LMFDB - Embedded newform 630.3.o.b.127.3

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			127.3
Root			$0.323042 + 0.323042i$ of defining polynomial
Character	$\chi$	$=$	630.127
Dual form			630.3.o.b.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(0.578661 - 4.96640i) q^{5} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(0.578661 - 4.96640i) q^{5} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-5.54506 + 4.38774i) q^{10} +12.4065 q^{11} +(3.13309 - 3.13309i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(5.80341 + 5.80341i) q^{17} +26.5813i q^{19} +(9.93280 + 1.15732i) q^{20} +(-12.4065 - 12.4065i) q^{22} +(10.4235 - 10.4235i) q^{23} +(-24.3303 - 5.74773i) q^{25} -6.26617 q^{26} +(-3.74166 + 3.74166i) q^{28} -14.5808i q^{29} +42.6563 q^{31} +(4.00000 + 4.00000i) q^{32} -11.6068i q^{34} +(10.3739 - 8.20871i) q^{35} +(11.9306 + 11.9306i) q^{37} +(26.5813 - 26.5813i) q^{38} +(-8.77548 - 11.0901i) q^{40} -37.5226 q^{41} +(24.0083 - 24.0083i) q^{43} +24.8131i q^{44} -20.8470 q^{46} +(-8.83609 - 8.83609i) q^{47} +7.00000i q^{49} +(18.5826 + 30.0780i) q^{50} +(6.26617 + 6.26617i) q^{52} +(1.97883 - 1.97883i) q^{53} +(7.17918 - 61.6158i) q^{55} +7.48331 q^{56} +(-14.5808 + 14.5808i) q^{58} -88.2651i q^{59} +102.471 q^{61} +(-42.6563 - 42.6563i) q^{62} -8.00000i q^{64} +(-13.7472 - 17.3732i) q^{65} +(-22.8107 - 22.8107i) q^{67} +(-11.6068 + 11.6068i) q^{68} +(-18.5826 - 2.16515i) q^{70} +10.7950 q^{71} +(80.4481 - 80.4481i) q^{73} -23.8612i q^{74} -53.1625 q^{76} +(23.2105 + 23.2105i) q^{77} +138.851i q^{79} +(-2.31464 + 19.8656i) q^{80} +(37.5226 + 37.5226i) q^{82} +(96.0834 - 96.0834i) q^{83} +(32.1803 - 25.4638i) q^{85} -48.0166 q^{86} +(24.8131 - 24.8131i) q^{88} +3.29855i q^{89} +11.7229 q^{91} +(20.8470 + 20.8470i) q^{92} +17.6722i q^{94} +(132.013 + 15.3815i) q^{95} +(-88.5219 - 88.5219i) q^{97} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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
$5$	0.578661	−	4.96640i	0.115732	−	0.993280i
$5$	0.578661	−	4.96640i	0.115732	−	0.993280i
$6$		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
$10$	−5.54506	+	4.38774i	−0.554506	+	0.438774i
$11$	12.4065			1.12787			0.563933	−	0.825820i	$-0.309288\pi$
$11$	12.4065			1.12787			0.563933	+	0.825820i	$0.309288\pi$
$12$		0			0
$13$	3.13309	−	3.13309i	0.241007	−	0.241007i	−0.576260	−	0.817267i	$-0.695488\pi$
$13$	3.13309	−	3.13309i	0.241007	−	0.241007i	0.817267	+	0.576260i	$0.195488\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	5.80341	+	5.80341i	0.341377	+	0.341377i	0.856885	−	0.515508i	$-0.172397\pi$
$17$	5.80341	+	5.80341i	0.341377	+	0.341377i	−0.515508	+	0.856885i	$0.672397\pi$
$18$		0			0
$19$			26.5813i			1.39901i	0.714626	+	0.699507i	$0.246597\pi$
$19$			26.5813i			1.39901i	−0.714626	+	0.699507i	$0.753403\pi$
$20$	9.93280	+	1.15732i	0.496640	+	0.0578661i
$21$		0			0
$22$	−12.4065	−	12.4065i	−0.563933	−	0.563933i
$23$	10.4235	−	10.4235i	0.453195	−	0.453195i	−0.443218	−	0.896414i	$-0.646163\pi$
$23$	10.4235	−	10.4235i	0.453195	−	0.453195i	0.896414	+	0.443218i	$0.146163\pi$
$24$		0			0
$25$	−24.3303	−	5.74773i	−0.973212	−	0.229909i
$26$	−6.26617			−0.241007
$27$		0			0
$28$	−3.74166	+	3.74166i	−0.133631	+	0.133631i
$29$		−	14.5808i		−	0.502787i	−0.967885	−	0.251393i	$-0.919111\pi$
$29$		−	14.5808i		−	0.502787i	0.967885	−	0.251393i	$-0.0808888\pi$
$30$		0			0
$31$	42.6563			1.37601			0.688005	−	0.725706i	$-0.258487\pi$
$31$	42.6563			1.37601			0.688005	+	0.725706i	$0.258487\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$		0			0
$34$		−	11.6068i		−	0.341377i
$35$	10.3739	−	8.20871i	0.296396	−	0.234535i
$36$		0			0
$37$	11.9306	+	11.9306i	0.322448	+	0.322448i	0.849706	−	0.527257i	$-0.176780\pi$
$37$	11.9306	+	11.9306i	0.322448	+	0.322448i	−0.527257	+	0.849706i	$0.676780\pi$
$38$	26.5813	−	26.5813i	0.699507	−	0.699507i
$39$		0			0
$40$	−8.77548	−	11.0901i	−0.219387	−	0.277253i
$41$	−37.5226			−0.915185			−0.457593	−	0.889162i	$-0.651288\pi$
$41$	−37.5226			−0.915185			−0.457593	+	0.889162i	$0.651288\pi$
$42$		0			0
$43$	24.0083	−	24.0083i	0.558332	−	0.558332i	−0.370500	−	0.928832i	$-0.620814\pi$
$43$	24.0083	−	24.0083i	0.558332	−	0.558332i	0.928832	+	0.370500i	$0.120814\pi$
$44$			24.8131i			0.563933i
$45$		0			0
$46$	−20.8470			−0.453195
$47$	−8.83609	−	8.83609i	−0.188002	−	0.188002i	0.606830	−	0.794832i	$-0.292441\pi$
$47$	−8.83609	−	8.83609i	−0.188002	−	0.188002i	−0.794832	+	0.606830i	$0.792441\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	18.5826	+	30.0780i	0.371652	+	0.601561i
$51$		0			0
$52$	6.26617	+	6.26617i	0.120503	+	0.120503i
$53$	1.97883	−	1.97883i	0.0373364	−	0.0373364i	−0.688192	−	0.725529i	$-0.741595\pi$
$53$	1.97883	−	1.97883i	0.0373364	−	0.0373364i	0.725529	+	0.688192i	$0.241595\pi$
$54$		0			0
$55$	7.17918	−	61.6158i	0.130530	−	1.12029i
$56$	7.48331			0.133631
$57$		0			0
$58$	−14.5808	+	14.5808i	−0.251393	+	0.251393i
$59$		−	88.2651i		−	1.49602i	−0.663688	−	0.748010i	$-0.731010\pi$
$59$		−	88.2651i		−	1.49602i	0.663688	−	0.748010i	$-0.268990\pi$
$60$		0			0
$61$	102.471			1.67985			0.839924	−	0.542704i	$-0.182600\pi$
$61$	102.471			1.67985			0.839924	+	0.542704i	$0.182600\pi$
$62$	−42.6563	−	42.6563i	−0.688005	−	0.688005i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−13.7472	−	17.3732i	−0.211495	−	0.267279i
$66$		0			0
$67$	−22.8107	−	22.8107i	−0.340458	−	0.340458i	0.516082	−	0.856539i	$-0.327390\pi$
$67$	−22.8107	−	22.8107i	−0.340458	−	0.340458i	−0.856539	+	0.516082i	$0.827390\pi$
$68$	−11.6068	+	11.6068i	−0.170688	+	0.170688i
$69$		0			0
$70$	−18.5826	−	2.16515i	−0.265465	−	0.0309307i
$71$	10.7950			0.152042			0.0760208	−	0.997106i	$-0.475778\pi$
$71$	10.7950			0.152042			0.0760208	+	0.997106i	$0.475778\pi$
$72$		0			0
$73$	80.4481	−	80.4481i	1.10203	−	1.10203i	0.107863	−	0.994166i	$-0.465599\pi$
$73$	80.4481	−	80.4481i	1.10203	−	1.10203i	0.994166	−	0.107863i	$-0.0344007\pi$
$74$		−	23.8612i		−	0.322448i
$75$		0			0
$76$	−53.1625			−0.699507
$77$	23.2105	+	23.2105i	0.301435	+	0.301435i
$78$		0			0
$79$			138.851i			1.75761i	0.477180	+	0.878806i	$0.341659\pi$
$79$			138.851i			1.75761i	−0.477180	+	0.878806i	$0.658341\pi$
$80$	−2.31464	+	19.8656i	−0.0289331	+	0.248320i
$81$		0			0
$82$	37.5226	+	37.5226i	0.457593	+	0.457593i
$83$	96.0834	−	96.0834i	1.15763	−	1.15763i	0.172648	−	0.984984i	$-0.444768\pi$
$83$	96.0834	−	96.0834i	1.15763	−	1.15763i	0.984984	−	0.172648i	$-0.0552324\pi$
$84$		0			0
$85$	32.1803	−	25.4638i	0.378591	−	0.299575i
$86$	−48.0166			−0.558332
$87$		0			0
$88$	24.8131	−	24.8131i	0.281967	−	0.281967i
$89$			3.29855i			0.0370623i	0.999828	+	0.0185312i	$0.00589899\pi$
$89$			3.29855i			0.0370623i	−0.999828	+	0.0185312i	$0.994101\pi$
