LMFDB - Embedded newform 525.3.o.k.376.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(376,525)]

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, 0, 5]))

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

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

chi := DirichletCharacter("525.376");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.o (of order $6$, 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	525.376
Dual form			525.3.o.k.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72474 - 2.98735i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-3.94949 - 6.84072i) q^{4} +5.97469i q^{6} +(6.50000 - 2.59808i) q^{7} -13.4495 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.44949 - 2.51059i) q^{11} +(11.8485 + 6.84072i) q^{12} -17.1455i q^{13} +(3.44949 - 23.8988i) q^{14} +(-7.39898 + 12.8154i) q^{16} +(-1.65153 + 0.953512i) q^{17} +(-5.17423 - 8.96204i) q^{18} +(-14.5454 - 8.39780i) q^{19} +(-7.50000 + 9.52628i) q^{21} -10.0000 q^{22} +(-10.0000 + 17.3205i) q^{23} +(20.1742 - 11.6476i) q^{24} +(-51.2196 - 29.5717i) q^{26} +5.19615i q^{27} +(-43.4444 - 34.2036i) q^{28} -31.3939 q^{29} +(29.3939 - 16.9706i) q^{31} +(-1.37628 - 2.38378i) q^{32} +(4.34847 + 2.51059i) q^{33} +6.57826i q^{34} -23.6969 q^{36} +(-24.7474 + 42.8638i) q^{37} +(-50.1742 + 28.9681i) q^{38} +(14.8485 + 25.7183i) q^{39} -76.7175i q^{41} +(15.5227 + 38.8355i) q^{42} -59.7980 q^{43} +(-11.4495 + 19.8311i) q^{44} +(34.4949 + 59.7469i) q^{46} +(58.0454 + 33.5125i) q^{47} -25.6308i q^{48} +(35.5000 - 33.7750i) q^{49} +(1.65153 - 2.86054i) q^{51} +(-117.288 + 67.7161i) q^{52} +(47.7423 + 82.6922i) q^{53} +(15.5227 + 8.96204i) q^{54} +(-87.4217 + 34.9428i) q^{56} +29.0908 q^{57} +(-54.1464 + 93.7844i) q^{58} +(60.1362 - 34.7197i) q^{59} +(-36.4546 - 21.0471i) q^{61} -117.080i q^{62} +(3.00000 - 20.7846i) q^{63} -68.6867 q^{64} +(15.0000 - 8.66025i) q^{66} +(-47.0403 - 81.4762i) q^{67} +(13.0454 + 7.53177i) q^{68} -34.6410i q^{69} +22.9898 q^{71} +(-20.1742 + 34.9428i) q^{72} +(37.1969 - 21.4757i) q^{73} +(85.3661 + 147.858i) q^{74} +132.668i q^{76} +(-15.9444 - 12.5529i) q^{77} +102.439 q^{78} +(-10.0959 + 17.4866i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-229.182 - 132.318i) q^{82} -0.857187i q^{83} +(94.7878 + 13.6814i) q^{84} +(-103.136 + 178.637i) q^{86} +(47.0908 - 27.1879i) q^{87} +(19.4949 + 33.7662i) q^{88} +(18.7423 + 10.8209i) q^{89} +(-44.5454 - 111.446i) q^{91} +157.980 q^{92} +(-29.3939 + 50.9117i) q^{93} +(200.227 - 115.601i) q^{94} +(4.12883 + 2.38378i) q^{96} -72.3785i q^{97} +(-39.6691 - 164.304i) q^{98} -8.69694 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 26 q^{7} - 44 q^{8} + 6 q^{9} + 4 q^{11} + 18 q^{12} + 4 q^{14} - 10 q^{16} - 36 q^{17} - 6 q^{18} + 30 q^{19} - 30 q^{21} - 40 q^{22} - 40 q^{23} + 66 q^{24} - 102 q^{26}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 26 * q^7 - 44 * q^8 + 6 * q^9 + 4 * q^11 + 18 * q^12 + 4 * q^14 - 10 * q^16 - 36 * q^17 - 6 * q^18 + 30 * q^19 - 30 * q^21 - 40 * q^22 - 40 * q^23 + 66 * q^24 - 102 * q^26 - 66 * q^28 - 8 * q^29 - 30 * q^32 - 12 * q^33 - 36 * q^36 - 50 * q^37 - 186 * q^38 + 30 * q^39 + 18 * q^42 - 200 * q^43 - 36 * q^44 + 40 * q^46 + 144 * q^47 + 142 * q^49 + 36 * q^51 - 234 * q^52 + 44 * q^53 + 18 * q^54 - 286 * q^56 - 60 * q^57 - 148 * q^58 - 24 * q^59 - 234 * q^61 + 12 * q^63 - 20 * q^64 + 60 * q^66 - 2 * q^67 - 36 * q^68 - 104 * q^71 - 66 * q^72 + 90 * q^73 + 170 * q^74 + 44 * q^77 + 204 * q^78 + 38 * q^79 - 18 * q^81 - 564 * q^82 + 144 * q^84 - 148 * q^86 + 12 * q^87 - 20 * q^88 - 72 * q^89 - 90 * q^91 + 240 * q^92 + 360 * q^94 + 90 * q^96 - 46 * q^98 + 24 * q^99

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.72474	−	2.98735i	0.862372	−	1.49367i	−0.00726029	−	0.999974i	$-0.502311\pi$
$2$	1.72474	−	2.98735i	0.862372	−	1.49367i	0.869633	−	0.493699i	$-0.164356\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	−3.94949	−	6.84072i	−0.987372	−	1.71018i
$5$		0			0
$5$		0			0
$6$			5.97469i			0.995782i
$7$	6.50000	−	2.59808i	0.928571	−	0.371154i
$7$	6.50000	−	2.59808i	0.928571	−	0.371154i
$8$	−13.4495			−1.68119
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.44949	−	2.51059i	−0.131772	−	0.228235i	0.792588	−	0.609758i	$-0.208733\pi$
$11$	−1.44949	−	2.51059i	−0.131772	−	0.228235i	−0.924360	+	0.381522i	$0.875400\pi$
$12$	11.8485	+	6.84072i	0.987372	+	0.570060i
$13$		−	17.1455i		−	1.31889i	−0.751754	−	0.659444i	$-0.770792\pi$
$13$		−	17.1455i		−	1.31889i	0.751754	−	0.659444i	$-0.229208\pi$
$14$	3.44949	−	23.8988i	0.246392	−	1.70705i
$15$		0			0
$16$	−7.39898	+	12.8154i	−0.462436	+	0.800963i
$17$	−1.65153	+	0.953512i	−0.0971489	+	0.0560889i	−0.547787	−	0.836618i	$-0.684530\pi$
$17$	−1.65153	+	0.953512i	−0.0971489	+	0.0560889i	0.450638	+	0.892707i	$0.351196\pi$
$18$	−5.17423	−	8.96204i	−0.287457	−	0.497891i
$19$	−14.5454	−	8.39780i	−0.765548	−	0.441989i	0.0657363	−	0.997837i	$-0.479060\pi$
$19$	−14.5454	−	8.39780i	−0.765548	−	0.441989i	−0.831284	+	0.555848i	$0.812394\pi$
$20$		0			0
$21$	−7.50000	+	9.52628i	−0.357143	+	0.453632i
$22$	−10.0000			−0.454545
$23$	−10.0000	+	17.3205i	−0.434783	+	0.753066i	−0.997278	−	0.0737349i	$-0.976508\pi$
$23$	−10.0000	+	17.3205i	−0.434783	+	0.753066i	0.562495	+	0.826801i	$0.309841\pi$
$24$	20.1742	−	11.6476i	0.840593	−	0.485317i
$25$		0			0
$26$	−51.2196	−	29.5717i	−1.96999	−	1.13737i
$27$			5.19615i			0.192450i
$28$	−43.4444	−	34.2036i	−1.55159	−	1.22156i
$29$	−31.3939			−1.08255			−0.541274	−	0.840846i	$-0.682058\pi$
$29$	−31.3939			−1.08255			−0.541274	+	0.840846i	$0.682058\pi$
$30$		0			0
$31$	29.3939	−	16.9706i	0.948190	−	0.547438i	0.0556715	−	0.998449i	$-0.482270\pi$
$31$	29.3939	−	16.9706i	0.948190	−	0.547438i	0.892518	+	0.451012i	$0.148937\pi$
$32$	−1.37628	−	2.38378i	−0.0430086	−	0.0744931i
$33$	4.34847	+	2.51059i	0.131772	+	0.0760785i
$34$			6.57826i			0.193478i
$35$		0			0
$36$	−23.6969			−0.658248
$37$	−24.7474	+	42.8638i	−0.668850	+	1.15848i	0.309376	+	0.950940i	$0.399880\pi$
$37$	−24.7474	+	42.8638i	−0.668850	+	1.15848i	−0.978226	+	0.207542i	$0.933454\pi$
$38$	−50.1742	+	28.9681i	−1.32037	+	0.762319i
$39$	14.8485	+	25.7183i	0.380730	+	0.659444i
$40$		0			0
$41$		−	76.7175i		−	1.87116i	−0.353117	−	0.935579i	$-0.614878\pi$
$41$		−	76.7175i		−	1.87116i	0.353117	−	0.935579i	$-0.385122\pi$
$42$	15.5227	+	38.8355i	0.369588	+	0.924655i
$43$	−59.7980			−1.39065			−0.695325	−	0.718695i	$-0.744740\pi$
$43$	−59.7980			−1.39065			−0.695325	+	0.718695i	$0.744740\pi$
$44$	−11.4495	+	19.8311i	−0.260216	+	0.450707i
$45$		0			0
$46$	34.4949	+	59.7469i	0.749889	+	1.29885i
$47$	58.0454	+	33.5125i	1.23501	+	0.713033i	0.968070	−	0.250681i	$-0.0806545\pi$
$47$	58.0454	+	33.5125i	1.23501	+	0.713033i	0.266939	+	0.963713i	$0.413988\pi$
$48$		−	25.6308i		−	0.533975i
$49$	35.5000	−	33.7750i	0.724490	−	0.689286i
$50$		0			0
$51$	1.65153	−	2.86054i	0.0323830	−	0.0560889i
$52$	−117.288	+	67.7161i	−2.25553	+	1.30223i
$53$	47.7423	+	82.6922i	0.900799	+	1.56023i	0.826459	+	0.562997i	$0.190352\pi$
$53$	47.7423	+	82.6922i	0.900799	+	1.56023i	0.0743398	+	0.997233i	$0.476315\pi$
$54$	15.5227	+	8.96204i	0.287457	+	0.165964i
$55$		0			0
$56$	−87.4217	+	34.9428i	−1.56110	+	0.623979i
$57$	29.0908			0.510365
$58$	−54.1464	+	93.7844i	−0.933559	+	1.61697i
$59$	60.1362	−	34.7197i	1.01926	−	0.588469i	0.105369	−	0.994433i	$-0.466398\pi$
$59$	60.1362	−	34.7197i	1.01926	−	0.588469i	0.913889	+	0.405964i	$0.133064\pi$
$60$		0			0
$61$	−36.4546	−	21.0471i	−0.597616	−	0.345034i	0.170487	−	0.985360i	$-0.445466\pi$
$61$	−36.4546	−	21.0471i	−0.597616	−	0.345034i	−0.768103	+	0.640326i	$0.778799\pi$
$62$		−	117.080i		−	1.88838i
