LMFDB - Embedded newform 315.3.ca.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +O(q^{10})$	\(q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +(-0.352512 + 1.15027i) q^{10} +(-2.22825 - 3.85944i) q^{11} +(10.0930 - 10.0930i) q^{13} +(0.589662 - 1.57771i) q^{14} +(7.65430 - 13.2576i) q^{16} +(2.55748 - 9.54465i) q^{17} +(11.1120 + 6.41554i) q^{19} +(-0.701025 + 19.6981i) q^{20} +(0.758230 + 0.758230i) q^{22} +(-3.20215 - 11.9506i) q^{23} +(-10.9293 - 22.4844i) q^{25} +(-1.71723 + 2.97433i) q^{26} +(2.64146 - 27.4680i) q^{28} -36.7743i q^{29} +(-8.59913 - 14.8941i) q^{31} +(-2.93176 + 10.9415i) q^{32} +2.37760i q^{34} +(13.3763 + 32.3431i) q^{35} +(54.2699 - 14.5416i) q^{37} +(-2.98215 - 0.799066i) q^{38} +(-2.14319 - 9.31149i) q^{40} +46.8347 q^{41} +(25.0932 - 25.0932i) q^{43} +(15.2143 + 8.78398i) q^{44} +(1.48846 + 2.57809i) q^{46} +(-44.9155 + 12.0351i) q^{47} +(-15.9642 - 46.3265i) q^{49} +(3.94038 + 4.54512i) q^{50} +(-14.5633 + 54.3510i) q^{52} +(-58.8689 - 15.7739i) q^{53} +(-22.2684 - 0.792499i) q^{55} +(2.20945 + 13.1932i) q^{56} +(2.29015 + 8.54695i) q^{58} +(99.7443 - 57.5874i) q^{59} +(-22.1961 + 38.4447i) q^{61} +(2.92612 + 2.92612i) q^{62} +58.5089i q^{64} +(-16.0080 - 69.5498i) q^{65} +(-18.2625 + 68.1567i) q^{67} +(10.0819 + 37.6260i) q^{68} +(-5.12307 - 6.68403i) q^{70} -85.0378 q^{71} +(-11.2757 - 3.02132i) q^{73} +(-11.7076 + 6.75940i) q^{74} -50.5815 q^{76} +(31.0522 + 2.98613i) q^{77} +(57.2212 + 33.0366i) q^{79} +(-35.8897 - 67.6074i) q^{80} +(-10.8851 + 2.91666i) q^{82} +(-65.5612 + 65.5612i) q^{83} +(-33.6712 - 36.1563i) q^{85} +(-4.26937 + 7.39477i) q^{86} +(-8.22613 - 2.20418i) q^{88} +(10.9662 + 6.33133i) q^{89} +(16.5030 + 98.5433i) q^{91} +(34.4872 + 34.4872i) q^{92} +(9.68960 - 5.59429i) q^{94} +(56.6660 - 30.0814i) q^{95} +(-125.573 - 125.573i) q^{97} +(6.59537 + 9.77284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.232416	+	0.0622758i	−0.116208	+	0.0311379i	−0.316454	−	0.948608i	$-0.602492\pi$
$2$	−0.232416	+	0.0622758i	−0.116208	+	0.0311379i	0.200246	+	0.979746i	$0.435826\pi$
$3$		0			0
$3$		0			0
$4$	−3.41396	+	1.97105i	−0.853491	+	0.492763i
$5$	2.65242	−	4.23847i	0.530485	−	0.847694i
$5$	2.65242	−	4.23847i	0.530485	−	0.847694i
$6$		0			0
$7$	−4.06422	+	5.69931i	−0.580603	+	0.814187i
$7$	−4.06422	+	5.69931i	−0.580603	+	0.814187i
$8$	1.35127	−	1.35127i	0.168909	−	0.168909i
$9$		0			0
$10$	−0.352512	+	1.15027i	−0.0352512	+	0.115027i
$11$	−2.22825	−	3.85944i	−0.202568	−	0.350858i	0.746787	−	0.665063i	$-0.231595\pi$
$11$	−2.22825	−	3.85944i	−0.202568	−	0.350858i	−0.949355	+	0.314205i	$0.898262\pi$
$12$		0			0
$13$	10.0930	−	10.0930i	0.776385	−	0.776385i	−0.202829	−	0.979214i	$-0.565014\pi$
$13$	10.0930	−	10.0930i	0.776385	−	0.776385i	0.979214	+	0.202829i	$0.0650137\pi$
$14$	0.589662	−	1.57771i	0.0421187	−	0.112694i
$15$		0			0
$16$	7.65430	−	13.2576i	0.478394	−	0.828603i
$17$	2.55748	−	9.54465i	0.150440	−	0.561450i	−0.849013	−	0.528372i	$-0.822802\pi$
$17$	2.55748	−	9.54465i	0.150440	−	0.561450i	0.999453	−	0.0330776i	$-0.0105309\pi$
$18$		0			0
$19$	11.1120	+	6.41554i	0.584845	+	0.337660i	0.763056	−	0.646332i	$-0.223698\pi$
$19$	11.1120	+	6.41554i	0.584845	+	0.337660i	−0.178212	+	0.983992i	$0.557031\pi$
$20$	−0.701025	+	19.6981i	−0.0350513	+	0.984903i
$21$		0			0
$22$	0.758230	+	0.758230i	0.0344650	+	0.0344650i
$23$	−3.20215	−	11.9506i	−0.139224	−	0.519590i	−0.999945	−	0.0105132i	$-0.996653\pi$
$23$	−3.20215	−	11.9506i	−0.139224	−	0.519590i	0.860721	−	0.509077i	$-0.170013\pi$
$24$		0			0
$25$	−10.9293	−	22.4844i	−0.437172	−	0.899378i
$26$	−1.71723	+	2.97433i	−0.0660472	+	0.114397i
$27$		0			0
$28$	2.64146	−	27.4680i	0.0943378	−	0.981001i
$29$		−	36.7743i		−	1.26808i	−0.773301	−	0.634040i	$-0.781396\pi$
$29$		−	36.7743i		−	1.26808i	0.773301	−	0.634040i	$-0.218604\pi$
$30$		0			0
$31$	−8.59913	−	14.8941i	−0.277391	−	0.480456i	0.693344	−	0.720606i	$-0.256136\pi$
$31$	−8.59913	−	14.8941i	−0.277391	−	0.480456i	−0.970736	+	0.240151i	$0.922803\pi$
$32$	−2.93176	+	10.9415i	−0.0916174	+	0.341921i
$33$		0			0
$34$			2.37760i			0.0699295i
$35$	13.3763	+	32.3431i	0.382181	+	0.924088i
$36$		0			0
$37$	54.2699	−	14.5416i	1.46675	−	0.393016i	0.564937	−	0.825134i	$-0.308900\pi$
$37$	54.2699	−	14.5416i	1.46675	−	0.393016i	0.901817	+	0.432118i	$0.142234\pi$
$38$	−2.98215	−	0.799066i	−0.0784777	−	0.0210280i
$39$		0			0
$40$	−2.14319	−	9.31149i	−0.0535796	−	0.232787i
$41$	46.8347			1.14231			0.571155	−	0.820843i	$-0.306496\pi$
$41$	46.8347			1.14231			0.571155	+	0.820843i	$0.306496\pi$
$42$		0			0
$43$	25.0932	−	25.0932i	0.583563	−	0.583563i	−0.352317	−	0.935881i	$-0.614606\pi$
$43$	25.0932	−	25.0932i	0.583563	−	0.583563i	0.935881	+	0.352317i	$0.114606\pi$
$44$	15.2143	+	8.78398i	0.345780	+	0.199636i
$45$		0			0
$46$	1.48846	+	2.57809i	0.0323579	+	0.0560455i
$47$	−44.9155	+	12.0351i	−0.955649	+	0.256065i	−0.702758	−	0.711429i	$-0.748048\pi$
$47$	−44.9155	+	12.0351i	−0.955649	+	0.256065i	−0.252891	+	0.967495i	$0.581382\pi$
$48$		0			0
$49$	−15.9642	−	46.3265i	−0.325801	−	0.945438i
$50$	3.94038	+	4.54512i	0.0788076	+	0.0909024i
$51$		0			0
$52$	−14.5633	+	54.3510i	−0.280063	+	1.04521i
$53$	−58.8689	−	15.7739i	−1.11073	−	0.297620i	−0.343606	−	0.939114i	$-0.611648\pi$
$53$	−58.8689	−	15.7739i	−1.11073	−	0.297620i	−0.767128	+	0.641494i	$0.778315\pi$
$54$		0			0
$55$	−22.2684	−	0.792499i	−0.404879	−	0.0144091i
$56$	2.20945	+	13.1932i	0.0394545	+	0.235593i
$57$		0			0
$58$	2.29015	+	8.54695i	0.0394853	+	0.147361i
$59$	99.7443	−	57.5874i	1.69058	−	0.976058i	0.736535	−	0.676399i	$-0.236460\pi$
$59$	99.7443	−	57.5874i	1.69058	−	0.976058i	0.954046	−	0.299659i	$-0.0968729\pi$
$60$		0			0
$61$	−22.1961	+	38.4447i	−0.363870	+	0.630241i	−0.988594	−	0.150604i	$-0.951878\pi$
$61$	−22.1961	+	38.4447i	−0.363870	+	0.630241i	0.624724	+	0.780845i	$0.285211\pi$
$62$	2.92612	+	2.92612i	0.0471955	+	0.0471955i
$63$		0			0
$64$			58.5089i			0.914201i
$65$	−16.0080	−	69.5498i	−0.246277	−	1.07000i
$66$		0			0
$67$	−18.2625	+	68.1567i	−0.272575	+	1.01726i	0.684874	+	0.728662i	$0.259857\pi$
$67$	−18.2625	+	68.1567i	−0.272575	+	1.01726i	−0.957449	+	0.288602i	$0.906809\pi$
$68$	10.0819	+	37.6260i	0.148263	+	0.553324i
$69$		0			0
$70$	−5.12307	−	6.68403i	−0.0731867	−	0.0954862i
$71$	−85.0378			−1.19772			−0.598858	−	0.800855i	$-0.704379\pi$
$71$	−85.0378			−1.19772			−0.598858	+	0.800855i	$0.704379\pi$
$72$		0			0
$73$	−11.2757	−	3.02132i	−0.154462	−	0.0413879i	0.180760	−	0.983527i	$-0.442144\pi$
$73$	−11.2757	−	3.02132i	−0.154462	−	0.0413879i	−0.335221	+	0.942139i	$0.608811\pi$
$74$	−11.7076	+	6.75940i	−0.158211	+	0.0913432i
$75$		0			0
$76$	−50.5815			−0.665546
$77$	31.0522	+	2.98613i	0.403275	+	0.0387809i
$78$		0			0
$79$	57.2212	+	33.0366i	0.724318	+	0.418185i	0.816340	−	0.577572i	$-0.196000\pi$
$79$	57.2212	+	33.0366i	0.724318	+	0.418185i	−0.0920217	+	0.995757i	$0.529333\pi$
$80$	−35.8897	−	67.6074i	−0.448621	−	0.845093i
$81$		0			0
$82$	−10.8851	+	2.91666i	−0.132746	+	0.0355691i
$83$	−65.5612	+	65.5612i	−0.789894	+	0.789894i	−0.981476	−	0.191583i	$-0.938638\pi$
$83$	−65.5612	+	65.5612i	−0.789894	+	0.789894i	0.191583	+	0.981476i	$0.438638\pi$
$84$		0			0
$85$	−33.6712	−	36.1563i	−0.396132	−	0.425368i
$86$	−4.26937	+	7.39477i	−0.0496439	+	0.0859857i
$87$		0			0
$88$	−8.22613	−	2.20418i	−0.0934787	−	0.0250475i