$90$		0			0
$91$	11.7229			0.128823
$92$	20.8470	+	20.8470i	0.226598	+	0.226598i
$93$		0			0
$94$			17.6722i			0.188002i
$95$	132.013	+	15.3815i	1.38961	+	0.161911i
$96$		0			0
$97$	−88.5219	−	88.5219i	−0.912597	−	0.912597i	0.0838786	−	0.996476i	$-0.473269\pi$
$97$	−88.5219	−	88.5219i	−0.912597	−	0.912597i	−0.996476	+	0.0838786i	$0.973269\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$		0			0
$100$	11.4955	−	48.6606i	0.114955	−	0.486606i
$101$	−142.067			−1.40661			−0.703304	−	0.710889i	$-0.748293\pi$
$101$	−142.067			−1.40661			−0.703304	+	0.710889i	$0.748293\pi$
$102$		0			0
$103$	60.4386	−	60.4386i	0.586782	−	0.586782i	−0.349976	−	0.936759i	$-0.613810\pi$
$103$	60.4386	−	60.4386i	0.586782	−	0.586782i	0.936759	+	0.349976i	$0.113810\pi$
$104$		−	12.5323i		−	0.120503i
$105$		0			0
$106$	−3.95766			−0.0373364
$107$	−78.7617	−	78.7617i	−0.736091	−	0.736091i	0.235728	−	0.971819i	$-0.424253\pi$
$107$	−78.7617	−	78.7617i	−0.736091	−	0.736091i	−0.971819	+	0.235728i	$0.924253\pi$
$108$		0			0
$109$		−	102.684i		−	0.942053i	−0.882119	−	0.471026i	$-0.843884\pi$
$109$		−	102.684i		−	0.942053i	0.882119	−	0.471026i	$-0.156116\pi$
$110$	−68.7950	+	54.4366i	−0.625409	+	0.494879i
$111$		0			0
$112$	−7.48331	−	7.48331i	−0.0668153	−	0.0668153i
$113$	34.2131	−	34.2131i	0.302771	−	0.302771i	−0.539326	−	0.842097i	$-0.681321\pi$
$113$	34.2131	−	34.2131i	0.302771	−	0.302771i	0.842097	+	0.539326i	$0.181321\pi$
$114$		0			0
$115$	−45.7356	−	57.7989i	−0.397701	−	0.502599i
$116$	29.1616			0.251393
$117$		0			0
$118$	−88.2651	+	88.2651i	−0.748010	+	0.748010i
$119$			21.7144i			0.182474i
$120$		0			0
$121$	32.9220			0.272083
$122$	−102.471	−	102.471i	−0.839924	−	0.839924i
$123$		0			0
$124$			85.3126i			0.688005i
$125$	−42.6245	+	117.508i	−0.340996	+	0.940065i
$126$		0			0
$127$	−149.547	−	149.547i	−1.17753	−	1.17753i	−0.980371	−	0.197161i	$-0.936828\pi$
$127$	−149.547	−	149.547i	−1.17753	−	1.17753i	−0.197161	−	0.980371i	$-0.563172\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−3.62599	+	31.1203i	−0.0278922	+	0.239387i
$131$	93.4871			0.713642			0.356821	−	0.934173i	$-0.383861\pi$
$131$	93.4871			0.713642			0.356821	+	0.934173i	$0.383861\pi$
$132$		0			0
$133$	−49.7290	+	49.7290i	−0.373902	+	0.373902i
$134$			45.6213i			0.340458i
$135$		0			0
$136$	23.2136			0.170688
$137$	66.0053	+	66.0053i	0.481790	+	0.481790i	0.905703	−	0.423913i	$-0.139344\pi$
$137$	66.0053	+	66.0053i	0.481790	+	0.481790i	−0.423913	+	0.905703i	$0.639344\pi$
$138$		0			0
$139$			111.764i			0.804059i	0.915627	+	0.402029i	$0.131695\pi$
$139$			111.764i			0.804059i	−0.915627	+	0.402029i	$0.868305\pi$
$140$	16.4174	+	20.7477i	0.117267	+	0.148198i
$141$		0			0
$142$	−10.7950	−	10.7950i	−0.0760208	−	0.0760208i
$143$	38.8707	−	38.8707i	0.271823	−	0.271823i
$144$		0			0
$145$	−72.4142	−	8.43735i	−0.499408	−	0.0581886i
$146$	−160.896			−1.10203
$147$		0			0
$148$	−23.8612	+	23.8612i	−0.161224	+	0.161224i
$149$			214.999i			1.44295i	0.692443	+	0.721473i	$0.256535\pi$
$149$			214.999i			1.44295i	−0.692443	+	0.721473i	$0.743465\pi$
$150$		0			0
$151$	−62.7527			−0.415581			−0.207790	−	0.978173i	$-0.566627\pi$
$151$	−62.7527			−0.415581			−0.207790	+	0.978173i	$0.566627\pi$
$152$	53.1625	+	53.1625i	0.349754	+	0.349754i
$153$		0			0
$154$		−	46.4210i		−	0.301435i
$155$	24.6835	−	211.848i	0.159249	−	1.36676i
$156$		0			0
$157$	181.318	+	181.318i	1.15489	+	1.15489i	0.985560	+	0.169329i	$0.0541601\pi$
$157$	181.318	+	181.318i	1.15489	+	1.15489i	0.169329	+	0.985560i	$0.445840\pi$
$158$	138.851	−	138.851i	0.878806	−	0.878806i
$159$		0			0
$160$	22.1803	−	17.5510i	0.138627	−	0.109694i
$161$	39.0011			0.242243
$162$		0			0
$163$	−52.0026	+	52.0026i	−0.319034	+	0.319034i	−0.848396	−	0.529362i	$-0.822431\pi$
$163$	−52.0026	+	52.0026i	−0.319034	+	0.319034i	0.529362	+	0.848396i	$0.322431\pi$
$164$		−	75.0452i		−	0.457593i
$165$		0			0
$166$	−192.167			−1.15763
$167$	153.475	+	153.475i	0.919013	+	0.919013i	0.996958	−	0.0779443i	$-0.0248356\pi$
$167$	153.475	+	153.475i	0.919013	+	0.919013i	−0.0779443	+	0.996958i	$0.524836\pi$
$168$		0			0
$169$			149.368i			0.883832i
$170$	−57.6441	−	6.71641i	−0.339083	−	0.0395083i
$171$		0			0
$172$	48.0166	+	48.0166i	0.279166	+	0.279166i
$173$	86.7956	−	86.7956i	0.501708	−	0.501708i	−0.410260	−	0.911969i	$-0.634562\pi$
$173$	86.7956	−	86.7956i	0.501708	−	0.501708i	0.911969	+	0.410260i	$0.134562\pi$
$174$		0			0
$175$	−34.7648	−	56.2708i	−0.198656	−	0.321548i
$176$	−49.6261			−0.281967
$177$		0			0
$178$	3.29855	−	3.29855i	0.0185312	−	0.0185312i
$179$			203.414i			1.13639i	0.822893	+	0.568196i	$0.192359\pi$
$179$			203.414i			1.13639i	−0.822893	+	0.568196i	$0.807641\pi$
$180$		0			0
$181$	−251.290			−1.38834			−0.694172	−	0.719810i	$-0.744229\pi$
$181$	−251.290			−1.38834			−0.694172	+	0.719810i	$0.744229\pi$
$182$	−11.7229	−	11.7229i	−0.0644117	−	0.0644117i
$183$		0			0
$184$		−	41.6940i		−	0.226598i
$185$	66.1559	−	52.3483i	0.357599	−	0.282964i
$186$		0			0
$187$	72.0001	+	72.0001i	0.385027	+	0.385027i
$188$	17.6722	−	17.6722i	0.0940010	−	0.0940010i
$189$		0			0
$190$	−116.632	−	147.395i	−0.613851	−	0.775762i
$191$	−367.604			−1.92463			−0.962315	−	0.271938i	$-0.912335\pi$
$191$	−367.604			−1.92463			−0.962315	+	0.271938i	$0.912335\pi$
$192$		0			0
$193$	95.7120	−	95.7120i	0.495917	−	0.495917i	−0.414247	−	0.910164i	$-0.635955\pi$
$193$	95.7120	−	95.7120i	0.495917	−	0.495917i	0.910164	+	0.414247i	$0.135955\pi$
$194$			177.044i			0.912597i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	194.449	+	194.449i	0.987048	+	0.987048i	0.999917	−	0.0128689i	$-0.00409643\pi$
$197$	194.449	+	194.449i	0.987048	+	0.987048i	−0.0128689	+	0.999917i	$0.504096\pi$
$198$		0			0
$199$			91.9043i			0.461831i	0.972974	+	0.230915i	$0.0741720\pi$
$199$			91.9043i			0.461831i	−0.972974	+	0.230915i	$0.925828\pi$
$200$	−60.1561	+	37.1652i	−0.300780	+	0.185826i
$201$		0			0
$202$	142.067	+	142.067i	0.703304	+	0.703304i
$203$	27.2782	−	27.2782i	0.134375	−	0.134375i
$204$		0			0
$205$	−21.7129	+	186.352i	−0.105916	+	0.909036i
$206$	−120.877			−0.586782
$207$		0			0
$208$	−12.5323	+	12.5323i	−0.0602517	+	0.0602517i
$209$			329.781i			1.57790i
$210$		0			0
$211$	296.539			1.40540			0.702700	−	0.711486i	$-0.251978\pi$
$211$	296.539			1.40540			0.702700	+	0.711486i	$0.251978\pi$
$212$	3.95766	+	3.95766i	0.0186682	+	0.0186682i
$213$		0			0
$214$			157.523i			0.736091i
$215$	−105.342	−	133.127i	−0.489963	−	0.619197i
$216$		0			0
$217$	79.8026	+	79.8026i	0.367754	+	0.367754i
$218$	−102.684	+	102.684i	−0.471026	+	0.471026i
$219$		0			0
$220$	123.232	+	14.3584i	0.560144	+	0.0652652i
$221$	36.3651			0.164548
$222$		0			0
