LMFDB - Embedded newform 99.4.f.d.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 21 x^{10} - 26 x^{9} + 281 x^{8} + 486 x^{7} + 3506 x^{6} + 15102 x^{5} + \cdots + 1936 $ x^12 - 3x^11 + 21x^10 - 26x^9 + 281x^8 + 486x^7 + 3506x^6 + 15102x^5 + 46669x^4 + 41850x^3 + 16292x^2 + 616*x + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.2
Root			$0.0936861 - 0.288336i$ of defining polynomial
Character	$\chi$	$=$	99.82
Dual form			99.4.f.d.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.402703 - 1.23939i) q^{2} +(5.09821 - 3.70407i) q^{4} +(2.50364 - 7.70540i) q^{5} +(-0.439746 + 0.319494i) q^{7} +(-15.0782 - 10.9549i) q^{8} +O(q^{10})$	\(q+(-0.402703 - 1.23939i) q^{2} +(5.09821 - 3.70407i) q^{4} +(2.50364 - 7.70540i) q^{5} +(-0.439746 + 0.319494i) q^{7} +(-15.0782 - 10.9549i) q^{8} -10.5582 q^{10} +(25.3612 + 26.2261i) q^{11} +(-21.5234 - 66.2421i) q^{13} +(0.573065 + 0.416356i) q^{14} +(8.07330 - 24.8471i) q^{16} +(13.1571 - 40.4934i) q^{17} +(-61.0435 - 44.3507i) q^{19} +(-15.7773 - 48.5574i) q^{20} +(22.2914 - 41.9939i) q^{22} -37.9924 q^{23} +(48.0221 + 34.8901i) q^{25} +(-73.4324 + 53.3518i) q^{26} +(-1.05849 + 3.25769i) q^{28} +(97.1697 - 70.5979i) q^{29} +(85.6557 + 263.621i) q^{31} -183.148 q^{32} -55.4856 q^{34} +(1.36087 + 4.18831i) q^{35} +(12.0481 - 8.75344i) q^{37} +(-30.3855 + 93.5170i) q^{38} +(-122.163 + 88.7563i) q^{40} +(230.473 + 167.448i) q^{41} +312.130 q^{43} +(226.440 + 39.7664i) q^{44} +(15.2997 + 47.0875i) q^{46} +(272.897 + 198.272i) q^{47} +(-105.902 + 325.931i) q^{49} +(23.9039 - 73.5686i) q^{50} +(-355.096 - 257.992i) q^{52} +(-52.4474 - 161.417i) q^{53} +(265.578 - 129.758i) q^{55} +10.1306 q^{56} +(-126.629 - 92.0014i) q^{58} +(-648.765 + 471.356i) q^{59} +(-119.521 + 367.847i) q^{61} +(292.236 - 212.322i) q^{62} +(9.16772 + 28.2153i) q^{64} -564.309 q^{65} +981.580 q^{67} +(-82.9126 - 255.179i) q^{68} +(4.64294 - 3.37329i) q^{70} +(165.441 - 509.176i) q^{71} +(-369.585 + 268.520i) q^{73} +(-15.7007 - 11.4073i) q^{74} -475.490 q^{76} +(-19.5316 - 3.43004i) q^{77} +(-191.437 - 589.183i) q^{79} +(-171.244 - 124.416i) q^{80} +(114.722 - 353.079i) q^{82} +(-61.3212 + 188.727i) q^{83} +(-279.077 - 202.762i) q^{85} +(-125.696 - 386.851i) q^{86} +(-95.0962 - 673.273i) q^{88} +1317.67 q^{89} +(30.6287 + 22.2531i) q^{91} +(-193.693 + 140.726i) q^{92} +(135.840 - 418.072i) q^{94} +(-494.571 + 359.327i) q^{95} +(-287.328 - 884.304i) q^{97} +446.604 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} - 28 q^{5} + 12 q^{7} + 112 q^{8}+O(q^{10}) $ 12 * q - 16 * q^4 - 28 * q^5 + 12 * q^7 + 112 * q^8	$ 12 q - 16 q^{4} - 28 q^{5} + 12 q^{7} + 112 q^{8} + 100 q^{10} + 54 q^{11} - 18 q^{13} - 156 q^{14} + 308 q^{16} + 80 q^{17} - 280 q^{19} + 15 q^{20} - 193 q^{22} + 392 q^{23} + 77 q^{25} - 406 q^{26} - 429 q^{28} - 13 q^{29} + 413 q^{31} - 1314 q^{32} + 1060 q^{34} + 1239 q^{35} + 654 q^{37} - 912 q^{38} - 1803 q^{40} + 1490 q^{41} + 416 q^{43} - 695 q^{44} - 2369 q^{46} + 150 q^{47} - 301 q^{49} + 1878 q^{50} - 1661 q^{52} - 1359 q^{53} + 3300 q^{55} + 858 q^{56} + 955 q^{58} - 1262 q^{59} - 1044 q^{61} + 701 q^{62} + 78 q^{64} - 4556 q^{65} - 528 q^{67} - 703 q^{68} + 3050 q^{70} - 558 q^{71} - 699 q^{73} + 3224 q^{74} - 868 q^{76} - 390 q^{77} - 1252 q^{79} + 1914 q^{80} + 2987 q^{82} + 4464 q^{83} - 2170 q^{85} + 3209 q^{86} + 1302 q^{88} - 316 q^{89} + 176 q^{91} - 4595 q^{92} + 1247 q^{94} - 1466 q^{95} + 1608 q^{97} - 2810 q^{98}+O(q^{100}) $ 12 * q - 16 * q^4 - 28 * q^5 + 12 * q^7 + 112 * q^8 + 100 * q^10 + 54 * q^11 - 18 * q^13 - 156 * q^14 + 308 * q^16 + 80 * q^17 - 280 * q^19 + 15 * q^20 - 193 * q^22 + 392 * q^23 + 77 * q^25 - 406 * q^26 - 429 * q^28 - 13 * q^29 + 413 * q^31 - 1314 * q^32 + 1060 * q^34 + 1239 * q^35 + 654 * q^37 - 912 * q^38 - 1803 * q^40 + 1490 * q^41 + 416 * q^43 - 695 * q^44 - 2369 * q^46 + 150 * q^47 - 301 * q^49 + 1878 * q^50 - 1661 * q^52 - 1359 * q^53 + 3300 * q^55 + 858 * q^56 + 955 * q^58 - 1262 * q^59 - 1044 * q^61 + 701 * q^62 + 78 * q^64 - 4556 * q^65 - 528 * q^67 - 703 * q^68 + 3050 * q^70 - 558 * q^71 - 699 * q^73 + 3224 * q^74 - 868 * q^76 - 390 * q^77 - 1252 * q^79 + 1914 * q^80 + 2987 * q^82 + 4464 * q^83 - 2170 * q^85 + 3209 * q^86 + 1302 * q^88 - 316 * q^89 + 176 * q^91 - 4595 * q^92 + 1247 * q^94 - 1466 * q^95 + 1608 * q^97 - 2810 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.402703	−	1.23939i	−0.142377	−	0.438192i	0.854287	−	0.519801i	$-0.173994\pi$
$2$	−0.402703	−	1.23939i	−0.142377	−	0.438192i	−0.996664	+	0.0816096i	$0.973994\pi$
$3$		0			0
$3$		0			0
$4$	5.09821	−	3.70407i	0.637276	−	0.463008i
$5$	2.50364	−	7.70540i	0.223932	−	0.689192i	−0.774466	−	0.632615i	$-0.781981\pi$
$5$	2.50364	−	7.70540i	0.223932	−	0.689192i	0.998398	−	0.0565768i	$-0.0180186\pi$
$6$		0			0
$7$	−0.439746	+	0.319494i	−0.0237440	+	0.0172510i	−0.599594	−	0.800304i	$-0.704671\pi$
$7$	−0.439746	+	0.319494i	−0.0237440	+	0.0172510i	0.575850	+	0.817555i	$0.304671\pi$
$8$	−15.0782	−	10.9549i	−0.666368	−	0.484145i
$9$		0			0
$10$	−10.5582			−0.333881
$11$	25.3612	+	26.2261i	0.695155	+	0.718860i
$11$	25.3612	+	26.2261i	0.695155	+	0.718860i
$12$		0			0
$13$	−21.5234	−	66.2421i	−0.459193	−	1.41325i	−0.866141	−	0.499799i	$-0.833407\pi$
$13$	−21.5234	−	66.2421i	−0.459193	−	1.41325i	0.406949	−	0.913451i	$-0.366593\pi$
$14$	0.573065	+	0.416356i	0.0109399	+	0.00794828i
$15$		0			0
$16$	8.07330	−	24.8471i	0.126145	−	0.388236i
$17$	13.1571	−	40.4934i	0.187710	−	0.577711i	−0.812275	−	0.583275i	$-0.801771\pi$
$17$	13.1571	−	40.4934i	0.187710	−	0.577711i	0.999985	+	0.00556378i	$0.00177101\pi$
$18$		0			0
$19$	−61.0435	−	44.3507i	−0.737070	−	0.535513i	0.154722	−	0.987958i	$-0.450552\pi$
$19$	−61.0435	−	44.3507i	−0.737070	−	0.535513i	−0.891792	+	0.452445i	$0.850552\pi$
$20$	−15.7773	−	48.5574i	−0.176395	−	0.542888i
$21$		0			0
$22$	22.2914	−	41.9939i	0.216024	−	0.406960i
$23$	−37.9924			−0.344433			−0.172217	−	0.985059i	$-0.555093\pi$
$23$	−37.9924			−0.344433			−0.172217	+	0.985059i	$0.555093\pi$
$24$		0			0
$25$	48.0221	+	34.8901i	0.384177	+	0.279121i
$26$	−73.4324	+	53.3518i	−0.553896	+	0.402429i
$27$		0			0
$28$	−1.05849	+	3.25769i	−0.00714413	+	0.0219874i
$29$	97.1697	−	70.5979i	0.622205	−	0.452059i	−0.231486	−	0.972838i	$-0.574359\pi$
$29$	97.1697	−	70.5979i	0.622205	−	0.452059i	0.853691	+	0.520780i	$0.174359\pi$
$30$		0			0
$31$	85.6557	+	263.621i	0.496265	+	1.52735i	0.814976	+	0.579495i	$0.196750\pi$
$31$	85.6557	+	263.621i	0.496265	+	1.52735i	−0.318711	+	0.947852i	$0.603250\pi$
$32$	−183.148			−1.01176
$33$		0			0
$34$	−55.4856			−0.279874
$35$	1.36087	+	4.18831i	0.00657224	+	0.0202273i
$36$		0			0
$37$	12.0481	−	8.75344i	0.0535322	−	0.0388934i	−0.560697	−	0.828021i	$-0.689467\pi$
$37$	12.0481	−	8.75344i	0.0535322	−	0.0388934i	0.614230	+	0.789127i	$0.289467\pi$
$38$	−30.3855	+	93.5170i	−0.129715	+	0.399223i
$39$		0			0
$40$	−122.163	+	88.7563i	−0.482890	+	0.350840i
$41$	230.473	+	167.448i	0.877898	+	0.637831i	0.932695	−	0.360667i	$-0.117451\pi$
$41$	230.473	+	167.448i	0.877898	+	0.637831i	−0.0547962	+	0.998498i	$0.517451\pi$
$42$		0			0
$43$	312.130			1.10696			0.553481	−	0.832862i	$-0.313299\pi$
$43$	312.130			1.10696			0.553481	+	0.832862i	$0.313299\pi$
$44$	226.440	+	39.7664i	0.775844	+	0.136250i
$45$		0			0
$46$	15.2997	+	47.0875i	0.0490394	+	0.150928i
$47$	272.897	+	198.272i	0.846940	+	0.615338i	0.924301	−	0.381665i	$-0.124649\pi$
$47$	272.897	+	198.272i	0.846940	+	0.615338i	−0.0773606	+	0.997003i	$0.524649\pi$
$48$		0			0
$49$	−105.902	+	325.931i	−0.308751	+	0.950237i
$50$	23.9039	−	73.5686i	0.0676104	−	0.208083i
$51$		0			0
$52$	−355.096	−	257.992i	−0.946979	−	0.688021i
$53$	−52.4474	−	161.417i	−0.135928	−	0.418345i	0.859805	−	0.510623i	$-0.170585\pi$
