LMFDB - Embedded newform 1710.2.l.l.1531.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1531.2
Root			$2.38600 + 4.13267i$ of defining polynomial
Character	$\chi$	$=$	1710.1531
Dual form			1710.2.l.l.1261.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +4.77200 q^{11} +(-1.88600 - 3.26665i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.38600 - 4.13267i) q^{19} -1.00000 q^{20} +(-2.38600 + 4.13267i) q^{22} +(2.38600 + 4.13267i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.77200 q^{26} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} -5.77200 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{35} -1.00000 q^{37} +(4.27200 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} +(2.38600 - 4.13267i) q^{41} +(-0.113999 + 0.197452i) q^{43} +(-2.38600 - 4.13267i) q^{44} -4.77200 q^{46} -6.00000 q^{49} +1.00000 q^{50} +(-1.88600 + 3.26665i) q^{52} +(0.613999 + 1.06348i) q^{53} +(2.38600 - 4.13267i) q^{55} -1.00000 q^{56} +6.00000 q^{58} +(1.77200 - 3.06920i) q^{59} +(2.88600 + 4.99870i) q^{61} +(2.88600 - 4.99870i) q^{62} +1.00000 q^{64} -3.77200 q^{65} +(1.11400 + 1.92950i) q^{67} +(-0.500000 - 0.866025i) q^{70} +(4.77200 - 8.26535i) q^{71} +(5.88600 - 10.1949i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-2.88600 + 3.26665i) q^{76} -4.77200 q^{77} +(7.65800 - 13.2640i) q^{79} +(0.500000 + 0.866025i) q^{80} +(2.38600 + 4.13267i) q^{82} -6.00000 q^{83} +(-0.113999 - 0.197452i) q^{86} +4.77200 q^{88} +(-4.15800 - 7.20187i) q^{89} +(1.88600 + 3.26665i) q^{91} +(2.38600 - 4.13267i) q^{92} +(-4.27200 - 0.866025i) q^{95} +(5.00000 - 8.66025i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8} + 2 q^{10} + 2 q^{11} + q^{13} + 2 q^{14} - 2 q^{16} + 3 q^{19} - 4 q^{20} - q^{22} + q^{23} - 2 q^{25} - 2 q^{26} + 2 q^{28} - 12 q^{29} - 6 q^{31} - 2 q^{32} - 2 q^{35} - 4 q^{37} + 2 q^{40} + q^{41} - 9 q^{43} - q^{44} - 2 q^{46} - 24 q^{49} + 4 q^{50} + q^{52} + 11 q^{53} + q^{55} - 4 q^{56} + 24 q^{58} - 10 q^{59} + 3 q^{61} + 3 q^{62} + 4 q^{64} + 2 q^{65} + 13 q^{67} - 2 q^{70} + 2 q^{71} + 15 q^{73} + 2 q^{74} - 3 q^{76} - 2 q^{77} + 5 q^{79} + 2 q^{80} + q^{82} - 24 q^{83} - 9 q^{86} + 2 q^{88} + 9 q^{89} - q^{91} + q^{92} + 20 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8 + 2 * q^10 + 2 * q^11 + q^13 + 2 * q^14 - 2 * q^16 + 3 * q^19 - 4 * q^20 - q^22 + q^23 - 2 * q^25 - 2 * q^26 + 2 * q^28 - 12 * q^29 - 6 * q^31 - 2 * q^32 - 2 * q^35 - 4 * q^37 + 2 * q^40 + q^41 - 9 * q^43 - q^44 - 2 * q^46 - 24 * q^49 + 4 * q^50 + q^52 + 11 * q^53 + q^55 - 4 * q^56 + 24 * q^58 - 10 * q^59 + 3 * q^61 + 3 * q^62 + 4 * q^64 + 2 * q^65 + 13 * q^67 - 2 * q^70 + 2 * q^71 + 15 * q^73 + 2 * q^74 - 3 * q^76 - 2 * q^77 + 5 * q^79 + 2 * q^80 + q^82 - 24 * q^83 - 9 * q^86 + 2 * q^88 + 9 * q^89 - q^91 + q^92 + 20 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	4.77200			1.43881			0.719406	−	0.694589i	$-0.244414\pi$
$11$	4.77200			1.43881			0.719406	+	0.694589i	$0.244414\pi$
$12$		0			0
$13$	−1.88600	−	3.26665i	−0.523083	−	0.906006i	−0.999639	−	0.0268618i	$-0.991449\pi$
$13$	−1.88600	−	3.26665i	−0.523083	−	0.906006i	0.476557	−	0.879144i	$-0.341885\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−1.38600	−	4.13267i	−0.317970	−	0.948101i
$19$	−1.38600	−	4.13267i	−0.317970	−	0.948101i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−2.38600	+	4.13267i	−0.508697	+	0.881089i
$23$	2.38600	+	4.13267i	0.497516	+	0.861722i	0.999996	−	0.00286638i	$-0.000912399\pi$
$23$	2.38600	+	4.13267i	0.497516	+	0.861722i	−0.502480	+	0.864589i	$0.667579\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.77200			0.739750
$27$		0			0
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	−5.77200			−1.03668			−0.518341	−	0.855174i	$-0.673450\pi$
$31$	−5.77200			−1.03668			−0.518341	+	0.855174i	$0.673450\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	4.27200	+	0.866025i	0.693010	+	0.140488i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	2.38600	−	4.13267i	0.372631	−	0.645415i	−0.617339	−	0.786698i	$-0.711789\pi$
$41$	2.38600	−	4.13267i	0.372631	−	0.645415i	0.989969	+	0.141282i	$0.0451225\pi$
$42$		0			0
$43$	−0.113999	+	0.197452i	−0.0173847	+	0.0301112i	−0.874587	−	0.484869i	$-0.838867\pi$
$43$	−0.113999	+	0.197452i	−0.0173847	+	0.0301112i	0.857202	+	0.514980i	$0.172201\pi$
$44$	−2.38600	−	4.13267i	−0.359703	−	0.623024i
$45$		0			0
$46$	−4.77200			−0.703593
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$	1.00000			0.141421
$51$		0			0
$52$	−1.88600	+	3.26665i	−0.261541	+	0.453003i
$53$	0.613999	+	1.06348i	0.0843393	+	0.146080i	0.905109	−	0.425179i	$-0.139789\pi$
$53$	0.613999	+	1.06348i	0.0843393	+	0.146080i	−0.820770	+	0.571258i	$0.806455\pi$
$54$		0			0
$55$	2.38600	−	4.13267i	0.321728	−	0.557250i
$56$	−1.00000			−0.133631
$57$		0			0
$58$	6.00000			0.787839
$59$	1.77200	−	3.06920i	0.230695	−	0.399575i	−0.727318	−	0.686301i	$-0.759233\pi$
$59$	1.77200	−	3.06920i	0.230695	−	0.399575i	0.958013	+	0.286725i	$0.0925667\pi$
$60$		0			0
$61$	2.88600	+	4.99870i	0.369515	+	0.640018i	0.989490	−	0.144603i	$-0.0461907\pi$
$61$	2.88600	+	4.99870i	0.369515	+	0.640018i	−0.619975	+	0.784621i	$0.712857\pi$
$62$	2.88600	−	4.99870i	0.366522	−	0.634836i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.77200			−0.467859
$66$		0			0
$67$	1.11400	+	1.92950i	0.136097	+	0.235726i	0.926016	−	0.377485i	$-0.123211\pi$
$67$	1.11400	+	1.92950i	0.136097	+	0.235726i	−0.789919	+	0.613211i	$0.789878\pi$
$68$		0			0
$69$		0			0
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	4.77200	−	8.26535i	0.566332	−	0.980917i	−0.430592	−	0.902547i	$-0.641695\pi$
$71$	4.77200	−	8.26535i	0.566332	−	0.980917i	0.996924	−	0.0783698i	$-0.0249715\pi$
$72$		0			0
$73$	5.88600	−	10.1949i	0.688904	−	1.19322i	−0.283288	−	0.959035i	$-0.591425\pi$
$73$	5.88600	−	10.1949i	0.688904	−	1.19322i	0.972193	−	0.234182i	$-0.0752413\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−2.88600	+	3.26665i	−0.331047	+	0.374710i
$77$	−4.77200			−0.543820
$78$		0			0
$79$	7.65800	−	13.2640i	0.861593	−	1.49232i	−0.00879850	−	0.999961i	$-0.502801\pi$
$79$	7.65800	−	13.2640i	0.861593	−	1.49232i	0.870391	−	0.492361i	$-0.163866\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	2.38600	+	4.13267i	0.263490	+	0.456378i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$		0			0
$86$	−0.113999	−	0.197452i	−0.0122928	−	0.0212918i
$87$		0			0
$88$	4.77200			0.508697
$89$	−4.15800	−	7.20187i	−0.440747	−	0.763397i	0.556998	−	0.830514i	$-0.311953\pi$