$223$	99.7016	−	99.7016i	0.447092	−	0.447092i	−0.447295	−	0.894387i	$-0.647612\pi$
$223$	99.7016	−	99.7016i	0.447092	−	0.447092i	0.894387	+	0.447295i	$0.147612\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−68.4262			−0.302771
$227$	45.7570	+	45.7570i	0.201573	+	0.201573i	0.800674	−	0.599101i	$-0.204475\pi$
$227$	45.7570	+	45.7570i	0.201573	+	0.201573i	−0.599101	+	0.800674i	$0.704475\pi$
$228$		0			0
$229$			248.102i			1.08342i	0.840567	+	0.541708i	$0.182222\pi$
$229$			248.102i			1.08342i	−0.840567	+	0.541708i	$0.817778\pi$
$230$	−12.0633	+	103.535i	−0.0524493	+	0.450150i
$231$		0			0
$232$	−29.1616	−	29.1616i	−0.125697	−	0.125697i
$233$	−306.481	+	306.481i	−1.31537	+	1.31537i	−0.397968	+	0.917399i	$0.630284\pi$
$233$	−306.481	+	306.481i	−1.31537	+	1.31537i	−0.917399	+	0.397968i	$0.869716\pi$
$234$		0			0
$235$	−48.9967	+	38.7705i	−0.208497	+	0.164981i
$236$	176.530			0.748010
$237$		0			0
$238$	21.7144	−	21.7144i	0.0912368	−	0.0912368i
$239$		−	136.398i		−	0.570702i	−0.958423	−	0.285351i	$-0.907890\pi$
$239$		−	136.398i		−	0.570702i	0.958423	−	0.285351i	$-0.0921102\pi$
$240$		0			0
$241$	332.727			1.38061			0.690305	−	0.723519i	$-0.257477\pi$
$241$	332.727			1.38061			0.690305	+	0.723519i	$0.257477\pi$
$242$	−32.9220	−	32.9220i	−0.136041	−	0.136041i
$243$		0			0
$244$			204.941i			0.839924i
$245$	34.7648	+	4.05063i	0.141897	+	0.0165332i
$246$		0			0
$247$	83.2814	+	83.2814i	0.337172	+	0.337172i
$248$	85.3126	−	85.3126i	0.344002	−	0.344002i
$249$		0			0
$250$	160.133	−	74.8836i	0.640530	−	0.299534i
$251$	−244.521			−0.974186			−0.487093	−	0.873350i	$-0.661943\pi$
$251$	−244.521			−0.974186			−0.487093	+	0.873350i	$0.661943\pi$
$252$		0			0
$253$	129.319	−	129.319i	0.511144	−	0.511144i
$254$			299.093i			1.17753i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−102.592	−	102.592i	−0.399191	−	0.399191i	0.478756	−	0.877948i	$-0.341088\pi$
$257$	−102.592	−	102.592i	−0.399191	−	0.399191i	−0.877948	+	0.478756i	$0.841088\pi$
$258$		0			0
$259$			44.6402i			0.172356i
$260$	34.7463	−	27.4943i	0.133640	−	0.105747i
$261$		0			0
$262$	−93.4871	−	93.4871i	−0.356821	−	0.356821i
$263$	−253.841	+	253.841i	−0.965174	+	0.965174i	−0.999414	−	0.0342400i	$-0.989099\pi$
$263$	−253.841	+	253.841i	−0.965174	+	0.965174i	0.0342400	+	0.999414i	$0.489099\pi$
$264$		0			0
$265$	−8.68259	−	10.9727i	−0.0327645	−	0.0414065i
$266$	99.4580			0.373902
$267$		0			0
$268$	45.6213	−	45.6213i	0.170229	−	0.170229i
$269$			207.747i			0.772295i	0.922437	+	0.386147i	$0.126194\pi$
$269$			207.747i			0.772295i	−0.922437	+	0.386147i	$0.873806\pi$
$270$		0			0
$271$	−476.286			−1.75751			−0.878756	−	0.477270i	$-0.841626\pi$
$271$	−476.286			−1.75751			−0.878756	+	0.477270i	$0.841626\pi$
$272$	−23.2136	−	23.2136i	−0.0853442	−	0.0853442i
$273$		0			0
$274$		−	132.011i		−	0.481790i
$275$	−301.855	−	71.3094i	−1.09765	−	0.259307i
$276$		0			0
$277$	−9.67870	−	9.67870i	−0.0349412	−	0.0349412i	0.689420	−	0.724362i	$-0.257865\pi$
$277$	−9.67870	−	9.67870i	−0.0349412	−	0.0349412i	−0.724362	+	0.689420i	$0.757865\pi$
$278$	111.764	−	111.764i	0.402029	−	0.402029i
$279$		0			0
$280$	4.33030	−	37.1652i	0.0154654	−	0.132733i
$281$	−101.463			−0.361079			−0.180540	−	0.983568i	$-0.557784\pi$
$281$	−101.463			−0.361079			−0.180540	+	0.983568i	$0.557784\pi$
$282$		0			0
$283$	276.026	−	276.026i	0.975358	−	0.975358i	−0.0243452	−	0.999704i	$-0.507750\pi$
$283$	276.026	−	276.026i	0.975358	−	0.975358i	0.999704	+	0.0243452i	$0.00775008\pi$
$284$			21.5899i			0.0760208i
$285$		0			0
$286$	−77.7415			−0.271823
$287$	−70.1983	−	70.1983i	−0.244594	−	0.244594i
$288$		0			0
$289$		−	221.641i		−	0.766924i
$290$	63.9768	+	80.8515i	0.220610	+	0.278798i
$291$		0			0
$292$	160.896	+	160.896i	0.551014	+	0.551014i
$293$	−104.873	+	104.873i	−0.357928	+	0.357928i	−0.863049	−	0.505121i	$-0.831448\pi$
$293$	−104.873	+	104.873i	−0.357928	+	0.357928i	0.505121	+	0.863049i	$0.331448\pi$
$294$		0			0
$295$	−438.360	−	51.0756i	−1.48597	−	0.173138i
$296$	47.7224			0.161224
$297$		0			0
$298$	214.999	−	214.999i	0.721473	−	0.721473i
$299$		−	65.3154i		−	0.218446i
$300$		0			0
$301$	89.8308			0.298441
$302$	62.7527	+	62.7527i	0.207790	+	0.207790i
$303$		0			0
$304$		−	106.325i		−	0.349754i
$305$	59.2958	−	508.911i	0.194412	−	1.66856i
$306$		0			0
$307$	158.138	+	158.138i	0.515108	+	0.515108i	0.916087	−	0.400979i	$-0.131330\pi$
$307$	158.138	+	158.138i	0.515108	+	0.515108i	−0.400979	+	0.916087i	$0.631330\pi$
$308$	−46.4210	+	46.4210i	−0.150717	+	0.150717i
$309$		0			0
$310$	−236.532	+	187.165i	−0.763006	+	0.603757i
$311$	519.537			1.67054			0.835269	−	0.549842i	$-0.185312\pi$
$311$	519.537			1.67054			0.835269	+	0.549842i	$0.185312\pi$
$312$		0			0
$313$	73.0852	−	73.0852i	0.233499	−	0.233499i	−0.580653	−	0.814152i	$-0.697202\pi$
$313$	73.0852	−	73.0852i	0.233499	−	0.233499i	0.814152	+	0.580653i	$0.197202\pi$
$314$		−	362.635i		−	1.15489i
$315$		0			0
$316$	−277.703			−0.878806
$317$	−279.849	−	279.849i	−0.882805	−	0.882805i	0.111014	−	0.993819i	$-0.464590\pi$
$317$	−279.849	−	279.849i	−0.882805	−	0.882805i	−0.993819	+	0.111014i	$0.964590\pi$
$318$		0			0
$319$		−	180.897i		−	0.567076i
$320$	−39.7312	−	4.62929i	−0.124160	−	0.0144665i
$321$		0			0
$322$	−39.0011	−	39.0011i	−0.121122	−	0.121122i
$323$	−154.262	+	154.262i	−0.477591	+	0.477591i
$324$		0			0
$325$	−94.2371	+	58.2208i	−0.289960	+	0.179141i
$326$	104.005			0.319034
$327$		0			0
$328$	−75.0452	+	75.0452i	−0.228796	+	0.228796i
$329$		−	33.0616i		−	0.100491i
$330$		0			0
$331$	−601.834			−1.81823			−0.909115	−	0.416546i	$-0.863241\pi$
$331$	−601.834			−1.81823			−0.909115	+	0.416546i	$0.863241\pi$
$332$	192.167	+	192.167i	0.578816	+	0.578816i
$333$		0			0
$334$		−	306.950i		−	0.919013i
$335$	−126.487	+	100.087i	−0.377572	+	0.298768i
$336$		0			0
$337$	17.0969	+	17.0969i	0.0507325	+	0.0507325i	0.732018	−	0.681285i	$-0.238579\pi$
$337$	17.0969	+	17.0969i	0.0507325	+	0.0507325i	−0.681285	+	0.732018i	$0.738579\pi$
$338$	149.368	−	149.368i	0.441916	−	0.441916i
$339$		0			0
$340$	50.9277	+	64.3605i	0.149787	+	0.189296i
$341$	529.217			1.55195
$342$		0			0
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$		−	96.0331i		−	0.279166i
$345$		0			0
$346$	−173.591			−0.501708
$347$	−233.692	−	233.692i	−0.673465	−	0.673465i	0.285048	−	0.958513i	$-0.407990\pi$
$347$	−233.692	−	233.692i	−0.673465	−	0.673465i	−0.958513	+	0.285048i	$0.907990\pi$
$348$		0			0
$349$			399.184i			1.14379i	0.820326	+	0.571896i	$0.193792\pi$
$349$			399.184i			1.14379i	−0.820326	+	0.571896i	$0.806208\pi$
$350$	−21.5060	+	91.0357i	−0.0614458	+	0.260102i
$351$		0			0
$352$	49.6261	+	49.6261i	0.140983	+	0.140983i
$353$	137.005	−	137.005i	0.388117	−	0.388117i	−0.485898	−	0.874015i	$-0.661507\pi$
