LMFDB - Embedded newform 756.4.x.a.125.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,4,Mod(125,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("756.125");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	756.x (of order $6$, 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:	$44.6054439643$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.5
Character	$\chi$	$=$	756.125
Dual form			756.4.x.a.629.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.03570 + 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +O(q^{10})$	$q+(-6.03570 + 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-0.00221312 + 0.00127775i) q^{11} +(6.06841 + 3.50360i) q^{13} +28.3143 q^{17} +49.1973i q^{19} +(-44.4689 - 25.6741i) q^{23} +(-10.3594 - 17.9431i) q^{25} +(-97.9469 + 56.5497i) q^{29} +(-28.4271 - 16.4124i) q^{31} +(179.663 + 133.052i) q^{35} -101.961 q^{37} +(11.2449 - 19.4767i) q^{41} +(-227.203 - 393.527i) q^{43} +(-231.260 - 400.554i) q^{47} +(-334.149 - 77.4179i) q^{49} +567.586i q^{53} -0.0308484i q^{55} +(145.654 - 252.280i) q^{59} +(592.003 - 341.793i) q^{61} +(-73.2542 + 42.2933i) q^{65} +(269.780 - 467.273i) q^{67} -307.517i q^{71} -495.192i q^{73} +(0.0188553 + 0.0434103i) q^{77} +(-324.865 - 562.683i) q^{79} +(-565.581 - 979.615i) q^{83} +(-170.897 + 296.002i) q^{85} -130.217 q^{89} +(77.2337 - 104.291i) q^{91} +(-514.315 - 296.940i) q^{95} +(1260.41 - 727.696i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7}+O(q^{10}) $ 48 * q + 6 * q^7	$ 48 q + 6 q^{7} + 12 q^{11} + 408 q^{23} - 600 q^{25} + 84 q^{29} + 336 q^{37} + 84 q^{43} + 318 q^{49} - 2964 q^{65} - 588 q^{67} - 2400 q^{77} + 204 q^{79} - 360 q^{85} - 1080 q^{91} - 300 q^{95}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^11 + 408 * q^23 - 600 * q^25 + 84 * q^29 + 336 * q^37 + 84 * q^43 + 318 * q^49 - 2964 * q^65 - 588 * q^67 - 2400 * q^77 + 204 * q^79 - 360 * q^85 - 1080 * q^91 - 300 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−6.03570	+	10.4541i	−0.539850	+	0.935047i	0.459062	+	0.888404i	$0.348186\pi$
$5$	−6.03570	+	10.4541i	−0.539850	+	0.935047i	−0.998912	+	0.0466430i	$0.985148\pi$
$6$		0			0
$7$	2.10370	−	18.4004i	0.113589	−	0.993528i
$7$	2.10370	−	18.4004i	0.113589	−	0.993528i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.00221312	+	0.00127775i	−6.06619e−5	+	3.50232e-5i	−0.500030	−	0.866008i	$-0.666678\pi$
$11$	−0.00221312	+	0.00127775i	−6.06619e−5	+	3.50232e-5i	0.499970	+	0.866043i	$0.333344\pi$
$12$		0			0
$13$	6.06841	+	3.50360i	0.129467	+	0.0747479i	0.563335	−	0.826229i	$-0.309518\pi$
$13$	6.06841	+	3.50360i	0.129467	+	0.0747479i	−0.433868	+	0.900977i	$0.642851\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	28.3143			0.403955			0.201977	−	0.979390i	$-0.435263\pi$
$17$	28.3143			0.403955			0.201977	+	0.979390i	$0.435263\pi$
$18$		0			0
$19$			49.1973i			0.594033i	0.954872	+	0.297016i	$0.0959916\pi$
$19$			49.1973i			0.594033i	−0.954872	+	0.297016i	$0.904008\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−44.4689	−	25.6741i	−0.403148	−	0.232758i	0.284693	−	0.958619i	$-0.408108\pi$
$23$	−44.4689	−	25.6741i	−0.403148	−	0.232758i	−0.687841	+	0.725861i	$0.741442\pi$
$24$		0			0
$25$	−10.3594	−	17.9431i	−0.0828756	−	0.143545i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−97.9469	+	56.5497i	−0.627182	+	0.362104i	−0.779660	−	0.626203i	$-0.784608\pi$
$29$	−97.9469	+	56.5497i	−0.627182	+	0.362104i	0.152478	+	0.988307i	$0.451275\pi$
$30$		0			0
$31$	−28.4271	−	16.4124i	−0.164699	−	0.0950889i	0.415385	−	0.909646i	$-0.363647\pi$
$31$	−28.4271	−	16.4124i	−0.164699	−	0.0950889i	−0.580084	+	0.814557i	$0.696980\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	179.663	+	133.052i	0.867674	+	0.642567i
$36$		0			0
$37$	−101.961			−0.453034			−0.226517	−	0.974007i	$-0.572734\pi$
$37$	−101.961			−0.453034			−0.226517	+	0.974007i	$0.572734\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	11.2449	−	19.4767i	0.0428331	−	0.0741891i	−0.843814	−	0.536636i	$-0.819695\pi$
$41$	11.2449	−	19.4767i	0.0428331	−	0.0741891i	0.886647	+	0.462447i	$0.153028\pi$
$42$		0			0
$43$	−227.203	−	393.527i	−0.805771	−	1.39564i	−0.915769	−	0.401705i	$-0.868418\pi$
$43$	−227.203	−	393.527i	−0.805771	−	1.39564i	0.109998	−	0.993932i	$-0.464916\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−231.260	−	400.554i	−0.717717	−	1.24312i	−0.961902	−	0.273394i	$-0.911854\pi$
$47$	−231.260	−	400.554i	−0.717717	−	1.24312i	0.244185	−	0.969729i	$-0.421480\pi$
$48$		0			0
$49$	−334.149	−	77.4179i	−0.974195	−	0.225708i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			567.586i			1.47102i	0.677515	+	0.735509i	$0.263057\pi$
$53$			567.586i			1.47102i	−0.677515	+	0.735509i	$0.736943\pi$
$54$		0			0
$55$		−	0.0308484i		−	7.56290e-5i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	145.654	−	252.280i	0.321399	−	0.556680i	−0.659378	−	0.751812i	$-0.729180\pi$
$59$	145.654	−	252.280i	0.321399	−	0.556680i	0.980777	+	0.195132i	$0.0625136\pi$
$60$		0			0
$61$	592.003	−	341.793i	1.24259	−	0.717412i	0.272972	−	0.962022i	$-0.411993\pi$
$61$	592.003	−	341.793i	1.24259	−	0.717412i	0.969621	+	0.244610i	$0.0786601\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−73.2542	+	42.2933i	−0.139786	+	0.0807053i
$66$		0			0
$67$	269.780	−	467.273i	0.491924	−	0.852037i	−0.508033	−	0.861338i	$-0.669627\pi$
$67$	269.780	−	467.273i	0.491924	−	0.852037i	0.999957	+	0.00930051i	$0.00296049\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	307.517i		−	0.514022i	−0.966408	−	0.257011i	$-0.917262\pi$
$71$		−	307.517i		−	0.514022i	0.966408	−	0.257011i	$-0.0827377\pi$
$72$		0			0
$73$		−	495.192i		−	0.793943i	−0.917831	−	0.396971i	$-0.870061\pi$
$73$		−	495.192i		−	0.793943i	0.917831	−	0.396971i	$-0.129939\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.0188553	+	0.0434103i	2.79060e−5	+	6.42476e-5i
$78$		0			0
$79$	−324.865	−	562.683i	−0.462661	−	0.801352i	0.536432	−	0.843944i	$-0.319772\pi$
