LMFDB - Embedded newform 171.4.u.c.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.2
Character	$\chi$	$=$	171.82
Dual form			171.4.u.c.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57889 + 2.16395i) q^{2} +(0.578834 - 3.28273i) q^{4} +(1.62337 + 9.20660i) q^{5} +(10.2044 - 17.6746i) q^{7} +(-7.85512 - 13.6055i) q^{8} +O(q^{10})$	\(q+(-2.57889 + 2.16395i) q^{2} +(0.578834 - 3.28273i) q^{4} +(1.62337 + 9.20660i) q^{5} +(10.2044 - 17.6746i) q^{7} +(-7.85512 - 13.6055i) q^{8} +(-24.1091 - 20.2299i) q^{10} +(-16.0000 - 27.7127i) q^{11} +(-67.0703 + 24.4116i) q^{13} +(11.9308 + 67.6627i) q^{14} +(74.7578 + 27.2096i) q^{16} +(60.7411 - 50.9678i) q^{17} +(-69.0817 - 45.6807i) q^{19} +31.1625 q^{20} +(101.231 + 36.8451i) q^{22} +(15.7121 - 89.1075i) q^{23} +(35.3355 - 12.8611i) q^{25} +(120.142 - 208.092i) q^{26} +(-52.1142 - 43.7290i) q^{28} +(-16.0172 - 13.4401i) q^{29} +(67.4581 - 116.841i) q^{31} +(-133.570 + 48.6157i) q^{32} +(-46.3530 + 262.881i) q^{34} +(179.288 + 65.2556i) q^{35} +235.126 q^{37} +(277.005 - 31.6837i) q^{38} +(112.508 - 94.4056i) q^{40} +(303.396 + 110.427i) q^{41} +(-59.8743 - 339.564i) q^{43} +(-100.235 + 36.4825i) q^{44} +(152.304 + 263.799i) q^{46} +(-232.960 - 195.477i) q^{47} +(-36.7603 - 63.6707i) q^{49} +(-63.2958 + 109.632i) q^{50} +(41.3142 + 234.304i) q^{52} +(-79.8475 + 452.838i) q^{53} +(229.166 - 192.293i) q^{55} -320.628 q^{56} +70.3904 q^{58} +(-229.657 + 192.705i) q^{59} +(6.66553 - 37.8021i) q^{61} +(78.8703 + 447.296i) q^{62} +(-78.9602 + 136.763i) q^{64} +(-333.628 - 577.861i) q^{65} +(-498.260 - 418.090i) q^{67} +(-132.155 - 228.899i) q^{68} +(-603.575 + 219.683i) q^{70} +(-109.301 - 619.876i) q^{71} +(-350.982 - 127.747i) q^{73} +(-606.365 + 508.801i) q^{74} +(-189.944 + 200.335i) q^{76} -653.081 q^{77} +(-962.560 - 350.343i) q^{79} +(-129.148 + 732.436i) q^{80} +(-1021.38 + 371.754i) q^{82} +(471.707 - 817.021i) q^{83} +(567.845 + 476.479i) q^{85} +(889.209 + 746.135i) q^{86} +(-251.363 + 435.374i) q^{88} +(712.415 - 259.298i) q^{89} +(-252.949 + 1434.55i) q^{91} +(-283.421 - 103.157i) q^{92} +1023.78 q^{94} +(308.418 - 710.164i) q^{95} +(815.791 - 684.530i) q^{97} +(232.581 + 84.6527i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} + 9 q^{4} - 12 q^{5} - 48 q^{7} + 57 q^{8}+O(q^{10}) $ 36 * q - 3 * q^2 + 9 * q^4 - 12 * q^5 - 48 * q^7 + 57 * q^8	$ 36 q - 3 q^{2} + 9 q^{4} - 12 q^{5} - 48 q^{7} + 57 q^{8} - 24 q^{10} + 108 q^{11} - 24 q^{13} + 87 q^{14} + 69 q^{16} + 462 q^{17} - 336 q^{19} - 54 q^{20} + 84 q^{22} + 306 q^{25} - 72 q^{26} + 1938 q^{28} - 342 q^{29} + 1032 q^{31} + 141 q^{32} - 867 q^{34} + 642 q^{35} + 264 q^{37} + 4464 q^{38} - 4209 q^{40} - 558 q^{41} + 1344 q^{43} + 1239 q^{44} + 2229 q^{46} - 2628 q^{47} - 1122 q^{49} - 1503 q^{50} - 2463 q^{52} - 1722 q^{53} + 1860 q^{55} - 2238 q^{56} + 1512 q^{58} + 1986 q^{59} + 1566 q^{61} - 7287 q^{62} - 2679 q^{64} - 1716 q^{65} - 1044 q^{67} + 4623 q^{68} + 60 q^{70} + 5874 q^{71} + 3024 q^{73} + 723 q^{74} - 6942 q^{76} - 2028 q^{77} - 3696 q^{79} - 8076 q^{80} + 3597 q^{82} + 4764 q^{83} + 3300 q^{85} + 627 q^{86} + 3012 q^{88} - 3228 q^{89} - 1272 q^{91} - 18183 q^{92} - 16410 q^{94} + 3780 q^{95} - 1230 q^{97} + 19761 q^{98}+O(q^{100}) $ 36 * q - 3 * q^2 + 9 * q^4 - 12 * q^5 - 48 * q^7 + 57 * q^8 - 24 * q^10 + 108 * q^11 - 24 * q^13 + 87 * q^14 + 69 * q^16 + 462 * q^17 - 336 * q^19 - 54 * q^20 + 84 * q^22 + 306 * q^25 - 72 * q^26 + 1938 * q^28 - 342 * q^29 + 1032 * q^31 + 141 * q^32 - 867 * q^34 + 642 * q^35 + 264 * q^37 + 4464 * q^38 - 4209 * q^40 - 558 * q^41 + 1344 * q^43 + 1239 * q^44 + 2229 * q^46 - 2628 * q^47 - 1122 * q^49 - 1503 * q^50 - 2463 * q^52 - 1722 * q^53 + 1860 * q^55 - 2238 * q^56 + 1512 * q^58 + 1986 * q^59 + 1566 * q^61 - 7287 * q^62 - 2679 * q^64 - 1716 * q^65 - 1044 * q^67 + 4623 * q^68 + 60 * q^70 + 5874 * q^71 + 3024 * q^73 + 723 * q^74 - 6942 * q^76 - 2028 * q^77 - 3696 * q^79 - 8076 * q^80 + 3597 * q^82 + 4764 * q^83 + 3300 * q^85 + 627 * q^86 + 3012 * q^88 - 3228 * q^89 - 1272 * q^91 - 18183 * q^92 - 16410 * q^94 + 3780 * q^95 - 1230 * q^97 + 19761 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−2.57889	+	2.16395i	−0.911777	+	0.765072i	−0.972456	−	0.233086i	$-0.925118\pi$
$2$	−2.57889	+	2.16395i	−0.911777	+	0.765072i	0.0606793	+	0.998157i	$0.480673\pi$
$3$		0			0
$3$		0			0
$4$	0.578834	−	3.28273i	0.0723543	−	0.410341i
$5$	1.62337	+	9.20660i	0.145199	+	0.823463i	0.967207	+	0.253988i	$0.0817424\pi$
$5$	1.62337	+	9.20660i	0.145199	+	0.823463i	−0.822009	+	0.569475i	$0.807147\pi$
$6$		0			0
$7$	10.2044	−	17.6746i	0.550987	−	0.954337i	−0.447217	−	0.894426i	$-0.647585\pi$
$7$	10.2044	−	17.6746i	0.550987	−	0.954337i	0.998204	−	0.0599116i	$-0.0190819\pi$
$8$	−7.85512	−	13.6055i	−0.347150	−	0.601282i
$9$		0			0
$10$	−24.1091	−	20.2299i	−0.762397	−	0.639727i
$11$	−16.0000	−	27.7127i	−0.438561	−	0.759610i	0.559018	−	0.829156i	$-0.311178\pi$
$11$	−16.0000	−	27.7127i	−0.438561	−	0.759610i	−0.997579	+	0.0695460i	$0.977845\pi$
$12$		0			0
$13$	−67.0703	+	24.4116i	−1.43092	+	0.520813i	−0.937195	−	0.348805i	$-0.886587\pi$
$13$	−67.0703	+	24.4116i	−1.43092	+	0.520813i	−0.493725	+	0.869618i	$0.664365\pi$
$14$	11.9308	+	67.6627i	0.227759	+	1.29169i
$15$		0			0
$16$	74.7578	+	27.2096i	1.16809	+	0.425150i
$17$	60.7411	−	50.9678i	0.866581	−	0.727148i	−0.0967945	−	0.995304i	$-0.530859\pi$
$17$	60.7411	−	50.9678i	0.866581	−	0.727148i	0.963375	+	0.268157i	$0.0864145\pi$
$18$		0			0
$19$	−69.0817	−	45.6807i	−0.834128	−	0.551572i
$19$	−69.0817	−	45.6807i	−0.834128	−	0.551572i
$20$	31.1625			0.348407
$21$		0			0
$22$	101.231	+	36.8451i	0.981025	+	0.357064i
$23$	15.7121	−	89.1075i	0.142443	−	0.807835i	−0.826942	−	0.562288i	$-0.809921\pi$
$23$	15.7121	−	89.1075i	0.142443	−	0.807835i	0.969385	−	0.245547i	$-0.0789676\pi$
$24$		0			0
$25$	35.3355	−	12.8611i	0.282684	−	0.102888i
$26$	120.142	−	208.092i	0.906221	−	1.56962i
$27$		0			0
$28$	−52.1142	−	43.7290i	−0.351738	−	0.295143i
$29$	−16.0172	−	13.4401i	−0.102563	−	0.0860606i	0.590064	−	0.807356i	$-0.299102\pi$
$29$	−16.0172	−	13.4401i	−0.102563	−	0.0860606i	−0.692627	+	0.721296i	$0.743547\pi$
$30$		0			0
$31$	67.4581	−	116.841i	0.390833	−	0.676943i	−0.601727	−	0.798702i	$-0.705520\pi$
$31$	67.4581	−	116.841i	0.390833	−	0.676943i	0.992560	+	0.121759i	$0.0388536\pi$
$32$	−133.570	+	48.6157i	−0.737879	+	0.268566i
$33$		0			0
$34$	−46.3530	+	262.881i	−0.233808	+	1.32599i
$35$	179.288	+	65.2556i	0.865864	+	0.315149i
$36$		0			0
$37$	235.126			1.04472			0.522358	−	0.852726i	$-0.325053\pi$
$37$	235.126			1.04472			0.522358	+	0.852726i	$0.325053\pi$
$38$	277.005	−	31.6837i	1.18253	−	0.135257i
$39$		0			0
$40$	112.508	−	94.4056i	0.444728	−	0.373171i
$41$	303.396	+	110.427i	1.15567	+	0.420630i	0.847549	−	0.530717i	$-0.178077\pi$
$41$	303.396	+	110.427i	1.15567	+	0.420630i	0.308121	+	0.951347i	$0.400300\pi$
$42$		0			0
$43$	−59.8743	−	339.564i	−0.212343	−	1.20426i	−0.885458	−	0.464719i	$-0.846155\pi$
$43$	−59.8743	−	339.564i	−0.212343	−	1.20426i	0.673115	−	0.739538i	$-0.264956\pi$
$44$	−100.235	+	36.4825i	−0.343431	+	0.124999i
$45$		0			0
$46$	152.304	+	263.799i	0.488175	+	0.845544i
$47$	−232.960	−	195.477i	−0.722993	−	0.606663i	0.205218	−	0.978716i	$-0.434210\pi$
$47$	−232.960	−	195.477i	−0.722993	−	0.606663i	−0.928212	+	0.372053i	$0.878654\pi$
$48$		0			0
$49$	−36.7603	−	63.6707i	−0.107173	−	0.185629i
$50$	−63.2958	+	109.632i	−0.179027	+	0.310085i
$51$		0			0
$52$	41.3142	+	234.304i	0.110178	+	0.624849i
$53$	−79.8475	+	452.838i	−0.206942	+	1.17362i	0.687414	+	0.726266i	$0.258746\pi$
$53$	−79.8475	+	452.838i	−0.206942	+	1.17362i	−0.894355	+	0.447358i	$0.852365\pi$
$54$		0			0
$55$	229.166	−	192.293i	0.561832	−	0.471433i
$56$	−320.628			−0.765101
$57$		0			0
$58$	70.3904			0.159357
$59$	−229.657	+	192.705i	−0.506758	+	0.425221i	−0.859987	−	0.510316i	$-0.829528\pi$
