LMFDB - Embedded newform 819.2.bm.f.550.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.2
Root			$0.874681 + 1.11128i$ of defining polynomial
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.f.478.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34523i q^{2} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.44601 + 1.00849i) q^{7} -2.94654i q^{8} +O(q^{10})$	\(q-1.34523i q^{2} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.44601 + 1.00849i) q^{7} -2.94654i q^{8} +(2.39973 + 4.15646i) q^{10} +(1.10736 - 0.639336i) q^{11} +(3.57420 + 0.474474i) q^{13} +(1.35664 + 3.29043i) q^{14} -3.58303 q^{16} +7.73920 q^{17} +(0.817422 + 0.471939i) q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} +1.64727 q^{23} +(3.86451 - 6.69354i) q^{25} +(0.638275 - 4.80810i) q^{26} +(-0.465638 + 0.191982i) q^{28} +(2.02242 - 3.50293i) q^{29} +(4.46193 + 2.57610i) q^{31} -1.07309i q^{32} -10.4110i q^{34} +(5.75861 - 7.47941i) q^{35} +1.05608i q^{37} +(0.634865 - 1.09962i) q^{38} +(5.25629 + 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(0.210805 - 0.121708i) q^{44} -2.21596i q^{46} +(-0.774415 + 0.447109i) q^{47} +(4.96591 - 4.93353i) q^{49} +(-9.00432 - 5.19865i) q^{50} +(0.680407 + 0.0903239i) q^{52} +(-0.0399961 + 0.0692754i) q^{53} +(-2.28101 + 3.95082i) q^{55} +(2.97154 + 7.20726i) q^{56} +(-4.71224 - 2.72061i) q^{58} +11.1847i q^{59} +(3.81196 - 6.60251i) q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(-11.8899 + 4.90994i) q^{65} +(5.47418 - 3.16052i) q^{67} +1.47328 q^{68} +(-10.0615 - 7.74664i) q^{70} +(-9.89346 + 5.71199i) q^{71} +(0.658617 + 0.380253i) q^{73} +1.42067 q^{74} +(0.155610 + 0.0898413i) q^{76} +(-2.06386 + 2.68058i) q^{77} +(1.42765 + 2.47277i) q^{79} +(11.0708 - 6.39172i) q^{80} +(2.82418 - 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(4.46270 - 2.57654i) q^{86} +(-1.88383 - 3.26289i) q^{88} -7.57626i q^{89} +(-9.22101 + 2.44396i) q^{91} +0.313586 q^{92} +(0.601462 + 1.04176i) q^{94} -3.36755 q^{95} +(-0.414443 + 0.239279i) q^{97} +(-6.63671 - 6.68028i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.34523i		−	0.951219i	−0.879657	−	0.475609i	$-0.842228\pi$
$2$		−	1.34523i		−	0.951219i	0.879657	−	0.475609i	$-0.157772\pi$
$3$		0			0
$3$		0			0
$4$	0.190366			0.0951832
$5$	−3.08979	+	1.78389i	−1.38179	+	0.797779i	−0.992372	−	0.123280i	$-0.960659\pi$
$5$	−3.08979	+	1.78389i	−1.38179	+	0.797779i	−0.389422	+	0.921059i	$0.627325\pi$
$6$		0			0
$7$	−2.44601	+	1.00849i	−0.924504	+	0.381172i
$7$	−2.44601	+	1.00849i	−0.924504	+	0.381172i
$8$		−	2.94654i		−	1.04176i
$9$		0			0
$10$	2.39973	+	4.15646i	0.758862	+	1.31439i
$11$	1.10736	−	0.639336i	0.333882	−	0.192767i	−0.323681	−	0.946166i	$-0.604920\pi$
$11$	1.10736	−	0.639336i	0.333882	−	0.192767i	0.657563	+	0.753399i	$0.271587\pi$
$12$		0			0
$13$	3.57420	+	0.474474i	0.991304	+	0.131595i
$13$	3.57420	+	0.474474i	0.991304	+	0.131595i
$14$	1.35664	+	3.29043i	0.362578	+	0.879406i
$15$		0			0
$16$	−3.58303			−0.895757
$17$	7.73920			1.87703			0.938515	−	0.345238i	$-0.112202\pi$
$17$	7.73920			1.87703			0.938515	+	0.345238i	$0.112202\pi$
$18$		0			0
$19$	0.817422	+	0.471939i	0.187530	+	0.108270i	0.590826	−	0.806799i	$-0.298802\pi$
$19$	0.817422	+	0.471939i	0.187530	+	0.108270i	−0.403296	+	0.915070i	$0.632135\pi$
$20$	−0.588191	+	0.339592i	−0.131524	+	0.0759352i
$21$		0			0
$22$	−0.860052	−	1.48965i	−0.183364	−	0.317595i
$23$	1.64727			0.343481			0.171740	−	0.985142i	$-0.445061\pi$
$23$	1.64727			0.343481			0.171740	+	0.985142i	$0.445061\pi$
$24$		0			0
$25$	3.86451	−	6.69354i	0.772903	−	1.33871i
$26$	0.638275	−	4.80810i	0.125176	−	0.942946i
$27$		0			0
$28$	−0.465638	+	0.191982i	−0.0879973	+	0.0362812i
$29$	2.02242	−	3.50293i	0.375554	−	0.650478i	−0.614856	−	0.788639i	$-0.710786\pi$
$29$	2.02242	−	3.50293i	0.375554	−	0.650478i	0.990410	+	0.138161i	$0.0441192\pi$
$30$		0			0
$31$	4.46193	+	2.57610i	0.801387	+	0.462681i	0.843956	−	0.536413i	$-0.180221\pi$
$31$	4.46193	+	2.57610i	0.801387	+	0.462681i	−0.0425691	+	0.999094i	$0.513554\pi$
$32$		−	1.07309i		−	0.189698i
$33$		0			0
$34$		−	10.4110i		−	1.78547i
$35$	5.75861	−	7.47941i	0.973383	−	1.26425i
$36$		0			0
$37$			1.05608i			0.173619i	0.996225	+	0.0868094i	$0.0276671\pi$
$37$			1.05608i			0.173619i	−0.996225	+	0.0868094i	$0.972333\pi$
$38$	0.634865	−	1.09962i	0.102989	−	0.178382i
$39$		0			0
$40$	5.25629	+	9.10417i	0.831093	+	1.43950i
$41$	3.63629	+	2.09941i	0.567893	+	0.327873i	0.756307	−	0.654217i	$-0.227002\pi$
$41$	3.63629	+	2.09941i	0.567893	+	0.327873i	−0.188415	+	0.982090i	$0.560335\pi$
$42$		0			0
$43$	1.91532	+	3.31744i	0.292084	+	0.505904i	0.974302	−	0.225244i	$-0.0723180\pi$
$43$	1.91532	+	3.31744i	0.292084	+	0.505904i	−0.682218	+	0.731148i	$0.738985\pi$
$44$	0.210805	−	0.121708i	0.0317800	−	0.0183482i
$45$		0			0
$46$		−	2.21596i		−	0.326725i
$47$	−0.774415	+	0.447109i	−0.112960	+	0.0652175i	−0.555416	−	0.831573i	$-0.687441\pi$
$47$	−0.774415	+	0.447109i	−0.112960	+	0.0652175i	0.442456	+	0.896790i	$0.354107\pi$
$48$		0			0
$49$	4.96591	−	4.93353i	0.709416	−	0.704790i
$50$	−9.00432	−	5.19865i	−1.27340	−	0.735200i
$51$		0			0
$52$	0.680407	+	0.0903239i	0.0943554	+	0.0125257i
$53$	−0.0399961	+	0.0692754i	−0.00549389	+	0.00951570i	−0.868759	−	0.495235i	$-0.835082\pi$
$53$	−0.0399961	+	0.0692754i	−0.00549389	+	0.00951570i	0.863265	+	0.504750i	$0.168415\pi$
$54$		0			0
$55$	−2.28101	+	3.95082i	−0.307571	+	0.532729i
$56$	2.97154	+	7.20726i	0.397089	+	0.963110i
$57$		0			0
$58$	−4.71224	−	2.72061i	−0.618747	−	0.357234i
$59$			11.1847i			1.45613i	0.685509	+	0.728064i	$0.259580\pi$
$59$			11.1847i			1.45613i	−0.685509	+	0.728064i	$0.740420\pi$
$60$		0			0
$61$	3.81196	−	6.60251i	0.488072	−	0.845365i	−0.511834	−	0.859084i	$-0.671034\pi$
$61$	3.81196	−	6.60251i	0.488072	−	0.845365i	0.999906	+	0.0137195i	$0.00436719\pi$
$62$	3.46543	−	6.00231i	0.440111	−	0.762294i
$63$		0			0
$64$	−8.60961			−1.07620
$65$	−11.8899	+	4.90994i	−1.47476	+	0.609003i
$66$		0			0
$67$	5.47418	−	3.16052i	0.668777	−	0.386119i	−0.126836	−	0.991924i	$-0.540482\pi$
$67$	5.47418	−	3.16052i	0.668777	−	0.386119i	0.795613	+	0.605805i	$0.207149\pi$
$68$	1.47328			0.178662
$69$		0			0
$70$	−10.0615	−	7.74664i	−1.20258	−	0.925900i
$71$	−9.89346	+	5.71199i	−1.17414	+	0.677889i	−0.954651	−	0.297727i	$-0.903772\pi$
$71$	−9.89346	+	5.71199i	−1.17414	+	0.677889i	−0.219487	+	0.975616i	$0.570438\pi$
$72$		0			0
$73$	0.658617	+	0.380253i	0.0770853	+	0.0445052i	0.538047	−	0.842915i	$-0.319162\pi$
$73$	0.658617	+	0.380253i	0.0770853	+	0.0445052i	−0.460962	+	0.887420i	$0.652496\pi$
$74$	1.42067			0.165149
$75$		0			0
$76$	0.155610	+	0.0898413i	0.0178497	+	0.0103055i
$77$	−2.06386	+	2.68058i	−0.235198	+	0.305481i
$78$		0			0
$79$	1.42765	+	2.47277i	0.160624	+	0.278208i	0.935093	−	0.354404i	$-0.115316\pi$
$79$	1.42765	+	2.47277i	0.160624	+	0.278208i	−0.774469	+	0.632612i	$0.781983\pi$
$80$	11.0708	−	6.39172i	1.23775	−	0.714616i
$81$		0			0
$82$	2.82418	−	4.89163i	0.311879	−	0.540190i
$83$			2.32483i			0.255183i	0.991827	+	0.127591i	$0.0407246\pi$
$83$			2.32483i			0.255183i	−0.991827	+	0.127591i	$0.959275\pi$
$84$		0			0
$85$	−23.9125	+	13.8059i	−2.59367	+	1.49746i
$86$	4.46270	−	2.57654i	0.481226	−	0.277836i
