LMFDB - Embedded newform 630.4.g.e.379.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,4,Mod(379,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.379"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$37.1712033036$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.1
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	630.379
Dual form			630.4.g.e.379.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000i q^{2} -4.00000 q^{4} +(-8.79796 + 6.89898i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +(13.7980 + 17.5959i) q^{10} -25.5959 q^{11} +89.1918i q^{13} +14.0000 q^{14} +16.0000 q^{16} -18.7878i q^{17} +11.7980 q^{19} +(35.1918 - 27.5959i) q^{20} +51.1918i q^{22} -159.373i q^{23} +(29.8082 - 121.394i) q^{25} +178.384 q^{26} -28.0000i q^{28} +19.7980 q^{29} -126.404 q^{31} -32.0000i q^{32} -37.5755 q^{34} +(-48.2929 - 61.5857i) q^{35} +282.969i q^{37} -23.5959i q^{38} +(-55.1918 - 70.3837i) q^{40} +144.384 q^{41} -326.929i q^{43} +102.384 q^{44} -318.747 q^{46} +117.435i q^{47} -49.0000 q^{49} +(-242.788 - 59.6163i) q^{50} -356.767i q^{52} -634.504i q^{53} +(225.192 - 176.586i) q^{55} -56.0000 q^{56} -39.5959i q^{58} -515.069 q^{59} +395.716 q^{61} +252.808i q^{62} -64.0000 q^{64} +(-615.333 - 784.706i) q^{65} -842.120i q^{67} +75.1510i q^{68} +(-123.171 + 96.5857i) q^{70} -402.100 q^{71} +303.171i q^{73} +565.939 q^{74} -47.1918 q^{76} -179.171i q^{77} -266.384 q^{79} +(-140.767 + 110.384i) q^{80} -288.767i q^{82} -753.253i q^{83} +(129.616 + 165.294i) q^{85} -653.857 q^{86} -204.767i q^{88} -842.967 q^{89} -624.343 q^{91} +637.494i q^{92} +234.869 q^{94} +(-103.798 + 81.3939i) q^{95} -1201.92i q^{97} +98.0000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 4 q^{5} + 16 q^{10} - 24 q^{11} + 56 q^{14} + 64 q^{16} + 8 q^{19} - 16 q^{20} + 276 q^{25} + 400 q^{26} + 40 q^{29} - 584 q^{31} + 320 q^{34} - 56 q^{35} - 64 q^{40} + 264 q^{41} + 96 q^{44}+ \cdots - 376 q^{95}+O(q^{100}) $ 4 * q - 16 * q^4 + 4 * q^5 + 16 * q^10 - 24 * q^11 + 56 * q^14 + 64 * q^16 + 8 * q^19 - 16 * q^20 + 276 * q^25 + 400 * q^26 + 40 * q^29 - 584 * q^31 + 320 * q^34 - 56 * q^35 - 64 * q^40 + 264 * q^41 + 96 * q^44 - 256 * q^46 - 196 * q^49 - 736 * q^50 + 744 * q^55 - 224 * q^56 + 448 * q^59 - 24 * q^61 - 256 * q^64 - 1168 * q^65 + 56 * q^70 + 312 * q^71 + 1088 * q^74 - 32 * q^76 - 752 * q^79 + 64 * q^80 + 832 * q^85 + 128 * q^86 + 1096 * q^89 - 1400 * q^91 + 2272 * q^94 - 376 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	−8.79796	+	6.89898i	−0.786913	+	0.617063i
$5$	−8.79796	+	6.89898i	−0.786913	+	0.617063i
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$			8.00000i			0.353553i
$9$		0			0
$10$	13.7980	+	17.5959i	0.436330	+	0.556432i
$11$	−25.5959			−0.701587			−0.350794	−	0.936453i	$-0.614088\pi$
$11$	−25.5959			−0.701587			−0.350794	+	0.936453i	$0.614088\pi$
$12$		0			0
$13$			89.1918i			1.90287i	0.307843	+	0.951437i	$0.400393\pi$
$13$			89.1918i			1.90287i	−0.307843	+	0.951437i	$0.599607\pi$
$14$	14.0000			0.267261
$15$		0			0
$16$	16.0000			0.250000
$17$		−	18.7878i		−	0.268041i	−0.990979	−	0.134021i	$-0.957211\pi$
$17$		−	18.7878i		−	0.268041i	0.990979	−	0.134021i	$-0.0427888\pi$
$18$		0			0
$19$	11.7980			0.142455			0.0712273	−	0.997460i	$-0.477308\pi$
$19$	11.7980			0.142455			0.0712273	+	0.997460i	$0.477308\pi$
$20$	35.1918	−	27.5959i	0.393457	−	0.308532i
$21$		0			0
$22$			51.1918i			0.496097i
$23$		−	159.373i		−	1.44486i	−0.691447	−	0.722428i	$-0.743026\pi$
$23$		−	159.373i		−	1.44486i	0.691447	−	0.722428i	$-0.256974\pi$
$24$		0			0
$25$	29.8082	−	121.394i	0.238465	−	0.971151i
$26$	178.384			1.34554
$27$		0			0
$28$		−	28.0000i		−	0.188982i
$29$	19.7980			0.126772			0.0633860	−	0.997989i	$-0.479810\pi$
$29$	19.7980			0.126772			0.0633860	+	0.997989i	$0.479810\pi$
$30$		0			0
$31$	−126.404			−0.732350			−0.366175	−	0.930546i	$-0.619333\pi$
$31$	−126.404			−0.732350			−0.366175	+	0.930546i	$0.619333\pi$
$32$		−	32.0000i		−	0.176777i
$33$		0			0
$34$	−37.5755			−0.189534
$35$	−48.2929	−	61.5857i	−0.233228	−	0.297425i
$36$		0			0
$37$			282.969i			1.25729i	0.777691	+	0.628647i	$0.216391\pi$
$37$			282.969i			1.25729i	−0.777691	+	0.628647i	$0.783609\pi$
$38$		−	23.5959i		−	0.100731i
$39$		0			0
$40$	−55.1918	−	70.3837i	−0.218165	−	0.278216i
$41$	144.384			0.549974			0.274987	−	0.961448i	$-0.411326\pi$
$41$	144.384			0.549974			0.274987	+	0.961448i	$0.411326\pi$
$42$		0			0
$43$		−	326.929i		−	1.15945i	−0.814814	−	0.579723i	$-0.803161\pi$
$43$		−	326.929i		−	1.15945i	0.814814	−	0.579723i	$-0.196839\pi$
$44$	102.384			0.350794
$45$		0			0
$46$	−318.747			−1.02167
$47$			117.435i			0.364460i	0.983256	+	0.182230i	$0.0583315\pi$
$47$			117.435i			0.364460i	−0.983256	+	0.182230i	$0.941668\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−242.788	−	59.6163i	−0.686707	−	0.168620i
$51$		0			0
$52$		−	356.767i		−	0.951437i
$53$		−	634.504i		−	1.64445i	−0.569163	−	0.822225i	$-0.692733\pi$
$53$		−	634.504i		−	1.64445i	0.569163	−	0.822225i	$-0.307267\pi$
$54$		0			0
$55$	225.192	−	176.586i	0.552088	−	0.432924i
$56$	−56.0000			−0.133631
$57$		0			0
$58$		−	39.5959i		−	0.0896414i
$59$	−515.069			−1.13655			−0.568274	−	0.822839i	$-0.692389\pi$
$59$	−515.069			−1.13655			−0.568274	+	0.822839i	$0.692389\pi$
$60$		0			0
$61$	395.716			0.830595			0.415297	−	0.909686i	$-0.363678\pi$
$61$	395.716			0.830595			0.415297	+	0.909686i	$0.363678\pi$
$62$			252.808i			0.517849i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−615.333	−	784.706i	−1.17419	−	1.49740i
$66$		0			0
$67$		−	842.120i		−	1.53554i	−0.640724	−	0.767772i	$-0.721366\pi$
$67$		−	842.120i		−	1.53554i	0.640724	−	0.767772i	$-0.278634\pi$
$68$			75.1510i			0.134021i
$69$		0			0
$70$	−123.171	+	96.5857i	−0.210311	+	0.164917i
$71$	−402.100			−0.672120			−0.336060	−	0.941841i	$-0.609094\pi$
$71$	−402.100			−0.672120			−0.336060	+	0.941841i	$0.609094\pi$
$72$		0			0
$73$			303.171i			0.486076i	0.970017	+	0.243038i	$0.0781439\pi$