$63$	3.00000	−	20.7846i	0.0476190	−	0.329914i
$64$	−68.6867			−1.07323
$65$		0			0
$66$	15.0000	−	8.66025i	0.227273	−	0.131216i
$67$	−47.0403	−	81.4762i	−0.702094	−	1.21606i	−0.967730	−	0.251989i	$-0.918915\pi$
$67$	−47.0403	−	81.4762i	−0.702094	−	1.21606i	0.265636	−	0.964073i	$-0.414418\pi$
$68$	13.0454	+	7.53177i	0.191844	+	0.110761i
$69$		−	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	$0.448238\pi$
$72$	−20.1742	+	34.9428i	−0.280198	+	0.485317i
$73$	37.1969	−	21.4757i	0.509547	−	0.294187i	−0.223100	−	0.974795i	$-0.571618\pi$
$73$	37.1969	−	21.4757i	0.509547	−	0.294187i	0.732647	+	0.680608i	$0.238284\pi$
$74$	85.3661	+	147.858i	1.15360	+	1.99809i
$75$		0			0
$76$			132.668i			1.74563i
$77$	−15.9444	−	12.5529i	−0.207070	−	0.163025i
$78$	102.439			1.31332
$79$	−10.0959	+	17.4866i	−0.127796	+	0.221350i	−0.922823	−	0.385225i	$-0.874124\pi$
$79$	−10.0959	+	17.4866i	−0.127796	+	0.221350i	0.795026	+	0.606575i	$0.207457\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−229.182	−	132.318i	−2.79490	−	1.61364i
$83$		−	0.857187i		−	0.0103276i	−0.999987	−	0.00516378i	$-0.998356\pi$
$83$		−	0.857187i		−	0.0103276i	0.999987	−	0.00516378i	$-0.00164369\pi$
$84$	94.7878	+	13.6814i	1.12843	+	0.162874i
$85$		0			0
$86$	−103.136	+	178.637i	−1.19926	+	2.07718i
$87$	47.0908	−	27.1879i	0.541274	−	0.312505i
$88$	19.4949	+	33.7662i	0.221533	+	0.383706i
$89$	18.7423	+	10.8209i	0.210588	+	0.121583i	0.601585	−	0.798809i	$-0.294536\pi$
$89$	18.7423	+	10.8209i	0.210588	+	0.121583i	−0.390997	+	0.920392i	$0.627870\pi$
$90$		0			0
$91$	−44.5454	−	111.446i	−0.489510	−	1.22468i
$92$	157.980			1.71717
$93$	−29.3939	+	50.9117i	−0.316063	+	0.547438i
$94$	200.227	−	115.601i	2.13007	−	1.22980i
$95$		0			0
$96$	4.12883	+	2.38378i	0.0430086	+	0.0248310i
$97$		−	72.3785i		−	0.746170i	−0.927797	−	0.373085i	$-0.878300\pi$
$97$		−	72.3785i		−	0.746170i	0.927797	−	0.373085i	$-0.121700\pi$
$98$	−39.6691	−	164.304i	−0.404787	−	1.67657i
$99$	−8.69694			−0.0878479
$100$		0			0
$101$	19.6515	−	11.3458i	0.194570	−	0.112335i	−0.399550	−	0.916711i	$-0.630834\pi$
$101$	19.6515	−	11.3458i	0.194570	−	0.112335i	0.594120	+	0.804376i	$0.297500\pi$
$102$	−5.69694	−	9.86739i	−0.0558523	−	0.0967391i
$103$	76.1969	+	43.9923i	0.739776	+	0.427110i	0.821988	−	0.569505i	$-0.192865\pi$
$103$	76.1969	+	43.9923i	0.739776	+	0.427110i	−0.0822118	+	0.996615i	$0.526198\pi$
$104$			230.599i			2.21730i
$105$		0			0
$106$	329.373			3.10730
$107$	90.3485	−	156.488i	0.844378	−	1.46251i	−0.0417819	−	0.999127i	$-0.513303\pi$
$107$	90.3485	−	156.488i	0.844378	−	1.46251i	0.886160	−	0.463379i	$-0.153363\pi$
$108$	35.5454	−	20.5222i	0.329124	−	0.190020i
$109$	17.1515	+	29.7073i	0.157353	+	0.272544i	0.933914	−	0.357499i	$-0.116370\pi$
$109$	17.1515	+	29.7073i	0.157353	+	0.272544i	−0.776560	+	0.630043i	$0.783037\pi$
$110$		0			0
$111$		−	85.7277i		−	0.772321i
$112$	−14.7980	+	102.523i	−0.132125	+	0.915386i
$113$	8.38367			0.0741918			0.0370959	−	0.999312i	$-0.488189\pi$
$113$	8.38367			0.0741918			0.0370959	+	0.999312i	$0.488189\pi$
$114$	50.1742	−	86.9043i	0.440125	−	0.762319i
$115$		0			0
$116$	123.990	+	214.757i	1.06888	+	1.85135i
$117$	−44.5454	−	25.7183i	−0.380730	−	0.219815i
$118$		−	239.530i		−	2.02992i
$119$	−8.25765	+	10.4886i	−0.0693920	+	0.0881397i
$120$		0			0
$121$	56.2980	−	97.5109i	0.465272	−	0.805875i
$122$	−125.750	+	72.6016i	−1.03074	+	0.595095i
$123$	66.4393	+	115.076i	0.540157	+	0.935579i
$124$	−232.182	−	134.050i	−1.87243	−	1.08105i
$125$		0			0
$126$	−56.9166	−	44.8102i	−0.451719	−	0.355636i
$127$	160.798			1.26613			0.633063	−	0.774100i	$-0.281797\pi$
$127$	160.798			1.26613			0.633063	+	0.774100i	$0.281797\pi$
$128$	−112.962	+	195.656i	−0.882516	+	1.52856i
$129$	89.6969	−	51.7866i	0.695325	−	0.401446i
$130$		0			0
$131$	44.6969	+	25.8058i	0.341198	+	0.196991i	0.660802	−	0.750561i	$-0.270216\pi$
$131$	44.6969	+	25.8058i	0.341198	+	0.196991i	−0.319604	+	0.947551i	$0.603550\pi$
$132$		−	39.6622i		−	0.300471i
$133$	−116.363	−	16.7956i	−0.874912	−	0.126283i
$134$	−324.530			−2.42187
$135$		0			0
$136$	22.2122	−	12.8242i	0.163325	−	0.0942959i
$137$	136.697	+	236.766i	0.997788	+	1.72822i	0.556466	+	0.830871i	$0.312157\pi$
$137$	136.697	+	236.766i	0.997788	+	1.72822i	0.441322	+	0.897349i	$0.354510\pi$
$138$	−103.485	−	59.7469i	−0.749889	−	0.432949i
$139$			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
$142$	39.6515	−	68.6785i	0.279236	−	0.483651i
$143$	−43.0454	+	24.8523i	−0.301017	+	0.173792i
$144$	22.1969	+	38.4462i	0.154145	+	0.266988i
$145$		0			0
$146$		−	148.160i		−	1.01480i
$147$	−24.0000	+	81.4064i	−0.163265	+	0.553785i
$148$	390.959			2.64162
$149$	100.328	−	173.773i	0.673343	−	1.16626i	−0.303608	−	0.952797i	$-0.598191\pi$
$149$	100.328	−	173.773i	0.673343	−	1.16626i	0.976950	−	0.213467i	$-0.0684755\pi$
$150$		0			0
$151$	−117.187	−	202.973i	−0.776071	−	1.34419i	−0.934191	−	0.356775i	$-0.883876\pi$
$151$	−117.187	−	202.973i	−0.776071	−	1.34419i	0.158119	−	0.987420i	$-0.449457\pi$
$152$	195.628	+	112.946i	1.28703	+	0.743066i
$153$			5.72107i			0.0373926i
$154$	−65.0000	+	25.9808i	−0.422078	+	0.168706i
$155$		0			0
$156$	117.288	−	203.148i	0.751845	−	1.30223i
$157$	−36.1515	+	20.8721i	−0.230265	+	0.132943i	−0.610694	−	0.791867i	$-0.709109\pi$
$157$	−36.1515	+	20.8721i	−0.230265	+	0.132943i	0.380430	+	0.924810i	$0.375776\pi$
$158$	34.8258	+	60.3200i	0.220416	+	0.381772i
$159$	−143.227	−	82.6922i	−0.900799	−	0.520077i
$160$		0			0
$161$	−20.0000	+	138.564i	−0.124224	+	0.860646i
$162$	−31.0454			−0.191638
$163$	−21.3332	+	36.9501i	−0.130878	+	0.226688i	−0.924015	−	0.382355i	$-0.875113\pi$
$163$	−21.3332	+	36.9501i	−0.130878	+	0.226688i	0.793137	+	0.609043i	$0.208446\pi$
$164$	−524.803	+	302.995i	−3.20002	+	1.84753i
$165$		0			0
$166$	−2.56072	−	1.47843i	−0.0154260	−	0.00890620i
$167$			161.570i			0.967487i	0.875210	+	0.483743i	$0.160723\pi$
$167$			161.570i			0.967487i	−0.875210	+	0.483743i	$0.839277\pi$
$168$	100.871	−	128.124i	0.600424	−	0.762640i
$169$	−124.969			−0.739464
$170$		0			0
$171$	−43.6362	+	25.1934i	−0.255183	+	0.147330i
$172$	236.171	+	409.061i	1.37309	+	2.37826i
$173$	120.909	+	69.8070i	0.698897	+	0.403508i	0.806936	−	0.590638i	$-0.201124\pi$
$173$	120.909	+	69.8070i	0.698897	+	0.403508i	−0.108039	+	0.994147i	$0.534457\pi$
$174$		−	187.569i		−	1.07798i
$175$		0			0
$176$	42.8990			0.243744
$177$	−60.1362	+	104.159i	−0.339753	+	0.588469i
$178$	64.6515	−	37.3266i	0.363211	−	0.209700i
$179$	37.6061	+	65.1357i	0.210090	+	0.363887i	0.951743	−	0.306898i	$-0.0992909\pi$
$179$	37.6061	+	65.1357i	0.210090	+	0.363887i	−0.741652	+	0.670784i	$0.765958\pi$
$180$		0			0
$181$		−	42.5837i		−	0.235269i	−0.993057	−	0.117635i	$-0.962469\pi$
$181$		−	42.5837i		−	0.235269i	0.993057	−	0.117635i	$-0.0375311\pi$
$182$	−409.757	−	59.1433i	−2.25141	−	0.324963i
$183$	72.9092			0.398411
$184$	134.495	−	232.952i	0.730951	−	1.26604i
$185$		0			0
$186$	101.394	+	175.619i	0.545128	+	0.944190i
$187$	4.78775	+	2.76421i	0.0256030	+	0.0147819i
$188$		−	529.430i		−	2.81611i
$189$	13.5000	+	33.7750i	0.0714286	+	0.178704i
$190$		0			0
$191$	6.86378	−	11.8884i	0.0359360	−	0.0622430i	−0.847498	−	0.530799i	$-0.821892\pi$
$191$	6.86378	−	11.8884i	0.0359360	−	0.0622430i	0.883434	+	0.468556i	$0.155225\pi$
$192$	103.030	−	59.4845i	0.536615	−	0.309815i
$193$	−31.0908	−	53.8509i	−0.161092	−	0.279020i	0.774168	−	0.632980i	$-0.218168\pi$
$193$	−31.0908	−	53.8509i	−0.161092	−	0.279020i	−0.935261	+	0.353960i	$0.884835\pi$
$194$	−216.220	−	124.834i	−1.11453	−	0.643477i
$195$		0			0
$196$	−371.252	−	109.451i	−1.89414	−	0.558426i
$197$	−16.3837			−0.0831658			−0.0415829	−	0.999135i	$-0.513240\pi$
$197$	−16.3837			−0.0831658			−0.0415829	+	0.999135i	$0.513240\pi$