$89$	10.9662	+	6.33133i	0.123216	+	0.0711385i	0.560341	−	0.828262i	$-0.310670\pi$
$89$	10.9662	+	6.33133i	0.123216	+	0.0711385i	−0.437125	+	0.899401i	$0.644003\pi$
$90$		0			0
$91$	16.5030	+	98.5433i	0.181351	+	1.08289i
$92$	34.4872	+	34.4872i	0.374861	+	0.374861i
$93$		0			0
$94$	9.68960	−	5.59429i	0.103081	−	0.0595138i
$95$	56.6660	−	30.0814i	0.596484	−	0.316646i
$96$		0			0
$97$	−125.573	−	125.573i	−1.29456	−	1.29456i	−0.931932	−	0.362632i	$-0.881878\pi$
$97$	−125.573	−	125.573i	−1.29456	−	1.29456i	−0.362632	−	0.931932i	$-0.618122\pi$
$98$	6.59537	+	9.77284i	0.0672997	+	0.0997229i
$99$		0			0
$100$	81.6302	+	55.2189i	0.816302	+	0.552189i
$101$	57.5790	+	99.7297i	0.570089	+	0.987422i	0.996556	+	0.0829196i	$0.0264245\pi$
$101$	57.5790	+	99.7297i	0.570089	+	0.987422i	−0.426468	+	0.904503i	$0.640242\pi$
$102$		0			0
$103$	25.0098	+	93.3379i	0.242814	+	0.906193i	0.974470	+	0.224519i	$0.0720810\pi$
$103$	25.0098	+	93.3379i	0.242814	+	0.906193i	−0.731656	+	0.681674i	$0.761252\pi$
$104$		−	27.2768i		−	0.262277i
$105$		0			0
$106$	14.6644			0.138344
$107$	−119.300	+	31.9665i	−1.11496	+	0.298752i	−0.768841	−	0.639440i	$-0.779166\pi$
$107$	−119.300	+	31.9665i	−1.11496	+	0.298752i	−0.346116	+	0.938192i	$0.612500\pi$
$108$		0			0
$109$	43.0410	−	24.8497i	0.394871	−	0.227979i	−0.289397	−	0.957209i	$-0.593455\pi$
$109$	43.0410	−	24.8497i	0.394871	−	0.227979i	0.684269	+	0.729230i	$0.260122\pi$
$110$	5.22488	−	1.20259i	0.0474990	−	0.0109326i
$111$		0			0
$112$	44.4506	+	97.5062i	0.396881	+	0.870591i
$113$	42.4036	−	42.4036i	0.375253	−	0.375253i	−0.494133	−	0.869386i	$-0.664514\pi$
$113$	42.4036	−	42.4036i	0.375253	−	0.375253i	0.869386	+	0.494133i	$0.164514\pi$
$114$		0			0
$115$	−59.1456	−	18.1258i	−0.514310	−	0.157615i
$116$	72.4841	+	125.546i	0.624863	+	1.08229i
$117$		0			0
$118$	−19.5959	+	19.5959i	−0.166067	+	0.166067i
$119$	44.0038	+	53.3674i	0.369779	+	0.448466i
$120$		0			0
$121$	50.5698	−	87.5895i	0.417933	−	0.723880i
$122$	2.76455	−	10.3174i	0.0226603	−	0.0845693i
$123$		0			0
$124$	58.7142	+	33.8987i	0.473502	+	0.273376i
$125$	−124.289	−	13.3148i	−0.994311	−	0.106518i
$126$		0			0
$127$	−62.2747	−	62.2747i	−0.490352	−	0.490352i	0.418065	−	0.908417i	$-0.362708\pi$
$127$	−62.2747	−	62.2747i	−0.490352	−	0.490352i	−0.908417	+	0.418065i	$0.862708\pi$
$128$	−15.3707	−	57.3643i	−0.120084	−	0.448158i
$129$		0			0
$130$	8.05178	+	15.1676i	0.0619368	+	0.116674i
$131$	−7.67305	+	13.2901i	−0.0585729	+	0.101451i	−0.893825	−	0.448416i	$-0.851988\pi$
$131$	−7.67305	+	13.2901i	−0.0585729	+	0.101451i	0.835252	+	0.549867i	$0.185322\pi$
$132$		0			0
$133$	−81.7260	+	37.2568i	−0.614481	+	0.280126i
$134$		−	16.9780i		−	0.126702i
$135$		0			0
$136$	−9.44158	−	16.3533i	−0.0694234	−	0.120245i
$137$	−58.8789	+	219.739i	−0.429773	+	1.60394i	0.323500	+	0.946228i	$0.395140\pi$
$137$	−58.8789	+	219.739i	−0.429773	+	1.60394i	−0.753273	+	0.657708i	$0.771526\pi$
$138$		0			0
$139$		−	102.047i		−	0.734151i	−0.930191	−	0.367076i	$-0.880359\pi$
$139$		−	102.047i		−	0.734151i	0.930191	−	0.367076i	$-0.119641\pi$
$140$	−109.416	−	84.0526i	−0.781544	−	0.600375i
$141$		0			0
$142$	19.7642	−	5.29579i	0.139184	−	0.0372943i
$143$	−61.4430	−	16.4636i	−0.429671	−	0.115130i
$144$		0			0
$145$	−155.867	−	97.5410i	−1.07494	−	0.672697i
$146$	2.80881			0.0192384
$147$		0			0
$148$	−156.613	+	156.613i	−1.05820	+	1.05820i
$149$	253.568	+	146.397i	1.70180	+	0.982532i	0.943944	+	0.330104i	$0.107084\pi$
$149$	253.568	+	146.397i	1.70180	+	0.982532i	0.757851	+	0.652428i	$0.226249\pi$
$150$		0			0
$151$	103.721	+	179.651i	0.686897	+	1.18974i	0.972837	+	0.231492i	$0.0743608\pi$
$151$	103.721	+	179.651i	0.686897	+	1.18974i	−0.285940	+	0.958247i	$0.592306\pi$
$152$	23.6846	−	6.34626i	0.155820	−	0.0417517i
$153$		0			0
$154$	−7.40300	+	1.23977i	−0.0480714	+	0.00805048i
$155$	−85.9369	−	3.05837i	−0.554431	−	0.0197314i
$156$		0			0
$157$	19.6048	−	73.1661i	0.124871	−	0.466026i	−0.874964	−	0.484188i	$-0.839115\pi$
$157$	19.6048	−	73.1661i	0.124871	−	0.466026i	0.999835	+	0.0181625i	$0.00578162\pi$
$158$	−15.3565	−	4.11476i	−0.0971931	−	0.0260428i
$159$		0			0
$160$	38.5988	+	41.4476i	0.241243	+	0.259047i
$161$	81.1243	+	30.3197i	0.503877	+	0.188321i
$162$		0			0
$163$	−50.8403	−	189.738i	−0.311903	−	1.16404i	−0.926838	−	0.375461i	$-0.877484\pi$
$163$	−50.8403	−	189.738i	−0.311903	−	1.16404i	0.614935	−	0.788578i	$-0.289182\pi$
$164$	−159.892	+	92.3136i	−0.974950	+	0.562888i
$165$		0			0
$166$	11.1546	−	19.3204i	0.0671965	−	0.116388i
$167$	−189.235	−	189.235i	−1.13314	−	1.13314i	−0.989652	−	0.143492i	$-0.954167\pi$
$167$	−189.235	−	189.235i	−1.13314	−	1.13314i	−0.143492	−	0.989652i	$-0.545833\pi$
$168$		0			0
$169$		−	34.7373i		−	0.205546i
$170$	10.0774	+	6.30641i	0.0592788	+	0.0370965i
$171$		0			0
$172$	−36.2073	+	135.127i	−0.210507	+	0.785624i
$173$	−49.4475	−	184.540i	−0.285823	−	1.06671i	−0.948236	−	0.317568i	$-0.897134\pi$
$173$	−49.4475	−	184.540i	−0.285823	−	1.06671i	0.662412	−	0.749140i	$-0.269533\pi$
$174$		0			0
$175$	172.565	+	29.0923i	0.986085	+	0.166242i
$176$	−68.2227			−0.387629
$177$		0			0
$178$	−2.94301	−	0.788577i	−0.0165338	−	0.00443021i
$179$	158.096	−	91.2766i	0.883216	−	0.509925i	0.0114988	−	0.999934i	$-0.496340\pi$
$179$	158.096	−	91.2766i	0.883216	−	0.509925i	0.871718	+	0.490009i	$0.163006\pi$
$180$		0			0
$181$	−103.223			−0.570290			−0.285145	−	0.958484i	$-0.592042\pi$
$181$	−103.223			−0.570290			−0.285145	+	0.958484i	$0.592042\pi$
$182$	−9.97241	−	21.8753i	−0.0547935	−	0.120194i
$183$		0			0
$184$	−20.4755	−	11.8215i	−0.111280	−	0.0642474i
$185$	82.3127	−	268.592i	0.444934	−	1.45185i
$186$		0			0
$187$	−42.5357	+	11.3974i	−0.227463	+	0.0609487i
$188$	129.618	−	129.618i	0.689458	−	0.689458i
$189$		0			0
$190$	−11.2968	+	10.5203i	−0.0594566	+	0.0553701i
$191$	129.306	−	223.965i	0.676996	−	1.17259i	−0.298885	−	0.954289i	$-0.596615\pi$
$191$	129.306	−	223.965i	0.676996	−	1.17259i	0.975881	−	0.218302i	$-0.0700519\pi$
$192$		0			0
$193$	88.4965	+	23.7126i	0.458531	+	0.122863i	0.480688	−	0.876891i	$-0.340387\pi$
$193$	88.4965	+	23.7126i	0.458531	+	0.122863i	−0.0221573	+	0.999754i	$0.507053\pi$
$194$	37.0053	+	21.3650i	0.190749	+	0.110129i
$195$		0			0
$196$	145.813	+	126.691i	0.743945	+	0.646380i
$197$	186.124	+	186.124i	0.944793	+	0.944793i	0.998554	−	0.0537607i	$-0.0171208\pi$
$197$	186.124	+	186.124i	0.944793	+	0.944793i	−0.0537607	+	0.998554i	$0.517121\pi$
$198$		0			0
$199$	234.511	−	135.395i	1.17844	−	0.680375i	0.222791	−	0.974866i	$-0.428483\pi$
$199$	234.511	−	135.395i	1.17844	−	0.680375i	0.955654	+	0.294491i	$0.0951500\pi$
$200$	−45.1511	−	15.6142i	−0.225756	−	0.0780709i
$201$		0			0
$202$	−19.5930	−	19.5930i	−0.0969952	−	0.0969952i
$203$	209.588	+	149.459i	1.03245	+	0.736250i
$204$		0			0
$205$	124.225	−	198.507i	0.605978	−	0.968329i
$206$	−11.6254	−	20.1357i	−0.0564338	−	0.0977463i
$207$		0			0
$208$	−56.5545	−	211.064i	−0.271897	−	1.01473i
$209$		−	57.1817i		−	0.273596i
$210$		0			0
$211$	294.597			1.39619			0.698096	−	0.716004i	$-0.254031\pi$
$211$	294.597			1.39619			0.698096	+	0.716004i	$0.254031\pi$
$212$	232.067	−	62.1823i	1.09466	−	0.293313i
$213$		0			0
$214$	25.7366	−	14.8590i	0.120265	−	0.0694348i
$215$	−39.7991	−	172.915i	−0.185112	−	0.804255i
$216$		0			0
$217$	119.835	+	11.5239i	0.552235	+	0.0531056i
$218$	−8.45589	+	8.45589i	−0.0387885	+	0.0387885i
$219$		0			0
