LMFDB - Embedded newform 390.2.bn.b.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			163.2
Root			$-1.09227 + 0.838128i$ of defining polynomial
Character	$\chi$	$=$	390.163
Dual form			390.2.bn.b.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.06394 - 0.860320i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.450069 - 0.259847i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.06394 - 0.860320i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.450069 - 0.259847i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +(0.286912 - 2.21758i) q^{10} +(0.222514 + 0.830435i) q^{11} +(0.707107 + 0.707107i) q^{12} +(1.76341 - 3.14490i) q^{13} -0.519695i q^{14} +(-1.77095 + 1.36519i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.09452 - 4.08479i) q^{17} -1.00000i q^{18} +(0.0538940 + 0.0144409i) q^{19} +(-1.77703 - 1.35727i) q^{20} +(-0.367480 + 0.367480i) q^{21} +(0.830435 + 0.222514i) q^{22} +(0.0474866 + 0.177222i) q^{23} +(0.965926 - 0.258819i) q^{24} +(3.51970 - 3.55130i) q^{25} +(-1.84186 - 3.09961i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.450069 - 0.259847i) q^{28} +(-6.27365 - 3.62210i) q^{29} +(0.296818 + 2.21628i) q^{30} +(3.09986 + 3.09986i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.429865 - 0.744548i) q^{33} +(-2.99027 - 2.99027i) q^{34} +(0.705364 - 0.923513i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-0.195463 - 0.112851i) q^{37} +(0.0394531 - 0.0394531i) q^{38} +(-0.889363 + 3.49414i) q^{39} +(-2.06394 + 0.860320i) q^{40} +(-0.0280536 + 0.00751694i) q^{41} +(0.134507 + 0.501987i) q^{42} +(4.63274 + 1.24134i) q^{43} +(0.607921 - 0.607921i) q^{44} +(1.35727 - 1.77703i) q^{45} +(0.177222 + 0.0474866i) q^{46} -5.53738i q^{47} +(0.258819 - 0.965926i) q^{48} +(-3.36496 + 5.82828i) q^{49} +(-1.31566 - 4.82380i) q^{50} +4.22888i q^{51} +(-3.60527 + 0.0452920i) q^{52} +(2.49867 + 2.49867i) q^{53} +(0.258819 + 0.965926i) q^{54} +(1.17370 + 1.52254i) q^{55} +(-0.450069 + 0.259847i) q^{56} -0.0557952 q^{57} +(-6.27365 + 3.62210i) q^{58} +(-1.31167 + 4.89521i) q^{59} +(2.06776 + 0.851088i) q^{60} +(7.21773 + 12.5015i) q^{61} +(4.23449 - 1.13463i) q^{62} +(0.259847 - 0.450069i) q^{63} +1.00000 q^{64} +(0.933954 - 8.00798i) q^{65} -0.859730 q^{66} +(-6.85698 + 11.8766i) q^{67} +(-4.08479 + 1.09452i) q^{68} +(-0.0917371 - 0.158893i) q^{69} +(-0.447104 - 1.07262i) q^{70} +(-1.78083 + 6.64614i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.40525 q^{73} +(-0.195463 + 0.112851i) q^{74} +(-2.48063 + 4.34125i) q^{75} +(-0.0144409 - 0.0538940i) q^{76} +(0.315933 + 0.315933i) q^{77} +(2.58133 + 2.51728i) q^{78} +16.0201i q^{79} +(-0.286912 + 2.21758i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.00751694 + 0.0280536i) q^{82} -4.83100i q^{83} +(0.501987 + 0.134507i) q^{84} +(-1.25521 - 9.37239i) q^{85} +(3.39140 - 3.39140i) q^{86} +(6.99735 + 1.87494i) q^{87} +(-0.222514 - 0.830435i) q^{88} +(-14.9100 + 3.99511i) q^{89} +(-0.860320 - 2.06394i) q^{90} +(-0.0235380 - 1.87364i) q^{91} +(0.129736 - 0.129736i) q^{92} +(-3.79654 - 2.19193i) q^{93} +(-4.79551 - 2.76869i) q^{94} +(0.123658 - 0.0165610i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(3.14672 + 5.45027i) q^{97} +(3.36496 + 5.82828i) q^{98} +(0.607921 + 0.607921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.06394	−	0.860320i	0.923022	−	0.384747i
$5$	2.06394	−	0.860320i	0.923022	−	0.384747i
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	0.450069	−	0.259847i	0.170110	−	0.0982131i	−0.412528	−	0.910945i	$-0.635354\pi$
$7$	0.450069	−	0.259847i	0.170110	−	0.0982131i	0.582638	+	0.812732i	$0.302021\pi$
$8$	−1.00000			−0.353553
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	0.286912	−	2.21758i	0.0907294	−	0.701262i
$11$	0.222514	+	0.830435i	0.0670906	+	0.250386i	0.991324	−	0.131443i	$-0.0419611\pi$
$11$	0.222514	+	0.830435i	0.0670906	+	0.250386i	−0.924233	+	0.381829i	$0.875294\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	1.76341	−	3.14490i	0.489082	−	0.872238i
$13$	1.76341	−	3.14490i	0.489082	−	0.872238i
$14$		−	0.519695i		−	0.138894i
$15$	−1.77095	+	1.36519i	−0.457256	+	0.352491i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.09452	−	4.08479i	0.265459	−	0.990707i	−0.696510	−	0.717547i	$-0.745265\pi$
$17$	1.09452	−	4.08479i	0.265459	−	0.990707i	0.961969	−	0.273159i	$-0.0880686\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.0538940	+	0.0144409i	0.0123641	+	0.00331296i	0.264996	−	0.964250i	$-0.414629\pi$
$19$	0.0538940	+	0.0144409i	0.0123641	+	0.00331296i	−0.252632	+	0.967563i	$0.581296\pi$
$20$	−1.77703	−	1.35727i	−0.397356	−	0.303494i
$21$	−0.367480	+	0.367480i	−0.0801907	+	0.0801907i
$22$	0.830435	+	0.222514i	0.177049	+	0.0474402i
$23$	0.0474866	+	0.177222i	0.00990164	+	0.0369534i	0.970700	−	0.240295i	$-0.0772442\pi$
$23$	0.0474866	+	0.177222i	0.00990164	+	0.0369534i	−0.960798	+	0.277248i	$0.910578\pi$
$24$	0.965926	−	0.258819i	0.197169	−	0.0528312i
$25$	3.51970	−	3.55130i	0.703940	−	0.710259i
$26$	−1.84186	−	3.09961i	−0.361218	−	0.607883i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.450069	−	0.259847i	−0.0850550	−	0.0491066i
$29$	−6.27365	−	3.62210i	−1.16499	−	0.672606i	−0.212494	−	0.977162i	$-0.568159\pi$
$29$	−6.27365	−	3.62210i	−1.16499	−	0.672606i	−0.952494	+	0.304556i	$0.901492\pi$
$30$	0.296818	+	2.21628i	0.0541913	+	0.404636i
$31$	3.09986	+	3.09986i	0.556752	+	0.556752i	0.928381	−	0.371629i	$-0.121201\pi$
$31$	3.09986	+	3.09986i	0.556752	+	0.556752i	−0.371629	+	0.928381i	$0.621201\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.429865	−	0.744548i	−0.0748299	−	0.129609i
$34$	−2.99027	−	2.99027i	−0.512828	−	0.512828i
$35$	0.705364	−	0.923513i	0.119228	−	0.156102i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−0.195463	−	0.112851i	−0.0321339	−	0.0185525i	0.483847	−	0.875153i	$-0.339239\pi$
$37$	−0.195463	−	0.112851i	−0.0321339	−	0.0185525i	−0.515981	+	0.856600i	$0.672572\pi$
$38$	0.0394531	−	0.0394531i	0.00640014	−	0.00640014i
$39$	−0.889363	+	3.49414i	−0.142412	+	0.559511i
$40$	−2.06394	+	0.860320i	−0.326338	+	0.136028i
$41$	−0.0280536	+	0.00751694i	−0.00438124	+	0.00117395i	−0.261009	−	0.965336i	$-0.584055\pi$
$41$	−0.0280536	+	0.00751694i	−0.00438124	+	0.00117395i	0.256628	+	0.966510i	$0.417389\pi$
$42$	0.134507	+	0.501987i	0.0207549	+	0.0774582i
$43$	4.63274	+	1.24134i	0.706487	+	0.189303i	0.594134	−	0.804366i	$-0.297495\pi$
$43$	4.63274	+	1.24134i	0.706487	+	0.189303i	0.112352	+	0.993668i	$0.464161\pi$
$44$	0.607921	−	0.607921i	0.0916475	−	0.0916475i
$45$	1.35727	−	1.77703i	0.202329	−	0.264904i
$46$	0.177222	+	0.0474866i	0.0261300	+	0.00700152i
$47$		−	5.53738i		−	0.807710i	−0.914823	−	0.403855i	$-0.867670\pi$
$47$		−	5.53738i		−	0.807710i	0.914823	−	0.403855i	$-0.132330\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	−3.36496	+	5.82828i	−0.480708	+	0.832611i
$50$	−1.31566	−	4.82380i	−0.186063	−	0.682188i
$51$			4.22888i			0.592162i
$52$	−3.60527	+	0.0452920i	−0.499961	+	0.00628087i
$53$	2.49867	+	2.49867i	0.343219	+	0.343219i	0.857576	−	0.514357i	$-0.171969\pi$
$53$	2.49867	+	2.49867i	0.343219	+	0.343219i	−0.514357	+	0.857576i	$0.671969\pi$
$54$	0.258819	+	0.965926i	0.0352208	+	0.131446i
$55$	1.17370	+	1.52254i	0.158261	+	0.205299i
$56$	−0.450069	+	0.259847i	−0.0601430	+	0.0347236i
$57$	−0.0557952			−0.00739025
$58$	−6.27365	+	3.62210i	−0.823771	+	0.475605i
$59$	−1.31167	+	4.89521i	−0.170765	+	0.637302i	0.826470	+	0.562981i	$0.190346\pi$
$59$	−1.31167	+	4.89521i	−0.170765	+	0.637302i	−0.997234	+	0.0743209i	$0.976321\pi$
$60$	2.06776	+	0.851088i	0.266947	+	0.109875i
$61$	7.21773	+	12.5015i	0.924135	+	1.60065i	0.792946	+	0.609292i	$0.208546\pi$
$61$	7.21773	+	12.5015i	0.924135	+	1.60065i	0.131189	+	0.991357i	$0.458120\pi$
$62$	4.23449	−	1.13463i	0.537781	−	0.144098i
$63$	0.259847	−	0.450069i	0.0327377	−	0.0567034i
$64$	1.00000			0.125000
$65$	0.933954	−	8.00798i	0.115843	−	0.993268i
$66$	−0.859730			−0.105825
$67$	−6.85698	+	11.8766i	−0.837713	+	1.45096i	0.0540887	+	0.998536i	$0.482775\pi$
$67$	−6.85698	+	11.8766i	−0.837713	+	1.45096i	−0.891802	+	0.452426i	$0.850559\pi$
$68$	−4.08479	+	1.09452i	−0.495353	+	0.132730i
$69$	−0.0917371	−	0.158893i	−0.0110438	−	0.0191285i
$70$	−0.447104	−	1.07262i	−0.0534391	−	0.128203i
$71$	−1.78083	+	6.64614i	−0.211345	+	0.788752i	0.776076	+	0.630640i	$0.217207\pi$
$71$	−1.78083	+	6.64614i	−0.211345	+	0.788752i	−0.987421	+	0.158112i	$0.949459\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	2.40525			0.281513			0.140756	−	0.990044i	$-0.455047\pi$
$73$	2.40525			0.281513			0.140756	+	0.990044i	$0.455047\pi$
$74$	−0.195463	+	0.112851i	−0.0227221	+	0.0131186i
$75$	−2.48063	+	4.34125i	−0.286438	+	0.501285i
$76$	−0.0144409	−	0.0538940i	−0.00165648	−	0.00618206i
$77$	0.315933	+	0.315933i	0.0360039	+	0.0360039i
$78$	2.58133	+	2.51728i	0.292279	+	0.285026i
$79$			16.0201i			1.80240i	0.433402	+	0.901201i	$0.357313\pi$
$79$			16.0201i			1.80240i	−0.433402	+	0.901201i	$0.642687\pi$
$80$	−0.286912	+	2.21758i	−0.0320777	+	0.247934i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−0.00751694	+	0.0280536i	−0.000830108	+	0.00309800i