$79$	−324.865	−	562.683i	−0.462661	−	0.801352i	−0.999093	+	0.0425920i	$0.986438\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−565.581	−	979.615i	−0.747959	−	1.29550i	−0.948800	−	0.315879i	$-0.897701\pi$
$83$	−565.581	−	979.615i	−0.747959	−	1.29550i	0.200841	−	0.979624i	$-0.435633\pi$
$84$		0			0
$85$	−170.897	+	296.002i	−0.218075	+	0.377717i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−130.217			−0.155089			−0.0775447	−	0.996989i	$-0.524708\pi$
$89$	−130.217			−0.155089			−0.0775447	+	0.996989i	$0.524708\pi$
$90$		0			0
$91$	77.2337	−	104.291i	0.0889702	−	0.120139i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−514.315	−	296.940i	−0.555449	−	0.320688i
$96$		0			0
$97$	1260.41	−	727.696i	1.31933	−	0.761715i	0.335709	−	0.941966i	$-0.391024\pi$
$97$	1260.41	−	727.696i	1.31933	−	0.761715i	0.983621	+	0.180251i	$0.0576909\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−197.600	−	342.254i	−0.194673	−	0.337183i	0.752120	−	0.659026i	$-0.229031\pi$
$101$	−197.600	−	342.254i	−0.194673	−	0.337183i	−0.946793	+	0.321842i	$0.895698\pi$
$102$		0			0
$103$	545.260	+	314.806i	0.521612	+	0.301153i	0.737594	−	0.675244i	$-0.235962\pi$
$103$	545.260	+	314.806i	0.521612	+	0.301153i	−0.215982	+	0.976397i	$0.569295\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	515.616i		−	0.465855i	−0.972494	−	0.232927i	$-0.925170\pi$
$107$		−	515.616i		−	0.465855i	0.972494	−	0.232927i	$-0.0748305\pi$
$108$		0			0
$109$	794.011			0.697729			0.348864	−	0.937173i	$-0.386567\pi$
$109$	794.011			0.697729			0.348864	+	0.937173i	$0.386567\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1782.31	−	1029.02i	−1.48377	−	0.856654i	−0.483939	−	0.875102i	$-0.660794\pi$
$113$	−1782.31	−	1029.02i	−1.48377	−	0.856654i	−0.999830	+	0.0184476i	$0.994128\pi$
$114$		0			0
$115$	536.802	−	309.923i	0.435279	−	0.251308i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	59.5649	−	520.994i	0.0458849	−	0.401340i
$120$		0			0
$121$	−665.500	+	1152.68i	−0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1258.82			−0.900738
$126$		0			0
$127$	−2071.63			−1.44746			−0.723729	−	0.690084i	$-0.757573\pi$
$127$	−2071.63			−1.44746			−0.723729	+	0.690084i	$0.757573\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	467.210	−	809.232i	0.311606	−	0.539717i	−0.667104	−	0.744964i	$-0.732467\pi$
$131$	467.210	−	809.232i	0.311606	−	0.539717i	0.978710	+	0.205247i	$0.0657999\pi$
$132$		0			0
$133$	905.249	+	103.496i	0.590188	+	0.0674758i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2320.59	+	1339.79i	−1.44716	+	0.835521i	−0.998312	−	0.0580849i	$-0.981501\pi$
$137$	−2320.59	+	1339.79i	−1.44716	+	0.835521i	−0.448853	+	0.893606i	$0.648167\pi$
$138$		0			0
$139$	794.727	+	458.836i	0.484949	+	0.279985i	0.722476	−	0.691395i	$-0.243004\pi$
$139$	794.727	+	458.836i	0.484949	+	0.279985i	−0.237528	+	0.971381i	$0.576337\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.0179068			−1.04716e−5
$144$		0			0
$145$		−	1365.27i		−	0.781926i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1187.44	−	685.572i	−0.652881	−	0.376941i	0.136678	−	0.990616i	$-0.456357\pi$
$149$	−1187.44	−	685.572i	−0.652881	−	0.376941i	−0.789559	+	0.613674i	$0.789691\pi$
$150$		0			0
$151$	127.186	+	220.292i	0.0685445	+	0.118723i	0.898261	−	0.439463i	$-0.144831\pi$
$151$	127.186	+	220.292i	0.0685445	+	0.118723i	−0.829716	+	0.558185i	$0.811498\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	343.155	−	198.121i	0.177825	−	0.102667i
$156$		0			0
$157$	511.747	+	295.457i	0.260139	+	0.150191i	0.624398	−	0.781106i	$-0.285344\pi$
$157$	511.747	+	295.457i	0.260139	+	0.150191i	−0.364259	+	0.931298i	$0.618678\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−565.963	+	764.234i	−0.277044	+	0.374100i
$162$		0			0
$163$	−2197.17			−1.05580			−0.527901	−	0.849306i	$-0.677021\pi$
$163$	−2197.17			−1.05580			−0.527901	+	0.849306i	$0.677021\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−210.903	+	365.295i	−0.0977256	+	0.169266i	−0.910743	−	0.412974i	$-0.864490\pi$
$167$	−210.903	+	365.295i	−0.0977256	+	0.169266i	0.813017	+	0.582240i	$0.197823\pi$
$168$		0			0
$169$	−1073.95	−	1860.14i	−0.488826	−	0.846671i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−872.428	−	1511.09i	−0.383407	−	0.664081i	0.608139	−	0.793830i	$-0.291916\pi$
$173$	−872.428	−	1511.09i	−0.383407	−	0.664081i	−0.991547	+	0.129749i	$0.958583\pi$
$174$		0			0
$175$	−351.953	+	152.871i	−0.152029	+	0.0660341i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			4311.61i			1.80036i	0.435518	+	0.900180i	$0.356565\pi$
$179$			4311.61i			1.80036i	−0.435518	+	0.900180i	$0.643435\pi$
$180$		0			0
$181$		−	1307.99i		−	0.537141i	−0.963260	−	0.268570i	$-0.913449\pi$
$181$		−	1307.99i		−	0.537141i	0.963260	−	0.268570i	$-0.0865512\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	615.405	−	1065.91i	0.244570	−	0.423608i
$186$		0			0
$187$	−0.0626630	+	0.0361785i	−2.45047e−5	+	1.41478e-5i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3495.99	−	2018.41i	1.32440	−	0.764644i	0.339975	−	0.940435i	$-0.389581\pi$
$191$	3495.99	−	2018.41i	1.32440	−	0.764644i	0.984428	+	0.175791i	$0.0562482\pi$
$192$		0			0
$193$	2209.64	−	3827.21i	0.824112	−	1.42740i	−0.0784849	−	0.996915i	$-0.525008\pi$
$193$	2209.64	−	3827.21i	0.824112	−	1.42740i	0.902596	−	0.430488i	$-0.141658\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			151.673i			0.0548540i	0.999624	+	0.0274270i	$0.00873138\pi$
$197$			151.673i			0.0548540i	−0.999624	+	0.0274270i	$0.991269\pi$
$198$		0			0
$199$		−	1838.65i		−	0.654966i	−0.944857	−	0.327483i	$-0.893800\pi$
$199$		−	1838.65i		−	0.654966i	0.944857	−	0.327483i	$-0.106200\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	834.485	+	1921.22i	0.288519	+	0.664254i
$204$		0			0
$205$	135.742	+	235.111i	0.0462468	+	0.0801019i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0628616	−	0.108879i	−2.08049e−5	−	3.60352e-5i
