LMFDB - Embedded newform 700.2.c.k.699.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(699,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("700.699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.c (of order $2$, degree $1$, not 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.29960650073923649536.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 $ x^16 - 7x^12 + 40x^8 - 112*x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			699.6
Root			$1.32968 - 0.481610i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.k.699.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.736813 - 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(3.37740 - 2.06155i) q^{6} +(2.51564 + 0.819496i) q^{7} +(2.82083 - 0.207107i) q^{8} -4.82843 q^{9} +O(q^{10})$	\(q+(-0.736813 - 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(3.37740 - 2.06155i) q^{6} +(2.51564 + 0.819496i) q^{7} +(2.82083 - 0.207107i) q^{8} -4.82843 q^{9} +1.47363i q^{11} +(-4.97703 - 2.55791i) q^{12} +5.83095 q^{13} +(-0.864335 - 3.64046i) q^{14} +(-2.32843 - 3.25245i) q^{16} +4.12311 q^{17} +(3.55765 + 5.82843i) q^{18} +5.11582 q^{19} +(-2.29289 + 7.03858i) q^{21} +(1.77882 - 1.08579i) q^{22} -2.08402 q^{23} +(0.579471 + 7.89250i) q^{24} +(-4.29632 - 7.03858i) q^{26} -5.11582i q^{27} +(-3.75757 + 3.72568i) q^{28} -8.24264 q^{29} -3.95687 q^{31} +(-2.21044 + 5.20711i) q^{32} -4.12311 q^{33} +(-3.03796 - 4.97703i) q^{34} +(4.41421 - 8.58892i) q^{36} -2.24264i q^{37} +(-3.76940 - 6.17534i) q^{38} +16.3146i q^{39} +4.12311i q^{41} +(10.1858 - 2.41835i) q^{42} -2.94725 q^{43} +(-2.62132 - 1.34721i) q^{44} +(1.53553 + 2.51564i) q^{46} +11.8706i q^{47} +(9.10013 - 6.51478i) q^{48} +(5.65685 + 4.12311i) q^{49} +11.5362i q^{51} +(-5.33074 + 10.3722i) q^{52} -3.75736i q^{53} +(-6.17534 + 3.76940i) q^{54} +(7.26592 + 1.79066i) q^{56} +14.3137i q^{57} +(6.07328 + 9.94975i) q^{58} -5.59587 q^{59} -11.6619i q^{61} +(2.91548 + 4.77637i) q^{62} +(-12.1466 - 3.95687i) q^{63} +(7.91421 - 1.16843i) q^{64} +(3.03796 + 4.97703i) q^{66} +12.7570 q^{67} +(-3.76940 + 7.33428i) q^{68} -5.83095i q^{69} -7.97852i q^{71} +(-13.6202 + 1.00000i) q^{72} -12.3693 q^{73} +(-2.70711 + 1.65241i) q^{74} +(-4.67695 + 9.10013i) q^{76} +(-1.20763 + 3.70711i) q^{77} +(19.6935 - 12.0208i) q^{78} -4.16804i q^{79} -0.171573 q^{81} +(4.97703 - 3.03796i) q^{82} +2.79793i q^{83} +(-10.4242 - 10.5134i) q^{84} +(2.17157 + 3.55765i) q^{86} -23.0624i q^{87} +(0.305198 + 4.15685i) q^{88} +12.3693i q^{89} +(14.6686 + 4.77844i) q^{91} +(1.90524 - 3.70711i) q^{92} -11.0711i q^{93} +(14.3291 - 8.74643i) q^{94} +(-14.5691 - 6.18466i) q^{96} +8.24621 q^{97} +(0.808986 - 9.86638i) q^{98} -7.11529i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 32 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 32 * q^9	$ 16 q + 8 q^{4} - 32 q^{9} - 24 q^{14} + 8 q^{16} - 48 q^{21} - 64 q^{29} + 48 q^{36} - 8 q^{44} - 32 q^{46} + 40 q^{56} + 104 q^{64} - 32 q^{74} - 48 q^{81} - 40 q^{84} + 80 q^{86}+O(q^{100}) $ 16 * q + 8 * q^4 - 32 * q^9 - 24 * q^14 + 8 * q^16 - 48 * q^21 - 64 * q^29 + 48 * q^36 - 8 * q^44 - 32 * q^46 + 40 * q^56 + 104 * q^64 - 32 * q^74 - 48 * q^81 - 40 * q^84 + 80 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.736813	−	1.20711i	−0.521005	−	0.853553i
$2$	−0.736813	−	1.20711i	−0.521005	−	0.853553i
$3$			2.79793i			1.61539i	0.589602	+	0.807694i	$0.299284\pi$
$3$			2.79793i			1.61539i	−0.589602	+	0.807694i	$0.700716\pi$
$4$	−0.914214	+	1.77882i	−0.457107	+	0.889412i
$5$		0			0
$5$		0			0
$6$	3.37740	−	2.06155i	1.37882	−	0.841625i
$7$	2.51564	+	0.819496i	0.950821	+	0.309740i
$7$	2.51564	+	0.819496i	0.950821	+	0.309740i
$8$	2.82083	−	0.207107i	0.997316	−	0.0732233i
$9$	−4.82843			−1.60948
$10$		0			0
$11$			1.47363i			0.444315i	0.975011	+	0.222157i	$0.0713099\pi$
$11$			1.47363i			0.444315i	−0.975011	+	0.222157i	$0.928690\pi$
$12$	−4.97703	−	2.55791i	−1.43674	−	0.738404i
$13$	5.83095			1.61722			0.808608	−	0.588348i	$-0.200222\pi$
$13$	5.83095			1.61722			0.808608	+	0.588348i	$0.200222\pi$
$14$	−0.864335	−	3.64046i	−0.231003	−	0.972953i
$15$		0			0
$16$	−2.32843	−	3.25245i	−0.582107	−	0.813112i
$17$	4.12311			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$17$	4.12311			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$18$	3.55765	+	5.82843i	0.838546	+	1.37377i
$19$	5.11582			1.17365			0.586824	−	0.809714i	$-0.300378\pi$
$19$	5.11582			1.17365			0.586824	+	0.809714i	$0.300378\pi$
$20$		0			0
$21$	−2.29289	+	7.03858i	−0.500350	+	1.53594i
$22$	1.77882	−	1.08579i	0.379246	−	0.231490i
$23$	−2.08402			−0.434549			−0.217274	−	0.976111i	$-0.569717\pi$
$23$	−2.08402			−0.434549			−0.217274	+	0.976111i	$0.569717\pi$
$24$	0.579471	+	7.89250i	0.118284	+	1.61105i
$25$		0			0
$26$	−4.29632	−	7.03858i	−0.842578	−	1.38038i
$27$		−	5.11582i		−	0.984539i
$28$	−3.75757	+	3.72568i	−0.710113	+	0.704087i
$29$	−8.24264			−1.53062			−0.765310	−	0.643662i	$-0.777414\pi$
$29$	−8.24264			−1.53062			−0.765310	+	0.643662i	$0.777414\pi$
$30$		0			0
$31$	−3.95687			−0.710676			−0.355338	−	0.934738i	$-0.615634\pi$
$31$	−3.95687			−0.710676			−0.355338	+	0.934738i	$0.615634\pi$
$32$	−2.21044	+	5.20711i	−0.390754	+	0.920495i
$33$	−4.12311			−0.717741
$34$	−3.03796	−	4.97703i	−0.521005	−	0.853553i
$35$		0			0
$36$	4.41421	−	8.58892i	0.735702	−	1.43149i
$37$		−	2.24264i		−	0.368688i	−0.982862	−	0.184344i	$-0.940984\pi$
$37$		−	2.24264i		−	0.368688i	0.982862	−	0.184344i	$-0.0590160\pi$
$38$	−3.76940	−	6.17534i	−0.611477	−	1.00177i
$39$			16.3146i			2.61243i
$40$		0			0
$41$			4.12311i			0.643921i	0.946753	+	0.321960i	$0.104342\pi$
$41$			4.12311i			0.643921i	−0.946753	+	0.321960i	$0.895658\pi$
$42$	10.1858	−	2.41835i	1.57170	−	0.373160i
$43$	−2.94725			−0.449452			−0.224726	−	0.974422i	$-0.572149\pi$
$43$	−2.94725			−0.449452			−0.224726	+	0.974422i	$0.572149\pi$
$44$	−2.62132	−	1.34721i	−0.395179	−	0.203099i
$45$		0			0
$46$	1.53553	+	2.51564i	0.226402	+	0.370910i
$47$			11.8706i			1.73151i	0.500470	+	0.865754i	$0.333161\pi$
$47$			11.8706i			1.73151i	−0.500470	+	0.865754i	$0.666839\pi$
$48$	9.10013	−	6.51478i	1.31349	−	0.940328i
$49$	5.65685	+	4.12311i	0.808122	+	0.589015i
$50$		0			0
$51$			11.5362i			1.61539i
$52$	−5.33074	+	10.3722i	−0.739240	+	1.43837i
$53$		−	3.75736i		−	0.516113i	−0.966130	−	0.258056i	$-0.916918\pi$
$53$		−	3.75736i		−	0.516113i	0.966130	−	0.258056i	$-0.0830821\pi$
$54$	−6.17534	+	3.76940i	−0.840357	+	0.512950i
$55$		0			0
$56$	7.26592	+	1.79066i	0.970949	+	0.239286i
$57$			14.3137i			1.89590i
$58$	6.07328	+	9.94975i	0.797461	+	1.30647i
$59$	−5.59587			−0.728520			−0.364260	−	0.931297i	$-0.618678\pi$
$59$	−5.59587			−0.728520			−0.364260	+	0.931297i	$0.618678\pi$
$60$		0			0
$61$		−	11.6619i		−	1.49315i	−0.665299	−	0.746577i	$-0.731696\pi$
$61$		−	11.6619i		−	1.49315i	0.665299	−	0.746577i	$-0.268304\pi$
$62$	2.91548	+	4.77637i	0.370266	+	0.606600i
$63$	−12.1466	−	3.95687i	−1.53032	−	0.498519i
$64$	7.91421	−	1.16843i	0.989277	−	0.146053i
$65$		0			0
$66$	3.03796	+	4.97703i	0.373947	+	0.612630i
$67$	12.7570			1.55851			0.779256	−	0.626706i	$-0.215597\pi$
$67$	12.7570			1.55851			0.779256	+	0.626706i	$0.215597\pi$
$68$	−3.76940	+	7.33428i	−0.457107	+	0.889412i
$69$		−	5.83095i		−	0.701964i
$70$		0			0
