LMFDB - Embedded newform 315.2.bf.b.109.8

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			109.8
Root			$-0.281555 + 1.05078i$ of defining polynomial
Character	$\chi$	$=$	315.109
Dual form			315.2.bf.b.289.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17942 - 1.25829i) q^{2} +(2.16659 - 3.75264i) q^{4} +(-2.23607 - 0.00136408i) q^{5} +(1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +O(q^{10})$	\(q+(2.17942 - 1.25829i) q^{2} +(2.16659 - 3.75264i) q^{4} +(-2.23607 - 0.00136408i) q^{5} +(1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +(-4.87505 + 2.81065i) q^{10} +(0.489068 - 0.847090i) q^{11} +5.14977i q^{13} +(-0.0275122 - 6.65819i) q^{14} +(-3.05502 - 5.29146i) q^{16} +(3.59380 + 2.07488i) q^{17} +(-1.15001 - 1.99187i) q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +(-4.39324 + 2.53644i) q^{23} +(5.00000 + 0.00610036i) q^{25} +(6.47990 + 11.2235i) q^{26} +(-5.77323 - 9.90478i) q^{28} +5.92664 q^{29} +(-0.316594 + 0.548357i) q^{31} +(-3.14643 - 1.81659i) q^{32} +10.4432 q^{34} +(-2.93998 + 5.13386i) q^{35} +(-7.84188 + 4.52751i) q^{37} +(-5.01270 - 2.89408i) q^{38} +(-0.00800937 + 13.1293i) q^{40} -2.65505 q^{41} +0.344947i q^{43} +(-2.11922 - 3.67059i) q^{44} +(-6.38315 + 11.0559i) q^{46} +(-3.67059 + 2.11922i) q^{47} +(-3.54998 - 6.03305i) q^{49} +(10.9048 - 6.27815i) q^{50} +(19.3252 + 11.1574i) q^{52} +(6.61053 + 3.81659i) q^{53} +(-1.09474 + 1.89348i) q^{55} +(-13.4855 - 7.71176i) q^{56} +(12.9167 - 7.45743i) q^{58} +(-0.908297 + 1.57322i) q^{59} +(-0.328128 - 0.568335i) q^{61} +1.59347i q^{62} +3.07689 q^{64} +(0.00702471 - 11.5152i) q^{65} +(-8.01924 - 4.62991i) q^{67} +(15.5726 - 8.99083i) q^{68} +(0.0524368 + 14.8882i) q^{70} +5.49351 q^{71} +(-4.65758 - 2.68905i) q^{73} +(-11.3938 + 19.7347i) q^{74} -9.96636 q^{76} +(-1.30320 - 2.23582i) q^{77} +(-5.44346 - 9.42835i) q^{79} +(6.82402 + 11.8362i) q^{80} +(-5.78648 + 3.34083i) q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +(0.434043 + 0.751785i) q^{86} +(-4.97379 - 2.87162i) q^{88} +(-8.15542 - 14.1256i) q^{89} +(11.8277 + 6.76369i) q^{91} +21.9817i q^{92} +(-5.33317 + 9.23733i) q^{94} +(2.56878 + 4.45553i) q^{95} +1.53844i q^{97} +(-15.3282 - 8.68165i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.542313	−	0.840176i	$-0.317549\pi$
$2$	2.17942	−	1.25829i	1.54108	−	0.889745i	0.998771	−	0.0495691i	$-0.0157848\pi$
$3$		0			0
$3$		0			0
$4$	2.16659	−	3.75264i	1.08329	−	1.87632i
$5$	−2.23607	−	0.00136408i	−1.00000	−	0.000610036i
$5$	−2.23607	−	0.00136408i	−1.00000	−	0.000610036i
$6$		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
$10$	−4.87505	+	2.81065i	−1.54163	+	0.888805i
$11$	0.489068	−	0.847090i	0.147459	−	0.255407i	−0.782828	−	0.622238i	$-0.786224\pi$
$11$	0.489068	−	0.847090i	0.147459	−	0.255407i	0.930288	+	0.366830i	$0.119557\pi$
$12$		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	$-0.165477\pi$
$17$	3.59380	+	2.07488i	0.871626	+	0.503233i	0.00373753	+	0.999993i	$0.498810\pi$
$18$		0			0
$19$	−1.15001	−	1.99187i	−0.263830	−	0.456967i	0.703427	−	0.710768i	$-0.251652\pi$
$19$	−1.15001	−	1.99187i	−0.263830	−	0.456967i	−0.967256	+	0.253801i	$0.918319\pi$
$20$	−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	$-0.844056\pi$
$23$	−4.39324	+	2.53644i	−0.916054	+	0.528884i	−0.0336802	+	0.999433i	$0.510723\pi$
$24$		0			0
$25$	5.00000	+	0.00610036i	0.999999	+	0.00122007i
$26$	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	−0.893055	−	0.449947i	$-0.851443\pi$
$31$	−0.316594	+	0.548357i	−0.0568620	+	0.0984879i	0.836193	+	0.548435i	$0.184776\pi$
$32$	−3.14643	−	1.81659i	−0.556216	−	0.321132i
$33$		0			0
$34$	10.4432			1.79100
$35$	−2.93998	+	5.13386i	−0.496947	+	0.867781i
$36$		0			0
$37$	−7.84188	+	4.52751i	−1.28920	+	0.744318i	−0.978511	−	0.206194i	$-0.933892\pi$
$37$	−7.84188	+	4.52751i	−1.28920	+	0.744318i	−0.310686	+	0.950513i	$0.600559\pi$
$38$	−5.01270	−	2.89408i	−0.813168	−	0.469483i
$39$		0			0
$40$	−0.00800937	+	13.1293i	−0.00126639	+	2.07593i
$41$	−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	$-0.766701\pi$
$47$	−3.67059	+	2.11922i	−0.535410	+	0.309119i	0.207806	+	0.978170i	$0.433368\pi$
$48$		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	$-0.157679\pi$
$53$	6.61053	+	3.81659i	0.908027	+	0.524250i	0.0282311	+	0.999601i	$0.491013\pi$
$54$		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	−0.919074	−	0.394084i	$-0.871062\pi$
$59$	−0.908297	+	1.57322i	−0.118250	+	0.204815i	0.800824	+	0.598900i	$0.204395\pi$
$60$		0			0
$61$	−0.328128	−	0.568335i	−0.0420125	−	0.0727678i	0.844255	−	0.535942i	$-0.180044\pi$
