LMFDB - Embedded newform 700.2.c.k.699.12

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			699.12
Root			$0.481610 + 1.32968i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.k.699.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.736813 + 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(-3.37740 + 2.06155i) q^{6} +(-2.51564 + 0.819496i) q^{7} +(-2.82083 + 0.207107i) q^{8} -4.82843 q^{9} +O(q^{10})$	\(q+(0.736813 + 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(-3.37740 + 2.06155i) q^{6} +(-2.51564 + 0.819496i) q^{7} +(-2.82083 + 0.207107i) q^{8} -4.82843 q^{9} +1.47363i q^{11} +(-4.97703 - 2.55791i) q^{12} +5.83095 q^{13} +(-2.84277 - 2.43283i) q^{14} +(-2.32843 - 3.25245i) q^{16} +4.12311 q^{17} +(-3.55765 - 5.82843i) q^{18} -5.11582 q^{19} +(-2.29289 - 7.03858i) q^{21} +(-1.77882 + 1.08579i) q^{22} +2.08402 q^{23} +(-0.579471 - 7.89250i) q^{24} +(4.29632 + 7.03858i) q^{26} -5.11582i q^{27} +(0.842091 - 5.22407i) q^{28} -8.24264 q^{29} +3.95687 q^{31} +(2.21044 - 5.20711i) q^{32} -4.12311 q^{33} +(3.03796 + 4.97703i) q^{34} +(4.41421 - 8.58892i) q^{36} +2.24264i q^{37} +(-3.76940 - 6.17534i) q^{38} +16.3146i q^{39} -4.12311i q^{41} +(6.80689 - 7.95388i) q^{42} +2.94725 q^{43} +(-2.62132 - 1.34721i) q^{44} +(1.53553 + 2.51564i) q^{46} +11.8706i q^{47} +(9.10013 - 6.51478i) q^{48} +(5.65685 - 4.12311i) q^{49} +11.5362i q^{51} +(-5.33074 + 10.3722i) q^{52} +3.75736i q^{53} +(6.17534 - 3.76940i) q^{54} +(6.92647 - 2.83267i) q^{56} -14.3137i q^{57} +(-6.07328 - 9.94975i) q^{58} +5.59587 q^{59} +11.6619i q^{61} +(2.91548 + 4.77637i) q^{62} +(12.1466 - 3.95687i) q^{63} +(7.91421 - 1.16843i) q^{64} +(-3.03796 - 4.97703i) q^{66} -12.7570 q^{67} +(-3.76940 + 7.33428i) q^{68} +5.83095i q^{69} -7.97852i q^{71} +(13.6202 - 1.00000i) q^{72} -12.3693 q^{73} +(-2.70711 + 1.65241i) q^{74} +(4.67695 - 9.10013i) q^{76} +(-1.20763 - 3.70711i) q^{77} +(-19.6935 + 12.0208i) q^{78} -4.16804i q^{79} -0.171573 q^{81} +(4.97703 - 3.03796i) q^{82} +2.79793i q^{83} +(14.6166 + 2.35611i) q^{84} +(2.17157 + 3.55765i) q^{86} -23.0624i q^{87} +(-0.305198 - 4.15685i) q^{88} -12.3693i q^{89} +(-14.6686 + 4.77844i) q^{91} +(-1.90524 + 3.70711i) q^{92} +11.0711i q^{93} +(-14.3291 + 8.74643i) q^{94} +(14.5691 + 6.18466i) q^{96} +8.24621 q^{97} +(9.14507 + 3.79047i) q^{98} -7.11529i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.200222\pi$
$14$	−2.84277	−	2.43283i	−0.759763	−	0.650200i
$15$		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	$-0.699622\pi$
$19$	−5.11582			−1.17365			−0.586824	+	0.809714i	$0.699622\pi$
$20$		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	$-0.430283\pi$
$23$	2.08402			0.434549			0.217274	+	0.976111i	$0.430283\pi$
$24$	−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
$28$	0.842091	−	5.22407i	0.159140	−	0.987256i
$29$	−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	$-0.384366\pi$
$31$	3.95687			0.710676			0.355338	+	0.934738i	$0.384366\pi$
$32$	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	$0.0590160\pi$
$37$			2.24264i			0.368688i	−0.982862	+	0.184344i	$0.940984\pi$
$38$	−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	$-0.895658\pi$
$41$		−	4.12311i		−	0.643921i	0.946753	−	0.321960i	$-0.104342\pi$
$42$	6.80689	−	7.95388i	1.05033	−	1.22731i
$43$	2.94725			0.449452			0.224726	−	0.974422i	$-0.427851\pi$
