LMFDB - Embedded newform 18.4.c.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,4,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	18.c (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:	$1.06203438010$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	18.7
Dual form			18.4.c.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +5.19615i q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 + 7.79423i) q^{5} +(-9.00000 - 5.19615i) q^{6} +(15.5000 - 26.8468i) q^{7} +8.00000 q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +5.19615i q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 + 7.79423i) q^{5} +(-9.00000 - 5.19615i) q^{6} +(15.5000 - 26.8468i) q^{7} +8.00000 q^{8} -27.0000 q^{9} -18.0000 q^{10} +(7.50000 - 12.9904i) q^{11} +(18.0000 - 10.3923i) q^{12} +(18.5000 + 32.0429i) q^{13} +(31.0000 + 53.6936i) q^{14} +(-40.5000 + 23.3827i) q^{15} +(-8.00000 + 13.8564i) q^{16} -42.0000 q^{17} +(27.0000 - 46.7654i) q^{18} -28.0000 q^{19} +(18.0000 - 31.1769i) q^{20} +(139.500 + 80.5404i) q^{21} +(15.0000 + 25.9808i) q^{22} +(-97.5000 - 168.875i) q^{23} +41.5692i q^{24} +(22.0000 - 38.1051i) q^{25} -74.0000 q^{26} -140.296i q^{27} -124.000 q^{28} +(-55.5000 + 96.1288i) q^{29} -93.5307i q^{30} +(102.500 + 177.535i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(67.5000 + 38.9711i) q^{33} +(42.0000 - 72.7461i) q^{34} +279.000 q^{35} +(54.0000 + 93.5307i) q^{36} -166.000 q^{37} +(28.0000 - 48.4974i) q^{38} +(-166.500 + 96.1288i) q^{39} +(36.0000 + 62.3538i) q^{40} +(130.500 + 226.033i) q^{41} +(-279.000 + 161.081i) q^{42} +(21.5000 - 37.2391i) q^{43} -60.0000 q^{44} +(-121.500 - 210.444i) q^{45} +390.000 q^{46} +(-88.5000 + 153.286i) q^{47} +(-72.0000 - 41.5692i) q^{48} +(-309.000 - 535.204i) q^{49} +(44.0000 + 76.2102i) q^{50} -218.238i q^{51} +(74.0000 - 128.172i) q^{52} +114.000 q^{53} +(243.000 + 140.296i) q^{54} +135.000 q^{55} +(124.000 - 214.774i) q^{56} -145.492i q^{57} +(-111.000 - 192.258i) q^{58} +(-79.5000 - 137.698i) q^{59} +(162.000 + 93.5307i) q^{60} +(-95.5000 + 165.411i) q^{61} -410.000 q^{62} +(-418.500 + 724.863i) q^{63} +64.0000 q^{64} +(-166.500 + 288.386i) q^{65} +(-135.000 + 77.9423i) q^{66} +(210.500 + 364.597i) q^{67} +(84.0000 + 145.492i) q^{68} +(877.500 - 506.625i) q^{69} +(-279.000 + 483.242i) q^{70} +156.000 q^{71} -216.000 q^{72} +182.000 q^{73} +(166.000 - 287.520i) q^{74} +(198.000 + 114.315i) q^{75} +(56.0000 + 96.9948i) q^{76} +(-232.500 - 402.702i) q^{77} -384.515i q^{78} +(-566.500 + 981.207i) q^{79} -144.000 q^{80} +729.000 q^{81} -522.000 q^{82} +(541.500 - 937.906i) q^{83} -644.323i q^{84} +(-189.000 - 327.358i) q^{85} +(43.0000 + 74.4782i) q^{86} +(-499.500 - 288.386i) q^{87} +(60.0000 - 103.923i) q^{88} -1050.00 q^{89} +486.000 q^{90} +1147.00 q^{91} +(-390.000 + 675.500i) q^{92} +(-922.500 + 532.606i) q^{93} +(-177.000 - 306.573i) q^{94} +(-126.000 - 218.238i) q^{95} +(144.000 - 83.1384i) q^{96} +(450.500 - 780.289i) q^{97} +1236.00 q^{98} +(-202.500 + 350.740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} + 9 q^{5} - 18 q^{6} + 31 q^{7} + 16 q^{8} - 54 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 + 9 * q^5 - 18 * q^6 + 31 * q^7 + 16 * q^8 - 54 * q^9	\( 2 q - 2 q^{2} - 4 q^{4} + 9 q^{5} - 18 q^{6} + 31 q^{7} + 16 q^{8} - 54 q^{9} - 36 q^{10} + 15 q^{11} + 36 q^{12} + 37 q^{13} + 62 q^{14} - 81 q^{15} - 16 q^{16} - 84 q^{17} + 54 q^{18} - 56 q^{19} + 36 q^{20} + 279 q^{21} + 30 q^{22} - 195 q^{23} + 44 q^{25} - 148 q^{26} - 248 q^{28} - 111 q^{29} + 205 q^{31} - 32 q^{32} + 135 q^{33} + 84 q^{34} + 558 q^{35} + 108 q^{36} - 332 q^{37} + 56 q^{38} - 333 q^{39} + 72 q^{40} + 261 q^{41} - 558 q^{42} + 43 q^{43} - 120 q^{44} - 243 q^{45} + 780 q^{46} - 177 q^{47} - 144 q^{48} - 618 q^{49} + 88 q^{50} + 148 q^{52} + 228 q^{53} + 486 q^{54} + 270 q^{55} + 248 q^{56} - 222 q^{58} - 159 q^{59} + 324 q^{60} - 191 q^{61} - 820 q^{62} - 837 q^{63} + 128 q^{64} - 333 q^{65} - 270 q^{66} + 421 q^{67} + 168 q^{68} + 1755 q^{69} - 558 q^{70} + 312 q^{71} - 432 q^{72} + 364 q^{73} + 332 q^{74} + 396 q^{75} + 112 q^{76} - 465 q^{77} - 1133 q^{79} - 288 q^{80} + 1458 q^{81} - 1044 q^{82} + 1083 q^{83} - 378 q^{85} + 86 q^{86} - 999 q^{87} + 120 q^{88} - 2100 q^{89} + 972 q^{90} + 2294 q^{91} - 780 q^{92} - 1845 q^{93} - 354 q^{94} - 252 q^{95} + 288 q^{96} + 901 q^{97} + 2472 q^{98} - 405 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 9 * q^5 - 18 * q^6 + 31 * q^7 + 16 * q^8 - 54 * q^9 - 36 * q^10 + 15 * q^11 + 36 * q^12 + 37 * q^13 + 62 * q^14 - 81 * q^15 - 16 * q^16 - 84 * q^17 + 54 * q^18 - 56 * q^19 + 36 * q^20 + 279 * q^21 + 30 * q^22 - 195 * q^23 + 44 * q^25 - 148 * q^26 - 248 * q^28 - 111 * q^29 + 205 * q^31 - 32 * q^32 + 135 * q^33 + 84 * q^34 + 558 * q^35 + 108 * q^36 - 332 * q^37 + 56 * q^38 - 333 * q^39 + 72 * q^40 + 261 * q^41 - 558 * q^42 + 43 * q^43 - 120 * q^44 - 243 * q^45 + 780 * q^46 - 177 * q^47 - 144 * q^48 - 618 * q^49 + 88 * q^50 + 148 * q^52 + 228 * q^53 + 486 * q^54 + 270 * q^55 + 248 * q^56 - 222 * q^58 - 159 * q^59 + 324 * q^60 - 191 * q^61 - 820 * q^62 - 837 * q^63 + 128 * q^64 - 333 * q^65 - 270 * q^66 + 421 * q^67 + 168 * q^68 + 1755 * q^69 - 558 * q^70 + 312 * q^71 - 432 * q^72 + 364 * q^73 + 332 * q^74 + 396 * q^75 + 112 * q^76 - 465 * q^77 - 1133 * q^79 - 288 * q^80 + 1458 * q^81 - 1044 * q^82 + 1083 * q^83 - 378 * q^85 + 86 * q^86 - 999 * q^87 + 120 * q^88 - 2100 * q^89 + 972 * q^90 + 2294 * q^91 - 780 * q^92 - 1845 * q^93 - 354 * q^94 - 252 * q^95 + 288 * q^96 + 901 * q^97 + 2472 * q^98 - 405 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$			5.19615i			1.00000i
$3$			5.19615i			1.00000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	4.50000	+	7.79423i	0.402492	+	0.697137i	0.994026	−	0.109143i	$-0.0348107\pi$
$5$	4.50000	+	7.79423i	0.402492	+	0.697137i	−0.591534	+	0.806280i	$0.701477\pi$
$6$	−9.00000	−	5.19615i	−0.612372	−	0.353553i
$7$	15.5000	−	26.8468i	0.836921	−	1.44959i	−0.0555351	−	0.998457i	$-0.517686\pi$
$7$	15.5000	−	26.8468i	0.836921	−	1.44959i	0.892456	−	0.451134i	$-0.148980\pi$
$8$	8.00000			0.353553
$9$	−27.0000			−1.00000
$10$	−18.0000			−0.569210
$11$	7.50000	−	12.9904i	0.205576	−	0.356068i	−0.744740	−	0.667355i	$-0.767427\pi$
$11$	7.50000	−	12.9904i	0.205576	−	0.356068i	0.950316	+	0.311287i	$0.100760\pi$
$12$	18.0000	−	10.3923i	0.433013	−	0.250000i
$13$	18.5000	+	32.0429i	0.394691	+	0.683624i	0.993062	−	0.117595i	$-0.0375185\pi$
$13$	18.5000	+	32.0429i	0.394691	+	0.683624i	−0.598371	+	0.801219i	$0.704185\pi$
$14$	31.0000	+	53.6936i	0.591793	+	1.02502i
$15$	−40.5000	+	23.3827i	−0.697137	+	0.402492i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−42.0000			−0.599206			−0.299603	−	0.954064i	$-0.596854\pi$
$17$	−42.0000			−0.599206			−0.299603	+	0.954064i	$0.596854\pi$
$18$	27.0000	−	46.7654i	0.353553	−	0.612372i
$19$	−28.0000			−0.338086			−0.169043	−	0.985609i	$-0.554068\pi$
$19$	−28.0000			−0.338086			−0.169043	+	0.985609i	$0.554068\pi$
$20$	18.0000	−	31.1769i	0.201246	−	0.348569i
$21$	139.500	+	80.5404i	1.44959	+	0.836921i
$22$	15.0000	+	25.9808i	0.145364	+	0.251778i
$23$	−97.5000	−	168.875i	−0.883920	−	1.53099i	−0.846947	−	0.531678i	$-0.821562\pi$
