LMFDB - Embedded newform 390.2.bd.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (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} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 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			37.3
Root			$2.69978 + 0.355433i$ of defining polynomial
Character	$\chi$	$=$	390.37
Dual form			390.2.bd.b.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.48905 - 1.66815i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.328411 - 0.568824i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.48905 - 1.66815i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.328411 - 0.568824i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.455475 + 2.18919i) q^{10} +(-1.26026 - 0.337686i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.54536 - 0.656060i) q^{13} +0.656821i q^{14} +(1.87006 - 1.22592i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.47202 - 5.49364i) q^{17} -1.00000 q^{18} +(0.425167 + 1.58674i) q^{19} +(-0.700141 - 2.12363i) q^{20} +(0.464443 - 0.464443i) q^{21} +(1.26026 - 0.337686i) q^{22} +(-0.0557460 + 0.208047i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(-0.565478 - 4.96792i) q^{25} +(-2.74234 + 2.34084i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.328411 - 0.568824i) q^{28} +(0.0656377 - 0.0378960i) q^{29} +(-1.00656 + 1.99671i) q^{30} +(5.13765 + 5.13765i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.12992 - 0.652360i) q^{33} +(4.02163 + 4.02163i) q^{34} +(-0.459867 - 1.39484i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.462173 + 0.800508i) q^{37} +(-1.16158 - 1.16158i) q^{38} +(3.59436 + 0.283902i) q^{39} +(1.66815 + 1.48905i) q^{40} +(-2.01318 + 7.51330i) q^{41} +(-0.169998 + 0.634441i) q^{42} +(9.17603 - 2.45871i) q^{43} +(-0.922576 + 0.922576i) q^{44} +(2.12363 - 0.700141i) q^{45} +(-0.0557460 - 0.208047i) q^{46} -7.92499 q^{47} +(-0.258819 - 0.965926i) q^{48} +(3.28429 + 5.68856i) q^{49} +(2.97368 + 4.01961i) q^{50} -5.68744i q^{51} +(1.20452 - 3.39840i) q^{52} +(2.58944 - 2.58944i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-2.43990 + 1.59948i) q^{55} +(0.568824 + 0.328411i) q^{56} +1.64272i q^{57} +(-0.0378960 + 0.0656377i) q^{58} +(-4.72918 + 1.26718i) q^{59} +(-0.126648 - 2.23248i) q^{60} +(1.60754 - 2.78433i) q^{61} +(-7.01816 - 1.88051i) q^{62} +(0.568824 - 0.328411i) q^{63} -1.00000 q^{64} +(4.18480 - 6.89111i) q^{65} +1.30472 q^{66} +(-11.5042 + 6.64195i) q^{67} +(-5.49364 - 1.47202i) q^{68} +(-0.107693 + 0.186530i) q^{69} +(1.09568 + 0.978038i) q^{70} +(-3.94410 + 1.05682i) q^{71} +(-0.500000 + 0.866025i) q^{72} -3.44819i q^{73} +(-0.800508 - 0.462173i) q^{74} +(0.739583 - 4.94500i) q^{75} +(1.58674 + 0.425167i) q^{76} +(-0.605967 + 0.605967i) q^{77} +(-3.25476 + 1.55131i) q^{78} +11.0648i q^{79} +(-2.18919 - 0.455475i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.01318 - 7.51330i) q^{82} +2.20398 q^{83} +(-0.169998 - 0.634441i) q^{84} +(-11.3561 - 5.72474i) q^{85} +(-6.71732 + 6.71732i) q^{86} +(0.0732094 - 0.0196164i) q^{87} +(0.337686 - 1.26026i) q^{88} +(1.59876 - 5.96664i) q^{89} +(-1.48905 + 1.66815i) q^{90} +(0.791152 - 2.23214i) q^{91} +(0.152301 + 0.152301i) q^{92} +(3.63287 + 6.29231i) q^{93} +(6.86325 - 3.96250i) q^{94} +(3.28003 + 1.65349i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-11.8381 - 6.83472i) q^{97} +(-5.68856 - 3.28429i) q^{98} +(-0.922576 - 0.922576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	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
$5$	1.48905	−	1.66815i	0.665922	−	0.746021i
$5$	1.48905	−	1.66815i	0.665922	−	0.746021i
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	0.328411	−	0.568824i	0.124128	−	0.214995i	−0.797264	−	0.603631i	$-0.793720\pi$
$7$	0.328411	−	0.568824i	0.124128	−	0.214995i	0.921392	+	0.388636i	$0.127053\pi$
$8$			1.00000i			0.353553i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−0.455475	+	2.18919i	−0.144034	+	0.692282i
$11$	−1.26026	−	0.337686i	−0.379983	−	0.101816i	0.0637713	−	0.997965i	$-0.479687\pi$
$11$	−1.26026	−	0.337686i	−0.379983	−	0.101816i	−0.443755	+	0.896148i	$0.646354\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	3.54536	−	0.656060i	0.983306	−	0.181958i
$13$	3.54536	−	0.656060i	0.983306	−	0.181958i
$14$			0.656821i			0.175543i
$15$	1.87006	−	1.22592i	0.482847	−	0.316531i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.47202	−	5.49364i	−0.357017	−	1.33240i	−0.877928	−	0.478793i	$-0.841074\pi$
$17$	−1.47202	−	5.49364i	−0.357017	−	1.33240i	0.520911	−	0.853611i	$-0.325592\pi$
$18$	−1.00000			−0.235702
$19$	0.425167	+	1.58674i	0.0975399	+	0.364024i	0.997392	−	0.0721707i	$-0.0229926\pi$
$19$	0.425167	+	1.58674i	0.0975399	+	0.364024i	−0.899852	+	0.436195i	$0.856326\pi$
$20$	−0.700141	−	2.12363i	−0.156556	−	0.474858i
$21$	0.464443	−	0.464443i	0.101350	−	0.101350i
$22$	1.26026	−	0.337686i	0.268689	−	0.0719949i
$23$	−0.0557460	+	0.208047i	−0.0116238	+	0.0433808i	−0.971494	−	0.237063i	$-0.923815\pi$
$23$	−0.0557460	+	0.208047i	−0.0116238	+	0.0433808i	0.959870	+	0.280444i	$0.0904818\pi$
$24$	−0.258819	+	0.965926i	−0.0528312	+	0.197169i
$25$	−0.565478	−	4.96792i	−0.113096	−	0.993584i
$26$	−2.74234	+	2.34084i	−0.537818	+	0.459077i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.328411	−	0.568824i	−0.0620638	−	0.107498i
$29$	0.0656377	−	0.0378960i	0.0121886	−	0.00703710i	−0.493893	−	0.869523i	$-0.664427\pi$
$29$	0.0656377	−	0.0378960i	0.0121886	−	0.00703710i	0.506082	+	0.862485i	$0.331093\pi$
$30$	−1.00656	+	1.99671i	−0.183772	+	0.364547i
$31$	5.13765	+	5.13765i	0.922749	+	0.922749i	0.997223	−	0.0744742i	$-0.0237278\pi$
$31$	5.13765	+	5.13765i	0.922749	+	0.922749i	−0.0744742	+	0.997223i	$0.523728\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.12992	−	0.652360i	−0.196694	−	0.113561i
$34$	4.02163	+	4.02163i	0.689703	+	0.689703i
$35$	−0.459867	−	1.39484i	−0.0777317	−	0.235772i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	0.462173	+	0.800508i	0.0759808	+	0.131603i	0.901512	−	0.432753i	$-0.142458\pi$
$37$	0.462173	+	0.800508i	0.0759808	+	0.131603i	−0.825532	+	0.564356i	$0.809125\pi$
$38$	−1.16158	−	1.16158i	−0.188433	−	0.188433i
$39$	3.59436	+	0.283902i	0.575558	+	0.0454607i
$40$	1.66815	+	1.48905i	0.263758	+	0.235439i
$41$	−2.01318	+	7.51330i	−0.314406	+	1.17338i	0.610135	+	0.792298i	$0.291115\pi$
$41$	−2.01318	+	7.51330i	−0.314406	+	1.17338i	−0.924541	+	0.381082i	$0.875551\pi$
$42$	−0.169998	+	0.634441i	−0.0262312	+	0.0978963i
$43$	9.17603	−	2.45871i	1.39933	−	0.374950i	0.521226	−	0.853418i	$-0.325475\pi$
$43$	9.17603	−	2.45871i	1.39933	−	0.374950i	0.878105	+	0.478469i	$0.158808\pi$
$44$	−0.922576	+	0.922576i	−0.139084	+	0.139084i
$45$	2.12363	−	0.700141i	0.316572	−	0.104371i
$46$	−0.0557460	−	0.208047i	−0.00821930	−	0.0306748i
$47$	−7.92499			−1.15598			−0.577990	−	0.816044i	$-0.696163\pi$
$47$	−7.92499			−1.15598			−0.577990	+	0.816044i	$0.696163\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	3.28429	+	5.68856i	0.469185	+	0.812652i
$50$	2.97368	+	4.01961i	0.420542	+	0.568458i
$51$		−	5.68744i		−	0.796400i
$52$	1.20452	−	3.39840i	0.167036	−	0.471274i
$53$	2.58944	−	2.58944i	0.355687	−	0.355687i	−0.506533	−	0.862220i	$-0.669073\pi$