$43$	2.94725			0.449452			0.224726	+	0.974422i	$0.427851\pi$
$44$	−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	$0.0830821\pi$
$53$			3.75736i			0.516113i	−0.966130	+	0.258056i	$0.916918\pi$
$54$	6.17534	−	3.76940i	0.840357	−	0.512950i
$55$		0			0
$56$	6.92647	−	2.83267i	0.925589	−	0.378531i
$57$		−	14.3137i		−	1.89590i
$58$	−6.07328	−	9.94975i	−0.797461	−	1.30647i
$59$	5.59587			0.728520			0.364260	−	0.931297i	$-0.381322\pi$
$59$	5.59587			0.728520			0.364260	+	0.931297i	$0.381322\pi$
$60$		0			0
$61$			11.6619i			1.49315i	0.665299	+	0.746577i	$0.268304\pi$
$61$			11.6619i			1.49315i	−0.665299	+	0.746577i	$0.731696\pi$
$62$	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	$-0.784403\pi$
$67$	−12.7570			−1.55851			−0.779256	+	0.626706i	$0.784403\pi$
$68$	−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	$0.950927\pi$
$84$	14.6166	+	2.35611i	1.59480	+	0.257073i
$85$		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	$-0.772427\pi$
$89$		−	12.3693i		−	1.31114i	0.755132	−	0.655572i	$-0.227573\pi$
$90$		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	$0.362508\pi$
$98$	9.14507	+	3.79047i	0.923792	+	0.382895i
$99$		−	7.11529i		−	0.715114i
$100$		0			0
$101$			14.0772i			1.40073i	0.713785	+	0.700365i	$0.246979\pi$
$101$			14.0772i			1.40073i	−0.713785	+	0.700365i	$0.753021\pi$
$102$	−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	$-0.342748\pi$
$107$	9.80971			0.948341			0.474170	+	0.880433i	$0.342748\pi$
$108$	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
$112$	8.52284	+	6.27384i	0.805333	+	0.592823i
$113$			4.31371i			0.405800i	0.979200	+	0.202900i	$0.0650366\pi$
$113$			4.31371i			0.405800i	−0.979200	+	0.202900i	$0.934963\pi$
$114$	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
$126$	13.7261	+	11.7467i	1.22282	+	1.04648i
$127$	2.94725			0.261526			0.130763	−	0.991414i	$-0.458257\pi$
$127$	2.94725			0.261526			0.130763	+	0.991414i	$0.458257\pi$
$128$	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	$-0.626715\pi$
$131$	−8.87385			−0.775312			−0.387656	+	0.921804i	$0.626715\pi$
$132$	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	$0.195412\pi$
$137$			13.4853i			1.15213i	−0.817406	+	0.576063i	$0.804588\pi$
$138$	−7.03858	+	4.29632i	−0.599164	+	0.365727i
$139$	10.7117			0.908553			0.454276	−	0.890861i	$-0.349898\pi$
$139$	10.7117			0.908553			0.454276	+	0.890861i	$0.349898\pi$
$140$		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
$154$	3.58508	−	4.18918i	0.288894	−	0.337574i
$155$		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	$-0.539997\pi$
$163$	−3.20009			−0.250650			−0.125325	+	0.992116i	$0.539997\pi$
$164$	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	$-0.0118271\pi$
$168$	7.92561	+	19.3798i	0.611474	+	1.49518i
$169$	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	$-0.959483\pi$
$181$		−	3.41569i		−	0.253886i	0.991910	−	0.126943i	$-0.0405166\pi$
$182$	−16.5761	−	14.1857i	−1.22870	−	1.05151i
$183$	−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	$-0.827732\pi$
$193$		−	14.3137i		−	1.03032i	0.857093	−	0.515162i	$-0.172268\pi$
$194$	6.07591	+	9.95406i	0.436225	+	0.714660i
$195$		0			0
$196$	2.16270	+	13.8319i	0.154479	+	0.987996i
$197$			14.4853i			1.03203i	0.856578	+	0.516017i	$0.172586\pi$
$197$			14.4853i			1.03203i	−0.856578	+	0.516017i	$0.827414\pi$