$73$			303.171i			0.486076i	−0.970017	+	0.243038i	$0.921856\pi$
$74$	565.939			0.889041
$75$		0			0
$76$	−47.1918			−0.0712273
$77$		−	179.171i		−	0.265175i
$78$		0			0
$79$	−266.384			−0.379373			−0.189687	−	0.981845i	$-0.560747\pi$
$79$	−266.384			−0.379373			−0.189687	+	0.981845i	$0.560747\pi$
$80$	−140.767	+	110.384i	−0.196728	+	0.154266i
$81$		0			0
$82$		−	288.767i		−	0.388890i
$83$		−	753.253i		−	0.996148i	−0.867135	−	0.498074i	$-0.834041\pi$
$83$		−	753.253i		−	0.996148i	0.867135	−	0.498074i	$-0.165959\pi$
$84$		0			0
$85$	129.616	+	165.294i	0.165398	+	0.210925i
$86$	−653.857			−0.819851
$87$		0			0
$88$		−	204.767i		−	0.248049i
$89$	−842.967			−1.00398			−0.501991	−	0.864873i	$-0.667399\pi$
$89$	−842.967			−1.00398			−0.501991	+	0.864873i	$0.667399\pi$
$90$		0			0
$91$	−624.343			−0.719219
$92$			637.494i			0.722428i
$93$		0			0
$94$	234.869			0.257712
$95$	−103.798	+	81.3939i	−0.112099	+	0.0879035i
$96$		0			0
$97$		−	1201.92i		−	1.25811i	−0.777362	−	0.629053i	$-0.783443\pi$
$97$		−	1201.92i		−	1.25811i	0.777362	−	0.629053i	$-0.216557\pi$
$98$			98.0000i			0.101015i
$99$		0			0
$100$	−119.233	+	485.576i	−0.119233	+	0.485576i
$101$	−575.371			−0.566847			−0.283424	−	0.958995i	$-0.591470\pi$
$101$	−575.371			−0.566847			−0.283424	+	0.958995i	$0.591470\pi$
$102$		0			0
$103$		−	254.220i		−	0.243195i	−0.992579	−	0.121597i	$-0.961198\pi$
$103$		−	254.220i		−	0.243195i	0.992579	−	0.121597i	$-0.0388017\pi$
$104$	−713.535			−0.672768
$105$		0			0
$106$	−1269.01			−1.16280
$107$			1142.61i			1.03234i	0.856487	+	0.516168i	$0.172642\pi$
$107$			1142.61i			1.03234i	−0.856487	+	0.516168i	$0.827358\pi$
$108$		0			0
$109$	2054.28			1.80518			0.902589	−	0.430502i	$-0.141664\pi$
$109$	2054.28			1.80518			0.902589	+	0.430502i	$0.141664\pi$
$110$	−353.171	−	450.384i	−0.306123	−	0.390385i
$111$		0			0
$112$			112.000i			0.0944911i
$113$			890.827i			0.741610i	0.928711	+	0.370805i	$0.120918\pi$
$113$			890.827i			0.741610i	−0.928711	+	0.370805i	$0.879082\pi$
$114$		0			0
$115$	1099.51	+	1402.16i	0.891567	+	1.13698i
$116$	−79.1918			−0.0633860
$117$		0			0
$118$			1030.14i			0.803661i
$119$	131.514			0.101310
$120$		0			0
$121$	−675.849			−0.507775
$122$		−	791.433i		−	0.587319i
$123$		0			0
$124$	505.616			0.366175
$125$	575.243	+	1273.66i	0.411610	+	0.911360i
$126$		0			0
$127$		−	2304.16i		−	1.60993i	−0.593323	−	0.804965i	$-0.702184\pi$
$127$		−	2304.16i		−	1.60993i	0.593323	−	0.804965i	$-0.297816\pi$
$128$			128.000i			0.0883883i
$129$		0			0
$130$	−1569.41	+	1230.67i	−1.05882	+	0.830281i
$131$	−955.192			−0.637065			−0.318532	−	0.947912i	$-0.603190\pi$
$131$	−955.192			−0.637065			−0.318532	+	0.947912i	$0.603190\pi$
$132$		0			0
$133$			82.5857i			0.0538428i
$134$	−1684.24			−1.08579
$135$		0			0
$136$	150.302			0.0947669
$137$		−	1489.53i		−	0.928900i	−0.885599	−	0.464450i	$-0.846252\pi$
$137$		−	1489.53i		−	0.928900i	0.885599	−	0.464450i	$-0.153748\pi$
$138$		0			0
$139$	752.284			0.459049			0.229525	−	0.973303i	$-0.426283\pi$
$139$	752.284			0.459049			0.229525	+	0.973303i	$0.426283\pi$
$140$	193.171	+	246.343i	0.116614	+	0.148713i
$141$		0			0
$142$			804.200i			0.475260i
$143$		−	2282.95i		−	1.33503i
$144$		0			0
$145$	−174.182	+	136.586i	−0.0997586	+	0.0782264i
$146$	606.343			0.343707
$147$		0			0
$148$		−	1131.88i		−	0.628647i
$149$	1709.01			0.939648			0.469824	−	0.882760i	$-0.344317\pi$
$149$	1709.01			0.939648			0.469824	+	0.882760i	$0.344317\pi$
$150$		0			0
$151$	−2773.61			−1.49479			−0.747395	−	0.664380i	$-0.768696\pi$
$151$	−2773.61			−1.49479			−0.747395	+	0.664380i	$0.768696\pi$
$152$			94.3837i			0.0503653i
$153$		0			0
$154$	−358.343			−0.187507
$155$	1112.10	−	872.059i	0.576296	−	0.451906i
$156$		0			0
$157$		−	353.478i		−	0.179685i	−0.995956	−	0.0898426i	$-0.971364\pi$
$157$		−	353.478i		−	0.179685i	0.995956	−	0.0898426i	$-0.0286364\pi$
$158$			532.767i			0.268258i
$159$		0			0
$160$	220.767	+	281.535i	0.109082	+	0.139108i
$161$	1115.61			0.546104
$162$		0			0
$163$			885.231i			0.425378i	0.977120	+	0.212689i	$0.0682221\pi$
$163$			885.231i			0.425378i	−0.977120	+	0.212689i	$0.931778\pi$
$164$	−577.535			−0.274987
$165$		0			0
$166$	−1506.51			−0.704383
$167$			3220.26i			1.49216i	0.665855	+	0.746081i	$0.268067\pi$
$167$			3220.26i			1.49216i	−0.665855	+	0.746081i	$0.731933\pi$
$168$		0			0
$169$	−5758.18			−2.62093
$170$	330.588	−	259.233i	0.149147	−	0.116954i
$171$		0			0
$172$			1307.71i			0.579723i
$173$		−	3780.62i		−	1.66148i	−0.556663	−	0.830738i	$-0.687919\pi$
$173$		−	3780.62i		−	1.66148i	0.556663	−	0.830738i	$-0.312081\pi$
$174$		0			0
$175$	849.757	+	208.657i	0.367061	+	0.0901314i
$176$	−409.535			−0.175397
$177$		0			0
$178$			1685.93i			0.709922i
$179$	4534.07			1.89325			0.946627	−	0.322330i	$-0.104466\pi$
$179$	4534.07			1.89325			0.946627	+	0.322330i	$0.104466\pi$
$180$		0			0
$181$	1805.49			0.741443			0.370721	−	0.928744i	$-0.379110\pi$
$181$	1805.49			0.741443			0.370721	+	0.928744i	$0.379110\pi$
$182$			1248.69i			0.508565i
$183$		0			0
$184$	1274.99			0.510833
$185$	−1952.20	−	2489.55i	−0.775830	−	0.989382i
$186$		0			0
$187$			480.890i			0.188054i
$188$		−	469.739i		−	0.182230i
$189$		0			0
$190$	162.788	+	207.596i	0.0621572	+	0.0792663i
$191$	−3359.15			−1.27256			−0.636282	−	0.771456i	$-0.719529\pi$
$191$	−3359.15			−1.27256			−0.636282	+	0.771456i	$0.719529\pi$
$192$		0			0
$193$		−	2800.56i		−	1.04450i	−0.852792	−	0.522251i	$-0.825092\pi$
$193$		−	2800.56i		−	1.04450i	0.852792	−	0.522251i	$-0.174908\pi$
$194$	−2403.84			−0.889616
$195$		0			0
$196$	196.000			0.0714286
$197$			3252.52i			1.17631i	0.808749	+	0.588154i	$0.200145\pi$
$197$			3252.52i			1.17631i	−0.808749	+	0.588154i	$0.799855\pi$
$198$		0			0
$199$	1525.31			0.543347			0.271674	−	0.962389i	$-0.412423\pi$
$199$	1525.31			0.543347			0.271674	+	0.962389i	$0.412423\pi$
$200$	971.151	+	238.465i	0.343354	+	0.0843102i
$201$		0			0
$202$			1150.74i			0.400822i
$203$			138.586i			0.0479153i
