−139.308	−	36.7443i	−0.647944	−	0.170903i
$216$		0			0
$217$	29.5472	−	29.5472i	0.136162	−	0.136162i
$218$	68.6170	+	68.6170i	0.314757	+	0.314757i
$219$		0			0
$220$	−14.7150	−	25.2584i	−0.0668862	−	0.114811i
$221$	3.50138			0.0158433
$222$		0			0
$223$	−101.768	−	101.768i	−0.456360	−	0.456360i	0.441099	−	0.897459i	$-0.354589\pi$
$223$	−101.768	−	101.768i	−0.456360	−	0.456360i	−0.897459	+	0.441099i	$0.854589\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−136.073			−0.602094
$227$	25.0589	−	25.0589i	0.110392	−	0.110392i	−0.649753	−	0.760145i	$-0.725128\pi$
$227$	25.0589	−	25.0589i	0.110392	−	0.110392i	0.760145	+	0.649753i	$0.225128\pi$
$228$		0			0
$229$		−	283.497i		−	1.23798i	−0.785399	−	0.618990i	$-0.787542\pi$
$229$		−	283.497i		−	1.23798i	0.785399	−	0.618990i	$-0.212458\pi$
$230$	−68.3199	+	39.8015i	−0.297043	+	0.173050i
$231$		0			0
$232$	27.0949	−	27.0949i	0.116788	−	0.116788i
$233$	−139.119	−	139.119i	−0.597077	−	0.597077i	0.342457	−	0.939534i	$-0.388741\pi$
$233$	−139.119	−	139.119i	−0.597077	−	0.597077i	−0.939534	+	0.342457i	$0.888741\pi$
$234$		0			0
$235$	−94.3531	+	357.720i	−0.401503	+	1.52221i
$236$	−234.330			−0.992924
$237$		0			0
$238$	−5.78110	−	5.78110i	−0.0242903	−	0.0242903i
$239$		−	183.280i		−	0.766864i	−0.923569	−	0.383432i	$-0.874742\pi$
$239$		−	183.280i		−	0.766864i	0.923569	−	0.383432i	$-0.125258\pi$
$240$		0			0
$241$	−280.094			−1.16222			−0.581108	−	0.813827i	$-0.697380\pi$
$241$	−280.094			−1.16222			−0.581108	+	0.813827i	$0.697380\pi$
$242$	112.455	−	112.455i	0.464689	−	0.464689i
$243$		0			0
$244$			90.8747i			0.372437i
$245$	17.6184	+	30.2422i	0.0719118	+	0.123438i
$246$		0			0
$247$	−3.79809	+	3.79809i	−0.0153769	+	0.0153769i
$248$	31.5873	+	31.5873i	0.127368	+	0.127368i
$249$		0			0
$250$	−126.458	−	123.525i	−0.505831	−	0.494100i
$251$	−148.745			−0.592611			−0.296305	−	0.955093i	$-0.595755\pi$
$251$	−148.745			−0.592611			−0.296305	+	0.955093i	$0.595755\pi$
$252$		0			0
$253$	23.1133	+	23.1133i	0.0913569	+	0.0913569i
$254$			285.926i			1.12569i
$255$		0			0
$256$	16.0000			0.0625000
$257$	241.684	−	241.684i	0.940404	−	0.940404i	−0.0579178	−	0.998321i	$-0.518446\pi$
$257$	241.684	−	241.684i	0.940404	−	0.940404i	0.998321	+	0.0579178i	$0.0184461\pi$
$258$		0			0
$259$			62.9739i			0.243142i
$260$	4.08683	−	15.4943i	0.0157186	−	0.0595936i
$261$		0			0
$262$	3.55384	−	3.55384i	0.0135643	−	0.0135643i
$263$	234.607	+	234.607i	0.892042	+	0.892042i	0.994715	−	0.102673i	$-0.0327395\pi$
$263$	234.607	+	234.607i	0.892042	+	0.892042i	−0.102673	+	0.994715i	$0.532740\pi$
$264$		0			0
$265$	−277.167	−	73.1062i	−1.04591	−	0.275872i
$266$	12.5420			0.0471503
$267$		0			0
$268$	−115.555	−	115.555i	−0.431174	−	0.431174i
$269$		−	357.902i		−	1.33049i	−0.746625	−	0.665245i	$-0.768327\pi$
$269$		−	357.902i		−	1.33049i	0.746625	−	0.665245i	$-0.231673\pi$
$270$		0			0
$271$	178.869			0.660035			0.330017	−	0.943975i	$-0.392945\pi$
$271$	178.869			0.660035			0.330017	+	0.943975i	$0.392945\pi$
$272$	6.18025	−	6.18025i	0.0227215	−	0.0227215i
$273$		0			0
$274$		−	150.211i		−	0.548214i
$275$	−36.0441	+	63.5733i	−0.131070	+	0.231176i
$276$		0			0
$277$	−119.355	+	119.355i	−0.430883	+	0.430883i	−0.888929	−	0.458045i	$-0.848550\pi$
$277$	−119.355	+	119.355i	−0.430883	+	0.430883i	0.458045	+	0.888929i	$0.348550\pi$
$278$	192.352	+	192.352i	0.691914	+	0.691914i
$279$		0			0
$280$	−32.3303	+	18.8348i	−0.115465	+	0.0672673i
$281$	42.3632			0.150759			0.0753793	−	0.997155i	$-0.475983\pi$
$281$	42.3632			0.150759			0.0753793	+	0.997155i	$0.475983\pi$
$282$		0			0
$283$	3.43964	+	3.43964i	0.0121542	+	0.0121542i	0.713158	−	0.701004i	$-0.247264\pi$
$283$	3.43964	+	3.43964i	0.0121542	+	0.0121542i	−0.701004	+	0.713158i	$0.747264\pi$
$284$		−	103.443i		−	0.364238i
$285$		0			0
$286$	−6.62451			−0.0231626
$287$	135.865	−	135.865i	0.473396	−	0.473396i
$288$		0			0
$289$			284.226i			0.983479i
$290$	−92.6270	−	24.4315i	−0.319403	−	0.0842467i
$291$		0			0
$292$	144.770	−	144.770i	0.495788	−	0.495788i
$293$	25.3982	+	25.3982i	0.0866834	+	0.0866834i	0.749119	−	0.662436i	$-0.230477\pi$
$293$	25.3982	+	25.3982i	0.0866834	+	0.0866834i	−0.662436	+	0.749119i	$0.730477\pi$
$294$		0			0
$295$	294.894	+	506.190i	0.999641	+	1.71590i
$296$	−67.3219			−0.227439
$297$		0			0
$298$	77.5005	+	77.5005i	0.260069	+	0.260069i
$299$			17.9182i			0.0599270i
$300$		0			0
$301$	76.2360			0.253276
$302$	−36.8195	+	36.8195i	−0.121919	+	0.121919i
$303$		0			0
$304$			13.4080i			0.0441051i
$305$	196.304	−	114.362i	0.643619	−	0.374957i
$306$		0			0
$307$	−323.839	+	323.839i	−1.05485	+	1.05485i	−0.0564445	+	0.998406i	$0.517976\pi$
$307$	−323.839	+	323.839i	−1.05485	+	1.05485i	−0.998406	+	0.0564445i	$0.982024\pi$
$308$	10.9377	+	10.9377i	0.0355119	+	0.0355119i
$309$		0			0
$310$	28.4824	−	107.985i	0.0918786	−	0.348338i
$311$	284.428			0.914561			0.457280	−	0.889323i	$-0.348824\pi$
$311$	284.428			0.914561			0.457280	+	0.889323i	$0.348824\pi$
$312$		0			0
$313$	178.964	+	178.964i	0.571771	+	0.571771i	0.932623	−	0.360852i	$-0.117514\pi$
$313$	178.964	+	178.964i	0.571771	+	0.571771i	−0.360852	+	0.932623i	$0.617514\pi$
$314$			151.531i			0.482582i