$198$	8.58892	−	5.24264i	0.610388	−	0.372578i
$199$	22.1023			1.56679			0.783394	−	0.621526i	$-0.213487\pi$
$199$	22.1023			1.56679			0.783394	+	0.621526i	$0.213487\pi$
$200$		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	$-0.103632\pi$
$224$	−1.29346	+	14.9106i	−0.0864229	+	0.996259i
$225$		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	$0.0254289\pi$
$229$			2.41526i			0.159605i	−0.996811	+	0.0798024i	$0.974571\pi$
$230$		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	$0.284558\pi$
$233$			23.7990i			1.55912i	−0.626325	+	0.779562i	$0.715442\pi$
$234$	−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
$238$	−11.7210	−	10.0308i	−0.759763	−	0.650200i
$239$			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	$-0.921931\pi$
$241$		−	7.53880i		−	0.485617i	0.970074	−	0.242808i	$-0.0780686\pi$
$242$	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	$-0.270147\pi$
$251$	20.9433			1.32193			0.660965	+	0.750417i	$0.270147\pi$
$252$	−4.06598	+	25.2240i	−0.256132	+	1.58896i
$253$			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	$-0.650124\pi$
$263$	−14.7363			−0.908677			−0.454338	+	0.890829i	$0.650124\pi$
$264$	11.6306	−	0.853923i	0.715814	−	0.0525553i
$265$		0			0
$266$	14.5431	+	12.4459i	0.891695	+	0.763107i
$267$	34.6085			2.11801
$268$	11.6626	−	22.6924i	0.712406	−	1.38616i
$269$			14.0772i			0.858300i	0.903233	+	0.429150i	$0.141187\pi$
$269$			14.0772i			0.858300i	−0.903233	+	0.429150i	$0.858813\pi$
$270$		0			0
$271$	4.23808			0.257445			0.128723	−	0.991681i	$-0.458912\pi$
$271$	4.23808			0.257445			0.128723	+	0.991681i	$0.458912\pi$
$272$	−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	$-0.716196\pi$
$277$		−	25.8995i		−	1.55615i	0.628171	−	0.778075i	$-0.283804\pi$
$278$	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	$0.340002\pi$
$294$	−10.6055	+	25.5873i	−0.618524	+	1.49228i
$295$		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	$0.965798\pi$
$308$	7.69832	+	1.24093i	0.438653	+	0.0707084i
$309$	−6.48528			−0.368935
$310$		0			0
$311$	−22.3835			−1.26925			−0.634625	−	0.772820i	$-0.718845\pi$
$311$	−22.3835			−1.26925			−0.634625	+	0.772820i	$0.718845\pi$
$312$	−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	$0.131961\pi$
$317$			14.3431i			0.805591i	−0.915290	+	0.402796i	$0.868039\pi$
$318$	−7.74599	−	12.6901i	−0.434374	−	0.711627i
$319$		−	12.1466i		−	0.680077i
$320$		0			0
$321$			27.4469i			1.53194i
$322$	−5.92440	−	5.07006i	−0.330154	−	0.282544i
$323$	−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
$336$	−17.5538	+	23.8463i	−0.957638	+	1.30092i
$337$		−	24.7990i		−	1.35089i	−0.737412	−	0.675444i	$-0.763952\pi$
$337$		−	24.7990i		−	1.35089i	0.737412	−	0.675444i	$-0.236048\pi$
$338$	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	$-0.184737\pi$
$347$	31.1556			1.67252			0.836260	+	0.548333i	$0.184737\pi$
$348$	41.0239	+	21.0839i	2.19911	+	1.13022i
$349$			2.41526i			0.129286i	0.997908	+	0.0646429i	$0.0205908\pi$
$349$			2.41526i			0.129286i	−0.997908	+	0.0646429i	$0.979409\pi$
$350$		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
$364$	4.91019	−	30.4613i	0.257364	−	1.59661i
$365$		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	$-0.911635\pi$
$373$		−	10.5858i		−	0.548111i	0.961714	−	0.274056i	$-0.0883652\pi$