$83$		−	4.83100i		−	0.530271i	−0.964211	−	0.265136i	$-0.914583\pi$
$83$		−	4.83100i		−	0.530271i	0.964211	−	0.265136i	$-0.0854167\pi$
$84$	0.501987	+	0.134507i	0.0547712	+	0.0146759i
$85$	−1.25521	−	9.37239i	−0.136146	−	1.01658i
$86$	3.39140	−	3.39140i	0.365704	−	0.365704i
$87$	6.99735	+	1.87494i	0.750195	+	0.201014i
$88$	−0.222514	−	0.830435i	−0.0237201	−	0.0885247i
$89$	−14.9100	+	3.99511i	−1.58045	+	0.423481i	−0.939066	−	0.343737i	$-0.888307\pi$
$89$	−14.9100	+	3.99511i	−1.58045	+	0.423481i	−0.641386	+	0.767218i	$0.721640\pi$
$90$	−0.860320	−	2.06394i	−0.0906856	−	0.217558i
$91$	−0.0235380	−	1.87364i	−0.00246745	−	0.196411i
$92$	0.129736	−	0.129736i	0.0135259	−	0.0135259i
$93$	−3.79654	−	2.19193i	−0.393683	−	0.227293i
$94$	−4.79551	−	2.76869i	−0.494619	−	0.285569i
$95$	0.123658	−	0.0165610i	0.0126870	−	0.00169912i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	3.14672	+	5.45027i	0.319501	+	0.553392i	0.980384	−	0.197097i	$-0.0631515\pi$
$97$	3.14672	+	5.45027i	0.319501	+	0.553392i	−0.660883	+	0.750489i	$0.729818\pi$
$98$	3.36496	+	5.82828i	0.339912	+	0.588745i
$99$	0.607921	+	0.607921i	0.0610983	+	0.0610983i
$100$	−4.83536	−	1.27250i	−0.483536	−	0.127250i
$101$	4.39076	+	2.53501i	0.436897	+	0.252243i	0.702281	−	0.711900i	$-0.252165\pi$
$101$	4.39076	+	2.53501i	0.436897	+	0.252243i	−0.265384	+	0.964143i	$0.585499\pi$
$102$	3.66232	+	2.11444i	0.362624	+	0.209361i
$103$	5.95248	−	5.95248i	0.586515	−	0.586515i	−0.350171	−	0.936686i	$-0.613876\pi$
$103$	5.95248	−	5.95248i	0.586515	−	0.586515i	0.936686	+	0.350171i	$0.113876\pi$
$104$	−1.76341	+	3.14490i	−0.172917	+	0.308383i
$105$	−0.442306	+	1.07461i	−0.0431647	+	0.104871i
$106$	3.41325	−	0.914577i	0.331524	−	0.0888315i
$107$	−1.81541	−	6.77519i	−0.175502	−	0.654982i	−0.996466	−	0.0840016i	$-0.973230\pi$
$107$	−1.81541	−	6.77519i	−0.175502	−	0.654982i	0.820964	−	0.570980i	$-0.193437\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	6.23531	−	6.23531i	0.597235	−	0.597235i	−0.342341	−	0.939576i	$-0.611220\pi$
$109$	6.23531	−	6.23531i	0.597235	−	0.597235i	0.939576	+	0.342341i	$0.111220\pi$
$110$	1.90540	−	0.255183i	0.181673	−	0.0243308i
$111$	0.218011	+	0.0584158i	0.0206927	+	0.00554458i
$112$			0.519695i			0.0491066i
$113$	1.51348	−	5.64837i	0.142376	−	0.531354i	−0.857482	−	0.514513i	$-0.827973\pi$
$113$	1.51348	−	5.64837i	0.142376	−	0.531354i	0.999858	−	0.0168406i	$-0.00536077\pi$
$114$	−0.0278976	+	0.0483200i	−0.00261285	+	0.00452559i
$115$	0.250478	+	0.324923i	0.0233571	+	0.0302992i
$116$			7.24419i			0.672606i
$117$	−0.0452920	−	3.60527i	−0.00418725	−	0.333307i
$118$	3.58354	+	3.58354i	0.329892	+	0.329892i
$119$	−0.568814	−	2.12284i	−0.0521431	−	0.194601i
$120$	1.77095	−	1.36519i	0.161665	−	0.124624i
$121$	8.88617	−	5.13043i	0.807834	−	0.466403i
$122$	14.4355			1.30692
$123$	0.0251522	−	0.0145216i	0.00226790	−	0.00130937i
$124$	1.13463	−	4.23449i	0.101893	−	0.380268i
$125$	4.20920	−	10.3577i	0.376482	−	0.926424i
$126$	−0.259847	−	0.450069i	−0.0231491	−	0.0400953i
$127$	−10.0408	+	2.69043i	−0.890979	+	0.238737i	−0.675138	−	0.737691i	$-0.735916\pi$
$127$	−10.0408	+	2.69043i	−0.890979	+	0.238737i	−0.215841	+	0.976429i	$0.569249\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.79617			−0.422279
$130$	−6.46814	−	4.81282i	−0.567293	−	0.422112i
$131$	−17.3948			−1.51979			−0.759894	−	0.650047i	$-0.774749\pi$
$131$	−17.3948			−1.51979			−0.759894	+	0.650047i	$0.774749\pi$
$132$	−0.429865	+	0.744548i	−0.0374149	+	0.0648046i
$133$	0.0280084	−	0.00750484i	0.00242864	−	0.000650752i
$134$	6.85698	+	11.8766i	0.592353	+	1.02599i
$135$	−0.851088	+	2.06776i	−0.0732500	+	0.177965i
$136$	−1.09452	+	4.08479i	−0.0938540	+	0.350268i
$137$	7.86958	−	4.54350i	0.672343	−	0.388178i	−0.124621	−	0.992204i	$-0.539771\pi$
$137$	7.86958	−	4.54350i	0.672343	−	0.388178i	0.796964	+	0.604027i	$0.206438\pi$
$138$	−0.183474			−0.0156184
$139$	2.33716	−	1.34936i	0.198236	−	0.114451i	−0.397597	−	0.917560i	$-0.630156\pi$
$139$	2.33716	−	1.34936i	0.198236	−	0.114451i	0.595832	+	0.803109i	$0.296822\pi$
$140$	−1.15247	−	0.149107i	−0.0974013	−	0.0126018i
$141$	1.43318	+	5.34870i	0.120695	+	0.450442i
$142$	4.86531	+	4.86531i	0.408288	+	0.408288i
$143$	3.00402	+	0.764612i	0.251209	+	0.0639401i
$144$			1.00000i			0.0833333i
$145$	−16.0646	−	2.07844i	−1.33409	−	0.172605i
$146$	1.20262	−	2.08300i	0.0995298	−	0.172391i
$147$	1.74183	−	6.50060i	0.143664	−	0.536161i
$148$			0.225701i			0.0185525i
$149$	4.01632	+	1.07617i	0.329029	+	0.0881632i	0.419552	−	0.907731i	$-0.362187\pi$
$149$	4.01632	+	1.07617i	0.329029	+	0.0881632i	−0.0905228	+	0.995894i	$0.528854\pi$
$150$	2.51932	+	4.31891i	0.205702	+	0.352638i
$151$	2.79391	−	2.79391i	0.227365	−	0.227365i	−0.584226	−	0.811591i	$-0.698602\pi$
$151$	2.79391	−	2.79391i	0.227365	−	0.227365i	0.811591	+	0.584226i	$0.198602\pi$
$152$	−0.0538940	−	0.0144409i	−0.00437138	−	0.00117131i
$153$	−1.09452	−	4.08479i	−0.0884864	−	0.330236i
$154$	0.431573	−	0.115640i	0.0347771	−	0.00931851i
$155$	9.06480	+	3.73106i	0.728102	+	0.299686i
$156$	3.47070	−	0.976860i	0.277878	−	0.0782114i
$157$	−9.39011	+	9.39011i	−0.749413	+	0.749413i	−0.974369	−	0.224956i	$-0.927776\pi$
$157$	−9.39011	+	9.39011i	−0.749413	+	0.749413i	0.224956	+	0.974369i	$0.427776\pi$
$158$	13.8738	+	8.01005i	1.10374	+	0.637245i
$159$	−3.06023	−	1.76683i	−0.242692	−	0.140118i
$160$	1.77703	+	1.35727i	0.140486	+	0.107301i
$161$	0.0674231	+	0.0674231i	0.00531368	+	0.00531368i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−11.4085	−	19.7602i	−0.893585	−	1.54773i	−0.835546	−	0.549420i	$-0.814849\pi$
$163$	−11.4085	−	19.7602i	−0.893585	−	1.54773i	−0.0580388	−	0.998314i	$-0.518485\pi$
$164$	0.0205367	+	0.0205367i	0.00160364	+	0.00160364i
$165$	−1.52776	−	1.16688i	−0.118936	−	0.0908416i
$166$	−4.18377	−	2.41550i	−0.324723	−	0.187479i
$167$	11.5320	+	6.65800i	0.892372	+	0.515211i	0.874718	−	0.484633i	$-0.161047\pi$
$167$	11.5320	+	6.65800i	0.892372	+	0.515211i	0.0176545	+	0.999844i	$0.494380\pi$
$168$	0.367480	−	0.367480i	0.0283517	−	0.0283517i
$169$	−6.78077	−	11.0915i	−0.521598	−	0.853191i
$170$	−8.74434	−	3.59915i	−0.670660	−	0.276043i
$171$	0.0538940	−	0.0144409i	0.00412138	−	0.00110432i
$172$	−1.24134	−	4.63274i	−0.0946513	−	0.353243i
$173$	−18.6279	−	4.99132i	−1.41625	−	0.379483i	−0.532099	−	0.846682i	$-0.678597\pi$
$173$	−18.6279	−	4.99132i	−1.41625	−	0.379483i	−0.884152	+	0.467199i	$0.845263\pi$
$174$	5.12242	−	5.12242i	0.388329	−	0.388329i
$175$	0.661313	−	2.51291i	0.0499905	−	0.189958i
$176$	−0.830435	−	0.222514i	−0.0625964	−	0.0167727i
$177$		−	5.06789i		−	0.380926i
$178$	−3.99511	+	14.9100i	−0.299446	+	1.11755i
$179$	−10.1381	+	17.5596i	−0.757754	+	1.31247i	0.186240	+	0.982504i	$0.440370\pi$
$179$	−10.1381	+	17.5596i	−0.757754	+	1.31247i	−0.943994	+	0.329964i	$0.892963\pi$
$180$	−2.21758	−	0.286912i	−0.165289	−	0.0213851i
$181$			14.3123i			1.06382i	0.846799	+	0.531912i	$0.178526\pi$
$181$			14.3123i			1.06382i	−0.846799	+	0.531912i	$0.821474\pi$
$182$	−1.63439	−	0.916435i	−0.121149	−	0.0679307i
$183$	−10.2074	−	10.2074i	−0.754553	−	0.754553i
$184$	−0.0474866	−	0.177222i	−0.00350076	−	0.0130650i
$185$	−0.500512	−	0.0647563i	−0.0367983	−	0.00476098i
$186$	−3.79654	+	2.19193i	−0.278376	+	0.160720i
$187$	3.63570			0.265869
$188$	−4.79551	+	2.76869i	−0.349749	+	0.201927i
$189$	−0.134507	+	0.501987i	−0.00978394	+	0.0365142i
$190$	0.0474866	−	0.115371i	0.00344504	−	0.00836991i
$191$	−6.39485	−	11.0762i	−0.462715	−	0.801446i	0.536380	−	0.843977i	$-0.319791\pi$
$191$	−6.39485	−	11.0762i	−0.462715	−	0.801446i	−0.999095	+	0.0425302i	$0.986458\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	1.10451	−	1.91307i	0.0795045	−	0.137706i	−0.823532	−	0.567270i	$-0.808000\pi$
$193$	1.10451	−	1.91307i	0.0795045	−	0.137706i	0.903036	+	0.429564i	$0.141333\pi$
$194$	6.29344			0.451842
$195$	1.17049	+	7.97684i	0.0838203	+	0.571233i
$196$	6.72992			0.480708
$197$	−6.06986	+	10.5133i	−0.432460	+	0.749042i	−0.997084	−	0.0763056i	$-0.975688\pi$
$197$	−6.06986	+	10.5133i	−0.432460	+	0.749042i	0.564625	+	0.825348i	$0.309021\pi$
$198$	0.830435	−	0.222514i	0.0590165	−	0.0158134i
$199$	−2.03805	−	3.53001i	−0.144474	−	0.250236i	0.784703	−	0.619872i	$-0.212816\pi$
$199$	−2.03805	−	3.53001i	−0.144474	−	0.250236i	−0.929176	+	0.369636i	$0.879482\pi$
$200$	−3.51970	+	3.55130i	−0.248880	+	0.251115i
$201$	3.54943	−	13.2467i	0.250358	−	0.934348i
$202$	4.39076	−	2.53501i	0.308933	−	0.178362i
$203$	−3.76477			−0.264235
$204$	3.66232	−	2.11444i	0.256414	−	0.148041i
$205$	−0.0514340	+	0.0396496i	−0.00359231	+	0.00276925i
$206$	−2.17876	−	8.13124i	−0.151801	−	0.566530i
$207$	0.129736	+	0.129736i	0.00901727	+	0.00901727i
$208$	1.84186	+	3.09961i	0.127710	+	0.214919i
$209$			0.0479688i			0.00331807i
$210$	0.709483	+	0.920352i	0.0489590	+	0.0635103i
$211$	7.38509	−	12.7914i	0.508411	−	0.880593i	−0.491542	−	0.870854i	$-0.663567\pi$
$211$	7.38509	−	12.7914i	0.508411	−	0.880593i	0.999953	−	0.00973918i	$-0.00310013\pi$
$212$	0.914577	−	3.41325i	0.0628134	−	0.234423i
$213$		−	6.88059i		−	0.471450i
