LMFDB - Embedded newform 315.2.bf.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(109,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("315.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.1
Root			$1.05078 - 0.281555i$ of defining polynomial
Character	$\chi$	$=$	315.289
Dual form			315.2.bf.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.17942 - 1.25829i) q^{2} +(2.16659 + 3.75264i) q^{4} +(1.11685 + 1.93717i) q^{5} +(-1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +O(q^{10})$	\(q+(-2.17942 - 1.25829i) q^{2} +(2.16659 + 3.75264i) q^{4} +(1.11685 + 1.93717i) q^{5} +(-1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +(0.00343282 - 5.62724i) q^{10} +(0.489068 + 0.847090i) q^{11} +5.14977i q^{13} +(-0.0275122 + 6.65819i) q^{14} +(-3.05502 + 5.29146i) q^{16} +(-3.59380 + 2.07488i) q^{17} +(-1.15001 + 1.99187i) q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +(4.39324 + 2.53644i) q^{23} +(-2.50528 + 4.32707i) q^{25} +(6.47990 - 11.2235i) q^{26} +(5.77323 - 9.90478i) q^{28} +5.92664 q^{29} +(-0.316594 - 0.548357i) q^{31} +(3.14643 - 1.81659i) q^{32} +10.4432 q^{34} +(2.98230 - 5.10939i) q^{35} +(7.84188 + 4.52751i) q^{37} +(5.01270 - 2.89408i) q^{38} +(11.3743 - 6.55773i) q^{40} -2.65505 q^{41} +0.344947i q^{43} +(-2.11922 + 3.67059i) q^{44} +(-6.38315 - 11.0559i) q^{46} +(3.67059 + 2.11922i) q^{47} +(-3.54998 + 6.03305i) q^{49} +(10.9048 - 6.27815i) q^{50} +(-19.3252 + 11.1574i) q^{52} +(-6.61053 + 3.81659i) q^{53} +(-1.09474 + 1.89348i) q^{55} +(-13.4855 + 7.71176i) q^{56} +(-12.9167 - 7.45743i) q^{58} +(-0.908297 - 1.57322i) q^{59} +(-0.328128 + 0.568335i) q^{61} +1.59347i q^{62} +3.07689 q^{64} +(-9.97599 + 5.75153i) q^{65} +(8.01924 - 4.62991i) q^{67} +(-15.5726 - 8.99083i) q^{68} +(-12.9288 + 7.38292i) q^{70} +5.49351 q^{71} +(4.65758 - 2.68905i) q^{73} +(-11.3938 - 19.7347i) q^{74} -9.96636 q^{76} +(1.30320 - 2.23582i) q^{77} +(-5.44346 + 9.42835i) q^{79} +(-13.6625 - 0.00833461i) q^{80} +(5.78648 + 3.34083i) q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +(0.434043 - 0.751785i) q^{86} +(4.97379 - 2.87162i) q^{88} +(-8.15542 + 14.1256i) q^{89} +(11.8277 - 6.76369i) q^{91} +21.9817i q^{92} +(-5.33317 - 9.23733i) q^{94} +(-5.14299 - 0.00313741i) q^{95} +1.53844i q^{97} +(15.3282 - 8.68165i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) $ 16 * q + 8 * q^4 - 2 * q^5	$ 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.17942	−	1.25829i	−1.54108	−	0.889745i	−0.998771	−	0.0495691i	$-0.984215\pi$
$2$	−2.17942	−	1.25829i	−1.54108	−	0.889745i	−0.542313	−	0.840176i	$-0.682451\pi$
$3$		0			0
$3$		0			0
$4$	2.16659	+	3.75264i	1.08329	+	1.87632i
$5$	1.11685	+	1.93717i	0.499472	+	0.866330i
$5$	1.11685	+	1.93717i	0.499472	+	0.866330i
$6$		0			0
$7$	−1.31340	−	2.29673i	−0.496417	−	0.868084i
$7$	−1.31340	−	2.29673i	−0.496417	−	0.868084i
$8$		−	5.87162i		−	2.07593i
$9$		0			0
$10$	0.00343282	−	5.62724i	0.00108555	−	1.77949i
$11$	0.489068	+	0.847090i	0.147459	+	0.255407i	0.930288	−	0.366830i	$-0.119557\pi$
$11$	0.489068	+	0.847090i	0.147459	+	0.255407i	−0.782828	+	0.622238i	$0.786224\pi$
$12$		0			0
$13$			5.14977i			1.42829i	0.699998	+	0.714144i	$0.253184\pi$
$13$			5.14977i			1.42829i	−0.699998	+	0.714144i	$0.746816\pi$
$14$	−0.0275122	+	6.65819i	−0.00735294	+	1.77948i
$15$		0			0
$16$	−3.05502	+	5.29146i	−0.763756	+	1.32286i
$17$	−3.59380	+	2.07488i	−0.871626	+	0.503233i	−0.867888	−	0.496760i	$-0.834523\pi$
$17$	−3.59380	+	2.07488i	−0.871626	+	0.503233i	−0.00373753	+	0.999993i	$0.501190\pi$
$18$		0			0
$19$	−1.15001	+	1.99187i	−0.263830	+	0.456967i	−0.967256	−	0.253801i	$-0.918319\pi$
$19$	−1.15001	+	1.99187i	−0.263830	+	0.456967i	0.703427	+	0.710768i	$0.251652\pi$
$20$	−4.84975	+	8.38820i	−1.08444	+	1.87566i
$21$		0			0
$22$		−	2.46156i		−	0.524805i
$23$	4.39324	+	2.53644i	0.916054	+	0.528884i	0.882374	−	0.470548i	$-0.155944\pi$
$23$	4.39324	+	2.53644i	0.916054	+	0.528884i	0.0336802	+	0.999433i	$0.489277\pi$
$24$		0			0
$25$	−2.50528	+	4.32707i	−0.501056	+	0.865415i
$26$	6.47990	−	11.2235i	1.27081	−	2.20111i
$27$		0			0
$28$	5.77323	−	9.90478i	1.09104	−	1.87183i
$29$	5.92664			1.10055			0.550275	−	0.834983i	$-0.314523\pi$
$29$	5.92664			1.10055			0.550275	+	0.834983i	$0.314523\pi$
$30$		0			0
$31$	−0.316594	−	0.548357i	−0.0568620	−	0.0984879i	0.836193	−	0.548435i	$-0.184776\pi$
$31$	−0.316594	−	0.548357i	−0.0568620	−	0.0984879i	−0.893055	+	0.449947i	$0.851443\pi$
$32$	3.14643	−	1.81659i	0.556216	−	0.321132i
$33$		0			0
$34$	10.4432			1.79100
$35$	2.98230	−	5.10939i	0.504101	−	0.863645i
$36$		0			0
$37$	7.84188	+	4.52751i	1.28920	+	0.744318i	0.978511	−	0.206194i	$-0.0661078\pi$
$37$	7.84188	+	4.52751i	1.28920	+	0.744318i	0.310686	+	0.950513i	$0.399441\pi$
$38$	5.01270	−	2.89408i	0.813168	−	0.469483i
$39$		0			0
$40$	11.3743	−	6.55773i	1.79844	−	1.03687i
$41$	−2.65505			−0.414650			−0.207325	−	0.978272i	$-0.566476\pi$
$41$	−2.65505			−0.414650			−0.207325	+	0.978272i	$0.566476\pi$
$42$		0			0
$43$			0.344947i			0.0526039i	0.999654	+	0.0263020i	$0.00837314\pi$
$43$			0.344947i			0.0526039i	−0.999654	+	0.0263020i	$0.991627\pi$
$44$	−2.11922	+	3.67059i	−0.319484	+	0.553362i
$45$		0			0
$46$	−6.38315	−	11.0559i	−0.941144	−	1.63011i
$47$	3.67059	+	2.11922i	0.535410	+	0.309119i	0.743217	−	0.669051i	$-0.233299\pi$
$47$	3.67059	+	2.11922i	0.535410	+	0.309119i	−0.207806	+	0.978170i	$0.566632\pi$
$48$		0			0
$49$	−3.54998	+	6.03305i	−0.507140	+	0.861864i
$50$	10.9048	−	6.27815i	1.54217	−	0.887864i
$51$		0			0
$52$	−19.3252	+	11.1574i	−2.67993	+	1.54726i
$53$	−6.61053	+	3.81659i	−0.908027	+	0.524250i	−0.879796	−	0.475352i	$-0.842321\pi$
$53$	−6.61053	+	3.81659i	−0.908027	+	0.524250i	−0.0282311	+	0.999601i	$0.508987\pi$
$54$		0			0
$55$	−1.09474	+	1.89348i	−0.147615	+	0.255317i
$56$	−13.4855	+	7.71176i	−1.80208	+	1.03053i
$57$		0			0
$58$	−12.9167	−	7.45743i	−1.69604	−	0.979209i
$59$	−0.908297	−	1.57322i	−0.118250	−	0.204815i	0.800824	−	0.598900i	$-0.204395\pi$
$59$	−0.908297	−	1.57322i	−0.118250	−	0.204815i	−0.919074	+	0.394084i	$0.871062\pi$
$60$		0			0
$61$	−0.328128	+	0.568335i	−0.0420125	+	0.0727678i	−0.886267	−	0.463175i	$-0.846710\pi$
$61$	−0.328128	+	0.568335i	−0.0420125	+	0.0727678i	0.844255	+	0.535942i	$0.180044\pi$
$62$			1.59347i			0.202371i
$63$		0			0
$64$	3.07689			0.384611
$65$	−9.97599	+	5.75153i	−1.23737	+	0.713390i
$66$		0			0
$67$	8.01924	−	4.62991i	0.979706	−	0.565633i	0.0775244	−	0.996990i	$-0.475298\pi$
$67$	8.01924	−	4.62991i	0.979706	−	0.565633i	0.902181	+	0.431357i	$0.141965\pi$
$68$	−15.5726	−	8.99083i	−1.88845	−	1.09030i
$69$		0			0
$70$	−12.9288	+	7.38292i	−1.54529	+	0.882427i
$71$	5.49351			0.651960			0.325980	−	0.945377i	$-0.394306\pi$
$71$	5.49351			0.651960			0.325980	+	0.945377i	$0.394306\pi$
$72$		0			0
$73$	4.65758	−	2.68905i	0.545128	−	0.314730i	−0.202027	−	0.979380i	$-0.564753\pi$
$73$	4.65758	−	2.68905i	0.545128	−	0.314730i	0.747155	+	0.664650i	$0.231419\pi$
$74$	−11.3938	−	19.7347i	−1.32451	−	2.29411i
$75$		0			0
$76$	−9.96636			−1.14322
$77$	1.30320	−	2.23582i	0.148514	−	0.254796i
$78$		0			0
$79$	−5.44346	+	9.42835i	−0.612437	+	1.06077i	0.378391	+	0.925646i	$0.376477\pi$
$79$	−5.44346	+	9.42835i	−0.612437	+	1.06077i	−0.990828	+	0.135127i	$0.956856\pi$
$80$	−13.6625	−	0.00833461i	−1.52751	−	0.000931838i
$81$		0			0
$82$	5.78648	+	3.34083i	0.639010	+	0.368933i
$83$		−	6.62663i		−	0.727367i	−0.931523	−	0.363683i	$-0.881519\pi$
