LMFDB - Embedded newform 648.4.i.d.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,4,Mod(217,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("648.217");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	648.i (of order $3$, degree $2$, not 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:	$38.2332376837$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	648.433
Dual form			648.4.i.d.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{5} +(-1.50000 - 2.59808i) q^{7} +O(q^{10})$	$q+(-2.00000 + 3.46410i) q^{5} +(-1.50000 - 2.59808i) q^{7} +(-14.0000 - 24.2487i) q^{11} +(5.50000 - 9.52628i) q^{13} +44.0000 q^{17} +29.0000 q^{19} +(-86.0000 + 148.956i) q^{23} +(54.5000 + 94.3968i) q^{25} +(-96.0000 - 166.277i) q^{29} +(-58.0000 + 100.459i) q^{31} +12.0000 q^{35} -69.0000 q^{37} +(-192.000 + 332.554i) q^{41} +(-164.000 - 284.056i) q^{43} +(-78.0000 - 135.100i) q^{47} +(167.000 - 289.252i) q^{49} -392.000 q^{53} +112.000 q^{55} +(-206.000 + 356.802i) q^{59} +(212.500 + 368.061i) q^{61} +(22.0000 + 38.1051i) q^{65} +(-128.500 + 222.569i) q^{67} -1000.00 q^{71} -359.000 q^{73} +(-42.0000 + 72.7461i) q^{77} +(-438.500 - 759.504i) q^{79} +(164.000 + 284.056i) q^{83} +(-88.0000 + 152.420i) q^{85} -1572.00 q^{89} -33.0000 q^{91} +(-58.0000 + 100.459i) q^{95} +(741.500 + 1284.32i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{5} - 3 q^{7}+O(q^{10}) $ 2 * q - 4 * q^5 - 3 * q^7	$ 2 q - 4 q^{5} - 3 q^{7} - 28 q^{11} + 11 q^{13} + 88 q^{17} + 58 q^{19} - 172 q^{23} + 109 q^{25} - 192 q^{29} - 116 q^{31} + 24 q^{35} - 138 q^{37} - 384 q^{41} - 328 q^{43} - 156 q^{47} + 334 q^{49} - 784 q^{53} + 224 q^{55} - 412 q^{59} + 425 q^{61} + 44 q^{65} - 257 q^{67} - 2000 q^{71} - 718 q^{73} - 84 q^{77} - 877 q^{79} + 328 q^{83} - 176 q^{85} - 3144 q^{89} - 66 q^{91} - 116 q^{95} + 1483 q^{97}+O(q^{100}) $ 2 * q - 4 * q^5 - 3 * q^7 - 28 * q^11 + 11 * q^13 + 88 * q^17 + 58 * q^19 - 172 * q^23 + 109 * q^25 - 192 * q^29 - 116 * q^31 + 24 * q^35 - 138 * q^37 - 384 * q^41 - 328 * q^43 - 156 * q^47 + 334 * q^49 - 784 * q^53 + 224 * q^55 - 412 * q^59 + 425 * q^61 + 44 * q^65 - 257 * q^67 - 2000 * q^71 - 718 * q^73 - 84 * q^77 - 877 * q^79 + 328 * q^83 - 176 * q^85 - 3144 * q^89 - 66 * q^91 - 116 * q^95 + 1483 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.00000	+	3.46410i	−0.178885	+	0.309839i	−0.941499	−	0.337016i	$-0.890582\pi$
$5$	−2.00000	+	3.46410i	−0.178885	+	0.309839i	0.762614	+	0.646854i	$0.223916\pi$
$6$		0			0
$7$	−1.50000	−	2.59808i	−0.0809924	−	0.140283i	0.822684	−	0.568499i	$-0.192476\pi$
$7$	−1.50000	−	2.59808i	−0.0809924	−	0.140283i	−0.903676	+	0.428216i	$0.859142\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−14.0000	−	24.2487i	−0.383742	−	0.664660i	0.607852	−	0.794050i	$-0.292031\pi$
$11$	−14.0000	−	24.2487i	−0.383742	−	0.664660i	−0.991594	+	0.129390i	$0.958698\pi$
$12$		0			0
$13$	5.50000	−	9.52628i	0.117340	−	0.203240i	−0.801372	−	0.598166i	$-0.795896\pi$
$13$	5.50000	−	9.52628i	0.117340	−	0.203240i	0.918713	+	0.394926i	$0.129230\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	44.0000			0.627739			0.313870	−	0.949466i	$-0.398375\pi$
$17$	44.0000			0.627739			0.313870	+	0.949466i	$0.398375\pi$
$18$		0			0
$19$	29.0000			0.350161			0.175080	−	0.984554i	$-0.443981\pi$
$19$	29.0000			0.350161			0.175080	+	0.984554i	$0.443981\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−86.0000	+	148.956i	−0.779663	+	1.35042i	0.152474	+	0.988308i	$0.451276\pi$
$23$	−86.0000	+	148.956i	−0.779663	+	1.35042i	−0.932136	+	0.362108i	$0.882057\pi$
$24$		0			0
$25$	54.5000	+	94.3968i	0.436000	+	0.755174i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−96.0000	−	166.277i	−0.614716	−	1.06472i	−0.990434	−	0.137985i	$-0.955937\pi$
$29$	−96.0000	−	166.277i	−0.614716	−	1.06472i	0.375719	−	0.926734i	$-0.377396\pi$
$30$		0			0
$31$	−58.0000	+	100.459i	−0.336036	+	0.582031i	−0.983683	−	0.179909i	$-0.942420\pi$
$31$	−58.0000	+	100.459i	−0.336036	+	0.582031i	0.647648	+	0.761940i	$0.275753\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	12.0000			0.0579534
$36$		0			0
$37$	−69.0000			−0.306582			−0.153291	−	0.988181i	$-0.548987\pi$
$37$	−69.0000			−0.306582			−0.153291	+	0.988181i	$0.548987\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−192.000	+	332.554i	−0.731350	+	1.26674i	0.224956	+	0.974369i	$0.427776\pi$
$41$	−192.000	+	332.554i	−0.731350	+	1.26674i	−0.956306	+	0.292367i	$0.905557\pi$
$42$		0			0
$43$	−164.000	−	284.056i	−0.581622	−	1.00740i	−0.995287	−	0.0969704i	$-0.969085\pi$
$43$	−164.000	−	284.056i	−0.581622	−	1.00740i	0.413665	−	0.910429i	$-0.364249\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−78.0000	−	135.100i	−0.242074	−	0.419284i	0.719231	−	0.694771i	$-0.244494\pi$
$47$	−78.0000	−	135.100i	−0.242074	−	0.419284i	−0.961305	+	0.275487i	$0.911161\pi$
$48$		0			0
$49$	167.000	−	289.252i	0.486880	−	0.843302i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−392.000			−1.01595			−0.507975	−	0.861372i	$-0.669606\pi$
$53$	−392.000			−1.01595			−0.507975	+	0.861372i	$0.669606\pi$
$54$		0			0
$55$	112.000			0.274583
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−206.000	+	356.802i	−0.454558	+	0.787317i	−0.998663	−	0.0516999i	$-0.983536\pi$
$59$	−206.000	+	356.802i	−0.454558	+	0.787317i	0.544105	+	0.839017i	$0.316869\pi$
$60$		0			0
$61$	212.500	+	368.061i	0.446030	+	0.772547i	0.998123	−	0.0612356i	$-0.0195041\pi$
$61$	212.500	+	368.061i	0.446030	+	0.772547i	−0.552093	+	0.833782i	$0.686171\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	22.0000	+	38.1051i	0.0419810	+	0.0727132i
$66$		0			0
$67$	−128.500	+	222.569i	−0.234310	+	0.405837i	−0.959072	−	0.283163i	$-0.908616\pi$
$67$	−128.500	+	222.569i	−0.234310	+	0.405837i	0.724762	+	0.688999i	$0.241950\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1000.00			−1.67152			−0.835762	−	0.549092i	$-0.814974\pi$