$23$	−97.5000	−	168.875i	−0.883920	−	1.53099i	−0.0369731	−	0.999316i	$-0.511772\pi$
$24$			41.5692i			0.353553i
$25$	22.0000	−	38.1051i	0.176000	−	0.304841i
$26$	−74.0000			−0.558177
$27$		−	140.296i		−	1.00000i
$28$	−124.000			−0.836921
$29$	−55.5000	+	96.1288i	−0.355382	+	0.615540i	−0.987183	−	0.159590i	$-0.948983\pi$
$29$	−55.5000	+	96.1288i	−0.355382	+	0.615540i	0.631801	+	0.775131i	$0.282316\pi$
$30$		−	93.5307i		−	0.569210i
$31$	102.500	+	177.535i	0.593856	+	1.02859i	0.993707	+	0.112009i	$0.0357285\pi$
$31$	102.500	+	177.535i	0.593856	+	1.02859i	−0.399851	+	0.916580i	$0.630938\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	67.5000	+	38.9711i	0.356068	+	0.205576i
$34$	42.0000	−	72.7461i	0.211851	−	0.366937i
$35$	279.000			1.34742
$36$	54.0000	+	93.5307i	0.250000	+	0.433013i
$37$	−166.000			−0.737574			−0.368787	−	0.929514i	$-0.620227\pi$
$37$	−166.000			−0.737574			−0.368787	+	0.929514i	$0.620227\pi$
$38$	28.0000	−	48.4974i	0.119532	−	0.207035i
$39$	−166.500	+	96.1288i	−0.683624	+	0.394691i
$40$	36.0000	+	62.3538i	0.142302	+	0.246475i
$41$	130.500	+	226.033i	0.497090	+	0.860985i	0.999994	−	0.00335732i	$-0.00106867\pi$
$41$	130.500	+	226.033i	0.497090	+	0.860985i	−0.502905	+	0.864342i	$0.667735\pi$
$42$	−279.000	+	161.081i	−1.02502	+	0.591793i
$43$	21.5000	−	37.2391i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	21.5000	−	37.2391i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−60.0000			−0.205576
$45$	−121.500	−	210.444i	−0.402492	−	0.697137i
$46$	390.000			1.25005
$47$	−88.5000	+	153.286i	−0.274661	+	0.475726i	−0.970049	−	0.242907i	$-0.921899\pi$
$47$	−88.5000	+	153.286i	−0.274661	+	0.475726i	0.695389	+	0.718634i	$0.255232\pi$
$48$	−72.0000	−	41.5692i	−0.216506	−	0.125000i
$49$	−309.000	−	535.204i	−0.900875	−	1.56036i
$50$	44.0000	+	76.2102i	0.124451	+	0.215555i
$51$		−	218.238i		−	0.599206i
$52$	74.0000	−	128.172i	0.197345	−	0.341812i
$53$	114.000			0.295455			0.147727	−	0.989028i	$-0.452804\pi$
$53$	114.000			0.295455			0.147727	+	0.989028i	$0.452804\pi$
$54$	243.000	+	140.296i	0.612372	+	0.353553i
$55$	135.000			0.330971
$56$	124.000	−	214.774i	0.295896	−	0.512508i
$57$		−	145.492i		−	0.338086i
$58$	−111.000	−	192.258i	−0.251293	−	0.435253i
$59$	−79.5000	−	137.698i	−0.175424	−	0.303843i	0.764884	−	0.644168i	$-0.222796\pi$
$59$	−79.5000	−	137.698i	−0.175424	−	0.303843i	−0.940308	+	0.340325i	$0.889463\pi$
$60$	162.000	+	93.5307i	0.348569	+	0.201246i
$61$	−95.5000	+	165.411i	−0.200451	+	0.347192i	−0.948674	−	0.316256i	$-0.897574\pi$
$61$	−95.5000	+	165.411i	−0.200451	+	0.347192i	0.748223	+	0.663448i	$0.230907\pi$
$62$	−410.000			−0.839840
$63$	−418.500	+	724.863i	−0.836921	+	1.44959i
$64$	64.0000			0.125000
$65$	−166.500	+	288.386i	−0.317720	+	0.550307i
$66$	−135.000	+	77.9423i	−0.251778	+	0.145364i
$67$	210.500	+	364.597i	0.383831	+	0.664815i	0.991606	−	0.129294i	$-0.0412712\pi$
$67$	210.500	+	364.597i	0.383831	+	0.664815i	−0.607775	+	0.794109i	$0.707938\pi$
$68$	84.0000	+	145.492i	0.149801	+	0.259464i
$69$	877.500	−	506.625i	1.53099	−	0.883920i
$70$	−279.000	+	483.242i	−0.476384	+	0.825121i
$71$	156.000			0.260758			0.130379	−	0.991464i	$-0.458381\pi$
$71$	156.000			0.260758			0.130379	+	0.991464i	$0.458381\pi$
$72$	−216.000			−0.353553
$73$	182.000			0.291801			0.145901	−	0.989299i	$-0.453392\pi$
$73$	182.000			0.291801			0.145901	+	0.989299i	$0.453392\pi$
$74$	166.000	−	287.520i	0.260772	−	0.451670i
$75$	198.000	+	114.315i	0.304841	+	0.176000i
$76$	56.0000	+	96.9948i	0.0845216	+	0.146396i
$77$	−232.500	−	402.702i	−0.344102	−	0.596002i
$78$		−	384.515i		−	0.558177i
$79$	−566.500	+	981.207i	−0.806788	+	1.39740i	0.108290	+	0.994119i	$0.465463\pi$
$79$	−566.500	+	981.207i	−0.806788	+	1.39740i	−0.915078	+	0.403278i	$0.867871\pi$
$80$	−144.000			−0.201246
$81$	729.000			1.00000
$82$	−522.000			−0.702991
$83$	541.500	−	937.906i	0.716113	−	1.24034i	−0.246416	−	0.969164i	$-0.579253\pi$
$83$	541.500	−	937.906i	0.716113	−	1.24034i	0.962529	−	0.271179i	$-0.0874136\pi$
$84$		−	644.323i		−	0.836921i
$85$	−189.000	−	327.358i	−0.241176	−	0.417728i
$86$	43.0000	+	74.4782i	0.0539164	+	0.0933859i
$87$	−499.500	−	288.386i	−0.615540	−	0.355382i
$88$	60.0000	−	103.923i	0.0726821	−	0.125889i
$89$	−1050.00			−1.25056			−0.625280	−	0.780401i	$-0.715015\pi$
$89$	−1050.00			−1.25056			−0.625280	+	0.780401i	$0.715015\pi$
$90$	486.000			0.569210
$91$	1147.00			1.32130
$92$	−390.000	+	675.500i	−0.441960	+	0.765497i
$93$	−922.500	+	532.606i	−1.02859	+	0.593856i
$94$	−177.000	−	306.573i	−0.194214	−	0.336389i
$95$	−126.000	−	218.238i	−0.136077	−	0.235693i
$96$	144.000	−	83.1384i	0.153093	−	0.0883883i
$97$	450.500	−	780.289i	0.471560	−	0.816766i	−0.527910	−	0.849300i	$-0.677024\pi$
$97$	450.500	−	780.289i	0.471560	−	0.816766i	0.999471	+	0.0325338i	$0.0103576\pi$
$98$	1236.00			1.27403
$99$	−202.500	+	350.740i	−0.205576	+	0.356068i
$100$	−176.000			−0.176000
$101$	−193.500	+	335.152i	−0.190633	+	0.330187i	−0.945460	−	0.325737i	$-0.894387\pi$
$101$	−193.500	+	335.152i	−0.190633	+	0.330187i	0.754827	+	0.655924i	$0.227721\pi$
$102$	378.000	+	218.238i	0.366937	+	0.211851i
$103$	−275.500	−	477.180i	−0.263552	−	0.456485i	0.703631	−	0.710565i	$-0.251561\pi$
$103$	−275.500	−	477.180i	−0.263552	−	0.456485i	−0.967183	+	0.254080i	$0.918227\pi$
$104$	148.000	+	256.344i	0.139544	+	0.241698i
$105$			1449.73i			1.34742i
$106$	−114.000	+	197.454i	−0.104459	+	0.180928i
$107$	−12.0000			−0.0108419			−0.00542095	−	0.999985i	$-0.501726\pi$
$107$	−12.0000			−0.0108419			−0.00542095	+	0.999985i	$0.501726\pi$
$108$	−486.000	+	280.592i	−0.433013	+	0.250000i
$109$	−502.000			−0.441127			−0.220564	−	0.975373i	$-0.570790\pi$
$109$	−502.000			−0.441127			−0.220564	+	0.975373i	$0.570790\pi$
$110$	−135.000	+	233.827i	−0.117016	+	0.202677i
$111$		−	862.561i		−	0.737574i
$112$	248.000	+	429.549i	0.209230	+	0.362398i
$113$	700.500	+	1213.30i	0.583164	+	1.01007i	0.995102	+	0.0988572i	$0.0315187\pi$
$113$	700.500	+	1213.30i	0.583164	+	1.01007i	−0.411938	+	0.911212i	$0.635148\pi$
$114$	252.000	+	145.492i	0.207035	+	0.119532i
$115$	877.500	−	1519.87i	0.711542	−	1.23243i
$116$	444.000			0.355382
$117$	−499.500	−	865.159i	−0.394691	−	0.683624i
$118$	318.000			0.248087
$119$	−651.000	+	1127.57i	−0.501488	+	0.868603i
$120$	−324.000	+	187.061i	−0.246475	+	0.142302i
$121$	553.000	+	957.824i	0.415477	+	0.719627i
$122$	−191.000	−	330.822i	−0.141740	−	0.245502i
$123$	−1174.50	+	678.098i	−0.860985	+	0.497090i
$124$	410.000	−	710.141i	0.296928	−	0.514295i
$125$	1521.00			1.08834
$126$	−837.000	−	1449.73i	−0.591793	−	1.02502i
$127$	−880.000			−0.614861			−0.307431	−	0.951571i	$-0.599469\pi$
$127$	−880.000			−0.614861			−0.307431	+	0.951571i	$0.599469\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	193.500	+	111.717i	0.132068	+	0.0762493i
$130$	−333.000	−	576.773i	−0.224662	−	0.389126i
$131$	−751.500	−	1301.64i	−0.501213	−	0.868126i	−0.999999	−	0.00140084i	$-0.999554\pi$
$131$	−751.500	−	1301.64i	−0.501213	−	0.868126i	0.498786	−	0.866725i	$-0.333779\pi$
$132$		−	311.769i		−	0.205576i
$133$	−434.000	+	751.710i	−0.282952	+	0.490087i
$134$	−842.000			−0.542819