$89$	−4.15800	−	7.20187i	−0.440747	−	0.763397i	−0.997745	+	0.0671171i	$0.978620\pi$
$90$		0			0
$91$	1.88600	+	3.26665i	0.197707	+	0.342438i
$92$	2.38600	−	4.13267i	0.248758	−	0.430861i
$93$		0			0
$94$		0			0
$95$	−4.27200	−	0.866025i	−0.438298	−	0.0888523i
$96$		0			0
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	3.00000	−	5.19615i	0.303046	−	0.524891i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	−1.88600	−	3.26665i	−0.184938	−	0.320321i
$105$		0			0
$106$	−1.22800			−0.119274
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	3.77200	−	6.53330i	0.361292	−	0.625777i	−0.626882	−	0.779115i	$-0.715669\pi$
$109$	3.77200	−	6.53330i	0.361292	−	0.625777i	0.988174	+	0.153338i	$0.0490023\pi$
$110$	2.38600	+	4.13267i	0.227496	+	0.394035i
$111$		0			0
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−3.54400			−0.333392			−0.166696	−	0.986008i	$-0.553310\pi$
$113$	−3.54400			−0.333392			−0.166696	+	0.986008i	$0.553310\pi$
$114$		0			0
$115$	4.77200			0.444991
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$		0			0
$118$	1.77200	+	3.06920i	0.163126	+	0.282543i
$119$		0			0
$120$		0			0
$121$	11.7720			1.07018
$122$	−5.77200			−0.522572
$123$		0			0
$124$	2.88600	+	4.99870i	0.259171	+	0.448897i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.15800	−	14.1301i	−0.723906	−	1.25384i	−0.959423	−	0.281971i	$-0.909012\pi$
$127$	−8.15800	−	14.1301i	−0.723906	−	1.25384i	0.235517	−	0.971870i	$-0.424322\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	1.88600	−	3.26665i	0.165413	−	0.286504i
$131$	7.15800	−	12.3980i	0.625398	−	1.08322i	−0.363066	−	0.931763i	$-0.618270\pi$
$131$	7.15800	−	12.3980i	0.625398	−	1.08322i	0.988464	−	0.151457i	$-0.0483965\pi$
$132$		0			0
$133$	1.38600	+	4.13267i	0.120182	+	0.358348i
$134$	−2.22800			−0.192470
$135$		0			0
$136$		0			0
$137$	7.77200	+	13.4615i	0.664007	+	1.15009i	0.979554	+	0.201184i	$0.0644788\pi$
$137$	7.77200	+	13.4615i	0.664007	+	1.15009i	−0.315547	+	0.948910i	$0.602188\pi$
$138$		0			0
$139$	1.11400	+	1.92950i	0.0944882	+	0.163658i	0.909395	−	0.415934i	$-0.136545\pi$
$139$	1.11400	+	1.92950i	0.0944882	+	0.163658i	−0.814907	+	0.579592i	$0.803212\pi$
$140$	1.00000			0.0845154
$141$		0			0
$142$	4.77200	+	8.26535i	0.400458	+	0.693613i
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$		0			0
$145$	−6.00000			−0.498273
$146$	5.88600	+	10.1949i	0.487129	+	0.843732i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	1.77200	−	3.06920i	0.145168	−	0.251438i	−0.784268	−	0.620423i	$-0.786961\pi$
$149$	1.77200	−	3.06920i	0.145168	−	0.251438i	0.929436	+	0.368984i	$0.120294\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−1.38600	−	4.13267i	−0.112420	−	0.335204i
$153$		0			0
$154$	2.38600	−	4.13267i	0.192269	−	0.333020i
$155$	−2.88600	+	4.99870i	−0.231809	+	0.401505i
$156$		0			0
$157$	−10.2720	+	17.7916i	−0.819795	+	1.41993i	0.0860381	+	0.996292i	$0.472579\pi$
$157$	−10.2720	+	17.7916i	−0.819795	+	1.41993i	−0.905833	+	0.423635i	$0.860754\pi$
$158$	7.65800	+	13.2640i	0.609238	+	1.05523i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−2.38600	−	4.13267i	−0.188043	−	0.325700i
$162$		0			0
$163$	7.31601			0.573034			0.286517	−	0.958075i	$-0.407503\pi$
$163$	7.31601			0.573034			0.286517	+	0.958075i	$0.407503\pi$
$164$	−4.77200			−0.372631
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	7.15800	+	12.3980i	0.553903	+	0.959388i	0.997988	+	0.0634033i	$0.0201955\pi$
$167$	7.15800	+	12.3980i	0.553903	+	0.959388i	−0.444085	+	0.895985i	$0.646471\pi$
$168$		0			0
$169$	−0.613999	+	1.06348i	−0.0472307	+	0.0818060i
$170$		0			0
$171$		0			0
$172$	0.227998			0.0173847
$173$	−7.15800	+	12.3980i	−0.544213	+	0.942604i	0.454443	+	0.890776i	$0.349838\pi$
$173$	−7.15800	+	12.3980i	−0.544213	+	0.942604i	−0.998656	+	0.0518286i	$0.983495\pi$
$174$		0			0
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−2.38600	+	4.13267i	−0.179852	+	0.311512i
$177$		0			0
$178$	8.31601			0.623311
$179$	26.3160			1.96695			0.983475	−	0.181042i	$-0.0579471\pi$
$179$	26.3160			1.96695			0.983475	+	0.181042i	$0.0579471\pi$
$180$		0			0
$181$	8.54400	+	14.7986i	0.635071	+	1.09997i	0.986500	+	0.163760i	$0.0523624\pi$
$181$	8.54400	+	14.7986i	0.635071	+	1.09997i	−0.351429	+	0.936214i	$0.614304\pi$
$182$	−3.77200			−0.279599
$183$		0			0
$184$	2.38600	+	4.13267i	0.175898	+	0.304665i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	2.88600	−	3.26665i	0.209373	−	0.236988i
$191$	9.54400			0.690580			0.345290	−	0.938496i	$-0.387781\pi$
$191$	9.54400			0.690580			0.345290	+	0.938496i	$0.387781\pi$
$192$		0			0
$193$	2.88600	−	4.99870i	0.207739	−	0.359814i	−0.743263	−	0.668999i	$-0.766723\pi$
$193$	2.88600	−	4.99870i	0.207739	−	0.359814i	0.951002	+	0.309185i	$0.100056\pi$
$194$	5.00000	+	8.66025i	0.358979	+	0.621770i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	−14.3160			−1.01997			−0.509987	−	0.860182i	$-0.670350\pi$
$197$	−14.3160			−1.01997			−0.509987	+	0.860182i	$0.670350\pi$
$198$		0			0
$199$	−12.6580	−	21.9243i	−0.897302	−	1.55417i	−0.830929	−	0.556378i	$-0.812191\pi$
$199$	−12.6580	−	21.9243i	−0.897302	−	1.55417i	−0.0663726	−	0.997795i	$-0.521143\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	6.00000			0.422159
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		0			0
$205$	−2.38600	−	4.13267i	−0.166646	−	0.288639i
$206$	6.50000	−	11.2583i	0.452876	−	0.784405i
$207$		0			0
$208$	3.77200			0.261541
$209$	−6.61400	−	19.7211i	−0.457500	−	1.36414i
$210$		0			0
$211$	1.72800	−	2.99298i	0.118960	−	0.206045i	−0.800396	−	0.599472i	$-0.795377\pi$
$211$	1.72800	−	2.99298i	0.118960	−	0.206045i	0.919356	+	0.393427i	$0.128711\pi$
$212$	0.613999	−	1.06348i	0.0421696	−	0.0730399i
$213$		0			0
$214$		0			0
$215$	0.113999	+	0.197452i	0.00777467	+	0.0134661i
$216$		0			0
$217$	5.77200			0.391829
$218$	3.77200	+	6.53330i	0.255472	+	0.442491i
$219$		0			0
$220$	−4.77200			−0.321728
$221$		0			0
$222$		0			0
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	−0.0552786	−	0.998471i	$-0.517605\pi$
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	0.892341	−	0.451363i	$-0.149062\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	1.77200	−	3.06920i	0.117872	−	0.204160i
$227$	25.0880			1.66515			0.832575	−	0.553913i	$-0.186866\pi$
$227$	25.0880			1.66515			0.832575	+	0.553913i	$0.186866\pi$
$228$		0			0
$229$	−18.8600			−1.24630			−0.623152	−	0.782101i	$-0.714148\pi$