$204$		0			0
$205$	−1270.28	+	996.100i	−0.432782	+	0.339369i
$206$	−508.441			−0.171965
$207$		0			0
$208$			1427.07i			0.475719i
$209$	−301.980			−0.0999443
$210$		0			0
$211$	−2934.29			−0.957370			−0.478685	−	0.877987i	$-0.658886\pi$
$211$	−2934.29			−0.957370			−0.478685	+	0.877987i	$0.658886\pi$
$212$			2538.02i			0.822225i
$213$		0			0
$214$	2285.21			0.729971
$215$	2255.47	+	2876.30i	0.715451	+	0.912383i
$216$		0			0
$217$		−	884.829i		−	0.276802i
$218$		−	4108.56i		−	1.27645i
$219$		0			0
$220$	−900.767	+	706.343i	−0.276044	+	0.216462i
$221$	1675.71			0.510049
$222$		0			0
$223$		−	3626.30i		−	1.08895i	−0.838778	−	0.544473i	$-0.816730\pi$
$223$		−	3626.30i		−	1.08895i	0.838778	−	0.544473i	$-0.183270\pi$
$224$	224.000			0.0668153
$225$		0			0
$226$	1781.65			0.524397
$227$		−	2189.45i		−	0.640171i	−0.947389	−	0.320086i	$-0.896288\pi$
$227$		−	2189.45i		−	0.640171i	0.947389	−	0.320086i	$-0.103712\pi$
$228$		0			0
$229$	5501.00			1.58741			0.793704	−	0.608304i	$-0.208150\pi$
$229$	5501.00			1.58741			0.793704	+	0.608304i	$0.208150\pi$
$230$	2804.32	−	2199.03i	0.803963	−	0.630433i
$231$		0			0
$232$			158.384i			0.0448207i
$233$		−	3927.72i		−	1.10435i	−0.833729	−	0.552174i	$-0.813798\pi$
$233$		−	3927.72i		−	1.10435i	0.833729	−	0.552174i	$-0.186202\pi$
$234$		0			0
$235$	−810.180	−	1033.19i	−0.224895	−	0.286798i
$236$	2060.28			0.568274
$237$		0			0
$238$		−	263.029i		−	0.0716370i
$239$	4435.11			1.20035			0.600174	−	0.799869i	$-0.295098\pi$
$239$	4435.11			1.20035			0.600174	+	0.799869i	$0.295098\pi$
$240$		0			0
$241$	4575.81			1.22304			0.611522	−	0.791227i	$-0.290557\pi$
$241$	4575.81			1.22304			0.611522	+	0.791227i	$0.290557\pi$
$242$			1351.70i			0.359051i
$243$		0			0
$244$	−1582.87			−0.415297
$245$	431.100	−	338.050i	0.112416	−	0.0881519i
$246$		0			0
$247$			1052.28i			0.271073i
$248$		−	1011.23i		−	0.258925i
$249$		0			0
$250$	2547.33	−	1150.49i	0.644429	−	0.291052i
$251$	−1646.96			−0.414163			−0.207081	−	0.978324i	$-0.566397\pi$
$251$	−1646.96			−0.414163			−0.207081	+	0.978324i	$0.566397\pi$
$252$		0			0
$253$			4079.31i			1.01369i
$254$	−4608.32			−1.13839
$255$		0			0
$256$	256.000			0.0625000
$257$			2811.64i			0.682432i	0.939985	+	0.341216i	$0.110839\pi$
$257$			2811.64i			0.682432i	−0.939985	+	0.341216i	$0.889161\pi$
$258$		0			0
$259$	−1980.79			−0.475212
$260$	2461.33	+	3138.82i	0.587097	+	0.748699i
$261$		0			0
$262$			1910.38i			0.450473i
$263$			3103.13i			0.727556i	0.931486	+	0.363778i	$0.118513\pi$
$263$			3103.13i			0.727556i	−0.931486	+	0.363778i	$0.881487\pi$
$264$		0			0
$265$	4377.43	+	5582.34i	1.01473	+	1.29404i
$266$	165.171			0.0380726
$267$		0			0
$268$			3368.48i			0.767772i
$269$	−61.1877			−0.0138687			−0.00693435	−	0.999976i	$-0.502207\pi$
$269$	−61.1877			−0.0138687			−0.00693435	+	0.999976i	$0.502207\pi$
$270$		0			0
$271$	97.6285			0.0218838			0.0109419	−	0.999940i	$-0.496517\pi$
$271$	97.6285			0.0218838			0.0109419	+	0.999940i	$0.496517\pi$
$272$		−	300.604i		−	0.0670103i
$273$		0			0
$274$	−2979.07			−0.656832
$275$	−762.967	+	3107.19i	−0.167304	+	0.681347i
$276$		0			0
$277$		−	4719.24i		−	1.02365i	−0.859089	−	0.511826i	$-0.828969\pi$
$277$		−	4719.24i		−	1.02365i	0.859089	−	0.511826i	$-0.171031\pi$
$278$		−	1504.57i		−	0.324597i
$279$		0			0
$280$	492.686	−	386.343i	0.105156	−	0.0824586i
$281$	−995.094			−0.211254			−0.105627	−	0.994406i	$-0.533685\pi$
$281$	−995.094			−0.211254			−0.105627	+	0.994406i	$0.533685\pi$
$282$		0			0
$283$		−	7995.58i		−	1.67946i	−0.543002	−	0.839732i	$-0.682712\pi$
$283$		−	7995.58i		−	1.67946i	0.543002	−	0.839732i	$-0.317288\pi$
$284$	1608.40			0.336060
$285$		0			0
$286$	−4565.89			−0.944010
$287$			1010.69i			0.207871i
$288$		0			0
$289$	4560.02			0.928154
$290$	273.171	+	348.363i	0.0553144	+	0.0705400i
$291$		0			0
$292$		−	1212.69i		−	0.243038i
$293$			8930.79i			1.78069i	0.455286	+	0.890345i	$0.349537\pi$
$293$			8930.79i			1.78069i	−0.455286	+	0.890345i	$0.650463\pi$
$294$		0			0
$295$	4531.56	−	3553.45i	0.894365	−	0.701322i
$296$	−2263.76			−0.444521
$297$		0			0
$298$		−	3418.02i		−	0.664432i
$299$	14214.8			2.74938
$300$		0			0
$301$	2288.50			0.438229
$302$			5547.22i			1.05698i
$303$		0			0
$304$	188.767			0.0356137
$305$	−3481.50	+	2730.04i	−0.653606	+	0.512530i
$306$		0			0
$307$		−	2515.79i		−	0.467700i	−0.972273	−	0.233850i	$-0.924868\pi$
$307$		−	2515.79i		−	0.467700i	0.972273	−	0.233850i	$-0.0751324\pi$
$308$			716.686i			0.132588i
$309$		0			0
$310$	−1744.12	−	2224.20i	−0.319546	−	0.407503i
$311$	−3759.39			−0.685452			−0.342726	−	0.939435i	$-0.611350\pi$
$311$	−3759.39			−0.685452			−0.342726	+	0.939435i	$0.611350\pi$
$312$		0			0
$313$			6825.91i			1.23266i	0.787487	+	0.616331i	$0.211382\pi$
$313$			6825.91i			1.23266i	−0.787487	+	0.616331i	$0.788618\pi$
$314$	−706.955			−0.127057
$315$		0			0
$316$	1065.53			0.189687
$317$		−	2464.94i		−	0.436734i	−0.975867	−	0.218367i	$-0.929927\pi$
$317$		−	2464.94i		−	0.436734i	0.975867	−	0.218367i	$-0.0700730\pi$
$318$		0			0
$319$	−506.747			−0.0889416
$320$	563.069	−	441.535i	0.0983642	−	0.0771329i
$321$		0			0
$322$		−	2231.23i		−	0.386154i
$323$		−	221.657i		−	0.0381837i
$324$		0			0
$325$	10827.3	+	2658.64i	1.84798	+	0.453769i
$326$	1770.46			0.300788
$327$		0			0
$328$			1155.07i			0.194445i
$329$	−822.043			−0.137753
$330$		0			0
$331$	3780.36			0.627756			0.313878	−	0.949463i	$-0.398372\pi$
$331$	3780.36			0.627756			0.313878	+	0.949463i	$0.398372\pi$
$332$			3013.01i			0.498074i
$333$		0			0
$334$	6440.52			1.05512
$335$	5809.77	+	7408.94i	0.947528	+	1.20834i
$336$		0			0
$337$		−	1914.39i		−	0.309446i	−0.987958	−	0.154723i	$-0.950551\pi$
$337$		−	1914.39i		−	0.309446i	0.987958	−	0.154723i	$-0.0494485\pi$
$338$			11516.4i			1.85328i
$339$		0			0
$340$	−518.465	−	661.176i	−0.0826992	−	0.105463i
$341$	3235.43			0.513807
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	2615.43			0.409926
$345$		0			0
$346$	−7561.24			−1.17484