$315$		0			0
$316$	74.3700			0.235348
$317$	−335.800	+	335.800i	−1.05931	+	1.05931i	−0.0611787	+	0.998127i	$0.519486\pi$
$317$	−335.800	+	335.800i	−1.05931	+	1.05931i	−0.998127	+	0.0611787i	$0.980514\pi$
$318$		0			0
$319$			39.6021i			0.124145i
$320$	−20.1353	−	34.5625i	−0.0629228	−	0.108008i
$321$		0			0
$322$	29.5846	−	29.5846i	0.0918775	−	0.0918775i
$323$	5.17903	+	5.17903i	0.0160342	+	0.0160342i
$324$		0			0
$325$	−38.6133	+	10.6708i	−0.118810	+	0.0328331i
$326$	−348.905			−1.07026
$327$		0			0
$328$	145.245	+	145.245i	0.442821	+	0.442821i
$329$		−	195.761i		−	0.595019i
$330$		0			0
$331$	444.301			1.34230			0.671150	−	0.741322i	$-0.265801\pi$
$331$	444.301			1.34230			0.671150	+	0.741322i	$0.265801\pi$
$332$	42.6663	−	42.6663i	0.128513	−	0.128513i
$333$		0			0
$334$		−	238.550i		−	0.714222i
$335$	−104.196	+	395.037i	−0.311033	+	1.17921i
$336$		0			0
$337$	431.469	−	431.469i	1.28032	−	1.28032i	0.339842	−	0.940483i	$-0.389626\pi$
$337$	431.469	−	431.469i	1.28032	−	1.28032i	0.940483	−	0.339842i	$-0.110374\pi$
$338$	166.432	+	166.432i	0.492403	+	0.492403i
$339$		0			0
$340$	−21.1279	−	5.57275i	−0.0621409	−	0.0163904i
$341$	−46.1682			−0.135391
$342$		0			0
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			81.4997i			0.236918i
$345$		0			0
$346$	220.041			0.635957
$347$	227.893	−	227.893i	0.656751	−	0.656751i	−0.297859	−	0.954610i	$-0.596272\pi$
$347$	227.893	−	227.893i	0.656751	−	0.656751i	0.954610	+	0.297859i	$0.0962725\pi$
$348$		0			0
$349$		−	280.016i		−	0.802337i	−0.916004	−	0.401168i	$-0.868604\pi$
$349$		−	280.016i		−	0.802337i	0.916004	−	0.401168i	$-0.131396\pi$
$350$	81.3725	+	46.1358i	0.232493	+	0.131816i
$351$		0			0
$352$	−11.6929	+	11.6929i	−0.0332184	+	0.0332184i
$353$	114.469	+	114.469i	0.324276	+	0.324276i	0.850405	−	0.526129i	$-0.176357\pi$
$353$	114.469	+	114.469i	0.324276	+	0.324276i	−0.526129	+	0.850405i	$0.676357\pi$
$354$		0			0
$355$	−223.454	+	130.179i	−0.629449	+	0.366702i
$356$	−201.902			−0.567141
$357$		0			0
$358$	49.0357	+	49.0357i	0.136971	+	0.136971i
$359$			700.748i			1.95195i	0.217893	+	0.975973i	$0.430082\pi$
$359$			700.748i			1.95195i	−0.217893	+	0.975973i	$0.569918\pi$
$360$		0			0
$361$	349.764			0.968876
$362$	327.143	−	327.143i	0.903709	−	0.903709i
$363$		0			0
$364$			8.47924i			0.0232946i
$365$	−494.913	−	130.540i	−1.35593	−	0.357643i
$366$		0			0
$367$	412.257	−	412.257i	1.12332	−	1.12332i	0.132075	−	0.991240i	$-0.457836\pi$
$367$	412.257	−	412.257i	1.12332	−	1.12332i	0.991240	−	0.132075i	$-0.0421641\pi$
$368$	31.6272	+	31.6272i	0.0859436	+	0.0859436i
$369$		0			0
$370$	84.7217	+	145.426i	0.228978	+	0.393043i
$371$	151.679			0.408838
$372$		0			0
$373$	−121.669	−	121.669i	−0.326191	−	0.326191i	0.524945	−	0.851136i	$-0.324086\pi$
$373$	−121.669	−	121.669i	−0.326191	−	0.326191i	−0.851136	+	0.524945i	$0.824086\pi$
$374$			9.03311i			0.0241527i
$375$		0			0
$376$	209.278			0.556589
$377$	−15.3504	+	15.3504i	−0.0407173	+	0.0407173i
$378$		0			0
$379$			709.113i			1.87101i	0.353312	+	0.935506i	$0.385055\pi$
$379$			709.113i			1.87101i	−0.353312	+	0.935506i	$0.614945\pi$
$380$	28.9633	−	16.8733i	0.0762192	−	0.0444035i
$381$		0			0
$382$	289.078	−	289.078i	0.756749	−	0.756749i
$383$	476.611	+	476.611i	1.24441	+	1.24441i	0.958151	+	0.286264i	$0.0924134\pi$
$383$	476.611	+	476.611i	1.24441	+	1.24441i	0.286264	+	0.958151i	$0.407587\pi$
$384$		0			0
$385$	9.86253	−	37.3917i	0.0256170	−	0.0971213i
$386$	262.425			0.679858
$387$		0			0
$388$	−105.177	−	105.177i	−0.271076	−	0.271076i
$389$			270.210i			0.694627i	0.937749	+	0.347313i	$0.112906\pi$
$389$			270.210i			0.694627i	−0.937749	+	0.347313i	$0.887094\pi$
$390$		0			0
$391$	24.4330			0.0624886
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	223.597i		−	0.567504i
$395$	−93.5914	−	160.651i	−0.236940	−	0.406712i
$396$		0			0
$397$	−169.270	+	169.270i	−0.426374	+	0.426374i	−0.887391	−	0.461017i	$-0.847485\pi$
$397$	−169.270	+	169.270i	−0.426374	+	0.426374i	0.461017	+	0.887391i	$0.347485\pi$
$398$	−58.3715	−	58.3715i	−0.146662	−	0.146662i
$399$		0			0
$400$	−49.3212	+	86.9909i	−0.123303	+	0.217477i
$401$	−397.414			−0.991058			−0.495529	−	0.868592i	$-0.665026\pi$
$401$	−397.414			−0.991058			−0.495529	+	0.868592i	$0.665026\pi$
$402$		0			0
$403$	−17.8956	−	17.8956i	−0.0444059	−	0.0444059i
$404$		−	258.834i		−	0.640679i
$405$		0			0
$406$	50.6899			0.124852
$407$	49.1991	−	49.1991i	0.120882	−	0.120882i
$408$		0			0
$409$		−	787.478i		−	1.92537i	−0.270616	−	0.962687i	$-0.587227\pi$
$409$		−	787.478i		−	1.92537i	0.270616	−	0.962687i	$-0.412773\pi$
$410$	130.968	−	496.538i	0.319435	−	1.21107i
$411$		0			0
$412$	62.0894	−	62.0894i	0.150703	−	0.150703i
$413$	−219.196	−	219.196i	−0.530740	−	0.530740i
$414$		0			0
$415$	−145.860	−	38.4723i	−0.351469	−	0.0927043i
$416$	−9.06469			−0.0217901
$417$		0			0
$418$	−9.79858	−	9.79858i	−0.0234416	−	0.0234416i
$419$		−	293.606i		−	0.700730i	−0.936613	−	0.350365i	$-0.886058\pi$
$419$		−	293.606i		−	0.700730i	0.936613	−	0.350365i	$-0.113942\pi$
$420$		0			0
$421$	−294.797			−0.700230			−0.350115	−	0.936707i	$-0.613857\pi$
$421$	−294.797			−0.700230			−0.350115	+	0.936707i	$0.613857\pi$
