LMFDB - Embedded newform 261.3.s.a.118.1

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			118.1
Character	$\chi$	$=$	261.118
Dual form			261.3.s.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58169 - 0.290886i) q^{2} +(2.68078 + 0.611870i) q^{4} +(2.49104 - 1.98654i) q^{5} +(1.30161 + 5.70272i) q^{7} +(3.06598 + 1.07283i) q^{8} +O(q^{10})$	\(q+(-2.58169 - 0.290886i) q^{2} +(2.68078 + 0.611870i) q^{4} +(2.49104 - 1.98654i) q^{5} +(1.30161 + 5.70272i) q^{7} +(3.06598 + 1.07283i) q^{8} +(-7.00893 + 4.40400i) q^{10} +(-16.1070 + 5.63608i) q^{11} +(2.84196 - 5.90140i) q^{13} +(-1.70150 - 15.1013i) q^{14} +(-17.5130 - 8.43380i) q^{16} +(14.7807 - 14.7807i) q^{17} +(9.65814 + 15.3708i) q^{19} +(7.89342 - 3.80127i) q^{20} +(43.2227 - 9.86529i) q^{22} +(-18.5750 + 23.2923i) q^{23} +(-3.30408 + 14.4761i) q^{25} +(-9.05369 + 14.4089i) q^{26} +16.0841i q^{28} +(19.9272 + 21.0691i) q^{29} +(-13.3687 - 1.50629i) q^{31} +(31.7582 + 19.9550i) q^{32} +(-42.4586 + 33.8596i) q^{34} +(14.5710 + 11.6200i) q^{35} +(17.2522 + 6.03682i) q^{37} +(-20.4631 - 42.4921i) q^{38} +(9.76869 - 3.41821i) q^{40} +(44.4102 + 44.4102i) q^{41} +(7.00239 + 62.1479i) q^{43} +(-46.6278 + 5.25369i) q^{44} +(54.7302 - 54.7302i) q^{46} +(16.6790 + 47.6658i) q^{47} +(13.3206 - 6.41487i) q^{49} +(12.7410 - 36.4117i) q^{50} +(11.2296 - 14.0814i) q^{52} +(-12.0961 - 15.1681i) q^{53} +(-28.9269 + 46.0368i) q^{55} +(-2.12736 + 18.8808i) q^{56} +(-45.3170 - 60.1904i) q^{58} -47.9911 q^{59} +(41.0683 + 25.8049i) q^{61} +(34.0756 + 7.77754i) q^{62} +(-15.3963 - 12.2781i) q^{64} +(-4.64390 - 20.3463i) q^{65} +(-6.15092 - 12.7725i) q^{67} +(48.6676 - 30.5799i) q^{68} +(-34.2377 - 34.2377i) q^{70} +(11.6321 - 24.1543i) q^{71} +(-12.2617 + 1.38156i) q^{73} +(-42.7839 - 20.6036i) q^{74} +(16.4864 + 47.1153i) q^{76} +(-53.1060 - 84.5178i) q^{77} +(33.5205 - 95.7961i) q^{79} +(-60.3795 + 13.7812i) q^{80} +(-101.735 - 127.571i) q^{82} +(9.73978 - 42.6728i) q^{83} +(7.45688 - 66.1816i) q^{85} -162.483i q^{86} -55.4303 q^{88} +(-53.9337 - 6.07686i) q^{89} +(37.3532 + 8.52561i) q^{91} +(-64.0472 + 51.0760i) q^{92} +(-29.1946 - 127.910i) q^{94} +(54.5935 + 19.1031i) q^{95} +(-124.213 + 78.0480i) q^{97} +(-36.2556 + 12.6864i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.58169	−	0.290886i	−1.29084	−	0.145443i	−0.560289	−	0.828298i	$-0.689310\pi$
$2$	−2.58169	−	0.290886i	−1.29084	−	0.145443i	−0.730554	+	0.682854i	$0.760738\pi$
$3$		0			0
$3$		0			0
$4$	2.68078	+	0.611870i	0.670194	+	0.152967i
$5$	2.49104	−	1.98654i	0.498207	−	0.397307i	−0.341892	−	0.939739i	$-0.611068\pi$
$5$	2.49104	−	1.98654i	0.498207	−	0.397307i	0.840100	+	0.542432i	$0.182496\pi$
$6$		0			0
$7$	1.30161	+	5.70272i	0.185944	+	0.814675i	0.978726	+	0.205170i	$0.0657746\pi$
$7$	1.30161	+	5.70272i	0.185944	+	0.814675i	−0.792782	+	0.609505i	$0.791368\pi$
$8$	3.06598	+	1.07283i	0.383247	+	0.134104i
$9$		0			0
$10$	−7.00893	+	4.40400i	−0.700893	+	0.440400i
$11$	−16.1070	+	5.63608i	−1.46427	+	0.512371i	−0.940591	−	0.339543i	$-0.889728\pi$
$11$	−16.1070	+	5.63608i	−1.46427	+	0.512371i	−0.523682	+	0.851914i	$0.675442\pi$
$12$		0			0
$13$	2.84196	−	5.90140i	0.218613	−	0.453954i	−0.762603	−	0.646866i	$-0.776079\pi$
$13$	2.84196	−	5.90140i	0.218613	−	0.453954i	0.981216	+	0.192913i	$0.0617934\pi$
$14$	−1.70150	−	15.1013i	−0.121536	−	1.07866i
$15$		0			0
$16$	−17.5130	−	8.43380i	−1.09456	−	0.527112i
$17$	14.7807	−	14.7807i	0.869452	−	0.869452i	−0.122959	−	0.992412i	$-0.539238\pi$
$17$	14.7807	−	14.7807i	0.869452	−	0.869452i	0.992412	+	0.122959i	$0.0392385\pi$
$18$		0			0
$19$	9.65814	+	15.3708i	0.508323	+	0.808992i	0.998020	−	0.0629012i	$-0.0200353\pi$
$19$	9.65814	+	15.3708i	0.508323	+	0.808992i	−0.489697	+	0.871893i	$0.662892\pi$
$20$	7.89342	−	3.80127i	0.394671	−	0.190063i
$21$		0			0
$22$	43.2227	−	9.86529i	1.96467	−	0.448422i
$23$	−18.5750	+	23.2923i	−0.807608	+	1.01271i	0.191902	+	0.981414i	$0.438534\pi$
$23$	−18.5750	+	23.2923i	−0.807608	+	1.01271i	−0.999510	+	0.0312943i	$0.990037\pi$
$24$		0			0
$25$	−3.30408	+	14.4761i	−0.132163	+	0.579045i
$26$	−9.05369	+	14.4089i	−0.348219	+	0.554187i
$27$		0			0
$28$			16.0841i			0.574434i
$29$	19.9272	+	21.0691i	0.687144	+	0.726521i
$29$	19.9272	+	21.0691i	0.687144	+	0.726521i
$30$		0			0
$31$	−13.3687	−	1.50629i	−0.431249	−	0.0485900i	−0.106327	−	0.994331i	$-0.533909\pi$
$31$	−13.3687	−	1.50629i	−0.431249	−	0.0485900i	−0.324921	+	0.945741i	$0.605338\pi$
$32$	31.7582	+	19.9550i	0.992443	+	0.623593i
$33$		0			0
$34$	−42.4586	+	33.8596i	−1.24878	+	0.995871i
$35$	14.5710	+	11.6200i	0.416315	+	0.332000i
$36$		0			0
$37$	17.2522	+	6.03682i	0.466277	+	0.163157i	0.553184	−	0.833059i	$-0.313413\pi$
$37$	17.2522	+	6.03682i	0.466277	+	0.163157i	−0.0869071	+	0.996216i	$0.527698\pi$
$38$	−20.4631	−	42.4921i	−0.538503	−	1.11821i
$39$		0			0
$40$	9.76869	−	3.41821i	0.244217	−	0.0854553i
$41$	44.4102	+	44.4102i	1.08318	+	1.08318i	0.996211	+	0.0869640i	$0.0277165\pi$
$41$	44.4102	+	44.4102i	1.08318	+	1.08318i	0.0869640	+	0.996211i	$0.472283\pi$
$42$		0			0
$43$	7.00239	+	62.1479i	0.162846	+	1.44530i	0.763509	+	0.645797i	$0.223475\pi$
$43$	7.00239	+	62.1479i	0.162846	+	1.44530i	−0.600663	+	0.799503i	$0.705096\pi$
$44$	−46.6278	+	5.25369i	−1.05972	+	0.119402i
$45$		0			0
$46$	54.7302	−	54.7302i	1.18979	−	1.18979i
$47$	16.6790	+	47.6658i	0.354872	+	1.01417i	0.973541	+	0.228515i	$0.0733868\pi$
$47$	16.6790	+	47.6658i	0.354872	+	1.01417i	−0.618668	+	0.785652i	$0.712327\pi$
$48$		0			0
$49$	13.3206	−	6.41487i	0.271849	−	0.130916i
$50$	12.7410	−	36.4117i	0.254820	−	0.728234i
$51$		0			0
$52$	11.2296	−	14.0814i	0.215953	−	0.270796i
$53$	−12.0961	−	15.1681i	−0.228229	−	0.286190i	0.654511	−	0.756053i	$-0.272875\pi$
$53$	−12.0961	−	15.1681i	−0.228229	−	0.286190i	−0.882739	+	0.469863i	$0.844303\pi$
$54$		0			0
$55$	−28.9269	+	46.0368i	−0.525943	+	0.837033i
$56$	−2.12736	+	18.8808i	−0.0379886	+	0.337158i
$57$		0			0
$58$	−45.3170	−	60.1904i	−0.781327	−	1.03777i
$59$	−47.9911			−0.813408			−0.406704	−	0.913560i	$-0.633322\pi$
$59$	−47.9911			−0.813408			−0.406704	+	0.913560i	$0.633322\pi$
$60$		0			0
$61$	41.0683	+	25.8049i	0.673251	+	0.423031i	0.824805	−	0.565417i	$-0.191285\pi$
$61$	41.0683	+	25.8049i	0.673251	+	0.423031i	−0.151554	+	0.988449i	$0.548428\pi$
$62$	34.0756	+	7.77754i	0.549607	+	0.125444i
$63$		0			0
$64$	−15.3963	−	12.2781i	−0.240567	−	0.191846i
$65$	−4.64390	−	20.3463i	−0.0714446	−	0.313019i
$66$		0			0
$67$	−6.15092	−	12.7725i	−0.0918048	−	0.190635i	0.850010	−	0.526766i	$-0.176596\pi$
$67$	−6.15092	−	12.7725i	−0.0918048	−	0.190635i	−0.941815	+	0.336132i	$0.890881\pi$
$68$	48.6676	−	30.5799i	0.715700	−	0.449704i
$69$		0			0
$70$	−34.2377	−	34.2377i	−0.489110	−	0.489110i
$71$	11.6321	−	24.1543i	0.163832	−	0.340202i	−0.802850	−	0.596182i	$-0.796684\pi$
$71$	11.6321	−	24.1543i	0.163832	−	0.340202i	0.966682	+	0.255980i	$0.0823981\pi$
$72$		0			0
$73$	−12.2617	+	1.38156i	−0.167968	+	0.0189255i	−0.195548	−	0.980694i	$-0.562649\pi$
$73$	−12.2617	+	1.38156i	−0.167968	+	0.0189255i	0.0275798	+	0.999620i	$0.491220\pi$
$74$	−42.7839	−	20.6036i	−0.578160	−	0.278427i
$75$		0			0
$76$	16.4864	+	47.1153i	0.216926	+	0.619938i
$77$	−53.1060	−	84.5178i	−0.689689	−	1.09763i
$78$		0			0
$79$	33.5205	−	95.7961i	0.424310	−	1.21261i	−0.511247	−	0.859434i	$-0.670816\pi$
$79$	33.5205	−	95.7961i	0.424310	−	1.21261i	0.935557	−	0.353175i	$-0.114898\pi$
$80$	−60.3795	+	13.7812i	−0.754744	+	0.172265i
$81$		0			0
$82$	−101.735	−	127.571i	−1.24067	−	1.55575i