$87$		0			0
$88$	−1.88383	−	3.26289i	−0.200817	−	0.347825i
$89$		−	7.57626i		−	0.803082i	−0.915841	−	0.401541i	$-0.868475\pi$
$89$		−	7.57626i		−	0.803082i	0.915841	−	0.401541i	$-0.131525\pi$
$90$		0			0
$91$	−9.22101	+	2.44396i	−0.966625	+	0.256196i
$92$	0.313586			0.0326936
$93$		0			0
$94$	0.601462	+	1.04176i	0.0620361	+	0.107450i
$95$	−3.36755			−0.345503
$96$		0			0
$97$	−0.414443	+	0.239279i	−0.0420803	+	0.0242951i	−0.520893	−	0.853622i	$-0.674401\pi$
$97$	−0.414443	+	0.239279i	−0.0420803	+	0.0242951i	0.478812	+	0.877917i	$0.341067\pi$
$98$	−6.63671	−	6.68028i	−0.670409	−	0.674810i
$99$		0			0
$100$	0.735674	−	1.27422i	0.0735674	−	0.127422i
$101$	−1.43918	−	2.49273i	−0.143204	−	0.248036i	0.785498	−	0.618865i	$-0.212407\pi$
$101$	−1.43918	−	2.49273i	−0.143204	−	0.248036i	−0.928701	+	0.370829i	$0.879074\pi$
$102$		0			0
$103$	−5.66755	−	9.81649i	−0.558441	−	0.967248i	−0.997627	−	0.0688516i	$-0.978066\pi$
$103$	−5.66755	−	9.81649i	−0.558441	−	0.967248i	0.439186	−	0.898396i	$-0.355267\pi$
$104$	1.39806	−	10.5315i	0.137091	−	1.03270i
$105$		0			0
$106$	0.0931910	+	0.0538039i	0.00905151	+	0.00522589i
$107$	6.57206			0.635345			0.317673	−	0.948200i	$-0.397099\pi$
$107$	6.57206			0.635345			0.317673	+	0.948200i	$0.397099\pi$
$108$		0			0
$109$	−5.05684	−	2.91957i	−0.484358	−	0.279644i	0.237873	−	0.971296i	$-0.423550\pi$
$109$	−5.05684	−	2.91957i	−0.484358	−	0.279644i	−0.722231	+	0.691652i	$0.756883\pi$
$110$	5.31475	+	3.06847i	0.506741	+	0.292567i
$111$		0			0
$112$	8.76412	−	3.61343i	0.828131	−	0.341437i
$113$	3.26617	+	5.65717i	0.307255	+	0.532181i	0.977761	−	0.209723i	$-0.0672562\pi$
$113$	3.26617	+	5.65717i	0.307255	+	0.532181i	−0.670506	+	0.741904i	$0.733923\pi$
$114$		0			0
$115$	−5.08973	+	2.93855i	−0.474619	+	0.274022i
$116$	0.385001	−	0.666841i	0.0357464	−	0.0619146i
$117$		0			0
$118$	15.0460			1.38510
$119$	−18.9301	+	7.80487i	−1.73532	+	0.715471i
$120$		0			0
$121$	−4.68250	+	8.11033i	−0.425682	+	0.737302i
$122$	−8.88187	−	5.12795i	−0.804127	−	0.464263i
$123$		0			0
$124$	0.849402	+	0.490402i	0.0762786	+	0.0440394i
$125$			9.73656i			0.870865i
$126$		0			0
$127$	7.35818	−	12.7447i	0.652932	−	1.13091i	−0.329475	−	0.944164i	$-0.606872\pi$
$127$	7.35818	−	12.7447i	0.652932	−	1.13091i	0.982408	−	0.186748i	$-0.0597948\pi$
$128$			9.43568i			0.834005i
$129$		0			0
$130$	6.60498	+	15.9946i	0.579295	+	1.40282i
$131$	5.59335	+	9.68796i	0.488693	+	0.846441i	0.999915	−	0.0130074i	$-0.00414049\pi$
$131$	5.59335	+	9.68796i	0.488693	+	0.846441i	−0.511222	+	0.859448i	$0.670807\pi$
$132$		0			0
$133$	−2.47537	−	0.330008i	−0.214641	−	0.0286153i
$134$	−4.25161	−	7.36400i	−0.367283	−	0.636153i
$135$		0			0
$136$		−	22.8038i		−	1.95541i
$137$		−	17.6308i		−	1.50630i	−0.657848	−	0.753151i	$-0.728533\pi$
$137$		−	17.6308i		−	1.50630i	0.657848	−	0.753151i	$-0.271467\pi$
$138$		0			0
$139$	2.92855	+	5.07240i	0.248396	+	0.430235i	0.963081	−	0.269212i	$-0.0867631\pi$
$139$	2.92855	+	5.07240i	0.248396	+	0.430235i	−0.714685	+	0.699447i	$0.753430\pi$
$140$	1.09625	−	1.42383i	0.0926497	−	0.120335i
$141$		0			0
$142$	7.68392	+	13.3089i	0.644820	+	1.11686i
$143$	4.26128	−	1.75970i	0.356346	−	0.147153i
$144$		0			0
$145$			14.4311i			1.19844i
$146$	0.511526	−	0.885989i	0.0423342	−	0.0733250i
$147$		0			0
$148$			0.201043i			0.0165256i
$149$	−9.07505	−	5.23948i	−0.743457	−	0.429235i	0.0798677	−	0.996805i	$-0.474550\pi$
$149$	−9.07505	−	5.23948i	−0.743457	−	0.429235i	−0.823325	+	0.567570i	$0.807884\pi$
$150$		0			0
$151$	−4.08249	−	2.35703i	−0.332229	−	0.191812i	0.324602	−	0.945851i	$-0.394770\pi$
$151$	−4.08249	−	2.35703i	−0.332229	−	0.191812i	−0.656830	+	0.754039i	$0.728103\pi$
$152$	1.39059	−	2.40857i	0.112791	−	0.195361i
$153$		0			0
$154$	3.60599	+	2.77635i	0.290579	+	0.223725i
$155$	−18.3819			−1.47647
$156$		0			0
$157$	−4.50105	+	7.79604i	−0.359223	+	0.622192i	−0.987831	−	0.155530i	$-0.950291\pi$
$157$	−4.50105	+	7.79604i	−0.359223	+	0.622192i	0.628608	+	0.777722i	$0.283625\pi$
$158$	3.32643	−	1.92052i	0.264637	−	0.152788i
$159$		0			0
$160$	1.91428	+	3.31563i	0.151337	+	0.262123i
$161$	−4.02925	+	1.66125i	−0.317549	+	0.130925i
$162$		0			0
$163$	10.4203	+	6.01619i	0.816185	+	0.471224i	0.849099	−	0.528234i	$-0.177146\pi$
$163$	10.4203	+	6.01619i	0.816185	+	0.471224i	−0.0329144	+	0.999458i	$0.510479\pi$
$164$	0.692227	+	0.399657i	0.0540538	+	0.0312080i
$165$		0			0
$166$	3.12742			0.242735
$167$	16.8199	+	9.71099i	1.30157	+	0.751459i	0.980672	−	0.195657i	$-0.0626838\pi$
$167$	16.8199	+	9.71099i	1.30157	+	0.751459i	0.320893	+	0.947116i	$0.396017\pi$
$168$		0			0
$169$	12.5497	+	3.39173i	0.965365	+	0.260902i
$170$	18.5720	+	32.1677i	1.42441	+	2.46715i
$171$		0			0
$172$	0.364613	+	0.631528i	0.0278015	+	0.0481536i
$173$	−7.18976	+	12.4530i	−0.546627	+	0.946786i	0.451875	+	0.892081i	$0.350755\pi$
$173$	−7.18976	+	12.4530i	−0.546627	+	0.946786i	−0.998503	+	0.0547049i	$0.982578\pi$
$174$		0			0
$175$	−2.70230	+	20.2697i	−0.204275	+	1.53225i
$176$	−3.96771	+	2.29076i	−0.299077	+	0.172672i
$177$		0			0
$178$	−10.1918			−0.763907
$179$	−2.71303	−	4.69911i	−0.202781	−	0.351228i	0.746642	−	0.665226i	$-0.231665\pi$
$179$	−2.71303	−	4.69911i	−0.202781	−	0.351228i	−0.949424	+	0.313998i	$0.898331\pi$
$180$		0			0
$181$	−15.4902			−1.15138			−0.575688	−	0.817669i	$-0.695266\pi$
$181$	−15.4902			−1.15138			−0.575688	+	0.817669i	$0.695266\pi$
$182$	3.28768	+	12.4043i	0.243699	+	0.919471i
$183$		0			0
$184$		−	4.85376i		−	0.357824i
$185$	−1.88393	−	3.26307i	−0.138509	−	0.239905i
$186$		0			0
$187$	8.57010	−	4.94795i	0.626707	−	0.361830i
$188$	−0.147423	+	0.0851144i	−0.0107519	+	0.00620761i
$189$		0			0
$190$			4.53011i			0.328649i
$191$	2.37311	−	4.11035i	0.171712	−	0.297414i	−0.767306	−	0.641281i	$-0.778403\pi$
$191$	2.37311	−	4.11035i	0.171712	−	0.297414i	0.939019	+	0.343866i	$0.111737\pi$
$192$		0			0
$193$	18.2204	−	10.5196i	1.31154	−	0.757215i	0.329185	−	0.944266i	$-0.393226\pi$
$193$	18.2204	−	10.5196i	1.31154	−	0.757215i	0.982350	+	0.187050i	$0.0598928\pi$
$194$	0.321884	+	0.557519i	0.0231099	+	0.0400276i
$195$		0			0
$196$	0.945343	−	0.939178i	0.0675245	−	0.0670842i
$197$	−5.03342	−	2.90604i	−0.358616	−	0.207047i	0.309857	−	0.950783i	$-0.399719\pi$
$197$	−5.03342	−	2.90604i	−0.358616	−	0.207047i	−0.668474	+	0.743736i	$0.733052\pi$
$198$		0			0
$199$	−10.6182			−0.752703			−0.376352	−	0.926477i	$-0.622821\pi$
$199$	−10.6182			−0.752703			−0.376352	+	0.926477i	$0.622821\pi$
$200$	−19.7228	−	11.3869i	−1.39461	−	0.805178i
$201$		0			0
$202$	−3.35329	+	1.93602i	−0.235936	+	0.136218i
$203$	−1.41420	+	10.6078i	−0.0992571	+	0.744520i
$204$		0			0
$205$	−14.9805			−1.04628
$206$	−13.2054	+	7.62414i	−0.920064	+	0.531199i
$207$		0			0
$208$	−12.8064	−	1.70005i	−0.887967	−	0.117877i
$209$	1.20691			0.0834837
$210$		0			0
$211$	2.33275	−	4.04043i	0.160593	−	0.278155i	−0.774489	−	0.632588i	$-0.781993\pi$
$211$	2.33275	−	4.04043i	0.160593	−	0.278155i	0.935081	+	0.354433i	$0.115326\pi$
$212$	−0.00761392	+	0.0131877i	−0.000522926	+	0.000905735i
$213$		0			0
$214$		−	8.84091i		−	0.604352i
$215$	−11.8359	−	6.83344i	−0.807200	−	0.466037i
$216$		0			0
$217$	−13.5119	−	1.80136i	−0.917246	−	0.122284i
$218$	−3.92748	+	6.80260i	−0.266003	+	0.460730i