$53$	2.58944	−	2.58944i	0.355687	−	0.355687i	0.862220	+	0.506533i	$0.169073\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	−2.43990	+	1.59948i	−0.328996	+	0.215674i
$56$	0.568824	+	0.328411i	0.0760123	+	0.0438857i
$57$			1.64272i			0.217583i
$58$	−0.0378960	+	0.0656377i	−0.00497598	+	0.00861866i
$59$	−4.72918	+	1.26718i	−0.615686	+	0.164973i	−0.553166	−	0.833071i	$-0.686581\pi$
$59$	−4.72918	+	1.26718i	−0.615686	+	0.164973i	−0.0625204	+	0.998044i	$0.519914\pi$
$60$	−0.126648	−	2.23248i	−0.0163502	−	0.288212i
$61$	1.60754	−	2.78433i	0.205824	−	0.356497i	−0.744571	−	0.667543i	$-0.767346\pi$
$61$	1.60754	−	2.78433i	0.205824	−	0.356497i	0.950395	+	0.311046i	$0.100679\pi$
$62$	−7.01816	−	1.88051i	−0.891307	−	0.238825i
$63$	0.568824	−	0.328411i	0.0716651	−	0.0413758i
$64$	−1.00000			−0.125000
$65$	4.18480	−	6.89111i	0.519061	−	0.854737i
$66$	1.30472			0.160600
$67$	−11.5042	+	6.64195i	−1.40546	+	0.811443i	−0.994946	−	0.100411i	$-0.967984\pi$
$67$	−11.5042	+	6.64195i	−1.40546	+	0.811443i	−0.410515	+	0.911854i	$0.634651\pi$
$68$	−5.49364	−	1.47202i	−0.666202	−	0.178508i
$69$	−0.107693	+	0.186530i	−0.0129647	+	0.0224555i
$70$	1.09568	+	0.978038i	0.130959	+	0.116898i
$71$	−3.94410	+	1.05682i	−0.468079	+	0.125421i	−0.485146	−	0.874433i	$-0.661234\pi$
$71$	−3.94410	+	1.05682i	−0.468079	+	0.125421i	0.0170676	+	0.999854i	$0.494567\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		−	3.44819i		−	0.403581i	−0.979429	−	0.201790i	$-0.935324\pi$
$73$		−	3.44819i		−	0.403581i	0.979429	−	0.201790i	$-0.0646759\pi$
$74$	−0.800508	−	0.462173i	−0.0930571	−	0.0537265i
$75$	0.739583	−	4.94500i	0.0853997	−	0.570999i
$76$	1.58674	+	0.425167i	0.182012	+	0.0487699i
$77$	−0.605967	+	0.605967i	−0.0690564	+	0.0690564i
$78$	−3.25476	+	1.55131i	−0.368528	+	0.175651i
$79$			11.0648i			1.24489i	0.782663	+	0.622446i	$0.213861\pi$
$79$			11.0648i			1.24489i	−0.782663	+	0.622446i	$0.786139\pi$
$80$	−2.18919	−	0.455475i	−0.244759	−	0.0509237i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−2.01318	−	7.51330i	−0.222319	−	0.829705i
$83$	2.20398			0.241918			0.120959	−	0.992658i	$-0.461403\pi$
$83$	2.20398			0.241918			0.120959	+	0.992658i	$0.461403\pi$
$84$	−0.169998	−	0.634441i	−0.0185483	−	0.0692231i
$85$	−11.3561	−	5.72474i	−1.23175	−	0.620935i
$86$	−6.71732	+	6.71732i	−0.724347	+	0.724347i
$87$	0.0732094	−	0.0196164i	0.00784887	−	0.00210310i
$88$	0.337686	−	1.26026i	0.0359975	−	0.134344i
$89$	1.59876	−	5.96664i	0.169468	−	0.632462i	−0.827960	−	0.560787i	$-0.810499\pi$
$89$	1.59876	−	5.96664i	0.169468	−	0.632462i	0.997428	−	0.0716755i	$-0.0228346\pi$
$90$	−1.48905	+	1.66815i	−0.156959	+	0.175839i
$91$	0.791152	−	2.23214i	0.0829352	−	0.233992i
$92$	0.152301	+	0.152301i	0.0158785	+	0.0158785i
$93$	3.63287	+	6.29231i	0.376711	+	0.652482i
$94$	6.86325	−	3.96250i	0.707890	−	0.408700i
$95$	3.28003	+	1.65349i	0.336523	+	0.169645i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−11.8381	−	6.83472i	−1.20198	−	0.693961i	−0.240982	−	0.970530i	$-0.577469\pi$
$97$	−11.8381	−	6.83472i	−1.20198	−	0.693961i	−0.960994	+	0.276569i	$0.910803\pi$
$98$	−5.68856	−	3.28429i	−0.574632	−	0.331764i
$99$	−0.922576	−	0.922576i	−0.0927224	−	0.0927224i
$100$	−4.58508	−	1.99424i	−0.458508	−	0.199424i
$101$	−9.11777	+	5.26415i	−0.907252	+	0.523802i	−0.879546	−	0.475814i	$-0.842154\pi$
$101$	−9.11777	+	5.26415i	−0.907252	+	0.523802i	−0.0277059	+	0.999616i	$0.508820\pi$
$102$	2.84372	+	4.92547i	0.281570	+	0.487694i
$103$	−9.71646	−	9.71646i	−0.957391	−	0.957391i	0.0417373	−	0.999129i	$-0.486711\pi$
$103$	−9.71646	−	9.71646i	−0.957391	−	0.957391i	−0.999129	+	0.0417373i	$0.986711\pi$
$104$	0.656060	+	3.54536i	0.0643319	+	0.347651i
$105$	−0.0831851	−	1.46634i	−0.00811803	−	0.143100i
$106$	−0.947801	+	3.53724i	−0.0920586	+	0.343567i
$107$	−3.31625	+	12.3764i	−0.320594	+	1.19647i	0.598073	+	0.801442i	$0.295933\pi$
$107$	−3.31625	+	12.3764i	−0.320594	+	1.19647i	−0.918667	+	0.395033i	$0.870733\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	−13.0240	+	13.0240i	−1.24748	+	1.24748i	−0.290646	+	0.956831i	$0.593870\pi$
$109$	−13.0240	+	13.0240i	−1.24748	+	1.24748i	−0.956831	+	0.290646i	$0.906130\pi$
$110$	1.31328	−	2.60514i	0.125216	−	0.248391i
$111$	0.239238	+	0.892850i	0.0227075	+	0.0847456i
$112$	−0.656821			−0.0620638
$113$	0.603092	+	2.25077i	0.0567341	+	0.211735i	0.988474	−	0.151392i	$-0.0483757\pi$
$113$	0.603092	+	2.25077i	0.0567341	+	0.211735i	−0.931740	+	0.363127i	$0.881709\pi$
$114$	−0.821359	−	1.42263i	−0.0769273	−	0.133242i
$115$	0.264046	+	0.402784i	0.0246224	+	0.0375598i
$116$		−	0.0757919i		−	0.00703710i
$117$	3.39840	+	1.20452i	0.314182	+	0.111358i
$118$	3.46200	−	3.46200i	0.318703	−	0.318703i
$119$	−3.60834	−	0.966852i	−0.330776	−	0.0886312i
$120$	1.22592	+	1.87006i	0.111911	+	0.170712i
$121$	−8.05205	−	4.64885i	−0.732005	−	0.422623i
$122$			3.21507i			0.291079i
$123$	−3.88917	+	6.73624i	−0.350675	+	0.607386i
$124$	7.01816	−	1.88051i	0.630249	−	0.168875i
$125$	−9.12928	−	6.45416i	−0.816548	−	0.577278i
$126$	−0.328411	+	0.568824i	−0.0292571	+	0.0506749i
$127$	−1.21222	−	0.324813i	−0.107567	−	0.0288225i	0.204634	−	0.978839i	$-0.434400\pi$
$127$	−1.21222	−	0.324813i	−0.107567	−	0.0288225i	−0.312201	+	0.950016i	$0.601066\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	9.49972			0.836404
$130$	−0.178587	+	8.06028i	−0.0156631	+	0.706933i
$131$	14.7382			1.28768			0.643842	−	0.765159i	$-0.277340\pi$
$131$	14.7382			1.28768			0.643842	+	0.765159i	$0.277340\pi$
$132$	−1.12992	+	0.652360i	−0.0983469	+	0.0567806i
$133$	1.04221	+	0.279258i	0.0903708	+	0.0242148i
$134$	6.64195	−	11.5042i	0.573777	−	0.993811i
$135$	2.23248	−	0.126648i	0.192141	−	0.0109001i
$136$	5.49364	−	1.47202i	0.471076	−	0.126224i
$137$	8.11924	−	14.0629i	0.693674	−	1.20148i	−0.276952	−	0.960884i	$-0.589324\pi$
$137$	8.11924	−	14.0629i	0.693674	−	1.20148i	0.970626	−	0.240595i	$-0.0773424\pi$
$138$		−	0.215386i		−	0.0183349i
$139$	6.66282	+	3.84678i	0.565133	+	0.326280i	0.755203	−	0.655491i	$-0.227538\pi$
$139$	6.66282	+	3.84678i	0.565133	+	0.326280i	−0.190070	+	0.981770i	$0.560872\pi$
$140$	−1.43790	−	0.299166i	−0.121525	−	0.0252841i
$141$	−7.65496	−	2.05114i	−0.644664	−	0.172737i
$142$	2.88728	−	2.88728i	0.242295	−	0.242295i
$143$	−4.68963	−	0.370412i	−0.392166	−	0.0309754i
$144$		−	1.00000i		−	0.0833333i
$145$	0.0345214	−	0.165923i	0.00286684	−	0.0137791i
$146$	1.72410	+	2.98622i	0.142687	+	0.247142i
$147$	1.70008	+	6.34477i	0.140220	+	0.523308i
$148$	0.924347			0.0759808
$149$	3.77709	+	14.0963i	0.309431	+	1.15481i	0.929063	+	0.369921i	$0.120615\pi$
$149$	3.77709	+	14.0963i	0.309431	+	1.15481i	−0.619632	+	0.784893i	$0.712718\pi$
$150$	1.83200	+	4.65229i	0.149582	+	0.379858i
$151$	−8.69302	+	8.69302i	−0.707428	+	0.707428i	−0.965994	−	0.258566i	$-0.916750\pi$
$151$	−8.69302	+	8.69302i	−0.707428	+	0.707428i	0.258566	+	0.965994i	$0.416750\pi$
$152$	−1.58674	+	0.425167i	−0.128702	+	0.0344856i
$153$	1.47202	−	5.49364i	0.119006	−	0.444135i
$154$	0.221799	−	0.827767i	0.0178731	−	0.0667034i
$155$	16.2206	−	0.920190i	1.30287	−	0.0739114i
$156$	2.04304	−	2.97085i	0.163574	−	0.237859i
