LMFDB - Embedded newform 525.3.s.g.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(124,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("525.124");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	525.199
Dual form			525.3.s.g.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.98735 + 1.72474i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(3.94949 - 6.84072i) q^{4} -5.97469i q^{6} +(-2.59808 + 6.50000i) q^{7} +13.4495i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-2.98735 + 1.72474i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(3.94949 - 6.84072i) q^{4} -5.97469i q^{6} +(-2.59808 + 6.50000i) q^{7} +13.4495i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.44949 + 2.51059i) q^{11} +(6.84072 + 11.8485i) q^{12} +17.1455 q^{13} +(-3.44949 - 23.8988i) q^{14} +(-7.39898 - 12.8154i) q^{16} +(0.953512 - 1.65153i) q^{17} +(8.96204 + 5.17423i) q^{18} +(14.5454 - 8.39780i) q^{19} +(-7.50000 - 9.52628i) q^{21} -10.0000i q^{22} +(-17.3205 + 10.0000i) q^{23} +(-20.1742 - 11.6476i) q^{24} +(-51.2196 + 29.5717i) q^{26} +5.19615 q^{27} +(34.2036 + 43.4444i) q^{28} +31.3939 q^{29} +(29.3939 + 16.9706i) q^{31} +(-2.38378 - 1.37628i) q^{32} +(-2.51059 - 4.34847i) q^{33} +6.57826i q^{34} -23.6969 q^{36} +(42.8638 - 24.7474i) q^{37} +(-28.9681 + 50.1742i) q^{38} +(-14.8485 + 25.7183i) q^{39} +76.7175i q^{41} +(38.8355 + 15.5227i) q^{42} +59.7980i q^{43} +(11.4495 + 19.8311i) q^{44} +(34.4949 - 59.7469i) q^{46} +(33.5125 + 58.0454i) q^{47} +25.6308 q^{48} +(-35.5000 - 33.7750i) q^{49} +(1.65153 + 2.86054i) q^{51} +(67.7161 - 117.288i) q^{52} +(-82.6922 - 47.7423i) q^{53} +(-15.5227 + 8.96204i) q^{54} +(-87.4217 - 34.9428i) q^{56} +29.0908i q^{57} +(-93.7844 + 54.1464i) q^{58} +(-60.1362 - 34.7197i) q^{59} +(-36.4546 + 21.0471i) q^{61} -117.080 q^{62} +(20.7846 - 3.00000i) q^{63} +68.6867 q^{64} +(15.0000 + 8.66025i) q^{66} +(-81.4762 - 47.0403i) q^{67} +(-7.53177 - 13.0454i) q^{68} -34.6410i q^{69} +22.9898 q^{71} +(34.9428 - 20.1742i) q^{72} +(21.4757 - 37.1969i) q^{73} +(-85.3661 + 147.858i) q^{74} -132.668i q^{76} +(-12.5529 - 15.9444i) q^{77} -102.439i q^{78} +(10.0959 + 17.4866i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-132.318 - 229.182i) q^{82} +0.857187 q^{83} +(-94.7878 + 13.6814i) q^{84} +(-103.136 - 178.637i) q^{86} +(-27.1879 + 47.0908i) q^{87} +(-33.7662 - 19.4949i) q^{88} +(-18.7423 + 10.8209i) q^{89} +(-44.5454 + 111.446i) q^{91} +157.980i q^{92} +(-50.9117 + 29.3939i) q^{93} +(-200.227 - 115.601i) q^{94} +(4.12883 - 2.38378i) q^{96} -72.3785 q^{97} +(164.304 + 39.6691i) q^{98} +8.69694 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4} - 12 q^{9}+O(q^{10}) $ 8 * q + 12 * q^4 - 12 * q^9	$ 8 q + 12 q^{4} - 12 q^{9} + 8 q^{11} - 8 q^{14} - 20 q^{16} - 60 q^{19} - 60 q^{21} - 132 q^{24} - 204 q^{26} + 16 q^{29} - 72 q^{36} - 60 q^{39} + 72 q^{44} + 80 q^{46} - 284 q^{49} + 72 q^{51} - 36 q^{54} - 572 q^{56} + 48 q^{59} - 468 q^{61} + 40 q^{64} + 120 q^{66} - 208 q^{71} - 340 q^{74} - 76 q^{79} - 36 q^{81} - 288 q^{84} - 296 q^{86} + 144 q^{89} - 180 q^{91} - 720 q^{94} + 180 q^{96} - 48 q^{99}+O(q^{100}) $ 8 * q + 12 * q^4 - 12 * q^9 + 8 * q^11 - 8 * q^14 - 20 * q^16 - 60 * q^19 - 60 * q^21 - 132 * q^24 - 204 * q^26 + 16 * q^29 - 72 * q^36 - 60 * q^39 + 72 * q^44 + 80 * q^46 - 284 * q^49 + 72 * q^51 - 36 * q^54 - 572 * q^56 + 48 * q^59 - 468 * q^61 + 40 * q^64 + 120 * q^66 - 208 * q^71 - 340 * q^74 - 76 * q^79 - 36 * q^81 - 288 * q^84 - 296 * q^86 + 144 * q^89 - 180 * q^91 - 720 * q^94 + 180 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.98735	+	1.72474i	−1.49367	+	0.862372i	−0.999974	−	0.00726029i	$-0.997689\pi$
$2$	−2.98735	+	1.72474i	−1.49367	+	0.862372i	−0.493699	+	0.869633i	$0.664356\pi$
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	3.94949	−	6.84072i	0.987372	−	1.71018i
$5$		0			0
$5$		0			0
$6$		−	5.97469i		−	0.995782i
$7$	−2.59808	+	6.50000i	−0.371154	+	0.928571i
$7$	−2.59808	+	6.50000i	−0.371154	+	0.928571i
$8$			13.4495i			1.68119i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.44949	+	2.51059i	−0.131772	+	0.228235i	−0.924360	−	0.381522i	$-0.875400\pi$
$11$	−1.44949	+	2.51059i	−0.131772	+	0.228235i	0.792588	+	0.609758i	$0.208733\pi$
$12$	6.84072	+	11.8485i	0.570060	+	0.987372i
$13$	17.1455			1.31889			0.659444	−	0.751754i	$-0.270792\pi$
$13$	17.1455			1.31889			0.659444	+	0.751754i	$0.270792\pi$
$14$	−3.44949	−	23.8988i	−0.246392	−	1.70705i
$15$		0			0
$16$	−7.39898	−	12.8154i	−0.462436	−	0.800963i
$17$	0.953512	−	1.65153i	0.0560889	−	0.0971489i	−0.836618	−	0.547787i	$-0.815470\pi$
$17$	0.953512	−	1.65153i	0.0560889	−	0.0971489i	0.892707	+	0.450638i	$0.148804\pi$
$18$	8.96204	+	5.17423i	0.497891	+	0.287457i
$19$	14.5454	−	8.39780i	0.765548	−	0.441989i	−0.0657363	−	0.997837i	$-0.520940\pi$
$19$	14.5454	−	8.39780i	0.765548	−	0.441989i	0.831284	+	0.555848i	$0.187606\pi$
$20$		0			0
$21$	−7.50000	−	9.52628i	−0.357143	−	0.453632i
$22$		−	10.0000i		−	0.454545i
$23$	−17.3205	+	10.0000i	−0.753066	+	0.434783i	−0.826801	−	0.562495i	$-0.809841\pi$
$23$	−17.3205	+	10.0000i	−0.753066	+	0.434783i	0.0737349	+	0.997278i	$0.476508\pi$
$24$	−20.1742	−	11.6476i	−0.840593	−	0.485317i
$25$		0			0
$26$	−51.2196	+	29.5717i	−1.96999	+	1.13737i
$27$	5.19615			0.192450
$28$	34.2036	+	43.4444i	1.22156	+	1.55159i
$29$	31.3939			1.08255			0.541274	−	0.840846i	$-0.317942\pi$
$29$	31.3939			1.08255			0.541274	+	0.840846i	$0.317942\pi$
$30$		0			0
$31$	29.3939	+	16.9706i	0.948190	+	0.547438i	0.892518	−	0.451012i	$-0.148937\pi$
$31$	29.3939	+	16.9706i	0.948190	+	0.547438i	0.0556715	+	0.998449i	$0.482270\pi$
$32$	−2.38378	−	1.37628i	−0.0744931	−	0.0430086i
$33$	−2.51059	−	4.34847i	−0.0760785	−	0.131772i
$34$			6.57826i			0.193478i
$35$		0			0
$36$	−23.6969			−0.658248
$37$	42.8638	−	24.7474i	1.15848	−	0.668850i	0.207542	−	0.978226i	$-0.433454\pi$
$37$	42.8638	−	24.7474i	1.15848	−	0.668850i	0.950940	+	0.309376i	$0.100120\pi$
$38$	−28.9681	+	50.1742i	−0.762319	+	1.32037i
$39$	−14.8485	+	25.7183i	−0.380730	+	0.659444i
$40$		0			0
$41$			76.7175i			1.87116i	0.353117	+	0.935579i	$0.385122\pi$
$41$			76.7175i			1.87116i	−0.353117	+	0.935579i	$0.614878\pi$
$42$	38.8355	+	15.5227i	0.924655	+	0.369588i
$43$			59.7980i			1.39065i	0.718695	+	0.695325i	$0.244740\pi$
$43$			59.7980i			1.39065i	−0.718695	+	0.695325i	$0.755260\pi$
$44$	11.4495	+	19.8311i	0.260216	+	0.450707i
$45$		0			0
$46$	34.4949	−	59.7469i	0.749889	−	1.29885i
$47$	33.5125	+	58.0454i	0.713033	+	1.23501i	0.963713	+	0.266939i	$0.0860122\pi$
$47$	33.5125	+	58.0454i	0.713033	+	1.23501i	−0.250681	+	0.968070i	$0.580654\pi$
$48$	25.6308			0.533975
$49$	−35.5000	−	33.7750i	−0.724490	−	0.689286i
$50$		0			0
$51$	1.65153	+	2.86054i	0.0323830	+	0.0560889i
$52$	67.7161	−	117.288i	1.30223	−	2.25553i
$53$	−82.6922	−	47.7423i	−1.56023	−	0.900799i	−0.997233	−	0.0743398i	$-0.976315\pi$
$53$	−82.6922	−	47.7423i	−1.56023	−	0.900799i	−0.562997	−	0.826459i	$-0.690352\pi$
$54$	−15.5227	+	8.96204i	−0.287457	+	0.165964i
$55$		0			0
$56$	−87.4217	−	34.9428i	−1.56110	−	0.623979i
$57$			29.0908i			0.510365i
$58$	−93.7844	+	54.1464i	−1.61697	+	0.933559i
$59$	−60.1362	−	34.7197i	−1.01926	−	0.588469i	−0.105369	−	0.994433i	$-0.533602\pi$
$59$	−60.1362	−	34.7197i	−1.01926	−	0.588469i	−0.913889	+	0.405964i	$0.866936\pi$
$60$		0			0
$61$	−36.4546	+	21.0471i	−0.597616	+	0.345034i	−0.768103	−	0.640326i	$-0.778799\pi$
$61$	−36.4546	+	21.0471i	−0.597616	+	0.345034i	0.170487	+	0.985360i	$0.445466\pi$
$62$	−117.080			−1.88838
$63$	20.7846	−	3.00000i	0.329914	−	0.0476190i
$64$	68.6867			1.07323
$65$		0			0
$66$	15.0000	+	8.66025i	0.227273	+	0.131216i
$67$	−81.4762	−	47.0403i	−1.21606	−	0.702094i	−0.251989	−	0.967730i	$-0.581085\pi$
$67$	−81.4762	−	47.0403i	−1.21606	−	0.702094i	−0.964073	+	0.265636i	$0.914418\pi$