$229$	−18.8600			−1.24630			−0.623152	+	0.782101i	$0.714148\pi$
$230$	−2.38600	+	4.13267i	−0.157328	+	0.272501i
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−10.7720	+	18.6577i	−0.705697	+	1.22230i	0.260742	+	0.965409i	$0.416033\pi$
$233$	−10.7720	+	18.6577i	−0.705697	+	1.22230i	−0.966439	+	0.256895i	$0.917301\pi$
$234$		0			0
$235$		0			0
$236$	−3.54400			−0.230695
$237$		0			0
$238$		0			0
$239$	3.54400			0.229243			0.114621	−	0.993409i	$-0.463435\pi$
$239$	3.54400			0.229243			0.114621	+	0.993409i	$0.463435\pi$
$240$		0			0
$241$	1.65800	+	2.87175i	0.106801	+	0.184985i	0.914473	−	0.404648i	$-0.132606\pi$
$241$	1.65800	+	2.87175i	0.106801	+	0.184985i	−0.807671	+	0.589633i	$0.799272\pi$
$242$	−5.88600	+	10.1949i	−0.378366	+	0.655350i
$243$		0			0
$244$	2.88600	−	4.99870i	0.184757	−	0.320009i
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	−10.8860	+	12.3218i	−0.692660	+	0.784018i
$248$	−5.77200			−0.366522
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−7.77200	−	13.4615i	−0.490564	−	0.849682i	0.509377	−	0.860544i	$-0.329876\pi$
$251$	−7.77200	−	13.4615i	−0.490564	−	0.849682i	−0.999941	+	0.0108612i	$0.996543\pi$
$252$		0			0
$253$	11.3860	+	19.7211i	0.715832	+	1.23986i
$254$	16.3160			1.02376
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.773427	−	0.633885i	$-0.781459\pi$
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.162247	−	0.986750i	$-0.551874\pi$
$258$		0			0
$259$	1.00000			0.0621370
$260$	1.88600	+	3.26665i	0.116965	+	0.202589i
$261$		0			0
$262$	7.15800	+	12.3980i	0.442223	+	0.765953i
$263$	3.61400	−	6.25963i	0.222849	−	0.385985i	−0.732823	−	0.680419i	$-0.761798\pi$
$263$	3.61400	−	6.25963i	0.222849	−	0.385985i	0.955672	+	0.294434i	$0.0951311\pi$
$264$		0			0
$265$	1.22800			0.0754353
$266$	−4.27200	−	0.866025i	−0.261933	−	0.0530994i
$267$		0			0
$268$	1.11400	−	1.92950i	0.0680483	−	0.117863i
$269$	−4.22800	+	7.32311i	−0.257786	+	0.446498i	−0.965648	−	0.259852i	$-0.916326\pi$
$269$	−4.22800	+	7.32311i	−0.257786	+	0.446498i	0.707863	+	0.706350i	$0.249659\pi$
$270$		0			0
$271$	−14.7720	+	25.5859i	−0.897335	+	1.55423i	−0.0664476	+	0.997790i	$0.521167\pi$
$271$	−14.7720	+	25.5859i	−0.897335	+	1.55423i	−0.830888	+	0.556440i	$0.812167\pi$
$272$		0			0
$273$		0			0
$274$	−15.5440			−0.939048
$275$	−2.38600	−	4.13267i	−0.143881	−	0.249210i
$276$		0			0
$277$	−29.0880			−1.74773			−0.873864	−	0.486170i	$-0.838394\pi$
$277$	−29.0880			−1.74773			−0.873864	+	0.486170i	$0.838394\pi$
$278$	−2.22800			−0.133626
$279$		0			0
$280$	−0.500000	+	0.866025i	−0.0298807	+	0.0517549i
$281$	9.61400	+	16.6519i	0.573523	+	0.993371i	0.996200	+	0.0870909i	$0.0277571\pi$
$281$	9.61400	+	16.6519i	0.573523	+	0.993371i	−0.422677	+	0.906280i	$0.638910\pi$
$282$		0			0
$283$	−12.3160	+	21.3319i	−0.732111	+	1.26805i	0.223869	+	0.974619i	$0.428131\pi$
$283$	−12.3160	+	21.3319i	−0.732111	+	1.26805i	−0.955980	+	0.293433i	$0.905202\pi$
$284$	−9.54400			−0.566332
$285$		0			0
$286$	18.0000			1.06436
$287$	−2.38600	+	4.13267i	−0.140841	+	0.243944i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	3.00000	−	5.19615i	0.176166	−	0.305129i
$291$		0			0
$292$	−11.7720			−0.688904
$293$	28.7720			1.68088			0.840439	−	0.541906i	$-0.182297\pi$
$293$	28.7720			1.68088			0.840439	+	0.541906i	$0.182297\pi$
$294$		0			0
$295$	−1.77200	−	3.06920i	−0.103170	−	0.178696i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$	1.77200	+	3.06920i	0.102649	+	0.177794i
$299$	9.00000	−	15.5885i	0.520483	−	0.901504i
$300$		0			0
$301$	0.113999	−	0.197452i	0.00657080	−	0.0113810i
$302$	−4.00000	+	6.92820i	−0.230174	+	0.398673i
$303$		0			0
$304$	4.27200	+	0.866025i	0.245016	+	0.0496700i
$305$	5.77200			0.330504
$306$		0			0
$307$	3.22800	−	5.59106i	0.184232	−	0.319098i	−0.759086	−	0.650991i	$-0.774354\pi$
$307$	3.22800	−	5.59106i	0.184232	−	0.319098i	0.943317	+	0.331892i	$0.107687\pi$
$308$	2.38600	+	4.13267i	0.135955	+	0.235481i
$309$		0			0
$310$	−2.88600	−	4.99870i	−0.163914	−	0.283907i
$311$	−8.45600			−0.479496			−0.239748	−	0.970835i	$-0.577065\pi$
$311$	−8.45600			−0.479496			−0.239748	+	0.970835i	$0.577065\pi$
$312$		0			0
$313$	9.77200	+	16.9256i	0.552346	+	0.956692i	0.998105	+	0.0615384i	$0.0196007\pi$
$313$	9.77200	+	16.9256i	0.552346	+	0.956692i	−0.445759	+	0.895153i	$0.647066\pi$
$314$	−10.2720	−	17.7916i	−0.579683	−	1.00404i
$315$		0			0
$316$	−15.3160			−0.861593
$317$	14.3860	+	24.9173i	0.807998	+	1.39949i	0.914248	+	0.405155i	$0.132782\pi$
$317$	14.3860	+	24.9173i	0.807998	+	1.39949i	−0.106250	+	0.994339i	$0.533884\pi$
$318$		0			0
$319$	−14.3160	−	24.7960i	−0.801542	−	1.38831i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	4.77200			0.265933
$323$		0			0
$324$		0			0
$325$	−1.88600	+	3.26665i	−0.104617	+	0.181201i
$326$	−3.65800	+	6.33585i	−0.202598	+	0.350910i
$327$		0			0
$328$	2.38600	−	4.13267i	0.131745	−	0.228189i
$329$		0			0
$330$		0			0
$331$	−9.45600			−0.519749			−0.259874	−	0.965642i	$-0.583681\pi$
$331$	−9.45600			−0.519749			−0.259874	+	0.965642i	$0.583681\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$		0			0
$334$	−14.3160			−0.783337
$335$	2.22800			0.121729
$336$		0			0
$337$	2.34200	−	4.05646i	0.127577	−	0.220969i	−0.795160	−	0.606399i	$-0.792613\pi$
$337$	2.34200	−	4.05646i	0.127577	−	0.220969i	0.922737	+	0.385430i	$0.125947\pi$
$338$	−0.613999	−	1.06348i	−0.0333971	−	0.0578456i
$339$		0			0
$340$		0			0
$341$	−27.5440			−1.49159
$342$		0			0
$343$	13.0000			0.701934
$344$	−0.113999	+	0.197452i	−0.00614642	+	0.0106459i
$345$		0			0
$346$	−7.15800	−	12.3980i	−0.384817	−	0.666522i
$347$	4.77200	−	8.26535i	0.256174	−	0.443707i	−0.709039	−	0.705169i	$-0.750871\pi$
$347$	4.77200	−	8.26535i	0.256174	−	0.443707i	0.965214	+	0.261462i	$0.0842045\pi$
$348$		0			0
$349$	−17.7720			−0.951313			−0.475657	−	0.879631i	$-0.657790\pi$
$349$	−17.7720			−0.951313			−0.475657	+	0.879631i	$0.657790\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	−2.38600	−	4.13267i	−0.127174	−	0.220272i
$353$	−3.54400			−0.188628			−0.0943141	−	0.995542i	$-0.530066\pi$
$353$	−3.54400			−0.188628			−0.0943141	+	0.995542i	$0.530066\pi$
$354$		0			0
$355$	−4.77200	−	8.26535i	−0.253272	−	0.438679i
$356$	−4.15800	+	7.20187i	−0.220374	+	0.381698i
$357$		0			0
$358$	−13.1580	+	22.7903i	−0.695422	+	1.20451i
$359$	−6.54400	+	11.3345i	−0.345379	+	0.598215i	−0.985423	−	0.170124i	$-0.945583\pi$
$359$	−6.54400	+	11.3345i	−0.345379	+	0.598215i	0.640043	+	0.768339i	$0.278916\pi$
$360$		0			0
