LMFDB - Embedded newform 261.3.s.a.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	261.73
Dual form			261.3.s.a.118.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.56136 - 0.401269i) q^{2} +(8.62256 - 1.96804i) q^{4} +(-5.24106 - 4.17960i) q^{5} +(2.11977 - 9.28734i) q^{7} +(16.3872 - 5.73413i) q^{8} +O(q^{10})$	\(q+(3.56136 - 0.401269i) q^{2} +(8.62256 - 1.96804i) q^{4} +(-5.24106 - 4.17960i) q^{5} +(2.11977 - 9.28734i) q^{7} +(16.3872 - 5.73413i) q^{8} +(-20.3424 - 12.7820i) q^{10} +(0.700768 + 0.245209i) q^{11} +(3.39382 + 7.04735i) q^{13} +(3.82256 - 33.9262i) q^{14} +(24.1861 - 11.6474i) q^{16} +(17.4730 + 17.4730i) q^{17} +(-7.96846 + 12.6817i) q^{19} +(-53.4169 - 25.7242i) q^{20} +(2.59408 + 0.592082i) q^{22} +(11.9732 + 15.0139i) q^{23} +(4.43656 + 19.4379i) q^{25} +(14.9145 + 23.7363i) q^{26} -84.2524i q^{28} +(19.7681 - 21.2184i) q^{29} +(0.327624 - 0.0369143i) q^{31} +(22.6600 - 14.2382i) q^{32} +(69.2390 + 55.2162i) q^{34} +(-49.9272 + 39.8156i) q^{35} +(-15.2693 + 5.34296i) q^{37} +(-23.2898 + 48.3617i) q^{38} +(-109.853 - 38.4391i) q^{40} +(-28.0484 + 28.0484i) q^{41} +(0.679170 - 6.02780i) q^{43} +(6.52499 + 0.735190i) q^{44} +(48.6656 + 48.6656i) q^{46} +(-1.43620 + 4.10443i) q^{47} +(-37.6137 - 18.1138i) q^{49} +(23.6000 + 67.4450i) q^{50} +(43.1329 + 54.0870i) q^{52} +(37.6082 - 47.1592i) q^{53} +(-2.64789 - 4.21408i) q^{55} +(-18.5176 - 164.349i) q^{56} +(61.8871 - 83.4988i) q^{58} -91.1542 q^{59} +(6.43745 - 4.04492i) q^{61} +(1.15197 - 0.262930i) q^{62} +(-8.96447 + 7.14893i) q^{64} +(11.6679 - 51.1204i) q^{65} +(29.8663 - 62.0180i) q^{67} +(185.049 + 116.274i) q^{68} +(-161.832 + 161.832i) q^{70} +(38.1572 + 79.2343i) q^{71} +(-29.1293 - 3.28209i) q^{73} +(-52.2355 + 25.1553i) q^{74} +(-43.7503 + 125.031i) q^{76} +(3.76281 - 5.98848i) q^{77} +(7.28322 + 20.8142i) q^{79} +(-175.442 - 40.0435i) q^{80} +(-88.6354 + 111.145i) q^{82} +(-9.19165 - 40.2713i) q^{83} +(-18.5468 - 164.607i) q^{85} -21.7397i q^{86} +12.8897 q^{88} +(-98.0089 + 11.0429i) q^{89} +(72.6452 - 16.5808i) q^{91} +(132.788 + 105.895i) q^{92} +(-3.46785 + 15.1936i) q^{94} +(94.7678 - 33.1607i) q^{95} +(136.891 + 86.0143i) q^{97} +(-141.224 - 49.4166i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$1$

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 $

$2$	3.56136	−	0.401269i	1.78068	−	0.200634i	0.840616	−	0.541632i	$-0.182193\pi$
$2$	3.56136	−	0.401269i	1.78068	−	0.200634i	0.940064	+	0.340997i	$0.110765\pi$
$3$		0			0
$3$		0			0
$4$	8.62256	−	1.96804i	2.15564	−	0.492011i
$5$	−5.24106	−	4.17960i	−1.04821	−	0.835920i	−0.0614515	−	0.998110i	$-0.519573\pi$
$5$	−5.24106	−	4.17960i	−1.04821	−	0.835920i	−0.986760	+	0.162190i	$0.948144\pi$
$6$		0			0
$7$	2.11977	−	9.28734i	0.302825	−	1.32676i	−0.563017	−	0.826445i	$-0.690360\pi$
$7$	2.11977	−	9.28734i	0.302825	−	1.32676i	0.865842	−	0.500317i	$-0.166783\pi$
$8$	16.3872	−	5.73413i	2.04840	−	0.716766i
$9$		0			0
$10$	−20.3424	−	12.7820i	−2.03424	−	1.27820i
$11$	0.700768	+	0.245209i	0.0637061	+	0.0222917i	0.361944	−	0.932200i	$-0.382113\pi$
$11$	0.700768	+	0.245209i	0.0637061	+	0.0222917i	−0.298238	+	0.954492i	$0.596399\pi$
$12$		0			0
$13$	3.39382	+	7.04735i	0.261063	+	0.542104i	0.989761	−	0.142731i	$-0.0455885\pi$
$13$	3.39382	+	7.04735i	0.261063	+	0.542104i	−0.728698	+	0.684835i	$0.759874\pi$
$14$	3.82256	−	33.9262i	0.273040	−	2.42330i
$15$		0			0
$16$	24.1861	−	11.6474i	1.51163	−	0.727962i
$17$	17.4730	+	17.4730i	1.02782	+	1.02782i	0.999602	+	0.0282209i	$0.00898419\pi$
$17$	17.4730	+	17.4730i	1.02782	+	1.02782i	0.0282209	+	0.999602i	$0.491016\pi$
$18$		0			0
$19$	−7.96846	+	12.6817i	−0.419393	+	0.667460i	−0.987878	−	0.155234i	$-0.950387\pi$
$19$	−7.96846	+	12.6817i	−0.419393	+	0.667460i	0.568485	+	0.822694i	$0.307530\pi$
$20$	−53.4169	−	25.7242i	−2.67085	−	1.28621i
$21$		0			0
$22$	2.59408	+	0.592082i	0.117913	+	0.0269128i
$23$	11.9732	+	15.0139i	0.520575	+	0.652780i	0.970731	−	0.240170i	$-0.0772031\pi$
$23$	11.9732	+	15.0139i	0.520575	+	0.652780i	−0.450156	+	0.892950i	$0.648632\pi$
$24$		0			0
$25$	4.43656	+	19.4379i	0.177463	+	0.777514i
$26$	14.9145	+	23.7363i	0.573635	+	0.912935i
$27$		0			0
$28$		−	84.2524i		−	3.00901i
$29$	19.7681	−	21.2184i	0.681659	−	0.731670i
$29$	19.7681	−	21.2184i	0.681659	−	0.731670i
$30$		0			0
$31$	0.327624	−	0.0369143i	0.0105685	−	0.00119078i	−0.106679	−	0.994294i	$-0.534022\pi$
$31$	0.327624	−	0.0369143i	0.0105685	−	0.00119078i	0.117247	+	0.993103i	$0.462593\pi$
$32$	22.6600	−	14.2382i	0.708124	−	0.444944i
$33$		0			0
$34$	69.2390	+	55.2162i	2.03644	+	1.62401i
$35$	−49.9272	+	39.8156i	−1.42649	+	1.13759i
$36$		0			0
$37$	−15.2693	+	5.34296i	−0.412684	+	0.144404i	−0.528632	−	0.848851i	$-0.677295\pi$
$37$	−15.2693	+	5.34296i	−0.412684	+	0.144404i	0.115949	+	0.993255i	$0.463009\pi$
$38$	−23.2898	+	48.3617i	−0.612889	+	1.27268i
$39$		0			0
$40$	−109.853	−	38.4391i	−2.74632	−	0.960978i
$41$	−28.0484	+	28.0484i	−0.684106	+	0.684106i	−0.960923	−	0.276816i	$-0.910721\pi$
$41$	−28.0484	+	28.0484i	−0.684106	+	0.684106i	0.276816	+	0.960923i	$0.410721\pi$
$42$		0			0
$43$	0.679170	−	6.02780i	0.0157947	−	0.140181i	−0.983340	−	0.181776i	$-0.941815\pi$
$43$	0.679170	−	6.02780i	0.0157947	−	0.140181i	0.999135	+	0.0415949i	$0.0132439\pi$
$44$	6.52499	+	0.735190i	0.148295	+	0.0167089i
$45$		0			0
$46$	48.6656	+	48.6656i	1.05795	+	1.05795i
$47$	−1.43620	+	4.10443i	−0.0305575	+	0.0873282i	−0.958152	−	0.286261i	$-0.907587\pi$
$47$	−1.43620	+	4.10443i	−0.0305575	+	0.0873282i	0.927594	+	0.373590i	$0.121873\pi$
$48$		0			0
$49$	−37.6137	−	18.1138i	−0.767627	−	0.369670i
$50$	23.6000	+	67.4450i	0.472000	+	1.34890i
$51$		0			0
$52$	43.1329	+	54.0870i	0.829479	+	1.04013i
$53$	37.6082	−	47.1592i	0.709589	−	0.889797i	−0.288110	−	0.957597i	$-0.593027\pi$
$53$	37.6082	−	47.1592i	0.709589	−	0.889797i	0.997699	+	0.0678006i	$0.0215982\pi$
$54$		0			0
$55$	−2.64789	−	4.21408i	−0.0481434	−	0.0766197i
$56$	−18.5176	−	164.349i	−0.330672	−	2.93480i
$57$		0			0
$58$	61.8871	−	83.4988i	1.06702	−	1.43963i
$59$	−91.1542			−1.54499			−0.772493	−	0.635023i	$-0.780991\pi$
$59$	−91.1542			−1.54499			−0.772493	+	0.635023i	$0.780991\pi$
$60$		0			0
$61$	6.43745	−	4.04492i	0.105532	−	0.0663101i	−0.478232	−	0.878234i	$-0.658722\pi$
$61$	6.43745	−	4.04492i	0.105532	−	0.0663101i	0.583764	+	0.811923i	$0.301579\pi$
$62$	1.15197	−	0.262930i	0.0185802	−	0.00424081i
$63$		0			0
$64$	−8.96447	+	7.14893i	−0.140070	+	0.111702i
$65$	11.6679	−	51.1204i	0.179506	−	0.786467i
$66$		0			0
$67$	29.8663	−	62.0180i	0.445766	−	0.925642i	−0.550125	−	0.835082i	$-0.685420\pi$
$67$	29.8663	−	62.0180i	0.445766	−	0.925642i	0.995891	−	0.0905598i	$-0.0288656\pi$
$68$	185.049	+	116.274i	2.72131	+	1.70992i
$69$		0			0
$70$	−161.832	+	161.832i	−2.31189	+	2.31189i
$71$	38.1572	+	79.2343i	0.537426	+	1.11598i	0.976098	+	0.217329i	$0.0697346\pi$
$71$	38.1572	+	79.2343i	0.537426	+	1.11598i	−0.438672	+	0.898647i	$0.644551\pi$
$72$		0			0
$73$	−29.1293	−	3.28209i	−0.399032	−	0.0449601i	−0.0898315	−	0.995957i	$-0.528633\pi$
$73$	−29.1293	−	3.28209i	−0.399032	−	0.0449601i	−0.309200	+	0.950997i	$0.600061\pi$
$74$	−52.2355	+	25.1553i	−0.705885	+	0.339936i
$75$		0			0
$76$	−43.7503	+	125.031i	−0.575662	+	1.64515i
$77$	3.76281	−	5.98848i	0.0488677	−	0.0777724i
$78$		0			0
$79$	7.28322	+	20.8142i	0.0921927	+	0.263472i	0.980741	−	0.195311i	$-0.0625715\pi$
$79$	7.28322	+	20.8142i	0.0921927	+	0.263472i	−0.888549	+	0.458782i	$0.848286\pi$