$61$	−0.328128	−	0.568335i	−0.0420125	−	0.0727678i	−0.886267	+	0.463175i	$0.846710\pi$
$62$			1.59347i			0.202371i
$63$		0			0
$64$	3.07689			0.384611
$65$	0.00702471	−	11.5152i	0.000871308	−	1.42829i
$66$		0			0
$67$	−8.01924	−	4.62991i	−0.979706	−	0.565633i	−0.0775244	−	0.996990i	$-0.524702\pi$
$67$	−8.01924	−	4.62991i	−0.979706	−	0.565633i	−0.902181	+	0.431357i	$0.858035\pi$
$68$	15.5726	−	8.99083i	1.88845	−	1.09030i
$69$		0			0
$70$	0.0524368	+	14.8882i	0.00626740	+	1.77948i
$71$	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	$-0.435247\pi$
$73$	−4.65758	−	2.68905i	−0.545128	−	0.314730i	−0.747155	+	0.664650i	$0.768581\pi$
$74$	−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	−0.990828	−	0.135127i	$-0.956856\pi$
$79$	−5.44346	−	9.42835i	−0.612437	−	1.06077i	0.378391	−	0.925646i	$-0.376477\pi$
$80$	6.82402	+	11.8362i	0.762949	+	1.32333i
$81$		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	−0.867570	−	0.497315i	$-0.834319\pi$
$89$	−8.15542	−	14.1256i	−0.864472	−	1.49731i	0.00309785	−	0.999995i	$-0.499014\pi$
$90$		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
$95$	2.56878	+	4.45553i	0.263551	+	0.457127i
$96$		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
$100$	10.8558	−	18.7500i	1.08558	−	1.87500i
$101$	−2.75805	+	4.77708i	−0.274436	+	0.475338i	−0.969993	−	0.243134i	$-0.921825\pi$
$101$	−2.75805	+	4.77708i	−0.274436	+	0.475338i	0.695556	+	0.718471i	$0.255158\pi$
$102$		0			0
$103$	14.3079	−	8.26066i	1.40980	−	0.813947i	0.414429	−	0.910082i	$-0.363981\pi$
$103$	14.3079	−	8.26066i	1.40980	−	0.813947i	0.995368	+	0.0961349i	$0.0306480\pi$
$104$	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	$-0.703494\pi$
$107$	−2.06824	+	1.19410i	−0.199944	+	0.115438i	0.396685	+	0.917955i	$0.370160\pi$
$108$		0			0
$109$	−9.05479	+	15.6833i	−0.867291	+	1.50219i	−0.00253705	+	0.999997i	$0.500808\pi$
$109$	−9.05479	+	15.6833i	−0.867291	+	1.50219i	−0.864754	+	0.502196i	$0.832526\pi$
$110$	−0.00335777	+	5.50420i	−0.000320150	+	0.524805i
$111$		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
$115$	9.82705	−	5.66566i	0.916377	−	0.528325i
$116$	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
$130$	−14.4742	−	25.1054i	−1.26947	−	2.20189i
$131$	−2.01270	−	3.48610i	−0.175850	−	0.304582i	0.764605	−	0.644499i	$-0.222934\pi$
$131$	−2.01270	−	3.48610i	−0.175850	−	0.304582i	−0.940455	+	0.339918i	$0.889601\pi$
$132$		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	$-0.492625\pi$
$137$	−9.72709	−	5.61594i	−0.831041	−	0.479802i	−0.854209	+	0.519930i	$0.825958\pi$
$138$		0			0
$139$	4.98991			0.423238			0.211619	−	0.977352i	$-0.432126\pi$
$139$	4.98991			0.423238			0.211619	+	0.977352i	$0.432126\pi$
$140$	12.8958	+	22.1556i	1.08990	+	1.87249i
$141$		0			0
$142$	11.9727	−	6.91243i	1.00473	−	0.580078i
$143$	4.36232	+	2.51858i	0.364795	+	0.210615i
$144$		0			0
$145$	−13.2524	−	0.00808443i	−1.10055	−	0.000671376i
$146$	−13.5344			−1.12012
$147$		0			0
$148$			39.2370i			3.22526i
$149$	7.24712	+	12.5524i	0.593707	+	1.02833i	0.993728	+	0.111825i	$0.0356695\pi$
$149$	7.24712	+	12.5524i	0.593707	+	1.02833i	−0.400021	+	0.916506i	$0.630997\pi$
$150$		0			0
$151$	−3.94346	+	6.83028i	−0.320914	+	0.555840i	−0.980677	−	0.195634i	$-0.937324\pi$
$151$	−3.94346	+	6.83028i	−0.320914	+	0.555840i	0.659763	+	0.751474i	$0.270657\pi$
$152$	−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	$-0.249075\pi$
$157$	5.67792	+	3.27815i	0.453147	+	0.261625i	−0.256011	+	0.966674i	$0.582408\pi$
$158$	−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	$-0.826021\pi$
$163$	−10.6138	+	6.12790i	−0.831340	+	0.479974i	0.0229712	+	0.999736i	$0.492687\pi$
$164$	−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
$170$	−23.3518	−	0.0142454i	−1.79100	−	0.00109257i
$171$		0			0
$172$	1.29446	+	0.747358i	0.0987017	+	0.0569855i
$173$	−10.0013	+	5.77427i	−0.760387	+	0.439009i	−0.829435	−	0.558604i	$-0.811337\pi$
$173$	−10.0013	+	5.77427i	−0.760387	+	0.439009i	0.0690479	+	0.997613i	$0.478004\pi$
$174$		0			0
$175$	6.58099	−	11.4757i	0.497476	−	0.867478i
$176$	−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	−0.983019	−	0.183502i	$-0.941257\pi$
$179$	−4.44978	+	7.70725i	−0.332592	+	0.576067i	0.650427	+	0.759569i	$0.274590\pi$
$180$		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
$185$	17.5412	−	10.1131i	1.28965	−	0.743532i
$186$		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	0.854543	−	0.519381i	$-0.173837\pi$
$191$	−0.311309	−	0.539203i	−0.0225255	−	0.0390154i	−0.877068	+	0.480365i	$0.840504\pi$
$192$		0			0