$220$	77.5854	−	41.1866i	0.352661	−	0.187212i
$221$	−70.5215	−	122.147i	−0.319102	−	0.552701i
$222$		0			0
$223$	8.97417	−	8.97417i	0.0402429	−	0.0402429i	−0.686699	−	0.726942i	$-0.740941\pi$
$223$	8.97417	−	8.97417i	0.0402429	−	0.0402429i	0.726942	+	0.686699i	$0.240941\pi$
$224$	−50.4435	−	61.1775i	−0.225194	−	0.273114i
$225$		0			0
$226$	−7.21458	+	12.4960i	−0.0319229	+	0.0552921i
$227$	−93.1104	+	347.493i	−0.410178	+	1.53080i	0.384124	+	0.923281i	$0.374503\pi$
$227$	−93.1104	+	347.493i	−0.410178	+	1.53080i	−0.794302	+	0.607523i	$0.792163\pi$
$228$		0			0
$229$	−201.351	−	116.250i	−0.879261	−	0.507642i	−0.00884639	−	0.999961i	$-0.502816\pi$
$229$	−201.351	−	116.250i	−0.879261	−	0.507642i	−0.870415	+	0.492319i	$0.836149\pi$
$230$	14.8752	+	0.529387i	0.0646748	+	0.00230168i
$231$		0			0
$232$	−49.6921	−	49.6921i	−0.214190	−	0.214190i
$233$	−8.52601	−	31.8195i	−0.0365923	−	0.136564i	0.945213	−	0.326454i	$-0.105854\pi$
$233$	−8.52601	−	31.8195i	−0.0365923	−	0.136564i	−0.981805	+	0.189889i	$0.939187\pi$
$234$		0			0
$235$	−68.1246	+	222.295i	−0.289892	+	0.945937i
$236$	−227.016	+	393.203i	−0.961931	+	1.66611i
$237$		0			0
$238$	−13.5507	−	9.66309i	−0.0569357	−	0.0406012i
$239$		−	133.557i		−	0.558817i	−0.960172	−	0.279408i	$-0.909862\pi$
$239$		−	133.557i		−	0.558817i	0.960172	−	0.279408i	$-0.0901383\pi$
$240$		0			0
$241$	−230.800	−	399.758i	−0.957678	−	1.65875i	−0.728117	−	0.685453i	$-0.759604\pi$
$241$	−230.800	−	399.758i	−0.957678	−	1.65875i	−0.229561	−	0.973294i	$-0.573729\pi$
$242$	−6.29855	+	23.5065i	−0.0260271	+	0.0971343i
$243$		0			0
$244$		−	174.998i		−	0.717206i
$245$	−238.697	−	55.2135i	−0.974275	−	0.225361i
$246$		0			0
$247$	176.906	−	47.4018i	0.716219	−	0.191910i
$248$	−31.7458	−	8.50627i	−0.128007	−	0.0342995i
$249$		0			0
$250$	29.7159	−	4.64561i	0.118864	−	0.0185824i
$251$	125.961			0.501837			0.250919	−	0.968008i	$-0.419267\pi$
$251$	125.961			0.501837			0.250919	+	0.968008i	$0.419267\pi$
$252$		0			0
$253$	−38.9873	+	38.9873i	−0.154100	+	0.154100i
$254$	18.3519	+	10.5955i	0.0722515	+	0.0417144i
$255$		0			0
$256$	−109.873	−	190.305i	−0.429191	−	0.743381i
$257$	236.058	−	63.2516i	0.918515	−	0.246115i	0.231564	−	0.972820i	$-0.425616\pi$
$257$	236.058	−	63.2516i	0.918515	−	0.246115i	0.686950	+	0.726704i	$0.258949\pi$
$258$		0			0
$259$	−137.688	+	368.401i	−0.531613	+	1.42240i
$260$	191.737	+	205.888i	0.737450	+	0.791876i
$261$		0			0
$262$	0.955690	−	3.56669i	0.00364767	−	0.0136133i
$263$	−116.745	−	31.2818i	−0.443898	−	0.118942i	0.0299446	−	0.999552i	$-0.490467\pi$
$263$	−116.745	−	31.2818i	−0.443898	−	0.118942i	−0.473843	+	0.880609i	$0.657134\pi$
$264$		0			0
$265$	−223.002	+	207.675i	−0.841519	+	0.783680i
$266$	16.6742	−	13.7486i	0.0626851	−	0.0516866i
$267$		0			0
$268$	−71.9928	−	268.681i	−0.268630	−	1.00254i
$269$	−221.456	+	127.858i	−0.823258	+	0.475308i	−0.851539	−	0.524292i	$-0.824330\pi$
$269$	−221.456	+	127.858i	−0.823258	+	0.475308i	0.0282806	+	0.999600i	$0.490997\pi$
$270$		0			0
$271$	−24.1359	+	41.8046i	−0.0890625	+	0.154261i	−0.907115	−	0.420883i	$-0.861720\pi$
$271$	−24.1359	+	41.8046i	−0.0890625	+	0.154261i	0.818053	+	0.575143i	$0.195054\pi$
$272$	−106.964	−	106.964i	−0.393249	−	0.393249i
$273$		0			0
$274$		−	54.7377i		−	0.199773i
$275$	−62.4241	+	92.2818i	−0.226997	+	0.335570i
$276$		0			0
$277$	−26.8253	+	100.113i	−0.0968423	+	0.361420i	−0.997292	−	0.0735390i	$-0.976571\pi$
$277$	−26.8253	+	100.113i	−0.0968423	+	0.361420i	0.900450	+	0.434960i	$0.143237\pi$
$278$	6.35506	+	23.7174i	0.0228599	+	0.0853143i
$279$		0			0
$280$	61.7794	+	25.6293i	0.220641	+	0.0915330i
$281$	−357.942			−1.27382			−0.636908	−	0.770940i	$-0.719787\pi$
$281$	−357.942			−1.27382			−0.636908	+	0.770940i	$0.719787\pi$
$282$		0			0
$283$	174.344	+	46.7152i	0.616055	+	0.165072i	0.553334	−	0.832960i	$-0.313355\pi$
$283$	174.344	+	46.7152i	0.616055	+	0.165072i	0.0627214	+	0.998031i	$0.480022\pi$
$284$	290.316	−	167.614i	1.02224	−	0.590190i
$285$		0			0
$286$	15.3056			0.0535162
$287$	−190.346	+	266.925i	−0.663228	+	0.930053i
$288$		0			0
$289$	165.722	+	95.6795i	0.573431	+	0.331071i
$290$	42.3004	+	12.9634i	0.145864	+	0.0447014i
$291$		0			0
$292$	44.4500	−	11.9103i	0.152226	−	0.0407889i
$293$	−116.627	+	116.627i	−0.398046	+	0.398046i	−0.877543	−	0.479497i	$-0.840819\pi$
$293$	−116.627	+	116.627i	−0.398046	+	0.398046i	0.479497	+	0.877543i	$0.340819\pi$
$294$		0			0
$295$	20.4816	−	575.510i	0.0694290	−	1.95088i
$296$	53.6838	−	92.9832i	0.181364	−	0.314132i
$297$		0			0
$298$	−68.0502	−	18.2340i	−0.228356	−	0.0611879i
$299$	−152.936	−	88.2979i	−0.511493	−	0.295311i
$300$		0			0
$301$	41.0297	+	244.998i	0.136311	+	0.813948i
$302$	−35.2944	−	35.2944i	−0.116869	−	0.116869i
$303$		0			0
$304$	170.110	−	98.2130i	0.559572	−	0.323069i
$305$	104.073	+	196.049i	0.341224	+	0.642784i
$306$		0			0
$307$	102.316	+	102.316i	0.333276	+	0.333276i	0.853829	−	0.520553i	$-0.174274\pi$
$307$	102.316	+	102.316i	0.333276	+	0.333276i	−0.520553	+	0.853829i	$0.674274\pi$
$308$	−111.897	+	51.0110i	−0.363302	+	0.165620i
$309$		0			0
$310$	20.1636	−	4.64097i	0.0650438	−	0.0149709i
$311$	5.34944	+	9.26551i	0.0172008	+	0.0297926i	0.874498	−	0.485030i	$-0.161191\pi$
$311$	5.34944	+	9.26551i	0.0172008	+	0.0297926i	−0.857297	+	0.514822i	$0.827858\pi$
$312$		0			0
$313$	123.581	+	461.210i	0.394827	+	1.47351i	0.822075	+	0.569380i	$0.192816\pi$
$313$	123.581	+	461.210i	0.394827	+	1.47351i	−0.427248	+	0.904135i	$0.640517\pi$
$314$			18.2259i			0.0580442i
$315$		0			0
$316$	−260.468			−0.824265
$317$	71.5544	−	19.1729i	0.225724	−	0.0604825i	−0.144184	−	0.989551i	$-0.546056\pi$
$317$	71.5544	−	19.1729i	0.225724	−	0.0604825i	0.369908	+	0.929068i	$0.379389\pi$
$318$		0			0
$319$	−141.928	+	81.9422i	−0.444916	+	0.256872i
$320$	247.988	+	155.190i	0.774963	+	0.484970i
$321$		0			0
$322$	−20.7428	−	1.99473i	−0.0644186	−	0.00619480i
$323$	89.6530	−	89.6530i	0.277563	−	0.277563i
$324$		0			0
$325$	−337.245	−	116.626i	−1.03768	−	0.358850i
$326$	23.6322	+	40.9322i	0.0724914	+	0.125559i
$327$		0			0
$328$	63.2865	−	63.2865i	0.192947	−	0.192947i
$329$	113.955	−	304.900i	0.346367	−	0.926749i
$330$		0			0
$331$	−186.461	+	322.960i	−0.563327	+	0.975711i	0.433876	+	0.900972i	$0.357145\pi$
$331$	−186.461	+	322.960i	−0.563327	+	0.975711i	−0.997203	+	0.0747382i	$0.976188\pi$
$332$	94.5989	−	353.048i	0.284937	−	1.06340i
$333$		0			0
$334$	55.7660	+	32.1965i	0.166964	+	0.0963968i
$335$	240.440	+	258.186i	0.717732	+	0.770703i
$336$		0			0
$337$	−1.52001	−	1.52001i	−0.00451041	−	0.00451041i	0.704848	−	0.709358i	$-0.251015\pi$
$337$	−1.52001	−	1.52001i	−0.00451041	−	0.00451041i	−0.709358	+	0.704848i	$0.751015\pi$
$338$	2.16329	+	8.07351i	0.00640027	+	0.0238861i
$339$		0			0
$340$	186.218	+	57.0684i	0.547701	+	0.167848i
$341$	−38.3220	+	66.3756i	−0.112381	+	0.194650i
$342$		0			0
$343$	328.911	+	97.2959i	0.958925	+	0.283661i
$344$		−	67.8156i		−	0.197138i
$345$		0			0
$346$	22.9848	+	39.8108i	0.0664300	+	0.115060i
$347$	54.2716	−	202.544i	0.156402	−	0.583701i	−0.842579	−	0.538573i	$-0.818964\pi$
$347$	54.2716	−	202.544i	0.156402	−	0.583701i	0.998981	−	0.0451282i	$-0.0143696\pi$
$348$		0			0
$349$			256.040i			0.733639i	0.930292	+	0.366820i	$0.119553\pi$
$349$			256.040i			0.733639i	−0.930292	+	0.366820i	$0.880447\pi$
$350$	−41.9186	+	3.98508i	−0.119768	+	0.0113860i
$351$		0			0
$352$	48.7606	−	13.0654i	0.138524	−	0.0371175i