$80$	−175.442	−	40.0435i	−2.19302	−	0.500543i
$81$		0			0
$82$	−88.6354	+	111.145i	−1.08092	+	1.35543i
$83$	−9.19165	−	40.2713i	−0.110743	−	0.485196i	−0.999633	−	0.0270764i	$-0.991380\pi$
$83$	−9.19165	−	40.2713i	−0.110743	−	0.485196i	0.888891	−	0.458120i	$-0.151477\pi$
$84$		0			0
$85$	−18.5468	−	164.607i	−0.218197	−	1.93655i
$86$		−	21.7397i		−	0.252787i
$87$		0			0
$88$	12.8897			0.146474
$89$	−98.0089	+	11.0429i	−1.10122	+	0.124078i	−0.643817	−	0.765180i	$-0.722650\pi$
$89$	−98.0089	+	11.0429i	−1.10122	+	0.124078i	−0.457407	+	0.889258i	$0.651222\pi$
$90$		0			0
$91$	72.6452	−	16.5808i	0.798299	−	0.182207i
$92$	132.788	+	105.895i	1.44335	+	1.15103i
$93$		0			0
$94$	−3.46785	+	15.1936i	−0.0368920	+	0.161635i
$95$	94.7678	−	33.1607i	0.997556	−	0.349060i
$96$		0			0
$97$	136.891	+	86.0143i	1.41125	+	0.886745i	0.999696	−	0.0246414i	$-0.00784441\pi$
$97$	136.891	+	86.0143i	1.41125	+	0.886745i	0.411551	+	0.911387i	$0.364987\pi$
$98$	−141.224	−	49.4166i	−1.44107	−	0.504251i
$99$		0			0
$100$	76.5091	+	158.873i	0.765091	+	1.58873i
$101$	−0.930887	+	8.26185i	−0.00921670	+	0.0818005i	−0.997478	−	0.0709693i	$-0.977391\pi$
$101$	−0.930887	+	8.26185i	−0.00921670	+	0.0818005i	0.988262	+	0.152770i	$0.0488193\pi$
$102$		0			0
$103$	−65.6998	+	31.6393i	−0.637862	+	0.307178i	−0.724721	−	0.689043i	$-0.758031\pi$
$103$	−65.6998	+	31.6393i	−0.637862	+	0.307178i	0.0868590	+	0.996221i	$0.472317\pi$
$104$	96.0257	+	96.0257i	0.923324	+	0.923324i
$105$		0			0
$106$	115.013	−	183.042i	1.08503	−	1.72681i
$107$	73.2735	+	35.2867i	0.684799	+	0.329782i	0.743730	−	0.668480i	$-0.233055\pi$
$107$	73.2735	+	35.2867i	0.684799	+	0.329782i	−0.0589308	+	0.998262i	$0.518769\pi$
$108$		0			0
$109$	119.739	+	27.3296i	1.09852	+	0.250730i	0.733106	−	0.680114i	$-0.238070\pi$
$109$	119.739	+	27.3296i	1.09852	+	0.250730i	0.365415	+	0.930845i	$0.380927\pi$
$110$	−11.1211	−	13.9454i	−0.101100	−	0.126776i
$111$		0			0
$112$	−56.9043	−	249.314i	−0.508074	−	2.22602i
$113$	−84.5371	−	134.540i	−0.748116	−	1.19062i	−0.976178	−	0.216973i	$-0.930382\pi$
$113$	−84.5371	−	134.540i	−0.748116	−	1.19062i	0.228062	−	0.973647i	$-0.426761\pi$
$114$		0			0
$115$		−	128.732i		−	1.11941i
$116$	128.693	−	221.862i	1.10942	−	1.91260i
$117$		0			0
$118$	−324.633	+	36.5773i	−2.75113	+	0.309977i
$119$	199.316	−	125.239i	1.67493	−	1.05243i
$120$		0			0
$121$	−94.1707	−	75.0986i	−0.778270	−	0.620650i
$122$	21.3030	−	16.9886i	0.174615	−	0.139250i
$123$		0			0
$124$	2.75231	−	0.963073i	0.0221960	−	0.00776672i
$125$	−14.7239	+	30.5745i	−0.117791	+	0.244596i
$126$		0			0
$127$	91.0577	+	31.8625i	0.716990	+	0.250886i	0.664025	−	0.747711i	$-0.268847\pi$
$127$	91.0577	+	31.8625i	0.716990	+	0.250886i	0.0529652	+	0.998596i	$0.483133\pi$
$128$	−104.751	+	104.751i	−0.818369	+	0.818369i
$129$		0			0
$130$	21.0405	−	186.740i	0.161850	−	1.43646i
$131$	−75.6558	−	8.52436i	−0.577525	−	0.0650714i	−0.181630	−	0.983367i	$-0.558137\pi$
$131$	−75.6558	−	8.52436i	−0.577525	−	0.0650714i	−0.395895	+	0.918296i	$0.629566\pi$
$132$		0			0
$133$	100.888	+	100.888i	0.758558	+	0.758558i
$134$	81.4787	−	232.853i	0.608050	−	1.73771i
$135$		0			0
$136$	386.526	+	186.141i	2.84210	+	1.36868i
$137$	50.4454	+	144.165i	0.368215	+	1.05230i	0.967742	+	0.251943i	$0.0810695\pi$
$137$	50.4454	+	144.165i	0.368215	+	1.05230i	−0.599528	+	0.800354i	$0.704645\pi$
$138$		0			0
$139$	−84.2699	−	105.671i	−0.606258	−	0.760224i	0.380080	−	0.924953i	$-0.375896\pi$
$139$	−84.2699	−	105.671i	−0.606258	−	0.760224i	−0.986339	+	0.164729i	$0.947325\pi$
$140$	−352.142	+	441.572i	−2.51530	+	3.15408i
$141$		0			0
$142$	167.686	+	266.871i	1.18089	+	1.87937i
$143$	0.650207	+	5.77075i	0.00454690	+	0.0403549i
$144$		0			0
$145$	−192.290	+	28.5841i	−1.32614	+	0.197132i
$146$	−105.057			−0.719569
$147$		0			0
$148$	−121.145	+	76.1206i	−0.818549	+	0.514328i
$149$	−58.0928	+	13.2593i	−0.389885	+	0.0889886i	−0.412969	−	0.910745i	$-0.635508\pi$
$149$	−58.0928	+	13.2593i	−0.389885	+	0.0889886i	0.0230848	+	0.999734i	$0.492651\pi$
$150$		0			0
$151$	−203.074	+	161.946i	−1.34486	+	1.07249i	−0.354340	+	0.935117i	$0.615294\pi$
$151$	−203.074	+	161.946i	−1.34486	+	1.07249i	−0.990519	+	0.137373i	$0.956134\pi$
$152$	−57.8621	+	253.510i	−0.380672	+	1.66783i
$153$		0			0
$154$	10.9977	−	22.8370i	0.0714138	−	0.148292i
$155$	−1.87138	−	1.17587i	−0.0120734	−	0.00758624i
$156$		0			0
$157$	−132.437	+	132.437i	−0.843550	+	0.843550i	−0.989319	−	0.145769i	$-0.953434\pi$
$157$	−132.437	+	132.437i	−0.843550	+	0.843550i	0.145769	+	0.989319i	$0.453434\pi$
$158$	34.2903	+	71.2045i	0.217027	+	0.450661i
$159$		0			0
$160$	−178.272	−	20.0865i	−1.11420	−	0.125540i
$161$	164.820	−	79.3732i	1.02373	−	0.493001i
$162$		0			0
$163$	84.1241	−	240.413i	0.516098	−	1.47492i	−0.331073	−	0.943605i	$-0.607411\pi$
$163$	84.1241	−	240.413i	0.516098	−	1.47492i	0.847171	−	0.531320i	$-0.178304\pi$
$164$	−186.648	+	297.049i	−1.13810	+	1.81127i
$165$		0			0
$166$	−48.8944	−	139.732i	−0.294545	−	0.841760i
$167$	37.5325	+	8.56655i	0.224746	+	0.0512967i	0.333411	−	0.942782i	$-0.391800\pi$
$167$	37.5325	+	8.56655i	0.224746	+	0.0512967i	−0.108665	+	0.994078i	$0.534658\pi$
$168$		0			0
$169$	67.2227	−	84.2946i	0.397768	−	0.498785i
$170$	−132.103	−	578.783i	−0.777079	−	3.40460i
$171$		0			0
$172$	−6.00679	−	53.3117i	−0.0349232	−	0.309952i
$173$			38.3828i			0.221866i	0.993828	+	0.110933i	$0.0353839\pi$
$173$			38.3828i			0.221866i	−0.993828	+	0.110933i	$0.964616\pi$
$174$		0			0
$175$	189.930			1.08532
$176$	19.8048	−	2.23147i	0.112528	−	0.0126788i
$177$		0			0
$178$	−344.614	+	78.6558i	−1.93603	+	0.441887i
$179$	−136.077	−	108.518i	−0.760206	−	0.606244i	0.164742	−	0.986337i	$-0.447321\pi$
$179$	−136.077	−	108.518i	−0.760206	−	0.606244i	−0.924949	+	0.380092i	$0.875892\pi$
$180$		0			0
$181$	37.8882	−	165.999i	0.209327	−	0.917122i	−0.755689	−	0.654931i	$-0.772698\pi$
$181$	37.8882	−	165.999i	0.209327	−	0.917122i	0.965016	−	0.262191i	$-0.0844451\pi$
$182$	252.062	−	88.2005i	1.38496	−	0.484618i
$183$		0			0
$184$	282.300	+	177.381i	1.53424	+	0.964025i
$185$	102.359	+	35.8168i	0.553290	+	0.193605i
$186$		0			0
$187$	7.95997	+	16.5290i	0.0425667	+	0.0883906i
$188$	−4.30604	+	38.2172i	−0.0229045	+	0.203283i
$189$		0			0
$190$	324.196	−	156.124i	1.70629	−	0.821708i
$191$	20.1345	+	20.1345i	0.105416	+	0.105416i	0.757848	−	0.652431i	$-0.226251\pi$
$191$	20.1345	+	20.1345i	0.105416	+	0.105416i	−0.652431	+	0.757848i	$0.726251\pi$
$192$		0			0
$193$	−157.961	+	251.393i	−0.818449	+	1.30255i	0.131867	+	0.991267i	$0.457903\pi$
$193$	−157.961	+	251.393i	−0.818449	+	1.30255i	−0.950316	+	0.311287i	$0.899240\pi$
$194$	522.033	+	251.398i	2.69089	+	1.29587i
$195$		0			0
$196$	−359.975	−	82.1620i	−1.83661	−	0.419194i
$197$	−152.105	−	190.734i	−0.772108	−	0.968192i	0.227877	−	0.973690i	$-0.426822\pi$
$197$	−152.105	−	190.734i	−0.772108	−	0.968192i	−0.999985	+	0.00549749i	$0.998250\pi$
$198$		0			0
$199$	−70.5672	−	309.175i	−0.354609	−	1.55364i	−0.766399	−	0.642365i	$-0.777953\pi$
$199$	−70.5672	−	309.175i	−0.354609	−	1.55364i	0.411789	−	0.911279i	$-0.364904\pi$
$200$	184.162	+	293.092i	0.920811	+	1.46546i
$201$		0			0
$202$			29.7970i			0.147510i
$203$	−155.159	−	228.571i	−0.764329	−	1.12597i
$204$		0			0
$205$	264.234	−	29.7720i	1.28895	−	0.145229i
$206$	−221.285	+	139.042i	−1.07420	+	0.674963i
$207$		0			0
$208$	164.166	+	130.918i	0.789261	+	0.629415i
$209$	−8.69372	+	6.93301i	−0.0415967	+	0.0331723i
$210$		0			0
$211$	353.376	−	123.652i	1.67477	−	0.586027i	0.684978	−	0.728563i	$-0.259812\pi$