$59$	−229.657	+	192.705i	−0.506758	+	0.425221i	0.353228	+	0.935537i	$0.385084\pi$
$60$		0			0
$61$	6.66553	−	37.8021i	0.0139907	−	0.0793453i	−0.977013	−	0.213180i	$-0.931618\pi$
$61$	6.66553	−	37.8021i	0.0139907	−	0.0793453i	0.991004	+	0.133835i	$0.0427291\pi$
$62$	78.8703	+	447.296i	0.161557	+	0.916236i
$63$		0			0
$64$	−78.9602	+	136.763i	−0.154219	+	0.267116i
$65$	−333.628	−	577.861i	−0.636638	−	1.10269i
$66$		0			0
$67$	−498.260	−	418.090i	−0.908540	−	0.762356i	0.0633006	−	0.997995i	$-0.479837\pi$
$67$	−498.260	−	418.090i	−0.908540	−	0.762356i	−0.971841	+	0.235639i	$0.924282\pi$
$68$	−132.155	−	228.899i	−0.235678	−	0.408206i
$69$		0			0
$70$	−603.575	+	219.683i	−1.03059	+	0.375103i
$71$	−109.301	−	619.876i	−0.182699	−	1.03614i	−0.928876	−	0.370390i	$-0.879224\pi$
$71$	−109.301	−	619.876i	−0.182699	−	1.03614i	0.746177	−	0.665747i	$-0.231887\pi$
$72$		0			0
$73$	−350.982	−	127.747i	−0.562731	−	0.204817i	0.0449630	−	0.998989i	$-0.485683\pi$
$73$	−350.982	−	127.747i	−0.562731	−	0.204817i	−0.607694	+	0.794171i	$0.707905\pi$
$74$	−606.365	+	508.801i	−0.952548	+	0.799282i
$75$		0			0
$76$	−189.944	+	200.335i	−0.286685	+	0.302369i
$77$	−653.081			−0.966565
$78$		0			0
$79$	−962.560	−	350.343i	−1.37084	−	0.498945i	−0.451452	−	0.892295i	$-0.649094\pi$
$79$	−962.560	−	350.343i	−1.37084	−	0.498945i	−0.919389	+	0.393350i	$0.871316\pi$
$80$	−129.148	+	732.436i	−0.180490	+	1.02361i
$81$		0			0
$82$	−1021.38	+	371.754i	−1.37553	+	0.500650i
$83$	471.707	−	817.021i	0.623814	−	1.08048i	−0.364955	−	0.931025i	$-0.618915\pi$
$83$	471.707	−	817.021i	0.623814	−	1.08048i	0.988769	−	0.149453i	$-0.0477512\pi$
$84$		0			0
$85$	567.845	+	476.479i	0.724606	+	0.608016i
$86$	889.209	+	746.135i	1.11495	+	0.935556i
$87$		0			0
$88$	−251.363	+	435.374i	−0.304493	+	0.527398i
$89$	712.415	−	259.298i	0.848492	−	0.308826i	0.119067	−	0.992886i	$-0.462010\pi$
$89$	712.415	−	259.298i	0.848492	−	0.308826i	0.729425	+	0.684060i	$0.239787\pi$
$90$		0			0
$91$	−252.949	+	1434.55i	−0.291388	+	1.65254i
$92$	−283.421	−	103.157i	−0.321182	−	0.116901i
$93$		0			0
$94$	1023.78			1.12335
$95$	308.418	−	710.164i	0.333085	−	0.766961i
$96$		0			0
$97$	815.791	−	684.530i	0.853928	−	0.716531i	−0.106723	−	0.994289i	$-0.534036\pi$
$97$	815.791	−	684.530i	0.853928	−	0.716531i	0.960651	+	0.277758i	$0.0895913\pi$
$98$	232.581	+	84.6527i	0.239737	+	0.0872572i
$99$		0			0
$100$	−21.7660	−	123.441i	−0.0217660	−	0.123441i
$101$	−1790.75	+	651.779i	−1.76422	+	0.642123i	−0.999996	−	0.00282937i	$-0.999099\pi$
$101$	−1790.75	+	651.779i	−1.76422	+	0.642123i	−0.764223	+	0.644952i	$0.776877\pi$
$102$		0			0
$103$	548.637	+	950.267i	0.524842	+	0.909054i	0.999582	+	0.0289272i	$0.00920910\pi$
$103$	548.637	+	950.267i	0.524842	+	0.909054i	−0.474739	+	0.880127i	$0.657458\pi$
$104$	858.977	+	720.767i	0.809900	+	0.679587i
$105$		0			0
$106$	−774.000	−	1340.61i	−0.709222	−	1.22841i
$107$	−220.646	+	382.171i	−0.199352	+	0.345288i	−0.948319	−	0.317320i	$-0.897217\pi$
$107$	−220.646	+	382.171i	−0.199352	+	0.345288i	0.748966	+	0.662608i	$0.230550\pi$
$108$		0			0
$109$	−15.2672	−	86.5847i	−0.0134159	−	0.0760855i	0.977365	−	0.211561i	$-0.0678548\pi$
$109$	−15.2672	−	86.5847i	−0.0134159	−	0.0760855i	−0.990781	+	0.135476i	$0.956744\pi$
$110$	−174.882	+	991.808i	−0.151585	+	0.859683i
$111$		0			0
$112$	1243.78	−	1043.65i	1.04934	−	0.880500i
$113$	−1352.50			−1.12595			−0.562974	−	0.826475i	$-0.690343\pi$
$113$	−1352.50			−1.12595			−0.562974	+	0.826475i	$0.690343\pi$
$114$		0			0
$115$	845.884			0.685905
$116$	−53.3915	+	44.8008i	−0.0427351	+	0.0358590i
$117$		0			0
$118$	175.257	−	993.930i	0.136726	−	0.775413i
$119$	−281.007	−	1593.67i	−0.216469	−	1.22766i
$120$		0			0
$121$	153.503	−	265.875i	0.115329	−	0.199755i
$122$	64.6121	+	111.911i	0.0479484	+	0.0830491i
$123$		0			0
$124$	−344.510	−	289.078i	−0.249499	−	0.209355i
$125$	760.058	+	1316.46i	0.543853	+	0.941982i
$126$		0			0
$127$	2188.16	−	796.425i	1.52888	−	0.556467i	0.565533	−	0.824725i	$-0.308670\pi$
$127$	2188.16	−	796.425i	1.52888	−	0.556467i	0.963347	+	0.268259i	$0.0864481\pi$
$128$	−289.781	−	1643.43i	−0.200104	−	1.13484i
$129$		0			0
$130$	2110.85	+	768.287i	1.42411	+	0.518333i
$131$	1415.19	−	1187.49i	0.943864	−	0.791996i	−0.0343898	−	0.999408i	$-0.510949\pi$
$131$	1415.19	−	1187.49i	0.943864	−	0.791996i	0.978254	+	0.207413i	$0.0665043\pi$
$132$		0			0
$133$	−1512.32	+	754.845i	−0.985979	+	0.492130i
$134$	2189.69			1.41164
$135$		0			0
$136$	−1170.57	−	426.052i	−0.738055	−	0.268630i
$137$	92.3356	−	523.661i	0.0575822	−	0.326565i	−0.942386	−	0.334527i	$-0.891423\pi$
$137$	92.3356	−	523.661i	0.0575822	−	0.326565i	0.999968	+	0.00796227i	$0.00253450\pi$
$138$		0			0
$139$	−1468.28	+	534.411i	−0.895958	+	0.326102i	−0.748632	−	0.662986i	$-0.769289\pi$
$139$	−1468.28	+	534.411i	−0.895958	+	0.326102i	−0.147326	+	0.989088i	$0.547067\pi$
$140$	317.995	−	550.783i	0.191968	−	0.332498i
$141$		0			0
$142$	1623.26	+	1362.07i	0.959300	+	0.804948i
$143$	1749.64	+	1468.12i	1.02316	+	0.858533i
$144$		0			0
$145$	97.7353	−	169.283i	0.0559757	−	0.0969528i
$146$	1181.58	−	430.061i	0.669785	−	0.243782i
$147$		0			0
$148$	136.099	−	771.856i	0.0755896	−	0.428690i
$149$	−2286.99	−	832.395i	−1.25743	−	0.457667i	−0.374525	−	0.927217i	$-0.622194\pi$
$149$	−2286.99	−	832.395i	−1.25743	−	0.457667i	−0.882906	+	0.469549i	$0.844416\pi$
$150$		0			0
$151$	−3524.32			−1.89937			−0.949686	−	0.313204i	$-0.898597\pi$
$151$	−3524.32			−1.89937			−0.949686	+	0.313204i	$0.898597\pi$
$152$	−78.8617	+	1298.72i	−0.0420824	+	0.693024i
$153$		0			0
$154$	1684.23	−	1413.23i	0.881291	−	0.739491i
$155$	1185.22	+	431.383i	0.614186	+	0.223545i
$156$		0			0
$157$	−18.8502	−	106.905i	−0.00958224	−	0.0543436i	0.979642	−	0.200754i	$-0.0643391\pi$
$157$	−18.8502	−	106.905i	−0.00958224	−	0.0543436i	−0.989224	+	0.146410i	$0.953228\pi$
$158$	3240.46	−	1179.43i	1.63163	−	0.593865i
$159$		0			0
$160$	−664.419	−	1150.81i	−0.328293	−	0.568621i
$161$	−1414.60	−	1186.99i	−0.692463	−	0.581045i
$162$		0			0
$163$	1313.40	+	2274.87i	0.631125	+	1.09314i	0.987322	+	0.158729i	$0.0507397\pi$
$163$	1313.40	+	2274.87i	0.631125	+	1.09314i	−0.356197	+	0.934411i	$0.615927\pi$
$164$	538.118	−	932.048i	0.256219	−	0.443785i
$165$		0			0
$166$	551.509	+	3127.76i	0.257864	+	1.46242i
$167$	25.8477	−	146.589i	0.0119770	−	0.0679247i	−0.978233	−	0.207507i	$-0.933465\pi$
$167$	25.8477	−	146.589i	0.0119770	−	0.0679247i	0.990210	+	0.139583i	$0.0445761\pi$
$168$		0			0
$169$	2219.51	−	1862.39i	1.01024	−	0.847695i
$170$	−2495.49			−1.12585
$171$		0			0
$172$	−1149.36			−0.509520
$173$	−255.349	+	214.263i	−0.112219	+	0.0941626i	−0.697170	−	0.716905i	$-0.745558\pi$
$173$	−255.349	+	214.263i	−0.112219	+	0.0941626i	0.584952	+	0.811068i	$0.301113\pi$
$174$		0			0
$175$	133.264	−	755.779i	0.0575647	−	0.326466i
$176$	−442.069	−	2507.10i	−0.189331	−	1.07375i
$177$		0			0
$178$	−1276.14	+	2210.33i	−0.537362	+	0.930738i
$179$	1649.27	+	2856.63i	0.688673	+	1.19282i	0.972267	+	0.233873i	$0.0751399\pi$
$179$	1649.27	+	2856.63i	0.688673	+	1.19282i	−0.283594	+	0.958944i	$0.591527\pi$
$180$		0			0
$181$	−2551.09	−	2140.62i	−1.04763	−	0.879068i	−0.0547894	−	0.998498i	$-0.517449\pi$
$181$	−2551.09	−	2140.62i	−1.04763	−	0.879068i	−0.992843	+	0.119430i	$0.961893\pi$
$182$	−2451.96	−	4246.91i	−0.998632	−	1.72968i
$183$		0			0
$184$	−1335.77	+	486.180i	−0.535186	+	0.194792i
$185$	381.697	+	2164.71i	0.151691	+	0.860285i
$186$		0			0
$187$	−2384.31	−	867.819i	−0.932397	−	0.339365i
$188$	−776.542	+	651.596i	−0.301251	+	0.252779i
$189$		0			0
$190$	741.381	+	2498.84i	0.283081	+	0.954131i
$191$	−28.5897			−0.0108308			−0.00541539	−	0.999985i	$-0.501724\pi$
$191$	−28.5897			−0.0108308			−0.00541539	+	0.999985i	$0.501724\pi$
$192$		0			0
$193$	2405.43	+	875.505i	0.897133	+	0.326530i	0.749103	−	0.662453i	$-0.230485\pi$
$193$	2405.43	+	875.505i	0.897133	+	0.326530i	0.148030	+	0.988983i	$0.452707\pi$