$83$		−	6.62663i		−	0.727367i	0.931523	−	0.363683i	$-0.118481\pi$
$84$		0			0
$85$	−8.03316	−	4.64448i	−0.871318	−	0.503765i
$86$	0.434043	−	0.751785i	0.0468041	−	0.0810671i
$87$		0			0
$88$	4.97379	−	2.87162i	0.530208	−	0.306116i
$89$	−8.15542	+	14.1256i	−0.864472	+	1.49731i	0.00309785	+	0.999995i	$0.499014\pi$
$89$	−8.15542	+	14.1256i	−0.864472	+	1.49731i	−0.867570	+	0.497315i	$0.834319\pi$
$90$		0			0
$91$	11.8277	−	6.76369i	1.23987	−	0.709027i
$92$			21.9817i			2.29175i
$93$		0			0
$94$	−5.33317	−	9.23733i	−0.550075	−	0.952758i
$95$	−5.14299	−	0.00313741i	−0.527659	−	0.000321892i
$96$		0			0
$97$			1.53844i			0.156205i	0.996945	+	0.0781027i	$0.0248862\pi$
$97$			1.53844i			0.156205i	−0.996945	+	0.0781027i	$0.975114\pi$
$98$	15.3282	−	8.68165i	1.54838	−	0.876979i
$99$		0			0
$100$	−21.6659	−	0.0264339i	−2.16659	−	0.00264339i
$101$	−2.75805	−	4.77708i	−0.274436	−	0.475338i	0.695556	−	0.718471i	$-0.255158\pi$
$101$	−2.75805	−	4.77708i	−0.274436	−	0.475338i	−0.969993	+	0.243134i	$0.921825\pi$
$102$		0			0
$103$	−14.3079	−	8.26066i	−1.40980	−	0.813947i	−0.414429	−	0.910082i	$-0.636019\pi$
$103$	−14.3079	−	8.26066i	−1.40980	−	0.813947i	−0.995368	+	0.0961349i	$0.969352\pi$
$104$	30.2375			2.96503
$105$		0			0
$106$	19.2095			1.86579
$107$	2.06824	+	1.19410i	0.199944	+	0.115438i	0.596630	−	0.802517i	$-0.296506\pi$
$107$	2.06824	+	1.19410i	0.199944	+	0.115438i	−0.396685	+	0.917955i	$0.629840\pi$
$108$		0			0
$109$	−9.05479	−	15.6833i	−0.867291	−	1.50219i	−0.864754	−	0.502196i	$-0.832526\pi$
$109$	−9.05479	−	15.6833i	−0.867291	−	1.50219i	−0.00253705	−	0.999997i	$-0.500808\pi$
$110$	4.76846	−	2.74919i	0.454655	−	0.262125i
$111$		0			0
$112$	16.1655	+	0.0667973i	1.52750	+	0.00631176i
$113$		−	4.04373i		−	0.380402i	−0.981745	−	0.190201i	$-0.939086\pi$
$113$		−	4.04373i		−	0.380402i	0.981745	−	0.190201i	$-0.0609140\pi$
$114$		0			0
$115$	−0.00691983	+	11.3433i	−0.000645277	+	1.05777i
$116$	12.8406	+	22.2405i	1.19222	+	2.06498i
$117$		0			0
$118$			4.57160i			0.420850i
$119$	9.48555	+	5.52887i	0.869539	+	0.506831i
$120$		0			0
$121$	5.02163	−	8.69771i	0.456511	−	0.790701i
$122$	1.43026	−	0.825761i	0.129490	−	0.0747608i
$123$		0			0
$124$	1.37186	−	2.37613i	0.123196	−	0.213383i
$125$	−11.1803	−	0.0204612i	−0.999998	−	0.00183011i
$126$		0			0
$127$		−	6.85023i		−	0.607860i	−0.952694	−	0.303930i	$-0.901701\pi$
$127$		−	6.85023i		−	0.607860i	0.952694	−	0.303930i	$-0.0982989\pi$
$128$	−12.9987	−	7.50481i	−1.14893	−	0.663337i
$129$		0			0
$130$	28.9790	+	0.0176782i	2.54163	+	0.00155048i
$131$	−2.01270	+	3.48610i	−0.175850	+	0.304582i	−0.940455	−	0.339918i	$-0.889601\pi$
$131$	−2.01270	+	3.48610i	−0.175850	+	0.304582i	0.764605	+	0.644499i	$0.222934\pi$
$132$		0			0
$133$	6.08521	+	0.0251446i	0.527655	+	0.00218031i
$134$	−23.3031			−2.01308
$135$		0			0
$136$	12.1829	+	21.1014i	1.04468	+	1.80943i
$137$	9.72709	−	5.61594i	0.831041	−	0.479802i	−0.0231680	−	0.999732i	$-0.507375\pi$
$137$	9.72709	−	5.61594i	0.831041	−	0.479802i	0.854209	+	0.519930i	$0.174042\pi$
$138$		0			0
$139$	4.98991			0.423238			0.211619	−	0.977352i	$-0.432126\pi$
$139$	4.98991			0.423238			0.211619	+	0.977352i	$0.432126\pi$
$140$	25.6351	+	0.121565i	2.16656	+	0.0102741i
$141$		0			0
$142$	−11.9727	−	6.91243i	−1.00473	−	0.580078i
$143$	−4.36232	+	2.51858i	−0.364795	+	0.210615i
$144$		0			0
$145$	6.61919	+	11.4809i	0.549693	+	0.953440i
$146$	−13.5344			−1.12012
$147$		0			0
$148$			39.2370i			3.22526i
$149$	7.24712	−	12.5524i	0.593707	−	1.02833i	−0.400021	−	0.916506i	$-0.630997\pi$
$149$	7.24712	−	12.5524i	0.593707	−	1.02833i	0.993728	−	0.111825i	$-0.0356695\pi$
$150$		0			0
$151$	−3.94346	−	6.83028i	−0.320914	−	0.555840i	0.659763	−	0.751474i	$-0.270657\pi$
$151$	−3.94346	−	6.83028i	−0.320914	−	0.555840i	−0.980677	+	0.195634i	$0.937324\pi$
$152$	11.6955	+	6.75240i	0.948631	+	0.547692i
$153$		0			0
$154$	−5.65354	+	3.23300i	−0.455575	+	0.260522i
$155$	0.708674	−	1.22573i	0.0569221	−	0.0984531i
$156$		0			0
$157$	−5.67792	+	3.27815i	−0.453147	+	0.261625i	−0.709159	−	0.705049i	$-0.750925\pi$
$157$	−5.67792	+	3.27815i	−0.453147	+	0.261625i	0.256011	+	0.966674i	$0.417592\pi$
$158$	23.7272	−	13.6989i	1.88763	−	1.08983i
$159$		0			0
$160$	7.03316	+	4.06632i	0.556020	+	0.321471i
$161$	0.0554586	−	13.4215i	0.00437075	−	1.05776i
$162$		0			0
$163$	10.6138	+	6.12790i	0.831340	+	0.479974i	0.854311	−	0.519762i	$-0.173979\pi$
$163$	10.6138	+	6.12790i	0.831340	+	0.479974i	−0.0229712	+	0.999736i	$0.507313\pi$
$164$	−5.75240	−	9.96346i	−0.449187	−	0.778015i
$165$		0			0
$166$	−8.33822	+	14.4422i	−0.647171	+	1.12093i
$167$		−	2.13239i		−	0.165009i	−0.996591	−	0.0825047i	$-0.973708\pi$
$167$		−	2.13239i		−	0.165009i	0.996591	−	0.0825047i	$-0.0262920\pi$
$168$		0			0
$169$	−13.5201			−1.04001
$170$	11.6635	+	20.2303i	0.894553	+	1.55160i
$171$		0			0
$172$	−1.29446	+	0.747358i	−0.0987017	+	0.0569855i
$173$	10.0013	+	5.77427i	0.760387	+	0.439009i	0.829435	−	0.558604i	$-0.188663\pi$
$173$	10.0013	+	5.77427i	0.760387	+	0.439009i	−0.0690479	+	0.997613i	$0.521996\pi$
$174$		0			0
$175$	13.2286	+	0.0708017i	0.999986	+	0.00535211i
$176$	−5.97645			−0.450492
$177$		0			0
$178$	35.5482	−	20.5238i	2.66445	−	1.53832i
$179$	−4.44978	−	7.70725i	−0.332592	−	0.576067i	0.650427	−	0.759569i	$-0.274590\pi$
$179$	−4.44978	−	7.70725i	−0.332592	−	0.576067i	−0.983019	+	0.183502i	$0.941257\pi$
$180$		0			0
$181$	−3.17940			−0.236323			−0.118161	−	0.992994i	$-0.537700\pi$
$181$	−3.17940			−0.236323			−0.118161	+	0.992994i	$0.537700\pi$
$182$	−34.2881	−	0.141681i	−2.54160	−	0.0105021i
$183$		0			0
$184$	14.8930	−	25.7954i	1.09793	−	1.90167i
$185$	−0.0123518	+	20.2476i	−0.000908123	+	1.48864i
$186$		0			0
$187$	−3.51523	−	2.02952i	−0.257059	−	0.148413i
$188$			18.3659i			1.33947i
$189$		0			0
$190$	11.2048	+	6.47821i	0.812881	+	0.469979i
$191$	−0.311309	+	0.539203i	−0.0225255	+	0.0390154i	−0.877068	−	0.480365i	$-0.840504\pi$
$191$	−0.311309	+	0.539203i	−0.0225255	+	0.0390154i	0.854543	+	0.519381i	$0.173837\pi$
$192$		0			0
$193$	−13.1529	+	7.59383i	−0.946767	+	0.546616i	−0.892075	−	0.451887i	$-0.850751\pi$
$193$	−13.1529	+	7.59383i	−0.946767	+	0.546616i	−0.0546916	+	0.998503i	$0.517418\pi$
$194$	1.93581	−	3.35292i	0.138983	−	0.240726i
$195$		0			0
$196$	−30.3312	−	0.250666i	−2.16651	−	0.0179047i
$197$		−	23.9410i		−	1.70573i	−0.522136	−	0.852863i	$-0.674864\pi$
$197$		−	23.9410i		−	1.70573i	0.522136	−	0.852863i	$-0.325136\pi$
$198$		0			0
$199$	6.97662	+	12.0839i	0.494560	+	0.856602i	0.999980	−	0.00627071i	$-0.00199604\pi$
$199$	6.97662	+	12.0839i	0.494560	+	0.856602i	−0.505421	+	0.862873i	$0.668663\pi$
$200$	25.4069	+	14.7101i	1.79654	+	1.04016i
$201$		0			0
$202$			13.8817i			0.976714i
$203$	−7.78403	−	13.6119i	−0.546332	−	0.955370i
$204$		0			0
$205$	−2.96530	−	5.14330i	−0.207106	−	0.359224i
$206$	20.7886	+	36.0069i	1.44841	+	2.50872i
$207$		0			0
$208$	−27.2498	−	15.7327i	−1.88943	−	1.09086i
$209$	−2.24973			−0.155617
$210$		0			0
$211$	4.82315			0.332040			0.166020	−	0.986122i	$-0.446908\pi$
$211$	4.82315			0.332040			0.166020	+	0.986122i	$0.446908\pi$
$212$	−28.6446	−	16.5380i	−1.96732	−	1.13583i
$213$		0			0
$214$	−3.00505	−	5.20489i	−0.205421	−	0.355799i
$215$	−0.668222	+	0.385255i	−0.0455724	+	0.0262742i
$216$		0			0
$217$	−0.843617	+	1.44734i	−0.0572685	+	0.0982521i
$218$			45.5742i			3.08667i
$219$		0			0