$193$	13.1529	+	7.59383i	0.946767	+	0.546616i	0.892075	−	0.451887i	$-0.149249\pi$
$193$	13.1529	+	7.59383i	0.946767	+	0.546616i	0.0546916	+	0.998503i	$0.482582\pi$
$194$	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	−0.505421	−	0.862873i	$-0.668663\pi$
$199$	6.97662	−	12.0839i	0.494560	−	0.856602i	0.999980	+	0.00627071i	$0.00199604\pi$
$200$	0.0358190	−	29.3581i	0.00253279	−	2.07593i
$201$		0			0
$202$			13.8817i			0.976714i
$203$	7.78403	−	13.6119i	0.546332	−	0.955370i
$204$		0			0
$205$	5.93688	+	0.00362171i	0.414650	+	0.000252951i
$206$	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
$215$	0.000470536	−	0.771325i	3.20903e−5	−	0.0526039i
$216$		0			0
$217$	0.843617	+	1.44734i	0.0572685	+	0.0982521i
$218$			45.5742i			3.08667i
$219$		0			0
$220$	4.73370	+	8.21057i	0.319146	+	0.553557i
$221$	−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	$-0.589230\pi$
$227$	−18.7913	−	10.8492i	−1.24722	−	0.720084i	−0.970554	+	0.240882i	$0.922563\pi$
$228$		0			0
$229$	−1.03844	−	1.79864i	−0.0686223	−	0.118857i	0.829673	−	0.558250i	$-0.188527\pi$
$229$	−1.03844	−	1.79864i	−0.0686223	−	0.118857i	−0.898295	+	0.439393i	$0.855194\pi$
$230$	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	$-0.737729\pi$
$233$	−5.85348	+	3.37951i	−0.383474	+	0.221399i	0.295854	+	0.955233i	$0.404396\pi$
$234$		0			0
$235$	8.21057	−	4.73370i	0.535599	−	0.308793i
$236$	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	−0.686419	−	0.727206i	$-0.740819\pi$
$241$	4.44875	−	7.70546i	0.286569	−	0.496352i	0.972988	+	0.230854i	$0.0741519\pi$
$242$	21.8885	+	12.6373i	1.40705	+	0.812358i
$243$		0			0
$244$	−2.84367			−0.182047
$245$	7.92976	+	13.4951i	0.506614	+	0.862173i
$246$		0			0
$247$	10.2577	−	5.92227i	0.652680	−	0.376825i
$248$	3.21974	+	1.85892i	0.204454	+	0.118042i
$249$		0			0
$250$	−24.3924	+	14.0235i	−1.54271	+	0.886923i
$251$	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	$-0.728958\pi$
$257$	−5.39917	+	3.11721i	−0.336791	+	0.194446i	0.322061	+	0.946719i	$0.395624\pi$
$258$		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	$-0.000806060\pi$
$263$	24.2903	+	14.0240i	1.49780	+	0.864756i	0.497805	+	0.867289i	$0.334139\pi$
$264$		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	−0.956664	−	0.291194i	$-0.905948\pi$
$269$	−3.70915	+	6.42444i	−0.226151	+	0.391705i	0.730513	+	0.682899i	$0.239281\pi$
$270$		0			0
$271$	15.6058	+	27.0300i	0.947985	+	1.64196i	0.749662	+	0.661821i	$0.230216\pi$
$271$	15.6058	+	27.0300i	0.947985	+	1.64196i	0.198323	+	0.980137i	$0.436450\pi$
$272$		−	25.3553i		−	1.53739i
$273$		0			0
$274$	−28.2659			−1.70761
$275$	2.45050	−	4.23246i	0.147771	−	0.255227i
$276$		0			0
$277$	10.7843	+	6.22629i	0.647963	+	0.374102i	0.787675	−	0.616090i	$-0.211284\pi$
$277$	10.7843	+	6.22629i	0.647963	+	0.374102i	−0.139712	+	0.990192i	$0.544618\pi$
$278$	10.8751	−	6.27875i	0.652246	−	0.376574i
$279$		0			0
$280$	30.1441	+	17.2624i	1.80145	+	1.03163i
$281$	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	$-0.228896\pi$
$283$	9.38944	+	5.42100i	0.558144	+	0.322245i	−0.194256	+	0.980951i	$0.562229\pi$
$284$	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
$290$	−28.8927	+	16.6577i	−1.69664	+	0.978174i
$291$		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
$305$	0.732941	+	1.27128i	0.0419681	+	0.0727934i
$306$		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
$310$	0.00217362	−	3.56310i	0.000123454	−	0.202371i
$311$	11.0851	−	19.2000i	0.628581	−	1.08873i	−0.359256	−	0.933239i	$-0.616969\pi$
$311$	11.0851	−	19.2000i	0.628581	−	1.08873i	0.987837	−	0.155495i	$-0.0496972\pi$
$312$		0			0
$313$	−5.96321	+	3.44286i	−0.337060	+	0.194602i	−0.658971	−	0.752168i	$-0.729008\pi$
$313$	−5.96321	+	3.44286i	−0.337060	+	0.194602i	0.321911	+	0.946770i	$0.395675\pi$
$314$	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	$-0.784077\pi$
$317$	−11.1186	+	6.41935i	−0.624485	+	0.360547i	0.154128	+	0.988051i	$0.450743\pi$
$318$		0			0
$319$	2.89853	−	5.02040i	0.162286	−	0.281088i
$320$	−6.88013	−	0.00419713i	−0.384611	−	0.000234627i
$321$		0			0
$322$	17.0090	+	29.1812i	0.947872	+	1.62621i
$323$		−	9.54453i		−	0.531072i
$324$		0			0
$325$	−0.0314155	+	25.7488i	−0.00174262	+	1.42829i
$326$	−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	0.959134	−	0.282952i	$-0.0913137\pi$
$331$	4.26678	+	7.39028i	0.234524	+	0.406207i	−0.724611	+	0.689159i	$0.757980\pi$
$332$	−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
$340$	−34.8336	+	20.0829i	−1.88912	+	1.08915i
$341$	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	$-0.450837\pi$