$68$	−7.53177	−	13.0454i	−0.110761	−	0.191844i
$69$		−	34.6410i		−	0.502044i
$70$		0			0
$71$	22.9898			0.323800			0.161900	−	0.986807i	$-0.448238\pi$
$71$	22.9898			0.323800			0.161900	+	0.986807i	$0.448238\pi$
$72$	34.9428	−	20.1742i	0.485317	−	0.280198i
$73$	21.4757	−	37.1969i	0.294187	−	0.509547i	−0.680608	−	0.732647i	$-0.738284\pi$
$73$	21.4757	−	37.1969i	0.294187	−	0.509547i	0.974795	+	0.223100i	$0.0716178\pi$
$74$	−85.3661	+	147.858i	−1.15360	+	1.99809i
$75$		0			0
$76$		−	132.668i		−	1.74563i
$77$	−12.5529	−	15.9444i	−0.163025	−	0.207070i
$78$		−	102.439i		−	1.31332i
$79$	10.0959	+	17.4866i	0.127796	+	0.221350i	0.922823	−	0.385225i	$-0.125876\pi$
$79$	10.0959	+	17.4866i	0.127796	+	0.221350i	−0.795026	+	0.606575i	$0.792543\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−132.318	−	229.182i	−1.61364	−	2.79490i
$83$	0.857187			0.0103276			0.00516378	−	0.999987i	$-0.498356\pi$
$83$	0.857187			0.0103276			0.00516378	+	0.999987i	$0.498356\pi$
$84$	−94.7878	+	13.6814i	−1.12843	+	0.162874i
$85$		0			0
$86$	−103.136	−	178.637i	−1.19926	−	2.07718i
$87$	−27.1879	+	47.0908i	−0.312505	+	0.541274i
$88$	−33.7662	−	19.4949i	−0.383706	−	0.221533i
$89$	−18.7423	+	10.8209i	−0.210588	+	0.121583i	−0.601585	−	0.798809i	$-0.705464\pi$
$89$	−18.7423	+	10.8209i	−0.210588	+	0.121583i	0.390997	+	0.920392i	$0.372130\pi$
$90$		0			0
$91$	−44.5454	+	111.446i	−0.489510	+	1.22468i
$92$			157.980i			1.71717i
$93$	−50.9117	+	29.3939i	−0.547438	+	0.316063i
$94$	−200.227	−	115.601i	−2.13007	−	1.22980i
$95$		0			0
$96$	4.12883	−	2.38378i	0.0430086	−	0.0248310i
$97$	−72.3785			−0.746170			−0.373085	−	0.927797i	$-0.621700\pi$
$97$	−72.3785			−0.746170			−0.373085	+	0.927797i	$0.621700\pi$
$98$	164.304	+	39.6691i	1.67657	+	0.404787i
$99$	8.69694			0.0878479
$100$		0			0
$101$	19.6515	+	11.3458i	0.194570	+	0.112335i	0.594120	−	0.804376i	$-0.297500\pi$
$101$	19.6515	+	11.3458i	0.194570	+	0.112335i	−0.399550	+	0.916711i	$0.630834\pi$
$102$	−9.86739	−	5.69694i	−0.0967391	−	0.0558523i
$103$	−43.9923	−	76.1969i	−0.427110	−	0.739776i	0.569505	−	0.821988i	$-0.307135\pi$
$103$	−43.9923	−	76.1969i	−0.427110	−	0.739776i	−0.996615	+	0.0822118i	$0.973802\pi$
$104$			230.599i			2.21730i
$105$		0			0
$106$	329.373			3.10730
$107$	−156.488	+	90.3485i	−1.46251	+	0.844378i	−0.999127	−	0.0417819i	$-0.986697\pi$
$107$	−156.488	+	90.3485i	−1.46251	+	0.844378i	−0.463379	+	0.886160i	$0.653363\pi$
$108$	20.5222	−	35.5454i	0.190020	−	0.329124i
$109$	−17.1515	+	29.7073i	−0.157353	+	0.272544i	−0.933914	−	0.357499i	$-0.883630\pi$
$109$	−17.1515	+	29.7073i	−0.157353	+	0.272544i	0.776560	+	0.630043i	$0.216963\pi$
$110$		0			0
$111$			85.7277i			0.772321i
$112$	102.523	−	14.7980i	0.915386	−	0.132125i
$113$		−	8.38367i		−	0.0741918i	−0.999312	−	0.0370959i	$-0.988189\pi$
$113$		−	8.38367i		−	0.0741918i	0.999312	−	0.0370959i	$-0.0118107\pi$
$114$	−50.1742	−	86.9043i	−0.440125	−	0.762319i
$115$		0			0
$116$	123.990	−	214.757i	1.06888	−	1.85135i
$117$	−25.7183	−	44.5454i	−0.219815	−	0.380730i
$118$	239.530			2.02992
$119$	8.25765	+	10.4886i	0.0693920	+	0.0881397i
$120$		0			0
$121$	56.2980	+	97.5109i	0.465272	+	0.805875i
$122$	72.6016	−	125.750i	0.595095	−	1.03074i
$123$	−115.076	−	66.4393i	−0.935579	−	0.540157i
$124$	232.182	−	134.050i	1.87243	−	1.08105i
$125$		0			0
$126$	−56.9166	+	44.8102i	−0.451719	+	0.355636i
$127$			160.798i			1.26613i	0.774100	+	0.633063i	$0.218203\pi$
$127$			160.798i			1.26613i	−0.774100	+	0.633063i	$0.781797\pi$
$128$	−195.656	+	112.962i	−1.52856	+	0.882516i
$129$	−89.6969	−	51.7866i	−0.695325	−	0.401446i
$130$		0			0
$131$	44.6969	−	25.8058i	0.341198	−	0.196991i	−0.319604	−	0.947551i	$-0.603550\pi$
$131$	44.6969	−	25.8058i	0.341198	−	0.196991i	0.660802	+	0.750561i	$0.270216\pi$
$132$	−39.6622			−0.300471
$133$	16.7956	+	116.363i	0.126283	+	0.874912i
$134$	324.530			2.42187
$135$		0			0
$136$	22.2122	+	12.8242i	0.163325	+	0.0942959i
$137$	236.766	+	136.697i	1.72822	+	0.997788i	0.897349	+	0.441322i	$0.145490\pi$
$137$	236.766	+	136.697i	1.72822	+	0.997788i	0.830871	+	0.556466i	$0.187843\pi$
$138$	59.7469	+	103.485i	0.432949	+	0.749889i
$139$			225.656i			1.62343i	0.584057	+	0.811713i	$0.301465\pi$
$139$			225.656i			1.62343i	−0.584057	+	0.811713i	$0.698535\pi$
$140$		0			0
$141$	−116.091			−0.823339
$142$	−68.6785	+	39.6515i	−0.483651	+	0.279236i
$143$	−24.8523	+	43.0454i	−0.173792	+	0.301017i
$144$	−22.1969	+	38.4462i	−0.154145	+	0.266988i
$145$		0			0
$146$			148.160i			1.01480i
$147$	81.4064	−	24.0000i	0.553785	−	0.163265i
$148$		−	390.959i		−	2.64162i
$149$	−100.328	−	173.773i	−0.673343	−	1.16626i	−0.976950	−	0.213467i	$-0.931525\pi$
$149$	−100.328	−	173.773i	−0.673343	−	1.16626i	0.303608	−	0.952797i	$-0.401809\pi$
$150$		0			0
$151$	−117.187	+	202.973i	−0.776071	+	1.34419i	0.158119	+	0.987420i	$0.449457\pi$
$151$	−117.187	+	202.973i	−0.776071	+	1.34419i	−0.934191	+	0.356775i	$0.883876\pi$
$152$	112.946	+	195.628i	0.743066	+	1.28703i
$153$	−5.72107			−0.0373926
$154$	65.0000	+	25.9808i	0.422078	+	0.168706i
$155$		0			0
$156$	117.288	+	203.148i	0.751845	+	1.30223i
$157$	20.8721	−	36.1515i	0.132943	−	0.230265i	−0.791867	−	0.610694i	$-0.790891\pi$
$157$	20.8721	−	36.1515i	0.132943	−	0.230265i	0.924810	+	0.380430i	$0.124224\pi$
$158$	−60.3200	−	34.8258i	−0.381772	−	0.220416i
$159$	143.227	−	82.6922i	0.900799	−	0.520077i
$160$		0			0
$161$	−20.0000	−	138.564i	−0.124224	−	0.860646i
$162$		−	31.0454i		−	0.191638i
$163$	−36.9501	+	21.3332i	−0.226688	+	0.130878i	−0.609043	−	0.793137i	$-0.708446\pi$
$163$	−36.9501	+	21.3332i	−0.226688	+	0.130878i	0.382355	+	0.924015i	$0.375113\pi$
$164$	524.803	+	302.995i	3.20002	+	1.84753i
$165$		0			0
$166$	−2.56072	+	1.47843i	−0.0154260	+	0.00890620i
$167$	161.570			0.967487			0.483743	−	0.875210i	$-0.339277\pi$
$167$	161.570			0.967487			0.483743	+	0.875210i	$0.339277\pi$
$168$	128.124	−	100.871i	0.762640	−	0.600424i
$169$	124.969			0.739464
$170$		0			0
$171$	−43.6362	−	25.1934i	−0.255183	−	0.147330i
$172$	409.061	+	236.171i	2.37826	+	1.37309i
$173$	−69.8070	−	120.909i	−0.403508	−	0.698897i	0.590638	−	0.806936i	$-0.298876\pi$
$173$	−69.8070	−	120.909i	−0.403508	−	0.698897i	−0.994147	+	0.108039i	$0.965543\pi$
$174$		−	187.569i		−	1.07798i
$175$		0			0
$176$	42.8990			0.243744
$177$	104.159	−	60.1362i	0.588469	−	0.339753i
$178$	37.3266	−	64.6515i	0.209700	−	0.363211i
$179$	−37.6061	+	65.1357i	−0.210090	+	0.363887i	−0.951743	−	0.306898i	$-0.900709\pi$
$179$	−37.6061	+	65.1357i	−0.210090	+	0.363887i	0.741652	+	0.670784i	$0.234042\pi$
$180$		0			0
$181$			42.5837i			0.235269i	0.993057	+	0.117635i	$0.0375311\pi$
$181$			42.5837i			0.235269i	−0.993057	+	0.117635i	$0.962469\pi$
$182$	−59.1433	−	409.757i	−0.324963	−	2.25141i
$183$		−	72.9092i		−	0.398411i
$184$	−134.495	−	232.952i	−0.730951	−	1.26604i
$185$		0			0
$186$	101.394	−	175.619i	0.545128	−	0.944190i
$187$	2.76421	+	4.78775i	0.0147819	+	0.0256030i
$188$	529.430			2.81611
$189$	−13.5000	+	33.7750i	−0.0714286	+	0.178704i
$190$		0			0
$191$	6.86378	+	11.8884i	0.0359360	+	0.0622430i	0.883434	−	0.468556i	$-0.155225\pi$
$191$	6.86378	+	11.8884i	0.0359360	+	0.0622430i	−0.847498	+	0.530799i	$0.821892\pi$
$192$	−59.4845	+	103.030i	−0.309815	+	0.536615i
$193$	53.8509	+	31.0908i	0.279020	+	0.161092i	0.632980	−	0.774168i	$-0.281832\pi$
$193$	53.8509	+	31.0908i	0.279020	+	0.161092i	−0.353960	+	0.935261i	$0.615165\pi$
$194$	216.220	−	124.834i	1.11453	−	0.643477i
$195$		0			0
$196$	−371.252	+	109.451i	−1.89414	+	0.558426i
$197$		−	16.3837i		−	0.0831658i	−0.999135	−	0.0415829i	$-0.986760\pi$
$197$		−	16.3837i		−	0.0831658i	0.999135	−	0.0415829i	$-0.0132401\pi$
$198$	−25.9808	+	15.0000i	−0.131216	+	0.0757576i
$199$	−240.257	−	138.713i	−1.20732	−	0.697048i	−0.245149	−	0.969485i	$-0.578837\pi$
$199$	−240.257	−	138.713i	−1.20732	−	0.697048i	−0.962173	+	0.272438i	$0.912170\pi$