$374$	−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
$378$	−12.4459	+	14.5431i	−0.640148	+	0.748016i
$379$		−	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
$392$	−15.1031	+	12.8022i	−0.762823	+	0.646607i
$393$		−	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
$406$	23.4319	+	20.0529i	1.16291	+	0.995210i
$407$	−3.30481			−0.163814
$408$	−2.38922	−	32.5416i	−0.118284	−	1.61105i
$409$		−	7.53880i		−	0.372770i	−0.982477	−	0.186385i	$-0.940323\pi$
$409$		−	7.53880i		−	0.372770i	0.982477	−	0.186385i	$-0.0596771\pi$
$410$		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	$-0.381010\pi$
$419$	14.9498			0.730344			0.365172	+	0.930940i	$0.381010\pi$
$420$		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	$0.468413\pi$
$434$	−11.2485	−	9.62639i	−0.539945	−	0.462082i
$435$		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	$-0.542634\pi$
$439$	−5.59587			−0.267076			−0.133538	+	0.991044i	$0.542634\pi$
$440$		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	$-0.621693\pi$
$443$	−15.7042			−0.746130			−0.373065	+	0.927805i	$0.621693\pi$
$444$	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
$448$	−18.9518	+	9.42500i	−0.895387	+	0.445290i
$449$	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	$-0.905444\pi$
$457$		−	12.5147i		−	0.585414i	0.956202	−	0.292707i	$-0.0945560\pi$
$458$	−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	$0.106314\pi$
$461$			14.0772i			0.655639i	−0.944740	+	0.327819i	$0.893686\pi$
$462$	11.7210	+	10.0308i	0.545313	+	0.466675i
$463$	24.2931			1.12900			0.564499	−	0.825434i	$-0.309069\pi$
$463$	24.2931			1.12900			0.564499	+	0.825434i	$0.309069\pi$
$464$	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
$476$	3.47203	−	21.5394i	0.159140	−	0.987256i
$477$		−	18.1421i		−	0.830671i
$478$	−10.6729	+	6.51472i	−0.488169	+	0.297976i
$479$	−16.7876			−0.767045			−0.383522	−	0.923532i	$-0.625289\pi$
$479$	−16.7876			−0.767045			−0.383522	+	0.923532i	$0.625289\pi$
$480$		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	$-0.752041\pi$
$487$	−31.4084			−1.42325			−0.711626	+	0.702559i	$0.752041\pi$
$488$	−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	$-0.142264\pi$
$504$	−33.4440	+	13.6773i	−1.48971	+	0.609236i
$505$		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	$0.0585010\pi$
$509$			8.24621i			0.365507i	−0.983159	+	0.182753i	$0.941499\pi$
$510$		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
$518$	5.45596	−	6.37532i	0.239721	−	0.280115i
$519$			6.75773i			0.296632i
$520$		0			0
$521$		−	28.8617i		−	1.26446i	−0.774782	−	0.632228i	$-0.782141\pi$
$521$		−	28.8617i		−	1.26446i	0.774782	−	0.632228i	$-0.217859\pi$
$522$	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
$532$	−4.30798	+	26.7254i	−0.186775	+	1.15869i
$533$		−	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
$546$	39.6906	−	46.3787i	1.69860	−	1.98483i
$547$	9.80971			0.419433			0.209716	−	0.977762i	$-0.432746\pi$
$547$	9.80971			0.419433			0.209716	+	0.977762i	$0.432746\pi$
$548$	−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	$0.249400\pi$
$557$			33.3137i			1.41155i	−0.708437	+	0.705774i	$0.750600\pi$
$558$	−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
$574$	−10.0308	+	11.7210i	−0.418678	+	0.489227i
$575$		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	$0.789018\pi$
$588$	−38.7009	+	6.05110i	−1.59600	+	0.249543i