$347$		−	9118.93i		−	1.41075i	−0.708835	−	0.705375i	$-0.750779\pi$
$347$		−	9118.93i		−	1.41075i	0.708835	−	0.705375i	$-0.249221\pi$
$348$		0			0
$349$	−4832.45			−0.741189			−0.370594	−	0.928795i	$-0.620846\pi$
$349$	−4832.45			−0.741189			−0.370594	+	0.928795i	$0.620846\pi$
$350$	417.314	−	1699.51i	0.0637325	−	0.259551i
$351$		0			0
$352$			819.069i			0.124024i
$353$		−	2806.58i		−	0.423170i	−0.977360	−	0.211585i	$-0.932138\pi$
$353$		−	2806.58i		−	0.423170i	0.977360	−	0.211585i	$-0.0678625\pi$
$354$		0			0
$355$	3537.66	−	2774.08i	0.528900	−	0.414740i
$356$	3371.87			0.501991
$357$		0			0
$358$		−	9068.15i		−	1.33873i
$359$	−1075.06			−0.158049			−0.0790246	−	0.996873i	$-0.525181\pi$
$359$	−1075.06			−0.158049			−0.0790246	+	0.996873i	$0.525181\pi$
$360$		0			0
$361$	−6719.81			−0.979707
$362$		−	3610.98i		−	0.524279i
$363$		0			0
$364$	2497.37			0.359609
$365$	−2091.57	−	2667.29i	−0.299940	−	0.382500i
$366$		0			0
$367$		−	367.020i		−	0.0522025i	−0.999659	−	0.0261012i	$-0.991691\pi$
$367$		−	367.020i		−	0.0522025i	0.999659	−	0.0261012i	$-0.00830922\pi$
$368$		−	2549.98i		−	0.361214i
$369$		0			0
$370$	−4979.11	+	3904.40i	−0.699598	+	0.548595i
$371$	4441.53			0.621544
$372$		0			0
$373$		−	1304.56i		−	0.181092i	−0.995892	−	0.0905461i	$-0.971139\pi$
$373$		−	1304.56i		−	0.181092i	0.995892	−	0.0905461i	$-0.0288613\pi$
$374$	961.780			0.132974
$375$		0			0
$376$	−939.478			−0.128856
$377$			1765.82i			0.241231i
$378$		0			0
$379$	−5340.61			−0.723822			−0.361911	−	0.932213i	$-0.617876\pi$
$379$	−5340.61			−0.723822			−0.361911	+	0.932213i	$0.617876\pi$
$380$	415.192	−	325.576i	0.0560497	−	0.0439518i
$381$		0			0
$382$			6718.31i			0.899839i
$383$		−	6662.27i		−	0.888841i	−0.895818	−	0.444420i	$-0.853410\pi$
$383$		−	6662.27i		−	0.888841i	0.895818	−	0.444420i	$-0.146590\pi$
$384$		0			0
$385$	1236.10	+	1576.34i	0.163630	+	0.208670i
$386$	−5601.13			−0.738575
$387$		0			0
$388$			4807.67i			0.629053i
$389$	−6313.48			−0.822895			−0.411448	−	0.911433i	$-0.634977\pi$
$389$	−6313.48			−0.822895			−0.411448	+	0.911433i	$0.634977\pi$
$390$		0			0
$391$	−2994.27			−0.387281
$392$		−	392.000i		−	0.0505076i
$393$		0			0
$394$	6505.05			0.831776
$395$	2343.63	−	1837.78i	0.298534	−	0.234098i
$396$		0			0
$397$			14210.6i			1.79650i	0.439490	+	0.898248i	$0.355159\pi$
$397$			14210.6i			1.79650i	−0.439490	+	0.898248i	$0.644841\pi$
$398$		−	3050.61i		−	0.384204i
$399$		0			0
$400$	476.931	−	1942.30i	0.0596163	−	0.242788i
$401$	−5578.59			−0.694717			−0.347359	−	0.937732i	$-0.612921\pi$
$401$	−5578.59			−0.694717			−0.347359	+	0.937732i	$0.612921\pi$
$402$		0			0
$403$		−	11274.2i		−	1.39357i
$404$	2301.49			0.283424
$405$		0			0
$406$	277.171			0.0338812
$407$		−	7242.86i		−	0.882101i
$408$		0			0
$409$	−11914.0			−1.44037			−0.720184	−	0.693783i	$-0.755943\pi$
$409$	−11914.0			−1.44037			−0.720184	+	0.693783i	$0.755943\pi$
$410$	1992.20	+	2540.56i	0.239970	+	0.306023i
$411$		0			0
$412$			1016.88i			0.121597i
$413$		−	3605.49i		−	0.429575i
$414$		0			0
$415$	5196.68	+	6627.09i	0.614686	+	0.783882i
$416$	2854.14			0.336384
$417$		0			0
$418$			603.959i			0.0706713i
$419$	−12093.0			−1.40998			−0.704990	−	0.709217i	$-0.749049\pi$
$419$	−12093.0			−1.40998			−0.704990	+	0.709217i	$0.749049\pi$
$420$		0			0
$421$	−12188.5			−1.41100			−0.705500	−	0.708710i	$-0.749277\pi$
$421$	−12188.5			−1.41100			−0.705500	+	0.708710i	$0.749277\pi$
$422$			5868.59i			0.676963i
$423$		0			0
$424$	5076.03			0.581401
$425$	−2280.72	−	560.028i	−0.260308	−	0.0639185i
$426$		0			0
$427$			2770.01i			0.313935i
$428$		−	4570.42i		−	0.516168i
$429$		0			0
$430$	5752.61	−	4510.95i	0.645152	−	0.505900i
$431$	−4968.16			−0.555238			−0.277619	−	0.960691i	$-0.589545\pi$
$431$	−4968.16			−0.555238			−0.277619	+	0.960691i	$0.589545\pi$
$432$		0			0
$433$			14483.7i			1.60749i	0.594974	+	0.803745i	$0.297162\pi$
$433$			14483.7i			1.60749i	−0.594974	+	0.803745i	$0.702838\pi$
$434$	−1769.66			−0.195729
$435$		0			0
$436$	−8217.13			−0.902589
$437$		−	1880.28i		−	0.205826i
$438$		0			0
$439$	9937.64			1.08040			0.540202	−	0.841535i	$-0.318348\pi$
$439$	9937.64			1.08040			0.540202	+	0.841535i	$0.318348\pi$
$440$	1412.69	+	1801.53i	0.153062	+	0.195193i
$441$		0			0
$442$		−	3351.43i		−	0.360659i
$443$			17139.6i			1.83821i	0.394013	+	0.919105i	$0.371087\pi$
$443$			17139.6i			1.83821i	−0.394013	+	0.919105i	$0.628913\pi$
$444$		0			0
$445$	7416.39	−	5815.61i	0.790047	−	0.619520i
$446$	−7252.60			−0.770001
$447$		0			0
$448$		−	448.000i		−	0.0472456i
$449$	1555.34			0.163477			0.0817385	−	0.996654i	$-0.473953\pi$
$449$	1555.34			0.163477			0.0817385	+	0.996654i	$0.473953\pi$
$450$		0			0
$451$	−3695.63			−0.385855
$452$		−	3563.31i		−	0.370805i
$453$		0			0
$454$	−4378.90			−0.452669
$455$	5492.94	−	4307.33i	0.565963	−	0.443804i
$456$		0			0
$457$			18409.2i			1.88435i	0.335124	+	0.942174i	$0.391222\pi$
$457$			18409.2i			1.88435i	−0.335124	+	0.942174i	$0.608778\pi$
$458$		−	11002.0i		−	1.12247i
$459$		0			0
$460$	−4398.06	−	5608.64i	−0.445784	−	0.568488i
$461$	−6616.52			−0.668465			−0.334232	−	0.942491i	$-0.608477\pi$
$461$	−6616.52			−0.668465			−0.334232	+	0.942491i	$0.608477\pi$
$462$		0			0
$463$			12605.5i			1.26529i	0.774443	+	0.632644i	$0.218030\pi$
$463$			12605.5i			1.26529i	−0.774443	+	0.632644i	$0.781970\pi$
$464$	316.767			0.0316930
$465$		0			0
$466$	−7855.43			−0.780892
$467$		−	16291.5i		−	1.61431i	−0.590340	−	0.807155i	$-0.701006\pi$
$467$		−	16291.5i		−	1.61431i	0.590340	−	0.807155i	$-0.298994\pi$
$468$		0			0
$469$	5894.84			0.580381
$470$	−2066.37	+	1620.36i	−0.202797	+	0.159025i
$471$		0			0
$472$		−	4120.55i		−	0.401830i
$473$			8368.04i			0.813452i
$474$		0			0
$475$	351.675	−	1432.20i	0.0339705	−	0.138345i
$476$	−526.057			−0.0506550
$477$		0			0
$478$		−	8870.22i		−	0.848775i
$479$	11506.3			1.09757			0.548785	−	0.835963i	$-0.315091\pi$
$479$	11506.3			1.09757			0.548785	+	0.835963i	$0.315091\pi$
$480$		0			0
$481$	−25238.6			−2.39247