$214$	−6.77519	−	1.81541i	−0.463142	−	0.124099i
$215$	10.6297	−	1.42359i	0.724936	−	0.0970879i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	2.20064	+	0.589661i	0.149389	+	0.0400288i
$218$	−2.28228	−	8.51759i	−0.154576	−	0.576884i
$219$	−2.32329	+	0.622524i	−0.156993	+	0.0420662i
$220$	0.731706	−	1.77772i	0.0493316	−	0.119854i
$221$	−10.9162	−	10.6453i	−0.734301	−	0.716080i
$222$	0.159595	−	0.159595i	0.0107113	−	0.0107113i
$223$	2.75364	+	1.58981i	0.184397	+	0.106462i	0.589357	−	0.807873i	$-0.299381\pi$
$223$	2.75364	+	1.58981i	0.184397	+	0.106462i	−0.404960	+	0.914334i	$0.632714\pi$
$224$	0.450069	+	0.259847i	0.0300715	+	0.0173618i
$225$	1.27250	−	4.83536i	0.0848334	−	0.322358i
$226$	−4.13489	−	4.13489i	−0.275049	−	0.275049i
$227$	14.4830	+	25.0852i	0.961267	+	1.66496i	0.719326	+	0.694673i	$0.244451\pi$
$227$	14.4830	+	25.0852i	0.961267	+	1.66496i	0.241942	+	0.970291i	$0.422216\pi$
$228$	0.0278976	+	0.0483200i	0.00184756	+	0.00320007i
$229$	−8.53343	−	8.53343i	−0.563905	−	0.563905i	0.366509	−	0.930414i	$-0.380553\pi$
$229$	−8.53343	−	8.53343i	−0.563905	−	0.563905i	−0.930414	+	0.366509i	$0.880553\pi$
$230$	0.406630	−	0.0544584i	0.0268124	−	0.00359088i
$231$	−0.386938	−	0.223399i	−0.0254586	−	0.0146985i
$232$	6.27365	+	3.62210i	0.411886	+	0.237802i
$233$	7.11568	−	7.11568i	0.466164	−	0.466164i	−0.434505	−	0.900669i	$-0.643077\pi$
$233$	7.11568	−	7.11568i	0.466164	−	0.466164i	0.900669	+	0.434505i	$0.143077\pi$
$234$	−3.14490	−	1.76341i	−0.205588	−	0.115278i
$235$	−4.76392	−	11.4288i	−0.310764	−	0.745534i
$236$	4.89521	−	1.31167i	0.318651	−	0.0853823i
$237$	−4.14631	−	15.4742i	−0.269331	−	1.00516i
$238$	−2.12284	−	0.568814i	−0.137604	−	0.0368708i
$239$	15.7046	−	15.7046i	1.01584	−	1.01584i	0.0159718	−	0.999872i	$-0.494916\pi$
$239$	15.7046	−	15.7046i	1.01584	−	1.01584i	0.999872	−	0.0159718i	$-0.00508419\pi$
$240$	−0.296818	−	2.21628i	−0.0191595	−	0.143060i
$241$	24.1684	+	6.47591i	1.55682	+	0.417150i	0.931656	−	0.363341i	$-0.118364\pi$
$241$	24.1684	+	6.47591i	1.55682	+	0.417150i	0.625168	+	0.780490i	$0.285031\pi$
$242$		−	10.2609i		−	0.659593i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	7.21773	−	12.5015i	0.462068	−	0.800325i
$245$	−1.93089	+	14.9242i	−0.123360	+	0.953470i
$246$		−	0.0290432i		−	0.00185173i
$247$	0.140452	−	0.144026i	0.00893676	−	0.00916415i
$248$	−3.09986	−	3.09986i	−0.196841	−	0.196841i
$249$	1.25035	+	4.66639i	0.0792380	+	0.295720i
$250$	−6.86546	−	8.82414i	−0.434210	−	0.558088i
$251$	−23.7056	+	13.6864i	−1.49628	+	0.863878i	−0.999991	−	0.00427828i	$-0.998638\pi$
$251$	−23.7056	+	13.6864i	−1.49628	+	0.863878i	−0.496290	+	0.868157i	$0.665305\pi$
$252$	−0.519695			−0.0327377
$253$	−0.136605	+	0.0788691i	−0.00858830	+	0.00495846i
$254$	−2.69043	+	10.0408i	−0.168813	+	0.630017i
$255$	3.63819	+	8.72817i	0.227832	+	0.546579i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.249933	+	0.0669693i	−0.0155904	+	0.00417743i	−0.266606	−	0.963806i	$-0.585902\pi$
$257$	−0.249933	+	0.0669693i	−0.0155904	+	0.00417743i	0.251015	+	0.967983i	$0.419236\pi$
$258$	−2.39808	+	4.15360i	−0.149298	+	0.258592i
$259$	−0.117296			−0.00728840
$260$	−7.40209	+	3.19516i	−0.459058	+	0.198156i
$261$	−7.24419			−0.448404
$262$	−8.69738	+	15.0643i	−0.537326	+	0.930676i
$263$	6.00425	−	1.60883i	0.370238	−	0.0992050i	−0.0689024	−	0.997623i	$-0.521950\pi$
$263$	6.00425	−	1.60883i	0.370238	−	0.0992050i	0.439140	+	0.898418i	$0.355283\pi$
$264$	0.429865	+	0.744548i	0.0264564	+	0.0458238i
$265$	7.30676	+	3.00745i	0.448851	+	0.184746i
$266$	0.00750484	−	0.0280084i	0.000460151	−	0.00171731i
$267$	13.3679	−	7.71796i	0.818102	−	0.472332i
$268$	13.7140			0.837713
$269$	0.338208	−	0.195264i	0.0206209	−	0.0119055i	−0.489654	−	0.871917i	$-0.662877\pi$
$269$	0.338208	−	0.195264i	0.0206209	−	0.0119055i	0.510275	+	0.860011i	$0.329544\pi$
$270$	1.36519	+	1.77095i	0.0830829	+	0.107776i
$271$	−4.36922	−	16.3061i	−0.265411	−	0.990528i	−0.961998	−	0.273056i	$-0.911966\pi$
$271$	−4.36922	−	16.3061i	−0.265411	−	0.990528i	0.696587	−	0.717472i	$-0.254701\pi$
$272$	2.99027	+	2.99027i	0.181312	+	0.181312i
$273$	0.507669	+	1.80370i	0.0307255	+	0.109165i
$274$		−	9.08700i		−	0.548966i
$275$	3.73231	+	2.13267i	0.225067	+	0.128605i
$276$	−0.0917371	+	0.158893i	−0.00552192	+	0.00956425i
$277$	−0.273563	+	1.02095i	−0.0164368	+	0.0613430i	−0.973657	−	0.228017i	$-0.926776\pi$
$277$	−0.273563	+	1.02095i	−0.0164368	+	0.0613430i	0.957220	+	0.289360i	$0.0934425\pi$
$278$		−	2.69872i		−	0.161859i
$279$	4.23449	+	1.13463i	0.253512	+	0.0679284i
$280$	−0.705364	+	0.923513i	−0.0421535	+	0.0551904i
$281$	9.59800	−	9.59800i	0.572568	−	0.572568i	−0.360277	−	0.932845i	$-0.617318\pi$
$281$	9.59800	−	9.59800i	0.572568	−	0.572568i	0.932845	+	0.360277i	$0.117318\pi$
$282$	5.34870	+	1.43318i	0.318510	+	0.0853446i
$283$	2.48624	+	9.27878i	0.147792	+	0.551566i	0.999615	+	0.0277374i	$0.00883024\pi$
$283$	2.48624	+	9.27878i	0.147792	+	0.551566i	−0.851823	+	0.523829i	$0.824503\pi$
$284$	6.64614	−	1.78083i	0.394376	−	0.105673i
$285$	−0.115158	+	0.0480017i	−0.00682136	+	0.00284337i
$286$	2.16418	−	2.21925i	0.127971	−	0.131227i
$287$	−0.0106728	+	0.0106728i	−0.000629996	+	0.000629996i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−0.765102	−	0.441732i	−0.0450060	−	0.0259842i
$290$	−9.83229	+	12.8731i	−0.577372	+	0.755937i
$291$	−4.45013	−	4.45013i	−0.260871	−	0.260871i
$292$	−1.20262	−	2.08300i	−0.0703782	−	0.121899i
$293$	−2.91359	−	5.04648i	−0.170214	−	0.294819i	0.768281	−	0.640113i	$-0.221112\pi$
$293$	−2.91359	−	5.04648i	−0.170214	−	0.294819i	−0.938494	+	0.345294i	$0.887779\pi$
$294$	−4.75877	−	4.75877i	−0.277537	−	0.277537i
$295$	1.50424	+	11.2319i	0.0875803	+	0.653945i
$296$	0.195463	+	0.112851i	0.0113611	+	0.00655931i
$297$	−0.744548	−	0.429865i	−0.0432031	−	0.0249433i
$298$	2.94015	−	2.94015i	0.170318	−	0.170318i
$299$	0.641085	+	0.163175i	0.0370749	+	0.00943666i
$300$	4.99995	−	0.0223420i	0.288672	−	0.00128991i
$301$	2.40761	−	0.645118i	0.138772	−	0.0371840i
$302$	−1.02264	−	3.81656i	−0.0588465	−	0.219618i
$303$	−4.89726	−	1.31222i	−0.281340	−	0.0753848i
$304$	−0.0394531	+	0.0394531i	−0.00226279	+	0.00226279i
$305$	25.6522	+	19.5927i	1.46884	+	1.12188i
$306$	−4.08479	−	1.09452i	−0.233512	−	0.0625693i
$307$		−	4.52688i		−	0.258363i	−0.991621	−	0.129181i	$-0.958765\pi$
$307$		−	4.52688i		−	0.258363i	0.991621	−	0.129181i	$-0.0412349\pi$
$308$	0.115640	−	0.431573i	0.00658918	−	0.0245912i
$309$	−4.20904	+	7.29027i	−0.239444	+	0.414729i
$310$	7.76359	−	5.98482i	0.440942	−	0.339915i
$311$			27.6370i			1.56715i	0.621297	+	0.783575i	$0.286606\pi$
$311$			27.6370i			1.56715i	−0.621297	+	0.783575i	$0.713394\pi$
$312$	0.889363	−	3.49414i	0.0503503	−	0.197817i
$313$	22.4963	+	22.4963i	1.27157	+	1.27157i	0.945266	+	0.326301i	$0.105802\pi$
$313$	22.4963	+	22.4963i	1.27157	+	1.27157i	0.326301	+	0.945266i	$0.394198\pi$
$314$	3.43702	+	12.8271i	0.193962	+	0.723877i
$315$	0.149107	−	1.15247i	0.00840120	−	0.0649342i
$316$	13.8738	−	8.01005i	0.780463	−	0.450600i
$317$	−1.80472			−0.101363			−0.0506817	−	0.998715i	$-0.516139\pi$
$317$	−1.80472			−0.101363			−0.0506817	+	0.998715i	$0.516139\pi$
$318$	−3.06023	+	1.76683i	−0.171609	+	0.0990787i
$319$	1.61194	−	6.01583i	0.0902512	−	0.336822i
$320$	2.06394	−	0.860320i	0.115378	−	0.0480933i
$321$	3.50709	+	6.07447i	0.195747	+	0.339044i
$322$	0.0921016	−	0.0246786i	0.00513262	−	0.00137528i
$323$	0.117976	−	0.204340i	0.00656434	−	0.0113698i
$324$	−1.00000			−0.0555556
$325$	−4.96180	−	17.3315i	−0.275231	−	0.961378i
$326$	−22.8171			−1.26372
$327$	−4.40903	+	7.63667i	−0.243820	+	0.422309i
$328$	0.0280536	−	0.00751694i	0.00154900	−	0.000415054i
$329$	−1.43887	−	2.49220i	−0.0793277	−	0.137400i
$330$	−1.77443	+	0.739642i	−0.0976792	+	0.0407160i
$331$	5.25635	−	19.6170i	0.288915	−	1.07825i	−0.657015	−	0.753877i	$-0.728181\pi$
$331$	5.25635	−	19.6170i	0.288915	−	1.07825i	0.945930	−	0.324369i	$-0.105152\pi$
$332$	−4.18377	+	2.41550i	−0.229614	+	0.132568i
$333$	−0.225701			−0.0123684
$334$	11.5320	−	6.65800i	0.631002	−	0.364309i
$335$	−3.93469	+	30.4119i	−0.214975	+	1.66158i
$336$	−0.134507	−	0.501987i	−0.00733796	−	0.0273856i
$337$	−16.0244	−	16.0244i	−0.872903	−	0.872903i	0.119885	−	0.992788i	$-0.461747\pi$
$337$	−16.0244	−	16.0244i	−0.872903	−	0.872903i	−0.992788	+	0.119885i	$0.961747\pi$
$338$	−12.9959	+	0.326579i	−0.706884	+	0.0177636i
$339$			5.84762i			0.317599i
$340$	−7.48913	+	5.77324i	−0.406155	+	0.313098i
$341$	−1.88447	+	3.26400i	−0.102050	+	0.176755i
$342$	0.0144409	−	0.0538940i	0.000780872	−	0.00291425i
$343$			7.13537i			0.385274i
$344$	−4.63274	−	1.24134i	−0.249781	−	0.0669285i
$345$	−0.326039	−	0.249023i	−0.0175533	−	0.0134070i
$346$	−13.6366	+	13.6366i	−0.733106	+	0.733106i
$347$	−34.8393	−	9.33516i	−1.87027	−	0.501138i	−0.999963	−	0.00863072i	$-0.997253\pi$
$347$	−34.8393	−	9.33516i	−1.87027	−	0.501138i	−0.870309	−	0.492507i	$-0.836081\pi$
$348$	−1.87494	−	6.99735i	−0.100507	−	0.375097i
$349$	−3.51575	+	0.942042i	−0.188194	+	0.0504264i	−0.351685	−	0.936118i	$-0.614391\pi$
$349$	−3.51575	+	0.942042i	−0.188194	+	0.0504264i	0.163491	+	0.986545i	$0.447724\pi$