$198$	−15.0000	+	25.9808i	−0.0757576	+	0.131216i
$199$	240.257	−	138.713i	1.20732	−	0.697048i	0.245149	−	0.969485i	$-0.421163\pi$
$199$	240.257	−	138.713i	1.20732	−	0.697048i	0.962173	+	0.272438i	$0.0878298\pi$
$200$		0			0
$201$	141.121	+	81.4762i	0.702094	+	0.405354i
$202$		−	78.2746i		−	0.387498i
$203$	−204.060	+	81.5637i	−1.00522	+	0.401792i
$204$	−26.0908			−0.127896
$205$		0			0
$206$	262.841	−	151.751i	1.27593	−	0.736656i
$207$	30.0000	+	51.9615i	0.144928	+	0.251022i
$208$	219.727	+	126.859i	1.05638	+	0.609901i
$209$			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	$0.451908\pi$
$212$	377.116	−	653.184i	1.77885	−	3.08106i
$213$	−34.4847	+	19.9097i	−0.161900	+	0.0934730i
$214$	−311.656	−	539.804i	−1.45634	−	2.52245i
$215$		0			0
$216$		−	69.8856i		−	0.323544i
$217$	146.969	−	186.676i	0.677278	−	0.860259i
$218$	118.328			0.542789
$219$	−37.1969	+	64.4270i	−0.169849	+	0.294187i
$220$		0			0
$221$	16.3485	+	28.3164i	0.0739750	+	0.128128i
$222$	−256.098	−	147.858i	−1.15360	−	0.666029i
$223$		−	300.274i		−	1.34652i	−0.739406	−	0.673260i	$-0.764893\pi$
$223$		−	300.274i		−	1.34652i	0.739406	−	0.673260i	$-0.235107\pi$
$224$	−15.1390	−	11.9189i	−0.0675850	−	0.0532094i
$225$		0			0
$226$	14.4597	−	25.0449i	0.0639810	−	0.110818i
$227$	58.8184	−	33.9588i	0.259112	−	0.149598i	−0.364818	−	0.931079i	$-0.618869\pi$
$227$	58.8184	−	33.9588i	0.259112	−	0.149598i	0.623929	+	0.781481i	$0.285535\pi$
$228$	−114.894	−	199.002i	−0.503921	−	0.872816i
$229$	303.393	+	175.164i	1.32486	+	0.764909i	0.984500	−	0.175385i	$-0.0561171\pi$
$229$	303.393	+	175.164i	1.32486	+	0.764909i	0.340362	+	0.940295i	$0.389450\pi$
$230$		0			0
$231$	34.7878	+	5.02118i	0.150596	+	0.0217367i
$232$	422.232			1.81996
$233$	46.5301	−	80.5925i	0.199700	−	0.345891i	−0.748731	−	0.662874i	$-0.769337\pi$
$233$	46.5301	−	80.5925i	0.199700	−	0.345891i	0.948431	+	0.316983i	$0.102670\pi$
$234$	−153.659	+	88.7150i	−0.656662	+	0.379124i
$235$		0			0
$236$	−475.015	−	274.250i	−2.01277	−	1.16208i
$237$		−	34.9733i		−	0.147567i
$238$	17.0908	+	42.7587i	0.0718101	+	0.179658i
$239$	−112.363			−0.470139			−0.235070	−	0.971979i	$-0.575532\pi$
$239$	−112.363			−0.470139			−0.235070	+	0.971979i	$0.575532\pi$
$240$		0			0
$241$	−342.560	+	197.777i	−1.42141	+	0.820652i	−0.996420	−	0.0845448i	$-0.973056\pi$
$241$	−342.560	+	197.777i	−1.42141	+	0.820652i	−0.424992	+	0.905197i	$0.639723\pi$
$242$	−194.199	−	336.363i	−0.802476	−	1.38993i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$			332.501i			1.36271i
$245$		0			0
$246$	458.363			1.86327
$247$	−143.985	+	249.389i	−0.582934	+	1.00967i
$248$	−395.333	+	228.245i	−1.59408	+	0.920344i
$249$	0.742346	+	1.28578i	0.00298131	+	0.00516378i
$250$		0			0
$251$		−	113.423i		−	0.451884i	−0.974141	−	0.225942i	$-0.927454\pi$
$251$		−	113.423i		−	0.451884i	0.974141	−	0.225942i	$-0.0725459\pi$
$252$	−154.030	+	61.5665i	−0.611231	+	0.244311i
$253$	57.9796			0.229168
$254$	277.335	−	480.359i	1.09187	−	1.89118i
$255$		0			0
$256$	252.288	+	436.975i	0.985499	+	1.70693i
$257$	163.348	+	94.3093i	0.635597	+	0.366962i	0.782917	−	0.622127i	$-0.213731\pi$
$257$	163.348	+	94.3093i	0.635597	+	0.366962i	−0.147319	+	0.989089i	$0.547065\pi$
$258$		−	357.274i		−	1.38478i
$259$	−49.4949	+	342.911i	−0.191100	+	1.32398i
$260$		0			0
$261$	−47.0908	+	81.5637i	−0.180425	+	0.312505i
$262$	154.182	−	89.0168i	0.588480	−	0.339759i
$263$	9.97959	+	17.2852i	0.0379452	+	0.0657230i	0.884374	−	0.466778i	$-0.154585\pi$
$263$	9.97959	+	17.2852i	0.0379452	+	0.0657230i	−0.846429	+	0.532501i	$0.821252\pi$
$264$	−58.4847	−	33.7662i	−0.221533	−	0.127902i
$265$		0			0
$266$	−250.871	+	318.649i	−0.943125	+	1.19793i
$267$	−37.4847			−0.140392
$268$	−371.570	+	643.579i	−1.38646	+	2.40141i
$269$	−334.590	+	193.176i	−1.24383	+	0.718126i	−0.969872	−	0.243616i	$-0.921666\pi$
$269$	−334.590	+	193.176i	−1.24383	+	0.718126i	−0.273958	+	0.961742i	$0.588333\pi$
$270$		0			0
$271$	−33.6367	−	19.4202i	−0.124121	−	0.0716612i	0.436654	−	0.899629i	$-0.356163\pi$
$271$	−33.6367	−	19.4202i	−0.124121	−	0.0716612i	−0.560775	+	0.827968i	$0.689497\pi$
$272$		−	28.2201i		−	0.103750i
$273$	163.333	+	128.592i	0.598290	+	0.471031i
$274$	943.069			3.44186
$275$		0			0
$276$	−236.969	+	136.814i	−0.858585	+	0.495704i
$277$	263.606	+	456.578i	0.951645	+	1.64830i	0.741866	+	0.670548i	$0.233941\pi$
$277$	263.606	+	456.578i	0.951645	+	1.64830i	0.209779	+	0.977749i	$0.432726\pi$
$278$	674.113	+	389.199i	2.42487	+	1.40000i
$279$		−	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	$0.305763\pi$
$282$	−200.227	+	346.803i	−0.710025	+	1.22980i
$283$	406.272	−	234.561i	1.43559	−	0.828838i	0.438051	−	0.898950i	$-0.355669\pi$
$283$	406.272	−	234.561i	1.43559	−	0.828838i	0.997539	+	0.0701121i	$0.0223357\pi$
$284$	−90.7980	−	157.267i	−0.319711	−	0.553756i
$285$		0			0
$286$			171.455i			0.599494i
$287$	−199.318	−	498.664i	−0.694487	−	1.73750i
$288$	−8.25765			−0.0286724
$289$	−142.682	+	247.132i	−0.493708	+	0.855127i
$290$		0			0
$291$	62.6816	+	108.568i	0.215401	+	0.373085i
$292$	−293.818	−	169.636i	−1.00623	−	0.580945i
$293$			192.555i			0.657183i	0.944472	+	0.328591i	$0.106574\pi$
$293$			192.555i			0.657183i	−0.944472	+	0.328591i	$0.893426\pi$
$294$	201.795	+	212.102i	0.686378	+	0.721434i
$295$		0			0
$296$	332.841	−	576.497i	1.12446	−	1.94762i
$297$	13.0454	−	7.53177i	0.0439239	−	0.0253595i
$298$	−346.081	−	599.429i	−1.16134	−	2.01151i
$299$	296.969	+	171.455i	0.993209	+	0.573429i
$300$		0			0
$301$	−388.687	+	155.360i	−1.29132	+	0.516145i
$302$	−808.469			−2.67705
$303$	−19.6515	+	34.0374i	−0.0648565	+	0.112335i
$304$	215.242	−	124.270i	0.708034	−	0.408784i
$305$		0			0
$306$	17.0908	+	9.86739i	0.0558523	+	0.0322464i
$307$		−	35.6555i		−	0.116142i	−0.998312	−	0.0580708i	$-0.981505\pi$
$307$		−	35.6555i		−	0.116142i	0.998312	−	0.0580708i	$-0.0184949\pi$
$308$	−22.8990	+	158.649i	−0.0743473	+	0.515093i
$309$	−152.394			−0.493184
$310$		0			0
$311$	−176.060	+	101.648i	−0.566110	+	0.326844i	−0.755594	−	0.655040i	$-0.772652\pi$
$311$	−176.060	+	101.648i	−0.566110	+	0.326844i	0.189484	+	0.981884i	$0.439318\pi$
$312$	−199.704	−	345.898i	−0.640078	−	1.10865i
$313$	−51.5755	−	29.7771i	−0.164778	−	0.0951346i	0.415343	−	0.909665i	$-0.363661\pi$
$313$	−51.5755	−	29.7771i	−0.164778	−	0.0951346i	−0.580121	+	0.814530i	$0.696995\pi$
$314$			143.996i			0.458587i
$315$		0			0
$316$	159.495			0.504731
$317$	−211.879	+	366.984i	−0.668387	+	1.15768i	0.309969	+	0.950747i	$0.399681\pi$
$317$	−211.879	+	366.984i	−0.668387	+	1.15768i	−0.978355	+	0.206933i	$0.933652\pi$
$318$	−494.060	+	285.246i	−1.55365	+	0.896999i
$319$	45.5051	+	78.8171i	0.142649	+	0.247076i
$320$		0			0
$321$			312.976i			0.975004i
$322$	379.444	+	298.735i	1.17840	+	0.927747i
$323$	32.0296			0.0991628
$324$	−35.5454	+	61.5665i	−0.109708	+	0.190020i
$325$		0			0
$326$	73.5885	+	127.459i	0.225732	+	0.390979i
$327$	−51.4546	−	29.7073i	−0.157353	−	0.0908481i
$328$			1031.81i			3.14577i
$329$	464.363	+	67.0251i	1.41144	+	0.203724i
$330$		0			0
$331$	200.758	−	347.722i	0.606519	−	1.05052i	−0.385291	−	0.922795i	$-0.625899\pi$
$331$	200.758	−	347.722i	0.606519	−	1.05052i	0.991810	−	0.127726i	$-0.0407678\pi$
$332$	−5.86378	+	3.38545i	−0.0176620	+	0.0101971i
$333$	74.2423	+	128.592i	0.222950	+	0.386161i
$334$	482.666	+	278.668i	1.44511	+	0.834334i
$335$		0			0
$336$	−66.5908	−	166.600i	−0.198187	−	0.495834i
$337$	−445.333			−1.32146			−0.660731	−	0.750623i	$-0.729754\pi$
$337$	−445.333			−1.32146			−0.660731	+	0.750623i	$0.729754\pi$
$338$	−215.540	+	373.327i	−0.637693	+	1.10452i
$339$	−12.5755	+	7.26047i	−0.0370959	+	0.0214173i
$340$		0			0
