LMFDB - Embedded newform 936.2.ed.c.739.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			739.12
Character	$\chi$	$=$	936.739
Dual form			936.2.ed.c.19.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39432 - 0.236374i) q^{2} +(1.88825 - 0.659163i) q^{4} +(-1.86647 + 1.86647i) q^{5} +(4.71214 - 1.26261i) q^{7} +(2.47702 - 1.36542i) q^{8} +(-2.16128 + 3.04365i) q^{10} +(1.99964 + 0.535801i) q^{11} +(-3.15234 + 1.75007i) q^{13} +(6.27177 - 2.87431i) q^{14} +(3.13101 - 2.48933i) q^{16} +(-3.84928 - 2.22238i) q^{17} +(2.62661 - 0.703799i) q^{19} +(-2.29407 + 4.75469i) q^{20} +(2.91478 + 0.274415i) q^{22} +(3.41537 + 5.91559i) q^{23} -1.96745i q^{25} +(-3.98170 + 3.18529i) q^{26} +(8.06544 - 5.49020i) q^{28} +(0.143621 - 0.0829197i) q^{29} +(3.77330 - 3.77330i) q^{31} +(3.77721 - 4.21102i) q^{32} +(-5.89244 - 2.18884i) q^{34} +(-6.43844 + 11.1517i) q^{35} +(-1.19716 + 4.46786i) q^{37} +(3.49598 - 1.60218i) q^{38} +(-2.07478 + 7.17181i) q^{40} +(2.06622 - 7.71126i) q^{41} +(-7.03012 - 4.05884i) q^{43} +(4.12900 - 0.306357i) q^{44} +(6.16041 + 7.44092i) q^{46} +(1.87036 + 1.87036i) q^{47} +(14.5479 - 8.39921i) q^{49} +(-0.465055 - 2.74326i) q^{50} +(-4.79885 + 5.38248i) q^{52} +8.22085i q^{53} +(-4.73233 + 2.73221i) q^{55} +(9.94806 - 9.56155i) q^{56} +(0.180654 - 0.149565i) q^{58} +(-0.352439 - 1.31532i) q^{59} +(0.601045 + 0.347013i) q^{61} +(4.36928 - 6.15310i) q^{62} +(4.27127 - 6.76434i) q^{64} +(2.61731 - 9.15022i) q^{65} +(1.26441 - 4.71883i) q^{67} +(-8.73333 - 1.65912i) q^{68} +(-6.34127 + 17.0709i) q^{70} +(-2.46409 - 9.19612i) q^{71} +(-11.2670 + 11.2670i) q^{73} +(-0.613136 + 6.51261i) q^{74} +(4.49579 - 3.06032i) q^{76} +10.0991 q^{77} +9.91660i q^{79} +(-1.19767 + 10.4902i) q^{80} +(1.05824 - 11.2404i) q^{82} +(-3.88441 - 3.88441i) q^{83} +(11.3326 - 3.03656i) q^{85} +(-10.7616 - 3.99758i) q^{86} +(5.68474 - 1.40315i) q^{88} +(-13.1559 - 3.52510i) q^{89} +(-12.6446 + 12.2267i) q^{91} +(10.3484 + 8.91886i) q^{92} +(3.04998 + 2.16577i) q^{94} +(-3.58888 + 6.21613i) q^{95} +(-1.52421 + 0.408410i) q^{97} +(18.2990 - 15.1499i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{2} + 4 q^{8} - 6 q^{10} - 20 q^{11} + 28 q^{14} + 4 q^{16} - 12 q^{17} + 20 q^{19} - 4 q^{20} + 14 q^{22} + 12 q^{26} - 2 q^{28} + 18 q^{32} - 12 q^{35} + 52 q^{40} + 36 q^{41} + 12 q^{43} - 12 q^{44}+ \cdots + 6 q^{98}+O(q^{100}) $ 48 * q - 2 * q^2 + 4 * q^8 - 6 * q^10 - 20 * q^11 + 28 * q^14 + 4 * q^16 - 12 * q^17 + 20 * q^19 - 4 * q^20 + 14 * q^22 + 12 * q^26 - 2 * q^28 + 18 * q^32 - 12 * q^35 + 52 * q^40 + 36 * q^41 + 12 * q^43 - 12 * q^44 - 14 * q^46 + 24 * q^49 + 32 * q^50 + 24 * q^52 + 54 * q^56 - 22 * q^58 - 96 * q^59 + 108 * q^62 + 52 * q^65 - 12 * q^67 + 6 * q^68 - 52 * q^70 - 48 * q^73 + 114 * q^76 + 16 * q^80 - 60 * q^82 - 48 * q^83 - 24 * q^86 + 102 * q^88 - 80 * q^89 - 152 * q^91 + 100 * q^92 - 10 * q^94 - 64 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.39432	−	0.236374i	0.985933	−	0.167142i
$2$	1.39432	−	0.236374i	0.985933	−	0.167142i
$3$		0			0
$3$		0			0
$4$	1.88825	−	0.659163i	0.944127	−	0.329581i
$5$	−1.86647	+	1.86647i	−0.834713	+	0.834713i	−0.988157	−	0.153445i	$-0.950963\pi$
$5$	−1.86647	+	1.86647i	−0.834713	+	0.834713i	0.153445	+	0.988157i	$0.450963\pi$
$6$		0			0
$7$	4.71214	−	1.26261i	1.78102	−	0.477223i	0.790251	−	0.612784i	$-0.209950\pi$
$7$	4.71214	−	1.26261i	1.78102	−	0.477223i	0.990769	+	0.135561i	$0.0432836\pi$
$8$	2.47702	−	1.36542i	0.875759	−	0.482748i
$9$		0			0
$10$	−2.16128	+	3.04365i	−0.683455	+	0.962486i
$11$	1.99964	+	0.535801i	0.602913	+	0.161550i	0.547348	−	0.836905i	$-0.315637\pi$
$11$	1.99964	+	0.535801i	0.602913	+	0.161550i	0.0555651	+	0.998455i	$0.482304\pi$
$12$		0			0
$13$	−3.15234	+	1.75007i	−0.874303	+	0.485381i
$13$	−3.15234	+	1.75007i	−0.874303	+	0.485381i
$14$	6.27177	−	2.87431i	1.67620	−	0.768193i
$15$		0			0
$16$	3.13101	−	2.48933i	0.782752	−	0.622333i
$17$	−3.84928	−	2.22238i	−0.933587	−	0.539007i	−0.0456428	−	0.998958i	$-0.514534\pi$
$17$	−3.84928	−	2.22238i	−0.933587	−	0.539007i	−0.887944	+	0.459951i	$0.847867\pi$
$18$		0			0
$19$	2.62661	−	0.703799i	0.602586	−	0.161462i	0.0553871	−	0.998465i	$-0.482361\pi$
$19$	2.62661	−	0.703799i	0.602586	−	0.161462i	0.547199	+	0.837002i	$0.315694\pi$
$20$	−2.29407	+	4.75469i	−0.512969	+	1.06318i
$21$		0			0
$22$	2.91478	+	0.274415i	0.621434	+	0.0585055i
$23$	3.41537	+	5.91559i	0.712154	+	1.23349i	0.964047	+	0.265732i	$0.0856135\pi$
$23$	3.41537	+	5.91559i	0.712154	+	1.23349i	−0.251893	+	0.967755i	$0.581053\pi$
$24$		0			0
$25$		−	1.96745i		−	0.393490i
$26$	−3.98170	+	3.18529i	−0.780876	+	0.624686i
$27$		0			0
$28$	8.06544	−	5.49020i	1.52423	−	1.03755i
$29$	0.143621	−	0.0829197i	0.0266698	−	0.0153978i	−0.486606	−	0.873622i	$-0.661765\pi$
$29$	0.143621	−	0.0829197i	0.0266698	−	0.0153978i	0.513276	+	0.858224i	$0.328432\pi$
$30$		0			0
$31$	3.77330	−	3.77330i	0.677705	−	0.677705i	−0.281775	−	0.959480i	$-0.590923\pi$
$31$	3.77330	−	3.77330i	0.677705	−	0.677705i	0.959480	+	0.281775i	$0.0909233\pi$
$32$	3.77721	−	4.21102i	0.667723	−	0.744410i
$33$		0			0
$34$	−5.89244	−	2.18884i	−1.01054	−	0.375383i
$35$	−6.43844	+	11.1517i	−1.08830	+	1.88498i
$36$		0			0
$37$	−1.19716	+	4.46786i	−0.196812	+	0.734512i	0.794978	+	0.606638i	$0.207482\pi$
$37$	−1.19716	+	4.46786i	−0.196812	+	0.734512i	−0.991790	+	0.127874i	$0.959185\pi$
$38$	3.49598	−	1.60218i	0.567122	−	0.259909i
$39$		0			0
$40$	−2.07478	+	7.17181i	−0.328051	+	1.13396i
$41$	2.06622	−	7.71126i	0.322690	−	1.20430i	−0.593924	−	0.804521i	$-0.702422\pi$
$41$	2.06622	−	7.71126i	0.322690	−	1.20430i	0.916614	−	0.399774i	$-0.130911\pi$
$42$		0			0
$43$	−7.03012	−	4.05884i	−1.07208	−	0.618968i	−0.143334	−	0.989674i	$-0.545782\pi$
$43$	−7.03012	−	4.05884i	−1.07208	−	0.618968i	−0.928750	+	0.370707i	$0.879116\pi$
$44$	4.12900	−	0.306357i	0.622471	−	0.0461851i
$45$		0			0
$46$	6.16041	+	7.44092i	0.908303	+	1.09710i
$47$	1.87036	+	1.87036i	0.272820	+	0.272820i	0.830234	−	0.557415i	$-0.188207\pi$
$47$	1.87036	+	1.87036i	0.272820	+	0.272820i	−0.557415	+	0.830234i	$0.688207\pi$
$48$		0			0
$49$	14.5479	−	8.39921i	2.07826	−	1.19989i
$50$	−0.465055	−	2.74326i	−0.0657687	−	0.387955i
$51$		0			0