$220$	−9.47742	−	0.00578157i	−0.638967	−	0.000389793i
$221$	−10.6852	−	18.5073i	−0.718762	−	1.24493i
$222$		0			0
$223$		−	15.8227i		−	1.05956i	−0.848134	−	0.529782i	$-0.822274\pi$
$223$		−	15.8227i		−	1.05956i	0.848134	−	0.529782i	$-0.177726\pi$
$224$	−8.30475	−	4.84061i	−0.554884	−	0.323427i
$225$		0			0
$226$	−5.08818	+	8.81299i	−0.338461	+	0.586232i
$227$	18.7913	−	10.8492i	1.24722	−	0.720084i	0.276667	−	0.960966i	$-0.410770\pi$
$227$	18.7913	−	10.8492i	1.24722	−	0.720084i	0.970554	+	0.240882i	$0.0774368\pi$
$228$		0			0
$229$	−1.03844	+	1.79864i	−0.0686223	+	0.118857i	−0.898295	−	0.439393i	$-0.855194\pi$
$229$	−1.03844	+	1.79864i	−0.0686223	+	0.118857i	0.829673	+	0.558250i	$0.188527\pi$
$230$	14.2882	−	24.7131i	0.942139	−	1.62954i
$231$		0			0
$232$		−	34.7990i		−	2.28467i
$233$	5.85348	+	3.37951i	0.383474	+	0.221399i	0.679329	−	0.733834i	$-0.262271\pi$
$233$	5.85348	+	3.37951i	0.383474	+	0.221399i	−0.295854	+	0.955233i	$0.595604\pi$
$234$		0			0
$235$	−0.00578157	+	9.47742i	−0.000377148	+	0.618238i
$236$	3.93581	−	6.81702i	0.256199	−	0.443750i
$237$		0			0
$238$	−13.7161	−	23.9853i	−0.889082	−	1.55474i
$239$	−2.90478			−0.187894			−0.0939472	−	0.995577i	$-0.529949\pi$
$239$	−2.90478			−0.187894			−0.0939472	+	0.995577i	$0.529949\pi$
$240$		0			0
$241$	4.44875	+	7.70546i	0.286569	+	0.496352i	0.972988	−	0.230854i	$-0.0741519\pi$
$241$	4.44875	+	7.70546i	0.286569	+	0.496352i	−0.686419	+	0.727206i	$0.740819\pi$
$242$	−21.8885	+	12.6373i	−1.40705	+	0.812358i
$243$		0			0
$244$	−2.84367			−0.182047
$245$	−15.6519	−	0.138901i	−0.999961	−	0.00887404i
$246$		0			0
$247$	−10.2577	−	5.92227i	−0.652680	−	0.376825i
$248$	−3.21974	+	1.85892i	−0.204454	+	0.118042i
$249$		0			0
$250$	24.3409	+	14.1127i	1.53945	+	0.892564i
$251$	21.1747			1.33653			0.668267	−	0.743921i	$-0.267036\pi$
$251$	21.1747			1.33653			0.668267	+	0.743921i	$0.267036\pi$
$252$		0			0
$253$			4.96196i			0.311956i
$254$	−8.61958	+	14.9295i	−0.540840	+	0.936763i
$255$		0			0
$256$	15.8096	+	27.3830i	0.988097	+	1.71143i
$257$	5.39917	+	3.11721i	0.336791	+	0.194446i	0.658852	−	0.752273i	$-0.271042\pi$
$257$	5.39917	+	3.11721i	0.336791	+	0.194446i	−0.322061	+	0.946719i	$0.604376\pi$
$258$		0			0
$259$	0.0989929	−	23.9571i	0.00615112	−	1.48862i
$260$	−43.1973	−	24.9751i	−2.67898	−	1.54889i
$261$		0			0
$262$	8.77304	−	5.06512i	0.542000	−	0.312924i
$263$	−24.2903	+	14.0240i	−1.49780	+	0.864756i	−0.999997	−	0.00253231i	$-0.999194\pi$
$263$	−24.2903	+	14.0240i	−1.49780	+	0.864756i	−0.497805	+	0.867289i	$0.665861\pi$
$264$		0			0
$265$	−14.7764	−	8.54318i	−0.907707	−	0.524803i
$266$	−13.2306	−	7.71176i	−0.811221	−	0.472839i
$267$		0			0
$268$	34.7487	+	20.0622i	2.12262	+	1.22549i
$269$	−3.70915	−	6.42444i	−0.226151	−	0.391705i	0.730513	−	0.682899i	$-0.239281\pi$
$269$	−3.70915	−	6.42444i	−0.226151	−	0.391705i	−0.956664	+	0.291194i	$0.905948\pi$
$270$		0			0
$271$	15.6058	−	27.0300i	0.947985	−	1.64196i	0.198323	−	0.980137i	$-0.436450\pi$
$271$	15.6058	−	27.0300i	0.947985	−	1.64196i	0.749662	−	0.661821i	$-0.230216\pi$
$272$		−	25.3553i		−	1.53739i
$273$		0			0
$274$	−28.2659			−1.70761
$275$	−4.89067	−	0.00596698i	−0.294919	−	0.000359822i
$276$		0			0
$277$	−10.7843	+	6.22629i	−0.647963	+	0.374102i	−0.787675	−	0.616090i	$-0.788716\pi$
$277$	−10.7843	+	6.22629i	−0.647963	+	0.374102i	0.139712	+	0.990192i	$0.455382\pi$
$278$	−10.8751	−	6.27875i	−0.652246	−	0.376574i
$279$		0			0
$280$	−30.0004	−	17.5109i	−1.79287	−	1.04648i
$281$	0.0409225			0.00244123			0.00122061	−	0.999999i	$-0.499611\pi$
$281$	0.0409225			0.00244123			0.00122061	+	0.999999i	$0.499611\pi$
$282$		0			0
$283$	−9.38944	+	5.42100i	−0.558144	+	0.322245i	−0.752400	−	0.658706i	$-0.771104\pi$
$283$	−9.38944	+	5.42100i	−0.558144	+	0.322245i	0.194256	+	0.980951i	$0.437771\pi$
$284$	11.9022	+	20.6152i	0.706264	+	1.22329i
$285$		0			0
$286$	12.6764			0.749574
$287$	3.48714	+	6.09795i	0.205839	+	0.359951i
$288$		0			0
$289$	0.110288	−	0.191024i	0.00648752	−	0.0112367i
$290$	0.0203451	−	33.3507i	0.00119471	−	1.95842i
$291$		0			0
$292$	20.1821	+	11.6521i	1.18107	+	0.681890i
$293$			29.6455i			1.73191i	0.500125	+	0.865953i	$0.333287\pi$
$293$			29.6455i			1.73191i	−0.500125	+	0.865953i	$0.666713\pi$
$294$		0			0
$295$	2.03316	−	3.51658i	0.118375	−	0.204743i
$296$	26.5838	−	46.0445i	1.54515	−	2.67628i
$297$		0			0
$298$	−31.5891	+	18.2380i	−1.82991	+	1.05650i
$299$	−13.0621	+	22.6242i	−0.755399	+	1.30839i
$300$		0			0
$301$	0.792252	−	0.453052i	0.0456646	−	0.0261135i
$302$			19.8481i			1.14213i
$303$		0			0
$304$	−7.02660	−	12.1704i	−0.403003	−	0.698022i
$305$	−1.46743		0.000895188i	−0.0840250		5.12583e-5i
$306$		0			0
$307$			31.6055i			1.80382i	0.431923	+	0.901910i	$0.357835\pi$
$307$			31.6055i			1.80382i	−0.431923	+	0.901910i	$0.642165\pi$
$308$	11.2137	+	0.0463361i	0.638962	+	0.00264024i
$309$		0			0
$310$	−3.08683	+	1.77967i	−0.175320	+	0.101078i
$311$	11.0851	+	19.2000i	0.628581	+	1.08873i	0.987837	+	0.155495i	$0.0496972\pi$
$311$	11.0851	+	19.2000i	0.628581	+	1.08873i	−0.359256	+	0.933239i	$0.616969\pi$
$312$		0			0
$313$	5.96321	+	3.44286i	0.337060	+	0.194602i	0.658971	−	0.752168i	$-0.270992\pi$
$313$	5.96321	+	3.44286i	0.337060	+	0.194602i	−0.321911	+	0.946770i	$0.604325\pi$
$314$	16.4995			0.931118
$315$		0			0
$316$	−47.1749			−2.65380
$317$	11.1186	+	6.41935i	0.624485	+	0.360547i	0.778613	−	0.627504i	$-0.215923\pi$
$317$	11.1186	+	6.41935i	0.624485	+	0.360547i	−0.154128	+	0.988051i	$0.549257\pi$
$318$		0			0
$319$	2.89853	+	5.02040i	0.162286	+	0.281088i
$320$	3.43643	+	5.96047i	0.192102	+	0.333200i
$321$		0			0
$322$	−17.0090	+	29.1812i	−0.947872	+	1.62621i
$323$		−	9.54453i		−	0.531072i
$324$		0			0
$325$	−22.2834	−	12.9016i	−1.23606	−	0.715653i
$326$	−15.4214	−	26.7106i	−0.854110	−	1.47936i
$327$		0			0
$328$			15.5895i			0.860784i
$329$	0.0463361	−	11.2137i	0.00255459	−	0.618233i
$330$		0			0
$331$	4.26678	−	7.39028i	0.234524	−	0.406207i	−0.724611	−	0.689159i	$-0.757980\pi$
$331$	4.26678	−	7.39028i	0.234524	−	0.406207i	0.959134	+	0.282952i	$0.0913137\pi$
$332$	24.8673	−	14.3572i	1.36477	−	0.787952i
$333$		0			0
$334$	−2.68317	+	4.64738i	−0.146816	+	0.254293i
$335$	17.9252	+	10.3637i	0.979360	+	0.566231i
$336$		0			0
$337$		−	29.1131i		−	1.58589i	−0.609292	−	0.792946i	$-0.708546\pi$
$337$		−	29.1131i		−	1.58589i	0.609292	−	0.792946i	$-0.291454\pi$
$338$	29.4660	+	17.0122i	1.60274	+	0.925343i
$339$		0			0
$340$	0.0245285	−	40.2082i	0.00133024	−	2.18060i
$341$	0.309672	−	0.536367i	0.0167697	−	0.0290459i
$342$		0			0
$343$	18.5188	+	0.229575i	0.999923	+	0.0123959i
$344$	2.02540			0.109202
$345$		0			0
$346$	−14.5314	−	25.1691i	−0.781213	−	1.35310i
$347$	11.6418	−	6.72137i	0.624962	−	0.360822i	−0.153836	−	0.988096i	$-0.549163\pi$
$347$	11.6418	−	6.72137i	0.624962	−	0.360822i	0.778798	+	0.627274i	$0.215829\pi$
$348$		0			0
$349$	24.7397			1.32429			0.662144	−	0.749377i	$-0.269647\pi$
$349$	24.7397			1.32429			0.662144	+	0.749377i	$0.269647\pi$
$350$	−28.7415	−	16.7997i	−1.53630	−	0.897981i
$351$		0			0
$352$	3.07764	+	1.77687i	0.164039	+	0.0947077i
$353$	14.5103	−	8.37751i	0.772303	−	0.445890i	−0.0613923	−	0.998114i	$-0.519554\pi$
$353$	14.5103	−	8.37751i	0.772303	−	0.445890i	0.833696	+	0.552224i	$0.186221\pi$
$354$		0			0
$355$	6.13544	+	10.6419i	0.325635	+	0.564813i
$356$	−70.6777			−3.74591
$357$		0			0
$358$			22.3965i			1.18369i
