LMFDB - Embedded newform 525.3.s.g.124.4

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			124.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	525.124
Dual form			525.3.s.g.199.4

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.98735	+	1.72474i	1.49367	+	0.862372i	0.999974	−	0.00726029i	$-0.00231104\pi$
$2$	2.98735	+	1.72474i	1.49367	+	0.862372i	0.493699	+	0.869633i	$0.335644\pi$
$3$	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	0.792588	−	0.609758i	$-0.208733\pi$
$11$	−1.44949	−	2.51059i	−0.131772	−	0.228235i	−0.924360	+	0.381522i	$0.875400\pi$
$12$	−6.84072	+	11.8485i	−0.570060	+	0.987372i
$13$	−17.1455			−1.31889			−0.659444	−	0.751754i	$-0.729208\pi$
$13$	−17.1455			−1.31889			−0.659444	+	0.751754i	$0.729208\pi$
$14$	−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	$-0.184530\pi$
$17$	−0.953512	−	1.65153i	−0.0560889	−	0.0971489i	−0.892707	+	0.450638i	$0.851196\pi$
$18$	−8.96204	+	5.17423i	−0.497891	+	0.287457i
$19$	14.5454	+	8.39780i	0.765548	+	0.441989i	0.831284	−	0.555848i	$-0.187606\pi$
$19$	14.5454	+	8.39780i	0.765548	+	0.441989i	−0.0657363	+	0.997837i	$0.520940\pi$
$20$		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	$-0.190159\pi$
$23$	17.3205	+	10.0000i	0.753066	+	0.434783i	−0.0737349	+	0.997278i	$0.523492\pi$
$24$	−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	0.0556715	−	0.998449i	$-0.482270\pi$
$31$	29.3939	−	16.9706i	0.948190	−	0.547438i	0.892518	+	0.451012i	$0.148937\pi$
$32$	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	$-0.566546\pi$
$37$	−42.8638	−	24.7474i	−1.15848	−	0.668850i	−0.950940	+	0.309376i	$0.899880\pi$
$38$	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	$-0.614878\pi$
$41$		−	76.7175i		−	1.87116i	0.353117	−	0.935579i	$-0.385122\pi$
$42$	−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	0.250681	+	0.968070i	$0.419346\pi$
$47$	−33.5125	+	58.0454i	−0.713033	+	1.23501i	−0.963713	+	0.266939i	$0.913988\pi$
$48$	−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	0.562997	−	0.826459i	$-0.309648\pi$
$53$	82.6922	−	47.7423i	1.56023	−	0.900799i	0.997233	−	0.0743398i	$-0.0236849\pi$
$54$	−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	−0.913889	−	0.405964i	$-0.866936\pi$
$59$	−60.1362	+	34.7197i	−1.01926	+	0.588469i	−0.105369	+	0.994433i	$0.533602\pi$
$60$		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	$0.778799\pi$
$62$	117.080			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	$-0.418915\pi$
$67$	81.4762	−	47.0403i	1.21606	−	0.702094i	0.964073	+	0.265636i	$0.0855819\pi$
$68$	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	$-0.261716\pi$
$73$	−21.4757	−	37.1969i	−0.294187	−	0.509547i	−0.974795	+	0.223100i	$0.928382\pi$
$74$	−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	−0.795026	−	0.606575i	$-0.792543\pi$
$79$	10.0959	−	17.4866i	0.127796	−	0.221350i	0.922823	+	0.385225i	$0.125876\pi$
$80$		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	$-0.501644\pi$
$83$	−0.857187			−0.0103276			−0.00516378	+	0.999987i	$0.501644\pi$
$84$	−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	0.390997	−	0.920392i	$-0.372130\pi$
$89$	−18.7423	−	10.8209i	−0.210588	−	0.121583i	−0.601585	+	0.798809i	$0.705464\pi$
$90$		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	$-0.378300\pi$
$97$	72.3785			0.746170			0.373085	+	0.927797i	$0.378300\pi$