$422$	−55.0602	+	55.0602i	−0.130474	+	0.130474i
$423$		0			0
$424$			162.151i			0.382433i
$425$	14.5505	+	52.6527i	0.0342365	+	0.123889i
$426$		0			0
$427$	−85.0055	+	85.0055i	−0.199076	+	0.199076i
$428$	218.842	+	218.842i	0.511314	+	0.511314i
$429$		0			0
$430$	176.052	−	102.564i	0.409424	−	0.238520i
$431$	314.916			0.730663			0.365332	−	0.930877i	$-0.380956\pi$
$431$	314.916			0.730663			0.365332	+	0.930877i	$0.380956\pi$
$432$		0			0
$433$	236.366	+	236.366i	0.545880	+	0.545880i	0.925246	−	0.379367i	$-0.123858\pi$
$433$	236.366	+	236.366i	0.545880	+	0.545880i	−0.379367	+	0.925246i	$0.623858\pi$
$434$			59.0944i			0.136162i
$435$		0			0
$436$	−137.234			−0.314757
$437$	−26.5035	+	26.5035i	−0.0606488	+	0.0606488i
$438$		0			0
$439$		−	254.993i		−	0.580850i	−0.956898	−	0.290425i	$-0.906203\pi$
$439$		−	254.993i		−	0.580850i	0.956898	−	0.290425i	$-0.0937967\pi$
$440$	39.9734	+	10.5435i	0.0908486	+	0.0239625i
$441$		0			0
$442$	−3.50138	+	3.50138i	−0.00792167	+	0.00792167i
$443$	292.628	+	292.628i	0.660559	+	0.660559i	0.955512	−	0.294953i	$-0.0953039\pi$
$443$	292.628	+	292.628i	0.660559	+	0.660559i	−0.294953	+	0.955512i	$0.595304\pi$
$444$		0			0
$445$	254.085	+	436.141i	0.570978	+	0.980093i
$446$	203.537			0.456360
$447$		0			0
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$		−	400.989i		−	0.893072i	−0.894766	−	0.446536i	$-0.852657\pi$
$449$		−	400.989i		−	0.893072i	0.894766	−	0.446536i	$-0.147343\pi$
$450$		0			0
$451$	−212.292			−0.470714
$452$	136.073	−	136.073i	0.301047	−	0.301047i
$453$		0			0
$454$			50.1179i			0.110392i
$455$	18.3165	−	10.6708i	0.0402561	−	0.0234522i
$456$		0			0
$457$	−172.040	+	172.040i	−0.376454	+	0.376454i	−0.869821	−	0.493367i	$-0.835766\pi$
$457$	−172.040	+	172.040i	−0.376454	+	0.376454i	0.493367	+	0.869821i	$0.335766\pi$
$458$	283.497	+	283.497i	0.618990	+	0.618990i
$459$		0			0
$460$	28.5184	−	108.121i	0.0619965	−	0.235046i
$461$	−153.918			−0.333878			−0.166939	−	0.985967i	$-0.553388\pi$
$461$	−153.918			−0.333878			−0.166939	+	0.985967i	$0.553388\pi$
$462$		0			0
$463$	−291.763	−	291.763i	−0.630158	−	0.630158i	0.317949	−	0.948108i	$-0.397006\pi$
$463$	−291.763	−	291.763i	−0.630158	−	0.630158i	−0.948108	+	0.317949i	$0.897006\pi$
$464$			54.1898i			0.116788i
$465$		0			0
$466$	278.238			0.597077
$467$	503.234	−	503.234i	1.07759	−	1.07759i	0.0808645	−	0.996725i	$-0.474232\pi$
$467$	503.234	−	503.234i	1.07759	−	1.07759i	0.996725	−	0.0808645i	$-0.0257681\pi$
$468$		0			0
$469$		−	216.183i		−	0.460944i
$470$	−263.367	−	452.073i	−0.560355	−	0.961857i
$471$		0			0
$472$	234.330	−	234.330i	0.496462	−	0.496462i
$473$	−59.5603	−	59.5603i	−0.125920	−	0.125920i
$474$		0			0
$475$	−72.8981	−	41.3310i	−0.153470	−	0.0870127i
$476$	11.5622			0.0242903
$477$		0			0
$478$	183.280	+	183.280i	0.383432	+	0.383432i
$479$			670.857i			1.40054i	0.713880	+	0.700268i	$0.246936\pi$
$479$			670.857i			1.40054i	−0.713880	+	0.700268i	$0.753064\pi$
$480$		0			0
$481$	38.1408			0.0792947
$482$	280.094	−	280.094i	0.581108	−	0.581108i
$483$		0			0
$484$			224.910i			0.464689i
$485$	−94.8388	+	359.561i	−0.195544	+	0.741363i
$486$		0			0
$487$	−431.350	+	431.350i	−0.885729	+	0.885729i	−0.994110	−	0.108380i	$-0.965434\pi$
$487$	−431.350	+	431.350i	−0.885729	+	0.885729i	0.108380	+	0.994110i	$0.465434\pi$
$488$	−90.8747	−	90.8747i	−0.186219	−	0.186219i
$489$		0			0
$490$	−47.8606	−	12.6238i	−0.0976747	−	0.0257629i
$491$	643.019			1.30961			0.654806	−	0.755797i	$-0.272750\pi$
$491$	643.019			1.30961			0.654806	+	0.755797i	$0.272750\pi$
$492$		0			0
$493$	20.9317	+	20.9317i	0.0424577	+	0.0424577i
$494$		−	7.59618i		−	0.0153769i
$495$		0			0
$496$	−63.1746			−0.127368
$497$	96.7625	−	96.7625i	0.194693	−	0.194693i
$498$		0			0
$499$			350.058i			0.701520i	0.936465	+	0.350760i	$0.114077\pi$
$499$			350.058i			0.701520i	−0.936465	+	0.350760i	$0.885923\pi$
$500$	249.983	−	2.93258i	0.499966	−	0.00586517i
$501$		0			0
$502$	148.745	−	148.745i	0.296305	−	0.296305i
$503$	−160.423	−	160.423i	−0.318932	−	0.318932i	0.529425	−	0.848357i	$-0.322408\pi$
$503$	−160.423	−	160.423i	−0.318932	−	0.318932i	−0.848357	+	0.529425i	$0.822408\pi$
$504$		0			0
$505$	−559.124	+	325.732i	−1.10718	+	0.645014i
$506$	−46.2266			−0.0913569
$507$		0			0
$508$	−285.926	−	285.926i	−0.562847	−	0.562847i
$509$			402.935i			0.791620i	0.918332	+	0.395810i	$0.129536\pi$
$509$			402.935i			0.791620i	−0.918332	+	0.395810i	$0.870464\pi$
$510$		0			0
$511$	270.840			0.530020
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			483.367i			0.940404i
$515$	−212.260	−	55.9862i	−0.412155	−	0.108711i
$516$		0			0
$517$	−152.941	+	152.941i	−0.295824	+	0.295824i
$518$	−62.9739	−	62.9739i	−0.121571	−	0.121571i
$519$		0			0
$520$	11.4075	+	19.5812i	0.0219375	+	0.0376561i
$521$	725.448			1.39241			0.696207	−	0.717841i	$-0.254869\pi$
$521$	725.448			1.39241			0.696207	+	0.717841i	$0.254869\pi$
$522$		0			0
$523$	454.490	+	454.490i	0.869005	+	0.869005i	0.992362	−	0.123357i	$-0.0393661\pi$
$523$	454.490	+	454.490i	0.869005	+	0.869005i	−0.123357	+	0.992362i	$0.539366\pi$
$524$			7.10768i			0.0135643i
$525$		0			0
$526$	−469.214			−0.892042