$211$	353.376	−	123.652i	1.67477	−	0.586027i	0.989789	+	0.142537i	$0.0455259\pi$
$212$	231.468	−	480.648i	1.09183	−	2.26721i
$213$		0			0
$214$	275.113	+	96.2661i	1.28557	+	0.449842i
$215$	−28.7534	+	28.7534i	−0.133737	+	0.133737i
$216$		0			0
$217$	0.351652	−	3.12100i	0.00162052	−	0.0143825i
$218$	437.400	+	49.2831i	2.00642	+	0.226069i
$219$		0			0
$220$	−31.1250	−	31.1250i	−0.141477	−	0.141477i
$221$	−63.8380	+	182.438i	−0.288860	+	0.825513i
$222$		0			0
$223$	−249.428	−	120.118i	−1.11851	−	0.538647i	−0.219079	−	0.975707i	$-0.570305\pi$
$223$	−249.428	−	120.118i	−1.11851	−	0.538647i	−0.899432	+	0.437061i	$0.856020\pi$
$224$	−84.2010	−	240.633i	−0.375897	−	1.07425i
$225$		0			0
$226$	−355.054	−	445.223i	−1.57103	−	1.97001i
$227$	163.809	−	205.410i	0.721624	−	0.904888i	−0.276805	−	0.960926i	$-0.589276\pi$
$227$	163.809	−	205.410i	0.721624	−	0.904888i	0.998429	+	0.0560385i	$0.0178470\pi$
$228$		0			0
$229$	164.093	+	261.153i	0.716564	+	1.14040i	0.984230	+	0.176893i	$0.0566046\pi$
$229$	164.093	+	261.153i	0.716564	+	1.14040i	−0.267667	+	0.963512i	$0.586253\pi$
$230$	−51.6562	−	458.462i	−0.224592	−	1.99331i
$231$		0			0
$232$	202.275	−	461.064i	0.871875	−	1.98734i
$233$	−92.4111			−0.396614			−0.198307	−	0.980140i	$-0.563544\pi$
$233$	−92.4111			−0.396614			−0.198307	+	0.980140i	$0.563544\pi$
$234$		0			0
$235$	24.6821	−	15.5088i	0.105030	−	0.0659948i
$236$	−785.982	+	179.395i	−3.33043	+	0.760150i
$237$		0			0
$238$	659.583	−	526.000i	2.77136	−	2.21008i
$239$	91.6570	−	401.575i	0.383502	−	1.68023i	−0.302910	−	0.953019i	$-0.597958\pi$
$239$	91.6570	−	401.575i	0.383502	−	1.68023i	0.686412	−	0.727213i	$-0.259185\pi$
$240$		0			0
$241$	−53.8613	+	111.844i	−0.223491	+	0.464084i	−0.982321	−	0.187205i	$-0.940057\pi$
$241$	−53.8613	+	111.844i	−0.223491	+	0.464084i	0.758830	+	0.651289i	$0.225771\pi$
$242$	−365.510	−	229.665i	−1.51037	−	0.949031i
$243$		0			0
$244$	47.5467	−	47.5467i	0.194864	−	0.194864i
$245$	121.427	+	252.146i	0.495621	+	1.02917i
$246$		0			0
$247$	−116.416	−	13.1169i	−0.471320	−	0.0531051i
$248$	5.15717	−	2.48356i	0.0207950	−	0.0100144i
$249$		0			0
$250$	−40.1686	+	114.795i	−0.160674	+	0.459181i
$251$	−17.8330	+	28.3810i	−0.0710477	+	0.113072i	−0.880358	−	0.474309i	$-0.842698\pi$
$251$	−17.8330	+	28.3810i	−0.0710477	+	0.113072i	0.809311	+	0.587381i	$0.199841\pi$
$252$		0			0
$253$	4.70889	+	13.4572i	0.0186122	+	0.0531906i
$254$	337.075	+	76.9351i	1.32707	+	0.302894i
$255$		0			0
$256$	−302.428	+	379.233i	−1.18136	+	1.48138i
$257$	60.1375	+	263.480i	0.233998	+	1.02521i	0.946287	+	0.323327i	$0.104801\pi$
$257$	60.1375	+	263.480i	0.233998	+	1.02521i	−0.712289	+	0.701886i	$0.752342\pi$
$258$		0			0
$259$	17.2544	+	153.137i	0.0666193	+	0.591262i
$260$		−	463.751i		−	1.78366i
$261$		0			0
$262$	−272.858			−1.04144
$263$	−177.612	+	20.0120i	−0.675329	+	0.0760914i	−0.442967	−	0.896538i	$-0.646074\pi$
$263$	−177.612	+	20.0120i	−0.675329	+	0.0760914i	−0.232362	+	0.972629i	$0.574646\pi$
$264$		0			0
$265$	−394.214	+	89.9767i	−1.48760	+	0.339535i
$266$	399.783	+	318.816i	1.50294	+	1.19856i
$267$		0			0
$268$	135.470	−	593.532i	0.505484	−	2.21467i
$269$	369.061	−	129.140i	1.37197	−	0.480074i	0.459124	−	0.888372i	$-0.348163\pi$
$269$	369.061	−	129.140i	1.37197	−	0.480074i	0.912849	+	0.408298i	$0.133878\pi$
$270$		0			0
$271$	28.6724	+	18.0161i	0.105802	+	0.0664799i	0.583894	−	0.811830i	$-0.301528\pi$
$271$	28.6724	+	18.0161i	0.105802	+	0.0664799i	−0.478092	+	0.878310i	$0.658671\pi$
$272$	626.117	+	219.088i	2.30190	+	0.805470i
$273$		0			0
$274$	237.503	+	493.180i	0.866799	+	1.79993i
$275$	−1.65734	+	14.7093i	−0.00602669	+	0.0534884i
$276$		0			0
$277$	−106.776	+	51.4207i	−0.385473	+	0.185634i	−0.616576	−	0.787295i	$-0.711481\pi$
$277$	−106.776	+	51.4207i	−0.385473	+	0.185634i	0.231103	+	0.972929i	$0.425767\pi$
$278$	−342.518	−	342.518i	−1.23208	−	1.23208i
$279$		0			0
$280$	−589.860	+	938.756i	−2.10664	+	3.35270i
$281$	−257.658	−	124.081i	−0.916932	−	0.441571i	−0.0849569	−	0.996385i	$-0.527075\pi$
$281$	−257.658	−	124.081i	−0.916932	−	0.441571i	−0.831975	+	0.554814i	$0.812790\pi$
$282$		0			0
$283$	−221.399	−	50.5329i	−0.782329	−	0.178561i	−0.187340	−	0.982295i	$-0.559986\pi$
$283$	−221.399	−	50.5329i	−0.782329	−	0.178561i	−0.594989	+	0.803734i	$0.702844\pi$
$284$	484.950	+	608.108i	1.70757	+	2.14122i
$285$		0			0
$286$	4.63124	+	20.2908i	0.0161932	+	0.0709469i
$287$	201.038	+	319.951i	0.700482	+	1.11481i
$288$		0			0
$289$			321.610i			1.11284i
$290$	−673.345	+	178.958i	−2.32188	+	0.617098i
$291$		0			0
$292$	−257.629	+	29.0278i	−0.882290	+	0.0994102i
$293$	160.239	−	100.685i	0.546891	−	0.343634i	−0.230079	−	0.973172i	$-0.573899\pi$
$293$	160.239	−	100.685i	0.546891	−	0.343634i	0.776970	+	0.629538i	$0.216756\pi$
$294$		0			0
$295$	477.744	+	380.988i	1.61947	+	1.29149i
$296$	−219.584	+	175.112i	−0.741837	+	0.591595i
$297$		0			0
$298$	−201.569	+	70.5320i	−0.676405	+	0.236685i
$299$	−65.1735	+	135.334i	−0.217971	+	0.452622i
$300$		0			0
$301$	−54.5425	−	19.0853i	−0.181204	−	0.0634062i
$302$	−658.235	+	658.235i	−2.17959	+	2.17959i
$303$		0			0
$304$	−45.0165	+	399.533i	−0.148081	+	1.31425i
$305$	−50.6452	−	5.70634i	−0.166050	−	0.0187093i
$306$		0			0
$307$	−287.766	−	287.766i	−0.937349	−	0.937349i	0.0608010	−	0.998150i	$-0.480634\pi$
$307$	−287.766	−	287.766i	−0.937349	−	0.937349i	−0.998150	+	0.0608010i	$0.980634\pi$
$308$	20.6595	−	59.0414i	0.0670762	−	0.191693i
$309$		0			0
$310$	−7.13650	−	3.43676i	−0.0230210	−	0.0110863i
$311$	7.89034	+	22.5493i	0.0253709	+	0.0725058i	0.955872	−	0.293782i	$-0.0949141\pi$
$311$	7.89034	+	22.5493i	0.0253709	+	0.0725058i	−0.930501	+	0.366288i	$0.880628\pi$
$312$		0			0
$313$	256.380	+	321.491i	0.819107	+	1.02713i	0.999056	+	0.0434514i	$0.0138354\pi$
$313$	256.380	+	321.491i	0.819107	+	1.02713i	−0.179949	+	0.983676i	$0.557593\pi$
$314$	−418.514	+	524.800i	−1.33285	+	1.67134i
$315$		0			0
$316$	103.763	+	165.138i	0.328365	+	0.522590i
$317$	53.9274	+	478.619i	0.170118	+	1.50984i	0.731248	+	0.682111i	$0.238938\pi$
$317$	53.9274	+	478.619i	0.170118	+	1.50984i	−0.561131	+	0.827727i	$0.689633\pi$
$318$		0			0
$319$	19.0558	−	10.0219i	0.0597361	−	0.0314165i
$320$	76.8630			0.240197
$321$		0			0
$322$	555.134	−	348.814i	1.72402	−	1.08327i
$323$	−360.821	+	82.3550i	−1.11709	+	0.254969i
$324$		0			0
$325$	−121.928	+	97.2347i	−0.375164	+	0.299184i
$326$	203.126	−	889.953i	0.623086	−	2.72992i
$327$		0			0
$328$	−298.801	+	620.467i	−0.910980	+	1.89167i
$329$	35.0748	+	22.0389i	0.106610	+	0.0669877i
$330$		0			0
$331$	−253.593	+	253.593i	−0.766142	+	0.766142i	−0.977425	−	0.211283i	$-0.932236\pi$
$331$	−253.593	+	253.593i	−0.766142	+	0.766142i	0.211283	+	0.977425i	$0.432236\pi$
$332$	−158.511	−	329.152i	−0.477443	−	0.991421i
$333$		0			0
$334$	137.104	+	15.4479i	0.410492	+	0.0462513i
$335$	−415.742	+	200.211i	−1.24102	+	0.597644i
$336$		0			0
$337$	7.65449	−	21.8753i	0.0227136	−	0.0649118i	−0.931968	−	0.362540i	$-0.881910\pi$
$337$	7.65449	−	21.8753i	0.0227136	−	0.0649118i	0.954682	+	0.297628i	$0.0961955\pi$
$338$	205.580	−	327.178i	0.608223	−	0.967982i
$339$		0			0
$340$	−483.874	−	1382.83i	−1.42316	−	4.06716i
$341$	0.238640	+	0.0544680i	0.000699823	+	0.000159730i
$342$		0			0
$343$	43.0726	−	54.0114i	0.125576	−	0.157468i
$344$	−23.4345	−	102.673i	−0.0681236	−	0.298469i
$345$		0			0
$346$	15.4018	+	136.695i	0.0445139	+	0.395072i
$347$			307.231i			0.885393i	0.896672	+	0.442696i	$0.145978\pi$