$157$	−3.31162	−	3.31162i	−0.264296	−	0.264296i	0.562501	−	0.826797i	$-0.309839\pi$
$157$	−3.31162	−	3.31162i	−0.264296	−	0.264296i	−0.826797	+	0.562501i	$0.809839\pi$
$158$	−5.53242	−	9.58244i	−0.440136	−	0.762338i
$159$	3.17140	−	1.83101i	0.251509	−	0.145209i
$160$	2.12363	−	0.700141i	0.167888	−	0.0553510i
$161$	0.100034	+	0.100034i	0.00788382	+	0.00788382i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−1.58838	−	0.917052i	−0.124412	−	0.0718291i	0.436503	−	0.899703i	$-0.356217\pi$
$163$	−1.58838	−	0.917052i	−0.124412	−	0.0718291i	−0.560914	+	0.827874i	$0.689550\pi$
$164$	5.50012	+	5.50012i	0.429487	+	0.429487i
$165$	−2.77074	+	0.913487i	−0.215702	+	0.0711149i
$166$	−1.90870	+	1.10199i	−0.148144	+	0.0855309i
$167$	10.0982	+	17.4905i	0.781420	+	1.35346i	0.931115	+	0.364726i	$0.118837\pi$
$167$	10.0982	+	17.4905i	0.781420	+	1.35346i	−0.149695	+	0.988732i	$0.547829\pi$
$168$	0.464443	+	0.464443i	0.0358325	+	0.0358325i
$169$	12.1392	−	4.65194i	0.933782	−	0.357841i
$170$	12.6971	−	0.720302i	0.973822	−	0.0552447i
$171$	−0.425167	+	1.58674i	−0.0325133	+	0.121341i
$172$	2.45871	−	9.17603i	0.187475	−	0.699665i
$173$	−9.81276	+	2.62932i	−0.746051	+	0.199904i	−0.611766	−	0.791039i	$-0.709540\pi$
$173$	−9.81276	+	2.62932i	−0.746051	+	0.199904i	−0.134285	+	0.990943i	$0.542874\pi$
$174$	−0.0535930	+	0.0535930i	−0.00406287	+	0.00406287i
$175$	−3.01158	−	1.30986i	−0.227654	−	0.0990161i
$176$	0.337686	+	1.26026i	0.0254541	+	0.0949958i
$177$	−4.89600			−0.368006
$178$	1.59876	+	5.96664i	0.119832	+	0.447218i
$179$	0.597467	+	1.03484i	0.0446568	+	0.0773478i	0.887490	−	0.460827i	$-0.152447\pi$
$179$	0.597467	+	1.03484i	0.0446568	+	0.0773478i	−0.842833	+	0.538175i	$0.819114\pi$
$180$	0.455475	−	2.18919i	0.0339491	−	0.163172i
$181$		−	21.0296i		−	1.56312i	−0.623831	−	0.781559i	$-0.714425\pi$
$181$		−	21.0296i		−	1.56312i	0.623831	−	0.781559i	$-0.285575\pi$
$182$	0.430914	+	2.32867i	0.0319415	+	0.172612i
$183$	2.27340	−	2.27340i	0.168054	−	0.168054i
$184$	−0.208047	−	0.0557460i	−0.0153374	−	0.00410965i
$185$	2.02357	+	0.421017i	0.148776	+	0.0309538i
$186$	−6.29231	−	3.63287i	−0.461374	−	0.266375i
$187$			7.42051i			0.542641i
$188$	−3.96250	+	6.86325i	−0.288995	+	0.500554i
$189$	0.634441	−	0.169998i	0.0461488	−	0.0123655i
$190$	−3.66733	+	0.208047i	−0.266056	+	0.0150933i
$191$	4.06177	−	7.03518i	0.293899	−	0.509048i	−0.680829	−	0.732442i	$-0.738380\pi$
$191$	4.06177	−	7.03518i	0.293899	−	0.509048i	0.974728	+	0.223394i	$0.0717137\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	3.88620	−	2.24370i	0.279735	−	0.161505i	−0.353568	−	0.935409i	$-0.615032\pi$
$193$	3.88620	−	2.24370i	0.279735	−	0.161505i	0.633303	+	0.773904i	$0.281698\pi$
$194$	13.6694			0.981409
$195$	5.82576	−	5.57320i	0.417191	−	0.399105i
$196$	6.56859			0.469185
$197$	9.97443	−	5.75874i	0.710649	−	0.410293i	−0.100652	−	0.994922i	$-0.532093\pi$
$197$	9.97443	−	5.75874i	0.710649	−	0.410293i	0.811301	+	0.584628i	$0.198760\pi$
$198$	1.26026	+	0.337686i	0.0895629	+	0.0239983i
$199$	1.75484	−	3.03947i	0.124397	−	0.215462i	−0.797100	−	0.603847i	$-0.793634\pi$
$199$	1.75484	−	3.03947i	0.124397	−	0.215462i	0.921497	+	0.388385i	$0.126967\pi$
$200$	4.96792	−	0.565478i	0.351285	−	0.0399853i
$201$	−12.8313	+	3.43813i	−0.905047	+	0.242507i
$202$	5.26415	−	9.11777i	0.370384	−	0.641524i
$203$		−	0.0497817i		−	0.00349399i
$204$	−4.92547	−	2.84372i	−0.344852	−	0.199100i
$205$	9.53562	+	14.5460i	0.665996	+	1.01593i
$206$	13.2729	+	3.55647i	0.924769	+	0.247791i
$207$	−0.152301	+	0.152301i	−0.0105856	+	0.0105856i
$208$	−2.34084	−	2.74234i	−0.162308	−	0.190147i
$209$		−	2.14329i		−	0.148254i
$210$	0.805210	+	1.22829i	0.0555648	+	0.0847604i
$211$	9.02202	+	15.6266i	0.621102	+	1.07578i	0.989281	+	0.146025i	$0.0466479\pi$
$211$	9.02202	+	15.6266i	0.621102	+	1.07578i	−0.368179	+	0.929755i	$0.620019\pi$
$212$	−0.947801	−	3.53724i	−0.0650952	−	0.242939i
$213$	−4.08323			−0.279778
$214$	−3.31625	−	12.3764i	−0.226694	−	0.846035i
$215$	9.56203	−	18.9682i	0.652125	−	1.29362i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	4.60967	−	1.23516i	0.312925	−	0.0838480i
$218$	4.76713	−	17.7912i	0.322871	−	1.20497i
$219$	0.892458	−	3.33070i	0.0603067	−	0.225068i
$220$	0.165240	+	2.91276i	0.0111405	+	0.196378i
$221$	−8.82299	−	18.5112i	−0.593498	−	1.24520i
$222$	−0.653612	−	0.653612i	−0.0438675	−	0.0438675i
$223$	13.7968	+	23.8968i	0.923905	+	1.60025i	0.793313	+	0.608814i	$0.208354\pi$
$223$	13.7968	+	23.8968i	0.923905	+	1.60025i	0.130592	+	0.991436i	$0.458312\pi$
$224$	0.568824	−	0.328411i	0.0380061	−	0.0219429i
$225$	1.99424	−	4.58508i	0.132949	−	0.305672i
$226$	−1.64768	−	1.64768i	−0.109602	−	0.109602i
$227$	10.7895	+	6.22930i	0.716122	+	0.413453i	0.813324	−	0.581812i	$-0.197656\pi$
$227$	10.7895	+	6.22930i	0.716122	+	0.413453i	−0.0972019	+	0.995265i	$0.530989\pi$
$228$	1.42263	+	0.821359i	0.0942163	+	0.0543958i
$229$	−12.4079	−	12.4079i	−0.819937	−	0.819937i	0.166162	−	0.986099i	$-0.446863\pi$
$229$	−12.4079	−	12.4079i	−0.819937	−	0.819937i	−0.986099	+	0.166162i	$0.946863\pi$
$230$	−0.430063	−	0.216799i	−0.0283575	−	0.0142953i
$231$	−0.742155	+	0.428484i	−0.0488302	+	0.0281922i
$232$	0.0378960	+	0.0656377i	0.00248799	+	0.00430933i
$233$	21.0823	+	21.0823i	1.38115	+	1.38115i	0.842582	+	0.538567i	$0.181034\pi$
$233$	21.0823	+	21.0823i	1.38115	+	1.38115i	0.538567	+	0.842582i	$0.318966\pi$
$234$	−3.54536	+	0.656060i	−0.231768	+	0.0428880i
$235$	−11.8007	+	13.2201i	−0.769792	+	0.862385i
$236$	−1.26718	+	4.72918i	−0.0824863	+	0.307843i
$237$	−2.86379	+	10.6878i	−0.186023	+	0.694248i
$238$	3.60834	−	0.966852i	0.233894	−	0.0626717i
$239$	0.526226	−	0.526226i	0.0340388	−	0.0340388i	−0.689883	−	0.723921i	$-0.742338\pi$
$239$	0.526226	−	0.526226i	0.0340388	−	0.0340388i	0.723921	+	0.689883i	$0.242338\pi$
$240$	−1.99671	−	1.00656i	−0.128887	−	0.0649731i
$241$	4.41998	+	16.4956i	0.284716	+	1.06258i	0.949046	+	0.315136i	$0.102050\pi$
$241$	4.41998	+	16.4956i	0.284716	+	1.06258i	−0.664330	+	0.747439i	$0.731283\pi$
$242$	9.29771			0.597679
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−1.60754	−	2.78433i	−0.102912	−	0.178249i
$245$	14.3799	+	2.99183i	0.918696	+	0.191141i
$246$		−	7.77834i		−	0.495929i
$247$	2.54837	+	5.34664i	0.162149	+	0.340199i
$248$	−5.13765	+	5.13765i	−0.326241	+	0.326241i
$249$	2.12888	+	0.570431i	0.134912	+	0.0361496i
$250$	11.1333	+	1.02483i	0.704130	+	0.0648159i
$251$	−12.1516	−	7.01575i	−0.767004	−	0.442830i	0.0648005	−	0.997898i	$-0.479359\pi$
$251$	−12.1516	−	7.01575i	−0.767004	−	0.442830i	−0.831805	+	0.555068i	$0.812692\pi$
$252$		−	0.656821i		−	0.0413758i
$253$	0.140509	−	0.243369i	0.00883373	−	0.0153005i
$254$	1.21222	−	0.324813i	0.0760613	−	0.0203806i
$255$	−9.48752	−	8.46886i	−0.594132	−	0.530341i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	16.7017	+	4.47521i	1.04182	+	0.279156i	0.738869	−	0.673849i	$-0.235360\pi$
$257$	16.7017	+	4.47521i	1.04182	+	0.279156i	0.302955	+	0.953005i	$0.402027\pi$
$258$	−8.22700	+	4.74986i	−0.512191	+	0.295713i
$259$	0.607130			0.0377252
$260$	−3.87548	−	7.06970i	−0.240347	−	0.438444i
$261$	0.0757919			0.00469140
$262$	−12.7637	+	7.36910i	−0.788542	+	0.455265i
$263$	−25.0956	−	6.72435i	−1.54746	−	0.414641i	−0.618794	−	0.785553i	$-0.712378\pi$