$71$	−1000.00			−1.67152			−0.835762	+	0.549092i	$0.814974\pi$
$72$		0			0
$73$	−359.000			−0.575586			−0.287793	−	0.957693i	$-0.592921\pi$
$73$	−359.000			−0.575586			−0.287793	+	0.957693i	$0.592921\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−42.0000	+	72.7461i	−0.0621603	+	0.107665i
$78$		0			0
$79$	−438.500	−	759.504i	−0.624495	−	1.08166i	−0.988638	−	0.150314i	$-0.951971\pi$
$79$	−438.500	−	759.504i	−0.624495	−	1.08166i	0.364143	−	0.931343i	$-0.381362\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	164.000	+	284.056i	0.216884	+	0.375653i	0.953854	−	0.300272i	$-0.0970775\pi$
$83$	164.000	+	284.056i	0.216884	+	0.375653i	−0.736970	+	0.675925i	$0.763744\pi$
$84$		0			0
$85$	−88.0000	+	152.420i	−0.112293	+	0.194498i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1572.00			−1.87227			−0.936133	−	0.351646i	$-0.885622\pi$
$89$	−1572.00			−1.87227			−0.936133	+	0.351646i	$0.885622\pi$
$90$		0			0
$91$	−33.0000			−0.0380147
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−58.0000	+	100.459i	−0.0626387	+	0.108493i
$96$		0			0
$97$	741.500	+	1284.32i	0.776164	+	1.34436i	0.934138	+	0.356912i	$0.116171\pi$
$97$	741.500	+	1284.32i	0.776164	+	1.34436i	−0.157974	+	0.987443i	$0.550496\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	288.000	+	498.831i	0.283733	+	0.491441i	0.972301	−	0.233731i	$-0.0750936\pi$
$101$	288.000	+	498.831i	0.283733	+	0.491441i	−0.688568	+	0.725172i	$0.741760\pi$
$102$		0			0
$103$	−39.5000	+	68.4160i	−0.0377869	+	0.0654488i	−0.884300	−	0.466918i	$-0.845364\pi$
$103$	−39.5000	+	68.4160i	−0.0377869	+	0.0654488i	0.846513	+	0.532367i	$0.178697\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1836.00			−1.65881			−0.829406	−	0.558647i	$-0.811321\pi$
$107$	−1836.00			−1.65881			−0.829406	+	0.558647i	$0.811321\pi$
$108$		0			0
$109$	1450.00			1.27417			0.637086	−	0.770792i	$-0.280139\pi$
$109$	1450.00			1.27417			0.637086	+	0.770792i	$0.280139\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−318.000	+	550.792i	−0.264734	+	0.458532i	−0.967494	−	0.252895i	$-0.918617\pi$
$113$	−318.000	+	550.792i	−0.264734	+	0.458532i	0.702760	+	0.711427i	$0.251951\pi$
$114$		0			0
$115$	−344.000	−	595.825i	−0.278941	−	0.483139i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−66.0000	−	114.315i	−0.0508421	−	0.0880611i
$120$		0			0
$121$	273.500	−	473.716i	0.205485	−	0.355910i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−936.000			−0.669747
$126$		0			0
$127$	−1460.00			−1.02011			−0.510055	−	0.860142i	$-0.670375\pi$
$127$	−1460.00			−1.02011			−0.510055	+	0.860142i	$0.670375\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−232.000	+	401.836i	−0.154732	+	0.268004i	−0.932962	−	0.359976i	$-0.882785\pi$
$131$	−232.000	+	401.836i	−0.154732	+	0.268004i	0.778229	+	0.627980i	$0.216118\pi$
$132$		0			0
$133$	−43.5000	−	75.3442i	−0.0283604	−	0.0491216i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−18.0000	−	31.1769i	−0.0112251	−	0.0194425i	0.860358	−	0.509690i	$-0.170240\pi$
$137$	−18.0000	−	31.1769i	−0.0112251	−	0.0194425i	−0.871583	+	0.490247i	$0.836906\pi$
$138$		0			0
$139$	574.500	−	995.063i	0.350564	−	0.607195i	−0.635784	−	0.771867i	$-0.719323\pi$
$139$	574.500	−	995.063i	0.350564	−	0.607195i	0.986348	+	0.164672i	$0.0526564\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−308.000			−0.180114
$144$		0			0
$145$	768.000			0.439855
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−868.000	+	1503.42i	−0.477244	+	0.826611i	−0.999660	−	0.0260802i	$-0.991697\pi$
$149$	−868.000	+	1503.42i	−0.477244	+	0.826611i	0.522416	+	0.852691i	$0.325031\pi$
$150$		0			0
$151$	−368.500	−	638.261i	−0.198597	−	0.343980i	0.749477	−	0.662030i	$-0.230305\pi$
$151$	−368.500	−	638.261i	−0.198597	−	0.343980i	−0.948074	+	0.318051i	$0.896972\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−232.000	−	401.836i	−0.120224	−	0.208234i
$156$		0			0
$157$	−1427.00	+	2471.64i	−0.725395	+	1.25642i	0.233416	+	0.972377i	$0.425009\pi$
$157$	−1427.00	+	2471.64i	−0.725395	+	1.25642i	−0.958811	+	0.284044i	$0.908324\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	516.000			0.252587
$162$		0			0
$163$	−2013.00			−0.967303			−0.483651	−	0.875261i	$-0.660690\pi$
$163$	−2013.00			−0.967303			−0.483651	+	0.875261i	$0.660690\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−606.000	+	1049.62i	−0.280801	+	0.486361i	−0.971582	−	0.236703i	$-0.923933\pi$
$167$	−606.000	+	1049.62i	−0.280801	+	0.486361i	0.690782	+	0.723063i	$0.257267\pi$
$168$		0			0
$169$	1038.00	+	1797.87i	0.472462	+	0.818329i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−960.000	−	1662.77i	−0.421893	−	0.730740i	0.574232	−	0.818693i	$-0.305301\pi$
$173$	−960.000	−	1662.77i	−0.421893	−	0.730740i	−0.996125	+	0.0879530i	$0.971967\pi$
$174$		0			0
$175$	163.500	−	283.190i	0.0706254	−	0.122327i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3240.00			1.35290			0.676450	−	0.736489i	$-0.263518\pi$
$179$	3240.00			1.35290			0.676450	+	0.736489i	$0.263518\pi$
$180$		0			0
$181$	4545.00			1.86645			0.933224	−	0.359294i	$-0.116983\pi$
$181$	4545.00			1.86645			0.933224	+	0.359294i	$0.116983\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	138.000	−	239.023i	0.0548430	−	0.0949909i
$186$		0			0
$187$	−616.000	−	1066.94i	−0.240890	−	0.417233i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1074.00	−	1860.22i	−0.406869	−	0.704717i	0.587668	−	0.809102i	$-0.300046\pi$
$191$	−1074.00	−	1860.22i	−0.406869	−	0.704717i	−0.994537	+	0.104385i	$0.966713\pi$
$192$		0			0
$193$	420.500	−	728.327i	0.156830	−	0.271638i	−0.776894	−	0.629632i	$-0.783206\pi$
$193$	420.500	−	728.327i	0.156830	−	0.271638i	0.933724	+	0.357994i	$0.116539\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1524.00			0.551170			0.275585	−	0.961277i	$-0.411128\pi$
$197$	1524.00			0.551170			0.275585	+	0.961277i	$0.411128\pi$
$198$		0			0
$199$	−5321.00			−1.89546			−0.947728	−	0.319080i	$-0.896626\pi$