$210$		0			0
$211$	1229.27	−	2129.15i	0.401072	−	0.694678i	−0.592783	−	0.805362i	$-0.701971\pi$
$211$	1229.27	−	2129.15i	0.401072	−	0.694678i	0.993856	+	0.110684i	$0.0353042\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5485.32			1.73998
$216$		0			0
$217$	−361.797	+	488.543i	−0.113181	+	0.152832i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	171.823	+	99.2019i	0.0522989	+	0.0301948i
$222$		0			0
$223$	−4491.19	+	2592.99i	−1.34867	+	0.778653i	−0.988061	−	0.154066i	$-0.950763\pi$
$223$	−4491.19	+	2592.99i	−1.34867	+	0.778653i	−0.360606	+	0.932718i	$0.617430\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−497.531	−	861.749i	−0.145473	−	0.251966i	0.784077	−	0.620664i	$-0.213137\pi$
$227$	−497.531	−	861.749i	−0.145473	−	0.251966i	−0.929549	+	0.368698i	$0.879804\pi$
$228$		0			0
$229$	101.864	+	58.8111i	0.0293946	+	0.0169710i	0.514625	−	0.857415i	$-0.327931\pi$
$229$	101.864	+	58.8111i	0.0293946	+	0.0169710i	−0.485231	+	0.874386i	$0.661264\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			1484.08i			0.417276i	0.977993	+	0.208638i	$0.0669030\pi$
$233$			1484.08i			0.417276i	−0.977993	+	0.208638i	$0.933097\pi$
$234$		0			0
$235$	5583.26			1.54984
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2392.08	−	1381.07i	−0.647409	−	0.373782i	0.140054	−	0.990144i	$-0.455272\pi$
$239$	−2392.08	−	1381.07i	−0.647409	−	0.373782i	−0.787463	+	0.616362i	$0.788606\pi$
$240$		0			0
$241$	−3362.99	+	1941.62i	−0.898877	+	0.518967i	−0.876836	−	0.480790i	$-0.840350\pi$
$241$	−3362.99	+	1941.62i	−0.898877	+	0.518967i	−0.0220413	+	0.999757i	$0.507017\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2826.16	−	3025.97i	0.736967	−	0.789070i
$246$		0			0
$247$	−172.367	+	298.549i	−0.0444027	+	0.0769078i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5549.57			1.39556			0.697780	−	0.716312i	$-0.254171\pi$
$251$	5549.57			1.39556			0.697780	+	0.716312i	$0.254171\pi$
$252$		0			0
$253$	0.131220			3.26076e−5
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−809.585	+	1402.24i	−0.196500	+	0.340348i	−0.947391	−	0.320078i	$-0.896291\pi$
$257$	−809.585	+	1402.24i	−0.196500	+	0.340348i	0.750891	+	0.660426i	$0.229624\pi$
$258$		0			0
$259$	−214.495	+	1876.12i	−0.0514598	+	0.450102i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	594.813	−	343.415i	0.139459	−	0.0805167i	−0.428647	−	0.903472i	$-0.641010\pi$
$263$	594.813	−	343.415i	0.139459	−	0.0805167i	0.568106	+	0.822955i	$0.307676\pi$
$264$		0			0
$265$	−5933.62	−	3425.78i	−1.37547	−	0.794128i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1805.03			0.409124			0.204562	−	0.978854i	$-0.434423\pi$
$269$	1805.03			0.409124			0.204562	+	0.978854i	$0.434423\pi$
$270$		0			0
$271$			6726.19i			1.50770i	0.657046	+	0.753851i	$0.271806\pi$
$271$			6726.19i			1.50770i	−0.657046	+	0.753851i	$0.728194\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.0458534	+	0.0264735i	1.00548e−5	+	5.80513e-6i
$276$		0			0
$277$	−336.124	−	582.184i	−0.0729088	−	0.126282i	0.827266	−	0.561810i	$-0.189895\pi$
$277$	−336.124	−	582.184i	−0.0729088	−	0.126282i	−0.900175	+	0.435528i	$0.856562\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2007.12	−	1158.81i	0.426102	−	0.246010i	−0.271583	−	0.962415i	$-0.587547\pi$
$281$	2007.12	−	1158.81i	0.426102	−	0.246010i	0.697685	+	0.716405i	$0.254214\pi$
$282$		0			0
$283$	8014.87	+	4627.39i	1.68352	+	0.971978i	0.959294	+	0.282411i	$0.0911342\pi$
$283$	8014.87	+	4627.39i	1.68352	+	0.971978i	0.724222	+	0.689567i	$0.242199\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−334.723	−	247.883i	−0.0688435	−	0.0509829i
$288$		0			0
$289$	−4111.30			−0.836821
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4392.72	+	7608.42i	−0.875855	+	1.51703i	−0.0200056	+	0.999800i	$0.506368\pi$
$293$	−4392.72	+	7608.42i	−0.875855	+	1.51703i	−0.855849	+	0.517225i	$0.826965\pi$
$294$		0			0
$295$	1758.25	+	3045.38i	0.347015	+	0.601047i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−179.904	−	311.602i	−0.0347963	−	0.0602689i
$300$		0			0
$301$	−7719.03	+	3352.76i	−1.47813	+	0.642027i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			8251.85i			1.54918i
$306$		0			0
$307$		−	599.516i		−	0.111453i	−0.998446	−	0.0557267i	$-0.982252\pi$
$307$		−	599.516i		−	0.111453i	0.998446	−	0.0557267i	$-0.0177476\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4494.29	+	7784.34i	−0.819447	+	1.41932i	0.0866437	+	0.996239i	$0.472386\pi$
$311$	−4494.29	+	7784.34i	−0.819447	+	1.41932i	−0.906090	+	0.423084i	$0.860948\pi$
$312$		0			0
$313$	7102.69	−	4100.74i	1.28264	−	0.740535i	0.305314	−	0.952252i	$-0.401239\pi$
$313$	7102.69	−	4100.74i	1.28264	−	0.740535i	0.977331	+	0.211717i	$0.0679054\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5894.42	−	3403.15i	1.04436	−	0.602964i	0.123298	−	0.992370i	$-0.460653\pi$
$317$	5894.42	−	3403.15i	1.04436	−	0.602964i	0.921066	+	0.389405i	$0.127319\pi$
$318$		0			0
$319$	0.144512	−	0.250302i	2.53640e−5	−	4.39318e-5i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1392.99i			0.239962i
$324$		0			0
$325$		−	145.181i		−	0.0247791i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7856.85	+	3412.63i	−1.31660	+	0.571867i
$330$		0			0
$331$	3875.41	+	6712.41i	0.643540	+	1.11464i	0.984637	+	0.174616i	$0.0558684\pi$
$331$	3875.41	+	6712.41i	0.643540	+	1.11464i	−0.341097	+	0.940028i	$0.610798\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3256.63	+	5640.64i	0.531130	+	0.919944i
$336$		0			0
$337$	−1544.24	+	2674.70i	−0.249614	+	0.432344i	−0.963419	−	0.268001i	$-0.913637\pi$
$337$	−1544.24	+	2674.70i	−0.249614	+	0.432344i	0.713805	+	0.700345i	$0.246970\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.0838835			1.33213e−5
$342$		0			0
$343$	−2127.47	+	5985.61i	−0.334906	+	0.942252i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10112.9	−	5838.71i	−1.56453	−	0.903281i	−0.996789	−	0.0800721i	$-0.974485\pi$
