LMFDB - Embedded newform 390.2.bd.b.253.3

Newspace parameters

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
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			253.3
Root			$2.69978 - 0.355433i$ of defining polynomial
Character	$\chi$	$=$	390.253
Dual form			390.2.bd.b.37.3

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.965926 - 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.48905 + 1.66815i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.328411 + 0.568824i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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	0.921392	−	0.388636i	$-0.127053\pi$
$7$	0.328411	+	0.568824i	0.124128	+	0.214995i	−0.797264	+	0.603631i	$0.793720\pi$
$8$		−	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	−0.443755	−	0.896148i	$-0.646354\pi$
$11$	−1.26026	+	0.337686i	−0.379983	+	0.101816i	0.0637713	+	0.997965i	$0.479687\pi$
$12$	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	0.520911	+	0.853611i	$0.325592\pi$
$17$	−1.47202	+	5.49364i	−0.357017	+	1.33240i	−0.877928	+	0.478793i	$0.841074\pi$
$18$	−1.00000			−0.235702
$19$	0.425167	−	1.58674i	0.0975399	−	0.364024i	−0.899852	−	0.436195i	$-0.856326\pi$
$19$	0.425167	−	1.58674i	0.0975399	−	0.364024i	0.997392	+	0.0721707i	$0.0229926\pi$
$20$	−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	0.959870	−	0.280444i	$-0.0904818\pi$
$23$	−0.0557460	−	0.208047i	−0.0116238	−	0.0433808i	−0.971494	+	0.237063i	$0.923815\pi$
$24$	−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	0.506082	−	0.862485i	$-0.331093\pi$
$29$	0.0656377	+	0.0378960i	0.0121886	+	0.00703710i	−0.493893	+	0.869523i	$0.664427\pi$
$30$	−1.00656	−	1.99671i	−0.183772	−	0.364547i
$31$	5.13765	−	5.13765i	0.922749	−	0.922749i	−0.0744742	−	0.997223i	$-0.523728\pi$
$31$	5.13765	−	5.13765i	0.922749	−	0.922749i	0.997223	+	0.0744742i	$0.0237278\pi$
$32$	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	−0.825532	−	0.564356i	$-0.809125\pi$
$37$	0.462173	−	0.800508i	0.0759808	−	0.131603i	0.901512	+	0.432753i	$0.142458\pi$
$38$	−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	−0.924541	−	0.381082i	$-0.875551\pi$
$41$	−2.01318	−	7.51330i	−0.314406	−	1.17338i	0.610135	−	0.792298i	$-0.291115\pi$
$42$	−0.169998	−	0.634441i	−0.0262312	−	0.0978963i
$43$	9.17603	+	2.45871i	1.39933	+	0.374950i	0.878105	−	0.478469i	$-0.158808\pi$
$43$	9.17603	+	2.45871i	1.39933	+	0.374950i	0.521226	+	0.853418i	$0.325475\pi$
$44$	−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	0.862220	−	0.506533i	$-0.169073\pi$
$53$	2.58944	+	2.58944i	0.355687	+	0.355687i	−0.506533	+	0.862220i	$0.669073\pi$
$54$	−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	−0.0625204	−	0.998044i	$-0.519914\pi$
$59$	−4.72918	−	1.26718i	−0.615686	−	0.164973i	−0.553166	+	0.833071i	$0.686581\pi$
$60$	−0.126648	+	2.23248i	−0.0163502	+	0.288212i
$61$	1.60754	+	2.78433i	0.205824	+	0.356497i	0.950395	−	0.311046i	$-0.100679\pi$
$61$	1.60754	+	2.78433i	0.205824	+	0.356497i	−0.744571	+	0.667543i	$0.767346\pi$
$62$	−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	−0.410515	−	0.911854i	$-0.634651\pi$
$67$	−11.5042	−	6.64195i	−1.40546	−	0.811443i	−0.994946	+	0.100411i	$0.967984\pi$
$68$	−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	0.0170676	−	0.999854i	$-0.494567\pi$
$71$	−3.94410	−	1.05682i	−0.468079	−	0.125421i	−0.485146	+	0.874433i	$0.661234\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$			3.44819i			0.403581i	0.979429	+	0.201790i	$0.0646759\pi$