$347$			307.231i			0.885393i	−0.896672	+	0.442696i	$0.854022\pi$
$348$		0			0
$349$	81.9545			0.234827			0.117413	−	0.993083i	$-0.462540\pi$
$349$	81.9545			0.234827			0.117413	+	0.993083i	$0.462540\pi$
$350$	676.411	−	76.2132i	1.93260	−	0.217752i
$351$		0			0
$352$	19.3707	−	4.42124i	0.0550305	−	0.0125603i
$353$	−34.5942	−	27.5880i	−0.0980006	−	0.0781529i	0.573264	−	0.819371i	$-0.305677\pi$
$353$	−34.5942	−	27.5880i	−0.0980006	−	0.0781529i	−0.671264	+	0.741218i	$0.734248\pi$
$354$		0			0
$355$	131.184	−	574.754i	0.369532	−	1.61902i
$356$	−823.354	+	288.104i	−2.31279	+	0.809281i
$357$		0			0
$358$	−528.164	−	331.867i	−1.47532	−	0.927004i
$359$	329.635	+	115.344i	0.918204	+	0.321294i	0.747680	−	0.664060i	$-0.231168\pi$
$359$	329.635	+	115.344i	0.918204	+	0.321294i	0.170525	+	0.985353i	$0.445454\pi$
$360$		0			0
$361$	59.3020	+	123.142i	0.164271	+	0.341113i
$362$	68.3233	−	606.386i	0.188738	−	1.67510i
$363$		0			0
$364$	593.756	−	285.938i	1.63120	−	0.785543i
$365$	138.951	+	138.951i	0.380687	+	0.380687i
$366$		0			0
$367$	117.163	−	186.464i	0.319246	−	0.508076i	−0.648094	−	0.761560i	$-0.724434\pi$
$367$	117.163	−	186.464i	0.319246	−	0.508076i	0.967340	+	0.253484i	$0.0815765\pi$
$368$	464.458	+	223.671i	1.26211	+	0.607802i
$369$		0			0
$370$	378.908	+	86.4833i	1.02408	+	0.233739i
$371$	−358.263	−	449.247i	−0.965668	−	1.21091i
$372$		0			0
$373$	58.3911	+	255.828i	0.156545	+	0.685867i	0.990896	+	0.134633i	$0.0429855\pi$
$373$	58.3911	+	255.828i	0.156545	+	0.685867i	−0.834351	+	0.551234i	$0.814157\pi$
$374$	34.9809	+	55.6718i	0.0935318	+	0.148855i
$375$		0			0
$376$			75.4955i			0.200786i
$377$	216.623	+	67.3012i	0.574597	+	0.178518i
$378$		0			0
$379$	−224.710	+	25.3187i	−0.592901	+	0.0668039i	−0.403317	−	0.915061i	$-0.632143\pi$
$379$	−224.710	+	25.3187i	−0.592901	+	0.0668039i	−0.189584	+	0.981864i	$0.560714\pi$
$380$	751.879	−	472.437i	1.97863	−	1.24326i
$381$		0			0
$382$	79.7857	+	63.6270i	0.208863	+	0.166563i
$383$	−106.140	+	84.6436i	−0.277127	+	0.221002i	−0.752183	−	0.658954i	$-0.770999\pi$
$383$	−106.140	+	84.6436i	−0.277127	+	0.221002i	0.475056	+	0.879956i	$0.342428\pi$
$384$		0			0
$385$	−44.7505	+	15.6589i	−0.116235	+	0.0406724i
$386$	−461.679	+	958.686i	−1.19606	+	2.48364i
$387$		0			0
$388$	1349.63	+	472.256i	3.47843	+	1.21715i
$389$	11.0445	−	11.0445i	0.0283920	−	0.0283920i	−0.692768	−	0.721160i	$-0.743609\pi$
$389$	11.0445	−	11.0445i	0.0283920	−	0.0283920i	0.721160	+	0.692768i	$0.243609\pi$
$390$		0			0
$391$	−53.1305	+	471.546i	−0.135884	+	1.20600i
$392$	−720.251	−	81.1528i	−1.83737	−	0.207022i
$393$		0			0
$394$	−618.237	−	618.237i	−1.56913	−	1.56913i
$395$	48.8235	−	139.530i	0.123604	−	0.353240i
$396$		0			0
$397$	−258.406	−	124.442i	−0.650896	−	0.313455i	0.0791405	−	0.996863i	$-0.474782\pi$
$397$	−258.406	−	124.442i	−0.650896	−	0.313455i	−0.730036	+	0.683409i	$0.760497\pi$
$398$	−375.378	−	1072.77i	−0.943160	−	2.69540i
$399$		0			0
$400$	333.703	+	418.451i	0.834258	+	1.04613i
$401$	−94.6371	+	118.671i	−0.236003	+	0.295938i	−0.885703	−	0.464253i	$-0.846323\pi$
$401$	−94.6371	+	118.671i	−0.236003	+	0.295938i	0.649700	+	0.760191i	$0.274894\pi$
$402$		0			0
$403$	1.37204	+	2.18360i	0.00340458	+	0.00541835i
$404$	8.23305	+	73.0703i	0.0203788	+	0.180867i
$405$		0			0
$406$	−644.295	−	751.765i	−1.58693	−	1.85164i
$407$	−12.0104			−0.0295095
$408$		0			0
$409$	−138.561	+	87.0640i	−0.338781	+	0.212870i	−0.690668	−	0.723172i	$-0.742683\pi$
$409$	−138.561	+	87.0640i	−0.338781	+	0.212870i	0.351886	+	0.936043i	$0.385540\pi$
$410$	929.086	−	212.058i	2.26606	−	0.517214i
$411$		0			0
$412$	−504.233	+	402.112i	−1.22387	+	0.976000i
$413$	−193.226	+	846.580i	−0.467860	+	2.04983i
$414$		0			0
$415$	−120.144	+	249.481i	−0.289503	+	0.601160i
$416$	177.246	+	111.371i	0.426071	+	0.267718i
$417$		0			0
$418$	−28.1795	+	28.1795i	−0.0674150	+	0.0674150i
$419$	14.3641	+	29.8274i	0.0342819	+	0.0711870i	0.917406	−	0.397952i	$-0.130279\pi$
$419$	14.3641	+	29.8274i	0.0342819	+	0.0711870i	−0.883125	+	0.469139i	$0.844564\pi$
$420$		0			0
$421$	−442.876	−	49.9001i	−1.05196	−	0.118528i	−0.430986	−	0.902358i	$-0.641834\pi$
$421$	−442.876	−	49.9001i	−1.05196	−	0.118528i	−0.620974	+	0.783831i	$0.713263\pi$
$422$	1208.88	−	582.167i	2.86465	−	1.37954i
$423$		0			0
$424$	345.877	−	988.459i	0.815747	−	2.33127i
$425$	−262.117	+	417.157i	−0.616747	+	0.981547i
$426$		0			0
$427$	−23.9206	−	68.3611i	−0.0560201	−	0.160096i
$428$	701.251	+	160.056i	1.63844	+	0.373962i
$429$		0			0
$430$	−90.8633	+	113.939i	−0.211310	+	0.264974i
$431$	−56.6584	−	248.237i	−0.131458	−	0.575955i	−0.997154	−	0.0753857i	$-0.975981\pi$
$431$	−56.6584	−	248.237i	−0.131458	−	0.575955i	0.865696	−	0.500569i	$-0.166876\pi$
$432$		0			0
$433$	41.5408	+	368.685i	0.0959371	+	0.851465i	0.945864	+	0.324564i	$0.105218\pi$
$433$	41.5408	+	368.685i	0.0959371	+	0.851465i	−0.849927	+	0.526901i	$0.823354\pi$
$434$		−	11.2561i		−	0.0259358i
$435$		0			0
$436$	1086.24			2.49138
$437$	−285.811	+	32.2032i	−0.654030	+	0.0736915i
$438$		0			0
$439$	472.512	−	107.848i	1.07634	−	0.245667i	0.352622	−	0.935766i	$-0.385290\pi$
$439$	472.512	−	107.848i	1.07634	−	0.245667i	0.723715	+	0.690099i	$0.242433\pi$
$440$	−67.5556	−	53.8738i	−0.153535	−	0.122440i
$441$		0			0
$442$	−154.143	+	675.345i	−0.348740	+	1.52793i
$443$	133.331	−	46.6547i	0.300974	−	0.105315i	−0.175567	−	0.984467i	$-0.556176\pi$
$443$	133.331	−	46.6547i	0.300974	−	0.105315i	0.476541	+	0.879152i	$0.341890\pi$
$444$		0			0
$445$	559.825	+	351.761i	1.25803	+	0.790475i
$446$	−936.503	−	327.696i	−2.09978	−	0.734745i
$447$		0			0
$448$	47.3918	+	98.4102i	0.105785	+	0.219666i
$449$	−55.2993	+	490.795i	−0.123161	+	1.09309i	0.768332	+	0.640051i	$0.221087\pi$
$449$	−55.2993	+	490.795i	−0.123161	+	1.09309i	−0.891493	+	0.453034i	$0.850342\pi$
$450$		0			0
$451$	−26.5331	+	12.7777i	−0.0588317	+	0.0283319i
$452$	−993.706	−	993.706i	−2.19847	−	2.19847i
$453$		0			0
$454$	500.957	−	797.269i	1.10343	−	1.75610i
$455$	−450.039	−	216.727i	−0.989096	−	0.476324i
$456$		0			0
$457$	890.248	+	203.193i	1.94803	+	0.444624i	0.983653	+	0.180077i	$0.0576347\pi$
$457$	890.248	+	203.193i	1.94803	+	0.444624i	0.964373	+	0.264547i	$0.0852225\pi$
$458$	689.187	+	864.213i	1.50478	+	1.88693i
$459$		0			0
$460$	−253.351	−	1110.00i	−0.550762	−	2.41305i
$461$	70.6093	+	112.374i	0.153166	+	0.243762i	0.914489	−	0.404611i	$-0.132593\pi$
$461$	70.6093	+	112.374i	0.153166	+	0.243762i	−0.761323	+	0.648372i	$0.775450\pi$
$462$		0			0
$463$			36.6184i			0.0790895i	0.999218	+	0.0395447i	$0.0125908\pi$
$463$			36.6184i			0.0790895i	−0.999218	+	0.0395447i	$0.987409\pi$
$464$	230.973	−	743.437i	0.497788	−	1.60223i
$465$		0			0
$466$	−329.109	+	37.0817i	−0.706243	+	0.0795745i
$467$	−125.291	+	78.7258i	−0.268290	+	0.168578i	−0.659458	−	0.751742i	$-0.729214\pi$
$467$	−125.291	+	78.7258i	−0.268290	+	0.168578i	0.391168	+	0.920319i	$0.372071\pi$
$468$		0			0
$469$	−512.672	−	408.843i	−1.09312	−	0.871733i
$470$	81.6786	−	65.1365i	0.173784	−	0.138588i
$471$		0			0
$472$	−1493.76	+	522.690i	−3.16475	+	1.10739i
$473$	1.95401	−	4.05755i	0.00413111	−	0.00857833i
$474$		0			0
$475$	−281.858	−	98.6265i	−0.593386	−	0.207635i
$476$	1472.14	−	1472.14i	3.09273	−	3.09273i
$477$		0			0
$478$	165.284	−	1466.93i	0.345782	−	3.06890i
$479$	541.118	+	60.9693i	1.12968	+	0.127285i	0.656959	−	0.753926i	$-0.271842\pi$
$479$	541.118	+	60.9693i	1.12968	+	0.127285i	0.472723	+	0.881211i	$0.343271\pi$
$480$		0			0