$347$	−10112.9	−	5838.71i	−1.56453	−	0.903281i	−0.567739	−	0.823209i	$-0.692182\pi$
$348$		0			0
$349$	−6683.19	+	3858.54i	−1.02505	+	0.591814i	−0.915563	−	0.402174i	$-0.868255\pi$
$349$	−6683.19	+	3858.54i	−1.02505	+	0.591814i	−0.109489	+	0.993988i	$0.534921\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2760.12	−	4780.66i	−0.416165	−	0.720818i	0.579385	−	0.815054i	$-0.303293\pi$
$353$	−2760.12	−	4780.66i	−0.416165	−	0.720818i	−0.995550	+	0.0942355i	$0.969959\pi$
$354$		0			0
$355$	3214.83	+	1856.08i	0.480635	+	0.277495i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	6290.95i		−	0.924857i	−0.886657	−	0.462429i	$-0.846978\pi$
$359$		−	6290.95i		−	0.924857i	0.886657	−	0.462429i	$-0.153022\pi$
$360$		0			0
$361$	4438.63			0.647125
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5176.81	+	2988.83i	0.742374	+	0.428610i
$366$		0			0
$367$	−3342.42	+	1929.75i	−0.475404	+	0.274474i	−0.718499	−	0.695528i	$-0.755171\pi$
$367$	−3342.42	+	1929.75i	−0.475404	+	0.274474i	0.243095	+	0.970002i	$0.421837\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10443.8	+	1194.03i	1.46150	+	0.167092i
$372$		0			0
$373$	−4308.29	+	7462.17i	−0.598055	+	1.03586i	0.395052	+	0.918659i	$0.370726\pi$
$373$	−4308.29	+	7462.17i	−0.598055	+	1.03586i	−0.993108	+	0.117204i	$0.962607\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−792.509			−0.108266
$378$		0			0
$379$	11100.5			1.50447			0.752237	−	0.658893i	$-0.228975\pi$
$379$	11100.5			1.50447			0.752237	+	0.658893i	$0.228975\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3294.29	−	5705.87i	0.439505	−	0.761244i	−0.558147	−	0.829742i	$-0.688487\pi$
$383$	3294.29	−	5705.87i	0.439505	−	0.761244i	0.997651	+	0.0684980i	$0.0218207\pi$
$384$		0			0
$385$	−0.567622	−	0.0648959i	−7.51395e−5	−	8.59065e-6i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6913.20	−	3991.34i	0.901062	−	0.520228i	0.0235174	−	0.999723i	$-0.492513\pi$
$389$	6913.20	−	3991.34i	0.901062	−	0.520228i	0.877545	+	0.479495i	$0.159180\pi$
$390$		0			0
$391$	−1259.11	−	726.945i	−0.162854	−	0.0940235i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7843.16			0.999069
$396$		0			0
$397$			9040.06i			1.14284i	0.820658	+	0.571420i	$0.193607\pi$
$397$			9040.06i			1.14284i	−0.820658	+	0.571420i	$0.806393\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	836.173	+	482.765i	0.104131	+	0.0601200i	0.551161	−	0.834399i	$-0.314185\pi$
$401$	836.173	+	482.765i	0.104131	+	0.0601200i	−0.447030	+	0.894519i	$0.647518\pi$
$402$		0			0
$403$	−115.005	−	199.194i	−0.0142154	−	0.0246218i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.225652	−	0.130280i	2.74819e−5	−	1.58667e-5i
$408$		0			0
$409$	−2868.77	−	1656.28i	−0.346825	−	0.200240i	0.316461	−	0.948606i	$-0.397505\pi$
$409$	−2868.77	−	1656.28i	−0.346825	−	0.200240i	−0.663286	+	0.748366i	$0.730839\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4335.64	−	3210.82i	−0.516569	−	0.382552i
$414$		0			0
$415$	13654.7			1.61514
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4172.32	+	7226.67i	−0.486470	+	0.842591i	−0.999879	−	0.0155530i	$-0.995049\pi$
$419$	−4172.32	+	7226.67i	−0.486470	+	0.842591i	0.513409	+	0.858144i	$0.328382\pi$
$420$		0			0
$421$	3350.59	+	5803.38i	0.387880	+	0.671828i	0.992164	−	0.124941i	$-0.0398741\pi$
$421$	3350.59	+	5803.38i	0.387880	+	0.671828i	−0.604284	+	0.796769i	$0.706541\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−293.321	−	508.046i	−0.0334780	−	0.0579856i
$426$		0			0
$427$	−5043.73	−	11612.1i	−0.571623	−	1.31604i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	9168.55i		−	1.02467i	−0.858785	−	0.512336i	$-0.828780\pi$
$431$		−	9168.55i		−	1.02467i	0.858785	−	0.512336i	$-0.171220\pi$
$432$		0			0
$433$			1346.90i			0.149487i	0.997203	+	0.0747436i	$0.0238138\pi$
$433$			1346.90i			0.149487i	−0.997203	+	0.0747436i	$0.976186\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1263.10	−	2187.75i	0.138266	−	0.239483i
$438$		0			0
$439$	4892.07	−	2824.44i	0.531858	−	0.307069i	−0.209914	−	0.977720i	$-0.567319\pi$
$439$	4892.07	−	2824.44i	0.531858	−	0.307069i	0.741773	+	0.670651i	$0.233985\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7525.68	−	4344.95i	0.807124	−	0.465993i	−0.0388322	−	0.999246i	$-0.512364\pi$
$443$	7525.68	−	4344.95i	0.807124	−	0.465993i	0.845956	+	0.533253i	$0.179030\pi$
$444$		0			0
$445$	785.950	−	1361.31i	0.0837249	−	0.145016i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			14492.3i			1.52324i	0.648026	+	0.761618i	$0.275595\pi$
$449$			14492.3i			1.52324i	−0.648026	+	0.761618i	$0.724405\pi$
$450$		0			0
$451$			0.0574724i			6.00060e-6i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	624.109	+	1436.88i	0.0643048	+	0.148048i
$456$		0			0
$457$	−4131.68	−	7156.27i	−0.422914	−	0.732508i	0.573309	−	0.819339i	$-0.305659\pi$
$457$	−4131.68	−	7156.27i	−0.422914	−	0.732508i	−0.996223	+	0.0868308i	$0.972326\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4948.33	−	8570.75i	−0.499928	−	0.865900i	0.500072	−	0.865984i	$-0.333307\pi$
$461$	−4948.33	−	8570.75i	−0.499928	−	0.865900i	−1.00000		8.36677e-5i	$0.999973\pi$
$462$		0			0
$463$	1987.79	−	3442.95i	0.199525	−	0.345588i	−0.748849	−	0.662740i	$-0.769393\pi$
$463$	1987.79	−	3442.95i	0.199525	−	0.345588i	0.948375	+	0.317152i	$0.102727\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17044.5			1.68892			0.844460	−	0.535619i	$-0.179921\pi$
$467$	17044.5			1.68892			0.844460	+	0.535619i	$0.179921\pi$
$468$		0			0
$469$	−8030.47	−	5947.07i	−0.790645	−	0.585522i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.00566	+	0.580616i	9.77592e−5	+	5.64413e-5i
$474$		0			0
$475$	882.751	−	509.656i	0.0852703	−	0.0492308i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5364.93	+	9292.33i	0.511753	+	0.886383i	0.999907	+	0.0136250i	$0.00433712\pi$
$479$	5364.93	+	9292.33i	0.511753	+	0.886383i	−0.488154	+	0.872758i	$0.662330\pi$