$359$	16.2462	−	28.1393i	0.857442	−	1.48513i	−0.0169190	−	0.999857i	$-0.505386\pi$
$359$	16.2462	−	28.1393i	0.857442	−	1.48513i	0.874361	−	0.485276i	$-0.161281\pi$
$360$		0			0
$361$	6.85497	+	11.8732i	0.360788	+	0.624903i
$362$	6.92925	+	4.00060i	0.364193	+	0.210267i
$363$		0			0
$364$	51.0073	+	29.7308i	2.67351	+	1.55832i
$365$	10.4110	+	6.01926i	0.544936	+	0.315062i
$366$		0			0
$367$	20.7516	−	11.9809i	1.08322	−	0.625400i	0.151460	−	0.988463i	$-0.451603\pi$
$367$	20.7516	−	11.9809i	1.08322	−	0.625400i	0.931764	+	0.363064i	$0.118269\pi$
$368$	−26.8429	+	15.4978i	−1.39928	+	0.807877i
$369$		0			0
$370$	25.5043	−	44.1126i	1.32591	−	2.29331i
$371$	17.4480	+	10.1699i	0.905853	+	0.527997i
$372$		0			0
$373$	−9.59160	−	5.53771i	−0.496634	−	0.286732i	0.230688	−	0.973028i	$-0.425902\pi$
$373$	−9.59160	−	5.53771i	−0.496634	−	0.286732i	−0.727323	+	0.686296i	$0.759236\pi$
$374$	5.10744	+	8.84635i	0.264100	+	0.457434i
$375$		0			0
$376$	12.4432	−	21.5523i	0.641710	−	1.11147i
$377$			30.5208i			1.57190i
$378$		0			0
$379$	32.7423			1.68186			0.840929	−	0.541145i	$-0.182009\pi$
$379$	32.7423			1.68186			0.840929	+	0.541145i	$0.182009\pi$
$380$	−11.1310	−	19.3066i	−0.571006	−	0.990406i
$381$		0			0
$382$	1.35695	−	0.783435i	0.0694275	−	0.0400840i
$383$	−20.1371	−	11.6262i	−1.02896	−	0.594069i	−0.112271	−	0.993678i	$-0.535813\pi$
$383$	−20.1371	−	11.6262i	−1.02896	−	0.594069i	−0.916686	+	0.399609i	$0.869146\pi$
$384$		0			0
$385$	5.78666	+	0.0274411i	0.294916	+	0.00139853i
$386$	38.2210			1.94540
$387$		0			0
$388$	−5.77323	+	3.33317i	−0.293091	+	0.169216i
$389$	18.8131	+	32.5852i	0.953861	+	1.65214i	0.736954	+	0.675943i	$0.236263\pi$
$389$	18.8131	+	32.5852i	0.953861	+	1.65214i	0.216907	+	0.976192i	$0.430403\pi$
$390$		0			0
$391$	−21.0513			−1.06461
$392$	35.4237	+	20.8441i	1.78917	+	1.05279i
$393$		0			0
$394$	−30.1247	+	52.1775i	−1.51766	+	2.62867i
$395$	−24.3439	−	0.0148507i	−1.22487	−	0.000747218i
$396$		0			0
$397$	−0.0498605	−	0.0287870i	−0.00250243	−	0.00144478i	0.498748	−	0.866747i	$-0.333793\pi$
$397$	−0.0498605	−	0.0287870i	−0.00250243	−	0.00144478i	−0.501251	+	0.865302i	$0.667127\pi$
$398$		−	35.1144i		−	1.76013i
$399$		0			0
$400$	−15.2428	−	26.4759i	−0.762142	−	1.32380i
$401$	−4.53797	+	7.85999i	−0.226615	+	0.392509i	−0.956803	−	0.290738i	$-0.906099\pi$
$401$	−4.53797	+	7.85999i	−0.226615	+	0.392509i	0.730188	+	0.683247i	$0.239433\pi$
$402$		0			0
$403$	2.82391	−	1.63039i	0.140669	−	0.0812153i
$404$	11.9511	−	20.6999i	0.594590	−	1.02986i
$405$		0			0
$406$	−0.163055	+	39.4607i	−0.00809228	+	1.95840i
$407$			8.85704i			0.439027i
$408$		0			0
$409$	8.30602	+	14.3865i	0.410706	+	0.711364i	0.994967	−	0.100202i	$-0.0319488\pi$
$409$	8.30602	+	14.3865i	0.410706	+	0.711364i	−0.584261	+	0.811566i	$0.698615\pi$
$410$	−0.00911433	+	14.9406i	−0.000450125	+	0.737865i
$411$		0			0
$412$		−	71.5897i		−	3.52697i
$413$	−2.42031	+	4.15237i	−0.119096	+	0.204325i
$414$		0			0
$415$	12.8369	−	7.40097i	0.630140	−	0.363299i
$416$	9.35504	+	16.2034i	0.458669	+	0.794437i
$417$		0			0
$418$	4.90310	+	2.83081i	0.239818	+	0.138459i
$419$	−29.8759			−1.45953			−0.729766	−	0.683697i	$-0.760371\pi$
$419$	−29.8759			−1.45953			−0.729766	+	0.683697i	$0.760371\pi$
$420$		0			0
$421$	−19.3201			−0.941602			−0.470801	−	0.882239i	$-0.656035\pi$
$421$	−19.3201			−0.941602			−0.470801	+	0.882239i	$0.656035\pi$
$422$	−10.5117	−	6.06893i	−0.511701	−	0.295431i
$423$		0			0
$424$	22.4096	+	38.8145i	1.08831	+	1.88500i
$425$	0.0253151	−	20.7488i	0.00122796	−	1.00647i
$426$		0			0
$427$	1.73628	+	0.00717444i	0.0840243	+	0.000347195i
$428$			10.3485i			0.500213i
$429$		0			0
$430$	1.94110	+	0.00118414i	0.0936082	+	5.71044e-5i
$431$	−10.9981	−	19.0493i	−0.529761	−	0.917572i	−0.999397	−	0.0347127i	$-0.988948\pi$
$431$	−10.9981	−	19.0493i	−0.529761	−	0.917572i	0.469637	−	0.882860i	$-0.344385\pi$
$432$		0			0
$433$		−	2.72706i		−	0.131054i	−0.997851	−	0.0655272i	$-0.979127\pi$
$433$		−	2.72706i		−	0.131054i	0.997851	−	0.0655272i	$-0.0208729\pi$
$434$	3.65978	−	2.09286i	0.175675	−	0.100460i
$435$		0			0
$436$	39.2360	−	67.9587i	1.87906	−	3.25463i
$437$	−10.1045	+	5.83385i	−0.483365	+	0.279071i
$438$		0			0
$439$	−3.77183	+	6.53300i	−0.180020	+	0.311803i	−0.941887	−	0.335930i	$-0.890949\pi$
$439$	−3.77183	+	6.53300i	−0.180020	+	0.311803i	0.761867	+	0.647733i	$0.224283\pi$
$440$	11.1178	+	6.42792i	0.530021	+	0.306439i
$441$		0			0
$442$			53.7802i			2.55806i
$443$	−9.03987	−	5.21917i	−0.429497	−	0.247970i	0.269635	−	0.962963i	$-0.413097\pi$
$443$	−9.03987	−	5.21917i	−0.429497	−	0.247970i	−0.699132	+	0.714992i	$0.746430\pi$
$444$		0			0
$445$	−36.4721	−	0.0222493i	−1.72894	−	0.00105472i
$446$	−19.9095	+	34.4843i	−0.942743	+	1.63288i
$447$		0			0
$448$	−4.04118	−	7.06680i	−0.190928	−	0.333875i
$449$	−1.73107			−0.0816944			−0.0408472	−	0.999165i	$-0.513006\pi$
$449$	−1.73107			−0.0816944			−0.0408472	+	0.999165i	$0.513006\pi$
$450$		0			0
$451$	−1.29850	−	2.24907i	−0.0611440	−	0.105905i
$452$	15.1747	−	8.76109i	0.713756	−	0.412087i
$453$		0			0
$454$	−54.6055			−2.56276
$455$	26.3122	+	15.3582i	1.23353	+	0.720002i
$456$		0			0
$457$	26.7268	+	15.4307i	1.25023	+	0.721819i	0.971154	−	0.238452i	$-0.0766398\pi$
$457$	26.7268	+	15.4307i	1.25023	+	0.721819i	0.279072	+	0.960270i	$0.409973\pi$
$458$	4.52642	−	2.61333i	0.211506	−	0.122113i
$459$		0			0
$460$	−42.5823	+	24.5503i	−1.98541	+	1.14466i
$461$	−10.7294			−0.499718			−0.249859	−	0.968282i	$-0.580384\pi$
$461$	−10.7294			−0.499718			−0.249859	+	0.968282i	$0.580384\pi$
$462$		0			0
$463$			11.1060i			0.516141i	0.966126	+	0.258071i	$0.0830867\pi$
$463$			11.1060i			0.516141i	−0.966126	+	0.258071i	$0.916913\pi$
$464$	−18.1060	+	31.3606i	−0.840552	+	1.45588i
$465$		0			0
$466$	−8.50481	−	14.7308i	−0.393978	−	0.682389i
$467$	−23.8932	−	13.7947i	−1.10564	−	0.638344i	−0.167946	−	0.985796i	$-0.553714\pi$
$467$	−23.8932	−	13.7947i	−1.10564	−	0.638344i	−0.937698	+	0.347452i	$0.887047\pi$
$468$		0			0
$469$	−21.1661	−	12.3372i	−0.977360	−	0.569677i
$470$	11.9379	−	20.6480i	0.550656	−	0.952422i
$471$		0			0
$472$	−9.23733	+	5.33317i	−0.425182	+	0.245479i
$473$	−0.292201	+	0.168702i	−0.0134354	+	0.00775694i
$474$		0			0
$475$	−5.73788	−	9.96636i	−0.263272	−	0.457288i
$476$	−0.196582	+	47.5746i	−0.00901034	+	2.18058i
$477$		0			0
$478$	6.33074	+	3.65505i	0.289561	+	0.167178i
$479$	5.00869	+	8.67530i	0.228853	+	0.396385i	0.957468	−	0.288538i	$-0.0931692\pi$
$479$	5.00869	+	8.67530i	0.228853	+	0.396385i	−0.728616	+	0.684923i	$0.759836\pi$
$480$		0			0
$481$	−23.3156	+	40.3839i	−1.06310	+	1.84135i
$482$		−	22.3913i		−	1.01989i
$483$		0			0
$484$	43.5192			1.97814
$485$	−2.98023	+	1.71822i	−0.135325	+	0.0780202i
$486$		0			0
$487$	26.6165	−	15.3671i	1.20611	−	0.696348i	0.244203	−	0.969724i	$-0.421474\pi$
$487$	26.6165	−	15.3671i	1.20611	−	0.696348i	0.961907	+	0.273376i	$0.0881403\pi$
$488$	3.33704	+	1.92664i	0.151061	+	0.0872150i
$489$		0			0
$490$	33.9372	+	19.9973i	1.53313	+	0.903386i
$491$	−4.14054			−0.186860			−0.0934301	−	0.995626i	$-0.529783\pi$
$491$	−4.14054			−0.186860			−0.0934301	+	0.995626i	$0.529783\pi$
$492$		0			0
$493$	−21.2992	+	12.2971i	−0.959268	+	0.553833i
$494$	14.9039	+	25.8143i	0.670557	+	1.16144i
$495$		0			0
$496$	3.86881			0.173715
$497$	−7.21516	−	12.6171i	−0.323644	−	0.565956i
$498$		0			0
$499$	−0.774139	+	1.34085i	−0.0346552	+	0.0600246i	−0.882833	−	0.469687i	$-0.844367\pi$