$52$	−4.79885	+	5.38248i	−0.665480	+	0.746415i
$53$			8.22085i			1.12922i	0.825358	+	0.564610i	$0.190974\pi$
$53$			8.22085i			1.12922i	−0.825358	+	0.564610i	$0.809026\pi$
$54$		0			0
$55$	−4.73233	+	2.73221i	−0.638107	+	0.368411i
$56$	9.94806	−	9.56155i	1.32937	−	1.27772i
$57$		0			0
$58$	0.180654	−	0.149565i	0.0237210	−	0.0196388i
$59$	−0.352439	−	1.31532i	−0.0458837	−	0.171240i	0.939182	−	0.343420i	$-0.111586\pi$
$59$	−0.352439	−	1.31532i	−0.0458837	−	0.171240i	−0.985065	+	0.172180i	$0.944919\pi$
$60$		0			0
$61$	0.601045	+	0.347013i	0.0769559	+	0.0444305i	0.537984	−	0.842955i	$-0.319186\pi$
$61$	0.601045	+	0.347013i	0.0769559	+	0.0444305i	−0.461028	+	0.887385i	$0.652519\pi$
$62$	4.36928	−	6.15310i	0.554899	−	0.781445i
$63$		0			0
$64$	4.27127	−	6.76434i	0.533908	−	0.845542i
$65$	2.61731	−	9.15022i	0.324638	−	1.13495i
$66$		0			0
$67$	1.26441	−	4.71883i	0.154472	−	0.576497i	−0.844678	−	0.535275i	$-0.820208\pi$
$67$	1.26441	−	4.71883i	0.154472	−	0.576497i	0.999150	−	0.0412224i	$-0.0131252\pi$
$68$	−8.73333	−	1.65912i	−1.05907	−	0.201198i
$69$		0			0
$70$	−6.34127	+	17.0709i	−0.757927	+	2.04037i
$71$	−2.46409	−	9.19612i	−0.292434	−	1.09138i	−0.943234	−	0.332129i	$-0.892233\pi$
$71$	−2.46409	−	9.19612i	−0.292434	−	1.09138i	0.650800	−	0.759249i	$-0.274434\pi$
$72$		0			0
$73$	−11.2670	+	11.2670i	−1.31870	+	1.31870i	−0.403895	+	0.914805i	$0.632344\pi$
$73$	−11.2670	+	11.2670i	−1.31870	+	1.31870i	−0.914805	+	0.403895i	$0.867656\pi$
$74$	−0.613136	+	6.51261i	−0.0712756	+	0.757075i
$75$		0			0
$76$	4.49579	−	3.06032i	0.515703	−	0.351042i
$77$	10.0991			1.15090
$78$		0			0
$79$			9.91660i			1.11570i	0.829940	+	0.557852i	$0.188374\pi$
$79$			9.91660i			1.11570i	−0.829940	+	0.557852i	$0.811626\pi$
$80$	−1.19767	+	10.4902i	−0.133904	+	1.17284i
$81$		0			0
$82$	1.05824	−	11.2404i	0.116863	−	1.24129i
$83$	−3.88441	−	3.88441i	−0.426369	−	0.426369i	0.461020	−	0.887390i	$-0.347483\pi$
$83$	−3.88441	−	3.88441i	−0.426369	−	0.426369i	−0.887390	+	0.461020i	$0.847483\pi$
$84$		0			0
$85$	11.3326	−	3.03656i	1.22919	−	0.329361i
$86$	−10.7616	−	3.99758i	−1.16046	−	0.431071i
$87$		0			0
$88$	5.68474	−	1.40315i	0.605995	−	0.149576i
$89$	−13.1559	−	3.52510i	−1.39452	−	0.373660i	−0.518145	−	0.855293i	$-0.673377\pi$
$89$	−13.1559	−	3.52510i	−1.39452	−	0.373660i	−0.876373	+	0.481632i	$0.840044\pi$
$90$		0			0
$91$	−12.6446	+	12.2267i	−1.32552	+	1.28171i
$92$	10.3484	+	8.91886i	1.07890	+	0.929856i
$93$		0			0
$94$	3.04998	+	2.16577i	0.314581	+	0.223382i
$95$	−3.58888	+	6.21613i	−0.368212	+	0.637761i
$96$		0			0
$97$	−1.52421	+	0.408410i	−0.154760	+	0.0414678i	−0.335367	−	0.942088i	$-0.608860\pi$
$97$	−1.52421	+	0.408410i	−0.154760	+	0.0414678i	0.180607	+	0.983555i	$0.442194\pi$
$98$	18.2990	−	15.1499i	1.84848	−	1.53037i
$99$		0			0
$100$	−1.29687	−	3.71505i	−0.129687	−	0.371505i
$101$	1.42809	+	2.47353i	0.142101	+	0.246126i	0.928287	−	0.371863i	$-0.121281\pi$
$101$	1.42809	+	2.47353i	0.142101	+	0.246126i	−0.786187	+	0.617989i	$0.787948\pi$
$102$		0			0
$103$	−10.1257			−0.997716			−0.498858	−	0.866684i	$-0.666247\pi$
$103$	−10.1257			−0.997716			−0.498858	+	0.866684i	$0.666247\pi$
$104$	−5.41885	+	8.63922i	−0.531362	+	0.847145i
$105$		0			0
$106$	1.94320	+	11.4625i	0.188740	+	1.11334i
$107$	−5.08478	−	8.80709i	−0.491564	−	0.851414i	0.508389	−	0.861128i	$-0.330241\pi$
$107$	−5.08478	−	8.80709i	−0.491564	−	0.851414i	−0.999953	+	0.00971375i	$0.996908\pi$
$108$		0			0
$109$	−5.06478	+	5.06478i	−0.485118	+	0.485118i	−0.906761	−	0.421644i	$-0.861453\pi$
$109$	−5.06478	+	5.06478i	−0.485118	+	0.485118i	0.421644	+	0.906761i	$0.361453\pi$
$110$	−5.95256	+	4.92818i	−0.567554	+	0.469883i
$111$		0			0
$112$	11.6107	−	15.6833i	1.09711	−	1.48194i
$113$	0.373640	−	0.647164i	0.0351491	−	0.0608801i	−0.847916	−	0.530131i	$-0.822143\pi$
$113$	0.373640	−	0.647164i	0.0351491	−	0.0608801i	0.883065	+	0.469251i	$0.155476\pi$
$114$		0			0
$115$	−17.4160	−	4.66660i	−1.62405	−	0.435163i
$116$	0.216536	−	0.251243i	0.0201048	−	0.0233273i
$117$		0			0
$118$	−0.802321	−	1.75067i	−0.0738596	−	0.161162i
$119$	−20.9443	−	5.61202i	−1.91996	−	0.514453i
$120$		0			0
$121$	−5.81481	−	3.35718i	−0.528619	−	0.305198i
$122$	0.920073	+	0.341776i	0.0832995	+	0.0309429i
$123$		0			0
$124$	4.63773	−	9.61217i	0.416481	−	0.863199i
$125$	−5.66017	−	5.66017i	−0.506261	−	0.506261i
$126$		0			0
$127$	−8.06962	−	13.9770i	−0.716063	−	1.24026i	−0.962548	−	0.271111i	$-0.912609\pi$
$127$	−8.06962	−	13.9770i	−0.716063	−	1.24026i	0.246485	−	0.969147i	$-0.420724\pi$
$128$	4.35660	−	10.4413i	0.385072	−	0.922886i
$129$		0			0
$130$	1.48649	−	13.3770i	0.130374	−	1.17324i
$131$	−16.6579			−1.45540			−0.727702	−	0.685894i	$-0.759412\pi$
$131$	−16.6579			−1.45540			−0.727702	+	0.685894i	$0.759412\pi$
$132$		0			0
$133$	11.4883	−	6.63279i	0.996164	−	0.575136i
$134$	0.647577	−	6.87843i	0.0559421	−	0.594206i
$135$		0			0
$136$	−12.5692	−	0.249012i	−1.07780	−	0.0213526i
$137$	0.760062	+	2.83659i	0.0649365	+	0.242346i	0.990763	−	0.135601i	$-0.0432966\pi$
$137$	0.760062	+	2.83659i	0.0649365	+	0.242346i	−0.925827	+	0.377948i	$0.876630\pi$
$138$		0			0
$139$	1.89159	−	3.27634i	0.160443	−	0.277895i	−0.774585	−	0.632470i	$-0.782041\pi$
$139$	1.89159	−	3.27634i	0.160443	−	0.277895i	0.935028	+	0.354575i	$0.115374\pi$
$140$	−4.80663	+	25.3013i	−0.406234	+	2.13835i
$141$		0			0
$142$	−5.60946	−	12.2399i	−0.470735	−	1.02715i
$143$	−7.24123	+	1.81047i	−0.605542	+	0.151399i
$144$		0			0
$145$	−0.113298	+	0.422832i	−0.00940885	+	0.0351143i
$146$	−13.0465	+	18.3730i	−1.07974	+	1.52056i
$147$		0			0
$148$	0.684505	+	9.22558i	0.0562660	+	0.758338i
$149$	−4.90868	−	18.3194i	−0.402134	−	1.50079i	−0.809280	−	0.587423i	$-0.800143\pi$
$149$	−4.90868	−	18.3194i	−0.402134	−	1.50079i	0.407146	−	0.913363i	$-0.366524\pi$
$150$		0			0
$151$	7.95676	+	7.95676i	0.647512	+	0.647512i	0.952391	−	0.304879i	$-0.0986160\pi$
$151$	7.95676	+	7.95676i	0.647512	+	0.647512i	−0.304879	+	0.952391i	$0.598616\pi$
$152$	5.54520	−	5.32975i	0.449775	−	0.432300i
$153$		0			0
$154$	14.0813	−	2.38716i	1.13471	−	0.192363i
$155$			14.0855i			1.13138i
$156$		0			0
$157$			9.73082i			0.776604i	0.921532	+	0.388302i	$0.126938\pi$
$157$			9.73082i			0.776604i	−0.921532	+	0.388302i	$0.873062\pi$