$480$		0			0
$481$	−618.740	−	357.230i	−0.0586530	−	0.0338633i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			17568.6i			1.64485i
$486$		0			0
$487$	−12461.1			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$487$	−12461.1			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4052.21	+	2339.55i	0.372452	+	0.215035i	0.674529	−	0.738248i	$-0.264347\pi$
$491$	4052.21	+	2339.55i	0.372452	+	0.215035i	−0.302077	+	0.953283i	$0.597680\pi$
$492$		0			0
$493$	−2773.30	+	1601.16i	−0.253353	+	0.146273i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5658.43	−	646.925i	−0.510695	−	0.0583874i
$498$		0			0
$499$	2685.54	−	4651.49i	0.240924	−	0.417293i	−0.720054	−	0.693918i	$-0.755883\pi$
$499$	2685.54	−	4651.49i	0.240924	−	0.417293i	0.960978	+	0.276625i	$0.0892161\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22263.9			−1.97355			−0.986777	−	0.162086i	$-0.948178\pi$
$503$	−22263.9			−1.97355			−0.986777	+	0.162086i	$0.948178\pi$
$504$		0			0
$505$	4770.63			0.420376
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7249.76	−	12556.9i	0.631316	−	1.09347i	−0.355967	−	0.934498i	$-0.615848\pi$
$509$	7249.76	−	12556.9i	0.631316	−	1.09347i	0.987283	−	0.158973i	$-0.0508182\pi$
$510$		0			0
$511$	−9111.72	−	1041.74i	−0.788804	−	0.0901834i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6582.05	+	3800.15i	−0.563184	+	0.325155i
$516$		0			0
$517$	1.02361	+	0.590983i	8.70762e−5	+	5.02735e-5i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7009.79			0.589452			0.294726	−	0.955582i	$-0.404772\pi$
$521$	7009.79			0.589452			0.294726	+	0.955582i	$0.404772\pi$
$522$		0			0
$523$			3631.76i			0.303644i	0.988408	+	0.151822i	$0.0485141\pi$
$523$			3631.76i			0.303644i	−0.988408	+	0.151822i	$0.951486\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−804.894	−	464.706i	−0.0665308	−	0.0384116i
$528$		0			0
$529$	−4765.18	−	8253.53i	−0.391648	−	0.678354i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	136.477	−	78.7951i	0.0110910	−	0.00640336i
$534$		0			0
$535$	5390.32	+	3112.10i	0.435596	+	0.251492i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.838432	−	0.255622i	6.70015e−5	−	2.04275e-5i
$540$		0			0
$541$	−12760.4			−1.01407			−0.507037	−	0.861925i	$-0.669259\pi$
$541$	−12760.4			−1.01407			−0.507037	+	0.861925i	$0.669259\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4792.42	+	8300.71i	−0.376669	+	0.652410i
$546$		0			0
$547$	−3919.62	−	6788.98i	−0.306382	−	0.530669i	0.671186	−	0.741289i	$-0.265785\pi$
$547$	−3919.62	−	6788.98i	−0.306382	−	0.530669i	−0.977568	+	0.210620i	$0.932452\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2782.09	−	4818.72i	−0.215101	−	0.372567i
$552$		0			0
$553$	−11037.0	+	4793.93i	−0.848718	+	0.368641i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			9443.19i			0.718350i	0.933270	+	0.359175i	$0.116942\pi$
$557$			9443.19i			0.718350i	−0.933270	+	0.359175i	$0.883058\pi$
$558$		0			0
$559$		−	3184.11i		−	0.240919i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8022.13	−	13894.7i	0.600519	−	1.04013i	−0.392223	−	0.919870i	$-0.628294\pi$
$563$	8022.13	−	13894.7i	0.600519	−	1.04013i	0.992742	−	0.120260i	$-0.0383728\pi$
$564$		0			0
$565$	21515.0	−	12421.7i	1.60202	−	0.924929i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19213.9	+	11093.2i	−1.41562	+	0.817310i	−0.995910	−	0.0903469i	$-0.971202\pi$
$569$	−19213.9	+	11093.2i	−1.41562	+	0.817310i	−0.419712	+	0.907657i	$0.637869\pi$
$570$		0			0
$571$	−3211.11	+	5561.80i	−0.235343	+	0.407625i	−0.959372	−	0.282144i	$-0.908955\pi$
$571$	−3211.11	+	5561.80i	−0.235343	+	0.407625i	0.724030	+	0.689769i	$0.242288\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			1063.88i			0.0771597i
$576$		0			0
$577$		−	21441.1i		−	1.54697i	−0.633813	−	0.773486i	$-0.718511\pi$
$577$		−	21441.1i		−	1.54697i	0.633813	−	0.773486i	$-0.281489\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19215.1	+	8346.09i	−1.37208	+	0.595963i
$582$		0			0
$583$	−0.725230	−	1.25614i	−5.15197e−5	−	8.92347e-5i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−342.762	−	593.681i	−0.0241010	−	0.0417442i	0.853723	−	0.520727i	$-0.174339\pi$
$587$	−342.762	−	593.681i	−0.0241010	−	0.0417442i	−0.877824	+	0.478983i	$0.841006\pi$
$588$		0			0
$589$	807.445	−	1398.54i	0.0564859	−	0.0978365i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	11503.8			0.796635			0.398317	−	0.917248i	$-0.369594\pi$
$593$	11503.8			0.796635			0.398317	+	0.917248i	$0.369594\pi$
$594$		0			0
$595$	5087.04	+	3767.27i	0.350501	+	0.259568i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5124.45	−	2958.60i	−0.349548	−	0.201812i	0.314938	−	0.949112i	$-0.398016\pi$
$599$	−5124.45	−	2958.60i	−0.349548	−	0.201812i	−0.664486	+	0.747300i	$0.731350\pi$
$600$		0			0
$601$	−10168.3	+	5870.67i	−0.690139	+	0.398452i	−0.803664	−	0.595083i	$-0.797119\pi$
$601$	−10168.3	+	5870.67i	−0.690139	+	0.398452i	0.113525	+	0.993535i	$0.463786\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8033.52	−	13914.5i	−0.539850	−	0.935047i
$606$		0			0
$607$	24018.0	+	13866.8i	1.60603	+	0.927241i	0.990247	+	0.139325i	$0.0444933\pi$
$607$	24018.0	+	13866.8i	1.60603	+	0.927241i	0.615782	+	0.787916i	$0.288840\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	3240.96i		−	0.214592i
$612$		0			0
$613$	−19338.2			−1.27416			−0.637081	−	0.770797i	$-0.719858\pi$
$613$	−19338.2			−1.27416			−0.637081	+	0.770797i	$0.719858\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9927.33	−	5731.55i	−0.647746	−	0.373976i	0.139846	−	0.990173i	$-0.455339\pi$
$617$	−9927.33	−	5731.55i	−0.647746	−	0.373976i	−0.787592	+	0.616197i	$0.788673\pi$
$618$		0			0
$619$	−3429.59	+	1980.07i	−0.222693	+	0.128572i	−0.607196	−	0.794552i	$-0.707706\pi$
$619$	−3429.59	+	1980.07i	−0.222693	+	0.128572i	0.384504	+	0.923123i	$0.374373\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−273.937	+	2396.04i	−0.0176165	+	0.154086i