$199$	−5321.00			−1.89546			−0.947728	+	0.319080i	$0.896626\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−288.000	+	498.831i	−0.0995746	+	0.172468i
$204$		0			0
$205$	−768.000	−	1330.22i	−0.261656	−	0.453201i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−406.000	−	703.213i	−0.134371	−	0.232738i
$210$		0			0
$211$	1748.50	−	3028.49i	0.570482	−	0.988104i	−0.426034	−	0.904707i	$-0.640090\pi$
$211$	1748.50	−	3028.49i	0.570482	−	0.988104i	0.996516	−	0.0833969i	$-0.0265769\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1312.00			0.416175
$216$		0			0
$217$	348.000			0.108865
$218$		0			0
$219$		0			0
$220$		0			0
$221$	242.000	−	419.156i	0.0736592	−	0.127581i
$222$		0			0
$223$	−902.000	−	1562.31i	−0.270863	−	0.469148i	0.698220	−	0.715883i	$-0.253976\pi$
$223$	−902.000	−	1562.31i	−0.270863	−	0.469148i	−0.969083	+	0.246735i	$0.920642\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	660.000	+	1143.15i	0.192977	+	0.334246i	0.946235	−	0.323479i	$-0.104852\pi$
$227$	660.000	+	1143.15i	0.192977	+	0.334246i	−0.753259	+	0.657724i	$0.771519\pi$
$228$		0			0
$229$	−2057.00	+	3562.83i	−0.593582	+	1.02812i	0.400163	+	0.916444i	$0.368954\pi$
$229$	−2057.00	+	3562.83i	−0.593582	+	1.02812i	−0.993745	+	0.111671i	$0.964380\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5008.00			1.40809			0.704045	−	0.710155i	$-0.251375\pi$
$233$	5008.00			1.40809			0.704045	+	0.710155i	$0.251375\pi$
$234$		0			0
$235$	624.000			0.173214
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1268.00	−	2196.24i	0.343180	−	0.594406i	−0.641841	−	0.766838i	$-0.721829\pi$
$239$	1268.00	−	2196.24i	0.343180	−	0.594406i	0.985021	+	0.172432i	$0.0551625\pi$
$240$		0			0
$241$	2143.50	+	3712.65i	0.572925	+	0.992336i	0.996264	+	0.0863639i	$0.0275248\pi$
$241$	2143.50	+	3712.65i	0.572925	+	0.992336i	−0.423338	+	0.905972i	$0.639142\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	668.000	+	1157.01i	0.174192	+	0.301709i
$246$		0			0
$247$	159.500	−	276.262i	0.0410880	−	0.0711665i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1424.00			0.358096			0.179048	−	0.983840i	$-0.442698\pi$
$251$	1424.00			0.358096			0.179048	+	0.983840i	$0.442698\pi$
$252$		0			0
$253$	4816.00			1.19676
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2924.00	−	5064.52i	0.709705	−	1.22924i	−0.255262	−	0.966872i	$-0.582162\pi$
$257$	2924.00	−	5064.52i	0.709705	−	1.22924i	0.964967	−	0.262373i	$-0.0845050\pi$
$258$		0			0
$259$	103.500	+	179.267i	0.0248308	+	0.0430082i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1900.00	+	3290.90i	0.445472	+	0.771579i	0.998085	−	0.0618584i	$-0.0197027\pi$
$263$	1900.00	+	3290.90i	0.445472	+	0.771579i	−0.552613	+	0.833438i	$0.686369\pi$
$264$		0			0
$265$	784.000	−	1357.93i	0.181739	−	0.314781i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1820.00			0.412518			0.206259	−	0.978497i	$-0.433871\pi$
$269$	1820.00			0.412518			0.206259	+	0.978497i	$0.433871\pi$
$270$		0			0
$271$	−1615.00			−0.362008			−0.181004	−	0.983482i	$-0.557935\pi$
$271$	−1615.00			−0.362008			−0.181004	+	0.983482i	$0.557935\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1526.00	−	2643.11i	0.334623	−	0.579584i
$276$		0			0
$277$	−377.000	−	652.983i	−0.0817752	−	0.141639i	0.822237	−	0.569145i	$-0.192726\pi$
$277$	−377.000	−	652.983i	−0.0817752	−	0.141639i	−0.904013	+	0.427506i	$0.859392\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	272.000	+	471.118i	0.0577443	+	0.100016i	0.893453	−	0.449158i	$-0.148276\pi$
$281$	272.000	+	471.118i	0.0577443	+	0.100016i	−0.835708	+	0.549174i	$0.814943\pi$
$282$		0			0
$283$	−424.000	+	734.390i	−0.0890607	+	0.154258i	−0.907114	−	0.420884i	$-0.861720\pi$
$283$	−424.000	+	734.390i	−0.0890607	+	0.154258i	0.818054	+	0.575142i	$0.195053\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1152.00			0.236935
$288$		0			0
$289$	−2977.00			−0.605943
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3354.00	−	5809.30i	0.668747	−	1.15830i	−0.309508	−	0.950897i	$-0.600164\pi$
$293$	3354.00	−	5809.30i	0.668747	−	1.15830i	0.978255	−	0.207406i	$-0.0665023\pi$
$294$		0			0
$295$	−824.000	−	1427.21i	−0.162628	−	0.281679i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	946.000	+	1638.52i	0.182972	+	0.316917i
$300$		0			0
$301$	−492.000	+	852.169i	−0.0942140	+	0.163183i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1700.00			−0.319153
$306$		0			0
$307$	2112.00			0.392633			0.196316	−	0.980541i	$-0.437102\pi$
$307$	2112.00			0.392633			0.196316	+	0.980541i	$0.437102\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2910.00	−	5040.27i	0.530582	−	0.918995i	−0.468781	−	0.883314i	$-0.655307\pi$
$311$	2910.00	−	5040.27i	0.530582	−	0.918995i	0.999363	−	0.0356805i	$-0.0113599\pi$
$312$		0			0
$313$	3706.50	+	6419.85i	0.669341	+	1.15933i	0.978089	+	0.208189i	$0.0667568\pi$
$313$	3706.50	+	6419.85i	0.669341	+	1.15933i	−0.308748	+	0.951144i	$0.599910\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4428.00	+	7669.52i	0.784547	+	1.35887i	0.929270	+	0.369402i	$0.120438\pi$
$317$	4428.00	+	7669.52i	0.784547	+	1.35887i	−0.144723	+	0.989472i	$0.546229\pi$
$318$		0			0
$319$	−2688.00	+	4655.75i	−0.471784	+	0.817154i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1276.00			0.219810
$324$		0			0
$325$	1199.00			0.204642
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−234.000	+	405.300i	−0.0392123	+	0.0679176i
$330$		0			0
$331$	−1565.50	−	2711.53i	−0.259963	−	0.450269i	0.706269	−	0.707944i	$-0.250377\pi$
$331$	−1565.50	−	2711.53i	−0.259963	−	0.450269i	−0.966232	+	0.257675i	$0.917044\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−514.000	−	890.274i	−0.0838293	−	0.145197i
$336$		0			0
$337$	3409.50	−	5905.43i	0.551120	−	0.954567i	−0.447075	−	0.894497i	$-0.647534\pi$
$337$	3409.50	−	5905.43i	0.551120	−	0.954567i	0.998194	−	0.0600704i	$-0.0191325\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3248.00			0.515804