$53$	−52.4474	−	161.417i	−0.135928	−	0.418345i	−0.995733	+	0.0922780i	$0.970585\pi$
$54$		0			0
$55$	265.578	−	129.758i	0.651100	−	0.318119i
$56$	10.1306			0.0241743
$57$		0			0
$58$	−126.629	−	92.0014i	−0.286676	−	0.208282i
$59$	−648.765	+	471.356i	−1.43156	+	1.04009i	−0.441836	+	0.897096i	$0.645673\pi$
$59$	−648.765	+	471.356i	−1.43156	+	1.04009i	−0.989724	+	0.142994i	$0.954327\pi$
$60$		0			0
$61$	−119.521	+	367.847i	−0.250870	+	0.772099i	0.743745	+	0.668463i	$0.233048\pi$
$61$	−119.521	+	367.847i	−0.250870	+	0.772099i	−0.994615	+	0.103636i	$0.966952\pi$
$62$	292.236	−	212.322i	0.598614	−	0.434918i
$63$		0			0
$64$	9.16772	+	28.2153i	0.0179057	+	0.0551081i
$65$	−564.309			−1.07683
$66$		0			0
$67$	981.580			1.78984			0.894919	−	0.446229i	$-0.147233\pi$
$67$	981.580			1.78984			0.894919	+	0.446229i	$0.147233\pi$
$68$	−82.9126	−	255.179i	−0.147862	−	0.455073i
$69$		0			0
$70$	4.64294	−	3.37329i	0.00792768	−	0.00575980i
$71$	165.441	−	509.176i	0.276539	−	0.851100i	−0.712269	−	0.701907i	$-0.752332\pi$
$71$	165.441	−	509.176i	0.276539	−	0.851100i	0.988808	−	0.149193i	$-0.0476676\pi$
$72$		0			0
$73$	−369.585	+	268.520i	−0.592558	+	0.430518i	−0.843229	−	0.537554i	$-0.819348\pi$
$73$	−369.585	+	268.520i	−0.592558	+	0.430518i	0.250672	+	0.968072i	$0.419348\pi$
$74$	−15.7007	−	11.4073i	−0.0246645	−	0.0179198i
$75$		0			0
$76$	−475.490			−0.717664
$77$	−19.5316	−	3.43004i	−0.0289069	−	0.00507649i
$78$		0			0
$79$	−191.437	−	589.183i	−0.272637	−	0.839092i	−0.989835	−	0.142222i	$-0.954575\pi$
$79$	−191.437	−	589.183i	−0.272637	−	0.839092i	0.717197	−	0.696870i	$-0.245425\pi$
$80$	−171.244	−	124.416i	−0.239321	−	0.173877i
$81$		0			0
$82$	114.722	−	353.079i	0.154499	−	0.475500i
$83$	−61.3212	+	188.727i	−0.0810948	+	0.249584i	−0.983381	−	0.181553i	$-0.941888\pi$
$83$	−61.3212	+	188.727i	−0.0810948	+	0.249584i	0.902286	+	0.431137i	$0.141888\pi$
$84$		0			0
$85$	−279.077	−	202.762i	−0.356120	−	0.258736i
$86$	−125.696	−	386.851i	−0.157606	−	0.485061i
$87$		0			0
$88$	−95.0962	−	673.273i	−0.115197	−	0.815581i
$89$	1317.67			1.56935			0.784676	−	0.619906i	$-0.212829\pi$
$89$	1317.67			1.56935			0.784676	+	0.619906i	$0.212829\pi$
$90$		0			0
$91$	30.6287	+	22.2531i	0.0352831	+	0.0256347i
$92$	−193.693	+	140.726i	−0.219499	+	0.159475i
$93$		0			0
$94$	135.840	−	418.072i	0.149051	−	0.458732i
$95$	−494.571	+	359.327i	−0.534125	+	0.388065i
$96$		0			0
$97$	−287.328	−	884.304i	−0.300760	−	0.925644i	−0.981226	−	0.192864i	$-0.938222\pi$
$97$	−287.328	−	884.304i	−0.300760	−	0.925644i	0.680466	−	0.732780i	$-0.261778\pi$
$98$	446.604			0.460345
$99$		0			0
$100$	374.062			0.374062
$101$	−471.033	−	1449.69i	−0.464054	−	1.42821i	−0.860168	−	0.510011i	$-0.829641\pi$
$101$	−471.033	−	1449.69i	−0.464054	−	1.42821i	0.396113	−	0.918202i	$-0.370359\pi$
$102$		0			0
$103$	115.550	−	83.9520i	0.110539	−	0.0803110i	−0.531143	−	0.847282i	$-0.678237\pi$
$103$	115.550	−	83.9520i	0.110539	−	0.0803110i	0.641681	+	0.766971i	$0.278237\pi$
$104$	−401.145	+	1234.60i	−0.378226	+	1.16406i
$105$		0			0
$106$	−178.938	+	130.006i	−0.163962	+	0.119125i
$107$	1252.74	+	910.166i	1.13184	+	0.822327i	0.985961	−	0.166976i	$-0.0534001\pi$
$107$	1252.74	+	910.166i	1.13184	+	0.822327i	0.145875	+	0.989303i	$0.453400\pi$
$108$		0			0
$109$	−650.244			−0.571395			−0.285697	−	0.958320i	$-0.592225\pi$
$109$	−650.244			−0.571395			−0.285697	+	0.958320i	$0.592225\pi$
$110$	−267.770	−	276.901i	−0.232099	−	0.240014i
$111$		0			0
$112$	4.38829	+	13.5058i	0.00370227	+	0.0113944i
$113$	64.3134	+	46.7264i	0.0535406	+	0.0388996i	0.614234	−	0.789124i	$-0.289465\pi$
$113$	64.3134	+	46.7264i	0.0535406	+	0.0388996i	−0.560693	+	0.828024i	$0.689465\pi$
$114$		0			0
$115$	−95.1191	+	292.747i	−0.0771296	+	0.237381i
$116$	233.892	−	719.846i	0.187210	−	0.576173i
$117$		0			0
$118$	845.454	+	614.259i	0.659580	+	0.479213i
$119$	7.15161	+	22.0104i	0.00550914	+	0.0169554i
$120$		0			0
$121$	−44.6148	+	1330.25i	−0.0335198	+	0.999438i
$122$	504.039			0.374045
$123$		0			0
$124$	1413.16	+	1026.72i	1.02343	+	0.743567i
$125$	1208.40	−	877.953i	0.864659	−	0.628212i
$126$		0			0
$127$	−126.921	+	390.621i	−0.0886802	+	0.272930i	−0.985555	−	0.169355i	$-0.945832\pi$
$127$	−126.921	+	390.621i	−0.0886802	+	0.272930i	0.896875	+	0.442284i	$0.145832\pi$
$128$	−1154.08	+	838.487i	−0.796931	+	0.579004i
$129$		0			0
$130$	227.249	+	699.400i	0.153316	+	0.471857i
$131$	−2714.85			−1.81067			−0.905334	−	0.424699i	$-0.860380\pi$
$131$	−2714.85			−1.81067			−0.905334	+	0.424699i	$0.860380\pi$
$132$		0			0
$133$	41.0134			0.0267392
$134$	−395.285	−	1216.56i	−0.254832	−	0.784292i
$135$		0			0
$136$	−641.988	+	466.432i	−0.404779	+	0.294090i
$137$	−821.452	+	2528.17i	−0.512273	+	1.57661i	0.275917	+	0.961181i	$0.411019\pi$
$137$	−821.452	+	2528.17i	−0.512273	+	1.57661i	−0.788190	+	0.615432i	$0.788981\pi$
$138$		0			0
$139$	161.672	−	117.462i	0.0986538	−	0.0716762i	−0.537365	−	0.843350i	$-0.680580\pi$
$139$	161.672	−	117.462i	0.0986538	−	0.0716762i	0.636019	+	0.771674i	$0.280580\pi$
$140$	22.4518	+	16.3122i	0.0135537	+	0.00984736i
$141$		0			0
$142$	−697.693			−0.412318
$143$	1191.41	−	2244.45i	0.696719	−	1.31252i
$144$		0			0
$145$	−300.708	−	925.483i	−0.172223	−	0.530049i
$146$	481.634	+	349.928i	0.273016	+	0.198358i
$147$		0			0
$148$	29.0003	−	89.2537i	0.0161068	−	0.0495717i
$149$	−776.768	+	2390.65i	−0.427083	+	1.31443i	0.473903	+	0.880577i	$0.342845\pi$
$149$	−776.768	+	2390.65i	−0.427083	+	1.31443i	−0.900986	+	0.433849i	$0.857155\pi$
$150$		0			0
$151$	2403.32	+	1746.11i	1.29523	+	0.941038i	0.999897	−	0.0143566i	$-0.00457000\pi$
$151$	2403.32	+	1746.11i	1.29523	+	0.941038i	0.295331	+	0.955395i	$0.404570\pi$
$152$	434.566	+	1337.46i	0.231894	+	0.713697i
$153$		0			0
$154$	3.61425	+	25.5886i	0.00189120	+	0.0133895i
$155$	2245.76			1.16377
$156$		0			0
$157$	−1660.59	−	1206.49i	−0.844137	−	0.613301i	0.0793864	−	0.996844i	$-0.474704\pi$
$157$	−1660.59	−	1206.49i	−0.844137	−	0.613301i	−0.923523	+	0.383543i	$0.874704\pi$
$158$	−653.136	+	474.531i	−0.328866	+	0.238935i
$159$		0			0
$160$	−458.535	+	1411.23i	−0.226565	+	0.697296i
$161$	16.7070	−	12.1383i	0.00817823	−	0.00594183i
$162$		0			0
$163$	−716.204	−	2204.25i	−0.344156	−	1.05920i	−0.962034	−	0.272929i	$-0.912008\pi$
$163$	−716.204	−	2204.25i	−0.344156	−	1.05920i	0.617878	−	0.786274i	$-0.287992\pi$
$164$	1795.24			0.854785
$165$		0			0
$166$	258.601			0.120912
$167$	−382.525	−	1177.29i	−0.177249	−	0.545517i	0.822480	−	0.568794i	$-0.192590\pi$
$167$	−382.525	−	1177.29i	−0.177249	−	0.545517i	−0.999729	+	0.0232771i	$0.992590\pi$
$168$		0			0
$169$	−2147.35	+	1560.14i	−0.977400	+	0.710123i
$170$	−138.916	+	427.539i	−0.0626727	+	0.192887i
$171$		0			0
$172$	1591.30	−	1156.15i	0.705440	−	0.512532i
$173$	−1853.26	−	1346.47i	−0.814454	−	0.591736i	0.100664	−	0.994920i	$-0.467903\pi$
$173$	−1853.26	−	1346.47i	−0.814454	−	0.591736i	−0.915119	+	0.403185i	$0.867903\pi$
$174$		0			0
$175$	−32.2647			−0.0139370
$176$	856.391	−	418.422i	0.366778	−	0.179203i
$177$		0			0
$178$	−530.628	−	1633.11i	−0.223440	−	0.687677i
$179$	437.029	+	317.520i	0.182487	+	0.132584i	0.675278	−	0.737563i	$-0.264024\pi$
$179$	437.029	+	317.520i	0.182487	+	0.132584i	−0.492792	+	0.870147i	$0.664024\pi$
$180$		0			0
$181$	−692.312	+	2130.72i	−0.284305	+	0.875000i	0.702302	+	0.711880i	$0.252156\pi$
$181$	−692.312	+	2130.72i	−0.284305	+	0.875000i	−0.986606	+	0.163120i	$0.947844\pi$
$182$	15.2460	−	46.9224i	0.00620940	−	0.0191106i
$183$		0			0
$184$	572.856	+	416.204i	0.229519	+	0.166755i
$185$	−37.2848	−	114.751i	−0.0148175	−	0.0456034i
$186$		0			0
$187$	1395.66	−	681.903i	0.545781	−	0.266662i
$188$	2125.70			0.824642
$189$		0			0
$190$	644.512	+	468.265i	0.246094	+	0.178798i
$191$	511.507	−	371.632i	0.193777	−	0.140787i	−0.486666	−	0.873588i	$-0.661787\pi$