$481$	−89.4749	−	89.4749i	−0.186019	−	0.186019i
$482$	−146.940	+	419.930i	−0.304855	+	0.871225i
$483$		0			0
$484$	−959.789	−	462.210i	−1.98304	−	0.954980i
$485$	−357.948	−	1022.96i	−0.738036	−	2.10919i
$486$		0			0
$487$	−143.770	−	180.282i	−0.295216	−	0.370190i	0.611997	−	0.790860i	$-0.290366\pi$
$487$	−143.770	−	180.282i	−0.295216	−	0.370190i	−0.907214	+	0.420670i	$0.861795\pi$
$488$	82.2977	−	103.198i	0.168643	−	0.211471i
$489$		0			0
$490$	533.624	+	849.257i	1.08903	+	1.73318i
$491$	−55.3414	−	491.168i	−0.112712	−	1.00034i	−0.915013	−	0.403424i	$-0.867820\pi$
$491$	−55.3414	−	491.168i	−0.112712	−	1.00034i	0.802302	−	0.596919i	$-0.203608\pi$
$492$		0			0
$493$	716.157	−	25.3412i	1.45265	−	0.0514020i
$494$	−419.863			−0.849926
$495$		0			0
$496$	7.49397	−	4.70877i	0.0151088	−	0.00949349i
$497$	816.761	−	186.420i	1.64338	−	0.375091i
$498$		0			0
$499$	116.986	−	93.2931i	0.234441	−	0.186960i	−0.499222	−	0.866474i	$-0.666381\pi$
$499$	116.986	−	93.2931i	0.234441	−	0.186960i	0.733663	+	0.679514i	$0.237809\pi$
$500$	−66.7859	+	292.608i	−0.133572	+	0.585216i
$501$		0			0
$502$	−52.1212	+	108.231i	−0.103827	+	0.215599i
$503$	579.852	+	364.345i	1.15279	+	0.724344i	0.966124	−	0.258080i	$-0.0830897\pi$
$503$	579.852	+	364.345i	1.15279	+	0.724344i	0.186664	+	0.982424i	$0.440233\pi$
$504$		0			0
$505$	39.4101	−	39.4101i	0.0780398	−	0.0780398i
$506$	22.1700	+	46.0365i	0.0438143	+	0.0909813i
$507$		0			0
$508$	847.857	+	95.5305i	1.66901	+	0.188052i
$509$	285.063	−	137.279i	0.560046	−	0.269704i	−0.132372	−	0.991200i	$-0.542259\pi$
$509$	285.063	−	137.279i	0.560046	−	0.269704i	0.692419	+	0.721496i	$0.256545\pi$
$510$		0			0
$511$	−92.2295	+	263.577i	−0.180488	+	0.515806i
$512$	−609.618	+	970.201i	−1.19066	+	1.89492i
$513$		0			0
$514$	319.898	+	914.215i	0.622369	+	1.77863i
$515$	476.576	+	108.775i	0.925390	+	0.211214i
$516$		0			0
$517$	−2.01289	+	2.52408i	−0.00389340	+	0.00488217i
$518$	122.898	+	538.452i	0.237255	+	1.03948i
$519$		0			0
$520$	−101.927	−	904.625i	−0.196013	−	1.73966i
$521$		−	561.548i		−	1.07783i	−0.842361	−	0.538914i	$-0.818835\pi$
$521$		−	561.548i		−	1.07783i	0.842361	−	0.538914i	$-0.181165\pi$
$522$		0			0
$523$	−649.609			−1.24208			−0.621041	−	0.783778i	$-0.713290\pi$
$523$	−649.609			−1.24208			−0.621041	+	0.783778i	$0.713290\pi$
$524$	−669.123	+	75.3920i	−1.27695	+	0.143878i
$525$		0			0
$526$	−624.509	+	142.540i	−1.18728	+	0.270989i
$527$	6.36957	+	5.07956i	0.0120865	+	0.00963863i
$528$		0			0
$529$	35.6531	−	156.206i	0.0673971	−	0.295286i
$530$	−1367.83	+	478.625i	−2.58082	+	0.903066i
$531$		0			0
$532$	1068.47	+	671.362i	2.00840	+	1.26196i
$533$	−292.858	−	102.475i	−0.549452	−	0.192261i
$534$		0			0
$535$	−236.546	−	491.193i	−0.442143	−	0.918119i
$536$	133.806	−	1187.56i	0.249638	−	2.21560i
$537$		0			0
$538$	1262.54	−	608.006i	2.34672	−	1.13012i
$539$	−21.9168	−	21.9168i	−0.0406620	−	0.0406620i
$540$		0			0
$541$	412.119	−	655.884i	0.761774	−	1.21236i	−0.210290	−	0.977639i	$-0.567441\pi$
$541$	412.119	−	655.884i	0.761774	−	1.21236i	0.972064	−	0.234717i	$-0.0754162\pi$
$542$	109.342	+	52.6563i	0.201738	+	0.0971519i
$543$		0			0
$544$	644.722	+	147.153i	1.18515	+	0.270503i
$545$	−513.331	−	643.697i	−0.941892	−	1.18109i
$546$		0			0
$547$	−116.423	−	510.082i	−0.212839	−	0.932508i	−0.962627	−	0.270830i	$-0.912702\pi$
$547$	−116.423	−	510.082i	−0.212839	−	0.932508i	0.749788	−	0.661678i	$-0.230155\pi$
$548$	718.691	+	1143.79i	1.31148	+	2.08721i
$549$		0			0
$550$			53.0502i			0.0964549i
$551$	111.565	+	419.772i	0.202477	+	0.761837i
$552$		0			0
$553$	208.748	−	23.5202i	0.377482	−	0.0425320i
$554$	−359.635	+	225.973i	−0.649160	+	0.407894i
$555$		0			0
$556$	−934.588	−	745.309i	−1.68091	−	1.34048i
$557$	133.141	−	106.177i	0.239033	−	0.190622i	−0.496645	−	0.867954i	$-0.665435\pi$
$557$	133.141	−	106.177i	0.239033	−	0.190622i	0.735678	+	0.677331i	$0.236864\pi$
$558$		0			0
$559$	44.7850	−	15.6709i	0.0801163	−	0.0280339i
$560$	−743.794	+	1544.50i	−1.32820	+	2.75804i
$561$		0			0
$562$	−967.402	−	338.509i	−1.72136	−	0.602329i
$563$	622.112	−	622.112i	1.10499	−	1.10499i	0.111195	−	0.993799i	$-0.464532\pi$
$563$	622.112	−	622.112i	1.10499	−	1.10499i	0.993799	−	0.111195i	$-0.0354679\pi$
$564$		0			0
$565$	−119.260	+	1058.46i	−0.211080	+	1.87339i
$566$	−808.759	−	91.1252i	−1.42890	−	0.160999i
$567$		0			0
$568$	1079.63	+	1079.63i	1.90076	+	1.90076i
$569$	−62.1379	+	177.580i	−0.109205	+	0.312091i	−0.985498	−	0.169689i	$-0.945724\pi$
$569$	−62.1379	+	177.580i	−0.109205	+	0.312091i	0.876292	+	0.481780i	$0.160010\pi$
$570$		0			0
$571$	485.208	+	233.664i	0.849751	+	0.409218i	0.807485	−	0.589888i	$-0.200828\pi$
$571$	485.208	+	233.664i	0.849751	+	0.409218i	0.0422657	+	0.999106i	$0.486542\pi$
$572$	16.9635	+	48.4790i	0.0296565	+	0.0847535i
$573$		0			0
$574$	844.356	+	1058.79i	1.47100	+	1.84458i
$575$	−238.719	+	299.344i	−0.415163	+	0.520599i
$576$		0			0
$577$	−276.433	−	439.941i	−0.479087	−	0.762462i	0.516502	−	0.856286i	$-0.327234\pi$
$577$	−276.433	−	439.941i	−0.479087	−	0.762462i	−0.995589	+	0.0938238i	$0.970091\pi$
$578$	129.052	+	1145.37i	0.223274	+	1.98161i
$579$		0			0
$580$	−1601.78	+	624.904i	−2.76169	+	1.07742i
$581$	−393.497			−0.677276
$582$		0			0
$583$	37.9185	−	23.8258i	0.0650403	−	0.0408675i
$584$	−496.168	+	113.247i	−0.849603	+	0.193916i
$585$		0			0
$586$	530.267	−	422.874i	0.904893	−	0.721628i
$587$	235.013	−	1029.66i	0.400363	−	1.75411i	−0.225568	−	0.974227i	$-0.572424\pi$
$587$	235.013	−	1029.66i	0.400363	−	1.75411i	0.625931	−	0.779878i	$-0.284719\pi$
$588$		0			0
$589$	−2.14252	+	4.44899i	−0.00363755	+	0.00755346i
$590$	1854.30	+	1165.13i	3.14288	+	1.97480i
$591$		0			0
$592$	−307.072	+	307.072i	−0.518703	+	0.518703i
$593$	−85.9928	−	178.566i	−0.145013	−	0.301123i	0.815793	−	0.578344i	$-0.196301\pi$
$593$	−85.9928	−	178.566i	−0.145013	−	0.301123i	−0.960806	+	0.277221i	$0.910587\pi$
$594$		0			0
$595$	−1568.08	−	176.680i	−2.63542	−	0.296941i
$596$	−474.814	+	228.658i	−0.796667	+	0.383655i
$597$		0			0
$598$	−177.801	+	508.126i	−0.297326	+	0.849708i
$599$	154.573	−	246.002i	0.258052	−	0.410687i	−0.692421	−	0.721493i	$-0.743456\pi$
$599$	154.573	−	246.002i	0.258052	−	0.410687i	0.950473	+	0.310806i	$0.100599\pi$
$600$		0			0
$601$	−168.543	−	481.670i	−0.280438	−	0.801447i	−0.994816	−	0.101687i	$-0.967576\pi$
$601$	−168.543	−	481.670i	−0.280438	−	0.801447i	0.714378	−	0.699760i	$-0.246710\pi$
$602$	−201.904	−	46.0833i	−0.335389	−	0.0765503i
$603$		0			0
$604$	−1432.30	+	1796.05i	−2.37136	+	2.97359i
$605$	179.671	+	787.192i	0.296978	+	1.30114i
$606$		0			0
$607$	2.33822	+	20.7523i	0.00385209	+	0.0341883i	0.995491	−	0.0948538i	$-0.0302384\pi$
$607$	2.33822	+	20.7523i	0.00385209	+	0.0341883i	−0.991639	+	0.129042i	$0.958810\pi$
$608$			400.825i			0.659251i
$609$		0			0
$610$	−182.656			−0.299435
$611$	−33.7995	+	3.80829i	−0.0553184	+	0.00623289i
$612$		0			0
$613$	−480.301	+	109.626i	−0.783525	+	0.178835i	−0.595527	−	0.803335i	$-0.703057\pi$
$613$	−480.301	+	109.626i	−0.783525	+	0.178835i	−0.187998	+	0.982169i	$0.560200\pi$
$614$	−1140.31	−	909.367i	−1.85718	−	1.48105i
$615$		0			0
$616$	27.3232	−	119.711i	0.0443559	−	0.194336i
$617$	−814.785	+	285.105i	−1.32056	+	0.462083i	−0.896296	−	0.443456i	$-0.853752\pi$
$617$	−814.785	+	285.105i	−1.32056	+	0.462083i	−0.424262	+	0.905539i	$0.639467\pi$
$618$		0			0
$619$	−111.989	−	70.3677i	−0.180920	−	0.113680i	0.438527	−	0.898718i	$-0.355500\pi$
$619$	−111.989	−	70.3677i	−0.180920	−	0.113680i	−0.619447	+	0.785038i	$0.712643\pi$