$83$	9.73978	−	42.6728i	0.117347	−	0.514130i	−0.881753	−	0.471711i	$-0.843637\pi$
$83$	9.73978	−	42.6728i	0.117347	−	0.514130i	0.999100	−	0.0424187i	$-0.0135063\pi$
$84$		0			0
$85$	7.45688	−	66.1816i	0.0877280	−	0.778607i
$86$		−	162.483i		−	1.88934i
$87$		0			0
$88$	−55.4303			−0.629890
$89$	−53.9337	−	6.07686i	−0.605996	−	0.0682794i	−0.196365	−	0.980531i	$-0.562914\pi$
$89$	−53.9337	−	6.07686i	−0.605996	−	0.0682794i	−0.409631	+	0.912251i	$0.634342\pi$
$90$		0			0
$91$	37.3532	+	8.52561i	0.410474	+	0.0936881i
$92$	−64.0472	+	51.0760i	−0.696165	+	0.555173i
$93$		0			0
$94$	−29.1946	−	127.910i	−0.310581	−	1.36074i
$95$	54.5935	+	19.1031i	0.574669	+	0.201085i
$96$		0			0
$97$	−124.213	+	78.0480i	−1.28054	+	0.804619i	−0.988417	−	0.151761i	$-0.951506\pi$
$97$	−124.213	+	78.0480i	−1.28054	+	0.804619i	−0.292126	+	0.956380i	$0.594363\pi$
$98$	−36.2556	+	12.6864i	−0.369955	+	0.129453i
$99$		0			0
$100$	−17.7150	+	36.7856i	−0.177150	+	0.367856i
$101$	15.1390	+	134.362i	0.149891	+	1.33032i	0.813205	+	0.581978i	$0.197721\pi$
$101$	15.1390	+	134.362i	0.149891	+	1.33032i	−0.663314	+	0.748342i	$0.730850\pi$
$102$		0			0
$103$	42.8611	+	20.6408i	0.416127	+	0.200396i	0.630219	−	0.776417i	$-0.282965\pi$
$103$	42.8611	+	20.6408i	0.416127	+	0.200396i	−0.214092	+	0.976813i	$0.568679\pi$
$104$	15.0446	−	15.0446i	0.144660	−	0.144660i
$105$		0			0
$106$	26.8162	+	42.6778i	0.252983	+	0.402620i
$107$	−119.175	+	57.3917i	−1.11379	+	0.536371i	−0.897967	−	0.440063i	$-0.854956\pi$
$107$	−119.175	+	57.3917i	−1.11379	+	0.536371i	−0.215818	+	0.976434i	$0.569242\pi$
$108$		0			0
$109$	−42.9080	+	9.79348i	−0.393652	+	0.0898485i	−0.414765	−	0.909929i	$-0.636136\pi$
$109$	−42.9080	+	9.79348i	−0.393652	+	0.0898485i	0.0211130	+	0.999777i	$0.493279\pi$
$110$	88.0715	−	110.438i	0.800650	−	1.00398i
$111$		0			0
$112$	25.3006	−	110.849i	0.225898	−	0.989724i
$113$	48.1620	−	76.6493i	0.426212	−	0.678313i	−0.562726	−	0.826644i	$-0.690247\pi$
$113$	48.1620	−	76.6493i	0.426212	−	0.678313i	0.988938	+	0.148331i	$0.0473901\pi$
$114$		0			0
$115$			94.9218i			0.825407i
$116$	40.5287	+	68.6744i	0.349386	+	0.592021i
$117$		0			0
$118$	123.898	+	13.9599i	1.04998	+	0.118305i
$119$	103.529	+	65.0515i	0.869991	+	0.546651i
$120$		0			0
$121$	133.068	−	106.119i	1.09974	−	0.877012i
$122$	−98.5191	−	78.5664i	−0.807534	−	0.643987i
$123$		0			0
$124$	−34.9169	−	12.2179i	−0.281588	−	0.0985317i
$125$	55.0873	+	114.390i	0.440698	+	0.915120i
$126$		0			0
$127$	−198.494	+	69.4561i	−1.56295	+	0.546898i	−0.966702	−	0.255905i	$-0.917626\pi$
$127$	−198.494	+	69.4561i	−1.56295	+	0.546898i	−0.596244	+	0.802804i	$0.703341\pi$
$128$	−69.9093	−	69.9093i	−0.546166	−	0.546166i
$129$		0			0
$130$	6.07065	+	53.8785i	0.0466973	+	0.414450i
$131$	164.999	−	18.5909i	1.25953	−	0.141915i	0.543158	−	0.839631i	$-0.317228\pi$
$131$	164.999	−	18.5909i	1.25953	−	0.141915i	0.716375	+	0.697715i	$0.245800\pi$
$132$		0			0
$133$	−75.0845	+	75.0845i	−0.564545	+	0.564545i
$134$	12.1644	+	34.7638i	0.0907791	+	0.259432i
$135$		0			0
$136$	61.1745	−	29.4601i	0.449813	−	0.216618i
$137$	56.9427	−	162.733i	0.415640	−	1.18783i	−0.525788	−	0.850616i	$-0.676229\pi$
$137$	56.9427	−	162.733i	0.415640	−	1.18783i	0.941428	−	0.337215i	$-0.109485\pi$
$138$		0			0
$139$	97.5376	−	122.308i	0.701709	−	0.879915i	−0.295441	−	0.955361i	$-0.595467\pi$
$139$	97.5376	−	122.308i	0.701709	−	0.879915i	0.997150	+	0.0754457i	$0.0240379\pi$
$140$	31.9517	+	40.0662i	0.228227	+	0.286187i
$141$		0			0
$142$	−37.0566	+	58.9752i	−0.260962	+	0.415319i
$143$	−12.5147	+	111.071i	−0.0875156	+	0.776723i
$144$		0			0
$145$	91.4939	+	12.8979i	0.630992	+	0.0889512i
$146$	32.0577			0.219573
$147$		0			0
$148$	42.5557	+	26.7395i	0.287538	+	0.180672i
$149$	−101.993	−	23.2793i	−0.684519	−	0.156237i	−0.133901	−	0.990995i	$-0.542751\pi$
$149$	−101.993	−	23.2793i	−0.684519	−	0.156237i	−0.550617	+	0.834758i	$0.685608\pi$
$150$		0			0
$151$	−87.2999	−	69.6194i	−0.578145	−	0.461055i	0.290234	−	0.956956i	$-0.406267\pi$
$151$	−87.2999	−	69.6194i	−0.578145	−	0.461055i	−0.868379	+	0.495900i	$0.834838\pi$
$152$	13.1213	+	57.4883i	0.0863245	+	0.378212i
$153$		0			0
$154$	112.518	+	233.646i	0.730637	+	1.51718i
$155$	−36.2942	+	22.8052i	−0.234156	+	0.147130i
$156$		0			0
$157$	154.052	+	154.052i	0.981223	+	0.981223i	0.999827	−	0.0186037i	$-0.00592209\pi$
$157$	154.052	+	154.052i	0.981223	+	0.981223i	−0.0186037	+	0.999827i	$0.505922\pi$
$158$	−114.405	+	237.565i	−0.724083	+	1.50357i
$159$		0			0
$160$	118.752	−	13.3801i	0.742201	−	0.0836259i
$161$	−157.007	−	75.6105i	−0.975198	−	0.469631i
$162$		0			0
$163$	−18.9751	−	54.2278i	−0.116412	−	0.332686i	0.870904	−	0.491453i	$-0.163534\pi$
$163$	−18.9751	−	54.2278i	−0.116412	−	0.332686i	−0.987316	+	0.158767i	$0.949248\pi$
$164$	91.8805	+	146.227i	0.560247	+	0.891628i
$165$		0			0
$166$	−37.5580	+	107.335i	−0.226253	+	0.646594i
$167$	−131.159	+	29.9362i	−0.785384	+	0.179259i	−0.596364	−	0.802714i	$-0.703388\pi$
$167$	−131.159	+	29.9362i	−0.785384	+	0.179259i	−0.189020	+	0.981973i	$0.560531\pi$
$168$		0			0
$169$	78.6200	+	98.5864i	0.465207	+	0.583352i
$170$	−38.5026	+	168.691i	−0.226486	+	0.992300i
$171$		0			0
$172$	−19.2546	+	170.889i	−0.111945	+	0.993542i
$173$			21.1826i			0.122443i	0.998124	+	0.0612213i	$0.0194995\pi$
$173$			21.1826i			0.122443i	−0.998124	+	0.0612213i	$0.980500\pi$
$174$		0			0
$175$	−86.8540			−0.496308
$176$	329.615	+	37.1387i	1.87281	+	0.211015i
$177$		0			0
$178$	137.472	+	31.3771i	0.772315	+	0.176276i
$179$	71.5446	−	57.0549i	0.399690	−	0.318742i	−0.402932	−	0.915230i	$-0.632009\pi$
$179$	71.5446	−	57.0549i	0.399690	−	0.318742i	0.802622	+	0.596487i	$0.203437\pi$
$180$		0			0
$181$	−43.7618	−	191.733i	−0.241778	−	1.05930i	−0.939398	−	0.342829i	$-0.888615\pi$
$181$	−43.7618	−	191.733i	−0.241778	−	1.05930i	0.697620	−	0.716468i	$-0.254242\pi$
$182$	−93.9541	−	32.8760i	−0.516232	−	0.180637i
$183$		0			0
$184$	−81.9393	+	51.4858i	−0.445322	+	0.279814i
$185$	54.9684	−	19.2343i	0.297126	−	0.103969i
$186$		0			0
$187$	−154.767	+	321.378i	−0.827633	+	1.71860i
$188$	15.5474	+	137.987i	0.0826988	+	0.733973i
$189$		0			0
$190$	−135.387	−	65.1987i	−0.712561	−	0.343151i
$191$	173.129	−	173.129i	0.906436	−	0.906436i	−0.0895465	−	0.995983i	$-0.528542\pi$
$191$	173.129	−	173.129i	0.906436	−	0.906436i	0.995983	+	0.0895465i	$0.0285418\pi$
$192$		0			0
$193$	−107.871	−	171.676i	−0.558917	−	0.889511i	0.441051	−	0.897482i	$-0.354606\pi$
$193$	−107.871	−	171.676i	−0.558917	−	0.889511i	−0.999968	+	0.00797056i	$0.997463\pi$
$194$	343.381	−	165.364i	1.77001	−	0.852390i
$195$		0			0
$196$	39.6346	−	9.04635i	0.202218	−	0.0461548i
$197$	−39.4510	+	49.4700i	−0.200259	+	0.251117i	−0.871813	−	0.489839i	$-0.837056\pi$
$197$	−39.4510	+	49.4700i	−0.200259	+	0.251117i	0.671554	+	0.740956i	$0.265627\pi$
$198$		0			0
$199$	−10.0083	+	43.8490i	−0.0502928	+	0.220347i	−0.993829	−	0.110922i	$-0.964620\pi$
$199$	−10.0083	+	43.8490i	−0.0502928	+	0.220347i	0.943536	+	0.331269i	$0.107477\pi$
$200$	−25.6607	+	40.8388i	−0.128304	+	0.204194i
$201$		0			0
$202$		−	351.285i		−	1.73903i
$203$	−94.2140	+	141.063i	−0.464108	+	0.694891i
$204$		0			0
$205$	198.850	+	22.4050i	0.970000	+	0.109293i
$206$	−104.650	−	65.7557i	−0.508008	−	0.319203i
$207$		0			0
$208$	−99.5424	+	79.3824i	−0.478569	+	0.381646i
$209$	−242.195	−	193.144i	−1.15883	−	0.924134i
$210$		0			0
$211$	267.044	+	93.4429i	1.26561	+	0.442857i	0.877865	−	0.478908i	$-0.158967\pi$