$200$		0			0
$201$	141.121	−	81.4762i	0.702094	−	0.405354i
$202$	−78.2746			−0.387498
$203$	−81.5637	+	204.060i	−0.401792	+	1.00522i
$204$	26.0908			0.127896
$205$		0			0
$206$	262.841	+	151.751i	1.27593	+	0.736656i
$207$	51.9615	+	30.0000i	0.251022	+	0.144928i
$208$	−126.859	−	219.727i	−0.609901	−	1.05638i
$209$			48.6901i			0.232967i
$210$		0			0
$211$	63.5153			0.301020			0.150510	−	0.988608i	$-0.451908\pi$
$211$	63.5153			0.301020			0.150510	+	0.988608i	$0.451908\pi$
$212$	−653.184	+	377.116i	−3.08106	+	1.77885i
$213$	−19.9097	+	34.4847i	−0.0934730	+	0.161900i
$214$	311.656	−	539.804i	1.45634	−	2.52245i
$215$		0			0
$216$			69.8856i			0.323544i
$217$	−186.676	+	146.969i	−0.860259	+	0.677278i
$218$		−	118.328i		−	0.542789i
$219$	37.1969	+	64.4270i	0.169849	+	0.294187i
$220$		0			0
$221$	16.3485	−	28.3164i	0.0739750	−	0.128128i
$222$	−147.858	−	256.098i	−0.666029	−	1.15360i
$223$	300.274			1.34652			0.673260	−	0.739406i	$-0.264893\pi$
$223$	300.274			1.34652			0.673260	+	0.739406i	$0.264893\pi$
$224$	15.1390	−	11.9189i	0.0675850	−	0.0532094i
$225$		0			0
$226$	14.4597	+	25.0449i	0.0639810	+	0.110818i
$227$	−33.9588	+	58.8184i	−0.149598	+	0.259112i	−0.931079	−	0.364818i	$-0.881131\pi$
$227$	−33.9588	+	58.8184i	−0.149598	+	0.259112i	0.781481	+	0.623929i	$0.214465\pi$
$228$	199.002	+	114.894i	0.872816	+	0.503921i
$229$	−303.393	+	175.164i	−1.32486	+	0.764909i	−0.984500	−	0.175385i	$-0.943883\pi$
$229$	−303.393	+	175.164i	−1.32486	+	0.764909i	−0.340362	+	0.940295i	$0.610550\pi$
$230$		0			0
$231$	34.7878	−	5.02118i	0.150596	−	0.0217367i
$232$			422.232i			1.81996i
$233$	80.5925	−	46.5301i	0.345891	−	0.199700i	−0.316983	−	0.948431i	$-0.602670\pi$
$233$	80.5925	−	46.5301i	0.345891	−	0.199700i	0.662874	+	0.748731i	$0.269337\pi$
$234$	153.659	+	88.7150i	0.656662	+	0.379124i
$235$		0			0
$236$	−475.015	+	274.250i	−2.01277	+	1.16208i
$237$	−34.9733			−0.147567
$238$	−42.7587	−	17.0908i	−0.179658	−	0.0718101i
$239$	112.363			0.470139			0.235070	−	0.971979i	$-0.424468\pi$
$239$	112.363			0.470139			0.235070	+	0.971979i	$0.424468\pi$
$240$		0			0
$241$	−342.560	−	197.777i	−1.42141	−	0.820652i	−0.424992	−	0.905197i	$-0.639723\pi$
$241$	−342.560	−	197.777i	−1.42141	−	0.820652i	−0.996420	+	0.0845448i	$0.973056\pi$
$242$	−336.363	−	194.199i	−1.38993	−	0.802476i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			332.501i			1.36271i
$245$		0			0
$246$	458.363			1.86327
$247$	249.389	−	143.985i	1.00967	−	0.582934i
$248$	−228.245	+	395.333i	−0.920344	+	1.59408i
$249$	−0.742346	+	1.28578i	−0.00298131	+	0.00516378i
$250$		0			0
$251$			113.423i			0.451884i	0.974141	+	0.225942i	$0.0725459\pi$
$251$			113.423i			0.451884i	−0.974141	+	0.225942i	$0.927454\pi$
$252$	61.5665	−	154.030i	0.244311	−	0.611231i
$253$		−	57.9796i		−	0.229168i
$254$	−277.335	−	480.359i	−1.09187	−	1.89118i
$255$		0			0
$256$	252.288	−	436.975i	0.985499	−	1.70693i
$257$	94.3093	+	163.348i	0.366962	+	0.635597i	0.989089	−	0.147319i	$-0.0470645\pi$
$257$	94.3093	+	163.348i	0.366962	+	0.635597i	−0.622127	+	0.782917i	$0.713731\pi$
$258$	357.274			1.38478
$259$	49.4949	+	342.911i	0.191100	+	1.32398i
$260$		0			0
$261$	−47.0908	−	81.5637i	−0.180425	−	0.312505i
$262$	−89.0168	+	154.182i	−0.339759	+	0.588480i
$263$	−17.2852	−	9.97959i	−0.0657230	−	0.0379452i	0.466778	−	0.884374i	$-0.345415\pi$
$263$	−17.2852	−	9.97959i	−0.0657230	−	0.0379452i	−0.532501	+	0.846429i	$0.678748\pi$
$264$	58.4847	−	33.7662i	0.221533	−	0.127902i
$265$		0			0
$266$	−250.871	−	318.649i	−0.943125	−	1.19793i
$267$		−	37.4847i		−	0.140392i
$268$	−643.579	+	371.570i	−2.40141	+	1.38646i
$269$	334.590	+	193.176i	1.24383	+	0.718126i	0.969872	−	0.243616i	$-0.0783336\pi$
$269$	334.590	+	193.176i	1.24383	+	0.718126i	0.273958	+	0.961742i	$0.411667\pi$
$270$		0			0
$271$	−33.6367	+	19.4202i	−0.124121	+	0.0716612i	−0.560775	−	0.827968i	$-0.689497\pi$
$271$	−33.6367	+	19.4202i	−0.124121	+	0.0716612i	0.436654	+	0.899629i	$0.356163\pi$
$272$	−28.2201			−0.103750
$273$	−128.592	−	163.333i	−0.471031	−	0.598290i
$274$	−943.069			−3.44186
$275$		0			0
$276$	−236.969	−	136.814i	−0.858585	−	0.495704i
$277$	456.578	+	263.606i	1.64830	+	0.951645i	0.977749	+	0.209779i	$0.0672744\pi$
$277$	456.578	+	263.606i	1.64830	+	0.951645i	0.670548	+	0.741866i	$0.266059\pi$
$278$	−389.199	−	674.113i	−1.40000	−	2.42487i
$279$		−	101.823i		−	0.364958i
$280$		0			0
$281$	322.050			1.14609			0.573043	−	0.819526i	$-0.305763\pi$
$281$	322.050			1.14609			0.573043	+	0.819526i	$0.305763\pi$
$282$	346.803	−	200.227i	1.22980	−	0.710025i
$283$	234.561	−	406.272i	0.828838	−	1.43559i	−0.0701121	−	0.997539i	$-0.522336\pi$
$283$	234.561	−	406.272i	0.828838	−	1.43559i	0.898950	−	0.438051i	$-0.144331\pi$
$284$	90.7980	−	157.267i	0.319711	−	0.553756i
$285$		0			0
$286$		−	171.455i		−	0.599494i
$287$	−498.664	−	199.318i	−1.73750	−	0.694487i
$288$			8.25765i			0.0286724i
$289$	142.682	+	247.132i	0.493708	+	0.855127i
$290$		0			0
$291$	62.6816	−	108.568i	0.215401	−	0.373085i
$292$	−169.636	−	293.818i	−0.580945	−	1.00623i
$293$	−192.555			−0.657183			−0.328591	−	0.944472i	$-0.606574\pi$
$293$	−192.555			−0.657183			−0.328591	+	0.944472i	$0.606574\pi$
$294$	−201.795	+	212.102i	−0.686378	+	0.721434i
$295$		0			0
$296$	332.841	+	576.497i	1.12446	+	1.94762i
$297$	−7.53177	+	13.0454i	−0.0253595	+	0.0439239i
$298$	599.429	+	346.081i	2.01151	+	1.16134i
$299$	−296.969	+	171.455i	−0.993209	+	0.573429i
$300$		0			0
$301$	−388.687	−	155.360i	−1.29132	−	0.516145i
$302$		−	808.469i		−	2.67705i
$303$	−34.0374	+	19.6515i	−0.112335	+	0.0648565i
$304$	−215.242	−	124.270i	−0.708034	−	0.408784i
$305$		0			0
$306$	17.0908	−	9.86739i	0.0558523	−	0.0322464i
$307$	−35.6555			−0.116142			−0.0580708	−	0.998312i	$-0.518495\pi$
$307$	−35.6555			−0.116142			−0.0580708	+	0.998312i	$0.518495\pi$
$308$	−158.649	+	22.8990i	−0.515093	+	0.0743473i
$309$	152.394			0.493184
$310$		0			0
$311$	−176.060	−	101.648i	−0.566110	−	0.326844i	0.189484	−	0.981884i	$-0.439318\pi$
$311$	−176.060	−	101.648i	−0.566110	−	0.326844i	−0.755594	+	0.655040i	$0.772652\pi$
$312$	−345.898	−	199.704i	−1.10865	−	0.640078i
$313$	29.7771	+	51.5755i	0.0951346	+	0.164778i	0.909665	−	0.415343i	$-0.136339\pi$
$313$	29.7771	+	51.5755i	0.0951346	+	0.164778i	−0.814530	+	0.580121i	$0.803005\pi$
$314$			143.996i			0.458587i
$315$		0			0
$316$	159.495			0.504731
$317$	366.984	−	211.879i	1.15768	−	0.668387i	0.206933	−	0.978355i	$-0.433652\pi$
$317$	366.984	−	211.879i	1.15768	−	0.668387i	0.950747	+	0.309969i	$0.100319\pi$
$318$	−285.246	+	494.060i	−0.896999	+	1.55365i
$319$	−45.5051	+	78.8171i	−0.142649	+	0.247076i
$320$		0			0
$321$		−	312.976i		−	0.975004i
$322$	298.735	+	379.444i	0.927747	+	1.17840i
$323$		−	32.0296i		−	0.0991628i
$324$	35.5454	+	61.5665i	0.109708	+	0.190020i
$325$		0			0
$326$	73.5885	−	127.459i	0.225732	−	0.390979i
$327$	−29.7073	−	51.4546i	−0.0908481	−	0.157353i
$328$	−1031.81			−3.14577
$329$	−464.363	+	67.0251i	−1.41144	+	0.203724i
$330$		0			0
$331$	200.758	+	347.722i	0.606519	+	1.05052i	0.991810	+	0.127726i	$0.0407678\pi$
$331$	200.758	+	347.722i	0.606519	+	1.05052i	−0.385291	+	0.922795i	$0.625899\pi$
$332$	3.38545	−	5.86378i	0.0101971	−	0.0176620i
$333$	−128.592	−	74.2423i	−0.386161	−	0.222950i
$334$	−482.666	+	278.668i	−1.44511	+	0.834334i
$335$		0			0
$336$	−66.5908	+	166.600i	−0.198187	+	0.495834i
$337$		−	445.333i		−	1.32146i	−0.750623	−	0.660731i	$-0.770246\pi$
$337$		−	445.333i		−	1.32146i	0.750623	−	0.660731i	$-0.229754\pi$
$338$	−373.327	+	215.540i	−1.10452	+	0.637693i
$339$	12.5755	+	7.26047i	0.0370959	+	0.0214173i
$340$		0			0
$341$	−85.2122	+	49.1973i	−0.249889	+	0.144274i
$342$	173.809			0.508212
$343$	311.769	−	143.000i	0.908948	−	0.416910i
$344$	−804.252			−2.33794
$345$		0			0
$346$	417.075	+	240.798i	1.20542	+	0.695949i