$71$		−	7.97852i		−	0.946877i	−0.880827	−	0.473438i	$-0.843013\pi$
$71$		−	7.97852i		−	0.946877i	0.880827	−	0.473438i	$-0.156987\pi$
$72$	−13.6202	+	1.00000i	−1.60516	+	0.117851i
$73$	−12.3693			−1.44772			−0.723860	−	0.689947i	$-0.757634\pi$
$73$	−12.3693			−1.44772			−0.723860	+	0.689947i	$0.757634\pi$
$74$	−2.70711	+	1.65241i	−0.314695	+	0.192088i
$75$		0			0
$76$	−4.67695	+	9.10013i	−0.536483	+	1.04386i
$77$	−1.20763	+	3.70711i	−0.137622	+	0.422464i
$78$	19.6935	−	12.0208i	2.22985	−	1.36109i
$79$		−	4.16804i		−	0.468941i	−0.972123	−	0.234471i	$-0.924664\pi$
$79$		−	4.16804i		−	0.468941i	0.972123	−	0.234471i	$-0.0753357\pi$
$80$		0			0
$81$	−0.171573			−0.0190637
$82$	4.97703	−	3.03796i	0.549621	−	0.335486i
$83$			2.79793i			0.307113i	0.988140	+	0.153557i	$0.0490727\pi$
$83$			2.79793i			0.307113i	−0.988140	+	0.153557i	$0.950927\pi$
$84$	−10.4242	−	10.5134i	−1.13737	−	1.14711i
$85$		0			0
$86$	2.17157	+	3.55765i	0.234167	+	0.383631i
$87$		−	23.0624i		−	2.47254i
$88$	0.305198	+	4.15685i	0.0325342	+	0.443122i
$89$			12.3693i			1.31114i	0.755132	+	0.655572i	$0.227573\pi$
$89$			12.3693i			1.31114i	−0.755132	+	0.655572i	$0.772427\pi$
$90$		0			0
$91$	14.6686	+	4.77844i	1.53768	+	0.500916i
$92$	1.90524	−	3.70711i	0.198635	−	0.386493i
$93$		−	11.0711i		−	1.14802i
$94$	14.3291	−	8.74643i	1.47793	−	0.902125i
$95$		0			0
$96$	−14.5691	−	6.18466i	−1.48696	−	0.631219i
$97$	8.24621			0.837276			0.418638	−	0.908153i	$-0.362508\pi$
$97$	8.24621			0.837276			0.418638	+	0.908153i	$0.362508\pi$
$98$	0.808986	−	9.86638i	0.0817199	−	0.996655i
$99$		−	7.11529i		−	0.715114i
$100$		0			0
$101$		−	14.0772i		−	1.40073i	−0.713785	−	0.700365i	$-0.753021\pi$
$101$		−	14.0772i		−	1.40073i	0.713785	−	0.700365i	$-0.246979\pi$
$102$	13.9254	−	8.50000i	1.37882	−	0.841625i
$103$			2.31788i			0.228388i	0.993458	+	0.114194i	$0.0364285\pi$
$103$			2.31788i			0.228388i	−0.993458	+	0.114194i	$0.963571\pi$
$104$	16.4481	−	1.20763i	1.61287	−	0.118418i
$105$		0			0
$106$	−4.53553	+	2.76847i	−0.440530	+	0.268898i
$107$	−9.80971			−0.948341			−0.474170	−	0.880433i	$-0.657252\pi$
$107$	−9.80971			−0.948341			−0.474170	+	0.880433i	$0.657252\pi$
$108$	9.10013	+	4.67695i	0.875661	+	0.450040i
$109$	2.82843			0.270914			0.135457	−	0.990783i	$-0.456750\pi$
$109$	2.82843			0.270914			0.135457	+	0.990783i	$0.456750\pi$
$110$		0			0
$111$	6.27476			0.595574
$112$	−3.19211	−	10.0901i	−0.301626	−	0.953426i
$113$		−	4.31371i		−	0.405800i	−0.979200	−	0.202900i	$-0.934963\pi$
$113$		−	4.31371i		−	0.405800i	0.979200	−	0.202900i	$-0.0650366\pi$
$114$	17.2782	−	10.5465i	1.61825	−	0.987773i
$115$		0			0
$116$	7.53553	−	14.6622i	0.699657	−	1.36135i
$117$	−28.1543			−2.60287
$118$	4.12311	+	6.75481i	0.379563	+	0.621830i
$119$	10.3722	+	3.37887i	0.950821	+	0.309740i
$120$		0			0
$121$	8.82843			0.802584
$122$	−14.0772	+	8.59264i	−1.27449	+	0.777941i
$123$	−11.5362			−1.04018
$124$	3.61743	−	7.03858i	0.324855	−	0.632083i
$125$		0			0
$126$	4.17338	+	17.5777i	0.371794	+	1.56594i
$127$	−2.94725			−0.261526			−0.130763	−	0.991414i	$-0.541743\pi$
$127$	−2.94725			−0.261526			−0.130763	+	0.991414i	$0.541743\pi$
$128$	−7.24171	−	8.69239i	−0.640083	−	0.768306i
$129$		−	8.24621i		−	0.726038i
$130$		0			0
$131$	8.87385			0.775312			0.387656	−	0.921804i	$-0.373285\pi$
$131$	8.87385			0.775312			0.387656	+	0.921804i	$0.373285\pi$
$132$	3.76940	−	7.33428i	0.328084	−	0.638367i
$133$	12.8695	+	4.19239i	1.11593	+	0.363526i
$134$	−9.39949	−	15.3990i	−0.811993	−	1.33027i
$135$		0			0
$136$	11.6306	−	0.853923i	0.997316	−	0.0732233i
$137$		−	13.4853i		−	1.15213i	−0.817406	−	0.576063i	$-0.804588\pi$
$137$		−	13.4853i		−	1.15213i	0.817406	−	0.576063i	$-0.195412\pi$
$138$	−7.03858	+	4.29632i	−0.599164	+	0.365727i
$139$	−10.7117			−0.908553			−0.454276	−	0.890861i	$-0.650102\pi$
$139$	−10.7117			−0.908553			−0.454276	+	0.890861i	$0.650102\pi$
$140$		0			0
$141$	−33.2132			−2.79706
$142$	−9.63093	+	5.87868i	−0.808210	+	0.493328i
$143$			8.59264i			0.718553i
$144$	11.2426	+	15.7042i	0.936887	+	1.30868i
$145$		0			0
$146$	9.11387	+	14.9311i	0.754269	+	1.23571i
$147$	−11.5362	+	15.8275i	−0.951487	+	1.30543i
$148$	3.98926	+	2.05025i	0.327915	+	0.168530i
$149$	−2.00000			−0.163846			−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000			−0.163846			−0.0819232	+	0.996639i	$0.526106\pi$
$150$		0			0
$151$			5.03127i			0.409439i	0.978821	+	0.204720i	$0.0656283\pi$
$151$			5.03127i			0.409439i	−0.978821	+	0.204720i	$0.934372\pi$
$152$	14.4309	−	1.05952i	1.17050	−	0.0859384i
$153$	−19.9081			−1.60948
$154$	5.36467	−	1.27371i	0.432297	−	0.102638i
$155$		0			0
$156$	−29.0208	−	14.9150i	−2.32352	−	1.19416i
$157$	10.6615			0.850878			0.425439	−	0.904987i	$-0.360120\pi$
$157$	10.6615			0.850878			0.425439	+	0.904987i	$0.360120\pi$
$158$	−5.03127	+	3.07107i	−0.400267	+	0.244321i
$159$	10.5128			0.833722
$160$		0			0
$161$	−5.24264	−	1.70785i	−0.413178	−	0.134597i
$162$	0.126417	+	0.207107i	0.00993227	+	0.0162718i
$163$	3.20009			0.250650			0.125325	−	0.992116i	$-0.460003\pi$
$163$	3.20009			0.250650			0.125325	+	0.992116i	$0.460003\pi$
$164$	−7.33428	−	3.76940i	−0.572711	−	0.294341i
$165$		0			0
$166$	3.37740	−	2.06155i	0.262137	−	0.160008i
$167$		−	0.960099i		−	0.0742947i	−0.999310	−	0.0371473i	$-0.988173\pi$
$167$		−	0.960099i		−	0.0742947i	0.999310	−	0.0371473i	$-0.0118271\pi$
$168$	−5.01013	+	20.3295i	−0.386540	+	1.56846i
$169$	21.0000			1.61538
$170$		0			0
$171$	−24.7013			−1.88896
$172$	2.69442	−	5.24264i	0.205447	−	0.399748i
$173$	2.41526			0.183629			0.0918144	−	0.995776i	$-0.470733\pi$
$173$	2.41526			0.183629			0.0918144	+	0.995776i	$0.470733\pi$
$174$	−27.8387	+	16.9926i	−2.11045	+	1.28821i
$175$		0			0
$176$	4.79289	−	3.43123i	0.361278	−	0.258639i
$177$		−	15.6569i		−	1.17684i
$178$	14.9311	−	9.11387i	1.11913	−	0.683114i
$179$			2.69442i			0.201390i	0.994917	+	0.100695i	$0.0321067\pi$
$179$			2.69442i			0.201390i	−0.994917	+	0.100695i	$0.967893\pi$
$180$		0			0
$181$			3.41569i			0.253886i	0.991910	+	0.126943i	$0.0405166\pi$
$181$			3.41569i			0.253886i	−0.991910	+	0.126943i	$0.959483\pi$
$182$	−5.03989	−	21.2273i	−0.373582	−	1.57347i
$183$	32.6292			2.41202
$184$	−5.87868	+	0.431615i	−0.433382	+	0.0318191i
$185$		0			0
$186$	−13.3640	+	8.15731i	−0.979893	+	0.598123i
$187$			6.07591i			0.444315i
$188$	−21.1157	−	10.8523i	−1.54002	−	0.791484i
$189$	4.19239	−	12.8695i	0.304951	−	0.936121i
$190$		0			0
$191$			4.67371i			0.338178i	0.985601	+	0.169089i	$0.0540825\pi$
$191$			4.67371i			0.338178i	−0.985601	+	0.169089i	$0.945917\pi$
$192$	3.26918	+	22.1434i	0.235933	+	1.59806i
$193$			14.3137i			1.03032i	0.857093	+	0.515162i	$0.172268\pi$
$193$			14.3137i			1.03032i	−0.857093	+	0.515162i	$0.827732\pi$
$194$	−6.07591	−	9.95406i	−0.436225	−	0.714660i
$195$		0			0
$196$	−12.5059	+	6.29315i	−0.893275	+	0.449511i
$197$		−	14.4853i		−	1.03203i	−0.856578	−	0.516017i	$-0.827414\pi$
$197$		−	14.4853i		−	1.03203i	0.856578	−	0.516017i	$-0.172586\pi$
$198$	−8.58892	+	5.24264i	−0.610388	+	0.372578i
$199$	−22.1023			−1.56679			−0.783394	−	0.621526i	$-0.786513\pi$
$199$	−22.1023			−1.56679			−0.783394	+	0.621526i	$0.786513\pi$
$200$		0			0
$201$			35.6931i			2.51760i
$202$	−16.9926	+	10.3722i	−1.19560	+	0.729788i
$203$	−20.7355	−	6.75481i	−1.45535	−	0.474095i