$219$		0			0
$220$	−0.434227	+	0.752104i	−0.0292756	+	0.0507068i
$221$	27.6614	+	3.67205i	1.86071	+	0.247009i
$222$		0			0
$223$	20.9798	+	12.1127i	1.40491	+	0.811126i	0.994891	−	0.100950i	$-0.0321883\pi$
$223$	20.9798	+	12.1127i	1.40491	+	0.811126i	0.410020	+	0.912076i	$0.365522\pi$
$224$	1.08220	+	2.62480i	0.0723075	+	0.175377i
$225$		0			0
$226$	7.61017	−	4.39373i	0.506221	−	0.292267i
$227$		−	15.3753i		−	1.02049i	−0.860028	−	0.510247i	$-0.829554\pi$
$227$		−	15.3753i		−	1.02049i	0.860028	−	0.510247i	$-0.170446\pi$
$228$		0			0
$229$	−14.1608	+	8.17573i	−0.935771	+	0.540268i	−0.888632	−	0.458621i	$-0.848344\pi$
$229$	−14.1608	+	8.17573i	−0.935771	+	0.540268i	−0.0471389	+	0.998888i	$0.515010\pi$
$230$	3.95302	+	6.84683i	0.260654	+	0.451467i
$231$		0			0
$232$	−10.3215	−	5.95913i	−0.677641	−	0.391236i
$233$	14.5554	+	25.2106i	0.953554	+	1.65160i	0.737643	+	0.675191i	$0.235939\pi$
$233$	14.5554	+	25.2106i	0.953554	+	1.65160i	0.215911	+	0.976413i	$0.430728\pi$
$234$		0			0
$235$	1.59518	−	2.76294i	0.104058	−	0.180234i
$236$			2.12920i			0.138599i
$237$		0			0
$238$	10.4993	+	25.4653i	0.680570	+	1.65067i
$239$		−	8.65409i		−	0.559787i	−0.960031	−	0.279893i	$-0.909701\pi$
$239$		−	8.65409i		−	0.559787i	0.960031	−	0.279893i	$-0.0902991\pi$
$240$		0			0
$241$		−	18.1982i		−	1.17225i	−0.810222	−	0.586124i	$-0.800653\pi$
$241$		−	18.1982i		−	1.17225i	0.810222	−	0.586124i	$-0.199347\pi$
$242$	10.9102	+	6.29902i	0.701336	+	0.404916i
$243$		0			0
$244$	0.725669	−	1.25690i	0.0464562	−	0.0804645i
$245$	−6.54274	+	24.1022i	−0.418000	+	1.53983i
$246$		0			0
$247$	2.69770	+	2.07465i	0.171651	+	0.132007i
$248$	7.59057	−	13.1473i	0.482002	−	0.834851i
$249$		0			0
$250$	13.0979			0.828383
$251$	−7.93598	−	13.7455i	−0.500915	−	0.867610i	−0.999999	−	0.00105678i	$-0.999664\pi$
$251$	−7.93598	−	13.7455i	−0.500915	−	0.867610i	0.499085	−	0.866553i	$-0.333670\pi$
$252$		0			0
$253$	1.82413	−	1.05316i	0.114682	−	0.0662117i
$254$	−17.1446	−	9.89841i	−1.07574	−	0.621082i
$255$		0			0
$256$	−4.52609			−0.282880
$257$	−24.3267			−1.51746			−0.758730	−	0.651406i	$-0.774180\pi$
$257$	−24.3267			−1.51746			−0.758730	+	0.651406i	$0.774180\pi$
$258$		0			0
$259$	−1.06504	−	2.58319i	−0.0661786	−	0.160511i
$260$	−2.26344	+	0.934688i	−0.140372	+	0.0579669i
$261$		0			0
$262$	13.0325	−	7.52432i	0.805150	−	0.464854i
$263$	7.71727	+	13.3667i	0.475867	+	0.824226i	0.999618	−	0.0276456i	$-0.00880099\pi$
$263$	7.71727	+	13.3667i	0.475867	+	0.824226i	−0.523751	+	0.851872i	$0.675468\pi$
$264$		0			0
$265$		−	0.285395i		−	0.0175317i
$266$	−0.443935	+	3.32993i	−0.0272194	+	0.204171i
$267$		0			0
$268$	1.04210	−	0.601656i	0.0636563	−	0.0367520i
$269$	13.0407			0.795106			0.397553	−	0.917579i	$-0.369859\pi$
$269$	13.0407			0.795106			0.397553	+	0.917579i	$0.369859\pi$
$270$		0			0
$271$			26.9706i			1.63835i	0.573544	+	0.819174i	$0.305568\pi$
$271$			26.9706i			1.63835i	−0.573544	+	0.819174i	$0.694432\pi$
$272$	−27.7298			−1.68136
$273$		0			0
$274$	−23.7174			−1.43282
$275$		−	9.88289i		−	0.595961i
$276$		0			0
$277$	−12.7015			−0.763156			−0.381578	−	0.924337i	$-0.624619\pi$
$277$	−12.7015			−0.763156			−0.381578	+	0.924337i	$0.624619\pi$
$278$	6.82352	−	3.93956i	0.409248	−	0.236279i
$279$		0			0
$280$	−22.0384	−	16.9680i	−1.31704	−	1.01403i
$281$		−	26.7216i		−	1.59408i	−0.603930	−	0.797038i	$-0.706399\pi$
$281$		−	26.7216i		−	1.59408i	0.603930	−	0.797038i	$-0.293601\pi$
$282$		0			0
$283$	7.37113	+	12.7672i	0.438168	+	0.758929i	0.997548	−	0.0699819i	$-0.0222941\pi$
$283$	7.37113	+	12.7672i	0.438168	+	0.758929i	−0.559380	+	0.828911i	$0.688961\pi$
$284$	−1.88338	+	1.08737i	−0.111758	+	0.0645236i
$285$		0			0
$286$	−2.36719	−	5.73238i	−0.139975	−	0.338963i
$287$	−11.0116	−	1.46803i	−0.649995	−	0.0866553i
$288$		0			0
$289$	42.8952			2.52324
$290$	19.4131			1.13997
$291$		0			0
$292$	0.125379	+	0.0723874i	0.00733723	+	0.00423615i
$293$	10.0312	−	5.79153i	0.586030	−	0.338345i	−0.177496	−	0.984121i	$-0.556800\pi$
$293$	10.0312	−	5.79153i	0.586030	−	0.338345i	0.763526	+	0.645777i	$0.223466\pi$
$294$		0			0
$295$	−19.9523	−	34.5584i	−1.16167	−	2.01207i
$296$	3.11179			0.180869
$297$		0			0
$298$	−7.04829	+	12.2080i	−0.408297	+	0.707190i
$299$	5.88768	+	0.781589i	0.340493	+	0.0452005i
$300$		0			0
$301$	−8.03048	−	6.18290i	−0.462869	−	0.356376i
$302$	−3.17074	+	5.49188i	−0.182455	+	0.316022i
$303$		0			0
$304$	−2.92885	−	1.69097i	−0.167981	−	0.0969838i
$305$			27.2004i			1.55749i
$306$		0			0
$307$			29.3335i			1.67415i	0.547086	+	0.837076i	$0.315737\pi$
$307$			29.3335i			1.67415i	−0.547086	+	0.837076i	$0.684263\pi$
$308$	−0.392889	+	0.510293i	−0.0223869	+	0.0290766i
$309$		0			0
$310$			24.7278i			1.40444i
$311$	0.0753271	−	0.130470i	0.00427141	−	0.00739830i	−0.863882	−	0.503695i	$-0.831974\pi$
$311$	0.0753271	−	0.130470i	0.00427141	−	0.00739830i	0.868153	+	0.496296i	$0.165307\pi$
$312$		0			0
$313$	5.26057	+	9.11157i	0.297345	+	0.515016i	0.975528	−	0.219877i	$-0.0705656\pi$
$313$	5.26057	+	9.11157i	0.297345	+	0.515016i	−0.678183	+	0.734893i	$0.737232\pi$
$314$	10.4874	+	6.05493i	0.591841	+	0.341699i
$315$		0			0
$316$	0.271777	+	0.470732i	0.0152887	+	0.0264808i
$317$	−1.30489	+	0.753380i	−0.0732901	+	0.0423140i	−0.536197	−	0.844093i	$-0.680140\pi$
$317$	−1.30489	+	0.753380i	−0.0732901	+	0.0423140i	0.462907	+	0.886407i	$0.346806\pi$
$318$		0			0
$319$		−	5.17202i		−	0.289578i
$320$	26.6018	−	15.3586i	1.48709	−	0.858571i
$321$		0			0
$322$	2.23476	+	5.42025i	0.124538	+	0.302059i
$323$	6.32619	+	3.65243i	0.351999	+	0.203227i
$324$		0			0
$325$	16.9884	−	22.0904i	0.942349	−	1.22535i
$326$	8.09314	−	14.0177i	0.448237	−	0.776370i
$327$		0			0
$328$	6.18600	−	10.7145i	0.341565	−	0.591607i
$329$	1.44332	−	1.87462i	0.0795729	−	0.103351i
$330$		0			0
$331$	−21.8679	−	12.6254i	−1.20197	−	0.693957i	−0.240976	−	0.970531i	$-0.577467\pi$
$331$	−21.8679	−	12.6254i	−1.20197	−	0.693957i	−0.960993	+	0.276574i	$0.910801\pi$
$332$			0.442569i			0.0242891i
$333$		0			0
$334$	13.0635	−	22.6266i	0.714802	−	1.23807i
$335$	−11.2760	+	19.5306i	−0.616075	+	1.06707i
$336$		0			0
$337$	32.1811			1.75302			0.876509	−	0.481386i	$-0.159866\pi$
$337$	32.1811			1.75302			0.876509	+	0.481386i	$0.159866\pi$
$338$	4.56264	−	16.8823i	0.248175	−	0.918273i
$339$		0			0
$340$	−4.55213	+	2.62817i	−0.246874	+	0.142533i
$341$	6.58797			0.356759
$342$		0			0
$343$	−7.17127	+	17.0755i	−0.387212	+	0.921991i
$344$	9.77495	−	5.64357i	0.527030	−	0.304281i
$345$		0			0
$346$	16.7521	+	9.67185i	0.900600	+	0.519962i
$347$	−24.7638			−1.32939			−0.664695	−	0.747115i	$-0.731438\pi$
$347$	−24.7638			−1.32939			−0.664695	+	0.747115i	$0.731438\pi$
$348$		0			0
$349$	−10.0075	−	5.77782i	−0.535688	−	0.309280i	0.207642	−	0.978205i	$-0.433421\pi$
$349$	−10.0075	−	5.77782i	−0.535688	−	0.309280i	−0.743330	+	0.668925i	$0.766755\pi$
$350$	27.2674	+	3.63520i	1.45750	+	0.194310i
$351$		0			0
$352$	−0.686067	−	1.18830i	−0.0365675	−	0.0633368i
$353$	17.3971	−	10.0442i	0.925953	−	0.534599i	0.0404237	−	0.999183i	$-0.487129\pi$
$353$	17.3971	−	10.0442i	0.925953	−	0.534599i	0.885529	+	0.464583i	$0.153796\pi$
$354$		0			0
$355$	20.3791	−	35.2977i	1.08161	−	1.87340i
$356$		−	1.44227i		−	0.0764399i