$158$	2.34403	+	13.8269i	0.186481	+	1.10001i
$159$		0			0
$160$	0.809682	+	14.9098i	0.0640110	+	1.17873i
$161$	23.5628	+	23.5628i	1.85701	+	1.85701i
$162$		0			0
$163$	6.44596	+	24.0567i	0.504887	+	1.88426i	0.465520	+	0.885038i	$0.345867\pi$
$163$	6.44596	+	24.0567i	0.504887	+	1.88426i	0.0393670	+	0.999225i	$0.487466\pi$
$164$	−1.18141	−	15.9228i	−0.0922529	−	1.24336i
$165$		0			0
$166$	−6.33428	−	4.49793i	−0.491635	−	0.349107i
$167$	−2.58274	+	9.63891i	−0.199858	+	0.745881i	0.791097	+	0.611690i	$0.209510\pi$
$167$	−2.58274	+	9.63891i	−0.199858	+	0.745881i	−0.990956	+	0.134191i	$0.957157\pi$
$168$		0			0
$169$	6.87453	−	11.0336i	0.528810	−	0.848740i
$170$	15.0835	−	6.91267i	1.15685	−	0.530178i
$171$		0			0
$172$	−15.9501	−	3.03013i	−1.21618	−	0.231046i
$173$	−5.29984	+	9.17959i	−0.402939	+	0.697911i	−0.994079	−	0.108658i	$-0.965345\pi$
$173$	−5.29984	+	9.17959i	−0.402939	+	0.697911i	0.591140	+	0.806569i	$0.298678\pi$
$174$		0			0
$175$	−2.48413	−	9.27090i	−0.187783	−	0.700814i
$176$	7.59467	−	3.30017i	0.572470	−	0.248759i
$177$		0			0
$178$	−19.1767	−	1.80541i	−1.43736	−	0.135321i
$179$	13.8149	−	7.97602i	1.03257	−	0.596156i	0.114851	−	0.993383i	$-0.463361\pi$
$179$	13.8149	−	7.97602i	1.03257	−	0.596156i	0.917720	+	0.397227i	$0.130027\pi$
$180$		0			0
$181$	−7.36580			−0.547496			−0.273748	−	0.961801i	$-0.588263\pi$
$181$	−7.36580			−0.547496			−0.273748	+	0.961801i	$0.588263\pi$
$182$	−14.7405	+	20.0368i	−1.09264	+	1.48523i
$183$		0			0
$184$	16.5372	+	9.98964i	1.21914	+	0.736446i
$185$	−6.10468	−	10.5736i	−0.448825	−	0.777388i
$186$		0			0
$187$	−6.50641	−	6.50641i	−0.475796	−	0.475796i
$188$	4.76458	+	2.29884i	0.347493	+	0.167660i
$189$		0			0
$190$	−3.53472	+	9.51559i	−0.256435	+	0.690333i
$191$	−5.05273	−	2.91720i	−0.365603	−	0.211081i	0.305933	−	0.952053i	$-0.401032\pi$
$191$	−5.05273	−	2.91720i	−0.365603	−	0.211081i	−0.671536	+	0.740972i	$0.734365\pi$
$192$		0			0
$193$	17.5387	+	4.69948i	1.26246	+	0.338276i	0.827139	−	0.561998i	$-0.189967\pi$
$193$	17.5387	+	4.69948i	1.26246	+	0.338276i	0.435324	+	0.900274i	$0.356634\pi$
$194$	−2.02869	+	0.929738i	−0.145652	+	0.0667513i
$195$		0			0
$196$	21.9336	−	25.4492i	1.56669	−	1.81780i
$197$	7.77095	+	2.08222i	0.553657	+	0.148352i	0.524791	−	0.851231i	$-0.324144\pi$
$197$	7.77095	+	2.08222i	0.553657	+	0.148352i	0.0288665	+	0.999583i	$0.490810\pi$
$198$		0			0
$199$	−1.64080	+	2.84194i	−0.116313	+	0.201460i	−0.918304	−	0.395876i	$-0.870441\pi$
$199$	−1.64080	+	2.84194i	−0.116313	+	0.201460i	0.801991	+	0.597336i	$0.203774\pi$
$200$	−2.68639	−	4.87342i	−0.189957	−	0.344603i
$201$		0			0
$202$	2.57590	+	3.11133i	0.181240	+	0.218912i
$203$	0.572067	−	0.572067i	0.0401512	−	0.0401512i
$204$		0			0
$205$	10.5363	+	18.2494i	0.735887	+	1.27459i
$206$	−14.1185	+	2.39346i	−0.983681	+	0.166760i
$207$		0			0
$208$	−5.51352	+	13.3267i	−0.382294	+	0.924041i
$209$	5.62937			0.389392
$210$		0			0
$211$	6.16814	+	10.6835i	0.424632	+	0.735484i	0.996386	−	0.0849408i	$-0.0270701\pi$
$211$	6.16814	+	10.6835i	0.424632	+	0.735484i	−0.571754	+	0.820425i	$0.693737\pi$
$212$	5.41888	+	15.5231i	0.372170	+	1.06613i
$213$		0			0
$214$	−9.17158	−	11.0780i	−0.626956	−	0.757276i
$215$	20.6973	−	5.54582i	1.41154	−	0.378221i
$216$		0			0
$217$	13.0161	−	22.5445i	0.883590	−	1.53042i
$218$	−5.86473	+	8.25910i	−0.397210	+	0.559377i
$219$		0			0
$220$	−7.13487	+	8.27849i	−0.481033	+	0.558136i
$221$	16.0236	+	0.269216i	1.07786	+	0.0181094i
$222$		0			0
$223$	−24.4285	−	6.54560i	−1.63585	−	0.438326i	−0.680250	−	0.732980i	$-0.738129\pi$
$223$	−24.4285	−	6.54560i	−1.63585	−	0.438326i	−0.955604	+	0.294655i	$0.904795\pi$
$224$	12.4819	−	24.6120i	0.833979	−	1.64446i
$225$		0			0
$226$	0.368001	−	0.990673i	0.0244791	−	0.0658986i
$227$	21.3233	−	5.71357i	1.41528	−	0.379223i	0.531473	−	0.847075i	$-0.321639\pi$
$227$	21.3233	−	5.71357i	1.41528	−	0.379223i	0.883807	+	0.467852i	$0.154972\pi$
$228$		0			0
$229$	−11.7201	−	11.7201i	−0.774485	−	0.774485i	0.204402	−	0.978887i	$-0.434475\pi$
$229$	−11.7201	−	11.7201i	−0.774485	−	0.774485i	−0.978887	+	0.204402i	$0.934475\pi$
$230$	−25.3865	−	2.39004i	−1.67394	−	0.157595i
$231$		0			0
$232$	0.242532	−	0.401497i	0.0159230	−	0.0263595i
$233$		−	4.91123i		−	0.321746i	−0.986975	−	0.160873i	$-0.948569\pi$
$233$		−	4.91123i		−	0.321746i	0.986975	−	0.160873i	$-0.0514309\pi$
$234$		0			0
$235$	−6.98195			−0.455452
$236$	−1.53250	−	2.25135i	−0.0997576	−	0.146550i
$237$		0			0
$238$	−30.5296	−	2.87424i	−1.97894	−	0.186310i
$239$	−10.2089	+	10.2089i	−0.660358	+	0.660358i	−0.955465	−	0.295106i	$-0.904645\pi$
$239$	−10.2089	+	10.2089i	−0.660358	+	0.660358i	0.295106	+	0.955465i	$0.404645\pi$
$240$		0			0
$241$	0.695205	+	2.59454i	0.0447821	+	0.167129i	0.984695	−	0.174284i	$-0.0557611\pi$
$241$	0.695205	+	2.59454i	0.0447821	+	0.167129i	−0.939913	+	0.341413i	$0.889094\pi$
$242$	−8.90126	−	3.30651i	−0.572195	−	0.212551i
$243$		0			0
$244$	1.36366	+	0.259063i	0.0872996	+	0.0165848i
$245$	−11.4763	+	42.8301i	−0.733193	+	2.73631i
$246$		0			0
$247$	−7.04829	+	6.81536i	−0.448472	+	0.433651i
$248$	4.19441	−	14.4987i	0.266346	−	0.920667i
$249$		0			0
$250$	−9.23001	−	6.55417i	−0.583757	−	0.414522i
$251$	2.76530	+	1.59655i	0.174544	+	0.100773i	0.584727	−	0.811230i	$-0.301202\pi$
$251$	2.76530	+	1.59655i	0.174544	+	0.100773i	−0.410183	+	0.912003i	$0.634535\pi$
$252$		0			0
$253$	3.65992	+	13.6590i	0.230097	+	0.858734i
$254$	−14.5554	−	17.5809i	−0.913289	−	1.10313i
$255$		0			0
$256$	3.60644	−	15.5883i	0.225402	−	0.974266i
$257$	11.7430	−	6.77983i	0.732509	−	0.422914i	−0.0868303	−	0.996223i	$-0.527674\pi$
$257$	11.7430	−	6.77983i	0.732509	−	0.422914i	0.819339	+	0.573309i	$0.194340\pi$
$258$		0			0
$259$			22.5647i			1.40210i
$260$	−1.08933	−	19.0032i	−0.0675575	−	1.17853i
$261$		0			0
$262$	−23.2264	+	3.93749i	−1.43493	+	0.243259i
$263$	15.4394	−	8.91391i	0.952031	−	0.549655i	0.0583199	−	0.998298i	$-0.481426\pi$
$263$	15.4394	−	8.91391i	0.952031	−	0.549655i	0.893711	+	0.448642i	$0.148092\pi$
$264$		0			0
$265$	−15.3440	−	15.3440i	−0.942575	−	0.942575i
$266$	14.4506	−	11.9638i	0.886022	−	0.733546i
$267$		0			0
$268$	−0.722955	−	9.74380i	−0.0441615	−	0.595198i