$350$	−1.84559	−	1.82917i	−0.0986510	−	0.0977733i
$351$	0.976860	+	3.47070i	0.0521410	+	0.185252i
$352$	−0.607921	+	0.607921i	−0.0324023	+	0.0324023i
$353$	24.5055	+	14.1482i	1.30429	+	0.753034i	0.981137	−	0.193311i	$-0.0619227\pi$
$353$	24.5055	+	14.1482i	1.30429	+	0.753034i	0.323156	+	0.946346i	$0.395256\pi$
$354$	−4.38892	−	2.53395i	−0.233269	−	0.134678i
$355$	2.04228	+	15.2493i	0.108393	+	0.809350i
$356$	10.9148	+	10.9148i	0.578486	+	0.578486i
$357$	1.09886	+	1.90329i	0.0581581	+	0.100733i
$358$	10.1381	+	17.5596i	0.535813	+	0.928055i
$359$	4.76749	+	4.76749i	0.251619	+	0.251619i	0.821634	−	0.570015i	$-0.193063\pi$
$359$	4.76749	+	4.76749i	0.251619	+	0.251619i	−0.570015	+	0.821634i	$0.693063\pi$
$360$	−1.35727	+	1.77703i	−0.0715342	+	0.0936576i
$361$	−16.4518	−	9.49844i	−0.865884	−	0.499918i
$362$	12.3948	+	7.15615i	0.651457	+	0.376119i
$363$	−7.25553	+	7.25553i	−0.380816	+	0.380816i
$364$	−1.61085	+	0.957204i	−0.0844315	+	0.0501711i
$365$	4.96429	−	2.06928i	0.259843	−	0.108311i
$366$	−13.9436	+	3.73617i	−0.728843	+	0.195293i
$367$	−8.05298	−	30.0541i	−0.420362	−	1.56881i	−0.773847	−	0.633373i	$-0.781670\pi$
$367$	−8.05298	−	30.0541i	−0.420362	−	1.56881i	0.353485	−	0.935440i	$-0.384997\pi$
$368$	−0.177222	−	0.0474866i	−0.00923836	−	0.00247541i
$369$	−0.0205367	+	0.0205367i	−0.00106910	+	0.00106910i
$370$	−0.306336	+	0.401078i	−0.0159257	+	0.0208510i
$371$	1.77385	+	0.475301i	0.0920935	+	0.0246764i
$372$			4.38387i			0.227293i
$373$	−5.84130	+	21.8000i	−0.302451	+	1.12876i	0.632666	+	0.774425i	$0.281961\pi$
$373$	−5.84130	+	21.8000i	−0.302451	+	1.12876i	−0.935117	+	0.354338i	$0.884706\pi$
$374$	1.81785	−	3.14861i	0.0939987	−	0.162811i
$375$	−1.38500	+	11.0942i	−0.0715210	+	0.572903i
$376$			5.53738i			0.285569i
$377$	−22.4541	+	13.3428i	−1.15645	+	0.687188i
$378$	0.367480	+	0.367480i	0.0189011	+	0.0189011i
$379$	−3.85119	−	14.3728i	−0.197822	−	0.738283i	−0.991518	−	0.129968i	$-0.958512\pi$
$379$	−3.85119	−	14.3728i	−0.197822	−	0.738283i	0.793696	−	0.608315i	$-0.208154\pi$
$380$	−0.0761711	−	0.0988102i	−0.00390750	−	0.00506886i
$381$	9.00236	−	5.19751i	0.461205	−	0.266277i
$382$	−12.7897			−0.654378
$383$	−9.84116	+	5.68179i	−0.502860	+	0.290326i	−0.729894	−	0.683561i	$-0.760430\pi$
$383$	−9.84116	+	5.68179i	−0.502860	+	0.290326i	0.227034	+	0.973887i	$0.427097\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	0.923871	+	0.380264i	0.0470848	+	0.0193800i
$386$	−1.10451	−	1.91307i	−0.0562182	−	0.0973727i
$387$	4.63274	−	1.24134i	0.235496	−	0.0631008i
$388$	3.14672	−	5.45027i	0.159750	−	0.276696i
$389$	0.783134			0.0397065			0.0198532	−	0.999803i	$-0.493680\pi$
$389$	0.783134			0.0397065			0.0198532	+	0.999803i	$0.493680\pi$
$390$	7.49339	+	2.97475i	0.379442	+	0.150632i
$391$	0.775891			0.0392385
$392$	3.36496	−	5.82828i	0.169956	−	0.294373i
$393$	16.8021	−	4.50210i	0.847552	−	0.227101i
$394$	6.06986	+	10.5133i	0.305795	+	0.529653i
$395$	13.7824	+	33.0645i	0.693468	+	1.66366i
$396$	0.222514	−	0.830435i	0.0111818	−	0.0417309i
$397$	−12.3334	+	7.12070i	−0.618996	+	0.357378i	−0.776478	−	0.630144i	$-0.782996\pi$
$397$	−12.3334	+	7.12070i	−0.618996	+	0.357378i	0.157482	+	0.987522i	$0.449662\pi$
$398$	−4.07610			−0.204317
$399$	−0.0251117	+	0.0144982i	−0.00125716	+	0.000725819i
$400$	1.31566	+	4.82380i	0.0657831	+	0.241190i
$401$	−8.08823	−	30.1857i	−0.403907	−	1.50740i	−0.806062	−	0.591830i	$-0.798405\pi$
$401$	−8.08823	−	30.1857i	−0.403907	−	1.50740i	0.402155	−	0.915571i	$-0.368261\pi$
$402$	−9.69723	−	9.69723i	−0.483654	−	0.483654i
$403$	15.2151	−	4.28243i	0.757917	−	0.213323i
$404$		−	5.07001i		−	0.252243i
$405$	0.286912	−	2.21758i	0.0142568	−	0.110193i
$406$	−1.88239	+	3.26039i	−0.0934212	+	0.161810i
$407$	0.0502218	−	0.187430i	0.00248940	−	0.00929057i
$408$		−	4.22888i		−	0.209361i
$409$	32.5735	+	8.72803i	1.61065	+	0.431573i	0.948237	−	0.317563i	$-0.102864\pi$
$409$	32.5735	+	8.72803i	1.61065	+	0.431573i	0.662416	+	0.749136i	$0.269531\pi$
$410$	0.00862055	+	0.0643680i	0.000425739	+	0.00317891i
$411$	−6.42548	+	6.42548i	−0.316946	+	0.316946i
$412$	−8.13124	−	2.17876i	−0.400597	−	0.107340i
$413$	0.681667	+	2.54402i	0.0335426	+	0.125183i
$414$	0.177222	−	0.0474866i	0.00871001	−	0.00233384i
$415$	−4.15620	−	9.97090i	−0.204020	−	0.489452i
$416$	3.60527	−	0.0452920i	0.176763	−	0.00222062i
$417$	−1.90829	+	1.90829i	−0.0934492	+	0.0934492i
$418$	0.0415422	+	0.0239844i	0.00203189	+	0.00117311i
$419$	9.64226	+	5.56696i	0.471055	+	0.271964i	0.716681	−	0.697401i	$-0.245660\pi$
$419$	9.64226	+	5.56696i	0.471055	+	0.271964i	−0.245626	+	0.969365i	$0.578994\pi$
$420$	1.15179	−	0.154255i	0.0562016	−	0.00752686i
$421$	20.6313	+	20.6313i	1.00551	+	1.00551i	0.999985	+	0.00552546i	$0.00175882\pi$
$421$	20.6313	+	20.6313i	1.00551	+	1.00551i	0.00552546	+	0.999985i	$0.498241\pi$
$422$	−7.38509	−	12.7914i	−0.359501	−	0.622673i
$423$	−2.76869	−	4.79551i	−0.134618	−	0.233166i
$424$	−2.49867	−	2.49867i	−0.121346	−	0.121346i
$425$	−10.6539	−	18.2642i	−0.516791	−	0.885943i
$426$	−5.95877	−	3.44030i	−0.288703	−	0.166683i
$427$	6.49695	+	3.75102i	0.314409	+	0.181524i
$428$	−4.95978	+	4.95978i	−0.239740	+	0.239740i
$429$	−3.09956	+	0.0389389i	−0.149648	+	0.00187999i
$430$	4.08196	−	9.91734i	0.196850	−	0.478257i
$431$	16.8679	−	4.51975i	0.812500	−	0.217709i	0.171435	−	0.985195i	$-0.445160\pi$
$431$	16.8679	−	4.51975i	0.812500	−	0.217709i	0.641065	+	0.767487i	$0.278493\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	−2.14717	−	0.575332i	−0.103186	−	0.0276487i	0.206856	−	0.978371i	$-0.433677\pi$
$433$	−2.14717	−	0.575332i	−0.103186	−	0.0276487i	−0.310043	+	0.950723i	$0.600343\pi$
$434$	1.61098	−	1.61098i	0.0773296	−	0.0773296i
$435$	16.0552	−	2.15021i	0.769786	−	0.103094i
$436$	−8.51759	−	2.28228i	−0.407919	−	0.109302i
$437$			0.0102370i			0.000489701i
$438$	−0.622524	+	2.32329i	−0.0297453	+	0.111011i
$439$	−18.9701	+	32.8571i	−0.905392	+	1.56819i	−0.0850025	+	0.996381i	$0.527090\pi$
$439$	−18.9701	+	32.8571i	−0.905392	+	1.56819i	−0.820390	+	0.571805i	$0.806243\pi$
$440$	−1.17370	−	1.52254i	−0.0559538	−	0.0725840i
$441$			6.72992i			0.320472i
$442$	−14.6772	+	4.13103i	−0.698122	+	0.196493i
$443$	15.4941	+	15.4941i	0.736149	+	0.736149i	0.971830	−	0.235681i	$-0.0757322\pi$
$443$	15.4941	+	15.4941i	0.736149	+	0.736149i	−0.235681	+	0.971830i	$0.575732\pi$
$444$	−0.0584158	−	0.218011i	−0.00277229	−	0.0103463i
$445$	−27.3362	+	21.0730i	−1.29586	+	0.998956i
$446$	2.75364	−	1.58981i	0.130388	−	0.0752798i
$447$	−4.15800			−0.196666
$448$	0.450069	−	0.259847i	0.0212638	−	0.0122766i
$449$	4.09810	−	15.2943i	0.193402	−	0.721784i	−0.799273	−	0.600968i	$-0.794782\pi$
$449$	4.09810	−	15.2943i	0.193402	−	0.721784i	0.992675	−	0.120817i	$-0.0385513\pi$
$450$	−3.55130	−	3.51970i	−0.167410	−	0.165920i
$451$	−0.0124847	−	0.0216241i	−0.000587880	−	0.00101824i
$452$	−5.64837	+	1.51348i	−0.265677	+	0.0711879i
$453$	−1.97560	+	3.42183i	−0.0928216	+	0.160772i
$454$	28.9659			1.35944
$455$	−1.66051	−	3.84683i	−0.0778459	−	0.180342i
$456$	0.0557952			0.00261285
$457$	−19.5983	+	33.9453i	−0.916771	+	1.58789i	−0.112483	+	0.993654i	$0.535880\pi$
$457$	−19.5983	+	33.9453i	−0.916771	+	1.58789i	−0.804288	+	0.594240i	$0.797453\pi$
$458$	−11.6569	+	3.12345i	−0.544691	+	0.145949i
$459$	2.11444	+	3.66232i	0.0986937	+	0.170943i
$460$	0.156153	−	0.379381i	0.00728066	−	0.0176887i
$461$	−2.72197	+	10.1585i	−0.126775	+	0.473130i	−0.999897	−	0.0143717i	$-0.995425\pi$
$461$	−2.72197	+	10.1585i	−0.126775	+	0.473130i	0.873122	+	0.487502i	$0.162092\pi$
$462$	−0.386938	+	0.223399i	−0.0180020	+	0.0103934i
$463$	−31.3265			−1.45586			−0.727932	−	0.685649i	$-0.759518\pi$
$463$	−31.3265			−1.45586			−0.727932	+	0.685649i	$0.759518\pi$
$464$	6.27365	−	3.62210i	0.291247	−	0.168152i
$465$	−9.72160	−	1.25778i	−0.450828	−	0.0583283i
$466$	−2.60452	−	9.72020i	−0.120652	−	0.450280i
$467$	−17.1532	−	17.1532i	−0.793754	−	0.793754i	0.188349	−	0.982102i	$-0.439687\pi$
$467$	−17.1532	−	17.1532i	−0.793754	−	0.793754i	−0.982102	+	0.188349i	$0.939687\pi$
$468$	−3.09961	+	1.84186i	−0.143279	+	0.0851399i
$469$			7.12707i			0.329098i
$470$	−12.2796	−	1.58874i	−0.566416	−	0.0732830i
$471$	6.63981	−	11.5005i	0.305946	−	0.529915i
$472$	1.31167	−	4.89521i	0.0603744	−	0.225320i
$473$			4.12341i			0.189595i
$474$	−15.4742	−	4.14631i	−0.710755	−	0.190446i
$475$	0.240974	−	0.140566i	0.0110567	−	0.00644961i
$476$	−1.55403	+	1.55403i	−0.0712288	+	0.0712288i
$477$	3.41325	+	0.914577i	0.156282	+	0.0418756i
$478$	−5.74827	−	21.4528i	−0.262920	−	0.981230i
$479$	11.2332	−	3.00994i	0.513260	−	0.137528i	0.00711279	−	0.999975i	$-0.497736\pi$
$479$	11.2332	−	3.00994i	0.513260	−	0.137528i	0.506147	+	0.862447i	$0.331069\pi$
$480$	−2.06776	−	0.851088i	−0.0943801	−	0.0388467i
$481$	−0.699585	+	0.415709i	−0.0318983	+	0.0189547i
$482$	17.6925	−	17.6925i	0.805871	−	0.805871i
$483$	−0.0825761	−	0.0476753i	−0.00375734	−	0.00216930i
$484$	−8.88617	−	5.13043i	−0.403917	−	0.233201i
$485$	11.1836	+	8.54186i	0.507822	+	0.387866i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−4.57010	−	7.91564i	−0.207091	−	0.358692i	0.743706	−	0.668507i	$-0.233066\pi$