$191$	511.507	−	371.632i	0.193777	−	0.140787i	0.680443	+	0.732801i	$0.261787\pi$
$192$		0			0
$193$	1274.62	−	3922.89i	0.475386	−	1.46309i	−0.370051	−	0.929011i	$-0.620660\pi$
$193$	1274.62	−	3922.89i	0.475386	−	1.46309i	0.845437	−	0.534076i	$-0.179340\pi$
$194$	−980.292	+	712.224i	−0.362788	+	0.263581i
$195$		0			0
$196$	667.363	+	2053.93i	0.243208	+	0.748518i
$197$	−3297.43			−1.19255			−0.596274	−	0.802781i	$-0.703353\pi$
$197$	−3297.43			−1.19255			−0.596274	+	0.802781i	$0.703353\pi$
$198$		0			0
$199$	47.3923			0.0168822			0.00844109	−	0.999964i	$-0.497313\pi$
$199$	47.3923			0.0168822			0.00844109	+	0.999964i	$0.497313\pi$
$200$	−341.867	−	1052.16i	−0.120868	−	0.371994i
$201$		0			0
$202$	−1607.05	+	1167.59i	−0.559760	+	0.406689i
$203$	−20.1743	+	62.0902i	−0.00697517	+	0.0214674i
$204$		0			0
$205$	1867.28	−	1356.66i	0.636178	−	0.462210i
$206$	−150.582	−	109.404i	−0.0509298	−	0.0370027i
$207$		0			0
$208$	−1819.69			−0.606599
$209$	−384.994	−	2725.72i	−0.127419	−	0.902115i
$210$		0			0
$211$	−469.344	−	1444.49i	−0.153132	−	0.471293i	0.844834	−	0.535028i	$-0.179699\pi$
$211$	−469.344	−	1444.49i	−0.153132	−	0.471293i	−0.997967	+	0.0637346i	$0.979699\pi$
$212$	−865.286	−	628.667i	−0.280321	−	0.203665i
$213$		0			0
$214$	623.572	−	1919.16i	0.199189	−	0.613042i
$215$	781.459	−	2405.08i	0.247884	−	0.762909i
$216$		0			0
$217$	−121.892	−	88.5598i	−0.0381317	−	0.0277043i
$218$	261.855	+	805.907i	0.0813535	+	0.250380i
$219$		0			0
$220$	873.340	−	1645.25i	0.267639	−	0.504195i
$221$	−2965.55			−0.902645
$222$		0			0
$223$	−827.855	−	601.472i	−0.248598	−	0.180617i	0.456507	−	0.889720i	$-0.349100\pi$
$223$	−827.855	−	601.472i	−0.248598	−	0.180617i	−0.705105	+	0.709103i	$0.749100\pi$
$224$	80.5384	−	58.5146i	0.0240232	−	0.0174539i
$225$		0			0
$226$	32.0132	−	98.5264i	0.00942250	−	0.0289995i
$227$	2058.48	−	1495.57i	0.601876	−	0.437288i	−0.244668	−	0.969607i	$-0.578679\pi$
$227$	2058.48	−	1495.57i	0.601876	−	0.437288i	0.846544	+	0.532318i	$0.178679\pi$
$228$		0			0
$229$	−1105.69	−	3402.95i	−0.319065	−	0.981980i	−0.974049	−	0.226337i	$-0.927325\pi$
$229$	−1105.69	−	3402.95i	−0.319065	−	0.981980i	0.654984	−	0.755642i	$-0.272675\pi$
$230$	401.133			0.115000
$231$		0			0
$232$	−2238.54			−0.633479
$233$	−534.492	−	1645.00i	−0.150282	−	0.462521i	0.847370	−	0.531003i	$-0.178185\pi$
$233$	−534.492	−	1645.00i	−0.150282	−	0.462521i	−0.997652	+	0.0684817i	$0.978185\pi$
$234$		0			0
$235$	2211.00	−	1606.38i	0.613743	−	0.445911i
$236$	−1561.61	+	4806.14i	−0.430729	+	1.32565i
$237$		0			0
$238$	24.3996	−	17.7273i	0.00664533	−	0.00482811i
$239$	4356.80	+	3165.40i	1.17916	+	0.856707i	0.992076	−	0.125638i	$-0.0400978\pi$
$239$	4356.80	+	3165.40i	1.17916	+	0.856707i	0.187079	+	0.982345i	$0.440098\pi$
$240$		0			0
$241$	−3515.37			−0.939605			−0.469803	−	0.882771i	$-0.655675\pi$
$241$	−3515.37			−0.939605			−0.469803	+	0.882771i	$0.655675\pi$
$242$	1666.67	−	480.401i	0.442718	−	0.127609i
$243$		0			0
$244$	753.189	+	2318.08i	0.197615	+	0.608195i
$245$	2246.29	+	1632.03i	0.585757	+	0.425577i
$246$		0			0
$247$	−1624.02	+	4998.22i	−0.418356	+	1.28757i
$248$	1596.42	−	4913.28i	0.408762	−	1.25804i
$249$		0			0
$250$	−1574.75	−	1144.13i	−0.398385	−	0.289443i
$251$	445.948	+	1372.49i	0.112143	+	0.345141i	0.991340	−	0.131317i	$-0.0419204\pi$
$251$	445.948	+	1372.49i	0.112143	+	0.345141i	−0.879197	+	0.476458i	$0.841920\pi$
$252$		0			0
$253$	−963.534	−	996.391i	−0.239434	−	0.247599i
$254$	535.245			0.132221
$255$		0			0
$256$	1695.98	+	1232.20i	0.414057	+	0.300830i
$257$	−4955.96	+	3600.72i	−1.20290	+	0.873956i	−0.994567	−	0.104103i	$-0.966803\pi$
$257$	−4955.96	+	3600.72i	−1.20290	+	0.873956i	−0.208330	+	0.978059i	$0.566803\pi$
$258$		0			0
$259$	−2.50142	+	7.69857i	−0.000600118	+	0.00184697i
$260$	−2876.96	+	2090.24i	−0.686238	+	0.498581i
$261$		0			0
$262$	1093.28	+	3364.77i	0.257798	+	0.793420i
$263$	−2135.26			−0.500631			−0.250315	−	0.968164i	$-0.580534\pi$
$263$	−2135.26			−0.500631			−0.250315	+	0.968164i	$0.580534\pi$
$264$		0			0
$265$	−1375.09			−0.318759
$266$	−16.5162	−	50.8317i	−0.00380704	−	0.0117169i
$267$		0			0
$268$	5004.30	−	3635.84i	1.14062	−	0.828710i
$269$	0.642583	−	1.97767i	0.000145647	−	0.000448255i	−0.950984	−	0.309241i	$-0.899925\pi$
$269$	0.642583	−	1.97767i	0.000145647	−	0.000448255i	0.951129	+	0.308793i	$0.0999250\pi$
$270$		0			0
$271$	−3652.12	+	2653.42i	−0.818637	+	0.594775i	−0.916322	−	0.400442i	$-0.868856\pi$
$271$	−3652.12	+	2653.42i	−0.818637	+	0.594775i	0.0976844	+	0.995217i	$0.468856\pi$
$272$	−899.921	−	653.831i	−0.200609	−	0.145751i
$273$		0			0
$274$	3464.20			0.763795
$275$	302.869	+	2144.29i	0.0664135	+	0.470201i
$276$		0			0
$277$	1493.35	+	4596.05i	0.323922	+	0.996930i	0.971925	+	0.235292i	$0.0756046\pi$
$277$	1493.35	+	4596.05i	0.323922	+	0.996930i	−0.648002	+	0.761638i	$0.724395\pi$
$278$	−210.687	−	153.073i	−0.0454539	−	0.0330242i
$279$		0			0
$280$	25.3633	−	78.0604i	0.00541339	−	0.0166607i
$281$	−60.8452	+	187.262i	−0.0129172	+	0.0397549i	−0.957307	−	0.289072i	$-0.906653\pi$
$281$	−60.8452	+	187.262i	−0.0129172	+	0.0397549i	0.944390	+	0.328827i	$0.106653\pi$
$282$		0			0
$283$	2215.82	+	1609.89i	0.465430	+	0.338155i	0.795658	−	0.605747i	$-0.207125\pi$
$283$	2215.82	+	1609.89i	0.465430	+	0.338155i	−0.330228	+	0.943901i	$0.607125\pi$
$284$	−1042.57	−	3208.69i	−0.217835	−	0.670426i
$285$		0			0
$286$	−3261.55	−	572.778i	−0.674333	−	0.118423i
$287$	−154.848			−0.0318481
$288$		0			0
$289$	2508.09	+	1822.24i	0.510502	+	0.370901i
$290$	−1025.94	+	745.390i	−0.207742	+	0.150934i
$291$		0			0
$292$	−889.610	+	2737.94i	−0.178289	+	0.548718i
$293$	5372.42	−	3903.29i	1.07120	−	0.778269i	0.0950687	−	0.995471i	$-0.469693\pi$
$293$	5372.42	−	3903.29i	1.07120	−	0.778269i	0.976127	+	0.217202i	$0.0696929\pi$
$294$		0			0
$295$	2007.71	+	6179.10i	0.396249	+	1.21953i
$296$	−277.556			−0.0545022
$297$		0			0
$298$	3275.76			0.636777
$299$	817.724	+	2516.69i	0.158161	+	0.486770i
$300$		0			0
$301$	−137.258	+	99.7235i	−0.0262837	+	0.0190962i
$302$	1196.30	−	3681.82i	0.227944	−	0.701540i
$303$		0			0
$304$	−1594.81	+	1158.70i	−0.300883	+	0.218604i
$305$	2535.18	+	1841.91i	0.475947	+	0.345795i
$306$		0			0
$307$	3278.70			0.609530			0.304765	−	0.952428i	$-0.401422\pi$
$307$	3278.70			0.609530			0.304765	+	0.952428i	$0.401422\pi$
$308$	−112.281	+	54.8591i	−0.0207721	+	0.0101490i
$309$		0			0
$310$	−904.374	−	2783.38i	−0.165693	−	0.509952i
$311$	5309.42	+	3857.52i	0.968069	+	0.703343i	0.955011	−	0.296572i	$-0.0958433\pi$
$311$	5309.42	+	3857.52i	0.968069	+	0.703343i	0.0130582	+	0.999915i	$0.495843\pi$
$312$		0			0
$313$	209.313	−	644.199i	0.0377989	−	0.116333i	−0.930377	−	0.366605i	$-0.880520\pi$
$313$	209.313	−	644.199i	0.0377989	−	0.116333i	0.968176	+	0.250272i	$0.0805200\pi$
$314$	−826.589	+	2543.98i	−0.148558	+	0.457214i
$315$		0			0
$316$	−3158.36	−	2294.68i	−0.562252	−	0.408500i
$317$	−1176.03	−	3619.46i	−0.208368	−	0.641290i	−0.999558	−	0.0297204i	$-0.990538\pi$
$317$	−1176.03	−	3619.46i	−0.208368	−	0.641290i	0.791190	−	0.611570i	$-0.209462\pi$
$318$		0			0
$319$	4315.85	+	757.929i	0.757496	+	0.133028i
$320$	240.363			0.0419897
$321$		0			0
$322$	−21.7721	−	15.8184i	−0.00376805	−	0.00273765i
$323$	−2599.06	+	1888.33i	−0.447727	+	0.325293i
$324$		0			0
$325$	1277.60	−	3932.04i	0.218056	−	0.671108i
$326$	−2443.51	+	1775.32i	−0.415134	+	0.301612i
$327$		0			0
$328$	−1640.73	−	5049.64i	−0.276201	−	0.850060i
$329$	−183.352			−0.0307250
$330$		0			0
$331$	3339.46			0.554542			0.277271	−	0.960792i	$-0.410570\pi$
$331$	3339.46			0.554542			0.277271	+	0.960792i	$0.410570\pi$
$332$	386.430	+	1189.31i	0.0638798	+	0.196602i
$333$		0			0
$334$	−1305.08	+	948.196i	−0.213805	+	0.155338i
$335$	2457.52	−	7563.47i	0.400802	−	1.23354i
$336$		0			0