$357$		0			0
$358$	−6.32136	+	3.64964i	−0.334094	+	0.192890i
$359$	−13.0346	+	7.52551i	−0.687938	+	0.397181i	−0.802839	−	0.596196i	$-0.796678\pi$
$359$	−13.0346	+	7.52551i	−0.687938	+	0.397181i	0.114901	+	0.993377i	$0.463345\pi$
$360$		0			0
$361$	−9.05455	−	15.6829i	−0.476555	−	0.825418i
$362$			20.8378i			1.09521i
$363$		0			0
$364$	−1.75537	+	0.465248i	−0.0920064	+	0.0243856i
$365$	−2.71331			−0.142021
$366$		0			0
$367$	−4.50178	−	7.79731i	−0.234991	−	0.407016i	0.724279	−	0.689507i	$-0.242173\pi$
$367$	−4.50178	−	7.79731i	−0.234991	−	0.407016i	−0.959270	+	0.282491i	$0.908839\pi$
$368$	−5.90223			−0.307675
$369$		0			0
$370$	−4.38956	+	2.53431i	−0.228202	+	0.131753i
$371$	0.0279677	−	0.209784i	0.00145201	−	0.0108914i
$372$		0			0
$373$	8.06953	−	13.9768i	0.417824	−	0.723693i	−0.577896	−	0.816110i	$-0.696126\pi$
$373$	8.06953	−	13.9768i	0.417824	−	0.723693i	0.995720	+	0.0924174i	$0.0294594\pi$
$374$	−6.65611	−	11.5287i	−0.344179	−	0.596136i
$375$		0			0
$376$	1.31742	+	2.28184i	0.0679409	+	0.117677i
$377$	8.89057	−	11.5606i	0.457888	−	0.595400i
$378$		0			0
$379$	−13.5668	−	7.83277i	−0.696878	−	0.402342i	0.109306	−	0.994008i	$-0.465137\pi$
$379$	−13.5668	−	7.83277i	−0.696878	−	0.402342i	−0.806183	+	0.591666i	$0.798471\pi$
$380$	−0.641068			−0.0328861
$381$		0			0
$382$	−5.52935	−	3.19237i	−0.282906	−	0.163336i
$383$	−21.3327	−	12.3164i	−1.09005	−	0.629339i	−0.156459	−	0.987685i	$-0.550008\pi$
$383$	−21.3327	−	12.3164i	−1.09005	−	0.629339i	−0.933589	+	0.358345i	$0.883341\pi$
$384$		0			0
$385$	1.59502	−	11.9641i	0.0812896	−	0.609747i
$386$	−14.1512	−	24.5106i	−0.720277	−	1.24756i
$387$		0			0
$388$	−0.0788960	+	0.0455506i	−0.00400534	+	0.00231248i
$389$	9.42834	−	16.3304i	0.478036	−	0.827982i	−0.521647	−	0.853161i	$-0.674682\pi$
$389$	9.42834	−	16.3304i	0.478036	−	0.827982i	0.999683	+	0.0251791i	$0.00801560\pi$
$390$		0			0
$391$	12.7486			0.644724
$392$	−14.5368	−	14.6323i	−0.734221	−	0.739040i
$393$		0			0
$394$	−3.90929	+	6.77108i	−0.196947	+	0.341122i
$395$	−8.82229	−	5.09355i	−0.443897	−	0.256284i
$396$		0			0
$397$	−12.5600	−	7.25149i	−0.630366	−	0.363942i	0.150528	−	0.988606i	$-0.451903\pi$
$397$	−12.5600	−	7.25149i	−0.630366	−	0.363942i	−0.780894	+	0.624664i	$0.785236\pi$
$398$			14.2839i			0.715985i
$399$		0			0
$400$	−13.8467	+	23.9831i	−0.692333	+	1.19916i
$401$		−	20.9889i		−	1.04814i	−0.851676	−	0.524069i	$-0.824413\pi$
$401$		−	20.9889i		−	1.04814i	0.851676	−	0.524069i	$-0.175587\pi$
$402$		0			0
$403$	14.7255	+	11.3245i	0.733531	+	0.564116i
$404$	−0.273971	−	0.474532i	−0.0136306	−	0.0236089i
$405$		0			0
$406$	14.2699	+	1.90241i	0.708201	+	0.0944152i
$407$	0.675191	+	1.16947i	0.0334680	+	0.0579683i
$408$		0			0
$409$			21.4276i			1.05953i	0.848146	+	0.529763i	$0.177719\pi$
$409$			21.4276i			1.05953i	−0.848146	+	0.529763i	$0.822281\pi$
$410$			20.1521i			0.995242i
$411$		0			0
$412$	−1.07891	−	1.86873i	−0.0531542	−	0.0920657i
$413$	−11.2796	−	27.3580i	−0.555035	−	1.34620i
$414$		0			0
$415$	−4.14723	−	7.18321i	−0.203580	−	0.352610i
$416$	0.509155	−	3.83545i	0.0249634	−	0.188048i
$417$		0			0
$418$		−	1.62357i		−	0.0794113i
$419$	3.98203	−	6.89708i	0.194535	−	0.336944i	−0.752213	−	0.658920i	$-0.771014\pi$
$419$	3.98203	−	6.89708i	0.194535	−	0.336944i	0.946748	+	0.321976i	$0.104347\pi$
$420$		0			0
$421$		−	2.81786i		−	0.137334i	−0.997640	−	0.0686670i	$-0.978125\pi$
$421$		−	2.81786i		−	0.137334i	0.997640	−	0.0686670i	$-0.0218746\pi$
$422$	−5.43530	−	3.13807i	−0.264586	−	0.152759i
$423$		0			0
$424$	0.204122	+	0.117850i	0.00991306	+	0.00572331i
$425$	29.9082	−	51.8026i	1.45076	−	2.51279i
$426$		0			0
$427$	−2.66555	+	19.9941i	−0.128995	+	0.967582i
$428$	1.25110			0.0604742
$429$		0			0
$430$	−9.19253	+	15.9219i	−0.443303	+	0.767823i
$431$	−4.96775	+	2.86813i	−0.239288	+	0.138153i	−0.614849	−	0.788645i	$-0.710783\pi$
$431$	−4.96775	+	2.86813i	−0.239288	+	0.138153i	0.375561	+	0.926797i	$0.377450\pi$
$432$		0			0
$433$	−12.2628	−	21.2398i	−0.589314	−	1.02072i	−0.994322	−	0.106409i	$-0.966065\pi$
$433$	−12.2628	−	21.2398i	−0.589314	−	1.02072i	0.405009	−	0.914313i	$-0.367268\pi$
$434$	−2.42324	+	18.1765i	−0.116319	+	0.872502i
$435$		0			0
$436$	−0.962653	−	0.555788i	−0.0461027	−	0.0266174i
$437$	1.34652	+	0.777413i	0.0644128	+	0.0371887i
$438$		0			0
$439$	−36.6423			−1.74884			−0.874420	−	0.485169i	$-0.838758\pi$
$439$	−36.6423			−1.74884			−0.874420	+	0.485169i	$0.838758\pi$
$440$	11.6412	+	6.72108i	0.554975	+	0.320415i
$441$		0			0
$442$	4.93973	−	37.2108i	0.234959	−	1.76994i
$443$	13.5467	+	23.4635i	0.643622	+	1.11479i	0.984618	+	0.174721i	$0.0559022\pi$
$443$	13.5467	+	23.4635i	0.643622	+	1.11479i	−0.340996	+	0.940065i	$0.610764\pi$
$444$		0			0
$445$	13.5152	+	23.4090i	0.640682	+	1.10969i
$446$	16.2943	−	28.2226i	0.771558	−	1.33638i
$447$		0			0
$448$	21.0592	−	8.68267i	0.994953	−	0.410218i
$449$	−23.7571	+	13.7162i	−1.12117	+	0.647307i	−0.941699	−	0.336456i	$-0.890772\pi$
$449$	−23.7571	+	13.7162i	−1.12117	+	0.647307i	−0.179470	+	0.983764i	$0.557438\pi$
$450$		0			0
$451$	5.36892			0.252812
$452$	0.621768	+	1.07693i	0.0292455	+	0.0506547i
$453$		0			0
$454$	−20.6832			−0.970712
$455$	24.1312	−	24.0006i	1.13129	−	1.12516i
$456$		0			0
$457$		−	39.6639i		−	1.85540i	−0.373327	−	0.927700i	$-0.621783\pi$
$457$		−	39.6639i		−	1.85540i	0.373327	−	0.927700i	$-0.378217\pi$
$458$	10.9982	+	19.0495i	0.513913	+	0.890123i
$459$		0			0
$460$	−0.968913	+	0.559402i	−0.0451758	+	0.0260823i
$461$	4.23988	−	2.44790i	0.197471	−	0.114010i	−0.398004	−	0.917384i	$-0.630297\pi$
$461$	4.23988	−	2.44790i	0.197471	−	0.114010i	0.595475	+	0.803374i	$0.296964\pi$
$462$		0			0
$463$			4.71193i			0.218982i	0.993988	+	0.109491i	$0.0349221\pi$
$463$			4.71193i			0.218982i	−0.993988	+	0.109491i	$0.965078\pi$
$464$	−7.24638	+	12.5511i	−0.336405	+	0.582670i
$465$		0			0
$466$	33.9140	−	19.5803i	1.57104	−	0.907038i
$467$	−16.0081	−	27.7268i	−0.740765	−	1.28304i	−0.952147	−	0.305639i	$-0.901130\pi$
$467$	−16.0081	−	27.7268i	−0.740765	−	1.28304i	0.211383	−	0.977403i	$-0.432203\pi$
$468$		0			0
$469$	−10.2025	+	13.2513i	−0.471110	+	0.611887i
$470$	−3.71678	−	2.14588i	−0.171442	−	0.0989822i
$471$		0			0
$472$	32.9563			1.51693
$473$	4.24191	+	2.44907i	0.195043	+	0.112608i
$474$		0			0
$475$	6.31788	−	3.64763i	0.289884	−	0.167365i
$476$	−3.60366	+	1.48578i	−0.165174	+	0.0681008i
$477$		0			0
$478$	−11.6417			−0.532480
$479$	−15.6097	+	9.01224i	−0.713224	+	0.411780i	−0.812254	−	0.583305i	$-0.801759\pi$
$479$	−15.6097	+	9.01224i	−0.713224	+	0.411780i	0.0990298	+	0.995084i	$0.468426\pi$
$480$		0			0
$481$	−0.501083	+	3.77464i	−0.0228474	+	0.172109i
$482$	−24.4807			−1.11506
$483$		0			0
$484$	−0.891390	+	1.54393i	−0.0405177	+	0.0701788i
$485$	0.853693	−	1.47864i	0.0387642	−	0.0671416i
$486$		0			0
$487$			17.6004i			0.797550i	0.917049	+	0.398775i	$0.130565\pi$
$487$			17.6004i			0.797550i	−0.917049	+	0.398775i	$0.869435\pi$
$488$	−19.4545	−	11.2321i	−0.880666	−	0.508453i
$489$		0			0
$490$	32.4229	+	8.80146i	1.46472	+	0.397609i
$491$	−1.93180	+	3.34598i	−0.0871810	+	0.151002i	−0.906318	−	0.422595i	$-0.861119\pi$
$491$	−1.93180	+	3.34598i	−0.0871810	+	0.151002i	0.819138	+	0.573597i	$0.194453\pi$
$492$		0			0