$527$	−24.4022	+	24.4022i	−0.0463040	+	0.0463040i
$528$		0			0
$529$		−	403.965i		−	0.763638i
$530$	350.273	−	204.060i	0.660892	−	0.385020i
$531$		0			0
$532$	−12.5420	+	12.5420i	−0.0235752	+	0.0235752i
$533$	−82.2878	−	82.2878i	−0.154386	−	0.154386i
$534$		0			0
$535$	197.331	−	748.138i	0.368843	−	1.39839i
$536$	231.109			0.431174
$537$		0			0
$538$	357.902	+	357.902i	0.665245	+	0.665245i
$539$			20.4625i			0.0379638i
$540$		0			0
$541$	−173.852			−0.321354			−0.160677	−	0.987007i	$-0.551368\pi$
$541$	−173.852			−0.321354			−0.160677	+	0.987007i	$0.551368\pi$
$542$	−178.869	+	178.869i	−0.330017	+	0.330017i
$543$		0			0
$544$			12.3605i			0.0227215i
$545$	172.703	+	296.447i	0.316886	+	0.543940i
$546$		0			0
$547$	−293.440	+	293.440i	−0.536453	+	0.536453i	−0.922485	−	0.386032i	$-0.873845\pi$
$547$	−293.440	+	293.440i	−0.536453	+	0.536453i	0.386032	+	0.922485i	$0.373845\pi$
$548$	150.211	+	150.211i	0.274107	+	0.274107i
$549$		0			0
$550$	−27.5292	−	99.6174i	−0.0500530	−	0.181123i
$551$	−45.4109			−0.0824154
$552$		0			0
$553$	69.5668	+	69.5668i	0.125799	+	0.125799i
$554$		−	238.709i		−	0.430883i
$555$		0			0
$556$	−384.704			−0.691914
$557$	−234.581	+	234.581i	−0.421151	+	0.421151i	−0.885600	−	0.464449i	$-0.846253\pi$
$557$	−234.581	+	234.581i	−0.421151	+	0.421151i	0.464449	+	0.885600i	$0.346253\pi$
$558$		0			0
$559$		−	46.1731i		−	0.0825994i
$560$	13.4955	−	51.1652i	0.0240990	−	0.0913663i
$561$		0			0
$562$	−42.3632	+	42.3632i	−0.0753793	+	0.0753793i
$563$	−177.541	−	177.541i	−0.315348	−	0.315348i	0.531629	−	0.846977i	$-0.321580\pi$
$563$	−177.541	−	177.541i	−0.315348	−	0.315348i	−0.846977	+	0.531629i	$0.821580\pi$
$564$		0			0
$565$	−465.182	−	122.698i	−0.823331	−	0.217164i
$566$	−6.87928			−0.0121542
$567$		0			0
$568$	103.443	+	103.443i	0.182119	+	0.182119i
$569$			253.619i			0.445727i	0.974850	+	0.222864i	$0.0715405\pi$
$569$			253.619i			0.445727i	−0.974850	+	0.222864i	$0.928460\pi$
$570$		0			0
$571$	219.857			0.385038			0.192519	−	0.981293i	$-0.438334\pi$
$571$	219.857			0.385038			0.192519	+	0.981293i	$0.438334\pi$
$572$	6.62451	−	6.62451i	0.0115813	−	0.0115813i
$573$		0			0
$574$			271.729i			0.473396i
$575$	−269.448	+	74.4618i	−0.468606	+	0.129499i
$576$		0			0
$577$	419.350	−	419.350i	0.726776	−	0.726776i	−0.243200	−	0.969976i	$-0.578197\pi$
$577$	419.350	−	419.350i	0.726776	−	0.726776i	0.969976	+	0.243200i	$0.0781972\pi$
$578$	−284.226	−	284.226i	−0.491740	−	0.491740i
$579$		0			0
$580$	117.059	−	68.1955i	0.201825	−	0.117578i
$581$	79.8213			0.137386
$582$		0			0
$583$	−118.501	−	118.501i	−0.203261	−	0.203261i
$584$			289.540i			0.495788i
$585$		0			0
$586$	−50.7965			−0.0866834
$587$	493.116	−	493.116i	0.840061	−	0.840061i	−0.148805	−	0.988867i	$-0.547543\pi$
$587$	493.116	−	493.116i	0.840061	−	0.840061i	0.988867	+	0.148805i	$0.0475427\pi$
$588$		0			0
$589$		−	52.9401i		−	0.0898814i
$590$	−801.084	−	211.296i	−1.35777	−	0.358129i
$591$		0			0
$592$	67.3219	−	67.3219i	0.113719	−	0.113719i
$593$	−528.205	−	528.205i	−0.890733	−	0.890733i	0.103859	−	0.994592i	$-0.466881\pi$
$593$	−528.205	−	528.205i	−0.890733	−	0.890733i	−0.994592	+	0.103859i	$0.966881\pi$
$594$		0			0
$595$	−14.5505	−	24.9762i	−0.0244546	−	0.0419768i
$596$	−155.001			−0.260069
$597$		0			0
$598$	−17.9182	−	17.9182i	−0.0299635	−	0.0299635i
$599$		−	436.395i		−	0.728540i	−0.931293	−	0.364270i	$-0.881319\pi$
$599$		−	436.395i		−	0.728540i	0.931293	−	0.364270i	$-0.118681\pi$
$600$		0			0
$601$	907.900			1.51065			0.755324	−	0.655351i	$-0.227479\pi$
$601$	907.900			1.51065			0.755324	+	0.655351i	$0.227479\pi$
$602$	−76.2360	+	76.2360i	−0.126638	+	0.126638i
$603$		0			0
$604$		−	73.6389i		−	0.121919i
$605$	485.841	−	283.039i	0.803042	−	0.467833i
$606$		0			0
$607$	−46.6746	+	46.6746i	−0.0768939	+	0.0768939i	−0.744508	−	0.667614i	$-0.767316\pi$
$607$	−46.6746	+	46.6746i	−0.0768939	+	0.0768939i	0.667614	+	0.744508i	$0.267316\pi$
$608$	−13.4080	−	13.4080i	−0.0220526	−	0.0220526i
$609$		0			0
$610$	−81.9420	+	310.666i	−0.134331	+	0.509288i
$611$	−118.565			−0.194050
$612$		0			0
$613$	404.981	+	404.981i	0.660653	+	0.660653i	0.955534	−	0.294881i	$-0.0952799\pi$
$613$	404.981	+	404.981i	0.660653	+	0.660653i	−0.294881	+	0.955534i	$0.595280\pi$
$614$		−	647.678i		−	1.05485i
$615$		0			0
$616$	−21.8753			−0.0355119
$617$	−821.889	+	821.889i	−1.33207	+	1.33207i	−0.428558	+	0.903514i	$0.640978\pi$
$617$	−821.889	+	821.889i	−1.33207	+	1.33207i	−0.903514	+	0.428558i	$0.859022\pi$
$618$		0			0
$619$		−	355.855i		−	0.574886i	−0.957798	−	0.287443i	$-0.907195\pi$
$619$		−	355.855i		−	0.574886i	0.957798	−	0.287443i	$-0.0928052\pi$
$620$	79.5025	+	136.467i	0.128230	+	0.220108i
$621$		0			0
$622$	−284.428	+	284.428i	−0.457280	+	0.457280i
$623$	−188.862	−	188.862i	−0.303150	−	0.303150i
$624$		0			0
$625$	−320.927	−	536.312i	−0.513484	−	0.858099i
$626$	−357.929			−0.571771
$627$		0			0
$628$	−151.531	−	151.531i	−0.241291	−	0.241291i
$629$		−	52.0083i		−	0.0826841i
$630$		0			0
$631$	−588.910			−0.933297			−0.466648	−	0.884443i	$-0.654539\pi$
$631$	−588.910			−0.933297			−0.466648	+	0.884443i	$0.654539\pi$
$632$	−74.3700	+	74.3700i	−0.117674	+	0.117674i
$633$		0			0
$634$		−	671.600i		−	1.05931i