$337$	−7795.17	+	5663.52i	−1.26003	+	0.915465i	−0.998759	−	0.0498006i	$-0.984141\pi$
$337$	−7795.17	+	5663.52i	−1.26003	+	0.915465i	−0.261270	+	0.965266i	$0.584141\pi$
$338$	2798.37	+	2033.14i	0.450329	+	0.327183i
$339$		0			0
$340$	−2173.84			−0.346744
$341$	−4741.42	+	8932.17i	−0.752968	+	1.41849i
$342$		0			0
$343$	−115.176	−	354.476i	−0.0181310	−	0.0558015i
$344$	−4706.35	−	3419.36i	−0.737643	−	0.535929i
$345$		0			0
$346$	−922.493	+	2839.14i	−0.143334	+	0.441137i
$347$	−822.954	+	2532.79i	−0.127315	+	0.391837i	−0.994316	−	0.106471i	$-0.966045\pi$
$347$	−822.954	+	2532.79i	−0.127315	+	0.391837i	0.867000	+	0.498307i	$0.166045\pi$
$348$		0			0
$349$	−4363.82	−	3170.50i	−0.669312	−	0.486284i	0.200483	−	0.979697i	$-0.435749\pi$
$349$	−4363.82	−	3170.50i	−0.669312	−	0.486284i	−0.869795	+	0.493413i	$0.835749\pi$
$350$	12.9931	+	39.9886i	0.00198431	+	0.00610709i
$351$		0			0
$352$	−4644.85	−	4803.25i	−0.703328	−	0.727312i
$353$	−3003.14			−0.452807			−0.226403	−	0.974034i	$-0.572697\pi$
$353$	−3003.14			−0.452807			−0.226403	+	0.974034i	$0.572697\pi$
$354$		0			0
$355$	−3509.20	−	2549.58i	−0.524645	−	0.381177i
$356$	6717.74	−	4880.72i	1.00011	−	0.726623i
$357$		0			0
$358$	217.539	−	669.517i	0.0321154	−	0.0988410i
$359$	1640.26	−	1191.72i	0.241141	−	0.175199i	−0.460650	−	0.887582i	$-0.652384\pi$
$359$	1640.26	−	1191.72i	0.241141	−	0.175199i	0.701792	+	0.712382i	$0.252384\pi$
$360$		0			0
$361$	−360.225	−	1108.66i	−0.0525185	−	0.161635i
$362$	2919.59			0.423896
$363$		0			0
$364$	238.579			0.0343542
$365$	1143.74	+	3520.08i	0.164017	+	0.504793i
$366$		0			0
$367$	1975.14	−	1435.02i	0.280930	−	0.204107i	−0.438393	−	0.898783i	$-0.644452\pi$
$367$	1975.14	−	1435.02i	0.280930	−	0.204107i	0.719323	+	0.694676i	$0.244452\pi$
$368$	−306.724	+	944.000i	−0.0434486	+	0.133721i
$369$		0			0
$370$	−127.206	+	92.4209i	−0.0178734	+	0.0129858i
$371$	74.6351	+	54.2256i	0.0104444	+	0.00758828i
$372$		0			0
$373$	10410.5			1.44513			0.722565	−	0.691302i	$-0.242963\pi$
$373$	10410.5			1.44513			0.722565	+	0.691302i	$0.242963\pi$
$374$	−1407.18	−	1455.17i	−0.194556	−	0.201190i
$375$		0			0
$376$	−1942.74	−	5979.15i	−0.266461	−	0.820083i
$377$	−6767.97	−	4917.22i	−0.924584	−	0.671750i
$378$		0			0
$379$	1508.05	−	4641.31i	0.204389	−	0.629045i	−0.795349	−	0.606152i	$-0.792712\pi$
$379$	1508.05	−	4641.31i	0.204389	−	0.629045i	0.999738	−	0.0228927i	$-0.00728761\pi$
$380$	−1190.46	+	3663.85i	−0.160708	+	0.494609i
$381$		0			0
$382$	−666.583	−	484.301i	−0.0892810	−	0.0648665i
$383$	−3695.60	−	11373.9i	−0.493045	−	1.51744i	−0.819982	−	0.572389i	$-0.806017\pi$
$383$	−3695.60	−	11373.9i	−0.493045	−	1.51744i	0.326937	−	0.945046i	$-0.393983\pi$
$384$		0			0
$385$	−75.3298	+	141.911i	−0.00997185	+	0.0187856i
$386$	−5375.30			−0.708796
$387$		0			0
$388$	−4740.38	−	3444.09i	−0.620248	−	0.450637i
$389$	5806.74	−	4218.84i	0.756846	−	0.549881i	−0.141095	−	0.989996i	$-0.545062\pi$
$389$	5806.74	−	4218.84i	0.756846	−	0.549881i	0.897941	+	0.440115i	$0.145062\pi$
$390$		0			0
$391$	−499.870	+	1538.44i	−0.0646534	+	0.198983i
$392$	5167.36	−	3754.31i	0.665794	−	0.483728i
$393$		0			0
$394$	1327.88	+	4086.81i	0.169791	+	0.522564i
$395$	−5019.18			−0.639348
$396$		0			0
$397$	−2881.37			−0.364262			−0.182131	−	0.983274i	$-0.558299\pi$
$397$	−2881.37			−0.364262			−0.182131	+	0.983274i	$0.558299\pi$
$398$	−19.0850	−	58.7377i	−0.00240364	−	0.00739763i
$399$		0			0
$400$	1254.61	−	911.530i	0.156827	−	0.113941i
$401$	1224.69	−	3769.21i	0.152514	−	0.469389i	−0.845387	−	0.534155i	$-0.820630\pi$
$401$	1224.69	−	3769.21i	0.152514	−	0.469389i	0.997901	+	0.0647655i	$0.0206299\pi$
$402$		0			0
$403$	15619.2	−	11348.0i	1.93064	−	1.40269i
$404$	−7771.17	−	5646.09i	−0.957005	−	0.695305i
$405$		0			0
$406$	85.0784			0.0103999
$407$	535.122	+	93.9757i	0.0651721	+	0.0114452i
$408$		0			0
$409$	2794.07	+	8599.27i	0.337795	+	1.03962i	0.965329	+	0.261036i	$0.0840641\pi$
$409$	2794.07	+	8599.27i	0.337795	+	1.03962i	−0.627534	+	0.778589i	$0.715936\pi$
$410$	−2433.39	−	1767.96i	−0.293114	−	0.212959i
$411$		0			0
$412$	278.135	−	856.010i	0.0332590	−	0.102361i
$413$	134.696	−	414.553i	0.0160484	−	0.0493918i
$414$		0			0
$415$	1300.69	+	945.008i	0.153852	+	0.111780i
$416$	3941.95	+	12132.1i	0.464592	+	1.42987i
$417$		0			0
$418$	−3223.20	+	1574.81i	−0.377157	+	0.184274i
$419$	840.109			0.0979523			0.0489761	−	0.998800i	$-0.484404\pi$
$419$	840.109			0.0979523			0.0489761	+	0.998800i	$0.484404\pi$
$420$		0			0
$421$	−1622.04	−	1178.48i	−0.187775	−	0.136427i	0.489926	−	0.871764i	$-0.337024\pi$
$421$	−1622.04	−	1178.48i	−0.187775	−	0.136427i	−0.677701	+	0.735337i	$0.737024\pi$
$422$	−1601.29	+	1163.40i	−0.184714	+	0.134203i
$423$		0			0
$424$	−977.497	+	3008.43i	−0.111961	+	0.344581i
$425$	2044.65	−	1485.52i	0.233365	−	0.169550i
$426$		0			0
$427$	−64.9662	−	199.945i	−0.00736285	−	0.0226605i
$428$	9758.02			1.10204
$429$		0			0
$430$	−3295.54			−0.369593
$431$	3683.31	+	11336.0i	0.411644	+	1.26691i	0.915218	+	0.402958i	$0.132018\pi$
$431$	3683.31	+	11336.0i	0.411644	+	1.26691i	−0.503574	+	0.863952i	$0.667982\pi$
$432$		0			0
$433$	−777.349	+	564.777i	−0.0862749	+	0.0626824i	−0.630087	−	0.776525i	$-0.716981\pi$
$433$	−777.349	+	564.777i	−0.0862749	+	0.0626824i	0.543812	+	0.839207i	$0.316981\pi$
$434$	−60.6740	+	186.735i	−0.00671070	+	0.0206534i
$435$		0			0
$436$	−3315.08	+	2408.55i	−0.364137	+	0.264561i
$437$	2319.19	+	1684.99i	0.253871	+	0.184448i
$438$		0			0
$439$	−7590.46			−0.825223			−0.412611	−	0.910907i	$-0.635383\pi$
$439$	−7590.46			−0.825223			−0.412611	+	0.910907i	$0.635383\pi$
$440$	−5425.92	−	952.875i	−0.587888	−	0.103242i
$441$		0			0
$442$	1194.24	+	3675.48i	0.128516	+	0.395531i
$443$	343.603	+	249.642i	0.0368512	+	0.0267739i	0.606058	−	0.795420i	$-0.292750\pi$
$443$	343.603	+	249.642i	0.0368512	+	0.0267739i	−0.569207	+	0.822194i	$0.692750\pi$
$444$		0			0
$445$	3298.96	−	10153.1i	0.351428	−	1.08158i
$446$	−412.080	+	1268.25i	−0.0437501	+	0.134649i
$447$		0			0
$448$	−13.0461	−	9.47853i	−0.00137582	−	0.000999595i
$449$	1462.74	+	4501.85i	0.153744	+	0.473175i	0.998031	−	0.0627155i	$-0.0199761\pi$
$449$	1462.74	+	4501.85i	0.153744	+	0.473175i	−0.844288	+	0.535890i	$0.819976\pi$
$450$		0			0
$451$	1453.57	+	10291.1i	0.151764	+	1.07448i
$452$	500.961			0.0521310
$453$		0			0
$454$	−2682.55	−	1948.99i	−0.277309	−	0.201477i
$455$	248.152	−	180.293i	0.0255683	−	0.0185764i
$456$		0			0
$457$	−4688.02	+	14428.2i	−0.479861	+	1.47686i	0.359428	+	0.933173i	$0.382972\pi$
$457$	−4688.02	+	14428.2i	−0.479861	+	1.47686i	−0.839288	+	0.543687i	$0.817028\pi$
$458$	−3772.33	+	2740.76i	−0.384868	+	0.279623i
$459$		0			0
$460$	599.416	+	1844.81i	0.0607563	+	0.186989i
$461$	12952.3			1.30856			0.654282	−	0.756251i	$-0.272971\pi$
$461$	12952.3			1.30856			0.654282	+	0.756251i	$0.272971\pi$
$462$		0			0
$463$	−6774.30			−0.679975			−0.339988	−	0.940430i	$-0.610423\pi$
$463$	−6774.30			−0.679975			−0.339988	+	0.940430i	$0.610423\pi$
$464$	−969.671	−	2984.34i	−0.0970169	−	0.298587i
$465$		0			0
$466$	−1823.56	+	1324.89i	−0.181276	+	0.131705i
$467$	−1602.94	+	4933.34i	−0.158834	+	0.488839i	−0.998529	−	0.0542181i	$-0.982733\pi$
$467$	−1602.94	+	4933.34i	−0.158834	+	0.488839i	0.839696	+	0.543057i	$0.182733\pi$
$468$		0			0
$469$	−431.645	+	313.609i	−0.0424979	+	0.0308766i
$470$	−2881.32	−	2093.40i	−0.282777	−	0.205450i
$471$		0			0
$472$	14945.9			1.45750
$473$	7916.00	+	8185.94i	0.769509	+	0.795750i
$474$		0			0
$475$	−1384.04	−	4259.62i	−0.133692	−	0.411463i
$476$	117.988	+	85.7236i	0.0113613	+	0.00825449i
$477$		0			0
$478$	2168.68	−	6674.51i	0.207517	−	0.638671i
$479$	850.728	−	2618.27i	0.0811498	−	0.249753i	−0.902248	−	0.431218i	$-0.858084\pi$
$479$	850.728	−	2618.27i	0.0811498	−	0.249753i	0.983397	+	0.181465i	$0.0580839\pi$