$98$	−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	−0.399550	−	0.916711i	$-0.630834\pi$
$101$	19.6515	−	11.3458i	0.194570	−	0.112335i	0.594120	+	0.804376i	$0.297500\pi$
$102$	9.86739	−	5.69694i	0.0967391	−	0.0558523i
$103$	43.9923	−	76.1969i	0.427110	−	0.739776i	−0.569505	−	0.821988i	$-0.692865\pi$
$103$	43.9923	−	76.1969i	0.427110	−	0.739776i	0.996615	+	0.0822118i	$0.0261984\pi$
$104$		−	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	$-0.0133035\pi$
$107$	156.488	+	90.3485i	1.46251	+	0.844378i	0.463379	+	0.886160i	$0.346637\pi$
$108$	−20.5222	−	35.5454i	−0.190020	−	0.329124i
$109$	−17.1515	−	29.7073i	−0.157353	−	0.272544i	0.776560	−	0.630043i	$-0.216963\pi$
$109$	−17.1515	−	29.7073i	−0.157353	−	0.272544i	−0.933914	+	0.357499i	$0.883630\pi$
$110$		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	0.660802	−	0.750561i	$-0.270216\pi$
$131$	44.6969	+	25.8058i	0.341198	+	0.196991i	−0.319604	+	0.947551i	$0.603550\pi$
$132$	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	−0.830871	+	0.556466i	$0.812157\pi$
$137$	−236.766	+	136.697i	−1.72822	+	0.997788i	−0.897349	+	0.441322i	$0.854510\pi$
$138$	−59.7469	+	103.485i	−0.432949	+	0.749889i
$139$		−	225.656i		−	1.62343i	−0.584057	−	0.811713i	$-0.698535\pi$
$139$		−	225.656i		−	1.62343i	0.584057	−	0.811713i	$-0.301465\pi$
$140$		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	0.303608	+	0.952797i	$0.401809\pi$
$149$	−100.328	+	173.773i	−0.673343	+	1.16626i	−0.976950	+	0.213467i	$0.931525\pi$
$150$		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	$-0.449457\pi$
$152$	−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	$-0.209109\pi$
$157$	−20.8721	−	36.1515i	−0.132943	−	0.230265i	−0.924810	+	0.380430i	$0.875776\pi$
$158$	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	$-0.291554\pi$
$163$	36.9501	+	21.3332i	0.226688	+	0.130878i	−0.382355	+	0.924015i	$0.624887\pi$
$164$	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	$-0.660723\pi$
$167$	−161.570			−0.967487			−0.483743	+	0.875210i	$0.660723\pi$
$168$	−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	$-0.701124\pi$
$173$	69.8070	−	120.909i	0.403508	−	0.698897i	0.994147	+	0.108039i	$0.0344573\pi$
$174$			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	0.741652	−	0.670784i	$-0.234042\pi$
$179$	−37.6061	−	65.1357i	−0.210090	−	0.363887i	−0.951743	+	0.306898i	$0.900709\pi$
$180$		0			0
$181$		−	42.5837i		−	0.235269i	−0.993057	−	0.117635i	$-0.962469\pi$
$181$		−	42.5837i		−	0.235269i	0.993057	−	0.117635i	$-0.0375311\pi$
$182$	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	−0.847498	−	0.530799i	$-0.821892\pi$
$191$	6.86378	−	11.8884i	0.0359360	−	0.0622430i	0.883434	+	0.468556i	$0.155225\pi$
$192$	59.4845	+	103.030i	0.309815	+	0.536615i
$193$	−53.8509	+	31.0908i	−0.279020	+	0.161092i	−0.632980	−	0.774168i	$-0.718168\pi$
$193$	−53.8509	+	31.0908i	−0.279020	+	0.161092i	0.353960	+	0.935261i	$0.384835\pi$
$194$	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	−0.962173	−	0.272438i	$-0.912170\pi$
$199$	−240.257	+	138.713i	−1.20732	+	0.697048i	−0.245149	+	0.969485i	$0.578837\pi$
$200$		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	$-0.735107\pi$
$223$	−300.274			−1.34652			−0.673260	+	0.739406i	$0.735107\pi$
$224$	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	$-0.118869\pi$
$227$	33.9588	+	58.8184i	0.149598	+	0.259112i	−0.781481	+	0.623929i	$0.785535\pi$