$347$	278.903	+	161.025i	0.803756	+	0.464049i	0.844783	−	0.535109i	$-0.179729\pi$
$347$	278.903	+	161.025i	0.803756	+	0.464049i	−0.0410266	+	0.999158i	$0.513063\pi$
$348$	214.757	+	371.969i	0.617117	+	1.06888i
$349$		−	45.0687i		−	0.129137i	−0.997913	−	0.0645683i	$-0.979433\pi$
$349$		−	45.0687i		−	0.129137i	0.997913	−	0.0645683i	$-0.0205670\pi$
$350$		0			0
$351$	89.0908			0.253820
$352$	6.91053	−	3.98979i	0.0196322	−	0.0113346i
$353$	−325.687	+	564.106i	−0.922625	+	1.59803i	−0.127287	+	0.991866i	$0.540627\pi$
$353$	−325.687	+	564.106i	−0.922625	+	1.59803i	−0.795337	+	0.606167i	$0.792706\pi$
$354$	−207.439	+	359.295i	−0.585987	+	1.01496i
$355$		0			0
$356$			170.948i			0.480191i
$357$	−22.8843	+	3.30306i	−0.0641016	+	0.00925227i
$358$		−	259.444i		−	0.724704i
$359$	−3.48011	−	6.02772i	−0.00969389	−	0.0167903i	0.861138	−	0.508372i	$-0.169752\pi$
$359$	−3.48011	−	6.02772i	−0.00969389	−	0.0167903i	−0.870832	+	0.491581i	$0.836419\pi$
$360$		0			0
$361$	−39.4541	+	68.3365i	−0.109291	+	0.189298i
$362$	−73.4460	−	127.212i	−0.202890	−	0.351415i
$363$	−195.022			−0.537250
$364$	586.439	+	744.877i	1.61110	+	2.04637i
$365$		0			0
$366$	125.750	+	217.805i	0.343579	+	0.595095i
$367$	−254.594	+	440.969i	−0.693716	+	1.20155i	0.276896	+	0.960900i	$0.410694\pi$
$367$	−254.594	+	440.969i	−0.693716	+	1.20155i	−0.970612	+	0.240651i	$0.922639\pi$
$368$	256.308	+	147.980i	0.696490	+	0.402118i
$369$	199.318	−	115.076i	0.540157	−	0.311860i
$370$		0			0
$371$	525.166	−	413.461i	1.41554	−	1.11445i
$372$			464.363i			1.24829i
$373$	154.344	−	89.1107i	0.413792	−	0.238903i	−0.278626	−	0.960400i	$-0.589879\pi$
$373$	154.344	−	89.1107i	0.413792	−	0.238903i	0.692418	+	0.721497i	$0.256546\pi$
$374$	−16.5153	−	9.53512i	−0.0441586	−	0.0254950i
$375$		0			0
$376$	−780.681	+	450.726i	−2.07628	+	1.19874i
$377$	538.265			1.42776
$378$	−17.9241	−	124.182i	−0.0474182	−	0.328523i
$379$	215.899			0.569654			0.284827	−	0.958579i	$-0.408064\pi$
$379$	215.899			0.569654			0.284827	+	0.958579i	$0.408064\pi$
$380$		0			0
$381$	−241.197	−	139.255i	−0.633063	−	0.365499i
$382$	−41.0089	−	23.6765i	−0.107353	−	0.0619804i
$383$	84.6778	+	146.666i	0.221091	+	0.382941i	0.955140	−	0.296156i	$-0.0957049\pi$
$383$	84.6778	+	146.666i	0.221091	+	0.382941i	−0.734049	+	0.679097i	$0.762372\pi$
$384$		−	391.312i		−	1.01904i
$385$		0			0
$386$	−214.495			−0.555686
$387$	155.360	−	89.6969i	0.401446	−	0.231775i
$388$	−285.858	+	495.121i	−0.736748	+	1.27608i
$389$	26.4699	−	45.8472i	0.0680460	−	0.117859i	−0.829995	−	0.557771i	$-0.811657\pi$
$389$	26.4699	−	45.8472i	0.0680460	−	0.117859i	0.898041	+	0.439912i	$0.144990\pi$
$390$		0			0
$391$			38.1405i			0.0975460i
$392$	454.256	−	477.457i	1.15882	−	1.21800i
$393$			89.3939i			0.227465i
$394$	28.2577	+	48.9437i	0.0717199	+	0.124223i
$395$		0			0
$396$	34.3485	−	59.4933i	0.0867386	−	0.150236i
$397$	−198.468	−	343.757i	−0.499920	−	0.865887i	0.500080	−	0.865979i	$-0.333304\pi$
$397$	−198.468	−	343.757i	−0.499920	−	0.865887i	−1.00000		9.22678e-5i	$0.999971\pi$
$398$	956.975			2.40446
$399$	−189.090	−	75.5802i	−0.473911	−	0.189424i
$400$		0			0
$401$	−207.398	−	359.225i	−0.517203	−	0.895822i	−0.999800	−	0.0199797i	$-0.993640\pi$
$401$	−207.398	−	359.225i	−0.517203	−	0.895822i	0.482597	−	0.875842i	$-0.339694\pi$
$402$	−281.051	+	486.795i	−0.699133	+	1.21093i
$403$	503.974	+	290.969i	1.25056	+	0.722008i
$404$	155.227	−	89.6204i	0.384225	−	0.221833i
$405$		0			0
$406$	−108.293	−	750.275i	−0.266731	−	1.84797i
$407$			143.485i			0.352542i
$408$	−38.4727	+	22.2122i	−0.0942959	+	0.0544418i
$409$	−440.651	−	254.410i	−1.07739	−	0.622029i	−0.147196	−	0.989107i	$-0.547025\pi$
$409$	−440.651	−	254.410i	−1.07739	−	0.622029i	−0.930190	+	0.367078i	$0.880358\pi$
$410$		0			0
$411$	−410.091	+	236.766i	−0.997788	+	0.576073i
$412$	−694.989			−1.68687
$413$	381.916	−	300.681i	0.924737	−	0.728041i
$414$	−206.969			−0.499926
$415$		0			0
$416$	−40.8712	−	23.5970i	−0.0982480	−	0.0567235i
$417$	−338.484	−	195.424i	−0.811713	−	0.468643i
$418$	−83.9780	−	145.454i	−0.200904	−	0.347976i
$419$		−	234.946i		−	0.560729i	−0.959894	−	0.280365i	$-0.909545\pi$
$419$		−	234.946i		−	0.560729i	0.959894	−	0.280365i	$-0.0904554\pi$
$420$		0			0
$421$	−537.919			−1.27772			−0.638859	−	0.769324i	$-0.720593\pi$
$421$	−537.919			−1.27772			−0.638859	+	0.769324i	$0.720593\pi$
$422$	−189.742	+	109.548i	−0.449626	+	0.259592i
$423$	100.538	−	174.136i	0.237678	−	0.411670i
$424$	642.110	−	1112.17i	1.51441	−	2.62304i
$425$		0			0
$426$		−	137.357i		−	0.322434i
$427$	−42.0941	−	291.637i	−0.0985811	−	0.682990i
$428$			1427.32i			3.33486i
$429$	−43.0454	−	74.5568i	−0.100339	−	0.173792i
$430$		0			0
$431$	−16.6663	+	28.8669i	−0.0386690	+	0.0669766i	−0.884712	−	0.466138i	$-0.845645\pi$
$431$	−16.6663	+	28.8669i	−0.0386690	+	0.0669766i	0.846043	+	0.533114i	$0.178978\pi$
$432$	−38.4462	−	66.5908i	−0.0889959	−	0.154145i
$433$	−443.405			−1.02403			−0.512015	−	0.858976i	$-0.671101\pi$
$433$	−443.405			−1.02403			−0.512015	+	0.858976i	$0.671101\pi$
$434$	304.182	−	761.017i	0.700879	−	1.75350i
$435$		0			0
$436$	135.480	+	234.658i	0.310733	+	0.538205i
$437$	−167.956	+	290.908i	−0.384338	+	0.665694i
$438$	−222.240	−	128.310i	−0.507398	−	0.292946i
$439$	320.985	−	185.321i	0.731172	−	0.422143i	−0.0876785	−	0.996149i	$-0.527945\pi$
$439$	320.985	−	185.321i	0.731172	−	0.422143i	0.818851	+	0.574006i	$0.194611\pi$
$440$		0			0
$441$	−34.5000	+	142.894i	−0.0782313	+	0.324023i
$442$			112.788i			0.255176i
$443$	681.011	−	393.182i	1.53727	−	0.887543i	0.538273	−	0.842771i	$-0.319077\pi$
$443$	681.011	−	393.182i	1.53727	−	0.887543i	0.998997	−	0.0447724i	$-0.0142563\pi$
$444$	586.439	+	338.581i	1.32081	+	0.762569i
$445$		0			0
$446$	−897.022	+	517.896i	−2.01126	+	1.16120i
$447$	347.547			0.777509
$448$	−178.453	+	446.464i	−0.398333	+	0.996571i
$449$	−93.3439			−0.207893			−0.103946	−	0.994583i	$-0.533147\pi$
$449$	−93.3439			−0.207893			−0.103946	+	0.994583i	$0.533147\pi$
$450$		0			0
$451$	−192.606	−	111.201i	−0.427065	−	0.246566i
$452$	−57.3503	−	33.1112i	−0.126881	−	0.0732549i
$453$	−202.973	−	351.560i	−0.448065	−	0.776071i
$454$		−	234.281i		−	0.516038i
$455$		0			0
$456$	−391.257			−0.858019
$457$	−457.585	+	264.187i	−1.00128	+	0.578089i	−0.908627	−	0.417609i	$-0.862868\pi$
$457$	−457.585	+	264.187i	−1.00128	+	0.578089i	−0.0926531	+	0.995698i	$0.529535\pi$
$458$	604.227	−	1046.55i	1.31927	−	2.28505i
$459$	4.95459	−	8.58161i	0.0107943	−	0.0186963i
$460$		0			0
$461$		−	730.505i		−	1.58461i	−0.610126	−	0.792305i	$-0.708881\pi$
$461$		−	730.505i		−	1.58461i	0.610126	−	0.792305i	$-0.291119\pi$
$462$	−95.2628	+	75.0000i	−0.206197	+	0.162338i
$463$			217.908i			0.470644i	0.971917	+	0.235322i	$0.0756145\pi$
$463$			217.908i			0.470644i	−0.971917	+	0.235322i	$0.924386\pi$
$464$	−232.283	−	402.325i	−0.500609	−	0.867081i
$465$		0			0
$466$	−160.505	+	278.003i	−0.344432	+	0.596573i
$467$	100.091	+	173.363i	0.214328	+	0.371228i	0.953065	−	0.302767i	$-0.0979104\pi$
$467$	100.091	+	173.363i	0.214328	+	0.371228i	−0.738736	+	0.673995i	$0.764577\pi$
$468$	−406.297			−0.868155
$469$	517.443	−	407.381i	1.10329	−	0.868616i
$470$		0			0
$471$	36.1515	+	62.6163i	0.0767548	+	0.132943i
$472$	466.962	−	808.802i	0.989326	−	1.71356i
$473$	−150.128	−	86.6765i	−0.317396	−	0.183248i
$474$	104.477	−	60.3200i	0.220416	−	0.127257i
$475$		0			0
$476$	104.363	−	15.0635i	0.219251	−	0.0316461i
$477$			286.454i			0.600533i
$478$	−335.668	+	193.798i	−0.702234	+	0.405435i
$479$	−227.864	−	131.557i	−0.475707	−	0.274650i	0.242919	−	0.970047i	$-0.421895\pi$
$479$	−227.864	−	131.557i	−0.475707	−	0.274650i	−0.718626	+	0.695397i	$0.755229\pi$
$480$		0			0
$481$	734.923	−	424.308i	1.52791	−	0.882138i
$482$	1364.46			2.83083
$483$	225.167	+	90.0000i	0.466183	+	0.186335i
$484$	889.393			1.83759
$485$		0			0
$486$	46.5681	+	26.8861i	0.0958192	+	0.0553212i