$342$		0			0
$343$	−2031.00			−0.319719
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5652.00	−	9789.55i	0.874396	−	1.51450i	0.0169903	−	0.999856i	$-0.494592\pi$
$347$	5652.00	−	9789.55i	0.874396	−	1.51450i	0.857405	−	0.514642i	$-0.172075\pi$
$348$		0			0
$349$	−1117.50	−	1935.57i	−0.171399	−	0.296873i	0.767510	−	0.641037i	$-0.221496\pi$
$349$	−1117.50	−	1935.57i	−0.171399	−	0.296873i	−0.938909	+	0.344165i	$0.888162\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−148.000	−	256.344i	−0.0223151	−	0.0386510i	0.854652	−	0.519201i	$-0.173770\pi$
$353$	−148.000	−	256.344i	−0.0223151	−	0.0386510i	−0.876967	+	0.480550i	$0.840437\pi$
$354$		0			0
$355$	2000.00	−	3464.10i	0.299011	−	0.517903i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5700.00			0.837979			0.418990	−	0.907991i	$-0.362384\pi$
$359$	5700.00			0.837979			0.418990	+	0.907991i	$0.362384\pi$
$360$		0			0
$361$	−6018.00			−0.877387
$362$		0			0
$363$		0			0
$364$		0			0
$365$	718.000	−	1243.61i	0.102964	−	0.178339i
$366$		0			0
$367$	−3471.50	−	6012.81i	−0.493762	−	0.855222i	0.506212	−	0.862409i	$-0.331045\pi$
$367$	−3471.50	−	6012.81i	−0.493762	−	0.855222i	−0.999974	+	0.00718757i	$0.997712\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	588.000	+	1018.45i	0.0822842	+	0.142520i
$372$		0			0
$373$	438.500	−	759.504i	0.0608704	−	0.105431i	−0.833984	−	0.551788i	$-0.813946\pi$
$373$	438.500	−	759.504i	0.0608704	−	0.105431i	0.894855	+	0.446358i	$0.147279\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2112.00			−0.288524
$378$		0			0
$379$	10361.0			1.40424			0.702122	−	0.712056i	$-0.252236\pi$
$379$	10361.0			1.40424			0.702122	+	0.712056i	$0.252236\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2592.00	+	4489.48i	−0.345809	+	0.598960i	−0.985500	−	0.169673i	$-0.945729\pi$
$383$	−2592.00	+	4489.48i	−0.345809	+	0.598960i	0.639691	+	0.768632i	$0.279062\pi$
$384$		0			0
$385$	−168.000	−	290.985i	−0.0222392	−	0.0385193i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4130.00	−	7153.37i	−0.538302	−	0.932366i	−0.998996	−	0.0448067i	$-0.985733\pi$
$389$	−4130.00	−	7153.37i	−0.538302	−	0.932366i	0.460694	−	0.887559i	$-0.347601\pi$
$390$		0			0
$391$	−3784.00	+	6554.08i	−0.489425	+	0.847709i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3508.00			0.446852
$396$		0			0
$397$	−5098.00			−0.644487			−0.322243	−	0.946657i	$-0.604437\pi$
$397$	−5098.00			−0.644487			−0.322243	+	0.946657i	$0.604437\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1596.00	+	2764.35i	−0.198754	+	0.344252i	−0.948125	−	0.317898i	$-0.897023\pi$
$401$	−1596.00	+	2764.35i	−0.198754	+	0.344252i	0.749371	+	0.662151i	$0.230356\pi$
$402$		0			0
$403$	638.000	+	1105.05i	0.0788612	+	0.136592i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	966.000	+	1673.16i	0.117648	+	0.203773i
$408$		0			0
$409$	319.500	−	553.390i	0.0386265	−	0.0669031i	−0.846066	−	0.533078i	$-0.821035\pi$
$409$	319.500	−	553.390i	0.0386265	−	0.0669031i	0.884692	+	0.466175i	$0.154368\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1236.00			0.147263
$414$		0			0
$415$	−1312.00			−0.155189
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5670.00	+	9820.73i	−0.661092	+	1.14505i	0.319237	+	0.947675i	$0.396573\pi$
$419$	−5670.00	+	9820.73i	−0.661092	+	1.14505i	−0.980329	+	0.197370i	$0.936760\pi$
$420$		0			0
$421$	57.5000	+	99.5929i	0.00665648	+	0.0115294i	0.869334	−	0.494224i	$-0.164548\pi$
$421$	57.5000	+	99.5929i	0.00665648	+	0.0115294i	−0.862678	+	0.505754i	$0.831214\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2398.00	+	4153.46i	0.273694	+	0.474052i
$426$		0			0
$427$	637.500	−	1104.18i	0.0722501	−	0.125141i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3796.00			−0.424239			−0.212119	−	0.977244i	$-0.568037\pi$
$431$	−3796.00			−0.424239			−0.212119	+	0.977244i	$0.568037\pi$
$432$		0			0
$433$	−6062.00			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−6062.00			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2494.00	+	4319.73i	−0.273007	+	0.472863i
$438$		0			0
$439$	5274.00	+	9134.84i	0.573381	+	0.993125i	0.996215	+	0.0869182i	$0.0277019\pi$
$439$	5274.00	+	9134.84i	0.573381	+	0.993125i	−0.422834	+	0.906207i	$0.638965\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7708.00	−	13350.6i	−0.826677	−	1.43185i	−0.900630	−	0.434586i	$-0.856895\pi$
$443$	−7708.00	−	13350.6i	−0.826677	−	1.43185i	0.0739530	−	0.997262i	$-0.476439\pi$
$444$		0			0
$445$	3144.00	−	5445.57i	0.334921	−	0.580100i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12820.0			1.34747			0.673734	−	0.738974i	$-0.264689\pi$
$449$	12820.0			1.34747			0.673734	+	0.738974i	$0.264689\pi$
$450$		0			0
$451$	10752.0			1.12260
$452$		0			0
$453$		0			0
$454$		0			0
$455$	66.0000	−	114.315i	0.00680028	−	0.0117784i
$456$		0			0
$457$	−235.000	−	407.032i	−0.0240543	−	0.0416634i	0.853748	−	0.520687i	$-0.174324\pi$
$457$	−235.000	−	407.032i	−0.0240543	−	0.0416634i	−0.877802	+	0.479024i	$0.840991\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6398.00	−	11081.7i	−0.646387	−	1.11958i	−0.983979	−	0.178283i	$-0.942946\pi$
$461$	−6398.00	−	11081.7i	−0.646387	−	1.11958i	0.337592	−	0.941293i	$-0.390388\pi$
$462$		0			0
$463$	−7301.50	+	12646.6i	−0.732893	+	1.26941i	0.222749	+	0.974876i	$0.428497\pi$
$463$	−7301.50	+	12646.6i	−0.732893	+	1.26941i	−0.955642	+	0.294532i	$0.904836\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12084.0			−1.19739			−0.598695	−	0.800977i	$-0.704314\pi$
$467$	−12084.0			−1.19739			−0.598695	+	0.800977i	$0.704314\pi$
$468$		0			0
$469$	771.000			0.0759093
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4592.00	+	7953.58i	−0.446386	+	0.773163i
$474$		0			0
$475$	1580.50	+	2737.51i	0.152670	+	0.264432i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	764.000	+	1323.29i	0.0728769	+	0.126227i	0.900161	−	0.435557i	$-0.143449\pi$