$194$	−622.551	+	3530.66i	−0.230395	+	1.30663i
$195$		0			0
$196$	−230.292	+	83.8195i	−0.0839257	+	0.0305465i
$197$	1690.10	−	2927.34i	0.611242	−	1.05870i	−0.379789	−	0.925073i	$-0.624004\pi$
$197$	1690.10	−	2927.34i	0.611242	−	1.05870i	0.991031	−	0.133629i	$-0.0426631\pi$
$198$		0			0
$199$	−1648.60	−	1383.34i	−0.587268	−	0.492776i	0.300057	−	0.953921i	$-0.402994\pi$
$199$	−1648.60	−	1383.34i	−0.587268	−	0.492776i	−0.887325	+	0.461145i	$0.847439\pi$
$200$	−452.545	−	379.730i	−0.159999	−	0.134255i
$201$		0			0
$202$	3207.73	−	5555.96i	1.11730	−	1.93523i
$203$	−400.994	+	145.950i	−0.138642	+	0.0504615i
$204$		0			0
$205$	−524.133	+	2972.51i	−0.178571	+	1.01273i
$206$	−3471.20	−	1263.42i	−1.17403	−	0.427312i
$207$		0			0
$208$	−5678.26			−1.89287
$209$	−160.632	+	2645.33i	−0.0531634	+	0.875509i
$210$		0			0
$211$	−336.854	+	282.654i	−0.109905	+	0.0922214i	−0.696084	−	0.717960i	$-0.745076\pi$
$211$	−336.854	+	282.654i	−0.109905	+	0.0922214i	0.586179	+	0.810182i	$0.300632\pi$
$212$	1440.33	+	524.236i	0.466613	+	0.169833i
$213$		0			0
$214$	−257.974	−	1463.05i	−0.0824054	−	0.467344i
$215$	3029.03	−	1102.48i	0.960829	−	0.349713i
$216$		0			0
$217$	−1376.74	−	2384.58i	−0.430688	−	0.745973i
$218$	226.738	+	190.255i	0.0704431	+	0.0591088i
$219$		0			0
$220$	−498.598	−	863.597i	−0.152798	−	0.264653i
$221$	−2829.72	+	4901.22i	−0.861301	+	1.49182i
$222$		0			0
$223$	714.755	+	4053.58i	0.214635	+	1.21725i	0.881539	+	0.472111i	$0.156508\pi$
$223$	714.755	+	4053.58i	0.214635	+	1.21725i	−0.666905	+	0.745143i	$0.732381\pi$
$224$	−503.748	+	2856.89i	−0.150259	+	0.852162i
$225$		0			0
$226$	3487.94	−	2926.73i	1.02661	−	0.861431i
$227$	−402.574			−0.117708			−0.0588541	−	0.998267i	$-0.518745\pi$
$227$	−402.574			−0.117708			−0.0588541	+	0.998267i	$0.518745\pi$
$228$		0			0
$229$	6101.41			1.76067			0.880334	−	0.474355i	$-0.157319\pi$
$229$	6101.41			1.76067			0.880334	+	0.474355i	$0.157319\pi$
$230$	−2181.44	+	1830.45i	−0.625392	+	0.524766i
$231$		0			0
$232$	−57.0410	+	323.495i	−0.0161419	+	0.0915453i
$233$	−796.766	−	4518.68i	−0.224025	−	1.27051i	−0.864540	−	0.502564i	$-0.832390\pi$
$233$	−796.766	−	4518.68i	−0.224025	−	1.27051i	0.640515	−	0.767946i	$-0.278721\pi$
$234$		0			0
$235$	1421.49	−	2462.10i	0.394587	−	0.683445i
$236$	499.665	+	865.445i	0.137820	+	0.238710i
$237$		0			0
$238$	4173.31	+	3501.82i	1.13662	+	0.953737i
$239$	−1360.96	−	2357.26i	−0.368341	−	0.637985i	0.620965	−	0.783838i	$-0.286741\pi$
$239$	−1360.96	−	2357.26i	−0.368341	−	0.637985i	−0.989306	+	0.145853i	$0.953407\pi$
$240$		0			0
$241$	−3845.79	+	1399.75i	−1.02792	+	0.374133i	−0.800289	−	0.599614i	$-0.795321\pi$
$241$	−3845.79	+	1399.75i	−1.02792	+	0.374133i	−0.227632	+	0.973747i	$0.573098\pi$
$242$	179.472	+	1017.83i	0.0476730	+	0.270367i
$243$		0			0
$244$	−120.236	−	43.7623i	−0.0315464	−	0.0114819i
$245$	526.515	−	441.799i	0.137297	−	0.115206i
$246$		0			0
$247$	5748.47	+	1377.42i	1.48084	+	0.354831i
$248$	−2119.56			−0.542711
$249$		0			0
$250$	−4808.86	−	1750.28i	−1.21656	−	0.442790i
$251$	−328.294	+	1861.85i	−0.0825567	+	0.468203i	0.915300	+	0.402772i	$0.131953\pi$
$251$	−328.294	+	1861.85i	−0.0825567	+	0.468203i	−0.997857	+	0.0654306i	$0.979158\pi$
$252$		0			0
$253$	−2720.81	+	990.292i	−0.676109	+	0.246084i
$254$	−3919.61	+	6788.96i	−0.968261	+	1.67708i
$255$		0			0
$256$	3335.82	+	2799.08i	0.814409	+	0.683370i
$257$	3091.76	+	2594.30i	0.750424	+	0.629681i	0.935615	−	0.353022i	$-0.114846\pi$
$257$	3091.76	+	2594.30i	0.750424	+	0.629681i	−0.185191	+	0.982703i	$0.559290\pi$
$258$		0			0
$259$	2399.32	−	4155.75i	0.575625	−	0.997011i
$260$	−2090.08	+	760.726i	−0.498542	+	0.181455i
$261$		0			0
$262$	−1079.97	+	6124.82i	−0.254660	+	1.44425i
$263$	2152.56	+	783.469i	0.504688	+	0.183691i	0.581801	−	0.813331i	$-0.302348\pi$
$263$	2152.56	+	783.469i	0.504688	+	0.183691i	−0.0771136	+	0.997022i	$0.524570\pi$
$264$		0			0
$265$	−4298.72			−0.996484
$266$	2266.68	−	5219.26i	0.522478	−	1.20306i
$267$		0			0
$268$	−1660.89	+	1393.65i	−0.378563	+	0.317652i
$269$	−5282.24	−	1922.58i	−1.19726	−	0.435769i	−0.334996	−	0.942220i	$-0.608735\pi$
$269$	−5282.24	−	1922.58i	−1.19726	−	0.435769i	−0.862269	+	0.506451i	$0.830957\pi$
$270$		0			0
$271$	1496.50	+	8487.07i	0.335446	+	1.90241i	0.422784	+	0.906230i	$0.361053\pi$
$271$	1496.50	+	8487.07i	0.335446	+	1.90241i	−0.0873382	+	0.996179i	$0.527836\pi$
$272$	5927.68	−	2157.50i	1.32139	−	0.480947i
$273$		0			0
$274$	895.053	+	1550.28i	0.197343	+	0.341809i
$275$	−921.781	−	773.466i	−0.202129	−	0.169606i
$276$		0			0
$277$	465.386	+	806.072i	0.100947	+	0.174845i	0.912075	−	0.410023i	$-0.134479\pi$
$277$	465.386	+	806.072i	0.100947	+	0.174845i	−0.811128	+	0.584869i	$0.801146\pi$
$278$	2630.11	−	4555.48i	0.567422	−	0.982804i
$279$		0			0
$280$	−520.498	−	2951.89i	−0.111092	−	0.630033i
$281$	−1381.22	+	7833.27i	−0.293226	+	1.66297i	0.381100	+	0.924534i	$0.375545\pi$
$281$	−1381.22	+	7833.27i	−0.293226	+	1.66297i	−0.674326	+	0.738434i	$0.735566\pi$
$282$		0			0
$283$	3575.95	−	3000.58i	0.751125	−	0.630269i	−0.184675	−	0.982800i	$-0.559123\pi$
$283$	3575.95	−	3000.58i	0.751125	−	0.630269i	0.935800	+	0.352531i	$0.114679\pi$
$284$	−2098.15			−0.438389
$285$		0			0
$286$	−7689.06			−1.58973
$287$	5047.73	−	4235.55i	1.03818	−	0.871138i
$288$		0			0
$289$	238.627	−	1353.32i	0.0485704	−	0.275457i
$290$	114.270	+	648.056i	0.0231385	+	0.131225i
$291$		0			0
$292$	−622.520	+	1078.24i	−0.124761	+	0.216092i
$293$	−2039.87	−	3533.16i	−0.406725	−	0.704469i	0.587795	−	0.809010i	$-0.299996\pi$
$293$	−2039.87	−	3533.16i	−0.406725	−	0.704469i	−0.994521	+	0.104541i	$0.966663\pi$
$294$		0			0
$295$	−2146.97	−	1801.52i	−0.423734	−	0.355555i
$296$	−1846.94	−	3199.00i	−0.362674	−	0.628169i
$297$		0			0
$298$	7699.16	−	2802.26i	1.49664	−	0.544734i
$299$	1121.44	+	6360.03i	0.216906	+	1.23013i
$300$		0			0
$301$	−6612.63	−	2406.80i	−1.26627	−	0.460883i
$302$	9088.85	−	7626.45i	1.73180	−	1.45316i
$303$		0			0
$304$	−3921.44	−	5294.67i	−0.739836	−	0.998915i
$305$	358.849			0.0673693
$306$		0			0
$307$	−2693.68	−	980.418i	−0.500770	−	0.182265i	0.0792706	−	0.996853i	$-0.474741\pi$
$307$	−2693.68	−	980.418i	−0.500770	−	0.182265i	−0.580040	+	0.814588i	$0.696963\pi$
$308$	−378.026	+	2143.89i	−0.0699351	+	0.396622i
$309$		0			0
$310$	−3990.04	+	1452.25i	−0.731029	+	0.266073i
$311$	−1373.32	+	2378.67i	−0.250399	+	0.433704i	−0.963636	−	0.267220i	$-0.913895\pi$
$311$	−1373.32	+	2378.67i	−0.250399	+	0.433704i	0.713237	+	0.700923i	$0.247228\pi$
$312$		0			0
$313$	488.741	+	410.103i	0.0882597	+	0.0740587i	0.685850	−	0.727743i	$-0.259431\pi$
$313$	488.741	+	410.103i	0.0882597	+	0.0740587i	−0.597590	+	0.801802i	$0.703875\pi$
$314$	279.950	+	234.906i	0.0503136	+	0.0422181i
$315$		0			0
$316$	−1707.24	+	2957.03i	−0.303924	+	0.526412i
$317$	8180.00	−	2977.28i	1.44932	−	0.527510i	0.506920	−	0.861993i	$-0.330784\pi$
$317$	8180.00	−	2977.28i	1.44932	−	0.527510i	0.942402	+	0.334483i	$0.108562\pi$
$318$		0			0
$319$	−116.186	+	658.922i	−0.0203923	+	0.115651i
$320$	−1387.31	−	504.938i	−0.242352	−	0.0882090i
$321$		0			0
$322$	6216.71			1.07591
$323$	−6524.34	+	746.250i	−1.12391	+	0.128553i
$324$		0			0
$325$	−2056.00	+	1725.19i	−0.350912	+	0.294451i
$326$	−8309.83	−	3024.53i	−1.41178	−	0.513844i
$327$		0			0
$328$	−880.799	−	4995.26i	−0.148274	−	0.840906i
$329$	−5832.18	+	2122.74i	−0.977321	+	0.355716i
$330$		0			0
$331$	−1243.66	−	2154.08i	−0.206519	−	0.357701i	0.744097	−	0.668072i	$-0.232880\pi$
$331$	−1243.66	−	2154.08i	−0.206519	−	0.357701i	−0.950616	+	0.310371i	$0.899547\pi$
$332$	−2409.02	−	2021.41i	−0.398229	−	0.334154i
$333$		0			0
$334$	250.553	+	433.971i	0.0410469	+	0.0710954i
$335$	3040.33	−	5266.00i	0.495853	−	0.858842i
$336$		0			0
$337$	685.996	+	3890.48i	0.110886	+	0.628866i	0.988705	+	0.149874i	$0.0478867\pi$
$337$	685.996	+	3890.48i	0.110886	+	0.628866i	−0.877819	+	0.478992i	$0.841002\pi$