$499$	−0.774139	+	1.34085i	−0.0346552	+	0.0600246i	0.848178	+	0.529712i	$0.177700\pi$
$500$	−24.1464	−	42.0000i	−1.07986	−	1.87830i
$501$		0			0
$502$	−46.1486	−	26.6439i	−2.05971	−	1.18918i
$503$		−	15.1658i		−	0.676210i	−0.941108	−	0.338105i	$-0.890214\pi$
$503$		−	15.1658i		−	0.676210i	0.941108	−	0.338105i	$-0.109786\pi$
$504$		0			0
$505$	6.17370	−	10.6781i	0.274726	−	0.475170i
$506$	6.24359	−	10.8142i	0.277561	−	0.480750i
$507$		0			0
$508$	25.7064	−	14.8416i	1.14054	−	0.658491i
$509$	10.2327	−	17.7236i	0.453558	−	0.785586i	−0.545046	−	0.838406i	$-0.683488\pi$
$509$	10.2327	−	17.7236i	0.453558	−	0.785586i	0.998604	+	0.0528204i	$0.0168211\pi$
$510$		0			0
$511$	−12.2933	−	7.16542i	−0.543823	−	0.316980i
$512$		−	49.5528i		−	2.18994i
$513$		0			0
$514$	−7.84471	−	13.5874i	−0.346015	−	0.599316i
$515$	0.0225364	−	36.9428i	0.000993074	−	1.62789i
$516$		0			0
$517$			4.14576i			0.182330i
$518$	−30.3608	+	52.0882i	−1.33398	+	2.28862i
$519$		0			0
$520$	33.7708	+	58.5752i	1.48095	+	2.56869i
$521$	1.37337	+	2.37875i	0.0601685	+	0.104215i	0.894541	−	0.446987i	$-0.147503\pi$
$521$	1.37337	+	2.37875i	0.0601685	+	0.104215i	−0.834372	+	0.551202i	$0.814170\pi$
$522$		0			0
$523$	−34.5258	−	19.9335i	−1.50971	−	0.871629i	−0.999936	−	0.0113184i	$-0.996397\pi$
$523$	−34.5258	−	19.9335i	−1.50971	−	0.871629i	−0.509770	−	0.860311i	$-0.670269\pi$
$524$	−17.4427			−0.761990
$525$		0			0
$526$	70.5850			3.07765
$527$	2.27556	+	1.31379i	0.0991247	+	0.0572297i
$528$		0			0
$529$	1.36705	+	2.36780i	0.0594370	+	0.102948i
$530$	21.4542	+	37.2122i	0.931911	+	1.61639i
$531$		0			0
$532$	13.0898	+	22.8901i	0.567514	+	0.992411i
$533$		−	13.6729i		−	0.592239i
$534$		0			0
$535$	−0.00325770	+	5.34017i	−0.000140843	+	0.230876i
$536$	−27.1851	−	47.0859i	−1.17422	−	2.03380i
$537$		0			0
$538$			18.6688i			0.804867i
$539$	−6.84671	−	0.0565834i	−0.294909	−	0.00243722i
$540$		0			0
$541$	−13.2493	+	22.9485i	−0.569633	+	0.986633i	0.426969	+	0.904266i	$0.359581\pi$
$541$	−13.2493	+	22.9485i	−0.569633	+	0.986633i	−0.996602	+	0.0823667i	$0.973752\pi$
$542$	−68.0232	+	39.2732i	−2.92185	+	1.68693i
$543$		0			0
$544$	−7.53844	+	13.0570i	−0.323208	+	0.559813i
$545$	20.2685	−	35.0567i	0.868207	−	1.50166i
$546$		0			0
$547$		−	12.9090i		−	0.551950i	−0.961165	−	0.275975i	$-0.910999\pi$
$547$		−	12.9090i		−	0.551950i	0.961165	−	0.275975i	$-0.0890008\pi$
$548$	42.1492	+	24.3348i	1.80052	+	1.03953i
$549$		0			0
$550$	10.6513	+	6.16689i	0.454174	+	0.262957i
$551$	−6.81568	+	11.8051i	−0.290358	+	0.502914i
$552$		0			0
$553$	28.8038	+	0.119020i	1.22486	+	0.00506124i
$554$	31.3379			1.33142
$555$		0			0
$556$	10.8111	+	18.7253i	0.458492	+	0.794131i
$557$	6.22247	−	3.59254i	0.263654	−	0.152221i	−0.362346	−	0.932044i	$-0.618024\pi$
$557$	6.22247	−	3.59254i	0.263654	−	0.152221i	0.626000	+	0.779823i	$0.284691\pi$
$558$		0			0
$559$	−1.77640			−0.0751336
$560$	17.9251	+	31.3900i	0.757474	+	1.32647i
$561$		0			0
$562$	−0.0891873	−	0.0514923i	−0.00376214	−	0.00217207i
$563$	−2.06720	+	1.19350i	−0.0871220	+	0.0502999i	−0.542928	−	0.839779i	$-0.682684\pi$
$563$	−2.06720	+	1.19350i	−0.0871220	+	0.0502999i	0.455806	+	0.890079i	$0.349351\pi$
$564$		0			0
$565$	7.83341	−	4.51625i	0.329554	−	0.190000i
$566$	27.2847			1.14686
$567$		0			0
$568$		−	32.2558i		−	1.35342i
$569$	−14.9271	+	25.8545i	−0.625776	+	1.08388i	0.362615	+	0.931939i	$0.381884\pi$
$569$	−14.9271	+	25.8545i	−0.625776	+	1.08388i	−0.988390	+	0.151936i	$0.951449\pi$
$570$		0			0
$571$	9.73170	+	16.8558i	0.407259	+	0.705393i	0.994582	−	0.103960i	$-0.0331513\pi$
$571$	9.73170	+	16.8558i	0.407259	+	0.705393i	−0.587322	+	0.809353i	$0.699818\pi$
$572$	−18.9027	−	10.9135i	−0.790361	−	0.456315i
$573$		0			0
$574$	0.0730463	−	17.6778i	0.00304889	−	0.737859i
$575$	−21.9817	+	12.6554i	−0.916699	+	0.527766i
$576$		0			0
$577$	−3.43108	+	1.98094i	−0.142838	+	0.0824675i	−0.569716	−	0.821842i	$-0.692947\pi$
$577$	−3.43108	+	1.98094i	−0.142838	+	0.0824675i	0.426878	+	0.904309i	$0.359613\pi$
$578$	−0.480727	+	0.277548i	−0.0199956	+	0.0115445i
$579$		0			0
$580$	−28.7428	+	49.7139i	−1.19348	+	2.06426i
$581$	−15.2196	+	8.70339i	−0.631416	+	0.361078i
$582$		0			0
$583$	−6.46600	−	3.73315i	−0.267794	−	0.154611i
$584$	−15.7891	−	27.3475i	−0.653357	−	1.13165i
$585$		0			0
$586$	37.3026	−	64.6100i	1.54096	−	2.66901i
$587$		−	13.9419i		−	0.575446i	−0.957714	−	0.287723i	$-0.907102\pi$
$587$		−	13.9419i		−	0.575446i	0.957714	−	0.287723i	$-0.0928982\pi$
$588$		0			0
$589$	1.45634			0.0600075
$590$	−8.85599	+	5.10581i	−0.364595	+	0.210203i
$591$		0			0
$592$	−47.9143	+	27.6633i	−1.96926	+	1.13696i
$593$	33.3396	+	19.2486i	1.36909	+	0.790447i	0.990812	−	0.135243i	$-0.0431816\pi$
$593$	33.3396	+	19.2486i	1.36909	+	0.790447i	0.378282	+	0.925690i	$0.376515\pi$
$594$		0			0
$595$	−0.116420	+	24.5501i	−0.00477274	+	1.00646i
$596$	62.8061			2.57264
$597$		0			0
$598$	56.9356	−	32.8718i	2.32827	−	1.34423i
$599$	−8.74985	−	15.1552i	−0.357509	−	0.619224i	0.630035	−	0.776567i	$-0.283041\pi$
$599$	−8.74985	−	15.1552i	−0.357509	−	0.619224i	−0.987544	+	0.157343i	$0.949707\pi$
$600$		0			0
$601$	34.5192			1.40807			0.704033	−	0.710167i	$-0.251381\pi$
$601$	34.5192			1.40807			0.704033	+	0.710167i	$0.251381\pi$
$602$	−2.29672	−	0.00949025i	−0.0936074	−	0.000386794i
$603$		0			0
$604$	17.0877	−	29.5968i	0.695289	−	1.20428i
$605$	22.4574	+	0.0136998i	0.913023	+	0.000556977i
$606$		0			0
$607$	−9.45318	−	5.45780i	−0.383693	−	0.221525i	0.295731	−	0.955271i	$-0.404437\pi$
$607$	−9.45318	−	5.45780i	−0.383693	−	0.221525i	−0.679424	+	0.733746i	$0.737770\pi$
$608$			8.35639i			0.338896i
$609$		0			0
$610$	3.19703	+	1.84841i	0.129444	+	0.0748398i
$611$	−10.9135	+	18.9027i	−0.441512	+	0.764721i
$612$		0			0
$613$	22.6183	−	13.0587i	0.913543	−	0.527435i	0.0319739	−	0.999489i	$-0.489821\pi$
$613$	22.6183	−	13.0587i	0.913543	−	0.527435i	0.881570	+	0.472054i	$0.156487\pi$
$614$	39.7689	−	68.8817i	1.60494	−	2.77984i
$615$		0			0
$616$	−13.1279	−	7.65190i	−0.528938	−	0.308304i
$617$		−	11.6689i		−	0.469772i	−0.972023	−	0.234886i	$-0.924528\pi$
$617$		−	11.6689i		−	0.469772i	0.972023	−	0.234886i	$-0.0754717\pi$
$618$		0			0
$619$	−0.411816	−	0.713286i	−0.0165523	−	0.0286694i	0.857631	−	0.514266i	$-0.171936\pi$
$619$	−0.411816	−	0.713286i	−0.0165523	−	0.0286694i	−0.874183	+	0.485597i	$0.838602\pi$
$620$	6.13513	+	0.00374265i	0.246393	+	0.000150309i
$621$		0			0
$622$		−	55.7933i		−	2.23711i
$623$	43.1540	+	0.178316i	1.72893	+	0.00714408i
$624$		0			0
$625$	−12.4471	−	21.6811i	−0.497885	−	0.867243i
$626$	−8.66423	−	15.0069i	−0.346292	−	0.599796i
$627$		0			0
$628$	−24.6034	−	14.2048i	−0.981783	−	0.566833i
$629$	−37.5763			−1.49826
$630$		0			0
$631$	−20.5920			−0.819755			−0.409877	−	0.912141i	$-0.634429\pi$
$631$	−20.5920			−0.819755			−0.409877	+	0.912141i	$0.634429\pi$
$632$	55.3597	+	31.9619i	2.20209	+	1.27138i
$633$		0			0
$634$	−16.1548	−	27.9810i	−0.641590	−	1.11127i
$635$	13.2701	−	7.65070i	0.526607	−	0.303609i
$636$		0			0
$637$	−31.0688	−	18.2816i	−1.23099	−	0.724342i
$638$		−	14.5888i		−	0.577575i
$639$		0			0
$640$	0.0204744	−	33.5625i	0.000809320	−	1.32667i
$641$	14.8371	+	25.6986i	0.586029	+	1.01503i	0.994746	+	0.102371i	$0.0326429\pi$
$641$	14.8371	+	25.6986i	0.586029	+	1.01503i	−0.408717	+	0.912661i	$0.634024\pi$
$642$		0			0
$643$		−	11.1286i		−	0.438870i	−0.975627	−	0.219435i	$-0.929579\pi$