$204$	−20.5208	−	10.5465i	−1.43674	−	0.738404i
$205$		0			0
$206$	2.79793	−	1.70785i	0.194941	−	0.118991i
$207$	10.0625			0.699395
$208$	−13.5769	−	18.9649i	−0.941392	−	1.31498i
$209$			7.53880i			0.521470i
$210$		0			0
$211$		−	25.7668i		−	1.77386i	−0.461907	−	0.886928i	$-0.652835\pi$
$211$		−	25.7668i		−	1.77386i	0.461907	−	0.886928i	$-0.347165\pi$
$212$	6.68368	+	3.43503i	0.459037	+	0.235919i
$213$	22.3234			1.52957
$214$	7.22792	+	11.8414i	0.494091	+	0.809459i
$215$		0			0
$216$	−1.05952	−	14.4309i	−0.0720912	−	0.981896i
$217$	−9.95406	−	3.24264i	−0.675725	−	0.220125i
$218$	−2.08402	−	3.41421i	−0.141148	−	0.231240i
$219$		−	34.6085i		−	2.33863i
$220$		0			0
$221$	24.0416			1.61722
$222$	−4.62332	−	7.57430i	−0.310297	−	0.508354i
$223$		−	9.55274i		−	0.639699i	−0.947468	−	0.319849i	$-0.896368\pi$
$223$		−	9.55274i		−	0.639699i	0.947468	−	0.319849i	$-0.103632\pi$
$224$	−9.82786	+	11.2877i	−0.656652	+	0.754194i
$225$		0			0
$226$	−5.20711	+	3.17840i	−0.346372	+	0.211424i
$227$		−	2.31788i		−	0.153843i	−0.997037	−	0.0769217i	$-0.975491\pi$
$227$		−	2.31788i		−	0.153843i	0.997037	−	0.0769217i	$-0.0245091\pi$
$228$	−25.4616	−	13.0858i	−1.68623	−	0.866627i
$229$		−	2.41526i		−	0.159605i	−0.996811	−	0.0798024i	$-0.974571\pi$
$229$		−	2.41526i		−	0.159605i	0.996811	−	0.0798024i	$-0.0254289\pi$
$230$		0			0
$231$	−10.3722	−	3.37887i	−0.682443	−	0.222313i
$232$	−23.2511	+	1.70711i	−1.52651	+	0.112077i
$233$		−	23.7990i		−	1.55912i	−0.626325	−	0.779562i	$-0.715442\pi$
$233$		−	23.7990i		−	1.55912i	0.626325	−	0.779562i	$-0.284558\pi$
$234$	20.7445	+	33.9853i	1.35611	+	2.22169i
$235$		0			0
$236$	5.11582	−	9.95406i	0.333011	−	0.647954i
$237$	11.6619			0.757522
$238$	−3.56374	−	15.0100i	−0.231003	−	0.972953i
$239$			8.84175i			0.571926i	0.958241	+	0.285963i	$0.0923134\pi$
$239$			8.84175i			0.571926i	−0.958241	+	0.285963i	$0.907687\pi$
$240$		0			0
$241$			7.53880i			0.485617i	0.970074	+	0.242808i	$0.0780686\pi$
$241$			7.53880i			0.485617i	−0.970074	+	0.242808i	$0.921931\pi$
$242$	−6.50490	−	10.6569i	−0.418151	−	0.685049i
$243$		−	15.8275i		−	1.01533i
$244$	20.7445	+	10.6615i	1.32803	+	0.682531i
$245$		0			0
$246$	8.50000	+	13.9254i	0.541940	+	0.887851i
$247$	29.8301			1.89804
$248$	−11.1617	+	0.819496i	−0.708768	+	0.0520380i
$249$	−7.82843			−0.496106
$250$		0			0
$251$	−20.9433			−1.32193			−0.660965	−	0.750417i	$-0.729853\pi$
$251$	−20.9433			−1.32193			−0.660965	+	0.750417i	$0.729853\pi$
$252$	18.1431	−	17.9892i	1.14291	−	1.13321i
$253$		−	3.07107i		−	0.193076i
$254$	2.17157	+	3.55765i	0.136257	+	0.223227i
$255$		0			0
$256$	−5.15685	+	15.1462i	−0.322303	+	0.946636i
$257$	23.3238			1.45490			0.727450	−	0.686161i	$-0.240706\pi$
$257$	23.3238			1.45490			0.727450	+	0.686161i	$0.240706\pi$
$258$	−9.95406	+	6.07591i	−0.619713	+	0.378270i
$259$	1.83783	−	5.64167i	0.114197	−	0.350556i
$260$		0			0
$261$	39.7990			2.46350
$262$	−6.53836	−	10.7117i	−0.403942	−	0.661770i
$263$	14.7363			0.908677			0.454338	−	0.890829i	$-0.349876\pi$
$263$	14.7363			0.908677			0.454338	+	0.890829i	$0.349876\pi$
$264$	−11.6306	+	0.853923i	−0.715814	+	0.0525553i
$265$		0			0
$266$	−4.42178	−	18.6239i	−0.271117	−	1.14190i
$267$	−34.6085			−2.11801
$268$	−11.6626	+	22.6924i	−0.712406	+	1.38616i
$269$		−	14.0772i		−	0.858300i	−0.903233	−	0.429150i	$-0.858813\pi$
$269$		−	14.0772i		−	0.858300i	0.903233	−	0.429150i	$-0.141187\pi$
$270$		0			0
$271$	−4.23808			−0.257445			−0.128723	−	0.991681i	$-0.541088\pi$
$271$	−4.23808			−0.257445			−0.128723	+	0.991681i	$0.541088\pi$
$272$	−9.60035	−	13.4102i	−0.582107	−	0.813112i
$273$	−13.3698	+	41.0416i	−0.809174	+	2.48395i
$274$	−16.2782	+	9.93613i	−0.983400	+	0.600264i
$275$		0			0
$276$	10.3722	+	5.33074i	0.624335	+	0.320873i
$277$			25.8995i			1.55615i	0.628171	+	0.778075i	$0.283804\pi$
$277$			25.8995i			1.55615i	−0.628171	+	0.778075i	$0.716196\pi$
$278$	7.89250	+	12.9301i	0.473361	+	0.775498i
$279$	19.1055			1.14382
$280$		0			0
$281$	−0.970563			−0.0578989			−0.0289495	−	0.999581i	$-0.509216\pi$
$281$	−0.970563			−0.0578989			−0.0289495	+	0.999581i	$0.509216\pi$
$282$	24.4719	+	40.0919i	1.45728	+	2.38744i
$283$			12.6319i			0.750887i	0.926845	+	0.375444i	$0.122510\pi$
$283$			12.6319i			0.750887i	−0.926845	+	0.375444i	$0.877490\pi$
$284$	14.1924	+	7.29408i	0.842163	+	0.432824i
$285$		0			0
$286$	10.3722	−	6.33117i	0.613323	−	0.374370i
$287$	−3.37887	+	10.3722i	−0.199448	+	0.612254i
$288$	10.6729	−	25.1421i	0.628909	−	1.48151i
$289$		0			0
$290$		0			0
$291$			23.0723i			1.35252i
$292$	11.3082	−	22.0028i	0.661762	−	1.28762i
$293$	16.4924			0.963498			0.481749	−	0.876309i	$-0.340002\pi$
$293$	16.4924			0.963498			0.481749	+	0.876309i	$0.340002\pi$
$294$	27.6055	+	2.26349i	1.60998	+	0.132009i
$295$		0			0
$296$	−0.464466	−	6.32612i	−0.0269965	−	0.367698i
$297$	7.53880			0.437445
$298$	1.47363	+	2.41421i	0.0853648	+	0.139852i
$299$	−12.1518			−0.702758
$300$		0			0
$301$	−7.41421	−	2.41526i	−0.427348	−	0.139213i
$302$	6.07328	−	3.70711i	0.349478	−	0.213320i
$303$	39.3870			2.26272
$304$	−11.9118	−	16.6389i	−0.683189	−	0.954308i
$305$		0			0
$306$	14.6686	+	24.0312i	0.838546	+	1.37377i
$307$			3.75803i			0.214482i	0.994233	+	0.107241i	$0.0342017\pi$
$307$			3.75803i			0.214482i	−0.994233	+	0.107241i	$0.965798\pi$
$308$	−5.49026	−	5.53725i	−0.312836	−	0.315514i
$309$	−6.48528			−0.368935
$310$		0			0
$311$	22.3835			1.26925			0.634625	−	0.772820i	$-0.281155\pi$
$311$	22.3835			1.26925			0.634625	+	0.772820i	$0.281155\pi$
$312$	3.37887	+	46.0208i	0.191291	+	2.60542i
$313$	28.1543			1.59138			0.795688	−	0.605706i	$-0.207109\pi$
$313$	28.1543			1.59138			0.795688	+	0.605706i	$0.207109\pi$
$314$	−7.85551	−	12.8695i	−0.443312	−	0.726270i
$315$		0			0
$316$	7.41421	+	3.81048i	0.417082	+	0.214356i
$317$		−	14.3431i		−	0.805591i	−0.915290	−	0.402796i	$-0.868039\pi$
$317$		−	14.3431i		−	0.805591i	0.915290	−	0.402796i	$-0.131961\pi$
$318$	−7.74599	−	12.6901i	−0.434374	−	0.711627i
$319$		−	12.1466i		−	0.680077i
$320$		0			0
$321$		−	27.4469i		−	1.53194i
$322$	1.80129	+	7.58679i	0.100382	+	0.422795i
$323$	21.0930			1.17365
$324$	0.156854	−	0.305198i	0.00871412	−	0.0169554i
$325$		0			0
$326$	−2.35786	−	3.86285i	−0.130590	−	0.213943i
$327$			7.91375i			0.437631i
$328$	0.853923	+	11.6306i	0.0471500	+	0.642192i
$329$	−9.72792	+	29.8622i	−0.536318	+	1.64635i
$330$		0			0
$331$		−	18.1458i		−	0.997383i	−0.866779	−	0.498692i	$-0.833814\pi$
$331$		−	18.1458i		−	0.997383i	0.866779	−	0.498692i	$-0.166186\pi$
$332$	−4.97703	−	2.55791i	−0.273150	−	0.140383i
$333$			10.8284i			0.593394i
$334$	−1.15894	+	0.707413i	−0.0634145	+	0.0387079i
$335$		0			0
$336$	28.2315	−	8.93131i	1.54015	−	0.487243i
$337$			24.7990i			1.35089i	0.737412	+	0.675444i	$0.236048\pi$
$337$			24.7990i			1.35089i	−0.737412	+	0.675444i	$0.763952\pi$
$338$	−15.4731	−	25.3492i	−0.841624	−	1.37882i
$339$	12.0695			0.655523
$340$		0			0
$341$		−	5.83095i		−	0.315764i
$342$	18.2003	+	29.8172i	0.984158	+	1.61233i
$343$	10.8517	+	15.0080i	0.585938	+	0.810356i
$344$	−8.31371	+	0.610396i	−0.448245	+	0.0329103i
$345$		0			0
$346$	−1.77959	−	2.91548i	−0.0956716	−	0.156737i
$347$	−31.1556			−1.67252			−0.836260	−	0.548333i	$-0.815263\pi$
$347$	−31.1556			−1.67252			−0.836260	+	0.548333i	$0.815263\pi$