$353$	137.005	−	137.005i	0.388117	−	0.388117i	0.874015	+	0.485898i	$0.161507\pi$
$354$		0			0
$355$	6.24662	−	53.6121i	0.0175961	−	0.151020i
$356$	−6.59709			−0.0185312
$357$		0			0
$358$	203.414	−	203.414i	0.568196	−	0.568196i
$359$		−	473.333i		−	1.31848i	−0.751934	−	0.659239i	$-0.770879\pi$
$359$		−	473.333i		−	1.31848i	0.751934	−	0.659239i	$-0.229121\pi$
$360$		0			0
$361$	−345.564			−0.957241
$362$	251.290	+	251.290i	0.694172	+	0.694172i
$363$		0			0
$364$			23.4459i			0.0644117i
$365$	−352.985	−	446.090i	−0.967083	−	1.22216i
$366$		0			0
$367$	−256.657	−	256.657i	−0.699338	−	0.699338i	0.264930	−	0.964268i	$-0.414651\pi$
$367$	−256.657	−	256.657i	−0.699338	−	0.699338i	−0.964268	+	0.264930i	$0.914651\pi$
$368$	−41.6940	+	41.6940i	−0.113299	+	0.113299i
$369$		0			0
$370$	−118.504	−	13.8075i	−0.320282	−	0.0373177i
$371$	7.40410			0.0199571
$372$		0			0
$373$	−278.764	+	278.764i	−0.747355	+	0.747355i	−0.973982	−	0.226627i	$-0.927230\pi$
$373$	−278.764	+	278.764i	−0.747355	+	0.747355i	0.226627	+	0.973982i	$0.427230\pi$
$374$		−	144.000i		−	0.385027i
$375$		0			0
$376$	−35.3444			−0.0940010
$377$	−45.6830	−	45.6830i	−0.121175	−	0.121175i
$378$		0			0
$379$			168.579i			0.444800i	0.974955	+	0.222400i	$0.0713891\pi$
$379$			168.579i			0.444800i	−0.974955	+	0.222400i	$0.928611\pi$
$380$	−30.7631	+	264.027i	−0.0809555	+	0.694807i
$381$		0			0
$382$	367.604	+	367.604i	0.962315	+	0.962315i
$383$	166.588	−	166.588i	0.434956	−	0.434956i	−0.455354	−	0.890310i	$-0.650487\pi$
$383$	166.588	−	166.588i	0.434956	−	0.434956i	0.890310	+	0.455354i	$0.150487\pi$
$384$		0			0
$385$	128.704	−	101.842i	0.334295	−	0.264524i
$386$	−191.424			−0.495917
$387$		0			0
$388$	177.044	−	177.044i	0.456299	−	0.456299i
$389$		−	73.9237i		−	0.190035i	−0.995476	−	0.0950176i	$-0.969709\pi$
$389$		−	73.9237i		−	0.190035i	0.995476	−	0.0950176i	$-0.0302907\pi$
$390$		0			0
$391$	120.984			0.309421
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$		0			0
$394$		−	388.897i		−	0.987048i
$395$	689.591	+	80.3478i	1.74580	+	0.203412i
$396$		0			0
$397$	73.4533	+	73.4533i	0.185021	+	0.185021i	0.793540	−	0.608519i	$-0.208236\pi$
$397$	73.4533	+	73.4533i	0.185021	+	0.185021i	−0.608519	+	0.793540i	$0.708236\pi$
$398$	91.9043	−	91.9043i	0.230915	−	0.230915i
$399$		0			0
$400$	97.3212	+	22.9909i	0.243303	+	0.0574773i
$401$	534.615			1.33321			0.666603	−	0.745413i	$-0.267748\pi$
$401$	534.615			1.33321			0.666603	+	0.745413i	$0.267748\pi$
$402$		0			0
$403$	133.646	−	133.646i	0.331627	−	0.331627i
$404$		−	284.135i		−	0.703304i
$405$		0			0
$406$	−54.5564			−0.134375
$407$	148.017	+	148.017i	0.363679	+	0.363679i
$408$		0			0
$409$			14.4205i			0.0352578i	0.999845	+	0.0176289i	$0.00561175\pi$
$409$			14.4205i			0.0352578i	−0.999845	+	0.0176289i	$0.994388\pi$
$410$	208.065	−	164.639i	0.507476	−	0.401560i
$411$		0			0
$412$	120.877	+	120.877i	0.293391	+	0.293391i
$413$	165.129	−	165.129i	0.399828	−	0.399828i
$414$		0			0
$415$	−421.589	−	532.789i	−1.01588	−	1.28383i
$416$	25.0647			0.0602517
$417$		0			0
$418$	329.781	−	329.781i	0.788951	−	0.788951i
$419$			337.860i			0.806349i	0.915123	+	0.403174i	$0.132093\pi$
$419$			337.860i			0.806349i	−0.915123	+	0.403174i	$0.867907\pi$
$420$		0			0
$421$	372.730			0.885345			0.442672	−	0.896683i	$-0.354031\pi$
$421$	372.730			0.885345			0.442672	+	0.896683i	$0.354031\pi$
$422$	−296.539	−	296.539i	−0.702700	−	0.702700i
$423$		0			0
$424$		−	7.91531i		−	0.0186682i
$425$	−107.842	−	174.555i	−0.253746	−	0.410718i
$426$		0			0
$427$	191.705	+	191.705i	0.448958	+	0.448958i
$428$	157.523	−	157.523i	0.368046	−	0.368046i
$429$		0			0
$430$	−27.7853	+	238.470i	−0.0646170	+	0.554580i
$431$	591.932			1.37339			0.686696	−	0.726944i	$-0.259060\pi$
$431$	591.932			1.37339			0.686696	+	0.726944i	$0.259060\pi$
$432$		0			0
$433$	−239.916	+	239.916i	−0.554079	+	0.554079i	−0.927615	−	0.373537i	$-0.878145\pi$
$433$	−239.916	+	239.916i	−0.554079	+	0.554079i	0.373537	+	0.927615i	$0.378145\pi$
$434$		−	159.605i		−	0.367754i
$435$		0			0
$436$	205.368			0.471026
$437$	277.070	+	277.070i	0.634027	+	0.634027i
$438$		0			0
$439$		−	243.928i		−	0.555644i	−0.960633	−	0.277822i	$-0.910388\pi$
$439$		−	243.928i		−	0.555644i	0.960633	−	0.277822i	$-0.0896125\pi$
$440$	−108.873	−	137.590i	−0.247439	−	0.312705i
$441$		0			0
$442$	−36.3651	−	36.3651i	−0.0822741	−	0.0822741i
$443$	−459.426	+	459.426i	−1.03708	+	1.03708i	−0.0377942	+	0.999286i	$0.512033\pi$
$443$	−459.426	+	459.426i	−1.03708	+	1.03708i	−0.999286	+	0.0377942i	$0.987967\pi$
$444$		0			0
$445$	16.3819	+	1.90874i	0.0368133	+	0.00428931i
$446$	−199.403			−0.447092
$447$		0			0
$448$	14.9666	−	14.9666i	0.0334077	−	0.0334077i
$449$			136.444i			0.303885i	0.988389	+	0.151943i	$0.0485529\pi$
$449$			136.444i			0.303885i	−0.988389	+	0.151943i	$0.951447\pi$
$450$		0			0
$451$	−465.525			−1.03221
$452$	68.4262	+	68.4262i	0.151385	+	0.151385i
$453$		0			0
$454$		−	91.5140i		−	0.201573i
$455$	6.78361	−	58.2208i	0.0149090	−	0.127958i
$456$		0			0
$457$	269.807	+	269.807i	0.590388	+	0.590388i	0.937736	−	0.347348i	$-0.112918\pi$
$457$	269.807	+	269.807i	0.590388	+	0.590388i	−0.347348	+	0.937736i	$0.612918\pi$
$458$	248.102	−	248.102i	0.541708	−	0.541708i
$459$		0			0
$460$	115.598	−	91.4712i	0.251300	−	0.198850i
$461$	238.818			0.518043			0.259022	−	0.965872i	$-0.416600\pi$
$461$	238.818			0.518043			0.259022	+	0.965872i	$0.416600\pi$
$462$		0			0
$463$	308.280	−	308.280i	0.665831	−	0.665831i	−0.290917	−	0.956748i	$-0.593960\pi$
$463$	308.280	−	308.280i	0.665831	−	0.665831i	0.956748	+	0.290917i	$0.0939603\pi$
$464$			58.3233i			0.125697i
$465$		0			0
$466$	612.961			1.31537
$467$	−228.918	−	228.918i	−0.490188	−	0.490188i	0.418177	−	0.908365i	$-0.362669\pi$
$467$	−228.918	−	228.918i	−0.490188	−	0.490188i	−0.908365	+	0.418177i	$0.862669\pi$
$468$		0			0
$469$		−	85.3497i		−	0.181982i
$470$	87.7672	+	10.2262i	0.186739	+	0.0217579i
$471$		0			0
$472$	−176.530	−	176.530i	−0.374005	−	0.374005i
$473$	297.860	−	297.860i	0.629724	−	0.629724i
$474$		0			0
$475$	152.782	−	646.730i	0.321646	−	1.36154i
$476$	−43.4287			−0.0912368
$477$		0			0
$478$	−136.398	+	136.398i	−0.285351	+	0.285351i
$479$		−	342.177i		−	0.714357i	−0.934036	−	0.357178i	$-0.883739\pi$
$479$		−	342.177i		−	0.714357i	0.934036	−	0.357178i	$-0.116261\pi$
$480$		0			0
$481$	74.7591			0.155424
$482$	−332.727	−	332.727i	−0.690305	−	0.690305i
$483$		0			0
$484$			65.8440i			0.136041i
$485$	−490.860	+	388.411i	−1.01208	+	0.800848i
$486$		0			0
$487$	−456.499	−	456.499i	−0.937370	−	0.937370i	0.0607814	−	0.998151i	$-0.480641\pi$
$487$	−456.499	−	456.499i	−0.937370	−	0.937370i	−0.998151	+	0.0607814i	$0.980641\pi$
