LMFDB - Embedded newform 240.3.l.c.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(161,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))

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

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

chi := DirichletCharacter("240.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.l (of order $2$, degree $1$, 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:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 9 $ x^4 - 4*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.3
Root			$-1.58114 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	240.161
Dual form			240.3.l.c.161.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.581139 - 2.94317i) q^{3} -2.23607i q^{5} -11.4868 q^{7} +(-8.32456 - 3.42079i) q^{9} +O(q^{10})$	\(q+(0.581139 - 2.94317i) q^{3} -2.23607i q^{5} -11.4868 q^{7} +(-8.32456 - 3.42079i) q^{9} +8.48528i q^{11} -10.0000 q^{13} +(-6.58114 - 1.29947i) q^{15} +3.55415i q^{17} +10.9737 q^{19} +(-6.67544 + 33.8078i) q^{21} -17.6590i q^{23} -5.00000 q^{25} +(-14.9057 + 22.5127i) q^{27} -26.8328i q^{29} -8.00000 q^{31} +(24.9737 + 4.93113i) q^{33} +25.6853i q^{35} -59.9473 q^{37} +(-5.81139 + 29.4317i) q^{39} -20.5247i q^{41} -42.4605 q^{43} +(-7.64911 + 18.6143i) q^{45} -88.2952i q^{47} +82.9473 q^{49} +(10.4605 + 2.06546i) q^{51} +3.55415i q^{53} +18.9737 q^{55} +(6.37722 - 32.2974i) q^{57} -77.7445i q^{59} +21.9473 q^{61} +(95.6228 + 39.2940i) q^{63} +22.3607i q^{65} +53.5395 q^{67} +(-51.9737 - 10.2624i) q^{69} +69.2592i q^{71} +12.0527 q^{73} +(-2.90569 + 14.7159i) q^{75} -97.4690i q^{77} +9.02633 q^{79} +(57.5964 + 56.9530i) q^{81} -0.688486i q^{83} +7.94733 q^{85} +(-78.9737 - 15.5936i) q^{87} -7.10831i q^{89} +114.868 q^{91} +(-4.64911 + 23.5454i) q^{93} -24.5379i q^{95} +111.947 q^{97} +(29.0263 - 70.6362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 8 * q^7 - 8 * q^9	$ 4 q - 4 q^{3} - 8 q^{7} - 8 q^{9} - 40 q^{13} - 20 q^{15} - 32 q^{19} - 52 q^{21} - 20 q^{25} - 28 q^{27} - 32 q^{31} + 24 q^{33} - 88 q^{37} + 40 q^{39} - 56 q^{43} + 20 q^{45} + 180 q^{49} - 72 q^{51} + 152 q^{57} - 64 q^{61} + 256 q^{63} + 328 q^{67} - 132 q^{69} + 200 q^{73} + 20 q^{75} + 112 q^{79} + 28 q^{81} - 120 q^{85} - 240 q^{87} + 80 q^{91} + 32 q^{93} + 296 q^{97} + 192 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 8 * q^7 - 8 * q^9 - 40 * q^13 - 20 * q^15 - 32 * q^19 - 52 * q^21 - 20 * q^25 - 28 * q^27 - 32 * q^31 + 24 * q^33 - 88 * q^37 + 40 * q^39 - 56 * q^43 + 20 * q^45 + 180 * q^49 - 72 * q^51 + 152 * q^57 - 64 * q^61 + 256 * q^63 + 328 * q^67 - 132 * q^69 + 200 * q^73 + 20 * q^75 + 112 * q^79 + 28 * q^81 - 120 * q^85 - 240 * q^87 + 80 * q^91 + 32 * q^93 + 296 * q^97 + 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.581139	−	2.94317i	0.193713	−	0.981058i
$3$	0.581139	−	2.94317i	0.193713	−	0.981058i
$4$		0			0
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		0			0
$7$	−11.4868			−1.64098			−0.820488	−	0.571664i	$-0.806298\pi$
$7$	−11.4868			−1.64098			−0.820488	+	0.571664i	$0.806298\pi$
$8$		0			0
$9$	−8.32456	−	3.42079i	−0.924951	−	0.380087i
$10$		0			0
$11$			8.48528i			0.771389i	0.922627	+	0.385695i	$0.126038\pi$
$11$			8.48528i			0.771389i	−0.922627	+	0.385695i	$0.873962\pi$
$12$		0			0
$13$	−10.0000			−0.769231			−0.384615	−	0.923077i	$-0.625666\pi$
$13$	−10.0000			−0.769231			−0.384615	+	0.923077i	$0.625666\pi$
$14$		0			0
$15$	−6.58114	−	1.29947i	−0.438743	−	0.0866311i
$16$		0			0
$17$			3.55415i			0.209068i	0.994521	+	0.104534i	$0.0333351\pi$
$17$			3.55415i			0.209068i	−0.994521	+	0.104534i	$0.966665\pi$
$18$		0			0
$19$	10.9737			0.577561			0.288781	−	0.957395i	$-0.406750\pi$
$19$	10.9737			0.577561			0.288781	+	0.957395i	$0.406750\pi$
$20$		0			0
$21$	−6.67544	+	33.8078i	−0.317878	+	1.60989i
$22$		0			0
$23$		−	17.6590i		−	0.767785i	−0.923378	−	0.383892i	$-0.874583\pi$
$23$		−	17.6590i		−	0.767785i	0.923378	−	0.383892i	$-0.125417\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$		0			0
$27$	−14.9057	+	22.5127i	−0.552063	+	0.833803i
$28$		0			0
$29$		−	26.8328i		−	0.925270i	−0.886549	−	0.462635i	$-0.846904\pi$
$29$		−	26.8328i		−	0.925270i	0.886549	−	0.462635i	$-0.153096\pi$
$30$		0			0
$31$	−8.00000			−0.258065			−0.129032	−	0.991640i	$-0.541187\pi$
$31$	−8.00000			−0.258065			−0.129032	+	0.991640i	$0.541187\pi$
$32$		0			0
$33$	24.9737	+	4.93113i	0.756778	+	0.149428i
$34$		0			0
$35$			25.6853i			0.733867i
$36$		0			0
$37$	−59.9473			−1.62020			−0.810099	−	0.586293i	$-0.800587\pi$
$37$	−59.9473			−1.62020			−0.810099	+	0.586293i	$0.800587\pi$
$38$		0			0
$39$	−5.81139	+	29.4317i	−0.149010	+	0.754660i
$40$		0			0
$41$		−	20.5247i		−	0.500603i	−0.968168	−	0.250301i	$-0.919470\pi$
$41$		−	20.5247i		−	0.500603i	0.968168	−	0.250301i	$-0.0805297\pi$
$42$		0			0
$43$	−42.4605			−0.987453			−0.493727	−	0.869617i	$-0.664366\pi$
$43$	−42.4605			−0.987453			−0.493727	+	0.869617i	$0.664366\pi$
$44$		0			0
$45$	−7.64911	+	18.6143i	−0.169980	+	0.413650i
$46$		0			0
$47$		−	88.2952i		−	1.87862i	−0.343067	−	0.939311i	$-0.611466\pi$
$47$		−	88.2952i		−	1.87862i	0.343067	−	0.939311i	$-0.388534\pi$
$48$		0			0
$49$	82.9473			1.69280
$50$		0			0
$51$	10.4605	+	2.06546i	0.205108	+	0.0404992i
$52$		0			0
$53$			3.55415i			0.0670595i	0.999438	+	0.0335298i	$0.0106749\pi$
$53$			3.55415i			0.0670595i	−0.999438	+	0.0335298i	$0.989325\pi$
$54$		0			0
$55$	18.9737			0.344976
$56$		0			0
$57$	6.37722	−	32.2974i	0.111881	−	0.566621i
$58$		0			0
$59$		−	77.7445i		−	1.31770i	−0.752273	−	0.658852i	$-0.771042\pi$
$59$		−	77.7445i		−	1.31770i	0.752273	−	0.658852i	$-0.228958\pi$
$60$		0			0
$61$	21.9473			0.359792			0.179896	−	0.983686i	$-0.442424\pi$
$61$	21.9473			0.359792			0.179896	+	0.983686i	$0.442424\pi$
$62$		0			0
$63$	95.6228	+	39.2940i	1.51782	+	0.623714i
$64$		0			0
$65$			22.3607i			0.344010i
$66$		0			0
$67$	53.5395			0.799097			0.399549	−	0.916712i	$-0.369167\pi$