$635$	−257.821	+	977.472i	−0.406017	+	1.53933i
$636$		0			0
$637$	−7.93160	+	7.93160i	−0.0124515	+	0.0124515i
$638$	−39.6021	−	39.6021i	−0.0620723	−	0.0620723i
$639$		0			0
$640$	54.6978	+	14.4272i	0.0854654	+	0.0225426i
$641$	703.566			1.09761			0.548804	−	0.835951i	$-0.315083\pi$
$641$	703.566			1.09761			0.548804	+	0.835951i	$0.315083\pi$
$642$		0			0
$643$	75.8005	+	75.8005i	0.117886	+	0.117886i	0.763589	−	0.645703i	$-0.223436\pi$
$643$	75.8005	+	75.8005i	0.117886	+	0.117886i	−0.645703	+	0.763589i	$0.723436\pi$
$644$			59.1691i			0.0918775i
$645$		0			0
$646$	−10.3581			−0.0160342
$647$	−362.070	+	362.070i	−0.559613	+	0.559613i	−0.929197	−	0.369584i	$-0.879500\pi$
$647$	−362.070	+	362.070i	−0.559613	+	0.559613i	0.369584	+	0.929197i	$0.379500\pi$
$648$		0			0
$649$			342.499i			0.527733i
$650$	27.9426	−	49.2841i	0.0429886	−	0.0758217i
$651$		0			0
$652$	348.905	−	348.905i	0.535131	−	0.535131i
$653$	−804.153	−	804.153i	−1.23147	−	1.23147i	−0.963397	−	0.268077i	$-0.913612\pi$
$653$	−804.153	−	804.153i	−1.23147	−	1.23147i	−0.268077	−	0.963397i	$-0.586388\pi$
$654$		0			0
$655$	15.3537	−	8.94470i	0.0234408	−	0.0136560i
$656$	−290.491			−0.442821
$657$		0			0
$658$	195.761	+	195.761i	0.297510	+	0.297510i
$659$		−	803.984i		−	1.22001i	−0.792399	−	0.610003i	$-0.791168\pi$
$659$		−	803.984i		−	1.22001i	0.792399	−	0.610003i	$-0.208832\pi$
$660$		0			0
$661$	−923.281			−1.39679			−0.698397	−	0.715710i	$-0.746103\pi$
$661$	−923.281			−1.39679			−0.698397	+	0.715710i	$0.746103\pi$
$662$	−444.301	+	444.301i	−0.671150	+	0.671150i
$663$		0			0
$664$			85.3325i			0.128513i
$665$	42.8762	+	11.3092i	0.0644756	+	0.0170062i
$666$		0			0
$667$	−107.117	+	107.117i	−0.160595	+	0.160595i
$668$	238.550	+	238.550i	0.357111	+	0.357111i
$669$		0			0
$670$	−290.841	−	499.233i	−0.434091	−	0.745123i
$671$	132.823			0.197948
$672$		0			0
$673$	−750.322	−	750.322i	−1.11489	−	1.11489i	−0.992479	−	0.122413i	$-0.960937\pi$
$673$	−750.322	−	750.322i	−1.11489	−	1.11489i	−0.122413	−	0.992479i	$-0.539063\pi$
$674$			862.939i			1.28032i
$675$		0			0
$676$	−332.864			−0.492403
$677$	405.042	−	405.042i	0.598290	−	0.598290i	−0.341567	−	0.939857i	$-0.610958\pi$
$677$	405.042	−	405.042i	0.598290	−	0.598290i	0.939857	+	0.341567i	$0.110958\pi$
$678$		0			0
$679$		−	196.769i		−	0.289792i
$680$	26.7007	−	15.5552i	0.0392657	−	0.0228752i
$681$		0			0
$682$	46.1682	−	46.1682i	0.0676954	−	0.0676954i
$683$	−666.271	−	666.271i	−0.975506	−	0.975506i	0.0242009	−	0.999707i	$-0.492296\pi$
$683$	−666.271	−	666.271i	−0.975506	−	0.975506i	−0.999707	+	0.0242009i	$0.992296\pi$
$684$		0			0
$685$	135.445	−	513.513i	0.197731	−	0.749654i
$686$	26.1916			0.0381802
$687$		0			0
$688$	−81.4997	−	81.4997i	−0.118459	−	0.118459i
$689$		−	91.8658i		−	0.133332i
$690$		0			0
$691$	521.895			0.755275			0.377637	−	0.925954i	$-0.376737\pi$
$691$	521.895			0.755275			0.377637	+	0.925954i	$0.376737\pi$
$692$	−220.041	+	220.041i	−0.317978	+	0.317978i
$693$		0			0
$694$			455.785i			0.656751i
$695$	484.133	+	831.022i	0.696595	+	1.19572i
$696$		0			0
$697$	−112.207	+	112.207i	−0.160985	+	0.160985i
$698$	280.016	+	280.016i	0.401168	+	0.401168i
$699$		0			0
$700$	−127.508	+	35.2368i	−0.182155	+	0.0503383i
$701$	−525.400			−0.749501			−0.374750	−	0.927126i	$-0.622272\pi$
$701$	−525.400			−0.749501			−0.374750	+	0.927126i	$0.622272\pi$
$702$		0			0
$703$	56.4156	+	56.4156i	0.0802497	+	0.0802497i
$704$		−	23.3857i		−	0.0332184i
$705$		0			0
$706$	−228.939			−0.324276
$707$	242.117	−	242.117i	0.342458	−	0.342458i
$708$		0			0
$709$			269.858i			0.380618i	0.981724	+	0.190309i	$0.0609489\pi$
$709$			269.858i			0.380618i	−0.981724	+	0.190309i	$0.939051\pi$
$710$	93.2753	−	353.633i	0.131374	−	0.498075i
$711$		0			0
$712$	201.902	−	201.902i	0.283571	−	0.283571i
$713$	−124.877	−	124.877i	−0.175144	−	0.175144i
$714$		0			0
$715$	−22.6466	−	5.97334i	−0.0316736	−	0.00835432i
$716$	−98.0715			−0.136971
$717$		0			0
$718$	−700.748	−	700.748i	−0.975973	−	0.975973i
$719$		−	42.9232i		−	0.0596985i	−0.999554	−	0.0298493i	$-0.990497\pi$
$719$		−	42.9232i		−	0.0596985i	0.999554	−	0.0298493i	$-0.00950273\pi$
$720$		0			0
$721$	116.159			0.161108
$722$	−349.764	+	349.764i	−0.484438	+	0.484438i
$723$		0			0
$724$			654.285i			0.903709i
$725$	−294.626	−	167.044i	−0.406381	−	0.230406i
$726$		0			0
$727$	109.192	−	109.192i	0.150195	−	0.150195i	−0.628010	−	0.778205i	$-0.716130\pi$
$727$	109.192	−	109.192i	0.150195	−	0.150195i	0.778205	+	0.628010i	$0.216130\pi$
$728$	−8.47924	−	8.47924i	−0.0116473	−	0.0116473i
$729$		0			0
$730$	625.453	−	364.374i	0.856785	−	0.499142i
$731$	−62.9611			−0.0861301
$732$		0			0
$733$	414.682	+	414.682i	0.565733	+	0.565733i	0.930930	−	0.365197i	$-0.118999\pi$
$733$	414.682	+	414.682i	0.565733	+	0.565733i	−0.365197	+	0.930930i	$0.618999\pi$
$734$			824.513i			1.12332i
$735$		0			0
$736$	−63.2545			−0.0859436
$737$	−168.895	+	168.895i	−0.229166	+	0.229166i
$738$		0			0
$739$			1042.54i			1.41074i	0.708838	+	0.705372i	$0.249220\pi$
$739$			1042.54i			1.41074i	−0.708838	+	0.705372i	$0.750780\pi$
$740$	−230.148	−	60.7044i	−0.311010	−	0.0820329i
$741$		0			0