$135$	1093.50	−	631.333i	0.697137	−	0.402492i
$136$	−336.000			−0.211851
$137$	1330.50	−	2304.49i	0.829725	−	1.43713i	−0.0685295	−	0.997649i	$-0.521831\pi$
$137$	1330.50	−	2304.49i	0.829725	−	1.43713i	0.898254	−	0.439476i	$-0.144836\pi$
$138$			2026.50i			1.25005i
$139$	60.5000	+	104.789i	0.0369176	+	0.0639431i	0.883894	−	0.467688i	$-0.154913\pi$
$139$	60.5000	+	104.789i	0.0369176	+	0.0639431i	−0.846976	+	0.531631i	$0.821579\pi$
$140$	−558.000	−	966.484i	−0.336854	−	0.583449i
$141$	−796.500	−	459.859i	−0.475726	−	0.274661i
$142$	−156.000	+	270.200i	−0.0921918	+	0.159681i
$143$	555.000			0.324555
$144$	216.000	−	374.123i	0.125000	−	0.216506i
$145$	−999.000			−0.572155
$146$	−182.000	+	315.233i	−0.103167	+	0.178691i
$147$	2781.00	−	1605.61i	1.56036	−	0.900875i
$148$	332.000	+	575.041i	0.184393	+	0.319379i
$149$	1414.50	+	2449.99i	0.777721	+	1.34705i	0.933253	+	0.359221i	$0.116957\pi$
$149$	1414.50	+	2449.99i	0.777721	+	1.34705i	−0.155532	+	0.987831i	$0.549709\pi$
$150$	−396.000	+	228.631i	−0.215555	+	0.124451i
$151$	−230.500	+	399.238i	−0.124224	+	0.215162i	−0.921429	−	0.388546i	$-0.872977\pi$
$151$	−230.500	+	399.238i	−0.124224	+	0.215162i	0.797205	+	0.603708i	$0.206311\pi$
$152$	−224.000			−0.119532
$153$	1134.00			0.599206
$154$	930.000			0.486633
$155$	−922.500	+	1597.82i	−0.478045	+	0.827998i
$156$	666.000	+	384.515i	0.341812	+	0.197345i
$157$	1488.50	+	2578.16i	0.756658	+	1.31057i	0.944546	+	0.328379i	$0.106502\pi$
$157$	1488.50	+	2578.16i	0.756658	+	1.31057i	−0.187889	+	0.982190i	$0.560164\pi$
$158$	−1133.00	−	1962.41i	−0.570485	−	0.988109i
$159$			592.361i			0.295455i
$160$	144.000	−	249.415i	0.0711512	−	0.123238i
$161$	−6045.00			−2.95909
$162$	−729.000	+	1262.67i	−0.353553	+	0.612372i
$163$	−3316.00			−1.59343			−0.796715	−	0.604355i	$-0.793431\pi$
$163$	−3316.00			−1.59343			−0.796715	+	0.604355i	$0.793431\pi$
$164$	522.000	−	904.131i	0.248545	−	0.430492i
$165$			701.481i			0.330971i
$166$	1083.00	+	1875.81i	0.506368	+	0.877055i
$167$	340.500	+	589.763i	0.157777	+	0.273277i	0.934067	−	0.357099i	$-0.116234\pi$
$167$	340.500	+	589.763i	0.157777	+	0.273277i	−0.776290	+	0.630376i	$0.782901\pi$
$168$	1116.00	+	644.323i	0.512508	+	0.295896i
$169$	414.000	−	717.069i	0.188439	−	0.326386i
$170$	756.000			0.341074
$171$	756.000			0.338086
$172$	−172.000			−0.0762493
$173$	1990.50	−	3447.65i	0.874768	−	1.51514i	0.0177589	−	0.999842i	$-0.494347\pi$
$173$	1990.50	−	3447.65i	0.874768	−	1.51514i	0.857009	−	0.515301i	$-0.172320\pi$
$174$	999.000	−	576.773i	0.435253	−	0.251293i
$175$	−682.000	−	1181.26i	−0.294596	−	0.510256i
$176$	120.000	+	207.846i	0.0513940	+	0.0890170i
$177$	715.500	−	413.094i	0.303843	−	0.175424i
$178$	1050.00	−	1818.65i	0.442139	−	0.765808i
$179$	2004.00			0.836793			0.418397	−	0.908264i	$-0.362592\pi$
$179$	2004.00			0.836793			0.418397	+	0.908264i	$0.362592\pi$
$180$	−486.000	+	841.777i	−0.201246	+	0.348569i
$181$	1274.00			0.523181			0.261590	−	0.965179i	$-0.415753\pi$
$181$	1274.00			0.523181			0.261590	+	0.965179i	$0.415753\pi$
$182$	−1147.00	+	1986.66i	−0.467150	+	0.809128i
$183$	−859.500	−	496.233i	−0.347192	−	0.200451i
$184$	−780.000	−	1351.00i	−0.312513	−	0.541288i
$185$	−747.000	−	1293.84i	−0.296868	−	0.514190i
$186$		−	2130.42i		−	0.839840i
$187$	−315.000	+	545.596i	−0.123182	+	0.213358i
$188$	708.000			0.274661
$189$	−3766.50	−	2174.59i	−1.44959	−	0.836921i
$190$	504.000			0.192442
$191$	−580.500	+	1005.46i	−0.219914	+	0.380902i	−0.954781	−	0.297309i	$-0.903911\pi$
$191$	−580.500	+	1005.46i	−0.219914	+	0.380902i	0.734868	+	0.678210i	$0.237244\pi$
$192$			332.554i			0.125000i
$193$	−1805.50	−	3127.22i	−0.673382	−	1.16633i	−0.976939	−	0.213519i	$-0.931508\pi$
$193$	−1805.50	−	3127.22i	−0.673382	−	1.16633i	0.303557	−	0.952813i	$-0.401826\pi$
$194$	901.000	+	1560.58i	0.333443	+	0.577541i
$195$	−1498.50	−	865.159i	−0.550307	−	0.317720i
$196$	−1236.00	+	2140.81i	−0.450437	+	0.780180i
$197$	2046.00			0.739957			0.369978	−	0.929040i	$-0.379365\pi$
$197$	2046.00			0.739957			0.369978	+	0.929040i	$0.379365\pi$
$198$	−405.000	−	701.481i	−0.145364	−	0.251778i
$199$	2996.00			1.06724			0.533620	−	0.845724i	$-0.320831\pi$
$199$	2996.00			1.06724			0.533620	+	0.845724i	$0.320831\pi$
$200$	176.000	−	304.841i	0.0622254	−	0.107778i
$201$	−1894.50	+	1093.79i	−0.664815	+	0.383831i
$202$	−387.000	−	670.304i	−0.134798	−	0.233477i
$203$	1720.50	+	2979.99i	0.594854	+	1.03032i
$204$	−756.000	+	436.477i	−0.259464	+	0.149801i
$205$	−1174.50	+	2034.29i	−0.400149	+	0.693079i
$206$	1102.00			0.372718
$207$	2632.50	+	4559.62i	0.883920	+	1.53099i
$208$	−592.000			−0.197345
$209$	−210.000	+	363.731i	−0.0695024	+	0.120382i
$210$	−2511.00	−	1449.73i	−0.825121	−	0.476384i
$211$	−377.500	−	653.849i	−0.123167	−	0.213331i	0.797848	−	0.602858i	$-0.205972\pi$
$211$	−377.500	−	653.849i	−0.123167	−	0.213331i	−0.921015	+	0.389528i	$0.872638\pi$
$212$	−228.000	−	394.908i	−0.0738637	−	0.127936i
$213$			810.600i			0.260758i
$214$	12.0000	−	20.7846i	0.00383319	−	0.00663928i
$215$	387.000			0.122759
$216$		−	1122.37i		−	0.353553i
$217$	6355.00			1.98804
$218$	502.000	−	869.490i	0.155962	−	0.270134i
$219$			945.700i			0.291801i
$220$	−270.000	−	467.654i	−0.0827427	−	0.143315i
$221$	−777.000	−	1345.80i	−0.236501	−	0.409631i
$222$	1494.00	+	862.561i	0.451670	+	0.260772i
$223$	1731.50	−	2999.05i	0.519954	−	0.900587i	−0.479777	−	0.877391i	$-0.659282\pi$
$223$	1731.50	−	2999.05i	0.519954	−	0.900587i	0.999731	−	0.0231966i	$-0.00738438\pi$
$224$	−992.000			−0.295896
$225$	−594.000	+	1028.84i	−0.176000	+	0.304841i
$226$	−2802.00			−0.824718
$227$	−3112.50	+	5391.01i	−0.910061	+	1.57627i	−0.0960856	+	0.995373i	$0.530632\pi$
$227$	−3112.50	+	5391.01i	−0.910061	+	1.57627i	−0.813976	+	0.580899i	$0.802701\pi$
$228$	−504.000	+	290.985i	−0.146396	+	0.0845216i
$229$	732.500	+	1268.73i	0.211375	+	0.366113i	0.952145	−	0.305646i	$-0.0988724\pi$
$229$	732.500	+	1268.73i	0.211375	+	0.366113i	−0.740770	+	0.671759i	$0.765539\pi$
$230$	1755.00	+	3039.75i	0.503136	+	0.871457i
$231$	2092.50	−	1208.11i	0.596002	−	0.344102i
$232$	−444.000	+	769.031i	−0.125647	+	0.217626i
$233$	2634.00			0.740597			0.370298	−	0.928913i	$-0.379255\pi$
$233$	2634.00			0.740597			0.370298	+	0.928913i	$0.379255\pi$
$234$	1998.00			0.558177
$235$	−1593.00			−0.442195
$236$	−318.000	+	550.792i	−0.0877120	+	0.151922i
$237$	−5098.50	−	2943.62i	−1.39740	−	0.806788i
$238$	−1302.00	−	2255.13i	−0.354606	−	0.614195i
$239$	−3457.50	−	5988.57i	−0.935762	−	1.62079i	−0.773270	−	0.634077i	$-0.781380\pi$
$239$	−3457.50	−	5988.57i	−0.935762	−	1.62079i	−0.162492	−	0.986710i	$-0.551953\pi$
$240$		−	748.246i		−	0.201246i
$241$	744.500	−	1289.51i	0.198994	−	0.344667i	−0.749209	−	0.662334i	$-0.769566\pi$
$241$	744.500	−	1289.51i	0.198994	−	0.344667i	0.948202	+	0.317667i	$0.102899\pi$
$242$	−2212.00			−0.587573
$243$			3788.00i			1.00000i
$244$	764.000			0.200451
$245$	2781.00	−	4816.83i	0.725190	−	1.25607i
$246$		−	2712.39i		−	0.702991i
$247$	−518.000	−	897.202i	−0.133439	−	0.231124i
$248$	820.000	+	1420.28i	0.209960	+	0.363661i
$249$	4873.50	+	2813.72i	1.24034	+	0.716113i
$250$	−1521.00	+	2634.45i	−0.384786	+	0.666469i