$480$		0			0
$481$	−839.161	−	609.686i	−0.0795477	−	0.0577948i
$482$	1415.65	+	4356.92i	0.133778	+	0.411727i
$483$		0			0
$484$	4699.89	+	6947.16i	0.441387	+	0.652438i
$485$	−7533.28			−0.705296
$486$		0			0
$487$	7540.35	+	5478.38i	0.701614	+	0.509752i	0.880457	−	0.474125i	$-0.157236\pi$
$487$	7540.35	+	5478.38i	0.701614	+	0.509752i	−0.178844	+	0.983877i	$0.557236\pi$
$488$	5831.90	−	4237.13i	0.540979	−	0.393044i
$489$		0			0
$490$	1118.13	−	3441.26i	0.103086	−	0.317266i
$491$	−7918.15	+	5752.87i	−0.727782	+	0.528765i	−0.888861	−	0.458177i	$-0.848503\pi$
$491$	−7918.15	+	5752.87i	−0.727782	+	0.528765i	0.161079	+	0.986942i	$0.448503\pi$
$492$		0			0
$493$	−1580.28	−	4863.59i	−0.144365	−	0.444311i
$494$	6848.76			0.623766
$495$		0			0
$496$	7241.74			0.655572
$497$	89.9265	+	276.765i	0.00811621	+	0.0249791i
$498$		0			0
$499$	−7078.28	+	5142.67i	−0.635005	+	0.461358i	−0.858130	−	0.513432i	$-0.828374\pi$
$499$	−7078.28	+	5142.67i	−0.635005	+	0.461358i	0.223126	+	0.974790i	$0.428374\pi$
$500$	2908.67	−	8951.98i	0.260160	−	0.800689i
$501$		0			0
$502$	1521.46	−	1105.41i	0.135271	−	0.0982805i
$503$	−16851.6	−	12243.4i	−1.49379	−	1.08530i	−0.972774	−	0.231757i	$-0.925553\pi$
$503$	−16851.6	−	12243.4i	−1.49379	−	1.08530i	−0.521018	−	0.853546i	$-0.674447\pi$
$504$		0			0
$505$	−12349.7			−1.08823
$506$	−846.902	+	1595.45i	−0.0744059	+	0.140170i
$507$		0			0
$508$	799.820	+	2461.59i	0.0698549	+	0.214991i
$509$	−2020.32	−	1467.85i	−0.175931	−	0.127822i	0.496335	−	0.868131i	$-0.334679\pi$
$509$	−2020.32	−	1467.85i	−0.175931	−	0.127822i	−0.672266	+	0.740310i	$0.734679\pi$
$510$		0			0
$511$	76.7332	−	236.161i	0.00664281	−	0.0204445i
$512$	−2682.35	+	8255.42i	−0.231531	+	0.712581i
$513$		0			0
$514$	6458.49	+	4692.36i	0.554225	+	0.402668i
$515$	−357.589	−	1100.54i	−0.0305966	−	0.0941666i
$516$		0			0
$517$	1721.13	+	12185.4i	0.146412	+	1.03659i
$518$	10.5489			0.000894770
$519$		0			0
$520$	8508.75	+	6181.97i	0.717564	+	0.521341i
$521$	1260.27	−	915.642i	0.105976	−	0.0769961i	−0.533535	−	0.845778i	$-0.679137\pi$
$521$	1260.27	−	915.642i	0.105976	−	0.0769961i	0.639511	+	0.768782i	$0.279137\pi$
$522$		0			0
$523$	209.566	−	644.979i	0.0175214	−	0.0539254i	−0.941914	−	0.335855i	$-0.890975\pi$
$523$	209.566	−	644.979i	0.0175214	−	0.0539254i	0.959435	+	0.281930i	$0.0909746\pi$
$524$	−13840.9	+	10056.0i	−1.15390	+	0.838355i
$525$		0			0
$526$	859.876	+	2646.43i	0.0712783	+	0.219372i
$527$	11801.9			0.975519
$528$		0			0
$529$	−10723.6			−0.881366
$530$	553.753	+	1704.28i	0.0453839	+	0.139677i
$531$		0			0
$532$	209.095	−	151.916i	0.0170402	−	0.0123805i
$533$	6131.58	−	18871.1i	0.498289	−	1.53358i
$534$		0			0
$535$	10149.6	−	7374.11i	0.820196	−	0.595907i
$536$	−14800.4	−	10753.2i	−1.19269	−	0.866540i
$537$		0			0
$538$	−2.70988			−0.000217158
$539$	−11233.7	+	5488.64i	−0.897717	+	0.438613i
$540$		0			0
$541$	3113.03	+	9580.92i	0.247393	+	0.761397i	0.995234	+	0.0975190i	$0.0310907\pi$
$541$	3113.03	+	9580.92i	0.247393	+	0.761397i	−0.747841	+	0.663878i	$0.768909\pi$
$542$	4759.36	+	3457.87i	0.377181	+	0.274038i
$543$		0			0
$544$	−2409.69	+	7416.27i	−0.189917	+	0.584504i
$545$	−1627.97	+	5010.39i	−0.127954	+	0.393801i
$546$		0			0
$547$	−7192.79	−	5225.87i	−0.562233	−	0.408486i	0.270042	−	0.962848i	$-0.412962\pi$
$547$	−7192.79	−	5225.87i	−0.562233	−	0.408486i	−0.832276	+	0.554362i	$0.812962\pi$
$548$	5176.57	+	15931.9i	0.403526	+	1.24193i
$549$		0			0
$550$	2535.65	−	1238.89i	0.196583	−	0.0960477i
$551$	−9062.64			−0.700692
$552$		0			0
$553$	272.424	+	197.928i	0.0209487	+	0.0152201i
$554$	5094.93	−	3701.68i	0.390727	−	0.283880i
$555$		0			0
$556$	389.154	−	1197.69i	0.0296831	−	0.0913551i
$557$	10783.4	−	7834.61i	0.820302	−	0.595984i	−0.0964971	−	0.995333i	$-0.530764\pi$
$557$	10783.4	−	7834.61i	0.820302	−	0.595984i	0.916799	+	0.399349i	$0.130764\pi$
$558$		0			0
$559$	−6718.08	−	20676.1i	−0.508309	−	1.56441i
$560$	115.054			0.00868200
$561$		0			0
$562$	256.594			0.0192594
$563$	4277.13	+	13163.7i	0.320177	+	0.985403i	0.973571	+	0.228385i	$0.0733446\pi$
$563$	4277.13	+	13163.7i	0.320177	+	0.985403i	−0.653394	+	0.757018i	$0.726655\pi$
$564$		0			0
$565$	521.063	−	378.574i	0.0387987	−	0.0281889i
$566$	1102.96	−	3394.57i	0.0819100	−	0.252093i
$567$		0			0
$568$	−8072.55	+	5865.05i	−0.596332	+	0.433261i
$569$	696.201	+	505.820i	0.0512940	+	0.0372673i	0.613137	−	0.789977i	$-0.289907\pi$
$569$	696.201	+	505.820i	0.0512940	+	0.0372673i	−0.561843	+	0.827244i	$0.689907\pi$
$570$		0			0
$571$	−20409.1			−1.49579			−0.747895	−	0.663817i	$-0.768935\pi$
$571$	−20409.1			−1.49579			−0.747895	+	0.663817i	$0.768935\pi$
$572$	−2239.55	−	15855.8i	−0.163706	−	1.15903i
$573$		0			0
$574$	62.3579	+	191.918i	0.00453444	+	0.0139556i
$575$	−1824.47	−	1325.56i	−0.132323	−	0.0961384i
$576$		0			0
$577$	5400.99	−	16622.5i	0.389681	−	1.19932i	−0.543345	−	0.839509i	$-0.682843\pi$
$577$	5400.99	−	16622.5i	0.389681	−	1.19932i	0.933027	−	0.359807i	$-0.117157\pi$
$578$	1248.45	−	3842.34i	0.0898420	−	0.276505i
$579$		0			0
$580$	−4961.12	−	3604.47i	−0.355171	−	0.258047i
$581$	−33.3314	−	102.584i	−0.00238007	−	0.00732511i
$582$		0			0
$583$	2903.19	−	5469.22i	0.206240	−	0.388528i
$584$	8514.29			0.603294
$585$		0			0
$586$	−7001.20	−	5086.67i	−0.493545	−	0.358581i
$587$	−4427.82	+	3217.00i	−0.311339	+	0.226201i	−0.732471	−	0.680798i	$-0.761633\pi$
$587$	−4427.82	+	3217.00i	−0.311339	+	0.226201i	0.421132	+	0.906999i	$0.361633\pi$
$588$		0			0
$589$	6463.06	−	19891.2i	0.452132	−	1.39152i
$590$	6849.82	−	4976.69i	0.477971	−	0.347266i
$591$		0			0
$592$	−120.230	−	370.029i	−0.00834697	−	0.0256893i
$593$	5410.65			0.374686			0.187343	−	0.982295i	$-0.440012\pi$
$593$	5410.65			0.374686			0.187343	+	0.982295i	$0.440012\pi$
$594$		0			0
$595$	187.504			0.0129192
$596$	4894.99	+	15065.2i	0.336420	+	1.03540i
$597$		0			0
$598$	2789.87	−	2026.96i	0.190780	−	0.138610i
$599$	−312.658	+	962.262i	−0.0213270	+	0.0656377i	−0.961154	−	0.276014i	$-0.910986\pi$
$599$	−312.658	+	962.262i	−0.0213270	+	0.0656377i	0.939827	+	0.341652i	$0.110986\pi$
$600$		0			0
$601$	4898.46	−	3558.94i	0.332466	−	0.241551i	−0.409010	−	0.912530i	$-0.634126\pi$
$601$	4898.46	−	3558.94i	0.332466	−	0.241551i	0.741476	+	0.670979i	$0.234126\pi$
$602$	178.871	+	129.957i	0.0121100	+	0.00879843i
$603$		0			0
$604$	18720.4			1.26113
$605$	10138.4	+	3674.24i	0.681299	+	0.246908i
$606$		0			0
$607$	−2138.42	−	6581.38i	−0.142991	−	0.440082i	0.853756	−	0.520674i	$-0.174319\pi$
$607$	−2138.42	−	6581.38i	−0.142991	−	0.440082i	−0.996747	+	0.0805912i	$0.974319\pi$
$608$	11180.0	+	8122.73i	0.745736	+	0.541809i
$609$		0			0
$610$	1261.93	−	3883.82i	0.0837608	−	0.257789i
$611$	7260.25	−	22344.8i	0.480718	−	1.47950i
$612$		0			0
$613$	5859.67	+	4257.30i	0.386084	+	0.280507i	0.763849	−	0.645395i	$-0.223307\pi$
$613$	5859.67	+	4257.30i	0.386084	+	0.280507i	−0.377765	+	0.925902i	$0.623307\pi$
$614$	−1320.34	−	4063.60i	−0.0867830	−	0.267091i
$615$		0			0
$616$	256.925	+	265.686i	0.0168048	+	0.0173779i
$617$	−26187.8			−1.70872			−0.854361	−	0.519680i	$-0.826051\pi$
$617$	−26187.8			−1.70872			−0.854361	+	0.519680i	$0.826051\pi$
$618$		0			0
$619$	−6821.27	−	4955.94i	−0.442924	−	0.321803i	0.343872	−	0.939017i	$-0.388261\pi$
$619$	−6821.27	−	4955.94i	−0.442924	−	0.321803i	−0.786796	+	0.617214i	$0.788261\pi$
$620$	11449.3	−	8318.44i	0.741640	−	0.538833i
$621$		0			0
$622$	2642.86	−	8133.89i	0.170368	−	0.524339i
$623$	−579.438	+	420.986i	−0.0372627	+	0.0270730i
$624$		0			0
$625$	−1446.74	−	4452.60i	−0.0925912	−	0.284966i
$626$	−882.706			−0.0563579
$627$		0			0
$628$	−12935.0			−0.821912
$629$	−195.939	−	603.037i	−0.0124206	−	0.0382268i
$630$		0			0
$631$	−9244.96	+	6716.85i	−0.583258	+	0.423762i	−0.839897	−	0.542745i	$-0.817385\pi$