$228$	−199.002	+	114.894i	−0.872816	+	0.503921i
$229$	−303.393	−	175.164i	−1.32486	−	0.764909i	−0.340362	−	0.940295i	$-0.610550\pi$
$229$	−303.393	−	175.164i	−1.32486	−	0.764909i	−0.984500	+	0.175385i	$0.943883\pi$
$230$		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	$-0.397330\pi$
$233$	−80.5925	−	46.5301i	−0.345891	−	0.199700i	−0.662874	+	0.748731i	$0.730663\pi$
$234$	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	−0.996420	−	0.0845448i	$-0.973056\pi$
$241$	−342.560	+	197.777i	−1.42141	+	0.820652i	−0.424992	+	0.905197i	$0.639723\pi$
$242$	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	$-0.927454\pi$
$251$		−	113.423i		−	0.451884i	0.974141	−	0.225942i	$-0.0725459\pi$
$252$	−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	$-0.952935\pi$
$257$	−94.3093	+	163.348i	−0.366962	+	0.635597i	0.622127	+	0.782917i	$0.286269\pi$
$258$	−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	$-0.654585\pi$
$263$	17.2852	−	9.97959i	0.0657230	−	0.0379452i	0.532501	+	0.846429i	$0.321252\pi$
$264$	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	0.273958	−	0.961742i	$-0.411667\pi$
$269$	334.590	−	193.176i	1.24383	−	0.718126i	0.969872	+	0.243616i	$0.0783336\pi$
$270$		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	$0.689497\pi$
$272$	28.2201			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	−0.670548	+	0.741866i	$0.733941\pi$
$277$	−456.578	+	263.606i	−1.64830	+	0.951645i	−0.977749	+	0.209779i	$0.932726\pi$
$278$	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	−0.898950	−	0.438051i	$-0.855669\pi$
$283$	−234.561	−	406.272i	−0.828838	−	1.43559i	0.0701121	−	0.997539i	$-0.477664\pi$
$284$	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	$-0.393426\pi$
$293$	192.555			0.657183			0.328591	+	0.944472i	$0.393426\pi$
$294$	−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	$-0.481505\pi$
$307$	35.6555			0.116142			0.0580708	+	0.998312i	$0.481505\pi$
$308$	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	−0.755594	−	0.655040i	$-0.772652\pi$
$311$	−176.060	+	101.648i	−0.566110	+	0.326844i	0.189484	+	0.981884i	$0.439318\pi$
$312$	345.898	−	199.704i	1.10865	−	0.640078i
$313$	−29.7771	+	51.5755i	−0.0951346	+	0.164778i	−0.909665	−	0.415343i	$-0.863661\pi$
$313$	−29.7771	+	51.5755i	−0.0951346	+	0.164778i	0.814530	+	0.580121i	$0.196995\pi$
$314$		−	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	$-0.566348\pi$
$317$	−366.984	−	211.879i	−1.15768	−	0.668387i	−0.950747	+	0.309969i	$0.899681\pi$
$318$	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	−0.385291	−	0.922795i	$-0.625899\pi$
$331$	200.758	−	347.722i	0.606519	−	1.05052i	0.991810	−	0.127726i	$-0.0407678\pi$
$332$	−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	$-0.820271\pi$
$347$	−278.903	+	161.025i	−0.803756	+	0.464049i	0.0410266	+	0.999158i	$0.486937\pi$
$348$	−214.757	+	371.969i	−0.617117	+	1.06888i
$349$			45.0687i			0.129137i	0.997913	+	0.0645683i	$0.0205670\pi$
$349$			45.0687i			0.129137i	−0.997913	+	0.0645683i	$0.979433\pi$
$350$		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	0.795337	+	0.606167i	$0.207294\pi$
$353$	325.687	+	564.106i	0.922625	+	1.59803i	0.127287	+	0.991866i	$0.459373\pi$
$354$	−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	−0.870832	−	0.491581i	$-0.836419\pi$
$359$	−3.48011	+	6.02772i	−0.00969389	+	0.0167903i	0.861138	+	0.508372i	$0.169752\pi$