$487$	−4.57010	−	7.91564i	−0.207091	−	0.358692i	−0.950797	+	0.309815i	$0.899733\pi$
$488$	−7.21773	−	12.5015i	−0.326731	−	0.565915i
$489$	16.1341	+	16.1341i	0.729609	+	0.729609i
$490$	11.9593	+	9.13428i	0.540264	+	0.412645i
$491$	−6.88995	−	3.97792i	−0.310939	−	0.179521i	0.336407	−	0.941717i	$-0.390788\pi$
$491$	−6.88995	−	3.97792i	−0.310939	−	0.179521i	−0.647347	+	0.762196i	$0.724121\pi$
$492$	−0.0251522	−	0.0145216i	−0.00113395	−	0.000654685i
$493$	−21.6621	+	21.6621i	−0.975612	+	0.975612i
$494$	−0.0545041	−	0.193648i	−0.00245225	−	0.00871264i
$495$	1.77772	+	0.731706i	0.0799025	+	0.0328877i
$496$	−4.23449	+	1.13463i	−0.190134	+	0.0509463i
$497$	0.925487	+	3.45397i	0.0415138	+	0.154932i
$498$	4.66639	+	1.25035i	0.209106	+	0.0560297i
$499$	21.9284	−	21.9284i	0.981650	−	0.981650i	−0.0181843	−	0.999835i	$-0.505789\pi$
$499$	21.9284	−	21.9284i	0.981650	−	0.981650i	0.999835	+	0.0181843i	$0.00578857\pi$
$500$	−11.0747	+	1.53359i	−0.495274	+	0.0685842i
$501$	−12.8623	−	3.44643i	−0.574644	−	0.153975i
$502$			27.3728i			1.22171i
$503$	4.95760	−	18.5020i	0.221049	−	0.824964i	−0.762901	−	0.646516i	$-0.776225\pi$
$503$	4.95760	−	18.5020i	0.221049	−	0.824964i	0.983949	−	0.178449i	$-0.0571078\pi$
$504$	−0.259847	+	0.450069i	−0.0115745	+	0.0200477i
$505$	11.2432	+	1.45465i	0.500315	+	0.0647309i
$506$			0.157738i			0.00701232i
$507$	9.42041	+	8.95856i	0.418375	+	0.397864i
$508$	7.35039	+	7.35039i	0.326121	+	0.326121i
$509$	−8.14806	−	30.4090i	−0.361156	−	1.34785i	−0.872557	−	0.488512i	$-0.837540\pi$
$509$	−8.14806	−	30.4090i	−0.361156	−	1.34785i	0.511401	−	0.859342i	$-0.329127\pi$
$510$	9.37791	+	1.21332i	0.415261	+	0.0537265i
$511$	1.08253	−	0.624997i	0.0478882	−	0.0276482i
$512$	−1.00000			−0.0441942
$513$	−0.0483200	+	0.0278976i	−0.00213338	+	0.00123171i
$514$	−0.0669693	+	0.249933i	−0.00295389	+	0.0110241i
$515$	7.16453	−	17.4066i	0.315707	−	0.767027i
$516$	2.39808	+	4.15360i	0.105570	+	0.182852i
$517$	4.59843	−	1.23215i	0.202239	−	0.0541898i
$518$	−0.0586479	+	0.101581i	−0.00257684	+	0.00446322i
$519$	19.2850			0.846517
$520$	−0.933954	+	8.00798i	−0.0409566	+	0.351173i
$521$	38.1901			1.67314			0.836568	−	0.547862i	$-0.184558\pi$
$521$	38.1901			1.67314			0.836568	+	0.547862i	$0.184558\pi$
$522$	−3.62210	+	6.27365i	−0.158535	+	0.274590i
$523$	1.41502	−	0.379154i	0.0618747	−	0.0165793i	−0.227749	−	0.973720i	$-0.573137\pi$
$523$	1.41502	−	0.379154i	0.0618747	−	0.0165793i	0.289624	+	0.957141i	$0.406470\pi$
$524$	8.69738	+	15.0643i	0.379947	+	0.658087i
$525$	0.0116110	+	2.59845i	0.000506746	+	0.113406i
$526$	1.60883	−	6.00425i	0.0701485	−	0.261798i
$527$	16.0551	−	9.26943i	0.699372	−	0.403783i
$528$	0.859730			0.0374149
$529$	19.8894	−	11.4832i	0.864758	−	0.499268i
$530$	6.25791	−	4.82411i	0.271826	−	0.209546i
$531$	1.31167	+	4.89521i	0.0569215	+	0.212434i
$532$	−0.0205036	−	0.0205036i	−0.000888944	−	0.000888944i
$533$	−0.0258300	+	0.101481i	−0.00111882	+	0.00439564i
$534$		−	15.4359i		−	0.667978i
$535$	−9.57571	−	12.4218i	−0.413994	−	0.537039i
$536$	6.85698	−	11.8766i	0.296176	−	0.512993i
$537$	5.24784	−	19.5852i	0.226461	−	0.845165i
$538$		−	0.390528i		−	0.0168369i
$539$	−5.58876	−	1.49750i	−0.240725	−	0.0645021i
$540$	2.21628	−	0.296818i	0.0953735	−	0.0127730i
$541$	−21.3618	+	21.3618i	−0.918417	+	0.918417i	−0.996914	−	0.0784970i	$-0.974988\pi$
$541$	−21.3618	+	21.3618i	−0.918417	+	0.918417i	0.0784970	+	0.996914i	$0.474988\pi$
$542$	−16.3061	−	4.36922i	−0.700409	−	0.187674i
$543$	−3.70429	−	13.8246i	−0.158966	−	0.593271i
$544$	4.08479	−	1.09452i	0.175134	−	0.0469270i
$545$	7.50495	−	18.2337i	0.321477	−	0.781045i
$546$	1.81589	+	0.462197i	0.0777128	+	0.0197802i
$547$	13.4041	−	13.4041i	0.573116	−	0.573116i	−0.359882	−	0.932998i	$-0.617183\pi$
$547$	13.4041	−	13.4041i	0.573116	−	0.573116i	0.932998	+	0.359882i	$0.117183\pi$
$548$	−7.86958	−	4.54350i	−0.336172	−	0.194089i
$549$	12.5015	+	7.21773i	0.533550	+	0.308045i
$550$	3.71310	−	2.16594i	0.158327	−	0.0923559i
$551$	−0.285806	−	0.285806i	−0.0121758	−	0.0121758i
$552$	0.0917371	+	0.158893i	0.00390459	+	0.00676295i
$553$	4.16278	+	7.21015i	0.177019	+	0.306607i
$554$	0.747388	+	0.747388i	0.0317535	+	0.0317535i
$555$	0.500217	−	0.0669921i	0.0212330	−	0.00284366i
$556$	−2.33716	−	1.34936i	−0.0991178	−	0.0572257i
$557$	−28.8536	−	16.6586i	−1.22256	−	0.705848i	−0.257101	−	0.966385i	$-0.582767\pi$
$557$	−28.8536	−	16.6586i	−1.22256	−	0.705848i	−0.965464	+	0.260536i	$0.916101\pi$
$558$	3.09986	−	3.09986i	0.131228	−	0.131228i
$559$	12.0733	−	12.3805i	0.510647	−	0.523640i
$560$	0.447104	+	1.07262i	0.0188936	+	0.0453264i
$561$	−3.51181	+	0.940988i	−0.148269	+	0.0397285i
$562$	−3.51311	−	13.1111i	−0.148192	−	0.553059i
$563$	−25.7554	−	6.90115i	−1.08546	−	0.290849i	−0.328631	−	0.944458i	$-0.606587\pi$
$563$	−25.7554	−	6.90115i	−1.08546	−	0.290849i	−0.756832	+	0.653610i	$0.773254\pi$
$564$	3.91552	−	3.91552i	0.164873	−	0.164873i
$565$	−1.73568	−	12.9600i	−0.0730206	−	0.545230i
$566$	9.27878	+	2.48624i	0.390016	+	0.104505i
$567$		−	0.519695i		−	0.0218251i
$568$	1.78083	−	6.64614i	0.0747219	−	0.278866i
$569$	20.0582	−	34.7418i	0.840883	−	1.45645i	−0.0482653	−	0.998835i	$-0.515369\pi$
$569$	20.0582	−	34.7418i	0.840883	−	1.45645i	0.889149	−	0.457618i	$-0.151297\pi$
$570$	−0.0160083	+	0.123730i	−0.000670513	+	0.00518250i
$571$		−	5.59408i		−	0.234105i	−0.993126	−	0.117053i	$-0.962655\pi$
$571$		−	5.59408i		−	0.234105i	0.993126	−	0.117053i	$-0.0373446\pi$
$572$	−0.839836	−	2.98386i	−0.0351153	−	0.124762i
$573$	9.04369	+	9.04369i	0.377806	+	0.377806i
$574$	0.00390652	+	0.0145793i	0.000163055	+	0.000608529i
$575$	0.796508	+	0.455131i	0.0332167	+	0.0189803i
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	12.9781			0.540287			0.270144	−	0.962820i	$-0.412929\pi$
$577$	12.9781			0.540287			0.270144	+	0.962820i	$0.412929\pi$
$578$	−0.765102	+	0.441732i	−0.0318240	+	0.0183736i
$579$	−0.571737	+	2.13375i	−0.0237606	+	0.0886757i
$580$	6.23232	+	14.9516i	0.258783	+	0.620831i
$581$	−1.25532	−	2.17428i	−0.0520796	−	0.0902045i
$582$	−6.07899	+	1.62886i	−0.251982	+	0.0675185i
$583$	−1.51899	+	2.63097i	−0.0629103	+	0.108964i
$584$	−2.40525			−0.0995298
$585$	−3.19516	−	7.40209i	−0.132104	−	0.306039i
$586$	−5.82718			−0.240718
$587$	20.9109	−	36.2188i	0.863086	−	1.49491i	−0.00584852	−	0.999983i	$-0.501862\pi$
$587$	20.9109	−	36.2188i	0.863086	−	1.49491i	0.868935	−	0.494926i	$-0.164805\pi$
$588$	−6.50060	+	1.74183i	−0.268080	+	0.0718319i
$589$	0.122299	+	0.211829i	0.00503925	+	0.00872824i
$590$	10.4792	+	4.31323i	0.431422	+	0.177573i
$591$	3.14199	−	11.7261i	0.129244	−	0.482346i
$592$	0.195463	−	0.112851i	0.00803348	−	0.00463813i
$593$	6.42791			0.263963			0.131981	−	0.991252i	$-0.457866\pi$
$593$	6.42791			0.263963			0.131981	+	0.991252i	$0.457866\pi$
$594$	−0.744548	+	0.429865i	−0.0305492	+	0.0176376i
$595$	−3.00032	−	3.89206i	−0.123001	−	0.159559i
$596$	−1.07617	−	4.01632i	−0.0440816	−	0.164515i
$597$	2.88224	+	2.88224i	0.117962	+	0.117962i
$598$	0.461856	−	0.473608i	0.0188867	−	0.0193673i
$599$		−	17.8641i		−	0.729906i	−0.931026	−	0.364953i	$-0.881085\pi$
$599$		−	17.8641i		−	0.729906i	0.931026	−	0.364953i	$-0.118915\pi$
$600$	2.48063	−	4.34125i	0.101271	−	0.177231i
$601$	−16.6635	+	28.8620i	−0.679717	+	1.17730i	0.295349	+	0.955389i	$0.404564\pi$
$601$	−16.6635	+	28.8620i	−0.679717	+	1.17730i	−0.975066	+	0.221914i	$0.928769\pi$
$602$	0.645118	−	2.40761i	0.0262930	−	0.0981270i
$603$			13.7140i			0.558476i
$604$	−3.81656	−	1.02264i	−0.155293	−	0.0416108i
$605$	13.9267	−	18.2339i	0.566201	−	0.741312i
$606$	−3.58504	+	3.58504i	−0.145632	+	0.145632i
$607$	−16.3187	−	4.37259i	−0.662357	−	0.177478i	−0.0880472	−	0.996116i	$-0.528063\pi$
$607$	−16.3187	−	4.37259i	−0.662357	−	0.177478i	−0.574309	+	0.818638i	$0.694729\pi$
$608$	0.0144409	+	0.0538940i	0.000585654	+	0.00218569i
$609$	3.63649	−	0.974394i	0.147358	−	0.0394844i
$610$	29.7939	−	12.4191i	1.20632	−	0.502835i
$611$	−17.4145	−	9.76467i	−0.704515	−	0.395036i
$612$	−2.99027	+	2.99027i	−0.120875	+	0.120875i
$613$	−34.3825	−	19.8507i	−1.38869	−	0.801763i	−0.395526	−	0.918455i	$-0.629438\pi$
$613$	−34.3825	−	19.8507i	−1.38869	−	0.801763i	−0.993168	+	0.116692i	$0.962771\pi$
$614$	−3.92039	−	2.26344i	−0.158214	−	0.0913450i
$615$	0.0394194	−	0.0516107i	0.00158954	−	0.00208114i
$616$	−0.315933	−	0.315933i	−0.0127293	−	0.0127293i
$617$	11.6945	+	20.2554i	0.470802	+	0.815453i	0.999442	−	0.0333930i	$-0.0106313\pi$
$617$	11.6945	+	20.2554i	0.470802	+	0.815453i	−0.528640	+	0.848846i	$0.677298\pi$
$618$	4.20904	+	7.29027i	0.169312	+	0.293258i
$619$	−9.00079	−	9.00079i	−0.361772	−	0.361772i	0.502693	−	0.864465i	$-0.332343\pi$
$619$	−9.00079	−	9.00079i	−0.361772	−	0.361772i	−0.864465	+	0.502693i	$0.832343\pi$
$620$	−1.30121	−	9.71588i	−0.0522578	−	0.390199i
$621$	−0.158893	−	0.0917371i	−0.00637617	−	0.00368128i
$622$	23.9343	+	13.8185i	0.959680	+	0.554071i
$623$	−5.67239	+	5.67239i	−0.227259	+	0.227259i
$624$	−2.58133	−	2.51728i	−0.103336	−	0.100772i
$625$	−0.223417	−	24.9990i	−0.00893670	−	0.999960i