$67$	53.5395			0.799097			0.399549	+	0.916712i	$0.369167\pi$
$68$		0			0
$69$	−51.9737	−	10.2624i	−0.753242	−	0.148730i
$70$		0			0
$71$			69.2592i			0.975482i	0.872988	+	0.487741i	$0.162179\pi$
$71$			69.2592i			0.975482i	−0.872988	+	0.487741i	$0.837821\pi$
$72$		0			0
$73$	12.0527			0.165105			0.0825525	−	0.996587i	$-0.473693\pi$
$73$	12.0527			0.165105			0.0825525	+	0.996587i	$0.473693\pi$
$74$		0			0
$75$	−2.90569	+	14.7159i	−0.0387426	+	0.196212i
$76$		0			0
$77$		−	97.4690i		−	1.26583i
$78$		0			0
$79$	9.02633			0.114257			0.0571287	−	0.998367i	$-0.481805\pi$
$79$	9.02633			0.114257			0.0571287	+	0.998367i	$0.481805\pi$
$80$		0			0
$81$	57.5964	+	56.9530i	0.711067	+	0.703124i
$82$		0			0
$83$		−	0.688486i		−	0.00829501i	−0.999991	−	0.00414750i	$-0.998680\pi$
$83$		−	0.688486i		−	0.00829501i	0.999991	−	0.00414750i	$-0.00132020\pi$
$84$		0			0
$85$	7.94733			0.0934980
$86$		0			0
$87$	−78.9737	−	15.5936i	−0.907743	−	0.179237i
$88$		0			0
$89$		−	7.10831i		−	0.0798686i	−0.999202	−	0.0399343i	$-0.987285\pi$
$89$		−	7.10831i		−	0.0798686i	0.999202	−	0.0399343i	$-0.0127149\pi$
$90$		0			0
$91$	114.868			1.26229
$92$		0			0
$93$	−4.64911	+	23.5454i	−0.0499904	+	0.253176i
$94$		0			0
$95$		−	24.5379i		−	0.258293i
$96$		0			0
$97$	111.947			1.15410			0.577048	−	0.816710i	$-0.304205\pi$
$97$	111.947			1.15410			0.577048	+	0.816710i	$0.304205\pi$
$98$		0			0
$99$	29.0263	−	70.6362i	0.293195	−	0.713497i
$100$		0			0
$101$			155.489i			1.53950i	0.638348	+	0.769748i	$0.279618\pi$
$101$			155.489i			1.53950i	−0.638348	+	0.769748i	$0.720382\pi$
$102$		0			0
$103$	−7.59217			−0.0737104			−0.0368552	−	0.999321i	$-0.511734\pi$
$103$	−7.59217			−0.0737104			−0.0368552	+	0.999321i	$0.511734\pi$
$104$		0			0
$105$	75.5964	+	14.9267i	0.719966	+	0.142160i
$106$		0			0
$107$		−	16.2821i		−	0.152169i	−0.997101	−	0.0760845i	$-0.975758\pi$
$107$		−	16.2821i		−	0.152169i	0.997101	−	0.0760845i	$-0.0242419\pi$
$108$		0			0
$109$	−93.8420			−0.860936			−0.430468	−	0.902606i	$-0.641651\pi$
$109$	−93.8420			−0.860936			−0.430468	+	0.902606i	$0.641651\pi$
$110$		0			0
$111$	−34.8377	+	176.435i	−0.313853	+	1.58951i
$112$		0			0
$113$		−	195.738i		−	1.73220i	−0.499874	−	0.866098i	$-0.666620\pi$
$113$		−	195.738i		−	1.73220i	0.499874	−	0.866098i	$-0.333380\pi$
$114$		0			0
$115$	−39.4868			−0.343364
$116$		0			0
$117$	83.2456	+	34.2079i	0.711500	+	0.292375i
$118$		0			0
$119$		−	40.8260i		−	0.343075i
$120$		0			0
$121$	49.0000			0.404959
$122$		0			0
$123$	−60.4078	−	11.9277i	−0.491121	−	0.0969733i
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	77.5395			0.610547			0.305274	−	0.952265i	$-0.401252\pi$
$127$	77.5395			0.610547			0.305274	+	0.952265i	$0.401252\pi$
$128$		0			0
$129$	−24.6754	+	124.969i	−0.191283	+	0.968749i
$130$		0			0
$131$			101.600i			0.775572i	0.921749	+	0.387786i	$0.126760\pi$
$131$			101.600i			0.775572i	−0.921749	+	0.387786i	$0.873240\pi$
$132$		0			0
$133$	−126.053			−0.947764
$134$		0			0
$135$	50.3399	+	33.3301i	0.372888	+	0.246890i
$136$		0			0
$137$		−	176.014i		−	1.28477i	−0.766381	−	0.642386i	$-0.777945\pi$
$137$		−	176.014i		−	1.28477i	0.766381	−	0.642386i	$-0.222055\pi$
$138$		0			0
$139$	−188.816			−1.35839			−0.679193	−	0.733960i	$-0.737670\pi$
$139$	−188.816			−1.35839			−0.679193	+	0.733960i	$0.737670\pi$
$140$		0			0
$141$	−259.868	−	51.3118i	−1.84304	−	0.363913i
$142$		0			0
$143$		−	84.8528i		−	0.593376i
$144$		0			0
$145$	−60.0000			−0.413793
$146$		0			0
$147$	48.2039	−	244.128i	0.327918	−	1.66074i
$148$		0			0
$149$		−	72.5899i		−	0.487181i	−0.969878	−	0.243590i	$-0.921675\pi$
$149$		−	72.5899i		−	0.487181i	0.969878	−	0.243590i	$-0.0783252\pi$
$150$		0			0
$151$	−93.9473			−0.622168			−0.311084	−	0.950382i	$-0.600692\pi$
$151$	−93.9473			−0.622168			−0.311084	+	0.950382i	$0.600692\pi$
$152$		0			0
$153$	12.1580	−	29.5868i	0.0794641	−	0.193378i
$154$		0			0
$155$			17.8885i			0.115410i
$156$		0			0
$157$	−123.842			−0.788803			−0.394401	−	0.918938i	$-0.629048\pi$
$157$	−123.842			−0.788803			−0.394401	+	0.918938i	$0.629048\pi$
$158$		0			0
$159$	10.4605	+	2.06546i	0.0657893	+	0.0129903i
$160$		0			0
$161$			202.847i			1.25992i
$162$		0			0
$163$	−159.381			−0.977801			−0.488900	−	0.872340i	$-0.662602\pi$
$163$	−159.381			−0.977801			−0.488900	+	0.872340i	$0.662602\pi$
$164$		0			0
$165$	11.0263	−	55.8428i	0.0668263	−	0.338441i
$166$		0			0
$167$			10.7742i			0.0645161i	0.999480	+	0.0322581i	$0.0102698\pi$
$167$			10.7742i			0.0645161i	−0.999480	+	0.0322581i	$0.989730\pi$
$168$		0			0
$169$	−69.0000			−0.408284
$170$		0			0
$171$	−91.3509	−	37.5386i	−0.534216	−	0.219524i
$172$		0			0
$173$			283.345i			1.63783i	0.573913	+	0.818916i	$0.305425\pi$
$173$			283.345i			1.63783i	−0.573913	+	0.818916i	$0.694575\pi$
$174$		0			0
$175$	57.4342			0.328195
$176$		0			0
$177$	−228.816	−	45.1804i	−1.29274	−	0.255256i
$178$		0			0
$179$			306.624i			1.71298i	0.516163	+	0.856491i	$0.327360\pi$
$179$			306.624i			1.71298i	−0.516163	+	0.856491i	$0.672640\pi$
$180$		0			0
$181$	265.684			1.46787			0.733934	−	0.679221i	$-0.237682\pi$
$181$	265.684			1.46787			0.733934	+	0.679221i	$0.237682\pi$
$182$		0			0
$183$	12.7544	−	64.5948i	0.0696964	−	0.352977i
$184$		0			0
$185$			134.046i			0.724575i
$186$		0			0
$187$	−30.1580			−0.161273
$188$		0			0
$189$	171.219	−	258.599i	0.905922	−	1.36825i
$190$		0			0
$191$		−	159.620i		−	0.835706i	−0.908515	−	0.417853i	$-0.862783\pi$
$191$		−	159.620i		−	0.835706i	0.908515	−	0.417853i	$-0.137217\pi$
$192$		0			0
$193$	−92.0527			−0.476957			−0.238478	−	0.971148i	$-0.576649\pi$
$193$	−92.0527			−0.476957			−0.238478	+	0.971148i	$0.576649\pi$
$194$		0			0
$195$	65.8114	+	12.9947i	0.337494	+	0.0666393i
$196$		0			0
$197$			69.8360i			0.354497i	0.984166	+	0.177249i	$0.0567197\pi$
$197$			69.8360i			0.354497i	−0.984166	+	0.177249i	$0.943280\pi$
$198$		0			0
$199$	−148.921			−0.748347			−0.374173	−	0.927359i	$-0.622074\pi$