$360$		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	0.970612	+	0.240651i	$0.0773611\pi$
$367$	254.594	+	440.969i	0.693716	+	1.20155i	−0.276896	+	0.960900i	$0.589306\pi$
$368$	−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	$-0.410121\pi$
$373$	−154.344	−	89.1107i	−0.413792	−	0.238903i	−0.692418	+	0.721497i	$0.743454\pi$
$374$	−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	$-0.904295\pi$
$383$	−84.6778	+	146.666i	−0.221091	+	0.382941i	0.734049	+	0.679097i	$0.237628\pi$
$384$			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	0.898041	−	0.439912i	$-0.144990\pi$
$389$	26.4699	+	45.8472i	0.0680460	+	0.117859i	−0.829995	+	0.557771i	$0.811657\pi$
$390$		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	$-0.666696\pi$
$397$	198.468	−	343.757i	0.499920	−	0.865887i	1.00000		9.22678e-5i	$2.93697e-5\pi$
$398$	−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	0.482597	+	0.875842i	$0.339694\pi$
$401$	−207.398	+	359.225i	−0.517203	+	0.895822i	−0.999800	+	0.0199797i	$0.993640\pi$
$402$	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	−0.930190	−	0.367078i	$-0.880358\pi$
$409$	−440.651	+	254.410i	−1.07739	+	0.622029i	−0.147196	+	0.989107i	$0.547025\pi$
$410$		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	$0.0904554\pi$
$419$			234.946i			0.560729i	−0.959894	+	0.280365i	$0.909545\pi$
$420$		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	0.846043	−	0.533114i	$-0.178978\pi$
$431$	−16.6663	−	28.8669i	−0.0386690	−	0.0669766i	−0.884712	+	0.466138i	$0.845645\pi$
$432$	38.4462	−	66.5908i	0.0889959	−	0.154145i
$433$	443.405			1.02403			0.512015	−	0.858976i	$-0.328899\pi$
$433$	443.405			1.02403			0.512015	+	0.858976i	$0.328899\pi$
$434$	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	0.818851	−	0.574006i	$-0.194611\pi$
$439$	320.985	+	185.321i	0.731172	+	0.422143i	−0.0876785	+	0.996149i	$0.527945\pi$
$440$		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	−0.998997	−	0.0447724i	$-0.985744\pi$
$443$	−681.011	−	393.182i	−1.53727	−	0.887543i	−0.538273	−	0.842771i	$-0.680923\pi$
$444$	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	$-0.137132\pi$
$457$	457.585	+	264.187i	1.00128	+	0.578089i	0.0926531	+	0.995698i	$0.470465\pi$
$458$	−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	$0.291119\pi$
$461$			730.505i			1.58461i	−0.610126	+	0.792305i	$0.708881\pi$
$462$	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	$-0.902090\pi$
$467$	−100.091	+	173.363i	−0.214328	+	0.371228i	0.738736	+	0.673995i	$0.235423\pi$
$468$	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	−0.718626	−	0.695397i	$-0.755229\pi$
$479$	−227.864	+	131.557i	−0.475707	+	0.274650i	0.242919	+	0.970047i	$0.421895\pi$
$480$		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	$-0.766523\pi$
$487$	−260.297	+	150.283i	−0.534491	+	0.308589i	0.208352	+	0.978054i	$0.433190\pi$
$488$	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	−0.783028	−	0.621987i	$-0.786326\pi$
$499$	73.4240	−	127.174i	0.147142	−	0.254858i	0.930170	+	0.367129i	$0.119659\pi$
$500$		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	$-0.532630\pi$
$503$	−102.944			−0.204660			−0.102330	+	0.994751i	$0.532630\pi$
$504$	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	0.999435	+	0.0335965i	$0.0106961\pi$
$509$	777.879	+	449.108i	1.52825	+	0.882335i	0.528813	+	0.848738i	$0.322637\pi$