$626$	30.7305	−	8.23422i	1.22824	−	0.329106i
$627$	−0.0124152	−	0.0463343i	−0.000495817	−	0.00185041i
$628$	12.8271	+	3.43702i	0.511858	+	0.137152i
$629$	−0.674908	+	0.674908i	−0.0269104	+	0.0269104i
$630$	−0.923513	−	0.705364i	−0.0367936	−	0.0281024i
$631$	−5.22065	−	1.39887i	−0.207831	−	0.0556881i	0.153401	−	0.988164i	$-0.450977\pi$
$631$	−5.22065	−	1.39887i	−0.207831	−	0.0556881i	−0.361232	+	0.932476i	$0.617644\pi$
$632$		−	16.0201i		−	0.637245i
$633$	−3.82280	+	14.2669i	−0.151943	+	0.567058i
$634$	−0.902361	+	1.56294i	−0.0358373	+	0.0620721i
$635$	−18.4090	+	14.1912i	−0.730540	+	0.563161i
$636$			3.53365i			0.140118i
$637$	12.3955	+	20.8601i	0.491129	+	0.826507i
$638$	−4.40390	−	4.40390i	−0.174352	−	0.174352i
$639$	1.78083	+	6.64614i	0.0704485	+	0.262917i
$640$	0.286912	−	2.21758i	0.0113412	−	0.0876577i
$641$	−7.68152	+	4.43492i	−0.303402	+	0.175169i	−0.643970	−	0.765051i	$-0.722714\pi$
$641$	−7.68152	+	4.43492i	−0.303402	+	0.175169i	0.340568	+	0.940220i	$0.389381\pi$
$642$	7.01419			0.276828
$643$	15.2956	−	8.83093i	0.603201	−	0.348258i	−0.167099	−	0.985940i	$-0.553440\pi$
$643$	15.2956	−	8.83093i	0.603201	−	0.348258i	0.770300	+	0.637682i	$0.220107\pi$
$644$	0.0246786	−	0.0921016i	0.000972471	−	0.00362931i
$645$	−9.89901	+	4.12624i	−0.389773	+	0.162470i
$646$	−0.117976	−	0.204340i	−0.00464169	−	0.00803964i
$647$	42.4705	−	11.3799i	1.66969	−	0.447391i	0.704660	−	0.709545i	$-0.251100\pi$
$647$	42.4705	−	11.3799i	1.66969	−	0.447391i	0.965026	+	0.262154i	$0.0844329\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−4.35702			−0.171028
$650$	−17.4904	−	4.36870i	−0.686030	−	0.171355i
$651$	−2.27827			−0.0892926
$652$	−11.4085	+	19.7602i	−0.446792	+	0.773867i
$653$	−22.0209	+	5.90050i	−0.861746	+	0.230904i	−0.662515	−	0.749048i	$-0.730511\pi$
$653$	−22.0209	+	5.90050i	−0.861746	+	0.230904i	−0.199231	+	0.979953i	$0.563844\pi$
$654$	4.40903	+	7.63667i	0.172407	+	0.298617i
$655$	−35.9018	+	14.9651i	−1.40280	+	0.584733i
$656$	0.00751694	−	0.0280536i	0.000293487	−	0.00109531i
$657$	2.08300	−	1.20262i	0.0812657	−	0.0469188i
$658$	−2.87775			−0.112186
$659$	−0.951098	+	0.549117i	−0.0370495	+	0.0213906i	−0.518410	−	0.855132i	$-0.673476\pi$
$659$	−0.951098	+	0.549117i	−0.0370495	+	0.0213906i	0.481361	+	0.876523i	$0.340143\pi$
$660$	−0.246666	+	1.90652i	−0.00960148	+	0.0742113i
$661$	−6.39522	−	23.8673i	−0.248745	−	0.928330i	−0.971464	−	0.237187i	$-0.923774\pi$
$661$	−6.39522	−	23.8673i	−0.248745	−	0.928330i	0.722719	−	0.691142i	$-0.242892\pi$
$662$	−14.3606	−	14.3606i	−0.558142	−	0.558142i
$663$	13.2994	+	7.45725i	0.516506	+	0.289616i
$664$			4.83100i			0.187479i
$665$	0.0513512	−	0.0395857i	0.00199131	−	0.00153507i
$666$	−0.112851	+	0.195463i	−0.00437287	+	0.00757404i
$667$	0.344002	−	1.28383i	0.0133198	−	0.0497102i
$668$		−	13.3160i		−	0.515211i
$669$	−3.07128	−	0.822948i	−0.118743	−	0.0318170i
$670$	24.3701	+	18.6135i	0.941499	+	0.719101i
$671$	−8.77561	+	8.77561i	−0.338779	+	0.338779i
$672$	−0.501987	−	0.134507i	−0.0193646	−	0.00518872i
$673$	1.94265	+	7.25006i	0.0748836	+	0.279469i	0.993207	−	0.116362i	$-0.0371232\pi$
$673$	1.94265	+	7.25006i	0.0748836	+	0.279469i	−0.918323	+	0.395831i	$0.870457\pi$
$674$	−21.8897	+	5.86533i	−0.843160	+	0.225924i
$675$	0.0223420	+	4.99995i	0.000859943	+	0.192448i
$676$	−6.21512	+	11.4181i	−0.239043	+	0.439156i
$677$	−29.5301	+	29.5301i	−1.13493	+	1.13493i	−0.145589	+	0.989345i	$0.546508\pi$
$677$	−29.5301	+	29.5301i	−1.13493	+	1.13493i	−0.989345	+	0.145589i	$0.953492\pi$
$678$	5.06419	+	2.92381i	0.194489	+	0.112288i
$679$	2.83248	+	1.63533i	0.108701	+	0.0627583i
$680$	1.25521	+	9.37239i	0.0481350	+	0.359415i
$681$	−20.4820	−	20.4820i	−0.784871	−	0.784871i
$682$	1.88447	+	3.26400i	0.0721601	+	0.124985i
$683$	−11.3030	−	19.5774i	−0.432499	−	0.749110i	0.564589	−	0.825372i	$-0.309035\pi$
$683$	−11.3030	−	19.5774i	−0.432499	−	0.749110i	−0.997088	+	0.0762622i	$0.975701\pi$
$684$	−0.0394531	−	0.0394531i	−0.00150853	−	0.00150853i
$685$	12.3335	−	16.1479i	0.471238	−	0.616978i
$686$	6.17941	+	3.56768i	0.235931	+	0.136215i
$687$	10.4513	+	6.03405i	0.398741	+	0.230213i
$688$	−3.39140	+	3.39140i	−0.129296	+	0.129296i
$689$	12.2642	−	3.45189i	0.467230	−	0.131506i
$690$	−0.378680	+	0.157846i	−0.0144161	+	0.00600911i
$691$	18.9019	−	5.06476i	0.719063	−	0.192672i	0.119310	−	0.992857i	$-0.461932\pi$
$691$	18.9019	−	5.06476i	0.719063	−	0.192672i	0.599754	+	0.800185i	$0.295265\pi$
$692$	4.99132	+	18.6279i	0.189742	+	0.708126i
$693$	0.431573	+	0.115640i	0.0163941	+	0.00439279i
$694$	−25.5041	+	25.5041i	−0.968124	+	0.968124i
$695$	3.66288	−	4.79571i	0.138941	−	0.181912i
$696$	−6.99735	−	1.87494i	−0.265234	−	0.0710692i
$697$			0.122821i			0.00465216i
$698$	−0.942042	+	3.51575i	−0.0356568	+	0.133073i
$699$	−5.03155	+	8.71490i	−0.190311	+	0.329628i
$700$	−2.50690	+	0.683743i	−0.0947520	+	0.0258431i
$701$			29.4470i			1.11220i	0.831116	+	0.556098i	$0.187702\pi$
$701$			29.4470i			1.11220i	−0.831116	+	0.556098i	$0.812298\pi$
$702$	3.49414	+	0.889363i	0.131878	+	0.0335668i
$703$	−0.00890462	−	0.00890462i	−0.000335844	−	0.000335844i
$704$	0.222514	+	0.830435i	0.00838633	+	0.0312982i
$705$	7.55959	+	9.80640i	0.284710	+	0.369330i
$706$	24.5055	−	14.1482i	0.922275	−	0.532476i
$707$	2.63486			0.0990941
$708$	−4.38892	+	2.53395i	−0.164946	+	0.0952315i
$709$	−10.6145	+	39.6139i	−0.398636	+	1.48773i	0.416861	+	0.908970i	$0.363130\pi$
$709$	−10.6145	+	39.6139i	−0.398636	+	1.48773i	−0.815497	+	0.578761i	$0.803537\pi$
$710$	14.2274	+	5.85599i	0.533946	+	0.219771i
$711$	8.01005	+	13.8738i	0.300400	+	0.520308i
$712$	14.9100	−	3.99511i	0.558774	−	0.149723i
$713$	−0.402163	+	0.696567i	−0.0150611	+	0.0260866i
$714$	2.19773			0.0822480
$715$	6.85793	−	1.00630i	0.256472	−	0.0376336i
$716$	20.2761			0.757754
$717$	−11.1048	+	19.2341i	−0.414717	+	0.718310i
$718$	6.51252	−	1.74502i	0.243045	−	0.0651237i
$719$	−15.8538	−	27.4596i	−0.591246	−	1.02407i	−0.994065	−	0.108789i	$-0.965303\pi$
$719$	−15.8538	−	27.4596i	−0.591246	−	1.02407i	0.402819	−	0.915280i	$-0.368031\pi$
$720$	0.860320	+	2.06394i	0.0320622	+	0.0769185i
$721$	1.13229	−	4.22576i	0.0421687	−	0.157376i
$722$	−16.4518	+	9.49844i	−0.612272	+	0.353495i
$723$	−25.0210			−0.930540
$724$	12.3948	−	7.15615i	0.460649	−	0.265956i
$725$	−34.9445	+	9.53092i	−1.29781	+	0.353969i
$726$	2.65571	+	9.91123i	0.0985625	+	0.367840i
$727$	−13.5130	−	13.5130i	−0.501169	−	0.501169i	0.410632	−	0.911801i	$-0.365308\pi$
$727$	−13.5130	−	13.5130i	−0.501169	−	0.501169i	−0.911801	+	0.410632i	$0.865308\pi$
$728$	0.0235380	+	1.87364i	0.000872377	+	0.0694417i
$729$		−	1.00000i		−	0.0370370i
$730$	0.690093	−	5.33384i	0.0255415	−	0.197414i
$731$	10.1412	−	17.5651i	0.375087	−	0.649669i
$732$	−3.73617	+	13.9436i	−0.138093	+	0.515369i
$733$		−	10.4942i		−	0.387612i	−0.981040	−	0.193806i	$-0.937917\pi$
$733$		−	10.4942i		−	0.387612i	0.981040	−	0.193806i	$-0.0620833\pi$
$734$	−30.0541	−	8.05298i	−1.10932	−	0.297241i
$735$	−1.99756	−	14.9154i	−0.0736811	−	0.550162i
$736$	−0.129736	+	0.129736i	−0.00478213	+	0.00478213i
$737$	−11.3886	−	3.05155i	−0.419503	−	0.112405i
$738$	0.00751694	+	0.0280536i	0.000276703	+	0.00103267i
$739$	−10.6866	+	2.86346i	−0.393112	+	0.105334i	−0.449960	−	0.893049i	$-0.648562\pi$
$739$	−10.6866	+	2.86346i	−0.393112	+	0.105334i	0.0568477	+	0.998383i	$0.481895\pi$
$740$	0.194175	+	0.465834i	0.00713802	+	0.0171244i
$741$	−0.0983897	+	0.175470i	−0.00361444	+	0.00644606i
$742$	1.29855	−	1.29855i	0.0476711	−	0.0476711i
$743$	31.4823	+	18.1763i	1.15498	+	0.666825i	0.950095	−	0.311962i	$-0.100986\pi$
$743$	31.4823	+	18.1763i	1.15498	+	0.666825i	0.204881	+	0.978787i	$0.434319\pi$
$744$	3.79654	+	2.19193i	0.139188	+	0.0803602i
$745$	9.21528	−	1.23417i	0.337622	−	0.0452164i
$746$	15.9587	+	15.9587i	0.584291	+	0.584291i
$747$	−2.41550	−	4.18377i	−0.0883785	−	0.153076i
$748$	−1.81785	−	3.14861i	−0.0664671	−	0.115124i
$749$	−2.57757	−	2.57757i	−0.0941824	−	0.0941824i
$750$	8.91538	+	6.74656i	0.325544	+	0.246349i
$751$	−42.3079	−	24.4265i	−1.54384	−	0.891335i	−0.998591	−	0.0530591i	$-0.983103\pi$
$751$	−42.3079	−	24.4265i	−1.54384	−	0.891335i	−0.545246	−	0.838276i	$-0.683564\pi$
$752$	4.79551	+	2.76869i	0.174874	+	0.100964i
$753$	19.3555	−	19.3555i	0.705354	−	0.705354i
$754$	0.328104	+	26.1172i	0.0119488	+	0.951134i
$755$	3.36281	−	8.17013i	0.122385	−	0.297341i
$756$	0.501987	−	0.134507i	0.0182571	−	0.00489197i
$757$	6.98099	+	26.0534i	0.253728	+	0.946927i	0.968794	+	0.247869i	$0.0797303\pi$
$757$	6.98099	+	26.0534i	0.253728	+	0.946927i	−0.715065	+	0.699058i	$0.753603\pi$
$758$	−14.3728	−	3.85119i	−0.522045	−	0.139881i
$759$	0.111538	−	0.111538i	0.00404857	−	0.00404857i
$760$	−0.123658	+	0.0165610i	−0.00448554	+	0.000600730i
$761$	−21.6967	−	5.81362i	−0.786505	−	0.210743i	−0.156855	−	0.987622i	$-0.550135\pi$
$761$	−21.6967	−	5.81362i	−0.786505	−	0.210743i	−0.629651	+	0.776878i	$0.716802\pi$
$762$		−	10.3950i		−	0.376572i
$763$	1.18609	−	4.42655i	0.0429394	−	0.160252i
$764$	−6.39485	+	11.0762i	−0.231358	+	0.400723i
$765$	−5.77324	−	7.48913i	−0.208732	−	0.270770i
$766$			11.3636i			0.410583i