$348$	41.0239	+	21.0839i	2.19911	+	1.13022i
$349$		−	2.41526i		−	0.129286i	−0.997908	−	0.0646429i	$-0.979409\pi$
$349$		−	2.41526i		−	0.129286i	0.997908	−	0.0646429i	$-0.0205908\pi$
$350$		0			0
$351$		−	29.8301i		−	1.59221i
$352$	−7.67333	−	3.25736i	−0.408990	−	0.173618i
$353$	−11.6619			−0.620701			−0.310350	−	0.950622i	$-0.600446\pi$
$353$	−11.6619			−0.620701			−0.310350	+	0.950622i	$0.600446\pi$
$354$	−18.8995	+	11.5362i	−1.00450	+	0.613141i
$355$		0			0
$356$	−22.0028	−	11.3082i	−1.16615	−	0.599333i
$357$	−9.45384	+	29.0208i	−0.500350	+	1.53594i
$358$	3.25245	−	1.98528i	0.171897	−	0.104925i
$359$			22.5667i			1.19102i	0.803347	+	0.595512i	$0.203051\pi$
$359$			22.5667i			1.19102i	−0.803347	+	0.595512i	$0.796949\pi$
$360$		0			0
$361$	7.17157			0.377451
$362$	4.12311	−	2.51673i	0.216706	−	0.132276i
$363$			24.7013i			1.29648i
$364$	−21.9102	+	21.7243i	−1.14841	+	1.13866i
$365$		0			0
$366$	−24.0416	−	39.3870i	−1.25668	−	2.05879i
$367$		−	14.4697i		−	0.755313i	−0.925946	−	0.377656i	$-0.876730\pi$
$367$		−	14.4697i		−	0.755313i	0.925946	−	0.377656i	$-0.123270\pi$
$368$	4.85249	+	6.77817i	0.252954	+	0.353337i
$369$		−	19.9081i		−	1.03638i
$370$		0			0
$371$	3.07914	−	9.45215i	0.159861	−	0.490731i
$372$	19.6935	+	10.1213i	1.02106	+	0.524766i
$373$			10.5858i			0.548111i	0.961714	+	0.274056i	$0.0883652\pi$
$373$			10.5858i			0.548111i	−0.961714	+	0.274056i	$0.911635\pi$
$374$	7.33428	−	4.47681i	0.379246	−	0.231490i
$375$		0			0
$376$	2.45849	+	33.4851i	0.126787	+	1.72686i
$377$	−48.0624			−2.47534
$378$	−18.6239	+	4.42178i	−0.957910	+	0.227432i
$379$		−	22.8195i		−	1.17216i	−0.810253	−	0.586080i	$-0.800671\pi$
$379$		−	22.8195i		−	1.17216i	0.810253	−	0.586080i	$-0.199329\pi$
$380$		0			0
$381$		−	8.24621i		−	0.422466i
$382$	5.64167	−	3.44365i	0.288653	−	0.176193i
$383$		−	12.5495i		−	0.641250i	−0.947206	−	0.320625i	$-0.896107\pi$
$383$		−	12.5495i		−	0.641250i	0.947206	−	0.320625i	$-0.103893\pi$
$384$	24.3207	−	20.2618i	1.24111	−	1.03398i
$385$		0			0
$386$	17.2782	−	10.5465i	0.879436	−	0.536804i
$387$	14.2306			0.723382
$388$	−7.53880	+	14.6686i	−0.382724	+	0.744683i
$389$	15.5563			0.788738			0.394369	−	0.918952i	$-0.370963\pi$
$389$	15.5563			0.788738			0.394369	+	0.918952i	$0.370963\pi$
$390$		0			0
$391$	−8.59264			−0.434549
$392$	16.8110	+	10.4590i	0.849082	+	0.528261i
$393$			24.8284i			1.25243i
$394$	−17.4853	+	10.6729i	−0.880896	+	0.537695i
$395$		0			0
$396$	12.6569	+	6.50490i	0.636031	+	0.326883i
$397$	30.5696			1.53424			0.767122	−	0.641502i	$-0.221688\pi$
$397$	30.5696			1.53424			0.767122	+	0.641502i	$0.221688\pi$
$398$	16.2852	+	26.6798i	0.816305	+	1.33734i
$399$	−11.7300	+	36.0081i	−0.587235	+	1.80266i
$400$		0			0
$401$	28.4558			1.42102			0.710509	−	0.703689i	$-0.248465\pi$
$401$	28.4558			1.42102			0.710509	+	0.703689i	$0.248465\pi$
$402$	43.0854	−	26.2992i	2.14891	−	1.31168i
$403$	−23.0723			−1.14932
$404$	25.0408	+	12.8695i	1.24583	+	0.640283i
$405$		0			0
$406$	7.12440	+	30.0070i	0.353578	+	1.48922i
$407$	3.30481			0.163814
$408$	2.38922	+	32.5416i	0.118284	+	1.61105i
$409$			7.53880i			0.372770i	0.982477	+	0.186385i	$0.0596771\pi$
$409$			7.53880i			0.372770i	−0.982477	+	0.186385i	$0.940323\pi$
$410$		0			0
$411$	37.7309			1.86113
$412$	−4.12311	−	2.11904i	−0.203131	−	0.104398i
$413$	−14.0772	−	4.58579i	−0.692692	−	0.225652i
$414$	−7.41421	−	12.1466i	−0.364389	−	0.596971i
$415$		0			0
$416$	−12.8890	+	30.3624i	−0.631933	+	1.48864i
$417$		−	29.9706i		−	1.46766i
$418$	9.10013	−	5.55468i	0.445102	−	0.271688i
$419$	−14.9498			−0.730344			−0.365172	−	0.930940i	$-0.618990\pi$
$419$	−14.9498			−0.730344			−0.365172	+	0.930940i	$0.618990\pi$
$420$		0			0
$421$	−23.3137			−1.13624			−0.568120	−	0.822946i	$-0.692329\pi$
$421$	−23.3137			−1.13624			−0.568120	+	0.822946i	$0.692329\pi$
$422$	−31.1032	+	18.9853i	−1.51408	+	0.924189i
$423$		−	57.3164i		−	2.78682i
$424$	−0.778175	−	10.5989i	−0.0377915	−	0.514728i
$425$		0			0
$426$	−16.4481	−	26.9467i	−0.796915	−	1.30557i
$427$	9.55688	−	29.3371i	0.462490	−	1.41972i
$428$	8.96817	−	17.4497i	0.433493	−	0.843465i
$429$	−24.0416			−1.16074
$430$		0			0
$431$		−	25.1564i		−	1.21174i	−0.795564	−	0.605870i	$-0.792825\pi$
$431$		−	25.1564i		−	1.21174i	0.795564	−	0.605870i	$-0.207175\pi$
$432$	−16.6389	+	11.9118i	−0.800541	+	0.573107i
$433$	4.12311			0.198144			0.0990719	−	0.995080i	$-0.468413\pi$
$433$	4.12311			0.198144			0.0990719	+	0.995080i	$0.468413\pi$
$434$	3.42006	+	14.4048i	0.164168	+	0.691454i
$435$		0			0
$436$	−2.58579	+	5.03127i	−0.123837	+	0.240954i
$437$	−10.6615			−0.510007
$438$	−41.7762	+	25.5000i	−1.99614	+	1.21844i
$439$	5.59587			0.267076			0.133538	−	0.991044i	$-0.457366\pi$
$439$	5.59587			0.267076			0.133538	+	0.991044i	$0.457366\pi$
$440$		0			0
$441$	−27.3137	−	19.9081i	−1.30065	−	0.948005i
$442$	−17.7142	−	29.0208i	−0.842578	−	1.38038i
$443$	15.7042			0.746130			0.373065	−	0.927805i	$-0.378307\pi$
$443$	15.7042			0.746130			0.373065	+	0.927805i	$0.378307\pi$
$444$	−5.73647	+	11.1617i	−0.272241	+	0.529710i
$445$		0			0
$446$	−11.5312	+	7.03858i	−0.546017	+	0.333286i
$447$		−	5.59587i		−	0.264675i
$448$	20.8668	+	3.54632i	0.985864	+	0.167548i
$449$	0.656854			0.0309989			0.0154994	−	0.999880i	$-0.495066\pi$
$449$	0.656854			0.0309989			0.0154994	+	0.999880i	$0.495066\pi$
$450$		0			0
$451$	−6.07591			−0.286104
$452$	7.67333	+	3.94365i	0.360923	+	0.185494i
$453$	−14.0772			−0.661403
$454$	−2.79793	+	1.70785i	−0.131313	+	0.0801532i
$455$		0			0
$456$	2.96447	+	40.3766i	0.138824	+	1.89081i
$457$			12.5147i			0.585414i	0.956202	+	0.292707i	$0.0945560\pi$
$457$			12.5147i			0.585414i	−0.956202	+	0.292707i	$0.905444\pi$
$458$	−2.91548	+	1.77959i	−0.136231	+	0.0831550i
$459$		−	21.0930i		−	0.984539i
$460$		0			0
$461$		−	14.0772i		−	0.655639i	−0.944740	−	0.327819i	$-0.893686\pi$
$461$		−	14.0772i		−	0.655639i	0.944740	−	0.327819i	$-0.106314\pi$
$462$	3.56374	+	15.0100i	0.165800	+	0.698328i
$463$	−24.2931			−1.12900			−0.564499	−	0.825434i	$-0.690931\pi$
$463$	−24.2931			−1.12900			−0.564499	+	0.825434i	$0.690931\pi$
$464$	19.1924	+	26.8088i	0.890984	+	1.24457i
$465$		0			0
$466$	−28.7279	+	17.5354i	−1.33080	+	0.812312i
$467$		−	30.2972i		−	1.40199i	−0.713167	−	0.700994i	$-0.752740\pi$
$467$		−	30.2972i		−	1.40199i	0.713167	−	0.700994i	$-0.247260\pi$
$468$	25.7391	−	50.0816i	1.18979	−	2.31502i
$469$	32.0919	+	10.4543i	1.48187	+	0.482734i
$470$		0			0
$471$			29.8301i			1.37450i
$472$	−15.7850	+	1.15894i	−0.726564	+	0.0533446i
$473$		−	4.34315i		−	0.199698i
$474$	−8.59264	−	14.0772i	−0.394673	−	0.646586i
$475$		0			0
$476$	−15.4928	+	15.3614i	−0.710113	+	0.704087i
$477$			18.1421i			0.830671i
$478$	10.6729	−	6.51472i	0.488169	−	0.297976i
$479$	16.7876			0.767045			0.383522	−	0.923532i	$-0.374711\pi$
$479$	16.7876			0.767045			0.383522	+	0.923532i	$0.374711\pi$
$480$		0			0
$481$		−	13.0767i		−	0.596248i
$482$	9.10013	−	5.55468i	0.414500	−	0.253009i
$483$	4.77844	−	14.6686i	0.217426	−	0.667442i
$484$	−8.07107	+	15.7042i	−0.366867	+	0.713828i
$485$		0			0
$486$	−19.1055	+	11.6619i	−0.866642	+	0.528995i
$487$	31.4084			1.42325			0.711626	−	0.702559i	$-0.247959\pi$
$487$	31.4084			1.42325			0.711626	+	0.702559i	$0.247959\pi$
$488$	−2.41526	−	32.8963i	−0.109334	−	1.48915i