$643$		−	11.1286i		−	0.438870i	0.975627	−	0.219435i	$-0.0704214\pi$
$644$	50.4861	−	28.8706i	1.98943	−	1.13766i
$645$		0			0
$646$	−12.0098	+	20.8016i	−0.472519	+	0.818426i
$647$	9.45991	−	5.46168i	0.371907	−	0.214721i	−0.302384	−	0.953186i	$-0.597783\pi$
$647$	9.45991	−	5.46168i	0.371907	−	0.214721i	0.674291	+	0.738465i	$0.264449\pi$
$648$		0			0
$649$	0.888437	−	1.53882i	0.0348742	−	0.0604039i
$650$	32.3310	+	56.1571i	1.26813	+	2.20266i
$651$		0			0
$652$			53.1065i			2.07981i
$653$	6.21006	+	3.58538i	0.243019	+	0.140307i	0.616563	−	0.787305i	$-0.288524\pi$
$653$	6.21006	+	3.58538i	0.243019	+	0.140307i	−0.373545	+	0.927612i	$0.621858\pi$
$654$		0			0
$655$	−9.00106	−	0.00549097i	−0.351700	−	0.000214550i
$656$	8.11125	−	14.0491i	0.316691	−	0.548525i
$657$		0			0
$658$	−14.2111	+	24.3812i	−0.554007	+	0.950477i
$659$	14.1232			0.550161			0.275080	−	0.961421i	$-0.411296\pi$
$659$	14.1232			0.550161			0.275080	+	0.961421i	$0.411296\pi$
$660$		0			0
$661$	−14.4608	−	25.0469i	−0.562461	−	0.974212i	−0.997281	−	0.0736941i	$-0.976521\pi$
$661$	−14.4608	−	25.0469i	−0.562461	−	0.974212i	0.434819	−	0.900518i	$-0.356812\pi$
$662$	−18.5982	+	10.7377i	−0.722841	+	0.417333i
$663$		0			0
$664$	−38.9090			−1.50996
$665$	6.74758	+	11.8162i	0.261660	+	0.458212i
$666$		0			0
$667$	26.0372	+	15.0326i	1.00816	+	0.582063i
$668$	8.00210	−	4.62001i	0.309610	−	0.178754i
$669$		0			0
$670$	−26.0261	−	45.1421i	−1.00548	−	1.74399i
$671$	−0.641907			−0.0247806
$672$		0			0
$673$			14.4081i			0.555392i	0.960669	+	0.277696i	$0.0895709\pi$
$673$			14.4081i			0.555392i	−0.960669	+	0.277696i	$0.910429\pi$
$674$	−36.6327	+	63.4497i	−1.41104	+	2.44399i
$675$		0			0
$676$	−29.2925	−	50.7361i	−1.12663	−	1.95139i
$677$	−26.0991	−	15.0683i	−1.00307	−	0.579123i	−0.0939148	−	0.995580i	$-0.529938\pi$
$677$	−26.0991	−	15.0683i	−1.00307	−	0.579123i	−0.909155	+	0.416457i	$0.863271\pi$
$678$		0			0
$679$	3.53340	−	2.02059i	0.135599	−	0.0775430i
$680$	−27.2706	+	47.1676i	−1.04578	+	1.80880i
$681$		0			0
$682$	−1.34981	+	0.779314i	−0.0516870	+	0.0298415i
$683$	−13.4380	+	7.75842i	−0.514190	+	0.296868i	−0.734554	−	0.678550i	$-0.762609\pi$
$683$	−13.4380	+	7.75842i	−0.514190	+	0.296868i	0.220364	+	0.975418i	$0.429275\pi$
$684$		0			0
$685$	21.7428	+	12.5709i	0.830748	+	0.480309i
$686$	−40.0715	−	23.8024i	−1.52994	−	0.908780i
$687$		0			0
$688$	−1.82527	−	1.05382i	−0.0695878	−	0.0401766i
$689$	−19.6546	−	34.0427i	−0.748780	−	1.29692i
$690$		0			0
$691$	−22.8917	+	39.6496i	−0.870842	+	1.50834i	−0.00971588	+	0.999953i	$0.503093\pi$
$691$	−22.8917	+	39.6496i	−0.870842	+	1.50834i	−0.861127	+	0.508391i	$0.830241\pi$
$692$			50.0418i			1.90230i
$693$		0			0
$694$	−33.8297			−1.28416
$695$	5.57299	+	9.66632i	0.211396	+	0.366664i
$696$		0			0
$697$	9.54174	−	5.50893i	0.361419	−	0.208666i
$698$	−53.9183	−	31.1298i	−2.04084	−	1.17828i
$699$		0			0
$700$	28.3951	+	49.7954i	1.07324	+	1.88209i
$701$	−24.0419			−0.908050			−0.454025	−	0.890989i	$-0.650012\pi$
$701$	−24.0419			−0.908050			−0.454025	+	0.890989i	$0.650012\pi$
$702$		0			0
$703$	−18.0364	+	10.4133i	−0.680257	+	0.392747i
$704$	1.50481	+	2.60640i	0.0567145	+	0.0982325i
$705$		0			0
$706$	−42.1653			−1.58691
$707$	−7.34928	+	12.6087i	−0.276398	+	0.474200i
$708$		0			0
$709$	9.19854	−	15.9323i	0.345459	−	0.598352i	−0.639978	−	0.768393i	$-0.721057\pi$
$709$	9.19854	−	15.9323i	0.345459	−	0.598352i	0.985437	+	0.170041i	$0.0543901\pi$
$710$	0.0188583	−	30.9133i	0.000707738	−	1.16016i
$711$		0			0
$712$	82.9401	+	47.8855i	3.10831	+	1.79458i
$713$		−	3.21209i		−	0.120294i
$714$		0			0
$715$	−9.75100	−	5.63768i	−0.364667	−	0.210837i
$716$	19.2817	−	33.3969i	0.720590	−	1.24810i
$717$		0			0
$718$	−70.8147	+	40.8849i	−2.64278	+	1.52581i
$719$	8.12275	−	14.0690i	0.302927	−	0.524686i	−0.673870	−	0.738850i	$-0.735369\pi$
$719$	8.12275	−	14.0690i	0.302927	−	0.524686i	0.976798	+	0.214164i	$0.0687027\pi$
$720$		0			0
$721$	−0.180617	+	43.7109i	−0.00672654	+	1.62788i
$722$		−	34.5021i		−	1.28404i
$723$		0			0
$724$	−6.88844	−	11.9311i	−0.256007	−	0.443417i
$725$	−14.8479	+	25.6450i	−0.551437	+	0.952432i
$726$		0			0
$727$			42.6977i			1.58357i	0.610800	+	0.791785i	$0.290848\pi$
$727$			42.6977i			1.58357i	−0.610800	+	0.791785i	$0.709152\pi$
$728$	−39.7138	−	69.4474i	−1.47189	−	2.57389i
$729$		0			0
$730$	−15.1160	−	26.2185i	−0.559467	−	0.970392i
$731$	−0.715725	−	1.23967i	−0.0264720	−	0.0458509i
$732$		0			0
$733$	40.4538	+	23.3560i	1.49420	+	0.862674i	0.999978	−	0.00666408i	$-0.00212126\pi$
$733$	40.4538	+	23.3560i	1.49420	+	0.862674i	0.494218	+	0.869338i	$0.335455\pi$
$734$	−60.3020			−2.22579
$735$		0			0
$736$	18.4307			0.679366
$737$	7.84390	+	4.52868i	0.288934	+	0.166816i
$738$		0			0
$739$	3.52410	+	6.10393i	0.129636	+	0.224537i	0.923536	−	0.383513i	$-0.125286\pi$
$739$	3.52410	+	6.10393i	0.129636	+	0.224537i	−0.793899	+	0.608049i	$0.791952\pi$
$740$	−76.0089	+	43.8219i	−2.79414	+	1.61093i
$741$		0			0
$742$	−25.2297	−	44.1192i	−0.926212	−	1.61967i
$743$			8.55510i			0.313856i	0.987610	+	0.156928i	$0.0501591\pi$
$743$			8.55510i			0.313856i	−0.987610	+	0.156928i	$0.949841\pi$
$744$		0			0
$745$	32.4101	+	0.0197713i	1.18741	+	0.000724366i
$746$	13.9361	+	24.1380i	0.510237	+	0.883756i
$747$		0			0
$748$		−	17.5885i		−	0.643099i
$749$	0.0261087	−	6.31853i	0.000953990	−	0.230874i
$750$		0			0
$751$	1.48823	−	2.57768i	0.0543062	−	0.0940611i	−0.837594	−	0.546293i	$-0.816039\pi$
$751$	1.48823	−	2.57768i	0.0543062	−	0.0940611i	0.891901	+	0.452232i	$0.149372\pi$
$752$	−22.4275	+	12.9485i	−0.817846	+	0.472183i
$753$		0			0
$754$	38.4041	−	66.5178i	1.39859	−	2.42243i
$755$	8.82716	−	15.2676i	0.321253	−	0.555644i
$756$		0			0
$757$		−	43.6750i		−	1.58740i	−0.608313	−	0.793698i	$-0.708153\pi$
$757$		−	43.6750i		−	1.58740i	0.608313	−	0.793698i	$-0.291847\pi$
$758$	−71.3592	−	41.1993i	−2.59188	−	1.49643i
$759$		0			0
$760$	−0.0184217	+	30.1977i	−0.000668224	+	1.09538i
$761$	13.3628	−	23.1451i	0.484402	−	0.839008i	−0.515438	−	0.856927i	$-0.672371\pi$
$761$	13.3628	−	23.1451i	0.484402	−	0.839008i	0.999839	+	0.0179187i	$0.00570401\pi$
$762$		0			0
$763$	−24.1280	+	41.3949i	−0.873491	+	1.49860i
$764$	−2.69791			−0.0976071
$765$		0			0
$766$	29.2581	+	50.6766i	1.05714	+	1.83102i
$767$	8.10170	−	4.67752i	0.292535	−	0.168895i
$768$		0			0
$769$	4.04661			0.145925			0.0729623	−	0.997335i	$-0.476755\pi$
$769$	4.04661			0.145925			0.0729623	+	0.997335i	$0.476755\pi$
$770$	−12.5770	−	7.34110i	−0.453245	−	0.264555i
$771$		0			0
$772$	−56.9938	−	32.9054i	−2.05125	−	1.18429i
$773$	−5.46553	+	3.15553i	−0.196581	+	0.113496i	−0.595060	−	0.803681i	$-0.702872\pi$
$773$	−5.46553	+	3.15553i	−0.196581	+	0.113496i	0.398478	+	0.917178i	$0.369538\pi$
$774$		0			0
$775$	3.16594	+	0.00386268i	0.113724	+	0.000138752i
$776$	9.03316			0.324272
$777$		0			0
$778$		−	94.6892i		−	3.39477i
$779$	3.05333	−	5.28852i	0.109397	−	0.189481i
$780$		0			0
$781$	2.68670	+	4.65350i	0.0961376	+	0.166515i
$782$	45.8796	+	26.4886i	1.64065	+	0.947230i
$783$		0			0
$784$	−21.0783	−	37.2157i	−0.752798	−	1.32913i
$785$	−12.6917	−	7.33791i	−0.452988	−	0.261901i
$786$		0			0
$787$	−25.9595	+	14.9877i	−0.925358	+	0.534256i	−0.885340	−	0.464943i	$-0.846075\pi$
$787$	−25.9595	+	14.9877i	−0.925358	+	0.534256i	−0.0400174	+	0.999199i	$0.512741\pi$
$788$	89.8419	−	51.8702i	3.20048	−	1.84780i
$789$		0			0
$790$	53.0369	+	30.6640i	1.88697	+	1.09098i