$361$	−15.1580	+	11.4558i	−0.797790	+	0.602936i
$362$	−17.0880			−0.898126
$363$		0			0
$364$	1.88600	−	3.26665i	0.0988533	−	0.171219i
$365$	−5.88600	−	10.1949i	−0.308087	−	0.533623i
$366$		0			0
$367$	8.88600	+	15.3910i	0.463845	+	0.803404i	0.999149	−	0.0412561i	$-0.0131360\pi$
$367$	8.88600	+	15.3910i	0.463845	+	0.803404i	−0.535303	+	0.844660i	$0.679803\pi$
$368$	−4.77200			−0.248758
$369$		0			0
$370$	−0.500000	−	0.866025i	−0.0259938	−	0.0450225i
$371$	−0.613999	−	1.06348i	−0.0318772	−	0.0552130i
$372$		0			0
$373$	−8.77200			−0.454197			−0.227099	−	0.973872i	$-0.572924\pi$
$373$	−8.77200			−0.454197			−0.227099	+	0.973872i	$0.572924\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−11.3160	+	19.5999i	−0.582804	+	1.00945i
$378$		0			0
$379$	−17.7720			−0.912886			−0.456443	−	0.889753i	$-0.650877\pi$
$379$	−17.7720			−0.912886			−0.456443	+	0.889753i	$0.650877\pi$
$380$	1.38600	+	4.13267i	0.0711003	+	0.212002i
$381$		0			0
$382$	−4.77200	+	8.26535i	−0.244157	+	0.422892i
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$		0			0
$385$	−2.38600	+	4.13267i	−0.121602	+	0.210621i
$386$	2.88600	+	4.99870i	0.146894	+	0.254427i
$387$		0			0
$388$	−10.0000			−0.507673
$389$	12.5440	+	21.7269i	0.636006	+	1.10160i	0.986301	+	0.164956i	$0.0527481\pi$
$389$	12.5440	+	21.7269i	0.636006	+	1.10160i	−0.350295	+	0.936640i	$0.613919\pi$
$390$		0			0
$391$		0			0
$392$	−6.00000			−0.303046
$393$		0			0
$394$	7.15800	−	12.3980i	0.360615	−	0.624603i
$395$	−7.65800	−	13.2640i	−0.385316	−	0.667387i
$396$		0			0
$397$	16.0440	−	27.7890i	0.805225	−	1.39469i	−0.110913	−	0.993830i	$-0.535378\pi$
$397$	16.0440	−	27.7890i	0.805225	−	1.39469i	0.916139	−	0.400861i	$-0.131289\pi$
$398$	25.3160			1.26898
$399$		0			0
$400$	1.00000			0.0500000
$401$	−12.5440	+	21.7269i	−0.626418	+	1.08499i	0.361847	+	0.932237i	$0.382146\pi$
$401$	−12.5440	+	21.7269i	−0.626418	+	1.08499i	−0.988265	+	0.152750i	$0.951187\pi$
$402$		0			0
$403$	10.8860	+	18.8551i	0.542270	+	0.939240i
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$		0			0
$406$	−6.00000			−0.297775
$407$	−4.77200			−0.236539
$408$		0			0
$409$	−14.7020	−	25.4646i	−0.726967	−	1.25914i	−0.958159	−	0.286236i	$-0.907596\pi$
$409$	−14.7020	−	25.4646i	−0.726967	−	1.25914i	0.231192	−	0.972908i	$-0.425738\pi$
$410$	4.77200			0.235672
$411$		0			0
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$	−1.77200	+	3.06920i	−0.0871945	+	0.151025i
$414$		0			0
$415$	−3.00000	+	5.19615i	−0.147264	+	0.255069i
$416$	−1.88600	+	3.26665i	−0.0924688	+	0.160161i
$417$		0			0
$418$	20.3860	+	4.13267i	0.997112	+	0.202136i
$419$	−17.8600			−0.872519			−0.436259	−	0.899821i	$-0.643697\pi$
$419$	−17.8600			−0.872519			−0.436259	+	0.899821i	$0.643697\pi$
$420$		0			0
$421$	0.227998	−	0.394904i	0.0111119	−	0.0192465i	−0.860416	−	0.509592i	$-0.829796\pi$
$421$	0.227998	−	0.394904i	0.0111119	−	0.0192465i	0.871528	+	0.490346i	$0.163130\pi$
$422$	1.72800	+	2.99298i	0.0841176	+	0.145696i
$423$		0			0
$424$	0.613999	+	1.06348i	0.0298184	+	0.0516470i
$425$		0			0
$426$		0			0
$427$	−2.88600	−	4.99870i	−0.139663	−	0.241904i
$428$		0			0
$429$		0			0
$430$	−0.227998			−0.0109950
$431$	15.5440	+	26.9230i	0.748728	+	1.29684i	0.948432	+	0.316979i	$0.102669\pi$
$431$	15.5440	+	26.9230i	0.748728	+	1.29684i	−0.199704	+	0.979856i	$0.563998\pi$
$432$		0			0
$433$	7.65800	+	13.2640i	0.368020	+	0.637430i	0.989256	−	0.146194i	$-0.0467024\pi$
$433$	7.65800	+	13.2640i	0.368020	+	0.637430i	−0.621236	+	0.783624i	$0.713369\pi$
$434$	−2.88600	+	4.99870i	−0.138532	+	0.239945i
$435$		0			0
$436$	−7.54400			−0.361292
$437$	13.7720	−	15.5885i	0.658804	−	0.745697i
$438$		0			0
$439$	10.6580	−	18.4602i	0.508679	−	0.881057i	−0.491271	−	0.871007i	$-0.663467\pi$
$439$	10.6580	−	18.4602i	0.508679	−	0.881057i	0.999949	−	0.0100505i	$-0.00319922\pi$
$440$	2.38600	−	4.13267i	0.113748	−	0.197018i
$441$		0			0
$442$		0			0
$443$	2.45600	+	4.25391i	0.116688	+	0.202109i	0.918453	−	0.395530i	$-0.129439\pi$
$443$	2.45600	+	4.25391i	0.116688	+	0.202109i	−0.801765	+	0.597639i	$0.796106\pi$
$444$		0			0
$445$	−8.31601			−0.394216
$446$	12.5000	+	21.6506i	0.591892	+	1.02519i
$447$		0			0
$448$	−1.00000			−0.0472456
$449$	−10.7720			−0.508362			−0.254181	−	0.967157i	$-0.581806\pi$
$449$	−10.7720			−0.508362			−0.254181	+	0.967157i	$0.581806\pi$
$450$		0			0
$451$	11.3860	−	19.7211i	0.536146	−	0.928632i
$452$	1.77200	+	3.06920i	0.0833480	+	0.144363i
$453$		0			0
$454$	−12.5440	+	21.7269i	−0.588719	+	1.01969i
$455$	3.77200			0.176834
$456$		0			0
$457$	16.8600			0.788678			0.394339	−	0.918965i	$-0.370974\pi$
$457$	16.8600			0.788678			0.394339	+	0.918965i	$0.370974\pi$
$458$	9.43000	−	16.3332i	0.440635	−	0.763203i
$459$		0			0
$460$	−2.38600	−	4.13267i	−0.111248	−	0.192687i
$461$	−8.31601	+	14.4037i	−0.387315	+	0.670849i	−0.992087	−	0.125549i	$-0.959931\pi$
$461$	−8.31601	+	14.4037i	−0.387315	+	0.670849i	0.604772	+	0.796398i	$0.293264\pi$
$462$		0			0
$463$	−23.6320			−1.09827			−0.549136	−	0.835733i	$-0.685043\pi$
$463$	−23.6320			−1.09827			−0.549136	+	0.835733i	$0.685043\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	−10.7720	−	18.6577i	−0.499003	−	0.864299i
$467$	−25.0880			−1.16093			−0.580467	−	0.814284i	$-0.697130\pi$
$467$	−25.0880			−1.16093			−0.580467	+	0.814284i	$0.697130\pi$
$468$		0			0
$469$	−1.11400	−	1.92950i	−0.0514397	−	0.0890962i
$470$		0			0
$471$		0			0
$472$	1.77200	−	3.06920i	0.0815630	−	0.141271i
$473$	−0.544004	+	0.942242i	−0.0250133	+	0.0433243i
$474$		0			0
$475$	−2.88600	+	3.26665i	−0.132419	+	0.149884i
$476$		0			0
$477$		0			0
$478$	−1.77200	+	3.06920i	−0.0810495	+	0.140382i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	1.88600	+	3.26665i	0.0859942	+	0.148946i
$482$	−3.31601			−0.151040
$483$		0			0
$484$	−5.88600	−	10.1949i	−0.267545	−	0.463402i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	16.3160			0.739349			0.369674	−	0.929161i	$-0.379469\pi$
$487$	16.3160			0.739349			0.369674	+	0.929161i	$0.379469\pi$
$488$	2.88600	+	4.99870i	0.130643	+	0.226281i
$489$		0			0
$490$	−3.00000	−	5.19615i	−0.135526	−	0.234738i
$491$	16.1580	−	27.9865i	0.729200	−	1.26301i	−0.228021	−	0.973656i	$-0.573226\pi$
$491$	16.1580	−	27.9865i	0.729200	−	1.26301i	0.957222	−	0.289356i	$-0.0934412\pi$
$492$		0			0
$493$		0			0
$494$	−5.22800	−	15.5885i	−0.235219	−	0.701358i
$495$		0			0
$496$	2.88600	−	4.99870i	0.129585	−	0.224448i
$497$	−4.77200	+	8.26535i	−0.214054	+	0.370752i
$498$		0			0