$73$			3.44819i			0.403581i	−0.979429	+	0.201790i	$0.935324\pi$
$74$	−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	$-0.786139\pi$
$79$		−	11.0648i		−	1.24489i	0.782663	−	0.622446i	$-0.213861\pi$
$80$	−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	0.997428	+	0.0716755i	$0.0228346\pi$
$89$	1.59876	+	5.96664i	0.169468	+	0.632462i	−0.827960	+	0.560787i	$0.810499\pi$
$90$	−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	−0.960994	−	0.276569i	$-0.910803\pi$
$97$	−11.8381	+	6.83472i	−1.20198	+	0.693961i	−0.240982	+	0.970530i	$0.577469\pi$
$98$	−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	−0.0277059	−	0.999616i	$-0.508820\pi$
$101$	−9.11777	−	5.26415i	−0.907252	−	0.523802i	−0.879546	+	0.475814i	$0.842154\pi$
$102$	2.84372	−	4.92547i	0.281570	−	0.487694i
$103$	−9.71646	+	9.71646i	−0.957391	+	0.957391i	−0.999129	−	0.0417373i	$-0.986711\pi$
$103$	−9.71646	+	9.71646i	−0.957391	+	0.957391i	0.0417373	+	0.999129i	$0.486711\pi$
$104$	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	−0.918667	−	0.395033i	$-0.870733\pi$
$107$	−3.31625	−	12.3764i	−0.320594	−	1.19647i	0.598073	−	0.801442i	$-0.295933\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	−13.0240	−	13.0240i	−1.24748	−	1.24748i	−0.956831	−	0.290646i	$-0.906130\pi$
$109$	−13.0240	−	13.0240i	−1.24748	−	1.24748i	−0.290646	−	0.956831i	$-0.593870\pi$
$110$	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	−0.931740	−	0.363127i	$-0.881709\pi$
$113$	0.603092	−	2.25077i	0.0567341	−	0.211735i	0.988474	+	0.151392i	$0.0483757\pi$
$114$	−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	−0.312201	−	0.950016i	$-0.601066\pi$
$127$	−1.21222	+	0.324813i	−0.107567	+	0.0288225i	0.204634	+	0.978839i	$0.434400\pi$
$128$	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	0.970626	+	0.240595i	$0.0773424\pi$
$137$	8.11924	+	14.0629i	0.693674	+	1.20148i	−0.276952	+	0.960884i	$0.589324\pi$
$138$			0.215386i			0.0183349i
$139$	6.66282	−	3.84678i	0.565133	−	0.326280i	−0.190070	−	0.981770i	$-0.560872\pi$
$139$	6.66282	−	3.84678i	0.565133	−	0.326280i	0.755203	+	0.655491i	$0.227538\pi$
$140$	−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	−0.619632	−	0.784893i	$-0.712718\pi$
$149$	3.77709	−	14.0963i	0.309431	−	1.15481i	0.929063	−	0.369921i	$-0.120615\pi$
$150$	1.83200	−	4.65229i	0.149582	−	0.379858i
$151$	−8.69302	−	8.69302i	−0.707428	−	0.707428i	0.258566	−	0.965994i	$-0.416750\pi$
$151$	−8.69302	−	8.69302i	−0.707428	−	0.707428i	−0.965994	+	0.258566i	$0.916750\pi$
$152$	−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	−0.826797	−	0.562501i	$-0.809839\pi$
$157$	−3.31162	+	3.31162i	−0.264296	+	0.264296i	0.562501	+	0.826797i	$0.309839\pi$
$158$	−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	−0.560914	−	0.827874i	$-0.689550\pi$
$163$	−1.58838	+	0.917052i	−0.124412	+	0.0718291i	0.436503	+	0.899703i	$0.356217\pi$
$164$	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	−0.149695	−	0.988732i	$-0.547829\pi$
$167$	10.0982	−	17.4905i	0.781420	−	1.35346i	0.931115	−	0.364726i	$-0.118837\pi$
$168$	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	−0.134285	−	0.990943i	$-0.542874\pi$
$173$	−9.81276	−	2.62932i	−0.746051	−	0.199904i	−0.611766	+	0.791039i	$0.709540\pi$
$174$	−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	−0.842833	−	0.538175i	$-0.819114\pi$