$791$	−9.28737	+	5.31102i	−0.330221	+	0.188838i
$792$		0			0
$793$	−2.92679	−	1.68978i	−0.103933	−	0.0600060i
$794$	0.0724448	+	0.125478i	0.00257097	+	0.00445305i
$795$		0			0
$796$	−30.2309	+	52.3615i	−1.07151	+	1.85590i
$797$			0.676527i			0.0239638i	0.999928	+	0.0119819i	$0.00381405\pi$
$797$			0.676527i			0.0239638i	−0.999928	+	0.0119819i	$0.996186\pi$
$798$		0			0
$799$	−17.5885			−0.622236
$800$	−0.0221638	+	18.1659i	−0.000783608	+	0.642263i
$801$		0			0
$802$	19.7803	−	11.4202i	0.698466	−	0.403260i
$803$	4.55574	+	2.63026i	0.160769	+	0.0928198i
$804$		0			0
$805$	26.0616	−	14.8824i	0.918552	−	0.524534i
$806$	−8.20600			−0.289044
$807$		0			0
$808$	−28.0492	+	16.1942i	−0.986768	+	0.569711i
$809$	25.0612	+	43.4072i	0.881104	+	1.52612i	0.850115	+	0.526596i	$0.176532\pi$
$809$	25.0612	+	43.4072i	0.881104	+	1.52612i	0.0309881	+	0.999520i	$0.490135\pi$
$810$		0			0
$811$	−36.4884			−1.28128			−0.640641	−	0.767841i	$-0.721331\pi$
$811$	−36.4884			−1.28128			−0.640641	+	0.767841i	$0.721331\pi$
$812$	34.2159	−	58.7021i	1.20074	−	2.06004i
$813$		0			0
$814$	11.1447	−	19.3032i	0.390622	−	0.676578i
$815$	−0.0167179	+	27.4048i	−0.000585604	+	0.959949i
$816$		0			0
$817$	−0.687090	−	0.396691i	−0.0240382	−	0.0138785i
$818$		−	41.8055i		−	1.46170i
$819$		0			0
$820$	12.8764	−	22.2711i	0.449662	−	0.777741i
$821$	19.3654	−	33.5419i	0.675858	−	1.17062i	−0.300359	−	0.953826i	$-0.597107\pi$
$821$	19.3654	−	33.5419i	0.675858	−	1.17062i	0.976217	−	0.216794i	$-0.0695600\pi$
$822$		0			0
$823$	18.1702	−	10.4906i	0.633375	−	0.365679i	−0.148683	−	0.988885i	$-0.547503\pi$
$823$	18.1702	−	10.4906i	0.633375	−	0.365679i	0.782058	+	0.623206i	$0.214170\pi$
$824$	−48.5034	+	84.0104i	−1.68970	+	2.92664i
$825$		0			0
$826$	10.4998	−	6.00433i	0.365333	−	0.208917i
$827$			37.8114i			1.31483i	0.753528	+	0.657416i	$0.228350\pi$
$827$			37.8114i			1.31483i	−0.753528	+	0.657416i	$0.771650\pi$
$828$		0			0
$829$	−26.6591	−	46.1749i	−0.925908	−	1.60372i	−0.790095	−	0.612985i	$-0.789969\pi$
$829$	−26.6591	−	46.1749i	−0.925908	−	1.60372i	−0.135813	−	0.990734i	$-0.543365\pi$
$830$	−37.2896	−	0.0227480i	−1.29434	−	0.000789596i
$831$		0			0
$832$			15.8453i			0.549336i
$833$	0.240057	−	29.0474i	0.00831747	−	1.00643i
$834$		0			0
$835$	4.13081	−	2.38157i	0.142953	−	0.0824175i
$836$	−4.87423	−	8.44241i	−0.168579	−	0.291987i
$837$		0			0
$838$	65.1121	+	37.5925i	2.24926	+	1.29861i
$839$	52.6452			1.81752			0.908758	−	0.417324i	$-0.137032\pi$
$839$	52.6452			1.81752			0.908758	+	0.417324i	$0.137032\pi$
$840$		0			0
$841$	6.12510			0.211210
$842$	42.1066	+	24.3102i	1.45109	+	0.837786i
$843$		0			0
$844$	10.4498	+	18.0996i	0.359696	+	0.623012i
$845$	−15.1000	−	26.1908i	−0.519455	−	0.900991i
$846$		0			0
$847$	−26.5717	−	0.109797i	−0.913015	−	0.00377266i
$848$		−	46.6392i		−	1.60160i
$849$		0			0
$850$	−26.1632	+	45.1886i	−0.897391	+	1.54996i
$851$	22.9675	+	39.7809i	0.787316	+	1.36367i
$852$		0			0
$853$		−	5.01225i		−	0.171616i	−0.996312	−	0.0858081i	$-0.972653\pi$
$853$		−	5.01225i		−	0.171616i	0.996312	−	0.0858081i	$-0.0273472\pi$
$854$	−3.77505	−	2.20037i	−0.129180	−	0.0752953i
$855$		0			0
$856$	7.01129	−	12.1439i	0.239641	−	0.415071i
$857$	−33.2737	+	19.2106i	−1.13661	+	0.656222i	−0.945589	−	0.325364i	$-0.894513\pi$
$857$	−33.2737	+	19.2106i	−1.13661	+	0.656222i	−0.191021	+	0.981586i	$0.561180\pi$
$858$		0			0
$859$	11.6709	−	20.2146i	0.398207	−	0.689714i	−0.595298	−	0.803505i	$-0.702966\pi$
$859$	11.6709	−	20.2146i	0.398207	−	0.689714i	0.993505	+	0.113791i	$0.0362994\pi$
$860$	−2.89348	−	1.67291i	−0.0986670	−	0.0570457i
$861$		0			0
$862$			55.3553i			1.88541i
$863$	−47.0908	−	27.1879i	−1.60299	−	0.925486i	−0.990885	−	0.134707i	$-0.956991\pi$
$863$	−47.0908	−	27.1879i	−1.60299	−	0.925486i	−0.612103	−	0.790778i	$-0.709676\pi$
$864$		0			0
$865$	−0.0157532	+	25.8233i	−0.000535624	+	0.878019i
$866$	−3.43144	+	5.94342i	−0.116605	+	0.201966i
$867$		0			0
$868$	−7.25913	−	0.0299953i	−0.246391	−	0.00101811i
$869$	−10.6489			−0.361239
$870$		0			0
$871$	23.8430	+	41.2972i	0.807888	+	1.39930i
$872$	−92.0866	+	53.1662i	−3.11845	+	1.80044i
$873$		0			0
$874$	29.3627			0.993208
$875$	14.6372	+	25.7051i	0.494828	+	0.868991i
$876$		0			0
$877$	24.6434	+	14.2279i	0.832148	+	0.480441i	0.854587	−	0.519307i	$-0.173810\pi$
$877$	24.6434	+	14.2279i	0.832148	+	0.480441i	−0.0224397	+	0.999748i	$0.507143\pi$
$878$	16.4408	−	9.49211i	0.554851	−	0.320343i
$879$		0			0
$880$	−6.67482	−	11.5774i	−0.225008	−	0.390275i
$881$	6.50466			0.219148			0.109574	−	0.993979i	$-0.465051\pi$
$881$	6.50466			0.219148			0.109574	+	0.993979i	$0.465051\pi$
$882$		0			0
$883$		−	34.7640i		−	1.16990i	−0.811069	−	0.584951i	$-0.801114\pi$
$883$		−	34.7640i		−	1.16990i	0.811069	−	0.584951i	$-0.198886\pi$
$884$	46.3007	−	80.1952i	1.55726	−	2.69726i
$885$		0			0
$886$	13.1345	+	22.7496i	0.441261	+	0.764286i
$887$	25.4214	+	14.6770i	0.853566	+	0.492807i	0.861853	−	0.507159i	$-0.169304\pi$
$887$	25.4214	+	14.6770i	0.853566	+	0.492807i	−0.00828615	+	0.999966i	$0.502638\pi$
$888$		0			0
$889$	−15.7332	+	8.99707i	−0.527673	+	0.301752i
$890$	79.4601	+	45.9410i	2.66351	+	1.53995i
$891$		0			0
$892$	59.3768	−	34.2812i	1.98808	−	1.14782i
$893$	−8.44241	+	4.87423i	−0.282514	+	0.163110i
$894$		0			0
$895$	9.96053	−	17.2279i	0.332944	−	0.575864i
$896$	−0.164091	+	39.7114i	−0.00548189	+	1.32666i
$897$		0			0
$898$	3.77274	+	2.17819i	0.125898	+	0.0726872i
$899$	−1.87634	−	3.24992i	−0.0625795	−	0.108391i
$900$		0			0
$901$	15.8380	−	27.4322i	0.527640	−	0.913899i
$902$			6.53556i			0.217610i
$903$		0			0
$904$	−23.7432			−0.789688
$905$	−3.55092	−	6.15904i	−0.118036	−	0.204733i
$906$		0			0
$907$	31.4256	−	18.1436i	1.04347	−	0.602447i	0.122655	−	0.992449i	$-0.460859\pi$
$907$	31.4256	−	18.1436i	1.04347	−	0.602447i	0.920814	+	0.390002i	$0.127526\pi$
$908$	81.4259	+	47.0113i	2.70221	+	1.56012i
$909$		0			0
$910$	−38.0203	−	66.5803i	−1.26036	−	2.20711i
$911$	−51.6732			−1.71201			−0.856004	−	0.516968i	$-0.827060\pi$
$911$	−51.6732			−1.71201			−0.856004	+	0.516968i	$0.827060\pi$
$912$		0			0
$913$	5.61335	−	3.24087i	0.185775	−	0.107257i
$914$	−38.8326	−	67.2601i	−1.28447	−	2.22477i
$915$		0			0
$916$	−8.99952			−0.297353
$917$	10.6501	+	0.0440071i	0.351698	+	0.00145324i
$918$		0			0
$919$	−20.5188	+	35.5397i	−0.676854	+	1.17235i	0.299069	+	0.954231i	$0.403324\pi$
$919$	−20.5188	+	35.5397i	−0.676854	+	1.17235i	−0.975923	+	0.218114i	$0.930010\pi$
$920$	66.6035	+	0.0406306i	2.19585	+	0.00133955i
$921$		0			0
$922$	23.3839	+	13.5007i	0.770107	+	0.444621i
$923$			28.2903i			0.931187i
$924$		0			0
$925$	−39.2370	+	22.5897i	−1.29010	+	0.742745i
$926$	13.9746	−	24.2047i	0.459234	−	0.795417i
$927$		0			0
$928$	18.6478	−	10.7663i	0.612144	−	0.353421i
$929$	1.49260	−	2.58526i	0.0489706	−	0.0848196i	−0.840501	−	0.541810i	$-0.817739\pi$
$929$	1.49260	−	2.58526i	0.0489706	−	0.0848196i	0.889472	+	0.456990i	$0.151073\pi$
$930$		0			0
$931$	−7.93455	−	14.0091i	−0.260044	−	0.459131i
$932$			29.2880i			0.959361i
$933$		0			0
$934$	34.7155	+	60.1291i	1.13593	+	1.96748i
$935$	0.00553686	−	9.07628i	0.000181075	−	0.296826i
$936$		0			0
$937$			26.1169i			0.853201i	0.904440	+	0.426601i	$0.140289\pi$
$937$			26.1169i			0.853201i	−0.904440	+	0.426601i	$0.859711\pi$
$938$	30.6062	+	53.5210i	0.999327	+	1.74752i
$939$		0			0
$940$	−35.5778	+	20.5120i	−1.16042	+	0.669026i
$941$	5.10580	+	8.84351i	0.166444	+	0.288290i	0.937167	−	0.348880i	$-0.113438\pi$