$347$	−11.6418	−	6.72137i	−0.624962	−	0.360822i	−0.778798	+	0.627274i	$0.784171\pi$
$348$		0			0
$349$	24.7397			1.32429			0.662144	−	0.749377i	$-0.269647\pi$
$349$	24.7397			1.32429			0.662144	+	0.749377i	$0.269647\pi$
$350$	−0.0969435	−	33.2911i	−0.00518185	−	1.77948i
$351$		0			0
$352$	−3.07764	+	1.77687i	−0.164039	+	0.0947077i
$353$	−14.5103	−	8.37751i	−0.772303	−	0.445890i	0.0613923	−	0.998114i	$-0.480446\pi$
$353$	−14.5103	−	8.37751i	−0.772303	−	0.445890i	−0.833696	+	0.552224i	$0.813779\pi$
$354$		0			0
$355$	−12.2839	−	0.00749361i	−0.651960	−	0.000397719i
$356$	−70.6777			−3.74591
$357$		0			0
$358$			22.3965i			1.18369i
$359$	16.2462	+	28.1393i	0.857442	+	1.48513i	0.874361	+	0.485276i	$0.161281\pi$
$359$	16.2462	+	28.1393i	0.857442	+	1.48513i	−0.0169190	+	0.999857i	$0.505386\pi$
$360$		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	$-0.548397\pi$
$367$	−20.7516	−	11.9809i	−1.08322	−	0.625400i	−0.931764	+	0.363064i	$0.881731\pi$
$368$	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	$-0.574098\pi$
$373$	9.59160	−	5.53771i	0.496634	−	0.286732i	0.727323	+	0.686296i	$0.240764\pi$
$374$	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	$0.182009\pi$
$380$	22.2855	+	0.0135949i	1.14322	+	0.000697406i
$381$		0			0
$382$	−1.35695	−	0.783435i	−0.0694275	−	0.0400840i
$383$	20.1371	−	11.6262i	1.02896	−	0.594069i	0.112271	−	0.993678i	$-0.464187\pi$
$383$	20.1371	−	11.6262i	1.02896	−	0.594069i	0.916686	+	0.399609i	$0.130854\pi$
$384$		0			0
$385$	2.91100	+	5.00123i	0.148358	+	0.254886i
$386$	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	0.216907	−	0.976192i	$-0.430403\pi$
$389$	18.8131	−	32.5852i	0.953861	−	1.65214i	0.736954	−	0.675943i	$-0.236263\pi$
$390$		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
$395$	12.1591	+	21.0899i	0.611790	+	1.06115i
$396$		0			0
$397$	0.0498605	−	0.0287870i	0.00250243	−	0.00144478i	−0.498748	−	0.866747i	$-0.666207\pi$
$397$	0.0498605	−	0.0287870i	0.00250243	−	0.00144478i	0.501251	+	0.865302i	$0.332873\pi$
$398$		−	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	0.730188	−	0.683247i	$-0.239433\pi$
$401$	−4.53797	−	7.85999i	−0.226615	−	0.392509i	−0.956803	+	0.290738i	$0.906099\pi$
$402$		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	−0.584261	−	0.811566i	$-0.698615\pi$
$409$	8.30602	−	14.3865i	0.410706	−	0.711364i	0.994967	+	0.100202i	$0.0319488\pi$
$410$	12.9435	−	7.46242i	0.639235	−	0.368543i
$411$		0			0
$412$		−	71.5897i		−	3.52697i
$413$	2.42031	+	4.15237i	0.119096	+	0.204325i
$414$		0			0
$415$	−0.00903927	+	14.8176i	−0.000443720	+	0.727367i
$416$	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
$425$	17.9564	+	10.3963i	0.871011	+	0.504296i
$426$		0			0
$427$	−1.73628	+	0.00717444i	−0.0840243	+	0.000347195i
$428$			10.3485i			0.500213i
$429$		0			0
$430$	−0.969525	−	1.68163i	−0.0467546	−	0.0810956i
$431$	−10.9981	+	19.0493i	−0.529761	+	0.917572i	0.469637	+	0.882860i	$0.344385\pi$
$431$	−10.9981	+	19.0493i	−0.529761	+	0.917572i	−0.999397	+	0.0347127i	$0.988948\pi$
$432$		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	0.761867	−	0.647733i	$-0.224283\pi$
$439$	−3.77183	−	6.53300i	−0.180020	−	0.311803i	−0.941887	+	0.335930i	$0.890949\pi$
$440$	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	$-0.586903\pi$
$443$	9.03987	−	5.21917i	0.429497	−	0.247970i	0.699132	+	0.714992i	$0.253570\pi$
$444$		0			0
$445$	18.2168	+	31.5969i	0.863559	+	1.49784i
$446$	−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
$455$	−26.4382	−	15.1402i	−1.23944	−	0.709783i
$456$		0			0
$457$	−26.7268	+	15.4307i	−1.25023	+	0.721819i	−0.971154	−	0.238452i	$-0.923360\pi$
$457$	−26.7268	+	15.4307i	−1.25023	+	0.721819i	−0.279072	+	0.960270i	$0.590027\pi$
$458$	−4.52642	−	2.61333i	−0.211506	−	0.122113i
$459$		0			0
$460$	0.0299848	−	49.1525i	0.00139805	−	2.29175i
$461$	−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	$-0.446286\pi$
$467$	23.8932	−	13.7947i	1.10564	−	0.638344i	0.937698	+	0.347452i	$0.112953\pi$
$468$		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	−0.728616	−	0.684923i	$-0.759836\pi$
$479$	5.00869	−	8.67530i	0.228853	−	0.396385i	0.957468	+	0.288538i	$0.0931692\pi$
$480$		0			0
$481$	−23.3156	−	40.3839i	−1.06310	−	1.84135i
$482$		−	22.3913i		−	1.01989i
$483$		0			0
$484$	43.5192			1.97814
$485$	0.00209857	−	3.44007i	9.52910e−5	−	0.156205i
$486$		0			0
$487$	−26.6165	−	15.3671i	−1.20611	−	0.696348i	−0.244203	−	0.969724i	$-0.578526\pi$
$487$	−26.6165	−	15.3671i	−1.20611	−	0.696348i	−0.961907	+	0.273376i	$0.911860\pi$
$488$	−3.33704	+	1.92664i	−0.151061	+	0.0872150i
$489$		0			0