$179$	0.597467	−	1.03484i	0.0446568	−	0.0773478i	0.887490	+	0.460827i	$0.152447\pi$
$180$	0.455475	+	2.18919i	0.0339491	+	0.163172i
$181$			21.0296i			1.56312i	0.623831	+	0.781559i	$0.285575\pi$
$181$			21.0296i			1.56312i	−0.623831	+	0.781559i	$0.714425\pi$
$182$	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	0.974728	−	0.223394i	$-0.0717137\pi$
$191$	4.06177	+	7.03518i	0.293899	+	0.509048i	−0.680829	+	0.732442i	$0.738380\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	3.88620	+	2.24370i	0.279735	+	0.161505i	0.633303	−	0.773904i	$-0.281698\pi$
$193$	3.88620	+	2.24370i	0.279735	+	0.161505i	−0.353568	+	0.935409i	$0.615032\pi$
$194$	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	0.811301	−	0.584628i	$-0.198760\pi$
$197$	9.97443	+	5.75874i	0.710649	+	0.410293i	−0.100652	+	0.994922i	$0.532093\pi$
$198$	1.26026	−	0.337686i	0.0895629	−	0.0239983i
$199$	1.75484	+	3.03947i	0.124397	+	0.215462i	0.921497	−	0.388385i	$-0.126967\pi$
$199$	1.75484	+	3.03947i	0.124397	+	0.215462i	−0.797100	+	0.603847i	$0.793634\pi$
$200$	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	−0.368179	−	0.929755i	$-0.620019\pi$
$211$	9.02202	−	15.6266i	0.621102	−	1.07578i	0.989281	−	0.146025i	$-0.0466479\pi$
$212$	−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	0.130592	−	0.991436i	$-0.458312\pi$
$223$	13.7968	−	23.8968i	0.923905	−	1.60025i	0.793313	−	0.608814i	$-0.208354\pi$
$224$	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	−0.0972019	−	0.995265i	$-0.530989\pi$
$227$	10.7895	−	6.22930i	0.716122	−	0.413453i	0.813324	+	0.581812i	$0.197656\pi$
$228$	1.42263	−	0.821359i	0.0942163	−	0.0543958i
$229$	−12.4079	+	12.4079i	−0.819937	+	0.819937i	−0.986099	−	0.166162i	$-0.946863\pi$
$229$	−12.4079	+	12.4079i	−0.819937	+	0.819937i	0.166162	+	0.986099i	$0.446863\pi$
$230$	−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	0.538567	−	0.842582i	$-0.318966\pi$
$233$	21.0823	−	21.0823i	1.38115	−	1.38115i	0.842582	−	0.538567i	$-0.181034\pi$
$234$	−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	0.723921	−	0.689883i	$-0.242338\pi$
$239$	0.526226	+	0.526226i	0.0340388	+	0.0340388i	−0.689883	+	0.723921i	$0.742338\pi$
$240$	−1.99671	+	1.00656i	−0.128887	+	0.0649731i
$241$	4.41998	−	16.4956i	0.284716	−	1.06258i	−0.664330	−	0.747439i	$-0.731283\pi$
$241$	4.41998	−	16.4956i	0.284716	−	1.06258i	0.949046	−	0.315136i	$-0.102050\pi$
$242$	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	−0.831805	−	0.555068i	$-0.812692\pi$
$251$	−12.1516	+	7.01575i	−0.767004	+	0.442830i	0.0648005	+	0.997898i	$0.479359\pi$
$252$			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	0.302955	−	0.953005i	$-0.402027\pi$
$257$	16.7017	−	4.47521i	1.04182	−	0.279156i	0.738869	+	0.673849i	$0.235360\pi$
$258$	−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	−0.928668	−	0.370912i	$-0.879045\pi$
$263$	−25.0956	+	6.72435i	−1.54746	+	0.414641i	−0.618794	+	0.785553i	$0.712378\pi$
$264$	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	−0.983942	−	0.178490i	$-0.942879\pi$
$269$	−21.6715	+	12.5121i	−1.32134	+	0.762873i	−0.337394	+	0.941364i	$0.609545\pi$
$270$	−1.87006	−	1.22592i	−0.113808	−	0.0746071i
$271$	2.53478	−	0.679193i	0.153977	−	0.0412580i	−0.181007	−	0.983482i	$-0.557936\pi$
$271$	2.53478	−	0.679193i	0.153977	−	0.0412580i	0.334984	+	0.942224i	$0.391269\pi$
$272$	−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	0.224406	+	0.974496i	$0.427956\pi$