$589$	−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	$-0.950863\pi$
$601$		−	7.53880i		−	0.307514i	0.988109	−	0.153757i	$-0.0491373\pi$
$602$	−8.37836	−	7.17015i	−0.341477	−	0.292234i
$603$	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	$0.364721\pi$
$613$			45.1127i			1.82208i	−0.412313	+	0.911042i	$0.635279\pi$
$614$	−4.53635	+	2.76897i	−0.183072	+	0.111746i
$615$		0			0
$616$	4.17429	+	10.2070i	0.168187	+	0.411253i
$617$		−	22.0000i		−	0.885687i	−0.896599	−	0.442843i	$-0.853970\pi$
$617$		−	22.0000i		−	0.885687i	0.896599	−	0.442843i	$-0.146030\pi$
$618$	−4.77844	−	7.82843i	−0.192217	−	0.314906i
$619$	−20.0656			−0.806504			−0.403252	−	0.915089i	$-0.632120\pi$
$619$	−20.0656			−0.806504			−0.403252	+	0.915089i	$0.632120\pi$
$620$		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	$-0.0947057\pi$
$644$	1.75494	−	10.8871i	0.0691542	−	0.429011i
$645$		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	$0.00969477\pi$
$653$			1.55635i			0.0609047i	−0.999536	+	0.0304523i	$0.990305\pi$
$654$	−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
$658$	28.8792	−	33.7455i	1.12583	−	1.31554i
$659$		−	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	$-0.727695\pi$
$661$		−	38.8158i		−	1.50976i	0.655863	−	0.754880i	$-0.272305\pi$
$662$	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
$672$	−41.7189	−	3.61901i	−1.60934	−	0.139606i
$673$			4.00000i			0.154189i	0.997024	+	0.0770943i	$0.0245643\pi$
$673$			4.00000i			0.154189i	−0.997024	+	0.0770943i	$0.975436\pi$
$674$	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	$-0.432317\pi$
$683$	11.0305			0.422070			0.211035	+	0.977478i	$0.432317\pi$
$684$	−22.5823	+	43.9393i	−0.863456	+	1.68006i
$685$		0			0
$686$	−26.1119	−	2.04110i	−0.996959	−	0.0779295i
$687$	−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	$-0.382150\pi$
$691$	19.0231			0.723673			0.361837	+	0.932241i	$0.382150\pi$
$692$	−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
$714$	28.0655	−	32.7947i	1.05033	−	1.22731i
$715$		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	$-0.693131\pi$
$719$	−30.5784			−1.14038			−0.570191	+	0.821512i	$0.693131\pi$
$720$		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	$-0.0347598\pi$
$728$	40.3879	−	16.5171i	1.49688	−	0.612166i
$729$	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
$742$	9.14101	−	10.6813i	0.335577	−	0.392123i
$743$	20.4827			0.751436			0.375718	−	0.926734i	$-0.377396\pi$
$743$	20.4827			0.751436			0.375718	+	0.926734i	$0.377396\pi$
$744$	−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
$756$	−26.7254	−	4.30798i	−0.971992	−	0.156680i
$757$		−	15.4142i		−	0.560239i	−0.959965	−	0.280120i	$-0.909626\pi$
$757$		−	15.4142i		−	0.560239i	0.959965	−	0.280120i	$-0.0903741\pi$
$758$	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	$0.188962\pi$
$761$			30.8626i			1.11877i	−0.828908	+	0.559384i	$0.811038\pi$
$762$	−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	$0.100370\pi$
$769$			17.1998i			0.620242i	−0.950697	+	0.310121i	$0.899630\pi$
$770$		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
$784$	−26.5818	−	8.79828i	−0.949349	−	0.314224i
$785$		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	$0.222404\pi$
$798$	−34.8228	+	40.6906i	−1.23271	+	1.44043i
$799$			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	$-0.379647\pi$