$251$	−4620.00			−1.16180			−0.580900	−	0.813975i	$-0.697299\pi$
$251$	−4620.00			−1.16180			−0.580900	+	0.813975i	$0.697299\pi$
$252$	3348.00			0.836921
$253$	−2925.00			−0.726850
$254$	880.000	−	1524.20i	0.217386	−	0.376524i
$255$	1701.00	−	982.073i	0.417728	−	0.241176i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1675.50	−	2902.05i	−0.406672	−	0.704377i	0.587842	−	0.808976i	$-0.299978\pi$
$257$	−1675.50	−	2902.05i	−0.406672	−	0.704377i	−0.994515	+	0.104598i	$0.966644\pi$
$258$	−387.000	+	223.435i	−0.0933859	+	0.0539164i
$259$	−2573.00	+	4456.57i	−0.617291	+	1.06918i
$260$	1332.00			0.317720
$261$	1498.50	−	2595.48i	0.355382	−	0.615540i
$262$	3006.00			0.708822
$263$	301.500	−	522.213i	0.0706893	−	0.122437i	−0.828514	−	0.559968i	$-0.810813\pi$
$263$	301.500	−	522.213i	0.0706893	−	0.122437i	0.899204	+	0.437530i	$0.144147\pi$
$264$	540.000	+	311.769i	0.125889	+	0.0726821i
$265$	513.000	+	888.542i	0.118918	+	0.205972i
$266$	−868.000	−	1503.42i	−0.200077	−	0.346544i
$267$		−	5455.96i		−	1.25056i
$268$	842.000	−	1458.39i	0.191915	−	0.332407i
$269$	−1470.00			−0.333188			−0.166594	−	0.986026i	$-0.553277\pi$
$269$	−1470.00			−0.333188			−0.166594	+	0.986026i	$0.553277\pi$
$270$			2525.33i			0.569210i
$271$	2072.00			0.464447			0.232223	−	0.972662i	$-0.425400\pi$
$271$	2072.00			0.464447			0.232223	+	0.972662i	$0.425400\pi$
$272$	336.000	−	581.969i	0.0749007	−	0.129732i
$273$			5959.99i			1.32130i
$274$	2661.00	+	4608.99i	0.586704	+	1.01620i
$275$	−330.000	−	571.577i	−0.0723627	−	0.125336i
$276$	−3510.00	−	2026.50i	−0.765497	−	0.441960i
$277$	−3569.50	+	6182.56i	−0.774262	+	1.34106i	0.160947	+	0.986963i	$0.448545\pi$
$277$	−3569.50	+	6182.56i	−0.774262	+	1.34106i	−0.935209	+	0.354097i	$0.884788\pi$
$278$	−242.000			−0.0522093
$279$	−2767.50	−	4793.45i	−0.593856	−	1.02859i
$280$	2232.00			0.476384
$281$	−4213.50	+	7298.00i	−0.894507	+	1.54933i	−0.0600924	+	0.998193i	$0.519140\pi$
$281$	−4213.50	+	7298.00i	−0.894507	+	1.54933i	−0.834414	+	0.551138i	$0.814194\pi$
$282$	1593.00	−	919.719i	0.336389	−	0.194214i
$283$	228.500	+	395.774i	0.0479962	+	0.0831318i	0.889025	−	0.457858i	$-0.151383\pi$
$283$	228.500	+	395.774i	0.0479962	+	0.0831318i	−0.841029	+	0.540990i	$0.818050\pi$
$284$	−312.000	−	540.400i	−0.0651894	−	0.112911i
$285$	1134.00	−	654.715i	0.235693	−	0.136077i
$286$	−555.000	+	961.288i	−0.114748	+	0.198749i
$287$	8091.00			1.66410
$288$	432.000	+	748.246i	0.0883883	+	0.153093i
$289$	−3149.00			−0.640953
$290$	999.000	−	1730.32i	0.202287	−	0.350372i
$291$	4054.50	+	2340.87i	0.816766	+	0.471560i
$292$	−364.000	−	630.466i	−0.0729503	−	0.126354i
$293$	2944.50	+	5100.02i	0.587097	+	1.01688i	0.994610	+	0.103683i	$0.0330628\pi$
$293$	2944.50	+	5100.02i	0.587097	+	1.01688i	−0.407513	+	0.913199i	$0.633604\pi$
$294$			6422.44i			1.27403i
$295$	715.500	−	1239.28i	0.141214	−	0.244589i
$296$	−1328.00			−0.260772
$297$	−1822.50	−	1052.22i	−0.356068	−	0.205576i
$298$	−5658.00			−1.09986
$299$	3607.50	−	6248.37i	0.697750	−	1.20854i
$300$		−	914.523i		−	0.176000i
$301$	−666.500	−	1154.41i	−0.127629	−	0.221060i
$302$	−461.000	−	798.475i	−0.0878396	−	0.152143i
$303$	−1741.50	−	1005.46i	−0.330187	−	0.190633i
$304$	224.000	−	387.979i	0.0422608	−	0.0731978i
$305$	−1719.00			−0.322720
$306$	−1134.00	+	1964.15i	−0.211851	+	0.366937i
$307$	−1204.00			−0.223830			−0.111915	−	0.993718i	$-0.535698\pi$
$307$	−1204.00			−0.223830			−0.111915	+	0.993718i	$0.535698\pi$
$308$	−930.000	+	1610.81i	−0.172051	+	0.298001i
$309$	2479.50	−	1431.54i	0.456485	−	0.263552i
$310$	−1845.00	−	3195.63i	−0.338029	−	0.585483i
$311$	1642.50	+	2844.89i	0.299478	+	0.518711i	0.976017	−	0.217696i	$-0.0698542\pi$
$311$	1642.50	+	2844.89i	0.299478	+	0.518711i	−0.676539	+	0.736407i	$0.736521\pi$
$312$	−1332.00	+	769.031i	−0.241698	+	0.139544i
$313$	5028.50	−	8709.62i	0.908075	−	1.57283i	0.0913406	−	0.995820i	$-0.470885\pi$
$313$	5028.50	−	8709.62i	0.908075	−	1.57283i	0.816735	−	0.577013i	$-0.195782\pi$
$314$	−5954.00			−1.07008
$315$	−7533.00			−1.34742
$316$	4532.00			0.806788
$317$	−1147.50	+	1987.53i	−0.203312	+	0.352147i	−0.949594	−	0.313483i	$-0.898504\pi$
$317$	−1147.50	+	1987.53i	−0.203312	+	0.352147i	0.746281	+	0.665631i	$0.231837\pi$
$318$	−1026.00	−	592.361i	−0.180928	−	0.104459i
$319$	832.500	+	1441.93i	0.146116	+	0.253081i
$320$	288.000	+	498.831i	0.0503115	+	0.0871421i
$321$		−	62.3538i		−	0.0108419i
$322$	6045.00	−	10470.2i	1.04619	−	1.81206i
$323$	1176.00			0.202583
$324$	−1458.00	−	2525.33i	−0.250000	−	0.433013i
$325$	1628.00			0.277862
$326$	3316.00	−	5743.48i	0.563363	−	0.975773i
$327$		−	2608.47i		−	0.441127i
$328$	1044.00	+	1808.26i	0.175748	+	0.304404i
$329$	2743.50	+	4751.88i	0.459739	+	0.796291i
$330$	−1215.00	−	701.481i	−0.202677	−	0.117016i
$331$	3339.50	−	5784.18i	0.554548	−	0.960506i	−0.443390	−	0.896329i	$-0.646224\pi$
$331$	3339.50	−	5784.18i	0.554548	−	0.960506i	0.997939	−	0.0641773i	$-0.0204423\pi$
$332$	−4332.00			−0.716113
$333$	4482.00			0.737574
$334$	−1362.00			−0.223130
$335$	−1894.50	+	3281.37i	−0.308978	+	0.535165i
$336$	−2232.00	+	1288.65i	−0.362398	+	0.209230i
$337$	−1091.50	−	1890.53i	−0.176433	−	0.305590i	0.764224	−	0.644951i	$-0.223122\pi$
$337$	−1091.50	−	1890.53i	−0.176433	−	0.305590i	−0.940656	+	0.339361i	$0.889789\pi$
$338$	828.000	+	1434.14i	0.133246	+	0.230789i
$339$	−6304.50	+	3639.90i	−1.01007	+	0.583164i
$340$	−756.000	+	1309.43i	−0.120588	+	0.208864i
$341$	3075.00			0.488330
$342$	−756.000	+	1309.43i	−0.119532	+	0.207035i
$343$	−8525.00			−1.34200
$344$	172.000	−	297.913i	0.0269582	−	0.0466930i
$345$	7897.50	+	4559.62i	1.23243	+	0.711542i
$346$	3981.00	+	6895.29i	0.618555	+	1.07137i
$347$	−1945.50	−	3369.70i	−0.300980	−	0.521312i	0.675379	−	0.737471i	$-0.263980\pi$
$347$	−1945.50	−	3369.70i	−0.300980	−	0.521312i	−0.976358	+	0.216159i	$0.930647\pi$
$348$			2307.09i			0.355382i
$349$	−1397.50	+	2420.54i	−0.214345	+	0.371257i	−0.953070	−	0.302751i	$-0.902095\pi$
$349$	−1397.50	+	2420.54i	−0.214345	+	0.371257i	0.738725	+	0.674007i	$0.235428\pi$
$350$	2728.00			0.416622
$351$	4495.50	−	2595.48i	0.683624	−	0.394691i
$352$	−480.000			−0.0726821
$353$	−2377.50	+	4117.95i	−0.358475	+	0.620896i	−0.987706	−	0.156322i	$-0.950036\pi$
$353$	−2377.50	+	4117.95i	−0.358475	+	0.620896i	0.629232	+	0.777218i	$0.283370\pi$
$354$			1652.38i			0.248087i
$355$	702.000	+	1215.90i	0.104953	+	0.181784i
$356$	2100.00	+	3637.31i	0.312640	+	0.541508i
$357$	−5859.00	−	3382.70i	−0.868603	−	0.501488i
$358$	−2004.00	+	3471.03i	−0.295851	+	0.512429i
$359$	4608.00			0.677440			0.338720	−	0.940887i	$-0.390006\pi$
$359$	4608.00			0.677440			0.338720	+	0.940887i	$0.390006\pi$
$360$	−972.000	−	1683.55i	−0.142302	−	0.246475i
$361$	−6075.00			−0.885698
$362$	−1274.00	+	2206.63i	−0.184972	+	0.320381i
$363$	−4977.00	+	2873.47i	−0.719627	+	0.415477i
$364$	−2294.00	−	3973.32i	−0.330325	−	0.572140i
$365$	819.000	+	1418.55i	0.117448	+	0.203425i
$366$	1719.00	−	992.465i	0.245502	−	0.141740i
$367$	−1922.50	+	3329.87i	−0.273443	+	0.473618i	−0.969741	−	0.244135i	$-0.921496\pi$
$367$	−1922.50	+	3329.87i	−0.273443	+	0.473618i	0.696298	+	0.717753i	$0.254829\pi$
$368$	3120.00			0.441960
$369$	−3523.50	−	6102.88i	−0.497090	−	0.860985i