$742$	−151.679	+	151.679i	−0.204419	+	0.204419i
$743$	403.117	+	403.117i	0.542553	+	0.542553i	0.924277	−	0.381724i	$-0.124669\pi$
$743$	403.117	+	403.117i	0.542553	+	0.542553i	−0.381724	+	0.924277i	$0.624669\pi$
$744$		0			0
$745$	195.062	+	334.827i	0.261828	+	0.449432i
$746$	243.338			0.326191
$747$		0			0
$748$	−9.03311	−	9.03311i	−0.0120763	−	0.0120763i
$749$			409.417i			0.546618i
$750$		0			0
$751$	346.283			0.461096			0.230548	−	0.973061i	$-0.425948\pi$
$751$	346.283			0.461096			0.230548	+	0.973061i	$0.425948\pi$
$752$	−209.278	+	209.278i	−0.278295	+	0.278295i
$753$		0			0
$754$		−	30.7008i		−	0.0407173i
$755$	−159.072	+	92.6713i	−0.210691	+	0.122744i
$756$		0			0
$757$	284.836	−	284.836i	0.376270	−	0.376270i	−0.493485	−	0.869754i	$-0.664277\pi$
$757$	284.836	−	284.836i	0.376270	−	0.376270i	0.869754	+	0.493485i	$0.164277\pi$
$758$	−709.113	−	709.113i	−0.935506	−	0.935506i
$759$		0			0
$760$	−12.0900	+	45.8366i	−0.0159079	+	0.0603114i
$761$	−321.609			−0.422614			−0.211307	−	0.977420i	$-0.567772\pi$
$761$	−321.609			−0.422614			−0.211307	+	0.977420i	$0.567772\pi$
$762$		0			0
$763$	−128.371	−	128.371i	−0.168245	−	0.168245i
$764$			578.156i			0.756749i
$765$		0			0
$766$	−953.222			−1.24441
$767$	−132.758	+	132.758i	−0.173087	+	0.173087i
$768$		0			0
$769$		−	634.413i		−	0.824984i	−0.910961	−	0.412492i	$-0.864658\pi$
$769$		−	634.413i		−	0.824984i	0.910961	−	0.412492i	$-0.135342\pi$
$770$	27.5292	+	47.2542i	0.0357522	+	0.0613691i
$771$		0			0
$772$	−262.425	+	262.425i	−0.339929	+	0.339929i
$773$	−793.682	−	793.682i	−1.02676	−	1.02676i	−0.999632	−	0.0271240i	$-0.991365\pi$
$773$	−793.682	−	793.682i	−1.02676	−	1.02676i	−0.0271240	−	0.999632i	$-0.508635\pi$
$774$		0			0
$775$	194.740	−	343.476i	0.251278	−	0.443195i
$776$	210.355			0.271076
$777$		0			0
$778$	−270.210	−	270.210i	−0.347313	−	0.347313i
$779$		−	243.430i		−	0.312491i
$780$		0			0
$781$	−151.194			−0.193590
$782$	−24.4330	+	24.4330i	−0.0312443	+	0.0312443i
$783$		0			0
$784$			28.0000i			0.0357143i
$785$	−136.636	+	518.025i	−0.174058	+	0.659905i
$786$		0			0
$787$	30.7537	−	30.7537i	0.0390771	−	0.0390771i	−0.687298	−	0.726375i	$-0.741203\pi$
$787$	30.7537	−	30.7537i	0.0390771	−	0.0390771i	0.726375	+	0.687298i	$0.241203\pi$
$788$	223.597	+	223.597i	0.283752	+	0.283752i
$789$		0			0
$790$	254.242	+	67.0597i	0.321826	+	0.0848856i
$791$	254.570			0.321833
$792$		0			0
$793$	51.4844	+	51.4844i	0.0649236	+	0.0649236i
$794$		−	338.541i		−	0.426374i
$795$		0			0
$796$	116.743			0.146662
$797$	−613.430	+	613.430i	−0.769674	+	0.769674i	−0.978049	−	0.208375i	$-0.933183\pi$
$797$	−613.430	+	613.430i	−0.769674	+	0.769674i	0.208375	+	0.978049i	$0.433183\pi$
$798$		0			0
$799$			161.674i			0.202345i
$800$	−37.6697	−	136.312i	−0.0470871	−	0.170390i
$801$		0			0
$802$	397.414	−	397.414i	0.495529	−	0.495529i
$803$	−211.597	−	211.597i	−0.263508	−	0.263508i
$804$		0			0
$805$	127.815	−	74.4618i	0.158776	−	0.0924991i
$806$	35.7911			0.0444059
$807$		0			0
$808$	258.834	+	258.834i	0.320340	+	0.320340i
$809$			23.8289i			0.0294548i	0.999892	+	0.0147274i	$0.00468804\pi$
$809$			23.8289i			0.0294548i	−0.999892	+	0.0147274i	$0.995312\pi$
$810$		0			0
$811$	676.685			0.834383			0.417192	−	0.908819i	$-0.363014\pi$
$811$	676.685			0.834383			0.417192	+	0.908819i	$0.363014\pi$
$812$	−50.6899	+	50.6899i	−0.0624260	+	0.0624260i
$813$		0			0
$814$			98.3982i			0.120882i
$815$	−1192.77	−	314.609i	−1.46352	−	0.386023i
$816$		0			0
$817$	68.2965	−	68.2965i	0.0835942	−	0.0835942i
$818$	787.478	+	787.478i	0.962687	+	0.962687i
$819$		0			0
$820$	365.570	+	627.506i	0.445817	+	0.765252i
$821$	7.29733			0.00888834			0.00444417	−	0.999990i	$-0.498585\pi$
$821$	7.29733			0.00888834			0.00444417	+	0.999990i	$0.498585\pi$
$822$		0			0
$823$	3.19071	+	3.19071i	0.00387692	+	0.00387692i	0.709043	−	0.705166i	$-0.249127\pi$
$823$	3.19071	+	3.19071i	0.00387692	+	0.00387692i	−0.705166	+	0.709043i	$0.749127\pi$
$824$			124.179i			0.150703i
$825$		0			0
$826$	438.391			0.530740
$827$	−355.496	+	355.496i	−0.429863	+	0.429863i	−0.888581	−	0.458719i	$-0.848309\pi$
$827$	−355.496	+	355.496i	−0.429863	+	0.429863i	0.458719	+	0.888581i	$0.348309\pi$
$828$		0			0
$829$			1466.78i			1.76933i	0.466225	+	0.884666i	$0.345614\pi$
$829$			1466.78i			1.76933i	−0.466225	+	0.884666i	$0.654386\pi$
$830$	184.332	−	107.387i	0.222087	−	0.129382i
$831$		0			0
$832$	9.06469	−	9.06469i	0.0108951	−	0.0108951i
$833$	10.8154	+	10.8154i	0.0129837	+	0.0129837i
$834$		0			0
$835$	215.101	−	815.511i	0.257606	−	0.976660i
$836$	19.5972			0.0234416
$837$		0			0
$838$	293.606	+	293.606i	0.350365	+	0.350365i
$839$		−	807.662i		−	0.962648i	−0.876543	−	0.481324i	$-0.840156\pi$
$839$		−	807.662i		−	0.962648i	0.876543	−	0.481324i	$-0.159844\pi$
$840$		0			0
$841$	657.467			0.781768
$842$	294.797	−	294.797i	0.350115	−	0.350115i
$843$		0			0
$844$		−	110.120i		−	0.130474i
$845$	418.895	+	719.040i	0.495734	+	0.850935i
$846$		0			0
$847$	−210.384	+	210.384i	−0.248387	+	0.248387i
$848$	−162.151	−	162.151i	−0.191216	−	0.191216i
$849$		0			0
$850$	−67.2032	−	38.1022i	−0.0790626	−	0.0448261i
$851$	266.151			0.312751
$852$		0			0