$811$	21.0257			0.738311			0.369156	+	0.929368i	$0.379647\pi$
$812$	−6.94105	+	43.0601i	−0.243583	+	1.51111i
$813$			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	$-0.613199\pi$
$823$	−19.9770			−0.696354			−0.348177	+	0.937429i	$0.613199\pi$
$824$	−0.480049	−	6.53836i	−0.0167233	−	0.227775i
$825$		0			0
$826$	−15.9078	−	13.6138i	−0.553502	−	0.473684i
$827$	−33.5972			−1.16829			−0.584144	−	0.811650i	$-0.698570\pi$
$827$	−33.5972			−1.16829			−0.584144	+	0.811650i	$0.698570\pi$
$828$	9.19932	−	17.8995i	0.319698	−	0.622050i
$829$			43.2319i			1.50151i	0.660583	+	0.750753i	$0.270309\pi$
$829$			43.2319i			1.50151i	−0.660583	+	0.750753i	$0.729691\pi$
$830$		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	$-0.413519\pi$
$839$	15.5463			0.536718			0.268359	+	0.963319i	$0.413519\pi$
$840$		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	$0.681753\pi$
$854$	28.3714	−	33.1521i	0.970849	−	1.13444i
$855$		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	$-0.280218\pi$
$859$	37.3332			1.27379			0.636897	+	0.770949i	$0.280218\pi$
$860$		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	$-0.371543\pi$
$863$	23.0723			0.785392			0.392696	+	0.919668i	$0.371543\pi$
$864$	−26.6386	−	11.3082i	−0.906264	−	0.384713i
$865$		0			0
$866$	3.03796	+	4.97703i	0.103234	+	0.169126i
$867$		0			0
$868$	3.33205	−	20.6710i	0.113097	−	0.701619i
$869$	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	$0.162687\pi$
$877$			28.9706i			0.978266i	−0.872209	+	0.489133i	$0.837313\pi$
$878$	−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	$-0.937059\pi$
$881$		−	11.6619i		−	0.392900i	0.980514	−	0.196450i	$-0.0629413\pi$
$882$	−44.1563	−	18.3020i	−1.48682	−	0.616261i
$883$	45.8919			1.54438			0.772192	−	0.635389i	$-0.219160\pi$
$883$	45.8919			1.54438			0.772192	+	0.635389i	$0.219160\pi$
$884$	−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
$896$	−25.3409	−	15.9323i	−0.846580	−	0.532262i
$897$			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	$-0.612458\pi$
$907$	−20.8402			−0.691988			−0.345994	+	0.938237i	$0.612458\pi$
$908$	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
$924$	−3.47203	+	21.5394i	−0.114221	+	0.708594i
$925$		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	$-0.964253\pi$
$929$		−	6.83139i		−	0.224130i	0.993701	−	0.112065i	$-0.0357466\pi$
$930$		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	$0.698130\pi$
$938$	36.2651	+	31.0355i	1.18410	+	1.01334i
$939$			78.7739i			2.57069i
$940$		0			0
$941$		−	24.7386i		−	0.806456i	−0.915099	−	0.403228i	$-0.867888\pi$
$941$		−	24.7386i		−	0.806456i	0.915099	−	0.403228i	$-0.132112\pi$
$942$	−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	$-0.276540\pi$
$947$	39.7445			1.29152			0.645762	+	0.763539i	$0.276540\pi$
$948$	−10.6615	+	20.7445i	−0.346268	+	0.673749i
$949$	−72.1249			−2.34127
$950$		0			0
$951$	−40.1312			−1.30134
$952$	28.5586	−	11.6794i	0.925589	−	0.378531i
$953$		−	19.7696i		−	0.640399i	−0.947350	−	0.320199i	$-0.896250\pi$
$953$		−	19.7696i		−	0.640399i	0.947350	−	0.320199i	$-0.103750\pi$
$954$	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
$966$	14.1857	−	16.5761i	0.456417	−	0.533326i
$967$	0.863230			0.0277596			0.0138798	−	0.999904i	$-0.495582\pi$
$967$	0.863230			0.0277596			0.0138798	+	0.999904i	$0.495582\pi$