$493$	15.6519	−	27.1099i	0.704926	−	1.22097i
$494$	2.79087	−	3.62902i	0.125567	−	0.163277i
$495$		0			0
$496$	−15.9872	−	9.23023i	−0.717848	−	0.414450i
$497$	18.4390	−	23.9490i	0.827103	−	1.07426i
$498$		0			0
$499$	−10.9528	+	6.32363i	−0.490317	+	0.283084i	−0.724706	−	0.689058i	$-0.758024\pi$
$499$	−10.9528	+	6.32363i	−0.490317	+	0.283084i	0.234389	+	0.972143i	$0.424691\pi$
$500$			1.85351i			0.0828917i
$501$		0			0
$502$	−18.4908	+	10.6757i	−0.825287	+	0.476480i
$503$	11.0180	+	19.0837i	0.491268	+	0.850902i	0.999949	−	0.0100533i	$-0.00320011\pi$
$503$	11.0180	+	19.0837i	0.491268	+	0.850902i	−0.508681	+	0.860955i	$0.669867\pi$
$504$		0			0
$505$	8.89351	+	5.13467i	0.395756	+	0.228490i
$506$	−1.41674	−	2.45387i	−0.0629818	−	0.109088i
$507$		0			0
$508$	1.40075	−	2.42617i	0.0621482	−	0.107644i
$509$			15.6702i			0.694568i	0.937760	+	0.347284i	$0.112896\pi$
$509$			15.6702i			0.694568i	−0.937760	+	0.347284i	$0.887104\pi$
$510$		0			0
$511$	−1.99446	−	0.265895i	−0.0882299	−	0.0117625i
$512$			24.9600i			1.10309i
$513$		0			0
$514$			32.7249i			1.44344i
$515$	35.0230	+	20.2206i	1.54330	+	0.891025i
$516$		0			0
$517$	−0.571705	+	0.990222i	−0.0251436	+	0.0435499i
$518$	−3.47497	+	1.43272i	−0.152681	+	0.0629503i
$519$		0			0
$520$	14.4673	+	35.0341i	0.634435	+	1.53635i
$521$	−12.6207	+	21.8598i	−0.552925	+	0.957694i	0.445137	+	0.895463i	$0.353155\pi$
$521$	−12.6207	+	21.8598i	−0.552925	+	0.957694i	−0.998062	+	0.0622317i	$0.980178\pi$
$522$		0			0
$523$	−13.2477			−0.579279			−0.289640	−	0.957136i	$-0.593535\pi$
$523$	−13.2477			−0.579279			−0.289640	+	0.957136i	$0.593535\pi$
$524$	1.06479	+	1.84426i	0.0465154	+	0.0805670i
$525$		0			0
$526$	17.9812	−	10.3815i	0.784019	−	0.452654i
$527$	34.5318	+	19.9369i	1.50423	+	0.868466i
$528$		0			0
$529$	−20.2865			−0.882021
$530$	−0.383920			−0.0166764
$531$		0			0
$532$	−0.471226	−	0.0628224i	−0.0204303	−	0.00272370i
$533$	12.0007	+	9.22903i	0.519807	+	0.399754i
$534$		0			0
$535$	−20.3063	+	11.7238i	−0.877916	+	0.506865i
$536$	−9.31258	−	16.1299i	−0.402242	−	0.696704i
$537$		0			0
$538$		−	17.5427i		−	0.756320i
$539$	2.34488	−	8.63809i	0.101001	−	0.372069i
$540$		0			0
$541$	−12.4737	+	7.20170i	−0.536287	+	0.309625i	−0.743573	−	0.668655i	$-0.766870\pi$
$541$	−12.4737	+	7.20170i	−0.536287	+	0.309625i	0.207286	+	0.978280i	$0.433537\pi$
$542$	36.2816			1.55843
$543$		0			0
$544$		−	8.30488i		−	0.356069i
$545$	20.8328			0.892377
$546$		0			0
$547$	2.00679			0.0858042			0.0429021	−	0.999079i	$-0.486340\pi$
$547$	2.00679			0.0858042			0.0429021	+	0.999079i	$0.486340\pi$
$548$		−	3.35631i		−	0.143375i
$549$		0			0
$550$	−13.2947			−0.566889
$551$	3.30634	−	1.90892i	0.140855	−	0.0813226i
$552$		0			0
$553$	−5.98581	−	4.60864i	−0.254542	−	0.195979i
$554$			17.0863i			0.725928i
$555$		0			0
$556$	0.557497	+	0.965614i	0.0236432	+	0.0409512i
$557$	7.42977	−	4.28958i	0.314810	−	0.181755i	−0.334267	−	0.942478i	$-0.608489\pi$
$557$	7.42977	−	4.28958i	0.314810	−	0.181755i	0.649077	+	0.760723i	$0.275155\pi$
$558$		0			0
$559$	5.27170	+	12.7659i	0.222969	+	0.539942i
$560$	−20.6333	+	26.7989i	−0.871915	+	1.13246i
$561$		0			0
$562$	−35.9466			−1.51631
$563$	−12.7744			−0.538375			−0.269188	−	0.963088i	$-0.586755\pi$
$563$	−12.7744			−0.538375			−0.269188	+	0.963088i	$0.586755\pi$
$564$		0			0
$565$	−20.1835	−	11.6530i	−0.849126	−	0.490243i
$566$	17.1747	−	9.91583i	0.721908	−	0.416794i
$567$		0			0
$568$	16.8306	+	29.1515i	0.706196	+	1.22317i
$569$	−5.79116			−0.242778			−0.121389	−	0.992605i	$-0.538735\pi$
$569$	−5.79116			−0.242778			−0.121389	+	0.992605i	$0.538735\pi$
$570$		0			0
$571$	−22.0666	+	38.2204i	−0.923458	+	1.59948i	−0.129435	+	0.991588i	$0.541316\pi$
$571$	−22.0666	+	38.2204i	−0.923458	+	1.59948i	−0.794023	+	0.607888i	$0.792017\pi$
$572$	0.811204	−	0.334987i	0.0339182	−	0.0140065i
$573$		0			0
$574$	−1.97484	+	14.8131i	−0.0824281	+	0.618287i
$575$	6.36592	−	11.0261i	0.265477	−	0.459820i
$576$		0			0
$577$	10.3343	+	5.96649i	0.430221	+	0.248388i	0.699441	−	0.714691i	$-0.253432\pi$
$577$	10.3343	+	5.96649i	0.430221	+	0.248388i	−0.269220	+	0.963079i	$0.586766\pi$
$578$		−	57.7037i		−	2.40016i
$579$		0			0
$580$			2.74719i			0.114071i
$581$	−2.34455	−	5.68654i	−0.0972685	−	0.235918i
$582$		0			0
$583$			0.102284i			0.00423617i
$584$	1.12043	−	1.94064i	0.0463637	−	0.0803043i
$585$		0			0
$586$	−7.79091	−	13.4943i	−0.321840	−	0.557443i
$587$	−17.6250	−	10.1758i	−0.727462	−	0.420000i	0.0900312	−	0.995939i	$-0.471303\pi$
$587$	−17.6250	−	10.1758i	−0.727462	−	0.420000i	−0.817493	+	0.575939i	$0.804637\pi$
$588$		0			0
$589$	2.43152	+	4.21152i	0.100189	+	0.173533i
$590$	−46.4889	+	26.8404i	−1.91392	+	1.10500i
$591$		0			0
$592$		−	3.78397i		−	0.155520i
$593$	−15.7443	+	9.09000i	−0.646543	+	0.373282i	−0.787130	−	0.616787i	$-0.788434\pi$
$593$	−15.7443	+	9.09000i	−0.646543	+	0.373282i	0.140588	+	0.990068i	$0.455101\pi$
$594$		0			0
$595$	44.5670	−	57.8846i	1.82707	−	2.37304i
$596$	−1.72759	−	0.997422i	−0.0707646	−	0.0408560i
$597$		0			0
$598$	1.05141	−	7.92026i	0.0429955	−	0.323884i
$599$	−19.1341	+	33.1412i	−0.781797	+	1.35411i	0.149096	+	0.988823i	$0.452364\pi$
$599$	−19.1341	+	33.1412i	−0.781797	+	1.35411i	−0.930894	+	0.365290i	$0.880970\pi$
$600$		0			0
$601$	13.4360	−	23.2718i	0.548064	−	0.949275i	−0.450343	−	0.892856i	$-0.648698\pi$
$601$	13.4360	−	23.2718i	0.548064	−	0.949275i	0.998407	−	0.0564195i	$-0.0179684\pi$
$602$	−8.31740	+	10.8028i	−0.338992	+	0.440290i
$603$		0			0
$604$	−0.777170	−	0.448699i	−0.0316226	−	0.0182573i
$605$		−	33.4122i		−	1.35840i
$606$		0			0
$607$	4.70105	−	8.14245i	0.190810	−	0.330492i	−0.754709	−	0.656059i	$-0.772222\pi$
$607$	4.70105	−	8.14245i	0.190810	−	0.330492i	0.945519	+	0.325568i	$0.105555\pi$
$608$	0.506435	−	0.877171i	0.0205386	−	0.0355740i
$609$		0			0
$610$	36.5908			1.48152
$611$	−2.98005	+	1.23061i	−0.120560	+	0.0497853i
$612$		0			0
$613$	11.5089	−	6.64469i	0.464842	−	0.268376i	−0.249236	−	0.968443i	$-0.580180\pi$
$613$	11.5089	−	6.64469i	0.464842	−	0.268376i	0.714078	+	0.700066i	$0.246846\pi$
$614$	39.4602			1.59248
$615$		0			0
$616$	7.89843	+	6.08123i	0.318237	+	0.245020i
$617$	9.72211	−	5.61306i	0.391397	−	0.225973i	−0.291368	−	0.956611i	$-0.594110\pi$
$617$	9.72211	−	5.61306i	0.391397	−	0.225973i	0.682765	+	0.730638i	$0.260777\pi$
$618$		0			0
$619$	−8.04109	−	4.64253i	−0.323199	−	0.186599i	0.329619	−	0.944114i	$-0.393080\pi$
$619$	−8.04109	−	4.64253i	−0.323199	−	0.186599i	−0.652817	+	0.757515i	$0.726413\pi$
$620$	−3.49929			−0.140535
$621$		0			0
$622$	−0.175512	−	0.101332i	−0.00703740	−	0.00406304i
$623$	7.64055	+	18.5316i	0.306112	+	0.742453i
$624$		0			0
$625$	1.95363	+	3.38379i	0.0781452	+	0.135351i
$626$	12.2571	−	7.07665i	0.489893	−	0.282840i
$627$		0			0
$628$	−0.856848	+	1.48410i	−0.0341920	+	0.0592222i
$629$			8.17322i			0.325888i
$630$		0			0
$631$	9.00894	−	5.20132i	0.358640	−	0.207061i	−0.309844	−	0.950787i	$-0.600277\pi$
$631$	9.00894	−	5.20132i	0.358640	−	0.207061i	0.668484	+	0.743726i	$0.266943\pi$
$632$	7.28611	−	4.20664i	0.289826	−	0.167331i
$633$		0			0
$634$	1.01347	+	1.75538i	0.0402499	+	0.0697149i
$635$			52.5046i			2.08358i
$636$		0			0
$637$	20.0900	−	15.2772i	0.795994	−	0.605305i
$638$	−6.95754			−0.275452