$482$		−	9151.62i		−	0.864823i
$483$		0			0
$484$	2703.40			0.253888
$485$	8292.01	+	10574.4i	0.776332	+	0.990021i
$486$		0			0
$487$			16502.9i			1.53556i	0.640714	+	0.767780i	$0.278639\pi$
$487$			16502.9i			1.53556i	−0.640714	+	0.767780i	$0.721361\pi$
$488$			3165.73i			0.293660i
$489$		0			0
$490$	−676.100	−	862.200i	−0.0623328	−	0.0794903i
$491$	−9269.67			−0.852004			−0.426002	−	0.904722i	$-0.640078\pi$
$491$	−9269.67			−0.852004			−0.426002	+	0.904722i	$0.640078\pi$
$492$		0			0
$493$		−	371.959i		−	0.0339801i
$494$	2104.56			0.191678
$495$		0			0
$496$	−2022.47			−0.183087
$497$		−	2814.70i		−	0.254037i
$498$		0			0
$499$	−13167.3			−1.18126			−0.590631	−	0.806941i	$-0.701121\pi$
$499$	−13167.3			−1.18126			−0.590631	+	0.806941i	$0.701121\pi$
$500$	−2300.97	−	5094.66i	−0.205805	−	0.455680i
$501$		0			0
$502$			3293.91i			0.292857i
$503$		−	16299.1i		−	1.44481i	−0.691469	−	0.722406i	$-0.743036\pi$
$503$		−	16299.1i		−	1.44481i	0.691469	−	0.722406i	$-0.256964\pi$
$504$		0			0
$505$	5062.09	−	3969.48i	0.446060	−	0.349781i
$506$	8158.62			0.716788
$507$		0			0
$508$			9216.64i			0.804965i
$509$	−10595.4			−0.922656			−0.461328	−	0.887230i	$-0.652627\pi$
$509$	−10595.4			−0.922656			−0.461328	+	0.887230i	$0.652627\pi$
$510$		0			0
$511$	−2122.20			−0.183719
$512$		−	512.000i		−	0.0441942i
$513$		0			0
$514$	5623.27			0.482552
$515$	1753.86	+	2236.62i	0.150067	+	0.191373i
$516$		0			0
$517$		−	3005.85i		−	0.255700i
$518$			3961.57i			0.336026i
$519$		0			0
$520$	6277.65	−	4922.66i	0.529410	−	0.415140i
$521$	3930.10			0.330481			0.165241	−	0.986253i	$-0.447160\pi$
$521$	3930.10			0.330481			0.165241	+	0.986253i	$0.447160\pi$
$522$		0			0
$523$		−	15430.7i		−	1.29013i	−0.764129	−	0.645064i	$-0.776831\pi$
$523$		−	15430.7i		−	1.29013i	0.764129	−	0.645064i	$-0.223169\pi$
$524$	3820.77			0.318532
$525$		0			0
$526$	6206.26			0.514459
$527$			2374.85i			0.196300i
$528$		0			0
$529$	−13232.9			−1.08761
$530$	11164.7	−	8754.86i	0.915024	−	0.717522i
$531$		0			0
$532$		−	330.343i		−	0.0269214i
$533$			12877.8i			1.04653i
$534$		0			0
$535$	−7882.82	−	10052.6i	−0.637017	−	0.812359i
$536$	6736.96			0.542896
$537$		0			0
$538$			122.375i			0.00980665i
$539$	1254.20			0.100227
$540$		0			0
$541$	−24132.0			−1.91777			−0.958885	−	0.283794i	$-0.908407\pi$
$541$	−24132.0			−1.91777			−0.958885	+	0.283794i	$0.908407\pi$
$542$		−	195.257i		−	0.0154742i
$543$		0			0
$544$	−601.208			−0.0473834
$545$	−18073.5	+	14172.4i	−1.42052	+	1.11391i
$546$		0			0
$547$		−	3505.64i		−	0.274022i	−0.990569	−	0.137011i	$-0.956250\pi$
$547$		−	3505.64i		−	0.274022i	0.990569	−	0.137011i	$-0.0437496\pi$
$548$			5958.13i			0.464450i
$549$		0			0
$550$	6214.38	+	1525.93i	0.481785	+	0.118302i
$551$	233.576			0.0180593
$552$		0			0
$553$		−	1864.69i		−	0.143390i
$554$	−9438.48			−0.723831
$555$		0			0
$556$	−3009.13			−0.229525
$557$		−	14427.0i		−	1.09747i	−0.835995	−	0.548737i	$-0.815109\pi$
$557$		−	14427.0i		−	1.09747i	0.835995	−	0.548737i	$-0.184891\pi$
$558$		0			0
$559$	29159.4			2.20628
$560$	−772.686	−	985.371i	−0.0583070	−	0.0743563i
$561$		0			0
$562$			1990.19i			0.149379i
$563$			9972.47i			0.746518i	0.927727	+	0.373259i	$0.121760\pi$
$563$			9972.47i			0.746518i	−0.927727	+	0.373259i	$0.878240\pi$
$564$		0			0
$565$	−6145.79	−	7837.46i	−0.457620	−	0.583583i
$566$	−15991.2			−1.18756
$567$		0			0
$568$		−	3216.80i		−	0.237630i
$569$	−25180.3			−1.85521			−0.927605	−	0.373563i	$-0.878136\pi$
$569$	−25180.3			−1.85521			−0.927605	+	0.373563i	$0.878136\pi$
$570$		0			0
$571$	6146.38			0.450470			0.225235	−	0.974305i	$-0.427685\pi$
$571$	6146.38			0.450470			0.225235	+	0.974305i	$0.427685\pi$
$572$			9131.79i			0.667516i
$573$		0			0
$574$	2021.37			0.146987
$575$	−19347.0	−	4750.63i	−1.40317	−	0.344548i
$576$		0			0
$577$		−	12735.9i		−	0.918895i	−0.888205	−	0.459447i	$-0.848048\pi$
$577$		−	12735.9i		−	0.918895i	0.888205	−	0.459447i	$-0.151952\pi$
$578$		−	9120.04i		−	0.656304i
$579$		0			0
$580$	696.727	−	546.343i	0.0498793	−	0.0391132i
$581$	5272.77			0.376508
$582$		0			0
$583$			16240.7i			1.15372i
$584$	−2425.37			−0.171854
$585$		0			0
$586$	17861.6			1.25914
$587$			13223.9i			0.929829i	0.885355	+	0.464915i	$0.153915\pi$
$587$			13223.9i			0.929829i	−0.885355	+	0.464915i	$0.846085\pi$
$588$		0			0
$589$	−1491.31			−0.104327
$590$	−7106.91	−	9063.12i	−0.495910	−	0.632411i
$591$		0			0
$592$			4527.51i			0.314324i
$593$			2498.96i			0.173052i	0.996250	+	0.0865261i	$0.0275766\pi$
$593$			2498.96i			0.173052i	−0.996250	+	0.0865261i	$0.972423\pi$
$594$		0			0
$595$	−1157.06	+	907.314i	−0.0797222	+	0.0625147i
$596$	−6836.04			−0.469824
$597$		0			0
$598$		−	28429.6i		−	1.94410i
$599$	−9468.29			−0.645850			−0.322925	−	0.946425i	$-0.604666\pi$
$599$	−9468.29			−0.645850			−0.322925	+	0.946425i	$0.604666\pi$
$600$		0			0
$601$	−12334.1			−0.837137			−0.418569	−	0.908185i	$-0.637468\pi$
$601$	−12334.1			−0.837137			−0.418569	+	0.908185i	$0.637468\pi$
$602$		−	4577.00i		−	0.309875i
$603$		0			0
$604$	11094.4			0.747395
$605$	5946.09	−	4662.67i	0.399575	−	0.313330i
$606$		0			0
$607$		−	25245.6i		−	1.68812i	−0.536248	−	0.844060i	$-0.680159\pi$
$607$		−	25245.6i		−	1.68812i	0.536248	−	0.844060i	$-0.319841\pi$
$608$		−	377.535i		−	0.0251827i
$609$		0			0
$610$	5460.08	+	6962.99i	0.362413	+	0.462169i
$611$	−10474.2			−0.693521
$612$		0			0
$613$		−	4007.86i		−	0.264071i	−0.991245	−	0.132036i	$-0.957849\pi$
$613$		−	4007.86i		−	0.264071i	0.991245	−	0.132036i	$-0.0421513\pi$
$614$	−5031.58			−0.330714
$615$		0			0
$616$	1433.37			0.0937535
$617$		−	14349.2i		−	0.936266i	−0.883658	−	0.468133i	$-0.844927\pi$
$617$		−	14349.2i		−	0.936266i	0.883658	−	0.468133i	$-0.155073\pi$
$618$		0			0
$619$	6004.19			0.389869			0.194934	−	0.980816i	$-0.437551\pi$
$619$	6004.19			0.389869			0.194934	+	0.980816i	$0.437551\pi$
$620$	−4448.39	+	3488.24i	−0.288148	+	0.225953i
$621$		0			0
$622$			7518.78i			0.484688i
$623$		−	5900.77i		−	0.379469i