$488$	204.941	−	204.941i	0.419962	−	0.419962i
$489$		0			0
$490$	−30.7142	−	38.8154i	−0.0626820	−	0.0792152i
$491$	−795.504			−1.62017			−0.810085	−	0.586312i	$-0.800579\pi$
$491$	−795.504			−1.62017			−0.810085	+	0.586312i	$0.800579\pi$
$492$		0			0
$493$	84.6184	−	84.6184i	0.171640	−	0.171640i
$494$		−	166.563i		−	0.337172i
$495$		0			0
$496$	−170.625			−0.344002
$497$	20.1955	+	20.1955i	0.0406348	+	0.0406348i
$498$		0			0
$499$		−	145.240i		−	0.291062i	−0.989354	−	0.145531i	$-0.953511\pi$
$499$		−	145.240i		−	0.291062i	0.989354	−	0.145531i	$-0.0464890\pi$
$500$	−235.016	−	85.2490i	−0.470032	−	0.170498i
$501$		0			0
$502$	244.521	+	244.521i	0.487093	+	0.487093i
$503$	−169.609	+	169.609i	−0.337195	+	0.337195i	−0.855311	−	0.518115i	$-0.826634\pi$
$503$	−169.609	+	169.609i	−0.337195	+	0.337195i	0.518115	+	0.855311i	$0.326634\pi$
$504$		0			0
$505$	−82.2089	+	705.564i	−0.162790	+	1.39716i
$506$	−258.639			−0.511144
$507$		0			0
$508$	299.093	−	299.093i	0.588766	−	0.588766i
$509$			734.035i			1.44211i	0.692877	+	0.721056i	$0.256343\pi$
$509$			734.035i			1.44211i	−0.692877	+	0.721056i	$0.743657\pi$
$510$		0			0
$511$	301.009			0.589059
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			205.184i			0.399191i
$515$	−265.189	−	335.136i	−0.514930	−	0.650749i
$516$		0			0
$517$	−109.625	−	109.625i	−0.212041	−	0.212041i
$518$	44.6402	−	44.6402i	0.0861780	−	0.0861780i
$519$		0			0
$520$	−62.2407	−	7.25198i	−0.119694	−	0.0139461i
$521$	−96.5998			−0.185412			−0.0927061	−	0.995694i	$-0.529552\pi$
$521$	−96.5998			−0.185412			−0.0927061	+	0.995694i	$0.529552\pi$
$522$		0			0
$523$	256.326	−	256.326i	0.490108	−	0.490108i	−0.418232	−	0.908340i	$-0.637350\pi$
$523$	256.326	−	256.326i	0.490108	−	0.490108i	0.908340	+	0.418232i	$0.137350\pi$
$524$			186.974i			0.356821i
$525$		0			0
$526$	507.681			0.965174
$527$	247.552	+	247.552i	0.469738	+	0.469738i
$528$		0			0
$529$			311.702i			0.589228i
$530$	−2.29014	+	19.6553i	−0.00432102	+	0.0370855i
$531$		0			0
$532$	−99.4580	−	99.4580i	−0.186951	−	0.186951i
$533$	−117.562	+	117.562i	−0.220566	+	0.220566i
$534$		0			0
$535$	−436.739	+	345.586i	−0.816334	+	0.645955i
$536$	−91.2426			−0.170229
$537$		0			0
$538$	207.747	−	207.747i	0.386147	−	0.386147i
$539$			86.8457i			0.161124i
$540$		0			0
$541$	−967.814			−1.78894			−0.894468	−	0.447133i	$-0.852445\pi$
$541$	−967.814			−1.78894			−0.894468	+	0.447133i	$0.852445\pi$
$542$	476.286	+	476.286i	0.878756	+	0.878756i
$543$		0			0
$544$			46.4272i			0.0853442i
$545$	−509.969	−	59.4191i	−0.935723	−	0.109026i
$546$		0			0
$547$	107.907	+	107.907i	0.197271	+	0.197271i	0.798829	−	0.601558i	$-0.205453\pi$
$547$	107.907	+	107.907i	0.197271	+	0.197271i	−0.601558	+	0.798829i	$0.705453\pi$
$548$	−132.011	+	132.011i	−0.240895	+	0.240895i
$549$		0			0
$550$	230.545	+	373.164i	0.419173	+	0.678480i
$551$	387.577			0.703406
$552$		0			0
$553$	−259.767	+	259.767i	−0.469741	+	0.469741i
$554$			19.3574i			0.0349412i
$555$		0			0
$556$	−223.528			−0.402029
$557$	−106.902	−	106.902i	−0.191925	−	0.191925i	0.604603	−	0.796527i	$-0.293332\pi$
$557$	−106.902	−	106.902i	−0.191925	−	0.191925i	−0.796527	+	0.604603i	$0.793332\pi$
$558$		0			0
$559$		−	150.440i		−	0.269123i
$560$	−41.4955	+	32.8348i	−0.0740990	+	0.0586337i
$561$		0			0
$562$	101.463	+	101.463i	0.180540	+	0.180540i
$563$	290.841	−	290.841i	0.516592	−	0.516592i	−0.399946	−	0.916539i	$-0.630971\pi$
$563$	290.841	−	290.841i	0.516592	−	0.516592i	0.916539	+	0.399946i	$0.130971\pi$
$564$		0			0
$565$	−150.118	−	189.714i	−0.265696	−	0.335777i
$566$	−552.053			−0.975358
$567$		0			0
$568$	21.5899	−	21.5899i	0.0380104	−	0.0380104i
$569$			53.2185i			0.0935299i	0.998906	+	0.0467649i	$0.0148912\pi$
$569$			53.2185i			0.0935299i	−0.998906	+	0.0467649i	$0.985109\pi$
$570$		0			0
$571$	437.943			0.766976			0.383488	−	0.923546i	$-0.374723\pi$
$571$	437.943			0.766976			0.383488	+	0.923546i	$0.374723\pi$
$572$	77.7415	+	77.7415i	0.135912	+	0.135912i
$573$		0			0
$574$			140.397i			0.244594i
$575$	−313.518	+	193.695i	−0.545249	+	0.336862i
$576$		0			0
$577$	−219.701	−	219.701i	−0.380764	−	0.380764i	0.490613	−	0.871377i	$-0.336773\pi$
$577$	−219.701	−	219.701i	−0.380764	−	0.380764i	−0.871377	+	0.490613i	$0.836773\pi$
$578$	−221.641	+	221.641i	−0.383462	+	0.383462i
$579$		0			0
$580$	16.8747	−	144.828i	0.0290943	−	0.249704i
$581$	359.511			0.618780
$582$		0			0
$583$	24.5504	−	24.5504i	0.0421105	−	0.0421105i
$584$		−	321.792i		−	0.551014i
$585$		0			0
$586$	209.746			0.357928
$587$	−677.250	−	677.250i	−1.15375	−	1.15375i	−0.985795	−	0.167952i	$-0.946285\pi$
$587$	−677.250	−	677.250i	−1.15375	−	1.15375i	−0.167952	−	0.985795i	$-0.553715\pi$
$588$		0			0
$589$			1133.86i			1.92506i
$590$	387.285	+	489.436i	0.656415	+	0.829552i
$591$		0			0
$592$	−47.7224	−	47.7224i	−0.0806121	−	0.0806121i
$593$	558.797	−	558.797i	0.942322	−	0.942322i	−0.0561035	−	0.998425i	$-0.517868\pi$
$593$	558.797	−	558.797i	0.942322	−	0.942322i	0.998425	+	0.0561035i	$0.0178677\pi$
$594$		0			0
$595$	107.842	+	12.5653i	0.181247	+	0.0211181i
$596$	−429.998			−0.721473
$597$		0			0
$598$	−65.3154	+	65.3154i	−0.109223	+	0.109223i
$599$		−	538.111i		−	0.898349i	−0.893444	−	0.449175i	$-0.851718\pi$
$599$		−	538.111i		−	0.898349i	0.893444	−	0.449175i	$-0.148282\pi$
$600$		0			0
$601$	573.831			0.954793			0.477397	−	0.878688i	$-0.341580\pi$
$601$	573.831			0.954793			0.477397	+	0.878688i	$0.341580\pi$
$602$	−89.8308	−	89.8308i	−0.149221	−	0.149221i
$603$		0			0
$604$		−	125.505i		−	0.207790i
$605$	19.0507	−	163.504i	0.0314887	−	0.270254i
$606$		0			0
$607$	409.542	+	409.542i	0.674699	+	0.674699i	0.958796	−	0.284097i	$-0.0916937\pi$
$607$	409.542	+	409.542i	0.674699	+	0.674699i	−0.284097	+	0.958796i	$0.591694\pi$
$608$	−106.325	+	106.325i	−0.174877	+	0.174877i
$609$		0			0
$610$	−568.207	+	449.615i	−0.931486	+	0.737074i
$611$	−55.3685			−0.0906195
$612$		0			0
$613$	−571.915	+	571.915i	−0.932977	+	0.932977i	−0.997891	−	0.0649138i	$-0.979323\pi$
$613$	−571.915	+	571.915i	−0.932977	+	0.932977i	0.0649138	+	0.997891i	$0.479323\pi$
$614$		−	316.277i		−	0.515108i
$615$		0			0
$616$	92.8420			0.150717
$617$	479.790	+	479.790i	0.777617	+	0.777617i	0.979425	−	0.201808i	$-0.0646817\pi$
$617$	479.790	+	479.790i	0.777617	+	0.777617i	−0.201808	+	0.979425i	$0.564682\pi$
$618$		0			0
$619$		−	308.772i		−	0.498824i	−0.968398	−	0.249412i	$-0.919763\pi$
$619$		−	308.772i		−	0.498824i	0.968398	−	0.249412i	$-0.0802373\pi$
$620$	423.697	+	49.3671i	0.683382	+	0.0796243i
$621$		0			0
$622$	−519.537	−	519.537i	−0.835269	−	0.835269i
$623$	−6.17102	+	6.17102i	−0.00990532	+	0.00990532i
$624$		0			0
$625$	558.927	+	279.688i	0.894284	+	0.447501i