$639$		0			0
$640$	−16.8322	−	29.1542i	−0.665351	−	1.15242i
$641$	14.8591			0.586899			0.293449	−	0.955975i	$-0.405197\pi$
$641$	14.8591			0.586899			0.293449	+	0.955975i	$0.405197\pi$
$642$		0			0
$643$	1.98945	−	1.14861i	0.0784563	−	0.0452968i	−0.460259	−	0.887785i	$-0.652243\pi$
$643$	1.98945	−	1.14861i	0.0784563	−	0.0452968i	0.538715	+	0.842488i	$0.318910\pi$
$644$	−0.767033	+	0.316247i	−0.0302254	+	0.0124619i
$645$		0			0
$646$	4.91334	−	8.51016i	0.193313	−	0.334828i
$647$	−3.99932	−	6.92703i	−0.157230	−	0.272330i	0.776639	−	0.629946i	$-0.216923\pi$
$647$	−3.99932	−	6.92703i	−0.157230	−	0.272330i	−0.933869	+	0.357616i	$0.883590\pi$
$648$		0			0
$649$	7.15081	+	12.3856i	0.280694	+	0.486176i
$650$	−29.7166	−	22.8533i	−1.16558	−	0.896380i
$651$		0			0
$652$	1.98368	+	1.14528i	0.0776871	+	0.0448526i
$653$	−3.98444			−0.155923			−0.0779615	−	0.996956i	$-0.524841\pi$
$653$	−3.98444			−0.155923			−0.0779615	+	0.996956i	$0.524841\pi$
$654$		0			0
$655$	−34.5645	−	19.9558i	−1.35055	−	0.779738i
$656$	−13.0289	−	7.52225i	−0.508694	−	0.293695i
$657$		0			0
$658$	−2.52178	−	1.94159i	−0.0983094	−	0.0756912i
$659$	−13.7501	−	23.8159i	−0.535629	−	0.927737i	−0.999133	−	0.0416417i	$-0.986741\pi$
$659$	−13.7501	−	23.8159i	−0.535629	−	0.927737i	0.463504	−	0.886095i	$-0.346592\pi$
$660$		0			0
$661$	6.05023	−	3.49310i	0.235327	−	0.135866i	−0.377700	−	0.925928i	$-0.623285\pi$
$661$	6.05023	−	3.49310i	0.235327	−	0.135866i	0.613027	+	0.790062i	$0.289952\pi$
$662$	−16.9841	+	29.4173i	−0.660105	+	1.14333i
$663$		0			0
$664$	6.85019			0.265839
$665$	8.23704	−	3.39612i	0.319419	−	0.131696i
$666$		0			0
$667$	3.33148	−	5.77029i	0.128995	−	0.223427i
$668$	3.20195	+	1.84865i	0.123887	+	0.0715263i
$669$		0			0
$670$	26.2731	+	15.1688i	1.01502	+	0.586022i
$671$		−	9.74849i		−	0.376336i
$672$		0			0
$673$	2.72783	−	4.72474i	0.105150	−	0.182125i	−0.808649	−	0.588291i	$-0.799801\pi$
$673$	2.72783	−	4.72474i	0.105150	−	0.182125i	0.913800	+	0.406166i	$0.133134\pi$
$674$		−	43.2909i		−	1.66750i
$675$		0			0
$676$	2.38905	+	0.645671i	0.0918866	+	0.0248335i
$677$	16.8961	+	29.2649i	0.649371	+	1.12474i	0.983273	+	0.182135i	$0.0583009\pi$
$677$	16.8961	+	29.2649i	0.649371	+	1.12474i	−0.333903	+	0.942607i	$0.608366\pi$
$678$		0			0
$679$	0.772421	−	1.00324i	0.0296428	−	0.0385007i
$680$	40.6795	+	70.4590i	1.55999	+	2.70198i
$681$		0			0
$682$		−	8.86231i		−	0.339355i
$683$		−	12.2988i		−	0.470602i	−0.971923	−	0.235301i	$-0.924392\pi$
$683$		−	12.2988i		−	0.470602i	0.971923	−	0.235301i	$-0.0756076\pi$
$684$		0			0
$685$	31.4514	+	54.4754i	1.20170	+	2.08140i
$686$	22.9704	+	9.64698i	0.877015	+	0.368323i
$687$		0			0
$688$	−6.86265	−	11.8865i	−0.261636	−	0.453167i
$689$	−0.175823	+	0.228627i	−0.00669834	+	0.00870998i
$690$		0			0
$691$			11.0897i			0.421871i	0.977500	+	0.210935i	$0.0676509\pi$
$691$			11.0897i			0.421871i	−0.977500	+	0.210935i	$0.932349\pi$
$692$	−1.36869	+	2.37064i	−0.0520297	+	0.0901181i
$693$		0			0
$694$			33.3129i			1.26454i
$695$	−18.0972	−	10.4484i	−0.686465	−	0.396331i
$696$		0			0
$697$	28.1419	+	16.2478i	1.06595	+	0.615428i
$698$	−7.77247	+	13.4623i	−0.294193	+	0.509556i
$699$		0			0
$700$	−0.514427	+	3.85868i	−0.0194435	+	0.145844i
$701$	−10.6470			−0.402133			−0.201066	−	0.979578i	$-0.564441\pi$
$701$	−10.6470			−0.402133			−0.201066	+	0.979578i	$0.564441\pi$
$702$		0			0
$703$	−0.498406	+	0.863265i	−0.0187977	+	0.0325587i
$704$	−9.53396	+	5.50443i	−0.359325	+	0.207456i
$705$		0			0
$706$	−13.5117	−	23.4030i	−0.508521	−	0.880784i
$707$	6.03413	+	4.64585i	0.226937	+	0.174725i
$708$		0			0
$709$	35.2532	+	20.3535i	1.32396	+	0.764391i	0.984358	−	0.176178i	$-0.0563733\pi$
$709$	35.2532	+	20.3535i	1.32396	+	0.764391i	0.339605	+	0.940568i	$0.389707\pi$
$710$	−47.4833	−	27.4145i	−1.78202	−	1.02885i
$711$		0			0
$712$	−22.3237			−0.836618
$713$	7.35003	+	4.24354i	0.275261	+	0.158922i
$714$		0			0
$715$	−10.0273	+	13.0387i	−0.375001	+	0.487621i
$716$	−0.516470	−	0.894552i	−0.0193014	−	0.0334310i
$717$		0			0
$718$	10.1235	+	17.5344i	0.377806	+	0.654380i
$719$	4.88769	−	8.46572i	0.182280	−	0.315718i	−0.760377	−	0.649482i	$-0.774986\pi$
$719$	4.88769	−	8.46572i	0.182280	−	0.315718i	0.942657	+	0.333764i	$0.108319\pi$
$720$		0			0
$721$	23.7627	+	18.2956i	0.884968	+	0.681363i
$722$	−21.0971	+	12.1804i	−0.785153	+	0.453308i
$723$		0			0
$724$	−2.94881			−0.109592
$725$	−15.6313	−	27.0743i	−0.580533	−	1.00551i
$726$		0			0
$727$	−12.2091			−0.452811			−0.226406	−	0.974033i	$-0.572697\pi$
$727$	−12.2091			−0.452811			−0.226406	+	0.974033i	$0.572697\pi$
$728$	7.20122	+	27.1701i	0.266895	+	1.00699i
$729$		0			0
$730$			3.65002i			0.135093i
$731$	14.8231	+	25.6743i	0.548251	+	0.949598i
$732$		0			0
$733$	−19.3256	+	11.1577i	−0.713809	+	0.412118i	−0.812470	−	0.583003i	$-0.801877\pi$
$733$	−19.3256	+	11.1577i	−0.713809	+	0.412118i	0.0986608	+	0.995121i	$0.468544\pi$
$734$	−10.4891	+	6.05591i	−0.387161	+	0.223528i
$735$		0			0
$736$		−	1.76768i		−	0.0651576i
$737$	4.04126	−	6.99968i	0.148862	−	0.257836i
$738$		0			0
$739$	−36.6960	+	21.1865i	−1.34989	+	0.779357i	−0.988233	−	0.152956i	$-0.951121\pi$
$739$	−36.6960	+	21.1865i	−1.34989	+	0.779357i	−0.361653	+	0.932313i	$0.617787\pi$
$740$	−0.358637	−	0.621178i	−0.0131838	−	0.0228350i
$741$		0			0
$742$	−0.282206	−	0.0376229i	−0.0103601	−	0.00138118i
$743$	26.8296	+	15.4901i	0.984282	+	0.568276i	0.903560	−	0.428461i	$-0.140944\pi$
$743$	26.8296	+	15.4901i	0.984282	+	0.568276i	0.0807220	+	0.996737i	$0.474277\pi$
$744$		0			0
$745$	37.3866			1.36974
$746$	−18.8020	−	10.8553i	−0.688390	−	0.397442i
$747$		0			0
$748$	1.63146	−	0.941923i	0.0596520	−	0.0344401i
$749$	−16.0753	+	6.62783i	−0.587379	+	0.242176i
$750$		0			0
$751$	−22.5660			−0.823444			−0.411722	−	0.911309i	$-0.635073\pi$
$751$	−22.5660			−0.823444			−0.411722	+	0.911309i	$0.635073\pi$
$752$	2.77475	−	1.60200i	0.101185	−	0.0584190i
$753$		0			0
$754$	−15.5516	−	11.9598i	−0.566356	−	0.435551i
$755$	16.8187			0.612095
$756$		0			0
$757$	−16.1404	+	27.9560i	−0.586633	+	1.01608i	0.408037	+	0.912965i	$0.366213\pi$
$757$	−16.1404	+	27.9560i	−0.586633	+	1.01608i	−0.994670	+	0.103112i	$0.967120\pi$
$758$	−10.5368	+	18.2504i	−0.382716	+	0.662883i
$759$		0			0
$760$			9.92260i			0.359931i
$761$	25.7657	+	14.8758i	0.934006	+	0.539249i	0.888076	−	0.459696i	$-0.152042\pi$
$761$	25.7657	+	14.8758i	0.934006	+	0.539249i	0.0459296	+	0.998945i	$0.485375\pi$
$762$		0			0
$763$	15.3134	+	2.04154i	0.554383	+	0.0739086i
$764$	0.451761	−	0.782473i	0.0163441	−	0.0283089i
$765$		0			0
$766$	−16.5684	+	28.6972i	−0.598639	+	1.03687i
$767$	−5.30687	+	39.9764i	−0.191620	+	1.44347i
$768$		0			0
$769$	−36.2090	−	20.9053i	−1.30573	−	0.753863i	−0.324349	−	0.945938i	$-0.605145\pi$
$769$	−36.2090	−	20.9053i	−1.30573	−	0.753863i	−0.981380	+	0.192075i	$0.938478\pi$
$770$	−16.0944	−	2.14566i	−0.580003	−	0.0773242i
$771$		0			0
$772$	3.46856	−	2.00257i	0.124836	−	0.0720742i
$773$			41.4336i			1.49026i	0.666917	+	0.745132i	$0.267613\pi$
$773$			41.4336i			1.49026i	−0.666917	+	0.745132i	$0.732387\pi$
$774$		0			0
$775$	34.4864	−	19.9107i	1.23879	−	0.715215i
$776$	0.705044	+	1.22117i	0.0253096	+	0.0438375i
$777$		0			0
$778$	−21.9680	−	12.6832i	−0.787592	−	0.454716i