$211$	267.044	+	93.4429i	1.26561	+	0.442857i	0.387748	+	0.921765i	$0.373253\pi$
$212$	−23.1461	−	48.0634i	−0.109180	−	0.226714i
$213$		0			0
$214$	324.367	−	113.501i	1.51573	−	0.530378i
$215$	140.902	+	140.902i	0.655359	+	0.655359i
$216$		0			0
$217$	−8.81087	−	78.1986i	−0.0406031	−	0.360362i
$218$	113.624	−	12.8023i	0.521210	−	0.0587263i
$219$		0			0
$220$	−105.715	+	105.715i	−0.480523	+	0.480523i
$221$	−45.2205	−	129.233i	−0.204618	−	0.584764i
$222$		0			0
$223$	−9.38970	+	4.52184i	−0.0421063	+	0.0202773i	−0.454818	−	0.890584i	$-0.650296\pi$
$223$	−9.38970	+	4.52184i	−0.0421063	+	0.0202773i	0.412712	+	0.910862i	$0.364582\pi$
$224$	−72.4610	+	207.082i	−0.323487	+	0.924472i
$225$		0			0
$226$	−146.635	+	183.875i	−0.648829	+	0.813605i
$227$	−41.9912	−	52.6552i	−0.184983	−	0.231961i	0.680690	−	0.732572i	$-0.261680\pi$
$227$	−41.9912	−	52.6552i	−0.184983	−	0.231961i	−0.865673	+	0.500611i	$0.833109\pi$
$228$		0			0
$229$	−137.469	+	218.781i	−0.600303	+	0.955376i	0.398959	+	0.916969i	$0.369371\pi$
$229$	−137.469	+	218.781i	−0.600303	+	0.955376i	−0.999262	+	0.0384078i	$0.987771\pi$
$230$	27.6114	−	245.058i	0.120050	−	1.06547i
$231$		0			0
$232$	38.4927	+	85.9760i	0.165917	+	0.370586i
$233$	−139.905			−0.600452			−0.300226	−	0.953868i	$-0.597062\pi$
$233$	−139.905			−0.600452			−0.300226	+	0.953868i	$0.597062\pi$
$234$		0			0
$235$	136.238	+	85.6040i	0.579736	+	0.364272i
$236$	−128.653	−	29.3643i	−0.545141	−	0.124425i
$237$		0			0
$238$	−248.356	−	198.058i	−1.04351	−	0.832175i
$239$	−22.0091	−	96.4282i	−0.0920883	−	0.403465i	0.907784	−	0.419438i	$-0.137773\pi$
$239$	−22.0091	−	96.4282i	−0.0920883	−	0.403465i	−0.999872	+	0.0159726i	$0.994916\pi$
$240$		0			0
$241$	−158.413	−	328.947i	−0.657314	−	1.36493i	−0.916865	−	0.399197i	$-0.869289\pi$
$241$	−158.413	−	328.947i	−0.657314	−	1.36493i	0.259552	−	0.965729i	$-0.416425\pi$
$242$	−374.409	+	235.257i	−1.54715	+	0.972136i
$243$		0			0
$244$	94.3057	+	94.3057i	0.386499	+	0.386499i
$245$	20.4388	−	42.4415i	0.0834235	−	0.173231i
$246$		0			0
$247$	118.158	−	13.3132i	0.478371	−	0.0538994i
$248$	−39.3722	−	18.9606i	−0.158759	−	0.0764542i
$249$		0			0
$250$	−108.944	−	311.343i	−0.435775	−	1.24537i
$251$	−117.710	−	187.335i	−0.468965	−	0.746353i	0.525571	−	0.850750i	$-0.323852\pi$
$251$	−117.710	−	187.335i	−0.468965	−	0.746353i	−0.994536	+	0.104396i	$0.966709\pi$
$252$		0			0
$253$	167.910	−	479.859i	0.663676	−	1.89668i
$254$	532.653	−	121.575i	2.09706	−	0.478640i
$255$		0			0
$256$	209.261	+	262.405i	0.817425	+	1.02502i
$257$	29.0472	−	127.264i	0.113024	−	0.495191i	−0.886452	−	0.462821i	$-0.846837\pi$
$257$	29.0472	−	127.264i	0.113024	−	0.495191i	0.999476	−	0.0323701i	$-0.0103055\pi$
$258$		0			0
$259$	−11.9706	+	106.242i	−0.0462187	+	0.410202i
$260$		−	57.3852i		−	0.220712i
$261$		0			0
$262$	−431.383			−1.64650
$263$	−53.5898	−	6.03812i	−0.203763	−	0.0229586i	0.00949275	−	0.999955i	$-0.496978\pi$
$263$	−53.5898	−	6.03812i	−0.203763	−	0.0229586i	−0.213256	+	0.976996i	$0.568407\pi$
$264$		0			0
$265$	−60.2638	−	13.7548i	−0.227411	−	0.0519050i
$266$	215.686	−	172.004i	0.810849	−	0.646630i
$267$		0			0
$268$	−8.67412	−	38.0038i	−0.0323661	−	0.141805i
$269$	−23.6596	−	8.27885i	−0.0879538	−	0.0307764i	0.285943	−	0.958246i	$-0.407693\pi$
$269$	−23.6596	−	8.27885i	−0.0879538	−	0.0307764i	−0.373897	+	0.927470i	$0.621979\pi$
$270$		0			0
$271$	261.030	−	164.016i	0.963211	−	0.605226i	0.0440174	−	0.999031i	$-0.485984\pi$
$271$	261.030	−	164.016i	0.963211	−	0.605226i	0.919194	+	0.393805i	$0.128841\pi$
$272$	−383.511	+	134.196i	−1.40997	+	0.493369i
$273$		0			0
$274$	−194.345	+	403.561i	−0.709288	+	1.47285i
$275$	−28.3698	−	251.789i	−0.103163	−	0.915596i
$276$		0			0
$277$	−448.792	−	216.127i	−1.62019	−	0.780241i	−0.620195	−	0.784448i	$-0.712947\pi$
$277$	−448.792	−	216.127i	−1.62019	−	0.780241i	−0.999991	+	0.00420714i	$0.998661\pi$
$278$	−287.389	+	287.389i	−1.03377	+	1.03377i
$279$		0			0
$280$	32.2081	+	51.2590i	0.115029	+	0.183068i
$281$	360.665	−	173.687i	1.28350	−	0.618103i	0.337216	−	0.941427i	$-0.390515\pi$
$281$	360.665	−	173.687i	1.28350	−	0.618103i	0.946288	+	0.323325i	$0.104801\pi$
$282$		0			0
$283$	72.2136	−	16.4823i	0.255172	−	0.0582413i	−0.0930214	−	0.995664i	$-0.529652\pi$
$283$	72.2136	−	16.4823i	0.255172	−	0.0582413i	0.348193	+	0.937423i	$0.386795\pi$
$284$	45.9624	−	57.6350i	0.161839	−	0.202940i
$285$		0			0
$286$	64.6182	−	283.111i	0.225938	−	0.989898i
$287$	−195.454	+	311.064i	−0.681026	+	1.08385i
$288$		0			0
$289$		−	147.938i		−	0.511895i
$290$	−232.457	−	59.9127i	−0.801575	−	0.206596i
$291$		0			0
$292$	−33.7161	−	3.79890i	−0.115466	−	0.0130099i
$293$	381.722	+	239.852i	1.30281	+	0.818608i	0.991298	−	0.131636i	$-0.0420230\pi$
$293$	381.722	+	239.852i	1.30281	+	0.818608i	0.311508	+	0.950243i	$0.399166\pi$
$294$		0			0
$295$	−119.548	+	95.3360i	−0.405246	+	0.323173i
$296$	46.4185	+	37.0176i	0.156819	+	0.125059i
$297$		0			0
$298$	256.543	+	89.7683i	0.860882	+	0.301236i
$299$	84.6676	+	175.814i	0.283169	+	0.588007i
$300$		0			0
$301$	−345.298	+	120.825i	−1.14717	+	0.401412i
$302$	205.130	+	205.130i	0.679237	+	0.679237i
$303$		0			0
$304$	−39.5081	−	350.644i	−0.129961	−	1.15343i
$305$	153.565	−	17.3026i	0.503492	−	0.0567299i
$306$		0			0
$307$	−14.8497	+	14.8497i	−0.0483703	+	0.0483703i	−0.730878	−	0.682508i	$-0.760889\pi$
$307$	−14.8497	+	14.8497i	−0.0483703	+	0.0483703i	0.682508	+	0.730878i	$0.260889\pi$
$308$	−90.6515	−	259.067i	−0.294323	−	0.841127i
$309$		0			0
$310$	100.334	−	48.3183i	0.323658	−	0.155866i
$311$	−51.0039	+	145.761i	−0.164000	+	0.468684i	−0.996330	−	0.0855959i	$-0.972721\pi$
$311$	−51.0039	+	145.761i	−0.164000	+	0.468684i	0.832330	+	0.554280i	$0.187006\pi$
$312$		0			0
$313$	106.381	−	133.398i	0.339876	−	0.426191i	−0.582292	−	0.812979i	$-0.697844\pi$
$313$	106.381	−	133.398i	0.339876	−	0.426191i	0.922169	+	0.386788i	$0.126416\pi$
$314$	−352.902	−	442.526i	−1.12389	−	1.40932i
$315$		0			0
$316$	148.476	−	236.298i	0.469860	−	0.747777i
$317$	4.18683	−	37.1591i	0.0132077	−	0.117221i	−0.985378	−	0.170380i	$-0.945500\pi$
$317$	4.18683	−	37.1591i	0.0132077	−	0.117221i	0.998586	+	0.0531589i	$0.0169290\pi$
$318$		0			0
$319$	−439.714	−	227.049i	−1.37841	−	0.711753i
$320$	−62.7436			−0.196074
$321$		0			0
$322$	383.348	+	240.874i	1.19052	+	0.748055i
$323$	369.946	+	84.4377i	1.14534	+	0.261417i
$324$		0			0
$325$	76.0393	+	60.6393i	0.233967	+	0.186582i
$326$	33.2137	+	145.519i	0.101883	+	0.446377i
$327$		0			0
$328$	88.5161	+	183.805i	0.269866	+	0.560383i
$329$	−250.116	+	157.158i	−0.760230	+	0.477684i
$330$		0			0
$331$	195.213	+	195.213i	0.589768	+	0.589768i	0.937569	−	0.347800i	$-0.113071\pi$
$331$	195.213	+	195.213i	0.589768	+	0.589768i	−0.347800	+	0.937569i	$0.613071\pi$
$332$	52.2204	−	108.437i	0.157290	−	0.326616i
$333$		0			0
$334$	347.320	−	39.1335i	1.03988	−	0.117166i
$335$	−40.6952	−	19.5978i	−0.121478	−	0.0585009i
$336$		0			0
$337$	86.0626	+	245.953i	0.255379	+	0.729830i	0.998179	+	0.0603174i	$0.0192113\pi$
$337$	86.0626	+	245.953i	0.255379	+	0.729830i	−0.742801	+	0.669513i	$0.766503\pi$
$338$	−174.295	−	277.389i	−0.515665	−	0.820676i
$339$		0			0
$340$	60.4848	−	172.855i	0.177896	−	0.508398i
$341$	223.819	−	51.0853i	0.656362	−	0.149810i
$342$		0			0
$343$	232.625	+	291.702i	0.678207	+	0.850444i
$344$	−45.2051	+	198.057i	−0.131410	+	0.575746i
$345$		0			0
$346$	6.16172	−	54.6867i	0.0178084	−	0.158054i
$347$			75.7571i			0.218320i	0.994024	+	0.109160i	$0.0348161\pi$
$347$			75.7571i			0.218320i	−0.994024	+	0.109160i	$0.965184\pi$