$277$	−7.60904	+	28.3973i	−0.457183	+	1.70623i	−0.681589	+	0.731735i	$0.738711\pi$
$278$	−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	0.326550	−	0.945180i	$-0.394114\pi$
$281$	−10.3701	−	10.3701i	−0.618630	−	0.618630i	−0.945180	+	0.326550i	$0.894114\pi$
$282$	7.65496	+	2.05114i	0.455846	+	0.122144i
$283$	3.02271	+	11.2809i	0.179681	+	0.670580i	0.995707	+	0.0925637i	$0.0295062\pi$
$283$	3.02271	+	11.2809i	0.179681	+	0.670580i	−0.816025	+	0.578016i	$0.803827\pi$
$284$	−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	−0.181841	−	0.983328i	$-0.558206\pi$
$293$	9.90790	−	5.72033i	0.578825	−	0.334185i	0.760666	+	0.649143i	$0.224872\pi$
$294$	−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	$0.0671590\pi$
$311$			7.38647i			0.418849i	−0.977825	+	0.209424i	$0.932841\pi$
$312$	−0.283902	−	3.59436i	−0.0160728	−	0.203490i
$313$	13.9012	+	13.9012i	0.785742	+	0.785742i	0.980793	−	0.195051i	$-0.0624873\pi$
$313$	13.9012	+	13.9012i	0.785742	+	0.785742i	−0.195051	+	0.980793i	$0.562487\pi$
$314$	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	$-0.761770\pi$
$317$		−	24.2313i		−	1.36097i	0.732763	−	0.680484i	$-0.238230\pi$
$318$	−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	0.460173	−	0.887830i	$-0.347788\pi$
$331$	7.54624	+	2.02201i	0.414779	+	0.111140i	−0.0453937	+	0.998969i	$0.514454\pi$
$332$	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	0.614206	−	0.789146i	$-0.289476\pi$
$337$	−3.21147	−	3.21147i	−0.174940	−	0.174940i	−0.789146	+	0.614206i	$0.789476\pi$
$338$	−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	0.707861	−	0.706352i	$-0.249660\pi$
$347$	18.0264	+	4.83017i	0.967710	+	0.259297i	0.259849	+	0.965649i	$0.416327\pi$
$348$	0.0196164	+	0.0732094i	0.00105155	+	0.00392444i
$349$	0.712266	+	2.65821i	0.0381267	+	0.142291i	0.982366	−	0.186971i	$-0.0598669\pi$
$349$	0.712266	+	2.65821i	0.0381267	+	0.142291i	−0.944239	+	0.329261i	$0.893200\pi$
$350$	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	−0.896543	−	0.442956i	$-0.853930\pi$
$353$	−1.21485	+	2.10419i	−0.0646602	+	0.111995i	0.831883	+	0.554951i	$0.187263\pi$
$354$	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	−0.133578	+	0.991038i	$0.542647\pi$
$359$	−21.3084	+	21.3084i	−1.12462	+	1.12462i	−0.991038	+	0.133578i	$0.957353\pi$
$360$	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	−0.999545	−	0.0301464i	$-0.990403\pi$
$367$	−2.85418	−	10.6519i	−0.148987	−	0.556027i	0.850559	−	0.525880i	$-0.176264\pi$
$368$	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	−0.943249	−	0.332086i	$-0.892248\pi$
$373$	0.766184	−	2.85944i	0.0396715	−	0.148056i	0.982921	+	0.184030i	$0.0589143\pi$
$374$	−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	−0.728109	−	0.685462i	$-0.759600\pi$
$379$	−19.7782	+	5.29955i	−1.01594	+	0.272220i	−0.287830	+	0.957682i	$0.592934\pi$
$380$	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	0.985464	+	0.169882i	$0.0543388\pi$
$383$	12.5222	+	21.6891i	0.639855	+	1.10826i	−0.345610	+	0.938378i	$0.612328\pi$
$384$	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	0.999573	+	0.0292254i	$0.00930406\pi$
$397$	10.4625	+	18.1215i	0.525096	+	0.909494i	−0.474476	+	0.880268i	$0.657363\pi$
$398$		−	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	0.542105	−	0.840311i	$-0.317628\pi$
$401$	28.6705	−	7.68224i	1.43174	−	0.383633i	0.889632	+	0.456678i	$0.150961\pi$