$968$	−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	$-0.728605\pi$
$971$	−41.0089			−1.31604			−0.658019	+	0.753001i	$0.728605\pi$
$972$	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	$-0.710924\pi$
$977$		−	49.2843i		−	1.57674i	0.615199	−	0.788372i	$-0.289076\pi$
$978$	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
$994$	−19.4104	+	22.6811i	−0.615660	+	0.719402i
$995$		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.699.12		16
4.3	odd	2	inner	700.2.c.k.699.7		16
5.2	odd	4		700.2.g.i.251.4	yes	8
5.3	odd	4		700.2.g.k.251.5	yes	8
5.4	even	2	inner	700.2.c.k.699.5		16
7.6	odd	2	inner	700.2.c.k.699.11		16
20.3	even	4		700.2.g.k.251.8	yes	8
20.7	even	4		700.2.g.i.251.1	✓	8
20.19	odd	2	inner	700.2.c.k.699.10		16
28.27	even	2	inner	700.2.c.k.699.8		16
35.13	even	4		700.2.g.k.251.6	yes	8
35.27	even	4		700.2.g.i.251.3	yes	8
35.34	odd	2	inner	700.2.c.k.699.6		16
140.27	odd	4		700.2.g.i.251.2	yes	8
140.83	odd	4		700.2.g.k.251.7	yes	8
140.139	even	2	inner	700.2.c.k.699.9		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.736813 + 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(-3.37740 + 2.06155i) q^{6} +(-2.51564 + 0.819496i) q^{7} +(-2.82083 + 0.207107i) q^{8} -4.82843 q^{9} +O(q^{10})\)	\(q+(0.736813 + 1.20711i) q^{2} +2.79793i q^{3} +(-0.914214 + 1.77882i) q^{4} +(-3.37740 + 2.06155i) q^{6} +(-2.51564 + 0.819496i) q^{7} +(-2.82083 + 0.207107i) q^{8} -4.82843 q^{9} +1.47363i q^{11} +(-4.97703 - 2.55791i) q^{12} +5.83095 q^{13} +(-2.84277 - 2.43283i) q^{14} +(-2.32843 - 3.25245i) q^{16} +4.12311 q^{17} +(-3.55765 - 5.82843i) q^{18} -5.11582 q^{19} +(-2.29289 - 7.03858i) q^{21} +(-1.77882 + 1.08579i) q^{22} +2.08402 q^{23} +(-0.579471 - 7.89250i) q^{24} +(4.29632 + 7.03858i) q^{26} -5.11582i q^{27} +(0.842091 - 5.22407i) q^{28} -8.24264 q^{29} +3.95687 q^{31} +(2.21044 - 5.20711i) q^{32} -4.12311 q^{33} +(3.03796 + 4.97703i) q^{34} +(4.41421 - 8.58892i) q^{36} +2.24264i q^{37} +(-3.76940 - 6.17534i) q^{38} +16.3146i q^{39} -4.12311i q^{41} +(6.80689 - 7.95388i) q^{42} +2.94725 q^{43} +(-2.62132 - 1.34721i) q^{44} +(1.53553 + 2.51564i) q^{46} +11.8706i q^{47} +(9.10013 - 6.51478i) q^{48} +(5.65685 - 4.12311i) q^{49} +11.5362i q^{51} +(-5.33074 + 10.3722i) q^{52} +3.75736i q^{53} +(6.17534 - 3.76940i) q^{54} +(6.92647 - 2.83267i) q^{56} -14.3137i q^{57} +(-6.07328 - 9.94975i) q^{58} +5.59587 q^{59} +11.6619i q^{61} +(2.91548 + 4.77637i) q^{62} +(12.1466 - 3.95687i) q^{63} +(7.91421 - 1.16843i) q^{64} +(-3.03796 - 4.97703i) q^{66} -12.7570 q^{67} +(-3.76940 + 7.33428i) q^{68} +5.83095i q^{69} -7.97852i q^{71} +(13.6202 - 1.00000i) q^{72} -12.3693 q^{73} +(-2.70711 + 1.65241i) q^{74} +(4.67695 - 9.10013i) q^{76} +(-1.20763 - 3.70711i) q^{77} +(-19.6935 + 12.0208i) q^{78} -4.16804i q^{79} -0.171573 q^{81} +(4.97703 - 3.03796i) q^{82} +2.79793i q^{83} +(14.6166 + 2.35611i) q^{84} +(2.17157 + 3.55765i) q^{86} -23.0624i q^{87} +(-0.305198 - 4.15685i) q^{88} -12.3693i q^{89} +(-14.6686 + 4.77844i) q^{91} +(-1.90524 + 3.70711i) q^{92} +11.0711i q^{93} +(-14.3291 + 8.74643i) q^{94} +(14.5691 + 6.18466i) q^{96} +8.24621 q^{97} +(9.14507 + 3.79047i) q^{98} -7.11529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 32 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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