$624$		0			0
$625$	8892.79	−	15402.8i	0.569139	−	0.985777i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2886.95			−0.183005
$630$		0			0
$631$	−5409.20			−0.341263			−0.170631	−	0.985335i	$-0.554581\pi$
$631$	−5409.20			−0.341263			−0.170631	+	0.985335i	$0.554581\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	12503.7	−	21657.1i	0.781410	−	1.35344i
$636$		0			0
$637$	−1756.51	−	1640.53i	−0.109255	−	0.102041i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20809.6	−	12014.4i	1.28226	−	0.740313i	0.304999	−	0.952353i	$-0.401344\pi$
$641$	20809.6	−	12014.4i	1.28226	−	0.740313i	0.977261	+	0.212040i	$0.0680107\pi$
$642$		0			0
$643$	−3581.87	−	2068.00i	−0.219682	−	0.126833i	0.386121	−	0.922448i	$-0.373815\pi$
$643$	−3581.87	−	2068.00i	−0.219682	−	0.126833i	−0.605803	+	0.795615i	$0.707148\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1393.75			−0.0846895			−0.0423447	−	0.999103i	$-0.513483\pi$
$647$	−1393.75			−0.0846895			−0.0423447	+	0.999103i	$0.513483\pi$
$648$		0			0
$649$			0.744436i			4.50257e-5i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7846.10	−	4529.95i	−0.470202	−	0.271471i	0.246122	−	0.969239i	$-0.420843\pi$
$653$	−7846.10	−	4529.95i	−0.470202	−	0.271471i	−0.716324	+	0.697768i	$0.754177\pi$
$654$		0			0
$655$	5639.89	+	9768.57i	0.336441	+	0.582732i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14018.1	+	8093.34i	−0.828629	+	0.478409i	−0.853383	−	0.521284i	$-0.825453\pi$
$659$	−14018.1	+	8093.34i	−0.828629	+	0.478409i	0.0247539	+	0.999694i	$0.492120\pi$
$660$		0			0
$661$	24821.5	+	14330.7i	1.46058	+	0.843269i	0.999038	−	0.0438473i	$-0.0139615\pi$
$661$	24821.5	+	14330.7i	1.46058	+	0.843269i	0.461546	+	0.887116i	$0.347295\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6545.78	+	8838.93i	−0.381706	+	0.515427i
$666$		0			0
$667$	5807.45			0.337130
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.873449	+	1.51286i	−5.02521e−5	+	8.70391e-5i
$672$		0			0
$673$	3670.88	+	6358.15i	0.210255	+	0.364173i	0.951794	−	0.306737i	$-0.0992371\pi$
$673$	3670.88	+	6358.15i	0.210255	+	0.364173i	−0.741539	+	0.670910i	$0.765904\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16478.4	−	28541.4i	−0.935474	−	1.62029i	−0.773787	−	0.633446i	$-0.781640\pi$
$677$	−16478.4	−	28541.4i	−0.935474	−	1.62029i	−0.161687	−	0.986842i	$-0.551693\pi$
$678$		0			0
$679$	−10738.4	−	24722.8i	−0.606924	−	1.39731i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	22213.0i		−	1.24444i	−0.782841	−	0.622222i	$-0.786230\pi$
$683$		−	22213.0i		−	1.24444i	0.782841	−	0.622222i	$-0.213770\pi$
$684$		0			0
$685$		−	32346.4i		−	1.80422i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1988.59	+	3444.34i	−0.109955	+	0.190448i
$690$		0			0
$691$	22072.1	−	12743.3i	1.21514	−	0.701563i	0.251267	−	0.967918i	$-0.419153\pi$
$691$	22072.1	−	12743.3i	1.21514	−	0.701563i	0.963875	+	0.266355i	$0.0858194\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9593.47	+	5538.79i	−0.523599	+	0.302300i
$696$		0			0
$697$	318.391	−	551.470i	0.0173026	−	0.0299690i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	22316.4i		−	1.20239i	−0.799101	−	0.601197i	$-0.794691\pi$
$701$		−	22316.4i		−	1.20239i	0.799101	−	0.601197i	$-0.205309\pi$
$702$		0			0
$703$		−	5016.19i		−	0.269117i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6713.29	+	2915.92i	−0.357114	+	0.155113i
$708$		0			0
$709$	−620.251	−	1074.31i	−0.0328547	−	0.0569061i	0.849130	−	0.528183i	$-0.177127\pi$
$709$	−620.251	−	1074.31i	−0.0328547	−	0.0569061i	−0.881985	+	0.471277i	$0.843793\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	842.748	+	1459.68i	0.0442653	+	0.0766698i
$714$		0			0
$715$	0.108080	−	0.187201i	5.65311e−6	−	9.79147e-6i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1718.52			−0.0891374			−0.0445687	−	0.999006i	$-0.514191\pi$
$719$	−1718.52			−0.0891374			−0.0445687	+	0.999006i	$0.514191\pi$
$720$		0			0
$721$	6939.62	−	9370.74i	0.358453	−	0.484028i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2029.35	+	1171.65i	0.103956	+	0.0600191i
$726$		0			0
$727$	2204.74	−	1272.91i	0.112475	−	0.0649376i	−0.442707	−	0.896666i	$-0.645982\pi$
$727$	2204.74	−	1272.91i	0.112475	−	0.0649376i	0.555182	+	0.831729i	$0.312649\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6433.10	−	11142.5i	−0.325495	−	0.563774i
$732$		0			0
$733$	19126.0	+	11042.4i	0.963761	+	0.556427i	0.897328	−	0.441363i	$-0.145505\pi$
$733$	19126.0	+	11042.4i	0.963761	+	0.556427i	0.0664323	+	0.997791i	$0.478838\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			1.37884i			6.89149e-5i
$738$		0			0
$739$	−5401.50			−0.268873			−0.134437	−	0.990922i	$-0.542922\pi$
$739$	−5401.50			−0.268873			−0.134437	+	0.990922i	$0.542922\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	26971.1	+	15571.7i	1.33173	+	0.768872i	0.985564	−	0.169303i	$-0.0541516\pi$
$743$	26971.1	+	15571.7i	1.33173	+	0.768872i	0.346161	+	0.938175i	$0.387485\pi$
$744$		0			0
$745$	14334.1	−	8275.82i	0.704915	−	0.406983i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−9487.53	−	1084.70i	−0.462840	−	0.0529161i
$750$		0			0
$751$	−2644.61	+	4580.61i	−0.128500	+	0.222568i	−0.923096	−	0.384571i	$-0.874350\pi$
$751$	−2644.61	+	4580.61i	−0.128500	+	0.222568i	0.794596	+	0.607139i	$0.207683\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3070.62			−0.148015
$756$		0			0
$757$	−20794.2			−0.998384			−0.499192	−	0.866491i	$-0.666370\pi$
$757$	−20794.2			−0.998384			−0.499192	+	0.866491i	$0.666370\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9126.94	−	15808.3i	0.434759	−	0.753024i	−0.562517	−	0.826785i	$-0.690167\pi$
$761$	9126.94	−	15808.3i	0.434759	−	0.753024i	0.997276	+	0.0737616i	$0.0235004\pi$
$762$		0			0
$763$	1670.36	−	14610.1i	0.0792546	−	0.693213i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1767.78	−	1020.63i	0.0832213	−	0.0480478i
$768$		0			0