$479$	764.000	+	1323.29i	0.0728769	+	0.126227i	−0.827284	+	0.561784i	$0.810115\pi$
$480$		0			0
$481$	−379.500	+	657.313i	−0.0359745	+	0.0623096i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5932.00			−0.555378
$486$		0			0
$487$	−8117.00			−0.755270			−0.377635	−	0.925955i	$-0.623263\pi$
$487$	−8117.00			−0.755270			−0.377635	+	0.925955i	$0.623263\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8298.00	+	14372.6i	−0.762696	+	1.32103i	0.178761	+	0.983893i	$0.442791\pi$
$491$	−8298.00	+	14372.6i	−0.762696	+	1.32103i	−0.941456	+	0.337135i	$0.890542\pi$
$492$		0			0
$493$	−4224.00	−	7316.18i	−0.385881	−	0.668366i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1500.00	+	2598.08i	0.135381	+	0.234486i
$498$		0			0
$499$	6720.00	−	11639.4i	0.602863	−	1.04419i	−0.389523	−	0.921017i	$-0.627360\pi$
$499$	6720.00	−	11639.4i	0.602863	−	1.04419i	0.992385	−	0.123172i	$-0.0393067\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8652.00			0.766946			0.383473	−	0.923552i	$-0.374728\pi$
$503$	8652.00			0.766946			0.383473	+	0.923552i	$0.374728\pi$
$504$		0			0
$505$	−2304.00			−0.203023
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2442.00	+	4229.67i	−0.212652	+	0.368324i	−0.952544	−	0.304402i	$-0.901543\pi$
$509$	−2442.00	+	4229.67i	−0.212652	+	0.368324i	0.739892	+	0.672726i	$0.234877\pi$
$510$		0			0
$511$	538.500	+	932.709i	0.0466181	+	0.0807449i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−158.000	−	273.664i	−0.0135191	−	0.0234157i
$516$		0			0
$517$	−2184.00	+	3782.80i	−0.185788	+	0.321794i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18028.0			−1.51597			−0.757986	−	0.652271i	$-0.773816\pi$
$521$	−18028.0			−1.51597			−0.757986	+	0.652271i	$0.773816\pi$
$522$		0			0
$523$	20593.0			1.72174			0.860869	−	0.508827i	$-0.169921\pi$
$523$	20593.0			1.72174			0.860869	+	0.508827i	$0.169921\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2552.00	+	4420.19i	−0.210943	+	0.365364i
$528$		0			0
$529$	−8708.50	−	15083.6i	−0.715748	−	1.23971i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2112.00	+	3658.09i	0.171634	+	0.297279i
$534$		0			0
$535$	3672.00	−	6360.09i	0.296737	−	0.513964i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9352.00			−0.747345
$540$		0			0
$541$	−7443.00			−0.591496			−0.295748	−	0.955266i	$-0.595569\pi$
$541$	−7443.00			−0.591496			−0.295748	+	0.955266i	$0.595569\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2900.00	+	5022.95i	−0.227931	+	0.394788i
$546$		0			0
$547$	11826.5	+	20484.1i	0.924433	+	1.60116i	0.792471	+	0.609909i	$0.208794\pi$
$547$	11826.5	+	20484.1i	0.924433	+	1.60116i	0.131961	+	0.991255i	$0.457873\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2784.00	−	4822.03i	−0.215249	−	0.372823i
$552$		0			0
$553$	−1315.50	+	2278.51i	−0.101159	+	0.175212i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12356.0			−0.939929			−0.469965	−	0.882685i	$-0.655733\pi$
$557$	−12356.0			−0.939929			−0.469965	+	0.882685i	$0.655733\pi$
$558$		0			0
$559$	−3608.00			−0.272991
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4144.00	−	7177.62i	0.310211	−	0.537301i	−0.668197	−	0.743984i	$-0.732934\pi$
$563$	4144.00	−	7177.62i	0.310211	−	0.537301i	0.978408	+	0.206683i	$0.0662670\pi$
$564$		0			0
$565$	−1272.00	−	2203.17i	−0.0947141	−	0.164050i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6614.00	−	11455.8i	−0.487299	−	0.844027i	0.512594	−	0.858631i	$-0.328685\pi$
$569$	−6614.00	−	11455.8i	−0.487299	−	0.844027i	−0.999893	+	0.0146039i	$0.995351\pi$
$570$		0			0
$571$	1405.50	−	2434.40i	0.103009	−	0.178417i	−0.809914	−	0.586549i	$-0.800486\pi$
$571$	1405.50	−	2434.40i	0.103009	−	0.178417i	0.912923	+	0.408131i	$0.133820\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−18748.0			−1.35973
$576$		0			0
$577$	8963.00			0.646680			0.323340	−	0.946283i	$-0.395194\pi$
$577$	8963.00			0.646680			0.323340	+	0.946283i	$0.395194\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	492.000	−	852.169i	0.0351318	−	0.0608501i
$582$		0			0
$583$	5488.00	+	9505.49i	0.389862	+	0.675261i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11422.0	+	19783.5i	0.803128	+	1.39106i	0.917547	+	0.397627i	$0.130166\pi$
$587$	11422.0	+	19783.5i	0.803128	+	1.39106i	−0.114419	+	0.993433i	$0.536501\pi$
$588$		0			0
$589$	−1682.00	+	2913.31i	−0.117667	+	0.203804i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−17528.0			−1.21381			−0.606904	−	0.794775i	$-0.707589\pi$
$593$	−17528.0			−1.21381			−0.606904	+	0.794775i	$0.707589\pi$
$594$		0			0
$595$	528.000			0.0363796
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7584.00	+	13135.9i	−0.517319	+	0.896022i	0.482479	+	0.875907i	$0.339736\pi$
$599$	−7584.00	+	13135.9i	−0.517319	+	0.896022i	−0.999798	+	0.0201146i	$0.993597\pi$
$600$		0			0
$601$	−11453.0	−	19837.2i	−0.777334	−	1.34638i	−0.933473	−	0.358647i	$-0.883238\pi$
$601$	−11453.0	−	19837.2i	−0.777334	−	1.34638i	0.156140	−	0.987735i	$-0.450095\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1094.00	+	1894.86i	0.0735164	+	0.127334i
$606$		0			0
$607$	−8609.50	+	14912.1i	−0.575698	+	0.997139i	0.420267	+	0.907400i	$0.361936\pi$
$607$	−8609.50	+	14912.1i	−0.575698	+	0.997139i	−0.995965	+	0.0897382i	$0.971397\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1716.00			−0.113620
$612$		0			0
$613$	−20569.0			−1.35526			−0.677630	−	0.735403i	$-0.736993\pi$
$613$	−20569.0			−1.35526			−0.677630	+	0.735403i	$0.736993\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8886.00	−	15391.0i	0.579800	−	1.00424i	−0.415701	−	0.909501i	$-0.636464\pi$
$617$	8886.00	−	15391.0i	0.579800	−	1.00424i	0.995502	−	0.0947427i	$-0.0302028\pi$
$618$		0			0
$619$	5549.50	+	9612.02i	0.360344	+	0.624135i	0.988017	−	0.154342i	$-0.0493258\pi$
$619$	5549.50	+	9612.02i	0.360344	+	0.624135i	−0.627673	+	0.778477i	$0.715992\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2358.00	+	4084.18i	0.151639	+	0.262647i