$402$	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	0.817401	+	0.576069i	$0.195414\pi$
$409$	−3.61041	+	13.4742i	−0.178523	+	0.666259i	−0.995925	+	0.0901897i	$0.971253\pi$
$410$	−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	0.647297	−	0.762238i	$-0.275899\pi$
$419$	6.36248	+	3.67338i	0.310827	+	0.179456i	−0.336469	+	0.941694i	$0.609233\pi$
$420$	−1.31148	+	0.661129i	−0.0639936	+	0.0322598i
$421$	11.2103	−	11.2103i	0.546356	−	0.546356i	−0.379029	−	0.925385i	$-0.623742\pi$
$421$	11.2103	−	11.2103i	0.546356	−	0.546356i	0.925385	+	0.379029i	$0.123742\pi$
$422$	−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	0.676672	+	0.736285i	$0.263422\pi$
$431$	9.52492	+	35.5475i	0.458799	+	1.71226i	−0.217872	+	0.975977i	$0.569912\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	8.17993	+	2.19180i	0.393102	+	0.105331i	0.449955	−	0.893051i	$-0.351440\pi$
$433$	8.17993	+	2.19180i	0.393102	+	0.105331i	−0.0568530	+	0.998383i	$0.518107\pi$
$434$	−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	−0.570317	−	0.821425i	$-0.693180\pi$
$439$	8.93023	−	15.4676i	0.426216	−	0.738229i	0.996533	+	0.0831963i	$0.0265129\pi$
$440$	−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	0.639921	−	0.768440i	$-0.278967\pi$
$443$	−2.70502	−	2.70502i	−0.128519	−	0.128519i	−0.768440	+	0.639921i	$0.778967\pi$
$444$	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	−0.0237652	−	0.999718i	$-0.507565\pi$
$449$	−11.5315	−	3.08986i	−0.544205	−	0.145819i	−0.520440	+	0.853898i	$0.674232\pi$
$450$	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	0.978167	+	0.207821i	$0.0666373\pi$
$457$	35.2137	+	20.3307i	1.64723	+	0.951028i	0.669062	+	0.743207i	$0.266696\pi$
$458$	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	0.878359	−	0.478001i	$-0.158639\pi$
$461$	30.0601	+	8.05459i	1.40004	+	0.375139i	0.521681	+	0.853141i	$0.325305\pi$
$462$	0.428484	+	0.742155i	0.0199349	+	0.0345282i
$463$		−	13.3638i		−	0.621069i	−0.950562	−	0.310534i	$-0.899492\pi$
$463$		−	13.3638i		−	0.621069i	0.950562	−	0.310534i	$-0.100508\pi$
$464$	−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	0.240123	−	0.970742i	$-0.422812\pi$
$467$	−15.7888	−	15.7888i	−0.730619	−	0.730619i	−0.970742	+	0.240123i	$0.922812\pi$
$468$	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	0.843674	+	0.536856i	$0.180388\pi$
$479$	8.34864	+	31.1575i	0.381459	+	1.42362i	−0.462215	+	0.886768i	$0.652945\pi$
$480$	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	−0.736296	−	0.676659i	$-0.763427\pi$
$487$	−11.4410	+	6.60545i	−0.518440	+	0.299321i	0.217856	+	0.975981i	$0.430094\pi$
$488$	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	−0.0557297	−	0.998446i	$-0.517749\pi$
$491$	−21.0123	−	12.1315i	−0.948274	−	0.547486i	−0.892544	+	0.450960i	$0.851082\pi$
$492$	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	0.998117	+	0.0613431i	$0.0195384\pi$
$499$	23.6665	+	23.6665i	1.05946	+	1.05946i	0.0613431	+	0.998117i	$0.480462\pi$
$500$	−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	−0.713314	−	0.700845i	$-0.752807\pi$
$503$	5.71583	−	21.3318i	0.254856	−	0.951137i	0.968170	−	0.250292i	$-0.0805267\pi$
$504$	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	−0.624459	−	0.781058i	$-0.714680\pi$
$509$	−17.4786	+	4.68339i	−0.774727	+	0.207588i	−0.150268	+	0.988645i	$0.548014\pi$
$510$	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	−0.941539	+	0.336905i	$0.890620\pi$