$370$	2988.00			0.419834
$371$	1767.00	−	3060.53i	0.247272	−	0.428288i
$372$	3690.00	+	2130.42i	0.514295	+	0.296928i
$373$	4158.50	+	7202.73i	0.577263	+	0.999848i	0.995792	+	0.0916449i	$0.0292125\pi$
$373$	4158.50	+	7202.73i	0.577263	+	0.999848i	−0.418529	+	0.908203i	$0.637454\pi$
$374$	−630.000	−	1091.19i	−0.0871030	−	0.150867i
$375$			7903.35i			1.08834i
$376$	−708.000	+	1226.29i	−0.0971072	+	0.168195i
$377$	−4107.00			−0.561064
$378$	7533.00	−	4349.18i	1.02502	−	0.591793i
$379$	12560.0			1.70228			0.851140	−	0.524939i	$-0.175912\pi$
$379$	12560.0			1.70228			0.851140	+	0.524939i	$0.175912\pi$
$380$	−504.000	+	872.954i	−0.0680386	+	0.117846i
$381$		−	4572.61i		−	0.614861i
$382$	−1161.00	−	2010.91i	−0.155502	−	0.269338i
$383$	−6043.50	−	10467.6i	−0.806288	−	1.39653i	−0.915418	−	0.402505i	$-0.868140\pi$
$383$	−6043.50	−	10467.6i	−0.806288	−	1.39653i	0.109130	−	0.994028i	$-0.465194\pi$
$384$	−576.000	−	332.554i	−0.0765466	−	0.0441942i
$385$	2092.50	−	3624.32i	0.276997	−	0.479772i
$386$	7222.00			0.952306
$387$	−580.500	+	1005.46i	−0.0762493	+	0.132068i
$388$	−3604.00			−0.471560
$389$	4270.50	−	7396.72i	0.556614	−	0.964084i	−0.441162	−	0.897428i	$-0.645433\pi$
$389$	4270.50	−	7396.72i	0.556614	−	0.964084i	0.997776	−	0.0666565i	$-0.0212332\pi$
$390$	2997.00	−	1730.32i	0.389126	−	0.224662i
$391$	4095.00	+	7092.75i	0.529650	+	0.917380i
$392$	−2472.00	−	4281.63i	−0.318507	−	0.551671i
$393$	6763.50	−	3904.91i	0.868126	−	0.501213i
$394$	−2046.00	+	3543.78i	−0.261614	+	0.453129i
$395$	−10197.0			−1.29890
$396$	1620.00			0.205576
$397$	−13174.0			−1.66545			−0.832726	−	0.553686i	$-0.813221\pi$
$397$	−13174.0			−1.66545			−0.832726	+	0.553686i	$0.813221\pi$
$398$	−2996.00	+	5189.22i	−0.377326	+	0.653549i
$399$	−3906.00	−	2255.13i	−0.490087	−	0.282952i
$400$	352.000	+	609.682i	0.0440000	+	0.0762102i
$401$	−4801.50	−	8316.44i	−0.597944	−	1.03567i	−0.993124	−	0.117066i	$-0.962651\pi$
$401$	−4801.50	−	8316.44i	−0.597944	−	1.03567i	0.395180	−	0.918604i	$-0.370682\pi$
$402$		−	4375.16i		−	0.542819i
$403$	−3792.50	+	6568.80i	−0.468779	+	0.811949i
$404$	1548.00			0.190633
$405$	3280.50	+	5681.99i	0.402492	+	0.697137i
$406$	−6882.00			−0.841251
$407$	−1245.00	+	2156.40i	−0.151627	+	0.262626i
$408$		−	1745.91i		−	0.211851i
$409$	−5735.50	−	9934.18i	−0.693404	−	1.20101i	−0.970716	−	0.240231i	$-0.922777\pi$
$409$	−5735.50	−	9934.18i	−0.693404	−	1.20101i	0.277312	−	0.960780i	$-0.410557\pi$
$410$	−2349.00	−	4068.59i	−0.282948	−	0.490081i
$411$	11974.5	+	6913.48i	1.43713	+	0.829725i
$412$	−1102.00	+	1908.72i	−0.131776	+	0.228242i
$413$	−4929.00			−0.587264
$414$	−10530.0			−1.25005
$415$	9747.00			1.15292
$416$	592.000	−	1025.37i	0.0697721	−	0.120849i
$417$	−544.500	+	314.367i	−0.0639431	+	0.0369176i
$418$	−420.000	−	727.461i	−0.0491456	−	0.0851227i
$419$	2986.50	+	5172.77i	0.348210	+	0.603118i	0.985932	−	0.167149i	$-0.0534562\pi$
$419$	2986.50	+	5172.77i	0.348210	+	0.603118i	−0.637721	+	0.770267i	$0.720123\pi$
$420$	5022.00	−	2899.45i	0.583449	−	0.336854i
$421$	4452.50	−	7711.96i	0.515443	−	0.892774i	−0.484396	−	0.874849i	$-0.660961\pi$
$421$	4452.50	−	7711.96i	0.515443	−	0.892774i	0.999839	−	0.0179250i	$-0.00570601\pi$
$422$	1510.00			0.174184
$423$	2389.50	−	4138.74i	0.274661	−	0.475726i
$424$	912.000			0.104459
$425$	−924.000	+	1600.41i	−0.105460	+	0.182662i
$426$	−1404.00	−	810.600i	−0.159681	−	0.0921918i
$427$	2960.50	+	5127.74i	0.335524	+	0.581144i
$428$	24.0000	+	41.5692i	0.00271048	+	0.00469468i
$429$			2883.86i			0.324555i
$430$	−387.000	+	670.304i	−0.0434019	+	0.0751742i
$431$	1416.00			0.158251			0.0791257	−	0.996865i	$-0.474787\pi$
$431$	1416.00			0.158251			0.0791257	+	0.996865i	$0.474787\pi$
$432$	1944.00	+	1122.37i	0.216506	+	0.125000i
$433$	10766.0			1.19488			0.597438	−	0.801915i	$-0.296186\pi$
$433$	10766.0			1.19488			0.597438	+	0.801915i	$0.296186\pi$
$434$	−6355.00	+	11007.2i	−0.702880	+	1.21742i
$435$		−	5190.96i		−	0.572155i
$436$	1004.00	+	1738.98i	0.110282	+	0.191014i
$437$	2730.00	+	4728.50i	0.298841	+	0.517608i
$438$	−1638.00	−	945.700i	−0.178691	−	0.103167i
$439$	−2174.50	+	3766.34i	−0.236408	+	0.409471i	−0.959681	−	0.281091i	$-0.909304\pi$
$439$	−2174.50	+	3766.34i	−0.236408	+	0.409471i	0.723273	+	0.690562i	$0.242637\pi$
$440$	1080.00			0.117016
$441$	8343.00	+	14450.5i	0.900875	+	1.56036i
$442$	3108.00			0.334463
$443$	7273.50	−	12598.1i	0.780078	−	1.35113i	−0.151818	−	0.988408i	$-0.548513\pi$
$443$	7273.50	−	12598.1i	0.780078	−	1.35113i	0.931896	−	0.362726i	$-0.118154\pi$
$444$	−2988.00	+	1725.12i	−0.319379	+	0.184393i
$445$	−4725.00	−	8183.94i	−0.503340	−	0.871811i
$446$	3463.00	+	5998.09i	0.367663	+	0.636811i
$447$	−12730.5	+	7349.96i	−1.34705	+	0.777721i
$448$	992.000	−	1718.19i	0.104615	−	0.181199i
$449$	−3330.00			−0.350005			−0.175003	−	0.984568i	$-0.555993\pi$
$449$	−3330.00			−0.350005			−0.175003	+	0.984568i	$0.555993\pi$
$450$	−1188.00	−	2057.68i	−0.124451	−	0.215555i
$451$	3915.00			0.408759
$452$	2802.00	−	4853.21i	0.291582	−	0.505035i
$453$	−2074.50	−	1197.71i	−0.215162	−	0.124224i
$454$	−6225.00	−	10782.0i	−0.643510	−	1.11459i
$455$	5161.50	+	8939.98i	0.531813	+	0.921127i
$456$		−	1163.94i		−	0.119532i
$457$	−4073.50	+	7055.51i	−0.416959	+	0.722194i	−0.995632	−	0.0933655i	$-0.970237\pi$
$457$	−4073.50	+	7055.51i	−0.416959	+	0.722194i	0.578673	+	0.815560i	$0.303571\pi$
$458$	−2930.00			−0.298930
$459$			5892.44i			0.599206i
$460$	−7020.00			−0.711542
$461$	−4015.50	+	6955.05i	−0.405684	+	0.702666i	−0.994401	−	0.105674i	$-0.966300\pi$
$461$	−4015.50	+	6955.05i	−0.405684	+	0.702666i	0.588717	+	0.808340i	$0.299633\pi$
$462$			4832.42i			0.486633i
$463$	−2141.50	−	3709.19i	−0.214955	−	0.372312i	0.738304	−	0.674468i	$-0.235627\pi$
$463$	−2141.50	−	3709.19i	−0.214955	−	0.372312i	−0.953259	+	0.302156i	$0.902294\pi$
$464$	−888.000	−	1538.06i	−0.0888456	−	0.153885i
$465$	−8302.50	−	4793.45i	−0.827998	−	0.478045i
$466$	−2634.00	+	4562.22i	−0.261841	+	0.453521i
$467$	5460.00			0.541025			0.270512	−	0.962716i	$-0.412807\pi$
$467$	5460.00			0.541025			0.270512	+	0.962716i	$0.412807\pi$
$468$	−1998.00	+	3460.64i	−0.197345	+	0.341812i
$469$	13051.0			1.28494
$470$	1593.00	−	2759.16i	0.156340	−	0.270788i
$471$	−13396.5	+	7734.47i	−1.31057	+	0.756658i
$472$	−636.000	−	1101.58i	−0.0620218	−	0.107425i
$473$	−322.500	−	558.586i	−0.0313500	−	0.0542999i
$474$	10197.0	−	5887.24i	0.988109	−	0.570485i
$475$	−616.000	+	1066.94i	−0.0595032	+	0.103063i
$476$	5208.00			0.501488
$477$	−3078.00			−0.295455
$478$	13830.0			1.32337
$479$	−214.500	+	371.525i	−0.0204609	+	0.0354393i	−0.876075	−	0.482176i	$-0.839847\pi$
$479$	−214.500	+	371.525i	−0.0204609	+	0.0354393i	0.855614	+	0.517615i	$0.173180\pi$
$480$	1296.00	+	748.246i	0.123238	+	0.0711512i
$481$	−3071.00	−	5319.13i	−0.291113	−	0.504223i
$482$	1489.00	+	2579.02i	0.140710	+	0.243716i
$483$		−	31410.7i		−	2.95909i
$484$	2212.00	−	3831.30i	0.207739	−	0.359814i
$485$	8109.00			0.759197
$486$	−6561.00	−	3788.00i	−0.612372	−	0.353553i
$487$	−11296.0			−1.05107			−0.525535	−	0.850772i	$-0.676135\pi$
$487$	−11296.0			−1.05107			−0.525535	+	0.850772i	$0.676135\pi$
$488$	−764.000	+	1323.29i	−0.0708702	+	0.122751i