$263$	−25.0956	−	6.72435i	−1.54746	−	0.414641i	−0.928668	+	0.370912i	$0.879045\pi$
$264$	0.652360	−	1.12992i	0.0401500	−	0.0695418i
$265$	−0.463788	−	8.17539i	−0.0284903	−	0.502210i
$266$	−1.04221	+	0.279258i	−0.0639018	+	0.0171224i
$267$	3.08856	−	5.34954i	0.189017	−	0.327387i
$268$			13.2839i			0.811443i
$269$	−21.6715	−	12.5121i	−1.32134	−	0.762873i	−0.337394	−	0.941364i	$-0.609545\pi$
$269$	−21.6715	−	12.5121i	−1.32134	−	0.762873i	−0.983942	+	0.178490i	$0.942879\pi$
$270$	−1.87006	+	1.22592i	−0.113808	+	0.0746071i
$271$	2.53478	+	0.679193i	0.153977	+	0.0412580i	0.334984	−	0.942224i	$-0.391269\pi$
$271$	2.53478	+	0.679193i	0.153977	+	0.0412580i	−0.181007	+	0.983482i	$0.557936\pi$
$272$	−4.02163	+	4.02163i	−0.243847	+	0.243847i
$273$	1.34191	−	1.95132i	0.0812164	−	0.118099i
$274$			16.2385i			0.981003i
$275$	−0.964948	+	6.45184i	−0.0581886	+	0.389060i
$276$	0.107693	+	0.186530i	0.00648235	+	0.0112278i
$277$	−7.60904	−	28.3973i	−0.457183	−	1.70623i	−0.681589	−	0.731735i	$-0.738711\pi$
$277$	−7.60904	−	28.3973i	−0.457183	−	1.70623i	0.224406	−	0.974496i	$-0.427956\pi$
$278$	−7.69356			−0.461429
$279$	1.88051	+	7.01816i	0.112583	+	0.420166i
$280$	1.39484	−	0.459867i	0.0833579	−	0.0274823i
$281$	−10.3701	+	10.3701i	−0.618630	+	0.618630i	−0.945180	−	0.326550i	$-0.894114\pi$
$281$	−10.3701	+	10.3701i	−0.618630	+	0.618630i	0.326550	+	0.945180i	$0.394114\pi$
$282$	7.65496	−	2.05114i	0.455846	−	0.122144i
$283$	3.02271	−	11.2809i	0.179681	−	0.670580i	−0.816025	−	0.578016i	$-0.803827\pi$
$283$	3.02271	−	11.2809i	0.179681	−	0.670580i	0.995707	−	0.0925637i	$-0.0295062\pi$
$284$	−1.05682	+	3.94410i	−0.0627106	+	0.234039i
$285$	2.74031	+	2.44608i	0.162322	+	0.144893i
$286$	4.24654	−	2.02403i	0.251103	−	0.119683i
$287$	3.61259	+	3.61259i	0.213245	+	0.213245i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−13.2908	+	7.67347i	−0.781814	+	0.451381i
$290$	0.0530650	+	0.160954i	0.00311608	+	0.00945154i
$291$	−9.66576	−	9.66576i	−0.566617	−	0.566617i
$292$	−2.98622	−	1.72410i	−0.174755	−	0.100895i
$293$	9.90790	+	5.72033i	0.578825	+	0.334185i	0.760666	−	0.649143i	$-0.224872\pi$
$293$	9.90790	+	5.72033i	0.578825	+	0.334185i	−0.181841	+	0.983328i	$0.558206\pi$
$294$	−4.64469	−	4.64469i	−0.270884	−	0.270884i
$295$	−4.92812	+	9.77589i	−0.286926	+	0.569174i
$296$	−0.800508	+	0.462173i	−0.0465286	+	0.0268633i
$297$	−0.652360	−	1.12992i	−0.0378538	−	0.0655646i
$298$	−10.3192	−	10.3192i	−0.597775	−	0.597775i
$299$	−0.0611485	+	0.774174i	−0.00353631	+	0.0447716i
$300$	−3.91270	−	3.11300i	−0.225900	−	0.179729i
$301$	1.61493	−	6.02701i	0.0930831	−	0.347391i
$302$	3.18187	−	11.8749i	0.183096	−	0.683323i
$303$	−10.1695	+	2.72492i	−0.584225	+	0.156543i
$304$	1.16158	−	1.16158i	0.0666210	−	0.0666210i
$305$	−2.25100	−	6.82762i	−0.128892	−	0.390948i
$306$	1.47202	+	5.49364i	0.0841496	+	0.314051i
$307$	−26.9028			−1.53543			−0.767713	−	0.640794i	$-0.778605\pi$
$307$	−26.9028			−1.53543			−0.767713	+	0.640794i	$0.778605\pi$
$308$	0.221799	+	0.827767i	0.0126382	+	0.0471664i
$309$	−6.87058	−	11.9002i	−0.390853	−	0.676978i
$310$	−13.5873	+	8.90720i	−0.771709	+	0.505895i
$311$		−	7.38647i		−	0.418849i	−0.977825	−	0.209424i	$-0.932841\pi$
$311$		−	7.38647i		−	0.418849i	0.977825	−	0.209424i	$-0.0671590\pi$
$312$	−0.283902	+	3.59436i	−0.0160728	+	0.203490i
$313$	13.9012	−	13.9012i	0.785742	−	0.785742i	−0.195051	−	0.980793i	$-0.562487\pi$
$313$	13.9012	−	13.9012i	0.785742	−	0.785742i	0.980793	+	0.195051i	$0.0624873\pi$
$314$	4.52376	+	1.21214i	0.255291	+	0.0684049i
$315$	0.299166	−	1.43790i	0.0168561	−	0.0810168i
$316$	9.58244	+	5.53242i	0.539054	+	0.311223i
$317$			24.2313i			1.36097i	0.732763	+	0.680484i	$0.238230\pi$
$317$			24.2313i			1.36097i	−0.732763	+	0.680484i	$0.761770\pi$
$318$	−1.83101	+	3.17140i	−0.102678	+	0.177844i
$319$	−0.0955177	+	0.0255939i	−0.00534797	+	0.00143298i
$320$	−1.48905	+	1.66815i	−0.0832403	+	0.0932527i
$321$	−6.40651	+	11.0964i	−0.357577	+	0.619341i
$322$	−0.136650	−	0.0366151i	−0.00761518	−	0.00204048i
$323$	8.09115	−	4.67143i	0.450203	−	0.259925i
$324$	1.00000			0.0555556
$325$	−5.26408	−	17.2421i	−0.291998	−	0.956419i
$326$	1.83410			0.101582
$327$	−15.9511	+	9.20939i	−0.882099	+	0.509280i
$328$	−7.51330	−	2.01318i	−0.414852	−	0.111159i
$329$	−2.60265	+	4.50793i	−0.143489	+	0.248530i
$330$	1.94279	−	2.17647i	0.106947	−	0.119811i
$331$	7.54624	−	2.02201i	0.414779	−	0.111140i	−0.0453937	−	0.998969i	$-0.514454\pi$
$331$	7.54624	−	2.02201i	0.414779	−	0.111140i	0.460173	+	0.887830i	$0.347788\pi$
$332$	1.10199	−	1.90870i	0.0604795	−	0.104754i
$333$			0.924347i			0.0506539i
$334$	−17.4905	−	10.0982i	−0.957040	−	0.552547i
$335$	−6.05049	+	29.0809i	−0.330573	+	1.58886i
$336$	−0.634441	−	0.169998i	−0.0346116	−	0.00927414i
$337$	−3.21147	+	3.21147i	−0.174940	+	0.174940i	−0.789146	−	0.614206i	$-0.789476\pi$
$337$	−3.21147	+	3.21147i	−0.174940	+	0.174940i	0.614206	+	0.789146i	$0.289476\pi$
$338$	−8.18686	+	10.0983i	−0.445307	+	0.549274i
$339$			2.33017i			0.126557i
$340$	−10.6358	+	6.97234i	−0.576810	+	0.378128i
$341$	−4.73987	−	8.20970i	−0.256678	−	0.444580i
$342$	−0.425167	−	1.58674i	−0.0229904	−	0.0858012i
$343$	8.91213			0.481210
$344$	2.45871	+	9.17603i	0.132565	+	0.494738i
$345$	0.150800	+	0.457400i	0.00811882	+	0.0246256i
$346$	7.18344	−	7.18344i	0.386184	−	0.386184i
$347$	18.0264	−	4.83017i	0.967710	−	0.259297i	0.259849	−	0.965649i	$-0.416327\pi$
$347$	18.0264	−	4.83017i	0.967710	−	0.259297i	0.707861	+	0.706352i	$0.249660\pi$
$348$	0.0196164	−	0.0732094i	0.00105155	−	0.00392444i
$349$	0.712266	−	2.65821i	0.0381267	−	0.142291i	−0.944239	−	0.329261i	$-0.893200\pi$
$349$	0.712266	−	2.65821i	0.0381267	−	0.142291i	0.982366	+	0.186971i	$0.0598669\pi$
$350$	3.26304	−	0.371418i	0.174417	−	0.0198531i
$351$	2.97085	+	2.04304i	0.158572	+	0.109050i
$352$	−0.922576	−	0.922576i	−0.0491735	−	0.0491735i
$353$	−1.21485	−	2.10419i	−0.0646602	−	0.111995i	0.831883	−	0.554951i	$-0.187263\pi$
$353$	−1.21485	−	2.10419i	−0.0646602	−	0.111995i	−0.896543	+	0.442956i	$0.853930\pi$
$354$	4.24006	−	2.44800i	0.225357	−	0.130110i
$355$	−4.11001	+	8.15302i	−0.218137	+	0.432717i
$356$	−4.36788	−	4.36788i	−0.231497	−	0.231497i
$357$	−3.23515	−	1.86781i	−0.171222	−	0.0988552i
$358$	−1.03484	−	0.597467i	−0.0546931	−	0.0315771i
$359$	−21.3084	−	21.3084i	−1.12462	−	1.12462i	−0.991038	−	0.133578i	$-0.957353\pi$
$359$	−21.3084	−	21.3084i	−1.12462	−	1.12462i	−0.133578	−	0.991038i	$-0.542647\pi$
$360$	0.700141	+	2.12363i	0.0369006	+	0.111925i
$361$	14.1175	−	8.15074i	0.743026	−	0.428986i
$362$	10.5148	+	18.2122i	0.552646	+	0.957211i
$363$	−6.57447	−	6.57447i	−0.345070	−	0.345070i
$364$	−1.53752	−	1.80123i	−0.0805878	−	0.0944100i
$365$	−5.75212	−	5.13452i	−0.301080	−	0.268753i
$366$	−0.832121	+	3.10552i	−0.0434957	+	0.162328i
$367$	−2.85418	+	10.6519i	−0.148987	+	0.556027i	0.850559	+	0.525880i	$0.176264\pi$
$367$	−2.85418	+	10.6519i	−0.148987	+	0.556027i	−0.999545	+	0.0301464i	$0.990403\pi$
$368$	0.208047	−	0.0557460i	0.0108452	−	0.00290596i
$369$	−5.50012	+	5.50012i	−0.286325	+	0.286325i
$370$	−1.96297	+	0.647172i	−0.102050	+	0.0336449i
$371$	−0.622536	−	2.32334i	−0.0323204	−	0.120622i