$199$	−148.921			−0.748347			−0.374173	+	0.927359i	$0.622074\pi$
$200$		0			0
$201$	31.1139	−	157.576i	0.154795	−	0.783961i
$202$		0			0
$203$			308.224i			1.51835i
$204$		0			0
$205$	−45.8947			−0.223876
$206$		0			0
$207$	−60.4078	+	147.004i	−0.291825	+	0.710163i
$208$		0			0
$209$			93.1146i			0.445525i
$210$		0			0
$211$	285.842			1.35470			0.677351	−	0.735660i	$-0.263128\pi$
$211$	285.842			1.35470			0.677351	+	0.735660i	$0.263128\pi$
$212$		0			0
$213$	203.842	+	40.2492i	0.957005	+	0.188963i
$214$		0			0
$215$			94.9446i			0.441603i
$216$		0			0
$217$	91.8947			0.423478
$218$		0			0
$219$	7.00427	−	35.4731i	0.0319830	−	0.161978i
$220$		0			0
$221$		−	35.5415i		−	0.160821i
$222$		0			0
$223$	71.3815			0.320096			0.160048	−	0.987109i	$-0.448835\pi$
$223$	71.3815			0.320096			0.160048	+	0.987109i	$0.448835\pi$
$224$		0			0
$225$	41.6228	+	17.1039i	0.184990	+	0.0760175i
$226$		0			0
$227$		−	29.1217i		−	0.128290i	−0.997941	−	0.0641448i	$-0.979568\pi$
$227$		−	29.1217i		−	0.128290i	0.997941	−	0.0641448i	$-0.0204319\pi$
$228$		0			0
$229$	−129.684			−0.566306			−0.283153	−	0.959075i	$-0.591380\pi$
$229$	−129.684			−0.566306			−0.283153	+	0.959075i	$0.591380\pi$
$230$		0			0
$231$	−286.868	−	56.6430i	−1.24185	−	0.245208i
$232$		0			0
$233$			185.876i			0.797751i	0.917005	+	0.398875i	$0.130599\pi$
$233$			185.876i			0.797751i	−0.917005	+	0.398875i	$0.869401\pi$
$234$		0			0
$235$	−197.434			−0.840145
$236$		0			0
$237$	5.24555	−	26.5661i	0.0221331	−	0.112093i
$238$		0			0
$239$		−	302.716i		−	1.26659i	−0.773908	−	0.633297i	$-0.781701\pi$
$239$		−	302.716i		−	1.26659i	0.773908	−	0.633297i	$-0.218299\pi$
$240$		0			0
$241$	−237.526			−0.985585			−0.492793	−	0.870147i	$-0.664024\pi$
$241$	−237.526			−0.985585			−0.492793	+	0.870147i	$0.664024\pi$
$242$		0			0
$243$	201.094	−	136.419i	0.827549	−	0.561394i
$244$		0			0
$245$		−	185.476i		−	0.757044i
$246$		0			0
$247$	−109.737			−0.444278
$248$		0			0
$249$	−2.02633	−	0.400106i	−0.00813789	−	0.00160685i
$250$		0			0
$251$			84.6294i			0.337169i	0.985687	+	0.168584i	$0.0539196\pi$
$251$			84.6294i			0.337169i	−0.985687	+	0.168584i	$0.946080\pi$
$252$		0			0
$253$	149.842			0.592261
$254$		0			0
$255$	4.61850	−	23.3904i	0.0181118	−	0.0917270i
$256$		0			0
$257$			292.054i			1.13640i	0.822892	+	0.568198i	$0.192359\pi$
$257$			292.054i			1.13640i	−0.822892	+	0.568198i	$0.807641\pi$
$258$		0			0
$259$	688.605			2.65871
$260$		0			0
$261$	−91.7893	+	223.371i	−0.351683	+	0.855829i
$262$		0			0
$263$		−	277.725i		−	1.05599i	−0.849247	−	0.527995i	$-0.822944\pi$
$263$		−	277.725i		−	1.05599i	0.849247	−	0.527995i	$-0.177056\pi$
$264$		0			0
$265$	7.94733			0.0299899
$266$		0			0
$267$	−20.9210	−	4.13091i	−0.0783558	−	0.0154716i
$268$		0			0
$269$		−	286.546i		−	1.06523i	−0.846359	−	0.532613i	$-0.821210\pi$
$269$		−	286.546i		−	1.06523i	0.846359	−	0.532613i	$-0.178790\pi$
$270$		0			0
$271$	324.105			1.19596			0.597980	−	0.801511i	$-0.295970\pi$
$271$	324.105			1.19596			0.597980	+	0.801511i	$0.295970\pi$
$272$		0			0
$273$	66.7544	−	338.078i	0.244522	−	1.23838i
$274$		0			0
$275$		−	42.4264i		−	0.154278i
$276$		0			0
$277$	415.842			1.50123			0.750617	−	0.660737i	$-0.229756\pi$
$277$	415.842			1.50123			0.750617	+	0.660737i	$0.229756\pi$
$278$		0			0
$279$	66.5964	+	27.3663i	0.238697	+	0.0980871i
$280$		0			0
$281$		−	431.726i		−	1.53639i	−0.640216	−	0.768195i	$-0.721155\pi$
$281$		−	431.726i		−	1.53639i	0.640216	−	0.768195i	$-0.278845\pi$
$282$		0			0
$283$	−141.540			−0.500140			−0.250070	−	0.968228i	$-0.580454\pi$
$283$	−141.540			−0.500140			−0.250070	+	0.968228i	$0.580454\pi$
$284$		0			0
$285$	−72.2192	−	14.2599i	−0.253401	−	0.0500348i
$286$		0			0
$287$			235.764i			0.821477i
$288$		0			0
$289$	276.368			0.956291
$290$		0			0
$291$	65.0569	−	329.481i	0.223563	−	1.13224i
$292$		0			0
$293$		−	164.998i		−	0.563133i	−0.959542	−	0.281566i	$-0.909146\pi$
$293$		−	164.998i		−	0.563133i	0.959542	−	0.281566i	$-0.0908540\pi$
$294$		0			0
$295$	−173.842			−0.589295
$296$		0			0
$297$	−191.026	−	126.479i	−0.643186	−	0.425855i
$298$		0			0
$299$			176.590i			0.590604i
$300$		0			0
$301$	487.737			1.62039
$302$		0			0
$303$	457.631	+	90.3607i	1.51033	+	0.298220i
$304$		0			0
$305$		−	49.0757i		−	0.160904i
$306$		0			0
$307$	−159.381			−0.519158			−0.259579	−	0.965722i	$-0.583584\pi$
$307$	−159.381			−0.519158			−0.259579	+	0.965722i	$0.583584\pi$
$308$		0			0
$309$	−4.41210	+	22.3451i	−0.0142787	+	0.0723142i
$310$		0			0
$311$			143.096i			0.460117i	0.973177	+	0.230058i	$0.0738917\pi$
$311$			143.096i			0.460117i	−0.973177	+	0.230058i	$0.926108\pi$
$312$		0			0
$313$	−501.684			−1.60282			−0.801412	−	0.598113i	$-0.795918\pi$
$313$	−501.684			−1.60282			−0.801412	+	0.598113i	$0.795918\pi$
$314$		0			0
$315$	87.8641	−	213.819i	0.278934	−	0.678791i
$316$		0			0
$317$			334.257i			1.05444i	0.849730	+	0.527219i	$0.176765\pi$
$317$			334.257i			1.05444i	−0.849730	+	0.527219i	$0.823235\pi$
$318$		0			0
$319$	227.684			0.713743
$320$		0			0
$321$	−47.9210	−	9.46215i	−0.149287	−	0.0294771i
$322$		0			0
$323$			39.0021i			0.120750i
$324$		0			0
$325$	50.0000			0.153846
$326$		0			0
$327$	−54.5352	+	276.193i	−0.166774	+	0.844628i
$328$		0			0
$329$			1014.23i			3.08277i
$330$		0			0
$331$	−389.421			−1.17650			−0.588249	−	0.808680i	$-0.700182\pi$
$331$	−389.421			−1.17650			−0.588249	+	0.808680i	$0.700182\pi$
$332$		0			0
$333$	499.035	+	205.067i	1.49860	+	0.615817i
$334$		0			0
$335$		−	119.718i		−	0.357367i
$336$		0			0
$337$	−129.684			−0.384819			−0.192409	−	0.981315i	$-0.561630\pi$
$337$	−129.684			−0.384819			−0.192409	+	0.981315i	$0.561630\pi$
$338$		0			0
$339$	−576.092	−	113.751i	−1.69939	−	0.335549i
$340$		0			0
$341$		−	67.8823i		−	0.199068i
$342$		0			0
$343$	−389.947			−1.13687
$344$		0			0
$345$	−22.9473	+	116.217i	−0.0665140	+	0.336860i
$346$		0			0
$347$			346.985i			0.999956i	0.866038	+	0.499978i	$0.166659\pi$
$347$			346.985i			0.999956i	−0.866038	+	0.499978i	$0.833341\pi$