$489$			8.95362i			0.404897i
$490$		0			0
$491$			9.55688i			0.431296i	0.976471	+	0.215648i	$0.0691863\pi$
$491$			9.55688i			0.431296i	−0.976471	+	0.215648i	$0.930814\pi$
$492$	10.5465	−	20.5208i	0.475474	−	0.925150i
$493$	−33.9853			−1.53062
$494$	−21.9792	−	36.0081i	−0.988890	−	1.62008i
$495$		0			0
$496$	9.21329	+	12.8695i	0.413689	+	0.577859i
$497$	6.53836	−	20.0711i	0.293286	−	0.900310i
$498$	5.76809	+	9.44975i	0.258474	+	0.423453i
$499$		−	8.84175i		−	0.395811i	−0.980221	−	0.197906i	$-0.936586\pi$
$499$		−	8.84175i		−	0.395811i	0.980221	−	0.197906i	$-0.0634140\pi$
$500$		0			0
$501$	2.68629			0.120015
$502$	15.4313	+	25.2808i	0.688733	+	1.12834i
$503$		−	19.3867i		−	0.864410i	−0.901775	−	0.432205i	$-0.857736\pi$
$503$		−	19.3867i		−	0.864410i	0.901775	−	0.432205i	$-0.142264\pi$
$504$	−35.0830	−	8.64605i	−1.56272	−	0.385126i
$505$		0			0
$506$	−3.70711	+	2.26280i	−0.164801	+	0.100594i
$507$			58.7566i			2.60947i
$508$	2.69442	−	5.24264i	0.119545	−	0.232605i
$509$		−	8.24621i		−	0.365507i	−0.983159	−	0.182753i	$-0.941499\pi$
$509$		−	8.24621i		−	0.365507i	0.983159	−	0.182753i	$-0.0585010\pi$
$510$		0			0
$511$	−31.1167	−	10.1366i	−1.37652	−	0.448417i
$512$	22.0827	−	4.93503i	0.975927	−	0.218100i
$513$		−	26.1716i		−	1.15550i
$514$	−17.1853	−	28.1543i	−0.758010	−	1.24183i
$515$		0			0
$516$	14.6686	+	7.53880i	0.645747	+	0.331877i
$517$	−17.4929			−0.769335
$518$	−8.16424	+	1.93839i	−0.358716	+	0.0851681i
$519$			6.75773i			0.296632i
$520$		0			0
$521$			28.8617i			1.26446i	0.774782	+	0.632228i	$0.217859\pi$
$521$			28.8617i			1.26446i	−0.774782	+	0.632228i	$0.782141\pi$
$522$	−29.3244	−	48.0416i	−1.28349	−	2.10273i
$523$			8.39380i			0.367035i	0.983016	+	0.183518i	$0.0587484\pi$
$523$			8.39380i			0.367035i	−0.983016	+	0.183518i	$0.941252\pi$
$524$	−8.11259	+	15.7850i	−0.354400	+	0.689571i
$525$		0			0
$526$	−10.8579	−	17.7882i	−0.473425	−	0.775604i
$527$	−16.3146			−0.710676
$528$	9.60035	+	13.4102i	0.417802	+	0.583604i
$529$	−18.6569			−0.811168
$530$		0			0
$531$	27.0192			1.17253
$532$	−19.2230	+	19.0599i	−0.833424	+	0.826351i
$533$			24.0416i			1.04136i
$534$	25.5000	+	41.7762i	1.10349	+	1.80783i
$535$		0			0
$536$	35.9853	−	2.64205i	1.55433	−	0.114119i
$537$	−7.53880			−0.325323
$538$	−16.9926	+	10.3722i	−0.732605	+	0.447179i
$539$	−6.07591	+	8.33609i	−0.261708	+	0.359061i
$540$		0			0
$541$	1.75736			0.0755548			0.0377774	−	0.999286i	$-0.487972\pi$
$541$	1.75736			0.0755548			0.0377774	+	0.999286i	$0.487972\pi$
$542$	3.12267	+	5.11582i	0.134130	+	0.219743i
$543$	−9.55688			−0.410125
$544$	−9.11387	+	21.4695i	−0.390754	+	0.920495i
$545$		0			0
$546$	59.3926	−	14.1013i	2.54177	−	0.603479i
$547$	−9.80971			−0.419433			−0.209716	−	0.977762i	$-0.567254\pi$
$547$	−9.80971			−0.419433			−0.209716	+	0.977762i	$0.567254\pi$
$548$	23.9879	+	12.3284i	1.02471	+	0.526644i
$549$			56.3087i			2.40319i
$550$		0			0
$551$	−42.1678			−1.79641
$552$	−1.20763	−	16.4481i	−0.0514001	−	0.700080i
$553$	3.41569	−	10.4853i	0.145250	−	0.445880i
$554$	31.2635	−	19.0831i	1.32826	−	0.810762i
$555$		0			0
$556$	9.79276	−	19.0542i	0.415306	−	0.808078i
$557$		−	33.3137i		−	1.41155i	−0.708437	−	0.705774i	$-0.750600\pi$
$557$		−	33.3137i		−	1.41155i	0.708437	−	0.705774i	$-0.249400\pi$
$558$	−14.0772	−	23.0624i	−0.595934	−	0.976307i
$559$	−17.1853			−0.726860
$560$		0			0
$561$	−17.0000			−0.717741
$562$	0.715123	+	1.17157i	0.0301656	+	0.0494198i
$563$			37.2509i			1.56994i	0.619536	+	0.784968i	$0.287321\pi$
$563$			37.2509i			1.56994i	−0.619536	+	0.784968i	$0.712679\pi$
$564$	30.3640	−	59.0804i	1.27855	−	2.48773i
$565$		0			0
$566$	15.2480	−	9.30733i	0.640922	−	0.391216i
$567$	−0.431615	−	0.140603i	−0.0181261	−	0.00590478i
$568$	−1.65241	−	22.5061i	−0.0693334	−	0.944335i
$569$	−26.3137			−1.10313			−0.551564	−	0.834133i	$-0.685969\pi$
$569$	−26.3137			−1.10313			−0.551564	+	0.834133i	$0.685969\pi$
$570$		0			0
$571$			24.2931i			1.01664i	0.861169	+	0.508318i	$0.169733\pi$
$571$			24.2931i			1.01664i	−0.861169	+	0.508318i	$0.830267\pi$
$572$	−15.2848	−	7.85551i	−0.639089	−	0.328455i
$573$	−13.0767			−0.546288
$574$	15.0100	−	3.56374i	0.626505	−	0.148748i
$575$		0			0
$576$	−38.2132	+	5.64167i	−1.59222	+	0.235070i
$577$	−15.7850			−0.657139			−0.328569	−	0.944480i	$-0.606566\pi$
$577$	−15.7850			−0.657139			−0.328569	+	0.944480i	$0.606566\pi$
$578$		0			0
$579$	−40.0488			−1.66437
$580$		0			0
$581$	−2.29289	+	7.03858i	−0.0951252	+	0.292010i
$582$	27.8508	−	17.0000i	1.15445	−	0.704673i
$583$	5.53694			0.229317
$584$	−34.8918	+	2.56177i	−1.44383	+	0.106007i
$585$		0			0
$586$	−12.1518	−	19.9081i	−0.501987	−	0.822397i
$587$			29.8172i			1.23069i	0.788260	+	0.615343i	$0.210982\pi$
$587$			29.8172i			1.23069i	−0.788260	+	0.615343i	$0.789018\pi$
$588$	−17.6078	−	34.9905i	−0.726133	−	1.44299i
$589$	−20.2426			−0.834083
$590$		0			0
$591$	40.5288			1.66713
$592$	−7.29408	+	5.22183i	−0.299785	+	0.214616i
$593$	−0.707413			−0.0290500			−0.0145250	−	0.999895i	$-0.504624\pi$
$593$	−0.707413			−0.0290500			−0.0145250	+	0.999895i	$0.504624\pi$
$594$	−5.55468	−	9.10013i	−0.227911	−	0.373383i
$595$		0			0
$596$	1.82843	−	3.55765i	0.0748953	−	0.145727i
$597$		−	61.8406i		−	2.53097i
$598$	8.95362	+	14.6686i	0.366141	+	0.599842i
$599$			6.75773i			0.276113i	0.990424	+	0.138057i	$0.0440856\pi$
$599$			6.75773i			0.276113i	−0.990424	+	0.138057i	$0.955914\pi$
$600$		0			0
$601$			7.53880i			0.307514i	0.988109	+	0.153757i	$0.0491373\pi$
$601$			7.53880i			0.307514i	−0.988109	+	0.153757i	$0.950863\pi$
$602$	2.54741	+	10.7293i	0.103825	+	0.437295i
$603$	−61.5961			−2.50839
$604$	−8.94975	−	4.59966i	−0.364160	−	0.187157i
$605$		0			0
$606$	−29.0208	−	47.5443i	−1.17889	−	1.93135i
$607$		−	31.6550i		−	1.28484i	−0.766354	−	0.642418i	$-0.777931\pi$
$607$		−	31.6550i		−	1.28484i	0.766354	−	0.642418i	$-0.222069\pi$
$608$	−11.3082	+	26.6386i	−0.458608	+	1.08034i
$609$	18.8995	−	58.0165i	0.765846	−	2.35095i
$610$		0			0
$611$			69.2170i			2.80022i
$612$	18.2003	−	35.4130i	0.735702	−	1.43149i
$613$		−	45.1127i		−	1.82208i	−0.412313	−	0.911042i	$-0.635279\pi$
$613$		−	45.1127i		−	1.82208i	0.412313	−	0.911042i	$-0.364721\pi$
$614$	4.53635	−	2.76897i	0.183072	−	0.111746i
$615$		0			0
$616$	−2.63876	+	10.7072i	−0.106319	+	0.431407i
$617$			22.0000i			0.885687i	0.896599	+	0.442843i	$0.146030\pi$
$617$			22.0000i			0.885687i	−0.896599	+	0.442843i	$0.853970\pi$
$618$	4.77844	+	7.82843i	0.192217	+	0.314906i
$619$	20.0656			0.806504			0.403252	−	0.915089i	$-0.367880\pi$
$619$	20.0656			0.806504			0.403252	+	0.915089i	$0.367880\pi$
$620$		0			0
$621$			10.6615i			0.427830i
$622$	−16.4924	−	27.0192i	−0.661286	−	1.08337i
$623$	−10.1366	+	31.1167i	−0.406114	+	1.24666i
$624$	53.0624	−	37.9874i	2.12420	−	1.52071i
$625$		0			0
$626$	−20.7445	−	33.9853i	−0.829116	−	1.35832i
$627$	−21.0930			−0.842375
$628$	−9.74686	+	18.9649i	−0.388942	+	0.756781i
$629$		−	9.24664i		−	0.368688i
$630$		0			0
$631$		−	6.25206i		−	0.248891i	−0.992226	−	0.124445i	$-0.960285\pi$
$631$		−	6.25206i		−	0.248891i	0.992226	−	0.124445i	$-0.0397152\pi$
$632$	−0.863230	−	11.7574i	−0.0343374	−	0.467683i
$633$	72.0937			2.86547
$634$	−17.3137	+	10.5682i	−0.687615	+	0.419717i
$635$		0			0
$636$	−9.61098	+	18.7005i	−0.381100	+	0.741522i