$767$	13.0819	+	12.7573i	0.472361	+	0.460640i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−3.23891	−	12.0878i	−0.116798	−	0.435897i	0.882617	−	0.470093i	$-0.155780\pi$
$769$	−3.23891	−	12.0878i	−0.116798	−	0.435897i	−0.999415	+	0.0341962i	$0.989113\pi$
$770$	0.791254	−	0.609964i	0.0285148	−	0.0219816i
$771$	0.224083	−	0.129375i	0.00807017	−	0.00465931i
$772$	−2.20902			−0.0795045
$773$	−17.7829	+	10.2670i	−0.639607	+	0.369278i	−0.784463	−	0.620175i	$-0.787061\pi$
$773$	−17.7829	+	10.2670i	−0.639607	+	0.369278i	0.144856	+	0.989453i	$0.453728\pi$
$774$	1.24134	−	4.63274i	0.0446190	−	0.166520i
$775$	21.9191	−	0.0979442i	0.787358	−	0.00351826i
$776$	−3.14672	−	5.45027i	−0.112961	−	0.195653i
$777$	0.113299	−	0.0303584i	0.00406458	−	0.00108910i
$778$	0.391567	−	0.678214i	0.0140384	−	0.0243151i
$779$	−0.00162047			−5.80594e−5
$780$	6.32290	−	5.00209i	0.226396	−	0.179104i
$781$	−5.91545			−0.211671
$782$	0.387946	−	0.671942i	0.0138729	−	0.0240286i
$783$	6.99735	−	1.87494i	0.250065	−	0.0670047i
$784$	−3.36496	−	5.82828i	−0.120177	−	0.208153i
$785$	−11.3021	+	27.4591i	−0.403391	+	0.980059i
$786$	4.50210	−	16.8021i	0.160584	−	0.599309i
$787$	22.0630	−	12.7381i	0.786462	−	0.454064i	−0.0522536	−	0.998634i	$-0.516640\pi$
$787$	22.0630	−	12.7381i	0.786462	−	0.454064i	0.838716	+	0.544570i	$0.183307\pi$
$788$	12.1397			0.432460
$789$	−5.38327	+	3.10803i	−0.191649	+	0.110649i
$790$	35.5259	+	4.59635i	1.26396	+	0.163531i
$791$	−0.786546	−	2.93543i	−0.0279664	−	0.104372i
$792$	−0.607921	−	0.607921i	−0.0216015	−	0.0216015i
$793$	52.0437	−	0.653810i	1.84812	−	0.0232175i
$794$			14.2414i			0.505409i
$795$	−7.83617	−	1.01385i	−0.277920	−	0.0359574i
$796$	−2.03805	+	3.53001i	−0.0722368	+	0.125118i
$797$	−5.98910	+	22.3516i	−0.212145	+	0.791735i	0.775008	+	0.631952i	$0.217746\pi$
$797$	−5.98910	+	22.3516i	−0.212145	+	0.791735i	−0.987152	+	0.159783i	$0.948921\pi$
$798$			0.0289965i			0.00102646i
$799$	−22.6190	−	6.06075i	−0.800203	−	0.214414i
$800$	4.83536	+	1.27250i	0.170956	+	0.0449897i
$801$	−10.9148	+	10.9148i	−0.385657	+	0.385657i
$802$	−30.1857	−	8.08823i	−1.06589	−	0.285605i
$803$	0.535202	+	1.99740i	0.0188869	+	0.0704868i
$804$	−13.2467	+	3.54943i	−0.467174	+	0.125179i
$805$	0.197163	+	0.0811518i	0.00694907	+	0.00286023i
$806$	3.89885	−	15.3179i	0.137331	−	0.539548i
$807$	−0.276145	+	0.276145i	−0.00972077	+	0.00972077i
$808$	−4.39076	−	2.53501i	−0.154466	−	0.0891812i
$809$	20.3578	+	11.7536i	0.715742	+	0.413234i	0.813184	−	0.582007i	$-0.197733\pi$
$809$	20.3578	+	11.7536i	0.715742	+	0.413234i	−0.0974414	+	0.995241i	$0.531066\pi$
$810$	−1.77703	−	1.35727i	−0.0624384	−	0.0476894i
$811$	−18.5083	−	18.5083i	−0.649915	−	0.649915i	0.303057	−	0.952972i	$-0.401993\pi$
$811$	−18.5083	−	18.5083i	−0.649915	−	0.649915i	−0.952972	+	0.303057i	$0.901993\pi$
$812$	1.88239	+	3.26039i	0.0660588	+	0.114417i
$813$	8.44068	+	14.6197i	0.296028	+	0.512735i
$814$	−0.137208	−	0.137208i	−0.00480915	−	0.00480915i
$815$	−40.5466	−	30.9688i	−1.42028	−	1.08479i
$816$	−3.66232	−	2.11444i	−0.128207	−	0.0740203i
$817$	0.231751	+	0.133801i	0.00810794	+	0.00468112i
$818$	23.8454	−	23.8454i	0.833736	−	0.833736i
$819$	−0.957204	−	1.61085i	−0.0334474	−	0.0562876i
$820$	0.0600546	+	0.0247184i	0.00209720	+	0.000863203i
$821$	49.9927	−	13.3955i	1.74476	−	0.467506i	0.761263	−	0.648444i	$-0.224580\pi$
$821$	49.9927	−	13.3955i	1.74476	−	0.467506i	0.983495	+	0.180938i	$0.0579132\pi$
$822$	2.35189	+	8.77737i	0.0820316	+	0.306146i
$823$	−28.2305	−	7.56435i	−0.984054	−	0.263677i	−0.269303	−	0.963055i	$-0.586793\pi$
$823$	−28.2305	−	7.56435i	−0.984054	−	0.263677i	−0.714751	+	0.699379i	$0.753460\pi$
$824$	−5.95248	+	5.95248i	−0.207364	+	0.207364i
$825$	−4.15711	−	1.09401i	−0.144732	−	0.0380885i
$826$	2.54402	+	0.681667i	0.0885176	+	0.0237182i
$827$			8.43549i			0.293331i	0.989186	+	0.146665i	$0.0468540\pi$
$827$			8.43549i			0.293331i	−0.989186	+	0.146665i	$0.953146\pi$
$828$	0.0474866	−	0.177222i	0.00165027	−	0.00615891i
$829$	−10.4506	+	18.1010i	−0.362965	+	0.628674i	−0.988447	−	0.151564i	$-0.951569\pi$
$829$	−10.4506	+	18.1010i	−0.362965	+	0.628674i	0.625482	+	0.780238i	$0.284902\pi$
$830$	−10.7132	−	1.38607i	−0.371859	−	0.0481112i
$831$		−	1.05697i		−	0.0366657i
$832$	1.76341	−	3.14490i	0.0611352	−	0.109030i
$833$	20.1243	+	20.1243i	0.697265	+	0.697265i
$834$	0.698481	+	2.60677i	0.0241864	+	0.0902650i
$835$	29.5293	+	3.82051i	1.02191	+	0.132214i
$836$	0.0415422	−	0.0239844i	0.00143677	−	0.000829517i
$837$	−4.38387			−0.151529
$838$	9.64226	−	5.56696i	0.333086	−	0.192307i
$839$	−8.60452	+	32.1125i	−0.297061	+	1.10865i	0.642505	+	0.766281i	$0.277895\pi$
$839$	−8.60452	+	32.1125i	−0.297061	+	1.10865i	−0.939567	+	0.342366i	$0.888772\pi$
$840$	0.442306	−	1.07461i	0.0152610	−	0.0370774i
$841$	11.7392	+	20.3328i	0.404799	+	0.701132i
$842$	28.1829	−	7.55160i	0.971248	−	0.260245i
$843$	−6.78681	+	11.7551i	−0.233750	+	0.404867i
$844$	−14.7702			−0.508411
$845$	−23.5373	−	17.0585i	−0.809709	−	0.586831i
$846$	−5.53738			−0.190379
$847$	2.66626	−	4.61810i	0.0916138	−	0.158680i
$848$	−3.41325	+	0.914577i	−0.117211	+	0.0314067i
$849$	−4.80305	−	8.31913i	−0.164840	−	0.285512i
$850$	−21.1442	+	0.0944816i	−0.725240	+	0.00324069i
$851$	0.0107178	−	0.0399993i	0.000367401	−	0.00137116i
$852$	−5.95877	+	3.44030i	−0.204144	+	0.117863i
$853$	−12.3935			−0.424344			−0.212172	−	0.977232i	$-0.568054\pi$
$853$	−12.3935			−0.424344			−0.212172	+	0.977232i	$0.568054\pi$
$854$	6.49695	−	3.75102i	0.222321	−	0.128357i
$855$	0.0988102	−	0.0761711i	0.00337924	−	0.00260500i
$856$	1.81541	+	6.77519i	0.0620493	+	0.231571i
$857$	−11.9224	−	11.9224i	−0.407262	−	0.407262i	0.473520	−	0.880783i	$-0.342983\pi$
$857$	−11.9224	−	11.9224i	−0.407262	−	0.407262i	−0.880783	+	0.473520i	$0.842983\pi$
$858$	−1.51606	+	2.70376i	−0.0517573	+	0.0923050i
$859$			37.7546i			1.28817i	0.764954	+	0.644085i	$0.222762\pi$
$859$			37.7546i			1.28817i	−0.764954	+	0.644085i	$0.777238\pi$
$860$	−6.54769	−	8.49376i	−0.223274	−	0.289635i
$861$	0.00754681	−	0.0130715i	0.000257195	−	0.000445474i
$862$	4.51975	−	16.8679i	0.153943	−	0.574524i
$863$		−	34.7009i		−	1.18123i	−0.806953	−	0.590615i	$-0.798885\pi$
$863$		−	34.7009i		−	1.18123i	0.806953	−	0.590615i	$-0.201115\pi$
$864$	−0.965926	−	0.258819i	−0.0328615	−	0.00880520i
$865$	−42.7410	+	5.72413i	−1.45324	+	0.194626i
$866$	−1.57183	+	1.57183i	−0.0534131	+	0.0534131i
$867$	0.853360	+	0.228657i	0.0289816	+	0.00776560i
$868$	−0.589661	−	2.20064i	−0.0200144	−	0.0746947i
$869$	−13.3037	+	3.56470i	−0.451295	+	0.120924i
$870$	6.16545	−	14.9793i	0.209028	−	0.507845i
$871$	25.2592	+	42.5079i	0.855874	+	1.44032i
$872$	−6.23531	+	6.23531i	−0.211154	+	0.211154i
$873$	5.45027	+	3.14672i	0.184464	+	0.106500i
$874$	0.00886548	+	0.00511849i	0.000299879	+	0.000173135i
$875$	−0.796999	−	5.75544i	−0.0269435	−	0.194570i
$876$	1.70077	+	1.70077i	0.0574636	+	0.0574636i
$877$	−15.4110	−	26.6926i	−0.520391	−	0.901344i	−0.999719	−	0.0237079i	$-0.992453\pi$
$877$	−15.4110	−	26.6926i	−0.520391	−	0.901344i	0.479328	−	0.877636i	$-0.340880\pi$
$878$	18.9701	+	32.8571i	0.640209	+	1.10887i
$879$	4.12044	+	4.12044i	0.138979	+	0.138979i
$880$	−1.90540	+	0.255183i	−0.0642311	+	0.00860222i
$881$	24.9249	+	14.3904i	0.839740	+	0.484824i	0.857176	−	0.515024i	$-0.172217\pi$
$881$	24.9249	+	14.3904i	0.839740	+	0.484824i	−0.0174360	+	0.999848i	$0.505550\pi$
$882$	5.82828	+	3.36496i	0.196248	+	0.113304i
$883$	−12.4407	+	12.4407i	−0.418662	+	0.418662i	−0.884742	−	0.466080i	$-0.845666\pi$
$883$	−12.4407	+	12.4407i	−0.418662	+	0.418662i	0.466080	+	0.884742i	$0.345666\pi$
$884$	−3.76101	+	14.7763i	−0.126497	+	0.496982i
$885$	−4.36001	−	10.4598i	−0.146560	−	0.351603i
$886$	21.1654	−	5.67125i	0.711065	−	0.190529i
$887$	9.95096	+	37.1375i	0.334121	+	1.24695i	0.904819	+	0.425796i	$0.140006\pi$
$887$	9.95096	+	37.1375i	0.334121	+	1.24695i	−0.570699	+	0.821159i	$0.693328\pi$
$888$	−0.218011	−	0.0584158i	−0.00731596	−	0.00196031i
$889$	−3.81996	+	3.81996i	−0.128117	+	0.128117i
$890$	4.58166	+	34.2103i	0.153577	+	1.14673i
$891$	0.830435	+	0.222514i	0.0278206	+	0.00745451i
$892$		−	3.17963i		−	0.106462i
$893$	0.0799645	−	0.298431i	0.00267591	−	0.00998663i
$894$	−2.07900	+	3.60093i	−0.0695321	+	0.120433i
$895$	−5.81745	+	44.9640i	−0.194456	+	1.50298i
$896$		−	0.519695i		−	0.0173618i
$897$	−0.661473	+	0.00830991i	−0.0220860	+	0.000277460i
$898$	−11.1962	−	11.1962i	−0.373623	−	0.373623i
$899$	−8.21947	−	30.6755i	−0.274135	−	1.02308i
$900$	−4.82380	+	1.31566i	−0.160793	+	0.0438554i
$901$	12.9414	−	7.47171i	0.431140	−	0.248919i
$902$	−0.0249693			−0.000831388
$903$	−2.15861	+	1.24627i	−0.0718339	+	0.0414733i
$904$	−1.51348	+	5.64837i	−0.0503375	+	0.187862i
$905$	12.3131	+	29.5397i	0.409303	+	0.981934i
$906$	1.97560	+	3.42183i	0.0656348	+	0.113683i
$907$	44.4572	−	11.9123i	1.47618	−	0.395540i	0.571132	−	0.820858i	$-0.306505\pi$
$907$	44.4572	−	11.9123i	1.47618	−	0.395540i	0.905044	+	0.425318i	$0.139838\pi$
$908$	14.4830	−	25.0852i	0.480634	−	0.832482i
$909$	5.07001			0.168162
$910$	−4.16171	−	0.485371i	−0.137959	−	0.0160899i
$911$	−34.0825			−1.12920			−0.564602	−	0.825363i	$-0.690970\pi$