$624$		0			0
$625$	−4940.50	+	8557.20i	−0.316192	+	0.547661i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3036.00			−0.192453
$630$		0			0
$631$	−25895.0			−1.63370			−0.816849	−	0.576851i	$-0.804281\pi$
$631$	−25895.0			−1.63370			−0.816849	+	0.576851i	$0.804281\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2920.00	−	5057.59i	0.182483	−	0.316070i
$636$		0			0
$637$	−1837.00	−	3181.78i	−0.114262	−	0.197907i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4540.00	+	7863.51i	0.279749	+	0.484540i	0.971322	−	0.237767i	$-0.0764154\pi$
$641$	4540.00	+	7863.51i	0.279749	+	0.484540i	−0.691573	+	0.722306i	$0.743082\pi$
$642$		0			0
$643$	11316.0	−	19599.9i	0.694027	−	1.20209i	−0.276480	−	0.961020i	$-0.589168\pi$
$643$	11316.0	−	19599.9i	0.694027	−	1.20209i	0.970508	−	0.241071i	$-0.0774986\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−30112.0			−1.82971			−0.914857	−	0.403778i	$-0.867697\pi$
$647$	−30112.0			−1.82971			−0.914857	+	0.403778i	$0.867697\pi$
$648$		0			0
$649$	11536.0			0.697731
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12684.0	+	21969.3i	−0.760128	+	1.31658i	0.182657	+	0.983177i	$0.441530\pi$
$653$	−12684.0	+	21969.3i	−0.760128	+	1.31658i	−0.942784	+	0.333403i	$0.891803\pi$
$654$		0			0
$655$	−928.000	−	1607.34i	−0.0553587	−	0.0958841i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6540.00	−	11327.6i	−0.386589	−	0.669592i	0.605399	−	0.795922i	$-0.293014\pi$
$659$	−6540.00	−	11327.6i	−0.386589	−	0.669592i	−0.991988	+	0.126330i	$0.959680\pi$
$660$		0			0
$661$	4716.50	−	8169.22i	0.277535	−	0.480705i	−0.693237	−	0.720710i	$-0.743816\pi$
$661$	4716.50	−	8169.22i	0.277535	−	0.480705i	0.970772	+	0.240005i	$0.0771492\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	348.000			0.0202930
$666$		0			0
$667$	33024.0			1.91708
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5950.00	−	10305.7i	0.342321	−	0.592917i
$672$		0			0
$673$	−7137.50	−	12362.5i	−0.408812	−	0.708083i	0.585945	−	0.810351i	$-0.300723\pi$
$673$	−7137.50	−	12362.5i	−0.408812	−	0.708083i	−0.994757	+	0.102268i	$0.967390\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14134.0	+	24480.8i	0.802384	+	1.38977i	0.918043	+	0.396480i	$0.129769\pi$
$677$	14134.0	+	24480.8i	0.802384	+	1.38977i	−0.115660	+	0.993289i	$0.536898\pi$
$678$		0			0
$679$	2224.50	−	3852.95i	0.125727	−	0.217765i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5840.00			−0.327176			−0.163588	−	0.986529i	$-0.552307\pi$
$683$	−5840.00			−0.327176			−0.163588	+	0.986529i	$0.552307\pi$
$684$		0			0
$685$	144.000			0.00803205
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2156.00	+	3734.30i	−0.119212	+	0.206481i
$690$		0			0
$691$	6188.00	+	10717.9i	0.340669	+	0.590057i	0.984557	−	0.175063i	$-0.0560130\pi$
$691$	6188.00	+	10717.9i	0.340669	+	0.590057i	−0.643888	+	0.765120i	$0.722680\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2298.00	+	3980.25i	0.125422	+	0.217237i
$696$		0			0
$697$	−8448.00	+	14632.4i	−0.459097	+	0.795180i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−11076.0			−0.596769			−0.298384	−	0.954446i	$-0.596448\pi$
$701$	−11076.0			−0.596769			−0.298384	+	0.954446i	$0.596448\pi$
$702$		0			0
$703$	−2001.00			−0.107353
$704$		0			0
$705$		0			0
$706$		0			0
$707$	864.000	−	1496.49i	0.0459605	−	0.0796059i
$708$		0			0
$709$	−3626.50	−	6281.28i	−0.192096	−	0.332720i	0.753849	−	0.657048i	$-0.228195\pi$
$709$	−3626.50	−	6281.28i	−0.192096	−	0.332720i	−0.945945	+	0.324328i	$0.894862\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9976.00	−	17278.9i	−0.523989	−	0.907576i
$714$		0			0
$715$	616.000	−	1066.94i	0.0322197	−	0.0558062i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	28456.0			1.47598			0.737990	−	0.674812i	$-0.235775\pi$
$719$	28456.0			1.47598			0.737990	+	0.674812i	$0.235775\pi$
$720$		0			0
$721$	237.000			0.0122418
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10464.0	−	18124.2i	0.536032	−	0.928435i
$726$		0			0
$727$	5214.00	+	9030.91i	0.265993	+	0.460713i	0.967823	−	0.251631i	$-0.0809670\pi$
$727$	5214.00	+	9030.91i	0.265993	+	0.460713i	−0.701831	+	0.712344i	$0.747634\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7216.00	−	12498.5i	−0.365107	−	0.632384i
$732$		0			0
$733$	11603.0	−	20097.0i	0.584675	−	1.01269i	−0.410241	−	0.911977i	$-0.634555\pi$
$733$	11603.0	−	20097.0i	0.584675	−	1.01269i	0.994916	−	0.100709i	$-0.0321112\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7196.00			0.359658
$738$		0			0
$739$	−3424.00			−0.170438			−0.0852191	−	0.996362i	$-0.527159\pi$
$739$	−3424.00			−0.170438			−0.0852191	+	0.996362i	$0.527159\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5846.00	+	10125.6i	−0.288653	+	0.499961i	−0.973488	−	0.228736i	$-0.926541\pi$
$743$	−5846.00	+	10125.6i	−0.288653	+	0.499961i	0.684836	+	0.728697i	$0.259874\pi$
$744$		0			0
$745$	−3472.00	−	6013.68i	−0.170744	−	0.295737i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2754.00	+	4770.07i	0.134351	+	0.232703i
$750$		0			0
$751$	−14674.5	+	25417.0i	−0.713023	+	1.23499i	0.250694	+	0.968066i	$0.419341\pi$
$751$	−14674.5	+	25417.0i	−0.713023	+	1.23499i	−0.963717	+	0.266925i	$0.913992\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2948.00			0.142104
$756$		0			0
$757$	−13555.0			−0.650812			−0.325406	−	0.945574i	$-0.605501\pi$
$757$	−13555.0			−0.650812			−0.325406	+	0.945574i	$0.605501\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5158.00	+	8933.92i	−0.245700	+	0.425564i	−0.962328	−	0.271891i	$-0.912351\pi$
$761$	−5158.00	+	8933.92i	−0.245700	+	0.425564i	0.716629	+	0.697455i	$0.245684\pi$
$762$		0			0
$763$	−2175.00	−	3767.21i	−0.103198	−	0.178745i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2266.00	+	3924.83i	0.106676	+	0.184768i
$768$		0			0
$769$	72.5000	−	125.574i	0.00339976	−	0.00588856i	−0.864321	−	0.502941i	$-0.832251\pi$