$626$	−146.170			−0.233499
$627$		0			0
$628$	−362.635	+	362.635i	−0.577444	+	0.577444i
$629$			138.476i			0.220153i
$630$		0			0
$631$	876.945			1.38977			0.694885	−	0.719121i	$-0.255455\pi$
$631$	876.945			1.38977			0.694885	+	0.719121i	$0.255455\pi$
$632$	277.703	+	277.703i	0.439403	+	0.439403i
$633$		0			0
$634$			559.698i			0.882805i
$635$	−829.245	+	656.172i	−1.30590	+	1.03334i
$636$		0			0
$637$	21.9316	+	21.9316i	0.0344295	+	0.0344295i
$638$	−180.897	+	180.897i	−0.283538	+	0.283538i
$639$		0			0
$640$	35.1019	+	44.3605i	0.0548468	+	0.0693133i
$641$	−492.966			−0.769057			−0.384529	−	0.923113i	$-0.625636\pi$
$641$	−492.966			−0.769057			−0.384529	+	0.923113i	$0.625636\pi$
$642$		0			0
$643$	−30.0997	+	30.0997i	−0.0468114	+	0.0468114i	−0.730125	−	0.683314i	$-0.760538\pi$
$643$	−30.0997	+	30.0997i	−0.0468114	+	0.0468114i	0.683314	+	0.730125i	$0.260538\pi$
$644$			78.0023i			0.121122i
$645$		0			0
$646$	308.524			0.477591
$647$	484.636	+	484.636i	0.749051	+	0.749051i	0.974301	−	0.225250i	$-0.0723198\pi$
$647$	484.636	+	484.636i	0.749051	+	0.749051i	−0.225250	+	0.974301i	$0.572320\pi$
$648$		0			0
$649$		−	1095.06i		−	1.68731i
$650$	152.458	+	36.0162i	0.234551	+	0.0554096i
$651$		0			0
$652$	−104.005	−	104.005i	−0.159517	−	0.159517i
$653$	113.485	−	113.485i	0.173791	−	0.173791i	−0.614852	−	0.788643i	$-0.710784\pi$
$653$	113.485	−	113.485i	0.173791	−	0.173791i	0.788643	+	0.614852i	$0.210784\pi$
$654$		0			0
$655$	54.0973	−	464.295i	0.0825914	−	0.708847i
$656$	150.090			0.228796
$657$		0			0
$658$	−33.0616	+	33.0616i	−0.0502456	+	0.0502456i
$659$		−	625.067i		−	0.948509i	−0.880388	−	0.474254i	$-0.842718\pi$
$659$		−	625.067i		−	0.948509i	0.880388	−	0.474254i	$-0.157282\pi$
$660$		0			0
$661$	608.913			0.921200			0.460600	−	0.887608i	$-0.347634\pi$
$661$	608.913			0.921200			0.460600	+	0.887608i	$0.347634\pi$
$662$	601.834	+	601.834i	0.909115	+	0.909115i
$663$		0			0
$664$		−	384.334i		−	0.578816i
$665$	218.198	+	275.750i	0.328117	+	0.414662i
$666$		0			0
$667$	−151.983	−	151.983i	−0.227861	−	0.227861i
$668$	−306.950	+	306.950i	−0.459507	+	0.459507i
$669$		0			0
$670$	226.574	+	26.3993i	0.338170	+	0.0394019i
$671$	1271.31			1.89464
$672$		0			0
$673$	−884.941	+	884.941i	−1.31492	+	1.31492i	−0.397179	+	0.917741i	$0.630011\pi$
$673$	−884.941	+	884.941i	−1.31492	+	1.31492i	−0.917741	+	0.397179i	$0.869989\pi$
$674$		−	34.1937i		−	0.0507325i
$675$		0			0
$676$	−298.735			−0.441916
$677$	390.548	+	390.548i	0.576881	+	0.576881i	0.934043	−	0.357162i	$-0.116255\pi$
$677$	390.548	+	390.548i	0.576881	+	0.576881i	−0.357162	+	0.934043i	$0.616255\pi$
$678$		0			0
$679$		−	331.219i		−	0.487804i
$680$	13.4328	−	115.288i	0.0197541	−	0.169541i
$681$		0			0
$682$	−529.217	−	529.217i	−0.775977	−	0.775977i
$683$	−869.027	+	869.027i	−1.27237	+	1.27237i	−0.327526	+	0.944842i	$0.606215\pi$
$683$	−869.027	+	869.027i	−1.27237	+	1.27237i	−0.944842	+	0.327526i	$0.893785\pi$
$684$		0			0
$685$	366.003	−	289.614i	0.534311	−	0.422794i
$686$	26.1916			0.0381802
$687$		0			0
$688$	−96.0331	+	96.0331i	−0.139583	+	0.139583i
$689$		−	12.3997i		−	0.0179966i
$690$		0			0
$691$	−148.448			−0.214831			−0.107415	−	0.994214i	$-0.534257\pi$
$691$	−148.448			−0.214831			−0.107415	+	0.994214i	$0.534257\pi$
$692$	173.591	+	173.591i	0.250854	+	0.250854i
$693$		0			0
$694$			467.385i			0.673465i
$695$	555.066	+	64.6736i	0.798656	+	0.0930555i
$696$		0			0
$697$	−217.759	−	217.759i	−0.312423	−	0.312423i
$698$	399.184	−	399.184i	0.571896	−	0.571896i
$699$		0			0
$700$	112.542	−	69.5296i	0.160774	−	0.0993280i
$701$	−65.2652			−0.0931029			−0.0465515	−	0.998916i	$-0.514823\pi$
$701$	−65.2652			−0.0931029			−0.0465515	+	0.998916i	$0.514823\pi$
$702$		0			0
$703$	−317.130	+	317.130i	−0.451110	+	0.451110i
$704$		−	99.2522i		−	0.140983i
$705$		0			0
$706$	−274.011			−0.388117
$707$	−265.784	−	265.784i	−0.375932	−	0.375932i
$708$		0			0
$709$			817.389i			1.15288i	0.817141	+	0.576438i	$0.195558\pi$
$709$			817.389i			1.15288i	−0.817141	+	0.576438i	$0.804442\pi$
$710$	−59.8587	+	47.3655i	−0.0843080	+	0.0667119i
$711$		0			0
$712$	6.59709	+	6.59709i	0.00926558	+	0.00926558i
$713$	444.628	−	444.628i	0.623601	−	0.623601i
$714$		0			0
$715$	−170.555	−	215.541i	−0.238538	−	0.301455i
$716$	−406.828			−0.568196
$717$		0			0
$718$	−473.333	+	473.333i	−0.659239	+	0.659239i
$719$			1151.64i			1.60173i	0.598846	+	0.800864i	$0.295626\pi$
$719$			1151.64i			1.60173i	−0.598846	+	0.800864i	$0.704374\pi$
$720$		0			0
$721$	226.141			0.313648
$722$	345.564	+	345.564i	0.478620	+	0.478620i
$723$		0			0
$724$		−	502.580i		−	0.694172i
$725$	−83.8066	+	354.756i	−0.115595	+	0.489318i
$726$		0			0
$727$	−82.3587	−	82.3587i	−0.113286	−	0.113286i	0.648192	−	0.761477i	$-0.275526\pi$
$727$	−82.3587	−	82.3587i	−0.113286	−	0.113286i	−0.761477	+	0.648192i	$0.775526\pi$
$728$	23.4459	−	23.4459i	0.0322059	−	0.0322059i
$729$		0			0
$730$	−93.1043	+	799.075i	−0.127540	+	1.09462i
$731$	278.660			0.381203
$732$		0			0
$733$	−482.749	+	482.749i	−0.658593	+	0.658593i	−0.955047	−	0.296454i	$-0.904196\pi$
$733$	−482.749	+	482.749i	−0.658593	+	0.658593i	0.296454	+	0.955047i	$0.404196\pi$
$734$			513.314i			0.699338i
$735$		0			0
$736$	83.3880			0.113299
$737$	−283.001	−	283.001i	−0.383991	−	0.383991i
$738$		0			0
$739$		−	430.657i		−	0.582757i	−0.956608	−	0.291379i	$-0.905886\pi$
$739$		−	430.657i		−	0.582757i	0.956608	−	0.291379i	$-0.0941139\pi$
$740$	104.697	+	132.312i	0.141482	+	0.178800i
$741$		0			0
$742$	−7.40410	−	7.40410i	−0.00997857	−	0.00997857i
$743$	−902.316	+	902.316i	−1.21442	+	1.21442i	−0.244866	+	0.969557i	$0.578744\pi$
$743$	−902.316	+	902.316i	−1.21442	+	1.21442i	−0.969557	+	0.244866i	$0.921256\pi$
$744$		0			0
$745$	1067.77	+	124.411i	1.43325	+	0.166995i
$746$	557.527			0.747355
$747$		0			0
$748$	−144.000	+	144.000i	−0.192514	+	0.192514i
$749$		−	294.699i		−	0.393457i
$750$		0			0
$751$	−262.783			−0.349910			−0.174955	−	0.984576i	$-0.555978\pi$
$751$	−262.783			−0.349910			−0.174955	+	0.984576i	$0.555978\pi$
$752$	35.3444	+	35.3444i	0.0470005	+	0.0470005i
$753$		0			0
$754$			91.3659i			0.121175i
$755$	−36.3126	+	311.655i	−0.0480961	+	0.412788i
$756$		0			0
$757$	−786.569	−	786.569i	−1.03906	−	1.03906i	−0.999205	−	0.0398555i	$-0.987310\pi$
$757$	−786.569	−	786.569i	−1.03906	−	1.03906i	−0.0398555	−	0.999205i	$-0.512690\pi$
$758$	168.579	−	168.579i	0.222400	−	0.222400i
$759$		0			0
$760$	294.790	−	233.263i	0.387881	−	0.306926i
$761$	−1469.36			−1.93082			−0.965412	−	0.260728i	$-0.916037\pi$
$761$	−1469.36			−1.93082			−0.965412	+	0.260728i	$0.916037\pi$
$762$		0			0
$763$	192.104	−	192.104i	0.251774	−	0.251774i
$764$		−	735.208i		−	0.962315i
$765$		0			0
$766$	−333.177			−0.434956