$490$	34.2631	+	19.4337i	1.54785	+	0.877924i
$491$	−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	0.848178	−	0.529712i	$-0.177700\pi$
$499$	−0.774139	−	1.34085i	−0.0346552	−	0.0600246i	−0.882833	+	0.469687i	$0.844367\pi$
$500$	−24.2999	+	41.9114i	−1.08673	+	1.87433i
$501$		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	0.998604	−	0.0528204i	$-0.0168211\pi$
$509$	10.2327	+	17.7236i	0.453558	+	0.785586i	−0.545046	+	0.838406i	$0.683488\pi$
$510$		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
$515$	−32.0047	+	18.4519i	−1.41029	+	0.813087i
$516$		0			0
$517$			4.14576i			0.182330i
$518$	30.3608	+	52.0882i	1.33398	+	2.28862i
$519$		0			0
$520$	−67.6130	−	0.0412464i	−2.96503	−	0.00180878i
$521$	1.37337	−	2.37875i	0.0601685	−	0.104215i	−0.834372	−	0.551202i	$-0.814170\pi$
$521$	1.37337	−	2.37875i	0.0601685	−	0.104215i	0.894541	+	0.446987i	$0.147503\pi$
$522$		0			0
$523$	34.5258	−	19.9335i	1.50971	−	0.871629i	0.509770	−	0.860311i	$-0.329731\pi$
$523$	34.5258	−	19.9335i	1.50971	−	0.871629i	0.999936	−	0.0113184i	$-0.00360283\pi$
$524$	−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
$530$	−42.9538	−	0.0262034i	−1.86579	−	0.00113820i
$531$		0			0
$532$	−13.0898	+	22.8901i	−0.567514	+	0.992411i
$533$		−	13.6729i		−	0.592239i
$534$		0			0
$535$	4.62635	−	2.66727i	0.200015	−	0.115316i
$536$	−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	−0.996602	−	0.0823667i	$-0.973752\pi$
$541$	−13.2493	−	22.9485i	−0.569633	−	0.986633i	0.426969	−	0.904266i	$-0.359581\pi$
$542$	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
$550$	0.0150164	−	12.3078i	0.000640301	−	0.524805i
$551$	−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	$-0.381976\pi$
$557$	−6.22247	−	3.59254i	−0.263654	−	0.152221i	−0.626000	+	0.779823i	$0.715309\pi$
$558$		0			0
$559$	−1.77640			−0.0751336
$560$	36.1473	−	0.127312i	1.52750	−	0.00537992i
$561$		0			0
$562$	0.0891873	−	0.0514923i	0.00376214	−	0.00217207i
$563$	2.06720	+	1.19350i	0.0871220	+	0.0502999i	0.542928	−	0.839779i	$-0.317316\pi$
$563$	2.06720	+	1.19350i	0.0871220	+	0.0502999i	−0.455806	+	0.890079i	$0.650649\pi$
$564$		0			0
$565$	−0.00551598	+	9.04205i	−0.000232059	+	0.380402i
$566$	27.2847			1.14686
$567$		0			0
$568$		−	32.2558i		−	1.35342i
$569$	−14.9271	−	25.8545i	−0.625776	−	1.08388i	−0.988390	−	0.151936i	$-0.951449\pi$
$569$	−14.9271	−	25.8545i	−0.625776	−	1.08388i	0.362615	−	0.931939i	$-0.381884\pi$
$570$		0			0
$571$	9.73170	−	16.8558i	0.407259	−	0.705393i	−0.587322	−	0.809353i	$-0.699818\pi$
$571$	9.73170	−	16.8558i	0.407259	−	0.705393i	0.994582	+	0.103960i	$0.0331513\pi$
$572$	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	$-0.307053\pi$
$577$	3.43108	+	1.98094i	0.142838	+	0.0824675i	−0.426878	+	0.904309i	$0.640387\pi$
$578$	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
$590$	0.00623605	−	10.2224i	0.000256734	−	0.420850i
$591$		0			0
$592$	47.9143	+	27.6633i	1.96926	+	1.13696i
$593$	−33.3396	+	19.2486i	−1.36909	+	0.790447i	−0.990812	−	0.135243i	$-0.956818\pi$
$593$	−33.3396	+	19.2486i	−1.36909	+	0.790447i	−0.378282	+	0.925690i	$0.623485\pi$
$594$		0			0
$595$	−21.2179	+	12.3500i	−0.869848	+	0.506300i
$596$	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	−0.987544	−	0.157343i	$-0.949707\pi$
$599$	−8.74985	+	15.1552i	−0.357509	+	0.619224i	0.630035	+	0.776567i	$0.283041\pi$
$600$		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
$605$	−11.2168	−	19.4555i	−0.456029	−	0.790979i
$606$		0			0
$607$	9.45318	−	5.45780i	0.383693	−	0.221525i	−0.295731	−	0.955271i	$-0.595563\pi$
$607$	9.45318	−	5.45780i	0.383693	−	0.221525i	0.679424	+	0.733746i	$0.262230\pi$
$608$			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	$-0.510179\pi$
$613$	−22.6183	−	13.0587i	−0.913543	−	0.527435i	−0.881570	+	0.472054i	$0.843513\pi$
$614$	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	−0.874183	−	0.485597i	$-0.838602\pi$
$619$	−0.411816	+	0.713286i	−0.0165523	+	0.0286694i	0.857631	+	0.514266i	$0.171936\pi$
$620$	−3.06432	−	5.31505i	−0.123066	−	0.213458i
$621$		0			0
$622$		−	55.7933i		−	2.23711i
$623$	−43.1540	+	0.178316i	−1.72893	+	0.00714408i
$624$		0			0
$625$	24.9999	+	0.0610036i	0.999997	+	0.00244014i
$626$	−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
$635$	−0.00934428	+	15.3176i	−0.000370817	+	0.607860i
$636$		0			0
$637$	31.0688	−	18.2816i	1.23099	−	0.724342i
$638$		−	14.5888i		−	0.577575i
$639$		0			0
$640$	−29.0762	+	16.7635i	−1.14934	+	0.662636i
$641$	14.8371	−	25.6986i	0.586029	−	1.01503i	−0.408717	−	0.912661i	$-0.634024\pi$
$641$	14.8371	−	25.6986i	0.586029	−	1.01503i	0.994746	−	0.102371i	$-0.0326429\pi$