$487$	260.297	+	150.283i	0.534491	+	0.308589i	0.742843	−	0.669465i	$-0.233477\pi$
$487$	260.297	+	150.283i	0.534491	+	0.308589i	−0.208352	+	0.978054i	$0.566810\pi$
$488$	−283.072	−	490.296i	−0.580066	−	1.00470i
$489$		−	73.9002i		−	0.151125i
$490$		0			0
$491$	268.061			0.545950			0.272975	−	0.962021i	$-0.411992\pi$
$491$	268.061			0.545950			0.272975	+	0.962021i	$0.411992\pi$
$492$	−908.985	+	524.803i	−1.84753	+	1.06667i
$493$	29.9344	−	51.8480i	0.0607189	−	0.105168i
$494$	−496.674	+	860.264i	−1.00541	+	1.74143i
$495$		0			0
$496$		−	502.259i		−	1.01262i
$497$	−59.7292	+	149.434i	−0.120180	+	0.300671i
$498$		−	5.12143i		−	0.0102840i
$499$	73.4240	+	127.174i	0.147142	+	0.254858i	0.930170	−	0.367129i	$-0.119659\pi$
$499$	73.4240	+	127.174i	0.147142	+	0.254858i	−0.783028	+	0.621987i	$0.786326\pi$
$500$		0			0
$501$	−139.924	+	242.355i	−0.279289	+	0.483743i
$502$	−195.625	−	338.833i	−0.389692	−	0.674966i
$503$	102.944			0.204660			0.102330	−	0.994751i	$-0.467370\pi$
$503$	102.944			0.204660			0.102330	+	0.994751i	$0.467370\pi$
$504$	40.3485	+	279.542i	0.0800565	+	0.554648i
$505$		0			0
$506$	100.000	+	173.205i	0.197628	+	0.342303i
$507$	−108.227	+	187.454i	−0.213465	+	0.369732i
$508$	1099.97	+	635.070i	2.16530	+	1.25014i
$509$	777.879	−	449.108i	1.52825	−	0.882335i	0.528813	−	0.848738i	$-0.322637\pi$
$509$	777.879	−	449.108i	1.52825	−	0.882335i	0.999435	−	0.0335965i	$-0.0106961\pi$
$510$		0			0
$511$	185.985	+	236.232i	0.363962	+	0.462294i
$512$			836.832i			1.63444i
$513$	75.5802	−	43.6362i	0.147330	−	0.0850609i
$514$	−563.469	−	325.319i	−1.09624	−	0.632916i
$515$		0			0
$516$	−708.514	+	409.061i	−1.37309	+	0.792754i
$517$	−194.304			−0.375830
$518$	−739.292	−	939.027i	−1.42720	−	1.81279i
$519$	241.818			0.465931
$520$		0			0
$521$	414.606	+	239.373i	0.795789	+	0.459449i	0.841997	−	0.539483i	$-0.181380\pi$
$521$	414.606	+	239.373i	0.795789	+	0.459449i	−0.0462075	+	0.998932i	$0.514714\pi$
$522$	281.353	+	162.439i	0.538991	+	0.311186i
$523$	313.991	+	543.848i	0.600365	+	1.03986i	0.992766	+	0.120068i	$0.0383113\pi$
$523$	313.991	+	543.848i	0.600365	+	1.03986i	−0.392401	+	0.919794i	$0.628355\pi$
$524$		−	407.679i		−	0.778013i
$525$		0			0
$526$	68.8490			0.130892
$527$	56.0548	−	32.3633i	0.106366	−	0.0614104i
$528$	−37.1516	+	64.3485i	−0.0703629	+	0.121872i
$529$	−64.5000	+	111.717i	−0.121928	+	0.211186i
$530$		0			0
$531$			208.318i			0.392313i
$532$	862.342	+	344.682i	1.62094	+	0.647898i
$533$			1315.36i			2.46785i
$534$	64.6515	+	111.980i	0.121070	+	0.209700i
$535$		0			0
$536$	632.668	−	1095.81i	1.18035	−	2.04443i
$537$	−65.1357	−	112.818i	−0.121296	−	0.210090i
$538$	−1332.72			−2.47717
$539$	136.252	−	40.1694i	0.252787	−	0.0745259i
$540$		0			0
$541$	−43.9801	−	76.1758i	−0.0812941	−	0.140806i	0.822512	−	0.568748i	$-0.192572\pi$
$541$	−43.9801	−	76.1758i	−0.0812941	−	0.140806i	−0.903806	+	0.427942i	$0.859239\pi$
$542$	66.9897	−	116.030i	0.123597	−	0.214077i
$543$	−63.8756	−	36.8786i	−0.117635	−	0.0679163i
$544$	−4.54592	+	2.62459i	−0.00835648	+	0.00482461i
$545$		0			0
$546$	665.855	+	266.145i	1.21952	+	0.487445i
$547$		−	1047.41i		−	1.91483i	−0.288715	−	0.957415i	$-0.593228\pi$
$547$		−	1047.41i		−	1.91483i	0.288715	−	0.957415i	$-0.406772\pi$
$548$	1870.21	−	1079.77i	3.41279	−	1.97038i
$549$	109.364	+	63.1412i	0.199205	+	0.115011i
$550$		0			0
$551$	456.637	−	263.639i	0.828742	−	0.478474i
$552$	465.904			0.844029
$553$	−139.893	+	20.1918i	−0.252971	+	0.0365133i
$554$	−1818.61			−3.28269
$555$		0			0
$556$	1543.65	+	891.227i	2.77635	+	1.60293i
$557$	606.935	+	350.414i	1.08965	+	0.629110i	0.933483	−	0.358621i	$-0.116753\pi$
$557$	606.935	+	350.414i	1.08965	+	0.629110i	0.156167	+	0.987731i	$0.450086\pi$
$558$	175.619	+	304.182i	0.314730	+	0.545128i
$559$			1025.27i			1.83411i
$560$		0			0
$561$	−9.57551			−0.0170686
$562$	−962.075	+	555.454i	−1.71188	+	0.988352i
$563$	236.023	−	408.804i	0.419224	−	0.726116i	−0.576638	−	0.817000i	$-0.695636\pi$
$563$	236.023	−	408.804i	0.419224	−	0.726116i	0.995862	+	0.0908833i	$0.0289690\pi$
$564$	−458.499	+	794.144i	−0.812942	+	1.40806i
$565$		0			0
$566$			1618.23i			2.85907i
$567$	−38.9711	−	49.5000i	−0.0687322	−	0.0873016i
$568$			309.201i			0.544368i
$569$	−91.0862	−	157.766i	−0.160081	−	0.277269i	0.774816	−	0.632186i	$-0.217842\pi$
$569$	−91.0862	−	157.766i	−0.160081	−	0.277269i	−0.934898	+	0.354917i	$0.884509\pi$
$570$		0			0
$571$	−321.212	+	556.355i	−0.562542	+	0.974352i	0.434731	+	0.900560i	$0.356843\pi$
$571$	−321.212	+	556.355i	−0.562542	+	0.974352i	−0.997274	+	0.0737918i	$0.976490\pi$
$572$	196.308	+	340.015i	0.343195	+	0.594431i
$573$	−23.7768			−0.0414953
$574$	1833.45	−	264.636i	3.19417	−	0.461039i
$575$		0			0
$576$	−103.030	−	178.453i	−0.178872	−	0.309815i
$577$	375.102	−	649.696i	0.650090	−	1.12599i	−0.333010	−	0.942923i	$-0.608064\pi$
$577$	375.102	−	649.696i	0.650090	−	1.12599i	0.983101	−	0.183066i	$-0.0586023\pi$
$578$	−852.479	−	492.179i	−1.47488	−	0.851520i
$579$	−93.2724	+	53.8509i	−0.161092	+	0.0930067i
$580$		0			0
$581$	−2.22704	+	5.57172i	−0.00383311	+	0.00958988i
$582$			432.439i			0.743023i
$583$	239.723	−	138.404i	0.411189	−	0.237400i
$584$	500.280	+	288.837i	0.856644	+	0.494583i
$585$		0			0
$586$	575.227	−	332.107i	0.981616	−	0.566736i
$587$	−975.092			−1.66114			−0.830572	−	0.556911i	$-0.811986\pi$
$587$	−975.092			−1.66114			−0.830572	+	0.556911i	$0.811986\pi$
$588$	157.336	−	651.666i	0.267579	−	1.10828i
$589$	570.061			0.967846
$590$		0			0
$591$	24.5755	+	14.1887i	0.0415829	+	0.0240079i
$592$	−634.297	−	366.212i	−1.07145	−	0.618601i
$593$	−101.177	−	175.243i	−0.170618	−	0.295519i	0.768018	−	0.640428i	$-0.221243\pi$
$593$	−101.177	−	175.243i	−0.170618	−	0.295519i	−0.938636	+	0.344909i	$0.887910\pi$
$594$		−	51.9615i		−	0.0874773i
$595$		0			0
$596$	−1584.98			−2.65936
$597$	416.138	−	240.257i	0.697048	−	0.402441i
$598$	591.433	−	1024.39i	0.989019	−	1.71303i
$599$	−392.176	+	679.269i	−0.654718	+	1.13400i	0.327247	+	0.944939i	$0.393879\pi$
$599$	−392.176	+	679.269i	−0.654718	+	1.13400i	−0.981964	+	0.189066i	$0.939454\pi$
$600$		0			0
$601$		−	252.476i		−	0.420094i	−0.977691	−	0.210047i	$-0.932638\pi$
$601$		−	252.476i		−	0.420094i	0.977691	−	0.210047i	$-0.0673617\pi$
$602$	1429.10	−	206.272i	2.37392	−	0.342645i
$603$			282.242i			0.468063i
$604$	925.656	+	1603.28i	1.53254	+	2.65444i
$605$		0			0
$606$	67.7878	−	117.412i	0.111861	−	0.193749i
$607$	−105.629	−	182.954i	−0.174017	−	0.301407i	0.765803	−	0.643075i	$-0.222342\pi$
$607$	−105.629	−	182.954i	−0.174017	−	0.301407i	−0.939821	+	0.341668i	$0.889008\pi$
$608$	−46.2307			−0.0760374
$609$	−235.454	−	299.067i	−0.386624	−	0.491079i
$610$		0			0
$611$	574.590	+	995.220i	0.940410	+	1.62884i
$612$	−22.5953	+	39.1362i	−0.0369204	+	0.0639481i
$613$	−570.824	−	329.565i	−0.931197	−	0.537627i	−0.0440072	−	0.999031i	$-0.514012\pi$
$613$	−570.824	−	329.565i	−0.931197	−	0.537627i	−0.887190	+	0.461404i	$0.847346\pi$
$614$	106.515	−	61.4966i	0.173478	−	0.100157i
$615$		0			0
$616$	214.444	−	168.831i	0.348123	−	0.274076i
$617$		−	155.757i		−	0.252443i	−0.992002	−	0.126221i	$-0.959715\pi$
$617$		−	155.757i		−	0.252443i	0.992002	−	0.126221i	$-0.0402850\pi$
$618$	−455.253	+	262.841i	−0.736656	+	0.425308i
$619$	−544.665	−	314.463i	−0.879912	−	0.508017i	−0.00928235	−	0.999957i	$-0.502955\pi$
$619$	−544.665	−	314.463i	−0.879912	−	0.508017i	−0.870629	+	0.491940i	$0.836288\pi$
$620$		0			0
$621$	−90.0000	+	51.9615i	−0.144928	+	0.0836740i
$622$	701.270			1.12744
$623$	−21.6418	−	149.939i	−0.0347380	−	0.240672i
$624$	439.454			0.704253
$625$		0			0
$626$	−177.909	−	102.716i	−0.284200	−	0.164083i
$627$	−73.0351	−	42.1668i	−0.116483	−	0.0672517i
$628$	−164.868	−	285.560i	−0.262529	−	0.454714i
$629$		−	94.3879i		−	0.150060i
$630$		0			0
$631$	−126.333			−0.200210			−0.100105	−	0.994977i	$-0.531918\pi$