$620$	−18.4502	−	6.45602i	−0.0297585	−	0.0104129i
$621$		0			0
$622$	37.1487	+	77.1400i	0.0597245	+	0.124019i
$623$	−105.197	+	933.650i	−0.168856	+	1.49864i
$624$		0			0
$625$	654.040	−	314.969i	1.04646	−	0.503951i
$626$	1042.07	+	1042.07i	1.66464	+	1.66464i
$627$		0			0
$628$	−881.306	+	1402.59i	−1.40335	+	2.23342i
$629$	−360.157	−	173.443i	−0.572587	−	0.275744i
$630$		0			0
$631$	901.413	+	205.742i	1.42855	+	0.326056i	0.865724	−	0.500522i	$-0.166858\pi$
$631$	901.413	+	205.742i	1.42855	+	0.326056i	0.562822	+	0.826578i	$0.309716\pi$
$632$	238.703	+	299.324i	0.377695	+	0.473615i
$633$		0			0
$634$	384.110	+	1682.89i	0.605851	+	2.65441i
$635$	−344.066	−	547.578i	−0.541836	−	0.862327i
$636$		0			0
$637$		−	326.552i		−	0.512640i
$638$	63.8431	−	43.3380i	0.100068	−	0.0679278i
$639$		0			0
$640$	986.826	−	111.189i	1.54192	−	0.173732i
$641$	836.101	−	525.357i	1.30437	−	0.819590i	0.312883	−	0.949792i	$-0.398705\pi$
$641$	836.101	−	525.357i	1.30437	−	0.819590i	0.991488	+	0.130202i	$0.0415625\pi$
$642$		0			0
$643$	597.523	+	476.509i	0.929274	+	0.741071i	0.966078	−	0.258251i	$-0.0831463\pi$
$643$	597.523	+	476.509i	0.929274	+	0.741071i	−0.0368040	+	0.999323i	$0.511718\pi$
$644$	1264.96	−	1008.77i	1.96423	−	1.56642i
$645$		0			0
$646$	−1251.97	+	438.082i	−1.93803	+	0.678145i
$647$	530.613	−	1101.83i	0.820112	−	1.70298i	0.115593	−	0.993297i	$-0.463123\pi$
$647$	530.613	−	1101.83i	0.820112	−	1.70298i	0.704520	−	0.709684i	$-0.251162\pi$
$648$		0			0
$649$	−63.8779	−	22.3518i	−0.0984251	−	0.0344404i
$650$	−395.214	+	395.214i	−0.608021	+	0.608021i
$651$		0			0
$652$	252.222	−	2238.53i	0.386844	−	3.43333i
$653$	−1154.35	−	130.064i	−1.76777	−	0.199179i	−0.832717	−	0.553699i	$-0.813216\pi$
$653$	−1154.35	−	130.064i	−1.76777	−	0.199179i	−0.935049	+	0.354520i	$0.884644\pi$
$654$		0			0
$655$	360.888	+	360.888i	0.550974	+	0.550974i
$656$	−351.689	+	1005.07i	−0.536111	+	1.53212i
$657$		0			0
$658$	133.757	+	64.4142i	0.203279	+	0.0978939i
$659$	103.295	+	295.200i	0.156745	+	0.447951i	0.995297	−	0.0968701i	$-0.0308831\pi$
$659$	103.295	+	295.200i	0.156745	+	0.447951i	−0.838552	+	0.544821i	$0.816597\pi$
$660$		0			0
$661$	−741.803	−	930.192i	−1.12224	−	1.40725i	−0.901963	−	0.431813i	$-0.857874\pi$
$661$	−741.803	−	930.192i	−1.12224	−	1.40725i	−0.220281	−	0.975436i	$-0.570697\pi$
$662$	−801.377	+	1004.90i	−1.21054	+	1.51797i
$663$		0			0
$664$	−381.546	−	607.228i	−0.574618	−	0.914499i
$665$	−107.088	−	950.433i	−0.161035	−	1.42922i
$666$		0			0
$667$	555.260	+	42.7445i	0.832474	+	0.0640847i
$668$	340.486			0.509709
$669$		0			0
$670$	−1400.27	+	879.846i	−2.08995	+	1.31320i
$671$	5.50301	−	1.25603i	0.00820120	−	0.00187187i
$672$		0			0
$673$	−444.801	+	354.717i	−0.660922	+	0.527068i	−0.895518	−	0.445025i	$-0.853195\pi$
$673$	−444.801	+	354.717i	−0.660922	+	0.527068i	0.234596	+	0.972093i	$0.424623\pi$
$674$	18.4825	−	80.9772i	0.0274221	−	0.120144i
$675$		0			0
$676$	413.736	−	859.133i	0.612036	−	1.27091i
$677$	−157.955	−	99.2497i	−0.233316	−	0.146602i	0.410300	−	0.911950i	$-0.365424\pi$
$677$	−157.955	−	99.2497i	−0.233316	−	0.146602i	−0.643616	+	0.765348i	$0.722567\pi$
$678$		0			0
$679$	1089.02	−	1089.02i	1.60386	−	1.60386i
$680$	−1247.81	−	2591.10i	−1.83501	−	3.81044i
$681$		0			0
$682$	0.871738	+	0.0982213i	0.00127821	+	0.000144020i
$683$	−102.817	+	49.5142i	−0.150538	+	0.0724951i	−0.507636	−	0.861572i	$-0.669480\pi$
$683$	−102.817	+	49.5142i	−0.150538	+	0.0724951i	0.357098	+	0.934067i	$0.383766\pi$
$684$		0			0
$685$	338.164	−	966.417i	0.493670	−	1.41083i
$686$	131.724	−	209.638i	0.192018	−	0.305594i
$687$		0			0
$688$	−53.7817	−	153.699i	−0.0781711	−	0.223400i
$689$	459.983	+	104.988i	0.667610	+	0.152378i
$690$		0			0
$691$	−301.568	+	378.155i	−0.436423	+	0.547257i	−0.950597	−	0.310429i	$-0.899527\pi$
$691$	−301.568	+	378.155i	−0.436423	+	0.547257i	0.514174	+	0.857686i	$0.328099\pi$
$692$	75.5389	+	330.958i	0.109160	+	0.478263i
$693$		0			0
$694$	123.282	+	1094.16i	0.177640	+	1.57660i
$695$			906.043i			1.30366i
$696$		0			0
$697$	−980.177			−1.40628
$698$	291.870	−	32.8858i	0.418151	−	0.0471143i
$699$		0			0
$700$	1637.69	−	373.791i	2.33955	−	0.533988i
$701$	382.725	+	305.213i	0.545969	+	0.435396i	0.857234	−	0.514927i	$-0.172181\pi$
$701$	382.725	+	305.213i	0.545969	+	0.435396i	−0.311264	+	0.950323i	$0.600752\pi$
$702$		0			0
$703$	53.9148	−	236.216i	0.0766925	−	0.336012i
$704$	−8.03499	+	2.81157i	−0.0114133	+	0.00399370i
$705$		0			0
$706$	−134.273	−	84.3691i	−0.190188	−	0.119503i
$707$	74.7573	+	26.1587i	0.105739	+	0.0369996i
$708$		0			0
$709$	461.431	+	958.172i	0.650820	+	1.35144i	0.921351	+	0.388731i	$0.127086\pi$
$709$	461.431	+	958.172i	0.650820	+	1.35144i	−0.270531	+	0.962711i	$0.587199\pi$
$710$	236.562	−	2099.54i	0.333186	−	2.95711i
$711$		0			0
$712$	−1542.77	+	742.959i	−2.16681	+	1.04348i
$713$	4.47694	+	4.47694i	0.00627902	+	0.00627902i
$714$		0			0
$715$	20.7117	−	32.9624i	0.0289674	−	0.0461013i
$716$	−1386.90	−	667.895i	−1.93701	−	0.932815i
$717$		0			0
$718$	1220.23	+	278.511i	1.69949	+	0.387898i
$719$	465.243	+	583.396i	0.647069	+	0.811399i	0.991867	−	0.127278i	$-0.0406240\pi$
$719$	465.243	+	583.396i	0.647069	+	0.811399i	−0.344798	+	0.938677i	$0.612053\pi$
$720$		0			0
$721$	154.577	+	677.244i	0.214392	+	0.939312i
$722$	260.609	+	414.757i	0.360954	+	0.574455i
$723$		0			0
$724$		−	1505.90i		−	2.07998i
$725$	500.143	+	290.113i	0.689853	+	0.400156i
$726$		0			0
$727$	137.483	−	15.4906i	0.189110	−	0.0213076i	−0.0169014	−	0.999857i	$-0.505380\pi$
$727$	137.483	−	15.4906i	0.189110	−	0.0213076i	0.206012	+	0.978550i	$0.433952\pi$
$728$	1095.38	−	688.270i	1.50464	−	0.945426i
$729$		0			0
$730$	550.610	+	439.097i	0.754260	+	0.601502i
$731$	117.191	−	93.4566i	0.160316	−	0.127848i
$732$		0			0
$733$	−96.2298	+	33.6723i	−0.131282	+	0.0459376i	−0.395121	−	0.918629i	$-0.629297\pi$
$733$	−96.2298	+	33.6723i	−0.131282	+	0.0459376i	0.263838	+	0.964567i	$0.415011\pi$
$734$	342.438	−	711.079i	0.466537	−	0.968773i
$735$		0			0
$736$	485.085	+	169.738i	0.659082	+	0.230623i
$737$	36.1367	−	36.1367i	0.0490322	−	0.0490322i
$738$		0			0
$739$	77.8075	−	690.560i	0.105288	−	0.934452i	−0.824376	−	0.566043i	$-0.808474\pi$
$739$	77.8075	−	690.560i	0.105288	−	0.934452i	0.929663	−	0.368410i	$-0.120098\pi$
$740$	953.082	+	107.387i	1.28795	+	0.145117i
$741$		0			0
$742$	−1456.17	−	1456.17i	−1.96250	−	1.96250i
$743$	213.456	−	610.021i	0.287289	−	0.821024i	−0.706294	−	0.707918i	$-0.749634\pi$
$743$	213.456	−	610.021i	0.287289	−	0.821024i	0.993583	−	0.113106i	$-0.0360799\pi$
$744$		0			0
$745$	359.886	+	173.312i	0.483069	+	0.232634i
$746$	310.608	+	887.666i	0.416364	+	1.18990i
$747$		0			0
$748$	101.165	+	126.857i	0.135247	+	0.169595i
$749$	483.042	−	605.716i	0.644916	−	0.808700i
$750$		0			0
$751$	203.554	+	323.954i	0.271044	+	0.431364i	0.954316	−	0.298800i	$-0.0965865\pi$
$751$	203.554	+	323.954i	0.271044	+	0.431364i	−0.683272	+	0.730164i	$0.739444\pi$
$752$	13.0698	+	115.998i	0.0173801	+	0.154253i
$753$		0			0
$754$	798.479	+	152.760i	1.05899	+	0.202599i
$755$	1741.19			2.30621
$756$		0			0
$757$	−572.593	+	359.784i	−0.756397	+	0.475276i	−0.854210	−	0.519929i	$-0.825958\pi$
$757$	−572.593	+	359.784i	−0.756397	+	0.475276i	0.0978121	+	0.995205i	$0.468816\pi$
$758$	−790.112	+	180.338i	−1.04236	+	0.237913i
$759$		0			0
$760$	1362.83	−	1086.82i	1.79320	−	1.43003i
$761$	−139.727	+	612.184i	−0.183610	+	0.804447i	0.796283	+	0.604924i	$0.206796\pi$