$767$	−276.542	−	276.542i	−0.360551	−	0.360551i
$768$		0			0
$769$			1018.45i			1.32439i	0.749333	+	0.662193i	$0.230374\pi$
$769$			1018.45i			1.32439i	−0.749333	+	0.662193i	$0.769626\pi$
$770$	−230.545	−	26.8620i	−0.299409	−	0.0348857i
$771$		0			0
$772$	191.424	+	191.424i	0.247958	+	0.247958i
$773$	−570.658	+	570.658i	−0.738238	+	0.738238i	−0.972237	−	0.233999i	$-0.924819\pi$
$773$	−570.658	+	570.658i	−0.738238	+	0.738238i	0.233999	+	0.972237i	$0.424819\pi$
$774$		0			0
$775$	−1037.84	−	245.177i	−1.33915	−	0.316357i
$776$	−354.088			−0.456299
$777$		0			0
$778$	−73.9237	+	73.9237i	−0.0950176	+	0.0950176i
$779$		−	997.398i		−	1.28036i
$780$		0			0
$781$	133.928			0.171483
$782$	−120.984	−	120.984i	−0.154710	−	0.154710i
$783$		0			0
$784$		−	28.0000i		−	0.0357143i
$785$	1005.42	−	795.574i	1.28079	−	1.01347i
$786$		0			0
$787$	1053.50	+	1053.50i	1.33862	+	1.33862i	0.897395	+	0.441227i	$0.145457\pi$
$787$	1053.50	+	1053.50i	1.33862	+	1.33862i	0.441227	+	0.897395i	$0.354543\pi$
$788$	−388.897	+	388.897i	−0.493524	+	0.493524i
$789$		0			0
$790$	−609.244	−	769.939i	−0.771194	−	0.974607i
$791$	128.014			0.161838
$792$		0			0
$793$	321.050	−	321.050i	0.404854	−	0.404854i
$794$		−	146.907i		−	0.185021i
$795$		0			0
$796$	−183.809			−0.230915
$797$	−874.260	−	874.260i	−1.09694	−	1.09694i	−0.994767	−	0.102172i	$-0.967421\pi$
$797$	−874.260	−	874.260i	−1.09694	−	1.09694i	−0.102172	−	0.994767i	$-0.532579\pi$
$798$		0			0
$799$		−	102.559i		−	0.128359i
$800$	−74.3303	−	120.312i	−0.0929129	−	0.150390i
$801$		0			0
$802$	−534.615	−	534.615i	−0.666603	−	0.666603i
$803$	998.082	−	998.082i	1.24294	−	1.24294i
$804$		0			0
$805$	22.5684	−	193.695i	0.0280353	−	0.240615i
$806$	−267.292			−0.331627
$807$		0			0
$808$	−284.135	+	284.135i	−0.351652	+	0.351652i
$809$			938.860i			1.16052i	0.814432	+	0.580260i	$0.197049\pi$
$809$			938.860i			1.16052i	−0.814432	+	0.580260i	$0.802951\pi$
$810$		0			0
$811$	422.265			0.520672			0.260336	−	0.965518i	$-0.416167\pi$
$811$	422.265			0.520672			0.260336	+	0.965518i	$0.416167\pi$
$812$	54.5564	+	54.5564i	0.0671877	+	0.0671877i
$813$		0			0
$814$		−	296.034i		−	0.363679i
$815$	228.174	+	288.358i	0.279968	+	0.353813i
$816$		0			0
$817$	638.171	+	638.171i	0.781115	+	0.781115i
$818$	14.4205	−	14.4205i	0.0176289	−	0.0176289i
$819$		0			0
$820$	−372.705	−	43.4257i	−0.454518	−	0.0529582i
$821$	−750.531			−0.914167			−0.457083	−	0.889424i	$-0.651106\pi$
$821$	−750.531			−0.914167			−0.457083	+	0.889424i	$0.651106\pi$
$822$		0			0
$823$	−755.539	+	755.539i	−0.918031	+	0.918031i	−0.996886	−	0.0788552i	$-0.974874\pi$
$823$	−755.539	+	755.539i	−0.918031	+	0.918031i	0.0788552	+	0.996886i	$0.474874\pi$
$824$		−	241.754i		−	0.293391i
$825$		0			0
$826$	−330.258			−0.399828
$827$	578.780	+	578.780i	0.699854	+	0.699854i	0.964379	−	0.264525i	$-0.0852150\pi$
$827$	578.780	+	578.780i	0.699854	+	0.699854i	−0.264525	+	0.964379i	$0.585215\pi$
$828$		0			0
$829$		−	318.623i		−	0.384346i	−0.981361	−	0.192173i	$-0.938447\pi$
$829$		−	318.623i		−	0.384346i	0.981361	−	0.192173i	$-0.0615534\pi$
$830$	−111.199	+	954.378i	−0.133975	+	1.14985i
$831$		0			0
$832$	−25.0647	−	25.0647i	−0.0301258	−	0.0301258i
$833$	−40.6238	+	40.6238i	−0.0487681	+	0.0487681i
$834$		0			0
$835$	851.030	−	673.410i	1.01920	−	0.806479i
$836$	−659.563			−0.788951
$837$		0			0
$838$	337.860	−	337.860i	0.403174	−	0.403174i
$839$		−	264.028i		−	0.314694i	−0.987543	−	0.157347i	$-0.949706\pi$
$839$		−	264.028i		−	0.314694i	0.987543	−	0.157347i	$-0.0502940\pi$
$840$		0			0
$841$	628.400			0.747205
$842$	−372.730	−	372.730i	−0.442672	−	0.442672i
$843$		0			0
$844$			593.079i			0.702700i
$845$	741.819	+	86.4332i	0.877893	+	0.102288i
$846$		0			0
$847$	61.5914	+	61.5914i	0.0727171	+	0.0727171i
$848$	−7.91531	+	7.91531i	−0.00933410	+	0.00933410i
$849$		0			0
$850$	−66.7128	+	282.397i	−0.0784856	+	0.332232i
$851$	248.717			0.292264
$852$		0			0
$853$	−426.618	+	426.618i	−0.500138	+	0.500138i	−0.911481	−	0.411343i	$-0.865060\pi$
$853$	−426.618	+	426.618i	−0.500138	+	0.500138i	0.411343	+	0.911481i	$0.365060\pi$
$854$		−	383.410i		−	0.448958i
$855$		0			0
$856$	−315.047			−0.368046
$857$	−670.381	−	670.381i	−0.782242	−	0.782242i	0.197967	−	0.980209i	$-0.436566\pi$
$857$	−670.381	−	670.381i	−0.782242	−	0.782242i	−0.980209	+	0.197967i	$0.936566\pi$
$858$		0			0
$859$		−	383.866i		−	0.446875i	−0.974718	−	0.223437i	$-0.928272\pi$
$859$		−	383.866i		−	0.446875i	0.974718	−	0.223437i	$-0.0717278\pi$
$860$	266.255	−	210.684i	0.309599	−	0.244982i
$861$		0			0
$862$	−591.932	−	591.932i	−0.686696	−	0.686696i
$863$	−563.290	+	563.290i	−0.652711	+	0.652711i	−0.953645	−	0.300934i	$-0.902702\pi$
$863$	−563.290	+	563.290i	−0.652711	+	0.652711i	0.300934	+	0.953645i	$0.402702\pi$
$864$		0			0
$865$	−380.836	−	481.287i	−0.440273	−	0.556401i
$866$	479.832			0.554079
$867$		0			0
$868$	−159.605	+	159.605i	−0.183877	+	0.183877i
$869$			1722.66i			1.98235i
$870$		0			0
$871$	−142.935			−0.164105
$872$	−205.368	−	205.368i	−0.235513	−	0.235513i
$873$		0			0
$874$		−	554.139i		−	0.634027i
$875$	−299.581	+	140.094i	−0.342378	+	0.160108i
$876$		0			0
$877$	−617.434	−	617.434i	−0.704029	−	0.704029i	0.261244	−	0.965273i	$-0.415867\pi$
$877$	−617.434	−	617.434i	−0.704029	−	0.704029i	−0.965273	+	0.261244i	$0.915867\pi$
$878$	−243.928	+	243.928i	−0.277822	+	0.277822i
$879$		0			0
$880$	−28.7167	+	246.463i	−0.0326326	+	0.280072i
$881$	456.278			0.517910			0.258955	−	0.965889i	$-0.416622\pi$
$881$	456.278			0.517910			0.258955	+	0.965889i	$0.416622\pi$
$882$		0			0
$883$	−161.141	+	161.141i	−0.182493	+	0.182493i	−0.792441	−	0.609948i	$-0.791190\pi$
$883$	−161.141	+	161.141i	−0.182493	+	0.182493i	0.609948	+	0.792441i	$0.291190\pi$
$884$			72.7303i			0.0822741i
$885$		0			0
$886$	918.853			1.03708
$887$	−701.018	−	701.018i	−0.790324	−	0.790324i	0.191222	−	0.981547i	$-0.438755\pi$
$887$	−701.018	−	701.018i	−0.790324	−	0.790324i	−0.981547	+	0.191222i	$0.938755\pi$
$888$		0			0
$889$		−	559.552i		−	0.629417i
$890$	−14.4732	−	18.2907i	−0.0162620	−	0.0205513i
$891$		0			0
$892$	199.403	+	199.403i	0.223546	+	0.223546i
$893$	234.875	−	234.875i	0.263017	−	0.263017i
$894$		0			0
$895$	1010.24	+	117.708i	1.12876	+	0.131517i
$896$	−29.9333			−0.0334077
$897$		0			0
$898$	136.444	−	136.444i	0.151943	−	0.151943i
$899$		−	621.964i		−	0.691839i
$900$		0			0
$901$	22.9679			0.0254916
$902$	465.525	+	465.525i	0.516103	+	0.516103i
$903$		0			0
$904$		−	136.852i		−	0.151385i
$905$	−145.412	+	1248.01i	−0.160676	+	1.37901i
$906$		0			0
$907$	−126.915	−	126.915i	−0.139928	−	0.139928i	0.633673	−	0.773601i	$-0.281546\pi$
$907$	−126.915	−	126.915i	−0.139928	−	0.139928i	−0.773601	+	0.633673i	$0.781546\pi$