$523$	−44.0321	+	11.7984i	−1.92539	+	0.515906i	−0.983849	+	0.179001i	$0.942713\pi$
$524$	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	0.532247	−	0.846589i	$-0.321348\pi$
$541$	−7.31140	−	7.31140i	−0.314342	−	0.314342i	−0.846589	+	0.532247i	$0.821348\pi$
$542$	−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	−0.394857	+	0.918742i	$0.629206\pi$
$547$	−30.7225	+	30.7225i	−1.31360	+	1.31360i	−0.918742	+	0.394857i	$0.870794\pi$
$548$	−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	−0.985576	−	0.169234i	$-0.945871\pi$
$557$	−8.17126	+	14.1530i	−0.346227	+	0.599683i	0.639349	+	0.768917i	$0.279204\pi$
$558$	−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	0.621085	−	0.783743i	$-0.286692\pi$
$563$	18.2012	+	4.87699i	0.767088	+	0.205541i	0.146003	+	0.989284i	$0.453359\pi$
$564$	−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	−0.723936	−	0.689867i	$-0.757669\pi$
$569$	5.61694	−	9.72882i	0.235474	−	0.407853i	0.959410	+	0.282014i	$0.0910023\pi$
$570$	−3.59622	+	0.748217i	−0.150629	+	0.0313394i
$571$			38.3139i			1.60339i	0.597735	+	0.801693i	$0.296067\pi$
$571$			38.3139i			1.60339i	−0.597735	+	0.801693i	$0.703933\pi$
$572$	−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	$0.122793\pi$
$577$			18.0766i			0.752540i	−0.926510	+	0.376270i	$0.877207\pi$
$578$	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	0.744071	−	0.668101i	$-0.232892\pi$
$587$	13.0229	+	7.51880i	0.537514	+	0.310334i	−0.206557	+	0.978435i	$0.566226\pi$
$588$	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	$-0.728761\pi$
$593$		−	36.6579i		−	1.50536i	0.658387	−	0.752680i	$-0.271239\pi$
$594$	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	$0.0593860\pi$
$599$			9.07935i			0.370972i	−0.982647	+	0.185486i	$0.940614\pi$
$600$	4.94500	−	0.739583i	0.201879	−	0.0301933i
$601$	17.2295	−	29.8423i	0.702805	−	1.21729i	−0.264673	−	0.964338i	$-0.585264\pi$
$601$	17.2295	−	29.8423i	0.702805	−	1.21729i	0.967478	−	0.252956i	$-0.0814027\pi$
$602$	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	0.774658	−	0.632381i	$-0.217922\pi$
$607$	27.8240	+	7.45542i	1.12934	+	0.302606i	0.354683	+	0.934987i	$0.384589\pi$
$608$	−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	−0.981116	−	0.193421i	$-0.938042\pi$
$613$	−7.99836	+	13.8536i	−0.323051	+	0.559540i	0.658065	+	0.752961i	$0.271375\pi$
$614$	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	−0.602871	−	0.797838i	$-0.705977\pi$
$617$	−5.29972	+	3.05979i	−0.213359	+	0.123183i	0.389513	+	0.921021i	$0.372643\pi$
$618$	11.9002	−	6.87058i	0.478696	−	0.276375i
$619$	−1.83202	+	1.83202i	−0.0736353	+	0.0736353i	−0.742965	−	0.669330i	$-0.766581\pi$
$619$	−1.83202	+	1.83202i	−0.0736353	+	0.0736353i	0.669330	+	0.742965i	$0.266581\pi$
$620$	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	−0.639444	−	0.768838i	$-0.720835\pi$
$631$	7.50451	−	28.0072i	0.298750	−	1.11495i	0.938193	−	0.346111i	$-0.112498\pi$
$632$	−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	−0.816169	−	0.577814i	$-0.803906\pi$
$641$	−18.3265	+	10.5808i	−0.723851	+	0.417916i	0.0923172	+	0.995730i	$0.470573\pi$
$642$			12.8130i			0.505690i
$643$	6.77343	+	11.7319i	0.267118	+	0.462662i	0.968116	−	0.250501i	$-0.0805953\pi$
$643$	6.77343	+	11.7319i	0.267118	+	0.462662i	−0.700998	+	0.713163i	$0.747262\pi$
$644$	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	−0.908463	−	0.417966i	$-0.862743\pi$