$637$	32.9848	+	24.0416i	1.30691	+	0.952564i
$638$	−14.6622	+	8.94975i	−0.580482	+	0.354324i
$639$			38.5237i			1.52397i
$640$		0			0
$641$	−26.8284			−1.05966			−0.529830	−	0.848104i	$-0.677744\pi$
$641$	−26.8284			−1.05966			−0.529830	+	0.848104i	$0.677744\pi$
$642$	−33.1314	+	20.2232i	−1.30759	+	0.798148i
$643$		−	14.8674i		−	0.586313i	−0.956064	−	0.293156i	$-0.905294\pi$
$643$		−	14.8674i		−	0.586313i	0.956064	−	0.293156i	$-0.0947057\pi$
$644$	7.83085	−	7.76440i	0.308579	−	0.305960i
$645$		0			0
$646$	−15.5416	−	25.4616i	−0.611477	−	1.00177i
$647$			21.8210i			0.857874i	0.903334	+	0.428937i	$0.141112\pi$
$647$			21.8210i			0.857874i	−0.903334	+	0.428937i	$0.858888\pi$
$648$	−0.483979	+	0.0355339i	−0.0190125	+	0.00139590i
$649$		−	8.24621i		−	0.323692i
$650$		0			0
$651$	9.07269	−	27.8508i	0.355587	−	1.09156i
$652$	−2.92556	+	5.69239i	−0.114574	+	0.222931i
$653$		−	1.55635i		−	0.0609047i	−0.999536	−	0.0304523i	$-0.990305\pi$
$653$		−	1.55635i		−	0.0609047i	0.999536	−	0.0304523i	$-0.00969477\pi$
$654$	9.55274	−	5.83095i	0.373542	−	0.228008i
$655$		0			0
$656$	13.4102	−	9.60035i	0.523580	−	0.374831i
$657$	59.7243			2.33007
$658$	43.2145	−	10.2602i	1.68468	−	0.399984i
$659$		−	29.9348i		−	1.16609i	−0.812438	−	0.583047i	$-0.801860\pi$
$659$		−	29.9348i		−	1.16609i	0.812438	−	0.583047i	$-0.198140\pi$
$660$		0			0
$661$			38.8158i			1.50976i	0.655863	+	0.754880i	$0.272305\pi$
$661$			38.8158i			1.50976i	−0.655863	+	0.754880i	$0.727695\pi$
$662$	−21.9039	+	13.3701i	−0.851320	+	0.519642i
$663$			67.2669i			2.61243i
$664$	0.579471	+	7.89250i	0.0224878	+	0.306289i
$665$		0			0
$666$	13.0711	−	7.97852i	0.506494	−	0.309162i
$667$	17.1778			0.665129
$668$	1.70785	+	0.877735i	0.0660786	+	0.0339606i
$669$	26.7279			1.03336
$670$		0			0
$671$	17.1853			0.663430
$672$	−31.5823	−	27.4977i	−1.21832	−	1.06075i
$673$		−	4.00000i		−	0.154189i	−0.997024	−	0.0770943i	$-0.975436\pi$
$673$		−	4.00000i		−	0.154189i	0.997024	−	0.0770943i	$-0.0245643\pi$
$674$	29.9350	−	18.2722i	1.15305	−	0.703819i
$675$		0			0
$676$	−19.1985	+	37.3553i	−0.738403	+	1.43674i
$677$	−11.6619			−0.448203			−0.224102	−	0.974566i	$-0.571945\pi$
$677$	−11.6619			−0.448203			−0.224102	+	0.974566i	$0.571945\pi$
$678$	−8.89294	−	14.5691i	−0.341531	−	0.559524i
$679$	20.7445	+	6.75773i	0.796100	+	0.259338i
$680$		0			0
$681$	6.48528			0.248517
$682$	−7.03858	+	4.29632i	−0.269521	+	0.164515i
$683$	−11.0305			−0.422070			−0.211035	−	0.977478i	$-0.567683\pi$
$683$	−11.0305			−0.422070			−0.211035	+	0.977478i	$0.567683\pi$
$684$	22.5823	−	43.9393i	0.863456	−	1.68006i
$685$		0			0
$686$	10.1206	−	24.1573i	0.386405	−	0.922329i
$687$	6.75773			0.257824
$688$	6.86246	+	9.58579i	0.261629	+	0.365455i
$689$		−	21.9090i		−	0.834666i
$690$		0			0
$691$	−19.0231			−0.723673			−0.361837	−	0.932241i	$-0.617850\pi$
$691$	−19.0231			−0.723673			−0.361837	+	0.932241i	$0.617850\pi$
$692$	−2.20806	+	4.29632i	−0.0839380	+	0.163322i
$693$	5.83095	−	17.8995i	0.221500	−	0.679946i
$694$	22.9558	+	37.6081i	0.871392	+	1.42759i
$695$		0			0
$696$	−4.77637	−	65.0551i	−0.181048	−	2.46591i
$697$			17.0000i			0.643921i
$698$	−2.91548	+	1.77959i	−0.110352	+	0.0673586i
$699$	66.5880			2.51859
$700$		0			0
$701$	−11.1716			−0.421944			−0.210972	−	0.977492i	$-0.567663\pi$
$701$	−11.1716			−0.421944			−0.210972	+	0.977492i	$0.567663\pi$
$702$	−36.0081	+	21.9792i	−1.35904	+	0.829551i
$703$		−	11.4729i		−	0.432710i
$704$	1.72183	+	11.6626i	0.0648937	+	0.439550i
$705$		0			0
$706$	8.59264	+	14.0772i	0.323388	+	0.529801i
$707$	11.5362	−	35.4130i	0.433862	−	1.33184i
$708$	27.8508	+	14.3137i	1.04670	+	0.537942i
$709$	28.0000			1.05156			0.525781	−	0.850620i	$-0.323773\pi$
$709$	28.0000			1.05156			0.525781	+	0.850620i	$0.323773\pi$
$710$		0			0
$711$			20.1251i			0.754750i
$712$	2.56177	+	34.8918i	0.0960064	+	1.30763i
$713$	8.24621			0.308823
$714$	41.9969	−	9.97111i	1.57170	−	0.373160i
$715$		0			0
$716$	−4.79289	−	2.46327i	−0.179119	−	0.0920568i
$717$	−24.7386			−0.923881
$718$	27.2404	−	16.6274i	1.01660	−	0.620530i
$719$	30.5784			1.14038			0.570191	−	0.821512i	$-0.306869\pi$
$719$	30.5784			1.14038			0.570191	+	0.821512i	$0.306869\pi$
$720$		0			0
$721$	−1.89949	+	5.83095i	−0.0707409	+	0.217156i
$722$	−5.28411	−	8.65685i	−0.196654	−	0.322175i
$723$	−21.0930			−0.784459
$724$	−6.07591	−	3.12267i	−0.225810	−	0.116053i
$725$		0			0
$726$	29.8172	−	18.2003i	1.10662	−	0.675475i
$727$		−	5.87707i		−	0.217969i	−0.994043	−	0.108984i	$-0.965240\pi$
$727$		−	5.87707i		−	0.217969i	0.994043	−	0.108984i	$-0.0347598\pi$
$728$	42.3672	+	10.4412i	1.57023	+	0.386978i
$729$	43.7696			1.62109
$730$		0			0
$731$	−12.1518			−0.449452
$732$	−29.8301	+	58.0416i	−1.10255	+	2.14528i
$733$	−24.7386			−0.913742			−0.456871	−	0.889533i	$-0.651030\pi$
$733$	−24.7386			−0.913742			−0.456871	+	0.889533i	$0.651030\pi$
$734$	−17.4665	+	10.6615i	−0.644700	+	0.393522i
$735$		0			0
$736$	4.60660	−	10.8517i	0.169802	−	0.400000i
$737$			18.7990i			0.692470i
$738$	−24.0312	+	14.6686i	−0.884601	+	0.539957i
$739$		−	43.1974i		−	1.58904i	−0.607236	−	0.794522i	$-0.707722\pi$
$739$		−	43.1974i		−	1.58904i	0.607236	−	0.794522i	$-0.292278\pi$
$740$		0			0
$741$			83.4625i			3.06607i
$742$	−13.6785	+	3.24762i	−0.502154	+	0.119224i
$743$	−20.4827			−0.751436			−0.375718	−	0.926734i	$-0.622604\pi$
$743$	−20.4827			−0.751436			−0.375718	+	0.926734i	$0.622604\pi$
$744$	−2.29289	−	31.2296i	−0.0840615	−	1.14493i
$745$		0			0
$746$	12.7782	−	7.79974i	0.467842	−	0.285569i
$747$		−	13.5096i		−	0.494291i
$748$	−10.8080	−	5.55468i	−0.395179	−	0.203099i
$749$	−24.6777	−	8.03901i	−0.901702	−	0.293739i
$750$		0			0
$751$		−	34.7132i		−	1.26670i	−0.773864	−	0.633352i	$-0.781678\pi$
$751$		−	34.7132i		−	1.26670i	0.773864	−	0.633352i	$-0.218322\pi$
$752$	38.6086	−	27.6399i	1.40791	−	1.00792i
$753$		−	58.5980i		−	2.13543i
$754$	35.4130	+	58.0165i	1.28967	+	2.11284i
$755$		0			0
$756$	19.0599	+	19.2230i	0.693202	+	0.699135i
$757$			15.4142i			0.560239i	0.959965	+	0.280120i	$0.0903741\pi$
$757$			15.4142i			0.560239i	−0.959965	+	0.280120i	$0.909626\pi$
$758$	−27.5456	+	16.8137i	−1.00050	+	0.610701i
$759$	8.59264			0.311893
$760$		0			0
$761$		−	30.8626i		−	1.11877i	−0.828908	−	0.559384i	$-0.811038\pi$
$761$		−	30.8626i		−	1.11877i	0.828908	−	0.559384i	$-0.188962\pi$
$762$	−9.95406	+	6.07591i	−0.360597	+	0.220107i
$763$	7.11529	+	2.31788i	0.257591	+	0.0839130i
$764$	−8.31371	−	4.27277i	−0.300779	−	0.154583i
$765$		0			0
$766$	−15.1486	+	9.24664i	−0.547341	+	0.334095i
$767$	−32.6292			−1.17817
$768$	−42.3780	−	14.4285i	−1.52918	−	0.520645i
$769$		−	17.1998i		−	0.620242i	−0.950697	−	0.310121i	$-0.899630\pi$
$769$		−	17.1998i		−	0.620242i	0.950697	−	0.310121i	$-0.100370\pi$
$770$		0			0
$771$			65.2584i			2.35023i
$772$	−25.4616	−	13.0858i	−0.916382	−	0.470968i
$773$	−13.0767			−0.470337			−0.235169	−	0.971955i	$-0.575564\pi$
$773$	−13.0767			−0.470337			−0.235169	+	0.971955i	$0.575564\pi$
$774$	−10.4853	−	17.1778i	−0.376886	−	0.617445i
$775$		0			0
$776$	23.2612	−	1.70785i	0.835028	−	0.0613081i
$777$	15.7850	+	5.14214i	0.566284	+	0.184473i
$778$	−11.4621	−	18.7782i	−0.410937	−	0.673230i
$779$			21.0930i			0.755737i
$780$		0			0
$781$	11.7574			0.420711
$782$	6.33117	+	10.3722i	0.226402	+	0.370910i