$353$	3.09864	+	0.830277i	0.00877800	+	0.00235206i	0.263205	−	0.964740i	$-0.415220\pi$
$353$	3.09864	+	0.830277i	0.00877800	+	0.00235206i	−0.254427	+	0.967092i	$0.581887\pi$
$354$		0			0
$355$	−225.556	+	360.430i	−0.635370	+	1.01530i
$356$	−49.9175			−0.140218
$357$		0			0
$358$	−31.0597	+	31.0597i	−0.0867589	+	0.0867589i
$359$	268.238	+	154.867i	0.747181	+	0.431385i	0.824674	−	0.565608i	$-0.191358\pi$
$359$	268.238	+	154.867i	0.747181	+	0.431385i	−0.0774934	+	0.996993i	$0.524692\pi$
$360$		0			0
$361$	−98.1816	−	170.055i	−0.271971	−	0.471068i
$362$	23.9906	−	6.42826i	0.0662724	−	0.0177576i
$363$		0			0
$364$	−250.574	−	303.895i	−0.688391	−	0.834876i
$365$	−42.7137	+	39.7780i	−0.117024	+	0.108981i
$366$		0			0
$367$	−90.8527	+	339.067i	−0.247555	+	0.923888i	0.724527	+	0.689247i	$0.242058\pi$
$367$	−90.8527	+	339.067i	−0.247555	+	0.923888i	−0.972082	+	0.234642i	$0.924608\pi$
$368$	−182.947	−	49.0204i	−0.497138	−	0.133208i
$369$		0			0
$370$	−2.40405	+	67.5512i	−0.00649743	+	0.182571i
$371$	329.156	−	271.404i	0.887214	−	0.731546i
$372$		0			0
$373$	−25.6741	−	95.8169i	−0.0688313	−	0.256882i	0.922933	−	0.384962i	$-0.125785\pi$
$373$	−25.6741	−	95.8169i	−0.0688313	−	0.256882i	−0.991764	+	0.128080i	$0.959119\pi$
$374$	9.17620	−	5.29788i	0.0245353	−	0.0141655i
$375$		0			0
$376$	−44.4305	+	76.9558i	−0.118166	+	0.204670i
$377$	−371.163	−	371.163i	−0.984517	−	0.984517i
$378$		0			0
$379$			466.795i			1.23165i	0.787884	+	0.615824i	$0.211177\pi$
$379$			466.795i			1.23165i	−0.787884	+	0.615824i	$0.788823\pi$
$380$	−134.164	+	214.388i	−0.353062	+	0.564180i
$381$		0			0
$382$	−16.1053	+	60.1057i	−0.0421604	+	0.157345i
$383$	59.3027	+	221.321i	0.154837	+	0.577861i	0.999119	+	0.0419615i	$0.0133607\pi$
$383$	59.3027	+	221.321i	0.154837	+	0.577861i	−0.844282	+	0.535899i	$0.819973\pi$
$384$		0			0
$385$	95.0202	−	123.693i	0.246806	−	0.321282i
$386$	−22.0448			−0.0571108
$387$		0			0
$388$	676.211	+	181.190i	1.74281	+	0.466985i
$389$	−465.749	+	268.900i	−1.19730	+	0.691260i	−0.959952	−	0.280165i	$-0.909611\pi$
$389$	−465.749	+	268.900i	−1.19730	+	0.691260i	−0.237346	+	0.971425i	$0.576277\pi$
$390$		0			0
$391$	−122.254			−0.312669
$392$	−84.1718	−	41.0277i	−0.214724	−	0.104663i
$393$		0			0
$394$	−54.8493	−	31.6673i	−0.139211	−	0.0803738i
$395$	291.800	−	154.903i	0.738733	−	0.392160i
$396$		0			0
$397$	−79.7937	+	21.3807i	−0.200992	+	0.0538555i	−0.357910	−	0.933756i	$-0.616511\pi$
$397$	−79.7937	+	21.3807i	−0.200992	+	0.0538555i	0.156919	+	0.987612i	$0.449844\pi$
$398$	−46.0723	+	46.0723i	−0.115759	+	0.115759i
$399$		0			0
$400$	−381.747	−	27.2061i	−0.954367	−	0.0680152i
$401$	72.9306	−	126.319i	0.181872	−	0.315011i	−0.760646	−	0.649167i	$-0.775118\pi$
$401$	72.9306	−	126.319i	0.181872	−	0.315011i	0.942518	+	0.334156i	$0.108451\pi$
$402$		0			0
$403$	−237.117	−	63.5354i	−0.588381	−	0.157656i
$404$	−393.145	−	226.982i	−0.973131	−	0.561837i
$405$		0			0
$406$	−58.0193	−	21.6844i	−0.142905	−	0.0534099i
$407$	−177.049	−	177.049i	−0.435010	−	0.435010i
$408$		0			0
$409$	−350.103	+	202.132i	−0.855998	+	0.494211i	−0.862670	−	0.505767i	$-0.831209\pi$
$409$	−350.103	+	202.132i	−0.855998	+	0.494211i	0.00667227	+	0.999978i	$0.497876\pi$
$410$	−16.5098	+	53.8726i	−0.0402678	+	0.131397i
$411$		0			0
$412$	−269.356	−	269.356i	−0.653777	−	0.653777i
$413$	−77.1744	+	802.522i	−0.186863	+	1.94315i
$414$		0			0
$415$	103.983	+	451.775i	0.250562	+	1.08862i
$416$	80.8420	+	140.022i	0.194332	+	0.336592i
$417$		0			0
$418$	3.56103	+	13.2899i	0.00851921	+	0.0317941i
$419$			404.689i			0.965844i	0.875663	+	0.482922i	$0.160425\pi$
$419$			404.689i			0.965844i	−0.875663	+	0.482922i	$0.839575\pi$
$420$		0			0
$421$	430.807			1.02329			0.511647	−	0.859196i	$-0.329035\pi$
$421$	430.807			1.02329			0.511647	+	0.859196i	$0.329035\pi$
$422$	−68.4691	+	18.3462i	−0.162249	+	0.0434745i
$423$		0			0
$424$	−100.863	+	58.2332i	−0.237884	+	0.137342i
$425$	−242.558	+	46.8128i	−0.570724	+	0.110148i
$426$		0			0
$427$	−128.899	−	282.750i	−0.301870	−	0.662178i
$428$	344.280	−	344.280i	0.804392	−	0.804392i
$429$		0			0
$430$	20.0184	+	37.7097i	0.0465543	+	0.0876970i
$431$	−32.0539	−	55.5190i	−0.0743710	−	0.128814i	0.826442	−	0.563023i	$-0.190362\pi$
$431$	−32.0539	−	55.5190i	−0.0743710	−	0.128814i	−0.900813	+	0.434208i	$0.857028\pi$
$432$		0			0
$433$	−58.9362	+	58.9362i	−0.136111	+	0.136111i	−0.771880	−	0.635769i	$-0.780683\pi$
$433$	−58.9362	+	58.9362i	−0.136111	+	0.136111i	0.635769	+	0.771880i	$0.280683\pi$
$434$	−28.5693	+	4.78447i	−0.0658278	+	0.0110241i
$435$		0			0
$436$	−97.9601	+	169.672i	−0.224679	+	0.389156i
$437$	41.0870	−	153.339i	0.0940207	−	0.350890i
$438$		0			0
$439$	262.656	+	151.644i	0.598304	+	0.345431i	0.768374	−	0.640001i	$-0.221066\pi$
$439$	262.656	+	151.644i	0.598304	+	0.345431i	−0.170070	+	0.985432i	$0.554399\pi$
$440$	−31.1615	+	29.0198i	−0.0708217	+	0.0659540i
$441$		0			0
$442$	23.9971	+	23.9971i	0.0542922	+	0.0542922i
$443$	55.0133	+	205.312i	0.124184	+	0.463459i	0.999809	−	0.0195310i	$-0.00621730\pi$
$443$	55.0133	+	205.312i	0.124184	+	0.463459i	−0.875626	+	0.482990i	$0.839551\pi$
$444$		0			0
$445$	55.9221	−	29.6865i	0.125668	−	0.0667112i
$446$	−1.52687	+	2.64461i	−0.00342347	+	0.00592963i
$447$		0			0
$448$	−333.460	−	237.793i	−0.744331	−	0.530788i
$449$			266.145i			0.592751i	0.955072	+	0.296375i	$0.0957779\pi$
$449$			266.145i			0.592751i	−0.955072	+	0.296375i	$0.904222\pi$
$450$		0			0
$451$	−104.359	−	180.755i	−0.231395	−	0.400788i
$452$	−61.1846	+	228.344i	−0.135364	+	0.505186i
$453$		0			0
$454$		−	86.5615i		−	0.190664i
$455$	461.446	+	191.431i	1.01417	+	0.420728i
$456$		0			0
$457$	304.655	−	81.6321i	0.666641	−	0.178626i	0.0904000	−	0.995906i	$-0.471185\pi$
$457$	304.655	−	81.6321i	0.666641	−	0.178626i	0.576241	+	0.817280i	$0.304519\pi$
$458$	54.0368	+	14.4791i	0.117984	+	0.0316138i
$459$		0			0
$460$	237.648	−	54.6984i	0.516626	−	0.118910i
$461$	613.866			1.33160			0.665799	−	0.746132i	$-0.268091\pi$
$461$	613.866			1.33160			0.665799	+	0.746132i	$0.268091\pi$
$462$		0			0
$463$	140.640	−	140.640i	0.303758	−	0.303758i	−0.538724	−	0.842482i	$-0.681093\pi$
$463$	140.640	−	140.640i	0.303758	−	0.303758i	0.842482	+	0.538724i	$0.181093\pi$
$464$	−487.540	−	281.482i	−1.05073	−	0.606641i
$465$		0			0
$466$	3.96317	+	6.86440i	0.00850465	+	0.0147305i
$467$	309.664	−	82.9741i	0.663091	−	0.177675i	0.0884506	−	0.996081i	$-0.471808\pi$
$467$	309.664	−	82.9741i	0.663091	−	0.177675i	0.574641	+	0.818406i	$0.305142\pi$
$468$		0			0
$469$	−314.223	−	381.088i	−0.669985	−	0.812553i
$470$	1.98967	−	55.9075i	0.00423334	−	0.118952i
$471$		0			0
$472$	56.9655	−	212.598i	0.120690	−	0.450420i
$473$	−152.760	−	40.9318i	−0.322959	−	0.0865366i
$474$		0			0
$475$	22.8031	−	319.966i	0.0480066	−	0.673612i
$476$	−255.417	−	95.4607i	−0.536591	−	0.200548i
$477$		0			0
$478$	8.31737	+	31.0409i	0.0174004	+	0.0649390i
$479$	−459.429	+	265.251i	−0.959141	+	0.553761i	−0.895909	−	0.444238i	$-0.853474\pi$
$479$	−459.429	+	265.251i	−0.959141	+	0.553761i	−0.0632327	+	0.997999i	$0.520141\pi$
$480$		0			0
$481$	400.978	−	694.514i	0.833634	−	1.44390i
$482$	78.5370	+	78.5370i	0.162940	+	0.162940i
$483$		0			0
$484$			398.703i			0.823767i
$485$	−865.309	+	199.165i	−1.78414	+	0.410648i
$486$		0			0
$487$	36.7674	−	137.218i	0.0754977	−	0.281761i	−0.917848	−	0.396932i	$-0.870075\pi$