$642$		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	$-0.402217\pi$
$647$	−9.45991	−	5.46168i	−0.371907	−	0.214721i	−0.674291	+	0.738465i	$0.735551\pi$
$648$		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	$-0.711476\pi$
$653$	−6.21006	+	3.58538i	−0.243019	+	0.140307i	0.373545	+	0.927612i	$0.378142\pi$
$654$		0			0
$655$	4.49577	+	7.79789i	0.175664	+	0.304689i
$656$	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	0.434819	+	0.900518i	$0.356812\pi$
$661$	−14.4608	+	25.0469i	−0.562461	+	0.974212i	−0.997281	+	0.0736941i	$0.976521\pi$
$662$	18.5982	+	10.7377i	0.722841	+	0.417333i
$663$		0			0
$664$	−38.9090			−1.50996
$665$	13.6070	−	0.0479243i	0.527656	−	0.00185843i
$666$		0			0
$667$	−26.0372	+	15.0326i	−1.00816	+	0.582063i
$668$	−8.00210	−	4.62001i	−0.309610	−	0.178754i
$669$		0			0
$670$	52.1072	+	0.0317873i	2.01308	+	0.00122805i
$671$	−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	$-0.470062\pi$
$677$	26.0991	−	15.0683i	1.00307	−	0.579123i	0.909155	+	0.416457i	$0.136729\pi$
$678$		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	$-0.237391\pi$
$683$	13.4380	+	7.75842i	0.514190	+	0.296868i	−0.220364	+	0.975418i	$0.570725\pi$
$684$		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	−0.861127	−	0.508391i	$-0.830241\pi$
$691$	−22.8917	−	39.6496i	−0.870842	−	1.50834i	−0.00971588	−	0.999953i	$-0.503093\pi$
$692$			50.0418i			1.90230i
$693$		0			0
$694$	−33.8297			−1.28416
$695$	−11.1578	−	0.00680665i	−0.423238	−	0.000258191i
$696$		0			0
$697$	−9.54174	−	5.50893i	−0.361419	−	0.208666i
$698$	53.9183	−	31.1298i	2.04084	−	1.17828i
$699$		0			0
$700$	−28.8057	−	49.5591i	−1.08875	−	1.87316i
$701$	−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	0.985437	−	0.170041i	$-0.0543901\pi$
$709$	9.19854	+	15.9323i	0.345459	+	0.598352i	−0.639978	+	0.768393i	$0.721057\pi$
$710$	−26.7812	+	15.4403i	−1.00508	+	0.579465i
$711$		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	0.976798	−	0.214164i	$-0.0687027\pi$
$719$	8.12275	+	14.0690i	0.302927	+	0.524686i	−0.673870	+	0.738850i	$0.735369\pi$
$720$		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
$725$	29.6332	+	0.0361547i	1.10055	+	0.00134275i
$726$		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
$730$	30.2639	+	0.0184621i	1.12012	+	0.000683313i
$731$	−0.715725	+	1.23967i	−0.0264720	+	0.0458509i
$732$		0			0
$733$	−40.4538	+	23.3560i	−1.49420	+	0.862674i	−0.999978	−	0.00666408i	$-0.997879\pi$
$733$	−40.4538	+	23.3560i	−1.49420	+	0.862674i	−0.494218	+	0.869338i	$0.664545\pi$
$734$	−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	−0.793899	−	0.608049i	$-0.791952\pi$
$739$	3.52410	−	6.10393i	0.129636	−	0.224537i	0.923536	+	0.383513i	$0.125286\pi$
$740$	0.0535225	−	87.7366i	0.00196753	−	3.22526i
$741$		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
$745$	−16.1879	−	28.0778i	−0.593080	−	1.02869i
$746$	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	0.891901	−	0.452232i	$-0.149372\pi$
$751$	1.48823	+	2.57768i	0.0543062	+	0.0940611i	−0.837594	+	0.546293i	$0.816039\pi$
$752$	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
$760$	26.1612	−	15.0829i	0.948965	−	0.547113i
$761$	13.3628	+	23.1451i	0.484402	+	0.839008i	0.999839	−	0.0179187i	$-0.00570401\pi$
$761$	13.3628	+	23.1451i	0.484402	+	0.839008i	−0.515438	+	0.856927i	$0.672371\pi$
$762$		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	$0.476755\pi$
$770$	12.6373	+	7.23692i	0.455416	+	0.260800i
$771$		0			0
$772$	56.9938	−	32.9054i	2.05125	−	1.18429i
$773$	5.46553	+	3.15553i	0.196581	+	0.113496i	0.595060	−	0.803681i	$-0.297128\pi$
$773$	5.46553	+	3.15553i	0.196581	+	0.113496i	−0.398478	+	0.917178i	$0.630462\pi$
$774$		0			0
$775$	−1.58631	+	2.73985i	−0.0569821	+	0.0984184i
$776$	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	$-0.153925\pi$
$787$	25.9595	+	14.9877i	0.925358	+	0.534256i	0.0400174	+	0.999199i	$0.487259\pi$
$788$	−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
$800$	−15.7211	−	9.10216i	−0.555824	−	0.321810i
$801$		0			0
$802$	−19.7803	−	11.4202i	−0.698466	−	0.403260i
$803$	−4.55574	+	2.63026i	−0.160769	+	0.0928198i
$804$		0			0
$805$	−0.105701	−	30.0114i	−0.00372548	−	1.05776i
$806$	−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	0.0309881	−	0.999520i	$-0.490135\pi$
$809$	25.0612	−	43.4072i	0.881104	−	1.52612i	0.850115	−	0.526596i	$-0.176532\pi$
$810$		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
$815$	23.7416	−	13.6879i	0.831633	−	0.479467i
$816$		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	0.976217	+	0.216794i	$0.0695600\pi$