$779$	1.98159	+	3.43221i	0.0709978	+	0.122972i
$780$		0			0
$781$	−7.30376	+	12.6505i	−0.261349	+	0.452670i
$782$		−	17.1497i		−	0.613273i
$783$		0			0
$784$	−17.7930	+	17.6770i	−0.635464	+	0.631320i
$785$		−	32.1175i		−	1.14632i
$786$		0			0
$787$		−	23.8627i		−	0.850612i	−0.905050	−	0.425306i	$-0.860167\pi$
$787$		−	23.8627i		−	0.850612i	0.905050	−	0.425306i	$-0.139833\pi$
$788$	−0.958193	−	0.553213i	−0.0341342	−	0.0197074i
$789$		0			0
$790$	−6.85198	+	11.8680i	−0.243782	+	0.422243i
$791$	−13.6942	−	10.5436i	−0.486911	−	0.374887i
$792$		0			0
$793$	16.7574	−	21.7900i	0.595073	−	0.773785i
$794$	−9.75490	+	16.8960i	−0.346188	+	0.599616i
$795$		0			0
$796$	−2.02135			−0.0716447
$797$	−25.4115	−	44.0141i	−0.900123	−	1.55906i	−0.827333	−	0.561712i	$-0.810143\pi$
$797$	−25.4115	−	44.0141i	−0.900123	−	1.55906i	−0.0727899	−	0.997347i	$-0.523190\pi$
$798$		0			0
$799$	−5.99335	+	3.46026i	−0.212029	+	0.122415i
$800$	−7.18279	−	4.14699i	−0.253950	−	0.146618i
$801$		0			0
$802$	−28.2349			−0.997008
$803$	0.972438			0.0343166
$804$		0			0
$805$	9.48602	−	12.3206i	0.334338	−	0.434246i
$806$	15.2341	−	19.8092i	0.536598	−	0.697748i
$807$		0			0
$808$	−7.34493	+	4.24060i	−0.258394	+	0.149184i
$809$	2.20588	+	3.82070i	0.0775547	+	0.134329i	0.902194	−	0.431330i	$-0.141955\pi$
$809$	2.20588	+	3.82070i	0.0775547	+	0.134329i	−0.824640	+	0.565658i	$0.808622\pi$
$810$		0			0
$811$			17.6493i			0.619750i	0.950777	+	0.309875i	$0.100287\pi$
$811$			17.6493i			0.619750i	−0.950777	+	0.309875i	$0.899713\pi$
$812$	−0.269215	+	2.01937i	−0.00944760	+	0.0708658i
$813$		0			0
$814$	1.57320	−	0.908285i	0.0551405	−	0.0318354i
$815$	−42.9288			−1.50373
$816$		0			0
$817$			3.61566i			0.126496i
$818$	28.8249			1.00784
$819$		0			0
$820$	−2.85178			−0.0995884
$821$		−	3.56043i		−	0.124260i	−0.998068	−	0.0621299i	$-0.980211\pi$
$821$		−	3.56043i		−	0.124260i	0.998068	−	0.0621299i	$-0.0197893\pi$
$822$		0			0
$823$	−21.8665			−0.762217			−0.381109	−	0.924530i	$-0.624458\pi$
$823$	−21.8665			−0.762217			−0.381109	+	0.924530i	$0.624458\pi$
$824$	−28.9247	+	16.6997i	−1.00764	+	0.581760i
$825$		0			0
$826$	−36.8026	+	15.1737i	−1.28053	+	0.527960i
$827$		−	18.1361i		−	0.630653i	−0.948983	−	0.315327i	$-0.897886\pi$
$827$		−	18.1361i		−	0.630653i	0.948983	−	0.315327i	$-0.102114\pi$
$828$		0			0
$829$	15.4497	+	26.7596i	0.536590	+	0.929401i	0.999085	+	0.0427787i	$0.0136210\pi$
$829$	15.4497	+	26.7596i	0.536590	+	0.929401i	−0.462495	+	0.886622i	$0.653046\pi$
$830$	−9.66305	+	5.57896i	−0.335409	+	0.193649i
$831$		0			0
$832$	−30.7724	−	4.08504i	−1.06684	−	0.141623i
$833$	38.4322	−	38.1816i	1.33160	−	1.32291i
$834$		0			0
$835$	−69.2933			−2.39799
$836$	0.229755			0.00794625
$837$		0			0
$838$	−9.27813	−	5.35673i	−0.320508	−	0.185045i
$839$	13.3333	−	7.69796i	0.460315	−	0.265763i	−0.251862	−	0.967763i	$-0.581043\pi$
$839$	13.3333	−	7.69796i	0.460315	−	0.265763i	0.712177	+	0.702000i	$0.247709\pi$
$840$		0			0
$841$	6.31965	+	10.9459i	0.217919	+	0.377446i
$842$	−3.79065			−0.130635
$843$		0			0
$844$	0.444076	−	0.769163i	0.0152857	−	0.0264757i
$845$	−44.8265	+	11.9076i	−1.54208	+	0.409636i
$846$		0			0
$847$	3.27428	−	24.5602i	0.112506	−	0.843897i
$848$	0.143307	−	0.248216i	0.00492119	−	0.00852376i
$849$		0			0
$850$	−69.6862	−	40.2333i	−2.39022	−	1.37999i
$851$			1.73966i			0.0596347i
$852$		0			0
$853$		−	23.7772i		−	0.814116i	−0.913402	−	0.407058i	$-0.866555\pi$
$853$		−	23.7772i		−	0.814116i	0.913402	−	0.407058i	$-0.133445\pi$
$854$	26.8966	+	3.58577i	0.920382	+	0.122702i
$855$		0			0
$856$		−	19.3648i		−	0.661877i
$857$	15.0525	−	26.0717i	0.514184	−	0.890592i	−0.485681	−	0.874136i	$-0.661428\pi$
$857$	15.0525	−	26.0717i	0.514184	−	0.890592i	0.999865	−	0.0164561i	$-0.00523837\pi$
$858$		0			0
$859$	7.56717	+	13.1067i	0.258188	+	0.447195i	0.965757	−	0.259450i	$-0.0835411\pi$
$859$	7.56717	+	13.1067i	0.258188	+	0.447195i	−0.707568	+	0.706645i	$0.750208\pi$
$860$	−2.25315	−	1.30086i	−0.0768318	−	0.0443589i
$861$		0			0
$862$	3.85828	+	6.68274i	0.131414	+	0.227615i
$863$	−15.8186	+	9.13287i	−0.538471	+	0.310886i	−0.744459	−	0.667668i	$-0.767293\pi$
$863$	−15.8186	+	9.13287i	−0.538471	+	0.310886i	0.205988	+	0.978555i	$0.433959\pi$
$864$		0			0
$865$		−	51.3029i		−	1.74435i
$866$	−28.5724	+	16.4963i	−0.970929	+	0.560566i
$867$		0			0
$868$	−2.57221	−	0.342919i	−0.0873064	−	0.0116394i
$869$	3.16186	+	1.82550i	0.107259	+	0.0619259i
$870$		0			0
$871$	21.0654	−	8.69895i	0.713772	−	0.294753i
$872$	−8.60263	+	14.9002i	−0.291322	+	0.504584i
$873$		0			0
$874$	1.04580	−	1.81137i	0.0353746	−	0.0612706i
$875$	−9.81919	−	23.8157i	−0.331949	−	0.805118i
$876$		0			0
$877$	−6.05906	−	3.49820i	−0.204600	−	0.118126i	0.394199	−	0.919025i	$-0.371022\pi$
$877$	−6.05906	−	3.49820i	−0.204600	−	0.118126i	−0.598799	+	0.800899i	$0.704355\pi$
$878$			49.2922i			1.66353i
$879$		0			0
$880$	8.17292	−	14.1559i	0.275509	−	0.477195i
$881$	−12.8873	+	22.3215i	−0.434184	+	0.752029i	−0.997229	−	0.0743977i	$-0.976297\pi$
$881$	−12.8873	+	22.3215i	−0.434184	+	0.752029i	0.563045	+	0.826427i	$0.309630\pi$
$882$		0			0
$883$	−16.4526			−0.553674			−0.276837	−	0.960917i	$-0.589286\pi$
$883$	−16.4526			−0.553674			−0.276837	+	0.960917i	$0.589286\pi$
$884$	5.26580	+	0.699034i	0.177108	+	0.0235111i
$885$		0			0
$886$	31.5637	−	18.2233i	1.06040	−	0.612225i
$887$	−55.2455			−1.85496			−0.927481	−	0.373871i	$-0.878030\pi$
$887$	−55.2455			−1.85496			−0.927481	+	0.373871i	$0.878030\pi$
$888$		0			0
$889$	−5.14527	+	38.5943i	−0.172567	+	1.29441i
$890$	31.4904	−	18.1810i	1.05556	−	0.609429i
$891$		0			0
$892$	3.99385	+	2.30585i	0.133724	+	0.0772056i
$893$	−0.844032			−0.0282444
$894$		0			0
$895$	16.7654	+	9.67949i	0.560404	+	0.323550i
$896$	−9.51575	−	23.0798i	−0.317899	−	0.771041i
$897$		0			0
$898$	18.4514	+	31.9587i	0.615731	+	1.06648i
$899$	18.0478	−	10.4199i	0.601927	−	0.347523i
$900$		0			0
$901$	−0.309538	+	0.536136i	−0.0103122	+	0.0178613i
$902$		−	7.22241i		−	0.240480i
$903$		0			0
$904$	16.6691	−	9.62388i	0.554405	−	0.320086i
$905$	47.8614	−	27.6328i	1.59097	−	0.918544i
$906$		0			0
$907$	23.9212	+	41.4327i	0.794290	+	1.37575i	0.923289	+	0.384107i	$0.125490\pi$
$907$	23.9212	+	41.4327i	0.794290	+	1.37575i	−0.128998	+	0.991645i	$0.541176\pi$
$908$		−	2.92694i		−	0.0971338i
$909$		0			0
$910$	−32.2862	−	32.4619i	−1.07028	−	1.07610i
$911$	23.0711			0.764380			0.382190	−	0.924084i	$-0.375170\pi$
$911$	23.0711			0.764380			0.382190	+	0.924084i	$0.375170\pi$
$912$		0			0
$913$	1.48635	+	2.57443i	0.0491909	+	0.0852011i
$914$	−53.3569			−1.76489
$915$		0			0
$916$	−2.69574	+	1.55638i	−0.0890697	+	0.0514244i
$917$	−23.4515	−	18.0560i	−0.774438	−	0.596262i
$918$		0			0
$919$	21.7184	−	37.6174i	0.716424	−	1.24088i	−0.245984	−	0.969274i	$-0.579111\pi$
$919$	21.7184	−	37.6174i	0.716424	−	1.24088i	0.962408	−	0.271609i	$-0.0875557\pi$
$920$	8.65856	+	14.9971i	0.285464	+	0.494439i
$921$		0			0
$922$	−3.29298	−	5.70360i	−0.108448	−	0.187838i
$923$	−38.0714	+	15.7216i	−1.25313	+	0.517482i
$924$		0			0
$925$	7.06892	+	4.08124i	0.232425	+	0.134190i
$926$	6.33861			0.208300
$927$		0			0
$928$	−3.75897	−	2.17024i	−0.123394	−	0.0712418i
$929$	−11.0695	−	6.39095i	−0.363177	−	0.209680i	0.307296	−	0.951614i	$-0.400576\pi$