$487$	36.7674	−	137.218i	0.0754977	−	0.281761i	0.993346	+	0.115171i	$0.0367415\pi$
$488$	21.9564	+	81.9423i	0.0449925	+	0.167914i
$489$		0			0
$490$	58.9156	−	2.03255i	0.120236	−	0.00414807i
$491$	98.2025			0.200005			0.100003	−	0.994987i	$-0.468115\pi$
$491$	98.2025			0.200005			0.100003	+	0.994987i	$0.468115\pi$
$492$		0			0
$493$	−350.998	−	94.0496i	−0.711963	−	0.190770i
$494$	−38.1638	+	22.0339i	−0.0772548	+	0.0446031i
$495$		0			0
$496$	−263.281			−0.530809
$497$	345.612	−	484.657i	0.695397	−	0.975164i
$498$		0			0
$499$	75.4381	+	43.5542i	0.151179	+	0.0872830i	0.573681	−	0.819079i	$-0.305515\pi$
$499$	75.4381	+	43.5542i	0.151179	+	0.0872830i	−0.422502	+	0.906362i	$0.638848\pi$
$500$	450.562	−	199.524i	0.901123	−	0.399047i
$501$		0			0
$502$	−29.2754	+	7.84433i	−0.0583176	+	0.0156261i
$503$	−360.582	+	360.582i	−0.716863	+	0.716863i	−0.967962	−	0.251098i	$-0.919208\pi$
$503$	−360.582	+	360.582i	−0.716863	+	0.716863i	0.251098	+	0.967962i	$0.419208\pi$
$504$		0			0
$505$	575.425	+	20.4786i	1.13946	+	0.0405516i
$506$	6.63332	−	11.4893i	0.0131093	−	0.0227060i
$507$		0			0
$508$	335.350	+	89.8569i	0.660139	+	0.176884i
$509$	203.239	+	117.340i	0.399291	+	0.230531i	0.686178	−	0.727434i	$-0.259287\pi$
$509$	203.239	+	117.340i	0.399291	+	0.230531i	−0.286887	+	0.957964i	$0.592620\pi$
$510$		0			0
$511$	63.0464	−	51.9845i	0.123378	−	0.101731i
$512$	205.362	+	205.362i	0.401098	+	0.401098i
$513$		0			0
$514$	−50.9247	+	29.4014i	−0.0990754	+	0.0572012i
$515$	461.947	+	141.568i	0.896984	+	0.274890i
$516$		0			0
$517$	146.531	+	146.531i	0.283426	+	0.283426i
$518$	9.05844	−	94.1970i	0.0174873	−	0.181848i
$519$		0			0
$520$	−115.612	−	72.3497i	−0.222331	−	0.139134i
$521$	−264.414	−	457.979i	−0.507513	−	0.879038i	−0.999962	−	0.00869711i	$-0.997232\pi$
$521$	−264.414	−	457.979i	−0.507513	−	0.879038i	0.492449	−	0.870341i	$-0.336102\pi$
$522$		0			0
$523$	−96.7747	−	361.168i	−0.185038	−	0.690570i	−0.994622	−	0.103567i	$-0.966974\pi$
$523$	−96.7747	−	361.168i	−0.185038	−	0.690570i	0.809585	−	0.587003i	$-0.199692\pi$
$524$		−	60.4960i		−	0.115450i
$525$		0			0
$526$	29.0816			0.0552882
$527$	−164.151	+	43.9842i	−0.311483	+	0.0834615i
$528$		0			0
$529$	325.565	−	187.965i	0.615435	−	0.355321i
$530$	38.8963	−	62.1548i	0.0733892	−	0.117273i
$531$		0			0
$532$	205.574	−	288.280i	0.386418	−	0.541879i
$533$	472.702	−	472.702i	0.886871	−	0.886871i
$534$		0			0
$535$	−180.946	+	590.440i	−0.338217	+	1.10363i
$536$	67.4207	+	116.776i	0.125785	+	0.217866i
$537$		0			0
$538$	43.5076	−	43.5076i	0.0808692	−	0.0808692i
$539$	−143.222	+	164.840i	−0.265718	+	0.305825i
$540$		0			0
$541$	90.3132	−	156.427i	0.166937	−	0.289144i	−0.770404	−	0.637556i	$-0.779946\pi$
$541$	90.3132	−	156.427i	0.166937	−	0.289144i	0.937342	+	0.348412i	$0.113279\pi$
$542$	3.00617	−	11.2192i	0.00554643	−	0.0206996i
$543$		0			0
$544$	96.9346	+	55.9652i	0.178189	+	0.102877i
$545$	8.83806	−	248.340i	0.0162166	−	0.455669i
$546$		0			0
$547$	−17.8276	−	17.8276i	−0.0325916	−	0.0325916i	0.690623	−	0.723215i	$-0.257336\pi$
$547$	−17.8276	−	17.8276i	−0.0325916	−	0.0325916i	−0.723215	+	0.690623i	$0.757336\pi$
$548$	−232.107	−	866.235i	−0.423553	−	1.58072i
$549$		0			0
$550$	8.76146	−	25.3353i	0.0159299	−	0.0460642i
$551$	235.927	−	408.638i	0.428180	−	0.741629i
$552$		0			0
$553$	−420.845	+	191.853i	−0.761022	+	0.346931i
$554$		−	24.9386i		−	0.0450155i
$555$		0			0
$556$	201.140	+	348.385i	0.361763	+	0.626591i
$557$	189.707	−	707.997i	0.340587	−	1.27109i	−0.557096	−	0.830448i	$-0.688085\pi$
$557$	189.707	−	707.997i	0.340587	−	1.27109i	0.897683	−	0.440641i	$-0.145249\pi$
$558$		0			0
$559$		−	506.532i		−	0.906139i
$560$	531.179	+	70.2250i	0.948534	+	0.125402i
$561$		0			0
$562$	83.1916	−	22.2911i	0.148028	−	0.0396639i
$563$	805.856	+	215.928i	1.43136	+	0.383532i	0.889499	−	0.456936i	$-0.151053\pi$
$563$	805.856	+	215.928i	1.43136	+	0.383532i	0.541861	+	0.840468i	$0.317720\pi$
$564$		0			0
$565$	−67.2542	−	292.199i	−0.119034	−	0.517166i
$566$	−43.4295			−0.0767306
$567$		0			0
$568$	−114.909	+	114.909i	−0.202305	+	0.202305i
$569$	394.493	+	227.761i	0.693309	+	0.400282i	0.804851	−	0.593478i	$-0.202245\pi$
$569$	394.493	+	227.761i	0.693309	+	0.400282i	−0.111541	+	0.993760i	$0.535579\pi$
$570$		0			0
$571$	−79.5469	−	137.779i	−0.139312	−	0.241295i	0.787925	−	0.615772i	$-0.211156\pi$
$571$	−79.5469	−	137.779i	−0.139312	−	0.241295i	−0.927236	+	0.374477i	$0.877822\pi$
$572$	242.215	−	64.9012i	0.423452	−	0.113464i
$573$		0			0
$574$	27.6166	−	73.8917i	0.0481126	−	0.128731i
$575$	−233.705	+	202.610i	−0.406443	+	0.352365i
$576$		0			0
$577$	−193.065	+	720.527i	−0.334601	+	1.24875i	0.569700	+	0.821852i	$0.307059\pi$
$577$	−193.065	+	720.527i	−0.334601	+	1.24875i	−0.904301	+	0.426895i	$0.859607\pi$
$578$	−44.4749	−	11.9170i	−0.0769462	−	0.0206177i
$579$		0			0
$580$	724.382	+	25.7797i	1.24893	+	0.0444478i
$581$	−107.198	−	640.109i	−0.184507	−	1.10174i
$582$		0			0
$583$	70.2962	+	262.349i	0.120577	+	0.449998i
$584$	−19.3192	+	11.1539i	−0.0330808	+	0.0190992i
$585$		0			0
$586$	19.8431	−	34.3692i	0.0338619	−	0.0586505i
$587$	198.400	+	198.400i	0.337990	+	0.337990i	0.855611	−	0.517620i	$-0.173182\pi$
$587$	198.400	+	198.400i	0.337990	+	0.337990i	−0.517620	+	0.855611i	$0.673182\pi$
$588$		0			0
$589$		−	220.672i		−	0.374656i
$590$	31.0801	+	135.033i	0.0526781	+	0.228870i
$591$		0			0
$592$	222.611	−	830.797i	0.376033	−	1.40337i
$593$	−126.975	−	473.876i	−0.214123	−	0.799116i	−0.986474	−	0.163920i	$-0.947586\pi$
$593$	−126.975	−	473.876i	−0.214123	−	0.799116i	0.772351	−	0.635196i	$-0.219081\pi$
$594$		0			0
$595$	342.913	−	44.9556i	0.576324	−	0.0755557i
$596$	−1154.23			−1.93662
$597$		0			0
$598$	41.0437	+	10.9976i	0.0686350	+	0.0183907i
$599$	−821.554	+	474.325i	−1.37154	+	0.791861i	−0.991122	−	0.132953i	$-0.957554\pi$
$599$	−821.554	+	474.325i	−1.37154	+	0.791861i	−0.380421	+	0.924814i	$0.624221\pi$
$600$		0			0
$601$	1121.80			1.86655			0.933275	−	0.359161i	$-0.116937\pi$
$601$	1121.80			1.86655			0.933275	+	0.359161i	$0.116937\pi$
$602$	−24.7934	−	54.3865i	−0.0411851	−	0.0903430i
$603$		0			0
$604$	−708.202	−	408.881i	−1.17252	−	0.676955i
$605$	−237.113	−	446.663i	−0.391923	−	0.738287i
$606$		0			0
$607$	293.221	−	78.5682i	0.483065	−	0.129437i	−0.00906430	−	0.999959i	$-0.502885\pi$
$607$	293.221	−	78.5682i	0.483065	−	0.129437i	0.492130	+	0.870522i	$0.336219\pi$
$608$	−102.773	+	102.773i	−0.169035	+	0.169035i
$609$		0			0
$610$	−36.3975	−	39.0837i	−0.0596680	−	0.0640717i
$611$	−331.862	+	574.802i	−0.543146	+	0.940756i
$612$		0			0
$613$	−306.525	−	82.1330i	−0.500040	−	0.133985i	−2.15317e−5	−	1.00000i	$-0.500007\pi$
$613$	−306.525	−	82.1330i	−0.500040	−	0.133985i	−0.500019	+	0.866015i	$0.666674\pi$
$614$	−30.1516	−	17.4080i	−0.0491069	−	0.0283519i
$615$		0			0
$616$	45.9951	−	37.9249i	0.0746674	−	0.0615665i
$617$	405.225	+	405.225i	0.656767	+	0.656767i	0.954614	−	0.297847i	$-0.0962685\pi$
$617$	405.225	+	405.225i	0.656767	+	0.656767i	−0.297847	+	0.954614i	$0.596269\pi$
$618$		0			0
$619$	−906.466	+	523.349i	−1.46440	+	0.845474i	−0.999210	−	0.0397346i	$-0.987349\pi$
$619$	−906.466	+	523.349i	−1.46440	+	0.845474i	−0.465194	+	0.885209i	$0.654015\pi$
$620$	299.413	−	158.945i	0.482925	−	0.256363i
$621$		0			0
$622$	−1.82031	−	1.82031i	−0.00292655	−	0.00292655i
$623$	−80.6532	+	36.7678i	−0.129459	+	0.0590173i
$624$		0			0