$631$	−126.333			−0.200210			−0.100105	+	0.994977i	$0.531918\pi$
$632$	−235.186	+	135.785i	−0.372130	+	0.214850i
$633$	−55.0059	+	95.2730i	−0.0868971	+	0.150510i
$634$	−730.873	+	1265.91i	−1.15280	+	1.99670i
$635$		0			0
$636$		−	1306.37i		−	2.05404i
$637$	−608.667	−	579.090i	−0.955520	−	0.909090i
$638$		−	313.939i		−	0.492067i
$639$	−34.4847	−	59.7292i	−0.0539667	−	0.0934730i
$640$		0			0
$641$	−62.6561	+	108.524i	−0.0977475	+	0.169304i	−0.910752	−	0.412954i	$-0.864497\pi$
$641$	−62.6561	+	108.524i	−0.0977475	+	0.169304i	0.813004	+	0.582257i	$0.197830\pi$
$642$	539.804	+	934.968i	0.840817	+	1.45634i
$643$	−895.765			−1.39310			−0.696552	−	0.717507i	$-0.745283\pi$
$643$	−895.765			−1.39310			−0.696552	+	0.717507i	$0.745283\pi$
$644$	−1026.87	−	410.443i	−1.59451	−	0.637334i
$645$		0			0
$646$	55.2429	+	95.6834i	0.0855153	+	0.148117i
$647$	−478.404	+	828.620i	−0.739419	+	1.28071i	0.213339	+	0.976978i	$0.431566\pi$
$647$	−478.404	+	828.620i	−0.739419	+	1.28071i	−0.952757	+	0.303732i	$0.901767\pi$
$648$	−104.828	−	60.5227i	−0.161772	−	0.0933992i
$649$	174.334	−	100.652i	0.268619	−	0.155087i
$650$		0			0
$651$	−58.7878	−	407.294i	−0.0903038	−	0.625643i
$652$			337.020i			0.516902i
$653$	−1048.34	+	605.257i	−1.60541	+	0.926886i	−0.615036	+	0.788499i	$0.710858\pi$
$653$	−1048.34	+	605.257i	−1.60541	+	0.926886i	−0.990378	+	0.138387i	$0.955808\pi$
$654$	177.492	+	102.475i	0.271395	+	0.156690i
$655$		0			0
$656$	983.166	−	567.631i	1.49873	−	0.865291i
$657$	−128.854			−0.196125
$658$	1271.61	−	1001.14i	1.93254	−	1.52148i
$659$	741.485			1.12517			0.562583	−	0.826741i	$-0.309808\pi$
$659$	741.485			1.12517			0.562583	+	0.826741i	$0.309808\pi$
$660$		0			0
$661$	318.424	+	183.842i	0.481731	+	0.278127i	0.721137	−	0.692792i	$-0.243620\pi$
$661$	318.424	+	183.842i	0.481731	+	0.278127i	−0.239407	+	0.970919i	$0.576953\pi$
$662$	−1199.47	−	692.511i	−1.81188	−	1.04609i
$663$	28.3164	+	49.0454i	0.0427095	+	0.0739750i
$664$			11.5287i			0.0173626i
$665$		0			0
$666$	512.196			0.769064
$667$	−543.758	+	313.939i	−0.815229	+	0.470673i
$668$	638.120	−	1105.26i	0.955270	−	1.65458i
$669$	−260.045	+	450.411i	−0.388707	+	0.673260i
$670$		0			0
$671$		−	122.030i		−	0.181863i
$672$	4.76756	+	33.0306i	0.00709458	+	0.0491527i
$673$			200.514i			0.297941i	0.988842	+	0.148970i	$0.0475959\pi$
$673$			200.514i			0.297941i	−0.988842	+	0.148970i	$0.952404\pi$
$674$	768.085	+	1330.36i	1.13959	+	1.97383i
$675$		0			0
$676$	493.565	−	854.880i	0.730126	−	1.26462i
$677$	−542.936	−	940.393i	−0.801974	−	1.38906i	−0.918315	−	0.395850i	$-0.870450\pi$
$677$	−542.936	−	940.393i	−0.801974	−	1.38906i	0.116342	−	0.993209i	$-0.462883\pi$
$678$	−50.0899			−0.0738788
$679$	188.045	−	470.460i	0.276944	−	0.692872i
$680$		0			0
$681$	−58.8184	−	101.876i	−0.0863706	−	0.149598i
$682$	169.706	−	293.939i	0.248835	−	0.430995i
$683$	34.3344	+	19.8230i	0.0502699	+	0.0290234i	0.524924	−	0.851149i	$-0.324094\pi$
$683$	34.3344	+	19.8230i	0.0502699	+	0.0290234i	−0.474654	+	0.880172i	$0.657427\pi$
$684$	−344.682	+	199.002i	−0.503921	+	0.290939i
$685$		0			0
$686$	−684.724	+	964.913i	−0.998140	+	1.40658i
$687$		−	606.787i		−	0.883241i
$688$	766.335	−	442.444i	1.11386	−	0.643087i
$689$	−1417.80	−	818.568i	−2.05777	−	1.18805i
$690$		0			0
$691$	−38.3648	+	22.1499i	−0.0555207	+	0.0320549i	−0.527503	−	0.849553i	$-0.676872\pi$
$691$	−38.3648	+	22.1499i	−0.0555207	+	0.0320549i	0.471983	+	0.881608i	$0.343538\pi$
$692$	−1102.81			−1.59365
$693$	−22.5953	+	56.5301i	−0.0326051	+	0.0815730i
$694$	−1110.91			−1.60073
$695$		0			0
$696$	−633.347	−	365.663i	−0.909982	−	0.525378i
$697$	126.701	+	73.1510i	0.181781	+	0.104951i
$698$	77.7320	+	134.636i	0.111364	+	0.192888i
$699$			161.185i			0.230594i
$700$		0			0
$701$	409.848			0.584662			0.292331	−	0.956317i	$-0.405569\pi$
$701$	409.848			0.584662			0.292331	+	0.956317i	$0.405569\pi$
$702$	−266.145	+	153.659i	−0.379124	+	0.218887i
$703$	415.648	−	719.923i	0.591249	−	1.02407i
$704$	−99.5607	+	172.444i	−0.141421	+	0.244949i
$705$		0			0
$706$		−	2246.90i		−	3.18258i
$707$	−124.804	+	98.2577i	−0.176526	+	0.138978i
$708$		−	950.030i		−	1.34185i
$709$	−228.364	−	395.538i	−0.322093	−	0.557881i	0.658827	−	0.752295i	$-0.271053\pi$
$709$	−228.364	−	395.538i	−0.322093	−	0.557881i	−0.980920	+	0.194414i	$0.937720\pi$
$710$		0			0
$711$	30.2878	−	52.4599i	0.0425988	−	0.0737833i
$712$	−145.536	−	252.075i	−0.204404	−	0.354038i
$713$	−678.823			−0.952065
$714$	62.6663	−	49.3369i	0.0877680	−	0.0690993i
$715$		0			0
$716$	297.050	+	514.506i	0.414874	+	0.718583i
$717$	−97.3094	+	168.545i	−0.135717	+	0.235070i
$718$	20.7926	+	12.0046i	0.0289590	+	0.0167195i
$719$	58.0148	−	33.4949i	0.0806882	−	0.0465853i	−0.459113	−	0.888378i	$-0.651833\pi$
$719$	58.0148	−	33.4949i	0.0806882	−	0.0465853i	0.539801	+	0.841793i	$0.318499\pi$
$720$		0			0
$721$	609.576	−	87.9846i	0.845458	−	0.122031i
$722$		−	272.193i		−	0.376998i
$723$	593.332	−	342.560i	0.820652	−	0.473804i
$724$	291.303	+	168.184i	0.402352	+	0.232298i
$725$		0			0
$726$	582.598	−	336.363i	0.802476	−	0.463310i
$727$	−433.766			−0.596651			−0.298326	−	0.954464i	$-0.596428\pi$
$727$	−433.766			−0.596651			−0.298326	+	0.954464i	$0.596428\pi$
$728$	−1498.89	−	599.113i	−2.05892	−	0.822957i
$729$	27.0000			0.0370370
$730$		0			0
$731$	98.7582	+	57.0181i	0.135100	+	0.0780001i
$732$	−498.751	−	287.954i	−0.681354	−	0.393380i
$733$	148.344	+	256.939i	0.202379	+	0.350531i	0.949295	−	0.314388i	$-0.101799\pi$
$733$	148.344	+	256.939i	0.202379	+	0.350531i	−0.746915	+	0.664919i	$0.768466\pi$
$734$		−	1756.44i		−	2.39297i
$735$		0			0
$736$	55.0510			0.0747976
$737$	236.198	−	136.369i	0.320486	−	0.185032i
$738$	−396.954	+	687.545i	−0.537878	+	0.931633i
$739$	569.080	−	985.676i	0.770068	−	1.33380i	−0.167457	−	0.985879i	$-0.553556\pi$
$739$	569.080	−	985.676i	0.770068	−	1.33380i	0.937525	−	0.347917i	$-0.113111\pi$
$740$		0			0
$741$			498.778i			0.673114i
$742$	−855.737	+	2140.93i	−1.15328	+	2.88535i
$743$			331.637i			0.446348i	0.974779	+	0.223174i	$0.0716418\pi$
$743$			331.637i			0.446348i	−0.974779	+	0.223174i	$0.928358\pi$
$744$	−395.333	−	684.736i	−0.531361	−	0.920344i
$745$		0			0
$746$	−307.386	+	532.409i	−0.412046	+	0.713685i
$747$	−1.28578	−	2.22704i	−0.00172126	−	0.00298131i
$748$	43.6689			0.0583809
$749$	−180.697	−	1251.91i	−0.241251	−	1.67144i
$750$		0			0
$751$	481.923	+	834.716i	0.641709	+	1.11147i	0.985051	+	0.172262i	$0.0551076\pi$
$751$	481.923	+	834.716i	0.641709	+	1.11147i	−0.343342	+	0.939210i	$0.611559\pi$
$752$	495.917	−	858.954i	0.659464	−	1.14223i
$753$	−170.134	−	98.2270i	−0.225942	−	0.130448i
$754$	−1607.98	+	928.370i	−2.13260	+	1.23126i
$755$		0			0
$756$	177.727	+	225.744i	0.235089	+	0.298603i
$757$			400.242i			0.528721i	0.964424	+	0.264361i	$0.0851609\pi$
$757$			400.242i			0.528721i	−0.964424	+	0.264361i	$0.914839\pi$
$758$	−644.965	+	372.371i	−0.850877	+	0.491254i
$759$	86.9694	+	50.2118i	0.114584	+	0.0661552i
$760$		0			0
$761$	224.925	−	129.861i	0.295565	−	0.170645i	−0.344884	−	0.938645i	$-0.612082\pi$
$761$	224.925	−	129.861i	0.295565	−	0.170645i	0.640449	+	0.768001i	$0.278748\pi$
$762$	960.718			1.26079
$763$	−148.537	−	188.667i	−0.194674	−	0.247270i
$764$	108.434			0.141929
$765$		0			0
$766$	−505.924	−	292.095i	−0.660475	−	0.381326i
$767$	−1031.07	−	595.287i	−1.34429	−	0.776124i
$768$	436.975	+	756.863i	0.568978	+	0.985499i
$769$			119.179i			0.154980i	0.996993	+	0.0774898i	$0.0246905\pi$
$769$			119.179i			0.154980i	−0.996993	+	0.0774898i	$0.975309\pi$
$770$		0			0
$771$	−326.697			−0.423731
$772$	425.367	−	245.586i	0.550993	−	0.318116i
$773$	209.140	−	362.241i	0.270556	−	0.468617i	−0.698448	−	0.715661i	$-0.746126\pi$
$773$	209.140	−	362.241i	0.270556	−	0.468617i	0.969004	+	0.247044i	$0.0794591\pi$
$774$	−309.409	+	535.912i	−0.399753	+	0.692392i
$775$		0			0