$769$	−28098.3	−	16222.6i	−1.31762	−	0.760730i	−0.334278	−	0.942475i	$-0.608492\pi$
$769$	−28098.3	−	16222.6i	−1.31762	−	0.760730i	−0.983346	+	0.181745i	$0.941826\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20600.1			−0.958519			−0.479259	−	0.877673i	$-0.659095\pi$
$773$	−20600.1			−0.958519			−0.479259	+	0.877673i	$0.659095\pi$
$774$		0			0
$775$			680.094i			0.0315222i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	958.201	+	553.217i	0.0440707	+	0.0254442i
$780$		0			0
$781$	0.392929	+	0.680572i	1.80027e−5	+	3.11816e-5i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6177.51	+	3566.59i	−0.280872	+	0.162162i
$786$		0			0
$787$	12253.1	+	7074.35i	0.554990	+	0.320424i	0.751132	−	0.660152i	$-0.229508\pi$
$787$	12253.1	+	7074.35i	0.554990	+	0.320424i	−0.196142	+	0.980575i	$0.562841\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−22683.8	+	30630.5i	−1.01965	+	1.37686i
$792$		0			0
$793$	4790.02			0.214500
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9980.73	+	17287.1i	−0.443583	+	0.768308i	−0.997952	−	0.0639626i	$-0.979626\pi$
$797$	−9980.73	+	17287.1i	−0.443583	+	0.768308i	0.554369	+	0.832271i	$0.312959\pi$
$798$		0			0
$799$	−6547.96	−	11341.4i	−0.289925	−	0.502165i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.632729	+	1.09592i	2.78064e−5	+	4.81621e-5i
$804$		0			0
$805$	−4573.43	−	10529.4i	−0.200239	−	0.461007i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			13027.7i			0.566169i	0.959095	+	0.283085i	$0.0913578\pi$
$809$			13027.7i			0.566169i	−0.959095	+	0.283085i	$0.908642\pi$
$810$		0			0
$811$			2467.58i			0.106841i	0.998572	+	0.0534207i	$0.0170124\pi$
$811$			2467.58i			0.106841i	−0.998572	+	0.0534207i	$0.982988\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13261.5	−	22969.5i	0.569974	−	0.987224i
$816$		0			0
$817$	19360.5	−	11177.8i	0.829054	−	0.478654i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17302.8	+	9989.80i	−0.735534	+	0.424661i	−0.820443	−	0.571728i	$-0.806273\pi$
$821$	−17302.8	+	9989.80i	−0.735534	+	0.424661i	0.0849092	+	0.996389i	$0.472940\pi$
$822$		0			0
$823$	−20481.8	+	35475.5i	−0.867497	+	1.50255i	−0.00295098	+	0.999996i	$0.500939\pi$
$823$	−20481.8	+	35475.5i	−0.867497	+	1.50255i	−0.864546	+	0.502553i	$0.832394\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	38066.2i		−	1.60059i	−0.599604	−	0.800297i	$-0.704675\pi$
$827$		−	38066.2i		−	1.60059i	0.599604	−	0.800297i	$-0.295325\pi$
$828$		0			0
$829$		−	5157.09i		−	0.216059i	−0.994148	−	0.108030i	$-0.965546\pi$
$829$		−	5157.09i		−	0.216059i	0.994148	−	0.108030i	$-0.0344542\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9461.19	−	2192.04i	−0.393531	−	0.0911759i
$834$		0			0
$835$	−2545.90	−	4409.62i	−0.105514	−	0.182756i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12192.2	+	21117.5i	0.501695	+	0.868960i	0.999998	+	0.00195781i	$0.000623192\pi$
$839$	12192.2	+	21117.5i	0.501695	+	0.868960i	−0.498304	+	0.867003i	$0.666043\pi$
$840$		0			0
$841$	−5798.77	+	10043.8i	−0.237762	+	0.411816i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	25928.2			1.05557
$846$		0			0
$847$	19809.7	+	14670.4i	0.803626	+	0.595135i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4534.08	+	2617.75i	0.182640	+	0.105447i
$852$		0			0
$853$	−35213.6	+	20330.6i	−1.41347	+	0.816068i	−0.995714	−	0.0924912i	$-0.970517\pi$
$853$	−35213.6	+	20330.6i	−1.41347	+	0.816068i	−0.417757	+	0.908559i	$0.637184\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5424.95	+	9396.29i	0.216234	+	0.374529i	0.953654	−	0.300906i	$-0.0972892\pi$
$857$	5424.95	+	9396.29i	0.216234	+	0.374529i	−0.737419	+	0.675435i	$0.763956\pi$
$858$		0			0
$859$	29442.4	+	16998.6i	1.16945	+	0.675184i	0.953551	−	0.301230i	$-0.0973974\pi$
$859$	29442.4	+	16998.6i	1.16945	+	0.675184i	0.215902	+	0.976415i	$0.430731\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	21617.2i		−	0.852675i	−0.904564	−	0.426337i	$-0.859804\pi$
$863$		−	21617.2i		−	0.852675i	0.904564	−	0.426337i	$-0.140196\pi$
$864$		0			0
$865$	21062.9			0.827930
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.43793	+	0.830190i	5.61317e−5	+	3.24077e-5i
$870$		0			0
$871$	3274.27	−	1890.40i	0.127376	−	0.0735406i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2648.18	+	23162.8i	−0.102314	+	0.894908i
$876$		0			0
$877$	7452.42	−	12908.0i	0.286945	−	0.497003i	−0.686134	−	0.727475i	$-0.740694\pi$
$877$	7452.42	−	12908.0i	0.286945	−	0.497003i	0.973079	+	0.230472i	$0.0740271\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18956.5			−0.724928			−0.362464	−	0.931998i	$-0.618064\pi$
$881$	−18956.5			−0.724928			−0.362464	+	0.931998i	$0.618064\pi$
$882$		0			0
$883$	−35931.1			−1.36940			−0.684700	−	0.728825i	$-0.740067\pi$
$883$	−35931.1			−1.36940			−0.684700	+	0.728825i	$0.740067\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19322.4	−	33467.3i	0.731434	−	1.26688i	−0.224837	−	0.974396i	$-0.572185\pi$
$887$	19322.4	−	33467.3i	0.731434	−	1.26688i	0.956270	−	0.292484i	$-0.0944819\pi$
$888$		0			0
$889$	−4358.09	+	38118.7i	−0.164416	+	1.43809i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	19706.1	−	11377.3i	0.738456	−	0.426348i
$894$		0			0
$895$	−45074.2	−	26023.6i	−1.68342	−	0.971924i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3712.46			0.137728
$900$		0			0
$901$			16070.8i			0.594224i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13674.0	+	7894.67i	0.502252	+	0.289975i
$906$		0			0
$907$	−286.156	−	495.636i	−0.0104759	−	0.0181448i	0.860740	−	0.509045i	$-0.170001\pi$
$907$	−286.156	−	495.636i	−0.0104759	−	0.0181448i	−0.871216	+	0.490900i	$0.836668\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24634.1	+	14222.5i	−0.895901	+	0.517248i	−0.875868	−	0.482551i	$-0.839710\pi$
$911$	−24634.1	+	14222.5i	−0.895901	+	0.517248i	−0.0200327	+	0.999799i	$0.506377\pi$
$912$		0			0