$821$	19.3654	+	33.5419i	0.675858	+	1.17062i	−0.300359	+	0.953826i	$0.597107\pi$
$822$		0			0
$823$	−18.1702	−	10.4906i	−0.633375	−	0.365679i	0.148683	−	0.988885i	$-0.452497\pi$
$823$	−18.1702	−	10.4906i	−0.633375	−	0.365679i	−0.782058	+	0.623206i	$0.785830\pi$
$824$	−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	−0.135813	+	0.990734i	$0.543365\pi$
$829$	−26.6591	+	46.1749i	−0.925908	+	1.60372i	−0.790095	+	0.612985i	$0.789969\pi$
$830$	18.6251	+	32.3052i	0.646487	+	1.12133i
$831$		0			0
$832$			15.8453i			0.549336i
$833$	−0.240057	−	29.0474i	−0.00831747	−	1.00643i
$834$		0			0
$835$	−0.00290876	+	4.76817i	−0.000100662	+	0.165009i
$836$	−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
$845$	30.2319	+	0.0184426i	1.04001	+	0.000634443i
$846$		0			0
$847$	26.5717	−	0.109797i	0.913015	−	0.00377266i
$848$		−	46.6392i		−	1.60160i
$849$		0			0
$850$	52.2161	+	0.0637075i	1.79100	+	0.00218515i
$851$	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	$-0.105487\pi$
$857$	33.2737	+	19.2106i	1.13661	+	0.656222i	0.191021	+	0.981586i	$0.438820\pi$
$858$		0			0
$859$	11.6709	+	20.2146i	0.398207	+	0.689714i	0.993505	−	0.113791i	$-0.0362994\pi$
$859$	11.6709	+	20.2146i	0.398207	+	0.689714i	−0.595298	+	0.803505i	$0.702966\pi$
$860$	−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	0.612103	−	0.790778i	$-0.290324\pi$
$863$	47.0908	−	27.1879i	1.60299	−	0.925486i	0.990885	−	0.134707i	$-0.0430094\pi$
$864$		0			0
$865$	22.3715	−	12.8980i	0.760654	−	0.438546i
$866$	−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
$875$	−14.7312	+	25.6514i	−0.498005	+	0.867174i
$876$		0			0
$877$	−24.6434	+	14.2279i	−0.832148	+	0.480441i	−0.854587	−	0.519307i	$-0.826190\pi$
$877$	−24.6434	+	14.2279i	−0.832148	+	0.480441i	0.0224397	+	0.999748i	$0.492857\pi$
$878$	−16.4408	−	9.49211i	−0.554851	−	0.320343i
$879$		0			0
$880$	13.3638	+	0.00815238i	0.450492	+	0.000274817i
$881$	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	$-0.830696\pi$
$887$	−25.4214	+	14.6770i	−0.853566	+	0.492807i	0.00828615	+	0.999966i	$0.497362\pi$
$888$		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
$905$	7.10934	+	0.00433696i	0.236323	+	0.000144165i
$906$		0			0
$907$	−31.4256	−	18.1436i	−1.04347	−	0.602447i	−0.122655	−	0.992449i	$-0.539141\pi$
$907$	−31.4256	−	18.1436i	−1.04347	−	0.602447i	−0.920814	+	0.390002i	$0.872474\pi$
$908$	−81.4259	+	47.0113i	−2.70221	+	1.56012i
$909$		0			0
$910$	−76.6708	+	0.270037i	−2.54161	+	0.00895165i
$911$	−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	−0.975923	−	0.218114i	$-0.930010\pi$
$919$	−20.5188	−	35.5397i	−0.676854	−	1.17235i	0.299069	−	0.954231i	$-0.403324\pi$
$920$	−33.2666	−	57.7007i	−1.09677	−	1.90233i
$921$		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	0.889472	−	0.456990i	$-0.151073\pi$
$929$	1.49260	+	2.58526i	0.0489706	+	0.0848196i	−0.840501	+	0.541810i	$0.817739\pi$
$930$		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
$935$	−7.86305	+	4.53334i	−0.257149	+	0.148256i
$936$		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
$940$	0.0250525	−	41.0673i	0.000817124	−	1.33947i
$941$	5.10580	−	8.84351i	0.166444	−	0.288290i	−0.770723	−	0.637171i	$-0.780105\pi$
$941$	5.10580	−	8.84351i	0.166444	−	0.288290i	0.937167	+	0.348880i	$0.113438\pi$
$942$		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	$-0.939635\pi$
$947$	−40.3086	+	23.2722i	−1.30985	+	0.756245i	−0.327783	+	0.944753i	$0.606301\pi$
$948$		0			0
$949$	13.8480	−	23.9854i	0.449525	−	0.778600i
$950$	−25.0458	−	14.5010i	−0.812594	−	0.470474i
$951$		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
$955$	0.695373	+	1.20612i	0.0225017	+	0.0390291i
$956$	−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
$970$	−4.32403	−	7.50000i	−0.138836	−	0.240810i
$971$	24.0908	+	41.7265i	0.773110	+	1.33907i	0.935850	+	0.352397i	$0.114633\pi$
$971$	24.0908	+	41.7265i	0.773110	+	1.33907i	−0.162740	+	0.986669i	$0.552033\pi$
$972$		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	$-0.403935\pi$
$977$	−11.9099	−	6.87617i	−0.381031	−	0.219988i	−0.678267	+	0.734816i	$0.737269\pi$
$978$		0			0
$979$	−15.9542			−0.509898
$980$	67.8229	−	0.519132i	2.16652	−	0.0165831i
$981$		0			0
$982$	−9.02399	+	5.21001i	−0.287967	+	0.166258i
$983$	33.0773	+	19.0972i	1.05500	+	0.609106i	0.924046	−	0.382282i	$-0.124862\pi$
$983$	33.0773	+	19.0972i	1.05500	+	0.609106i	0.130957	+	0.991388i	$0.458195\pi$
$984$		0			0
$985$	−0.0326575	+	53.5337i	−0.00104055	+	1.70572i
$986$	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	0.360316	+	0.932830i	$0.382669\pi$