$489$		−	17230.4i		−	1.59343i
$490$	5562.00	+	9633.67i	0.512787	+	0.888173i
$491$	7336.50	+	12707.2i	0.674321	+	1.16796i	0.976667	+	0.214760i	$0.0688969\pi$
$491$	7336.50	+	12707.2i	0.674321	+	1.16796i	−0.302346	+	0.953198i	$0.597770\pi$
$492$	4698.00	+	2712.39i	0.430492	+	0.248545i
$493$	2331.00	−	4037.41i	0.212947	−	0.368835i
$494$	2072.00			0.188712
$495$	−3645.00			−0.330971
$496$	−3280.00			−0.296928
$497$	2418.00	−	4188.10i	0.218234	−	0.377992i
$498$	−9747.00	+	5627.43i	−0.877055	+	0.506368i
$499$	−6719.50	−	11638.5i	−0.602818	−	1.04411i	−0.992392	−	0.123116i	$-0.960711\pi$
$499$	−6719.50	−	11638.5i	−0.602818	−	1.04411i	0.389574	−	0.920995i	$-0.372622\pi$
$500$	−3042.00	−	5268.90i	−0.272085	−	0.471265i
$501$	−3064.50	+	1769.29i	−0.273277	+	0.157777i
$502$	4620.00	−	8002.07i	0.410758	−	0.711454i
$503$	−17388.0			−1.54134			−0.770669	−	0.637236i	$-0.780078\pi$
$503$	−17388.0			−1.54134			−0.770669	+	0.637236i	$0.780078\pi$
$504$	−3348.00	+	5798.91i	−0.295896	+	0.512508i
$505$	−3483.00			−0.306914
$506$	2925.00	−	5066.25i	0.256980	−	0.445103i
$507$	3726.00	+	2151.21i	0.326386	+	0.188439i
$508$	1760.00	+	3048.41i	0.153715	+	0.266243i
$509$	1894.50	+	3281.37i	0.164975	+	0.285745i	0.936646	−	0.350276i	$-0.113912\pi$
$509$	1894.50	+	3281.37i	0.164975	+	0.285745i	−0.771671	+	0.636021i	$0.780579\pi$
$510$			3928.29i			0.341074i
$511$	2821.00	−	4886.12i	0.244215	−	0.422992i
$512$	512.000			0.0441942
$513$			3928.29i			0.338086i
$514$	6702.00			0.575122
$515$	2479.50	−	4294.62i	0.212155	−	0.367463i
$516$		−	893.738i		−	0.0762493i
$517$	1327.50	+	2299.30i	0.112927	+	0.195596i
$518$	−5146.00	−	8913.13i	−0.436491	−	0.756024i
$519$	17914.5	+	10342.9i	1.51514	+	0.874768i
$520$	−1332.00	+	2307.09i	−0.112331	+	0.194563i
$521$	9786.00			0.822903			0.411451	−	0.911432i	$-0.365022\pi$
$521$	9786.00			0.822903			0.411451	+	0.911432i	$0.365022\pi$
$522$	2997.00	+	5190.96i	0.251293	+	0.435253i
$523$	−8008.00			−0.669532			−0.334766	−	0.942301i	$-0.608657\pi$
$523$	−8008.00			−0.669532			−0.334766	+	0.942301i	$0.608657\pi$
$524$	−3006.00	+	5206.54i	−0.250606	+	0.434063i
$525$	6138.00	−	3543.78i	0.510256	−	0.294596i
$526$	603.000	+	1044.43i	0.0499849	+	0.0865764i
$527$	−4305.00	−	7456.48i	−0.355842	−	0.616336i
$528$	−1080.00	+	623.538i	−0.0890170	+	0.0513940i
$529$	−12929.0	+	22393.7i	−1.06263	+	1.84053i
$530$	−2052.00			−0.168176
$531$	2146.50	+	3717.85i	0.175424	+	0.303843i
$532$	3472.00			0.282952
$533$	−4828.50	+	8363.21i	−0.392393	+	0.679645i
$534$	9450.00	+	5455.96i	0.765808	+	0.442139i
$535$	−54.0000	−	93.5307i	−0.00436378	−	0.00755829i
$536$	1684.00	+	2916.77i	0.135705	+	0.235047i
$537$			10413.1i			0.836793i
$538$	1470.00	−	2546.11i	0.117800	−	0.204035i
$539$	−9270.00			−0.740793
$540$	−4374.00	−	2525.33i	−0.348569	−	0.201246i
$541$	−2938.00			−0.233483			−0.116742	−	0.993162i	$-0.537245\pi$
$541$	−2938.00			−0.233483			−0.116742	+	0.993162i	$0.537245\pi$
$542$	−2072.00	+	3588.81i	−0.164207	+	0.284414i
$543$			6619.90i			0.523181i
$544$	672.000	+	1163.94i	0.0529628	+	0.0917343i
$545$	−2259.00	−	3912.70i	−0.177550	−	0.307526i
$546$	−10323.0	−	5959.99i	−0.809128	−	0.467150i
$547$	5187.50	−	8985.01i	0.405487	−	0.702324i	−0.588891	−	0.808213i	$-0.700435\pi$
$547$	5187.50	−	8985.01i	0.405487	−	0.702324i	0.994378	+	0.105888i	$0.0337686\pi$
$548$	−10644.0			−0.829725
$549$	2578.50	−	4466.09i	0.200451	−	0.347192i
$550$	1320.00			0.102336
$551$	1554.00	−	2691.61i	0.120150	−	0.208106i
$552$	7020.00	−	4053.00i	0.541288	−	0.312513i
$553$	17561.5	+	30417.4i	1.35044	+	2.33902i
$554$	−7139.00	−	12365.1i	−0.547486	−	0.948273i
$555$	6723.00	−	3881.53i	0.514190	−	0.296868i
$556$	242.000	−	419.156i	0.0184588	−	0.0319716i
$557$	3306.00			0.251490			0.125745	−	0.992063i	$-0.459868\pi$
$557$	3306.00			0.251490			0.125745	+	0.992063i	$0.459868\pi$
$558$	11070.0			0.839840
$559$	1591.00			0.120379
$560$	−2232.00	+	3865.94i	−0.168427	+	0.291724i
$561$	−2835.00	−	1636.79i	−0.213358	−	0.123182i
$562$	−8427.00	−	14596.0i	−0.632512	−	1.09554i
$563$	10546.5	+	18267.1i	0.789488	+	1.36743i	0.926281	+	0.376834i	$0.122987\pi$
$563$	10546.5	+	18267.1i	0.789488	+	1.36743i	−0.136792	+	0.990600i	$0.543679\pi$
$564$			3678.88i			0.274661i
$565$	−6304.50	+	10919.7i	−0.469438	+	0.813090i
$566$	−914.000			−0.0678768
$567$	11299.5	−	19571.3i	0.836921	−	1.44959i
$568$	1248.00			0.0921918
$569$	−643.500	+	1114.57i	−0.0474111	+	0.0821185i	−0.888757	−	0.458379i	$-0.848430\pi$
$569$	−643.500	+	1114.57i	−0.0474111	+	0.0821185i	0.841346	+	0.540497i	$0.181764\pi$
$570$			2618.86i			0.192442i
$571$	−7517.50	−	13020.7i	−0.550959	−	0.954289i	−0.998206	−	0.0598783i	$-0.980929\pi$
$571$	−7517.50	−	13020.7i	−0.550959	−	0.954289i	0.447247	−	0.894411i	$-0.352405\pi$
$572$	−1110.00	−	1922.58i	−0.0811389	−	0.140537i
$573$	−5224.50	−	3016.37i	−0.380902	−	0.219914i
$574$	−8091.00	+	14014.0i	−0.588348	+	1.01905i
$575$	−8580.00			−0.622280
$576$	−1728.00			−0.125000
$577$	1190.00			0.0858585			0.0429292	−	0.999078i	$-0.486331\pi$
$577$	1190.00			0.0858585			0.0429292	+	0.999078i	$0.486331\pi$
$578$	3149.00	−	5454.23i	0.226611	−	0.392502i
$579$	16249.5	−	9381.65i	1.16633	−	0.673382i
$580$	1998.00	+	3460.64i	0.143039	+	0.247750i
$581$	−16786.5	−	29075.1i	−1.19866	−	2.07614i
$582$	−8109.00	+	4681.73i	−0.577541	+	0.333443i
$583$	855.000	−	1480.90i	0.0607384	−	0.105202i
$584$	1456.00			0.103167
$585$	4495.50	−	7786.43i	0.317720	−	0.550307i
$586$	−11778.0			−0.830281
$587$	8941.50	−	15487.1i	0.628714	−	1.08896i	−0.359096	−	0.933301i	$-0.616915\pi$
$587$	8941.50	−	15487.1i	0.628714	−	1.08896i	0.987810	−	0.155664i	$-0.0497518\pi$
$588$	−11124.0	−	6422.44i	−0.780180	−	0.450437i
$589$	−2870.00	−	4970.99i	−0.200775	−	0.347752i
$590$	1431.00	+	2478.56i	0.0998531	+	0.172951i
$591$			10631.3i			0.739957i
$592$	1328.00	−	2300.16i	0.0921967	−	0.159689i
$593$	20118.0			1.39317			0.696583	−	0.717476i	$-0.254703\pi$
$593$	20118.0			1.39317			0.696583	+	0.717476i	$0.254703\pi$
$594$	3645.00	−	2104.44i	0.251778	−	0.145364i
$595$	−11718.0			−0.807380
$596$	5658.00	−	9799.94i	0.388860	−	0.673526i
$597$			15567.7i			1.06724i
$598$	7215.00	+	12496.7i	0.493383	+	0.854565i
$599$	532.500	+	922.317i	0.0363228	+	0.0629129i	0.883615	−	0.468214i	$-0.155102\pi$
$599$	532.500	+	922.317i	0.0363228	+	0.0629129i	−0.847293	+	0.531127i	$0.821769\pi$
$600$	1584.00	+	914.523i	0.107778	+	0.0622254i
$601$	10362.5	−	17948.4i	0.703320	−	1.21819i	−0.263975	−	0.964530i	$-0.585034\pi$
$601$	10362.5	−	17948.4i	0.703320	−	1.21819i	0.967294	−	0.253656i	$-0.0816331\pi$
$602$	2666.00			0.180495
$603$	−5683.50	−	9844.11i	−0.383831	−	0.664815i
$604$	1844.00			0.124224
$605$	−4977.00	+	8620.42i	−0.334453	+	0.579289i
$606$	3483.00	−	2010.91i	0.233477	−	0.134798i
$607$	7872.50	+	13635.6i	0.526417	+	0.911780i	0.999526	+	0.0307768i	$0.00979812\pi$
$607$	7872.50	+	13635.6i	0.526417	+	0.911780i	−0.473110	+	0.881004i	$0.656869\pi$
$608$	448.000	+	775.959i	0.0298829	+	0.0517587i
$609$	−15484.5	+	8939.98i	−1.03032	+	0.594854i
$610$	1719.00	−	2977.40i	0.114099	−	0.197625i
$611$	−6549.00			−0.433624
$612$	−2268.00	−	3928.29i	−0.149801	−	0.259464i
$613$	5042.00			0.332210			0.166105	−	0.986108i	$-0.446881\pi$