$776$		−	973.454i		−	1.25445i
$777$	−557.230	−	222.727i	−0.717156	−	0.286650i
$778$			182.615i			0.234724i
$779$	644.258	+	1115.89i	0.827032	+	1.43246i
$780$		0			0
$781$	−33.3235	+	57.7179i	−0.0426677	+	0.0739026i
$782$	−65.7826	−	113.939i	−0.0841209	−	0.145702i
$783$	163.127			0.208336
$784$	−170.177	+	704.847i	−0.217062	+	0.899040i
$785$		0			0
$786$	−154.182	−	267.050i	−0.196160	−	0.339759i
$787$	79.8149	−	138.243i	0.101417	−	0.175659i	−0.810852	−	0.585251i	$-0.800996\pi$
$787$	79.8149	−	138.243i	0.101417	−	0.175659i	0.912269	+	0.409593i	$0.134329\pi$
$788$	−112.076	−	64.7071i	−0.142229	−	0.0821157i
$789$	29.9388	−	17.2852i	0.0379452	−	0.0219077i
$790$		0			0
$791$	54.4939	+	21.7814i	0.0688924	+	0.0275366i
$792$			116.969i			0.147689i
$793$	−625.034	+	360.863i	−0.788189	+	0.455061i
$794$	1185.79	+	684.614i	1.49343	+	0.862235i
$795$		0			0
$796$	−1897.79	+	1095.69i	−2.38415	+	1.37649i
$797$	−610.067			−0.765454			−0.382727	−	0.923861i	$-0.625015\pi$
$797$	−610.067			−0.765454			−0.382727	+	0.923861i	$0.625015\pi$
$798$	695.235	−	100.348i	0.871221	−	0.125750i
$799$	127.818			0.159973
$800$		0			0
$801$	56.2270	+	32.4627i	0.0701961	+	0.0405277i
$802$	1239.14	+	715.419i	1.54506	+	0.892043i
$803$	62.2575	+	107.833i	0.0775311	+	0.134288i
$804$		−	1287.16i		−	1.60094i
$805$		0			0
$806$	−2007.39			−2.49056
$807$	−579.527	+	334.590i	−0.718126	+	0.414610i
$808$	−152.595	+	264.303i	−0.188856	+	0.327108i
$809$	35.2531	−	61.0601i	0.0435761	−	0.0754760i	−0.843415	−	0.537263i	$-0.819458\pi$
$809$	35.2531	−	61.0601i	0.0435761	−	0.0754760i	0.886991	+	0.461787i	$0.152792\pi$
$810$		0			0
$811$		−	656.361i		−	0.809323i	−0.914467	−	0.404661i	$-0.867389\pi$
$811$		−	656.361i		−	0.809323i	0.914467	−	0.404661i	$-0.132611\pi$
$812$	1073.78	+	1363.89i	1.32239	+	1.67966i
$813$		−	67.2735i		−	0.0827472i
$814$	−247.474	−	428.638i	−0.304023	−	0.526583i
$815$		0			0
$816$	24.4393	−	42.3301i	0.0299501	−	0.0518751i
$817$	502.171	+	869.786i	0.614652	+	1.06461i
$818$	1755.17			2.14568
$819$	356.363	−	51.4366i	0.435120	−	0.0628042i
$820$		0			0
$821$	466.984	+	808.840i	0.568799	+	0.985189i	0.996685	+	0.0813564i	$0.0259252\pi$
$821$	466.984	+	808.840i	0.568799	+	0.985189i	−0.427886	+	0.903833i	$0.640741\pi$
$822$	816.722	−	1414.60i	0.993579	−	1.72093i
$823$	159.375	+	92.0153i	0.193652	+	0.111805i	0.593691	−	0.804693i	$-0.297670\pi$
$823$	159.375	+	92.0153i	0.193652	+	0.111805i	−0.400039	+	0.916498i	$0.631004\pi$
$824$	1024.81	−	591.674i	1.24370	−	0.718051i
$825$		0			0
$826$	−622.318	+	1556.95i	−0.753411	+	1.88492i
$827$		−	819.778i		−	0.991267i	−0.868532	−	0.495633i	$-0.834936\pi$
$827$		−	819.778i		−	0.991267i	0.868532	−	0.495633i	$-0.165064\pi$
$828$	410.443	−	236.969i	0.495704	−	0.286195i
$829$	−289.364	−	167.064i	−0.349052	−	0.201525i	0.315216	−	0.949020i	$-0.397923\pi$
$829$	−289.364	−	167.064i	−0.349052	−	0.201525i	−0.664267	+	0.747495i	$0.731256\pi$
$830$		0			0
$831$	−790.817	+	456.578i	−0.951645	+	0.549432i
$832$	1177.67			1.41547
$833$	−89.6301	+	26.4245i	−0.107599	+	0.0317221i
$834$	1348.23			1.61658
$835$		0			0
$836$	333.075	+	192.301i	0.398415	+	0.230025i
$837$	152.735	+	88.1816i	0.182479	+	0.105354i
$838$	405.221	+	701.864i	0.483558	+	0.837546i
$839$			1185.81i			1.41336i	0.707534	+	0.706679i	$0.249808\pi$
$839$			1185.81i			1.41336i	−0.707534	+	0.706679i	$0.750192\pi$
$840$		0			0
$841$	144.576			0.171909
$842$	1606.95	−	927.774i	1.90849	−	1.10187i
$843$	−278.903	+	483.075i	−0.330846	+	0.573043i
$844$	250.853	−	434.490i	0.297219	−	0.514799i
$845$		0			0
$846$			693.607i			0.819866i
$847$	−780.087	+	112.596i	−0.921000	+	0.132935i
$848$			1412.98i			1.66625i
$849$	406.272	+	703.684i	0.478530	+	0.828838i
$850$		0			0
$851$	−494.949	+	857.277i	−0.581609	+	1.00738i
$852$	157.267	+	272.394i	0.184585	+	0.319711i
$853$	−1094.34			−1.28293			−0.641466	−	0.767151i	$-0.721674\pi$
$853$	−1094.34			−1.28293			−0.641466	+	0.767151i	$0.721674\pi$
$854$	628.749	+	798.618i	0.736240	+	0.935150i
$855$		0			0
$856$	−1215.14	−	2104.69i	−1.41956	−	2.45874i
$857$	−413.925	+	716.939i	−0.482993	+	0.836568i	−0.999809	−	0.0195282i	$-0.993784\pi$
$857$	−413.925	+	716.939i	−0.482993	+	0.836568i	0.516817	+	0.856096i	$0.327117\pi$
$858$	257.183	+	148.485i	0.299747	+	0.173059i
$859$	344.969	−	199.168i	0.401594	−	0.231860i	−0.285577	−	0.958356i	$-0.592185\pi$
$859$	344.969	−	199.168i	0.401594	−	0.231860i	0.687172	+	0.726495i	$0.258852\pi$
$860$		0			0
$861$	730.832	−	575.381i	0.848818	−	0.668271i
$862$		−	114.981i		−	0.133388i
$863$	493.520	−	284.934i	0.571866	−	0.330167i	−0.186028	−	0.982544i	$-0.559562\pi$
$863$	493.520	−	284.934i	0.571866	−	0.330167i	0.757894	+	0.652377i	$0.226228\pi$
$864$	−12.3865	−	7.15134i	−0.0143362	−	0.00827701i
$865$		0			0
$866$	1324.60	−	764.761i	1.52957	−	0.883095i
$867$	−494.264			−0.570085
$868$	268.100	+	1857.45i	0.308871	+	2.13992i
$869$	−58.5357			−0.0673599
$870$		0			0
$871$	−1396.95	−	806.531i	−1.60385	−	0.925983i
$872$	−399.548	−	230.679i	−0.458198	−	0.264541i
$873$	108.568	+	188.045i	0.124362	+	0.215401i
$874$		−	1158.72i		−	1.32577i
$875$		0			0
$876$	587.636			0.670817
$877$	414.276	−	239.182i	0.472378	−	0.272728i	−0.244857	−	0.969559i	$-0.578741\pi$
$877$	414.276	−	239.182i	0.472378	−	0.272728i	0.717235	+	0.696832i	$0.245408\pi$
$878$	−639.262	+	1107.23i	−0.728088	+	1.26109i
$879$	166.757	−	288.832i	0.189712	−	0.328591i
$880$		0			0
$881$			371.532i			0.421716i	0.977517	+	0.210858i	$0.0676258\pi$
$881$			371.532i			0.421716i	−0.977517	+	0.210858i	$0.932374\pi$
$882$	−143.393	−	486.378i	−0.162577	−	0.551449i
$883$			626.748i			0.709794i	0.934905	+	0.354897i	$0.115484\pi$
$883$			626.748i			0.709794i	−0.934905	+	0.354897i	$0.884516\pi$
$884$	−129.136	−	223.670i	−0.146082	−	0.253021i
$885$		0			0
$886$	−1356.28	+	2349.14i	−1.53079	+	2.65140i
$887$	333.621	+	577.849i	0.376123	+	0.651464i	0.990494	−	0.137553i	$-0.0439236\pi$
$887$	333.621	+	577.849i	0.376123	+	0.651464i	−0.614371	+	0.789017i	$0.710590\pi$
$888$	−1152.99			−1.29842
$889$	−1045.19	−	417.765i	−1.17569	−	0.469927i
$890$		0			0
$891$	−13.0454	−	22.5953i	−0.0146413	−	0.0253595i
$892$	1185.93	−	2054.09i	1.32952	−	2.30279i
$893$	974.907	+	562.863i	1.09172	+	0.630305i
$894$	−1038.24	+	599.429i	−1.16134	+	0.670502i
$895$		0			0
$896$	−225.924	−	1565.25i	−0.252147	−	1.74693i
$897$		−	593.939i		−	0.662139i
$898$	278.850	−	160.994i	0.310524	−	0.179281i
$899$	922.788	+	532.772i	1.02646	+	0.592627i
$900$		0			0
$901$	−157.696	+	91.0458i	−0.175023	+	0.101050i
$902$	767.175			0.850526
$903$	569.652	−	448.485i	0.630844	−	0.496661i
$904$	112.756			0.124730
$905$		0			0
$906$	1212.70	+	700.155i	1.33852	+	0.772798i
$907$	476.207	+	274.938i	0.525035	+	0.303129i	0.738992	−	0.673714i	$-0.235302\pi$
$907$	476.207	+	274.938i	0.525035	+	0.303129i	−0.213957	+	0.976843i	$0.568635\pi$
$908$	268.240	+	464.605i	0.295418	+	0.511680i
$909$		−	68.0749i		−	0.0748899i
$910$		0			0
$911$	443.573			0.486908			0.243454	−	0.969912i	$-0.421719\pi$
$911$	443.573			0.486908			0.243454	+	0.969912i	$0.421719\pi$
$912$	372.811	−	215.242i	0.408784	−	0.236011i
$913$	−1.24248	+	2.15205i	−0.00136088	+	0.00235712i
$914$	911.309	−	1578.43i	0.997056	−	1.72695i
$915$		0			0
$916$			2767.24i			3.02100i
$917$	51.6116	+	357.576i	0.0562831	+	0.389941i
$918$			34.1816i			0.0372349i
$919$	−435.838	−	754.893i	−0.474252	−	0.821429i	0.525313	−	0.850909i	$-0.323948\pi$
$919$	−435.838	−	754.893i	−0.474252	−	0.821429i	−0.999565	+	0.0294801i	$0.990615\pi$
$920$		0			0
$921$	30.8786	−	53.4833i	0.0335272	−	0.0580708i
$922$	1259.93	+	2182.27i	1.36652	+	2.36689i
$923$	394.172			0.427056
$924$	103.045	−	257.804i	0.111521	−	0.279009i
$925$		0			0
$926$	−375.836	−	650.967i	−0.405870	−	0.702988i
$927$	−131.977	+	228.591i	−0.142370	+	0.246592i
$928$	−74.8361	−	43.2066i	−0.0806423	−	0.0465589i