$499$	14.8160	−	25.6621i	0.663256	−	1.14879i	−0.316500	−	0.948593i	$-0.602508\pi$
$499$	14.8160	−	25.6621i	0.663256	−	1.14879i	0.979755	−	0.200200i	$-0.0641591\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	15.5440			0.693763
$503$	−4.15800	−	7.20187i	−0.185396	−	0.321116i	0.758314	−	0.651890i	$-0.226024\pi$
$503$	−4.15800	−	7.20187i	−0.185396	−	0.321116i	−0.943710	+	0.330774i	$0.892690\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$	−22.7720			−1.01234
$507$		0			0
$508$	−8.15800	+	14.1301i	−0.361953	+	0.626921i
$509$	−8.31601	−	14.4037i	−0.368600	−	0.638435i	0.620747	−	0.784011i	$-0.286830\pi$
$509$	−8.31601	−	14.4037i	−0.368600	−	0.638435i	−0.989347	+	0.145577i	$0.953496\pi$
$510$		0			0
$511$	−5.88600	+	10.1949i	−0.260381	+	0.450994i
$512$	1.00000			0.0441942
$513$		0			0
$514$	30.0000			1.32324
$515$	−6.50000	+	11.2583i	−0.286424	+	0.496101i
$516$		0			0
$517$		0			0
$518$	−0.500000	+	0.866025i	−0.0219687	+	0.0380510i
$519$		0			0
$520$	−3.77200			−0.165413
$521$	33.5440			1.46959			0.734795	−	0.678290i	$-0.237278\pi$
$521$	33.5440			1.46959			0.734795	+	0.678290i	$0.237278\pi$
$522$		0			0
$523$	1.65800	+	2.87175i	0.0724994	+	0.125573i	0.899996	−	0.435898i	$-0.143569\pi$
$523$	1.65800	+	2.87175i	0.0724994	+	0.125573i	−0.827497	+	0.561471i	$0.810236\pi$
$524$	−14.3160			−0.625398
$525$		0			0
$526$	3.61400	+	6.25963i	0.157578	+	0.272933i
$527$		0			0
$528$		0			0
$529$	0.113999	−	0.197452i	0.00495648	−	0.00858488i
$530$	−0.613999	+	1.06348i	−0.0266704	+	0.0461945i
$531$		0			0
$532$	2.88600	−	3.26665i	0.125124	−	0.141627i
$533$	−18.0000			−0.779667
$534$		0			0
$535$		0			0
$536$	1.11400	+	1.92950i	0.0481174	+	0.0833418i
$537$		0			0
$538$	−4.22800	−	7.32311i	−0.182282	−	0.315722i
$539$	−28.6320			−1.23327
$540$		0			0
$541$	4.65800	+	8.06790i	0.200263	+	0.346866i	0.948613	−	0.316438i	$-0.102487\pi$
$541$	4.65800	+	8.06790i	0.200263	+	0.346866i	−0.748350	+	0.663304i	$0.769154\pi$
$542$	−14.7720	−	25.5859i	−0.634512	−	1.09901i
$543$		0			0
$544$		0			0
$545$	−3.77200	−	6.53330i	−0.161575	−	0.279856i
$546$		0			0
$547$	15.4300	+	26.7256i	0.659739	+	1.14270i	0.980683	+	0.195604i	$0.0626667\pi$
$547$	15.4300	+	26.7256i	0.659739	+	1.14270i	−0.320944	+	0.947098i	$0.604000\pi$
$548$	7.77200	−	13.4615i	0.332003	−	0.575047i
$549$		0			0
$550$	4.77200			0.203479
$551$	−17.3160	+	19.5999i	−0.737687	+	0.834984i
$552$		0			0
$553$	−7.65800	+	13.2640i	−0.325651	+	0.564045i
$554$	14.5440	−	25.1910i	0.617916	−	1.07026i
$555$		0			0
$556$	1.11400	−	1.92950i	0.0472441	−	0.0818292i
$557$	5.38600	+	9.32883i	0.228212	+	0.395275i	0.957278	−	0.289168i	$-0.0933787\pi$
$557$	5.38600	+	9.32883i	0.228212	+	0.395275i	−0.729066	+	0.684443i	$0.760045\pi$
$558$		0			0
$559$	0.860009			0.0363745
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$		0			0
$562$	−19.2280			−0.811084
$563$	−20.4560			−0.862117			−0.431059	−	0.902324i	$-0.641860\pi$
$563$	−20.4560			−0.862117			−0.431059	+	0.902324i	$0.641860\pi$
$564$		0			0
$565$	−1.77200	+	3.06920i	−0.0745487	+	0.129122i
$566$	−12.3160	−	21.3319i	−0.517680	−	0.896649i
$567$		0			0
$568$	4.77200	−	8.26535i	0.200229	−	0.346806i
$569$	−10.7720			−0.451586			−0.225793	−	0.974175i	$-0.572497\pi$
$569$	−10.7720			−0.451586			−0.225793	+	0.974175i	$0.572497\pi$
$570$		0			0
$571$	40.8600			1.70994			0.854969	−	0.518679i	$-0.173576\pi$
$571$	40.8600			1.70994			0.854969	+	0.518679i	$0.173576\pi$
$572$	−9.00000	+	15.5885i	−0.376309	+	0.651786i
$573$		0			0
$574$	−2.38600	−	4.13267i	−0.0995898	−	0.172495i
$575$	2.38600	−	4.13267i	0.0995031	−	0.172344i
$576$		0			0
$577$	−7.54400			−0.314061			−0.157030	−	0.987594i	$-0.550192\pi$
$577$	−7.54400			−0.314061			−0.157030	+	0.987594i	$0.550192\pi$
$578$	−17.0000			−0.707107
$579$		0			0
$580$	3.00000	+	5.19615i	0.124568	+	0.215758i
$581$	6.00000			0.248922
$582$		0			0
$583$	2.93000	+	5.07492i	0.121348	+	0.210182i
$584$	5.88600	−	10.1949i	0.243564	−	0.421866i
$585$		0			0
$586$	−14.3860	+	24.9173i	−0.594280	+	1.02932i
$587$	−4.22800	+	7.32311i	−0.174508	+	0.302257i	−0.939991	−	0.341199i	$-0.889167\pi$
$587$	−4.22800	+	7.32311i	−0.174508	+	0.302257i	0.765483	+	0.643456i	$0.222500\pi$
$588$		0			0
$589$	8.00000	+	23.8538i	0.329634	+	0.982879i
$590$	3.54400			0.145904
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−4.77200	−	8.26535i	−0.195963	−	0.339417i	0.751253	−	0.660014i	$-0.229450\pi$
$593$	−4.77200	−	8.26535i	−0.195963	−	0.339417i	−0.947216	+	0.320597i	$0.896116\pi$
$594$		0			0
$595$		0			0
$596$	−3.54400			−0.145168
$597$		0			0
$598$	9.00000	+	15.5885i	0.368037	+	0.637459i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	15.6320			0.637643			0.318822	−	0.947815i	$-0.396713\pi$
$601$	15.6320			0.637643			0.318822	+	0.947815i	$0.396713\pi$
$602$	0.113999	+	0.197452i	0.00464625	+	0.00804755i
$603$		0			0
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	5.88600	−	10.1949i	0.239300	−	0.414480i
$606$		0			0
$607$	−5.91199			−0.239960			−0.119980	−	0.992776i	$-0.538283\pi$
$607$	−5.91199			−0.239960			−0.119980	+	0.992776i	$0.538283\pi$
$608$	−2.88600	+	3.26665i	−0.117043	+	0.132480i
$609$		0			0
$610$	−2.88600	+	4.99870i	−0.116851	+	0.202391i
$611$		0			0
$612$		0			0
$613$	−3.93000	+	6.80697i	−0.158731	+	0.274931i	−0.934411	−	0.356195i	$-0.884074\pi$
$613$	−3.93000	+	6.80697i	−0.158731	+	0.274931i	0.775680	+	0.631126i	$0.217407\pi$
$614$	3.22800	+	5.59106i	0.130271	+	0.225637i
$615$		0			0
$616$	−4.77200			−0.192269
$617$	15.5440	+	26.9230i	0.625778	+	1.08388i	0.988390	+	0.151939i	$0.0485518\pi$
$617$	15.5440	+	26.9230i	0.625778	+	1.08388i	−0.362612	+	0.931940i	$0.618115\pi$
$618$		0			0
$619$	37.1760			1.49423			0.747115	−	0.664695i	$-0.231438\pi$
$619$	37.1760			1.49423			0.747115	+	0.664695i	$0.231438\pi$
$620$	5.77200			0.231809
$621$		0			0
$622$	4.22800	−	7.32311i	0.169527	−	0.293630i
$623$	4.15800	+	7.20187i	0.166587	+	0.288537i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−19.5440			−0.781135
$627$		0			0
$628$	20.5440			0.819795
$629$		0			0
$630$		0			0
$631$	0.569995	+	0.987261i	0.0226912	+	0.0393022i	0.877148	−	0.480220i	$-0.159443\pi$
$631$	0.569995	+	0.987261i	0.0226912	+	0.0393022i	−0.854457	+	0.519522i	$0.826110\pi$
$632$	7.65800	−	13.2640i	0.304619	−	0.527616i
$633$		0			0
$634$	−28.7720			−1.14268
$635$	−16.3160			−0.647481
$636$		0			0
$637$	11.3160	+	19.5999i	0.448356	+	0.776576i
$638$	28.6320			1.13355