$348$		0			0
$349$	−88.0863			−0.252396			−0.126198	−	0.992005i	$-0.540277\pi$
$349$	−88.0863			−0.252396			−0.126198	+	0.992005i	$0.540277\pi$
$350$	224.230	+	25.2646i	0.640656	+	0.0721846i
$351$		0			0
$352$	−623.997	−	142.423i	−1.77272	−	0.404611i
$353$	−333.963	+	266.327i	−0.946071	+	0.754467i	−0.969457	−	0.245260i	$-0.921127\pi$
$353$	−333.963	+	266.327i	−0.946071	+	0.754467i	0.0233860	+	0.999727i	$0.492555\pi$
$354$		0			0
$355$	−19.0074	−	83.2769i	−0.0535420	−	0.234583i
$356$	−140.866	−	49.2911i	−0.395691	−	0.138458i
$357$		0			0
$358$	−201.302	+	126.486i	−0.562296	+	0.353314i
$359$	−396.769	+	138.835i	−1.10521	+	0.386728i	−0.820361	−	0.571845i	$-0.806228\pi$
$359$	−396.769	+	138.835i	−1.10521	+	0.386728i	−0.284845	+	0.958574i	$0.591942\pi$
$360$		0			0
$361$	13.6489	−	28.3422i	0.0378086	−	0.0785103i
$362$	57.2067	+	507.723i	0.158030	+	1.40255i
$363$		0			0
$364$	94.9189	+	45.7105i	0.260766	+	0.125578i
$365$	−27.7998	+	27.7998i	−0.0761638	+	0.0761638i
$366$		0			0
$367$	−133.333	−	212.198i	−0.363305	−	0.578196i	0.614189	−	0.789159i	$-0.289483\pi$
$367$	−133.333	−	212.198i	−0.363305	−	0.578196i	−0.977494	+	0.210962i	$0.932340\pi$
$368$	521.746	−	251.259i	1.41779	−	0.682770i
$369$		0			0
$370$	−147.506	+	33.6673i	−0.398665	+	0.0909927i
$371$	70.7548	−	88.7237i	0.190714	−	0.239148i
$372$		0			0
$373$	109.293	−	478.845i	0.293012	−	1.28377i	−0.587299	−	0.809370i	$-0.699809\pi$
$373$	109.293	−	478.845i	0.293012	−	1.28377i	0.880311	−	0.474397i	$-0.157334\pi$
$374$	493.045	−	784.677i	1.31830	−	2.09807i
$375$		0			0
$376$			164.036i			0.436267i
$377$	180.970	−	57.7205i	0.480025	−	0.153105i
$378$		0			0
$379$	8.35834	+	0.941759i	0.0220537	+	0.00248485i	0.122984	−	0.992409i	$-0.460753\pi$
$379$	8.35834	+	0.941759i	0.0220537	+	0.00248485i	−0.100931	+	0.994893i	$0.532182\pi$
$380$	134.664	+	84.6153i	0.354380	+	0.222672i
$381$		0			0
$382$	−497.326	+	396.605i	−1.30190	+	1.03823i
$383$	81.7068	+	65.1590i	0.213334	+	0.170128i	0.724327	−	0.689457i	$-0.242151\pi$
$383$	81.7068	+	65.1590i	0.213334	+	0.170128i	−0.510993	+	0.859585i	$0.670722\pi$
$384$		0			0
$385$	−300.187	−	105.040i	−0.779706	−	0.272831i
$386$	228.551	+	474.591i	0.592101	+	1.22951i
$387$		0			0
$388$	−380.742	+	133.227i	−0.981293	+	0.343369i
$389$	−3.30195	−	3.30195i	−0.00848831	−	0.00848831i	0.702850	−	0.711338i	$-0.251911\pi$
$389$	−3.30195	−	3.30195i	−0.00848831	−	0.00848831i	−0.711338	+	0.702850i	$0.751911\pi$
$390$		0			0
$391$	69.7251	+	618.827i	0.178325	+	1.58268i
$392$	47.7228	−	5.37707i	0.121742	−	0.0137170i
$393$		0			0
$394$	116.240	−	116.240i	0.295026	−	0.295026i
$395$	−106.802	−	305.221i	−0.270384	−	0.772712i
$396$		0			0
$397$	596.541	−	287.279i	1.50262	−	0.723625i	0.511839	−	0.859082i	$-0.328965\pi$
$397$	596.541	−	287.279i	1.50262	−	0.723625i	0.990783	+	0.135457i	$0.0432503\pi$
$398$	38.5933	−	110.293i	0.0969680	−	0.277119i
$399$		0			0
$400$	179.953	−	225.654i	0.449883	−	0.564135i
$401$	297.015	+	372.445i	0.740687	+	0.928792i	0.999308	−	0.0371871i	$-0.0118398\pi$
$401$	297.015	+	372.445i	0.740687	+	0.928792i	−0.258622	+	0.965979i	$0.583268\pi$
$402$		0			0
$403$	−46.8826	+	74.6132i	−0.116334	+	0.185144i
$404$	−41.6279	+	369.458i	−0.103039	+	0.914501i
$405$		0			0
$406$	284.264	−	336.775i	0.700158	−	0.829494i
$407$	−311.906			−0.766354
$408$		0			0
$409$	−245.996	−	154.570i	−0.601458	−	0.377921i	0.196616	−	0.980481i	$-0.437005\pi$
$409$	−245.996	−	154.570i	−0.601458	−	0.377921i	−0.798074	+	0.602560i	$0.794148\pi$
$410$	−506.851	−	115.685i	−1.23622	−	0.282159i
$411$		0			0
$412$	102.271	+	81.5587i	0.248232	+	0.197958i
$413$	−62.4657	−	273.680i	−0.151249	−	0.662663i
$414$		0			0
$415$	−60.5088	−	125.648i	−0.145804	−	0.302766i
$416$	208.018	−	130.706i	0.500043	−	0.314198i
$417$		0			0
$418$	569.089	+	569.089i	1.36146	+	1.36146i
$419$	−148.802	+	308.990i	−0.355135	+	0.737446i	−0.999631	−	0.0271619i	$-0.991353\pi$
$419$	−148.802	+	308.990i	−0.355135	+	0.737446i	0.644496	+	0.764608i	$0.277067\pi$
$420$		0			0
$421$	528.745	−	59.5753i	1.25593	−	0.141509i	0.541189	−	0.840901i	$-0.317974\pi$
$421$	528.745	−	59.5753i	1.25593	−	0.141509i	0.714738	+	0.699392i	$0.246546\pi$
$422$	−662.244	−	318.920i	−1.56930	−	0.755734i
$423$		0			0
$424$	−20.8137	−	59.4821i	−0.0490889	−	0.140288i
$425$	165.131	+	262.804i	0.388542	+	0.618362i
$426$		0			0
$427$	−93.7034	+	267.789i	−0.219446	+	0.627141i
$428$	−354.598	+	80.9346i	−0.828500	+	0.189100i
$429$		0			0
$430$	−322.779	−	404.752i	−0.750649	−	0.941284i
$431$	125.008	−	547.695i	0.290041	−	1.27075i	−0.594425	−	0.804151i	$-0.702620\pi$
$431$	125.008	−	547.695i	0.290041	−	1.27075i	0.884467	−	0.466604i	$-0.154523\pi$
$432$		0			0
$433$	−14.0479	+	124.679i	−0.0324432	+	0.287942i	0.967006	+	0.254754i	$0.0819945\pi$
$433$	−14.0479	+	124.679i	−0.0324432	+	0.287942i	−0.999449	+	0.0331877i	$0.989434\pi$
$434$			204.447i			0.471077i
$435$		0			0
$436$	−121.019			−0.277567
$437$	−537.422	−	60.5529i	−1.22980	−	0.138565i
$438$		0			0
$439$	505.439	+	115.363i	1.15134	+	0.262786i	0.755258	−	0.655428i	$-0.227512\pi$
$439$	505.439	+	115.363i	1.15134	+	0.262786i	0.396084	+	0.918214i	$0.370369\pi$
$440$	−138.079	+	110.114i	−0.313816	+	0.250260i
$441$		0			0
$442$	79.1532	+	346.793i	0.179080	+	0.784599i
$443$	−57.1618	−	20.0018i	−0.129033	−	0.0451507i	0.264990	−	0.964251i	$-0.414631\pi$
$443$	−57.1618	−	20.0018i	−0.129033	−	0.0451507i	−0.394023	+	0.919100i	$0.628917\pi$
$444$		0			0
$445$	−146.423	+	92.0035i	−0.329040	+	0.206749i
$446$	25.5566	−	8.94264i	0.0573018	−	0.0200508i
$447$		0			0
$448$	49.9788	−	103.782i	0.111560	−	0.231656i
$449$	80.2125	+	711.905i	0.178647	+	1.58554i	0.688476	+	0.725260i	$0.258280\pi$
$449$	80.2125	+	711.905i	0.178647	+	1.58554i	−0.509829	+	0.860276i	$0.670291\pi$
$450$		0			0
$451$	−965.615	−	465.015i	−2.14105	−	1.03108i
$452$	176.011	−	176.011i	0.389405	−	0.389405i
$453$		0			0
$454$	93.0913	+	148.154i	0.205047	+	0.326330i
$455$	109.985	−	52.9658i	0.241724	−	0.116408i
$456$		0			0
$457$	−533.475	+	121.762i	−1.16734	+	0.266438i	−0.761908	−	0.647686i	$-0.775737\pi$
$457$	−533.475	+	121.762i	−1.16734	+	0.266438i	−0.405435	+	0.914124i	$0.632880\pi$
$458$	418.543	−	524.836i	0.913850	−	1.14593i
$459$		0			0
$460$	−58.0798	+	254.464i	−0.126260	+	0.553183i
$461$	313.897	−	499.564i	0.680904	−	1.08365i	−0.310214	−	0.950667i	$-0.600401\pi$
$461$	313.897	−	499.564i	0.680904	−	1.08365i	0.991118	−	0.132985i	$-0.0424564\pi$
$462$		0			0
$463$			75.7339i			0.163572i	0.996650	+	0.0817861i	$0.0260624\pi$
$463$			75.7339i			0.163572i	−0.996650	+	0.0817861i	$0.973938\pi$
$464$	−171.291	−	537.045i	−0.369162	−	1.15742i
$465$		0			0
$466$	361.192	+	40.6965i	0.775090	+	0.0873316i
$467$	146.168	+	91.8436i	0.312994	+	0.196667i	0.679363	−	0.733803i	$-0.262256\pi$
$467$	146.168	+	91.8436i	0.312994	+	0.196667i	−0.366369	+	0.930470i	$0.619399\pi$
$468$		0			0
$469$	64.8320	−	51.7018i	0.138235	−	0.110238i
$470$	−326.823	−	260.632i	−0.695367	−	0.554537i
$471$		0			0
$472$	−147.140	−	51.4864i	−0.311737	−	0.109081i
$473$	−463.058	−	961.550i	−0.978981	−	2.03288i
$474$		0			0
$475$	−254.422	+	89.0260i	−0.535624	+	0.187423i
$476$	237.735	+	237.735i	0.499443	+	0.499443i
$477$		0			0
$478$	28.7710	+	255.349i	0.0601903	+	0.534204i
$479$	14.8101	−	1.66870i	0.0309188	−	0.00348372i	−0.0964915	−	0.995334i	$-0.530762\pi$
$479$	14.8101	−	1.66870i	0.0309188	−	0.00348372i	0.127410	+	0.991850i	$0.459333\pi$
$480$		0			0
$481$	84.6559	−	84.6559i	0.176000	−	0.176000i