$372$	7.26573			0.376711
$373$	0.766184	+	2.85944i	0.0396715	+	0.148056i	0.982921	−	0.184030i	$-0.0589143\pi$
$373$	0.766184	+	2.85944i	0.0396715	+	0.148056i	−0.943249	+	0.332086i	$0.892248\pi$
$374$	−3.71025	−	6.42635i	−0.191853	−	0.332299i
$375$	−7.14775	−	8.59707i	−0.369108	−	0.443951i
$376$		−	7.92499i		−	0.408700i
$377$	0.207847	−	0.177417i	0.0107047	−	0.00913745i
$378$	−0.464443	+	0.464443i	−0.0238884	+	0.0238884i
$379$	−19.7782	−	5.29955i	−1.01594	−	0.272220i	−0.287830	−	0.957682i	$-0.592934\pi$
$379$	−19.7782	−	5.29955i	−1.01594	−	0.272220i	−0.728109	+	0.685462i	$0.759600\pi$
$380$	3.07198	−	2.01384i	0.157589	−	0.103308i
$381$	−1.08684	−	0.627490i	−0.0556807	−	0.0321473i
$382$			8.12353i			0.415636i
$383$	12.5222	−	21.6891i	0.639855	−	1.10826i	−0.345610	−	0.938378i	$-0.612328\pi$
$383$	12.5222	−	21.6891i	0.639855	−	1.10826i	0.985464	−	0.169882i	$-0.0543388\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	0.108533	+	1.91316i	0.00553136	+	0.0975037i
$386$	−2.24370	+	3.88620i	−0.114201	+	0.197803i
$387$	9.17603	+	2.45871i	0.466444	+	0.124983i
$388$	−11.8381	+	6.83472i	−0.600988	+	0.346981i
$389$	−13.9873			−0.709182			−0.354591	−	0.935022i	$-0.615380\pi$
$389$	−13.9873			−0.709182			−0.354591	+	0.935022i	$0.615380\pi$
$390$	−2.25866	+	7.73941i	−0.114371	+	0.391900i
$391$	1.22499			0.0619506
$392$	−5.68856	+	3.28429i	−0.287316	+	0.165882i
$393$	14.2360	+	3.81453i	0.718112	+	0.192418i
$394$	−5.75874	+	9.97443i	−0.290121	+	0.502505i
$395$	18.4579	+	16.4761i	0.928716	+	0.829001i
$396$	−1.26026	+	0.337686i	−0.0633306	+	0.0169694i
$397$	10.4625	−	18.1215i	0.525096	−	0.909494i	−0.474476	−	0.880268i	$-0.657363\pi$
$397$	10.4625	−	18.1215i	0.525096	−	0.909494i	0.999573	−	0.0292254i	$-0.00930406\pi$
$398$			3.50967i			0.175924i
$399$	0.934417	+	0.539486i	0.0467793	+	0.0270081i
$400$	−4.01961	+	2.97368i	−0.200980	+	0.148684i
$401$	28.6705	+	7.68224i	1.43174	+	0.383633i	0.889632	−	0.456678i	$-0.150961\pi$
$401$	28.6705	+	7.68224i	1.43174	+	0.383633i	0.542105	+	0.840311i	$0.317628\pi$
$402$	9.39313	−	9.39313i	0.468487	−	0.468487i
$403$	21.5854	+	14.8442i	1.07525	+	0.739443i
$404$			10.5283i			0.523802i
$405$	2.18919	+	0.455475i	0.108782	+	0.0226328i
$406$	0.0248909	+	0.0431123i	0.00123531	+	0.00213963i
$407$	−0.312139	−	1.16492i	−0.0154722	−	0.0577429i
$408$	5.68744			0.281570
$409$	−3.61041	−	13.4742i	−0.178523	−	0.666259i	−0.995925	−	0.0901897i	$-0.971253\pi$
$409$	−3.61041	−	13.4742i	−0.178523	−	0.666259i	0.817401	−	0.576069i	$-0.195414\pi$
$410$	−15.5311	−	7.82935i	−0.767024	−	0.386664i
$411$	11.4823	−	11.4823i	0.566382	−	0.566382i
$412$	−13.2729	+	3.55647i	−0.653910	+	0.175215i
$413$	−0.832310	+	3.10622i	−0.0409553	+	0.152847i
$414$	0.0557460	−	0.208047i	0.00273977	−	0.0102249i
$415$	3.28183	−	3.67657i	0.161098	−	0.180476i
$416$	3.39840	+	1.20452i	0.166620	+	0.0590563i
$417$	5.44017	+	5.44017i	0.266406	+	0.266406i
$418$	1.07164	+	1.85614i	0.0524158	+	0.0907867i
$419$	6.36248	−	3.67338i	0.310827	−	0.179456i	−0.336469	−	0.941694i	$-0.609233\pi$
$419$	6.36248	−	3.67338i	0.310827	−	0.179456i	0.647297	+	0.762238i	$0.275899\pi$
$420$	−1.31148	−	0.661129i	−0.0639936	−	0.0322598i
$421$	11.2103	+	11.2103i	0.546356	+	0.546356i	0.925385	−	0.379029i	$-0.123742\pi$
$421$	11.2103	+	11.2103i	0.546356	+	0.546356i	−0.379029	+	0.925385i	$0.623742\pi$
$422$	−15.6266	−	9.02202i	−0.760691	−	0.439185i
$423$	−6.86325	−	3.96250i	−0.333702	−	0.192663i
$424$	2.58944	+	2.58944i	0.125754	+	0.125754i
$425$	−26.4596	+	10.4194i	−1.28348	+	0.505415i
$426$	3.53618	−	2.04162i	0.171329	−	0.0989166i
$427$	−1.05586	−	1.82881i	−0.0510968	−	0.0885022i
$428$	9.06017	+	9.06017i	0.437940	+	0.437940i
$429$	−4.43396	−	1.57156i	−0.214074	−	0.0758754i
$430$	1.20312	+	21.2079i	0.0580196	+	1.02274i
$431$	9.52492	−	35.5475i	0.458799	−	1.71226i	−0.217872	−	0.975977i	$-0.569912\pi$
$431$	9.52492	−	35.5475i	0.458799	−	1.71226i	0.676672	−	0.736285i	$-0.263422\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	8.17993	−	2.19180i	0.393102	−	0.105331i	−0.0568530	−	0.998383i	$-0.518107\pi$
$433$	8.17993	−	2.19180i	0.393102	−	0.105331i	0.449955	+	0.893051i	$0.351440\pi$
$434$	−3.37452	+	3.37452i	−0.161982	+	0.161982i
$435$	0.0762890	−	0.151334i	0.00365778	−	0.00725592i
$436$	4.76713	+	17.7912i	0.228304	+	0.852042i
$437$	−0.353818			−0.0169254
$438$	0.892458	+	3.33070i	0.0426433	+	0.159147i
$439$	8.93023	+	15.4676i	0.426216	+	0.738229i	0.996533	−	0.0831963i	$-0.0265129\pi$
$439$	8.93023	+	15.4676i	0.426216	+	0.738229i	−0.570317	+	0.821425i	$0.693180\pi$
$440$	−1.59948	−	2.43990i	−0.0762523	−	0.116318i
$441$			6.56859i			0.312790i
$442$	16.8965	+	11.6197i	0.803686	+	0.552692i
$443$	−2.70502	+	2.70502i	−0.128519	+	0.128519i	−0.768440	−	0.639921i	$-0.778967\pi$
$443$	−2.70502	+	2.70502i	−0.128519	+	0.128519i	0.639921	+	0.768440i	$0.278967\pi$
$444$	0.892850	+	0.239238i	0.0423728	+	0.0113538i
$445$	−7.57265	−	11.5516i	−0.358978	−	0.547597i
$446$	−23.8968	−	13.7968i	−1.13155	−	0.653299i
$447$			14.5936i			0.690252i
$448$	−0.328411	+	0.568824i	−0.0155159	+	0.0268744i
$449$	−11.5315	+	3.08986i	−0.544205	+	0.145819i	−0.520440	−	0.853898i	$-0.674232\pi$
$449$	−11.5315	+	3.08986i	−0.544205	+	0.145819i	−0.0237652	+	0.999718i	$0.507565\pi$
$450$	0.565478	+	4.96792i	0.0266569	+	0.234190i
$451$	5.07427	−	8.78890i	0.238938	−	0.413853i
$452$	2.25077	+	0.603092i	0.105867	+	0.0283671i
$453$	−10.6467	+	6.14689i	−0.500227	+	0.288806i
$454$	−12.4586			−0.584711
$455$	−2.54550	−	4.64353i	−0.119335	−	0.217692i
$456$	−1.64272			−0.0769273
$457$	35.2137	−	20.3307i	1.64723	−	0.951028i	0.669062	−	0.743207i	$-0.266696\pi$
$457$	35.2137	−	20.3307i	1.64723	−	0.951028i	0.978167	−	0.207821i	$-0.0666373\pi$
$458$	16.9495	+	4.54161i	0.791998	+	0.212215i
$459$	2.84372	−	4.92547i	0.132733	−	0.229901i
$460$	0.480844	−	0.0272782i	0.0224195	−	0.00127185i
$461$	30.0601	−	8.05459i	1.40004	−	0.375139i	0.521681	−	0.853141i	$-0.325305\pi$
$461$	30.0601	−	8.05459i	1.40004	−	0.375139i	0.878359	+	0.478001i	$0.158639\pi$
$462$	0.428484	−	0.742155i	0.0199349	−	0.0345282i
$463$			13.3638i			0.621069i	0.950562	+	0.310534i	$0.100508\pi$
$463$			13.3638i			0.621069i	−0.950562	+	0.310534i	$0.899492\pi$
$464$	−0.0656377	−	0.0378960i	−0.00304716	−	0.00175928i
$465$	15.9060	+	3.30936i	0.737625	+	0.153468i
$466$	−28.7990	−	7.71667i	−1.33409	−	0.357468i
$467$	−15.7888	+	15.7888i	−0.730619	+	0.730619i	−0.970742	−	0.240123i	$-0.922812\pi$
$467$	−15.7888	+	15.7888i	−0.730619	+	0.730619i	0.240123	+	0.970742i	$0.422812\pi$
$468$	2.74234	−	2.34084i	0.126765	−	0.108206i
$469$			8.72514i			0.402890i
$470$	3.60964	−	17.3493i	0.166500	−	0.800263i
$471$	−2.34167	−	4.05589i	−0.107898	−	0.186886i
$472$	−1.26718	−	4.72918i	−0.0583267	−	0.217678i
$473$	−12.3945			−0.569898
$474$	−2.86379	−	10.6878i	−0.131538	−	0.490908i
$475$	7.64239	−	3.00946i	0.350657	−	0.138084i
$476$	−2.64149	+	2.64149i	−0.121072	+	0.121072i
$477$	3.53724	−	0.947801i	0.161959	−	0.0433968i
$478$	−0.192612	+	0.718839i	−0.00880988	+	0.0328789i
$479$	8.34864	−	31.1575i	0.381459	−	1.42362i	−0.462215	−	0.886768i	$-0.652945\pi$
$479$	8.34864	−	31.1575i	0.381459	−	1.42362i	0.843674	−	0.536856i	$-0.180388\pi$
$480$	2.23248	−	0.126648i	0.101898	−	0.00578066i