$338$	−1693.76	+	9605.79i	−0.272569	+	1.54582i
$339$		0			0
$340$	1892.84	−	1588.28i	0.301923	−	0.253343i
$341$	−4317.30			−0.685616
$342$		0			0
$343$	5499.76			0.865770
$344$	−4149.61	+	3481.93i	−0.650383	+	0.545736i
$345$		0			0
$346$	194.863	−	1105.12i	0.0302772	−	0.171711i
$347$	515.644	+	2924.36i	0.0797730	+	0.452415i	0.998363	+	0.0572025i	$0.0182181\pi$
$347$	515.644	+	2924.36i	0.0797730	+	0.452415i	−0.918590	+	0.395213i	$0.870671\pi$
$348$		0			0
$349$	3131.99	−	5424.77i	0.480377	−	0.832037i	−0.519370	−	0.854550i	$-0.673833\pi$
$349$	3131.99	−	5424.77i	0.480377	−	0.832037i	0.999747	+	0.0225124i	$0.00716653\pi$
$350$	1291.79	+	2237.45i	0.197284	+	0.341705i
$351$		0			0
$352$	3484.39	+	2923.75i	0.527610	+	0.442718i
$353$	−888.496	−	1538.92i	−0.133966	−	0.232035i	0.791236	−	0.611511i	$-0.209438\pi$
$353$	−888.496	−	1538.92i	−0.133966	−	0.232035i	−0.925202	+	0.379475i	$0.876105\pi$
$354$		0			0
$355$	5529.51	−	2012.58i	0.826693	−	0.300892i
$356$	−438.835	−	2488.76i	−0.0653320	−	0.370516i
$357$		0			0
$358$	−10434.9	−	3797.99i	−1.54051	−	0.560699i
$359$	1900.39	−	1594.62i	0.279384	−	0.234431i	−0.492318	−	0.870415i	$-0.663850\pi$
$359$	1900.39	−	1594.62i	0.279384	−	0.234431i	0.771702	+	0.635985i	$0.219406\pi$
$360$		0			0
$361$	2685.56	+	6311.39i	0.391538	+	0.920162i
$362$	11211.2			1.62776
$363$		0			0
$364$	4562.81	+	1660.73i	0.657023	+	0.239137i
$365$	606.341	−	3438.73i	0.0869517	−	0.493127i
$366$		0			0
$367$	11791.5	−	4291.76i	1.67714	−	0.610430i	0.684229	−	0.729267i	$-0.260139\pi$
$367$	11791.5	−	4291.76i	1.67714	−	0.610430i	0.992914	+	0.118837i	$0.0379166\pi$
$368$	3599.18	−	6233.97i	0.509838	−	0.883065i
$369$		0			0
$370$	−5668.68	−	4756.59i	−0.796488	−	0.668333i
$371$	7188.92	+	6032.22i	1.00601	+	0.844143i
$372$		0			0
$373$	1368.95	−	2371.10i	0.190032	−	0.329144i	−0.755229	−	0.655461i	$-0.772474\pi$
$373$	1368.95	−	2371.10i	0.190032	−	0.329144i	0.945260	+	0.326317i	$0.105808\pi$
$374$	8026.80	−	2921.52i	1.10978	−	0.403925i
$375$		0			0
$376$	−829.622	+	4705.02i	−0.113788	+	0.645326i
$377$	1402.38	+	510.423i	0.191581	+	0.0697298i
$378$		0			0
$379$	−5003.80			−0.678174			−0.339087	−	0.940755i	$-0.610118\pi$
$379$	−5003.80			−0.678174			−0.339087	+	0.940755i	$0.610118\pi$
$380$	−2152.75	−	1423.52i	−0.290616	−	0.192171i
$381$		0			0
$382$	73.7299	−	61.8667i	0.00987525	−	0.00828632i
$383$	8915.13	+	3244.84i	1.18940	+	0.432908i	0.859515	−	0.511111i	$-0.170766\pi$
$383$	8915.13	+	3244.84i	1.18940	+	0.432908i	0.329890	+	0.944019i	$0.392988\pi$
$384$		0			0
$385$	−1060.19	−	6012.65i	−0.140344	−	0.795930i
$386$	−8097.90	+	2947.40i	−1.06780	+	0.388649i
$387$		0			0
$388$	−1774.92	−	3074.25i	−0.232237	−	0.402246i
$389$	1997.78	+	1676.34i	0.260389	+	0.218492i	0.763631	−	0.645653i	$-0.223415\pi$
$389$	1997.78	+	1676.34i	0.260389	+	0.218492i	−0.503241	+	0.864146i	$0.667859\pi$
$390$		0			0
$391$	−3587.25	−	6213.30i	−0.463977	−	0.803631i
$392$	−577.513	+	1000.28i	−0.0744103	+	0.128882i
$393$		0			0
$394$	1976.02	+	11206.6i	0.252667	+	1.43294i
$395$	1662.88	−	9430.64i	0.211819	−	1.20128i
$396$		0			0
$397$	−3869.15	+	3246.61i	−0.489137	+	0.410434i	−0.853717	−	0.520738i	$-0.825657\pi$
$397$	−3869.15	+	3246.61i	−0.489137	+	0.410434i	0.364580	+	0.931172i	$0.381213\pi$
$398$	7245.05			0.912467
$399$		0			0
$400$	2991.55			0.373943
$401$	3128.55	−	2625.17i	0.389607	−	0.326919i	−0.426853	−	0.904321i	$-0.640378\pi$
$401$	3128.55	−	2625.17i	0.389607	−	0.326919i	0.816460	+	0.577402i	$0.195933\pi$
$402$		0			0
$403$	−1672.16	+	9483.31i	−0.206691	+	1.17220i
$404$	1103.07	+	6255.82i	0.135841	+	0.770392i
$405$		0			0
$406$	718.293	−	1244.12i	0.0878037	−	0.152080i
$407$	−3762.01	−	6515.99i	−0.458171	−	0.793576i
$408$		0			0
$409$	10307.6	+	8649.14i	1.24616	+	1.04565i	0.997017	+	0.0771884i	$0.0245943\pi$
$409$	10307.6	+	8649.14i	1.24616	+	1.04565i	0.249146	+	0.968466i	$0.419850\pi$
$410$	−5080.67	−	8799.98i	−0.611992	−	1.06000i
$411$		0			0
$412$	3437.04	−	1250.98i	0.410997	−	0.149591i
$413$	1062.46	+	6025.52i	0.126587	+	0.717909i
$414$		0			0
$415$	8287.74	+	3016.49i	0.980311	+	0.356804i
$416$	7771.83	−	6521.34i	0.915974	−	0.768594i
$417$		0			0
$418$	−5310.11	−	7169.63i	−0.621354	−	0.838943i
$419$	−2157.04			−0.251500			−0.125750	−	0.992062i	$-0.540134\pi$
$419$	−2157.04			−0.251500			−0.125750	+	0.992062i	$0.540134\pi$
$420$		0			0
$421$	−8354.35	−	3040.74i	−0.967141	−	0.352010i	−0.190313	−	0.981724i	$-0.560950\pi$
$421$	−8354.35	−	3040.74i	−0.967141	−	0.352010i	−0.776828	+	0.629713i	$0.783172\pi$
$422$	257.062	−	1457.87i	0.0296530	−	0.168171i
$423$		0			0
$424$	6788.28	−	2470.73i	0.777519	−	0.282994i
$425$	1490.81	−	2582.17i	0.170153	−	0.294714i
$426$		0			0
$427$	−600.118	−	503.559i	−0.0680134	−	0.0570700i
$428$	1126.85	+	945.536i	0.127262	+	0.106786i
$429$		0			0
$430$	−5425.85	+	9397.84i	−0.608506	+	1.05396i
$431$	1224.43	−	445.657i	0.136842	−	0.0498063i	−0.272691	−	0.962102i	$-0.587914\pi$
$431$	1224.43	−	445.657i	0.136842	−	0.0498063i	0.409533	+	0.912295i	$0.365692\pi$
$432$		0			0
$433$	−1932.23	+	10958.2i	−0.214451	+	1.21621i	0.667406	+	0.744694i	$0.267405\pi$
$433$	−1932.23	+	10958.2i	−0.214451	+	1.21621i	−0.881857	+	0.471517i	$0.843707\pi$
$434$	8710.59	+	3170.39i	0.963414	+	0.350654i
$435$		0			0
$436$	−293.072			−0.0321917
$437$	−5155.91	+	5437.96i	−0.564395	+	0.595270i
$438$		0			0
$439$	222.645	−	186.821i	0.0242056	−	0.0203109i	−0.630605	−	0.776104i	$-0.717193\pi$
$439$	222.645	−	186.821i	0.0242056	−	0.0203109i	0.654810	+	0.755793i	$0.272749\pi$
$440$	−4416.37	−	1607.43i	−0.478504	−	0.174161i
$441$		0			0
$442$	−3308.44	−	18763.1i	−0.356033	−	2.01916i
$443$	−7162.28	+	2606.86i	−0.768150	+	0.279584i	−0.696222	−	0.717826i	$-0.745137\pi$
$443$	−7162.28	+	2606.86i	−0.768150	+	0.279584i	−0.0719275	+	0.997410i	$0.522915\pi$
$444$		0			0
$445$	3543.76	+	6137.98i	0.377507	+	0.653861i
$446$	−10615.0	−	8907.05i	−1.12699	−	0.945653i
$447$		0			0
$448$	1611.49	+	2791.18i	0.169946	+	0.294354i
$449$	9281.59	−	16076.2i	0.975557	−	1.68972i	0.297475	−	0.954730i	$-0.403856\pi$
$449$	9281.59	−	16076.2i	0.975557	−	1.68972i	0.678083	−	0.734985i	$-0.262811\pi$
$450$		0			0
$451$	−1794.08	−	10174.8i	−0.187317	−	1.06233i
$452$	−782.871	+	4439.88i	−0.0814671	+	0.462023i
$453$		0			0
$454$	1038.20	−	871.149i	0.107324	−	0.0900552i
$455$	−13617.9			−1.40312
$456$		0			0
$457$	6177.29			0.632301			0.316150	−	0.948709i	$-0.397610\pi$
$457$	6177.29			0.632301			0.316150	+	0.948709i	$0.397610\pi$
$458$	−15734.9	+	13203.2i	−1.60534	+	1.34704i
$459$		0			0
$460$	489.626	−	2776.81i	0.0496281	−	0.281455i
$461$	1598.62	+	9066.20i	0.161508	+	0.915955i	0.952593	+	0.304249i	$0.0984054\pi$
$461$	1598.62	+	9066.20i	0.161508	+	0.915955i	−0.791085	+	0.611706i	$0.790484\pi$
$462$		0			0
$463$	1590.90	−	2755.52i	0.159688	−	0.276587i	−0.775068	−	0.631877i	$-0.782285\pi$
$463$	1590.90	−	2755.52i	0.159688	−	0.276587i	0.934756	+	0.355290i	$0.115618\pi$
$464$	−831.715	−	1440.57i	−0.0832143	−	0.144131i
$465$		0			0
$466$	11833.0	+	9929.04i	1.17629	+	0.987026i
$467$	3658.43	+	6336.59i	0.362509	+	0.627885i	0.988373	−	0.152048i	$-0.0485867\pi$
$467$	3658.43	+	6336.59i	0.362509	+	0.627885i	−0.625864	+	0.779932i	$0.715253\pi$
$468$		0			0
$469$	−12474.0	+	4540.17i	−1.22814	+	0.447006i
$470$	1661.98	+	9425.53i	0.163109	+	0.925037i
$471$		0			0
$472$	4425.82	+	1610.87i	0.431599	+	0.157089i
$473$	−8452.27	+	7092.29i	−0.821640	+	0.689438i
$474$		0			0
$475$	−3028.54	−	725.684i	−0.292545	−	0.0700982i
$476$	−5394.24			−0.519422
$477$		0			0
$478$	8610.77	+	3134.07i	0.823949	+	0.299893i
$479$	−807.972	+	4582.24i	−0.0770714	+	0.437093i	0.921716	+	0.387865i	$0.126787\pi$
$479$	−807.972	+	4582.24i	−0.0770714	+	0.437093i	−0.998788	+	0.0492284i	$0.984324\pi$
$480$		0			0
$481$	−15770.0	+	5739.81i	−1.49491	+	0.544101i
$482$	6888.89	−	11931.9i	0.650996	−	1.12756i