$769$	72.5000	−	125.574i	0.00339976	−	0.00588856i	0.867720	+	0.497053i	$0.165584\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	33576.0			1.56228			0.781142	−	0.624354i	$-0.214638\pi$
$773$	33576.0			1.56228			0.781142	+	0.624354i	$0.214638\pi$
$774$		0			0
$775$	−12644.0			−0.586046
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5568.00	+	9644.06i	−0.256090	+	0.443561i
$780$		0			0
$781$	14000.0	+	24248.7i	0.641433	+	1.11100i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5708.00	−	9886.55i	−0.259525	−	0.449511i
$786$		0			0
$787$	13397.5	−	23205.2i	0.606822	−	1.05105i	−0.384938	−	0.922942i	$-0.625777\pi$
$787$	13397.5	−	23205.2i	0.606822	−	1.05105i	0.991761	−	0.128105i	$-0.0408895\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1908.00			0.0857657
$792$		0			0
$793$	4675.00			0.209349
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2392.00	−	4143.07i	0.106310	−	0.184134i	−0.807963	−	0.589234i	$-0.799430\pi$
$797$	2392.00	−	4143.07i	0.106310	−	0.184134i	0.914273	+	0.405099i	$0.132763\pi$
$798$		0			0
$799$	−3432.00	−	5944.40i	−0.151959	−	0.263201i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5026.00	+	8705.29i	0.220876	+	0.382569i
$804$		0			0
$805$	−1032.00	+	1787.48i	−0.0451841	+	0.0782612i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18488.0			0.803465			0.401733	−	0.915757i	$-0.368408\pi$
$809$	18488.0			0.803465			0.401733	+	0.915757i	$0.368408\pi$
$810$		0			0
$811$	33304.0			1.44200			0.721000	−	0.692935i	$-0.243683\pi$
$811$	33304.0			1.44200			0.721000	+	0.692935i	$0.243683\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4026.00	−	6973.24i	0.173036	−	0.299708i
$816$		0			0
$817$	−4756.00	−	8237.63i	−0.203661	−	0.352752i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−21690.0	−	37568.2i	−0.922029	−	1.59700i	−0.796270	−	0.604941i	$-0.793197\pi$
$821$	−21690.0	−	37568.2i	−0.922029	−	1.59700i	−0.125759	−	0.992061i	$-0.540137\pi$
$822$		0			0
$823$	−16892.5	+	29258.7i	−0.715475	+	1.23924i	0.247302	+	0.968939i	$0.420456\pi$
$823$	−16892.5	+	29258.7i	−0.715475	+	1.23924i	−0.962776	+	0.270300i	$0.912877\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	38732.0			1.62859			0.814295	−	0.580452i	$-0.197124\pi$
$827$	38732.0			1.62859			0.814295	+	0.580452i	$0.197124\pi$
$828$		0			0
$829$	−8255.00			−0.345848			−0.172924	−	0.984935i	$-0.555322\pi$
$829$	−8255.00			−0.345848			−0.172924	+	0.984935i	$0.555322\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7348.00	−	12727.1i	0.305634	−	0.529374i
$834$		0			0
$835$	−2424.00	−	4198.49i	−0.100462	−	0.174006i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−18180.0	−	31488.7i	−0.748085	−	1.29572i	−0.948739	−	0.316059i	$-0.897640\pi$
$839$	−18180.0	−	31488.7i	−0.748085	−	1.29572i	0.200655	−	0.979662i	$-0.435693\pi$
$840$		0			0
$841$	−6237.50	+	10803.7i	−0.255751	+	0.442973i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8304.00			−0.338067
$846$		0			0
$847$	−1641.00			−0.0665708
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5934.00	−	10278.0i	0.239030	−	0.414013i
$852$		0			0
$853$	20262.5	+	35095.7i	0.813335	+	1.40874i	0.910517	+	0.413471i	$0.135684\pi$
$853$	20262.5	+	35095.7i	0.813335	+	1.40874i	−0.0971822	+	0.995267i	$0.530983\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22596.0	+	39137.4i	0.900659	+	1.55999i	0.826641	+	0.562730i	$0.190249\pi$
$857$	22596.0	+	39137.4i	0.900659	+	1.55999i	0.0740181	+	0.997257i	$0.476418\pi$
$858$		0			0
$859$	2212.50	−	3832.16i	0.0878807	−	0.152214i	−0.818734	−	0.574172i	$-0.805324\pi$
$859$	2212.50	−	3832.16i	0.0878807	−	0.152214i	0.906615	+	0.421959i	$0.138657\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32380.0			1.27721			0.638603	−	0.769537i	$-0.279513\pi$
$863$	32380.0			1.27721			0.638603	+	0.769537i	$0.279513\pi$
$864$		0			0
$865$	7680.00			0.301882
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12278.0	+	21266.1i	−0.479290	+	0.830154i
$870$		0			0
$871$	1413.50	+	2448.25i	0.0549881	+	0.0952422i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1404.00	+	2431.80i	0.0542444	+	0.0939541i
$876$		0			0
$877$	16282.5	−	28202.1i	0.626934	−	1.08588i	−0.361230	−	0.932477i	$-0.617643\pi$
$877$	16282.5	−	28202.1i	0.626934	−	1.08588i	0.988164	−	0.153404i	$-0.0490237\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	40052.0			1.53165			0.765826	−	0.643047i	$-0.222330\pi$
$881$	40052.0			1.53165			0.765826	+	0.643047i	$0.222330\pi$
$882$		0			0
$883$	26891.0			1.02486			0.512432	−	0.858728i	$-0.328745\pi$
$883$	26891.0			1.02486			0.512432	+	0.858728i	$0.328745\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23084.0	−	39982.7i	0.873827	−	1.51351i	0.0158207	−	0.999875i	$-0.494964\pi$
$887$	23084.0	−	39982.7i	0.873827	−	1.51351i	0.858007	−	0.513639i	$-0.171703\pi$
$888$		0			0
$889$	2190.00	+	3793.19i	0.0826212	+	0.143104i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2262.00	−	3917.90i	−0.0847648	−	0.146817i
$894$		0			0
$895$	−6480.00	+	11223.7i	−0.242014	+	0.419181i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	22272.0			0.826266
$900$		0			0
$901$	−17248.0			−0.637752
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9090.00	+	15744.3i	−0.333880	+	0.578298i
$906$		0			0
$907$	−23724.5	−	41092.0i	−0.868533	−	1.50434i	−0.863496	−	0.504355i	$-0.831730\pi$
$907$	−23724.5	−	41092.0i	−0.868533	−	1.50434i	−0.00503641	−	0.999987i	$-0.501603\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4264.00	+	7385.46i	0.155074	+	0.268596i	0.933086	−	0.359653i	$-0.117105\pi$
$911$	4264.00	+	7385.46i	0.155074	+	0.268596i	−0.778012	+	0.628250i	$0.783772\pi$
$912$		0			0
$913$	4592.00	−	7953.58i	0.166455	−	0.288308i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1392.00			0.0501286
$918$		0			0
$919$	−45596.0			−1.63664			−0.818321	−	0.574762i	$-0.805095\pi$
$919$	−45596.0			−1.63664			−0.818321	+	0.574762i	$0.805095\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5500.00	+	9526.28i	−0.196137	+	0.339720i