$341$	−85.2122	−	49.1973i	−0.249889	−	0.144274i
$342$			173.809i			0.508212i
$343$	143.000	−	311.769i	0.416910	−	0.908948i
$344$	804.252			2.33794
$345$		0			0
$346$	417.075	−	240.798i	1.20542	−	0.695949i
$347$	161.025	+	278.903i	0.464049	+	0.803756i	0.999158	−	0.0410266i	$-0.0130628\pi$
$347$	161.025	+	278.903i	0.464049	+	0.803756i	−0.535109	+	0.844783i	$0.679729\pi$
$348$	−371.969	−	214.757i	−1.06888	−	0.617117i
$349$		−	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
$352$	−3.98979	+	6.91053i	−0.0113346	+	0.0196322i
$353$	−564.106	+	325.687i	−1.59803	+	0.922625i	−0.606167	+	0.795337i	$0.707294\pi$
$353$	−564.106	+	325.687i	−1.59803	+	0.922625i	−0.991866	+	0.127287i	$0.959373\pi$
$354$	207.439	+	359.295i	0.585987	+	1.01496i
$355$		0			0
$356$		−	170.948i		−	0.480191i
$357$	3.30306	−	22.8843i	0.00925227	−	0.0641016i
$358$	259.444			0.724704
$359$	3.48011	−	6.02772i	0.00969389	−	0.0167903i	−0.861138	−	0.508372i	$-0.830248\pi$
$359$	3.48011	−	6.02772i	0.00969389	−	0.0167903i	0.870832	+	0.491581i	$0.163581\pi$
$360$		0			0
$361$	−39.4541	−	68.3365i	−0.109291	−	0.189298i
$362$	−127.212	−	73.4460i	−0.351415	−	0.202890i
$363$			195.022i			0.537250i
$364$	−586.439	+	744.877i	−1.61110	+	2.04637i
$365$		0			0
$366$	125.750	−	217.805i	0.343579	−	0.595095i
$367$	440.969	−	254.594i	1.20155	−	0.693716i	0.240651	−	0.970612i	$-0.422639\pi$
$367$	440.969	−	254.594i	1.20155	−	0.693716i	0.960900	+	0.276896i	$0.0893056\pi$
$368$	−147.980	−	256.308i	−0.402118	−	0.696490i
$369$	−199.318	−	115.076i	−0.540157	−	0.311860i
$370$		0			0
$371$	525.166	+	413.461i	1.41554	+	1.11445i
$372$	464.363			1.24829
$373$	89.1107	−	154.344i	0.238903	−	0.413792i	−0.721497	−	0.692418i	$-0.756546\pi$
$373$	89.1107	−	154.344i	0.238903	−	0.413792i	0.960400	+	0.278626i	$0.0898790\pi$
$374$	16.5153	−	9.53512i	0.0441586	−	0.0254950i
$375$		0			0
$376$	−780.681	−	450.726i	−2.07628	−	1.19874i
$377$			538.265i			1.42776i
$378$	124.182	+	17.9241i	0.328523	+	0.0474182i
$379$	−215.899			−0.569654			−0.284827	−	0.958579i	$-0.591936\pi$
$379$	−215.899			−0.569654			−0.284827	+	0.958579i	$0.591936\pi$
$380$		0			0
$381$	−241.197	+	139.255i	−0.633063	+	0.365499i
$382$	−23.6765	−	41.0089i	−0.0619804	−	0.107353i
$383$	−146.666	−	84.6778i	−0.382941	−	0.221091i	0.296156	−	0.955140i	$-0.404295\pi$
$383$	−146.666	−	84.6778i	−0.382941	−	0.221091i	−0.679097	+	0.734049i	$0.737628\pi$
$384$		−	391.312i		−	1.01904i
$385$		0			0
$386$	−214.495			−0.555686
$387$	−89.6969	+	155.360i	−0.231775	+	0.401446i
$388$	−495.121	+	285.858i	−1.27608	+	0.736748i
$389$	−26.4699	−	45.8472i	−0.0680460	−	0.117859i	0.829995	−	0.557771i	$-0.188343\pi$
$389$	−26.4699	−	45.8472i	−0.0680460	−	0.117859i	−0.898041	+	0.439912i	$0.855010\pi$
$390$		0			0
$391$		−	38.1405i		−	0.0975460i
$392$	−477.457	+	454.256i	−1.21800	+	1.15882i
$393$	−89.3939			−0.227465
$394$	−28.2577	+	48.9437i	−0.0717199	+	0.124223i
$395$		0			0
$396$	34.3485	+	59.4933i	0.0867386	+	0.150236i
$397$	−343.757	−	198.468i	−0.865887	−	0.499920i	9.22678e−5	−	1.00000i	$-0.499971\pi$
$397$	−343.757	−	198.468i	−0.865887	−	0.499920i	−0.865979	+	0.500080i	$0.833304\pi$
$398$		−	956.975i		−	2.40446i
$399$	189.090	−	75.5802i	0.473911	−	0.189424i
$400$		0			0
$401$	−207.398	+	359.225i	−0.517203	+	0.895822i	0.482597	+	0.875842i	$0.339694\pi$
$401$	−207.398	+	359.225i	−0.517203	+	0.895822i	−0.999800	+	0.0199797i	$0.993640\pi$
$402$	486.795	−	281.051i	1.21093	−	0.699133i
$403$	−290.969	−	503.974i	−0.722008	−	1.25056i
$404$	−155.227	−	89.6204i	−0.384225	−	0.221833i
$405$		0			0
$406$	−108.293	+	750.275i	−0.266731	+	1.84797i
$407$	143.485			0.352542
$408$	−22.2122	+	38.4727i	−0.0544418	+	0.0942959i
$409$	440.651	−	254.410i	1.07739	−	0.622029i	0.147196	−	0.989107i	$-0.452975\pi$
$409$	440.651	−	254.410i	1.07739	−	0.622029i	0.930190	+	0.367078i	$0.119642\pi$
$410$		0			0
$411$	−410.091	−	236.766i	−0.997788	−	0.576073i
$412$		−	694.989i		−	1.68687i
$413$	300.681	−	381.916i	0.728041	−	0.924737i
$414$	206.969			0.499926
$415$		0			0
$416$	−40.8712	+	23.5970i	−0.0982480	+	0.0567235i
$417$	−195.424	−	338.484i	−0.468643	−	0.811713i
$418$	145.454	+	83.9780i	0.347976	+	0.200904i
$419$		−	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	$0.720593\pi$
$422$	109.548	−	189.742i	0.259592	−	0.449626i
$423$	174.136	−	100.538i	0.411670	−	0.237678i
$424$	−642.110	−	1112.17i	−1.51441	−	2.62304i
$425$		0			0
$426$			137.357i			0.322434i
$427$	−291.637	−	42.0941i	−0.682990	−	0.0985811i
$428$	−1427.32			−3.33486
$429$	43.0454	−	74.5568i	0.100339	−	0.173792i
$430$		0			0
$431$	−16.6663	−	28.8669i	−0.0386690	−	0.0669766i	0.846043	−	0.533114i	$-0.178978\pi$
$431$	−16.6663	−	28.8669i	−0.0386690	−	0.0669766i	−0.884712	+	0.466138i	$0.845645\pi$
$432$	−66.5908	−	38.4462i	−0.154145	−	0.0889959i
$433$			443.405i			1.02403i	0.858976	+	0.512015i	$0.171101\pi$
$433$			443.405i			1.02403i	−0.858976	+	0.512015i	$0.828899\pi$
$434$	−304.182	−	761.017i	−0.700879	−	1.75350i
$435$		0			0
$436$	135.480	−	234.658i	0.310733	−	0.538205i
$437$	290.908	−	167.956i	0.665694	−	0.384338i
$438$	128.310	+	222.240i	0.292946	+	0.507398i
$439$	−320.985	−	185.321i	−0.731172	−	0.422143i	0.0876785	−	0.996149i	$-0.472055\pi$
$439$	−320.985	−	185.321i	−0.731172	−	0.422143i	−0.818851	+	0.574006i	$0.805389\pi$
$440$		0			0
$441$	−34.5000	−	142.894i	−0.0782313	−	0.324023i
$442$	112.788			0.255176
$443$	393.182	−	681.011i	0.887543	−	1.53727i	0.0447724	−	0.998997i	$-0.485744\pi$
$443$	393.182	−	681.011i	0.887543	−	1.53727i	0.842771	−	0.538273i	$-0.180923\pi$
$444$	−586.439	+	338.581i	−1.32081	+	0.762569i
$445$		0			0
$446$	−897.022	−	517.896i	−2.01126	−	1.16120i
$447$			347.547i			0.777509i
$448$	−446.464	+	178.453i	−0.996571	+	0.398333i
$449$	93.3439			0.207893			0.103946	−	0.994583i	$-0.466853\pi$
$449$	93.3439			0.207893			0.103946	+	0.994583i	$0.466853\pi$
$450$		0			0
$451$	−192.606	+	111.201i	−0.427065	+	0.246566i
$452$	−33.1112	−	57.3503i	−0.0732549	−	0.126881i
$453$	351.560	+	202.973i	0.776071	+	0.448065i
$454$		−	234.281i		−	0.516038i
$455$		0			0
$456$	−391.257			−0.858019
$457$	264.187	−	457.585i	0.578089	−	1.00128i	−0.417609	−	0.908627i	$-0.637132\pi$
$457$	264.187	−	457.585i	0.578089	−	1.00128i	0.995698	−	0.0926531i	$-0.0295347\pi$
$458$	1046.55	−	604.227i	2.28505	−	1.31927i
$459$	−4.95459	−	8.58161i	−0.0107943	−	0.0186963i
$460$		0			0
$461$			730.505i			1.58461i	0.610126	+	0.792305i	$0.291119\pi$
$461$			730.505i			1.58461i	−0.610126	+	0.792305i	$0.708881\pi$
$462$	75.0000	−	95.2628i	0.162338	−	0.206197i
$463$	−217.908			−0.470644			−0.235322	−	0.971917i	$-0.575614\pi$
$463$	−217.908			−0.470644			−0.235322	+	0.971917i	$0.575614\pi$
$464$	232.283	−	402.325i	0.500609	−	0.867081i
$465$		0			0
$466$	−160.505	−	278.003i	−0.344432	−	0.596573i
$467$	173.363	+	100.091i	0.371228	+	0.214328i	0.673995	−	0.738736i	$-0.264577\pi$
$467$	173.363	+	100.091i	0.371228	+	0.214328i	−0.302767	+	0.953065i	$0.597910\pi$
$468$			406.297i			0.868155i
$469$	−517.443	−	407.381i	−1.10329	−	0.868616i
$470$		0			0
$471$	36.1515	−	62.6163i	0.0767548	−	0.132943i
$472$	−808.802	+	466.962i	−1.71356	+	0.989326i
$473$	86.6765	+	150.128i	0.183248	+	0.317396i
$474$	−104.477	−	60.3200i	−0.220416	−	0.127257i
$475$		0			0
$476$	104.363	+	15.0635i	0.219251	+	0.0316461i
$477$	286.454			0.600533
$478$	−193.798	+	335.668i	−0.405435	+	0.702234i
$479$	227.864	−	131.557i	0.475707	−	0.274650i	−0.242919	−	0.970047i	$-0.578105\pi$
$479$	227.864	−	131.557i	0.475707	−	0.274650i	0.718626	+	0.695397i	$0.244771\pi$
$480$		0			0
$481$	734.923	+	424.308i	1.52791	+	0.882138i
$482$			1364.46i			2.83083i
$483$	−90.0000	−	225.167i	−0.186335	−	0.466183i
$484$	−889.393			−1.83759
$485$		0			0