$483$		0			0
$484$	−783.942	−	657.806i	−0.0736234	−	0.0617774i
$485$	7626.52	+	6399.41i	0.714026	+	0.599139i
$486$		0			0
$487$	−4405.58	+	7630.69i	−0.409930	+	0.710019i	−0.994881	−	0.101049i	$-0.967780\pi$
$487$	−4405.58	+	7630.69i	−0.409930	+	0.710019i	0.584952	+	0.811068i	$0.301113\pi$
$488$	−566.673	+	206.252i	−0.0525658	+	0.0191324i
$489$		0			0
$490$	−401.797	+	2278.70i	−0.0370436	+	0.210084i
$491$	17160.5	+	6245.93i	1.57728	+	0.574083i	0.974610	−	0.223908i	$-0.0718815\pi$
$491$	17160.5	+	6245.93i	1.57728	+	0.574083i	0.602669	+	0.797991i	$0.294104\pi$
$492$		0			0
$493$	−1657.92			−0.151458
$494$	−17805.4	+	8887.17i	−1.62166	+	0.809419i
$495$		0			0
$496$	8222.21	−	6899.25i	0.744331	−	0.624568i
$497$	−12071.4	−	4393.63i	−1.08949	−	0.396542i
$498$		0			0
$499$	−1492.49	−	8464.33i	−0.133894	−	0.759349i	−0.975624	−	0.219451i	$-0.929574\pi$
$499$	−1492.49	−	8464.33i	−0.133894	−	0.759349i	0.841730	−	0.539899i	$-0.181538\pi$
$500$	4761.53	−	1733.06i	0.425884	−	0.155009i
$501$		0			0
$502$	−3182.31	−	5511.92i	−0.282935	−	0.490058i
$503$	−5211.27	−	4372.77i	−0.461946	−	0.387619i	0.381900	−	0.924204i	$-0.375270\pi$
$503$	−5211.27	−	4372.77i	−0.461946	−	0.387619i	−0.843847	+	0.536585i	$0.819714\pi$
$504$		0			0
$505$	−8907.72	−	15428.6i	−0.784927	−	1.35953i
$506$	4873.73	−	8441.55i	0.428189	−	0.741645i
$507$		0			0
$508$	−1347.87	−	7644.14i	−0.117720	−	0.667626i
$509$	−1667.29	+	9455.70i	−0.145190	+	0.823412i	0.822025	+	0.569451i	$0.192844\pi$
$509$	−1667.29	+	9455.70i	−0.145190	+	0.823412i	−0.967215	+	0.253960i	$0.918267\pi$
$510$		0			0
$511$	−5839.44	+	4899.87i	−0.505522	+	0.424183i
$512$	−1309.55			−0.113036
$513$		0			0
$514$	−13587.3			−1.16597
$515$	−7858.08	+	6593.71i	−0.672366	+	0.564182i
$516$		0			0
$517$	−1689.84	+	9583.57i	−0.143751	+	0.815251i
$518$	2805.23	+	15909.3i	0.237944	+	1.34945i
$519$		0			0
$520$	−5241.37	+	9078.33i	−0.442018	+	0.765598i
$521$	5912.44	+	10240.6i	0.497176	+	0.861134i	0.999995	−	0.00325784i	$-0.00103700\pi$
$521$	5912.44	+	10240.6i	0.497176	+	0.861134i	−0.502819	+	0.864392i	$0.667704\pi$
$522$		0			0
$523$	−4961.93	−	4163.56i	−0.414857	−	0.348106i	0.411346	−	0.911479i	$-0.365059\pi$
$523$	−4961.93	−	4163.56i	−0.414857	−	0.348106i	−0.826203	+	0.563373i	$0.809503\pi$
$524$	−3079.05	−	5333.06i	−0.256696	−	0.444611i
$525$		0			0
$526$	−7246.62	+	2637.56i	−0.600699	+	0.218637i
$527$	−1857.64	−	10535.2i	−0.153549	−	0.870819i
$528$		0			0
$529$	3739.96	+	1361.23i	0.307385	+	0.111879i
$530$	11085.9	−	9302.21i	0.908571	−	0.762381i
$531$		0			0
$532$	1602.57	+	5401.48i	0.130602	+	0.440196i
$533$	−23044.6			−1.87274
$534$		0			0
$535$	−3876.68	−	1411.00i	−0.313278	−	0.114024i
$536$	−1774.42	+	10063.2i	−0.142991	+	0.810941i
$537$		0			0
$538$	17782.7	−	6472.38i	1.42503	−	0.518669i
$539$	−1176.33	+	2037.46i	−0.0940037	+	0.162819i
$540$		0			0
$541$	−3588.58	−	3011.18i	−0.285185	−	0.239299i	0.488961	−	0.872306i	$-0.337376\pi$
$541$	−3588.58	−	3011.18i	−0.285185	−	0.239299i	−0.774146	+	0.633007i	$0.781820\pi$
$542$	−22224.9	−	18648.9i	−1.76133	−	1.47793i
$543$		0			0
$544$	−5635.38	+	9760.76i	−0.444145	+	0.769281i
$545$	772.366	−	281.118i	0.0607056	−	0.0220950i
$546$		0			0
$547$	3666.28	−	20792.5i	0.286579	−	1.62527i	−0.413010	−	0.910726i	$-0.635523\pi$
$547$	3666.28	−	20792.5i	0.286579	−	1.62527i	0.699589	−	0.714545i	$-0.253366\pi$
$548$	−1665.59	−	606.226i	−0.129837	−	0.0472567i
$549$		0			0
$550$	4050.92			0.314058
$551$	492.547	+	1660.14i	0.0380821	+	0.128356i
$552$		0			0
$553$	−16014.5	+	13437.8i	−1.23148	+	1.03333i
$554$	−2944.48	−	1071.70i	−0.225810	−	0.0821882i
$555$		0			0
$556$	904.437	+	5129.32i	0.0689868	+	0.391244i
$557$	1170.32	−	425.962i	0.0890272	−	0.0324032i	−0.297123	−	0.954839i	$-0.596027\pi$
$557$	1170.32	−	425.962i	0.0890272	−	0.0324032i	0.386150	+	0.922436i	$0.373805\pi$
$558$		0			0
$559$	12305.1	+	21313.1i	0.931038	+	1.61261i
$560$	11627.6	+	9756.73i	0.877422	+	0.736245i
$561$		0			0
$562$	−13388.8	−	23190.1i	−1.00493	−	1.74059i
$563$	8144.70	−	14107.0i	0.609695	−	1.05602i	−0.381596	−	0.924329i	$-0.624625\pi$
$563$	8144.70	−	14107.0i	0.609695	−	1.05602i	0.991291	−	0.131693i	$-0.0420413\pi$
$564$		0			0
$565$	−2195.60	−	12451.9i	−0.163486	−	0.927177i
$566$	−2728.90	+	15476.4i	−0.202658	+	1.14933i
$567$		0			0
$568$	−7575.13	+	6356.29i	−0.559587	+	0.469549i
$569$	−14710.3			−1.08381			−0.541905	−	0.840440i	$-0.682297\pi$
$569$	−14710.3			−1.08381			−0.541905	+	0.840440i	$0.682297\pi$
$570$		0			0
$571$	6921.05			0.507245			0.253623	−	0.967303i	$-0.418378\pi$
$571$	6921.05			0.507245			0.253623	+	0.967303i	$0.418378\pi$
$572$	5832.19	−	4893.79i	0.426322	−	0.357726i
$573$		0			0
$574$	−3852.05	+	21846.1i	−0.280107	+	1.58857i
$575$	−590.824	−	3350.73i	−0.0428506	−	0.243018i
$576$		0			0
$577$	9724.56	−	16843.4i	0.701627	−	1.21525i	−0.266269	−	0.963899i	$-0.585791\pi$
$577$	9724.56	−	16843.4i	0.701627	−	1.21525i	0.967895	−	0.251354i	$-0.0808758\pi$
$578$	2313.12	+	4006.44i	0.166459	+	0.288315i
$579$		0			0
$580$	−499.137	−	418.825i	−0.0357337	−	0.0299841i
$581$	−9627.00	−	16674.4i	−0.687427	−	1.19066i
$582$		0			0
$583$	13826.9	−	5032.59i	0.982252	−	0.357511i
$584$	1018.95	+	5778.74i	0.0721993	+	0.409462i
$585$		0			0
$586$	12906.2	+	4697.47i	0.909812	+	0.331144i
$587$	15919.8	−	13358.3i	1.11939	−	0.939278i	0.120814	−	0.992675i	$-0.461449\pi$
$587$	15919.8	−	13358.3i	1.11939	−	0.939278i	0.998573	+	0.0533972i	$0.0170049\pi$
$588$		0			0
$589$	−9997.48	+	4990.03i	−0.699387	+	0.349084i
$590$	9435.22			0.658376
$591$		0			0
$592$	17577.5	+	6397.69i	1.22032	+	0.444161i
$593$	1666.18	−	9449.35i	0.115382	−	0.654365i	−0.871178	−	0.490967i	$-0.836644\pi$
$593$	1666.18	−	9449.35i	0.115382	−	0.654365i	0.986560	−	0.163398i	$-0.0522453\pi$
$594$		0			0
$595$	14216.1	−	5174.23i	0.979501	−	0.356509i
$596$	−4056.32	+	7025.74i	−0.278780	+	0.482862i
$597$		0			0
$598$	−16654.9	−	13975.1i	−1.13891	−	0.955659i
$599$	−1452.22	−	1218.56i	−0.0990585	−	0.0831199i	0.591913	−	0.806002i	$-0.298373\pi$
$599$	−1452.22	−	1218.56i	−0.0990585	−	0.0831199i	−0.690972	+	0.722882i	$0.742817\pi$
$600$		0			0
$601$	7235.61	−	12532.4i	0.491093	−	0.850597i	−0.508855	−	0.860852i	$-0.669931\pi$
$601$	7235.61	−	12532.4i	0.491093	−	0.850597i	0.999947	+	0.0102551i	$0.00326435\pi$
$602$	22261.5	−	8102.52i	1.50716	−	0.548561i
$603$		0			0
$604$	−2040.00	+	11569.4i	−0.137428	+	0.779391i
$605$	2696.99	+	981.625i	0.181237	+	0.0659648i
$606$		0			0
$607$	3966.32			0.265219			0.132609	−	0.991168i	$-0.457664\pi$
$607$	3966.32			0.265219			0.132609	+	0.991168i	$0.457664\pi$
$608$	11448.1	+	2743.13i	0.763619	+	0.182975i
$609$		0			0
$610$	−925.434	+	776.531i	−0.0614258	+	0.0515424i
$611$	20396.6	+	7423.75i	1.35050	+	0.491543i
$612$		0			0
$613$	3198.09	+	18137.3i	0.210717	+	1.19504i	0.888186	+	0.459485i	$0.151966\pi$
$613$	3198.09	+	18137.3i	0.210717	+	1.19504i	−0.677469	+	0.735552i	$0.736923\pi$
$614$	9068.28	−	3300.58i	0.596036	−	0.216939i
$615$		0			0
$616$	5130.03	+	8885.47i	0.335543	+	0.581178i
$617$	−4888.82	−	4102.20i	−0.318989	−	0.267664i	0.469206	−	0.883089i	$-0.344540\pi$
$617$	−4888.82	−	4102.20i	−0.318989	−	0.267664i	−0.788196	+	0.615425i	$0.788984\pi$
$618$		0			0
$619$	−655.623	−	1135.57i	−0.0425714	−	0.0737359i	0.843955	−	0.536415i	$-0.180222\pi$
$619$	−655.623	−	1135.57i	−0.0425714	−	0.0737359i	−0.886526	+	0.462679i	$0.846888\pi$
$620$	2102.16	−	3641.04i	0.136169	−	0.235851i
$621$		0			0
$622$	−1605.66	−	9106.13i	−0.103506	−	0.587014i
$623$	2686.80	−	15237.6i	0.172784	−	0.979907i
$624$		0			0
$625$	−7285.54	+	6113.29i	−0.466274	+	0.391251i
$626$	−2147.85			−0.137133
$627$		0			0
$628$	−361.851			−0.0229927
$629$	14281.8	−	11983.9i	0.905331	−	0.759663i
$630$		0			0
$631$	−2554.55	+	14487.6i	−0.161165	+	0.914011i	0.791766	+	0.610824i	$0.209162\pi$
$631$	−2554.55	+	14487.6i	−0.161165	+	0.914011i	−0.952931	+	0.303187i	$0.901949\pi$