$929$	1091.01	−	629.896i	1.17439	−	0.678037i	0.219684	−	0.975571i	$-0.429498\pi$
$929$	1091.01	−	629.896i	1.17439	−	0.678037i	0.954711	+	0.297534i	$0.0961642\pi$
$930$		0			0
$931$	−799.997	−	193.149i	−0.859288	−	0.207464i
$932$		−	735.081i		−	0.788713i
$933$	304.945	−	176.060i	0.326844	−	0.188703i
$934$	−598.015	−	345.264i	−0.640273	−	0.369662i
$935$		0			0
$936$	599.113	−	345.898i	0.640078	−	0.369549i
$937$	267.856			0.285866			0.142933	−	0.989732i	$-0.454347\pi$
$937$	267.856			0.285866			0.142933	+	0.989732i	$0.454347\pi$
$938$	−843.154	+	2109.45i	−0.898885	+	2.24888i
$939$	−103.151			−0.109852
$940$		0			0
$941$	−257.908	−	148.903i	−0.274079	−	0.158239i	0.356661	−	0.934234i	$-0.383915\pi$
$941$	−257.908	−	148.903i	−0.274079	−	0.158239i	−0.630740	+	0.775994i	$0.717248\pi$
$942$	−215.994	−	124.704i	−0.229293	−	0.132383i
$943$	−767.175	−	1328.79i	−0.813547	−	1.40910i
$944$			1027.56i			1.08852i
$945$		0			0
$946$	597.980			0.632114
$947$	1524.52	−	880.181i	1.60984	−	0.929441i	0.620434	−	0.784259i	$-0.286956\pi$
$947$	1524.52	−	880.181i	1.60984	−	0.929441i	0.989405	−	0.145182i	$-0.0463769\pi$
$948$	−138.127	+	239.242i	−0.145703	+	0.252365i
$949$	368.212	−	637.761i	0.388000	−	0.672035i
$950$		0			0
$951$			733.969i			0.771786i
$952$	−141.067	+	111.061i	−0.148179	+	0.116661i
$953$			380.032i			0.398774i	0.979921	+	0.199387i	$0.0638951\pi$
$953$			380.032i			0.398774i	−0.979921	+	0.199387i	$0.936105\pi$
$954$	−494.060	−	855.737i	−0.517883	−	0.896999i
$955$		0			0
$956$	443.778	−	768.645i	0.464202	−	0.804022i
$957$	−78.8171	−	136.515i	−0.0823586	−	0.142649i
$958$	907.611			0.947401
$959$	−1503.67	+	1183.83i	−1.56795	+	1.23444i
$960$		0			0
$961$	95.5000	+	165.411i	0.0993757	+	0.172124i
$962$	−1463.65	+	2535.11i	−1.52146	+	2.63525i
$963$	469.464	+	271.045i	0.487502	+	0.281459i
$964$	−2705.88	+	1562.24i	−2.80693	+	1.62058i
$965$		0			0
$966$	−827.878	+	119.494i	−0.857016	+	0.123700i
$967$			597.302i			0.617686i	0.951113	+	0.308843i	$0.0999417\pi$
$967$			597.302i			0.617686i	−0.951113	+	0.308843i	$0.900058\pi$
$968$	−1311.47	+	757.179i	−1.35483	+	0.782210i
$969$	48.0444	+	27.7384i	0.0495814	+	0.0286258i
$970$		0			0
$971$	1209.38	−	698.235i	1.24550	−	0.719088i	0.275289	−	0.961361i	$-0.411226\pi$
$971$	1209.38	−	698.235i	1.24550	−	0.719088i	0.970208	+	0.242273i	$0.0778930\pi$
$972$	−123.133			−0.126680
$973$	−1466.77	−	586.272i	−1.50747	−	0.602541i
$974$	−1036.80			−1.06447
$975$		0			0
$976$	539.454	+	311.454i	0.552719	+	0.319112i
$977$	1533.83	+	885.560i	1.56994	+	0.906407i	0.996174	+	0.0873898i	$0.0278526\pi$
$977$	1533.83	+	885.560i	1.56994	+	0.906407i	0.573769	+	0.819017i	$0.305481\pi$
$978$	127.459	+	220.766i	0.130326	+	0.225732i
$979$		−	62.7391i		−	0.0640849i
$980$		0			0
$981$	102.909			0.104902
$982$	−800.792	+	462.337i	−0.815470	+	0.470812i
$983$	−562.575	+	974.408i	−0.572304	+	0.991259i	0.424025	+	0.905650i	$0.360617\pi$
$983$	−562.575	+	974.408i	−0.572304	+	0.991259i	−0.996329	+	0.0856086i	$0.972717\pi$
$984$	893.574	−	1547.72i	0.908104	−	1.57288i
$985$		0			0
$986$			206.517i			0.209449i
$987$	301.613	−	754.590i	0.305585	−	0.764529i
$988$		−	2274.66i		−	2.30229i
$989$	−597.980	−	1035.73i	−0.604631	−	1.04725i
$990$		0			0
$991$	248.292	−	430.054i	0.250547	−	0.433960i	−0.713130	−	0.701032i	$-0.752723\pi$
$991$	248.292	−	430.054i	0.250547	−	0.433960i	0.963676	+	0.267072i	$0.0860563\pi$
$992$	−46.7123	−	80.9082i	−0.0470891	−	0.0815606i
$993$	−695.445			−0.700347
$994$	−79.3031	−	549.428i	−0.0797818	−	0.552744i
$995$		0			0
$996$	5.86378	+	10.1564i	0.00588733	+	0.0101971i
$997$	−248.418	+	430.272i	−0.249165	+	0.431567i	−0.963294	−	0.268447i	$-0.913490\pi$
$997$	−248.418	+	430.272i	−0.249165	+	0.431567i	0.714129	+	0.700014i	$0.246823\pi$
$998$	−438.686	−	253.275i	−0.439565	−	0.253783i
$999$	222.727	−	128.592i	0.222950	−	0.128720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.s.g.199.1		8
5.2	odd	4		525.3.o.j.451.1	yes	4
5.3	odd	4		525.3.o.k.451.2	yes	4
5.4	even	2	inner	525.3.s.g.199.4		8
7.5	odd	6	inner	525.3.s.g.124.4		8
35.12	even	12		525.3.o.j.376.1	✓	4
35.19	odd	6	inner	525.3.s.g.124.1		8
35.33	even	12		525.3.o.k.376.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.3.o.j.376.1	✓	4	35.12	even	12
525.3.o.j.451.1	yes	4	5.2	odd	4
525.3.o.k.376.2	yes	4	35.33	even	12
525.3.o.k.451.2	yes	4	5.3	odd	4
525.3.s.g.124.1		8	35.19	odd	6	inner
525.3.s.g.124.4		8	7.5	odd	6	inner
525.3.s.g.199.1		8	1.1	even	1	trivial
525.3.s.g.199.4		8	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.98735 + 1.72474i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(3.94949 - 6.84072i) q^{4} -5.97469i q^{6} +(-2.59808 + 6.50000i) q^{7} +13.4495i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-2.98735 + 1.72474i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(3.94949 - 6.84072i) q^{4} -5.97469i q^{6} +(-2.59808 + 6.50000i) q^{7} +13.4495i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.44949 + 2.51059i) q^{11} +(6.84072 + 11.8485i) q^{12} +17.1455 q^{13} +(-3.44949 - 23.8988i) q^{14} +(-7.39898 - 12.8154i) q^{16} +(0.953512 - 1.65153i) q^{17} +(8.96204 + 5.17423i) q^{18} +(14.5454 - 8.39780i) q^{19} +(-7.50000 - 9.52628i) q^{21} -10.0000i q^{22} +(-17.3205 + 10.0000i) q^{23} +(-20.1742 - 11.6476i) q^{24} +(-51.2196 + 29.5717i) q^{26} +5.19615 q^{27} +(34.2036 + 43.4444i) q^{28} +31.3939 q^{29} +(29.3939 + 16.9706i) q^{31} +(-2.38378 - 1.37628i) q^{32} +(-2.51059 - 4.34847i) q^{33} +6.57826i q^{34} -23.6969 q^{36} +(42.8638 - 24.7474i) q^{37} +(-28.9681 + 50.1742i) q^{38} +(-14.8485 + 25.7183i) q^{39} +76.7175i q^{41} +(38.8355 + 15.5227i) q^{42} +59.7980i q^{43} +(11.4495 + 19.8311i) q^{44} +(34.4949 - 59.7469i) q^{46} +(33.5125 + 58.0454i) q^{47} +25.6308 q^{48} +(-35.5000 - 33.7750i) q^{49} +(1.65153 + 2.86054i) q^{51} +(67.7161 - 117.288i) q^{52} +(-82.6922 - 47.7423i) q^{53} +(-15.5227 + 8.96204i) q^{54} +(-87.4217 - 34.9428i) q^{56} +29.0908i q^{57} +(-93.7844 + 54.1464i) q^{58} +(-60.1362 - 34.7197i) q^{59} +(-36.4546 + 21.0471i) q^{61} -117.080 q^{62} +(20.7846 - 3.00000i) q^{63} +68.6867 q^{64} +(15.0000 + 8.66025i) q^{66} +(-81.4762 - 47.0403i) q^{67} +(-7.53177 - 13.0454i) q^{68} -34.6410i q^{69} +22.9898 q^{71} +(34.9428 - 20.1742i) q^{72} +(21.4757 - 37.1969i) q^{73} +(-85.3661 + 147.858i) q^{74} -132.668i q^{76} +(-12.5529 - 15.9444i) q^{77} -102.439i q^{78} +(10.0959 + 17.4866i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-132.318 - 229.182i) q^{82} +0.857187 q^{83} +(-94.7878 + 13.6814i) q^{84} +(-103.136 - 178.637i) q^{86} +(-27.1879 + 47.0908i) q^{87} +(-33.7662 - 19.4949i) q^{88} +(-18.7423 + 10.8209i) q^{89} +(-44.5454 + 111.446i) q^{91} +157.980i q^{92} +(-50.9117 + 29.3939i) q^{93} +(-200.227 - 115.601i) q^{94} +(4.12883 - 2.38378i) q^{96} -72.3785 q^{97} +(164.304 + 39.6691i) q^{98} +8.69694 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4} - 12 q^{9}+O(q^{10}) \) 8 * q + 12 * q^4 - 12 * q^9	\( 8 q + 12 q^{4} - 12 q^{9} + 8 q^{11} - 8 q^{14} - 20 q^{16} - 60 q^{19} - 60 q^{21} - 132 q^{24} - 204 q^{26} + 16 q^{29} - 72 q^{36} - 60 q^{39} + 72 q^{44} + 80 q^{46} - 284 q^{49} + 72 q^{51} - 36 q^{54} - 572 q^{56} + 48 q^{59} - 468 q^{61} + 40 q^{64} + 120 q^{66} - 208 q^{71} - 340 q^{74} - 76 q^{79} - 36 q^{81} - 288 q^{84} - 296 q^{86} + 144 q^{89} - 180 q^{91} - 720 q^{94} + 180 q^{96} - 48 q^{99}+O(q^{100}) \) 8 * q + 12 * q^4 - 12 * q^9 + 8 * q^11 - 8 * q^14 - 20 * q^16 - 60 * q^19 - 60 * q^21 - 132 * q^24 - 204 * q^26 + 16 * q^29 - 72 * q^36 - 60 * q^39 + 72 * q^44 + 80 * q^46 - 284 * q^49 + 72 * q^51 - 36 * q^54 - 572 * q^56 + 48 * q^59 - 468 * q^61 + 40 * q^64 + 120 * q^66 - 208 * q^71 - 340 * q^74 - 76 * q^79 - 36 * q^81 - 288 * q^84 - 296 * q^86 + 144 * q^89 - 180 * q^91 - 720 * q^94 + 180 * q^96 - 48 * q^99

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