$783$			42.1678i			1.50696i
$784$	0.238620	−	27.9990i	0.00852213	−	0.999964i
$785$		0			0
$786$	29.9706	−	18.2939i	1.06901	−	0.652522i
$787$			39.1711i			1.39630i	0.715953	+	0.698149i	$0.245993\pi$
$787$			39.1711i			1.39630i	−0.715953	+	0.698149i	$0.754007\pi$
$788$	25.7668	+	13.2426i	0.917903	+	0.471750i
$789$			41.2311i			1.46786i
$790$		0			0
$791$	3.53506	−	10.8517i	0.125692	−	0.385843i
$792$	−1.47363	−	20.0711i	−0.0523630	−	0.713194i
$793$		−	68.0000i		−	2.41475i
$794$	−22.5241	−	36.9008i	−0.799349	−	1.30956i
$795$		0			0
$796$	20.2062	−	39.3160i	0.716189	−	1.39352i
$797$	43.2319			1.53135			0.765677	−	0.643226i	$-0.222404\pi$
$797$	43.2319			1.53135			0.765677	+	0.643226i	$0.222404\pi$
$798$	52.1084	−	12.3718i	1.84462	−	0.437958i
$799$			48.9438i			1.73151i
$800$		0			0
$801$		−	59.7243i		−	2.11026i
$802$	−20.9666	−	34.3492i	−0.740358	−	1.21291i
$803$		−	18.2277i		−	0.643243i
$804$	−63.4918	−	32.6311i	−2.23918	−	1.15081i
$805$		0			0
$806$	17.0000	+	27.8508i	0.598799	+	0.981002i
$807$	39.3870			1.38649
$808$	−2.91548	−	39.7093i	−0.102566	−	1.39697i
$809$	6.82843			0.240075			0.120037	−	0.992769i	$-0.461699\pi$
$809$	6.82843			0.240075			0.120037	+	0.992769i	$0.461699\pi$
$810$		0			0
$811$	−21.0257			−0.738311			−0.369156	−	0.929368i	$-0.620353\pi$
$811$	−21.0257			−0.738311			−0.369156	+	0.929368i	$0.620353\pi$
$812$	30.9723	−	30.7094i	1.08691	−	1.07769i
$813$		−	11.8579i		−	0.415873i
$814$	−2.43503	−	3.98926i	−0.0853477	−	0.139824i
$815$		0			0
$816$	37.5208	−	26.8611i	1.31349	−	0.940328i
$817$	−15.0776			−0.527498
$818$	9.10013	−	5.55468i	0.318179	−	0.194215i
$819$	−70.8261	−	23.0723i	−2.47486	−	0.806213i
$820$		0			0
$821$	17.4142			0.607760			0.303880	−	0.952710i	$-0.401718\pi$
$821$	17.4142			0.607760			0.303880	+	0.952710i	$0.401718\pi$
$822$	−27.8006	−	45.5452i	−0.969658	−	1.58857i
$823$	19.9770			0.696354			0.348177	−	0.937429i	$-0.386801\pi$
$823$	19.9770			0.696354			0.348177	+	0.937429i	$0.386801\pi$
$824$	0.480049	+	6.53836i	0.0167233	+	0.227775i
$825$		0			0
$826$	4.83670	+	20.3715i	0.168290	+	0.708815i
$827$	33.5972			1.16829			0.584144	−	0.811650i	$-0.301430\pi$
$827$	33.5972			1.16829			0.584144	+	0.811650i	$0.301430\pi$
$828$	−9.19932	+	17.8995i	−0.319698	+	0.622050i
$829$		−	43.2319i		−	1.50151i	−0.660583	−	0.750753i	$-0.729691\pi$
$829$		−	43.2319i		−	1.50151i	0.660583	−	0.750753i	$-0.270309\pi$
$830$		0			0
$831$	−72.4650			−2.51378
$832$	46.1474	−	6.81305i	1.59987	−	0.236200i
$833$	23.3238	+	17.0000i	0.808122	+	0.589015i
$834$	−36.1777	+	22.0827i	−1.25273	+	0.764661i
$835$		0			0
$836$	−13.4102	−	6.89207i	−0.463801	−	0.238367i
$837$			20.2426i			0.699688i
$838$	11.0152	+	18.0460i	0.380513	+	0.623387i
$839$	−15.5463			−0.536718			−0.268359	−	0.963319i	$-0.586481\pi$
$839$	−15.5463			−0.536718			−0.268359	+	0.963319i	$0.586481\pi$
$840$		0			0
$841$	38.9411			1.34280
$842$	17.1778	+	28.1421i	0.591987	+	0.969842i
$843$		−	2.71557i		−	0.0935292i
$844$	45.8345	+	23.5563i	1.57769	+	0.810842i
$845$		0			0
$846$	−69.1871	+	42.2315i	−2.37870	+	1.45195i
$847$	22.2091	+	7.23486i	0.763114	+	0.248593i
$848$	−12.2206	+	8.74874i	−0.419658	+	0.300433i
$849$	−35.3431			−1.21297
$850$		0			0
$851$			4.67371i			0.160213i
$852$	−20.4083	+	39.7093i	−0.699178	+	1.36042i
$853$	−31.5700			−1.08094			−0.540468	−	0.841364i	$-0.681753\pi$
$853$	−31.5700			−1.08094			−0.540468	+	0.841364i	$0.681753\pi$
$854$	−42.4547	+	10.0798i	−1.45277	+	0.344923i
$855$		0			0
$856$	−27.6716	+	2.03166i	−0.945795	+	0.0694406i
$857$	−52.1855			−1.78262			−0.891312	−	0.453390i	$-0.850214\pi$
$857$	−52.1855			−1.78262			−0.891312	+	0.453390i	$0.850214\pi$
$858$	17.7142	+	29.0208i	0.604752	+	0.990754i
$859$	−37.3332			−1.27379			−0.636897	−	0.770949i	$-0.719782\pi$
$859$	−37.3332			−1.27379			−0.636897	+	0.770949i	$0.719782\pi$
$860$		0			0
$861$	−29.0208	−	9.45384i	−0.989027	−	0.322186i
$862$	−30.3664	+	18.5355i	−1.03428	+	0.631323i
$863$	−23.0723			−0.785392			−0.392696	−	0.919668i	$-0.628457\pi$
$863$	−23.0723			−0.785392			−0.392696	+	0.919668i	$0.628457\pi$
$864$	26.6386	+	11.3082i	0.906264	+	0.384713i
$865$		0			0
$866$	−3.03796	−	4.97703i	−0.103234	−	0.169126i
$867$		0			0
$868$	14.8682	−	14.7420i	0.504660	−	0.500378i
$869$	6.14214			0.208358
$870$		0			0
$871$	74.3852			2.52045
$872$	7.97852	−	0.585786i	0.270187	−	0.0198372i
$873$	−39.8162			−1.34758
$874$	7.85551	+	12.8695i	0.265717	+	0.435318i
$875$		0			0
$876$	61.5624	+	31.6396i	2.08000	+	1.06900i
$877$		−	28.9706i		−	0.978266i	−0.872209	−	0.489133i	$-0.837313\pi$
$877$		−	28.9706i		−	0.978266i	0.872209	−	0.489133i	$-0.162687\pi$
$878$	−4.12311	−	6.75481i	−0.139148	−	0.227964i
$879$			46.1447i			1.55642i
$880$		0			0
$881$			11.6619i			0.392900i	0.980514	+	0.196450i	$0.0629413\pi$
$881$			11.6619i			0.392900i	−0.980514	+	0.196450i	$0.937059\pi$
$882$	−3.90613	+	47.6391i	−0.131526	+	1.60409i
$883$	−45.8919			−1.54438			−0.772192	−	0.635389i	$-0.780840\pi$
$883$	−45.8919			−1.54438			−0.772192	+	0.635389i	$0.780840\pi$
$884$	−21.9792	+	42.7658i	−0.739240	+	1.43837i
$885$		0			0
$886$	−11.5711	−	18.9567i	−0.388738	−	0.636862i
$887$			12.8307i			0.430813i	0.976524	+	0.215407i	$0.0691077\pi$
$887$			12.8307i			0.430813i	−0.976524	+	0.215407i	$0.930892\pi$
$888$	17.7001	−	1.29954i	0.593975	−	0.0436099i
$889$	−7.41421	−	2.41526i	−0.248665	−	0.0810052i
$890$		0			0
$891$		−	0.252834i		−	0.00847026i
$892$	16.9926	+	8.73324i	0.568956	+	0.292411i
$893$			60.7279i			2.03218i
$894$	−6.75481	+	4.12311i	−0.225915	+	0.137897i
$895$		0			0
$896$	−11.0941	−	27.8014i	−0.370629	−	0.928781i
$897$		−	34.0000i		−	1.13523i
$898$	−0.483979	−	0.792893i	−0.0161506	−	0.0264592i
$899$	32.6151			1.08777
$900$		0			0
$901$		−	15.4920i		−	0.516113i
$902$	4.47681	+	7.33428i	0.149062	+	0.244205i
$903$	6.75773	−	20.7445i	0.224883	−	0.690333i
$904$	−0.893398	−	12.1683i	−0.0297140	−	0.404710i
$905$		0			0
$906$	10.3722	+	16.9926i	0.344594	+	0.564543i
$907$	20.8402			0.691988			0.345994	−	0.938237i	$-0.387542\pi$
$907$	20.8402			0.691988			0.345994	+	0.938237i	$0.387542\pi$
$908$	4.12311	+	2.11904i	0.136830	+	0.0703228i
$909$			67.9706i			2.25444i
$910$		0			0
$911$		−	7.62096i		−	0.252494i	−0.991999	−	0.126247i	$-0.959707\pi$
$911$		−	7.62096i		−	0.252494i	0.991999	−	0.126247i	$-0.0402932\pi$
$912$	46.5546	−	33.3284i	1.54158	−	1.10361i
$913$	−4.12311			−0.136455
$914$	15.1066	−	9.22101i	0.499682	−	0.305004i
$915$		0			0
$916$	4.29632	+	2.20806i	0.141954	+	0.0729565i
$917$	22.3234	+	7.27208i	0.737183	+	0.240145i
$918$	−25.4616	+	15.5416i	−0.840357	+	0.512950i
$919$		−	29.6820i		−	0.979118i	−0.871970	−	0.489559i	$-0.837158\pi$
$919$		−	29.6820i		−	0.979118i	0.871970	−	0.489559i	$-0.162842\pi$
$920$		0			0
$921$	−10.5147			−0.346472
$922$	−16.9926	+	10.3722i	−0.559623	+	0.341591i
$923$		−	46.5224i		−	1.53130i
$924$	15.4928	−	15.3614i	0.509677	−	0.505352i
$925$		0			0
$926$	17.8995	+	29.3244i	0.588214	+	0.963660i
$927$		−	11.1917i		−	0.367585i
$928$	18.2199	−	42.9203i	0.598096	−	1.40893i
$929$			6.83139i			0.224130i	0.993701	+	0.112065i	$0.0357466\pi$
$929$			6.83139i			0.224130i	−0.993701	+	0.112065i	$0.964253\pi$
$930$		0			0
$931$	28.9394	+	21.0930i	0.948451	+	0.691297i
$932$	42.3342	+	21.7574i	1.38670	+	0.712686i
$933$			62.6274i			2.05033i