$853$	34.4347	+	34.4347i	0.0403690	+	0.0403690i	0.727003	−	0.686634i	$-0.240913\pi$
$853$	34.4347	+	34.4347i	0.0403690	+	0.0403690i	−0.686634	+	0.727003i	$0.740913\pi$
$854$		−	170.011i		−	0.199076i
$855$		0			0
$856$	−437.685			−0.511314
$857$	795.023	−	795.023i	0.927681	−	0.927681i	−0.0698747	−	0.997556i	$-0.522260\pi$
$857$	795.023	−	795.023i	0.927681	−	0.927681i	0.997556	+	0.0698747i	$0.0222599\pi$
$858$		0			0
$859$			367.334i			0.427629i	0.976874	+	0.213815i	$0.0685889\pi$
$859$			367.334i			0.427629i	−0.976874	+	0.213815i	$0.931411\pi$
$860$	−73.4885	+	278.616i	−0.0854517	+	0.323972i
$861$		0			0
$862$	−314.916	+	314.916i	−0.365332	+	0.365332i
$863$	97.5396	+	97.5396i	0.113024	+	0.113024i	0.761357	−	0.648333i	$-0.224534\pi$
$863$	97.5396	+	97.5396i	0.113024	+	0.113024i	−0.648333	+	0.761357i	$0.724534\pi$
$864$		0			0
$865$	752.236	+	198.412i	0.869637	+	0.229378i
$866$	−472.732			−0.545880
$867$		0			0
$868$	−59.0944	−	59.0944i	−0.0680811	−	0.0680811i
$869$		−	108.700i		−	0.125086i
$870$		0			0
$871$	−130.933			−0.150325
$872$	137.234	−	137.234i	0.157379	−	0.157379i
$873$		0			0
$874$		−	53.0071i		−	0.0606488i
$875$	236.581	+	231.094i	0.270378	+	0.264108i
$876$		0			0
$877$	−326.965	+	326.965i	−0.372822	+	0.372822i	−0.868504	−	0.495682i	$-0.834918\pi$
$877$	−326.965	+	326.965i	−0.372822	+	0.372822i	0.495682	+	0.868504i	$0.334918\pi$
$878$	254.993	+	254.993i	0.290425	+	0.290425i
$879$		0			0
$880$	−50.5169	+	29.4299i	−0.0574056	+	0.0334431i
$881$	−538.293			−0.611003			−0.305501	−	0.952192i	$-0.598824\pi$
$881$	−538.293			−0.611003			−0.305501	+	0.952192i	$0.598824\pi$
$882$		0			0
$883$	−951.591	−	951.591i	−1.07768	−	1.07768i	−0.996717	−	0.0809620i	$-0.974201\pi$
$883$	−951.591	−	951.591i	−1.07768	−	1.07768i	−0.0809620	−	0.996717i	$-0.525799\pi$
$884$		−	7.00276i		−	0.00792167i
$885$		0			0
$886$	−585.255			−0.660559
$887$	−300.730	+	300.730i	−0.339042	+	0.339042i	−0.856007	−	0.516965i	$-0.827062\pi$
$887$	−300.730	+	300.730i	−0.339042	+	0.339042i	0.516965	+	0.856007i	$0.327062\pi$
$888$		0			0
$889$		−	534.919i		−	0.601709i
$890$	−690.226	−	182.056i	−0.775535	−	0.204557i
$891$		0			0
$892$	−203.537	+	203.537i	−0.228180	+	0.228180i
$893$	−175.374	−	175.374i	−0.196388	−	0.196388i
$894$		0			0
$895$	123.419	+	211.850i	0.137898	+	0.236704i
$896$	−29.9333			−0.0334077
$897$		0			0
$898$	400.989	+	400.989i	0.446536	+	0.446536i
$899$		−	213.964i		−	0.238002i
$900$		0			0
$901$	−125.267			−0.139031
$902$	212.292	−	212.292i	0.235357	−	0.235357i
$903$		0			0
$904$			272.147i			0.301047i
$905$	1413.36	−	823.389i	1.56172	−	0.909822i
$906$		0			0
$907$	−801.951	+	801.951i	−0.884179	+	0.884179i	−0.993956	−	0.109777i	$-0.964986\pi$
$907$	−801.951	+	801.951i	−0.884179	+	0.884179i	0.109777	+	0.993956i	$0.464986\pi$
$908$	−50.1179	−	50.1179i	−0.0551959	−	0.0551959i
$909$		0			0
$910$	−7.64575	+	28.9873i	−0.00840193	+	0.0318541i
$911$	1437.85			1.57832			0.789160	−	0.614187i	$-0.210516\pi$
$911$	1437.85			1.57832			0.789160	+	0.614187i	$0.210516\pi$
$912$		0			0
$913$	−62.3613	−	62.3613i	−0.0683038	−	0.0683038i
$914$		−	344.079i		−	0.376454i
$915$		0			0
$916$	−566.995			−0.618990
$917$	−6.64862	+	6.64862i	−0.00725041	+	0.00725041i
$918$		0			0
$919$			1282.30i			1.39532i	0.716428	+	0.697661i	$0.245776\pi$
$919$			1282.30i			1.39532i	−0.716428	+	0.697661i	$0.754224\pi$
$920$	79.6030	+	136.640i	0.0865250	+	0.148521i
$921$		0			0
$922$	153.918	−	153.918i	0.166939	−	0.166939i
$923$	−58.6052	−	58.6052i	−0.0634942	−	0.0634942i
$924$		0			0
$925$	158.500	+	573.550i	0.171351	+	0.620054i
$926$	583.527			0.630158
$927$		0			0
$928$	−54.1898	−	54.1898i	−0.0583942	−	0.0583942i
$929$		−	520.920i		−	0.560732i	−0.959893	−	0.280366i	$-0.909544\pi$
$929$		−	520.920i		−	0.560732i	0.959893	−	0.280366i	$-0.0904558\pi$
$930$		0			0
$931$	−23.4639			−0.0252029
$932$	−278.238	+	278.238i	−0.298539	+	0.298539i
$933$		0			0
$934$			1006.47i			1.07759i
$935$	−8.14518	+	30.8807i	−0.00871142	+	0.0330275i
$936$		0			0
$937$	−49.7102	+	49.7102i	−0.0530525	+	0.0530525i	−0.733135	−	0.680083i	$-0.761944\pi$
$937$	−49.7102	+	49.7102i	−0.0530525	+	0.0530525i	0.680083	+	0.733135i	$0.261944\pi$
$938$	216.183	+	216.183i	0.230472	+	0.230472i
$939$		0			0
$940$	715.440	+	188.706i	0.761106	+	0.200751i
$941$	163.591			0.173848			0.0869242	−	0.996215i	$-0.472296\pi$
$941$	163.591			0.173848			0.0869242	+	0.996215i	$0.472296\pi$
$942$		0			0
$943$	−574.214	−	574.214i	−0.608922	−	0.608922i
$944$			468.660i			0.496462i
$945$		0			0
$946$	119.121			0.125920
$947$	1003.15	−	1003.15i	1.05929	−	1.05929i	0.0611651	−	0.998128i	$-0.480518\pi$
$947$	1003.15	−	1003.15i	1.05929	−	1.05929i	0.998128	−	0.0611651i	$-0.0194816\pi$
$948$		0			0
$949$		−	164.037i		−	0.172852i
$950$	114.229	−	31.5671i	0.120241	−	0.0332285i
$951$		0			0
$952$	−11.5622	+	11.5622i	−0.0121452	+	0.0121452i
$953$	265.856	+	265.856i	0.278967	+	0.278967i	0.832697	−	0.553729i	$-0.186796\pi$
$953$	265.856	+	265.856i	0.278967	+	0.278967i	−0.553729	+	0.832697i	$0.686796\pi$
$954$		0			0
$955$	1248.91	−	727.585i	1.30776	−	0.761869i
$956$	−366.561			−0.383432
$957$		0			0
$958$	−670.857	−	670.857i	−0.700268	−	0.700268i
$959$			281.019i			0.293033i