$348$		0			0
$349$	509.579			1.46011			0.730055	−	0.683388i	$-0.239494\pi$
$349$	509.579			1.46011			0.730055	+	0.683388i	$0.239494\pi$
$350$		0			0
$351$	149.057	−	225.127i	0.424664	−	0.641387i
$352$		0			0
$353$		−	637.679i		−	1.80646i	−0.429159	−	0.903229i	$-0.641190\pi$
$353$		−	637.679i		−	1.80646i	0.429159	−	0.903229i	$-0.358810\pi$
$354$		0			0
$355$	154.868			0.436249
$356$		0			0
$357$	−120.158	−	23.7256i	−0.336577	−	0.0664582i
$358$		0			0
$359$			166.952i			0.465046i	0.972591	+	0.232523i	$0.0746982\pi$
$359$			166.952i			0.465046i	−0.972591	+	0.232523i	$0.925302\pi$
$360$		0			0
$361$	−240.579			−0.666423
$362$		0			0
$363$	28.4758	−	144.216i	0.0784457	−	0.397288i
$364$		0			0
$365$		−	26.9506i		−	0.0738372i
$366$		0			0
$367$	505.828			1.37828			0.689140	−	0.724629i	$-0.257989\pi$
$367$	505.828			1.37828			0.689140	+	0.724629i	$0.257989\pi$
$368$		0			0
$369$	−70.2107	+	170.859i	−0.190273	+	0.463033i
$370$		0			0
$371$		−	40.8260i		−	0.110043i
$372$		0			0
$373$	−416.053			−1.11542			−0.557711	−	0.830035i	$-0.688320\pi$
$373$	−416.053			−1.11542			−0.557711	+	0.830035i	$0.688320\pi$
$374$		0			0
$375$	32.9057	+	6.49733i	0.0877485	+	0.0173262i
$376$		0			0
$377$			268.328i			0.711746i
$378$		0			0
$379$	−82.7630			−0.218372			−0.109186	−	0.994021i	$-0.534824\pi$
$379$	−82.7630			−0.218372			−0.109186	+	0.994021i	$0.534824\pi$
$380$		0			0
$381$	45.0612	−	228.212i	0.118271	−	0.598982i
$382$		0			0
$383$			334.592i			0.873608i	0.899557	+	0.436804i	$0.143890\pi$
$383$			334.592i			0.873608i	−0.899557	+	0.436804i	$0.856110\pi$
$384$		0			0
$385$	−217.947			−0.566097
$386$		0			0
$387$	353.465	+	145.248i	0.913346	+	0.375319i
$388$		0			0
$389$		−	542.964i		−	1.39580i	−0.716197	−	0.697898i	$-0.754119\pi$
$389$		−	542.964i		−	1.39580i	0.716197	−	0.697898i	$-0.245881\pi$
$390$		0			0
$391$	62.7630			0.160519
$392$		0			0
$393$	299.026	+	59.0437i	0.760881	+	0.150238i
$394$		0			0
$395$		−	20.1835i		−	0.0510975i
$396$		0			0
$397$	−214.000			−0.539043			−0.269521	−	0.962994i	$-0.586865\pi$
$397$	−214.000			−0.539043			−0.269521	+	0.962994i	$0.586865\pi$
$398$		0			0
$399$	−73.2541	+	370.995i	−0.183594	+	0.929812i
$400$		0			0
$401$		−	726.086i		−	1.81069i	−0.424677	−	0.905345i	$-0.639613\pi$
$401$		−	726.086i		−	1.81069i	0.424677	−	0.905345i	$-0.360387\pi$
$402$		0			0
$403$	80.0000			0.198511
$404$		0			0
$405$	127.351	−	128.790i	0.314447	−	0.317999i
$406$		0			0
$407$		−	508.670i		−	1.24980i
$408$		0			0
$409$	−346.158			−0.846352			−0.423176	−	0.906047i	$-0.639085\pi$
$409$	−346.158			−0.846352			−0.423176	+	0.906047i	$0.639085\pi$
$410$		0			0
$411$	−518.039	−	102.288i	−1.26044	−	0.248877i
$412$		0			0
$413$			893.038i			2.16232i
$414$		0			0
$415$	−1.53950			−0.00370964
$416$		0			0
$417$	−109.728	+	555.717i	−0.263137	+	1.33266i
$418$		0			0
$419$		−	580.907i		−	1.38641i	−0.720740	−	0.693206i	$-0.756198\pi$
$419$		−	580.907i		−	1.38641i	0.720740	−	0.693206i	$-0.243802\pi$
$420$		0			0
$421$	−269.315			−0.639704			−0.319852	−	0.947468i	$-0.603633\pi$
$421$	−269.315			−0.639704			−0.319852	+	0.947468i	$0.603633\pi$
$422$		0			0
$423$	−302.039	+	735.019i	−0.714041	+	1.73763i
$424$		0			0
$425$		−	17.7708i		−	0.0418136i
$426$		0			0
$427$	−252.105			−0.590411
$428$		0			0
$429$	−249.737	−	49.3113i	−0.582137	−	0.114945i
$430$		0			0
$431$		−	776.068i		−	1.80062i	−0.435247	−	0.900311i	$-0.643339\pi$
$431$		−	776.068i		−	1.80062i	0.435247	−	0.900311i	$-0.356661\pi$
$432$		0			0
$433$	−195.526			−0.451561			−0.225781	−	0.974178i	$-0.572493\pi$
$433$	−195.526			−0.451561			−0.225781	+	0.974178i	$0.572493\pi$
$434$		0			0
$435$	−34.8683	+	176.590i	−0.0801571	+	0.405955i
$436$		0			0
$437$		−	193.785i		−	0.443443i
$438$		0			0
$439$	−598.763			−1.36392			−0.681962	−	0.731387i	$-0.738873\pi$
$439$	−598.763			−1.36392			−0.681962	+	0.731387i	$0.738873\pi$
$440$		0			0
$441$	−690.500	−	283.745i	−1.56576	−	0.643413i
$442$		0			0
$443$		−	216.728i		−	0.489228i	−0.969621	−	0.244614i	$-0.921339\pi$
$443$		−	216.728i		−	0.489228i	0.969621	−	0.244614i	$-0.0786612\pi$
$444$		0			0
$445$	−15.8947			−0.0357183
$446$		0			0
$447$	−213.645	−	42.1848i	−0.477953	−	0.0943732i
$448$		0			0
$449$			246.203i			0.548336i	0.961682	+	0.274168i	$0.0884025\pi$
$449$			246.203i			0.548336i	−0.961682	+	0.274168i	$0.911598\pi$
$450$		0			0
$451$	174.158			0.386160
$452$		0			0
$453$	−54.5964	+	276.503i	−0.120522	+	0.610383i
$454$		0			0
$455$		−	256.853i		−	0.564513i
$456$		0			0
$457$	553.052			1.21018			0.605090	−	0.796157i	$-0.293137\pi$
$457$	553.052			1.21018			0.605090	+	0.796157i	$0.293137\pi$
$458$		0			0
$459$	−80.0135	−	52.9771i	−0.174321	−	0.115419i
$460$		0			0
$461$			124.749i			0.270605i	0.990804	+	0.135302i	$0.0432006\pi$
$461$			124.749i			0.270605i	−0.990804	+	0.135302i	$0.956799\pi$
$462$		0			0
$463$	−669.723			−1.44649			−0.723243	−	0.690593i	$-0.757349\pi$
$463$	−669.723			−1.44649			−0.723243	+	0.690593i	$0.757349\pi$
$464$		0			0
$465$	52.6491	+	10.3957i	0.113224	+	0.0223564i
$466$		0			0
$467$			486.880i			1.04257i	0.853383	+	0.521285i	$0.174547\pi$
$467$			486.880i			1.04257i	−0.853383	+	0.521285i	$0.825453\pi$
$468$		0			0
$469$	−614.999			−1.31130
$470$		0			0
$471$	−71.9694	+	364.489i	−0.152801	+	0.773861i
$472$		0			0
$473$		−	360.289i		−	0.761711i
$474$		0			0
$475$	−54.8683			−0.115512
$476$		0			0
$477$	12.1580	−	29.5868i	0.0254885	−	0.0620267i
$478$		0			0
$479$			520.580i			1.08680i	0.839472	+	0.543402i	$0.182864\pi$
$479$			520.580i			1.08680i	−0.839472	+	0.543402i	$0.817136\pi$
$480$		0			0
$481$	599.473			1.24631
$482$		0			0
$483$	597.013	+	117.882i	1.23605	+	0.244062i
$484$		0			0
$485$		−	250.322i		−	0.516128i
$486$		0			0
$487$	263.381			0.540824			0.270412	−	0.962745i	$-0.412840\pi$
$487$	263.381			0.540824			0.270412	+	0.962745i	$0.412840\pi$
$488$		0			0
$489$	−92.6228	+	469.088i	−0.189413	+	0.959279i
$490$		0			0