$486$	46.5681	−	26.8861i	0.0958192	−	0.0553212i
$487$	150.283	+	260.297i	0.308589	+	0.534491i	0.978054	−	0.208352i	$-0.0668100\pi$
$487$	150.283	+	260.297i	0.308589	+	0.534491i	−0.669465	+	0.742843i	$0.733477\pi$
$488$	490.296	+	283.072i	1.00470	+	0.580066i
$489$		−	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	$0.411992\pi$
$492$	524.803	−	908.985i	1.06667	−	1.84753i
$493$	51.8480	−	29.9344i	0.105168	−	0.0607189i
$494$	496.674	+	860.264i	1.00541	+	1.74143i
$495$		0			0
$496$			502.259i			1.01262i
$497$	149.434	−	59.7292i	0.300671	−	0.120180i
$498$	5.12143			0.0102840
$499$	−73.4240	+	127.174i	−0.147142	+	0.254858i	−0.930170	−	0.367129i	$-0.880341\pi$
$499$	−73.4240	+	127.174i	−0.147142	+	0.254858i	0.783028	+	0.621987i	$0.213674\pi$
$500$		0			0
$501$	−139.924	−	242.355i	−0.279289	−	0.483743i
$502$	−338.833	−	195.625i	−0.674966	−	0.389692i
$503$		−	102.944i		−	0.204660i	−0.994751	−	0.102330i	$-0.967370\pi$
$503$		−	102.944i		−	0.204660i	0.994751	−	0.102330i	$-0.0326297\pi$
$504$	−40.3485	+	279.542i	−0.0800565	+	0.554648i
$505$		0			0
$506$	100.000	−	173.205i	0.197628	−	0.342303i
$507$	187.454	−	108.227i	0.369732	−	0.213465i
$508$	−635.070	−	1099.97i	−1.25014	−	2.16530i
$509$	−777.879	−	449.108i	−1.52825	−	0.882335i	−0.999435	−	0.0335965i	$-0.989304\pi$
$509$	−777.879	−	449.108i	−1.52825	−	0.882335i	−0.528813	−	0.848738i	$-0.677363\pi$
$510$		0			0
$511$	185.985	−	236.232i	0.363962	−	0.462294i
$512$	836.832			1.63444
$513$	43.6362	−	75.5802i	0.0850609	−	0.147330i
$514$	563.469	−	325.319i	1.09624	−	0.632916i
$515$		0			0
$516$	−708.514	−	409.061i	−1.37309	−	0.792754i
$517$		−	194.304i		−	0.375830i
$518$	939.027	+	739.292i	1.81279	+	1.42720i
$519$	−241.818			−0.465931
$520$		0			0
$521$	414.606	−	239.373i	0.795789	−	0.459449i	−0.0462075	−	0.998932i	$-0.514714\pi$
$521$	414.606	−	239.373i	0.795789	−	0.459449i	0.841997	+	0.539483i	$0.181380\pi$
$522$	162.439	+	281.353i	0.311186	+	0.538991i
$523$	−543.848	−	313.991i	−1.03986	−	0.600365i	−0.120068	−	0.992766i	$-0.538311\pi$
$523$	−543.848	−	313.991i	−1.03986	−	0.600365i	−0.919794	+	0.392401i	$0.871645\pi$
$524$		−	407.679i		−	0.778013i
$525$		0			0
$526$	68.8490			0.130892
$527$	−32.3633	+	56.0548i	−0.0614104	+	0.106366i
$528$	−64.3485	+	37.1516i	−0.121872	+	0.0703629i
$529$	64.5000	+	111.717i	0.121928	+	0.211186i
$530$		0			0
$531$		−	208.318i		−	0.392313i
$532$	344.682	+	862.342i	0.647898	+	1.62094i
$533$	−1315.36			−2.46785
$534$	−64.6515	+	111.980i	−0.121070	+	0.209700i
$535$		0			0
$536$	632.668	+	1095.81i	1.18035	+	2.04443i
$537$	−112.818	−	65.1357i	−0.210090	−	0.121296i
$538$			1332.72i			2.47717i
$539$	−136.252	−	40.1694i	−0.252787	−	0.0745259i
$540$		0			0
$541$	−43.9801	+	76.1758i	−0.0812941	+	0.140806i	−0.903806	−	0.427942i	$-0.859239\pi$
$541$	−43.9801	+	76.1758i	−0.0812941	+	0.140806i	0.822512	+	0.568748i	$0.192572\pi$
$542$	−116.030	+	66.9897i	−0.214077	+	0.123597i
$543$	36.8786	+	63.8756i	0.0679163	+	0.117635i
$544$	4.54592	+	2.62459i	0.00835648	+	0.00482461i
$545$		0			0
$546$	665.855	−	266.145i	1.21952	−	0.487445i
$547$	−1047.41			−1.91483			−0.957415	−	0.288715i	$-0.906772\pi$
$547$	−1047.41			−1.91483			−0.957415	+	0.288715i	$0.906772\pi$
$548$	1079.77	−	1870.21i	1.97038	−	3.41279i
$549$	−109.364	+	63.1412i	−0.199205	+	0.115011i
$550$		0			0
$551$	456.637	+	263.639i	0.828742	+	0.478474i
$552$			465.904i			0.844029i
$553$	−20.1918	+	139.893i	−0.0365133	+	0.252971i
$554$	1818.61			3.28269
$555$		0			0
$556$	1543.65	−	891.227i	2.77635	−	1.60293i
$557$	350.414	+	606.935i	0.629110	+	1.08965i	0.987731	+	0.156167i	$0.0499138\pi$
$557$	350.414	+	606.935i	0.629110	+	1.08965i	−0.358621	+	0.933483i	$0.616753\pi$
$558$	−304.182	−	175.619i	−0.545128	−	0.314730i
$559$			1025.27i			1.83411i
$560$		0			0
$561$	−9.57551			−0.0170686
$562$	555.454	−	962.075i	0.988352	−	1.71188i
$563$	408.804	−	236.023i	0.726116	−	0.419224i	−0.0908833	−	0.995862i	$-0.528969\pi$
$563$	408.804	−	236.023i	0.726116	−	0.419224i	0.817000	+	0.576638i	$0.195636\pi$
$564$	458.499	+	794.144i	0.812942	+	1.40806i
$565$		0			0
$566$		−	1618.23i		−	2.85907i
$567$	−49.5000	−	38.9711i	−0.0873016	−	0.0687322i
$568$	−309.201			−0.544368
$569$	91.0862	−	157.766i	0.160081	−	0.277269i	−0.774816	−	0.632186i	$-0.782158\pi$
$569$	91.0862	−	157.766i	0.160081	−	0.277269i	0.934898	+	0.354917i	$0.115491\pi$
$570$		0			0
$571$	−321.212	−	556.355i	−0.562542	−	0.974352i	−0.997274	−	0.0737918i	$-0.976490\pi$
$571$	−321.212	−	556.355i	−0.562542	−	0.974352i	0.434731	−	0.900560i	$-0.356843\pi$
$572$	340.015	+	196.308i	0.594431	+	0.343195i
$573$			23.7768i			0.0414953i
$574$	−1833.45	−	264.636i	−3.19417	−	0.461039i
$575$		0			0
$576$	−103.030	+	178.453i	−0.178872	+	0.309815i
$577$	−649.696	+	375.102i	−1.12599	+	0.650090i	−0.942923	−	0.333010i	$-0.891936\pi$
$577$	−649.696	+	375.102i	−1.12599	+	0.650090i	−0.183066	+	0.983101i	$0.558602\pi$
$578$	492.179	+	852.479i	0.851520	+	1.47488i
$579$	93.2724	+	53.8509i	0.161092	+	0.0930067i
$580$		0			0
$581$	−2.22704	−	5.57172i	−0.00383311	−	0.00958988i
$582$	432.439			0.743023
$583$	138.404	−	239.723i	0.237400	−	0.411189i
$584$	−500.280	+	288.837i	−0.856644	+	0.494583i
$585$		0			0
$586$	575.227	+	332.107i	0.981616	+	0.566736i
$587$		−	975.092i		−	1.66114i	−0.556911	−	0.830572i	$-0.688014\pi$
$587$		−	975.092i		−	1.66114i	0.556911	−	0.830572i	$-0.311986\pi$
$588$	651.666	−	157.336i	1.10828	−	0.267579i
$589$	−570.061			−0.967846
$590$		0			0
$591$	24.5755	−	14.1887i	0.0415829	−	0.0240079i
$592$	−366.212	−	634.297i	−0.618601	−	1.07145i
$593$	175.243	+	101.177i	0.295519	+	0.170618i	0.640428	−	0.768018i	$-0.278757\pi$
$593$	175.243	+	101.177i	0.295519	+	0.170618i	−0.344909	+	0.938636i	$0.612090\pi$
$594$		−	51.9615i		−	0.0874773i
$595$		0			0
$596$	−1584.98			−2.65936
$597$	−240.257	+	416.138i	−0.402441	+	0.697048i
$598$	1024.39	−	591.433i	1.71303	−	0.989019i
$599$	392.176	+	679.269i	0.654718	+	1.13400i	0.981964	+	0.189066i	$0.0605459\pi$
$599$	392.176	+	679.269i	0.654718	+	1.13400i	−0.327247	+	0.944939i	$0.606121\pi$
$600$		0			0
$601$			252.476i			0.420094i	0.977691	+	0.210047i	$0.0673617\pi$
$601$			252.476i			0.420094i	−0.977691	+	0.210047i	$0.932638\pi$
$602$	−206.272	+	1429.10i	−0.342645	+	2.37392i
$603$	−282.242			−0.468063
$604$	−925.656	+	1603.28i	−1.53254	+	2.65444i
$605$		0			0
$606$	67.7878	+	117.412i	0.111861	+	0.193749i
$607$	−182.954	−	105.629i	−0.301407	−	0.174017i	0.341668	−	0.939821i	$-0.389008\pi$
$607$	−182.954	−	105.629i	−0.301407	−	0.174017i	−0.643075	+	0.765803i	$0.722342\pi$
$608$			46.2307i			0.0760374i
$609$	235.454	−	299.067i	0.386624	−	0.491079i
$610$		0			0
$611$	574.590	−	995.220i	0.940410	−	1.62884i
$612$	39.1362	−	22.5953i	0.0639481	−	0.0369204i
$613$	329.565	+	570.824i	0.537627	+	0.931197i	0.999031	+	0.0440072i	$0.0140124\pi$
$613$	329.565	+	570.824i	0.537627	+	0.931197i	−0.461404	+	0.887190i	$0.652654\pi$
$614$	−106.515	−	61.4966i	−0.173478	−	0.100157i
$615$		0			0
$616$	214.444	+	168.831i	0.348123	+	0.274076i
$617$	−155.757			−0.252443			−0.126221	−	0.992002i	$-0.540285\pi$
$617$	−155.757			−0.252443			−0.126221	+	0.992002i	$0.540285\pi$
$618$	−262.841	+	455.253i	−0.425308	+	0.736656i
$619$	544.665	−	314.463i	0.879912	−	0.508017i	0.00928235	−	0.999957i	$-0.497045\pi$
$619$	544.665	−	314.463i	0.879912	−	0.508017i	0.870629	+	0.491940i	$0.163712\pi$
$620$		0			0
$621$	−90.0000	−	51.9615i	−0.144928	−	0.0836740i
$622$			701.270i			1.12744i
$623$	149.939	+	21.6418i	0.240672	+	0.0347380i
$624$	−439.454			−0.704253
$625$		0			0
$626$	−177.909	+	102.716i	−0.284200	+	0.164083i
$627$	−42.1668	−	73.0351i	−0.0672517	−	0.116483i
$628$	285.560	+	164.868i	0.454714	+	0.262529i