$761$	−139.727	+	612.184i	−0.183610	+	0.804447i	−0.979893	+	0.199523i	$0.936061\pi$
$762$		0			0
$763$	507.639	−	1054.12i	0.665319	−	1.38155i
$764$	213.237	+	133.986i	0.279106	+	0.175374i
$765$		0			0
$766$	−344.037	+	344.037i	−0.449134	+	0.449134i
$767$	−309.361	−	642.395i	−0.403339	−	0.837543i
$768$		0			0
$769$	−322.552	−	36.3428i	−0.419443	−	0.0472599i	−0.100279	−	0.994959i	$-0.531974\pi$
$769$	−322.552	−	36.3428i	−0.419443	−	0.0472599i	−0.319164	+	0.947700i	$0.603402\pi$
$770$	−153.089	+	73.7240i	−0.198817	+	0.0957454i
$771$		0			0
$772$	−867.273	+	2478.52i	−1.12341	+	3.21052i
$773$	246.656	−	392.551i	0.319089	−	0.507828i	−0.648211	−	0.761461i	$-0.724483\pi$
$773$	246.656	−	392.551i	0.319089	−	0.507828i	0.967301	+	0.253633i	$0.0816255\pi$
$774$		0			0
$775$	2.17106	+	6.20453i	0.00280137	+	0.00800585i
$776$	2736.48	+	624.583i	3.52639	+	0.804875i
$777$		0			0
$778$	34.9016	−	43.7652i	0.0448606	−	0.0562534i
$779$	−132.200	−	579.204i	−0.169704	−	0.743523i
$780$		0			0
$781$	7.31037	+	64.8814i	0.00936027	+	0.0830747i
$782$			1700.67i			2.17476i
$783$		0			0
$784$	−1120.71			−1.42947
$785$	1247.65	−	140.576i	1.58936	−	0.179078i
$786$		0			0
$787$	1295.68	−	295.731i	1.64636	−	0.375770i	0.703953	−	0.710246i	$-0.251416\pi$
$787$	1295.68	−	295.731i	1.64636	−	0.375770i	0.942404	+	0.334476i	$0.108559\pi$
$788$	−1686.91	−	1345.26i	−2.14075	−	1.70719i
$789$		0			0
$790$	117.889	−	516.507i	0.149227	−	0.653806i
$791$	−1428.72	+	499.930i	−1.80622	+	0.632023i
$792$		0			0
$793$	50.3535	+	31.6392i	0.0634975	+	0.0398981i
$794$	−970.210	−	339.491i	−1.22193	−	0.427571i
$795$		0			0
$796$	−1216.94	−	2527.00i	−1.52882	−	3.17463i
$797$	29.7161	−	263.738i	0.0372849	−	0.330913i	−0.961198	−	0.275858i	$-0.911038\pi$
$797$	29.7161	−	263.738i	0.0372849	−	0.330913i	0.998483	−	0.0550550i	$-0.0175334\pi$
$798$		0			0
$799$	−96.8113	+	46.6219i	−0.121166	+	0.0583503i
$800$	377.293	+	377.293i	0.471616	+	0.471616i
$801$		0			0
$802$	−289.418	+	460.606i	−0.360870	+	0.574321i
$803$	−19.6081	−	9.44276i	−0.0244185	−	0.0117594i
$804$		0			0
$805$	−1195.58	−	272.883i	−1.48519	−	0.338985i
$806$	5.76256	+	7.22602i	0.00714957	+	0.00896528i
$807$		0			0
$808$	32.1199	+	140.727i	0.0397524	+	0.174166i
$809$	617.736	+	983.122i	0.763580	+	1.21523i	0.971489	+	0.237083i	$0.0761913\pi$
$809$	617.736	+	983.122i	0.763580	+	1.21523i	−0.207909	+	0.978148i	$0.566666\pi$
$810$		0			0
$811$		−	321.059i		−	0.395880i	−0.980214	−	0.197940i	$-0.936575\pi$
$811$		−	321.059i		−	0.395880i	0.980214	−	0.197940i	$-0.0634252\pi$
$812$	−1787.70	−	1665.51i	−2.20161	−	2.05112i
$813$		0			0
$814$	−42.7732	+	4.81939i	−0.0525470	+	0.00592062i
$815$	−1445.73	+	908.411i	−1.77390	+	1.11462i
$816$		0			0
$817$	71.0311	+	56.6454i	0.0869413	+	0.0693334i
$818$	−458.531	+	365.667i	−0.560552	+	0.447025i
$819$		0			0
$820$	2219.78	−	776.735i	2.70705	−	0.947238i
$821$	−286.021	+	593.929i	−0.348381	+	0.723421i	−0.999364	−	0.0356719i	$-0.988643\pi$
$821$	−286.021	+	593.929i	−0.348381	+	0.723421i	0.650982	+	0.759093i	$0.274357\pi$
$822$		0			0
$823$	−1135.65	−	397.380i	−1.37989	−	0.482843i	−0.464555	−	0.885545i	$-0.653786\pi$
$823$	−1135.65	−	397.380i	−1.37989	−	0.482843i	−0.915331	+	0.402702i	$0.868071\pi$
$824$	−895.212	+	895.212i	−1.08642	+	1.08642i
$825$		0			0
$826$	−348.442	+	3092.51i	−0.421843	+	3.74396i
$827$	−935.574	−	105.414i	−1.13129	−	0.127465i	−0.473588	−	0.880747i	$-0.657041\pi$
$827$	−935.574	−	105.414i	−1.13129	−	0.127465i	−0.657699	+	0.753281i	$0.728470\pi$
$828$		0			0
$829$	445.070	+	445.070i	0.536876	+	0.536876i	0.922610	−	0.385734i	$-0.126052\pi$
$829$	445.070	+	445.070i	0.536876	+	0.536876i	−0.385734	+	0.922610i	$0.626052\pi$
$830$	−327.767	+	936.703i	−0.394900	+	1.12856i
$831$		0			0
$832$	−80.8048	−	38.9135i	−0.0971212	−	0.0467711i
$833$	−340.722	−	973.726i	−0.409029	−	1.16894i
$834$		0			0
$835$	−160.905	−	201.769i	−0.192701	−	0.241639i
$836$	−61.3176	+	76.8899i	−0.0733465	+	0.0919736i
$837$		0			0
$838$	63.1245	+	100.462i	0.0753276	+	0.119883i
$839$	112.137	+	995.248i	0.133656	+	1.18623i	0.864122	+	0.503282i	$0.167874\pi$
$839$	112.137	+	995.248i	0.133656	+	1.18623i	−0.730466	+	0.682949i	$0.760697\pi$
$840$		0			0
$841$	−59.4431	−	838.897i	−0.0706814	−	0.997499i
$842$	−1597.26			−1.89699
$843$		0			0
$844$	2803.65	−	1761.65i	3.32186	−	2.08727i
$845$	−704.636	+	160.829i	−0.833889	+	0.190330i
$846$		0			0
$847$	−897.087	+	715.403i	−1.05913	+	0.844631i
$848$	360.313	−	1578.63i	0.424897	−	1.86160i
$849$		0			0
$850$	−766.102	+	1590.83i	−0.901297	+	1.87156i
$851$	−263.041	−	165.280i	−0.309097	−	0.194218i
$852$		0			0
$853$	−187.887	+	187.887i	−0.220266	+	0.220266i	−0.808610	−	0.588345i	$-0.799780\pi$
$853$	−187.887	+	187.887i	−0.220266	+	0.220266i	0.588345	+	0.808610i	$0.299780\pi$
$854$	−112.621	−	233.860i	−0.131875	−	0.273841i
$855$		0			0
$856$	1403.09	+	158.090i	1.63912	+	0.184684i
$857$	−391.026	+	188.308i	−0.456273	+	0.219729i	−0.647880	−	0.761742i	$-0.724344\pi$
$857$	−391.026	+	188.308i	−0.456273	+	0.219729i	0.191608	+	0.981472i	$0.438630\pi$
$858$		0			0
$859$	−188.502	+	538.706i	−0.219443	+	0.627132i	0.780555	+	0.625087i	$0.214937\pi$
$859$	−188.502	+	538.706i	−0.219443	+	0.627132i	−0.999998	+	0.00204487i	$0.999349\pi$
$860$	−191.340	+	304.516i	−0.222488	+	0.354088i
$861$		0			0
$862$	−301.391	−	861.325i	−0.349641	−	0.999217i
$863$	−1118.53	−	255.297i	−1.29610	−	0.295826i	−0.481803	−	0.876279i	$-0.660018\pi$
$863$	−1118.53	−	255.297i	−1.29610	−	0.295826i	−0.814293	+	0.580454i	$0.802875\pi$
$864$		0			0
$865$	160.425	−	201.166i	0.185462	−	0.232562i
$866$	295.883	+	1296.35i	0.341667	+	1.49694i
$867$		0			0
$868$	−3.11012	−	27.6031i	−0.00358309	−	0.0318008i
$869$			16.3719i			0.0188399i
$870$		0			0
$871$	538.423			0.618167
$872$	2118.90	−	238.742i	2.42993	−	0.273787i
$873$		0			0
$874$	−1004.95	+	229.374i	−1.14983	+	0.262442i
$875$	252.745	+	201.557i	0.288851	+	0.230351i
$876$		0			0
$877$	−242.063	+	1060.55i	−0.276012	+	1.20929i	0.626775	+	0.779200i	$0.284375\pi$
$877$	−242.063	+	1060.55i	−0.276012	+	1.20929i	−0.902787	+	0.430088i	$0.858483\pi$
$878$	1639.51	−	573.689i	1.86732	−	0.653404i
$879$		0			0
$880$	−113.125	−	71.0811i	−0.128551	−	0.0807740i
$881$	775.831	+	271.475i	0.880625	+	0.308144i	0.732453	−	0.680817i	$-0.238375\pi$
$881$	775.831	+	271.475i	0.880625	+	0.308144i	0.148172	+	0.988962i	$0.452661\pi$
$882$		0			0
$883$	−143.552	−	298.089i	−0.162573	−	0.337587i	0.803730	−	0.594995i	$-0.202846\pi$
$883$	−143.552	−	298.089i	−0.162573	−	0.337587i	−0.966303	+	0.257408i	$0.917132\pi$
$884$	−191.400	+	1698.72i	−0.216516	+	1.92163i
$885$		0			0
$886$	456.120	−	219.656i	0.514809	−	0.247919i
$887$	−629.240	−	629.240i	−0.709402	−	0.709402i	0.257007	−	0.966410i	$-0.417264\pi$
$887$	−629.240	−	629.240i	−0.709402	−	0.709402i	−0.966410	+	0.257007i	$0.917264\pi$
$888$		0			0
$889$	488.939	−	778.142i	0.549988	−	0.875301i
$890$	2134.89	+	1028.11i	2.39875	+	1.15518i
$891$		0			0
$892$	−2387.10	−	544.841i	−2.67613	−	0.610808i
$893$	−40.6070	−	50.9195i	−0.0454725	−	0.0570207i
$894$		0			0
$895$	259.626	+	1137.50i	0.290085	+	1.27094i
$896$	750.811	+	1194.91i	0.837959	+	1.33360i
$897$		0			0
$898$			1770.09i			1.97115i
$899$	5.69324	−	7.68138i	0.00633286	−	0.00854437i
$900$		0			0
$901$	1481.14	−	166.884i	1.64389	−	0.185221i
$902$	−89.3666	+	56.1528i	−0.0990761	+	0.0622536i
$903$		0			0
$904$	−2156.80	−	1719.99i	−2.38584	−	1.90264i
$905$	−892.384	+	711.653i	−0.986060	+	0.786356i
$906$		0			0