$491$		−	711.646i		−	1.44938i	−0.689074	−	0.724691i	$-0.741983\pi$
$491$		−	711.646i		−	1.44938i	0.689074	−	0.724691i	$-0.258017\pi$
$492$		0			0
$493$	95.3680			0.193444
$494$		0			0
$495$	−157.947	−	64.9049i	−0.319086	−	0.131121i
$496$		0			0
$497$		−	795.569i		−	1.60074i
$498$		0			0
$499$	−23.0790			−0.0462505			−0.0231253	−	0.999733i	$-0.507362\pi$
$499$	−23.0790			−0.0462505			−0.0231253	+	0.999733i	$0.507362\pi$
$500$		0			0
$501$	31.7103	+	6.26130i	0.0632941	+	0.0124976i
$502$		0			0
$503$			40.5844i			0.0806847i	0.999186	+	0.0403423i	$0.0128449\pi$
$503$			40.5844i			0.0806847i	−0.999186	+	0.0403423i	$0.987155\pi$
$504$		0			0
$505$	347.684			0.688483
$506$		0			0
$507$	−40.0986	+	203.079i	−0.0790899	+	0.400550i
$508$		0			0
$509$		−	484.591i		−	0.952045i	−0.879433	−	0.476023i	$-0.842078\pi$
$509$		−	484.591i		−	0.952045i	0.879433	−	0.476023i	$-0.157922\pi$
$510$		0			0
$511$	−138.447			−0.270933
$512$		0			0
$513$	−163.570	+	247.047i	−0.318850	+	0.481572i
$514$		0			0
$515$			16.9766i			0.0329643i
$516$		0			0
$517$	749.210			1.44915
$518$		0			0
$519$	833.934	+	164.663i	1.60681	+	0.317269i
$520$		0			0
$521$			539.857i			1.03619i	0.855322	+	0.518097i	$0.173359\pi$
$521$			539.857i			1.03619i	−0.855322	+	0.518097i	$0.826641\pi$
$522$		0			0
$523$	266.644			0.509836			0.254918	−	0.966963i	$-0.417952\pi$
$523$	266.644			0.509836			0.254918	+	0.966963i	$0.417952\pi$
$524$		0			0
$525$	33.3772	−	169.039i	0.0635757	−	0.321979i
$526$		0			0
$527$		−	28.4332i		−	0.0539530i
$528$		0			0
$529$	217.158			0.410507
$530$		0			0
$531$	−265.947	+	647.188i	−0.500842	+	1.21881i
$532$		0			0
$533$			205.247i			0.385079i
$534$		0			0
$535$	−36.4078			−0.0680520
$536$		0			0
$537$	902.447	+	178.191i	1.68053	+	0.331827i
$538$		0			0
$539$			703.831i			1.30581i
$540$		0			0
$541$	−337.895			−0.624574			−0.312287	−	0.949988i	$-0.601095\pi$
$541$	−337.895			−0.624574			−0.312287	+	0.949988i	$0.601095\pi$
$542$		0			0
$543$	154.399	−	781.954i	0.284345	−	1.44006i
$544$		0			0
$545$			209.837i			0.385022i
$546$		0			0
$547$	214.566			0.392259			0.196130	−	0.980578i	$-0.437163\pi$
$547$	214.566			0.392259			0.196130	+	0.980578i	$0.437163\pi$
$548$		0			0
$549$	−182.702	−	75.0771i	−0.332790	−	0.136753i
$550$		0			0
$551$		−	294.454i		−	0.534400i
$552$		0			0
$553$	−103.684			−0.187494
$554$		0			0
$555$	394.522	+	77.8995i	0.710850	+	0.140359i
$556$		0			0
$557$			674.821i			1.21153i	0.795644	+	0.605764i	$0.207133\pi$
$557$			674.821i			1.21153i	−0.795644	+	0.605764i	$0.792867\pi$
$558$		0			0
$559$	424.605			0.759580
$560$		0			0
$561$	−17.5260	+	88.7603i	−0.0312406	+	0.158218i
$562$		0			0
$563$		−	718.513i		−	1.27622i	−0.769944	−	0.638111i	$-0.779716\pi$
$563$		−	718.513i		−	1.27622i	0.769944	−	0.638111i	$-0.220284\pi$
$564$		0			0
$565$	−437.684			−0.774662
$566$		0			0
$567$	−661.601	−	654.210i	−1.16684	−	1.15381i
$568$		0			0
$569$		−	183.122i		−	0.321831i	−0.986968	−	0.160916i	$-0.948555\pi$
$569$		−	183.122i		−	0.321831i	0.986968	−	0.160916i	$-0.0514447\pi$
$570$		0			0
$571$	295.895			0.518204			0.259102	−	0.965850i	$-0.416573\pi$
$571$	295.895			0.518204			0.259102	+	0.965850i	$0.416573\pi$
$572$		0			0
$573$	−469.789	−	92.7613i	−0.819877	−	0.161887i
$574$		0			0
$575$			88.2952i			0.153557i
$576$		0			0
$577$	−984.947			−1.70701			−0.853507	−	0.521082i	$-0.825529\pi$
$577$	−984.947			−1.70701			−0.853507	+	0.521082i	$0.825529\pi$
$578$		0			0
$579$	−53.4954	+	270.927i	−0.0923927	+	0.467922i
$580$		0			0
$581$			7.90852i			0.0136119i
$582$		0			0
$583$	−30.1580			−0.0517290
$584$		0			0
$585$	76.4911	−	186.143i	0.130754	−	0.318193i
$586$		0			0
$587$			378.172i			0.644245i	0.946698	+	0.322122i	$0.104396\pi$
$587$			378.172i			0.644245i	−0.946698	+	0.322122i	$0.895604\pi$
$588$		0			0
$589$	−87.7893			−0.149048
$590$		0			0
$591$	205.540	+	40.5844i	0.347783	+	0.0686707i
$592$		0			0
$593$		−	265.221i		−	0.447253i	−0.974675	−	0.223626i	$-0.928210\pi$
$593$		−	265.221i		−	0.447253i	0.974675	−	0.223626i	$-0.0717895\pi$
$594$		0			0
$595$	−91.2897			−0.153428
$596$		0			0
$597$	−86.5438	+	438.301i	−0.144964	+	0.734172i
$598$		0			0
$599$		−	382.061i		−	0.637832i	−0.947783	−	0.318916i	$-0.896681\pi$
$599$		−	382.061i		−	0.637832i	0.947783	−	0.318916i	$-0.103319\pi$
$600$		0			0
$601$	1021.53			1.69971			0.849855	−	0.527016i	$-0.176689\pi$
$601$	1021.53			1.69971			0.849855	+	0.527016i	$0.176689\pi$
$602$		0			0
$603$	−445.693	−	183.147i	−0.739125	−	0.303727i
$604$		0			0
$605$		−	109.567i		−	0.181103i
$606$		0			0
$607$	835.487			1.37642			0.688210	−	0.725512i	$-0.258397\pi$
$607$	835.487			1.37642			0.688210	+	0.725512i	$0.258397\pi$
$608$		0			0
$609$	907.157	+	179.121i	1.48959	+	0.294123i
$610$		0			0
$611$			882.952i			1.44509i
$612$		0			0
$613$	833.263			1.35932			0.679660	−	0.733528i	$-0.262128\pi$
$613$	833.263			1.35932			0.679660	+	0.733528i	$0.262128\pi$
$614$		0			0
$615$	−26.6712	+	135.076i	−0.0433678	+	0.219636i
$616$		0			0
$617$		−	455.098i		−	0.737598i	−0.929509	−	0.368799i	$-0.879769\pi$
$617$		−	455.098i		−	0.737598i	0.929509	−	0.368799i	$-0.120231\pi$
$618$		0			0
$619$	−336.710			−0.543959			−0.271979	−	0.962303i	$-0.587678\pi$
$619$	−336.710			−0.543959			−0.271979	+	0.962303i	$0.587678\pi$
$620$		0			0
$621$	397.552	+	263.220i	0.640181	+	0.423865i
$622$		0			0
$623$			81.6520i			0.131063i
$624$		0			0
$625$	25.0000			0.0400000
$626$		0			0
$627$	274.053	+	54.1125i	0.437086	+	0.0863039i
$628$		0			0
$629$		−	213.062i		−	0.338731i
$630$		0			0
$631$	1100.89			1.74468			0.872341	−	0.488898i	$-0.162601\pi$
$631$	1100.89			1.74468			0.872341	+	0.488898i	$0.162601\pi$
$632$		0			0
$633$	166.114	−	841.283i	0.262423	−	1.32904i
$634$		0			0
$635$		−	173.384i		−	0.273045i
$636$		0			0
$637$	−829.473			−1.30216
$638$		0			0
$639$	236.921	−	576.552i	0.370768	−	0.902273i
$640$		0			0
$641$		−	337.011i		−	0.525758i	−0.964829	−	0.262879i	$-0.915328\pi$