$629$		−	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	$0.531918\pi$
$632$	135.785	−	235.186i	0.214850	−	0.372130i
$633$	−95.2730	+	55.0059i	−0.150510	+	0.0868971i
$634$	730.873	+	1265.91i	1.15280	+	1.99670i
$635$		0			0
$636$			1306.37i			2.05404i
$637$	−579.090	−	608.667i	−0.909090	−	0.955520i
$638$	313.939			0.492067
$639$	34.4847	−	59.7292i	0.0539667	−	0.0934730i
$640$		0			0
$641$	−62.6561	−	108.524i	−0.0977475	−	0.169304i	0.813004	−	0.582257i	$-0.197830\pi$
$641$	−62.6561	−	108.524i	−0.0977475	−	0.169304i	−0.910752	+	0.412954i	$0.864497\pi$
$642$	934.968	+	539.804i	1.45634	+	0.840817i
$643$			895.765i			1.39310i	0.717507	+	0.696552i	$0.245283\pi$
$643$			895.765i			1.39310i	−0.717507	+	0.696552i	$0.754717\pi$
$644$	1026.87	−	410.443i	1.59451	−	0.637334i
$645$		0			0
$646$	55.2429	−	95.6834i	0.0855153	−	0.148117i
$647$	828.620	−	478.404i	1.28071	−	0.739419i	0.303732	−	0.952757i	$-0.401767\pi$
$647$	828.620	−	478.404i	1.28071	−	0.739419i	0.976978	+	0.213339i	$0.0684338\pi$
$648$	60.5227	+	104.828i	0.0933992	+	0.161772i
$649$	−174.334	−	100.652i	−0.268619	−	0.155087i
$650$		0			0
$651$	−58.7878	+	407.294i	−0.0903038	+	0.625643i
$652$	337.020			0.516902
$653$	−605.257	+	1048.34i	−0.926886	+	1.60541i	−0.138387	+	0.990378i	$0.544192\pi$
$653$	−605.257	+	1048.34i	−0.926886	+	1.60541i	−0.788499	+	0.615036i	$0.789142\pi$
$654$	−177.492	+	102.475i	−0.271395	+	0.156690i
$655$		0			0
$656$	983.166	+	567.631i	1.49873	+	0.865291i
$657$		−	128.854i		−	0.196125i
$658$	1001.14	−	1271.61i	1.52148	−	1.93254i
$659$	−741.485			−1.12517			−0.562583	−	0.826741i	$-0.690192\pi$
$659$	−741.485			−1.12517			−0.562583	+	0.826741i	$0.690192\pi$
$660$		0			0
$661$	318.424	−	183.842i	0.481731	−	0.278127i	−0.239407	−	0.970919i	$-0.576953\pi$
$661$	318.424	−	183.842i	0.481731	−	0.278127i	0.721137	+	0.692792i	$0.243620\pi$
$662$	−692.511	−	1199.47i	−1.04609	−	1.81188i
$663$	−49.0454	−	28.3164i	−0.0739750	−	0.0427095i
$664$			11.5287i			0.0173626i
$665$		0			0
$666$	512.196			0.769064
$667$	313.939	−	543.758i	0.470673	−	0.815229i
$668$	1105.26	−	638.120i	1.65458	−	0.955270i
$669$	260.045	+	450.411i	0.388707	+	0.673260i
$670$		0			0
$671$			122.030i			0.181863i
$672$	33.0306	+	4.76756i	0.0491527	+	0.00709458i
$673$	−200.514			−0.297941			−0.148970	−	0.988842i	$-0.547596\pi$
$673$	−200.514			−0.297941			−0.148970	+	0.988842i	$0.547596\pi$
$674$	−768.085	+	1330.36i	−1.13959	+	1.97383i
$675$		0			0
$676$	493.565	+	854.880i	0.730126	+	1.26462i
$677$	−940.393	−	542.936i	−1.38906	−	0.801974i	−0.395850	−	0.918315i	$-0.629550\pi$
$677$	−940.393	−	542.936i	−1.38906	−	0.801974i	−0.993209	+	0.116342i	$0.962883\pi$
$678$			50.0899i			0.0738788i
$679$	−188.045	−	470.460i	−0.276944	−	0.692872i
$680$		0			0
$681$	−58.8184	+	101.876i	−0.0863706	+	0.149598i
$682$	−293.939	+	169.706i	−0.430995	+	0.248835i
$683$	−19.8230	−	34.3344i	−0.0290234	−	0.0502699i	0.851149	−	0.524924i	$-0.175906\pi$
$683$	−19.8230	−	34.3344i	−0.0290234	−	0.0502699i	−0.880172	+	0.474654i	$0.842573\pi$
$684$	344.682	+	199.002i	0.503921	+	0.290939i
$685$		0			0
$686$	−684.724	−	964.913i	−0.998140	−	1.40658i
$687$	−606.787			−0.883241
$688$	442.444	−	766.335i	0.643087	−	1.11386i
$689$	1417.80	−	818.568i	2.05777	−	1.18805i
$690$		0			0
$691$	−38.3648	−	22.1499i	−0.0555207	−	0.0320549i	0.471983	−	0.881608i	$-0.343538\pi$
$691$	−38.3648	−	22.1499i	−0.0555207	−	0.0320549i	−0.527503	+	0.849553i	$0.676872\pi$
$692$		−	1102.81i		−	1.59365i
$693$	−56.5301	+	22.5953i	−0.0815730	+	0.0326051i
$694$	1110.91			1.60073
$695$		0			0
$696$	−633.347	+	365.663i	−0.909982	+	0.525378i
$697$	73.1510	+	126.701i	0.104951	+	0.181781i
$698$	−134.636	−	77.7320i	−0.192888	−	0.111364i
$699$			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	$0.405569\pi$
$702$	153.659	−	266.145i	0.218887	−	0.379124i
$703$	719.923	−	415.648i	1.02407	−	0.591249i
$704$	99.5607	+	172.444i	0.141421	+	0.244949i
$705$		0			0
$706$			2246.90i			3.18258i
$707$	98.2577	−	124.804i	0.138978	−	0.176526i
$708$	950.030			1.34185
$709$	228.364	−	395.538i	0.322093	−	0.557881i	−0.658827	−	0.752295i	$-0.728947\pi$
$709$	228.364	−	395.538i	0.322093	−	0.557881i	0.980920	+	0.194414i	$0.0622804\pi$
$710$		0			0
$711$	30.2878	+	52.4599i	0.0425988	+	0.0737833i
$712$	−252.075	−	145.536i	−0.354038	−	0.204404i
$713$			678.823i			0.952065i
$714$	−62.6663	−	49.3369i	−0.0877680	−	0.0690993i
$715$		0			0
$716$	297.050	−	514.506i	0.414874	−	0.718583i
$717$	168.545	−	97.3094i	0.235070	−	0.135717i
$718$	−12.0046	−	20.7926i	−0.0167195	−	0.0289590i
$719$	−58.0148	−	33.4949i	−0.0806882	−	0.0465853i	0.459113	−	0.888378i	$-0.348167\pi$
$719$	−58.0148	−	33.4949i	−0.0806882	−	0.0465853i	−0.539801	+	0.841793i	$0.681501\pi$
$720$		0			0
$721$	609.576	+	87.9846i	0.845458	+	0.122031i
$722$	−272.193			−0.376998
$723$	342.560	−	593.332i	0.473804	−	0.820652i
$724$	−291.303	+	168.184i	−0.402352	+	0.232298i
$725$		0			0
$726$	582.598	+	336.363i	0.802476	+	0.463310i
$727$		−	433.766i		−	0.596651i	−0.954464	−	0.298326i	$-0.903572\pi$
$727$		−	433.766i		−	0.596651i	0.954464	−	0.298326i	$-0.0964282\pi$
$728$	599.113	+	1498.89i	0.822957	+	2.05892i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	98.7582	−	57.0181i	0.135100	−	0.0780001i
$732$	−287.954	−	498.751i	−0.393380	−	0.681354i
$733$	−256.939	−	148.344i	−0.350531	−	0.202379i	0.314388	−	0.949295i	$-0.398201\pi$
$733$	−256.939	−	148.344i	−0.350531	−	0.202379i	−0.664919	+	0.746915i	$0.731534\pi$
$734$		−	1756.44i		−	2.39297i
$735$		0			0
$736$	55.0510			0.0747976
$737$	−136.369	+	236.198i	−0.185032	+	0.320486i
$738$	−687.545	+	396.954i	−0.931633	+	0.537878i
$739$	−569.080	−	985.676i	−0.770068	−	1.33380i	−0.937525	−	0.347917i	$-0.886889\pi$
$739$	−569.080	−	985.676i	−0.770068	−	1.33380i	0.167457	−	0.985879i	$-0.446444\pi$
$740$		0			0
$741$		−	498.778i		−	0.673114i
$742$	2140.93	−	855.737i	2.88535	−	1.15328i
$743$	−331.637			−0.446348			−0.223174	−	0.974779i	$-0.571642\pi$
$743$	−331.637			−0.446348			−0.223174	+	0.974779i	$0.571642\pi$
$744$	395.333	−	684.736i	0.531361	−	0.920344i
$745$		0			0
$746$	−307.386	−	532.409i	−0.412046	−	0.713685i
$747$	−2.22704	−	1.28578i	−0.00298131	−	0.00172126i
$748$		−	43.6689i		−	0.0583809i
$749$	180.697	−	1251.91i	0.241251	−	1.67144i
$750$		0			0
$751$	481.923	−	834.716i	0.641709	−	1.11147i	−0.343342	−	0.939210i	$-0.611559\pi$
$751$	481.923	−	834.716i	0.641709	−	1.11147i	0.985051	−	0.172262i	$-0.0551076\pi$
$752$	−858.954	+	495.917i	−1.14223	+	0.659464i
$753$	98.2270	+	170.134i	0.130448	+	0.225942i
$754$	1607.98	+	928.370i	2.13260	+	1.23126i
$755$		0			0
$756$	177.727	−	225.744i	0.235089	−	0.298603i
$757$	400.242			0.528721			0.264361	−	0.964424i	$-0.414839\pi$
$757$	400.242			0.528721			0.264361	+	0.964424i	$0.414839\pi$
$758$	−372.371	+	644.965i	−0.491254	+	0.850877i
$759$	−86.9694	+	50.2118i	−0.114584	+	0.0661552i
$760$		0			0
$761$	224.925	+	129.861i	0.295565	+	0.170645i	0.640449	−	0.768001i	$-0.278748\pi$
$761$	224.925	+	129.861i	0.295565	+	0.170645i	−0.344884	+	0.938645i	$0.612082\pi$
$762$			960.718i			1.26079i
$763$	188.667	+	148.537i	0.247270	+	0.194674i
$764$	−108.434			−0.141929
$765$		0			0
$766$	−505.924	+	292.095i	−0.660475	+	0.381326i
$767$	−595.287	−	1031.07i	−0.776124	−	1.34429i
$768$	−756.863	−	436.975i	−0.985499	−	0.568978i
$769$			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
$772$	−245.586	+	425.367i	−0.318116	+	0.550993i
$773$	362.241	−	209.140i	0.468617	−	0.270556i	−0.247044	−	0.969004i	$-0.579459\pi$
$773$	362.241	−	209.140i	0.468617	−	0.270556i	0.715661	+	0.698448i	$0.246126\pi$
$774$	309.409	+	535.912i	0.399753	+	0.692392i
$775$		0			0
$776$			973.454i			1.25445i
$777$	−222.727	−	557.230i	−0.286650	−	0.717156i