$269$	−15.1420	−	8.74224i	−0.923225	−	0.533024i	−0.0385623	−	0.999256i	$-0.512278\pi$
$269$	−15.1420	−	8.74224i	−0.923225	−	0.533024i	−0.884662	+	0.466232i	$0.845611\pi$
$270$		0			0
$271$	−0.868914	+	3.24283i	−0.0527828	+	0.196988i	−0.987282	−	0.158976i	$-0.949181\pi$
$271$	−0.868914	+	3.24283i	−0.0527828	+	0.196988i	0.934500	+	0.355964i	$0.115847\pi$
$272$	−17.5844	+	2.62384i	−1.06621	+	0.159094i
$273$		0			0
$274$	1.73027	+	3.77545i	0.104529	+	0.228083i
$275$	1.05416	−	3.93419i	0.0635684	−	0.237241i
$276$		0			0
$277$	12.8269	−	22.2168i	0.770694	−	1.33488i	−0.166490	−	0.986043i	$-0.553243\pi$
$277$	12.8269	−	22.2168i	0.770694	−	1.33488i	0.937183	−	0.348837i	$-0.113423\pi$
$278$	1.86304	−	5.01538i	0.111738	−	0.300803i
$279$		0			0
$280$	−0.721412	+	36.4142i	−0.0431126	+	2.17616i
$281$	−13.6396	+	13.6396i	−0.813669	+	0.813669i	−0.985182	−	0.171513i	$-0.945135\pi$
$281$	−13.6396	+	13.6396i	−0.813669	+	0.813669i	0.171513	+	0.985182i	$0.445135\pi$
$282$		0			0
$283$	4.91655	−	2.83857i	0.292258	−	0.168736i	−0.346701	−	0.937976i	$-0.612698\pi$
$283$	4.91655	−	2.83857i	0.292258	−	0.168736i	0.638960	+	0.769240i	$0.279365\pi$
$284$	−10.7146	−	15.7404i	−0.635793	−	0.934020i
$285$		0			0
$286$	−9.66864	+	4.23601i	−0.571719	+	0.250481i
$287$		−	38.9453i		−	2.29887i
$288$		0			0
$289$	1.37796	+	2.38670i	0.0810565	+	0.140394i
$290$	−0.0580264	+	0.616344i	−0.00340743	+	0.0361930i
$291$		0			0
$292$	−13.8482	+	28.7017i	−0.810402	+	1.67964i
$293$	−5.74107	+	1.53832i	−0.335397	+	0.0898693i	−0.422587	−	0.906322i	$-0.638878\pi$
$293$	−5.74107	+	1.53832i	−0.335397	+	0.0898693i	0.0871901	+	0.996192i	$0.472211\pi$
$294$		0			0
$295$	3.11283	+	1.79719i	0.181236	+	0.104637i
$296$	3.13511	+	12.7016i	0.182225	+	0.738266i
$297$		0			0
$298$	−11.1745	−	24.3828i	−0.647322	−	1.41246i
$299$	−21.1191	−	12.6709i	−1.22135	−	0.732775i
$300$		0			0
$301$	−38.2516	−	10.2495i	−2.20479	−	0.590771i
$302$	12.9750	+	9.21350i	0.746630	+	0.530177i
$303$		0			0
$304$	6.47196	−	8.74211i	0.371192	−	0.501395i
$305$	−1.76953	+	0.474143i	−0.101323	+	0.0271493i
$306$		0			0
$307$	−4.23600	+	4.23600i	−0.241761	+	0.241761i	−0.817578	−	0.575817i	$-0.804684\pi$
$307$	−4.23600	+	4.23600i	−0.241761	+	0.241761i	0.575817	+	0.817578i	$0.304684\pi$
$308$	19.0696	−	6.65693i	1.08659	−	0.379314i
$309$		0			0
$310$	3.32946	+	19.6397i	0.189101	+	1.11546i
$311$	23.2153			1.31642			0.658209	−	0.752836i	$-0.271315\pi$
$311$	23.2153			1.31642			0.658209	+	0.752836i	$0.271315\pi$
$312$		0			0
$313$	23.0016			1.30013			0.650064	−	0.759880i	$-0.274742\pi$
$313$	23.0016			1.30013			0.650064	+	0.759880i	$0.274742\pi$
$314$	2.30012	+	13.5679i	0.129803	+	0.765680i
$315$		0			0
$316$	6.53665	+	18.7251i	0.367715	+	1.05337i
$317$	13.3702	−	13.3702i	0.750944	−	0.750944i	−0.223711	−	0.974655i	$-0.571817\pi$
$317$	13.3702	−	13.3702i	0.750944	−	0.750944i	0.974655	+	0.223711i	$0.0718173\pi$
$318$		0			0
$319$	0.331619	−	0.0888569i	0.0185671	−	0.00497503i
$320$	4.65325	+	20.5977i	0.260125	+	1.15144i
$321$		0			0
$322$	38.4237	+	27.2844i	2.14127	+	1.52050i
$323$	−11.6747	−	3.12822i	−0.649596	−	0.174059i
$324$		0			0
$325$	3.44317	+	6.20208i	0.190993	+	0.344030i
$326$	14.6741	+	32.0190i	0.812723	+	1.77337i
$327$		0			0
$328$	−5.41101	−	21.9222i	−0.298773	−	1.21045i
$329$	11.1749	+	6.45184i	0.616093	+	0.355701i
$330$		0			0
$331$	15.9030	−	4.26121i	0.874110	−	0.234217i	0.206246	−	0.978500i	$-0.433875\pi$
$331$	15.9030	−	4.26121i	0.874110	−	0.234217i	0.667864	+	0.744283i	$0.267209\pi$
$332$	−9.89520	−	4.77429i	−0.543070	−	0.262023i
$333$		0			0
$334$	−1.32277	+	14.0502i	−0.0723788	+	0.768793i
$335$	6.44759	+	11.1676i	0.352270	+	0.610149i
$336$		0			0
$337$		−	27.5380i		−	1.50009i	−0.661386	−	0.750046i	$-0.730031\pi$
$337$		−	27.5380i		−	1.50009i	0.661386	−	0.750046i	$-0.269969\pi$
$338$	6.97723	−	17.0094i	0.379511	−	0.925187i
$339$		0			0
$340$	19.3972	−	13.2038i	1.05196	−	0.716078i
$341$	9.56698	−	5.52350i	0.518081	−	0.299114i
$342$		0			0
$343$	33.7998	−	33.7998i	1.82502	−	1.82502i
$344$	−22.9558	−	0.454783i	−1.23769	−	0.0245203i
$345$		0			0
$346$	−5.21985	+	14.0520i	−0.280621	+	0.755442i
$347$	−9.78651	+	16.9507i	−0.525367	+	0.909963i	0.474196	+	0.880419i	$0.342739\pi$
$347$	−9.78651	+	16.9507i	−0.525367	+	0.909963i	−0.999563	+	0.0295437i	$0.990595\pi$
$348$		0			0
$349$	1.58449	−	5.91341i	0.0848160	−	0.316538i	−0.910463	−	0.413590i	$-0.864275\pi$
$349$	1.58449	−	5.91341i	0.0848160	−	0.316538i	0.995279	+	0.0970522i	$0.0309414\pi$
$350$	−5.65507	−	12.3394i	−0.302276	−	0.659569i
$351$		0			0
$352$	9.80933	−	6.39667i	0.522839	−	0.340944i
$353$	−3.59259	+	13.4077i	−0.191214	+	0.713621i	0.802000	+	0.597324i	$0.203769\pi$
$353$	−3.59259	+	13.4077i	−0.191214	+	0.713621i	−0.993214	+	0.116297i	$0.962897\pi$
$354$		0			0
$355$	21.7635	+	12.5652i	1.15509	+	0.666889i
$356$	−27.1652	+	2.01556i	−1.43975	+	0.106825i
$357$		0			0
$358$	17.3770	−	14.3866i	0.918404	−	0.760355i
$359$	12.7715	+	12.7715i	0.674055	+	0.674055i	0.958648	−	0.284593i	$-0.0918586\pi$
$359$	12.7715	+	12.7715i	0.674055	+	0.674055i	−0.284593	+	0.958648i	$0.591859\pi$
$360$		0			0
$361$	−10.0507	+	5.80279i	−0.528985	+	0.305410i
$362$	−10.2703	+	1.74109i	−0.539794	+	0.0915094i
$363$		0			0
$364$	−15.8168	+	31.4221i	−0.829027	+	1.64696i
$365$		−	42.0591i		−	2.20147i
$366$		0			0
$367$	−1.71553	+	0.990463i	−0.0895500	+	0.0517017i	−0.544106	−	0.839016i	$-0.683131\pi$
$367$	−1.71553	+	0.990463i	−0.0895500	+	0.0517017i	0.454556	+	0.890718i	$0.349798\pi$
$368$	25.4194	+	10.0198i	1.32508	+	0.522318i
$369$		0			0
$370$	−11.0112	−	13.3000i	−0.572445	−	0.691435i
$371$	10.3798	+	38.7378i	0.538890	+	2.01116i
$372$		0			0
$373$	17.8013	+	10.2776i	0.921715	+	0.532152i	0.884182	−	0.467143i	$-0.154717\pi$
$373$	17.8013	+	10.2776i	0.921715	+	0.532152i	0.0375332	+	0.999295i	$0.488050\pi$
$374$	−10.6100	−	7.53406i	−0.548628	−	0.389577i
$375$		0			0
$376$	7.18673	+	2.07909i	0.370627	+	0.107221i
$377$	−0.307628	+	0.512738i	−0.0158436	+	0.0264073i
$378$		0			0
$379$	−1.58993	+	5.93369i	−0.0816691	+	0.304793i	−0.994663	−	0.103181i	$-0.967098\pi$
$379$	−1.58993	+	5.93369i	−0.0816691	+	0.304793i	0.912993	+	0.407974i	$0.133765\pi$
$380$	−2.67928	+	14.1033i	−0.137444	+	0.723483i
$381$		0			0