$481$	2.16375	+	2.53488i	0.0986586	+	0.115580i
$482$	−12.0756	−	12.0756i	−0.550029	−	0.550029i
$483$	0.0707350	+	0.122517i	0.00321855	+	0.00557470i
$484$	−8.05205	+	4.64885i	−0.366002	+	0.211312i
$485$	−29.0288	+	9.57053i	−1.31813	+	0.434576i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−11.4410	−	6.60545i	−0.518440	−	0.299321i	0.217856	−	0.975981i	$-0.430094\pi$
$487$	−11.4410	−	6.60545i	−0.518440	−	0.299321i	−0.736296	+	0.676659i	$0.763427\pi$
$488$	2.78433	+	1.60754i	0.126041	+	0.0727697i
$489$	−1.29691	−	1.29691i	−0.0586482	−	0.0586482i
$490$	−13.9492	+	4.59893i	−0.630163	+	0.207759i
$491$	−21.0123	+	12.1315i	−0.948274	+	0.547486i	−0.892544	−	0.450960i	$-0.851082\pi$
$491$	−21.0123	+	12.1315i	−0.948274	+	0.547486i	−0.0557297	+	0.998446i	$0.517749\pi$
$492$	3.88917	+	6.73624i	0.175337	+	0.303693i
$493$	−0.304807	−	0.304807i	−0.0137278	−	0.0137278i
$494$	−4.88027	−	3.35614i	−0.219574	−	0.151000i
$495$	−2.91276	+	0.165240i	−0.130919	+	0.00742699i
$496$	1.88051	−	7.01816i	0.0844374	−	0.315125i
$497$	−0.694141	+	2.59057i	−0.0311365	+	0.116203i
$498$	−2.12888	+	0.570431i	−0.0953973	+	0.0255616i
$499$	23.6665	−	23.6665i	1.05946	−	1.05946i	0.0613431	−	0.998117i	$-0.480462\pi$
$499$	23.6665	−	23.6665i	1.05946	−	1.05946i	0.998117	−	0.0613431i	$-0.0195384\pi$
$500$	−10.1541	+	4.67911i	−0.454106	+	0.209256i
$501$	5.22720	+	19.5082i	0.233534	+	0.871560i
$502$	14.0315			0.626257
$503$	5.71583	+	21.3318i	0.254856	+	0.951137i	0.968170	+	0.250292i	$0.0805267\pi$
$503$	5.71583	+	21.3318i	0.254856	+	0.951137i	−0.713314	+	0.700845i	$0.752807\pi$
$504$	0.328411	+	0.568824i	0.0146286	+	0.0253374i
$505$	−4.79538	+	23.0484i	−0.213392	+	1.02564i
$506$			0.281018i			0.0124928i
$507$	12.9295	−	1.35158i	0.574221	−	0.0600256i
$508$	−0.887405	+	0.887405i	−0.0393722	+	0.0393722i
$509$	−17.4786	−	4.68339i	−0.774727	−	0.207588i	−0.150268	−	0.988645i	$-0.548014\pi$
$509$	−17.4786	−	4.68339i	−0.774727	−	0.207588i	−0.624459	+	0.781058i	$0.714680\pi$
$510$	12.4509	+	2.59049i	0.551334	+	0.114709i
$511$	−1.96141	−	1.13242i	−0.0867679	−	0.0500955i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.821359	+	1.42263i	−0.0362639	+	0.0628109i
$514$	−16.7017	+	4.47521i	−0.736681	+	0.197393i
$515$	−30.6768	+	1.74029i	−1.35178	+	0.0766863i
$516$	4.74986	−	8.22700i	0.209101	−	0.362173i
$517$	9.98757	+	2.67616i	0.439253	+	0.117697i
$518$	−0.525790	+	0.303565i	−0.0231019	+	0.0133379i
$519$	−10.1589			−0.445927
$520$	6.89111	+	4.18480i	0.302195	+	0.183516i
$521$	30.3276			1.32868			0.664339	−	0.747432i	$-0.268713\pi$
$521$	30.3276			1.32868			0.664339	+	0.747432i	$0.268713\pi$
$522$	−0.0656377	+	0.0378960i	−0.00287289	+	0.00165866i
$523$	−44.0321	−	11.7984i	−1.92539	−	0.515906i	−0.983849	−	0.179001i	$-0.942713\pi$
$523$	−44.0321	−	11.7984i	−1.92539	−	0.515906i	−0.941539	−	0.336905i	$-0.890620\pi$
$524$	7.36910	−	12.7637i	0.321921	−	0.557583i
$525$	−2.56995	−	2.04468i	−0.112162	−	0.0892373i
$526$	25.0956	−	6.72435i	1.09422	−	0.293196i
$527$	20.6617	−	35.7871i	0.900038	−	1.55891i
$528$			1.30472i			0.0567806i
$529$	19.8784	+	11.4768i	0.864279	+	0.498991i
$530$	4.48935	+	6.84820i	0.195005	+	0.297467i
$531$	−4.72918	−	1.26718i	−0.205229	−	0.0549909i
$532$	0.762948	−	0.762948i	0.0330780	−	0.0330780i
$533$	−2.20829	+	27.9581i	−0.0956515	+	1.21100i
$534$			6.17712i			0.267310i
$535$	15.7077	+	23.9611i	0.679105	+	1.03593i
$536$	−6.64195	−	11.5042i	−0.286888	−	0.496905i
$537$	0.309271	+	1.15422i	0.0133461	+	0.0498081i
$538$	25.0241			1.07887
$539$	−2.21812	−	8.27814i	−0.0955412	−	0.356565i
$540$	1.00656	−	1.99671i	0.0433154	−	0.0859246i
$541$	−7.31140	+	7.31140i	−0.314342	+	0.314342i	−0.846589	−	0.532247i	$-0.821348\pi$
$541$	−7.31140	+	7.31140i	−0.314342	+	0.314342i	0.532247	+	0.846589i	$0.321348\pi$
$542$	−2.53478	+	0.679193i	−0.108878	+	0.0291738i
$543$	5.44286	−	20.3130i	0.233576	−	0.871716i
$544$	1.47202	−	5.49364i	0.0631122	−	0.235538i
$545$	2.33270	+	41.1195i	0.0999219	+	1.76137i
$546$	−0.186473	+	2.36085i	−0.00798030	+	0.101035i
$547$	−30.7225	−	30.7225i	−1.31360	−	1.31360i	−0.918742	−	0.394857i	$-0.870794\pi$
$547$	−30.7225	−	30.7225i	−1.31360	−	1.31360i	−0.394857	−	0.918742i	$-0.629206\pi$
$548$	−8.11924	−	14.0629i	−0.346837	−	0.600739i
$549$	2.78433	−	1.60754i	0.118832	−	0.0686079i
$550$	−2.39025	−	6.06993i	−0.101921	−	0.258823i
$551$	0.0880381	+	0.0880381i	0.00375055	+	0.00375055i
$552$	−0.186530	−	0.107693i	−0.00793923	−	0.00458372i
$553$	6.29395	+	3.63381i	0.267646	+	0.154525i
$554$	20.7883	+	20.7883i	0.883210	+	0.883210i
$555$	1.84565	+	0.930409i	0.0783434	+	0.0394937i
$556$	6.66282	−	3.84678i	0.282566	−	0.163140i
$557$	−8.17126	−	14.1530i	−0.346227	−	0.599683i	0.639349	−	0.768917i	$-0.279204\pi$
$557$	−8.17126	−	14.1530i	−0.346227	−	0.599683i	−0.985576	+	0.169234i	$0.945871\pi$
$558$	−5.13765	−	5.13765i	−0.217494	−	0.217494i
$559$	30.9193	−	14.7370i	1.30775	−	0.623310i
$560$	−0.978038	+	1.09568i	−0.0413296	+	0.0463009i
$561$	−1.92057	+	7.16766i	−0.0810865	+	0.302619i
$562$	3.79573	−	14.1659i	0.160113	−	0.597551i
$563$	18.2012	−	4.87699i	0.767088	−	0.205541i	0.146003	−	0.989284i	$-0.453359\pi$
$563$	18.2012	−	4.87699i	0.767088	−	0.205541i	0.621085	+	0.783743i	$0.286692\pi$
$564$	−5.60382	+	5.60382i	−0.235963	+	0.235963i
$565$	4.65267	+	2.34545i	0.195739	+	0.0986739i
$566$	3.02271	+	11.2809i	0.127054	+	0.474171i
$567$	0.656821			0.0275839
$568$	−1.05682	−	3.94410i	−0.0443431	−	0.165491i
$569$	5.61694	+	9.72882i	0.235474	+	0.407853i	0.959410	−	0.282014i	$-0.0910023\pi$
$569$	5.61694	+	9.72882i	0.235474	+	0.407853i	−0.723936	+	0.689867i	$0.757669\pi$
$570$	−3.59622	−	0.748217i	−0.150629	−	0.0313394i
$571$		−	38.3139i		−	1.60339i	−0.597735	−	0.801693i	$-0.703933\pi$
$571$		−	38.3139i		−	1.60339i	0.597735	−	0.801693i	$-0.296067\pi$
$572$	−2.66560	+	3.87613i	−0.111454	+	0.162069i
$573$	5.74420	−	5.74420i	0.239968	−	0.239968i
$574$	−4.93489	−	1.32230i	−0.205978	−	0.0551918i
$575$	1.06508	+	0.159296i	0.0444170	+	0.00664309i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$		−	18.0766i		−	0.752540i	−0.926510	−	0.376270i	$-0.877207\pi$
$577$		−	18.0766i		−	0.752540i	0.926510	−	0.376270i	$-0.122793\pi$
$578$	7.67347	−	13.2908i	0.319174	−	0.552826i
$579$	4.33450	−	1.16143i	0.180136	−	0.0482672i
$580$	−0.126433	−	0.112858i	−0.00524983	−	0.00468616i
$581$	0.723809	−	1.25367i	0.0300287	−	0.0520112i
$582$	13.2037	+	3.53791i	0.547310	+	0.146651i
$583$	−4.13779	+	2.38896i	−0.171370	+	0.0989404i
$584$	3.44819			0.142687
$585$	7.06970	−	3.87548i	0.292296	−	0.160231i
$586$	−11.4407			−0.472609
$587$	13.0229	−	7.51880i	0.537514	−	0.310334i	−0.206557	−	0.978435i	$-0.566226\pi$
$587$	13.0229	−	7.51880i	0.537514	−	0.310334i	0.744071	+	0.668101i	$0.232892\pi$
$588$	6.34477	+	1.70008i	0.261654	+	0.0701099i
$589$	−5.96777	+	10.3365i	−0.245898	+	0.425907i
$590$	−0.620069	−	10.9302i	−0.0255278	−	0.449990i
$591$	11.1250	−	2.98094i	0.457623	−	0.122620i
$592$	0.462173	−	0.800508i	0.0189952	−	0.0329007i
$593$			36.6579i			1.50536i	0.658387	+	0.752680i	$0.271239\pi$
$593$			36.6579i			1.50536i	−0.658387	+	0.752680i	$0.728761\pi$
$594$	1.12992	+	0.652360i	0.0463612	+	0.0267666i
$595$	−6.98585	+	4.57958i	−0.286392	+	0.187745i