$625$	−386.101	+	491.478i	−0.617762	+	0.786365i
$626$	−57.4444	−	99.4966i	−0.0917642	−	0.158940i
$627$		0			0
$628$	77.2841	+	288.428i	0.123064	+	0.459281i
$629$		−	555.177i		−	0.882635i
$630$		0			0
$631$	−340.356			−0.539392			−0.269696	−	0.962946i	$-0.586923\pi$
$631$	−340.356			−0.539392			−0.269696	+	0.962946i	$0.586923\pi$
$632$	121.963	−	32.6799i	0.192979	−	0.0517087i
$633$		0			0
$634$	−15.4364	+	8.91221i	−0.0243476	+	0.0140571i
$635$	−429.129	+	98.7708i	−0.675793	+	0.155545i
$636$		0			0
$637$	−628.700	−	306.446i	−0.986971	−	0.481077i
$638$	27.8834	−	27.8834i	0.0437044	−	0.0437044i
$639$		0			0
$640$	−283.907	−	87.0060i	−0.443604	−	0.135947i
$641$	−29.6837	−	51.4137i	−0.0463085	−	0.0802086i	0.841942	−	0.539568i	$-0.181412\pi$
$641$	−29.6837	−	51.4137i	−0.0463085	−	0.0802086i	−0.888251	+	0.459359i	$0.848079\pi$
$642$		0			0
$643$	−147.606	+	147.606i	−0.229558	+	0.229558i	−0.812508	−	0.582950i	$-0.801898\pi$
$643$	−147.606	+	147.606i	−0.229558	+	0.229558i	0.582950	+	0.812508i	$0.301898\pi$
$644$	−336.717	+	56.3897i	−0.522852	+	0.0875616i
$645$		0			0
$646$	−15.2536	+	26.4200i	−0.0236124	+	0.0408979i
$647$	−188.763	+	704.471i	−0.291750	+	1.08883i	0.652014	+	0.758207i	$0.273925\pi$
$647$	−188.763	+	704.471i	−0.291750	+	1.08883i	−0.943764	+	0.330620i	$0.892742\pi$
$648$		0			0
$649$	−444.510	−	256.638i	−0.684915	−	0.395436i
$650$	85.6442	+	6.10364i	0.131760	+	0.00939021i
$651$		0			0
$652$	547.551	+	547.551i	0.839802	+	0.839802i
$653$	−71.0567	−	265.187i	−0.108816	−	0.406106i	0.889934	−	0.456089i	$-0.150750\pi$
$653$	−71.0567	−	265.187i	−0.108816	−	0.406106i	−0.998750	+	0.0499826i	$0.984083\pi$
$654$		0			0
$655$	35.9776	+	67.7731i	0.0549277	+	0.103470i
$656$	358.487	−	620.917i	0.546474	−	0.946520i
$657$		0			0
$658$	−7.49706	+	77.9605i	−0.0113937	+	0.118481i
$659$		−	153.073i		−	0.232281i	−0.993233	−	0.116140i	$-0.962948\pi$
$659$		−	153.073i		−	0.232281i	0.993233	−	0.116140i	$-0.0370523\pi$
$660$		0			0
$661$	−427.398	−	740.276i	−0.646594	−	1.11993i	−0.983931	−	0.178549i	$-0.942860\pi$
$661$	−427.398	−	740.276i	−0.646594	−	1.11993i	0.337337	−	0.941384i	$-0.390474\pi$
$662$	23.2240	−	86.6732i	0.0350816	−	0.130926i
$663$		0			0
$664$			177.182i			0.266841i
$665$	−58.8599	+	445.214i	−0.0885112	+	0.669495i
$666$		0			0
$667$	−439.474	+	117.757i	−0.658882	+	0.176547i
$668$	1019.03	+	273.049i	1.52550	+	0.408756i
$669$		0			0
$670$	−71.9609	−	45.0330i	−0.107404	−	0.0672134i
$671$	197.833			0.294833
$672$		0			0
$673$	−26.8360	+	26.8360i	−0.0398752	+	0.0398752i	−0.726763	−	0.686888i	$-0.758976\pi$
$673$	−26.8360	+	26.8360i	−0.0398752	+	0.0398752i	0.686888	+	0.726763i	$0.258976\pi$
$674$	0.447934	+	0.258615i	0.000664591	+	0.000383702i
$675$		0			0
$676$	68.4690	+	118.592i	0.101286	+	0.175432i
$677$	−235.342	+	63.0598i	−0.347625	+	0.0931459i	−0.428407	−	0.903586i	$-0.640925\pi$
$677$	−235.342	+	63.0598i	−0.347625	+	0.0931459i	0.0807817	+	0.996732i	$0.474258\pi$
$678$		0			0
$679$	1226.03	−	205.323i	1.80565	−	0.302390i
$680$	−94.3561	−	3.35800i	−0.138759	−	0.00493823i
$681$		0			0
$682$	4.77306	−	17.8133i	0.00699862	−	0.0261192i
$683$	1285.99	+	344.581i	1.88286	+	0.504511i	0.999348	+	0.0361036i	$0.0114946\pi$
$683$	1285.99	+	344.581i	1.88286	+	0.504511i	0.883513	+	0.468407i	$0.155172\pi$
$684$		0			0
$685$	775.187	+	832.398i	1.13166	+	1.21518i
$686$	−82.5035	−	2.12995i	−0.120267	−	0.00310489i
$687$		0			0
$688$	−140.606	−	524.748i	−0.204369	−	0.762715i
$689$	−753.370	+	434.958i	−1.09342	+	0.631289i
$690$		0			0
$691$	260.502	−	451.203i	0.376993	−	0.652972i	−0.613630	−	0.789594i	$-0.710291\pi$
$691$	260.502	−	451.203i	0.376993	−	0.652972i	0.990623	+	0.136622i	$0.0436246\pi$
$692$	532.551	+	532.551i	0.769582	+	0.769582i
$693$		0			0
$694$			50.4544i			0.0727008i
$695$	−432.523	−	270.672i	−0.622336	−	0.389456i
$696$		0			0
$697$	119.779	−	447.021i	0.171849	−	0.641350i
$698$	−15.9451	−	59.5079i	−0.0228440	−	0.0852549i
$699$		0			0
$700$	−646.472	+	240.814i	−0.923532	+	0.344020i
$701$	387.575			0.552889			0.276444	−	0.961030i	$-0.410844\pi$
$701$	387.575			0.552889			0.276444	+	0.961030i	$0.410844\pi$
$702$		0			0
$703$	696.342	+	186.584i	0.990529	+	0.265411i
$704$	225.811	−	130.372i	0.320755	−	0.185188i
$705$		0			0
$706$	−0.771879			−0.00109331
$707$	−802.404	−	77.1630i	−1.13494	−	0.109141i
$708$		0			0
$709$	−13.1567	−	7.59601i	−0.0185567	−	0.0107137i	0.490693	−	0.871333i	$-0.336744\pi$
$709$	−13.1567	−	7.59601i	−0.0185567	−	0.0107137i	−0.509250	+	0.860619i	$0.670077\pi$
$710$	29.9769	−	97.8166i	0.0422210	−	0.137770i
$711$		0			0
$712$	23.3737	−	6.26296i	0.0328282	−	0.00879629i
$713$	−150.458	+	150.458i	−0.211021	+	0.211021i
$714$		0			0
$715$	−232.753	+	216.756i	−0.325529	+	0.303155i
$716$	−359.822	+	623.230i	−0.502545	+	0.870433i
$717$		0			0
$718$	−71.9873	−	19.2890i	−0.100261	−	0.0268648i
$719$	35.5781	+	20.5410i	0.0494827	+	0.0285689i	0.524537	−	0.851387i	$-0.324238\pi$
$719$	35.5781	+	20.5410i	0.0494827	+	0.0285689i	−0.475055	+	0.879956i	$0.657572\pi$
$720$		0			0
$721$	−633.607	−	236.807i	−0.878789	−	0.328442i
$722$	33.4093	+	33.4093i	0.0462733	+	0.0462733i
$723$		0			0
$724$	352.398	−	203.457i	0.486737	−	0.281018i
$725$	−826.850	+	401.917i	−1.14048	+	0.554369i
$726$		0			0
$727$	−198.452	−	198.452i	−0.272974	−	0.272974i	0.557322	−	0.830296i	$-0.311829\pi$
$727$	−198.452	−	198.452i	−0.272974	−	0.272974i	−0.830296	+	0.557322i	$0.811829\pi$
$728$	155.459	+	110.859i	0.213543	+	0.152279i
$729$		0			0
$730$	7.45016	−	11.9051i	0.0102057	−	0.0163083i
$731$	−175.331	−	303.682i	−0.239850	−	0.415433i
$732$		0			0
$733$	−68.7887	−	256.723i	−0.0938454	−	0.350236i	0.902996	−	0.429648i	$-0.141362\pi$
$733$	−68.7887	−	256.723i	−0.0938454	−	0.350236i	−0.996842	+	0.0794121i	$0.974696\pi$
$734$		−	84.4626i		−	0.115072i
$735$		0			0
$736$	140.145			0.190414
$737$	303.740	−	81.3868i	0.412130	−	0.110430i
$738$		0			0
$739$	990.596	−	571.921i	1.34045	−	0.773912i	0.353581	−	0.935404i	$-0.384964\pi$
$739$	990.596	−	571.921i	1.34045	−	0.773912i	0.986874	+	0.161492i	$0.0516306\pi$
$740$	248.396	+	1079.21i	0.335671	+	1.45839i
$741$		0			0
$742$	−59.5994	+	83.5771i	−0.0803227	+	0.112638i
$743$	43.0155	−	43.0155i	0.0578943	−	0.0578943i	−0.677567	−	0.735461i	$-0.736966\pi$
$743$	43.0155	−	43.0155i	0.0578943	−	0.0578943i	0.735461	+	0.677567i	$0.236966\pi$
$744$		0			0
$745$	1293.07	−	686.431i	1.73566	−	0.921384i
$746$	11.9341	+	20.6705i	0.0159975	+	0.0277085i
$747$		0			0
$748$	122.750	−	122.750i	0.164105	−	0.164105i
$749$	302.676	−	809.849i	0.404107	−	1.08124i
$750$		0			0
$751$	−627.063	+	1086.11i	−0.834971	+	1.44621i	0.0590826	+	0.998253i	$0.481182\pi$
$751$	−627.063	+	1086.11i	−0.834971	+	1.44621i	−0.894054	+	0.447960i	$0.852151\pi$
$752$	−184.240	+	687.594i	−0.245000	+	0.914353i
$753$		0			0
$754$	109.379	+	63.1499i	0.145065	+	0.0837531i
$755$	1036.56	+	36.8896i	1.37292	+	0.0488604i
$756$		0			0
$757$	−686.443	−	686.443i	−0.906795	−	0.906795i	0.0892176	−	0.996012i	$-0.471563\pi$
$757$	−686.443	−	686.443i	−0.906795	−	0.906795i	−0.996012	+	0.0892176i	$0.971563\pi$
$758$	−29.0700	−	108.491i	−0.0383509	−	0.143128i
$759$		0			0
$760$	35.9231	−	117.219i	0.0472672	−	0.154236i
$761$	−296.933	+	514.302i	−0.390187	+	0.675825i	−0.992474	−	0.122455i	$-0.960923\pi$
$761$	−296.933	+	514.302i	−0.390187	+	0.675825i	0.602287	+	0.798280i	$0.294256\pi$
$762$		0			0