$632$	2794.44	+	15848.1i	0.175881	+	0.997471i
$633$		0			0
$634$	−14652.7	+	25379.2i	−0.917875	+	1.58981i
$635$	10884.6	+	18852.6i	0.680221	+	1.17818i
$636$		0			0
$637$	4019.83	+	3373.04i	0.250034	+	0.209803i
$638$	−1126.24	−	1950.71i	−0.0698878	−	0.121049i
$639$		0			0
$640$	14660.0	−	5335.79i	0.905447	−	0.329556i
$641$	−3473.47	−	19699.0i	−0.214031	−	1.21383i	−0.882580	−	0.470162i	$-0.844196\pi$
$641$	−3473.47	−	19699.0i	−0.214031	−	1.21383i	0.668549	−	0.743668i	$-0.266916\pi$
$642$		0			0
$643$	−6343.53	−	2308.86i	−0.389058	−	0.141606i	0.140082	−	0.990140i	$-0.455263\pi$
$643$	−6343.53	−	2308.86i	−0.389058	−	0.141606i	−0.529140	+	0.848534i	$0.677485\pi$
$644$	−4715.41	+	3956.70i	−0.288530	+	0.242105i
$645$		0			0
$646$	15210.7	−	16042.8i	0.926406	−	0.977085i
$647$	−10225.5			−0.621338			−0.310669	−	0.950518i	$-0.600553\pi$
$647$	−10225.5			−0.621338			−0.310669	+	0.950518i	$0.600553\pi$
$648$		0			0
$649$	9014.87	+	3281.14i	0.545246	+	0.198453i
$650$	1568.99	−	8898.18i	0.0946781	−	0.536946i
$651$		0			0
$652$	8228.04	−	2994.76i	0.494225	−	0.179883i
$653$	−14153.5	+	24514.5i	−0.848190	+	1.46911i	0.0346315	+	0.999400i	$0.488974\pi$
$653$	−14153.5	+	24514.5i	−0.848190	+	1.46911i	−0.882822	+	0.469708i	$0.844359\pi$
$654$		0			0
$655$	13230.1	+	11101.4i	0.789227	+	0.662240i
$656$	19676.5	+	16510.6i	1.17110	+	0.982667i
$657$		0			0
$658$	10447.1	−	18094.9i	0.618951	−	1.07205i
$659$	13540.6	−	4928.37i	0.800404	−	0.291323i	0.0907499	−	0.995874i	$-0.471074\pi$
$659$	13540.6	−	4928.37i	0.800404	−	0.291323i	0.709654	+	0.704551i	$0.248851\pi$
$660$		0			0
$661$	3595.23	−	20389.6i	0.211556	−	1.19979i	−0.675229	−	0.737608i	$-0.735955\pi$
$661$	3595.23	−	20389.6i	0.211556	−	1.19979i	0.886784	−	0.462183i	$-0.152934\pi$
$662$	7868.59	+	2863.93i	0.461966	+	0.168142i
$663$		0			0
$664$	−14821.3			−0.866230
$665$	−9404.61	−	12698.0i	−0.548414	−	0.740460i
$666$		0			0
$667$	−1449.28	+	1216.09i	−0.0841322	+	0.0705953i
$668$	−466.252	−	169.702i	−0.0270057	−	0.00982928i
$669$		0			0
$670$	3554.67	+	20159.6i	0.204969	+	1.16244i
$671$	−1154.25	+	420.112i	−0.0664072	+	0.0241702i
$672$		0			0
$673$	−8344.80	−	14453.6i	−0.477962	−	0.827854i	0.521719	−	0.853117i	$-0.325291\pi$
$673$	−8344.80	−	14453.6i	−0.477962	−	0.827854i	−0.999681	+	0.0252631i	$0.991958\pi$
$674$	−10187.9	−	8548.67i	−0.582231	−	0.488550i
$675$		0			0
$676$	−4828.99	−	8364.05i	−0.274749	−	0.475879i
$677$	1208.40	−	2093.01i	0.0686004	−	0.118819i	−0.829685	−	0.558232i	$-0.811480\pi$
$677$	1208.40	−	2093.01i	0.0686004	−	0.118819i	0.898285	+	0.439412i	$0.144813\pi$
$678$		0			0
$679$	−3774.10	−	21404.0i	−0.213309	−	1.20973i
$680$	2022.22	−	11468.6i	0.114042	−	0.646766i
$681$		0			0
$682$	11133.9	−	9342.43i	0.625129	−	0.524545i
$683$	13279.3			0.743950			0.371975	−	0.928243i	$-0.378681\pi$
$683$	13279.3			0.743950			0.371975	+	0.928243i	$0.378681\pi$
$684$		0			0
$685$	4971.03			0.277275
$686$	−14183.3	+	11901.2i	−0.789389	+	0.662376i
$687$		0			0
$688$	4763.34	−	27014.2i	0.263954	−	1.49696i
$689$	−5699.10	−	32321.2i	−0.315121	−	1.78714i
$690$		0			0
$691$	9928.26	−	17196.3i	0.546583	−	0.946710i	−0.451922	−	0.892057i	$-0.649262\pi$
$691$	9928.26	−	17196.3i	0.546583	−	0.946710i	0.998505	−	0.0546525i	$-0.0174051\pi$
$692$	555.564	+	962.265i	0.0305193	+	0.0528610i
$693$		0			0
$694$	−7657.97	−	6425.80i	−0.418865	−	0.351470i
$695$	−7303.68	−	12650.3i	−0.398625	−	0.690439i
$696$		0			0
$697$	24056.8	−	8755.97i	1.30734	−	0.475833i
$698$	3661.85	+	20767.4i	0.198572	+	1.12616i
$699$		0			0
$700$	−2403.88	−	874.941i	−0.129797	−	0.0472424i
$701$	1775.43	−	1489.76i	0.0956592	−	0.0802676i	−0.593704	−	0.804684i	$-0.702335\pi$
$701$	1775.43	−	1489.76i	0.0956592	−	0.0802676i	0.689363	+	0.724416i	$0.257890\pi$
$702$		0			0
$703$	−16242.9	−	10740.7i	−0.871426	−	0.576236i
$704$	5053.44			0.270538
$705$		0			0
$706$	5621.48	+	2046.05i	0.299670	+	0.109071i
$707$	−6753.63	+	38301.7i	−0.359259	+	2.03746i
$708$		0			0
$709$	4351.46	−	1583.80i	0.230497	−	0.0838941i	−0.224189	−	0.974546i	$-0.571973\pi$
$709$	4351.46	−	1583.80i	0.230497	−	0.0838941i	0.454687	+	0.890651i	$0.349751\pi$
$710$	−9904.92	+	17155.8i	−0.523556	+	0.906826i
$711$		0			0
$712$	−9123.97	−	7655.92i	−0.480246	−	0.402974i
$713$	−9351.49	−	7846.83i	−0.491186	−	0.412154i
$714$		0			0
$715$	−10676.1	+	18491.5i	−0.558409	+	0.967192i
$716$	10332.2	−	3760.61i	0.539291	−	0.196286i
$717$		0			0
$718$	−1450.24	+	8224.70i	−0.0753793	+	0.427497i
$719$	3484.78	+	1268.36i	0.180751	+	0.0657882i	0.430810	−	0.902442i	$-0.358228\pi$
$719$	3484.78	+	1268.36i	0.180751	+	0.0657882i	−0.250059	+	0.968231i	$0.580450\pi$
$720$		0			0
$721$	22394.1			1.15673
$722$	−20583.3	−	10465.0i	−1.06098	−	0.539428i
$723$		0			0
$724$	−8503.75	+	7135.49i	−0.436519	+	0.366283i
$725$	−738.831	−	268.912i	−0.0378476	−	0.0137754i
$726$		0			0
$727$	6196.95	+	35144.6i	0.316138	+	1.79291i	0.565768	+	0.824565i	$0.308580\pi$
$727$	6196.95	+	35144.6i	0.316138	+	1.79291i	−0.249630	+	0.968341i	$0.580309\pi$
$728$	21504.6	−	7827.04i	1.09480	−	0.398474i
$729$		0			0
$730$	5877.55	+	10180.2i	0.297997	+	0.516146i
$731$	−20943.7	−	17573.8i	−1.05968	−	0.889181i
$732$		0			0
$733$	11376.5	+	19704.7i	0.573261	+	0.992917i	0.996228	+	0.0867718i	$0.0276551\pi$
$733$	11376.5	+	19704.7i	0.573261	+	0.992917i	−0.422968	+	0.906145i	$0.639012\pi$
$734$	−21121.9	+	36584.2i	−1.06216	+	1.83971i
$735$		0			0
$736$	2233.35	+	12666.0i	0.111851	+	0.634340i
$737$	−3614.28	+	20497.6i	−0.180643	+	1.02448i
$738$		0			0
$739$	−23102.6	+	19385.4i	−1.14999	+	0.964957i	−0.999719	−	0.0236875i	$-0.992459\pi$
$739$	−23102.6	+	19385.4i	−1.14999	+	0.964957i	−0.150272	+	0.988645i	$0.548015\pi$
$740$	7327.10			0.363986
$741$		0			0
$742$	−31592.9			−1.56309
$743$	606.273	−	508.724i	0.0299354	−	0.0251188i	−0.627697	−	0.778458i	$-0.716002\pi$
$743$	606.273	−	508.724i	0.0299354	−	0.0251188i	0.657633	+	0.753339i	$0.271558\pi$
$744$		0			0
$745$	3950.90	−	22406.6i	0.194295	−	1.10190i
$746$	1600.55	+	9077.16i	0.0785526	+	0.445494i
$747$		0			0
$748$	−4228.94	+	7324.73i	−0.206718	+	0.358047i
$749$	4503.13	+	7799.66i	0.219681	+	0.380498i
$750$		0			0
$751$	−13341.4	−	11194.8i	−0.648251	−	0.543947i	0.258289	−	0.966068i	$-0.416841\pi$
$751$	−13341.4	−	11194.8i	−0.648251	−	0.543947i	−0.906540	+	0.422121i	$0.861286\pi$
$752$	−12096.7	−	20952.1i	−0.586599	−	1.01602i
$753$		0			0
$754$	−4721.11	+	1718.34i	−0.228027	+	0.0829952i
$755$	−5721.28	−	32447.0i	−0.275786	−	1.56406i
$756$		0			0
$757$	−1712.46	−	623.283i	−0.0822196	−	0.0299255i	0.300583	−	0.953756i	$-0.402819\pi$
$757$	−1712.46	−	623.283i	−0.0822196	−	0.0299255i	−0.382802	+	0.923830i	$0.625041\pi$
$758$	12904.3	−	10828.0i	0.618343	−	0.518852i
$759$		0			0
$760$	−12084.8	+	1382.25i	−0.576790	+	0.0659729i
$761$	33405.5			1.59126			0.795629	−	0.605785i	$-0.207141\pi$
$761$	33405.5			1.59126			0.795629	+	0.605785i	$0.207141\pi$
$762$		0			0
$763$	−1686.14	−	613.705i	−0.0800032	−	0.0291188i
$764$	−16.5487	+	93.8524i	−0.000783653	+	0.00444432i
$765$		0			0
$766$	−30012.9	+	10923.8i	−1.41568	+	0.515265i
$767$	10698.9	−	18531.1i	0.503671	−	0.872383i
$768$		0			0
$769$	−15471.2	−	12981.9i	−0.725495	−	0.608763i	0.203404	−	0.979095i	$-0.434799\pi$
$769$	−15471.2	−	12981.9i	−0.725495	−	0.608763i	−0.928899	+	0.370332i	$0.879244\pi$
$770$	15745.2	+	13211.8i	0.736906	+	0.618338i
$771$		0			0
$772$	4266.40	−	7389.61i	0.198900	−	0.344505i
$773$	−8189.82	+	2980.85i	−0.381070	+	0.138698i	−0.525451	−	0.850824i	$-0.676103\pi$
$773$	−8189.82	+	2980.85i	−0.381070	+	0.138698i	0.144381	+	0.989522i	$0.453881\pi$
$774$		0			0
$775$	880.966	−	4996.21i	0.0408326	−	0.231573i
$776$	−15721.5	−	5722.15i	−0.727279	−	0.264708i
$777$		0			0
$778$	−8779.57			−0.404579
$779$	−15914.7	−	21487.8i	−0.731969	−	0.988294i
$780$		0			0
$781$	−15429.7	+	12947.0i	−0.706935	+	0.593189i
$782$	22696.4	+	8260.81i	1.03788	+	0.377757i