$647$	−37.8041	+	10.1296i	−1.48623	+	0.398235i	−0.577769	+	0.816200i	$0.696077\pi$
$648$	−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	−0.479579	−	0.877499i	$-0.659210\pi$
$653$	−11.6566	+	3.12337i	−0.456157	+	0.122227i	0.0234221	+	0.999726i	$0.492544\pi$
$654$	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	−0.102149	−	0.994769i	$-0.532572\pi$
$659$	18.1821	−	10.4974i	0.708273	−	0.408921i	0.810421	+	0.585848i	$0.199238\pi$
$660$	−0.594268	−	2.85628i	−0.0231318	−	0.111180i
$661$	−20.7944	+	5.57184i	−0.808808	+	0.216719i	−0.639448	−	0.768835i	$-0.720837\pi$
$661$	−20.7944	+	5.57184i	−0.808808	+	0.216719i	−0.169360	+	0.985554i	$0.554170\pi$
$662$	−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	0.999848	+	0.0174635i	$0.00555908\pi$
$673$	3.70159	+	13.8145i	0.142686	+	0.532511i	−0.857162	+	0.515048i	$0.827774\pi$
$674$	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	−0.994124	−	0.108249i	$-0.965476\pi$
$677$	−23.0498	+	23.0498i	−0.885875	+	0.885875i	0.108249	+	0.994124i	$0.465476\pi$
$678$	−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	−0.660602	−	0.750736i	$-0.729699\pi$
$683$	−8.90514	+	5.14139i	−0.340746	+	0.196730i	0.319856	+	0.947466i	$0.396365\pi$
$684$	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	0.998070	−	0.0621008i	$-0.0197800\pi$
$691$	2.69876	+	10.0719i	0.102666	+	0.383153i	−0.895404	+	0.445254i	$0.853113\pi$
$692$	−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	$-0.638475\pi$
$701$		−	48.0206i		−	1.81371i	0.421440	−	0.906856i	$-0.361525\pi$
$702$	−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	−0.0680921	−	0.997679i	$-0.521691\pi$
$709$	−16.6659	−	4.46562i	−0.625901	−	0.167710i	−0.557809	+	0.829969i	$0.688358\pi$
$710$	−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	0.639671	−	0.768649i	$-0.279071\pi$
$719$	−9.27325	−	16.0617i	−0.345834	−	0.599002i	−0.985505	+	0.169647i	$0.945737\pi$
$720$	−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	0.775212	−	0.631701i	$-0.217643\pi$
$727$	3.86950	+	3.86950i	0.143512	+	0.143512i	−0.631701	+	0.775212i	$0.717643\pi$
$728$	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	0.903150	−	0.429326i	$-0.141249\pi$
$739$	−2.54621	−	9.50257i	−0.0936637	−	0.349558i	−0.996813	+	0.0797679i	$0.974582\pi$
$740$	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	0.424892	+	0.905244i	$0.360312\pi$
$743$	−15.5785	+	26.9827i	−0.571518	+	0.989899i	−0.996410	+	0.0846546i	$0.973021\pi$
$744$	−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	0.721059	−	0.692874i	$-0.243656\pi$
$751$	13.1964	+	7.61892i	0.481542	+	0.278018i	−0.239517	+	0.970892i	$0.576989\pi$
$752$	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	−0.702487	−	0.711696i	$-0.747927\pi$
$757$	−12.3801	−	46.2033i	−0.449964	−	1.67929i	0.252524	−	0.967591i	$-0.418739\pi$
$758$	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	−0.789714	−	0.613476i	$-0.789771\pi$
$761$	5.54307	−	20.6870i	0.200936	−	0.749904i	0.990650	−	0.136429i	$-0.0435624\pi$
$762$	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		−	0.904891i
$767$	−15.9353	−	7.59523i	−0.575390	−	0.274248i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	22.8775	−	6.13001i	0.824984	−	0.221054i	0.178460	−	0.983947i	$-0.442889\pi$
$769$	22.8775	−	6.13001i	0.824984	−	0.221054i

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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