$641$		−	337.011i		−	0.525758i	0.964829	−	0.262879i	$-0.0846719\pi$
$642$		0			0
$643$	599.381			0.932164			0.466082	−	0.884742i	$-0.345665\pi$
$643$	599.381			0.932164			0.466082	+	0.884742i	$0.345665\pi$
$644$		0			0
$645$	279.438	+	55.1760i	0.433238	+	0.0855441i
$646$		0			0
$647$		−	47.0224i		−	0.0726775i	−0.999340	−	0.0363388i	$-0.988430\pi$
$647$		−	47.0224i		−	0.0726775i	0.999340	−	0.0363388i	$-0.0115695\pi$
$648$		0			0
$649$	659.684			1.01646
$650$		0			0
$651$	53.4036	−	270.462i	0.0820331	−	0.415456i
$652$		0			0
$653$		−	559.228i		−	0.856399i	−0.903684	−	0.428199i	$-0.859148\pi$
$653$		−	559.228i		−	0.856399i	0.903684	−	0.428199i	$-0.140852\pi$
$654$		0			0
$655$	227.184			0.346846
$656$		0			0
$657$	−100.333	−	41.2296i	−0.152714	−	0.0627543i
$658$		0			0
$659$		−	665.759i		−	1.01026i	−0.863044	−	0.505129i	$-0.831445\pi$
$659$		−	665.759i		−	1.01026i	0.863044	−	0.505129i	$-0.168555\pi$
$660$		0			0
$661$	−557.947			−0.844096			−0.422048	−	0.906574i	$-0.638689\pi$
$661$	−557.947			−0.844096			−0.422048	+	0.906574i	$0.638689\pi$
$662$		0			0
$663$	−104.605	−	20.6546i	−0.157775	−	0.0311532i
$664$		0			0
$665$			281.862i			0.423853i
$666$		0			0
$667$	−473.842			−0.710408
$668$		0			0
$669$	41.4826	−	210.088i	0.0620068	−	0.314033i
$670$		0			0
$671$			186.229i			0.277540i
$672$		0			0
$673$	1019.42			1.51474			0.757370	−	0.652985i	$-0.226484\pi$
$673$	1019.42			1.51474			0.757370	+	0.652985i	$0.226484\pi$
$674$		0			0
$675$	74.5285	−	112.563i	0.110413	−	0.166761i
$676$		0			0
$677$		−	624.616i		−	0.922624i	−0.887238	−	0.461312i	$-0.847379\pi$
$677$		−	624.616i		−	0.922624i	0.887238	−	0.461312i	$-0.152621\pi$
$678$		0			0
$679$	−1285.92			−1.89384
$680$		0			0
$681$	−85.7103	−	16.9238i	−0.125860	−	0.0248513i
$682$		0			0
$683$			525.882i			0.769959i	0.922925	+	0.384980i	$0.125792\pi$
$683$			525.882i			0.769959i	−0.922925	+	0.384980i	$0.874208\pi$
$684$		0			0
$685$	−393.579			−0.574567
$686$		0			0
$687$	−75.3644	+	381.683i	−0.109701	+	0.555579i
$688$		0			0
$689$		−	35.5415i		−	0.0515843i
$690$		0			0
$691$	−932.000			−1.34877			−0.674385	−	0.738380i	$-0.735591\pi$
$691$	−932.000			−1.34877			−0.674385	+	0.738380i	$0.735591\pi$
$692$		0			0
$693$	−333.421	+	811.386i	−0.481126	+	1.17083i
$694$		0			0
$695$			422.205i			0.607489i
$696$		0			0
$697$	72.9480			0.104660
$698$		0			0
$699$	547.065	+	108.020i	0.782640	+	0.154535i
$700$		0			0
$701$			606.045i			0.864544i	0.901743	+	0.432272i	$0.142288\pi$
$701$			606.045i			0.864544i	−0.901743	+	0.432272i	$0.857712\pi$
$702$		0			0
$703$	−657.842			−0.935764
$704$		0			0
$705$	−114.737	+	581.083i	−0.162747	+	0.824232i
$706$		0			0
$707$		−	1786.08i		−	2.52627i
$708$		0			0
$709$	489.473			0.690371			0.345186	−	0.938534i	$-0.387816\pi$
$709$	489.473			0.690371			0.345186	+	0.938534i	$0.387816\pi$
$710$		0			0
$711$	−75.1402	−	30.8772i	−0.105682	−	0.0434278i
$712$		0			0
$713$			141.272i			0.198138i
$714$		0			0
$715$	−189.737			−0.265366
$716$		0			0
$717$	−890.947	−	175.920i	−1.24260	−	0.245356i
$718$		0			0
$719$		−	107.778i		−	0.149900i	−0.997187	−	0.0749500i	$-0.976120\pi$
$719$		−	107.778i		−	0.149900i	0.997187	−	0.0749500i	$-0.0238797\pi$
$720$		0			0
$721$	87.2100			0.120957
$722$		0			0
$723$	−138.036	+	699.080i	−0.190921	+	0.966916i
$724$		0			0
$725$			134.164i			0.185054i
$726$		0			0
$727$	150.172			0.206563			0.103282	−	0.994652i	$-0.467066\pi$
$727$	150.172			0.206563			0.103282	+	0.994652i	$0.467066\pi$
$728$		0			0
$729$	−284.641	−	671.134i	−0.390453	−	0.920623i
$730$		0			0
$731$		−	150.911i		−	0.206445i
$732$		0			0
$733$	−675.526			−0.921591			−0.460795	−	0.887506i	$-0.652436\pi$
$733$	−675.526			−0.921591			−0.460795	+	0.887506i	$0.652436\pi$
$734$		0			0
$735$	−545.888	−	107.787i	−0.742705	−	0.146649i
$736$		0			0
$737$			454.298i			0.616415i
$738$		0			0
$739$	936.921			1.26782			0.633911	−	0.773406i	$-0.281448\pi$
$739$	936.921			1.26782			0.633911	+	0.773406i	$0.281448\pi$
$740$		0			0
$741$	−63.7722	+	322.974i	−0.0860624	+	0.435863i
$742$		0			0
$743$			452.939i			0.609608i	0.952415	+	0.304804i	$0.0985910\pi$
$743$			452.939i			0.609608i	−0.952415	+	0.304804i	$0.901409\pi$
$744$		0			0
$745$	−162.316			−0.217874
$746$		0			0
$747$	−2.35516	+	5.73134i	−0.00315283	+	0.00767247i
$748$		0			0
$749$			187.029i			0.249706i
$750$		0			0
$751$	−654.369			−0.871330			−0.435665	−	0.900109i	$-0.643487\pi$
$751$	−654.369			−0.871330			−0.435665	+	0.900109i	$0.643487\pi$
$752$		0			0
$753$	249.079	+	49.1814i	0.330782	+	0.0653140i
$754$		0			0
$755$			210.073i			0.278242i
$756$		0			0
$757$	123.315			0.162900			0.0814500	−	0.996677i	$-0.474045\pi$
$757$	123.315			0.162900			0.0814500	+	0.996677i	$0.474045\pi$
$758$		0			0
$759$	87.0790	−	441.011i	0.114729	−	0.581042i
$760$		0			0
$761$			502.715i			0.660598i	0.943876	+	0.330299i	$0.107150\pi$
$761$			502.715i			0.660598i	−0.943876	+	0.330299i	$0.892850\pi$
$762$		0			0
$763$	1077.95			1.41278
$764$		0			0
$765$	−66.1580	−	27.1861i	−0.0864811	−	0.0355374i
$766$		0			0
$767$			777.445i			1.01362i
$768$		0			0
$769$	−286.316			−0.372323			−0.186161	−	0.982519i	$-0.559605\pi$
$769$	−286.316			−0.372323			−0.186161	+	0.982519i	$0.559605\pi$
$770$		0			0
$771$	859.565	+	169.724i	1.11487	+	0.220135i
$772$		0			0
$773$			972.030i			1.25748i	0.777617	+	0.628739i	$0.216428\pi$
$773$			972.030i			1.25748i	−0.777617	+	0.628739i	$0.783572\pi$
$774$		0			0
$775$	40.0000			0.0516129
$776$		0			0
$777$	400.175	−	2026.68i	0.515026	−	2.60835i
$778$		0			0
$779$		−	225.231i		−	0.289129i
$780$		0			0
$781$	−587.684			−0.752476
$782$		0			0
$783$	604.078	+	399.962i	0.771492	+	0.510807i
$784$		0			0
$785$			276.919i			0.352763i
$786$		0			0
$787$	−1492.70			−1.89669			−0.948346	−	0.317237i	$-0.897245\pi$
$787$	−1492.70			−1.89669			−0.948346	+	0.317237i	$0.897245\pi$
$788$		0			0
$789$	−817.394	−	161.397i	−1.03599	−	0.204559i
$790$		0			0
$791$			2248.41i			2.84249i
$792$		0			0
$793$	−219.473			−0.276763