$624$		0			0
$625$	−13847.9	−	7237.06i	−0.886269	−	0.463172i
$626$	13651.8			0.871624
$627$		0			0
$628$			1413.91i			0.0898426i
$629$	5316.36			0.337007
$630$		0			0
$631$	17130.6			1.08076			0.540378	−	0.841422i	$-0.318281\pi$
$631$	17130.6			1.08076			0.540378	+	0.841422i	$0.318281\pi$
$632$		−	2131.07i		−	0.134129i
$633$		0			0
$634$	−4929.87			−0.308817
$635$	15896.3	+	20271.9i	0.993429	+	1.26688i
$636$		0			0
$637$		−	4370.40i		−	0.271839i
$638$			1013.49i			0.0628912i
$639$		0			0
$640$	−883.069	−	1126.14i	−0.0545412	−	0.0695540i
$641$	−13484.7			−0.830911			−0.415456	−	0.909613i	$-0.636378\pi$
$641$	−13484.7			−0.830911			−0.415456	+	0.909613i	$0.636378\pi$
$642$		0			0
$643$		−	18209.9i		−	1.11684i	−0.829559	−	0.558419i	$-0.811408\pi$
$643$		−	18209.9i		−	1.11684i	0.829559	−	0.558419i	$-0.188592\pi$
$644$	−4462.46			−0.273052
$645$		0			0
$646$	−443.314			−0.0270000
$647$		−	13402.9i		−	0.814406i	−0.913338	−	0.407203i	$-0.866504\pi$
$647$		−	13402.9i		−	0.814406i	0.913338	−	0.407203i	$-0.133496\pi$
$648$		0			0
$649$	13183.7			0.797387
$650$	5317.29	−	21654.7i	0.320863	−	1.30672i
$651$		0			0
$652$		−	3540.92i		−	0.212689i
$653$			1922.32i			0.115201i	0.998340	+	0.0576003i	$0.0183449\pi$
$653$			1922.32i			0.115201i	−0.998340	+	0.0576003i	$0.981655\pi$
$654$		0			0
$655$	8403.74	−	6589.85i	0.501315	−	0.393109i
$656$	2310.14			0.137494
$657$		0			0
$658$			1644.09i			0.0974060i
$659$	22722.3			1.34315			0.671574	−	0.740937i	$-0.265618\pi$
$659$	22722.3			1.34315			0.671574	+	0.740937i	$0.265618\pi$
$660$		0			0
$661$	−16049.3			−0.944393			−0.472196	−	0.881493i	$-0.656539\pi$
$661$	−16049.3			−0.944393			−0.472196	+	0.881493i	$0.656539\pi$
$662$		−	7560.72i		−	0.443891i
$663$		0			0
$664$	6026.02			0.352191
$665$	−569.757	−	726.586i	−0.0332244	−	0.0423696i
$666$		0			0
$667$		−	3155.27i		−	0.183167i
$668$		−	12881.0i		−	0.746081i
$669$		0			0
$670$	14817.9	−	11619.5i	0.854425	−	0.670003i
$671$	−10128.7			−0.582735
$672$		0			0
$673$			16507.8i			0.945513i	0.881193	+	0.472757i	$0.156741\pi$
$673$			16507.8i			0.945513i	−0.881193	+	0.472757i	$0.843259\pi$
$674$	−3828.78			−0.218811
$675$		0			0
$676$	23032.7			1.31047
$677$		−	15118.9i		−	0.858298i	−0.903234	−	0.429149i	$-0.858813\pi$
$677$		−	15118.9i		−	0.858298i	0.903234	−	0.429149i	$-0.141187\pi$
$678$		0			0
$679$	8413.43			0.475520
$680$	−1322.35	+	1036.93i	−0.0745733	+	0.0584772i
$681$		0			0
$682$		−	6470.86i		−	0.363317i
$683$			68.6595i			0.00384654i	0.999998	+	0.00192327i	$0.000612195\pi$
$683$			68.6595i			0.00384654i	−0.999998	+	0.00192327i	$0.999388\pi$
$684$		0			0
$685$	10276.3	+	13104.8i	0.573191	+	0.730964i
$686$	−686.000			−0.0381802
$687$		0			0
$688$		−	5230.86i		−	0.289861i
$689$	56592.6			3.12918
$690$		0			0
$691$	−3167.95			−0.174406			−0.0872030	−	0.996191i	$-0.527793\pi$
$691$	−3167.95			−0.174406			−0.0872030	+	0.996191i	$0.527793\pi$
$692$			15122.5i			0.830738i
$693$		0			0
$694$	−18237.9			−0.997550
$695$	−6618.56	+	5189.99i	−0.361232	+	0.283263i
$696$		0			0
$697$		−	2712.64i		−	0.147416i
$698$			9664.89i			0.524100i
$699$		0			0
$700$	−3399.03	−	834.629i	−0.183530	−	0.0450657i
$701$	−6930.44			−0.373408			−0.186704	−	0.982416i	$-0.559781\pi$
$701$	−6930.44			−0.373408			−0.186704	+	0.982416i	$0.559781\pi$
$702$		0			0
$703$			3338.46i			0.179107i
$704$	1638.14			0.0876984
$705$		0			0
$706$	−5613.15			−0.299226
$707$		−	4027.60i		−	0.214248i
$708$		0			0
$709$	−20689.6			−1.09593			−0.547966	−	0.836501i	$-0.684598\pi$
$709$	−20689.6			−1.09593			−0.547966	+	0.836501i	$0.684598\pi$
$710$	−5548.16	−	7075.32i	−0.293266	−	0.373989i
$711$		0			0
$712$		−	6743.74i		−	0.354961i
$713$			20145.5i			1.05814i
$714$		0			0
$715$	15750.0	+	20085.3i	0.823800	+	1.05055i
$716$	−18136.3			−0.946627
$717$		0			0
$718$			2150.13i			0.111758i
$719$	−2807.47			−0.145620			−0.0728101	−	0.997346i	$-0.523197\pi$
$719$	−2807.47			−0.145620			−0.0728101	+	0.997346i	$0.523197\pi$
$720$		0			0
$721$	1779.54			0.0919190
$722$			13439.6i			0.692757i
$723$		0			0
$724$	−7221.97			−0.370721
$725$	590.141	−	2403.35i	0.0302307	−	0.123115i
$726$		0			0
$727$			3059.84i			0.156098i	0.996950	+	0.0780489i	$0.0248690\pi$
$727$			3059.84i			0.156098i	−0.996950	+	0.0780489i	$0.975131\pi$
$728$		−	4994.74i		−	0.254282i
$729$		0			0
$730$	−5334.58	+	4183.15i	−0.270468	+	0.212089i
$731$	−6142.25			−0.310779
$732$		0			0
$733$		−	483.122i		−	0.0243445i	−0.999926	−	0.0121723i	$-0.996125\pi$
$733$		−	483.122i		−	0.0243445i	0.999926	−	0.0121723i	$-0.00387465\pi$
$734$	−734.041			−0.0369127
$735$		0			0
$736$	−5099.95			−0.255417
$737$			21554.8i			1.07732i
$738$		0			0
$739$	−15972.4			−0.795066			−0.397533	−	0.917588i	$-0.630134\pi$
$739$	−15972.4			−0.795066			−0.397533	+	0.917588i	$0.630134\pi$
$740$	7808.80	+	9958.21i	0.387915	+	0.494691i
$741$		0			0
$742$		−	8883.06i		−	0.439498i
$743$			1310.03i			0.0646840i	0.999477	+	0.0323420i	$0.0102966\pi$
$743$			1310.03i			0.0646840i	−0.999477	+	0.0323420i	$0.989703\pi$
$744$		0			0
$745$	−15035.8	+	11790.4i	−0.739422	+	0.579823i
$746$	−2609.11			−0.128052
$747$		0			0
$748$		−	1923.56i		−	0.0940271i
$749$	−7998.24			−0.390186
$750$		0			0
$751$	−14752.9			−0.716830			−0.358415	−	0.933562i	$-0.616683\pi$
$751$	−14752.9			−0.716830			−0.358415	+	0.933562i	$0.616683\pi$
$752$			1878.96i			0.0911150i
$753$		0			0
$754$	3531.63			0.170576
$755$	24402.1	−	19135.1i	1.17627	−	0.922381i
$756$		0			0
$757$		−	3934.60i		−	0.188911i	−0.995529	−	0.0944555i	$-0.969889\pi$
$757$		−	3934.60i		−	0.188911i	0.995529	−	0.0944555i	$-0.0301110\pi$
$758$			10681.2i			0.511820i
$759$		0			0
$760$	−651.151	−	830.384i	−0.0310786	−	0.0396331i
$761$	−17102.3			−0.814662			−0.407331	−	0.913281i	$-0.633540\pi$
$761$	−17102.3			−0.814662			−0.407331	+	0.913281i	$0.633540\pi$
$762$		0			0
$763$			14380.0i			0.682293i
$764$	13436.6			0.636282
$765$		0			0
$766$	−13324.5			−0.628505
$767$		−	45940.0i		−	2.16271i