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	1.22800	−	2.12696i	0.0485030	−	0.0840097i	−0.840755	−	0.541416i	$-0.817888\pi$
$641$	1.22800	−	2.12696i	0.0485030	−	0.0840097i	0.889258	+	0.457407i	$0.151222\pi$
$642$		0			0
$643$	−12.6580	+	21.9243i	−0.499183	+	0.864610i	−1.00000		0.000943247i	$-0.999700\pi$
$643$	−12.6580	+	21.9243i	−0.499183	+	0.864610i	0.500817	+	0.865553i	$0.333033\pi$
$644$	−2.38600	+	4.13267i	−0.0940216	+	0.162850i
$645$		0			0
$646$		0			0
$647$	38.3160			1.50636			0.753179	−	0.657816i	$-0.228519\pi$
$647$	38.3160			1.50636			0.753179	+	0.657816i	$0.228519\pi$
$648$		0			0
$649$	8.45600	−	14.6462i	0.331927	−	0.574914i
$650$	−1.88600	−	3.26665i	−0.0739750	−	0.128129i
$651$		0			0
$652$	−3.65800	−	6.33585i	−0.143258	−	0.248131i
$653$	−3.68399			−0.144166			−0.0720829	−	0.997399i	$-0.522965\pi$
$653$	−3.68399			−0.144166			−0.0720829	+	0.997399i	$0.522965\pi$
$654$		0			0
$655$	−7.15800	−	12.3980i	−0.279686	−	0.484431i
$656$	2.38600	+	4.13267i	0.0931577	+	0.161354i
$657$		0			0
$658$		0			0
$659$	19.1580	+	33.1826i	0.746290	+	1.29261i	0.949590	+	0.313495i	$0.101500\pi$
$659$	19.1580	+	33.1826i	0.746290	+	1.29261i	−0.203300	+	0.979117i	$0.565167\pi$
$660$		0			0
$661$	−3.31601	−	5.74349i	−0.128978	−	0.223396i	0.794303	−	0.607522i	$-0.207836\pi$
$661$	−3.31601	−	5.74349i	−0.128978	−	0.223396i	−0.923281	+	0.384126i	$0.874503\pi$
$662$	4.72800	−	8.18913i	0.183759	−	0.318280i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	4.27200	+	0.866025i	0.165661	+	0.0335830i
$666$		0			0
$667$	14.3160	−	24.7960i	0.554318	−	0.960107i
$668$	7.15800	−	12.3980i	0.276951	−	0.479694i
$669$		0			0
$670$	−1.11400	+	1.92950i	−0.0430375	+	0.0745432i
$671$	13.7720	+	23.8538i	0.531662	+	0.920866i
$672$		0			0
$673$	−29.7720			−1.14763			−0.573813	−	0.818986i	$-0.694536\pi$
$673$	−29.7720			−1.14763			−0.573813	+	0.818986i	$0.694536\pi$
$674$	2.34200	+	4.05646i	0.0902104	+	0.156249i
$675$		0			0
$676$	1.22800			0.0472307
$677$	8.31601			0.319610			0.159805	−	0.987149i	$-0.448913\pi$
$677$	8.31601			0.319610			0.159805	+	0.987149i	$0.448913\pi$
$678$		0			0
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$		0			0
$681$		0			0
$682$	13.7720	−	23.8538i	0.527357	−	0.913409i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$	15.5440			0.593906
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$		0			0
$688$	−0.113999	−	0.197452i	−0.00434617	−	0.00752779i
$689$	2.31601	−	4.01144i	0.0882328	−	0.152824i
$690$		0			0
$691$	49.8600			1.89676			0.948382	−	0.317130i	$-0.102719\pi$
$691$	49.8600			1.89676			0.948382	+	0.317130i	$0.102719\pi$
$692$	14.3160			0.544213
$693$		0			0
$694$	4.77200	+	8.26535i	0.181143	+	0.313748i
$695$	2.22800			0.0845128
$696$		0			0
$697$		0			0
$698$	8.88600	−	15.3910i	0.336340	−	0.582558i
$699$		0			0
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−8.31601	+	14.4037i	−0.314091	+	0.544022i	−0.979244	−	0.202685i	$-0.935033\pi$
$701$	−8.31601	+	14.4037i	−0.314091	+	0.544022i	0.665153	+	0.746707i	$0.268366\pi$
$702$		0			0
$703$	1.38600	+	4.13267i	0.0522740	+	0.155867i
$704$	4.77200			0.179852
$705$		0			0
$706$	1.77200	−	3.06920i	0.0666902	−	0.115511i
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$		0			0
$709$	13.1140	+	22.7141i	0.492507	+	0.853046i	0.999963	−	0.00863116i	$-0.00274742\pi$
$709$	13.1140	+	22.7141i	0.492507	+	0.853046i	−0.507456	+	0.861678i	$0.669414\pi$
$710$	9.54400			0.358180
$711$		0			0
$712$	−4.15800	−	7.20187i	−0.155828	−	0.269902i
$713$	−13.7720	−	23.8538i	−0.515766	−	0.893332i
$714$		0			0
$715$	−18.0000			−0.673162
$716$	−13.1580	−	22.7903i	−0.491738	−	0.851715i
$717$		0			0
$718$	−6.54400	−	11.3345i	−0.244220	−	0.423002i
$719$	−11.3160	+	19.5999i	−0.422016	+	0.730953i	−0.996137	−	0.0878178i	$-0.972011\pi$
$719$	−11.3160	+	19.5999i	−0.422016	+	0.730953i	0.574121	+	0.818771i	$0.305344\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	−2.34200	−	18.8551i	−0.0871601	−	0.701714i
$723$		0			0
$724$	8.54400	−	14.7986i	0.317535	−	0.549987i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	8.20201	−	14.2063i	0.304196	−	0.526882i	−0.672886	−	0.739746i	$-0.734946\pi$
$727$	8.20201	−	14.2063i	0.304196	−	0.526882i	0.977082	+	0.212864i	$0.0682790\pi$
$728$	1.88600	+	3.26665i	0.0698998	+	0.121070i
$729$		0			0
$730$	11.7720			0.435701
$731$		0			0
$732$		0			0
$733$	−37.4040			−1.38155			−0.690774	−	0.723070i	$-0.742730\pi$
$733$	−37.4040			−1.38155			−0.690774	+	0.723070i	$0.742730\pi$
$734$	−17.7720			−0.655977
$735$		0			0
$736$	2.38600	−	4.13267i	0.0879492	−	0.152332i
$737$	5.31601	+	9.20759i	0.195818	+	0.339166i
$738$		0			0
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	1.22800			0.0450812
$743$	14.3860	−	24.9173i	0.527771	−	0.914127i	−0.471705	−	0.881757i	$-0.656361\pi$
$743$	14.3860	−	24.9173i	0.527771	−	0.914127i	0.999476	−	0.0323700i	$-0.0103055\pi$
$744$		0			0
$745$	−1.77200	−	3.06920i	−0.0649211	−	0.112447i
$746$	4.38600	−	7.59678i	0.160583	−	0.278138i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−21.1140	−	36.5705i	−0.770461	−	1.33448i	−0.937311	−	0.348495i	$-0.886693\pi$
$751$	−21.1140	−	36.5705i	−0.770461	−	1.33448i	0.166850	−	0.985982i	$-0.446640\pi$
$752$		0			0
$753$		0			0
$754$	−11.3160	−	19.5999i	−0.412105	−	0.713786i
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	−10.8160	+	18.7339i	−0.393114	+	0.680894i	−0.992859	−	0.119298i	$-0.961936\pi$
$757$	−10.8160	+	18.7339i	−0.393114	+	0.680894i	0.599744	+	0.800192i	$0.295269\pi$
$758$	8.88600	−	15.3910i	0.322754	−	0.559026i
$759$		0			0
$760$	−4.27200	−	0.866025i	−0.154962	−	0.0314140i
$761$	54.9480			1.99186			0.995932	−	0.0901077i	$-0.0287211\pi$
$761$	54.9480			1.99186			0.995932	+	0.0901077i	$0.0287211\pi$
$762$		0			0
$763$	−3.77200	+	6.53330i	−0.136556	+	0.236521i
$764$	−4.77200	−	8.26535i	−0.172645	−	0.299030i
$765$		0			0
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	−13.3680			−0.482690
$768$		0			0
$769$	3.43000	+	5.94094i	0.123689	+	0.214236i	0.921220	−	0.389043i	$-0.127194\pi$
$769$	3.43000	+	5.94094i	0.123689	+	0.214236i	−0.797531	+	0.603278i	$0.793861\pi$
$770$	−2.38600	−	4.13267i	−0.0859855	−	0.148931i
$771$		0			0
$772$	−5.77200			−0.207739
$773$	2.38600	+	4.13267i	0.0858185	+	0.148642i	0.905740	−	0.423834i	$-0.139316\pi$
$773$	2.38600	+	4.13267i	0.0858185	+	0.148642i	−0.819921	+	0.572476i	$0.805983\pi$
$774$		0			0
$775$	2.88600	+	4.99870i	0.103668	+	0.179559i
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$		0			0
$778$	−25.0880			−0.899449