$382$	−7.73468	−	2.87317i	−0.395741	−	0.147004i
$383$	3.16308	+	11.8048i	0.161626	+	0.603196i	0.998446	+	0.0557191i	$0.0177451\pi$
$383$	3.16308	+	11.8048i	0.161626	+	0.603196i	−0.836820	+	0.547477i	$0.815588\pi$
$384$		0			0
$385$	−18.8497	+	18.8497i	−0.960668	+	0.960668i
$386$	25.5654	+	2.40688i	1.30124	+	0.122507i
$387$		0			0
$388$	−2.60888	+	1.77588i	−0.132446	+	0.0901568i
$389$	−29.9634			−1.51920			−0.759601	−	0.650389i	$-0.774606\pi$
$389$	−29.9634			−1.51920			−0.759601	+	0.650389i	$0.774606\pi$
$390$		0			0
$391$		−	30.3610i		−	1.53542i
$392$	24.5669	−	40.6689i	1.24082	−	2.05409i
$393$		0			0
$394$	11.3274	+	1.06643i	0.570665	+	0.0537258i
$395$	−18.5091	−	18.5091i	−0.931293	−	0.931293i
$396$		0			0
$397$	−11.2356	+	3.01057i	−0.563899	+	0.151096i	−0.529497	−	0.848312i	$-0.677619\pi$
$397$	−11.2356	+	3.01057i	−0.563899	+	0.151096i	−0.0344019	+	0.999408i	$0.510953\pi$
$398$	−1.61603	+	4.35042i	−0.0810044	+	0.218067i
$399$		0			0
$400$	−4.89764	−	6.16011i	−0.244882	−	0.308005i
$401$	24.4339	+	6.54704i	1.22017	+	0.326943i	0.810744	−	0.585400i	$-0.199063\pi$
$401$	24.4339	+	6.54704i	1.22017	+	0.326943i	0.409425	+	0.912344i	$0.365729\pi$
$402$		0			0
$403$	−5.29121	+	18.4983i	−0.263574	+	0.921465i
$404$	4.32706	+	3.72931i	0.215279	+	0.185540i
$405$		0			0
$406$	0.662422	−	0.932865i	0.0328754	−	0.0462973i
$407$	−4.78777	+	8.29267i	−0.237321	+	0.411052i
$408$		0			0
$409$	20.0336	−	5.36799i	0.990599	−	0.265430i	0.273097	−	0.961987i	$-0.411952\pi$
$409$	20.0336	−	5.36799i	0.990599	−	0.265430i	0.717502	+	0.696556i	$0.245285\pi$
$410$	19.0047	+	22.9550i	0.938574	+	1.13367i
$411$		0			0
$412$	−19.1199	+	6.67449i	−0.941971	+	0.328829i
$413$	−3.32148	−	5.75297i	−0.163439	−	0.283085i
$414$		0			0
$415$	14.5003			0.711791
$416$	−4.53751	+	19.8849i	−0.222470	+	0.974940i
$417$		0			0
$418$	7.84914	−	1.33064i	0.383914	−	0.0650836i
$419$	15.5683	+	26.9651i	0.760560	+	1.31733i	0.942562	+	0.334031i	$0.108409\pi$
$419$	15.5683	+	26.9651i	0.760560	+	1.31733i	−0.182002	+	0.983298i	$0.558258\pi$
$420$		0			0
$421$	0.590979	−	0.590979i	0.0288026	−	0.0288026i	−0.692559	−	0.721361i	$-0.743517\pi$
$421$	0.590979	−	0.590979i	0.0288026	−	0.0288026i	0.721361	+	0.692559i	$0.243517\pi$
$422$	11.1257	+	13.4383i	0.541589	+	0.654164i
$423$		0			0
$424$	11.2249	+	20.3632i	0.545129	+	0.988926i
$425$	−4.37243	+	7.57327i	−0.212094	+	0.367357i
$426$		0			0
$427$	3.27035	+	0.876287i	0.158263	+	0.0424065i
$428$	−15.4067	−	13.2783i	−0.744709	−	0.641833i
$429$		0			0
$430$	27.5477	−	12.6249i	1.32847	−	0.608829i
$431$	−8.41002	−	2.25346i	−0.405096	−	0.108545i	0.0505166	−	0.998723i	$-0.483913\pi$
$431$	−8.41002	−	2.25346i	−0.405096	−	0.108545i	−0.455613	+	0.890178i	$0.650580\pi$
$432$		0			0
$433$	−8.71099	−	5.02929i	−0.418624	−	0.241692i	0.275865	−	0.961196i	$-0.411036\pi$
$433$	−8.71099	−	5.02929i	−0.418624	−	0.241692i	−0.694488	+	0.719504i	$0.744369\pi$
$434$	12.8196	−	34.5109i	0.615363	−	1.65658i
$435$		0			0
$436$	−6.22507	+	12.9021i	−0.298127	+	0.617898i
$437$	13.1342	+	13.1342i	0.628296	+	0.628296i
$438$		0			0
$439$	3.83901	+	6.64936i	0.183226	+	0.317357i	0.942977	−	0.332857i	$-0.108013\pi$
$439$	3.83901	+	6.64936i	0.183226	+	0.317357i	−0.759751	+	0.650214i	$0.774679\pi$
$440$	−7.99147	+	13.2294i	−0.380978	+	0.630685i
$441$		0			0
$442$	22.4056	−	3.41218i	1.06573	−	0.162301i
$443$	6.09878			0.289762			0.144881	−	0.989449i	$-0.453720\pi$
$443$	6.09878			0.289762			0.144881	+	0.989449i	$0.453720\pi$
$444$		0			0
$445$	31.1346	−	17.9756i	1.47592	−	0.852123i
$446$	−35.6084	−	3.35239i	−1.68610	−	0.158740i
$447$		0			0
$448$	11.5860	−	37.2674i	0.547389	−	1.76072i
$449$	6.24854	+	23.3199i	0.294887	+	1.10053i	0.941307	+	0.337551i	$0.109599\pi$
$449$	6.24854	+	23.3199i	0.294887	+	1.10053i	−0.646421	+	0.762981i	$0.723735\pi$
$450$		0			0
$451$	8.26340	−	14.3126i	0.389108	−	0.673955i
$452$	0.278942	−	1.46830i	0.0131203	−	0.0690630i
$453$		0			0
$454$	28.3810	−	13.0068i	1.33199	−	0.610441i
$455$	0.779944	−	46.4217i	0.0365643	−	2.17628i
$456$		0			0
$457$	−5.14536	+	19.2027i	−0.240690	+	0.898266i	0.734811	+	0.678272i	$0.237271\pi$
$457$	−5.14536	+	19.2027i	−0.240690	+	0.898266i	−0.975501	+	0.219995i	$0.929396\pi$
$458$	−19.1119	−	13.5712i	−0.893040	−	0.634142i
$459$		0			0
$460$	−35.9619	+	2.66824i	−1.67673	+	0.124407i
$461$	3.19035	+	11.9065i	0.148589	+	0.554543i	0.999569	+	0.0293448i	$0.00934209\pi$
$461$	3.19035	+	11.9065i	0.148589	+	0.554543i	−0.850980	+	0.525198i	$0.823991\pi$
$462$		0			0
$463$	−5.89215	−	5.89215i	−0.273832	−	0.273832i	0.556809	−	0.830641i	$-0.312026\pi$
$463$	−5.89215	−	5.89215i	−0.273832	−	0.273832i	−0.830641	+	0.556809i	$0.812026\pi$
$464$	0.243264	−	0.617143i	0.0112933	−	0.0286501i
$465$		0			0
$466$	−1.16089	−	6.84783i	−0.0537771	−	0.317220i
$467$		−	23.5141i		−	1.08810i	−0.839051	−	0.544052i	$-0.816889\pi$
$467$		−	23.5141i		−	1.08810i	0.839051	−	0.544052i	$-0.183111\pi$
$468$		0			0
$469$		−	23.8322i		−	1.10047i
$470$	−9.73506	+	1.65035i	−0.449045	+	0.0761251i
$471$		0			0
$472$	−2.66896	−	2.77685i	−0.122849	−	0.127815i
$473$	−11.8830	−	11.8830i	−0.546379	−	0.546379i
$474$		0			0
$475$	−1.38469	−	5.16773i	−0.0635339	−	0.237112i
$476$	−43.2474	+	3.20880i	−1.98224	+	0.147075i
$477$		0			0
$478$	−11.8213	+	16.6476i	−0.540696	+	0.761443i
$479$	0.824761	−	3.07805i	0.0376843	−	0.140640i	−0.944521	−	0.328452i	$-0.893473\pi$
$479$	0.824761	−	3.07805i	0.0376843	−	0.140640i	0.982205	+	0.187812i	$0.0601397\pi$
$480$		0			0
$481$	−4.04520	−	16.1793i	−0.184445	−	0.737715i
$482$	1.58262	+	3.45329i	0.0720864	+	0.157293i
$483$		0			0
$484$	−13.1928	−	2.50631i	−0.599672	−	0.113923i
$485$	2.08261	−	3.60718i	0.0945663	−	0.163794i
$486$		0			0
$487$	4.40943	+	16.4562i	0.199810	+	0.745702i	0.990969	+	0.134091i	$0.0428115\pi$
$487$	4.40943	+	16.4562i	0.199810	+	0.745702i	−0.791159	+	0.611611i	$0.790522\pi$
$488$	1.96262	+	0.0388820i	0.0888435	+	0.00176010i
$489$		0			0
$490$	−5.87768	+	62.4315i	−0.265527	+	2.82037i
$491$	−10.5370	+	6.08352i	−0.475527	+	0.274546i	−0.718551	−	0.695475i	$-0.755194\pi$
$491$	−10.5370	+	6.08352i	−0.475527	+	0.274546i	0.243024	+	0.970020i	$0.421861\pi$
$492$		0			0
$493$	−0.737117			−0.0331981