$960$		0			0
$961$	−711.561			−0.740438
$962$	−38.1408	+	38.1408i	−0.0396474	+	0.0396474i
$963$		0			0
$964$			560.188i			0.581108i
$965$	897.130	+	236.629i	0.929669	+	0.245212i
$966$		0			0
$967$	662.074	−	662.074i	0.684668	−	0.684668i	−0.276380	−	0.961048i	$-0.589135\pi$
$967$	662.074	−	662.074i	0.684668	−	0.684668i	0.961048	+	0.276380i	$0.0891349\pi$
$968$	−224.910	−	224.910i	−0.232345	−	0.232345i
$969$		0			0
$970$	−264.722	−	454.400i	−0.272910	−	0.468453i
$971$	−562.832			−0.579642			−0.289821	−	0.957081i	$-0.593596\pi$
$971$	−562.832			−0.579642			−0.289821	+	0.957081i	$0.593596\pi$
$972$		0			0
$973$	−359.858	−	359.858i	−0.369844	−	0.369844i
$974$		−	862.700i		−	0.885729i
$975$		0			0
$976$	181.749			0.186219
$977$	−1319.92	+	1319.92i	−1.35099	+	1.35099i	−0.466433	+	0.884556i	$0.654461\pi$
$977$	−1319.92	+	1319.92i	−1.35099	+	1.35099i	−0.884556	+	0.466433i	$0.845539\pi$
$978$		0			0
$979$			295.102i			0.301432i
$980$	60.4845	−	35.2368i	0.0617188	−	0.0359559i
$981$		0			0
$982$	−643.019	+	643.019i	−0.654806	+	0.654806i
$983$	−117.249	−	117.249i	−0.119277	−	0.119277i	0.644949	−	0.764226i	$-0.276879\pi$
$983$	−117.249	−	117.249i	−0.119277	−	0.119277i	−0.764226	+	0.644949i	$0.776879\pi$
$984$		0			0
$985$	201.618	−	764.391i	0.204688	−	0.776032i
$986$	−41.8633			−0.0424577
$987$		0			0
$988$	7.59618	+	7.59618i	0.00768844	+	0.00768844i
$989$		−	322.201i		−	0.325785i
$990$		0			0
$991$	−354.972			−0.358196			−0.179098	−	0.983831i	$-0.557318\pi$
$991$	−354.972			−0.358196			−0.179098	+	0.983831i	$0.557318\pi$
$992$	63.1746	−	63.1746i	0.0636841	−	0.0636841i
$993$		0			0
$994$			193.525i			0.194693i
$995$	−146.916	−	252.183i	−0.147654	−	0.253451i
$996$		0			0
$997$	−913.231	+	913.231i	−0.915979	+	0.915979i	−0.996734	−	0.0807549i	$-0.974267\pi$
$997$	−913.231	+	913.231i	−0.915979	+	0.915979i	0.0807549	+	0.996734i	$0.474267\pi$
$998$	−350.058	−	350.058i	−0.350760	−	0.350760i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.b.253.1		8
3.2	odd	2		210.3.l.a.43.4	✓	8
5.2	odd	4	inner	630.3.o.b.127.1		8
15.2	even	4		210.3.l.a.127.4	yes	8
15.8	even	4		1050.3.l.b.757.1		8
15.14	odd	2		1050.3.l.b.43.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.4	✓	8	3.2	odd	2
210.3.l.a.127.4	yes	8	15.2	even	4
630.3.o.b.127.1		8	5.2	odd	4	inner
630.3.o.b.253.1		8	1.1	even	1	trivial
1050.3.l.b.43.1		8	15.14	odd	2
1050.3.l.b.757.1		8	15.8	even	4

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.32032 + 2.51691i) q^{5} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.32032 + 2.51691i) q^{5} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.80341 - 6.83723i) q^{10} -2.92322 q^{11} +(-1.13309 - 1.13309i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-1.54506 + 1.54506i) q^{17} -3.35199i q^{19} +(5.03383 + 8.64064i) q^{20} +(2.92322 - 2.92322i) q^{22} +(-7.90681 - 7.90681i) q^{23} +(12.3303 - 21.7477i) q^{25} +2.26617 q^{26} +(-3.74166 - 3.74166i) q^{28} -13.5474i q^{29} +15.7936 q^{31} +(4.00000 - 4.00000i) q^{32} -3.09013i q^{34} +(-3.37386 + 12.7913i) q^{35} +(-16.8305 + 16.8305i) q^{37} +(3.35199 + 3.35199i) q^{38} +(-13.6745 - 3.60681i) q^{40} +72.6227 q^{41} +(20.3749 + 20.3749i) q^{43} +5.84643i q^{44} +15.8136 q^{46} +(52.3194 - 52.3194i) q^{47} -7.00000i q^{49} +(9.41742 + 34.0780i) q^{50} +(-2.26617 + 2.26617i) q^{52} +(40.5379 + 40.5379i) q^{53} +(12.6292 - 7.35748i) q^{55} +7.48331 q^{56} +(13.5474 + 13.5474i) q^{58} -117.165i q^{59} -45.4373 q^{61} +(-15.7936 + 15.7936i) q^{62} +8.00000i q^{64} +(7.74717 + 2.04341i) q^{65} +(57.7773 - 57.7773i) q^{67} +(3.09013 + 3.09013i) q^{68} +(-9.41742 - 16.1652i) q^{70} +51.7217 q^{71} +(72.3851 + 72.3851i) q^{73} -33.6610i q^{74} -6.70398 q^{76} +(-5.46884 + 5.46884i) q^{77} +37.1850i q^{79} +(17.2813 - 10.0677i) q^{80} +(-72.6227 + 72.6227i) q^{82} +(21.3331 + 21.3331i) q^{83} +(2.78638 - 10.5640i) q^{85} -40.7498 q^{86} +(-5.84643 - 5.84643i) q^{88} -100.951i q^{89} -4.23962 q^{91} +(-15.8136 + 15.8136i) q^{92} +104.639i q^{94} +(8.43666 + 14.4817i) q^{95} +(52.5887 - 52.5887i) q^{97} +(7.00000 + 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} + 8 q^{11} + 8 q^{13} - 32 q^{16} + 32 q^{17} - 8 q^{22} + 40 q^{23} - 48 q^{25} - 16 q^{26} + 144 q^{31} + 32 q^{32} + 28 q^{35} + 160 q^{37} + 320 q^{41} - 32 q^{43} - 80 q^{46} + 144 q^{47} + 112 q^{50} + 16 q^{52} + 200 q^{53} + 184 q^{55} - 64 q^{58} + 288 q^{61} - 144 q^{62} - 24 q^{65} + 80 q^{67} - 64 q^{68} - 112 q^{70} + 280 q^{71} + 312 q^{73} + 56 q^{77} - 320 q^{82} + 320 q^{83} + 80 q^{85} + 64 q^{86} + 16 q^{88} + 80 q^{92} + 472 q^{95} - 24 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 + 8 * q^11 + 8 * q^13 - 32 * q^16 + 32 * q^17 - 8 * q^22 + 40 * q^23 - 48 * q^25 - 16 * q^26 + 144 * q^31 + 32 * q^32 + 28 * q^35 + 160 * q^37 + 320 * q^41 - 32 * q^43 - 80 * q^46 + 144 * q^47 + 112 * q^50 + 16 * q^52 + 200 * q^53 + 184 * q^55 - 64 * q^58 + 288 * q^61 - 144 * q^62 - 24 * q^65 + 80 * q^67 - 64 * q^68 - 112 * q^70 + 280 * q^71 + 312 * q^73 + 56 * q^77 - 320 * q^82 + 320 * q^83 + 80 * q^85 + 64 * q^86 + 16 * q^88 + 80 * q^92 + 472 * q^95 - 24 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more