$929$	−11.0695	−	6.39095i	−0.363177	−	0.209680i	−0.670474	+	0.741933i	$0.733909\pi$
$930$		0			0
$931$	6.38757	−	1.68917i	0.209344	−	0.0553603i
$932$	2.77085	+	4.79926i	0.0907623	+	0.157205i
$933$		0			0
$934$	−37.2988	+	21.5345i	−1.22045	+	0.704629i
$935$	−17.6532	+	30.5762i	−0.577320	+	0.999948i
$936$		0			0
$937$	16.2533			0.530971			0.265486	−	0.964115i	$-0.414468\pi$
$937$	16.2533			0.530971			0.265486	+	0.964115i	$0.414468\pi$
$938$	17.8260	+	13.7247i	0.582038	+	0.448128i
$939$		0			0
$940$	0.303669	−	0.525971i	0.00990460	−	0.0171553i
$941$	−39.1000	−	22.5744i	−1.27462	−	0.735905i	−0.298770	−	0.954325i	$-0.596576\pi$
$941$	−39.1000	−	22.5744i	−1.27462	−	0.735905i	−0.975855	+	0.218420i	$0.929910\pi$
$942$		0			0
$943$	5.98997	+	3.45831i	0.195060	+	0.112618i
$944$		−	40.0752i		−	1.30434i
$945$		0			0
$946$	3.29455	−	5.70633i	0.107115	−	0.185529i
$947$		−	19.8557i		−	0.645225i	−0.946531	−	0.322612i	$-0.895439\pi$
$947$		−	19.8557i		−	0.645225i	0.946531	−	0.322612i	$-0.104561\pi$
$948$		0			0
$949$	2.17361	+	1.67160i	0.0705583	+	0.0542623i
$950$	−4.90689	−	8.49898i	−0.159200	−	0.275743i
$951$		0			0
$952$	22.9973	+	55.7784i	0.745348	+	1.80779i
$953$	−7.86433	−	13.6214i	−0.254751	−	0.441241i	0.710077	−	0.704124i	$-0.248660\pi$
$953$	−7.86433	−	13.6214i	−0.254751	−	0.441241i	−0.964828	+	0.262883i	$0.915327\pi$
$954$		0			0
$955$			16.9335i			0.547954i
$956$		−	1.64745i		−	0.0532823i
$957$		0			0
$958$	12.1235	+	20.9985i	0.391693	+	0.678432i
$959$	17.7804	+	43.1251i	0.574160	+	1.39258i
$960$		0			0
$961$	−2.22744	−	3.85804i	−0.0718529	−	0.124453i
$962$	5.07775	+	0.674070i	0.163713	+	0.0217329i
$963$		0			0
$964$		−	3.46432i		−	0.111578i
$965$	−37.5315	+	65.0064i	−1.20818	+	2.09263i
$966$		0			0
$967$		−	52.1912i		−	1.67835i	−0.543858	−	0.839177i	$-0.683037\pi$
$967$		−	52.1912i		−	1.67835i	0.543858	−	0.839177i	$-0.316963\pi$
$968$	23.8974	+	13.7972i	0.768091	+	0.443458i
$969$		0			0
$970$	−1.98910	−	1.14841i	−0.0638663	−	0.0368732i
$971$	−11.2292	+	19.4495i	−0.360362	+	0.624165i	−0.988020	−	0.154324i	$-0.950680\pi$
$971$	−11.2292	+	19.4495i	−0.360362	+	0.624165i	0.627658	+	0.778489i	$0.284013\pi$
$972$		0			0
$973$	−12.2787	−	9.45372i	−0.393637	−	0.303072i
$974$	23.6765			0.758645
$975$		0			0
$976$	−13.6584	+	23.6570i	−0.437193	+	0.757241i
$977$	35.5369	−	20.5172i	1.13693	−	0.656405i	0.191259	−	0.981540i	$-0.438743\pi$
$977$	35.5369	−	20.5172i	1.13693	−	0.656405i	0.945668	+	0.325135i	$0.105410\pi$
$978$		0			0
$979$	−4.84378	−	8.38967i	−0.154808	−	0.268135i
$980$	−1.24552	+	4.58825i	−0.0397866	+	0.146566i
$981$		0			0
$982$	4.50110	+	2.59871i	0.143636	+	0.0829282i
$983$	23.2379	+	13.4164i	0.741173	+	0.427916i	0.822496	−	0.568772i	$-0.192581\pi$
$983$	23.2379	+	13.4164i	0.741173	+	0.427916i	−0.0813229	+	0.996688i	$0.525915\pi$
$984$		0			0
$985$	20.7362			0.660711
$986$	−36.4689	−	21.0553i	−1.16141	−	0.670539i
$987$		0			0
$988$	0.513552	+	0.394943i	0.0163383	+	0.0125648i
$989$	3.15506	+	5.46473i	0.100325	+	0.173768i
$990$		0			0
$991$	−5.18755	−	8.98510i	−0.164788	−	0.285421i	0.771792	−	0.635875i	$-0.219361\pi$
$991$	−5.18755	−	8.98510i	−0.164788	−	0.285421i	−0.936580	+	0.350454i	$0.886027\pi$
$992$	2.76439	−	4.78807i	0.0877696	−	0.152021i
$993$		0			0
$994$	−32.2168	−	24.8047i	−1.02186	−	0.786756i
$995$	32.8079	−	18.9417i	1.04008	−	0.600491i
$996$		0			0
$997$	−53.9097			−1.70734			−0.853669	−	0.520816i	$-0.825628\pi$
$997$	−53.9097			−1.70734			−0.853669	+	0.520816i	$0.825628\pi$
$998$	8.50671	+	14.7341i	0.269275	+	0.466398i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.f.550.2		12
3.2	odd	2		91.2.k.b.4.5	✓	12
7.2	even	3		819.2.do.e.667.2		12
13.10	even	6		819.2.do.e.361.2		12
21.2	odd	6		91.2.u.b.30.5	yes	12
21.5	even	6		637.2.u.g.30.5		12
21.11	odd	6		637.2.q.g.589.2		12
21.17	even	6		637.2.q.i.589.2		12
21.20	even	2		637.2.k.i.459.5		12
39.20	even	12		1183.2.e.j.508.9		24
39.23	odd	6		91.2.u.b.88.5	yes	12
39.32	even	12		1183.2.e.j.508.4		24
91.23	even	6	inner	819.2.bm.f.478.5		12
273.23	odd	6		91.2.k.b.23.2	yes	12
273.32	even	12		8281.2.a.cp.1.9		12
273.59	odd	12		8281.2.a.co.1.4		12
273.62	even	6		637.2.u.g.361.5		12
273.101	even	6		637.2.q.i.491.2		12
273.137	even	12		8281.2.a.cp.1.4		12
273.149	even	12		1183.2.e.j.170.4		24
273.179	odd	6		637.2.q.g.491.2		12
273.227	odd	12		8281.2.a.co.1.9		12
273.254	even	12		1183.2.e.j.170.9		24
273.257	even	6		637.2.k.i.569.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.5	✓	12	3.2	odd	2
91.2.k.b.23.2	yes	12	273.23	odd	6
91.2.u.b.30.5	yes	12	21.2	odd	6
91.2.u.b.88.5	yes	12	39.23	odd	6
637.2.k.i.459.5		12	21.20	even	2
637.2.k.i.569.2		12	273.257	even	6
637.2.q.g.491.2		12	273.179	odd	6
637.2.q.g.589.2		12	21.11	odd	6
637.2.q.i.491.2		12	273.101	even	6
637.2.q.i.589.2		12	21.17	even	6
637.2.u.g.30.5		12	21.5	even	6
637.2.u.g.361.5		12	273.62	even	6
819.2.bm.f.478.5		12	91.23	even	6	inner
819.2.bm.f.550.2		12	1.1	even	1	trivial
819.2.do.e.361.2		12	13.10	even	6
819.2.do.e.667.2		12	7.2	even	3
1183.2.e.j.170.4		24	273.149	even	12
1183.2.e.j.170.9		24	273.254	even	12
1183.2.e.j.508.4		24	39.32	even	12
1183.2.e.j.508.9		24	39.20	even	12
8281.2.a.co.1.4		12	273.59	odd	12
8281.2.a.co.1.9		12	273.227	odd	12
8281.2.a.cp.1.4		12	273.137	even	12
8281.2.a.cp.1.9		12	273.32	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.34523i q^{2} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.44601 + 1.00849i) q^{7} -2.94654i q^{8} +O(q^{10})\)	\(q-1.34523i q^{2} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.44601 + 1.00849i) q^{7} -2.94654i q^{8} +(2.39973 + 4.15646i) q^{10} +(1.10736 - 0.639336i) q^{11} +(3.57420 + 0.474474i) q^{13} +(1.35664 + 3.29043i) q^{14} -3.58303 q^{16} +7.73920 q^{17} +(0.817422 + 0.471939i) q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} +1.64727 q^{23} +(3.86451 - 6.69354i) q^{25} +(0.638275 - 4.80810i) q^{26} +(-0.465638 + 0.191982i) q^{28} +(2.02242 - 3.50293i) q^{29} +(4.46193 + 2.57610i) q^{31} -1.07309i q^{32} -10.4110i q^{34} +(5.75861 - 7.47941i) q^{35} +1.05608i q^{37} +(0.634865 - 1.09962i) q^{38} +(5.25629 + 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(0.210805 - 0.121708i) q^{44} -2.21596i q^{46} +(-0.774415 + 0.447109i) q^{47} +(4.96591 - 4.93353i) q^{49} +(-9.00432 - 5.19865i) q^{50} +(0.680407 + 0.0903239i) q^{52} +(-0.0399961 + 0.0692754i) q^{53} +(-2.28101 + 3.95082i) q^{55} +(2.97154 + 7.20726i) q^{56} +(-4.71224 - 2.72061i) q^{58} +11.1847i q^{59} +(3.81196 - 6.60251i) q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(-11.8899 + 4.90994i) q^{65} +(5.47418 - 3.16052i) q^{67} +1.47328 q^{68} +(-10.0615 - 7.74664i) q^{70} +(-9.89346 + 5.71199i) q^{71} +(0.658617 + 0.380253i) q^{73} +1.42067 q^{74} +(0.155610 + 0.0898413i) q^{76} +(-2.06386 + 2.68058i) q^{77} +(1.42765 + 2.47277i) q^{79} +(11.0708 - 6.39172i) q^{80} +(2.82418 - 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(4.46270 - 2.57654i) q^{86} +(-1.88383 - 3.26289i) q^{88} -7.57626i q^{89} +(-9.22101 + 2.44396i) q^{91} +0.313586 q^{92} +(0.601462 + 1.04176i) q^{94} -3.36755 q^{95} +(-0.414443 + 0.239279i) q^{97} +(-6.63671 - 6.68028i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more