$510$		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	−0.0462075	−	0.998932i	$-0.514714\pi$
$521$	414.606	−	239.373i	0.795789	−	0.459449i	0.841997	+	0.539483i	$0.181380\pi$
$522$	−281.353	+	162.439i	−0.538991	+	0.311186i
$523$	−313.991	+	543.848i	−0.600365	+	1.03986i	0.392401	+	0.919794i	$0.371645\pi$
$523$	−313.991	+	543.848i	−0.600365	+	1.03986i	−0.992766	+	0.120068i	$0.961689\pi$
$524$			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	−0.903806	−	0.427942i	$-0.859239\pi$
$541$	−43.9801	+	76.1758i	−0.0812941	+	0.140806i	0.822512	+	0.568748i	$0.192572\pi$
$542$	−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	$-0.883247\pi$
$557$	−606.935	+	350.414i	−1.08965	+	0.629110i	−0.156167	+	0.987731i	$0.549914\pi$
$558$	−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	$-0.304364\pi$
$563$	−236.023	−	408.804i	−0.419224	−	0.726116i	−0.995862	+	0.0908833i	$0.971031\pi$
$564$	−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	−0.934898	−	0.354917i	$-0.884509\pi$
$569$	−91.0862	+	157.766i	−0.160081	+	0.277269i	0.774816	+	0.632186i	$0.217842\pi$
$570$		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	$-0.356843\pi$
$572$	−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	−0.983101	−	0.183066i	$-0.941398\pi$
$577$	−375.102	−	649.696i	−0.650090	−	1.12599i	0.333010	−	0.942923i	$-0.391936\pi$
$578$	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	$-0.188014\pi$
$587$	975.092			1.66114			0.830572	+	0.556911i	$0.188014\pi$
$588$	−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	$-0.778757\pi$
$593$	101.177	−	175.243i	0.170618	−	0.295519i	0.938636	+	0.344909i	$0.112090\pi$
$594$			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	−0.981964	−	0.189066i	$-0.939454\pi$
$599$	−392.176	−	679.269i	−0.654718	−	1.13400i	0.327247	−	0.944939i	$-0.393879\pi$
$600$		0			0
$601$			252.476i			0.420094i	0.977691	+	0.210047i	$0.0673617\pi$
$601$			252.476i			0.420094i	−0.977691	+	0.210047i	$0.932638\pi$
$602$	−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	$-0.777658\pi$
$607$	105.629	−	182.954i	0.174017	−	0.301407i	0.939821	+	0.341668i	$0.110992\pi$
$608$	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	$-0.485988\pi$
$613$	570.824	−	329.565i	0.931197	−	0.537627i	0.887190	+	0.461404i	$0.152654\pi$
$614$	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	−0.870629	−	0.491940i	$-0.836288\pi$
$619$	−544.665	+	314.463i	−0.879912	+	0.508017i	−0.00928235	+	0.999957i	$0.502955\pi$
$620$		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	0.813004	−	0.582257i	$-0.197830\pi$
$641$	−62.6561	−	108.524i	−0.0977475	−	0.169304i	−0.910752	+	0.412954i	$0.864497\pi$
$642$	−539.804	+	934.968i	−0.840817	+	1.45634i
$643$	895.765			1.39310			0.696552	−	0.717507i	$-0.254717\pi$
$643$	895.765			1.39310			0.696552	+	0.717507i	$0.254717\pi$
$644$	−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	0.952757	+	0.303732i	$0.0982329\pi$
$647$	478.404	+	828.620i	0.739419	+	1.28071i	−0.213339	+	0.976978i	$0.568434\pi$
$648$	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	0.990378	+	0.138387i	$0.0441917\pi$
$653$	1048.34	+	605.257i	1.60541	+	0.926886i	0.615036	+	0.788499i	$0.289142\pi$
$654$	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	−0.239407	−	0.970919i	$-0.576953\pi$
$661$	318.424	−	183.842i	0.481731	−	0.278127i	0.721137	+	0.692792i	$0.243620\pi$