$763$	−33.3017	+	346.298i	−0.0436458	+	0.453864i
$764$			1019.48i			1.33439i
$765$		0			0
$766$	−27.5658	−	47.7454i	−0.0359867	−	0.0623308i
$767$	425.490	−	1587.95i	0.554745	−	2.07034i
$768$		0			0
$769$			712.789i			0.926903i	0.886122	+	0.463452i	$0.153389\pi$
$769$			712.789i			0.926903i	−0.886122	+	0.463452i	$0.846611\pi$
$770$	−14.3811	+	34.6658i	−0.0186768	+	0.0450205i
$771$		0			0
$772$	−348.863	+	93.4774i	−0.451895	+	0.121085i
$773$	−79.8406	−	21.3932i	−0.103287	−	0.0276756i	0.206806	−	0.978382i	$-0.433693\pi$
$773$	−79.8406	−	21.3932i	−0.103287	−	0.0276756i	−0.310092	+	0.950706i	$0.600360\pi$
$774$		0			0
$775$	−240.904	+	356.129i	−0.310844	+	0.459521i
$776$	−339.366			−0.437328
$777$		0			0
$778$	91.5016	−	91.5016i	0.117611	−	0.117611i
$779$	520.429	+	300.470i	0.668073	+	0.385712i
$780$		0			0
$781$	189.485	+	328.198i	0.242619	+	0.420228i
$782$	28.4137	−	7.61343i	0.0363347	−	0.00973585i
$783$		0			0
$784$	−736.375	−	142.949i	−0.939254	−	0.182333i
$785$	−258.112	−	277.162i	−0.328805	−	0.353072i
$786$		0			0
$787$	−79.6677	+	297.324i	−0.101230	+	0.377794i	−0.997890	−	0.0649245i	$-0.979319\pi$
$787$	−79.6677	+	297.324i	−0.101230	+	0.377794i	0.896661	+	0.442719i	$0.145986\pi$
$788$	−1002.28	−	268.561i	−1.27193	−	0.340813i
$789$		0			0
$790$	−58.1723	+	54.1740i	−0.0736358	+	0.0685747i
$791$	69.3337	+	414.009i	0.0876533	+	0.523400i
$792$		0			0
$793$	163.998	+	612.047i	0.206806	+	0.771812i
$794$	17.2139	−	9.93842i	0.0216799	−	0.0125169i
$795$		0			0
$796$	−533.740	+	924.465i	−0.670528	+	1.16139i
$797$	3.52945	+	3.52945i	0.00442842	+	0.00442842i	0.709318	−	0.704889i	$-0.249003\pi$
$797$	3.52945	+	3.52945i	0.00442842	+	0.00442842i	−0.704889	+	0.709318i	$0.749003\pi$
$798$		0			0
$799$			459.482i			0.575072i
$800$	278.055	−	53.6636i	0.347569	−	0.0670795i
$801$		0			0
$802$	−9.08361	+	33.9005i	−0.0113262	+	0.0422700i
$803$	13.4645	+	50.2501i	0.0167677	+	0.0625780i
$804$		0			0
$805$	343.685	−	263.422i	0.426938	−	0.327232i
$806$	59.0667			0.0732837
$807$		0			0
$808$	212.567	+	56.9572i	0.263078	+	0.0704915i
$809$	1165.56	−	672.936i	1.44074	−	0.831812i	0.442842	−	0.896600i	$-0.353970\pi$
$809$	1165.56	−	672.936i	1.44074	−	0.831812i	0.997899	+	0.0647879i	$0.0206371\pi$
$810$		0			0
$811$	−325.024			−0.400769			−0.200385	−	0.979717i	$-0.564219\pi$
$811$	−325.024			−0.400769			−0.200385	+	0.979717i	$0.564219\pi$
$812$	−1010.12	−	97.1378i	−1.24399	−	0.119628i
$813$		0			0
$814$	52.1749	+	30.1232i	0.0640970	+	0.0370064i
$815$	−939.051	−	287.782i	−1.15221	−	0.353106i
$816$		0			0
$817$	439.824	−	117.850i	0.538340	−	0.144248i
$818$	68.7817	−	68.7817i	0.0840852	−	0.0840852i
$819$		0			0
$820$	−32.8323	+	922.552i	−0.0400394	+	1.12506i
$821$	−38.5615	+	66.7905i	−0.0469689	+	0.0813526i	−0.888554	−	0.458772i	$-0.848290\pi$
$821$	−38.5615	+	66.7905i	−0.0469689	+	0.0813526i	0.841585	+	0.540124i	$0.181623\pi$
$822$		0			0
$823$	−100.088	−	26.8184i	−0.121613	−	0.0325861i	0.197499	−	0.980303i	$-0.436718\pi$
$823$	−100.088	−	26.8184i	−0.121613	−	0.0325861i	−0.319112	+	0.947717i	$0.603385\pi$
$824$	159.920	+	92.3299i	0.194078	+	0.112051i
$825$		0			0
$826$	−32.0411	−	191.325i	−0.0387906	−	0.231629i
$827$	−489.613	−	489.613i	−0.592035	−	0.592035i	0.346146	−	0.938181i	$-0.387490\pi$
$827$	−489.613	−	489.613i	−0.592035	−	0.592035i	−0.938181	+	0.346146i	$0.887490\pi$
$828$		0			0
$829$	50.1987	−	28.9823i	0.0605534	−	0.0349605i	−0.469418	−	0.882976i	$-0.655536\pi$
$829$	50.1987	−	28.9823i	0.0605534	−	0.0349605i	0.529971	+	0.848016i	$0.322203\pi$
$830$	−52.3020	−	98.5243i	−0.0630145	−	0.118704i
$831$		0			0
$832$	590.530	+	590.530i	0.709772	+	0.709772i
$833$	−482.998	+	33.8940i	−0.579830	+	0.0406891i
$834$		0			0
$835$	−1304.00	+	300.136i	−1.56167	+	0.359444i
$836$	112.708	+	195.216i	0.134818	+	0.233512i
$837$		0			0
$838$	−25.2023	−	94.0562i	−0.0300743	−	0.112239i
$839$		−	389.998i		−	0.464836i	−0.972616	−	0.232418i	$-0.925336\pi$
$839$		−	389.998i		−	0.464836i	0.972616	−	0.232418i	$-0.0746638\pi$
$840$		0			0
$841$	−511.349			−0.608025
$842$	−100.127	+	26.8288i	−0.118915	+	0.0318632i
$843$		0			0
$844$	−1005.74	+	580.665i	−1.19164	+	0.687992i
$845$	−147.233	−	92.1380i	−0.174240	−	0.109039i
$846$		0			0
$847$	293.673	+	644.196i	0.346721	+	0.760562i
$848$	−659.725	+	659.725i	−0.777977	+	0.777977i
$849$		0			0
$850$	53.4591	−	25.9855i	0.0628930	−	0.0305712i
$851$	−347.561	−	601.992i	−0.408414	−	0.707394i
$852$		0			0
$853$	−862.758	+	862.758i	−1.01144	+	1.01144i	−0.0115062	+	0.999934i	$0.503663\pi$
$853$	−862.758	+	862.758i	−1.01144	+	1.01144i	−0.999934	+	0.0115062i	$0.996337\pi$
$854$	47.5666	+	57.6884i	0.0556986	+	0.0675508i
$855$		0			0
$856$	−118.012	+	204.403i	−0.137865	+	0.238789i
$857$	−99.8555	+	372.666i	−0.116518	+	0.434849i	−0.999396	−	0.0347522i	$-0.988936\pi$
$857$	−99.8555	+	372.666i	−0.116518	+	0.434849i	0.882878	+	0.469602i	$0.155602\pi$
$858$		0			0
$859$	−201.304	−	116.223i	−0.234347	−	0.135300i	0.378229	−	0.925712i	$-0.376533\pi$
$859$	−201.304	−	116.223i	−0.234347	−	0.135300i	−0.612576	+	0.790412i	$0.709867\pi$
$860$	476.697	+	511.879i	0.554298	+	0.595208i
$861$		0			0
$862$	10.9073	+	10.9073i	0.0126535	+	0.0126535i
$863$	126.253	+	471.181i	0.146295	+	0.545980i	0.999694	+	0.0247225i	$0.00787023\pi$
$863$	126.253	+	471.181i	0.146295	+	0.545980i	−0.853399	+	0.521258i	$0.825463\pi$
$864$		0			0
$865$	−913.325	−	279.898i	−1.05587	−	0.323581i
$866$	10.0274	−	17.3680i	0.0115790	−	0.0200554i
$867$		0			0
$868$	−431.826	+	196.859i	−0.497496	+	0.226796i
$869$		−	294.455i		−	0.338844i
$870$		0			0
$871$	503.582	+	872.229i	0.578165	+	1.00141i
$872$	24.5814	−	91.7389i	0.0281896	−	0.105205i
$873$		0			0
$874$			38.1972i			0.0437039i
$875$	581.022	−	654.246i	0.664025	−	0.747710i
$876$		0			0
$877$	−1002.06	+	268.502i	−1.14260	+	0.306159i	−0.779997	−	0.625783i	$-0.784779\pi$
$877$	−1002.06	+	268.502i	−1.14260	+	0.306159i	−0.362605	+	0.931943i	$0.618113\pi$
$878$	−70.4892	−	18.8875i	−0.0802838	−	0.0215120i
$879$		0			0
$880$	−180.955	+	289.160i	−0.205631	+	0.328591i
$881$	141.683			0.160821			0.0804103	−	0.996762i	$-0.474377\pi$
$881$	141.683			0.160821			0.0804103	+	0.996762i	$0.474377\pi$
$882$		0			0
$883$	1171.38	−	1171.38i	1.32659	−	1.32659i	0.418262	−	0.908326i	$-0.362639\pi$
$883$	1171.38	−	1171.38i	1.32659	−	1.32659i	0.908326	−	0.418262i	$-0.137361\pi$
$884$	481.516	+	278.003i	0.544701	+	0.314483i
$885$		0			0
$886$	−25.5720	−	44.2920i	−0.0288623	−	0.0499909i
$887$	−760.992	+	203.907i	−0.857939	+	0.229884i	−0.660865	−	0.750505i	$-0.729811\pi$
$887$	−760.992	+	203.907i	−0.857939	+	0.229884i	−0.197074	+	0.980389i	$0.563144\pi$
$888$		0			0
$889$	608.021	−	101.825i	0.683938	−	0.114539i
$890$	−11.1485	+	10.3822i	−0.0125264	+	0.0116654i
$891$		0			0
$892$	−12.9489	+	48.3260i	−0.0145167	+	0.0541771i
$893$	−576.315	−	154.423i	−0.645369	−	0.172926i
$894$		0			0
$895$	32.4635	−	912.189i	0.0362720	−	1.01921i
$896$	389.407	+	145.539i	0.434606	+	0.162431i
$897$		0			0
$898$	−16.5744	−	61.8564i	−0.0184570	−	0.0688824i
$899$	−547.721	+	316.227i	−0.609256	+	0.351754i
$900$		0			0
$901$	−301.112	+	521.542i	−0.334198	+	0.578848i
$902$	35.5115	+	35.5115i	0.0393697	+	0.0393697i
$903$		0			0
$904$		−	114.598i		−	0.126768i
$905$	−273.790	+	437.506i	−0.302530	+	0.483432i
$906$		0			0
$907$	7.44379	−	27.7806i	0.00820704	−	0.0306291i	−0.961701	−	0.274101i	$-0.911620\pi$