$631$	−9244.96	+	6716.85i	−0.583258	+	0.423762i	0.256639	+	0.966507i	$0.417385\pi$
$632$	−3567.94	+	10981.0i	−0.224565	+	0.691140i
$633$		0			0
$634$	−4012.34	+	2915.13i	−0.251341	+	0.182610i
$635$	2692.13	+	1955.95i	0.168243	+	0.122235i
$636$		0			0
$637$	23869.7			1.48470
$638$	−798.634	−	5654.25i	−0.0495583	−	0.350868i
$639$		0			0
$640$	3571.49	+	10991.9i	0.220587	+	0.678896i
$641$	−18412.5	−	13377.5i	−1.13456	−	0.824305i	−0.148206	−	0.988956i	$-0.547350\pi$
$641$	−18412.5	−	13377.5i	−1.13456	−	0.824305i	−0.986352	+	0.164652i	$0.947350\pi$
$642$		0			0
$643$	−223.272	+	687.160i	−0.0136936	+	0.0421445i	−0.957670	−	0.287869i	$-0.907053\pi$
$643$	−223.272	+	687.160i	−0.0136936	+	0.0421445i	0.943976	+	0.330013i	$0.107053\pi$
$644$	40.2145	−	123.768i	0.00246067	−	0.00757318i
$645$		0			0
$646$	3387.04	+	2460.83i	0.206287	+	0.149876i
$647$	−4013.07	−	12351.0i	−0.243849	−	0.750490i	−0.995824	−	0.0912978i	$-0.970898\pi$
$647$	−4013.07	−	12351.0i	−0.243849	−	0.750490i	0.751975	−	0.659192i	$-0.229102\pi$
$648$		0			0
$649$	−28815.3	−	5060.41i	−1.74283	−	0.306068i
$650$	−5387.83			−0.325120
$651$		0			0
$652$	−11816.0	−	8584.86i	−0.709742	−	0.515658i
$653$	−14462.7	+	10507.7i	−0.866720	+	0.629709i	−0.929705	−	0.368306i	$-0.879938\pi$
$653$	−14462.7	+	10507.7i	−0.866720	+	0.629709i	0.0629852	+	0.998014i	$0.479938\pi$
$654$		0			0
$655$	−6797.00	+	20919.0i	−0.405467	+	1.24790i
$656$	6021.28	−	4374.72i	0.358371	−	0.260372i
$657$		0			0
$658$	73.8364	+	227.245i	0.00437453	+	0.0134634i
$659$	−14584.5			−0.862114			−0.431057	−	0.902325i	$-0.641859\pi$
$659$	−14584.5			−0.862114			−0.431057	+	0.902325i	$0.641859\pi$
$660$		0			0
$661$	28799.8			1.69468			0.847340	−	0.531051i	$-0.178203\pi$
$661$	28799.8			1.69468			0.847340	+	0.531051i	$0.178203\pi$
$662$	−1344.81	−	4138.90i	−0.0789540	−	0.242996i
$663$		0			0
$664$	2992.11	−	2173.89i	0.174874	−	0.127053i
$665$	102.683	−	316.024i	0.00598776	−	0.0184284i
$666$		0			0
$667$	−3691.71	+	2682.18i	−0.214308	+	0.155704i
$668$	−6310.95	−	4585.17i	−0.365536	−	0.265577i
$669$		0			0
$670$	−10363.8			−0.597593
$671$	−12678.4	+	6194.50i	−0.729425	+	0.356388i
$672$		0			0
$673$	2962.02	+	9116.16i	0.169655	+	0.522143i	0.999349	−	0.0360746i	$-0.0114854\pi$
$673$	2962.02	+	9116.16i	0.169655	+	0.522143i	−0.829695	+	0.558218i	$0.811485\pi$
$674$	10158.5	+	7380.56i	0.580548	+	0.421793i
$675$		0			0
$676$	−5168.77	+	15907.8i	−0.294081	+	0.905089i
$677$	302.293	−	930.362i	0.0171611	−	0.0528164i	−0.942109	−	0.335306i	$-0.891160\pi$
$677$	302.293	−	930.362i	0.0171611	−	0.0528164i	0.959270	+	0.282490i	$0.0911603\pi$
$678$		0			0
$679$	408.881	+	297.069i	0.0231096	+	0.0167901i
$680$	1986.74	+	6114.55i	0.112041	+	0.344827i
$681$		0			0
$682$	12979.9	+	2279.46i	0.728775	+	0.127984i
$683$	32472.0			1.81919			0.909594	−	0.415499i	$-0.136393\pi$
$683$	32472.0			1.81919			0.909594	+	0.415499i	$0.136393\pi$
$684$		0			0
$685$	17423.9	+	12659.2i	0.971876	+	0.706109i
$686$	−392.953	+	285.497i	−0.0218703	+	0.0158897i
$687$		0			0
$688$	2519.92	−	7755.51i	0.139638	−	0.429762i
$689$	−9563.73	+	6948.45i	−0.528808	+	0.384202i
$690$		0			0
$691$	9145.60	+	28147.3i	0.503495	+	1.54960i	0.803286	+	0.595594i	$0.203083\pi$
$691$	9145.60	+	28147.3i	0.503495	+	1.54960i	−0.299791	+	0.954005i	$0.596917\pi$
$692$	−14435.7			−0.793011
$693$		0			0
$694$	3470.53			0.189826
$695$	−500.322	−	1539.83i	−0.0273069	−	0.0840420i
$696$		0			0
$697$	9812.91	−	7129.50i	0.533272	−	0.387445i
$698$	−2172.17	+	6685.26i	−0.117791	+	0.362523i
$699$		0			0
$700$	−164.492	+	119.510i	−0.00888174	+	0.00645296i
$701$	21631.7	+	15716.4i	1.16550	+	0.846788i	0.990464	−	0.137773i	$-0.0439945\pi$
$701$	21631.7	+	15716.4i	1.16550	+	0.846788i	0.175040	+	0.984561i	$0.443994\pi$
$702$		0			0
$703$	−1123.68			−0.0602849
$704$	−507.473	+	956.009i	−0.0271678	+	0.0511803i
$705$		0			0
$706$	1209.37	+	3722.06i	0.0644693	+	0.198416i
$707$	670.301	+	487.002i	0.0356567	+	0.0259061i
$708$		0			0
$709$	971.474	−	2989.89i	0.0514591	−	0.158375i	−0.922025	−	0.387131i	$-0.873466\pi$
$709$	971.474	−	2989.89i	0.0514591	−	0.158375i	0.973484	+	0.228757i	$0.0734660\pi$
$710$	−1746.77	+	5376.01i	−0.0923311	+	0.284166i
$711$		0			0
$712$	−19868.0	−	14435.0i	−1.04577	−	0.759793i
$713$	−3254.26	−	10015.6i	−0.170930	−	0.526069i
$714$		0			0
$715$	−14311.6	−	14799.6i	−0.748563	−	0.774089i
$716$	3404.18			0.177682
$717$		0			0
$718$	−2137.55	−	1553.02i	−0.111104	−	0.0807217i
$719$	−6899.82	+	5013.01i	−0.357886	+	0.260019i	−0.752170	−	0.658969i	$-0.770993\pi$
$719$	−6899.82	+	5013.01i	−0.357886	+	0.260019i	0.394284	+	0.918989i	$0.370993\pi$
$720$		0			0
$721$	−23.9905	+	73.8350i	−0.00123918	+	0.00381381i
$722$	−1229.00	+	892.919i	−0.0633498	+	0.0460263i
$723$		0			0
$724$	4362.77	+	13427.2i	0.223952	+	0.689252i
$725$	7129.46			0.365216
$726$		0			0
$727$	−34617.2			−1.76600			−0.882999	−	0.469374i	$-0.844480\pi$
$727$	−34617.2			−1.76600			−0.882999	+	0.469374i	$0.844480\pi$
$728$	−218.045	−	671.072i	−0.0111006	−	0.0341643i
$729$		0			0
$730$	3902.17	−	2835.09i	0.197844	−	0.143742i
$731$	4106.72	−	12639.2i	0.207787	−	0.639504i
$732$		0			0
$733$	−7928.59	+	5760.46i	−0.399521	+	0.290269i	−0.769346	−	0.638832i	$-0.779418\pi$
$733$	−7928.59	+	5760.46i	−0.399521	+	0.290269i	0.369825	+	0.929102i	$0.379418\pi$
$734$	−2573.95	−	1870.08i	−0.129436	−	0.0940408i
$735$		0			0
$736$	6958.22			0.348483
$737$	24894.1	+	25743.0i	1.24421	+	1.28664i
$738$		0			0
$739$	−570.498	−	1755.81i	−0.0283980	−	0.0874000i	0.935853	−	0.352391i	$-0.114631\pi$
$739$	−570.498	−	1755.81i	−0.0283980	−	0.0874000i	−0.964251	+	0.264991i	$0.914631\pi$
$740$	−615.130	−	446.918i	−0.0305576	−	0.0222014i
$741$		0			0
$742$	37.1510	−	114.339i	0.00183808	−	0.00565703i
$743$	−6702.83	+	20629.2i	−0.330959	+	1.01859i	0.637719	+	0.770269i	$0.279878\pi$
$743$	−6702.83	+	20629.2i	−0.330959	+	1.01859i	−0.968678	+	0.248319i	$0.920122\pi$
$744$		0			0
$745$	16476.2	+	11970.6i	0.810254	+	0.588684i
$746$	−4192.33	−	12902.7i	−0.205753	−	0.633244i
$747$		0			0
$748$	4589.57	−	8646.12i	0.224347	−	0.422638i
$749$	−841.677			−0.0410604
$750$		0			0
$751$	9879.50	+	7177.88i	0.480038	+	0.348768i	0.801340	−	0.598209i	$-0.204121\pi$
$751$	9879.50	+	7177.88i	0.480038	+	0.348768i	−0.321303	+	0.946977i	$0.604121\pi$
$752$	7129.65	−	5180.00i	0.345734	−	0.251190i
$753$		0			0
$754$	−3368.88	+	10368.3i	−0.162715	+	0.500787i
$755$	19471.6	−	14146.9i	0.938599	−	0.681932i
$756$		0			0
$757$	−230.800	−	710.330i	−0.0110813	−	0.0341049i	0.945363	−	0.326020i	$-0.105708\pi$
$757$	−230.800	−	710.330i	−0.0110813	−	0.0341049i	−0.956444	+	0.291915i	$0.905708\pi$
$758$	−6359.70			−0.304742
$759$		0			0
$760$	11393.6			0.543803
$761$	−1525.80	−	4695.94i	−0.0726811	−	0.223689i	0.908117	−	0.418717i	$-0.137520\pi$
$761$	−1525.80	−	4695.94i	−0.0726811	−	0.223689i	−0.980798	+	0.195028i	$0.937520\pi$
$762$		0			0
$763$	285.942	−	207.749i	0.0135672	−	0.00985716i
$764$	1231.22	−	3789.31i	0.0583038	−	0.179441i
$765$		0			0
$766$	−12608.5	+	9160.59i	−0.594729	+	0.432096i
$767$	45187.2	+	32830.4i	2.12727	+	1.54555i
$768$		0			0
$769$	−2022.76			−0.0948538			−0.0474269	−	0.998875i	$-0.515102\pi$
$769$	−2022.76			−0.0948538			−0.0474269	+	0.998875i	$0.515102\pi$
$770$	206.219	+	36.2152i	0.00965145	+	0.00169494i
$771$		0			0
$772$	−8032.35	−	24721.0i	−0.374469	−	1.15250i
$773$	−8789.54	−	6385.97i	−0.408975	−	0.297138i	0.364212	−	0.931316i	$-0.381338\pi$
$773$	−8789.54	−	6385.97i	−0.408975	−	0.297138i	−0.773187	+	0.634178i	$0.781338\pi$
$774$		0			0
$775$	−5084.40	+	15648.2i	−0.235661	+	0.725289i
$776$	−5355.12	+	16481.4i	−0.247729	+	0.762431i
$777$		0			0
$778$	−7567.19	−	5497.89i	−0.348711	−	0.253353i
$779$	−6642.42	−	20443.3i	−0.305506	−	0.940252i
$780$		0			0
$781$	17549.5	−	8574.46i	0.804059	−	0.392853i