$779$	−20.3860	−	4.13267i	−0.730404	−	0.148068i
$780$		0			0
$781$	22.7720	−	39.4423i	0.814846	−	1.41136i
$782$		0			0
$783$		0			0
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	10.2720	+	17.7916i	0.366623	+	0.635010i
$786$		0			0
$787$	8.68399			0.309551			0.154775	−	0.987950i	$-0.450535\pi$
$787$	8.68399			0.309551			0.154775	+	0.987950i	$0.450535\pi$
$788$	7.15800	+	12.3980i	0.254993	+	0.441661i
$789$		0			0
$790$	15.3160			0.544919
$791$	3.54400			0.126010
$792$		0			0
$793$	10.8860	−	18.8551i	0.386573	−	0.669564i
$794$	16.0440	+	27.7890i	0.569380	+	0.986196i
$795$		0			0
$796$	−12.6580	+	21.9243i	−0.448651	+	0.777086i
$797$	7.22800			0.256029			0.128014	−	0.991772i	$-0.459140\pi$
$797$	7.22800			0.256029			0.128014	+	0.991772i	$0.459140\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	−12.5440	−	21.7269i	−0.442944	−	0.767202i
$803$	28.0880	−	48.6499i	0.991204	−	1.71682i
$804$		0			0
$805$	−4.77200			−0.168191
$806$	−21.7720			−0.766886
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$	−16.6140	−	28.7763i	−0.583396	−	1.01047i	−0.995073	−	0.0991423i	$-0.968390\pi$
$811$	−16.6140	−	28.7763i	−0.583396	−	1.01047i	0.411677	−	0.911330i	$-0.364943\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$		0			0
$814$	2.38600	−	4.13267i	0.0836293	−	0.144850i
$815$	3.65800	−	6.33585i	0.128134	−	0.221935i
$816$		0			0
$817$	0.974008	+	0.197452i	0.0340762	+	0.00690798i
$818$	29.4040			1.02809
$819$		0			0
$820$	−2.38600	+	4.13267i	−0.0833228	+	0.144319i
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	−0.930005	−	1.61082i	−0.0324179	−	0.0561495i	0.849361	−	0.527812i	$-0.176987\pi$
$823$	−0.930005	−	1.61082i	−0.0324179	−	0.0561495i	−0.881779	+	0.471662i	$0.843654\pi$
$824$	−13.0000			−0.452876
$825$		0			0
$826$	−1.77200	−	3.06920i	−0.0616558	−	0.106791i
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	−0.956780	−	0.290813i	$-0.906074\pi$
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	0.226538	−	0.974002i	$-0.427259\pi$
$828$		0			0
$829$	−28.4040			−0.986512			−0.493256	−	0.869884i	$-0.664193\pi$
$829$	−28.4040			−0.986512			−0.493256	+	0.869884i	$0.664193\pi$
$830$	−3.00000	−	5.19615i	−0.104132	−	0.180361i
$831$		0			0
$832$	−1.88600	−	3.26665i	−0.0653853	−	0.113251i
$833$		0			0
$834$		0			0
$835$	14.3160			0.495426
$836$	−13.7720	+	15.5885i	−0.476315	+	0.539138i
$837$		0			0
$838$	8.93000	−	15.4672i	0.308482	−	0.534306i
$839$	−26.3160	+	45.5807i	−0.908529	+	1.57362i	−0.0924212	+	0.995720i	$0.529461\pi$
$839$	−26.3160	+	45.5807i	−0.908529	+	1.57362i	−0.816108	+	0.577899i	$0.803873\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	0.227998	+	0.394904i	0.00785733	+	0.0136093i
$843$		0			0
$844$	−3.45600			−0.118960
$845$	0.613999	+	1.06348i	0.0211222	+	0.0365847i
$846$		0			0
$847$	−11.7720			−0.404491
$848$	−1.22800			−0.0421696
$849$		0			0
$850$		0			0
$851$	−2.38600	−	4.13267i	−0.0817911	−	0.141666i
$852$		0			0
$853$	−9.65800	+	16.7282i	−0.330684	+	0.572761i	−0.982646	−	0.185490i	$-0.940613\pi$
$853$	−9.65800	+	16.7282i	−0.330684	+	0.572761i	0.651962	+	0.758251i	$0.273946\pi$
$854$	5.77200			0.197514
$855$		0			0
$856$		0			0
$857$	28.6320	−	49.5921i	0.978051	−	1.69403i	0.308575	−	0.951200i	$-0.400148\pi$
$857$	28.6320	−	49.5921i	0.978051	−	1.69403i	0.669476	−	0.742834i	$-0.266519\pi$
$858$		0			0
$859$	16.7280	+	28.9737i	0.570752	+	0.988571i	0.996489	+	0.0837244i	$0.0266815\pi$
$859$	16.7280	+	28.9737i	0.570752	+	0.988571i	−0.425737	+	0.904847i	$0.639985\pi$
$860$	0.113999	−	0.197452i	0.00388734	−	0.00673306i
$861$		0			0
$862$	−31.0880			−1.05886
$863$	50.3160			1.71278			0.856388	−	0.516332i	$-0.172703\pi$
$863$	50.3160			1.71278			0.856388	+	0.516332i	$0.172703\pi$
$864$		0			0
$865$	7.15800	+	12.3980i	0.243379	+	0.421545i
$866$	−15.3160			−0.520459
$867$		0			0
$868$	−2.88600	−	4.99870i	−0.0979573	−	0.169667i
$869$	36.5440	−	63.2961i	1.23967	−	2.14717i
$870$		0			0
$871$	4.20201	−	7.27809i	0.142380	−	0.246609i
$872$	3.77200	−	6.53330i	0.127736	−	0.221245i
$873$		0			0
$874$	6.61400	+	19.7211i	0.223722	+	0.667077i
$875$	1.00000			0.0338062
$876$		0			0
$877$	5.27200	−	9.13138i	0.178023	−	0.308345i	−0.763180	−	0.646185i	$-0.776363\pi$
$877$	5.27200	−	9.13138i	0.178023	−	0.308345i	0.941203	+	0.337841i	$0.109697\pi$
$878$	10.6580	+	18.4602i	0.359690	+	0.623002i
$879$		0			0
$880$	2.38600	+	4.13267i	0.0804321	+	0.139312i
$881$	−0.139991			−0.00471640			−0.00235820	−	0.999997i	$-0.500751\pi$
$881$	−0.139991			−0.00471640			−0.00235820	+	0.999997i	$0.500751\pi$
$882$		0			0
$883$	16.6580	+	28.8525i	0.560586	+	0.970964i	0.997445	+	0.0714341i	$0.0227576\pi$
$883$	16.6580	+	28.8525i	0.560586	+	0.970964i	−0.436859	+	0.899530i	$0.643909\pi$
$884$		0			0
$885$		0			0
$886$	−4.91199			−0.165022
$887$	−7.08801	−	12.2768i	−0.237992	−	0.412214i	0.722146	−	0.691741i	$-0.243156\pi$
$887$	−7.08801	−	12.2768i	−0.237992	−	0.412214i	−0.960138	+	0.279526i	$0.909823\pi$
$888$		0			0
$889$	8.15800	+	14.1301i	0.273611	+	0.473908i
$890$	4.15800	−	7.20187i	0.139377	−	0.241407i
$891$		0			0
$892$	−25.0000			−0.837062
$893$		0			0
$894$		0			0
$895$	13.1580	−	22.7903i	0.439824	−	0.761797i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$		0			0
$898$	5.38600	−	9.32883i	0.179733	−	0.311307i
$899$	17.3160	+	29.9922i	0.577521	+	1.00030i
$900$		0			0
$901$		0			0
$902$	11.3860	+	19.7211i	0.379112	+	0.656642i
$903$		0			0
$904$	−3.54400			−0.117872
$905$	17.0880			0.568025
$906$		0			0
$907$	18.7720	−	32.5141i	0.623314	−	1.07961i	−0.365550	−	0.930792i	$-0.619119\pi$
$907$	18.7720	−	32.5141i	0.623314	−	1.07961i	0.988864	−	0.148820i	$-0.0475475\pi$
$908$	−12.5440	−	21.7269i	−0.416287	−	0.721031i
$909$		0			0
$910$	−1.88600	+	3.26665i	−0.0625203	+	0.108288i
$911$	32.1760			1.06604			0.533019	−	0.846103i	$-0.321057\pi$
$911$	32.1760			1.06604			0.533019	+	0.846103i	$0.321057\pi$
$912$		0			0
$913$	−28.6320			−0.947581
$914$	−8.43000	+	14.6012i	−0.278840	+	0.482965i
$915$		0			0
$916$	9.43000	+	16.3332i	0.311576	+	0.539666i
$917$	−7.15800	+	12.3980i	−0.236378	+	0.409419i
$918$		0			0
$919$	26.4040			0.870988			0.435494	−	0.900192i	$-0.356574\pi$
$919$	26.4040			0.870988			0.435494	+	0.900192i	$0.356574\pi$
$920$	4.77200			0.157328
$921$		0			0
$922$	−8.31601	−	14.4037i	−0.273873	−	0.474362i
$923$	−36.0000			−1.18495
$924$		0			0
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	11.8160	−	20.4659i	0.388298	−	0.672552i
$927$		0			0