$482$	313.285	+	895.318i	0.649970	+	1.85751i
$483$		0			0
$484$	421.657	−	203.059i	0.871193	−	0.419544i
$485$	−154.373	+	441.174i	−0.318296	+	0.909636i
$486$		0			0
$487$	121.461	−	152.307i	0.249406	−	0.312745i	−0.641331	−	0.767264i	$-0.721618\pi$
$487$	121.461	−	152.307i	0.249406	−	0.312745i	0.890737	+	0.454519i	$0.150189\pi$
$488$	98.2302	+	123.177i	0.201291	+	0.252411i
$489$		0			0
$490$	−65.1121	+	103.625i	−0.132882	+	0.211480i
$491$	−4.56914	+	40.5522i	−0.00930578	+	0.0825911i	−0.997507	−	0.0705722i	$-0.977517\pi$
$491$	−4.56914	+	40.5522i	−0.00930578	+	0.0825911i	0.988201	+	0.153163i	$0.0489461\pi$
$492$		0			0
$493$	605.953	+	16.8788i	1.22911	+	0.0342370i
$494$	−308.918			−0.625341
$495$		0			0
$496$	221.422	+	139.129i	0.446415	+	0.280501i
$497$	152.886	+	34.8952i	0.307617	+	0.0702116i
$498$		0			0
$499$	510.903	+	407.432i	1.02385	+	0.816497i	0.983173	−	0.182676i	$-0.0584758\pi$
$499$	510.903	+	407.432i	1.02385	+	0.816497i	0.0406810	+	0.999172i	$0.487047\pi$
$500$	77.6850	+	340.360i	0.155370	+	0.680720i
$501$		0			0
$502$	249.398	+	517.880i	0.496808	+	1.03163i
$503$	543.585	−	341.557i	1.08069	−	0.679040i	0.130728	−	0.991418i	$-0.458269\pi$
$503$	543.585	−	341.557i	1.08069	−	0.679040i	0.949958	+	0.312379i	$0.101126\pi$
$504$		0			0
$505$	304.627	+	304.627i	0.603222	+	0.603222i
$506$	−573.075	+	1190.00i	−1.13256	+	2.35178i
$507$		0			0
$508$	−574.616	+	64.7437i	−1.13113	+	0.127448i
$509$	108.052	+	52.0353i	0.212284	+	0.102230i	0.537004	−	0.843580i	$-0.319556\pi$
$509$	108.052	+	52.0353i	0.212284	+	0.102230i	−0.324720	+	0.945810i	$0.605270\pi$
$510$		0			0
$511$	−23.8386	−	68.1267i	−0.0466508	−	0.133320i
$512$	−253.515	−	403.466i	−0.495146	−	0.788020i
$513$		0			0
$514$	−112.010	+	320.106i	−0.217918	+	0.622775i
$515$	147.772	−	33.7280i	0.286936	−	0.0654913i
$516$		0			0
$517$	−537.297	−	673.750i	−1.03926	−	1.30319i
$518$	61.8089	−	270.802i	0.119322	−	0.522785i
$519$		0			0
$520$	7.59003	−	67.3634i	0.0145962	−	0.129545i
$521$		−	424.304i		−	0.814404i	−0.913338	−	0.407202i	$-0.866505\pi$
$521$		−	424.304i		−	0.814404i	0.913338	−	0.407202i	$-0.133495\pi$
$522$		0			0
$523$	4.61578			0.00882558			0.00441279	−	0.999990i	$-0.498595\pi$
$523$	4.61578			0.00882558			0.00441279	+	0.999990i	$0.498595\pi$
$524$	453.700	+	51.1197i	0.865840	+	0.0975568i
$525$		0			0
$526$	136.596	+	31.1770i	0.259687	+	0.0592720i
$527$	−219.863	+	175.335i	−0.417197	+	0.332703i
$528$		0			0
$529$	−79.7873	−	349.571i	−0.150827	−	0.660815i
$530$	151.581	+	53.0405i	0.286002	+	0.100076i
$531$		0			0
$532$	−247.227	+	155.343i	−0.464712	+	0.291998i
$533$	388.294	−	135.870i	0.728507	−	0.254916i
$534$		0			0
$535$	−182.859	+	379.710i	−0.341792	+	0.709739i
$536$	−5.15582	−	45.7592i	−0.00961907	−	0.0853716i
$537$		0			0
$538$	58.6734	+	28.2556i	0.109058	+	0.0525198i
$539$	−178.400	+	178.400i	−0.330984	+	0.330984i
$540$		0			0
$541$	160.391	+	255.261i	0.296472	+	0.471833i	0.961431	−	0.275048i	$-0.0886936\pi$
$541$	160.391	+	255.261i	0.296472	+	0.471833i	−0.664958	+	0.746880i	$0.731551\pi$
$542$	−721.608	+	347.508i	−1.33138	+	0.641159i
$543$		0			0
$544$	764.356	−	174.459i	1.40507	−	0.320697i
$545$	−87.4304	+	109.634i	−0.160423	+	0.201164i
$546$		0			0
$547$	33.8389	−	148.258i	0.0618627	−	0.271038i	−0.934532	−	0.355880i	$-0.884181\pi$
$547$	33.8389	−	148.258i	0.0618627	−	0.271038i	0.996394	+	0.0848416i	$0.0270384\pi$
$548$	252.222	−	401.409i	0.460259	−	0.732498i
$549$		0			0
$550$			658.293i			1.19690i
$551$	−131.391	+	509.786i	−0.238459	+	0.925201i
$552$		0			0
$553$	589.929	+	66.4691i	1.06678	+	0.120197i
$554$	1095.77	+	688.518i	1.97793	+	1.24281i
$555$		0			0
$556$	336.313	−	268.201i	0.604880	−	0.482375i
$557$	24.5533	+	19.5806i	0.0440814	+	0.0351538i	0.645283	−	0.763944i	$-0.276740\pi$
$557$	24.5533	+	19.5806i	0.0440814	+	0.0351538i	−0.601201	+	0.799098i	$0.705311\pi$
$558$		0			0
$559$	386.660	+	135.298i	0.691699	+	0.242036i
$560$	−157.181	−	326.390i	−0.280680	−	0.582839i
$561$		0			0
$562$	−981.646	+	343.493i	−1.74670	+	0.611197i
$563$	667.667	+	667.667i	1.18591	+	1.18591i	0.978188	+	0.207721i	$0.0666048\pi$
$563$	667.667	+	667.667i	1.18591	+	1.18591i	0.207721	+	0.978188i	$0.433395\pi$
$564$		0			0
$565$	−32.2934	−	286.612i	−0.0571565	−	0.507278i
$566$	−191.227	+	21.5461i	−0.337857	+	0.0380674i
$567$		0			0
$568$	61.5773	−	61.5773i	0.108411	−	0.108411i
$569$	−296.283	−	846.727i	−0.520708	−	1.48810i	−0.841136	−	0.540824i	$-0.818112\pi$
$569$	−296.283	−	846.727i	−0.520708	−	1.48810i	0.320428	−	0.947273i	$-0.396173\pi$
$570$		0			0
$571$	−603.338	+	290.552i	−1.05663	+	0.508848i	−0.879776	−	0.475388i	$-0.842308\pi$
$571$	−603.338	+	290.552i	−1.05663	+	0.508848i	−0.176858	+	0.984236i	$0.556593\pi$
$572$	−101.510	+	290.100i	−0.177466	+	0.507168i
$573$		0			0
$574$	595.086	−	746.214i	1.03673	−	1.30002i
$575$	−275.809	−	345.853i	−0.479668	−	0.601484i
$576$		0			0
$577$	−4.39331	+	6.99192i	−0.00761406	+	0.0121177i	−0.850510	−	0.525960i	$-0.823706\pi$
$577$	−4.39331	+	6.99192i	−0.00761406	+	0.0121177i	0.842895	+	0.538077i	$0.180849\pi$
$578$	−43.0330	+	381.928i	−0.0744516	+	0.660776i
$579$		0			0
$580$	237.383	+	90.5588i	0.409281	+	0.156136i
$581$	256.028			0.440669
$582$		0			0
$583$	280.321	+	176.137i	0.480825	+	0.302122i
$584$	−39.0762	−	8.91890i	−0.0669114	−	0.0152721i
$585$		0			0
$586$	−915.717	−	730.260i	−1.56266	−	1.24618i
$587$	68.8550	+	301.673i	0.117300	+	0.513924i	0.999105	+	0.0423093i	$0.0134715\pi$
$587$	68.8550	+	301.673i	0.117300	+	0.513924i	−0.881805	+	0.471615i	$0.843671\pi$
$588$		0			0
$589$	−105.964	−	220.036i	−0.179905	−	0.373576i
$590$	336.366	−	211.353i	0.570112	−	0.358225i
$591$		0			0
$592$	−251.225	−	251.225i	−0.424366	−	0.424366i
$593$	−313.607	+	651.212i	−0.528849	+	1.09817i	0.449896	+	0.893081i	$0.351461\pi$
$593$	−313.607	+	651.212i	−0.528849	+	1.09817i	−0.978744	+	0.205084i	$0.934253\pi$
$594$		0			0
$595$	387.121	−	43.6181i	0.650624	−	0.0733077i
$596$	−259.177	−	124.813i	−0.434861	−	0.209418i
$597$		0			0
$598$	−167.443	−	478.526i	−0.280006	−	0.800210i
$599$	202.636	+	322.493i	0.338290	+	0.538386i	0.971938	−	0.235235i	$-0.0755861\pi$
$599$	202.636	+	322.493i	0.338290	+	0.538386i	−0.633648	+	0.773621i	$0.718443\pi$
$600$		0			0
$601$	−311.119	+	889.126i	−0.517668	+	1.47941i	0.327469	+	0.944862i	$0.393804\pi$
$601$	−311.119	+	889.126i	−0.517668	+	1.47941i	−0.845137	+	0.534549i	$0.820481\pi$
$602$	926.597	−	211.490i	1.53920	−	0.351312i
$603$		0			0
$604$	−191.434	−	240.050i	−0.316943	−	0.397434i
$605$	120.670	−	528.690i	0.199455	−	0.873868i
$606$		0			0
$607$	9.33482	−	82.8488i	0.0153786	−	0.136489i	−0.983677	−	0.179945i	$-0.942408\pi$
$607$	9.33482	−	82.8488i	0.0153786	−	0.136489i	0.999055	+	0.0434556i	$0.0138367\pi$
$608$			680.878i			1.11986i
$609$		0			0
$610$	−401.490			−0.658180
$611$	328.696	+	37.0352i	0.537964	+	0.0606140i
$612$		0			0
$613$	−730.866	−	166.815i	−1.19228	−	0.272129i	−0.420065	−	0.907494i	$-0.637993\pi$
$613$	−730.866	−	166.815i	−1.19228	−	0.272129i	−0.772212	+	0.635365i	$0.780850\pi$
$614$	42.6568	−	34.0177i	0.0694737	−	0.0554034i
$615$		0			0
$616$	−72.1486	−	316.104i	−0.117124	−	0.513155i
$617$	−516.148	−	180.608i	−0.836544	−	0.292719i	−0.122192	−	0.992506i	$-0.538992\pi$
$617$	−516.148	−	180.608i	−0.836544	−	0.292719i	−0.714351	+	0.699787i	$0.753278\pi$
$618$		0			0
$619$	−669.936	+	420.949i	−1.08229	+	0.680046i	−0.950341	−	0.311211i	$-0.899266\pi$
$619$	−669.936	+	420.949i	−1.08229	+	0.680046i	−0.131947	+	0.991257i	$0.542123\pi$