$934$	−36.5720	+	22.3234i	−1.19667	+	0.730443i
$935$		0			0
$936$	−79.4187	+	5.83095i	−2.59588	+	0.190591i
$937$	−35.6931			−1.16604			−0.583022	−	0.812457i	$-0.698130\pi$
$937$	−35.6931			−1.16604			−0.583022	+	0.812457i	$0.698130\pi$
$938$	−11.0263	−	46.4412i	−0.360021	−	1.51636i
$939$			78.7739i			2.57069i
$940$		0			0
$941$			24.7386i			0.806456i	0.915099	+	0.403228i	$0.132112\pi$
$941$			24.7386i			0.806456i	−0.915099	+	0.403228i	$0.867888\pi$
$942$	36.0081	−	21.9792i	1.17321	−	0.716121i
$943$		−	8.59264i		−	0.279815i
$944$	13.0296	+	18.2003i	0.424076	+	0.592368i
$945$		0			0
$946$	−5.24264	+	3.20009i	−0.170453	+	0.104044i
$947$	−39.7445			−1.29152			−0.645762	−	0.763539i	$-0.723460\pi$
$947$	−39.7445			−1.29152			−0.645762	+	0.763539i	$0.723460\pi$
$948$	−10.6615	+	20.7445i	−0.346268	+	0.673749i
$949$	−72.1249			−2.34127
$950$		0			0
$951$	40.1312			1.30134
$952$	29.9581	+	7.38306i	0.970949	+	0.239286i
$953$			19.7696i			0.640399i	0.947350	+	0.320199i	$0.103750\pi$
$953$			19.7696i			0.640399i	−0.947350	+	0.320199i	$0.896250\pi$
$954$	21.8995	−	13.3674i	0.709022	−	0.432784i
$955$		0			0
$956$	−15.7279	−	8.08325i	−0.508677	−	0.261431i
$957$	33.9853			1.09859
$958$	−12.3693	−	20.2644i	−0.399634	−	0.654714i
$959$	11.0511	−	33.9241i	0.356860	−	1.09547i
$960$		0			0
$961$	−15.3431			−0.494940
$962$	−15.7850	+	9.63510i	−0.508929	+	0.310648i
$963$	47.3655			1.52633
$964$	−13.4102	−	6.89207i	−0.431913	−	0.221979i
$965$		0			0
$966$	−21.2273	+	5.03989i	−0.682978	+	0.162156i
$967$	−0.863230			−0.0277596			−0.0138798	−	0.999904i	$-0.504418\pi$
$967$	−0.863230			−0.0277596			−0.0138798	+	0.999904i	$0.504418\pi$
$968$	24.9035	−	1.82843i	0.800430	−	0.0587679i
$969$			59.0169i			1.89590i
$970$		0			0
$971$	41.0089			1.31604			0.658019	−	0.753001i	$-0.271395\pi$
$971$	41.0089			1.31604			0.658019	+	0.753001i	$0.271395\pi$
$972$	28.1543	+	14.4697i	0.903050	+	0.464116i
$973$	−26.9467	−	8.77817i	−0.863871	−	0.281415i
$974$	−23.1421	−	37.9133i	−0.741522	−	1.21482i
$975$		0			0
$976$	−37.9298	+	27.1539i	−1.21410	+	0.869175i
$977$			49.2843i			1.57674i	0.615199	+	0.788372i	$0.289076\pi$
$977$			49.2843i			1.57674i	−0.615199	+	0.788372i	$0.710924\pi$
$978$	10.8080	−	6.59715i	0.345601	−	0.210953i
$979$	−18.2277			−0.582561
$980$		0			0
$981$	−13.6569			−0.436030
$982$	11.5362	−	7.04163i	0.368134	−	0.224707i
$983$		−	33.2940i		−	1.06191i	−0.847399	−	0.530957i	$-0.821833\pi$
$983$		−	33.2940i		−	1.06191i	0.847399	−	0.530957i	$-0.178167\pi$
$984$	−32.5416	+	2.38922i	−1.03739	+	0.0761655i
$985$		0			0
$986$	25.0408	+	41.0239i	0.797461	+	1.30647i
$987$	−83.5523	−	27.2181i	−2.65950	−	0.866361i
$988$	−27.2711	+	53.0624i	−0.867608	+	1.68814i
$989$	6.14214			0.195309
$990$		0			0
$991$			9.19932i			0.292226i	0.989268	+	0.146113i	$0.0466763\pi$
$991$			9.19932i			0.292226i	−0.989268	+	0.146113i	$0.953324\pi$
$992$	8.74643	−	20.6039i	0.277699	−	0.654173i
$993$	50.7707			1.61116
$994$	−29.0455	+	6.89612i	−0.921266	+	0.218732i
$995$		0			0
$996$	7.15685	−	13.9254i	0.226774	−	0.441243i
$997$	−14.0772			−0.445828			−0.222914	−	0.974838i	$-0.571557\pi$
$997$	−14.0772			−0.445828			−0.222914	+	0.974838i	$0.571557\pi$
$998$	−10.6729	+	6.51472i	−0.337846	+	0.206220i
$999$	−11.4729			−0.362988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.c.k.699.6		16
4.3	odd	2	inner	700.2.c.k.699.9		16
5.2	odd	4		700.2.g.k.251.6	yes	8
5.3	odd	4		700.2.g.i.251.3	yes	8
5.4	even	2	inner	700.2.c.k.699.11		16
7.6	odd	2	inner	700.2.c.k.699.5		16
20.3	even	4		700.2.g.i.251.2	yes	8
20.7	even	4		700.2.g.k.251.7	yes	8
20.19	odd	2	inner	700.2.c.k.699.8		16
28.27	even	2	inner	700.2.c.k.699.10		16
35.13	even	4		700.2.g.i.251.4	yes	8
35.27	even	4		700.2.g.k.251.5	yes	8
35.34	odd	2	inner	700.2.c.k.699.12		16
140.27	odd	4		700.2.g.k.251.8	yes	8
140.83	odd	4		700.2.g.i.251.1	✓	8
140.139	even	2	inner	700.2.c.k.699.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.c.k.699.5		16	7.6	odd	2	inner
700.2.c.k.699.6		16	1.1	even	1	trivial
700.2.c.k.699.7		16	140.139	even	2	inner
700.2.c.k.699.8		16	20.19	odd	2	inner
700.2.c.k.699.9		16	4.3	odd	2	inner
700.2.c.k.699.10		16	28.27	even	2	inner
700.2.c.k.699.11		16	5.4	even	2	inner
700.2.c.k.699.12		16	35.34	odd	2	inner
700.2.g.i.251.1	✓	8	140.83	odd	4
700.2.g.i.251.2	yes	8	20.3	even	4
700.2.g.i.251.3	yes	8	5.3	odd	4
700.2.g.i.251.4	yes	8	35.13	even	4
700.2.g.k.251.5	yes	8	35.27	even	4
700.2.g.k.251.6	yes	8	5.2	odd	4
700.2.g.k.251.7	yes	8	20.7	even	4
700.2.g.k.251.8	yes	8	140.27	odd	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.736813 - 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(3.37740 - 2.06155i) q^{6} +(2.51564 + 0.819496i) q^{7} +(2.82083 - 0.207107i) q^{8} -4.82843 q^{9} +O(q^{10})\)	\(q+(-0.736813 - 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(3.37740 - 2.06155i) q^{6} +(2.51564 + 0.819496i) q^{7} +(2.82083 - 0.207107i) q^{8} -4.82843 q^{9} +1.47363i q^{11} +(-4.97703 - 2.55791i) q^{12} +5.83095 q^{13} +(-0.864335 - 3.64046i) q^{14} +(-2.32843 - 3.25245i) q^{16} +4.12311 q^{17} +(3.55765 + 5.82843i) q^{18} +5.11582 q^{19} +(-2.29289 + 7.03858i) q^{21} +(1.77882 - 1.08579i) q^{22} -2.08402 q^{23} +(0.579471 + 7.89250i) q^{24} +(-4.29632 - 7.03858i) q^{26} -5.11582i q^{27} +(-3.75757 + 3.72568i) q^{28} -8.24264 q^{29} -3.95687 q^{31} +(-2.21044 + 5.20711i) q^{32} -4.12311 q^{33} +(-3.03796 - 4.97703i) q^{34} +(4.41421 - 8.58892i) q^{36} -2.24264i q^{37} +(-3.76940 - 6.17534i) q^{38} +16.3146i q^{39} +4.12311i q^{41} +(10.1858 - 2.41835i) q^{42} -2.94725 q^{43} +(-2.62132 - 1.34721i) q^{44} +(1.53553 + 2.51564i) q^{46} +11.8706i q^{47} +(9.10013 - 6.51478i) q^{48} +(5.65685 + 4.12311i) q^{49} +11.5362i q^{51} +(-5.33074 + 10.3722i) q^{52} -3.75736i q^{53} +(-6.17534 + 3.76940i) q^{54} +(7.26592 + 1.79066i) q^{56} +14.3137i q^{57} +(6.07328 + 9.94975i) q^{58} -5.59587 q^{59} -11.6619i q^{61} +(2.91548 + 4.77637i) q^{62} +(-12.1466 - 3.95687i) q^{63} +(7.91421 - 1.16843i) q^{64} +(3.03796 + 4.97703i) q^{66} +12.7570 q^{67} +(-3.76940 + 7.33428i) q^{68} -5.83095i q^{69} -7.97852i q^{71} +(-13.6202 + 1.00000i) q^{72} -12.3693 q^{73} +(-2.70711 + 1.65241i) q^{74} +(-4.67695 + 9.10013i) q^{76} +(-1.20763 + 3.70711i) q^{77} +(19.6935 - 12.0208i) q^{78} -4.16804i q^{79} -0.171573 q^{81} +(4.97703 - 3.03796i) q^{82} +2.79793i q^{83} +(-10.4242 - 10.5134i) q^{84} +(2.17157 + 3.55765i) q^{86} -23.0624i q^{87} +(0.305198 + 4.15685i) q^{88} +12.3693i q^{89} +(14.6686 + 4.77844i) q^{91} +(1.90524 - 3.70711i) q^{92} -11.0711i q^{93} +(14.3291 - 8.74643i) q^{94} +(-14.5691 - 6.18466i) q^{96} +8.24621 q^{97} +(0.808986 - 9.86638i) q^{98} -7.11529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 32 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 32 * q^9	\( 16 q + 8 q^{4} - 32 q^{9} - 24 q^{14} + 8 q^{16} - 48 q^{21} - 64 q^{29} + 48 q^{36} - 8 q^{44} - 32 q^{46} + 40 q^{56} + 104 q^{64} - 32 q^{74} - 48 q^{81} - 40 q^{84} + 80 q^{86}+O(q^{100}) \) 16 * q + 8 * q^4 - 32 * q^9 - 24 * q^14 + 8 * q^16 - 48 * q^21 - 64 * q^29 + 48 * q^36 - 8 * q^44 - 32 * q^46 + 40 * q^56 + 104 * q^64 - 32 * q^74 - 48 * q^81 - 40 * q^84 + 80 * q^86

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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