$913$	2.50340	+	1.44534i	9.07452e−5	+	5.23918e-5i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13907.3	−	10299.2i	−0.500829	−	0.370895i
$918$		0			0
$919$	20019.4			0.718585			0.359292	−	0.933225i	$-0.383018\pi$
$919$	20019.4			0.718585			0.359292	+	0.933225i	$0.383018\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1077.42	−	1866.14i	0.0384221	−	0.0665490i
$924$		0			0
$925$	1056.26	+	1829.49i	0.0375455	+	0.0650306i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15791.3	+	27351.3i	0.557690	+	0.965948i	0.997689	+	0.0679494i	$0.0216456\pi$
$929$	15791.3	+	27351.3i	0.557690	+	0.965948i	−0.439999	+	0.897999i	$0.645021\pi$
$930$		0			0
$931$	3808.75	−	16439.2i	0.134078	−	0.578704i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	0.873451i		−	3.05507e-5i
$936$		0			0
$937$			39841.1i			1.38906i	0.719463	+	0.694531i	$0.244388\pi$
$937$			39841.1i			1.38906i	−0.719463	+	0.694531i	$0.755612\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5443.60	−	9428.59i	0.188583	−	0.326635i	−0.756195	−	0.654346i	$-0.772944\pi$
$941$	5443.60	−	9428.59i	0.188583	−	0.326635i	0.944778	+	0.327711i	$0.106277\pi$
$942$		0			0
$943$	−1000.09	+	577.405i	−0.0345361	+	0.0199394i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19780.5	+	11420.3i	−0.678755	+	0.391879i	−0.799386	−	0.600818i	$-0.794842\pi$
$947$	−19780.5	+	11420.3i	−0.678755	+	0.391879i	0.120631	+	0.992697i	$0.461508\pi$
$948$		0			0
$949$	1734.95	−	3005.03i	0.0593456	−	0.102790i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	51243.3i		−	1.74180i	−0.491462	−	0.870899i	$-0.663537\pi$
$953$		−	51243.3i		−	1.74180i	0.491462	−	0.870899i	$-0.336463\pi$
$954$		0			0
$955$			48730.1i			1.65117i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19770.9	+	45518.3i	0.665731	+	1.53270i
$960$		0			0
$961$	−14356.8	−	24866.6i	−0.481916	−	0.834703i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	26673.5	+	46199.8i	0.889793	+	1.54117i
$966$		0			0
$967$	−7489.56	+	12972.3i	−0.249067	+	0.431397i	−0.963267	−	0.268544i	$-0.913457\pi$
$967$	−7489.56	+	12972.3i	−0.249067	+	0.431397i	0.714200	+	0.699942i	$0.246791\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12705.2			0.419908			0.209954	−	0.977711i	$-0.432669\pi$
$971$	12705.2			0.419908			0.209954	+	0.977711i	$0.432669\pi$
$972$		0			0
$973$	10114.6	−	13658.0i	0.333258	−	0.450007i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17602.3	+	10162.7i	0.576405	+	0.332788i	0.759703	−	0.650270i	$-0.225344\pi$
$977$	17602.3	+	10162.7i	0.576405	+	0.332788i	−0.183298	+	0.983057i	$0.558677\pi$
$978$		0			0
$979$	0.288185	−	0.166384i	9.40802e−6	−	5.43172e-6i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20257.1	+	35086.3i	0.657274	+	1.13843i	0.981318	+	0.192390i	$0.0616240\pi$
$983$	20257.1	+	35086.3i	0.657274	+	1.13843i	−0.324044	+	0.946042i	$0.605043\pi$
$984$		0			0
$985$	−1585.61	−	915.452i	−0.0512911	−	0.0296129i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			23333.0i			0.750197i
$990$		0			0
$991$	−5083.59			−0.162952			−0.0814761	−	0.996675i	$-0.525963\pi$
$991$	−5083.59			−0.162952			−0.0814761	+	0.996675i	$0.525963\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	19221.5	+	11097.5i	0.612424	+	0.353583i
$996$		0			0
$997$	15996.3	−	9235.49i	0.508133	−	0.293371i	−0.223933	−	0.974605i	$-0.571890\pi$
$997$	15996.3	−	9235.49i	0.508133	−	0.293371i	0.732066	+	0.681234i	$0.238556\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.4.x.a.125.5		48
3.2	odd	2		252.4.x.a.41.16	yes	48
7.6	odd	2	inner	756.4.x.a.125.20		48
9.2	odd	6	inner	756.4.x.a.629.20		48
9.4	even	3		2268.4.f.a.1133.40		48
9.5	odd	6		2268.4.f.a.1133.9		48
9.7	even	3		252.4.x.a.209.9	yes	48
21.20	even	2		252.4.x.a.41.9	✓	48
63.13	odd	6		2268.4.f.a.1133.10		48
63.20	even	6	inner	756.4.x.a.629.5		48
63.34	odd	6		252.4.x.a.209.16	yes	48
63.41	even	6		2268.4.f.a.1133.39		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.9	✓	48	21.20	even	2
252.4.x.a.41.16	yes	48	3.2	odd	2
252.4.x.a.209.9	yes	48	9.7	even	3
252.4.x.a.209.16	yes	48	63.34	odd	6
756.4.x.a.125.5		48	1.1	even	1	trivial
756.4.x.a.125.20		48	7.6	odd	2	inner
756.4.x.a.629.5		48	63.20	even	6	inner
756.4.x.a.629.20		48	9.2	odd	6	inner
2268.4.f.a.1133.9		48	9.5	odd	6
2268.4.f.a.1133.10		48	63.13	odd	6
2268.4.f.a.1133.39		48	63.41	even	6
2268.4.f.a.1133.40		48	9.4	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	756.x (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.03570 + 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +O(q^{10})\)	\(q+(-6.03570 + 10.4541i) q^{5} +(2.10370 - 18.4004i) q^{7} +(-0.00221312 + 0.00127775i) q^{11} +(6.06841 + 3.50360i) q^{13} +28.3143 q^{17} +49.1973i q^{19} +(-44.4689 - 25.6741i) q^{23} +(-10.3594 - 17.9431i) q^{25} +(-97.9469 + 56.5497i) q^{29} +(-28.4271 - 16.4124i) q^{31} +(179.663 + 133.052i) q^{35} -101.961 q^{37} +(11.2449 - 19.4767i) q^{41} +(-227.203 - 393.527i) q^{43} +(-231.260 - 400.554i) q^{47} +(-334.149 - 77.4179i) q^{49} +567.586i q^{53} -0.0308484i q^{55} +(145.654 - 252.280i) q^{59} +(592.003 - 341.793i) q^{61} +(-73.2542 + 42.2933i) q^{65} +(269.780 - 467.273i) q^{67} -307.517i q^{71} -495.192i q^{73} +(0.0188553 + 0.0434103i) q^{77} +(-324.865 - 562.683i) q^{79} +(-565.581 - 979.615i) q^{83} +(-170.897 + 296.002i) q^{85} -130.217 q^{89} +(77.2337 - 104.291i) q^{91} +(-514.315 - 296.940i) q^{95} +(1260.41 - 727.696i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7}+O(q^{10}) \) 48 * q + 6 * q^7	\( 48 q + 6 q^{7} + 12 q^{11} + 408 q^{23} - 600 q^{25} + 84 q^{29} + 336 q^{37} + 84 q^{43} + 318 q^{49} - 2964 q^{65} - 588 q^{67} - 2400 q^{77} + 204 q^{79} - 360 q^{85} - 1080 q^{91} - 300 q^{95}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^11 + 408 * q^23 - 600 * q^25 + 84 * q^29 + 336 * q^37 + 84 * q^43 + 318 * q^49 - 2964 * q^65 - 588 * q^67 - 2400 * q^77 + 204 * q^79 - 360 * q^85 - 1080 * q^91 - 300 * q^95

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