$620$	−111.251	+	38.9283i	−0.179436	+	0.0627875i
$621$		0			0
$622$	174.076	−	361.472i	0.279865	−	0.581145i
$623$	−35.5459	−	315.478i	−0.0570560	−	0.506386i
$624$		0			0
$625$	30.0154	+	14.4547i	0.0480247	+	0.0231275i
$626$	−313.447	+	313.447i	−0.500713	+	0.500713i
$627$		0			0
$628$	318.719	+	507.239i	0.507515	+	0.807705i
$629$	344.229	−	165.772i	0.547263	−	0.263548i
$630$		0			0
$631$	305.108	−	69.6389i	0.483531	−	0.110363i	0.0261949	−	0.999657i	$-0.491661\pi$
$631$	305.108	−	69.6389i	0.483531	−	0.110363i	0.457336	+	0.889294i	$0.348804\pi$
$632$	205.546	−	257.747i	0.325232	−	0.407828i
$633$		0			0
$634$	−21.6182	+	94.7153i	−0.0340980	+	0.149393i
$635$	−356.479	+	567.333i	−0.561384	+	0.893438i
$636$		0			0
$637$		−	96.8410i		−	0.152027i
$638$	1069.16	+	714.076i	1.67580	+	1.11924i
$639$		0			0
$640$	−313.024	−	35.2693i	−0.489100	−	0.0551083i
$641$	−166.181	−	104.418i	−0.259253	−	0.162899i	0.396134	−	0.918193i	$-0.370352\pi$
$641$	−166.181	−	104.418i	−0.259253	−	0.162899i	−0.655387	+	0.755293i	$0.727494\pi$
$642$		0			0
$643$	−28.9995	+	23.1263i	−0.0451003	+	0.0359663i	−0.645781	−	0.763523i	$-0.723468\pi$
$643$	−28.9995	+	23.1263i	−0.0451003	+	0.0359663i	0.600680	+	0.799489i	$0.294896\pi$
$644$	−374.636	−	298.763i	−0.581734	−	0.463917i
$645$		0			0
$646$	−930.522	−	325.604i	−1.44044	−	0.504030i
$647$	−341.548	−	709.232i	−0.527895	−	1.09619i	−0.979027	−	0.203729i	$-0.934694\pi$
$647$	−341.548	−	709.232i	−0.527895	−	1.09619i	0.451132	−	0.892457i	$-0.351020\pi$
$648$		0			0
$649$	772.992	−	270.482i	1.19105	−	0.416767i
$650$	−178.670	−	178.670i	−0.274878	−	0.274878i
$651$		0			0
$652$	−17.6877	−	156.983i	−0.0271284	−	0.240771i
$653$	−651.771	+	73.4370i	−0.998118	+	0.112461i	−0.595879	−	0.803074i	$-0.703196\pi$
$653$	−651.771	+	73.4370i	−0.998118	+	0.112461i	−0.402239	+	0.915535i	$0.631768\pi$
$654$		0			0
$655$	374.087	−	374.087i	0.571125	−	0.571125i
$656$	−403.207	−	1152.30i	−0.614646	−	1.75656i
$657$		0			0
$658$	691.435	−	332.978i	1.05081	−	0.506045i
$659$	49.7225	−	142.099i	0.0754514	−	0.215628i	−0.899980	−	0.435931i	$-0.856419\pi$
$659$	49.7225	−	142.099i	0.0754514	−	0.215628i	0.975431	+	0.220304i	$0.0707048\pi$
$660$		0			0
$661$	236.407	−	296.445i	0.357650	−	0.448479i	−0.570159	−	0.821534i	$-0.693118\pi$
$661$	236.407	−	296.445i	0.357650	−	0.448479i	0.927809	+	0.373055i	$0.121690\pi$
$662$	−447.195	−	560.764i	−0.675521	−	0.847076i
$663$		0			0
$664$	75.6427	−	120.385i	0.113920	−	0.181302i
$665$	−37.8803	+	336.197i	−0.0569628	+	0.505559i
$666$		0			0
$667$	−860.895	+	72.7909i	−1.29070	+	0.109132i
$668$	−369.925			−0.553780
$669$		0			0
$670$	99.3616	+	62.4330i	0.148301	+	0.0931836i
$671$	−806.926	−	184.176i	−1.20257	−	0.274479i
$672$		0			0
$673$	−387.895	−	309.336i	−0.576367	−	0.459637i	0.291405	−	0.956600i	$-0.405877\pi$
$673$	−387.895	−	309.336i	−0.576367	−	0.459637i	−0.867772	+	0.496963i	$0.834449\pi$
$674$	−150.642	−	660.007i	−0.223505	−	0.979239i
$675$		0			0
$676$	150.441	+	312.393i	0.222545	+	0.462120i
$677$	659.147	−	414.170i	0.973630	−	0.611772i	0.0515083	−	0.998673i	$-0.483597\pi$
$677$	659.147	−	414.170i	0.973630	−	0.611772i	0.922122	+	0.386900i	$0.126454\pi$
$678$		0			0
$679$	−606.763	−	606.763i	−0.893612	−	0.893612i
$680$	93.8645	−	194.912i	0.138036	−	0.286635i
$681$		0			0
$682$	−592.691	+	66.7803i	−0.869049	+	0.0979183i
$683$	−346.400	−	166.817i	−0.507174	−	0.244242i	0.162756	−	0.986666i	$-0.447962\pi$
$683$	−346.400	−	166.817i	−0.507174	−	0.244242i	−0.669930	+	0.742424i	$0.733676\pi$
$684$		0			0
$685$	−181.428	−	518.492i	−0.264859	−	0.756923i
$686$	−515.712	−	820.751i	−0.751767	−	1.19643i
$687$		0			0
$688$	401.510	−	1147.45i	0.583591	−	1.66781i
$689$	−123.889	+	28.2770i	−0.179811	+	0.0410406i
$690$		0			0
$691$	654.553	+	820.783i	0.947254	+	1.18782i	0.982087	+	0.188426i	$0.0603386\pi$
$691$	654.553	+	820.783i	0.947254	+	1.18782i	−0.0348332	+	0.999393i	$0.511090\pi$
$692$	−12.9610	+	56.7857i	−0.0187297	+	0.0820603i
$693$		0			0
$694$	22.0367	−	195.581i	0.0317532	−	0.281817i
$695$		−	498.436i		−	0.717175i
$696$		0			0
$697$	1312.83			1.88354
$698$	227.411	+	25.6231i	0.325804	+	0.0367093i
$699$		0			0
$700$	−232.836	−	53.1433i	−0.332623	−	0.0759190i
$701$	−70.4321	+	56.1677i	−0.100474	+	0.0801252i	−0.672438	−	0.740153i	$-0.734753\pi$
$701$	−70.4321	+	56.1677i	−0.100474	+	0.0801252i	0.571964	+	0.820278i	$0.306182\pi$
$702$		0			0
$703$	73.8336	+	323.486i	0.105026	+	0.460151i
$704$	317.188	+	110.989i	0.450552	+	0.157655i
$705$		0			0
$706$	939.659	−	590.427i	1.33096	−	0.836299i
$707$	−746.526	+	261.221i	−1.05591	+	0.369478i
$708$		0			0
$709$	−457.420	+	949.843i	−0.645162	+	1.33969i	0.279955	+	0.960013i	$0.409680\pi$
$709$	−457.420	+	949.843i	−0.645162	+	1.33969i	−0.925118	+	0.379681i	$0.876034\pi$
$710$	24.8471	+	220.524i	0.0349959	+	0.310597i
$711$		0			0
$712$	−158.840	−	76.4933i	−0.223090	−	0.107434i
$713$	283.408	−	283.408i	0.397487	−	0.397487i
$714$		0			0
$715$	189.473	+	301.544i	0.264997	+	0.421740i
$716$	226.705	−	109.175i	0.316627	−	0.152480i
$717$		0			0
$718$	1064.72	−	243.015i	1.48289	−	0.338461i
$719$	375.775	−	471.207i	0.522636	−	0.655364i	−0.448531	−	0.893767i	$-0.648053\pi$
$719$	375.775	−	471.207i	0.522636	−	0.655364i	0.971166	+	0.238403i	$0.0766240\pi$
$720$		0			0
$721$	−61.9204	+	271.291i	−0.0858813	+	0.376270i
$722$	−43.4815	+	69.2005i	−0.0602237	+	0.0958455i
$723$		0			0
$724$		−	540.769i		−	0.746919i
$725$	−370.840	+	218.854i	−0.511504	+	0.301868i
$726$		0			0
$727$	−652.396	−	73.5073i	−0.897380	−	0.101110i	−0.348789	−	0.937201i	$-0.613407\pi$
$727$	−652.396	−	73.5073i	−0.897380	−	0.101110i	−0.548591	+	0.836091i	$0.684836\pi$
$728$	105.377	+	66.2131i	0.144749	+	0.0909520i
$729$		0			0
$730$	79.8569	−	63.6837i	0.109393	−	0.0872380i
$731$	1022.09	+	815.089i	1.39821	+	1.11503i
$732$		0			0
$733$	−1069.34	−	374.177i	−1.45885	−	0.510473i	−0.519810	−	0.854282i	$-0.673997\pi$
$733$	−1069.34	−	374.177i	−1.45885	−	0.510473i	−0.939040	+	0.343809i	$0.888283\pi$
$734$	282.498	+	586.614i	0.384875	+	0.799201i
$735$		0			0
$736$	−1054.70	+	369.057i	−1.43302	+	0.501436i
$737$	171.060	+	171.060i	0.232103	+	0.232103i
$738$		0			0
$739$	72.0915	+	639.830i	0.0975527	+	0.865805i	0.943237	+	0.332121i	$0.107764\pi$
$739$	72.0915	+	639.830i	0.0975527	+	0.865805i	−0.845684	+	0.533684i	$0.820807\pi$
$740$	159.127	−	17.9293i	0.215036	−	0.0242288i
$741$		0			0
$742$	−208.475	+	208.475i	−0.280964	+	0.280964i
$743$	−147.582	−	421.766i	−0.198630	−	0.567653i	0.800884	−	0.598820i	$-0.204363\pi$
$743$	−147.582	−	421.766i	−0.198630	−	0.567653i	−0.999514	+	0.0311669i	$0.990078\pi$
$744$		0			0
$745$	−300.314	+	144.624i	−0.403106	+	0.194126i
$746$	−421.450	+	1204.44i	−0.564947	+	1.61453i
$747$		0			0
$748$	−611.538	+	766.844i	−0.817564	+	1.02519i
$749$	−482.408	−	604.921i	−0.644070	−	0.807638i
$750$		0			0
$751$	523.385	−	832.962i	0.696917	−	1.10914i	−0.291381	−	0.956607i	$-0.594115\pi$
$751$	523.385	−	832.962i	0.696917	−	1.10914i	0.988299	−	0.152531i	$-0.0487423\pi$
$752$	109.905	−	975.438i	0.146151	−	1.29712i
$753$		0			0
$754$	−483.997	+	96.3746i	−0.641905	+	0.127818i
$755$	−355.769			−0.471217
$756$		0			0
$757$	−315.734	−	198.389i	−0.417086	−	0.262073i	0.307100	−	0.951677i	$-0.400641\pi$
$757$	−315.734	−	198.389i	−0.417086	−	0.262073i	−0.724186	+	0.689605i	$0.757784\pi$
$758$	−21.3047	−	4.86265i	−0.0281064	−	0.00641511i
$759$		0			0
$760$	146.888	+	117.139i	0.193274	+	0.154131i
$761$	−0.0873012	−	0.382492i	−0.000114719	−	0.000502617i	0.974871	−	0.222772i	$-0.0715106\pi$