$662$	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	−0.116342	−	0.993209i	$-0.537117\pi$
$677$	542.936	−	940.393i	0.801974	−	1.38906i	0.918315	−	0.395850i	$-0.129550\pi$
$678$	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	$-0.675906\pi$
$683$	−34.3344	+	19.8230i	−0.0502699	+	0.0290234i	0.474654	+	0.880172i	$0.342573\pi$
$684$	−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	0.471983	−	0.881608i	$-0.343538\pi$
$691$	−38.3648	−	22.1499i	−0.0555207	−	0.0320549i	−0.527503	+	0.849553i	$0.676872\pi$
$692$	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	−0.980920	−	0.194414i	$-0.937720\pi$
$709$	−228.364	+	395.538i	−0.322093	+	0.557881i	0.658827	+	0.752295i	$0.271053\pi$
$710$		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	0.539801	−	0.841793i	$-0.318499\pi$
$719$	58.0148	+	33.4949i	0.0806882	+	0.0465853i	−0.459113	+	0.888378i	$0.651833\pi$
$720$		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	$-0.403572\pi$
$727$	433.766			0.596651			0.298326	+	0.954464i	$0.403572\pi$
$728$	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	$-0.898201\pi$
$733$	−148.344	+	256.939i	−0.202379	+	0.350531i	0.746915	+	0.664919i	$0.231534\pi$
$734$			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	0.937525	+	0.347917i	$0.113111\pi$
$739$	569.080	+	985.676i	0.770068	+	1.33380i	−0.167457	+	0.985879i	$0.553556\pi$
$740$		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	−0.343342	−	0.939210i	$-0.611559\pi$
$751$	481.923	−	834.716i	0.641709	−	1.11147i	0.985051	−	0.172262i	$-0.0551076\pi$
$752$	−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	0.640449	−	0.768001i	$-0.278748\pi$
$761$	224.925	+	129.861i	0.295565	+	0.170645i	−0.344884	+	0.938645i	$0.612082\pi$
$762$	−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	$-0.975309\pi$
$769$		−	119.179i		−	0.154980i	0.996993	−	0.0774898i	$-0.0246905\pi$
$770$		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	$-0.253874\pi$
$773$	−209.140	−	362.241i	−0.270556	−	0.468617i	−0.969004	+	0.247044i	$0.920541\pi$
$774$	−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	$-0.199004\pi$
$787$	−79.8149	−	138.243i	−0.101417	−	0.175659i	−0.912269	+	0.409593i	$0.865671\pi$
$788$	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	$-0.374985\pi$
$797$	610.067			0.765454			0.382727	+	0.923861i	$0.374985\pi$
$798$	−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	0.886991	−	0.461787i	$-0.152792\pi$
$809$	35.2531	+	61.0601i	0.0435761	+	0.0754760i	−0.843415	+	0.537263i	$0.819458\pi$
$810$		0			0
$811$			656.361i			0.809323i	0.914467	+	0.404661i	$0.132611\pi$
$811$			656.361i			0.809323i	−0.914467	+	0.404661i	$0.867389\pi$
$812$	−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	−0.427886	−	0.903833i	$-0.640741\pi$
$821$	466.984	−	808.840i	0.568799	−	0.985189i	0.996685	−	0.0813564i	$-0.0259252\pi$
$822$	−816.722	−	1414.60i	−0.993579	−	1.72093i
$823$	−159.375	+	92.0153i	−0.193652	+	0.111805i	−0.593691	−	0.804693i	$-0.702330\pi$
$823$	−159.375	+	92.0153i	−0.193652	+	0.111805i	0.400039	+	0.916498i	$0.368996\pi$
$824$	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	−0.664267	−	0.747495i	$-0.731256\pi$
$829$	−289.364	+	167.064i	−0.349052	+	0.201525i	0.315216	+	0.949020i	$0.397923\pi$
$830$		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	$-0.750192\pi$
$839$		−	1185.81i		−	1.41336i	0.707534	−	0.706679i	$-0.249808\pi$
$840$		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	$-0.278326\pi$