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	28.0180	−	48.5286i	0.919241	−	1.59217i	0.118671	−	0.992934i	$-0.462137\pi$
$929$	28.0180	−	48.5286i	0.919241	−	1.59217i	0.800570	−	0.599239i	$-0.204530\pi$
$930$		0			0
$931$	8.31601	+	24.7960i	0.272546	+	0.812658i
$932$	21.5440			0.705697
$933$		0			0
$934$	12.5440	−	21.7269i	0.410452	−	0.710924i
$935$		0			0
$936$		0			0
$937$	22.1140	+	38.3026i	0.722433	+	1.25129i	0.960022	+	0.279925i	$0.0903095\pi$
$937$	22.1140	+	38.3026i	0.722433	+	1.25129i	−0.237589	+	0.971366i	$0.576357\pi$
$938$	2.22800			0.0727467
$939$		0			0
$940$		0			0
$941$	12.5440	+	21.7269i	0.408923	+	0.708275i	0.994769	−	0.102147i	$-0.0325712\pi$
$941$	12.5440	+	21.7269i	0.408923	+	0.708275i	−0.585846	+	0.810422i	$0.699238\pi$
$942$		0			0
$943$	22.7720			0.741558
$944$	1.77200	+	3.06920i	0.0576737	+	0.0998939i
$945$		0			0
$946$	−0.544004	−	0.942242i	−0.0176871	−	0.0306349i
$947$	23.3160	−	40.3845i	0.757668	−	1.31232i	−0.186368	−	0.982480i	$-0.559672\pi$
$947$	23.3160	−	40.3845i	0.757668	−	1.31232i	0.944037	−	0.329840i	$-0.106995\pi$
$948$		0			0
$949$	−44.4040			−1.44142
$950$	−1.38600	−	4.13267i	−0.0449678	−	0.134082i
$951$		0			0
$952$		0			0
$953$	−30.0000	+	51.9615i	−0.971795	+	1.68320i	−0.281666	+	0.959512i	$0.590887\pi$
$953$	−30.0000	+	51.9615i	−0.971795	+	1.68320i	−0.690129	+	0.723686i	$0.742446\pi$
$954$		0			0
$955$	4.77200	−	8.26535i	0.154418	−	0.267460i
$956$	−1.77200	−	3.06920i	−0.0573106	−	0.0992649i
$957$		0			0
$958$	18.0000			0.581554
$959$	−7.77200	−	13.4615i	−0.250971	−	0.434695i
$960$		0			0
$961$	2.31601			0.0747099
$962$	−3.77200			−0.121614
$963$		0			0
$964$	1.65800	−	2.87175i	0.0534007	−	0.0924927i
$965$	−2.88600	−	4.99870i	−0.0929037	−	0.160914i
$966$		0			0
$967$	26.8860	−	46.5679i	0.864596	−	1.49752i	−0.00285275	−	0.999996i	$-0.500908\pi$
$967$	26.8860	−	46.5679i	0.864596	−	1.49752i	0.867448	−	0.497527i	$-0.165759\pi$
$968$	11.7720			0.378366
$969$		0			0
$970$	10.0000			0.321081
$971$	−2.45600	+	4.25391i	−0.0788167	+	0.136514i	−0.902740	−	0.430187i	$-0.858448\pi$
$971$	−2.45600	+	4.25391i	−0.0788167	+	0.136514i	0.823923	+	0.566702i	$0.191781\pi$
$972$		0			0
$973$	−1.11400	−	1.92950i	−0.0357132	−	0.0618570i
$974$	−8.15800	+	14.1301i	−0.261399	+	0.452757i
$975$		0			0
$976$	−5.77200			−0.184757
$977$	8.17601			0.261574			0.130787	−	0.991410i	$-0.458250\pi$
$977$	8.17601			0.261574			0.130787	+	0.991410i	$0.458250\pi$
$978$		0			0
$979$	−19.8420	−	34.3673i	−0.634153	−	1.09839i
$980$	6.00000			0.191663
$981$		0			0
$982$	16.1580	+	27.9865i	0.515623	+	0.893085i
$983$	10.1580	−	17.5942i	0.323990	−	0.561167i	−0.657317	−	0.753614i	$-0.728309\pi$
$983$	10.1580	−	17.5942i	0.323990	−	0.561167i	0.981307	+	0.192447i	$0.0616423\pi$
$984$		0			0
$985$	−7.15800	+	12.3980i	−0.228073	+	0.395034i
$986$		0			0
$987$		0			0
$988$	16.1140	+	3.26665i	0.512655	+	0.103926i
$989$	−1.08801			−0.0345966
$990$		0			0
$991$	−12.1140	+	20.9821i	−0.384814	+	0.666517i	−0.991743	−	0.128239i	$-0.959068\pi$
$991$	−12.1140	+	20.9821i	−0.384814	+	0.666517i	0.606929	+	0.794756i	$0.292401\pi$
$992$	2.88600	+	4.99870i	0.0916306	+	0.158709i
$993$		0			0
$994$	−4.77200	−	8.26535i	−0.151359	−	0.262161i
$995$	−25.3160			−0.802571
$996$		0			0
$997$	1.72800	+	2.99298i	0.0547262	+	0.0947886i	0.892091	−	0.451856i	$-0.149238\pi$
$997$	1.72800	+	2.99298i	0.0547262	+	0.0947886i	−0.837364	+	0.546645i	$0.815905\pi$
$998$	14.8160	+	25.6621i	0.468992	+	0.812319i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.l.1531.2		4
3.2	odd	2		570.2.i.g.391.1	yes	4
19.7	even	3	inner	1710.2.l.l.1261.2		4
57.26	odd	6		570.2.i.g.121.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.g.121.1	✓	4	57.26	odd	6
570.2.i.g.391.1	yes	4	3.2	odd	2
1710.2.l.l.1261.2		4	19.7	even	3	inner
1710.2.l.l.1531.2		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +4.77200 q^{11} +(-1.88600 - 3.26665i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.38600 - 4.13267i) q^{19} -1.00000 q^{20} +(-2.38600 + 4.13267i) q^{22} +(2.38600 + 4.13267i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.77200 q^{26} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} -5.77200 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{35} -1.00000 q^{37} +(4.27200 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} +(2.38600 - 4.13267i) q^{41} +(-0.113999 + 0.197452i) q^{43} +(-2.38600 - 4.13267i) q^{44} -4.77200 q^{46} -6.00000 q^{49} +1.00000 q^{50} +(-1.88600 + 3.26665i) q^{52} +(0.613999 + 1.06348i) q^{53} +(2.38600 - 4.13267i) q^{55} -1.00000 q^{56} +6.00000 q^{58} +(1.77200 - 3.06920i) q^{59} +(2.88600 + 4.99870i) q^{61} +(2.88600 - 4.99870i) q^{62} +1.00000 q^{64} -3.77200 q^{65} +(1.11400 + 1.92950i) q^{67} +(-0.500000 - 0.866025i) q^{70} +(4.77200 - 8.26535i) q^{71} +(5.88600 - 10.1949i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-2.88600 + 3.26665i) q^{76} -4.77200 q^{77} +(7.65800 - 13.2640i) q^{79} +(0.500000 + 0.866025i) q^{80} +(2.38600 + 4.13267i) q^{82} -6.00000 q^{83} +(-0.113999 - 0.197452i) q^{86} +4.77200 q^{88} +(-4.15800 - 7.20187i) q^{89} +(1.88600 + 3.26665i) q^{91} +(2.38600 - 4.13267i) q^{92} +(-4.27200 - 0.866025i) q^{95} +(5.00000 - 8.66025i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{8} + 2 q^{10} + 2 q^{11} + q^{13} + 2 q^{14} - 2 q^{16} + 3 q^{19} - 4 q^{20} - q^{22} + q^{23} - 2 q^{25} - 2 q^{26} + 2 q^{28} - 12 q^{29} - 6 q^{31} - 2 q^{32} - 2 q^{35} - 4 q^{37} + 2 q^{40} + q^{41} - 9 q^{43} - q^{44} - 2 q^{46} - 24 q^{49} + 4 q^{50} + q^{52} + 11 q^{53} + q^{55} - 4 q^{56} + 24 q^{58} - 10 q^{59} + 3 q^{61} + 3 q^{62} + 4 q^{64} + 2 q^{65} + 13 q^{67} - 2 q^{70} + 2 q^{71} + 15 q^{73} + 2 q^{74} - 3 q^{76} - 2 q^{77} + 5 q^{79} + 2 q^{80} + q^{82} - 24 q^{83} - 9 q^{86} + 2 q^{88} + 9 q^{89} - q^{91} + q^{92} + 20 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 4 * q^8 + 2 * q^10 + 2 * q^11 + q^13 + 2 * q^14 - 2 * q^16 + 3 * q^19 - 4 * q^20 - q^22 + q^23 - 2 * q^25 - 2 * q^26 + 2 * q^28 - 12 * q^29 - 6 * q^31 - 2 * q^32 - 2 * q^35 - 4 * q^37 + 2 * q^40 + q^41 - 9 * q^43 - q^44 - 2 * q^46 - 24 * q^49 + 4 * q^50 + q^52 + 11 * q^53 + q^55 - 4 * q^56 + 24 * q^58 - 10 * q^59 + 3 * q^61 + 3 * q^62 + 4 * q^64 + 2 * q^65 + 13 * q^67 - 2 * q^70 + 2 * q^71 + 15 * q^73 + 2 * q^74 - 3 * q^76 - 2 * q^77 + 5 * q^79 + 2 * q^80 + q^82 - 24 * q^83 - 9 * q^86 + 2 * q^88 + 9 * q^89 - q^91 + q^92 + 20 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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