$778$	−182.615			−0.234724
$779$	−644.258	+	1115.89i	−0.827032	+	1.43246i
$780$		0			0
$781$	−33.3235	−	57.7179i	−0.0426677	−	0.0739026i
$782$	−113.939	−	65.7826i	−0.145702	−	0.0841209i
$783$		−	163.127i		−	0.208336i
$784$	170.177	+	704.847i	0.217062	+	0.899040i
$785$		0			0
$786$	−154.182	+	267.050i	−0.196160	+	0.339759i
$787$	−138.243	+	79.8149i	−0.175659	+	0.101417i	−0.585251	−	0.810852i	$-0.699004\pi$
$787$	−138.243	+	79.8149i	−0.175659	+	0.101417i	0.409593	+	0.912269i	$0.365671\pi$
$788$	64.7071	+	112.076i	0.0821157	+	0.142229i
$789$	−29.9388	−	17.2852i	−0.0379452	−	0.0219077i
$790$		0			0
$791$	54.4939	−	21.7814i	0.0688924	−	0.0275366i
$792$	116.969			0.147689
$793$	−360.863	+	625.034i	−0.455061	+	0.788189i
$794$	−1185.79	+	684.614i	−1.49343	+	0.862235i
$795$		0			0
$796$	−1897.79	−	1095.69i	−2.38415	−	1.37649i
$797$		−	610.067i		−	0.765454i	−0.923861	−	0.382727i	$-0.874985\pi$
$797$		−	610.067i		−	0.765454i	0.923861	−	0.382727i	$-0.125015\pi$
$798$	100.348	−	695.235i	0.125750	−	0.871221i
$799$	−127.818			−0.159973
$800$		0			0
$801$	56.2270	−	32.4627i	0.0701961	−	0.0405277i
$802$	715.419	+	1239.14i	0.892043	+	1.54506i
$803$	−107.833	−	62.2575i	−0.134288	−	0.0775311i
$804$		−	1287.16i		−	1.60094i
$805$		0			0
$806$	−2007.39			−2.49056
$807$	334.590	−	579.527i	0.414610	−	0.718126i
$808$	−264.303	+	152.595i	−0.327108	+	0.188856i
$809$	−35.2531	−	61.0601i	−0.0435761	−	0.0754760i	0.843415	−	0.537263i	$-0.180542\pi$
$809$	−35.2531	−	61.0601i	−0.0435761	−	0.0754760i	−0.886991	+	0.461787i	$0.847208\pi$
$810$		0			0
$811$			656.361i			0.809323i	0.914467	+	0.404661i	$0.132611\pi$
$811$			656.361i			0.809323i	−0.914467	+	0.404661i	$0.867389\pi$
$812$	1363.89	+	1073.78i	1.67966	+	1.32239i
$813$	67.2735			0.0827472
$814$	247.474	−	428.638i	0.304023	−	0.526583i
$815$		0			0
$816$	24.4393	+	42.3301i	0.0299501	+	0.0518751i
$817$	869.786	+	502.171i	1.06461	+	0.614652i
$818$		−	1755.17i		−	2.14568i
$819$	−356.363	−	51.4366i	−0.435120	−	0.0628042i
$820$		0			0
$821$	466.984	−	808.840i	0.568799	−	0.985189i	−0.427886	−	0.903833i	$-0.640741\pi$
$821$	466.984	−	808.840i	0.568799	−	0.985189i	0.996685	−	0.0813564i	$-0.0259252\pi$
$822$	−1414.60	+	816.722i	−1.72093	+	0.993579i
$823$	−92.0153	−	159.375i	−0.111805	−	0.193652i	0.804693	−	0.593691i	$-0.202330\pi$
$823$	−92.0153	−	159.375i	−0.111805	−	0.193652i	−0.916498	+	0.400039i	$0.868996\pi$
$824$	−1024.81	−	591.674i	−1.24370	−	0.718051i
$825$		0			0
$826$	−622.318	−	1556.95i	−0.753411	−	1.88492i
$827$	−819.778			−0.991267			−0.495633	−	0.868532i	$-0.665064\pi$
$827$	−819.778			−0.991267			−0.495633	+	0.868532i	$0.665064\pi$
$828$	236.969	−	410.443i	0.286195	−	0.495704i
$829$	289.364	−	167.064i	0.349052	−	0.201525i	−0.315216	−	0.949020i	$-0.602077\pi$
$829$	289.364	−	167.064i	0.349052	−	0.201525i	0.664267	+	0.747495i	$0.268744\pi$
$830$		0			0
$831$	−790.817	−	456.578i	−0.951645	−	0.549432i
$832$			1177.67i			1.41547i
$833$	−26.4245	+	89.6301i	−0.0317221	+	0.107599i
$834$	−1348.23			−1.61658
$835$		0			0
$836$	333.075	−	192.301i	0.398415	−	0.230025i
$837$	88.1816	+	152.735i	0.105354	+	0.182479i
$838$	−701.864	−	405.221i	−0.837546	−	0.483558i
$839$			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
$842$	−927.774	+	1606.95i	−1.10187	+	1.90849i
$843$	−483.075	+	278.903i	−0.573043	+	0.330846i
$844$	−250.853	−	434.490i	−0.297219	−	0.514799i
$845$		0			0
$846$		−	693.607i		−	0.819866i
$847$	112.596	−	780.087i	0.132935	−	0.921000i
$848$	−1412.98			−1.66625
$849$	−406.272	+	703.684i	−0.478530	+	0.828838i
$850$		0			0
$851$	−494.949	−	857.277i	−0.581609	−	1.00738i
$852$	272.394	+	157.267i	0.319711	+	0.184585i
$853$			1094.34i			1.28293i	0.767151	+	0.641466i	$0.221674\pi$
$853$			1094.34i			1.28293i	−0.767151	+	0.641466i	$0.778326\pi$
$854$	−628.749	+	798.618i	−0.736240	+	0.935150i
$855$		0			0
$856$	−1215.14	+	2104.69i	−1.41956	+	2.45874i
$857$	716.939	−	413.925i	0.836568	−	0.482993i	−0.0195282	−	0.999809i	$-0.506216\pi$
$857$	716.939	−	413.925i	0.836568	−	0.482993i	0.856096	+	0.516817i	$0.172883\pi$
$858$	−148.485	−	257.183i	−0.173059	−	0.299747i
$859$	−344.969	−	199.168i	−0.401594	−	0.231860i	0.285577	−	0.958356i	$-0.407815\pi$
$859$	−344.969	−	199.168i	−0.401594	−	0.231860i	−0.687172	+	0.726495i	$0.741148\pi$
$860$		0			0
$861$	730.832	+	575.381i	0.848818	+	0.668271i
$862$	−114.981			−0.133388
$863$	284.934	−	493.520i	0.330167	−	0.571866i	−0.652377	−	0.757894i	$-0.726228\pi$
$863$	284.934	−	493.520i	0.330167	−	0.571866i	0.982544	+	0.186028i	$0.0595616\pi$
$864$	12.3865	−	7.15134i	0.0143362	−	0.00827701i
$865$		0			0
$866$	1324.60	+	764.761i	1.52957	+	0.883095i
$867$		−	494.264i		−	0.570085i
$868$	−1857.45	−	268.100i	−2.13992	−	0.308871i
$869$	58.5357			0.0673599
$870$		0			0
$871$	−1396.95	+	806.531i	−1.60385	+	0.925983i
$872$	−230.679	−	399.548i	−0.264541	−	0.458198i
$873$	−188.045	−	108.568i	−0.215401	−	0.124362i
$874$		−	1158.72i		−	1.32577i
$875$		0			0
$876$	587.636			0.670817
$877$	−239.182	+	414.276i	−0.272728	+	0.472378i	−0.969559	−	0.244857i	$-0.921259\pi$
$877$	−239.182	+	414.276i	−0.272728	+	0.472378i	0.696832	+	0.717235i	$0.254592\pi$
$878$	−1107.23	+	639.262i	−1.26109	+	0.728088i
$879$	−166.757	−	288.832i	−0.189712	−	0.328591i
$880$		0			0
$881$		−	371.532i		−	0.421716i	−0.977517	−	0.210858i	$-0.932374\pi$
$881$		−	371.532i		−	0.421716i	0.977517	−	0.210858i	$-0.0676258\pi$
$882$	−486.378	−	143.393i	−0.551449	−	0.162577i
$883$	−626.748			−0.709794			−0.354897	−	0.934905i	$-0.615484\pi$
$883$	−626.748			−0.709794			−0.354897	+	0.934905i	$0.615484\pi$
$884$	129.136	−	223.670i	0.146082	−	0.253021i
$885$		0			0
$886$	−1356.28	−	2349.14i	−1.53079	−	2.65140i
$887$	577.849	+	333.621i	0.651464	+	0.376123i	0.789017	−	0.614371i	$-0.210590\pi$
$887$	577.849	+	333.621i	0.651464	+	0.376123i	−0.137553	+	0.990494i	$0.543924\pi$
$888$			1152.99i			1.29842i
$889$	1045.19	−	417.765i	1.17569	−	0.469927i
$890$		0			0
$891$	−13.0454	+	22.5953i	−0.0146413	+	0.0253595i
$892$	−2054.09	+	1185.93i	−2.30279	+	1.32952i
$893$	−562.863	−	974.907i	−0.630305	−	1.09172i
$894$	1038.24	+	599.429i	1.16134	+	0.670502i
$895$		0			0
$896$	−225.924	+	1565.25i	−0.252147	+	1.74693i
$897$	−593.939			−0.662139
$898$	160.994	−	278.850i	0.179281	−	0.310524i
$899$	−922.788	+	532.772i	−1.02646	+	0.592627i
$900$		0			0
$901$	−157.696	−	91.0458i	−0.175023	−	0.101050i
$902$			767.175i			0.850526i
$903$	448.485	−	569.652i	0.496661	−	0.630844i
$904$	−112.756			−0.124730
$905$		0			0
$906$	1212.70	−	700.155i	1.33852	−	0.772798i
$907$	274.938	+	476.207i	0.303129	+	0.525035i	0.976843	−	0.213957i	$-0.0686353\pi$
$907$	274.938	+	476.207i	0.303129	+	0.525035i	−0.673714	+	0.738992i	$0.735302\pi$
$908$	−464.605	−	268.240i	−0.511680	−	0.295418i
$909$		−	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	$0.421719\pi$
$912$	−215.242	+	372.811i	−0.236011	+	0.408784i
$913$	−2.15205	+	1.24248i	−0.00235712	+	0.00136088i
$914$	−911.309	−	1578.43i	−0.997056	−	1.72695i
$915$		0			0
$916$		−	2767.24i		−	3.02100i
$917$	357.576	+	51.6116i	0.389941	+	0.0562831i
$918$	−34.1816			−0.0372349
$919$	435.838	−	754.893i	0.474252	−	0.821429i	−0.525313	−	0.850909i	$-0.676052\pi$
$919$	435.838	−	754.893i	0.474252	−	0.821429i	0.999565	+	0.0294801i	$0.00938516\pi$
$920$		0			0
$921$	30.8786	+	53.4833i	0.0335272	+	0.0580708i
$922$	2182.27	+	1259.93i	2.36689	+	1.36652i
$923$		−	394.172i		−	0.427056i
$924$	−103.045	−	257.804i	−0.111521	−	0.279009i
$925$		0			0
$926$	−375.836	+	650.967i	−0.405870	+	0.702988i
$927$	228.591	−	131.977i	0.246592	−	0.142370i
$928$	43.2066	+	74.8361i	0.0465589	+	0.0806423i
$929$	−1091.01	−	629.896i	−1.17439	−	0.678037i	−0.219684	−	0.975571i	$-0.570502\pi$