$613$	5042.00			0.332210			0.166105	+	0.986108i	$0.446881\pi$
$614$	1204.00	−	2085.39i	0.0791360	−	0.137068i
$615$	−10570.5	−	6102.88i	−0.693079	−	0.400149i
$616$	−1860.00	−	3221.61i	−0.121658	−	0.210718i
$617$	5026.50	+	8706.15i	0.327973	+	0.568066i	0.982110	−	0.188311i	$-0.0603012\pi$
$617$	5026.50	+	8706.15i	0.327973	+	0.568066i	−0.654137	+	0.756376i	$0.726968\pi$
$618$			5726.16i			0.372718i
$619$	2991.50	−	5181.43i	0.194246	−	0.336445i	−0.752407	−	0.658699i	$-0.771107\pi$
$619$	2991.50	−	5181.43i	0.194246	−	0.336445i	0.946653	+	0.322254i	$0.104441\pi$
$620$	7380.00			0.478045
$621$	−23692.5	+	13678.9i	−1.53099	+	0.883920i
$622$	−6570.00			−0.423526
$623$	−16275.0	+	28189.1i	−1.04662	+	1.81280i
$624$		−	3076.12i		−	0.197345i
$625$	4094.50	+	7091.88i	0.262048	+	0.453880i
$626$	10057.0	+	17419.2i	0.642106	+	1.11216i
$627$	−1890.00	−	1091.19i	−0.120382	−	0.0695024i
$628$	5954.00	−	10312.6i	0.378329	−	0.655285i
$629$	6972.00			0.441958
$630$	7533.00	−	13047.5i	0.476384	−	0.825121i
$631$	−19696.0			−1.24261			−0.621304	−	0.783570i	$-0.713397\pi$
$631$	−19696.0			−1.24261			−0.621304	+	0.783570i	$0.713397\pi$
$632$	−4532.00	+	7849.65i	−0.285243	+	0.494055i
$633$	3397.50	−	1961.55i	0.213331	−	0.123167i
$634$	−2295.00	−	3975.06i	−0.143764	−	0.249006i
$635$	−3960.00	−	6858.92i	−0.247477	−	0.428642i
$636$	2052.00	−	1184.72i	0.127936	−	0.0738637i
$637$	11433.0	−	19802.5i	0.711133	−	1.23172i
$638$	−3330.00			−0.206639
$639$	−4212.00			−0.260758
$640$	−1152.00			−0.0711512
$641$	5488.50	−	9506.36i	0.338195	−	0.585770i	−0.645899	−	0.763423i	$-0.723517\pi$
$641$	5488.50	−	9506.36i	0.338195	−	0.585770i	0.984093	+	0.177653i	$0.0568505\pi$
$642$	108.000	+	62.3538i	0.00663928	+	0.00383319i
$643$	7914.50	+	13708.3i	0.485408	+	0.840752i	0.999859	−	0.0167681i	$-0.00533770\pi$
$643$	7914.50	+	13708.3i	0.485408	+	0.840752i	−0.514451	+	0.857520i	$0.672004\pi$
$644$	12090.0	+	20940.5i	0.739771	+	1.28132i
$645$			2010.91i			0.122759i
$646$	−1176.00	+	2036.89i	−0.0716240	+	0.124056i
$647$	28224.0			1.71499			0.857496	−	0.514490i	$-0.172019\pi$
$647$	28224.0			1.71499			0.857496	+	0.514490i	$0.172019\pi$
$648$	5832.00			0.353553
$649$	−2385.00			−0.144252
$650$	−1628.00	+	2819.78i	−0.0982391	+	0.170155i
$651$			33021.5i			1.98804i
$652$	6632.00	+	11487.0i	0.398358	+	0.689976i
$653$	−14083.5	−	24393.3i	−0.843997	−	1.46185i	−0.886490	−	0.462749i	$-0.846863\pi$
$653$	−14083.5	−	24393.3i	−0.843997	−	1.46185i	0.0424927	−	0.999097i	$-0.486470\pi$
$654$	4518.00	+	2608.47i	0.270134	+	0.155962i
$655$	6763.50	−	11714.7i	0.403468	−	0.698828i
$656$	−4176.00			−0.248545
$657$	−4914.00			−0.291801
$658$	−10974.0			−0.650169
$659$	−5368.50	+	9298.51i	−0.317340	+	0.549649i	−0.979932	−	0.199331i	$-0.936123\pi$
$659$	−5368.50	+	9298.51i	−0.317340	+	0.549649i	0.662592	+	0.748980i	$0.269456\pi$
$660$	2430.00	−	1402.96i	0.143315	−	0.0827427i
$661$	−5063.50	−	8770.24i	−0.297954	−	0.516071i	0.677714	−	0.735326i	$-0.262971\pi$
$661$	−5063.50	−	8770.24i	−0.297954	−	0.516071i	−0.975668	+	0.219255i	$0.929637\pi$
$662$	6679.00	+	11568.4i	0.392125	+	0.679180i
$663$	6993.00	−	4037.41i	0.409631	−	0.236501i
$664$	4332.00	−	7503.24i	0.253184	−	0.438528i
$665$	−7812.00			−0.455543
$666$	−4482.00	+	7763.05i	−0.260772	+	0.451670i
$667$	21645.0			1.25652
$668$	1362.00	−	2359.05i	0.0788883	−	0.136638i
$669$	15583.5	+	8997.14i	0.900587	+	0.519954i
$670$	−3789.00	−	6562.74i	−0.218480	−	0.378419i
$671$	1432.50	+	2481.16i	0.0824159	+	0.142748i
$672$		−	5154.58i		−	0.295896i
$673$	−125.500	+	217.372i	−0.00718822	+	0.0124504i	−0.869597	−	0.493762i	$-0.835621\pi$
$673$	−125.500	+	217.372i	−0.00718822	+	0.0124504i	0.862409	+	0.506212i	$0.168955\pi$
$674$	4366.00			0.249513
$675$	−5346.00	−	3086.51i	−0.304841	−	0.176000i
$676$	−3312.00			−0.188439
$677$	−4225.50	+	7318.78i	−0.239881	+	0.415485i	−0.960680	−	0.277659i	$-0.910442\pi$
$677$	−4225.50	+	7318.78i	−0.239881	+	0.415485i	0.720799	+	0.693144i	$0.243775\pi$
$678$		−	14559.6i		−	0.824718i
$679$	−13965.5	−	24189.0i	−0.789318	−	1.36714i
$680$	−1512.00	−	2618.86i	−0.0852685	−	0.147689i
$681$	−28012.5	−	16173.0i	−1.57627	−	0.910061i
$682$	−3075.00	+	5326.06i	−0.172651	+	0.299040i
$683$	−25884.0			−1.45011			−0.725054	−	0.688692i	$-0.758185\pi$
$683$	−25884.0			−1.45011			−0.725054	+	0.688692i	$0.758185\pi$
$684$	−1512.00	−	2618.86i	−0.0845216	−	0.146396i
$685$	23949.0			1.33583
$686$	8525.00	−	14765.7i	0.474469	−	0.821805i
$687$	−6592.50	+	3806.18i	−0.366113	+	0.211375i
$688$	344.000	+	595.825i	0.0190623	+	0.0330169i
$689$	2109.00	+	3652.90i	0.116613	+	0.201980i
$690$	−15795.0	+	9119.25i	−0.871457	+	0.503136i
$691$	−3182.50	+	5512.25i	−0.175207	+	0.303467i	−0.940233	−	0.340532i	$-0.889393\pi$
$691$	−3182.50	+	5512.25i	−0.175207	+	0.303467i	0.765026	+	0.643999i	$0.222726\pi$
$692$	−15924.0			−0.874768
$693$	6277.50	+	10872.9i	0.344102	+	0.596002i
$694$	7782.00			0.425649
$695$	−544.500	+	943.102i	−0.0297181	+	0.0514732i
$696$	−3996.00	−	2307.09i	−0.217626	−	0.125647i
$697$	−5481.00	−	9493.37i	−0.297859	−	0.515907i
$698$	−2795.00	−	4841.08i	−0.151565	−	0.262518i
$699$			13686.7i			0.740597i
$700$	−2728.00	+	4725.03i	−0.147298	+	0.255128i
$701$	1122.00			0.0604527			0.0302264	−	0.999543i	$-0.490377\pi$
$701$	1122.00			0.0604527			0.0302264	+	0.999543i	$0.490377\pi$
$702$			10381.9i			0.558177i
$703$	4648.00			0.249364
$704$	480.000	−	831.384i	0.0256970	−	0.0445085i
$705$		−	8277.47i		−	0.442195i
$706$	−4755.00	−	8235.90i	−0.253480	−	0.439040i
$707$	5998.50	+	10389.7i	0.319090	+	0.552681i
$708$	−2862.00	−	1652.38i	−0.151922	−	0.0877120i
$709$	−2141.50	+	3709.19i	−0.113435	+	0.196476i	−0.917153	−	0.398535i	$-0.869519\pi$
$709$	−2141.50	+	3709.19i	−0.113435	+	0.196476i	0.803718	+	0.595011i	$0.202852\pi$
$710$	−2808.00			−0.148426
$711$	15295.5	−	26492.6i	0.806788	−	1.39740i
$712$	−8400.00			−0.442139
$713$	19987.5	−	34619.4i	1.04984	−	1.81838i
$714$	11718.0	−	6765.39i	0.614195	−	0.354606i
$715$	2497.50	+	4325.80i	0.130631	+	0.226260i
$716$	−4008.00	−	6942.06i	−0.209198	−	0.362342i
$717$	31117.5	−	17965.7i	1.62079	−	0.935762i
$718$	−4608.00	+	7981.29i	−0.239511	+	0.414846i
$719$	4032.00			0.209135			0.104568	−	0.994518i	$-0.466654\pi$
$719$	4032.00			0.209135			0.104568	+	0.994518i	$0.466654\pi$
$720$	3888.00			0.201246
$721$	−17081.0			−0.882288
$722$	6075.00	−	10522.2i	0.313141	−	0.542377i
$723$	6700.50	+	3868.54i	0.344667	+	0.198994i
$724$	−2548.00	−	4413.27i	−0.130795	−	0.226544i
$725$	2442.00	+	4229.67i	0.125095	+	0.216670i
$726$		−	11493.9i		−	0.587573i
$727$	−12002.5	+	20788.9i	−0.612308	+	1.06055i	0.378542	+	0.925584i	$0.376426\pi$
$727$	−12002.5	+	20788.9i	−0.612308	+	1.06055i	−0.990850	+	0.134965i	$0.956908\pi$
$728$	9176.00			0.467150
$729$	−19683.0			−1.00000
$730$	−3276.00			−0.166096
$731$	−903.000	+	1564.04i	−0.0456890	+	0.0791357i
$732$			3969.86i			0.200451i
$733$	18750.5	+	32476.8i	0.944837	+	1.63651i	0.756077	+	0.654482i	$0.227113\pi$
$733$	18750.5	+	32476.8i	0.944837	+	1.63651i	0.188760	+	0.982023i	$0.439553\pi$
$734$	−3845.00	−	6659.74i	−0.193354	−	0.334898i
$735$	25029.0	+	14450.5i	1.25607	+	0.725190i
$736$	−3120.00	+	5404.00i	−0.156256	+	0.270644i