$924$		0			0
$925$	−3760.50	−	6513.38i	−0.133670	−	0.231523i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1372.00	−	2376.37i	−0.0484541	−	0.0839250i	0.840781	−	0.541375i	$-0.182096\pi$
$929$	−1372.00	−	2376.37i	−0.0484541	−	0.0839250i	−0.889235	+	0.457450i	$0.848763\pi$
$930$		0			0
$931$	4843.00	−	8388.32i	0.170486	−	0.295291i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4928.00			0.172367
$936$		0			0
$937$	−10389.0			−0.362213			−0.181107	−	0.983463i	$-0.557968\pi$
$937$	−10389.0			−0.362213			−0.181107	+	0.983463i	$0.557968\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27594.0	−	47794.2i	0.955939	−	1.65574i	0.223735	−	0.974650i	$-0.428175\pi$
$941$	27594.0	−	47794.2i	0.955939	−	1.65574i	0.732204	−	0.681085i	$-0.238492\pi$
$942$		0			0
$943$	−33024.0	−	57199.2i	−1.14041	−	1.97525i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11022.0	+	19090.7i	0.378212	+	0.655083i	0.990802	−	0.135318i	$-0.0432057\pi$
$947$	11022.0	+	19090.7i	0.378212	+	0.655083i	−0.612590	+	0.790401i	$0.709872\pi$
$948$		0			0
$949$	−1974.50	+	3419.93i	−0.0675395	+	0.116982i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	4140.00			0.140722			0.0703608	−	0.997522i	$-0.477585\pi$
$953$	4140.00			0.140722			0.0703608	+	0.997522i	$0.477585\pi$
$954$		0			0
$955$	8592.00			0.291132
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−54.0000	+	93.5307i	−0.00181830	+	0.00314939i
$960$		0			0
$961$	8167.50	+	14146.5i	0.274160	+	0.474859i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1682.00	+	2913.31i	0.0561093	+	0.0971842i
$966$		0			0
$967$	9069.50	−	15708.8i	0.301609	−	0.522401i	−0.674892	−	0.737917i	$-0.735810\pi$
$967$	9069.50	−	15708.8i	0.301609	−	0.522401i	0.976500	+	0.215515i	$0.0691431\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23340.0			−0.771386			−0.385693	−	0.922627i	$-0.626038\pi$
$971$	−23340.0			−0.771386			−0.385693	+	0.922627i	$0.626038\pi$
$972$		0			0
$973$	−3447.00			−0.113572
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19548.0	−	33858.1i	0.640119	−	1.10872i	−0.345287	−	0.938497i	$-0.612219\pi$
$977$	19548.0	−	33858.1i	0.640119	−	1.10872i	0.985406	−	0.170221i	$-0.0544482\pi$
$978$		0			0
$979$	22008.0	+	38119.0i	0.718467	+	1.24442i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−546.000	−	945.700i	−0.0177159	−	0.0306848i	0.857032	−	0.515264i	$-0.172306\pi$
$983$	−546.000	−	945.700i	−0.0177159	−	0.0306848i	−0.874747	+	0.484579i	$0.838973\pi$
$984$		0			0
$985$	−3048.00	+	5279.29i	−0.0985963	+	0.170774i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	56416.0			1.81388
$990$		0			0
$991$	5887.00			0.188705			0.0943525	−	0.995539i	$-0.469922\pi$
$991$	5887.00			0.188705			0.0943525	+	0.995539i	$0.469922\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	10642.0	−	18432.5i	0.339069	−	0.587285i
$996$		0			0
$997$	17713.0	+	30679.8i	0.562664	+	0.974563i	0.997263	+	0.0739389i	$0.0235570\pi$
$997$	17713.0	+	30679.8i	0.562664	+	0.974563i	−0.434598	+	0.900624i	$0.643110\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.4.i.d.433.1		2
3.2	odd	2		648.4.i.i.433.1		2
9.2	odd	6		648.4.i.i.217.1		2
9.4	even	3		216.4.a.d.1.1	yes	1
9.5	odd	6		216.4.a.a.1.1	✓	1
9.7	even	3	inner	648.4.i.d.217.1		2
36.23	even	6		432.4.a.d.1.1		1
36.31	odd	6		432.4.a.k.1.1		1
72.5	odd	6		1728.4.a.x.1.1		1
72.13	even	6		1728.4.a.j.1.1		1
72.59	even	6		1728.4.a.w.1.1		1
72.67	odd	6		1728.4.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.4.a.a.1.1	✓	1	9.5	odd	6
216.4.a.d.1.1	yes	1	9.4	even	3
432.4.a.d.1.1		1	36.23	even	6
432.4.a.k.1.1		1	36.31	odd	6
648.4.i.d.217.1		2	9.7	even	3	inner
648.4.i.d.433.1		2	1.1	even	1	trivial
648.4.i.i.217.1		2	9.2	odd	6
648.4.i.i.433.1		2	3.2	odd	2
1728.4.a.i.1.1		1	72.67	odd	6
1728.4.a.j.1.1		1	72.13	even	6
1728.4.a.w.1.1		1	72.59	even	6
1728.4.a.x.1.1		1	72.5	odd	6

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	648.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{5} +(-1.50000 - 2.59808i) q^{7} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{5} +(-1.50000 - 2.59808i) q^{7} +(-14.0000 - 24.2487i) q^{11} +(5.50000 - 9.52628i) q^{13} +44.0000 q^{17} +29.0000 q^{19} +(-86.0000 + 148.956i) q^{23} +(54.5000 + 94.3968i) q^{25} +(-96.0000 - 166.277i) q^{29} +(-58.0000 + 100.459i) q^{31} +12.0000 q^{35} -69.0000 q^{37} +(-192.000 + 332.554i) q^{41} +(-164.000 - 284.056i) q^{43} +(-78.0000 - 135.100i) q^{47} +(167.000 - 289.252i) q^{49} -392.000 q^{53} +112.000 q^{55} +(-206.000 + 356.802i) q^{59} +(212.500 + 368.061i) q^{61} +(22.0000 + 38.1051i) q^{65} +(-128.500 + 222.569i) q^{67} -1000.00 q^{71} -359.000 q^{73} +(-42.0000 + 72.7461i) q^{77} +(-438.500 - 759.504i) q^{79} +(164.000 + 284.056i) q^{83} +(-88.0000 + 152.420i) q^{85} -1572.00 q^{89} -33.0000 q^{91} +(-58.0000 + 100.459i) q^{95} +(741.500 + 1284.32i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{5} - 3 q^{7}+O(q^{10}) \) 2 * q - 4 * q^5 - 3 * q^7	\( 2 q - 4 q^{5} - 3 q^{7} - 28 q^{11} + 11 q^{13} + 88 q^{17} + 58 q^{19} - 172 q^{23} + 109 q^{25} - 192 q^{29} - 116 q^{31} + 24 q^{35} - 138 q^{37} - 384 q^{41} - 328 q^{43} - 156 q^{47} + 334 q^{49} - 784 q^{53} + 224 q^{55} - 412 q^{59} + 425 q^{61} + 44 q^{65} - 257 q^{67} - 2000 q^{71} - 718 q^{73} - 84 q^{77} - 877 q^{79} + 328 q^{83} - 176 q^{85} - 3144 q^{89} - 66 q^{91} - 116 q^{95} + 1483 q^{97}+O(q^{100}) \) 2 * q - 4 * q^5 - 3 * q^7 - 28 * q^11 + 11 * q^13 + 88 * q^17 + 58 * q^19 - 172 * q^23 + 109 * q^25 - 192 * q^29 - 116 * q^31 + 24 * q^35 - 138 * q^37 - 384 * q^41 - 328 * q^43 - 156 * q^47 + 334 * q^49 - 784 * q^53 + 224 * q^55 - 412 * q^59 + 425 * q^61 + 44 * q^65 - 257 * q^67 - 2000 * q^71 - 718 * q^73 - 84 * q^77 - 877 * q^79 + 328 * q^83 - 176 * q^85 - 3144 * q^89 - 66 * q^91 - 116 * q^95 + 1483 * q^97

Introduction

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