$761$	−0.0873012	−	0.382492i	−0.000114719	−	0.000502617i	−0.974985	+	0.222270i	$0.928653\pi$
$762$		0			0
$763$	−111.699	−	231.945i	−0.146395	−	0.303991i
$764$	570.053	−	358.188i	0.746143	−	0.468833i
$765$		0			0
$766$	−191.987	−	191.987i	−0.250636	−	0.250636i
$767$	−136.389	+	283.214i	−0.177821	+	0.369250i
$768$		0			0
$769$	1349.61	−	152.064i	1.75502	−	0.197743i	0.824968	−	0.565179i	$-0.191193\pi$
$769$	1349.61	−	152.064i	1.75502	−	0.197743i	0.930049	+	0.367436i	$0.119764\pi$
$770$	744.433	+	358.500i	0.966797	+	0.465585i
$771$		0			0
$772$	−184.135	−	526.227i	−0.238517	−	0.681641i
$773$	−392.849	−	625.216i	−0.508214	−	0.808818i	0.489798	−	0.871836i	$-0.337070\pi$
$773$	−392.849	−	625.216i	−0.508214	−	0.808818i	−0.998012	+	0.0630179i	$0.979927\pi$
$774$		0			0
$775$	65.9766	−	188.550i	0.0851310	−	0.243291i
$776$	−464.566	+	106.034i	−0.598668	+	0.136642i
$777$		0			0
$778$	7.56411	+	9.48510i	0.00972251	+	0.0121916i
$779$	−253.702	+	1111.54i	−0.325677	+	1.42688i
$780$		0			0
$781$	−51.2226	+	454.613i	−0.0655859	+	0.582091i
$782$		−	1617.90i		−	2.06893i
$783$		0			0
$784$	−287.385			−0.366563
$785$	689.779	+	77.7195i	0.878700	+	0.0990057i
$786$		0			0
$787$	161.929	+	36.9592i	0.205755	+	0.0469622i	0.324156	−	0.946004i	$-0.394920\pi$
$787$	161.929	+	36.9592i	0.205755	+	0.0469622i	−0.118401	+	0.992966i	$0.537777\pi$
$788$	−136.029	+	108.479i	−0.172625	+	0.137664i
$789$		0			0
$790$	186.943	+	819.053i	0.236637	+	1.03678i
$791$	499.798	+	174.887i	0.631856	+	0.221096i
$792$		0			0
$793$	269.000	−	169.024i	0.339218	−	0.213145i
$794$	−1623.65	+	568.139i	−2.04490	+	0.715540i
$795$		0			0
$796$	−53.6598	+	111.426i	−0.0674118	+	0.139982i
$797$	32.0030	+	284.034i	0.0401543	+	0.356379i	0.997683	+	0.0680400i	$0.0216746\pi$
$797$	32.0030	+	284.034i	0.0401543	+	0.356379i	−0.957528	+	0.288339i	$0.906897\pi$
$798$		0			0
$799$	951.061	+	458.007i	1.19031	+	0.573225i
$800$	−393.802	+	393.802i	−0.492253	+	0.492253i
$801$		0			0
$802$	−658.461	−	1047.93i	−0.821024	−	1.30665i
$803$	189.712	−	91.3606i	0.236254	−	0.113774i
$804$		0			0
$805$	−541.313	+	123.551i	−0.672439	+	0.153480i
$806$	142.740	−	178.990i	0.177097	−	0.222072i
$807$		0			0
$808$	−97.7324	+	428.194i	−0.120956	+	0.529943i
$809$	163.180	−	259.700i	0.201706	−	0.321013i	−0.730519	−	0.682892i	$-0.760722\pi$
$809$	163.180	−	259.700i	0.201706	−	0.321013i	0.932225	+	0.361879i	$0.117865\pi$
$810$		0			0
$811$			105.172i			0.129682i	0.997896	+	0.0648411i	$0.0206541\pi$
$811$			105.172i			0.129682i	−0.997896	+	0.0648411i	$0.979346\pi$
$812$	−338.879	+	320.511i	−0.417338	+	0.394718i
$813$		0			0
$814$	805.243	+	90.7291i	0.989242	+	0.111461i
$815$	−154.993	−	97.3887i	−0.190176	−	0.119495i
$816$		0			0
$817$	−887.636	+	707.866i	−1.08646	+	0.866421i
$818$	590.123	+	470.607i	0.721422	+	0.575314i
$819$		0			0
$820$	519.363	+	181.733i	0.633370	+	0.221626i
$821$	478.718	+	994.069i	0.583092	+	1.21080i	0.958805	+	0.284066i	$0.0916835\pi$
$821$	478.718	+	994.069i	0.583092	+	1.21080i	−0.375713	+	0.926736i	$0.622602\pi$
$822$		0			0
$823$	760.371	−	266.065i	0.923902	−	0.323287i	0.173931	−	0.984758i	$-0.444353\pi$
$823$	760.371	−	266.065i	0.923902	−	0.323287i	0.749971	+	0.661471i	$0.230067\pi$
$824$	109.267	+	109.267i	0.132606	+	0.132606i
$825$		0			0
$826$	81.6570	+	724.726i	0.0988584	+	0.877392i
$827$	1061.21	−	119.570i	1.28321	−	0.144583i	0.556105	−	0.831112i	$-0.312295\pi$
$827$	1061.21	−	119.570i	1.28321	−	0.144583i	0.727102	+	0.686529i	$0.240867\pi$
$828$		0			0
$829$	−149.865	+	149.865i	−0.180777	+	0.180777i	−0.791695	−	0.610917i	$-0.790801\pi$
$829$	−149.865	+	149.865i	−0.180777	+	0.180777i	0.610917	+	0.791695i	$0.290801\pi$
$830$	119.666	+	341.985i	0.144175	+	0.412030i
$831$		0			0
$832$	−116.214	+	55.9656i	−0.139680	+	0.0672663i
$833$	102.072	−	291.704i	0.122535	−	0.350185i
$834$		0			0
$835$	−267.253	+	335.124i	−0.320063	+	0.401347i
$836$	−531.092	−	665.968i	−0.635277	−	0.796612i
$837$		0			0
$838$	474.040	−	754.430i	0.565680	−	0.900275i
$839$	−24.7378	+	219.554i	−0.0294849	+	0.261686i	0.970318	+	0.241833i	$0.0777485\pi$
$839$	−24.7378	+	219.554i	−0.0294849	+	0.261686i	−0.999803	+	0.0198533i	$0.993680\pi$
$840$		0			0
$841$	−46.8158	+	839.696i	−0.0556668	+	0.998449i
$842$	−1382.38			−1.64179
$843$		0			0
$844$	658.712	+	413.896i	0.780464	+	0.490398i
$845$	391.691	+	89.4009i	0.463540	+	0.105800i
$846$		0			0
$847$	778.368	+	620.727i	0.918970	+	0.732854i
$848$	83.9146	+	367.654i	0.0989559	+	0.433554i
$849$		0			0
$850$	−349.869	−	726.511i	−0.411611	−	0.854719i
$851$	−461.072	+	289.711i	−0.541800	+	0.340435i
$852$		0			0
$853$	55.5077	+	55.5077i	0.0650735	+	0.0650735i	0.738895	−	0.673821i	$-0.235348\pi$
$853$	55.5077	+	55.5077i	0.0650735	+	0.0650735i	−0.673821	+	0.738895i	$0.735348\pi$
$854$	319.809	−	664.090i	0.374484	−	0.777623i
$855$		0			0
$856$	−426.960	+	48.1068i	−0.498785	+	0.0561996i
$857$	1012.19	+	487.444i	1.18108	+	0.568780i	0.918227	−	0.396055i	$-0.129621\pi$
$857$	1012.19	+	487.444i	1.18108	+	0.568780i	0.262857	+	0.964835i	$0.415335\pi$
$858$		0			0
$859$	−359.765	−	1028.15i	−0.418819	−	1.19692i	−0.939316	−	0.343052i	$-0.888539\pi$
$859$	−359.765	−	1028.15i	−0.418819	−	1.19692i	0.520497	−	0.853863i	$-0.325747\pi$
$860$	291.514	+	463.941i	0.338969	+	0.539467i
$861$		0			0
$862$	−482.048	+	1377.61i	−0.559220	+	1.59816i
$863$	1206.77	−	275.437i	1.39834	−	0.319163i	0.544093	−	0.839025i	$-0.316874\pi$
$863$	1206.77	−	275.437i	1.39834	−	0.319163i	0.854250	+	0.519862i	$0.174017\pi$
$864$		0			0
$865$	42.0799	+	52.7666i	0.0486473	+	0.0610018i
$866$	72.5346	−	317.795i	0.0837582	−	0.366969i
$867$		0			0
$868$	24.2274	−	215.024i	0.0279118	−	0.247724i
$869$			1731.91i			1.99299i
$870$		0			0
$871$	−92.8564			−0.106609
$872$	−142.062	−	16.0065i	−0.162915	−	0.0183561i
$873$		0			0
$874$	1369.84	+	312.657i	1.56732	+	0.357731i
$875$	−580.632	+	463.039i	−0.663579	+	0.529187i
$876$		0			0
$877$	123.979	+	543.187i	0.141367	+	0.619369i	0.995118	+	0.0986885i	$0.0314647\pi$
$877$	123.979	+	543.187i	0.141367	+	0.619369i	−0.853751	+	0.520681i	$0.825678\pi$
$878$	−1271.33	−	444.857i	−1.44798	−	0.506671i
$879$		0			0
$880$	894.860	−	562.278i	1.01689	−	0.638952i
$881$	862.626	−	301.846i	0.979144	−	0.342617i	0.207193	−	0.978300i	$-0.433567\pi$
$881$	862.626	−	301.846i	0.979144	−	0.342617i	0.771950	+	0.635683i	$0.219281\pi$
$882$		0			0
$883$	−286.016	+	593.917i	−0.323913	+	0.672613i	−0.997805	−	0.0662169i	$-0.978907\pi$
$883$	−286.016	+	593.917i	−0.323913	+	0.672613i	0.673892	+	0.738830i	$0.264621\pi$
$884$	−42.1525	−	374.114i	−0.0476838	−	0.423205i
$885$		0			0
$886$	141.755	+	68.2658i	0.159995	+	0.0770495i
$887$	−106.910	+	106.910i	−0.120530	+	0.120530i	−0.764799	−	0.644269i	$-0.777162\pi$
$887$	−106.910	+	106.910i	−0.120530	+	0.120530i	0.644269	+	0.764799i	$0.277162\pi$
$888$		0			0
$889$	−654.451	−	1041.55i	−0.736165	−	1.17160i
$890$	404.780	−	194.932i	0.454809	−	0.219024i
$891$		0			0
$892$	−27.9385	+	6.37677i	−0.0313212	+	0.00714885i
$893$	−571.576	+	716.734i	−0.640063	+	0.802613i
$894$		0			0
$895$	64.8786	−	284.252i	0.0724901	−	0.317600i
$896$	307.679	−	489.668i	0.343391	−	0.546504i
$897$		0			0
$898$		−	1861.25i		−	2.07266i
$899$	−234.664	−	311.683i	−0.261028	−	0.346700i
$900$		0			0
$901$	−402.983	−	45.4053i	−0.447262	−	0.0503944i
$902$	2357.65	+	1481.41i	2.61380	+	1.64236i
$903$		0			0
$904$	229.896	−	183.336i	0.254309	−	0.202805i
$905$	−489.896	−	390.679i	−0.541322	−	0.431690i
$906$		0			0