$737$	6315.00			0.315626
$738$	14094.0			0.702991
$739$	−880.000			−0.0438042			−0.0219021	−	0.999760i	$-0.506972\pi$
$739$	−880.000			−0.0438042			−0.0219021	+	0.999760i	$0.506972\pi$
$740$	−2988.00	+	5175.37i	−0.148434	+	0.257095i
$741$	4662.00	−	2691.61i	0.231124	−	0.133439i
$742$	3534.00	+	6121.07i	0.174848	+	0.302846i
$743$	−811.500	−	1405.56i	−0.0400687	−	0.0694010i	0.845296	−	0.534299i	$-0.179424\pi$
$743$	−811.500	−	1405.56i	−0.0400687	−	0.0694010i	−0.885364	+	0.464898i	$0.846091\pi$
$744$	−7380.00	+	4260.84i	−0.363661	+	0.209960i
$745$	−12730.5	+	22049.9i	−0.626053	+	1.08436i
$746$	−16634.0			−0.816373
$747$	−14620.5	+	25323.4i	−0.716113	+	1.24034i
$748$	2520.00			0.123182
$749$	−186.000	+	322.161i	−0.00907382	+	0.0157163i
$750$	−13689.0	−	7903.35i	−0.666469	−	0.384786i
$751$	3444.50	+	5966.05i	0.167366	+	0.289886i	0.937493	−	0.348005i	$-0.113141\pi$
$751$	3444.50	+	5966.05i	0.167366	+	0.289886i	−0.770127	+	0.637890i	$0.779807\pi$
$752$	−1416.00	−	2452.58i	−0.0686652	−	0.118932i
$753$		−	24006.2i		−	1.16180i
$754$	4107.00	−	7113.53i	0.198366	−	0.343580i
$755$	−4149.00			−0.199997
$756$			17396.7i			0.836921i
$757$	−12850.0			−0.616963			−0.308482	−	0.951230i	$-0.599821\pi$
$757$	−12850.0			−0.616963			−0.308482	+	0.951230i	$0.599821\pi$
$758$	−12560.0	+	21754.6i	−0.601847	+	1.04243i
$759$		−	15198.7i		−	0.726850i
$760$	−1008.00	−	1745.91i	−0.0481105	−	0.0833299i
$761$	−2305.50	−	3993.24i	−0.109822	−	0.190217i	0.805876	−	0.592084i	$-0.201695\pi$
$761$	−2305.50	−	3993.24i	−0.109822	−	0.190217i	−0.915698	+	0.401867i	$0.868361\pi$
$762$	7920.00	+	4572.61i	0.376524	+	0.217386i
$763$	−7781.00	+	13477.1i	−0.369189	+	0.639454i
$764$	4644.00			0.219914
$765$	5103.00	+	8838.66i	0.241176	+	0.417728i
$766$	24174.0			1.14026
$767$	2941.50	−

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +5.19615i q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 + 7.79423i) q^{5} +(-9.00000 - 5.19615i) q^{6} +(15.5000 - 26.8468i) q^{7} +8.00000 q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +5.19615i q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 + 7.79423i) q^{5} +(-9.00000 - 5.19615i) q^{6} +(15.5000 - 26.8468i) q^{7} +8.00000 q^{8} -27.0000 q^{9} -18.0000 q^{10} +(7.50000 - 12.9904i) q^{11} +(18.0000 - 10.3923i) q^{12} +(18.5000 + 32.0429i) q^{13} +(31.0000 + 53.6936i) q^{14} +(-40.5000 + 23.3827i) q^{15} +(-8.00000 + 13.8564i) q^{16} -42.0000 q^{17} +(27.0000 - 46.7654i) q^{18} -28.0000 q^{19} +(18.0000 - 31.1769i) q^{20} +(139.500 + 80.5404i) q^{21} +(15.0000 + 25.9808i) q^{22} +(-97.5000 - 168.875i) q^{23} +41.5692i q^{24} +(22.0000 - 38.1051i) q^{25} -74.0000 q^{26} -140.296i q^{27} -124.000 q^{28} +(-55.5000 + 96.1288i) q^{29} -93.5307i q^{30} +(102.500 + 177.535i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(67.5000 + 38.9711i) q^{33} +(42.0000 - 72.7461i) q^{34} +279.000 q^{35} +(54.0000 + 93.5307i) q^{36} -166.000 q^{37} +(28.0000 - 48.4974i) q^{38} +(-166.500 + 96.1288i) q^{39} +(36.0000 + 62.3538i) q^{40} +(130.500 + 226.033i) q^{41} +(-279.000 + 161.081i) q^{42} +(21.5000 - 37.2391i) q^{43} -60.0000 q^{44} +(-121.500 - 210.444i) q^{45} +390.000 q^{46} +(-88.5000 + 153.286i) q^{47} +(-72.0000 - 41.5692i) q^{48} +(-309.000 - 535.204i) q^{49} +(44.0000 + 76.2102i) q^{50} -218.238i q^{51} +(74.0000 - 128.172i) q^{52} +114.000 q^{53} +(243.000 + 140.296i) q^{54} +135.000 q^{55} +(124.000 - 214.774i) q^{56} -145.492i q^{57} +(-111.000 - 192.258i) q^{58} +(-79.5000 - 137.698i) q^{59} +(162.000 + 93.5307i) q^{60} +(-95.5000 + 165.411i) q^{61} -410.000 q^{62} +(-418.500 + 724.863i) q^{63} +64.0000 q^{64} +(-166.500 + 288.386i) q^{65} +(-135.000 + 77.9423i) q^{66} +(210.500 + 364.597i) q^{67} +(84.0000 + 145.492i) q^{68} +(877.500 - 506.625i) q^{69} +(-279.000 + 483.242i) q^{70} +156.000 q^{71} -216.000 q^{72} +182.000 q^{73} +(166.000 - 287.520i) q^{74} +(198.000 + 114.315i) q^{75} +(56.0000 + 96.9948i) q^{76} +(-232.500 - 402.702i) q^{77} -384.515i q^{78} +(-566.500 + 981.207i) q^{79} -144.000 q^{80} +729.000 q^{81} -522.000 q^{82} +(541.500 - 937.906i) q^{83} -644.323i q^{84} +(-189.000 - 327.358i) q^{85} +(43.0000 + 74.4782i) q^{86} +(-499.500 - 288.386i) q^{87} +(60.0000 - 103.923i) q^{88} -1050.00 q^{89} +486.000 q^{90} +1147.00 q^{91} +(-390.000 + 675.500i) q^{92} +(-922.500 + 532.606i) q^{93} +(-177.000 - 306.573i) q^{94} +(-126.000 - 218.238i) q^{95} +(144.000 - 83.1384i) q^{96} +(450.500 - 780.289i) q^{97} +1236.00 q^{98} +(-202.500 + 350.740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} + 9 q^{5} - 18 q^{6} + 31 q^{7} + 16 q^{8} - 54 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 + 9 * q^5 - 18 * q^6 + 31 * q^7 + 16 * q^8 - 54 * q^9	\( 2 q - 2 q^{2} - 4 q^{4} + 9 q^{5} - 18 q^{6} + 31 q^{7} + 16 q^{8} - 54 q^{9} - 36 q^{10} + 15 q^{11} + 36 q^{12} + 37 q^{13} + 62 q^{14} - 81 q^{15} - 16 q^{16} - 84 q^{17} + 54 q^{18} - 56 q^{19} + 36 q^{20} + 279 q^{21} + 30 q^{22} - 195 q^{23} + 44 q^{25} - 148 q^{26} - 248 q^{28} - 111 q^{29} + 205 q^{31} - 32 q^{32} + 135 q^{33} + 84 q^{34} + 558 q^{35} + 108 q^{36} - 332 q^{37} + 56 q^{38} - 333 q^{39} + 72 q^{40} + 261 q^{41} - 558 q^{42} + 43 q^{43} - 120 q^{44} - 243 q^{45} + 780 q^{46} - 177 q^{47} - 144 q^{48} - 618 q^{49} + 88 q^{50} + 148 q^{52} + 228 q^{53} + 486 q^{54} + 270 q^{55} + 248 q^{56} - 222 q^{58} - 159 q^{59} + 324 q^{60} - 191 q^{61} - 820 q^{62} - 837 q^{63} + 128 q^{64} - 333 q^{65} - 270 q^{66} + 421 q^{67} + 168 q^{68} + 1755 q^{69} - 558 q^{70} + 312 q^{71} - 432 q^{72} + 364 q^{73} + 332 q^{74} + 396 q^{75} + 112 q^{76} - 465 q^{77} - 1133 q^{79} - 288 q^{80} + 1458 q^{81} - 1044 q^{82} + 1083 q^{83} - 378 q^{85} + 86 q^{86} - 999 q^{87} + 120 q^{88} - 2100 q^{89} + 972 q^{90} + 2294 q^{91} - 780 q^{92} - 1845 q^{93} - 354 q^{94} - 252 q^{95} + 288 q^{96} + 901 q^{97} + 2472 q^{98} - 405 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 9 * q^5 - 18 * q^6 + 31 * q^7 + 16 * q^8 - 54 * q^9 - 36 * q^10 + 15 * q^11 + 36 * q^12 + 37 * q^13 + 62 * q^14 - 81 * q^15 - 16 * q^16 - 84 * q^17 + 54 * q^18 - 56 * q^19 + 36 * q^20 + 279 * q^21 + 30 * q^22 - 195 * q^23 + 44 * q^25 - 148 * q^26 - 248 * q^28 - 111 * q^29 + 205 * q^31 - 32 * q^32 + 135 * q^33 + 84 * q^34 + 558 * q^35 + 108 * q^36 - 332 * q^37 + 56 * q^38 - 333 * q^39 + 72 * q^40 + 261 * q^41 - 558 * q^42 + 43 * q^43 - 120 * q^44 - 243 * q^45 + 780 * q^46 - 177 * q^47 - 144 * q^48 - 618 * q^49 + 88 * q^50 + 148 * q^52 + 228 * q^53 + 486 * q^54 + 270 * q^55 + 248 * q^56 - 222 * q^58 - 159 * q^59 + 324 * q^60 - 191 * q^61 - 820 * q^62 - 837 * q^63 + 128 * q^64 - 333 * q^65 - 270 * q^66 + 421 * q^67 + 168 * q^68 + 1755 * q^69 - 558 * q^70 + 312 * q^71 - 432 * q^72 + 364 * q^73 + 332 * q^74 + 396 * q^75 + 112 * q^76 - 465 * q^77 - 1133 * q^79 - 288 * q^80 + 1458 * q^81 - 1044 * q^82 + 1083 * q^83 - 378 * q^85 + 86 * q^86 - 999 * q^87 + 120 * q^88 - 2100 * q^89 + 972 * q^90 + 2294 * q^91 - 780 * q^92 - 1845 * q^93 - 354 * q^94 - 252 * q^95 + 288 * q^96 + 901 * q^97 + 2472 * q^98 - 405 * q^99

Introduction

L-functions

Modular forms

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