$783$		0			0
$784$	−1015.66	−	5760.12i	−0.0462675	−	0.262396i
$785$	953.630	−	347.093i	0.0433586	−	0.0157812i
$786$		0			0
$787$	−13674.7	−	23685.4i	−0.619380	−	1.07280i	−0.989599	−	0.143853i	$-0.954051\pi$
$787$	−13674.7	−	23685.4i	−0.619380	−	1.07280i	0.370219	−	0.928944i	$-0.379283\pi$
$788$	−8631.38	−	7242.59i	−0.390203	−	0.327420i
$789$		0			0
$790$	16119.0	+	27919.0i	0.725936	+	1.25736i
$791$	−13801.4	+	23904.8i	−0.620382	+	1.07453i
$792$		0			0
$793$	475.751	+	2698.12i	0.0213044	+	0.120823i
$794$	2952.65	−	16745.3i	0.131972	−	0.748449i
$795$		0			0
$796$	−5495.41	+	4611.19i	−0.244698	+	0.205326i
$797$	8187.05			0.363865			0.181932	−	0.983311i	$-0.441765\pi$
$797$	8187.05			0.363865			0.181932	+	0.983311i	$0.441765\pi$
$798$		0			0
$799$	−24113.2			−1.06767
$800$	−4094.53	+	3435.71i	−0.180954	+	0.151839i
$801$		0			0
$802$	−2387.48	+	13540.1i	−0.105118	+	0.596155i
$803$	2075.48	+	11770.6i	0.0912105	+	0.517281i
$804$		0			0
$805$	8631.75	−	14950.6i	0.377925	−	0.654584i
$806$	−16209.1	−	28074.9i	−0.708363	−	1.22692i
$807$		0			0
$808$	22934.3	+	19244.2i	0.998546	+	0.837880i
$809$	11951.7	+	20701.0i	0.519406	+	0.899638i	0.999746	+	0.0225552i	$0.00718016\pi$
$809$	11951.7	+	20701.0i	0.519406	+	0.899638i	−0.480339	+	0.877083i	$0.659487\pi$
$810$		0			0
$811$	4171.58	−	1518.33i	0.180621	−	0.0657408i	−0.250126	−	0.968213i	$-0.580472\pi$
$811$	4171.58	−	1518.33i	0.180621	−	0.0657408i	0.430748	+	0.902472i	$0.358250\pi$
$812$	247.005	+	1400.84i	0.0106751	+	0.0605415i
$813$		0			0
$814$	23802.1	+	8663.25i	1.02489	+	0.373030i
$815$	−18811.7	+	15784.9i	−0.808522	+	0.678431i
$816$		0			0
$817$	−11375.3	+	26192.8i	−0.487113	+	1.12163i
$818$	−45298.6			−1.93622
$819$		0			0
$820$	9454.56	+	3441.18i	0.402643	+	0.146550i
$821$	−5637.50	+	31971.8i	−0.239647	+	1.35910i	0.592956	+	0.805235i	$0.297961\pi$
$821$	−5637.50	+	31971.8i	−0.239647	+	1.35910i	−0.832603	+	0.553870i	$0.813150\pi$
$822$		0			0
$823$	−18245.6	+	6640.84i	−0.772783	+	0.281270i	−0.698160	−	0.715942i	$-0.745998\pi$
$823$	−18245.6	+	6640.84i	−0.772783	+	0.281270i	−0.0746232	+	0.997212i	$0.523775\pi$
$824$	8619.21	−	14928.9i	0.364399	−	0.631157i
$825$		0			0
$826$	−15778.9	−	13240.1i	−0.664671	−	0.557725i
$827$	−16512.1	−	13855.3i	−0.694295	−	0.582582i	0.225849	−	0.974162i	$-0.427484\pi$
$827$	−16512.1	−	13855.3i	−0.694295	−	0.582582i	−0.920144	+	0.391580i	$0.871929\pi$
$828$		0			0
$829$	2793.99	−	4839.32i	0.117056	−	0.202746i	−0.801544	−	0.597936i	$-0.795988\pi$
$829$	2793.99	−	4839.32i	0.117056	−	0.202746i	0.918600	+	0.395190i	$0.129321\pi$
$830$	−27900.7	+	10155.0i	−1.16681	+	0.424682i
$831$		0			0
$832$	1957.28	−	11100.3i	0.0815584	−	0.462540i
$833$	−5478.02	−	1993.84i	−0.227854	−	0.0829320i
$834$		0			0
$835$	1391.55			0.0576725
$836$	8590.93	+	2058.52i	0.355411	+	0.0851620i
$837$		0			0
$838$	5562.78	−	4667.73i	0.229312	−	0.192415i
$839$	−9296.81	−	3383.76i	−0.382553	−	0.139238i	0.143583	−	0.989638i	$-0.454137\pi$
$839$	−9296.81	−	3383.76i	−0.382553	−	0.139238i	−0.526136	+	0.850400i	$0.676360\pi$
$840$		0			0
$841$	−4159.19	−	23587.9i	−0.170535	−	0.967154i
$842$	28125.0	−	10236.7i	1.15113	−	0.418977i
$843$		0			0
$844$	732.895	+	1269.41i	0.0298902	+	0.0517713i
$845$	20749.3	+	17410.7i	0.844732	+	0.708814i
$846$		0			0
$847$	−3132.81	−	5426.19i	−0.127089	−	0.220125i
$848$	−18290.8	+	31680.5i	−0.740693	+	1.28292i
$849$		0			0
$850$	1743.02	+	9885.18i	0.0703356	+	0.398893i
$851$	3694.31	−	20951.5i	0.148813	−	0.843958i
$852$		0			0
$853$	33791.7	−	28354.6i	1.35640	−	1.13815i	0.379319	−	0.925266i	$-0.376158\pi$
$853$	33791.7	−	28354.6i	1.35640	−	1.13815i	0.977077	−	0.212886i	$-0.0682863\pi$
$854$	2637.32			0.105676
$855$		0			0
$856$	6932.81			0.276821
$857$	−10897.9	+	9144.41i	−0.434381	+	0.364489i	−0.833602	−	0.552366i	$-0.813725\pi$
$857$	−10897.9	+	9144.41i	−0.434381	+	0.364489i	0.399221	+	0.916855i	$0.369281\pi$
$858$		0			0
$859$	−3840.54	+	21780.8i	−0.152547	+	0.865135i	0.808448	+	0.588568i	$0.200308\pi$
$859$	−3840.54	+	21780.8i	−0.152547	+	0.865135i	−0.960995	+	0.276567i	$0.910803\pi$
$860$	−1865.83	−	10581.7i	−0.0739817	−	0.419571i
$861$		0			0
$862$	−2193.30	+	3798.91i	−0.0866637	+	0.150106i
$863$	22194.7	+	38442.4i	0.875454	+	1.51633i	0.856278	+	0.516515i	$0.172771\pi$
$863$	22194.7	+	38442.4i	0.875454	+	1.51633i	0.0191765	+	0.999816i	$0.493896\pi$
$864$		0			0
$865$	−2387.16	−	2003.07i	−0.0938335	−	0.0787356i
$866$	−18730.0	−	32441.4i	−0.734957	−	1.27298i
$867$		0			0
$868$	−8624.85	+	3139.19i	−0.337266	+	0.122755i
$869$	5691.95	+	32280.6i	0.222193	+	1.26012i
$870$		0			0
$871$	43624.7	+	15878.1i	1.69709	+	0.617691i
$872$	−1058.10	+	887.851i	−0.0410915	+	0.0344798i
$873$		0			0
$874$	1529.07	−	25181.0i	0.0591778	−	0.974556i
$875$	31023.8			1.19862
$876$		0			0
$877$	−6233.01	−	2268.63i	−0.239993	−	0.0873503i	0.219224	−	0.975675i	$-0.429648\pi$
$877$	−6233.01	−	2268.63i	−0.239993	−	0.0873503i	−0.459217	+	0.888324i	$0.651870\pi$
$878$	−169.906	+	963.586i	−0.00653081	+	0.0370381i
$879$		0			0
$880$	22364.2	−	8139.90i	0.856701	−	0.311814i
$881$	−4501.55	+	7796.91i	−0.172146	+	0.298166i	−0.939170	−	0.343453i	$-0.888404\pi$
$881$	−4501.55	+	7796.91i	−0.172146	+	0.298166i	0.767024	+	0.641619i	$0.221737\pi$
$882$		0			0
$883$	11402.2	+	9567.56i	0.434557	+	0.364637i	0.833668	−	0.552266i	$-0.186237\pi$
$883$	11402.2	+	9567.56i	0.434557	+	0.364637i	−0.399111	+	0.916903i	$0.630681\pi$
$884$	14451.4	+	12126.2i	0.549835	+	0.461367i
$885$		0			0
$886$	12829.7	−	22221.6i	0.486480	−	0.842608i
$887$	−3216.05	+	1170.55i	−0.121741	+	0.0443101i	−0.402172	−	0.915564i	$-0.631745\pi$
$887$	−3216.05	+	1170.55i	−0.121741	+	0.0443101i	0.280431	+	0.959874i	$0.409523\pi$
$888$		0			0
$889$	8252.43	−	46801.8i	0.311336	−	1.76567i
$890$	−22421.3	−	8160.68i	−0.844453	−	0.307356i
$891$		0			0
$892$	13720.5			0.515019
$893$	7163.76	+	24145.6i	0.268450	+	0.904817i
$894$		0			0
$895$	−23622.4	+	19821.6i	−0.882246	+	0.740293i
$896$	−32004.0	−	11648.5i	−1.19328	−	0.434318i
$897$		0			0
$898$	10851.8	+	61543.7i	0.403262	+	2.28701i
$899$	−2650.84	+	964.827i	−0.0983431	+	0.0357940i
$900$		0			0
$901$	18230.1	+	31575.5i	0.674066	+	1.16752i
$902$	26644.4	+	22357.3i	0.983550	+	0.825297i
$903$		0			0
$904$	10624.0	+	18401.3i	0.390873	+	0.677012i
$905$	15566.5	−	26961.9i	0.571765	−	0.990326i
$906$		0			0
$907$	−312.696	−	1773.39i	−0.0114475	−	0.0649221i	0.978549	−	0.206015i	$-0.0660495\pi$
$907$	−312.696	−	1773.39i	−0.0114475	−	0.0649221i	−0.989996	+	0.141093i	$0.954938\pi$
$908$	−233.023	+	1321.54i	−0.00851669	+	0.0483005i
$909$		0			0
$910$	35119.2	−	29468.5i	1.27933	−	1.07348i
$911$	−5096.53			−0.185352			−0.0926759	−	0.995696i	$-0.529542\pi$
$911$	−5096.53			−0.185352			−0.0926759	+	0.995696i	$0.529542\pi$
$912$		0			0
$913$	−30189.2			−1.09432
$914$	−15930.6	+	13367.3i	−0.576517	+	0.483756i
$915$		0			0
$916$	3531.71	−	20029.3i	0.127392	−	0.722475i
$917$	−6547.13	−	37130.6i	−0.235774	−	1.33714i
$918$		0			0
$919$	−14389.8	+	24923.8i	−0.516512	+	0.894624i	0.483305	+	0.875452i	$0.339436\pi$
$919$	−14389.8	+	24923.8i	−0.516512	+	0.894624i	−0.999816	+	0.0191720i	$0.993897\pi$
$920$	−6644.52	−	11508.6i	−0.238112	−	0.412422i
$921$		0			0
$922$	−23741.5	−	19921.5i	−0.848030	−	0.711582i
$923$	22463.0	+	38907.1i	0.801061	+	1.38748i
$924$		0			0
$925$	8308.29	−	3023.97i	0.295324	−	0.107489i
$926$	1860.04	+	10548.8i	0.0660094	+	0.374358i
$927$		0			0
$928$	2792.83	+	1016.51i	0.0987921	+	0.0359574i
$929$	−29737.1	+	24952.4i	−1.05021	+	0.881228i	−0.993115	−	0.117140i	$-0.962627\pi$
$929$	−29737.1	+	24952.4i	−1.05021	+	0.881228i	−0.0570918	+	0.998369i	$0.518183\pi$
$930$		0			0
$931$	−369.057	+	6077.72i	−0.0129918	+	0.213952i
$932$	−15294.8			−0.537552
$933$		0			0
$934$	−23146.8	−	8424.73i	−0.810905	−	0.295145i
$935$	4119.03	−	23360.2i	0.144071	−	0.817070i
$936$		0			0
$937$	−15052.9	+	5478.82i	−0.524822	+	0.191020i	−0.590825	−	0.806800i	$-0.701198\pi$