$494$	−8.21659	+	11.1688i	−0.369682	+	0.502509i
$495$		0			0
$496$	2.42124	−	21.2073i	0.108717	−	0.952234i
$497$	−23.2223	−	40.2222i	−1.04166	−	1.80421i
$498$		0			0
$499$	−28.9374	−	28.9374i	−1.29542	−	1.29542i	−0.931389	−	0.364027i	$-0.881402\pi$
$499$	−28.9374	−	28.9374i	−1.29542	−	1.29542i	−0.364027	−	0.931389i	$-0.618598\pi$
$500$	−14.4188	−	6.95687i	−0.644829	−	0.311121i
$501$		0			0
$502$	4.23309	+	1.57245i	0.188932	+	0.0701818i
$503$	21.8800	+	12.6324i	0.975580	+	0.563252i	0.900933	−	0.433958i	$-0.142884\pi$
$503$	21.8800	+	12.6324i	0.975580	+	0.563252i	0.0746475	+	0.997210i	$0.476217\pi$
$504$		0			0
$505$	−7.28228	−	1.95128i	−0.324057	−	0.0868309i
$506$	8.33174	+	18.1799i	0.370391	+	0.808196i
$507$		0			0
$508$	−24.4506	−	21.0729i	−1.08482	−	0.934960i
$509$	18.9678	+	5.08241i	0.840734	+	0.225274i	0.653391	−	0.757021i	$-0.273346\pi$
$509$	18.9678	+	5.08241i	0.840734	+	0.225274i	0.187343	+	0.982295i	$0.440012\pi$
$510$		0			0
$511$	−38.8657	+	67.3174i	−1.71932	+	2.97795i
$512$	1.34387	−	22.5875i	0.0593911	−	0.998235i
$513$		0			0
$514$	14.7709	−	12.2290i	0.651518	−	0.539398i
$515$	18.8994	−	18.8994i	0.832806	−	0.832806i
$516$		0			0
$517$	2.73790	+	4.74218i	0.120413	+	0.208561i
$518$	5.33372	+	31.4624i	0.234350	+	1.38238i
$519$		0			0
$520$	−6.01074	−	26.2390i	−0.263588	−	1.15066i
$521$	8.50132			0.372450			0.186225	−	0.982507i	$-0.440375\pi$
$521$	8.50132			0.372450			0.186225	+	0.982507i	$0.440375\pi$
$522$		0			0
$523$	−22.1486	−	38.3625i	−0.968490	−	1.67747i	−0.699932	−	0.714209i	$-0.746786\pi$
$523$	−22.1486	−	38.3625i	−0.968490	−	1.67747i	−0.268558	−	0.963264i	$-0.586547\pi$
$524$	−31.4543	+	10.9802i	−1.37409	+	0.479674i
$525$		0			0
$526$	19.4204	−	16.0783i	0.846768	−	0.701048i
$527$	−22.9102	+	6.13877i	−0.997984	+	0.267409i
$528$		0			0
$529$	−11.8295	+	20.4893i	−0.514326	+	0.890839i
$530$	−25.0214	−	17.7675i	−1.08686	−	0.771772i
$531$		0			0
$532$	17.3208	−	20.0971i	0.750952	−	0.871319i
$533$	6.98176	+	27.9246i	0.302414	+	1.20955i
$534$		0			0
$535$	25.9288	+	6.94761i	1.12100	+	0.300371i
$536$	−3.31121	−	13.4151i	−0.143023	−	0.579444i
$537$		0			0
$538$	−23.1792	−	8.61030i	−0.999328	−	0.371216i
$539$	33.5907	−	9.00061i	1.44686	−	0.387684i
$540$		0			0
$541$	12.5837	+	12.5837i	0.541018	+	0.541018i	0.923827	−	0.382810i	$-0.125044\pi$
$541$	12.5837	+	12.5837i	0.541018	+	0.541018i	−0.382810	+	0.923827i	$0.625044\pi$
$542$	−0.445022	+	4.72693i	−0.0191153	+	0.203039i
$543$		0			0
$544$	−23.8980	+	7.81496i	−1.02462	+	0.335064i
$545$		−	18.9065i		−	0.809867i
$546$		0			0
$547$	−2.39098			−0.102231			−0.0511154	−	0.998693i	$-0.516278\pi$
$547$	−2.39098			−0.102231			−0.0511154	+	0.998693i	$0.516278\pi$
$548$	3.30496	+	4.85520i	0.141181	+	0.207404i
$549$		0			0
$550$	0.539899	−	5.73470i	0.0230214	−	0.244528i
$551$	0.318878	−	0.318878i	0.0135847	−	0.0135847i
$552$		0			0
$553$	12.5208	+	46.7284i	0.532440	+	1.98709i
$554$	12.6333	−	34.0093i	0.536738	−	1.44492i
$555$		0			0
$556$	1.41217	−	7.43342i	0.0598894	−	0.315247i
$557$	3.10542	−	11.5896i	0.131581	−	0.491067i	−0.868408	−	0.495851i	$-0.834856\pi$
$557$	3.10542	−	11.5896i	0.131581	−	0.491067i	0.999989	+	0.00478427i	$0.00152289\pi$
$558$		0			0
$559$	29.2646	+	0.491682i	1.23776	+	0.0207959i
$560$	7.60150	+	50.9436i	0.321222	+	2.15276i
$561$		0			0
$562$	−15.7939	+	22.2420i	−0.666225	+	0.938222i
$563$	20.5535	+	11.8665i	0.866225	+	0.500115i	0.866092	−	0.499885i	$-0.166624\pi$
$563$	20.5535	+	11.8665i	0.866225	+	0.500115i	0.000133111		1.00000i	$0.499958\pi$
$564$		0			0
$565$	0.510525	+	1.90531i	0.0214779	+	0.0801568i
$566$	6.18428	−	5.12002i	0.259944	−	0.215211i
$567$		0			0
$568$	−18.6602	−	19.4145i	−0.782963	−	0.814613i
$569$	26.9109	−	15.5370i	1.12816	−	0.651346i	0.184692	−	0.982796i	$-0.440871\pi$
$569$	26.9109	−	15.5370i	1.12816	−	0.651346i	0.943473	+	0.331450i	$0.107538\pi$
$570$		0			0
$571$		−	10.8606i		−	0.454500i	−0.973836	−	0.227250i	$-0.927027\pi$
$571$		−	10.8606i		−	0.454500i	0.973836	−	0.227250i	$-0.0729735\pi$
$572$	−12.4799	+	8.19178i	−0.521811	+	0.342515i
$573$		0			0
$574$	−9.20567	−	54.3022i	−0.384237	−	2.26653i
$575$	11.6386	−	6.71958i	0.485365	−	0.280226i
$576$		0			0
$577$	24.2438	+	24.2438i	1.00928	+	1.00928i	0.999956	+	0.00932743i	$0.00296906\pi$
$577$	24.2438	+	24.2438i	1.00928	+	1.00928i	0.00932743	+	0.999956i	$0.497031\pi$
$578$	2.48547	+	3.00211i	0.103382	+	0.124871i
$579$		0			0
$580$	0.0647806	+	0.873097i	0.00268987	+	0.0362534i
$581$	−23.2084	−	13.3993i	−0.962845	−	0.555899i
$582$		0			0
$583$	−4.40474	+	16.4387i	−0.182426	+	0.680822i
$584$	−12.5244	+	43.2927i	−0.518264	+	1.79146i
$585$		0			0
$586$	−7.64127	+	3.50194i	−0.315658	+	0.144664i
$587$	−0.397645	+	1.48403i	−0.0164125	+	0.0612525i	−0.973646	−	0.228063i	$-0.926761\pi$
$587$	−0.397645	+	1.48403i	−0.0164125	+	0.0612525i	0.957234	+	0.289315i	$0.0934276\pi$
$588$		0			0
$589$	7.25536	−	12.5666i	0.298952	−	0.517800i
$590$	4.76509	+	1.77007i	0.196176	+	0.0728726i
$591$		0			0
$592$	7.37368	+	16.9690i	0.303056	+	0.697424i
$593$	−4.86193	+	4.86193i	−0.199656	+	0.199656i	−0.799852	−	0.600197i	$-0.795089\pi$
$593$	−4.86193	+	4.86193i	−0.199656	+	0.199656i	0.600197	+	0.799852i	$0.295089\pi$
$594$		0			0
$595$	49.5667	−	28.6174i	2.03204	−	1.17320i
$596$	−21.3443	−	31.3561i	−0.874297	−	1.28440i
$597$		0			0
$598$	−32.4418	−	12.6752i	−1.32665	−	0.518328i
$599$			4.73413i			0.193431i	0.995312	+	0.0967156i	$0.0308337\pi$
$599$			4.73413i			0.193431i	−0.995312	+	0.0967156i	$0.969166\pi$
$600$		0			0
$601$	−5.84939	−	10.1314i	−0.238602	−	0.413270i	0.721712	−	0.692194i	$-0.243356\pi$
$601$	−5.84939	−	10.1314i	−0.238602	−	0.413270i	−0.960313	+	0.278924i	$0.910022\pi$
$602$	−55.7577	−	5.24937i	−2.27252	−	0.213948i
$603$		0			0
$604$	20.2692	+	9.77959i	0.824742	+	0.397926i
$605$	17.1193	−	4.58710i	0.695998	−	0.186492i
$606$		0			0
$607$	5.29055	+	3.05450i	0.214737	+	0.123978i	0.603511	−	0.797355i	$-0.293768\pi$
$607$	5.29055	+	3.05450i	0.214737	+	0.123978i	−0.388774	+	0.921333i	$0.627101\pi$
$608$	6.95757	−	13.7191i	0.282167	−	0.556383i
$609$		0			0
$610$	−2.35521	+	1.07938i	−0.0953596	+	0.0437027i
$611$	−9.16926	−	2.62276i	−0.370948	−	0.106105i
$612$		0			0
$613$	34.2679	+	9.18205i	1.38407	+	0.370860i	0.872597	−	0.488442i	$-0.162434\pi$