$768$		0			0
$769$	32173.5			1.50872			0.754361	−	0.656460i	$-0.227947\pi$
$769$	32173.5			1.50872			0.754361	+	0.656460i	$0.227947\pi$
$770$	3152.69	−	2472.20i	0.147552	−	0.115704i
$771$		0			0
$772$			11202.3i			0.522251i
$773$			19329.5i			0.899398i	0.893180	+	0.449699i	$0.148469\pi$
$773$			19329.5i			0.899398i	−0.893180	+	0.449699i	$0.851531\pi$
$774$		0			0
$775$	−3767.87	+	15344.7i	−0.174640	+	0.711222i
$776$	9615.35			0.444808
$777$		0			0
$778$			12627.0i			0.581875i
$779$	1703.43			0.0783464
$780$		0			0
$781$	10292.1			0.471551
$782$			5988.54i			0.273849i
$783$		0			0
$784$	−784.000			−0.0357143
$785$	2438.63	+	3109.88i	0.110877	+	0.141397i
$786$		0			0
$787$		−	4050.20i		−	0.183449i	−0.995784	−	0.0917244i	$-0.970762\pi$
$787$		−	4050.20i		−	0.183449i	0.995784	−	0.0917244i	$-0.0292379\pi$
$788$		−	13010.1i		−	0.588154i
$789$		0			0
$790$	−3675.55	−	4687.27i	−0.165532	−	0.211095i
$791$	−6235.79			−0.280302
$792$		0			0
$793$			35294.7i			1.58052i
$794$	28421.2			1.27031
$795$		0			0
$796$	−6101.22			−0.271674
$797$			30864.7i			1.37175i	0.727720	+	0.685874i	$0.240580\pi$
$797$			30864.7i			1.37175i	−0.727720	+	0.685874i	$0.759420\pi$
$798$		0			0
$799$	2206.33			0.0976902
$800$	−3884.60	−	953.861i	−0.171677	−	0.0421551i
$801$		0			0
$802$			11157.2i			0.491239i
$803$		−	7759.95i		−	0.341025i
$804$		0			0
$805$	−9815.13	+	7696.60i	−0.429736	+	0.336981i
$806$	−22548.4			−0.985402
$807$		0			0
$808$		−	4602.97i		−	0.200411i
$809$	14213.1			0.617682			0.308841	−	0.951114i	$-0.400059\pi$
$809$	14213.1			0.617682			0.308841	+	0.951114i	$0.400059\pi$
$810$		0			0
$811$	1619.57			0.0701242			0.0350621	−	0.999385i	$-0.488837\pi$
$811$	1619.57			0.0701242			0.0350621	+	0.999385i	$0.488837\pi$
$812$		−	554.343i		−	0.0239577i
$813$		0			0
$814$	−14485.7			−0.623740
$815$	−6107.19	−	7788.22i	−0.262485	−	0.334736i
$816$		0			0
$817$		−	3857.09i		−	0.165168i
$818$			23828.0i			1.01849i
$819$		0			0
$820$	5081.13	−	3984.40i	0.216391	−	0.169684i
$821$	20628.1			0.876888			0.438444	−	0.898758i	$-0.355530\pi$
$821$	20628.1			0.876888			0.438444	+	0.898758i	$0.355530\pi$
$822$		0			0
$823$		−	11868.2i		−	0.502671i	−0.967900	−	0.251335i	$-0.919130\pi$
$823$		−	11868.2i		−	0.502671i	0.967900	−	0.251335i	$-0.0808697\pi$
$824$	2033.76			0.0859824
$825$		0			0
$826$	−7210.97			−0.303755
$827$			9149.35i			0.384709i	0.981326	+	0.192354i	$0.0616123\pi$
$827$			9149.35i			0.384709i	−0.981326	+	0.192354i	$0.938388\pi$
$828$		0			0
$829$	11693.7			0.489916			0.244958	−	0.969534i	$-0.421226\pi$
$829$	11693.7			0.489916			0.244958	+	0.969534i	$0.421226\pi$
$830$	13254.2	−	10393.4i	0.554288	−	0.434649i
$831$		0			0
$832$		−	5708.28i		−	0.237859i
$833$			920.600i			0.0382916i
$834$		0			0
$835$	−22216.5	−	28331.7i	−0.920759	−	1.17420i
$836$	1207.92			0.0499722
$837$		0			0
$838$			24186.0i			0.997007i
$839$	−41472.3			−1.70654			−0.853268	−	0.521473i	$-0.825383\pi$
$839$	−41472.3			−1.70654			−0.853268	+	0.521473i	$0.825383\pi$
$840$		0			0
$841$	−23997.0			−0.983929
$842$			24377.0i			0.997727i
$843$		0			0
$844$	11737.2			0.478685
$845$	50660.3	−	39725.6i	2.06245	−	1.61728i
$846$		0			0
$847$		−	4730.94i		−	0.191921i
$848$		−	10152.1i		−	0.411112i
$849$		0			0
$850$	−1120.06	+	4561.44i	−0.0451972	+	0.184066i
$851$	45097.8			1.81661
$852$		0			0
$853$		−	10326.4i		−	0.414501i	−0.978288	−	0.207251i	$-0.933548\pi$
$853$		−	10326.4i		−	0.414501i	0.978288	−	0.207251i	$-0.0664516\pi$
$854$	5540.03			0.221986
$855$		0			0
$856$	−9140.85			−0.364986
$857$			17375.4i			0.692571i	0.938129	+	0.346285i	$0.112557\pi$
$857$			17375.4i			0.692571i	−0.938129	+	0.346285i	$0.887443\pi$
$858$		0			0
$859$	−10624.9			−0.422022			−0.211011	−	0.977484i	$-0.567676\pi$
$859$	−10624.9			−0.422022			−0.211011	+	0.977484i	$0.567676\pi$
$860$	−9021.89	−	11505.2i	−0.357726	−	0.456191i
$861$		0			0
$862$			9936.31i			0.392613i
$863$			22377.1i			0.882648i	0.897348	+	0.441324i	$0.145491\pi$
$863$			22377.1i			0.882648i	−0.897348	+	0.441324i	$0.854509\pi$
$864$		0			0
$865$	26082.4	+	33261.8i	1.02524	+	1.30744i
$866$	28967.4			1.13667
$867$		0			0
$868$			3539.31i			0.138401i
$869$	6818.33			0.266164
$870$		0			0
$871$	75110.3			2.92195
$872$			16434.3i			0.638227i
$873$		0			0
$874$	−3760.56			−0.145541
$875$	−8915.65	+	4026.70i	−0.344462	+	0.155574i
$876$		0			0
$877$		−	22267.1i		−	0.857362i	−0.903456	−	0.428681i	$-0.858979\pi$
$877$		−	22267.1i		−	0.857362i	0.903456	−	0.428681i	$-0.141021\pi$
$878$		−	19875.3i		−	0.763961i
$879$		0			0
$880$	3603.07	−	2825.37i	0.138022	−	0.108231i
$881$	7273.13			0.278136			0.139068	−	0.990283i	$-0.455589\pi$
$881$	7273.13			0.278136			0.139068	+	0.990283i	$0.455589\pi$
$882$		0			0
$883$			43452.0i			1.65603i	0.560705	+	0.828016i	$0.310530\pi$
$883$			43452.0i			1.65603i	−0.560705	+	0.828016i	$0.689470\pi$
$884$	−6702.86			−0.255024
$885$		0			0
$886$	34279.2			1.29981
$887$		−	34206.2i		−	1.29485i	−0.762130	−	0.647424i	$-0.775846\pi$
$887$		−	34206.2i		−	1.29485i	0.762130	−	0.647424i	$-0.224154\pi$
$888$		0			0
$889$	16129.1			0.608496
$890$	−11631.2	−	14832.8i	−0.438067	−	0.558647i
$891$		0			0
$892$			14505.2i			0.544473i
$893$			1385.49i			0.0519190i
$894$		0			0
$895$	−39890.6	+	31280.5i	−1.48983	+	1.16826i
$896$	−896.000			−0.0334077
$897$		0			0
$898$		−	3110.69i		−	0.115596i
$899$	−2502.54			−0.0928415
$900$		0			0
$901$	−11920.9			−0.440780
$902$			7391.27i			0.272841i
$903$		0			0
$904$	−7126.61			−0.262199
$905$	−15884.6	+	12456.1i	−0.583451	+	0.457517i
$906$		0			0
$907$		−	24922.5i		−	0.912391i	−0.889880	−	0.456196i	$-0.849212\pi$
$907$		−	24922.5i		−	0.912391i	0.889880	−	0.456196i	$-0.150788\pi$
$908$			8757.80i			0.320086i
$909$		0			0
$910$	−8614.66	−	10985.9i	−0.313817	−	0.400196i
$911$	−29200.7			−1.06198			−0.530989	−	0.847379i	$-0.678179\pi$
$911$	−29200.7			−1.06198			−0.530989	+	0.847379i	$0.678179\pi$
$912$		0			0
$913$			19280.2i			0.698885i
$914$	36818.4			1.33244
$915$		0			0