$794$		0			0
$795$	4.61850	−	23.3904i	0.00580944	−	0.0294219i
$796$		0			0
$797$			94.3618i			0.118396i	0.998246	+	0.0591981i	$0.0188544\pi$
$797$			94.3618i			0.118396i	−0.998246	+	0.0591981i	$0.981146\pi$
$798$		0			0
$799$	313.815			0.392760
$800$		0			0
$801$	−24.3160	+	59.1735i	−0.0303571	+	0.0738746i
$802$		0			0
$803$			102.270i			0.127360i
$804$		0			0
$805$	453.579			0.563452
$806$		0			0
$807$	−843.354	−	166.523i	−1.04505	−	0.206348i
$808$		0			0
$809$			1103.35i			1.36384i	0.731427	+	0.681920i	$0.238855\pi$
$809$			1103.35i			1.36384i	−0.731427	+	0.681920i	$0.761145\pi$
$810$		0			0
$811$	10.1580			0.0125253			0.00626264	−	0.999980i	$-0.498007\pi$
$811$	10.1580			0.0125253			0.00626264	+	0.999980i	$0.498007\pi$
$812$		0			0
$813$	188.350	−	953.899i	0.231673	−	1.17331i
$814$		0			0
$815$			356.388i			0.437286i
$816$		0			0
$817$	−465.947			−0.570315
$818$		0			0
$819$	−956.228	−	392.940i	−1.16756	−	0.479780i
$820$		0			0
$821$		−	337.011i		−	0.410488i	−0.978711	−	0.205244i	$-0.934201\pi$
$821$		−	337.011i		−	0.410488i	0.978711	−	0.205244i	$-0.0657988\pi$
$822$		0			0
$823$	901.512			1.09540			0.547699	−	0.836675i	$-0.315504\pi$
$823$	901.512			1.09540			0.547699	+	0.836675i	$0.315504\pi$
$824$		0			0
$825$	−124.868	−	24.6556i	−0.151356	−	0.0298856i
$826$		0			0
$827$		−	531.354i		−	0.642508i	−0.946993	−	0.321254i	$-0.895896\pi$
$827$		−	531.354i		−	0.642508i	0.946993	−	0.321254i	$-0.104104\pi$
$828$		0			0
$829$	−197.631			−0.238397			−0.119199	−	0.992870i	$-0.538033\pi$
$829$	−197.631			−0.238397			−0.119199	+	0.992870i	$0.538033\pi$
$830$		0			0
$831$	241.662	−	1223.90i	0.290809	−	1.47280i
$832$		0			0
$833$			294.808i			0.353911i
$834$		0			0
$835$	24.0918			0.0288525
$836$		0			0
$837$	119.246	−	180.101i	0.142468	−	0.215175i
$838$		0			0
$839$		−	943.950i		−	1.12509i	−0.826767	−	0.562545i	$-0.809822\pi$
$839$		−	943.950i		−	1.12509i	0.826767	−	0.562545i	$-0.190178\pi$
$840$		0			0
$841$	121.000			0.143876
$842$		0			0
$843$	−1270.64	−	250.893i	−1.50729	−	0.297619i
$844$		0			0
$845$			154.289i			0.182590i
$846$		0			0
$847$	−562.855			−0.664528
$848$		0			0
$849$	−82.2541	+	416.575i	−0.0968835	+	0.490666i
$850$		0			0
$851$			1058.61i			1.24396i
$852$		0			0
$853$	−1196.42			−1.40260			−0.701301	−	0.712865i	$-0.747397\pi$
$853$	−1196.42			−1.40260			−0.701301	+	0.712865i	$0.747397\pi$
$854$		0			0
$855$	−83.9388	+	204.267i	−0.0981740	+	0.238909i
$856$		0			0
$857$			1266.04i			1.47729i	0.674095	+	0.738645i	$0.264534\pi$
$857$			1266.04i			1.47729i	−0.674095	+	0.738645i	$0.735466\pi$
$858$		0			0
$859$	470.868			0.548159			0.274079	−	0.961707i	$-0.411627\pi$
$859$	470.868			0.548159			0.274079	+	0.961707i	$0.411627\pi$
$860$		0			0
$861$	693.895	+	137.012i	0.805917	+	0.159131i
$862$		0			0
$863$		−	285.057i		−	0.330310i	−0.986268	−	0.165155i	$-0.947188\pi$
$863$		−	285.057i		−	0.330310i	0.986268	−	0.165155i	$-0.0528124\pi$
$864$		0			0
$865$	633.579			0.732461
$866$		0			0
$867$	160.608	−	813.399i	0.185246	−	0.938177i
$868$		0			0
$869$			76.5910i			0.0881369i
$870$		0			0
$871$	−535.395			−0.614690
$872$		0			0
$873$	−931.912	−	382.948i	−1.06748	−	0.438657i
$874$		0			0
$875$		−	128.427i		−	0.146773i
$876$		0			0
$877$	244.579			0.278882			0.139441	−	0.990230i	$-0.455469\pi$
$877$	244.579			0.278882			0.139441	+	0.990230i	$0.455469\pi$
$878$		0			0
$879$	−485.618	−	95.8867i	−0.552466	−	0.109086i
$880$		0			0
$881$			137.271i			0.155813i	0.996961	+	0.0779065i	$0.0248236\pi$
$881$			137.271i			0.155813i	−0.996961	+	0.0779065i	$0.975176\pi$
$882$		0			0
$883$	−1647.75			−1.86608			−0.933040	−	0.359772i	$-0.882854\pi$
$883$	−1647.75			−1.86608			−0.933040	+	0.359772i	$0.882854\pi$
$884$		0			0
$885$	−101.026	+	511.647i	−0.114154	+	0.578133i
$886$		0			0
$887$			514.419i			0.579954i	0.957034	+	0.289977i	$0.0936477\pi$
$887$			514.419i			0.579954i	−0.957034	+	0.289977i	$0.906352\pi$
$888$		0			0
$889$	−890.683			−1.00189
$890$		0			0
$891$	−483.263	+	488.722i	−0.542382	+	0.548510i
$892$		0			0
$893$		−	968.923i		−	1.08502i
$894$		0			0
$895$	685.631			0.766069
$896$		0			0
$897$	519.737	+	102.624i	0.579417	+	0.114408i
$898$		0			0
$899$			214.663i			0.238779i
$900$		0			0
$901$	−12.6320			−0.0140200
$902$		0			0
$903$	283.443	−	1435.49i	0.313890	−	1.58969i
$904$		0			0
$905$		−	594.087i		−	0.656450i
$906$		0			0
$907$	−347.303			−0.382914			−0.191457	−	0.981501i	$-0.561321\pi$
$907$	−347.303			−0.382914			−0.191457	+	0.981501i	$0.561321\pi$
$908$		0			0
$909$	531.895	−	1294.38i	0.585143	−	1.42396i
$910$		0			0
$911$			304.540i			0.334292i	0.985932	+	0.167146i	$0.0534551\pi$
$911$			304.540i			0.334292i	−0.985932	+	0.167146i	$0.946545\pi$
$912$		0			0
$913$	5.84200			0.00639868
$914$		0			0
$915$	−144.438	−	28.5198i	−0.157856	−	0.0311692i
$916$		0			0
$917$		−	1167.06i		−	1.27270i
$918$		0			0
$919$	−244.289			−0.265820			−0.132910	−	0.991128i	$-0.542432\pi$
$919$	−244.289			−0.265820			−0.132910	+	0.991128i	$0.542432\pi$
$920$		0			0
$921$	−92.6228	+	469.088i	−0.100568	+	0.509324i
$922$		0			0
$923$		−	692.592i		−	0.750371i
$924$		0			0
$925$	299.737			0.324040
$926$		0			0
$927$	63.2014	+	25.9712i	0.0681785	+	0.0280164i
$928$		0			0
$929$		−	1025.96i		−	1.10437i	−0.833723	−	0.552183i	$-0.813795\pi$
$929$		−	1025.96i		−	1.10437i	0.833723	−	0.552183i	$-0.186205\pi$
$930$		0			0
$931$	910.236			0.977697
$932$		0			0
$933$	421.157	+	83.1588i	0.451401	+	0.0891305i
$934$		0			0
$935$			67.4353i			0.0721234i
$936$		0			0
$937$	−332.053			−0.354379			−0.177189	−	0.984177i	$-0.556700\pi$
$937$	−332.053			−0.354379			−0.177189	+	0.984177i	$0.556700\pi$
$938$		0			0
$939$	−291.548	+	1476.54i	−0.310488	+	1.57246i
$940$		0			0
$941$			1636.99i			1.73963i	0.493381	+	0.869813i	$0.335761\pi$
$941$			1636.99i			1.73963i	−0.493381	+	0.869813i	$0.664239\pi$
$942$		0			0
$943$	−362.447			−0.384355
$944$		0			0
$945$	−578.246	−	382.858i	−0.611900	−	0.405141i
$946$		0			0