$613$	34.2679	+	9.18205i	1.38407	+	0.370860i	0.511470	+	0.859301i	$0.329101\pi$
$614$	−4.90505	+	6.90762i	−0.197952	+	0.278769i
$615$		0			0
$616$	25.0156	−	13.7895i	1.00791	−	0.555593i
$617$	−24.2158	+	6.48861i	−0.974892	+	0.261221i	−0.710892	−	0.703301i	$-0.751709\pi$
$617$	−24.2158	+	6.48861i	−0.974892	+	0.261221i	−0.264000	+	0.964523i	$0.585042\pi$
$618$		0			0
$619$	−10.1532	+	10.1532i	−0.408091	+	0.408091i	−0.881072	−	0.472982i	$-0.843178\pi$
$619$	−10.1532	+	10.1532i	−0.408091	+	0.408091i	0.472982	+	0.881072i	$0.343178\pi$
$620$	9.28466	+	26.5971i	0.372881	+	1.06816i
$621$		0			0
$622$	32.3695	−	5.48749i	1.29790	−	0.220028i
$623$	−66.4430			−2.66198
$624$		0			0
$625$	30.9664			1.23866
$626$	32.0716	−	5.43699i	1.28184	−	0.217306i
$627$		0			0
$628$	6.41420	+	18.3743i	0.255954	+	0.733213i
$629$	14.5375	−	14.5375i	0.579648	−	0.579648i
$630$		0			0
$631$	−13.5488	+	3.63038i	−0.539368	+	0.144523i	−0.518211	−	0.855253i	$-0.673402\pi$
$631$	−13.5488	+	3.63038i	−0.539368	+	0.144523i	−0.0211573	+	0.999776i	$0.506735\pi$
$632$	13.5403	+	24.5636i	0.538604	+	0.977088i
$633$		0			0
$634$	15.4819	−	21.8027i	0.614866	−	0.865895i
$635$	41.1494	+	11.0260i	1.63297	+	0.437552i
$636$		0			0
$637$	−31.1606	+	51.9369i	−1.23463	+	2.05781i
$638$	0.441379	−	0.202281i	0.0174744	−	0.00800838i
$639$		0			0
$640$	11.3569	+	27.6198i	0.448920	+	1.09177i
$641$	16.2594	+	9.38735i	0.642206	+	0.370778i	0.785464	−	0.618908i	$-0.212424\pi$
$641$	16.2594	+	9.38735i	0.642206	+	0.370778i	−0.143258	+	0.989685i	$0.545758\pi$
$642$		0			0
$643$	37.3113	−	9.99754i	1.47142	−	0.394265i	0.567999	−	0.823029i	$-0.307718\pi$
$643$	37.3113	−	9.99754i	1.47142	−	0.394265i	0.903416	+	0.428765i	$0.141051\pi$
$644$	60.0243	+	28.9608i	2.36529	+	1.14122i
$645$		0			0
$646$	−17.0177	−	1.60214i	−0.669551	−	0.0630355i
$647$	22.8502	+	39.5777i	0.898333	+	1.55596i	0.829624	+	0.558322i	$0.188555\pi$
$647$	22.8502	+	39.5777i	0.898333	+	1.55596i	0.0687090	+	0.997637i	$0.478112\pi$
$648$		0			0
$649$		−	2.81900i		−	0.110655i
$650$	6.26689	+	7.83381i	0.245808	+	0.307267i
$651$		0			0
$652$	28.0289	+	41.1761i	1.09769	+	1.61258i
$653$	17.6262	−	10.1765i	0.689767	−	0.398237i	−0.113758	−	0.993509i	$-0.536289\pi$
$653$	17.6262	−	10.1765i	0.689767	−	0.398237i	0.803525	+	0.595271i	$0.202955\pi$
$654$		0			0
$655$	31.0915	−	31.0915i	1.21484	−	1.21484i
$656$	−12.7265	−	29.2875i	−0.496887	−	1.14349i
$657$		0			0
$658$	17.1064	+	6.35446i	0.666879	+	0.247723i
$659$	2.92527	−	5.06672i	0.113952	−	0.197371i	−0.803408	−	0.595429i	$-0.796982\pi$
$659$	2.92527	−	5.06672i	0.113952	−	0.197371i	0.917361	+	0.398057i	$0.130316\pi$
$660$		0			0
$661$	9.08145	−	33.8924i	0.353227	−	1.31826i	−0.529473	−	0.848327i	$-0.677610\pi$
$661$	9.08145	−	33.8924i	0.353227	−	1.31826i	0.882701	−	0.469936i	$-0.155723\pi$
$662$	21.1667	−	9.70056i	0.822667	−	0.377023i
$663$		0			0
$664$	−14.9256	−	4.31792i	−0.579225	−	0.167568i
$665$	−9.06274	+	33.8226i	−0.351438	+	1.31158i
$666$		0			0
$667$	0.981038	+	0.566403i	0.0379860	+	0.0219312i
$668$	1.47674	+	19.9032i	0.0571369	+	0.770076i
$669$		0			0
$670$	11.6297	+	14.0471i	0.449296	+	0.542687i
$671$	1.01594	+	1.01594i	0.0392200	+	0.0392200i
$672$		0			0
$673$	−36.8546	+	21.2780i	−1.42064	+	0.820207i	−0.996353	−	0.0853213i	$-0.972808\pi$
$673$	−36.8546	+	21.2780i	−1.42064	+	0.820207i	−0.424286	+	0.905528i	$0.639475\pi$
$674$	−6.50928	−	38.3968i	−0.250728	−	1.47899i
$675$		0			0
$676$	5.70792	−	25.3657i	0.219535	−	0.975605i
$677$		−	28.9422i		−	1.11234i	−0.831069	−	0.556169i	$-0.812271\pi$
$677$		−	28.9422i		−	1.11234i	0.831069	−	0.556169i	$-0.187729\pi$
$678$		0			0
$679$	−6.66661	+	3.84897i	−0.255841	+	0.147710i
$680$	23.9249	−	22.9954i	0.917478	−	0.881832i
$681$		0			0
$682$	12.0338	−	9.96291i	0.460798	−	0.381499i
$683$	−8.32432	−	31.0668i	−0.318521	−	1.18874i	−0.920666	−	0.390351i	$-0.872354\pi$
$683$	−8.32432	−	31.0668i	−0.318521	−	1.18874i	0.602145	−	0.798387i	$-0.294313\pi$
$684$		0			0
$685$	−6.71306	−	3.87578i	−0.256493	−	0.148086i
$686$	39.1384	−	55.1172i	1.49431	−	2.10438i
$687$		0			0
$688$	−32.1152	+	4.79204i	−1.22438	+	0.182695i
$689$	−14.3870	−	25.9149i	−0.548103	−	0.987281i
$690$		0			0
$691$	−0.974151	+	3.63558i	−0.0370584	+	0.138304i	−0.981977	−	0.189003i	$-0.939474\pi$
$691$	−0.974151	+	3.63558i	−0.0370584	+	0.138304i	0.944918	+	0.327307i	$0.106141\pi$
$692$	−3.95660	+	20.8269i	−0.150407	+	0.791718i
$693$		0			0
$694$	−9.63880	+	25.9480i	−0.365884	+	0.984973i
$695$	2.58459	+	9.64581i	0.0980389	+	0.365886i
$696$		0			0
$697$	−25.0908	+	25.0908i	−0.950383	+	0.950383i
$698$	0.811513	−	8.61972i	0.0307162	−	0.326261i
$699$		0			0
$700$	−10.8017	−	15.8684i	−0.408266	−	0.599768i
$701$	26.5127			1.00137			0.500685	−	0.865630i	$-0.333082\pi$
$701$	26.5127			1.00137			0.500685	+	0.865630i	$0.333082\pi$
$702$		0			0
$703$			12.5779i			0.474385i
$704$	12.1653	−	11.2377i	0.458498	−	0.423536i
$705$		0			0
$706$	−1.83998	+	19.5438i	−0.0692484	+	0.735542i
$707$	9.85248	+	9.85248i	0.370541	+	0.370541i
$708$		0			0
$709$	−5.29377	+	1.41846i	−0.198812	+	0.0532715i	−0.356851	−	0.934161i	$-0.616150\pi$
$709$	−5.29377	+	1.41846i	−0.198812	+	0.0532715i	0.158039	+	0.987433i	$0.449483\pi$
$710$	33.3153	+	12.3755i	1.25030	+	0.464445i
$711$		0			0
$712$	−37.4006	+	9.23150i	−1.40165	+	0.345965i
$713$	35.2085	+	9.43410i	1.31857	+	0.353310i
$714$		0			0
$715$	10.1364	−	16.8948i	0.379079	−	0.631828i
$716$	20.8285	−	24.1670i	0.778397	−	0.903163i
$717$		0			0
$718$	20.8264	+	14.7887i	0.777236	+	0.551910i
$719$	10.1805	−	17.6332i	0.379670	−	0.657608i	−0.611344	−	0.791365i	$-0.709371\pi$
$719$	10.1805	−	17.6332i	0.379670	−	0.657608i	0.991014	+	0.133757i	$0.0427041\pi$
$720$		0			0
$721$	−47.7137	+	12.7849i	−1.77695	+	0.476133i
$722$	−12.6423	+	10.4667i	−0.470497	+	0.389529i
$723$		0			0
$724$	−13.9085	+	4.85526i	−0.516906	+	0.180444i
$725$	−0.163140	−	0.282568i	−0.00605888	−	0.0104943i
$726$		0			0
$727$	16.4107			0.608639			0.304320	−	0.952570i	$-0.401571\pi$
$727$	16.4107			0.608639			0.304320	+	0.952570i	$0.401571\pi$
$728$	−14.6264	+	47.5511i	−0.542089	+	1.76236i
$729$		0			0
$730$	−9.94168	−	58.6438i	−0.367958	−	2.17050i
$731$	18.0406	+	31.2472i	0.667256	+	1.15572i