$941$	5.10580	+	8.84351i	0.166444	+	0.288290i	−0.770723	+	0.637171i	$0.780105\pi$
$942$		0			0
$943$	−11.6643	−	6.73438i	−0.379842	−	0.219302i
$944$	11.0995			0.361257
$945$		0			0
$946$	0.849106			0.0276068
$947$	40.3086	+	23.2722i	1.30985	+	0.756245i	0.982072	−	0.188509i	$-0.0603653\pi$
$947$	40.3086	+	23.2722i	1.30985	+	0.756245i	0.327783	+	0.944753i	$0.393699\pi$
$948$		0			0
$949$	13.8480	+	23.9854i	0.449525	+	0.778600i
$950$	−0.0353099	+	28.9408i	−0.00114561	+	0.938964i
$951$		0			0
$952$	32.4634	−	55.6955i	1.05215	−	1.80510i
$953$			30.6348i			0.992358i	0.868220	+	0.496179i	$0.165264\pi$
$953$			30.6348i			0.992358i	−0.868220	+	0.496179i	$0.834736\pi$
$954$		0			0
$955$	−1.39222		0.000849303i	−0.0450511		2.74828e-5i
$956$	−6.29345	−	10.9006i	−0.203545	−	0.352550i
$957$		0			0
$958$		−	25.2095i		−	0.814483i
$959$	−25.6738	−	14.9646i	−0.829051	−	0.483232i
$960$		0			0
$961$	15.2995	−	26.4996i	0.493533	−	0.854825i
$962$	101.629	−	58.6757i	3.27666	−	1.89178i
$963$		0			0
$964$	−19.2772	+	33.3891i	−0.620877	+	1.07539i
$965$	−29.4004	−	16.9983i	−0.946433	−	0.547193i
$966$		0			0
$967$			57.4401i			1.84715i	0.383419	+	0.923575i	$0.374747\pi$
$967$			57.4401i			1.84715i	−0.383419	+	0.923575i	$0.625253\pi$
$968$	−51.0696	−	29.4851i	−1.64144	−	0.947686i
$969$		0			0
$970$	8.65720	+	0.00528121i	0.277966	+	0.000169569i
$971$	24.0908	−	41.7265i	0.773110	−	1.33907i	−0.162740	−	0.986669i	$-0.552033\pi$
$971$	24.0908	−	41.7265i	0.773110	−	1.33907i	0.935850	−	0.352397i	$-0.114633\pi$
$972$		0			0
$973$	−6.55373	−	11.4605i	−0.210103	−	0.367407i
$974$	−77.3449			−2.47829
$975$		0			0
$976$	−2.00488	−	3.47255i	−0.0641746	−	0.111154i
$977$	11.9099	−	6.87617i	0.381031	−	0.219988i	−0.297236	−	0.954804i	$-0.596065\pi$
$977$	11.9099	−	6.87617i	0.381031	−	0.219988i	0.678267	+	0.734816i	$0.262731\pi$
$978$		0			0
$979$	−15.9542			−0.509898
$980$	−33.3899	−	59.0367i	−1.06660	−	1.88586i
$981$		0			0
$982$	9.02399	+	5.21001i	0.287967	+	0.166258i
$983$	−33.0773	+	19.0972i	−1.05500	+	0.609106i	−0.924046	−	0.382282i	$-0.875138\pi$
$983$	−33.0773	+	19.0972i	−1.05500	+	0.609106i	−0.130957	+	0.991388i	$0.541805\pi$
$984$		0			0
$985$	46.3779	−	26.7386i	1.47772	−	0.851961i
$986$	61.8933			1.97108
$987$		0			0
$988$		−	51.3245i		−	1.63285i
$989$	−0.874937	+	1.51544i	−0.0278214	+	0.0481880i
$990$		0			0
$991$	−19.7600	−	34.2253i	−0.627697	−	1.08720i	−0.988013	−	0.154372i	$-0.950665\pi$
$991$	−19.7600	−	34.2253i	−0.627697	−	1.08720i	0.360316	−	0.932830i	$-0.382669\pi$
$992$	−1.99228	−	1.15025i	−0.0632551	−	0.0365204i
$993$		0			0
$994$	−0.151139	+	36.5768i	−0.00479382	+	1.16015i
$995$	−15.6167	+	27.0108i	−0.495082	+	0.856300i
$996$		0			0
$997$	9.98438	−	5.76448i	0.316208	−	0.182563i	−0.333493	−	0.942753i	$-0.608227\pi$
$997$	9.98438	−	5.76448i	0.316208	−	0.182563i	0.649701	+	0.760190i	$0.274894\pi$
$998$	3.37435	−	1.94818i	0.106813	−	0.0616687i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.b.289.1		16
3.2	odd	2		105.2.q.a.79.8	yes	16
5.4	even	2	inner	315.2.bf.b.289.8		16
7.2	even	3		2205.2.d.s.1324.8		8
7.4	even	3	inner	315.2.bf.b.109.8		16
7.5	odd	6		2205.2.d.o.1324.8		8
12.11	even	2		1680.2.di.d.289.5		16
15.2	even	4		525.2.i.h.226.1		8
15.8	even	4		525.2.i.k.226.4		8
15.14	odd	2		105.2.q.a.79.1	yes	16
21.2	odd	6		735.2.d.d.589.1		8
21.5	even	6		735.2.d.e.589.1		8
21.11	odd	6		105.2.q.a.4.1	✓	16
21.17	even	6		735.2.q.g.214.1		16
21.20	even	2		735.2.q.g.79.8		16
35.4	even	6	inner	315.2.bf.b.109.1		16
35.9	even	6		2205.2.d.s.1324.1		8
35.19	odd	6		2205.2.d.o.1324.1		8
60.59	even	2		1680.2.di.d.289.4		16
84.11	even	6		1680.2.di.d.529.4		16
105.2	even	12		3675.2.a.bz.1.4		4
105.23	even	12		3675.2.a.bp.1.1		4
105.32	even	12		525.2.i.h.151.1		8
105.44	odd	6		735.2.d.d.589.8		8
105.47	odd	12		3675.2.a.cb.1.4		4
105.53	even	12		525.2.i.k.151.4		8
105.59	even	6		735.2.q.g.214.8		16
105.68	odd	12		3675.2.a.bn.1.1		4
105.74	odd	6		105.2.q.a.4.8	yes	16
105.89	even	6		735.2.d.e.589.8		8
105.104	even	2		735.2.q.g.79.1		16
420.179	even	6		1680.2.di.d.529.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.1	✓	16	21.11	odd	6
105.2.q.a.4.8	yes	16	105.74	odd	6
105.2.q.a.79.1	yes	16	15.14	odd	2
105.2.q.a.79.8	yes	16	3.2	odd	2
315.2.bf.b.109.1		16	35.4	even	6	inner
315.2.bf.b.109.8		16	7.4	even	3	inner
315.2.bf.b.289.1		16	1.1	even	1	trivial
315.2.bf.b.289.8		16	5.4	even	2	inner
525.2.i.h.151.1		8	105.32	even	12
525.2.i.h.226.1		8	15.2	even	4
525.2.i.k.151.4		8	105.53	even	12
525.2.i.k.226.4		8	15.8	even	4
735.2.d.d.589.1		8	21.2	odd	6
735.2.d.d.589.8		8	105.44	odd	6
735.2.d.e.589.1		8	21.5	even	6
735.2.d.e.589.8		8	105.89	even	6
735.2.q.g.79.1		16	105.104	even	2
735.2.q.g.79.8		16	21.20	even	2
735.2.q.g.214.1		16	21.17	even	6
735.2.q.g.214.8		16	105.59	even	6
1680.2.di.d.289.4		16	60.59	even	2
1680.2.di.d.289.5		16	12.11	even	2
1680.2.di.d.529.4		16	84.11	even	6
1680.2.di.d.529.5		16	420.179	even	6
2205.2.d.o.1324.1		8	35.19	odd	6
2205.2.d.o.1324.8		8	7.5	odd	6
2205.2.d.s.1324.1		8	35.9	even	6
2205.2.d.s.1324.8		8	7.2	even	3
3675.2.a.bn.1.1		4	105.68	odd	12
3675.2.a.bp.1.1		4	105.23	even	12
3675.2.a.bz.1.4		4	105.2	even	12
3675.2.a.cb.1.4		4	105.47	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.17942 - 1.25829i) q^{2} +(2.16659 + 3.75264i) q^{4} +(1.11685 + 1.93717i) q^{5} +(-1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +O(q^{10})\)	\(q+(-2.17942 - 1.25829i) q^{2} +(2.16659 + 3.75264i) q^{4} +(1.11685 + 1.93717i) q^{5} +(-1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +(0.00343282 - 5.62724i) q^{10} +(0.489068 + 0.847090i) q^{11} +5.14977i q^{13} +(-0.0275122 + 6.65819i) q^{14} +(-3.05502 + 5.29146i) q^{16} +(-3.59380 + 2.07488i) q^{17} +(-1.15001 + 1.99187i) q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +(4.39324 + 2.53644i) q^{23} +(-2.50528 + 4.32707i) q^{25} +(6.47990 - 11.2235i) q^{26} +(5.77323 - 9.90478i) q^{28} +5.92664 q^{29} +(-0.316594 - 0.548357i) q^{31} +(3.14643 - 1.81659i) q^{32} +10.4432 q^{34} +(2.98230 - 5.10939i) q^{35} +(7.84188 + 4.52751i) q^{37} +(5.01270 - 2.89408i) q^{38} +(11.3743 - 6.55773i) q^{40} -2.65505 q^{41} +0.344947i q^{43} +(-2.11922 + 3.67059i) q^{44} +(-6.38315 - 11.0559i) q^{46} +(3.67059 + 2.11922i) q^{47} +(-3.54998 + 6.03305i) q^{49} +(10.9048 - 6.27815i) q^{50} +(-19.3252 + 11.1574i) q^{52} +(-6.61053 + 3.81659i) q^{53} +(-1.09474 + 1.89348i) q^{55} +(-13.4855 + 7.71176i) q^{56} +(-12.9167 - 7.45743i) q^{58} +(-0.908297 - 1.57322i) q^{59} +(-0.328128 + 0.568335i) q^{61} +1.59347i q^{62} +3.07689 q^{64} +(-9.97599 + 5.75153i) q^{65} +(8.01924 - 4.62991i) q^{67} +(-15.5726 - 8.99083i) q^{68} +(-12.9288 + 7.38292i) q^{70} +5.49351 q^{71} +(4.65758 - 2.68905i) q^{73} +(-11.3938 - 19.7347i) q^{74} -9.96636 q^{76} +(1.30320 - 2.23582i) q^{77} +(-5.44346 + 9.42835i) q^{79} +(-13.6625 - 0.00833461i) q^{80} +(5.78648 + 3.34083i) q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +(0.434043 - 0.751785i) q^{86} +(4.97379 - 2.87162i) q^{88} +(-8.15542 + 14.1256i) q^{89} +(11.8277 - 6.76369i) q^{91} +21.9817i q^{92} +(-5.33317 - 9.23733i) q^{94} +(-5.14299 - 0.00313741i) q^{95} +1.53844i q^{97} +(15.3282 - 8.68165i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) \) 16 * q + 8 * q^4 - 2 * q^5	\( 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

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