$911$	−34.0825			−1.12920			−0.564602	+	0.825363i	$0.690970\pi$
$912$	0.0278976	−	0.0483200i	0.000923781	−	0.00160004i
$913$	4.01183	−	1.07497i	0.132772	−	0.0355762i
$914$	19.5983	+	33.9453i	0.648255	+	1.12281i
$915$	−29.8491	−	12.2858i	−0.986781	−	0.406158i
$916$	−3.12345	+	11.6569i	−0.103202	+	0.385154i
$917$	−7.82884	+	4.51999i	−0.258531	+	0.149263i
$918$	4.22888			0.139574
$919$	−6.13874	+	3.54420i	−0.202498	+	0.116913i	−0.597820	−	0.801630i	$-0.703966\pi$
$919$	−6.13874	+	3.54420i	−0.202498	+	0.116913i	0.395322	+	0.918543i	$0.370633\pi$
$920$	−0.250478	−	0.324923i	−0.00825800	−	0.0107124i
$921$	1.17164	+	4.37263i	0.0386070	+	0.144083i
$922$	7.43657	+	7.43657i	0.244910	+	0.244910i
$923$	17.7611	+	17.3204i	0.584614	+	0.570108i
$924$			0.446797i			0.0146985i
$925$	−1.08874	+	0.296947i	−0.0357975	+	0.00976355i
$926$	−15.6632	+	27.1295i	−0.514726	+	0.891531i
$927$	2.17876	−	8.13124i	0.0715598	−	0.267065i
$928$		−	7.24419i		−	0.237802i
$929$	−23.6705	−	6.34249i	−0.776604	−	0.208090i	−0.151317	−	0.988485i	$-0.548351\pi$
$929$	−23.6705	−	6.34249i	−0.776604	−	0.208090i	−0.625287	+	0.780395i	$0.715018\pi$
$930$	−5.95007	+	7.79026i	−0.195110	+	0.255453i
$931$	−0.265516	+	0.265516i	−0.00870195	+	0.00870195i
$932$	−9.72020	−	2.60452i	−0.318396	−	0.0853139i
$933$	−7.15298	−	26.6953i	−0.234178	−	0.873964i
$934$	−23.4317	+	6.27849i	−0.766707	+	0.205439i
$935$	7.50386	−	3.12786i	0.245403	−	0.102292i
$936$	0.0452920	+	3.60527i	0.00148041	+	0.117842i
$937$	23.5857	−	23.5857i	0.770510	−	0.770510i	−0.207685	−	0.978196i	$-0.566593\pi$
$937$	23.5857	−	23.5857i	0.770510	−	0.770510i	0.978196	+	0.207685i	$0.0665930\pi$
$938$	6.17223	+	3.56354i	0.201530	+	0.116354i
$939$	−27.5522	−	15.9073i	−0.899133	−	0.519115i
$940$	−7.51569	+	9.84008i	−0.245135	+	0.320948i
$941$	−3.01039	−	3.01039i	−0.0981360	−	0.0981360i	0.656334	−	0.754470i	$-0.272106\pi$
$941$	−3.01039	−	3.01039i	−0.0981360	−	0.0981360i	−0.754470	+	0.656334i	$0.772106\pi$
$942$	−6.63981	−	11.5005i	−0.216337	−	0.374706i
$943$	−0.00266434	−	0.00461478i	−8.67629e−5	−	0.000150278i
$944$	−3.58354	−	3.58354i	−0.116634	−	0.116634i
$945$	0.154255	+	1.15179i	0.00501791	+	0.0374677i
$946$	3.57098	+	2.06170i	0.116102	+	0.0670318i
$947$	39.0911	+	22.5692i	1.27029	+	0.733402i	0.975042	−	0.222020i	$-0.0712649\pi$
$947$	39.0911	+	22.5692i	1.27029	+	0.733402i	0.295247	+	0.955421i	$0.404598\pi$
$948$	−11.3279	+	11.3279i	−0.367914	+	0.367914i
$949$	4.24143	−	7.56426i	0.137683	−	0.245546i
$950$	−0.00124657	−	0.278973i	−4.04442e−5	−	0.00905108i
$951$	1.74323	−	0.467097i	0.0565280	−	0.0151466i
$952$	0.568814	+	2.12284i	0.0184354	+	0.0688018i
$953$	12.2640	+	3.28613i	0.397271	+	0.106448i	0.451923	−	0.892057i	$-0.350738\pi$
$953$	12.2640	+	3.28613i	0.397271	+	0.106448i	−0.0546521	+	0.998505i	$0.517405\pi$
$954$	2.49867	−	2.49867i	0.0808974	−	0.0808974i
$955$	−22.7277	−	17.3590i	−0.735450	−	0.561725i
$956$	−21.4528	−	5.74827i	−0.693835	−	0.185912i
$957$			6.22805i			0.201324i
$958$	3.00994	−	11.2332i	0.0972467	−	0.362930i
$959$	2.36124	−	4.08978i	0.0762483	−	0.132066i
$960$	−1.77095	+	1.36519i	−0.0571570	+	0.0440614i
$961$		−	11.7817i		−	0.380055i
$962$	0.0102225	+	0.813713i	0.000329585	+	0.0262352i
$963$	−4.95978	−	4.95978i	−0.159827	−	0.159827i
$964$	−6.47591	−	24.1684i	−0.208575	−	0.778412i
$965$	0.633795	−	4.89870i	0.0204026	−	0.157695i
$966$	−0.0825761	+	0.0476753i	−0.00265684	+	0.00153393i
$967$	27.7803			0.893353			0.446677	−	0.894695i	$-0.352607\pi$
$967$	27.7803			0.893353			0.446677	+	0.894695i	$0.352607\pi$
$968$	−8.88617	+	5.13043i	−0.285612	+	0.164898i
$969$	−0.0610687	+	0.227911i	−0.00196181	+	0.00732157i
$970$	12.9893	−	5.41437i	0.417061	−	0.173845i
$971$	−0.0689099	−	0.119355i	−0.00221142	−	0.00383030i	0.864918	−	0.501914i	$-0.167371\pi$
$971$	−0.0689099	−	0.119355i	−0.00221142	−	0.00383030i	−0.867129	+	0.498084i	$0.834037\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	0.701257	−	1.21461i	0.0224813	−	0.0389387i
$974$	−9.14019			−0.292871
$975$	9.27845	+	15.4567i	0.297148	+	0.495011i
$976$	−14.4355			−0.462068
$977$	−12.6538	+	21.9169i	−0.404829	+	0.701185i	−0.994302	−	0.106604i	$-0.966002\pi$
$977$	−12.6538	+	21.9169i	−0.404829	+	0.701185i	0.589472	+	0.807789i	$0.299336\pi$
$978$	22.0396	−	5.90549i	0.704748	−	0.188837i
$979$	−6.63536	−	11.4928i	−0.212067	−	0.367311i
$980$	13.8901	−	5.78988i	0.443705	−	0.184951i
$981$	2.28228	−	8.51759i	0.0728677	−	0.271946i
$982$	−6.88995	+	3.97792i	−0.219867	+	0.126940i
$983$	19.2981			0.615512			0.307756	−	0.951465i	$-0.400422\pi$
$983$	19.2981			0.615512			0.307756	+	0.951465i	$0.400422\pi$
$984$	−0.0251522	+	0.0145216i	−0.000801822	+	0.000462932i
$985$	−3.48303	+	26.9209i	−0.110978	+	0.857770i
$986$	7.92888	+	29.5910i	0.252507	+	0.942369i
$987$	2.03487	+	2.03487i	0.0647708	+	0.0647708i
$988$	−0.194956	−	0.0496222i	−0.00620238	−	0.00157869i
$989$			0.879973i			0.0279815i
$990$	1.52254	−	1.17370i	0.0483894	−	0.0373025i
$991$	8.95513	−	15.5107i	0.284469	−	0.492715i	−0.688011	−	0.725700i	$-0.741516\pi$
$991$	8.95513	−	15.5107i	0.284469	−	0.492715i	0.972480	+	0.232985i	$0.0748493\pi$
$992$	−1.13463	+	4.23449i	−0.0360245	+	0.134445i
$993$			20.3090i			0.644486i
$994$	3.45397	+	0.925487i	0.109553	+	0.0293547i
$995$	−7.24336	−	5.53235i	−0.229630	−	0.175387i
$996$	3.41603	−	3.41603i	0.108241	−	0.108241i
$997$	36.2474	+	9.71246i	1.14797	+	0.307597i	0.782150	−	0.623090i	$-0.214123\pi$
$997$	36.2474	+	9.71246i	1.14797	+	0.307597i	0.365816	+	0.930687i	$0.380790\pi$
$998$	−8.02635	−	29.9548i	−0.254070	−	0.948201i
$999$	0.218011	−	0.0584158i	0.00689755	−	0.00184819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.b.163.2	yes	16
5.2	odd	4		390.2.bd.b.7.3	✓	16
13.2	odd	12		390.2.bd.b.223.3	yes	16
65.2	even	12	inner	390.2.bn.b.67.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.7.3	✓	16	5.2	odd	4
390.2.bd.b.223.3	yes	16	13.2	odd	12
390.2.bn.b.67.2	yes	16	65.2	even	12	inner
390.2.bn.b.163.2	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.06394 - 0.860320i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.450069 - 0.259847i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.06394 - 0.860320i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(0.450069 - 0.259847i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +(0.286912 - 2.21758i) q^{10} +(0.222514 + 0.830435i) q^{11} +(0.707107 + 0.707107i) q^{12} +(1.76341 - 3.14490i) q^{13} -0.519695i q^{14} +(-1.77095 + 1.36519i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.09452 - 4.08479i) q^{17} -1.00000i q^{18} +(0.0538940 + 0.0144409i) q^{19} +(-1.77703 - 1.35727i) q^{20} +(-0.367480 + 0.367480i) q^{21} +(0.830435 + 0.222514i) q^{22} +(0.0474866 + 0.177222i) q^{23} +(0.965926 - 0.258819i) q^{24} +(3.51970 - 3.55130i) q^{25} +(-1.84186 - 3.09961i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.450069 - 0.259847i) q^{28} +(-6.27365 - 3.62210i) q^{29} +(0.296818 + 2.21628i) q^{30} +(3.09986 + 3.09986i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.429865 - 0.744548i) q^{33} +(-2.99027 - 2.99027i) q^{34} +(0.705364 - 0.923513i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-0.195463 - 0.112851i) q^{37} +(0.0394531 - 0.0394531i) q^{38} +(-0.889363 + 3.49414i) q^{39} +(-2.06394 + 0.860320i) q^{40} +(-0.0280536 + 0.00751694i) q^{41} +(0.134507 + 0.501987i) q^{42} +(4.63274 + 1.24134i) q^{43} +(0.607921 - 0.607921i) q^{44} +(1.35727 - 1.77703i) q^{45} +(0.177222 + 0.0474866i) q^{46} -5.53738i q^{47} +(0.258819 - 0.965926i) q^{48} +(-3.36496 + 5.82828i) q^{49} +(-1.31566 - 4.82380i) q^{50} +4.22888i q^{51} +(-3.60527 + 0.0452920i) q^{52} +(2.49867 + 2.49867i) q^{53} +(0.258819 + 0.965926i) q^{54} +(1.17370 + 1.52254i) q^{55} +(-0.450069 + 0.259847i) q^{56} -0.0557952 q^{57} +(-6.27365 + 3.62210i) q^{58} +(-1.31167 + 4.89521i) q^{59} +(2.06776 + 0.851088i) q^{60} +(7.21773 + 12.5015i) q^{61} +(4.23449 - 1.13463i) q^{62} +(0.259847 - 0.450069i) q^{63} +1.00000 q^{64} +(0.933954 - 8.00798i) q^{65} -0.859730 q^{66} +(-6.85698 + 11.8766i) q^{67} +(-4.08479 + 1.09452i) q^{68} +(-0.0917371 - 0.158893i) q^{69} +(-0.447104 - 1.07262i) q^{70} +(-1.78083 + 6.64614i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.40525 q^{73} +(-0.195463 + 0.112851i) q^{74} +(-2.48063 + 4.34125i) q^{75} +(-0.0144409 - 0.0538940i) q^{76} +(0.315933 + 0.315933i) q^{77} +(2.58133 + 2.51728i) q^{78} +16.0201i q^{79} +(-0.286912 + 2.21758i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.00751694 + 0.0280536i) q^{82} -4.83100i q^{83} +(0.501987 + 0.134507i) q^{84} +(-1.25521 - 9.37239i) q^{85} +(3.39140 - 3.39140i) q^{86} +(6.99735 + 1.87494i) q^{87} +(-0.222514 - 0.830435i) q^{88} +(-14.9100 + 3.99511i) q^{89} +(-0.860320 - 2.06394i) q^{90} +(-0.0235380 - 1.87364i) q^{91} +(0.129736 - 0.129736i) q^{92} +(-3.79654 - 2.19193i) q^{93} +(-4.79551 - 2.76869i) q^{94} +(0.123658 - 0.0165610i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(3.14672 + 5.45027i) q^{97} +(3.36496 + 5.82828i) q^{98} +(0.607921 + 0.607921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more