$991$	−19.7600	+	34.2253i	−0.627697	+	1.08720i	−0.988013	+	0.154372i	$0.950665\pi$
$992$	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	$-0.391773\pi$
$997$	−9.98438	−	5.76448i	−0.316208	−	0.182563i	−0.649701	+	0.760190i	$0.725106\pi$
$998$	−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.109.8		16
3.2	odd	2		105.2.q.a.4.1	✓	16
5.4	even	2	inner	315.2.bf.b.109.1		16
7.2	even	3	inner	315.2.bf.b.289.1		16
7.3	odd	6		2205.2.d.o.1324.8		8
7.4	even	3		2205.2.d.s.1324.8		8
12.11	even	2		1680.2.di.d.529.4		16
15.2	even	4		525.2.i.h.151.1		8
15.8	even	4		525.2.i.k.151.4		8
15.14	odd	2		105.2.q.a.4.8	yes	16
21.2	odd	6		105.2.q.a.79.8	yes	16
21.5	even	6		735.2.q.g.79.8		16
21.11	odd	6		735.2.d.d.589.1		8
21.17	even	6		735.2.d.e.589.1		8
21.20	even	2		735.2.q.g.214.1		16
35.4	even	6		2205.2.d.s.1324.1		8
35.9	even	6	inner	315.2.bf.b.289.8		16
35.24	odd	6		2205.2.d.o.1324.1		8
60.59	even	2		1680.2.di.d.529.5		16
84.23	even	6		1680.2.di.d.289.5		16
105.2	even	12		525.2.i.h.226.1		8
105.17	odd	12		3675.2.a.cb.1.4		4
105.23	even	12		525.2.i.k.226.4		8
105.32	even	12		3675.2.a.bz.1.4		4
105.38	odd	12		3675.2.a.bn.1.1		4
105.44	odd	6		105.2.q.a.79.1	yes	16
105.53	even	12		3675.2.a.bp.1.1		4
105.59	even	6		735.2.d.e.589.8		8
105.74	odd	6		735.2.d.d.589.8		8
105.89	even	6		735.2.q.g.79.1		16
105.104	even	2		735.2.q.g.214.8		16
420.359	even	6		1680.2.di.d.289.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.1	✓	16	3.2	odd	2
105.2.q.a.4.8	yes	16	15.14	odd	2
105.2.q.a.79.1	yes	16	105.44	odd	6
105.2.q.a.79.8	yes	16	21.2	odd	6
315.2.bf.b.109.1		16	5.4	even	2	inner
315.2.bf.b.109.8		16	1.1	even	1	trivial
315.2.bf.b.289.1		16	7.2	even	3	inner
315.2.bf.b.289.8		16	35.9	even	6	inner
525.2.i.h.151.1		8	15.2	even	4
525.2.i.h.226.1		8	105.2	even	12
525.2.i.k.151.4		8	15.8	even	4
525.2.i.k.226.4		8	105.23	even	12
735.2.d.d.589.1		8	21.11	odd	6
735.2.d.d.589.8		8	105.74	odd	6
735.2.d.e.589.1		8	21.17	even	6
735.2.d.e.589.8		8	105.59	even	6
735.2.q.g.79.1		16	105.89	even	6
735.2.q.g.79.8		16	21.5	even	6
735.2.q.g.214.1		16	21.20	even	2
735.2.q.g.214.8		16	105.104	even	2
1680.2.di.d.289.4		16	420.359	even	6
1680.2.di.d.289.5		16	84.23	even	6
1680.2.di.d.529.4		16	12.11	even	2
1680.2.di.d.529.5		16	60.59	even	2
2205.2.d.o.1324.1		8	35.24	odd	6
2205.2.d.o.1324.8		8	7.3	odd	6
2205.2.d.s.1324.1		8	35.4	even	6
2205.2.d.s.1324.8		8	7.4	even	3
3675.2.a.bn.1.1		4	105.38	odd	12
3675.2.a.bp.1.1		4	105.53	even	12
3675.2.a.bz.1.4		4	105.32	even	12
3675.2.a.cb.1.4		4	105.17	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)

\(f(q)\)	\(=\)	\(q+(2.17942 - 1.25829i) q^{2} +(2.16659 - 3.75264i) q^{4} +(-2.23607 - 0.00136408i) q^{5} +(1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +O(q^{10})\)	\(q+(2.17942 - 1.25829i) q^{2} +(2.16659 - 3.75264i) q^{4} +(-2.23607 - 0.00136408i) q^{5} +(1.31340 - 2.29673i) q^{7} -5.87162i q^{8} +(-4.87505 + 2.81065i) q^{10} +(0.489068 - 0.847090i) q^{11} +5.14977i q^{13} +(-0.0275122 - 6.65819i) q^{14} +(-3.05502 - 5.29146i) q^{16} +(3.59380 + 2.07488i) q^{17} +(-1.15001 - 1.99187i) q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +(-4.39324 + 2.53644i) q^{23} +(5.00000 + 0.00610036i) q^{25} +(6.47990 + 11.2235i) q^{26} +(-5.77323 - 9.90478i) q^{28} +5.92664 q^{29} +(-0.316594 + 0.548357i) q^{31} +(-3.14643 - 1.81659i) q^{32} +10.4432 q^{34} +(-2.93998 + 5.13386i) q^{35} +(-7.84188 + 4.52751i) q^{37} +(-5.01270 - 2.89408i) q^{38} +(-0.00800937 + 13.1293i) q^{40} -2.65505 q^{41} +0.344947i q^{43} +(-2.11922 - 3.67059i) q^{44} +(-6.38315 + 11.0559i) q^{46} +(-3.67059 + 2.11922i) q^{47} +(-3.54998 - 6.03305i) q^{49} +(10.9048 - 6.27815i) q^{50} +(19.3252 + 11.1574i) q^{52} +(6.61053 + 3.81659i) q^{53} +(-1.09474 + 1.89348i) q^{55} +(-13.4855 - 7.71176i) q^{56} +(12.9167 - 7.45743i) q^{58} +(-0.908297 + 1.57322i) q^{59} +(-0.328128 - 0.568335i) q^{61} +1.59347i q^{62} +3.07689 q^{64} +(0.00702471 - 11.5152i) q^{65} +(-8.01924 - 4.62991i) q^{67} +(15.5726 - 8.99083i) q^{68} +(0.0524368 + 14.8882i) q^{70} +5.49351 q^{71} +(-4.65758 - 2.68905i) q^{73} +(-11.3938 + 19.7347i) q^{74} -9.96636 q^{76} +(-1.30320 - 2.23582i) q^{77} +(-5.44346 - 9.42835i) q^{79} +(6.82402 + 11.8362i) q^{80} +(-5.78648 + 3.34083i) q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +(0.434043 + 0.751785i) q^{86} +(-4.97379 - 2.87162i) q^{88} +(-8.15542 - 14.1256i) q^{89} +(11.8277 + 6.76369i) q^{91} +21.9817i q^{92} +(-5.33317 + 9.23733i) q^{94} +(2.56878 + 4.45553i) q^{95} +1.53844i q^{97} +(-15.3282 - 8.68165i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more