$907$	7.44379	−	27.7806i	0.00820704	−	0.0306291i	0.969908	+	0.243472i	$0.0782864\pi$
$908$	−367.051	−	1369.85i	−0.404241	−	1.50865i
$909$		0			0
$910$	−119.169	−	15.7548i	−0.130955	−	0.0173130i
$911$	1646.21			1.80704			0.903518	−	0.428549i	$-0.140975\pi$
$911$	1646.21			1.80704			0.903518	+	0.428549i	$0.140975\pi$
$912$		0			0
$913$	399.116	+	106.943i	0.437148	+	0.117133i
$914$	−65.7231	+	37.9453i	−0.0719071	+	0.0415156i
$915$		0			0
$916$	916.539			1.00059
$917$	−44.5595	−	97.7451i	−0.0485927	−	0.106592i
$918$		0			0
$919$	215.550	+	124.448i	0.234549	+	0.135417i	0.612669	−	0.790340i	$-0.290096\pi$
$919$	215.550	+	124.448i	0.234549	+	0.135417i	−0.378120	+	0.925757i	$0.623429\pi$
$920$	−104.415	+	55.4291i	−0.113494	+	0.0602490i
$921$		0			0
$922$	−142.673	+	38.2290i	−0.154742	+	0.0414631i
$923$	−858.287	+	858.287i	−0.929888	+	0.929888i
$924$		0			0
$925$	−920.091	−	1061.30i	−0.994693	−	1.14735i
$926$	−23.9286	+	41.4455i	−0.0258408	+	0.0447576i
$927$		0			0
$928$	402.365	+	107.813i	0.433583	+	0.116178i
$929$	1486.29	+	858.110i	1.59988	+	0.923692i	0.991509	+	0.130041i	$0.0415108\pi$
$929$	1486.29	+	858.110i	1.59988	+	0.923692i	0.608373	+	0.793651i	$0.291823\pi$
$930$		0			0
$931$	119.814	−	617.201i	0.128694	−	0.662945i
$932$	91.8253	+	91.8253i	0.0985250	+	0.0985250i
$933$		0			0
$934$	−66.8036	+	38.5691i	−0.0715242	+	0.0412945i
$935$	−64.5151	+	210.517i	−0.0690001	+	0.225152i
$936$		0			0
$937$	1113.44	+	1113.44i	1.18831	+	1.18831i	0.977535	+	0.210773i	$0.0675980\pi$
$937$	1113.44	+	1113.44i	1.18831	+	1.18831i	0.210773	+	0.977535i	$0.432402\pi$
$938$	96.7631	+	69.0025i	0.103159	+	0.0735634i
$939$		0			0
$940$	−205.581	−	893.185i	−0.218703	−	0.950197i
$941$	304.667	+	527.699i	0.323769	+	0.560785i	0.981263	−	0.192676i	$-0.0617165\pi$
$941$	304.667	+	527.699i	0.323769	+	0.560785i	−0.657493	+	0.753460i	$0.728383\pi$
$942$		0			0
$943$	−149.972	−	559.701i	−0.159037	−	0.593533i
$944$		−	1763.17i		−	1.86776i
$945$		0			0
$946$	38.0529			0.0402250
$947$	1459.40	−	391.045i	1.54108	−	0.412931i	0.614464	−	0.788945i	$-0.289372\pi$
$947$	1459.40	−	391.045i	1.54108	−	0.412931i	0.926614	+	0.376014i	$0.122706\pi$
$948$		0			0
$949$	−144.300	+	83.3116i	−0.152055	+	0.0877888i
$950$	14.6263	+	75.7853i	0.0153961	+	0.0797740i
$951$		0			0
$952$	131.575	+	12.6529i	0.138209	+	0.0132909i
$953$	−333.912	+	333.912i	−0.350380	+	0.350380i	−0.860251	−	0.509871i	$-0.829693\pi$
$953$	−333.912	+	333.912i	−0.350380	+	0.350380i	0.509871	+	0.860251i	$0.329693\pi$
$954$		0			0
$955$	−606.294	−	1142.11i	−0.634863	−	1.19593i
$956$	263.248	+	455.959i	0.275364	+	0.476945i
$957$		0			0
$958$	90.2600	−	90.2600i	0.0942171	−	0.0942171i
$959$	−1013.06	−	1228.64i	−1.05638	−	1.28117i
$960$		0			0
$961$	332.610	−	576.097i	0.346108	−	0.599477i
$962$	−49.9424	+	186.388i	−0.0519152	+	0.193750i
$963$		0			0
$964$	1575.89	+	909.839i	1.63474	+	0.943817i
$965$	335.235	−	312.194i	0.347394	−	0.323517i
$966$		0			0
$967$	28.0057	+	28.0057i	0.0289614	+	0.0289614i	0.721439	−	0.692478i	$-0.243481\pi$
$967$	28.0057	+	28.0057i	0.0289614	+	0.0289614i	−0.692478	+	0.721439i	$0.743481\pi$
$968$	−50.0237	−	186.691i	−0.0516774	−	0.192863i
$969$		0			0
$970$	188.709	−	100.177i	0.194545	−	0.103275i
$971$	−224.810	+	389.382i	−0.231524	+	0.401011i	−0.958257	−	0.285909i	$-0.907705\pi$
$971$	−224.810	+	389.382i	−0.231524	+	0.401011i	0.726733	+	0.686920i	$0.241038\pi$
$972$		0			0
$973$	581.597	+	414.741i	0.597736	+	0.426250i
$974$			34.1814i			0.0350938i
$975$		0			0
$976$	339.791	+	588.535i	0.348146	+	0.603007i
$977$	−455.305	+	1699.22i	−0.466024	+	1.73922i	0.187450	+	0.982274i	$0.439978\pi$
$977$	−455.305	+	1699.22i	−0.466024	+	1.73922i	−0.653474	+	0.756949i	$0.726689\pi$
$978$		0			0
$979$		−	56.4310i		−	0.0576415i
$980$	923.733	−	281.988i	0.942584	−	0.287743i
$981$		0			0
$982$	−22.8239	+	6.11563i	−0.0232422	+	0.00622773i
$983$	1268.01	+	339.761i	1.28993	+	0.345637i	0.837635	−	0.546230i	$-0.183937\pi$
$983$	1268.01	+	339.761i	1.28993	+	0.345637i	0.452299	+	0.891866i	$0.350604\pi$
$984$		0			0
$985$	1282.56	−	295.202i	1.30209	−	0.299698i
$986$	87.4346			0.0886761
$987$		0			0
$988$	−510.519	+	510.519i	−0.516720	+	0.516720i
$989$	−380.231	−	219.526i	−0.384460	−	0.221968i
$990$		0			0
$991$	−670.542	−	1161.41i	−0.676632	−	1.17196i	−0.975989	−	0.217820i	$-0.930106\pi$
$991$	−670.542	−	1161.41i	−0.676632	−	1.17196i	0.299357	−	0.954141i	$-0.403228\pi$
$992$	188.174	−	50.4211i	0.189692	−	0.0508277i
$993$		0			0
$994$	−50.1436	+	134.165i	−0.0504462	+	0.134975i
$995$	48.1545	−	1353.09i	0.0483965	−	1.35989i
$996$		0			0
$997$	147.587	−	550.802i	0.148031	−	0.552459i	−0.851571	−	0.524240i	$-0.824350\pi$
$997$	147.587	−	550.802i	0.148031	−	0.552459i	0.999602	−	0.0282195i	$-0.00898375\pi$
$998$	−20.2454	−	5.42474i	−0.0202860	−	0.00543561i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.8		64
3.2	odd	2		105.3.v.a.37.9	✓	64
5.3	odd	4	inner	315.3.ca.b.163.9		64
7.4	even	3	inner	315.3.ca.b.172.9		64
15.8	even	4		105.3.v.a.58.8	yes	64
21.11	odd	6		105.3.v.a.67.8	yes	64
35.18	odd	12	inner	315.3.ca.b.298.8		64
105.53	even	12		105.3.v.a.88.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.9	✓	64	3.2	odd	2
105.3.v.a.58.8	yes	64	15.8	even	4
105.3.v.a.67.8	yes	64	21.11	odd	6
105.3.v.a.88.9	yes	64	105.53	even	12
315.3.ca.b.37.8		64	1.1	even	1	trivial
315.3.ca.b.163.9		64	5.3	odd	4	inner
315.3.ca.b.172.9		64	7.4	even	3	inner
315.3.ca.b.298.8		64	35.18	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +O(q^{10})\)	\(q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +(-0.352512 + 1.15027i) q^{10} +(-2.22825 - 3.85944i) q^{11} +(10.0930 - 10.0930i) q^{13} +(0.589662 - 1.57771i) q^{14} +(7.65430 - 13.2576i) q^{16} +(2.55748 - 9.54465i) q^{17} +(11.1120 + 6.41554i) q^{19} +(-0.701025 + 19.6981i) q^{20} +(0.758230 + 0.758230i) q^{22} +(-3.20215 - 11.9506i) q^{23} +(-10.9293 - 22.4844i) q^{25} +(-1.71723 + 2.97433i) q^{26} +(2.64146 - 27.4680i) q^{28} -36.7743i q^{29} +(-8.59913 - 14.8941i) q^{31} +(-2.93176 + 10.9415i) q^{32} +2.37760i q^{34} +(13.3763 + 32.3431i) q^{35} +(54.2699 - 14.5416i) q^{37} +(-2.98215 - 0.799066i) q^{38} +(-2.14319 - 9.31149i) q^{40} +46.8347 q^{41} +(25.0932 - 25.0932i) q^{43} +(15.2143 + 8.78398i) q^{44} +(1.48846 + 2.57809i) q^{46} +(-44.9155 + 12.0351i) q^{47} +(-15.9642 - 46.3265i) q^{49} +(3.94038 + 4.54512i) q^{50} +(-14.5633 + 54.3510i) q^{52} +(-58.8689 - 15.7739i) q^{53} +(-22.2684 - 0.792499i) q^{55} +(2.20945 + 13.1932i) q^{56} +(2.29015 + 8.54695i) q^{58} +(99.7443 - 57.5874i) q^{59} +(-22.1961 + 38.4447i) q^{61} +(2.92612 + 2.92612i) q^{62} +58.5089i q^{64} +(-16.0080 - 69.5498i) q^{65} +(-18.2625 + 68.1567i) q^{67} +(10.0819 + 37.6260i) q^{68} +(-5.12307 - 6.68403i) q^{70} -85.0378 q^{71} +(-11.2757 - 3.02132i) q^{73} +(-11.7076 + 6.75940i) q^{74} -50.5815 q^{76} +(31.0522 + 2.98613i) q^{77} +(57.2212 + 33.0366i) q^{79} +(-35.8897 - 67.6074i) q^{80} +(-10.8851 + 2.91666i) q^{82} +(-65.5612 + 65.5612i) q^{83} +(-33.6712 - 36.1563i) q^{85} +(-4.26937 + 7.39477i) q^{86} +(-8.22613 - 2.20418i) q^{88} +(10.9662 + 6.33133i) q^{89} +(16.5030 + 98.5433i) q^{91} +(34.4872 + 34.4872i) q^{92} +(9.68960 - 5.59429i) q^{94} +(56.6660 - 30.0814i) q^{95} +(-125.573 - 125.573i) q^{97} +(6.59537 + 9.77284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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