$916$	−22004.0			−0.793704
$917$		−	6686.34i		−	0.240788i
$918$		0			0
$919$	31961.7			1.14725			0.573623	−	0.819119i	$-0.305537\pi$
$919$	31961.7			1.14725			0.573623	+	0.819119i	$0.305537\pi$
$920$	−11217.3	+	8796.11i	−0.401982	+	0.315217i
$921$		0			0
$922$			13233.0i			0.472676i
$923$		−	35864.0i		−	1.27896i
$924$		0			0
$925$	34350.8	+	8434.80i	1.22102	+	0.299821i
$926$	25211.0			0.894693
$927$		0			0
$928$		−	633.535i		−	0.0224103i
$929$	−21349.4			−0.753985			−0.376993	−	0.926216i	$-0.623042\pi$
$929$	−21349.4			−0.753985			−0.376993	+	0.926216i	$0.623042\pi$
$930$		0			0
$931$	−578.100			−0.0203507
$932$			15710.9i			0.552174i
$933$		0			0
$934$	−32583.1			−1.14149
$935$	−3317.65	−	4230.85i	−0.116041	−	0.147982i
$936$		0			0
$937$			3802.95i			0.132590i	0.997800	+	0.0662951i	$0.0211179\pi$
$937$			3802.95i			0.132590i	−0.997800	+	0.0662951i	$0.978882\pi$
$938$		−	11789.7i		−	0.410391i
$939$		0			0
$940$	3240.72	+	4132.74i	0.112447	+	0.143399i
$941$	42690.8			1.47894			0.739470	−	0.673190i	$-0.235076\pi$
$941$	42690.8			1.47894			0.739470	+	0.673190i	$0.235076\pi$
$942$		0			0
$943$		−	23010.9i		−	0.794633i
$944$	−8241.11			−0.284137
$945$		0			0
$946$	16736.1			0.575197
$947$			40333.0i			1.38400i	0.721899	+	0.691998i	$0.243270\pi$
$947$			40333.0i			1.38400i	−0.721899	+	0.691998i	$0.756730\pi$
$948$		0			0
$949$	−27040.4			−0.924941
$950$	−2864.40	−	703.351i	−0.0978246	−	0.0240208i
$951$		0			0
$952$			1052.11i			0.0358185i
$953$			39603.5i			1.34615i	0.739573	+	0.673077i	$0.235028\pi$
$953$			39603.5i			1.34615i	−0.739573	+	0.673077i	$0.764972\pi$
$954$		0			0
$955$	29553.7	−	23174.7i	1.00140	−	0.785253i
$956$	−17740.4			−0.600174
$957$		0			0
$958$		−	23012.6i		−	0.776099i
$959$	10426.7			0.351091
$960$		0			0
$961$	−13813.0			−0.463664
$962$			50477.1i			1.69173i
$963$		0			0
$964$	−18303.2			−0.611522
$965$	19321.0	+	24639.2i	0.644524	+	0.821933i
$966$		0			0
$967$		−	4139.69i		−	0.137666i	−0.997628	−	0.0688332i	$-0.978072\pi$
$967$		−	4139.69i		−	0.137666i	0.997628	−	0.0688332i	$-0.0219276\pi$
$968$		−	5406.79i		−	0.179526i
$969$		0			0
$970$	21148.9	−	16584.0i	0.700050	−	0.548949i
$971$	−42137.2			−1.39263			−0.696316	−	0.717735i	$-0.745179\pi$
$971$	−42137.2			−1.39263			−0.696316	+	0.717735i	$0.745179\pi$
$972$		0			0
$973$			5265.99i			0.173504i
$974$	33005.8			1.08580
$975$		0			0
$976$	6331.46			0.207649
$977$			39782.4i			1.30271i	0.758772	+	0.651357i	$0.225800\pi$
$977$			39782.4i			1.30271i	−0.758772	+	0.651357i	$0.774200\pi$
$978$		0			0
$979$	21576.5			0.704381
$980$	−1724.40	+	1352.20i	−0.0562081	+	0.0440760i
$981$		0			0
$982$			18539.3i			0.602458i
$983$			3799.91i			0.123294i	0.998098	+	0.0616471i	$0.0196353\pi$
$983$			3799.91i			0.123294i	−0.998098	+	0.0616471i	$0.980365\pi$
$984$		0			0
$985$	−22439.1	−	28615.6i	−0.725857	−	0.925653i
$986$	−743.918			−0.0240276
$987$		0			0
$988$		−	4209.13i		−	0.135537i
$989$	−52103.7			−1.67523
$990$		0			0
$991$	20113.7			0.644735			0.322367	−	0.946615i	$-0.395521\pi$
$991$	20113.7			0.644735			0.322367	+	0.946615i	$0.395521\pi$
$992$			4044.93i			0.129462i
$993$		0			0
$994$	−5629.40			−0.179632
$995$	−13419.6	+	10523.1i	−0.427567	+	0.335280i
$996$		0			0
$997$			40814.2i			1.29649i	0.761432	+	0.648244i	$0.224496\pi$
$997$			40814.2i			1.29649i	−0.761432	+	0.648244i	$0.775504\pi$
$998$			26334.6i			0.835279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.g.e.379.1		4
3.2	odd	2		210.4.g.a.169.4	yes	4
5.4	even	2	inner	630.4.g.e.379.3		4
15.2	even	4		1050.4.a.bc.1.2		2
15.8	even	4		1050.4.a.bg.1.2		2
15.14	odd	2		210.4.g.a.169.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.g.a.169.2	✓	4	15.14	odd	2
210.4.g.a.169.4	yes	4	3.2	odd	2
630.4.g.e.379.1		4	1.1	even	1	trivial
630.4.g.e.379.3		4	5.4	even	2	inner
1050.4.a.bc.1.2		2	15.2	even	4
1050.4.a.bg.1.2		2	15.8	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -4.00000 q^{4} +(-8.79796 + 6.89898i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +(13.7980 + 17.5959i) q^{10} -25.5959 q^{11} +89.1918i q^{13} +14.0000 q^{14} +16.0000 q^{16} -18.7878i q^{17} +11.7980 q^{19} +(35.1918 - 27.5959i) q^{20} +51.1918i q^{22} -159.373i q^{23} +(29.8082 - 121.394i) q^{25} +178.384 q^{26} -28.0000i q^{28} +19.7980 q^{29} -126.404 q^{31} -32.0000i q^{32} -37.5755 q^{34} +(-48.2929 - 61.5857i) q^{35} +282.969i q^{37} -23.5959i q^{38} +(-55.1918 - 70.3837i) q^{40} +144.384 q^{41} -326.929i q^{43} +102.384 q^{44} -318.747 q^{46} +117.435i q^{47} -49.0000 q^{49} +(-242.788 - 59.6163i) q^{50} -356.767i q^{52} -634.504i q^{53} +(225.192 - 176.586i) q^{55} -56.0000 q^{56} -39.5959i q^{58} -515.069 q^{59} +395.716 q^{61} +252.808i q^{62} -64.0000 q^{64} +(-615.333 - 784.706i) q^{65} -842.120i q^{67} +75.1510i q^{68} +(-123.171 + 96.5857i) q^{70} -402.100 q^{71} +303.171i q^{73} +565.939 q^{74} -47.1918 q^{76} -179.171i q^{77} -266.384 q^{79} +(-140.767 + 110.384i) q^{80} -288.767i q^{82} -753.253i q^{83} +(129.616 + 165.294i) q^{85} -653.857 q^{86} -204.767i q^{88} -842.967 q^{89} -624.343 q^{91} +637.494i q^{92} +234.869 q^{94} +(-103.798 + 81.3939i) q^{95} -1201.92i q^{97} +98.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 4 q^{5} + 16 q^{10} - 24 q^{11} + 56 q^{14} + 64 q^{16} + 8 q^{19} - 16 q^{20} + 276 q^{25} + 400 q^{26} + 40 q^{29} - 584 q^{31} + 320 q^{34} - 56 q^{35} - 64 q^{40} + 264 q^{41} + 96 q^{44}+ \cdots - 376 q^{95}+O(q^{100}) \) 4 * q - 16 * q^4 + 4 * q^5 + 16 * q^10 - 24 * q^11 + 56 * q^14 + 64 * q^16 + 8 * q^19 - 16 * q^20 + 276 * q^25 + 400 * q^26 + 40 * q^29 - 584 * q^31 + 320 * q^34 - 56 * q^35 - 64 * q^40 + 264 * q^41 + 96 * q^44 - 256 * q^46 - 196 * q^49 - 736 * q^50 + 744 * q^55 - 224 * q^56 + 448 * q^59 - 24 * q^61 - 256 * q^64 - 1168 * q^65 + 56 * q^70 + 312 * q^71 + 1088 * q^74 - 32 * q^76 - 752 * q^79 + 64 * q^80 + 832 * q^85 + 128 * q^86 + 1096 * q^89 - 1400 * q^91 + 2272 * q^94 - 376 * q^95

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