$908$	−91.5140	+	91.5140i	−0.100786	+	0.100786i
$909$		0			0
$910$	−65.0044	+	51.4372i	−0.0714334	+	0.0565244i
$911$	508.167			0.557813			0.278906	−	0.960318i	$-0.410028\pi$
$911$	508.167			0.557813			0.278906	+	0.960318i	$0.410028\pi$
$912$		0			0
$913$	1192.06	−	1192.06i	1.30565	−	1.30565i
$914$		−	539.614i		−	0.590388i
$915$		0			0
$916$	−496.205			−0.541708
$917$	174.898	+	174.898i	0.190729	+	0.190729i
$918$		0			0
$919$		−	671.030i		−	0.730174i	−0.930973	−	0.365087i	$-0.881039\pi$
$919$		−	671.030i		−	0.730174i	0.930973	−	0.365087i	$-0.118961\pi$
$920$	−207.069	−	24.1267i	−0.225075	−	0.0262247i
$921$		0			0
$922$	−238.818	−	238.818i	−0.259022	−	0.259022i
$923$	33.8215	−	33.8215i	0.0366430	−	0.0366430i
$924$		0			0
$925$	−221.701	−	358.849i	−0.239677	−	0.387944i
$926$	−616.560			−0.665831
$927$		0			0
$928$	58.3233	−	58.3233i	0.0628483	−	0.0628483i
$929$		−	198.819i		−	0.214014i	−0.994258	−	0.107007i	$-0.965873\pi$
$929$		−	198.819i		−	0.214014i	0.994258	−	0.107007i	$-0.0341267\pi$
$930$		0			0
$931$	−186.069			−0.199859
$932$	−612.961	−	612.961i	−0.657684	−	0.657684i
$933$		0			0
$934$			457.836i			0.490188i
$935$	399.245	−	315.918i	0.427000	−	0.337880i
$936$		0			0
$937$	691.159	+	691.159i	0.737630	+	0.737630i	0.972119	−	0.234489i	$-0.0753417\pi$
$937$	691.159	+	691.159i	0.737630	+	0.737630i	−0.234489	+	0.972119i	$0.575342\pi$
$938$	−85.3497	+	85.3497i	−0.0909911	+	0.0909911i
$939$		0			0
$940$	−77.5410	−	97.9934i	−0.0824904	−	0.104248i
$941$	−1460.09			−1.55164			−0.775819	−	0.630956i	$-0.782663\pi$
$941$	−1460.09			−1.55164			−0.775819	+	0.630956i	$0.782663\pi$
$942$		0			0
$943$	−391.117	+	391.117i	−0.414758	+	0.414758i
$944$			353.061i			0.374005i
$945$		0			0
$946$	−595.719			−0.629724
$947$	332.380	+	332.380i	0.350982	+	0.350982i	0.860475	−	0.509493i	$-0.170167\pi$
$947$	332.380	+	332.380i	0.350982	+	0.350982i	−0.509493	+	0.860475i	$0.670167\pi$
$948$		0			0
$949$		−	504.102i		−	0.531192i
$950$	−799.512	+	493.948i	−0.841592	+	0.519946i
$951$		0			0
$952$	43.4287	+	43.4287i	0.0456184	+	0.0456184i
$953$	473.427	−	473.427i	0.496776	−	0.496776i	−0.413657	−	0.910433i	$-0.635749\pi$
$953$	473.427	−	473.427i	0.496776	−	0.496776i	0.910433	+	0.413657i	$0.135749\pi$
$954$		0			0
$955$	−212.718	+	1825.67i	−0.222742	+	1.91170i
$956$	272.796			0.285351
$957$		0			0
$958$	−342.177	+	342.177i	−0.357178	+	0.357178i
$959$			246.969i			0.257528i
$960$		0			0
$961$	858.560			0.893402
$962$	−74.7591	−	74.7591i	−0.0777122	−	0.0777122i
$963$		0			0
$964$			665.454i			0.690305i
$965$	−419.959	−	530.729i	−0.435191	−	0.549978i
$966$		0			0
$967$	−696.942	−	696.942i	−0.720726	−	0.720726i	0.248027	−	0.968753i	$-0.420218\pi$
$967$	−696.942	−	696.942i	−0.720726	−	0.720726i	−0.968753	+	0.248027i	$0.920218\pi$
$968$	65.8440	−	65.8440i	0.0680207	−	0.0680207i
$969$		0			0
$970$	879.271	+	102.448i	0.906465	+	0.105617i
$971$	262.031			0.269857			0.134929	−	0.990855i	$-0.456919\pi$
$971$	262.031			0.269857			0.134929	+	0.990855i	$0.456919\pi$
$972$		0			0
$973$	−209.092	+	209.092i	−0.214894	+	0.214894i
$974$			912.998i			0.937370i
$975$		0			0
$976$	−409.883			−0.419962
$977$	−363.414	−	363.414i	−0.371969	−	0.371969i	0.496225	−	0.868194i	$-0.334719\pi$
$977$	−363.414	−	363.414i	−0.371969	−	0.371969i	−0.868194	+	0.496225i	$0.834719\pi$
$978$		0			0
$979$			40.9235i			0.0418014i
$980$	−8.10125	+	69.5296i	−0.00826659	+	0.0709486i
$981$		0			0
$982$	795.504	+	795.504i	0.810085	+	0.810085i
$983$	−589.265	+	589.265i	−0.599456	+	0.599456i	−0.940168	−	0.340712i	$-0.889332\pi$
$983$	−589.265	+	589.265i	−0.599456	+	0.599456i	0.340712	+	0.940168i	$0.389332\pi$
$984$		0			0
$985$	1078.23	−	853.190i	1.09465	−	0.866182i
$986$	−169.237			−0.171640
$987$		0			0
$988$	−166.563	+	166.563i	−0.168586	+	0.168586i
$989$		−	500.500i		−	0.506067i
$990$		0			0
$991$	1470.51			1.48386			0.741931	−	0.670476i	$-0.233910\pi$
$991$	1470.51			1.48386			0.741931	+	0.670476i	$0.233910\pi$
$992$	170.625	+	170.625i	0.172001	+	0.172001i
$993$		0			0
$994$		−	40.3910i		−	0.0406348i
$995$	456.434	+	53.1814i	0.458727	+	0.0534487i
$996$		0			0
$997$	639.149	+	639.149i	0.641073	+	0.641073i	0.950819	−	0.309747i	$-0.100244\pi$
$997$	639.149	+	639.149i	0.641073	+	0.641073i	−0.309747	+	0.950819i	$0.600244\pi$
$998$	−145.240	+	145.240i	−0.145531	+	0.145531i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.b.127.3		8
3.2	odd	2		210.3.l.a.127.2	yes	8
5.3	odd	4	inner	630.3.o.b.253.3		8
15.2	even	4		1050.3.l.b.43.3		8
15.8	even	4		210.3.l.a.43.2	✓	8
15.14	odd	2		1050.3.l.b.757.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.2	✓	8	15.8	even	4
210.3.l.a.127.2	yes	8	3.2	odd	2
630.3.o.b.127.3		8	1.1	even	1	trivial
630.3.o.b.253.3		8	5.3	odd	4	inner
1050.3.l.b.43.3		8	15.2	even	4
1050.3.l.b.757.3		8	15.14	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(0.578661 - 4.96640i) q^{5} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(0.578661 - 4.96640i) q^{5} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-5.54506 + 4.38774i) q^{10} +12.4065 q^{11} +(3.13309 - 3.13309i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(5.80341 + 5.80341i) q^{17} +26.5813i q^{19} +(9.93280 + 1.15732i) q^{20} +(-12.4065 - 12.4065i) q^{22} +(10.4235 - 10.4235i) q^{23} +(-24.3303 - 5.74773i) q^{25} -6.26617 q^{26} +(-3.74166 + 3.74166i) q^{28} -14.5808i q^{29} +42.6563 q^{31} +(4.00000 + 4.00000i) q^{32} -11.6068i q^{34} +(10.3739 - 8.20871i) q^{35} +(11.9306 + 11.9306i) q^{37} +(26.5813 - 26.5813i) q^{38} +(-8.77548 - 11.0901i) q^{40} -37.5226 q^{41} +(24.0083 - 24.0083i) q^{43} +24.8131i q^{44} -20.8470 q^{46} +(-8.83609 - 8.83609i) q^{47} +7.00000i q^{49} +(18.5826 + 30.0780i) q^{50} +(6.26617 + 6.26617i) q^{52} +(1.97883 - 1.97883i) q^{53} +(7.17918 - 61.6158i) q^{55} +7.48331 q^{56} +(-14.5808 + 14.5808i) q^{58} -88.2651i q^{59} +102.471 q^{61} +(-42.6563 - 42.6563i) q^{62} -8.00000i q^{64} +(-13.7472 - 17.3732i) q^{65} +(-22.8107 - 22.8107i) q^{67} +(-11.6068 + 11.6068i) q^{68} +(-18.5826 - 2.16515i) q^{70} +10.7950 q^{71} +(80.4481 - 80.4481i) q^{73} -23.8612i q^{74} -53.1625 q^{76} +(23.2105 + 23.2105i) q^{77} +138.851i q^{79} +(-2.31464 + 19.8656i) q^{80} +(37.5226 + 37.5226i) q^{82} +(96.0834 - 96.0834i) q^{83} +(32.1803 - 25.4638i) q^{85} -48.0166 q^{86} +(24.8131 - 24.8131i) q^{88} +3.29855i q^{89} +11.7229 q^{91} +(20.8470 + 20.8470i) q^{92} +17.6722i q^{94} +(132.013 + 15.3815i) q^{95} +(-88.5219 - 88.5219i) q^{97} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 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

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Database

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