$782$	2108.03			0.0963977
$783$		0			0
$784$	7243.47	+	5262.69i	0.329968	+	0.239736i
$785$	−13454.0	+	9774.90i	−0.611712	+	0.444435i
$786$		0			0
$787$	−5828.24	+	17937.5i	−0.263983	+	0.812455i	0.727943	+	0.685637i	$0.240476\pi$
$787$	−5828.24	+	17937.5i	−0.263983	+	0.812455i	−0.991926	+	0.126818i	$0.959524\pi$
$788$	−16811.0	+	12213.9i	−0.759982	+	0.552160i
$789$		0			0
$790$	2021.24	+	6220.73i	0.0910284	+	0.280157i
$791$	−43.2103			−0.00194233
$792$		0			0
$793$	26939.5			1.20637
$794$	1160.34	+	3571.15i	0.0518625	+	0.159616i
$795$		0			0
$796$	241.616	−	175.544i	0.0107586	−	0.00781659i
$797$	−11087.4	+	34123.6i	−0.492769	+	1.51659i	0.327635	+	0.944804i	$0.393748\pi$
$797$	−11087.4	+	34123.6i	−0.492769	+	1.51659i	−0.820405	+	0.571784i	$0.806252\pi$
$798$		0			0
$799$	11619.2	−	8441.86i	0.514467	−	0.373782i
$800$	−8795.14	−	6390.04i	−0.388694	−	0.282403i
$801$		0			0
$802$	−5164.71			−0.227397
$803$	−16415.4	−	2882.79i	−0.721402	−	0.126689i
$804$		0			0
$805$	−51.7025	−	159.124i	−0.00226369	−	0.00696694i
$806$	−20354.6	−	14788.5i	−0.889527	−	0.646279i
$807$		0			0
$808$	−8778.95	+	27018.8i	−0.382230	+	1.17638i
$809$	10924.1	−	33621.1i	0.474750	−	1.46113i	−0.371545	−	0.928415i	$-0.621172\pi$
$809$	10924.1	−	33621.1i	0.474750	−	1.46113i	0.846295	−	0.532715i	$-0.178828\pi$
$810$		0			0
$811$	7545.06	+	5481.81i	0.326687	+	0.237352i	0.739023	−	0.673680i	$-0.235287\pi$
$811$	7545.06	+	5481.81i	0.326687	+	0.237352i	−0.412337	+	0.911032i	$0.635287\pi$
$812$	127.133	+	391.276i	0.00549446	+	0.0169102i
$813$		0			0
$814$	−99.0226	−	701.071i	−0.00426381	−	0.0301874i
$815$	−18777.7			−0.807062
$816$		0			0
$817$	−19053.5	−	13843.2i	−0.815908	−	0.592792i
$818$	9532.69	−	6925.91i	0.407461	−	0.296037i
$819$		0			0
$820$	4494.63	−	13833.1i	0.191414	−	0.589111i
$821$	37644.4	−	27350.3i	1.60024	−	1.16265i	0.713200	−	0.700961i	$-0.247245\pi$
$821$	37644.4	−	27350.3i	1.60024	−	1.16265i	0.887044	−	0.461684i	$-0.152755\pi$
$822$		0			0
$823$	5557.40	+	17103.9i	0.235381	+	0.724430i	0.997071	+	0.0764869i	$0.0243704\pi$
$823$	5557.40	+	17103.9i	0.235381	+	0.724430i	−0.761689	+	0.647943i	$0.775630\pi$
$824$	−2661.97			−0.112542
$825$		0			0
$826$	−568.037			−0.0239280
$827$	−13371.2	−	41152.2i	−0.562226	−	1.73035i	−0.676053	−	0.736853i	$-0.736311\pi$
$827$	−13371.2	−	41152.2i	−0.562226	−	1.73035i	0.113826	−	0.993501i	$-0.463689\pi$
$828$		0			0
$829$	29047.1	−	21104.0i	1.21695	−	0.884163i	0.221103	−	0.975250i	$-0.429034\pi$
$829$	29047.1	−	21104.0i	1.21695	−	0.884163i	0.995843	+	0.0910873i	$0.0290342\pi$
$830$	647.444	−	1992.63i	0.0270760	−	0.0833314i
$831$		0			0
$832$	1671.72	−	1214.58i	0.0696593	−	0.0506104i
$833$	11804.7	+	8576.62i	0.491007	+	0.356738i
$834$		0			0
$835$	−10029.2			−0.415658
$836$	−12059.0	−	12470.3i	−0.498888	−	0.515900i
$837$		0			0
$838$	−338.314	−	1041.22i	−0.0139462	−	0.0429219i
$839$	23775.0	+	17273.6i	0.978314	+	0.710787i	0.957331	−	0.288993i	$-0.0933204\pi$
$839$	23775.0	+	17273.6i	0.978314	+	0.710787i	0.0209831	+	0.999780i	$0.493320\pi$
$840$		0			0
$841$	−3078.74	+	9475.37i	−0.126235	+	0.388510i
$842$	−807.400	+	2484.92i	−0.0330461	+	0.101706i
$843$		0			0
$844$	−7743.31	−	5625.84i	−0.315800	−	0.229442i
$845$	6645.33	+	20452.2i	0.270540	+	0.832636i
$846$		0			0
$847$	−405.388	−	599.227i	−0.0164455	−	0.0243089i
$848$	−4434.15			−0.179563
$849$		0			0
$850$	−2664.54	−	1935.90i	−0.107521	−	0.0781185i
$851$	−457.735	+	332.564i	−0.0184383	+	0.0133962i
$852$		0			0
$853$	5340.34	−	16435.9i	0.214361	−	0.659735i	−0.784838	−	0.619702i	$-0.787254\pi$
$853$	5340.34	−	16435.9i	0.214361	−	0.659735i	0.999198	−	0.0400331i	$-0.0127463\pi$
$854$	−221.649	+	161.037i	−0.00888134	+	0.00645267i
$855$		0			0
$856$	−8918.16	−	27447.3i	−0.356094	−	1.09595i
$857$	−25834.0			−1.02972			−0.514862	−	0.857273i	$-0.672157\pi$
$857$	−25834.0			−1.02972			−0.514862	+	0.857273i	$0.672157\pi$
$858$		0			0
$859$	−29861.7			−1.18611			−0.593055	−	0.805162i	$-0.702078\pi$
$859$	−29861.7			−1.18611			−0.593055	+	0.805162i	$0.702078\pi$
$860$	−4924.55	−	15156.2i	−0.195263	−	0.600956i
$861$		0			0
$862$	12566.5	−	9130.12i	0.496541	−	0.360758i
$863$	488.835	−	1504.48i	0.0192817	−	0.0593430i	−0.940953	−	0.338538i	$-0.890068\pi$
$863$	488.835	−	1504.48i	0.0192817	−	0.0593430i	0.960234	+	0.279195i	$0.0900676\pi$
$864$		0			0
$865$	−15015.0	+	10909.0i	−0.590202	+	0.428807i
$866$	1013.02	+	736.003i	0.0397504	+	0.0288804i
$867$		0			0
$868$	−949.463			−0.0371277
$869$	10596.9	−	19963.1i	0.413664	−	0.779287i
$870$		0			0
$871$	−21126.9	−	65021.9i	−0.821880	−	2.52949i
$872$	9804.49	+	7123.38i	0.380759	+	0.276638i
$873$		0			0
$874$	1154.42	−	3552.93i	0.0446782	−	0.137505i
$875$	−250.887	+	772.151i	−0.00969318	+	0.0298325i
$876$		0			0
$877$	17706.6	+	12864.6i	0.681765	+	0.495331i	0.873943	−	0.486029i	$-0.161555\pi$
$877$	17706.6	+	12864.6i	0.681765	+	0.495331i	−0.192178	+	0.981360i	$0.561555\pi$
$878$	3056.70	+	9407.56i	0.117493	+	0.361606i
$879$		0			0
$880$	−1080.02	−	7646.41i	−0.0413720	−	0.292910i
$881$	2989.02			0.114305			0.0571524	−	0.998365i	$-0.481798\pi$
$881$	2989.02			0.114305			0.0571524	+	0.998365i	$0.481798\pi$
$882$		0			0
$883$	−7314.67	−	5314.42i	−0.278775	−	0.202542i	0.439608	−	0.898190i	$-0.355117\pi$
$883$	−7314.67	−	5314.42i	−0.278775	−	0.202542i	−0.718383	+	0.695648i	$0.755117\pi$
$884$	−15119.0	+	10984.6i	−0.575235	+	0.417932i
$885$		0			0
$886$	171.035	−	526.391i	0.00648535	−	0.0199599i
$887$	−26473.9	+	19234.4i	−1.00215	+	0.728103i	−0.962548	−	0.271113i	$-0.912608\pi$
$887$	−26473.9	+	19234.4i	−1.00215	+	0.728103i	−0.0396001	+	0.999216i	$0.512608\pi$
$888$		0			0
$889$	−68.9884	−	212.324i	−0.00260270	−	0.00801027i
$890$	−13912.2			−0.523977
$891$		0			0
$892$	−6448.47			−0.242052
$893$	−7865.13	−	24206.4i	−0.294733	−	0.907095i
$894$		0			0
$895$	3540.79	−	2572.53i	0.132241	−	0.0960785i
$896$	239.609	−	737.442i	0.00893392	−	0.0274958i
$897$		0			0
$898$	4990.51	−	3625.82i	0.185452	−	0.134738i
$899$	26934.2	+	19568.9i	0.999229	+	0.725982i
$900$		0			0
$901$	−7226.36			−0.267198
$902$	12169.4	−	5945.80i	0.449219	−	0.219483i
$903$		0			0
$904$	−457.844	−	1409.10i	−0.0168448	−	0.0518428i
$905$	14684.7	+	10669.1i	0.539378	+	0.391881i
$906$		0			0
$907$	−3369.67	+	10370.8i	−0.123361	+	0.379665i	−0.993599	−	0.112966i	$-0.963965\pi$
$907$	−3369.67	+	10370.8i	−0.123361	+	0.379665i	0.870238	+	0.492631i	$0.163965\pi$
$908$	4954.85	−	15249.5i	0.181093	−	0.557347i
$909$		0			0
$910$	−323.386	−	234.953i	−0.0117804	−	0.00855893i
$911$	−7341.32	−	22594.2i	−0.266991	−	0.821713i	−0.991228	−	0.132162i	$-0.957808\pi$
$911$	−7341.32	−	22594.2i	−0.266991	−	0.821713i	0.724237	−	0.689551i	$-0.242192\pi$
$912$		0			0
$913$	−6504.75	+	3178.14i	−0.235790	+	0.115204i
$914$	19770.1			0.715468
$915$		0			0
$916$	−18241.8	−	13253.4i	−0.657997	−	0.478063i
$917$	1193.84	−	867.378i	0.0429926	−	0.0312359i
$918$		0			0
$919$	5238.38	−	16122.1i	0.188028	−	0.578692i	−0.811959	−	0.583715i	$-0.801599\pi$
$919$	5238.38	−	16122.1i	0.188028	−	0.578692i	0.999987	+	0.00502241i	$0.00159869\pi$
$920$	4641.25	−	3372.06i	0.166323	−	0.120841i
$921$		0			0
$922$	−5215.92	−	16053.0i	−0.186309	−	0.573401i
$923$	−37289.7			−1.32980
$924$		0			0
$925$	883.982			0.0314218
$926$	2728.03	+	8396.02i	0.0968129	+	0.297959i
$927$		0			0
$928$	−17796.4	+	12929.8i	−0.629521	+	0.457374i
$929$	−11895.8	+	36611.5i	−0.420117	+	1.29299i	0.487476	+	0.873136i	$0.337918\pi$
$929$	−11895.8	+	36611.5i	−0.420117	+	1.29299i	−0.907593	+	0.419851i	$0.862082\pi$
$930$		0			0
$931$	20919.9	−	15199.2i	0.736435	−	0.535052i
$932$	−8818.13	−	6406.75i	−0.309922	−	0.225172i
$933$		0			0
$934$	6759.86			0.236819
$935$	−1760.11	−	12461.4i	−0.0615632	−	0.435862i
$936$		0			0