$596$	14.0963	+	3.77709i	0.577407	+	0.154716i
$597$	2.48171	−	2.48171i	0.101570	−	0.101570i
$598$	−0.334131	−	0.701028i	−0.0136636	−	0.0286672i
$599$		−	9.07935i		−	0.370972i	−0.982647	−	0.185486i	$-0.940614\pi$
$599$		−	9.07935i		−	0.370972i	0.982647	−	0.185486i	$-0.0593860\pi$
$600$	4.94500	+	0.739583i	0.201879	+	0.0301933i
$601$	17.2295	+	29.8423i	0.702805	+	1.21729i	0.967478	+	0.252956i	$0.0814027\pi$
$601$	17.2295	+	29.8423i	0.702805	+	1.21729i	−0.264673	+	0.964338i	$0.585264\pi$
$602$	1.61493	+	6.02701i	0.0658197	+	0.245643i
$603$	−13.2839			−0.540962
$604$	3.18187	+	11.8749i	0.129468	+	0.483182i
$605$	−19.7449	+	6.50970i	−0.802744	+	0.264657i
$606$	7.44463	−	7.44463i	0.302417	−	0.302417i
$607$	27.8240	−	7.45542i	1.12934	−	0.302606i	0.354683	−	0.934987i	$-0.384589\pi$
$607$	27.8240	−	7.45542i	1.12934	−	0.302606i	0.774658	+	0.632381i	$0.217922\pi$
$608$	−0.425167	+	1.58674i	−0.0172428	+	0.0643509i
$609$	0.0128845	−	0.0480855i	0.000522105	−	0.00194852i
$610$	5.36323	+	4.78739i	0.217151	+	0.193836i
$611$	−28.0970	+	5.19927i	−1.13668	+	0.210340i
$612$	−4.02163	−	4.02163i	−0.162565	−	0.162565i
$613$	−7.99836	−	13.8536i	−0.323051	−	0.559540i	0.658065	−	0.752961i	$-0.271375\pi$
$613$	−7.99836	−	13.8536i	−0.323051	−	0.559540i	−0.981116	+	0.193421i	$0.938042\pi$
$614$	23.2985	−	13.4514i	0.940253	−	0.542855i
$615$	5.44593	+	16.5183i	0.219601	+	0.666083i
$616$	−0.605967	−	0.605967i	−0.0244151	−	0.0244151i
$617$	−5.29972	−	3.05979i	−0.213359	−	0.123183i	0.389513	−	0.921021i	$-0.372643\pi$
$617$	−5.29972	−	3.05979i	−0.213359	−	0.123183i	−0.602871	+	0.797838i	$0.705977\pi$
$618$	11.9002	+	6.87058i	0.478696	+	0.276375i
$619$	−1.83202	−	1.83202i	−0.0736353	−	0.0736353i	0.669330	−	0.742965i	$-0.266581\pi$
$619$	−1.83202	−	1.83202i	−0.0736353	−	0.0736353i	−0.742965	+	0.669330i	$0.766581\pi$
$620$	7.31339	−	14.5075i	0.293713	−	0.582637i
$621$	−0.186530	+	0.107693i	−0.00748518	+	0.00432157i
$622$	3.69324	+	6.39687i	0.148085	+	0.256491i
$623$	−2.86892	−	2.86892i	−0.114941	−	0.114941i
$624$	−1.55131	−	3.25476i	−0.0621022	−	0.130294i
$625$	−24.3605	+	5.61850i	−0.974419	+	0.224740i
$626$	−5.08819	+	18.9894i	−0.203365	+	0.758968i
$627$	0.554723	−	2.07025i	0.0221535	−	0.0826780i
$628$	−4.52376	+	1.21214i	−0.180518	+	0.0483696i
$629$	3.71738	−	3.71738i	0.148221	−	0.148221i
$630$	0.459867	+	1.39484i	0.0183215	+	0.0555720i
$631$	7.50451	+	28.0072i	0.298750	+	1.11495i	0.938193	+	0.346111i	$0.112498\pi$
$631$	7.50451	+	28.0072i	0.298750	+	1.11495i	−0.639444	+	0.768838i	$0.720835\pi$
$632$	−11.0648			−0.440136
$633$	4.67014	+	17.4292i	0.185622	+	0.692749i
$634$	−12.1157	−	20.9850i	−0.481175	−	0.833419i
$635$	−2.34689	+	1.53850i	−0.0931334	+	0.0610537i
$636$		−	3.66202i		−	0.145209i
$637$	15.3760	+	18.0133i	0.609221	+	0.713714i
$638$	0.0699238	−	0.0699238i	0.00276831	−	0.00276831i
$639$	−3.94410	−	1.05682i	−0.156026	−	0.0418071i
$640$	0.455475	−	2.18919i	0.0180042	−	0.0865352i
$641$	−18.3265	−	10.5808i	−0.723851	−	0.417916i	0.0923172	−	0.995730i	$-0.470573\pi$
$641$	−18.3265	−	10.5808i	−0.723851	−	0.417916i	−0.816169	+	0.577814i	$0.803906\pi$
$642$		−	12.8130i		−	0.505690i
$643$	6.77343	−	11.7319i	0.267118	−	0.462662i	−0.700998	−	0.713163i	$-0.747262\pi$
$643$	6.77343	−	11.7319i	0.267118	−	0.462662i	0.968116	+	0.250501i	$0.0805953\pi$
$644$	0.136650	−	0.0366151i	0.00538475	−	0.00144284i
$645$	14.1455	−	15.8470i	0.556980	−	0.623975i
$646$	−4.67143	+	8.09115i	−0.183795	+	0.318342i
$647$	−37.8041	−	10.1296i	−1.48623	−	0.398235i	−0.577769	−	0.816200i	$-0.696077\pi$
$647$	−37.8041	−	10.1296i	−1.48623	−	0.398235i	−0.908463	+	0.417966i	$0.862743\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	6.38791			0.250747
$650$	13.1799	+	12.3000i	0.516957	+	0.482448i
$651$	4.77229			0.187041
$652$	−1.58838	+	0.917052i	−0.0622058	+	0.0359145i
$653$	−11.6566	−	3.12337i	−0.456157	−	0.122227i	0.0234221	−	0.999726i	$-0.492544\pi$
$653$	−11.6566	−	3.12337i	−0.456157	−	0.122227i	−0.479579	+	0.877499i	$0.659210\pi$
$654$	9.20939	−	15.9511i	0.360115	−	0.623738i
$655$	21.9459	−	24.5856i	0.857497	−	0.960639i
$656$	7.51330	−	2.01318i	0.293345	−	0.0786015i
$657$	1.72410	−	2.98622i	0.0672634	−	0.116504i
$658$		−	5.20530i		−	0.202924i
$659$	18.1821	+	10.4974i	0.708273	+	0.408921i	0.810421	−	0.585848i	$-0.199238\pi$
$659$	18.1821	+	10.4974i	0.708273	+	0.408921i	−0.102149	+	0.994769i	$0.532572\pi$
$660$	−0.594268	+	2.85628i	−0.0231318	+	0.111180i
$661$	−20.7944	−	5.57184i	−0.808808	−	0.216719i	−0.169360	−	0.985554i	$-0.554170\pi$
$661$	−20.7944	−	5.57184i	−0.808808	−	0.216719i	−0.639448	+	0.768835i	$0.720837\pi$
$662$	−5.52423	+	5.52423i	−0.214705	+	0.214705i
$663$	−3.73130	−	20.1640i	−0.144912	−	0.783106i
$664$			2.20398i			0.0855309i
$665$	2.01774	−	1.32273i	0.0782446	−	0.0512934i
$666$	−0.462173	−	0.800508i	−0.0179088	−	0.0310190i
$667$	0.00422510	+	0.0157683i	0.000163596	+	0.000610550i
$668$	20.1963			0.781420
$669$	7.14177	+	26.6535i	0.276117	+	1.03048i
$670$	−9.30059	−	28.2101i	−0.359313	−	1.08985i
$671$	−2.96615	+	2.96615i	−0.114507	+	0.114507i
$672$	0.634441	−	0.169998i	0.0244741	−	0.00655781i
$673$	3.70159	−	13.8145i	0.142686	−	0.532511i	−0.857162	−	0.515048i	$-0.827774\pi$
$673$	3.70159	−	13.8145i	0.142686	−	0.532511i	0.999848	−	0.0174635i	$-0.00555908\pi$
$674$	1.17548	−	4.38695i	0.0452778	−	0.168979i
$675$	3.11300	−	3.91270i	0.119819	−	0.150600i
$676$	2.04089	−	12.8388i	0.0784958	−	0.493800i
$677$	−23.0498	−	23.0498i	−0.885875	−	0.885875i	0.108249	−	0.994124i	$-0.465476\pi$
$677$	−23.0498	−	23.0498i	−0.885875	−	0.885875i	−0.994124	+	0.108249i	$0.965476\pi$
$678$	−1.16508	−	2.01799i	−0.0447448	−	0.0775003i
$679$	−7.77551	+	4.48919i	−0.298397	+	0.172279i
$680$	5.72474	−	11.3561i	0.219534	−	0.435488i
$681$	8.80956	+	8.80956i	0.337583	+	0.337583i
$682$	8.20970	+	4.73987i	0.314366	+	0.181499i
$683$	−8.90514	−	5.14139i	−0.340746	−	0.196730i	0.319856	−	0.947466i	$-0.396365\pi$
$683$	−8.90514	−	5.14139i	−0.340746	−	0.196730i	−0.660602	+	0.750736i	$0.729699\pi$
$684$	1.16158	+	1.16158i	0.0444140	+	0.0444140i
$685$	−11.3692	−	34.4845i	−0.434396	−	1.31759i
$686$	−7.71813	+	4.45607i	−0.294680	+	0.170133i
$687$	−8.77371	−	15.1965i	−0.334738	−	0.579783i
$688$	−6.71732	−	6.71732i	−0.256095	−	0.256095i
$689$	7.48168	−	10.8793i	0.285029	−	0.414469i
$690$	−0.359297	−	0.320720i	−0.0136782	−	0.0122096i
$691$	2.69876	−	10.0719i	0.102666	−	0.383153i	−0.895404	−	0.445254i	$-0.853113\pi$
$691$	2.69876	−	10.0719i	0.102666	−	0.383153i	0.998070	+	0.0621008i	$0.0197800\pi$
$692$	−2.62932	+	9.81276i	−0.0999518	+	0.373025i
$693$	−0.827767	+	0.221799i	−0.0314443	+	0.00842546i
$694$	−13.1963	+	13.1963i	−0.500923	+	0.500923i
$695$	16.3383	−	5.38657i	0.619746	−	0.204324i
$696$	0.0196164	+	0.0732094i	0.000743558	+	0.00277499i
$697$	44.2388			1.67566
$698$	0.712266	+	2.65821i	0.0269597	+	0.100615i
$699$	14.9075	+	25.8205i	0.563852	+	0.976620i
$700$	−2.64016	+	1.95317i	−0.0997888	+	0.0738231i
$701$			48.0206i			1.81371i	0.421440	+	0.906856i	$0.361525\pi$
$701$			48.0206i			1.81371i	−0.421440	+	0.906856i	$0.638475\pi$
$702$	−3.59436	−	0.283902i	−0.135660	−	0.0107152i
$703$	−1.07370	+	1.07370i	−0.0404953	+	0.0404953i