$937$	−15052.9	+	5478.82i	−0.524822	+	0.191020i	0.0660029	+	0.997819i	$0.478975\pi$
$938$	22344.5	−	38701.8i	0.777796	−	1.34718i
$939$		0			0
$940$	−7259.60	−	6091.53i	−0.251896	−	0.211366i
$941$	28703.7	+	24085.2i	0.994381	+	0.834384i	0.986196	−	0.165582i	$-0.0529503\pi$
$941$	28703.7	+	24085.2i	0.994381	+	0.834384i	0.00818469	+	0.999967i	$0.497395\pi$
$942$		0			0
$943$	14606.9	−	25299.8i	0.504417	−	0.873675i
$944$	−22412.0	+	8157.32i	−0.772722	+	0.281248i
$945$		0			0
$946$	6450.14	−	36580.5i	0.221683	−	1.25723i
$947$	40481.4	+	14734.0i	1.38909	+	0.505588i	0.924921	−	0.380159i	$-0.124131\pi$
$947$	40481.4	+	14734.0i	1.38909	+	0.505588i	0.464170	+	0.885746i	$0.346353\pi$
$948$		0			0
$949$	26659.0			0.911895
$950$	9380.62	−	4682.14i	0.320366	−	0.159904i
$951$		0			0
$952$	−19475.3	+	16341.7i	−0.663022	+	0.556342i
$953$	−16554.0	−	6025.15i	−0.562682	−	0.204799i	0.0449904	−	0.998987i	$-0.485674\pi$
$953$	−16554.0	−	6025.15i	−0.562682	−	0.204799i	−0.607672	+	0.794188i	$0.707896\pi$
$954$		0			0
$955$	−46.4117	−	263.214i	−0.00157262	−	0.00891875i
$956$	−8526.02	+	3103.22i	−0.288443	+	0.104985i
$957$		0			0
$958$	−7832.05	−	13565.5i	−0.264136	−	0.457497i
$959$	−8313.26	−	6975.65i	−0.279926	−	0.234886i
$960$		0			0
$961$	5794.32	+	10036.1i	0.194499	+	0.336882i
$962$	28248.5	−	48927.8i	0.946744	−	1.63981i
$963$		0			0
$964$	2368.94	+	13434.9i	0.0791477	+	0.448869i
$965$	−4155.52	+	23567.1i	−0.138623	+	0.786168i
$966$		0			0
$967$	−16116.2	+	13523.1i	−0.535950	+	0.449715i	−0.870150	−	0.492787i	$-0.835978\pi$
$967$	−16116.2	+	13523.1i	−0.535950	+	0.449715i	0.334200	+	0.942502i	$0.391534\pi$
$968$	−4823.13			−0.160146
$969$		0			0
$970$	−33516.0			−1.10942
$971$	−5294.86	+	4442.91i	−0.174995	+	0.146838i	−0.726078	−	0.687612i	$-0.758659\pi$
$971$	−5294.86	+	4442.91i	−0.174995	+	0.146838i	0.551083	+	0.834450i	$0.314215\pi$
$972$		0			0
$973$	−5537.49	+	31404.6i	−0.182450	+	1.03472i
$974$	−5150.90	−	29212.2i	−0.169451	−	0.961005i
$975$		0			0
$976$	1526.88	−	2644.63i	0.0500761	−	0.0867343i
$977$	−14583.0	−	25258.5i	−0.477535	−	0.827116i	0.522133	−	0.852864i	$-0.325136\pi$
$977$	−14583.0	−	25258.5i	−0.477535	−	0.827116i	−0.999668	+	0.0257484i	$0.991803\pi$
$978$		0			0
$979$	−18584.5	−	15594.2i	−0.606703	−	0.509084i
$980$	−1145.54	−	1984.14i	−0.0373398	−	0.0646744i
$981$		0			0
$982$	−57771.1	+	21027.0i	−1.87734	+	0.683296i
$983$	−4831.04	−	27398.2i	−0.156751	−	0.888980i	−0.957167	−	0.289535i	$-0.906499\pi$
$983$	−4831.04	−	27398.2i	−0.156751	−	0.888980i	0.800416	−	0.599445i	$-0.204612\pi$
$984$		0			0
$985$	29694.5	+	10807.9i	0.960554	+	0.349613i
$986$	4275.59	−	3587.65i	0.138096	−	0.115876i
$987$		0			0
$988$	7849.12	−	18073.4i	0.252747	−	0.581975i
$989$	−31198.5			−1.00309
$990$		0			0
$991$	−36463.0	−	13271.5i	−1.16881	−	0.425411i	−0.316571	−	0.948569i	$-0.602531\pi$
$991$	−36463.0	−	13271.5i	−1.16881	−	0.425411i	−0.852235	+	0.523158i	$0.824754\pi$
$992$	−3330.11	+	18886.0i	−0.106584	+	0.604466i
$993$		0			0
$994$	40638.5	−	14791.2i	1.29675	−	0.471980i
$995$	10059.6	−	17423.7i	0.320513	−	0.555144i
$996$		0			0
$997$	11848.7	+	9942.21i	0.376380	+	0.315820i	0.811279	−	0.584659i	$-0.198772\pi$
$997$	11848.7	+	9942.21i	0.376380	+	0.315820i	−0.434899	+	0.900479i	$0.643216\pi$
$998$	22165.4	+	18598.9i	0.703038	+	0.589919i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.c.82.2		36
3.2	odd	2		57.4.i.b.25.5	yes	36
19.16	even	9	inner	171.4.u.c.73.2		36
57.23	odd	18		1083.4.a.s.1.13		18
57.35	odd	18		57.4.i.b.16.5	✓	36
57.53	even	18		1083.4.a.t.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.4.i.b.16.5	✓	36	57.35	odd	18
57.4.i.b.25.5	yes	36	3.2	odd	2
171.4.u.c.73.2		36	19.16	even	9	inner
171.4.u.c.82.2		36	1.1	even	1	trivial
1083.4.a.s.1.13		18	57.23	odd	18
1083.4.a.t.1.6		18	57.53	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.57889 + 2.16395i) q^{2} +(0.578834 - 3.28273i) q^{4} +(1.62337 + 9.20660i) q^{5} +(10.2044 - 17.6746i) q^{7} +(-7.85512 - 13.6055i) q^{8} +O(q^{10})\)	\(q+(-2.57889 + 2.16395i) q^{2} +(0.578834 - 3.28273i) q^{4} +(1.62337 + 9.20660i) q^{5} +(10.2044 - 17.6746i) q^{7} +(-7.85512 - 13.6055i) q^{8} +(-24.1091 - 20.2299i) q^{10} +(-16.0000 - 27.7127i) q^{11} +(-67.0703 + 24.4116i) q^{13} +(11.9308 + 67.6627i) q^{14} +(74.7578 + 27.2096i) q^{16} +(60.7411 - 50.9678i) q^{17} +(-69.0817 - 45.6807i) q^{19} +31.1625 q^{20} +(101.231 + 36.8451i) q^{22} +(15.7121 - 89.1075i) q^{23} +(35.3355 - 12.8611i) q^{25} +(120.142 - 208.092i) q^{26} +(-52.1142 - 43.7290i) q^{28} +(-16.0172 - 13.4401i) q^{29} +(67.4581 - 116.841i) q^{31} +(-133.570 + 48.6157i) q^{32} +(-46.3530 + 262.881i) q^{34} +(179.288 + 65.2556i) q^{35} +235.126 q^{37} +(277.005 - 31.6837i) q^{38} +(112.508 - 94.4056i) q^{40} +(303.396 + 110.427i) q^{41} +(-59.8743 - 339.564i) q^{43} +(-100.235 + 36.4825i) q^{44} +(152.304 + 263.799i) q^{46} +(-232.960 - 195.477i) q^{47} +(-36.7603 - 63.6707i) q^{49} +(-63.2958 + 109.632i) q^{50} +(41.3142 + 234.304i) q^{52} +(-79.8475 + 452.838i) q^{53} +(229.166 - 192.293i) q^{55} -320.628 q^{56} +70.3904 q^{58} +(-229.657 + 192.705i) q^{59} +(6.66553 - 37.8021i) q^{61} +(78.8703 + 447.296i) q^{62} +(-78.9602 + 136.763i) q^{64} +(-333.628 - 577.861i) q^{65} +(-498.260 - 418.090i) q^{67} +(-132.155 - 228.899i) q^{68} +(-603.575 + 219.683i) q^{70} +(-109.301 - 619.876i) q^{71} +(-350.982 - 127.747i) q^{73} +(-606.365 + 508.801i) q^{74} +(-189.944 + 200.335i) q^{76} -653.081 q^{77} +(-962.560 - 350.343i) q^{79} +(-129.148 + 732.436i) q^{80} +(-1021.38 + 371.754i) q^{82} +(471.707 - 817.021i) q^{83} +(567.845 + 476.479i) q^{85} +(889.209 + 746.135i) q^{86} +(-251.363 + 435.374i) q^{88} +(712.415 - 259.298i) q^{89} +(-252.949 + 1434.55i) q^{91} +(-283.421 - 103.157i) q^{92} +1023.78 q^{94} +(308.418 - 710.164i) q^{95} +(815.791 - 684.530i) q^{97} +(232.581 + 84.6527i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} + 9 q^{4} - 12 q^{5} - 48 q^{7} + 57 q^{8}+O(q^{10}) \) 36 * q - 3 * q^2 + 9 * q^4 - 12 * q^5 - 48 * q^7 + 57 * q^8	\( 36 q - 3 q^{2} + 9 q^{4} - 12 q^{5} - 48 q^{7} + 57 q^{8} - 24 q^{10} + 108 q^{11} - 24 q^{13} + 87 q^{14} + 69 q^{16} + 462 q^{17} - 336 q^{19} - 54 q^{20} + 84 q^{22} + 306 q^{25} - 72 q^{26} + 1938 q^{28} - 342 q^{29} + 1032 q^{31} + 141 q^{32} - 867 q^{34} + 642 q^{35} + 264 q^{37} + 4464 q^{38} - 4209 q^{40} - 558 q^{41} + 1344 q^{43} + 1239 q^{44} + 2229 q^{46} - 2628 q^{47} - 1122 q^{49} - 1503 q^{50} - 2463 q^{52} - 1722 q^{53} + 1860 q^{55} - 2238 q^{56} + 1512 q^{58} + 1986 q^{59} + 1566 q^{61} - 7287 q^{62} - 2679 q^{64} - 1716 q^{65} - 1044 q^{67} + 4623 q^{68} + 60 q^{70} + 5874 q^{71} + 3024 q^{73} + 723 q^{74} - 6942 q^{76} - 2028 q^{77} - 3696 q^{79} - 8076 q^{80} + 3597 q^{82} + 4764 q^{83} + 3300 q^{85} + 627 q^{86} + 3012 q^{88} - 3228 q^{89} - 1272 q^{91} - 18183 q^{92} - 16410 q^{94} + 3780 q^{95} - 1230 q^{97} + 19761 q^{98}+O(q^{100}) \) 36 * q - 3 * q^2 + 9 * q^4 - 12 * q^5 - 48 * q^7 + 57 * q^8 - 24 * q^10 + 108 * q^11 - 24 * q^13 + 87 * q^14 + 69 * q^16 + 462 * q^17 - 336 * q^19 - 54 * q^20 + 84 * q^22 + 306 * q^25 - 72 * q^26 + 1938 * q^28 - 342 * q^29 + 1032 * q^31 + 141 * q^32 - 867 * q^34 + 642 * q^35 + 264 * q^37 + 4464 * q^38 - 4209 * q^40 - 558 * q^41 + 1344 * q^43 + 1239 * q^44 + 2229 * q^46 - 2628 * q^47 - 1122 * q^49 - 1503 * q^50 - 2463 * q^52 - 1722 * q^53 + 1860 * q^55 - 2238 * q^56 + 1512 * q^58 + 1986 * q^59 + 1566 * q^61 - 7287 * q^62 - 2679 * q^64 - 1716 * q^65 - 1044 * q^67 + 4623 * q^68 + 60 * q^70 + 5874 * q^71 + 3024 * q^73 + 723 * q^74 - 6942 * q^76 - 2028 * q^77 - 3696 * q^79 - 8076 * q^80 + 3597 * q^82 + 4764 * q^83 + 3300 * q^85 + 627 * q^86 + 3012 * q^88 - 3228 * q^89 - 1272 * q^91 - 18183 * q^92 - 16410 * q^94 + 3780 * q^95 - 1230 * q^97 + 19761 * q^98

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