$907$	142.031	−	49.6988i	0.156594	−	0.0547947i	−0.250844	−	0.968028i	$-0.580708\pi$
$907$	142.031	−	49.6988i	0.156594	−	0.0547947i	0.407438	+	0.913233i	$0.366422\pi$
$908$	1008.19	−	2093.54i	1.11035	−	2.30566i
$909$		0			0
$910$	−1689.72	−	591.257i	−1.85683	−	0.649733i
$911$	396.137	−	396.137i	0.434837	−	0.434837i	−0.455433	−	0.890270i	$-0.650515\pi$
$911$	396.137	−	396.137i	0.434837	−	0.434837i	0.890270	+	0.455433i	$0.150515\pi$
$912$		0			0
$913$	3.43367	−	30.4747i	0.00376087	−	0.0333786i
$914$	3252.03	+	366.415i	3.55802	+	0.400892i
$915$		0			0
$916$	1928.86	+	1928.86i	2.10574	+	2.10574i
$917$	−239.542	+	684.571i	−0.261223	+	0.746533i
$918$		0			0
$919$	84.8857	+	40.8788i	0.0923675	+	0.0444818i	0.479497	−	0.877543i	$-0.340819\pi$
$919$	84.8857	+	40.8788i	0.0923675	+	0.0444818i	−0.387130	+	0.922025i	$0.626533\pi$
$920$	−738.168	−	2109.56i	−0.802356	−	2.29300i
$921$		0			0
$922$	296.558	+	371.871i	0.321646	+	0.403331i
$923$	−428.893	+	537.815i	−0.464673	+	0.582681i
$924$		0			0
$925$	−171.599	−	273.098i	−0.185512	−	0.295241i
$926$	14.6938	+	130.411i	0.0158681	+	0.140833i
$927$		0			0
$928$	145.833	−	762.272i	0.157147	−	0.821413i
$929$	−426.924			−0.459552			−0.229776	−	0.973243i	$-0.573799\pi$
$929$	−426.924			−0.459552			−0.229776	+	0.973243i	$0.573799\pi$
$930$		0			0
$931$	529.438	−	332.668i	0.568677	−	0.357323i
$932$	−796.820	+	181.869i	−0.854957	+	0.195138i
$933$		0			0
$934$	−414.618	+	330.647i	−0.443916	+	0.354011i
$935$	27.3662	−	119.899i	0.0292686	−	0.128234i
$936$		0			0
$937$	495.268	−	1028.43i	0.528568	−	1.09758i	−0.450260	−	0.892897i	$-0.648669\pi$
$937$	495.268	−	1028.43i	0.528568	−	1.09758i	0.978828	−	0.204685i	$-0.0656169\pi$
$938$	−1989.87	−	1250.32i	−2.12139	−	1.33296i
$939$		0			0
$940$	182.301	−	182.301i	0.193937	−	0.193937i
$941$	−54.6779	−	113.540i	−0.0581062	−	0.120659i	0.869894	−	0.493239i	$-0.164187\pi$
$941$	−54.6779	−	113.540i	−0.0581062	−	0.120659i	−0.928000	+	0.372581i	$0.878473\pi$
$942$		0			0
$943$	−756.946	−	85.2873i	−0.802700	−	0.0904425i
$944$	−2204.66	+	1061.71i	−2.33544	+	1.12469i
$945$		0			0
$946$	5.33078	−	15.2345i	0.00563507	−	0.0161041i
$947$	220.220	−	350.478i	0.232545	−	0.370093i	−0.709984	−	0.704218i	$-0.751298\pi$
$947$	220.220	−	350.478i	0.232545	−	0.370093i	0.942529	+	0.334125i	$0.108441\pi$
$948$		0			0
$949$	−75.7298	−	216.423i	−0.0797996	−	0.228054i
$950$	−1043.38	−	238.144i	−1.09829	−	0.250677i
$951$		0			0
$952$	2548.10	−	3195.22i	2.67658	−	3.35632i
$953$	−151.639	−	664.374i	−0.159117	−	0.697139i	−0.990044	−	0.140757i	$-0.955046\pi$
$953$	−151.639	−	664.374i	−0.159117	−	0.697139i	0.830927	−	0.556382i	$-0.187811\pi$
$954$		0			0
$955$	−21.3719	−	189.681i	−0.0223789	−	0.198618i
$956$		−	3642.99i		−	3.81066i
$957$		0			0
$958$	1951.58			2.03714
$959$	1445.84	−	162.907i	1.50765	−	0.169872i
$960$		0			0
$961$	−936.800	+	213.818i	−0.974818	+	0.222496i
$962$	−354.556	−	282.749i	−0.368561	−	0.293918i
$963$		0			0
$964$	−244.308	+	1070.38i	−0.253432	+	1.11036i
$965$	1878.60	−	657.352i	1.94674	−	0.681193i
$966$		0			0
$967$	253.964	+	159.576i	0.262631	+	0.165022i	0.656910	−	0.753969i	$-0.271863\pi$
$967$	253.964	+	159.576i	0.262631	+	0.165022i	−0.394280	+	0.918990i	$0.629006\pi$
$968$	−1973.82	−	690.669i	−2.03907	−	0.713501i
$969$		0			0
$970$	−1685.26	−	3499.48i	−1.73738	−	3.60771i
$971$	−154.759	+	1373.53i	−0.159381	+	1.41455i	0.618327	+	0.785921i	$0.287811\pi$
$971$	−154.759	+	1373.53i	−0.159381	+	1.41455i	−0.777708	+	0.628626i	$0.783618\pi$
$972$		0			0
$973$	−1160.04	+	558.644i	−1.19223	+	0.574146i
$974$	−584.360	−	584.360i	−0.599959	−	0.599959i
$975$		0			0
$976$	108.584	−	172.810i	0.111254	−	0.177059i
$977$	1397.72	+	673.106i	1.43062	+	0.688952i	0.979114	−	0.203314i	$-0.0651712\pi$
$977$	1397.72	+	673.106i	1.43062	+	0.688952i	0.451510	+	0.892266i	$0.350885\pi$
$978$		0			0
$979$	−71.3893	−	16.2941i	−0.0729206	−	0.0166437i
$980$	1543.25	+	1935.17i	1.57474	+	1.97466i
$981$		0			0
$982$	−394.181	−	1727.02i	−0.401406	−	1.75868i
$983$	−582.106	−	926.416i	−0.592173	−	0.942438i	−0.999574	−	0.0291883i	$-0.990708\pi$
$983$	−582.106	−	926.416i	−0.592173	−	0.942438i	0.407401	−	0.913249i	$-0.366435\pi$
$984$		0			0
$985$			1635.39i			1.66029i
$986$	2540.33	−	377.621i	2.57639	−	0.382983i
$987$		0			0
$988$	−1029.62	+	116.010i	−1.04213	+	0.117419i
$989$	98.6330	−	61.9752i	0.0997300	−	0.0626645i
$990$		0			0
$991$	75.5485	+	60.2479i	0.0762346	+	0.0607951i	0.660866	−	0.750504i	$-0.270189\pi$
$991$	75.5485	+	60.2479i	0.0762346	+	0.0607951i	−0.584631	+	0.811299i	$0.698761\pi$
$992$	6.89835	−	5.50125i	0.00695398	−	0.00554562i
$993$		0			0
$994$	2833.97	−	991.651i	2.85108	−	0.997636i
$995$	−922.383	+	1915.35i	−0.927018	+	1.92497i
$996$		0			0
$997$	937.382	+	328.004i	0.940203	+	0.328991i	0.756502	−	0.653991i	$-0.226907\pi$
$997$	937.382	+	328.004i	0.940203	+	0.328991i	0.183700	+	0.982982i	$0.441192\pi$
$998$	379.193	−	379.193i	0.379953	−	0.379953i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.73.4		48
3.2	odd	2		29.3.f.a.15.1	yes	48
29.2	odd	28	inner	261.3.s.a.118.4		48
87.2	even	28		29.3.f.a.2.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.2.1	✓	48	87.2	even	28
29.3.f.a.15.1	yes	48	3.2	odd	2
261.3.s.a.73.4		48	1.1	even	1	trivial
261.3.s.a.118.4		48	29.2	odd	28	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(3.56136 - 0.401269i) q^{2} +(8.62256 - 1.96804i) q^{4} +(-5.24106 - 4.17960i) q^{5} +(2.11977 - 9.28734i) q^{7} +(16.3872 - 5.73413i) q^{8} +O(q^{10})\)	\(q+(3.56136 - 0.401269i) q^{2} +(8.62256 - 1.96804i) q^{4} +(-5.24106 - 4.17960i) q^{5} +(2.11977 - 9.28734i) q^{7} +(16.3872 - 5.73413i) q^{8} +(-20.3424 - 12.7820i) q^{10} +(0.700768 + 0.245209i) q^{11} +(3.39382 + 7.04735i) q^{13} +(3.82256 - 33.9262i) q^{14} +(24.1861 - 11.6474i) q^{16} +(17.4730 + 17.4730i) q^{17} +(-7.96846 + 12.6817i) q^{19} +(-53.4169 - 25.7242i) q^{20} +(2.59408 + 0.592082i) q^{22} +(11.9732 + 15.0139i) q^{23} +(4.43656 + 19.4379i) q^{25} +(14.9145 + 23.7363i) q^{26} -84.2524i q^{28} +(19.7681 - 21.2184i) q^{29} +(0.327624 - 0.0369143i) q^{31} +(22.6600 - 14.2382i) q^{32} +(69.2390 + 55.2162i) q^{34} +(-49.9272 + 39.8156i) q^{35} +(-15.2693 + 5.34296i) q^{37} +(-23.2898 + 48.3617i) q^{38} +(-109.853 - 38.4391i) q^{40} +(-28.0484 + 28.0484i) q^{41} +(0.679170 - 6.02780i) q^{43} +(6.52499 + 0.735190i) q^{44} +(48.6656 + 48.6656i) q^{46} +(-1.43620 + 4.10443i) q^{47} +(-37.6137 - 18.1138i) q^{49} +(23.6000 + 67.4450i) q^{50} +(43.1329 + 54.0870i) q^{52} +(37.6082 - 47.1592i) q^{53} +(-2.64789 - 4.21408i) q^{55} +(-18.5176 - 164.349i) q^{56} +(61.8871 - 83.4988i) q^{58} -91.1542 q^{59} +(6.43745 - 4.04492i) q^{61} +(1.15197 - 0.262930i) q^{62} +(-8.96447 + 7.14893i) q^{64} +(11.6679 - 51.1204i) q^{65} +(29.8663 - 62.0180i) q^{67} +(185.049 + 116.274i) q^{68} +(-161.832 + 161.832i) q^{70} +(38.1572 + 79.2343i) q^{71} +(-29.1293 - 3.28209i) q^{73} +(-52.2355 + 25.1553i) q^{74} +(-43.7503 + 125.031i) q^{76} +(3.76281 - 5.98848i) q^{77} +(7.28322 + 20.8142i) q^{79} +(-175.442 - 40.0435i) q^{80} +(-88.6354 + 111.145i) q^{82} +(-9.19165 - 40.2713i) q^{83} +(-18.5468 - 164.607i) q^{85} -21.7397i q^{86} +12.8897 q^{88} +(-98.0089 + 11.0429i) q^{89} +(72.6452 - 16.5808i) q^{91} +(132.788 + 105.895i) q^{92} +(-3.46785 + 15.1936i) q^{94} +(94.7678 - 33.1607i) q^{95} +(136.891 + 86.0143i) q^{97} +(-141.224 - 49.4166i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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