$704$	1.26026	+	0.337686i	0.0474979	+	0.0127270i
$705$	−14.8202	+	9.71541i	−0.558161	+	0.365903i
$706$	2.10419	+	1.21485i	0.0791922	+	0.0457217i
$707$			6.91520i			0.260073i
$708$	−2.44800	+	4.24006i	−0.0920016	+	0.159351i
$709$	−16.6659	+	4.46562i	−0.625901	+	0.167710i	−0.557809	−	0.829969i	$-0.688358\pi$
$709$	−16.6659	+	4.46562i	−0.625901	+	0.167710i	−0.0680921	+	0.997679i	$0.521691\pi$
$710$	−0.517133	−	9.11573i	−0.0194077	−	0.342107i
$711$	−5.53242	+	9.58244i	−0.207482	+	0.359369i
$712$	5.96664	+	1.59876i	0.223609	+	0.0599159i
$713$	−1.35527	+	0.782468i	−0.0507554	+	0.0293037i
$714$	3.73563			0.139802
$715$	−7.60098	+	7.27146i	−0.284261	+	0.271937i
$716$	1.19493			0.0446568
$717$	0.644493	−	0.372098i	0.0240690	−	0.0138963i
$718$	29.1079	+	7.79943i	1.08630	+	0.291072i
$719$	−9.27325	+	16.0617i	−0.345834	+	0.599002i	−0.985505	−	0.169647i	$-0.945737\pi$
$719$	−9.27325	+	16.0617i	−0.345834	+	0.599002i	0.639671	+	0.768649i	$0.279071\pi$
$720$	−1.66815	−	1.48905i	−0.0621684	−	0.0554935i
$721$	−8.71794	+	2.33597i	−0.324673	+	0.0869959i
$722$	−8.15074	+	14.1175i	−0.303339	+	0.525399i
$723$			17.0775i			0.635119i
$724$	−18.2122	−	10.5148i	−0.676850	−	0.390780i
$725$	−0.225381	−	0.304654i	−0.00837043	−	0.0113146i
$726$	8.98090	+	2.40642i	0.333312	+	0.0893108i
$727$	3.86950	−	3.86950i	0.143512	−	0.143512i	−0.631701	−	0.775212i	$-0.717643\pi$
$727$	3.86950	−	3.86950i	0.143512	−	0.143512i	0.775212	+	0.631701i	$0.217643\pi$
$728$	2.23214	+	0.791152i	0.0827287	+	0.0293220i
$729$			1.00000i			0.0370370i
$730$	7.54874	+	1.57057i	0.279391	+	0.0581293i
$731$	−27.0145	−	46.7905i	−0.999169	−	1.73061i
$732$	−0.832121	−	3.10552i	−0.0307561	−	0.114783i
$733$	−45.7696			−1.69054			−0.845270	−	0.534339i	$-0.820561\pi$
$733$	−45.7696			−1.69054			−0.845270	+	0.534339i	$0.820561\pi$
$734$	−2.85418	−	10.6519i	−0.105350	−	0.393170i
$735$	13.1155	+	6.61167i	0.483774	+	0.243875i
$736$	−0.152301	+	0.152301i	−0.00561388	+	0.00561388i
$737$	16.7412	−	4.48579i	0.616670	−	0.165236i
$738$	2.01318	−	7.51330i	0.0741063	−	0.276568i
$739$	−2.54621	+	9.50257i	−0.0936637	+	0.349558i	−0.996813	−	0.0797679i	$-0.974582\pi$
$739$	−2.54621	+	9.50257i	−0.0936637	+	0.349558i	0.903150	+	0.429326i	$0.141249\pi$
$740$	1.37640	−	1.54195i	0.0505973	−	0.0566833i
$741$	1.07772	+	5.82403i	0.0395911	+	0.213951i
$742$	1.70080	+	1.70080i	0.0624383	+	0.0624383i
$743$	−15.5785	−	26.9827i	−0.571518	−	0.989899i	−0.996410	−	0.0846546i	$-0.973021\pi$
$743$	−15.5785	−	26.9827i	−0.571518	−	0.989899i	0.424892	−	0.905244i	$-0.360312\pi$
$744$	−6.29231	+	3.63287i	−0.230687	+	0.133187i
$745$	29.1391	+	14.6893i	1.06757	+	0.538173i
$746$	−2.09325	−	2.09325i	−0.0766395	−	0.0766395i
$747$	1.90870	+	1.10199i	0.0698357	+	0.0403196i
$748$	6.42635	+	3.71025i	0.234971	+	0.135660i
$749$	5.95091	+	5.95091i	0.217442	+	0.217442i
$750$	10.4887	+	3.87141i	0.382992	+	0.141364i
$751$	13.1964	−	7.61892i	0.481542	−	0.278018i	−0.239517	−	0.970892i	$-0.576989\pi$
$751$	13.1964	−	7.61892i	0.481542	−	0.278018i	0.721059	+	0.692874i	$0.243656\pi$
$752$	3.96250	+	6.86325i	0.144497	+	0.250277i
$753$	−9.92177	−	9.92177i	−0.361569	−	0.361569i
$754$	−0.0912926	+	0.257572i	−0.00332468	+	0.00938020i
$755$	1.55698	+	27.4456i	0.0566644	+	0.998848i
$756$	0.169998	−	0.634441i	0.00618276	−	0.0230744i
$757$	−12.3801	+	46.2033i	−0.449964	+	1.67929i	0.252524	+	0.967591i	$0.418739\pi$
$757$	−12.3801	+	46.2033i	−0.449964	+	1.67929i	−0.702487	+	0.711696i	$0.747927\pi$
$758$	19.7782	−	5.29955i	0.718377	−	0.192488i
$759$	0.198710	−	0.198710i	0.00721271	−	0.00721271i
$760$	−1.65349	+	3.28003i	−0.0599784	+	0.118979i
$761$	5.54307	+	20.6870i	0.200936	+	0.749904i	0.990650	+	0.136429i	$0.0435624\pi$
$761$	5.54307	+	20.6870i	0.200936	+	0.749904i	−0.789714	+	0.613476i	$0.789771\pi$
$762$	1.25498			0.0454631
$763$	3.13115	+	11.6856i	0.113355	+	0.423048i
$764$	−4.06177	−	7.03518i	−0.146950	−	0.254524i
$765$	−6.97234	−	10.6358i	−0.252086	−	0.384540i
$766$			25.0444i

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.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.48905 - 1.66815i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.328411 - 0.568824i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.48905 - 1.66815i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.328411 - 0.568824i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.455475 + 2.18919i) q^{10} +(-1.26026 - 0.337686i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.54536 - 0.656060i) q^{13} +0.656821i q^{14} +(1.87006 - 1.22592i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.47202 - 5.49364i) q^{17} -1.00000 q^{18} +(0.425167 + 1.58674i) q^{19} +(-0.700141 - 2.12363i) q^{20} +(0.464443 - 0.464443i) q^{21} +(1.26026 - 0.337686i) q^{22} +(-0.0557460 + 0.208047i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(-0.565478 - 4.96792i) q^{25} +(-2.74234 + 2.34084i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.328411 - 0.568824i) q^{28} +(0.0656377 - 0.0378960i) q^{29} +(-1.00656 + 1.99671i) q^{30} +(5.13765 + 5.13765i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.12992 - 0.652360i) q^{33} +(4.02163 + 4.02163i) q^{34} +(-0.459867 - 1.39484i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.462173 + 0.800508i) q^{37} +(-1.16158 - 1.16158i) q^{38} +(3.59436 + 0.283902i) q^{39} +(1.66815 + 1.48905i) q^{40} +(-2.01318 + 7.51330i) q^{41} +(-0.169998 + 0.634441i) q^{42} +(9.17603 - 2.45871i) q^{43} +(-0.922576 + 0.922576i) q^{44} +(2.12363 - 0.700141i) q^{45} +(-0.0557460 - 0.208047i) q^{46} -7.92499 q^{47} +(-0.258819 - 0.965926i) q^{48} +(3.28429 + 5.68856i) q^{49} +(2.97368 + 4.01961i) q^{50} -5.68744i q^{51} +(1.20452 - 3.39840i) q^{52} +(2.58944 - 2.58944i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-2.43990 + 1.59948i) q^{55} +(0.568824 + 0.328411i) q^{56} +1.64272i q^{57} +(-0.0378960 + 0.0656377i) q^{58} +(-4.72918 + 1.26718i) q^{59} +(-0.126648 - 2.23248i) q^{60} +(1.60754 - 2.78433i) q^{61} +(-7.01816 - 1.88051i) q^{62} +(0.568824 - 0.328411i) q^{63} -1.00000 q^{64} +(4.18480 - 6.89111i) q^{65} +1.30472 q^{66} +(-11.5042 + 6.64195i) q^{67} +(-5.49364 - 1.47202i) q^{68} +(-0.107693 + 0.186530i) q^{69} +(1.09568 + 0.978038i) q^{70} +(-3.94410 + 1.05682i) q^{71} +(-0.500000 + 0.866025i) q^{72} -3.44819i q^{73} +(-0.800508 - 0.462173i) q^{74} +(0.739583 - 4.94500i) q^{75} +(1.58674 + 0.425167i) q^{76} +(-0.605967 + 0.605967i) q^{77} +(-3.25476 + 1.55131i) q^{78} +11.0648i q^{79} +(-2.18919 - 0.455475i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.01318 - 7.51330i) q^{82} +2.20398 q^{83} +(-0.169998 - 0.634441i) q^{84} +(-11.3561 - 5.72474i) q^{85} +(-6.71732 + 6.71732i) q^{86} +(0.0732094 - 0.0196164i) q^{87} +(0.337686 - 1.26026i) q^{88} +(1.59876 - 5.96664i) q^{89} +(-1.48905 + 1.66815i) q^{90} +(0.791152 - 2.23214i) q^{91} +(0.152301 + 0.152301i) q^{92} +(3.63287 + 6.29231i) q^{93} +(6.86325 - 3.96250i) q^{94} +(3.28003 + 1.65349i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-11.8381 - 6.83472i) q^{97} +(-5.68856 - 3.28429i) q^{98} +(-0.922576 - 0.922576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

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