$947$		−	1209.32i		−	1.27700i	−0.769622	−	0.638500i	$-0.779555\pi$
$947$		−	1209.32i		−	1.27700i	0.769622	−	0.638500i	$-0.220445\pi$
$948$		0			0
$949$	−120.527			−0.127004
$950$		0			0
$951$	983.776	+	194.250i	1.03446	+	0.204258i
$952$		0			0
$953$		−	1205.26i		−	1.26470i	−0.774681	−	0.632352i	$-0.782090\pi$
$953$		−	1205.26i		−	1.26470i	0.774681	−	0.632352i	$-0.217910\pi$
$954$		0			0
$955$	−356.921			−0.373739
$956$		0			0
$957$	132.316	−	670.114i	0.138261	−	0.700223i
$958$		0			0
$959$			2021.84i			2.10828i
$960$		0			0
$961$	−897.000			−0.933403
$962$		0			0
$963$	−55.6975	+	135.541i	−0.0578375	+	0.140749i
$964$		0			0
$965$			205.836i			0.213302i
$966$		0			0
$967$	1845.93			1.90893			0.954464	−	0.298325i	$-0.0964281\pi$
$967$	1845.93			1.90893			0.954464	+	0.298325i	$0.0964281\pi$
$968$		0			0
$969$	114.790	+	22.6656i	0.118462	+	0.0233908i
$970$		0			0
$971$		−	1057.91i		−	1.08950i	−0.838598	−	0.544751i	$-0.816624\pi$
$971$		−	1057.91i		−	1.08950i	0.838598	−	0.544751i	$-0.183376\pi$
$972$		0			0
$973$	2168.89			2.22908
$974$		0			0
$975$	29.0569	−	147.159i	0.0298020	−	0.150932i
$976$		0			0
$977$		−	964.028i		−	0.986722i	−0.869825	−	0.493361i	$-0.835768\pi$
$977$		−	964.028i		−	0.986722i	0.869825	−	0.493361i	$-0.164232\pi$
$978$		0			0
$979$	60.3160			0.0616098
$980$		0			0
$981$	781.193	+	321.013i	0.796323	+	0.327231i
$982$		0			0
$983$		−	460.718i		−	0.468685i	−0.972154	−	0.234343i	$-0.924706\pi$
$983$		−	460.718i		−	0.468685i	0.972154	−	0.234343i	$-0.0752937\pi$
$984$		0			0
$985$	156.158			0.158536
$986$		0			0
$987$	2985.06	+	589.410i	3.02438	+	0.597173i
$988$		0			0
$989$			749.812i			0.758152i
$990$		0			0
$991$	−1237.89			−1.24914			−0.624568	−	0.780971i	$-0.714725\pi$
$991$	−1237.89			−1.24914			−0.624568	+	0.780971i	$0.714725\pi$
$992$		0			0
$993$	−226.307	+	1146.13i	−0.227903	+	1.15421i
$994$		0			0
$995$			332.997i			0.334671i
$996$		0			0
$997$	−9.36798			−0.00939617			−0.00469809	−	0.999989i	$-0.501495\pi$
$997$	−9.36798			−0.00939617			−0.00469809	+	0.999989i	$0.501495\pi$
$998$		0			0
$999$	893.557	−	1349.57i	0.894451	−	1.35093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.l.c.161.3		4
3.2	odd	2	inner	240.3.l.c.161.4		4
4.3	odd	2		30.3.d.a.11.3	yes	4
5.2	odd	4		1200.3.c.k.449.1		8
5.3	odd	4		1200.3.c.k.449.8		8
5.4	even	2		1200.3.l.u.401.2		4
8.3	odd	2		960.3.l.e.641.3		4
8.5	even	2		960.3.l.f.641.2		4
12.11	even	2		30.3.d.a.11.1	✓	4
15.2	even	4		1200.3.c.k.449.7		8
15.8	even	4		1200.3.c.k.449.2		8
15.14	odd	2		1200.3.l.u.401.1		4
20.3	even	4		150.3.b.b.149.5		8
20.7	even	4		150.3.b.b.149.4		8
20.19	odd	2		150.3.d.c.101.2		4
24.5	odd	2		960.3.l.f.641.1		4
24.11	even	2		960.3.l.e.641.4		4
36.7	odd	6		810.3.h.a.701.4		8
36.11	even	6		810.3.h.a.701.1		8
36.23	even	6		810.3.h.a.431.4		8
36.31	odd	6		810.3.h.a.431.1		8
60.23	odd	4		150.3.b.b.149.3		8
60.47	odd	4		150.3.b.b.149.6		8
60.59	even	2		150.3.d.c.101.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.1	✓	4	12.11	even	2
30.3.d.a.11.3	yes	4	4.3	odd	2
150.3.b.b.149.3		8	60.23	odd	4
150.3.b.b.149.4		8	20.7	even	4
150.3.b.b.149.5		8	20.3	even	4
150.3.b.b.149.6		8	60.47	odd	4
150.3.d.c.101.2		4	20.19	odd	2
150.3.d.c.101.4		4	60.59	even	2
240.3.l.c.161.3		4	1.1	even	1	trivial
240.3.l.c.161.4		4	3.2	odd	2	inner
810.3.h.a.431.1		8	36.31	odd	6
810.3.h.a.431.4		8	36.23	even	6
810.3.h.a.701.1		8	36.11	even	6
810.3.h.a.701.4		8	36.7	odd	6
960.3.l.e.641.3		4	8.3	odd	2
960.3.l.e.641.4		4	24.11	even	2
960.3.l.f.641.1		4	24.5	odd	2
960.3.l.f.641.2		4	8.5	even	2
1200.3.c.k.449.1		8	5.2	odd	4
1200.3.c.k.449.2		8	15.8	even	4
1200.3.c.k.449.7		8	15.2	even	4
1200.3.c.k.449.8		8	5.3	odd	4
1200.3.l.u.401.1		4	15.14	odd	2
1200.3.l.u.401.2		4	5.4	even	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.l (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.581139 - 2.94317i) q^{3} -2.23607i q^{5} -11.4868 q^{7} +(-8.32456 - 3.42079i) q^{9} +O(q^{10})\)	\(q+(0.581139 - 2.94317i) q^{3} -2.23607i q^{5} -11.4868 q^{7} +(-8.32456 - 3.42079i) q^{9} +8.48528i q^{11} -10.0000 q^{13} +(-6.58114 - 1.29947i) q^{15} +3.55415i q^{17} +10.9737 q^{19} +(-6.67544 + 33.8078i) q^{21} -17.6590i q^{23} -5.00000 q^{25} +(-14.9057 + 22.5127i) q^{27} -26.8328i q^{29} -8.00000 q^{31} +(24.9737 + 4.93113i) q^{33} +25.6853i q^{35} -59.9473 q^{37} +(-5.81139 + 29.4317i) q^{39} -20.5247i q^{41} -42.4605 q^{43} +(-7.64911 + 18.6143i) q^{45} -88.2952i q^{47} +82.9473 q^{49} +(10.4605 + 2.06546i) q^{51} +3.55415i q^{53} +18.9737 q^{55} +(6.37722 - 32.2974i) q^{57} -77.7445i q^{59} +21.9473 q^{61} +(95.6228 + 39.2940i) q^{63} +22.3607i q^{65} +53.5395 q^{67} +(-51.9737 - 10.2624i) q^{69} +69.2592i q^{71} +12.0527 q^{73} +(-2.90569 + 14.7159i) q^{75} -97.4690i q^{77} +9.02633 q^{79} +(57.5964 + 56.9530i) q^{81} -0.688486i q^{83} +7.94733 q^{85} +(-78.9737 - 15.5936i) q^{87} -7.10831i q^{89} +114.868 q^{91} +(-4.64911 + 23.5454i) q^{93} -24.5379i q^{95} +111.947 q^{97} +(29.0263 - 70.6362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 8 * q^7 - 8 * q^9	\( 4 q - 4 q^{3} - 8 q^{7} - 8 q^{9} - 40 q^{13} - 20 q^{15} - 32 q^{19} - 52 q^{21} - 20 q^{25} - 28 q^{27} - 32 q^{31} + 24 q^{33} - 88 q^{37} + 40 q^{39} - 56 q^{43} + 20 q^{45} + 180 q^{49} - 72 q^{51} + 152 q^{57} - 64 q^{61} + 256 q^{63} + 328 q^{67} - 132 q^{69} + 200 q^{73} + 20 q^{75} + 112 q^{79} + 28 q^{81} - 120 q^{85} - 240 q^{87} + 80 q^{91} + 32 q^{93} + 296 q^{97} + 192 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 8 * q^7 - 8 * q^9 - 40 * q^13 - 20 * q^15 - 32 * q^19 - 52 * q^21 - 20 * q^25 - 28 * q^27 - 32 * q^31 + 24 * q^33 - 88 * q^37 + 40 * q^39 - 56 * q^43 + 20 * q^45 + 180 * q^49 - 72 * q^51 + 152 * q^57 - 64 * q^61 + 256 * q^63 + 328 * q^67 - 132 * q^69 + 200 * q^73 + 20 * q^75 + 112 * q^79 + 28 * q^81 - 120 * q^85 - 240 * q^87 + 80 * q^91 + 32 * q^93 + 296 * q^97 + 192 * q^99

Introduction

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