$853$	1094.34			1.28293			0.641466	+	0.767151i	$0.278326\pi$
$854$	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	$-0.00621641\pi$
$857$	413.925	+	716.939i	0.482993	+	0.836568i	−0.516817	+	0.856096i	$0.672883\pi$
$858$	−257.183	+	148.485i	−0.299747	+	0.173059i
$859$	344.969	+	199.168i	0.401594	+	0.231860i	0.687172	−	0.726495i	$-0.258852\pi$
$859$	344.969	+	199.168i	0.401594	+	0.231860i	−0.285577	+	0.958356i	$0.592185\pi$
$860$		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	$-0.440438\pi$
$863$	−493.520	−	284.934i	−0.571866	−	0.330167i	−0.757894	+	0.652377i	$0.773772\pi$
$864$	−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	$-0.421259\pi$
$877$	−414.276	−	239.182i	−0.472378	−	0.272728i	−0.717235	+	0.696832i	$0.754592\pi$
$878$	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	$-0.932374\pi$
$881$		−	371.532i		−	0.421716i	0.977517	−	0.210858i	$-0.0676258\pi$
$882$	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	$-0.956076\pi$
$887$	−333.621	+	577.849i	−0.376123	+	0.651464i	0.614371	+	0.789017i	$0.289410\pi$
$888$	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	$-0.764698\pi$
$907$	−476.207	+	274.938i	−0.525035	+	0.303129i	0.213957	+	0.976843i	$0.431365\pi$
$908$	−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	−0.999565	−	0.0294801i	$-0.990615\pi$
$919$	−435.838	+	754.893i	−0.474252	+	0.821429i	0.525313	+	0.850909i	$0.323948\pi$
$920$		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	0.954711	−	0.297534i	$-0.0961642\pi$
$929$	1091.01	+	629.896i	1.17439	+	0.678037i	0.219684	+	0.975571i	$0.429498\pi$
$930$		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	$-0.545653\pi$
$937$	−267.856			−0.285866			−0.142933	+	0.989732i	$0.545653\pi$
$938$	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	−0.630740	−	0.775994i	$-0.717248\pi$
$941$	−257.908	+	148.903i	−0.274079	+	0.158239i	0.356661	+	0.934234i	$0.383915\pi$
$942$	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	−0.989405	−	0.145182i	$-0.953623\pi$
$947$	−1524.52	−	880.181i	−1.60984	−	0.929441i	−0.620434	−	0.784259i	$-0.713044\pi$
$948$	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	0.970208	−	0.242273i	$-0.0778930\pi$
$971$	1209.38	+	698.235i	1.24550	+	0.719088i	0.275289	+	0.961361i	$0.411226\pi$
$972$	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	−0.573769	+	0.819017i	$0.694519\pi$
$977$	−1533.83	+	885.560i	−1.56994	+	0.906407i	−0.996174	+	0.0873898i	$0.972147\pi$
$978$	−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	0.996329	+	0.0856086i	$0.0272835\pi$
$983$	562.575	+	974.408i	0.572304	+	0.991259i	−0.424025	+	0.905650i	$0.639383\pi$
$984$	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	0.963676	−	0.267072i	$-0.0860563\pi$
$991$	248.292	+	430.054i	0.250547	+	0.433960i	−0.713130	+	0.701032i	$0.752723\pi$
$992$	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	$-0.0865105\pi$
$997$	248.418	+	430.272i	0.249165	+	0.431567i	−0.714129	+	0.700014i	$0.753177\pi$
$998$	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.124.4		8
5.2	odd	4		525.3.o.j.376.1	✓	4
5.3	odd	4		525.3.o.k.376.2	yes	4
5.4	even	2	inner	525.3.s.g.124.1		8
7.3	odd	6	inner	525.3.s.g.199.1		8
35.3	even	12		525.3.o.k.451.2	yes	4
35.17	even	12		525.3.o.j.451.1	yes	4
35.24	odd	6	inner	525.3.s.g.199.4		8

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