$929$	−1091.01	−	629.896i	−1.17439	−	0.678037i	−0.954711	+	0.297534i	$0.903836\pi$
$930$		0			0
$931$	−799.997	+	193.149i	−0.859288	+	0.207464i
$932$	−735.081			−0.788713
$933$	176.060	−	304.945i	0.188703	−	0.326844i
$934$	598.015	−	345.264i	0.640273	−	0.369662i
$935$		0			0
$936$	599.113	+	345.898i	0.640078	+	0.369549i
$937$			267.856i			0.285866i	0.989732	+	0.142933i	$0.0456533\pi$
$937$			267.856i			0.285866i	−0.989732	+	0.142933i	$0.954347\pi$
$938$	−2109.45	+	843.154i	−2.24888	+	0.898885i
$939$	103.151			0.109852
$940$		0			0
$941$	−257.908	+	148.903i	−0.274079	+	0.158239i	−0.630740	−	0.775994i	$-0.717248\pi$
$941$	−257.908	+	148.903i	−0.274079	+	0.158239i	0.356661	+	0.934234i	$0.383915\pi$
$942$	−124.704	−	215.994i	−0.132383	−	0.229293i
$943$	1328.79	+	767.175i	1.40910	+	0.813547i
$944$			1027.56i			1.08852i
$945$		0			0
$946$	597.980			0.632114
$947$	−880.181	+	1524.52i	−0.929441	+	1.60984i	−0.145182	+	0.989405i	$0.546377\pi$
$947$	−880.181	+	1524.52i	−0.929441	+	1.60984i	−0.784259	+	0.620434i	$0.786956\pi$
$948$	−239.242	+	138.127i	−0.252365	+	0.145703i
$949$	−368.212	−	637.761i	−0.388000	−	0.672035i
$950$		0			0
$951$		−	733.969i		−	0.771786i
$952$	111.061	−	141.067i	0.116661	−	0.148179i
$953$	−380.032			−0.398774			−0.199387	−	0.979921i	$-0.563895\pi$
$953$	−380.032			−0.398774			−0.199387	+	0.979921i	$0.563895\pi$
$954$	494.060	−	855.737i	0.517883	−	0.896999i
$955$		0			0
$956$	443.778	+	768.645i	0.464202	+	0.804022i
$957$	−136.515	−	78.8171i	−0.142649	−	0.0823586i
$958$		−	907.611i		−	0.947401i
$959$	1503.67	+	1183.83i	1.56795	+	1.23444i
$960$		0			0
$961$	95.5000	−	165.411i	0.0993757	−	0.172124i
$962$	2535.11	−	1463.65i	2.63525	−	1.52146i
$963$	−271.045	−	469.464i	−0.281459	−	0.487502i
$964$	2705.88	+	1562.24i	2.80693	+	1.62058i
$965$		0			0
$966$	−827.878	−	119.494i	−0.857016	−	0.123700i
$967$	597.302			0.617686			0.308843	−	0.951113i	$-0.400058\pi$
$967$	597.302			0.617686			0.308843	+	0.951113i	$0.400058\pi$
$968$	−757.179	+	1311.47i	−0.782210	+	1.35483i
$969$	−48.0444	+	27.7384i	−0.0495814	+	0.0286258i
$970$		0			0
$971$	1209.38	+	698.235i	1.24550	+	0.719088i	0.970208	−	0.242273i	$-0.0778930\pi$
$971$	1209.38	+	698.235i	1.24550	+	0.719088i	0.275289	+	0.961361i	$0.411226\pi$
$972$		−	123.133i		−	0.126680i
$973$	586.272	+	1466.77i	0.602541	+	1.50747i
$974$	1036.80			1.06447
$975$		0			0
$976$	539.454	−	311.454i	0.552719	−	0.319112i
$977$	885.560	+	1533.83i	0.906407	+	1.56994i	0.819017	+	0.573769i	$0.194519\pi$
$977$	885.560	+	1533.83i	0.906407	+	1.56994i	0.0873898	+	0.996174i	$0.472147\pi$
$978$	−220.766	−	127.459i	−0.225732	−	0.130326i
$979$		−	62.7391i		−	0.0640849i
$980$		0			0
$981$	102.909			0.104902
$982$	462.337	−	800.792i	0.470812	−	0.815470i
$983$	−974.408	+	562.575i	−0.991259	+	0.572304i	−0.905650	−	0.424025i	$-0.860617\pi$
$983$	−974.408	+	562.575i	−0.991259	+	0.572304i	−0.0856086	+	0.996329i	$0.527283\pi$
$984$	−893.574	−	1547.72i	−0.908104	−	1.57288i
$985$		0			0
$986$		−	206.517i		−	0.209449i
$987$	−754.590	+	301.613i	−0.764529	+	0.305585i
$988$	2274.66			2.30229
$989$	597.980	−	1035.73i	0.604631	−	1.04725i
$990$		0			0
$991$	248.292	+	430.054i	0.250547	+	0.433960i	0.963676	−	0.267072i	$-0.0860563\pi$
$991$	248.292	+	430.054i	0.250547	+	0.433960i	−0.713130	+	0.701032i	$0.752723\pi$
$992$	−80.9082	−	46.7123i	−0.0815606	−	0.0470891i
$993$			695.445i			0.700347i
$994$	79.3031	−	549.428i	0.0797818	−	0.552744i
$995$		0			0
$996$	5.86378	−	10.1564i	0.00588733	−	0.0101971i
$997$	430.272	−	248.418i	0.431567	−	0.249165i	−0.268447	−	0.963294i	$-0.586510\pi$
$997$	430.272	−	248.418i	0.431567	−	0.249165i	0.700014	+	0.714129i	$0.253177\pi$
$998$	253.275	+	438.686i	0.253783	+	0.439565i
$999$	−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.o.k.376.2	yes	4
5.2	odd	4		525.3.s.g.124.4		8
5.3	odd	4		525.3.s.g.124.1		8
5.4	even	2		525.3.o.j.376.1	✓	4
7.3	odd	6	inner	525.3.o.k.451.2	yes	4
35.3	even	12		525.3.s.g.199.4		8
35.17	even	12		525.3.s.g.199.1		8
35.24	odd	6		525.3.o.j.451.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.3.o.j.376.1	✓	4	5.4	even	2
525.3.o.j.451.1	yes	4	35.24	odd	6
525.3.o.k.376.2	yes	4	1.1	even	1	trivial
525.3.o.k.451.2	yes	4	7.3	odd	6	inner
525.3.s.g.124.1		8	5.3	odd	4
525.3.s.g.124.4		8	5.2	odd	4
525.3.s.g.199.1		8	35.17	even	12
525.3.s.g.199.4		8	35.3	even	12

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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72474 - 2.98735i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-3.94949 - 6.84072i) q^{4} +5.97469i q^{6} +(6.50000 - 2.59808i) q^{7} -13.4495 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.44949 - 2.51059i) q^{11} +(11.8485 + 6.84072i) q^{12} -17.1455i q^{13} +(3.44949 - 23.8988i) q^{14} +(-7.39898 + 12.8154i) q^{16} +(-1.65153 + 0.953512i) q^{17} +(-5.17423 - 8.96204i) q^{18} +(-14.5454 - 8.39780i) q^{19} +(-7.50000 + 9.52628i) q^{21} -10.0000 q^{22} +(-10.0000 + 17.3205i) q^{23} +(20.1742 - 11.6476i) q^{24} +(-51.2196 - 29.5717i) q^{26} +5.19615i q^{27} +(-43.4444 - 34.2036i) q^{28} -31.3939 q^{29} +(29.3939 - 16.9706i) q^{31} +(-1.37628 - 2.38378i) q^{32} +(4.34847 + 2.51059i) q^{33} +6.57826i q^{34} -23.6969 q^{36} +(-24.7474 + 42.8638i) q^{37} +(-50.1742 + 28.9681i) q^{38} +(14.8485 + 25.7183i) q^{39} -76.7175i q^{41} +(15.5227 + 38.8355i) q^{42} -59.7980 q^{43} +(-11.4495 + 19.8311i) q^{44} +(34.4949 + 59.7469i) q^{46} +(58.0454 + 33.5125i) q^{47} -25.6308i q^{48} +(35.5000 - 33.7750i) q^{49} +(1.65153 - 2.86054i) q^{51} +(-117.288 + 67.7161i) q^{52} +(47.7423 + 82.6922i) q^{53} +(15.5227 + 8.96204i) q^{54} +(-87.4217 + 34.9428i) q^{56} +29.0908 q^{57} +(-54.1464 + 93.7844i) q^{58} +(60.1362 - 34.7197i) q^{59} +(-36.4546 - 21.0471i) q^{61} -117.080i q^{62} +(3.00000 - 20.7846i) q^{63} -68.6867 q^{64} +(15.0000 - 8.66025i) q^{66} +(-47.0403 - 81.4762i) q^{67} +(13.0454 + 7.53177i) q^{68} -34.6410i q^{69} +22.9898 q^{71} +(-20.1742 + 34.9428i) q^{72} +(37.1969 - 21.4757i) q^{73} +(85.3661 + 147.858i) q^{74} +132.668i q^{76} +(-15.9444 - 12.5529i) q^{77} +102.439 q^{78} +(-10.0959 + 17.4866i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-229.182 - 132.318i) q^{82} -0.857187i q^{83} +(94.7878 + 13.6814i) q^{84} +(-103.136 + 178.637i) q^{86} +(47.0908 - 27.1879i) q^{87} +(19.4949 + 33.7662i) q^{88} +(18.7423 + 10.8209i) q^{89} +(-44.5454 - 111.446i) q^{91} +157.980 q^{92} +(-29.3939 + 50.9117i) q^{93} +(200.227 - 115.601i) q^{94} +(4.12883 + 2.38378i) q^{96} -72.3785i q^{97} +(-39.6691 - 164.304i) q^{98} -8.69694 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 26 q^{7} - 44 q^{8} + 6 q^{9} + 4 q^{11} + 18 q^{12} + 4 q^{14} - 10 q^{16} - 36 q^{17} - 6 q^{18} + 30 q^{19} - 30 q^{21} - 40 q^{22} - 40 q^{23} + 66 q^{24} - 102 q^{26}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 26 * q^7 - 44 * q^8 + 6 * q^9 + 4 * q^11 + 18 * q^12 + 4 * q^14 - 10 * q^16 - 36 * q^17 - 6 * q^18 + 30 * q^19 - 30 * q^21 - 40 * q^22 - 40 * q^23 + 66 * q^24 - 102 * q^26 - 66 * q^28 - 8 * q^29 - 30 * q^32 - 12 * q^33 - 36 * q^36 - 50 * q^37 - 186 * q^38 + 30 * q^39 + 18 * q^42 - 200 * q^43 - 36 * q^44 + 40 * q^46 + 144 * q^47 + 142 * q^49 + 36 * q^51 - 234 * q^52 + 44 * q^53 + 18 * q^54 - 286 * q^56 - 60 * q^57 - 148 * q^58 - 24 * q^59 - 234 * q^61 + 12 * q^63 - 20 * q^64 + 60 * q^66 - 2 * q^67 - 36 * q^68 - 104 * q^71 - 66 * q^72 + 90 * q^73 + 170 * q^74 + 44 * q^77 + 204 * q^78 + 38 * q^79 - 18 * q^81 - 564 * q^82 + 144 * q^84 - 148 * q^86 + 12 * q^87 - 20 * q^88 - 72 * q^89 - 90 * q^91 + 240 * q^92 + 360 * q^94 + 90 * q^96 - 46 * q^98 + 24 * q^99

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