$907$	1362.30	+	476.689i	1.50198	+	0.525566i	0.951064	−	0.308993i	$-0.0999920\pi$
$907$	1362.30	+	476.689i	1.50198	+	0.525566i	0.550918	+	0.834559i	$0.314278\pi$
$908$	−80.3507	−	166.850i	−0.0884920	−	0.183756i
$909$		0			0
$910$	−299.353	+	104.748i	−0.328959	+	0.115108i
$911$	−350.673	−	350.673i	−0.384932	−	0.384932i	0.487943	−	0.872875i	$-0.337747\pi$
$911$	−350.673	−	350.673i	−0.384932	−	0.384932i	−0.872875	+	0.487943i	$0.837747\pi$
$912$		0			0
$913$	83.6286	+	742.225i	0.0915976	+	0.812951i
$914$	1412.68	−	159.171i	1.54561	−	0.174148i
$915$		0			0
$916$	−502.390	+	502.390i	−0.548461	+	0.548461i
$917$	320.783	+	916.745i	0.349818	+	0.999722i
$918$		0			0
$919$	343.497	−	165.419i	0.373772	−	0.179999i	−0.237561	−	0.971373i	$-0.576348\pi$
$919$	343.497	−	165.419i	0.373772	−	0.179999i	0.611333	+	0.791374i	$0.290634\pi$
$920$	−101.835	+	291.028i	−0.110691	+	0.316335i
$921$		0			0
$922$	−955.699	+	1198.41i	−1.03655	+	1.29979i
$923$	−109.486	−	137.291i	−0.118620	−	0.148745i
$924$		0			0
$925$	−144.393	+	229.800i	−0.156100	+	0.248432i
$926$	22.0299	−	195.521i	0.0237904	−	0.211146i
$927$		0			0
$928$	212.417	+	1066.76i	0.228897	+	1.14953i
$929$	699.063			0.752490			0.376245	−	0.926520i	$-0.377215\pi$
$929$	699.063			0.752490			0.376245	+	0.926520i	$0.377215\pi$
$930$		0			0
$931$	227.254	+	142.793i	0.244097	+	0.153376i
$932$	−375.055	−	85.6039i	−0.402420	−	0.0918496i
$933$		0			0
$934$	−350.644	−	279.630i	−0.375422	−	0.299389i
$935$	252.897	+	1108.01i	0.270478	+	1.18504i
$936$		0			0
$937$	484.352	+	1005.77i	0.516918	+	1.07339i	0.982132	+	0.188192i	$0.0602629\pi$
$937$	484.352	+	1005.77i	0.516918	+	1.07339i	−0.465215	+	0.885198i	$0.654023\pi$
$938$	−182.415	+	114.619i	−0.194473	+	0.122195i
$939$		0			0
$940$	312.845	+	312.845i	0.332814	+	0.332814i
$941$	−521.146	+	1082.17i	−0.553821	+	1.15002i	0.416709	+	0.909040i	$0.363183\pi$
$941$	−521.146	+	1082.17i	−0.553821	+	1.15002i	−0.970530	+	0.240981i	$0.922531\pi$
$942$		0			0
$943$	−1859.33	+	209.497i	−1.97172	+	0.222160i
$944$	840.466	+	404.747i	0.890324	+	0.428758i
$945$		0			0
$946$	915.769	+	2617.12i	0.968044	+	2.76651i
$947$	−490.268	−	780.257i	−0.517706	−	0.823925i	0.480896	−	0.876778i	$-0.340311\pi$
$947$	−490.268	−	780.257i	−0.517706	−	0.823925i	−0.998602	+	0.0528529i	$0.983169\pi$
$948$		0			0
$949$	−26.6941	+	76.2874i	−0.0281287	+	0.0803871i
$950$	682.733	−	155.829i	0.718666	−	0.164031i
$951$		0			0
$952$	247.628	+	310.516i	0.260114	+	0.326172i
$953$	−176.169	+	771.848i	−0.184858	+	0.809914i	0.794416	+	0.607373i	$0.207777\pi$
$953$	−176.169	+	771.848i	−0.184858	+	0.809914i	−0.979274	+	0.202540i	$0.935080\pi$
$954$		0			0
$955$	87.3440	−	775.199i	0.0914597	−	0.811727i
$956$		−	271.969i		−	0.284486i
$957$		0			0
$958$	−38.7205			−0.0404181
$959$	1002.14	+	112.914i	1.04498	+	0.117741i
$960$		0			0
$961$	−760.452	−	173.568i	−0.791314	−	0.180612i
$962$	−243.180	+	193.930i	−0.252786	+	0.201590i
$963$		0			0
$964$	−223.396	−	978.761i	−0.231738	−	1.01531i
$965$	−609.751	−	213.361i	−0.631866	−	0.221099i
$966$		0			0
$967$	−333.145	+	209.329i	−0.344514	+	0.216472i	−0.693163	−	0.720781i	$-0.743783\pi$
$967$	−333.145	+	209.329i	−0.344514	+	0.216472i	0.348649	+	0.937253i	$0.386640\pi$
$968$	521.832	−	182.597i	0.539083	−	0.188633i
$969$		0			0
$970$	526.875	−	1094.07i	0.543170	−	1.12790i
$971$	−54.9296	−	487.514i	−0.0565701	−	0.502074i	−0.989765	−	0.142704i	$-0.954420\pi$
$971$	−54.9296	−	487.514i	−0.0565701	−	0.502074i	0.933195	−	0.359370i	$-0.117008\pi$
$972$		0			0
$973$	824.446	+	397.032i	0.847324	+	0.408050i
$974$	−357.877	+	357.877i	−0.367430	+	0.367430i
$975$		0			0
$976$	−501.594	−	798.282i	−0.513928	−	0.817912i
$977$	−31.3582	+	15.1013i	−0.0320964	+	0.0154568i	−0.449863	−	0.893098i	$-0.648527\pi$
$977$	−31.3582	+	15.1013i	−0.0320964	+	0.0154568i	0.417767	+	0.908554i	$0.362813\pi$
$978$		0			0
$979$	902.959	−	206.095i	0.922328	−	0.210515i
$980$	80.7605	−	101.270i	0.0824086	−	0.103337i
$981$		0			0
$982$	23.5922	−	103.364i	0.0240246	−	0.105259i
$983$	270.847	−	431.051i	0.275531	−	0.438505i	−0.680079	−	0.733139i	$-0.738055\pi$
$983$	270.847	−	431.051i	0.275531	−	0.438505i	0.955610	+	0.294633i	$0.0951975\pi$
$984$		0			0
$985$			201.603i			0.204673i
$986$	−1559.47	−	219.839i	−1.58161	−	0.222961i
$987$		0			0
$988$	324.900	+	36.6074i	0.328846	+	0.0370520i
$989$	−1577.64	−	991.295i	−1.59518	−	1.00232i
$990$		0			0
$991$	1171.15	−	933.958i	1.18178	−	0.942440i	0.182613	−	0.983185i	$-0.441544\pi$
$991$	1171.15	−	933.958i	1.18178	−	0.942440i	0.999170	+	0.0407444i	$0.0129729\pi$
$992$	−394.508	−	314.609i	−0.397689	−	0.317146i
$993$		0			0
$994$	−384.553	−	134.561i	−0.386874	−	0.135373i
$995$	62.1768	+	129.111i	0.0624892	+	0.129760i
$996$		0			0
$997$	1755.99	−	614.449i	1.76128	−	0.616298i	0.761776	−	0.647840i	$-0.224328\pi$
$997$	1755.99	−	614.449i	1.76128	−	0.616298i	0.999502	+	0.0315424i	$0.0100419\pi$
$998$	−1200.48	−	1200.48i	−1.20288	−	1.20288i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.118.1		48
3.2	odd	2		29.3.f.a.2.4	✓	48
29.15	odd	28	inner	261.3.s.a.73.1		48
87.44	even	28		29.3.f.a.15.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.2.4	✓	48	3.2	odd	2
29.3.f.a.15.4	yes	48	87.44	even	28
261.3.s.a.73.1		48	29.15	odd	28	inner
261.3.s.a.118.1		48	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-2.58169 - 0.290886i) q^{2} +(2.68078 + 0.611870i) q^{4} +(2.49104 - 1.98654i) q^{5} +(1.30161 + 5.70272i) q^{7} +(3.06598 + 1.07283i) q^{8} +O(q^{10})\)	\(q+(-2.58169 - 0.290886i) q^{2} +(2.68078 + 0.611870i) q^{4} +(2.49104 - 1.98654i) q^{5} +(1.30161 + 5.70272i) q^{7} +(3.06598 + 1.07283i) q^{8} +(-7.00893 + 4.40400i) q^{10} +(-16.1070 + 5.63608i) q^{11} +(2.84196 - 5.90140i) q^{13} +(-1.70150 - 15.1013i) q^{14} +(-17.5130 - 8.43380i) q^{16} +(14.7807 - 14.7807i) q^{17} +(9.65814 + 15.3708i) q^{19} +(7.89342 - 3.80127i) q^{20} +(43.2227 - 9.86529i) q^{22} +(-18.5750 + 23.2923i) q^{23} +(-3.30408 + 14.4761i) q^{25} +(-9.05369 + 14.4089i) q^{26} +16.0841i q^{28} +(19.9272 + 21.0691i) q^{29} +(-13.3687 - 1.50629i) q^{31} +(31.7582 + 19.9550i) q^{32} +(-42.4586 + 33.8596i) q^{34} +(14.5710 + 11.6200i) q^{35} +(17.2522 + 6.03682i) q^{37} +(-20.4631 - 42.4921i) q^{38} +(9.76869 - 3.41821i) q^{40} +(44.4102 + 44.4102i) q^{41} +(7.00239 + 62.1479i) q^{43} +(-46.6278 + 5.25369i) q^{44} +(54.7302 - 54.7302i) q^{46} +(16.6790 + 47.6658i) q^{47} +(13.3206 - 6.41487i) q^{49} +(12.7410 - 36.4117i) q^{50} +(11.2296 - 14.0814i) q^{52} +(-12.0961 - 15.1681i) q^{53} +(-28.9269 + 46.0368i) q^{55} +(-2.12736 + 18.8808i) q^{56} +(-45.3170 - 60.1904i) q^{58} -47.9911 q^{59} +(41.0683 + 25.8049i) q^{61} +(34.0756 + 7.77754i) q^{62} +(-15.3963 - 12.2781i) q^{64} +(-4.64390 - 20.3463i) q^{65} +(-6.15092 - 12.7725i) q^{67} +(48.6676 - 30.5799i) q^{68} +(-34.2377 - 34.2377i) q^{70} +(11.6321 - 24.1543i) q^{71} +(-12.2617 + 1.38156i) q^{73} +(-42.7839 - 20.6036i) q^{74} +(16.4864 + 47.1153i) q^{76} +(-53.1060 - 84.5178i) q^{77} +(33.5205 - 95.7961i) q^{79} +(-60.3795 + 13.7812i) q^{80} +(-101.735 - 127.571i) q^{82} +(9.73978 - 42.6728i) q^{83} +(7.45688 - 66.1816i) q^{85} -162.483i q^{86} -55.4303 q^{88} +(-53.9337 - 6.07686i) q^{89} +(37.3532 + 8.52561i) q^{91} +(-64.0472 + 51.0760i) q^{92} +(-29.1946 - 127.910i) q^{94} +(54.5935 + 19.1031i) q^{95} +(-124.213 + 78.0480i) q^{97} +(-36.2556 + 12.6864i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 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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