$937$	15072.7	+	46389.1i	0.525512	+	1.61736i	0.763301	+	0.646043i	$0.223577\pi$
$937$	15072.7	+	46389.1i	0.525512	+	1.61736i	−0.237789	+	0.971317i	$0.576423\pi$
$938$	562.509	+	408.687i	0.0195806	+	0.0142261i
$939$		0			0
$940$	5321.98	−	16379.4i	0.184664	−	0.568337i
$941$	−2427.23	+	7470.24i	−0.0840865	+	0.258792i	−0.984256	−	0.176748i	$-0.943442\pi$
$941$	−2427.23	+	7470.24i	−0.0840865	+	0.258792i	0.900170	+	0.435539i	$0.143442\pi$
$942$		0			0
$943$	−8756.22	−	6361.77i	−0.302377	−	0.219690i
$944$	6474.13	+	19925.3i	0.223215	+	0.686985i
$945$		0			0
$946$	6957.80	−	13107.5i	0.239131	−	0.450489i
$947$	38877.6			1.33406			0.667029	−	0.745032i	$-0.267566\pi$
$947$	38877.6			1.33406			0.667029	+	0.745032i	$0.267566\pi$
$948$		0			0
$949$	25742.0	+	18702.7i	0.880528	+	0.639741i
$950$	−4721.99	+	3430.73i	−0.161265	+	0.117166i
$951$		0			0
$952$	133.289	−	410.222i	0.00453774	−	0.0139657i
$953$	−10438.9	+	7584.32i	−0.354827	+	0.257797i	−0.750891	−	0.660426i	$-0.770376\pi$
$953$	−10438.9	+	7584.32i	−0.354827	+	0.257797i	0.396064	+	0.918223i	$0.370376\pi$
$954$		0			0
$955$	−1582.94	−	4871.80i	−0.0536365	−	0.165076i
$956$	33936.8			1.14811
$957$		0			0
$958$	−3587.66			−0.120994
$959$	−446.505	−	1374.20i	−0.0150348	−	0.0462724i
$960$		0			0
$961$	−38057.8	+	27650.6i	−1.27749	+	0.928153i
$962$	−417.708	+	1285.57i	−0.0139994	+	0.0430858i
$963$		0			0
$964$	−17922.1	+	13021.2i	−0.598788	+	0.435045i
$965$	−27036.3	−	19643.0i	−0.901894	−	0.655264i
$966$		0			0
$967$	−5006.71			−0.166499			−0.0832497	−	0.996529i	$-0.526530\pi$
$967$	−5006.71			−0.166499			−0.0832497	+	0.996529i	$0.526530\pi$
$968$	15245.5	−	19569.0i	0.506209	−	0.649765i
$969$		0			0
$970$	3033.68	+	9336.69i	0.100418	+	0.309055i
$971$	−12665.8	−	9202.27i	−0.418605	−	0.304135i	0.358471	−	0.933541i	$-0.383298\pi$
$971$	−12665.8	−	9202.27i	−0.418605	−	0.304135i	−0.777076	+	0.629406i	$0.783298\pi$
$972$		0			0
$973$	−33.5664	+	103.307i	−0.00110595	+	0.00340376i
$974$	3753.35	−	11551.6i	0.123475	−	0.380018i
$975$		0			0
$976$	8175.00	+	5939.49i	0.268110	+	0.194793i
$977$	3454.62	+	10632.2i	0.113125	+	0.348163i	0.991551	−	0.129715i	$-0.0414062\pi$
$977$	3454.62	+	10632.2i	0.113125	+	0.348163i	−0.878426	+	0.477878i	$0.841406\pi$
$978$		0			0
$979$	33417.6	+	34557.2i	1.09094	+	1.12814i
$980$	17497.2			0.570335
$981$		0			0
$982$	10318.7	+	7497.00i	0.335320	+	0.243624i
$983$	−21979.6	+	15969.1i	−0.713165	+	0.518145i	−0.884193	−	0.467121i	$-0.845291\pi$
$983$	−21979.6	+	15969.1i	−0.713165	+	0.518145i	0.171028	+	0.985266i	$0.445291\pi$
$984$		0			0
$985$	−8255.56	+	25408.0i	−0.267050	+	0.821895i
$986$	−5391.52	+	3917.17i	−0.174139	+	0.126519i
$987$		0			0
$988$	10234.2	+	31497.5i	0.329546	+	1.01424i
$989$	−11858.6			−0.381274
$990$		0			0
$991$	59150.4			1.89604			0.948020	−	0.318212i	$-0.103082\pi$
$991$	59150.4			1.89604			0.948020	+	0.318212i	$0.103082\pi$
$992$	−15687.6	−	48281.6i	−0.502100	−	1.54531i
$993$		0			0
$994$	306.807	−	222.909i	0.00979008	−	0.00711291i
$995$	118.653	−	365.177i	0.00378046	−	0.0116351i
$996$		0			0
$997$	35480.0	−	25777.8i	1.12705	−	0.818846i	0.141783	−	0.989898i	$-0.454716\pi$
$997$	35480.0	−	25777.8i	1.12705	−	0.818846i	0.985262	+	0.171051i	$0.0547164\pi$
$998$	9224.24	+	6701.80i	0.292573	+	0.212567i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.d.82.2		12
3.2	odd	2		33.4.e.c.16.2	✓	12
11.3	even	5		1089.4.a.bi.1.4		6
11.8	odd	10		1089.4.a.bk.1.3		6
11.9	even	5	inner	99.4.f.d.64.2		12
33.8	even	10		363.4.a.u.1.4		6
33.14	odd	10		363.4.a.v.1.3		6
33.20	odd	10		33.4.e.c.31.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.c.16.2	✓	12	3.2	odd	2
33.4.e.c.31.2	yes	12	33.20	odd	10
99.4.f.d.64.2		12	11.9	even	5	inner
99.4.f.d.82.2		12	1.1	even	1	trivial
363.4.a.u.1.4		6	33.8	even	10
363.4.a.v.1.3		6	33.14	odd	10
1089.4.a.bi.1.4		6	11.3	even	5
1089.4.a.bk.1.3		6	11.8	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.402703 - 1.23939i) q^{2} +(5.09821 - 3.70407i) q^{4} +(2.50364 - 7.70540i) q^{5} +(-0.439746 + 0.319494i) q^{7} +(-15.0782 - 10.9549i) q^{8} +O(q^{10})\)	\(q+(-0.402703 - 1.23939i) q^{2} +(5.09821 - 3.70407i) q^{4} +(2.50364 - 7.70540i) q^{5} +(-0.439746 + 0.319494i) q^{7} +(-15.0782 - 10.9549i) q^{8} -10.5582 q^{10} +(25.3612 + 26.2261i) q^{11} +(-21.5234 - 66.2421i) q^{13} +(0.573065 + 0.416356i) q^{14} +(8.07330 - 24.8471i) q^{16} +(13.1571 - 40.4934i) q^{17} +(-61.0435 - 44.3507i) q^{19} +(-15.7773 - 48.5574i) q^{20} +(22.2914 - 41.9939i) q^{22} -37.9924 q^{23} +(48.0221 + 34.8901i) q^{25} +(-73.4324 + 53.3518i) q^{26} +(-1.05849 + 3.25769i) q^{28} +(97.1697 - 70.5979i) q^{29} +(85.6557 + 263.621i) q^{31} -183.148 q^{32} -55.4856 q^{34} +(1.36087 + 4.18831i) q^{35} +(12.0481 - 8.75344i) q^{37} +(-30.3855 + 93.5170i) q^{38} +(-122.163 + 88.7563i) q^{40} +(230.473 + 167.448i) q^{41} +312.130 q^{43} +(226.440 + 39.7664i) q^{44} +(15.2997 + 47.0875i) q^{46} +(272.897 + 198.272i) q^{47} +(-105.902 + 325.931i) q^{49} +(23.9039 - 73.5686i) q^{50} +(-355.096 - 257.992i) q^{52} +(-52.4474 - 161.417i) q^{53} +(265.578 - 129.758i) q^{55} +10.1306 q^{56} +(-126.629 - 92.0014i) q^{58} +(-648.765 + 471.356i) q^{59} +(-119.521 + 367.847i) q^{61} +(292.236 - 212.322i) q^{62} +(9.16772 + 28.2153i) q^{64} -564.309 q^{65} +981.580 q^{67} +(-82.9126 - 255.179i) q^{68} +(4.64294 - 3.37329i) q^{70} +(165.441 - 509.176i) q^{71} +(-369.585 + 268.520i) q^{73} +(-15.7007 - 11.4073i) q^{74} -475.490 q^{76} +(-19.5316 - 3.43004i) q^{77} +(-191.437 - 589.183i) q^{79} +(-171.244 - 124.416i) q^{80} +(114.722 - 353.079i) q^{82} +(-61.3212 + 188.727i) q^{83} +(-279.077 - 202.762i) q^{85} +(-125.696 - 386.851i) q^{86} +(-95.0962 - 673.273i) q^{88} +1317.67 q^{89} +(30.6287 + 22.2531i) q^{91} +(-193.693 + 140.726i) q^{92} +(135.840 - 418.072i) q^{94} +(-494.571 + 359.327i) q^{95} +(-287.328 - 884.304i) q^{97} +446.604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 28 q^{5} + 12 q^{7} + 112 q^{8}+O(q^{10}) \) 12 * q - 16 * q^4 - 28 * q^5 + 12 * q^7 + 112 * q^8	\( 12 q - 16 q^{4} - 28 q^{5} + 12 q^{7} + 112 q^{8} + 100 q^{10} + 54 q^{11} - 18 q^{13} - 156 q^{14} + 308 q^{16} + 80 q^{17} - 280 q^{19} + 15 q^{20} - 193 q^{22} + 392 q^{23} + 77 q^{25} - 406 q^{26} - 429 q^{28} - 13 q^{29} + 413 q^{31} - 1314 q^{32} + 1060 q^{34} + 1239 q^{35} + 654 q^{37} - 912 q^{38} - 1803 q^{40} + 1490 q^{41} + 416 q^{43} - 695 q^{44} - 2369 q^{46} + 150 q^{47} - 301 q^{49} + 1878 q^{50} - 1661 q^{52} - 1359 q^{53} + 3300 q^{55} + 858 q^{56} + 955 q^{58} - 1262 q^{59} - 1044 q^{61} + 701 q^{62} + 78 q^{64} - 4556 q^{65} - 528 q^{67} - 703 q^{68} + 3050 q^{70} - 558 q^{71} - 699 q^{73} + 3224 q^{74} - 868 q^{76} - 390 q^{77} - 1252 q^{79} + 1914 q^{80} + 2987 q^{82} + 4464 q^{83} - 2170 q^{85} + 3209 q^{86} + 1302 q^{88} - 316 q^{89} + 176 q^{91} - 4595 q^{92} + 1247 q^{94} - 1466 q^{95} + 1608 q^{97} - 2810 q^{98}+O(q^{100}) \) 12 * q - 16 * q^4 - 28 * q^5 + 12 * q^7 + 112 * q^8 + 100 * q^10 + 54 * q^11 - 18 * q^13 - 156 * q^14 + 308 * q^16 + 80 * q^17 - 280 * q^19 + 15 * q^20 - 193 * q^22 + 392 * q^23 + 77 * q^25 - 406 * q^26 - 429 * q^28 - 13 * q^29 + 413 * q^31 - 1314 * q^32 + 1060 * q^34 + 1239 * q^35 + 654 * q^37 - 912 * q^38 - 1803 * q^40 + 1490 * q^41 + 416 * q^43 - 695 * q^44 - 2369 * q^46 + 150 * q^47 - 301 * q^49 + 1878 * q^50 - 1661 * q^52 - 1359 * q^53 + 3300 * q^55 + 858 * q^56 + 955 * q^58 - 1262 * q^59 - 1044 * q^61 + 701 * q^62 + 78 * q^64 - 4556 * q^65 - 528 * q^67 - 703 * q^68 + 3050 * q^70 - 558 * q^71 - 699 * q^73 + 3224 * q^74 - 868 * q^76 - 390 * q^77 - 1252 * q^79 + 1914 * q^80 + 2987 * q^82 + 4464 * q^83 - 2170 * q^85 + 3209 * q^86 + 1302 * q^88 - 316 * q^89 + 176 * q^91 - 4595 * q^92 + 1247 * q^94 - 1466 * q^95 + 1608 * q^97 - 2810 * q^98

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