$732$		0			0
$733$	−26.6302	+	26.6302i	−0.983610	+	0.983610i	−0.999868	−	0.0162577i	$-0.994825\pi$
$733$	−26.6302	+	26.6302i	−0.983610	+	0.983610i	0.0162577	+	0.999868i	$0.494825\pi$
$734$	−2.15788	+	1.78653i	−0.0796488	+	0.0659420i
$735$		0			0
$736$	37.8112	+	7.96228i	1.39374	+	0.293494i
$737$	5.05671	−	8.75848i	0.186266	−	0.322623i
$738$		0			0
$739$	−16.2372	−	4.35076i	−0.597296	−	0.160045i	−0.0525107	−	0.998620i	$-0.516722\pi$
$739$	−16.2372	−	4.35076i	−0.597296	−	0.160045i	−0.544786	+	0.838575i	$0.683389\pi$
$740$	−18.4969	−	15.9417i	−0.679960	−	0.586029i
$741$		0			0
$742$	23.6293	+	51.5593i	0.867459	+	1.89280i
$743$	−13.7938	−	3.69604i	−0.506046	−	0.135594i	−0.00324119	−	0.999995i	$-0.501032\pi$
$743$	−13.7938	−	3.69604i	−0.506046	−	0.135594i	−0.502804	+	0.864400i	$0.667698\pi$
$744$		0			0
$745$	43.3546	+	25.0308i	1.58839	+	0.917058i
$746$	27.2500	+	10.1225i	0.997694	+	0.370609i
$747$		0			0
$748$	−16.5745	−	7.99697i	−0.606025	−	0.292398i
$749$	−35.0801	−	35.0801i	−1.28180	−	1.28180i
$750$		0			0
$751$	−20.9053	−	36.2090i	−0.762844	−	1.32129i	−0.941379	−	0.337351i	$-0.890469\pi$
$751$	−20.9053	−	36.2090i	−0.762844	−	1.32129i	0.178534	−	0.983934i	$-0.442864\pi$
$752$	10.5120	+	1.20016i	0.383335	+	0.0437654i
$753$		0			0
$754$	−0.307734	+	0.787636i	−0.0112070	+	0.0286840i
$755$	−29.7022			−1.08097
$756$		0			0
$757$	−33.0464	+	19.0794i	−1.20109	+	0.693451i	−0.960798	−	0.277249i	$-0.910577\pi$
$757$	−33.0464	+	19.0794i	−1.20109	+	0.693451i	−0.240294	+	0.970700i	$0.577244\pi$
$758$	−0.814296	+	8.64928i	−0.0295766	+	0.314156i
$759$		0			0
$760$	−0.402125	+	20.2978i	−0.0145866	+	0.736279i
$761$	0.805403	+	3.00580i	0.0291958	+	0.108960i	0.978986	−	0.203927i	$-0.0653705\pi$
$761$	0.805403	+	3.00580i	0.0291958	+	0.108960i	−0.949790	+	0.312887i	$0.898704\pi$
$762$		0			0
$763$	−17.4711	+	30.2608i	−0.632495	+	1.09551i
$764$	−11.4638	−	2.17784i	−0.414744	−	0.0787914i
$765$		0			0
$766$	7.20070	+	15.7120i	0.260172	+	0.567697i
$767$	3.41291	+	3.52955i	0.123233	+	0.127445i
$768$		0			0
$769$	2.20764	−	8.23902i	0.0796094	−	0.297106i	−0.914629	−	0.404293i	$-0.867518\pi$
$769$	2.20764	−	8.23902i	0.0796094	−	0.297106i	0.994239	+	0.107187i	$0.0341842\pi$
$770$	−21.8269	+	30.7380i	−0.786586	+	1.10772i
$771$		0			0
$772$	36.2152	−	2.68704i	1.30341	−	0.0967086i
$773$	7.00923	+	26.1588i	0.252105	+	0.940867i	0.969678	+	0.244385i	$0.0785860\pi$
$773$	7.00923	+	26.1588i	0.252105	+	0.940867i	−0.717574	+	0.696483i	$0.754747\pi$
$774$		0			0
$775$	−7.42379	−	7.42379i	−0.266670	−	0.266670i
$776$	−3.21784	+	3.09282i	−0.115514	+	0.111026i
$777$		0			0
$778$	−41.7785	+	7.08257i	−1.49783	+	0.253922i
$779$		−	21.7087i		−	0.777794i
$780$		0			0
$781$		−	19.7092i		−	0.705250i
$782$	−7.17657	−	42.3330i	−0.256633	−	1.51382i
$783$		0			0
$784$	24.6410	−	62.5124i	0.880037	−	2.23259i
$785$	−18.1623	−	18.1623i	−0.648241	−	0.648241i
$786$		0			0
$787$	−2.25972	−	8.43338i	−0.0805502	−	0.300617i	0.913884	−	0.405975i	$-0.133068\pi$
$787$	−2.25972	−	8.43338i	−0.0805502	−	0.300617i	−0.994434	+	0.105357i	$0.966401\pi$
$788$	16.0461	−	1.19056i	0.571617	−	0.0424119i
$789$		0			0
$790$	−30.1826	−	21.4325i	−1.07385	−	0.762534i
$791$	0.943526	−	3.52129i	0.0335479	−	0.125203i
$792$		0			0
$793$	−2.50199	−	0.0420367i	−0.0888484	−	0.00149277i
$794$	−14.9544	+	6.85351i	−0.530712	+	0.243222i
$795$		0			0
$796$	−1.22494	+	6.44786i	−0.0434168	+	0.228538i
$797$	−15.5889	+	27.0008i	−0.552188	+	0.956418i	0.445928	+	0.895069i	$0.352874\pi$
$797$	−15.5889	+	27.0008i	−0.552188	+	0.956418i	−0.998116	+	0.0613490i	$0.980460\pi$
$798$		0			0
$799$	−3.04288	−	11.3562i	−0.107649	−	0.401752i
$800$	−8.28497	−	7.43148i	−0.292918	−	0.262743i
$801$		0			0
$802$	35.6162	+	3.35312i	1.25765	+	0.118403i
$803$	−28.5667	+	16.4930i	−1.00810	+	0.582026i
$804$		0			0
$805$	−87.9587			−3.10014
$806$	−3.00512	+	27.0432i	−0.105851	+	0.952556i
$807$		0			0
$808$	6.91482	+	4.17704i	0.243263	+	0.146948i
$809$	−3.86999	−	6.70302i	−0.136062	−	0.235666i	0.789941	−	0.613183i	$-0.210111\pi$
$809$	−3.86999	−	6.70302i	−0.136062	−	0.235666i	−0.926003	+	0.377517i	$0.876778\pi$
$810$		0			0
$811$	7.65096	+	7.65096i	0.268661	+	0.268661i	0.828561	−	0.559899i	$-0.189160\pi$
$811$	7.65096	+	7.65096i	0.268661	+	0.268661i	−0.559899	+	0.828561i	$0.689160\pi$
$812$	0.703122	−	1.45729i	0.0246748	−	0.0511409i
$813$		0			0
$814$	−4.71551	+	12.6943i	−0.165279	+	0.444936i
$815$	−56.9323	−	32.8699i	−1.99425	−	1.15138i
$816$		0			0
$817$	−21.3220	−	5.71322i	−0.745963	−	0.199880i
$818$	26.6644	−	12.2201i	0.932300	−	0.427267i
$819$		0			0
$820$	31.9246	+	27.5144i	1.11485	+	0.960844i
$821$	2.11509	+	0.566738i	0.0738173	+	0.0197793i	0.295539	−	0.955331i	$-0.404501\pi$
$821$	2.11509	+	0.566738i	0.0738173	+	0.0197793i	−0.221721	+	0.975110i	$0.571168\pi$
$822$		0			0
$823$	22.8632	−	39.6002i	0.796960	−	1.38037i	−0.124627	−	0.992204i	$-0.539774\pi$
$823$	22.8632	−	39.6002i	0.796960	−	1.38037i	0.921587	−	0.388171i	$-0.126893\pi$
$824$	−25.0816	+	13.8258i	−0.873759	+	0.481646i
$825$		0			0
$826$	−5.99106	−	7.23637i	−0.208456	−	0.251786i
$827$	−1.50831	+	1.50831i	−0.0524490	+	0.0524490i	−0.732845	−	0.680396i	$-0.761808\pi$
$827$	−1.50831	+	1.50831i	−0.0524490	+	0.0524490i	0.680396	+	0.732845i	$0.261808\pi$
$828$		0			0
$829$	−2.20284	−	3.81543i	−0.0765077	−	0.132515i	0.825233	−	0.564792i	$-0.191044\pi$
$829$	−2.20284	−	3.81543i	−0.0765077	−	0.132515i	−0.901741	+	0.432277i	$0.857710\pi$
$830$	20.2180	−	3.42750i	0.701778	−	0.118970i
$831$		0			0
$832$	−1.62645	+	28.7985i	−0.0563871	+	0.998409i
$833$	−74.6650			−2.58699
$834$		0			0
$835$	−13.1702	−	22.8114i	−0.455772	−	0.789420i
$836$	10.6297	−	3.71067i	0.367635	−	0.128336i
$837$		0			0
$838$	28.0810	+	33.9180i	0.970042	+	1.17168i
$839$	9.23752	−	2.47519i	0.318915	−	0.0854529i	−0.0958107	−	0.995400i	$-0.530544\pi$
$839$	9.23752	−	2.47519i	0.318915	−	0.0854529i	0.414725	+	0.909947i	$0.363878\pi$
$840$		0			0
$841$	−14.4862	+	25.0909i	−0.499526	+	0.865204i
$842$	0.684322	−	0.963707i	0.0235833	−	0.0332115i
$843$		0			0
$844$	18.6892	+	16.1074i	0.643309	+	0.554440i
$845$	7.76283	+	33.4251i	0.267050	+	1.14986i
$846$		0			0
$847$	−31.6390	−	8.47765i	−1.08713	−	0.291295i
$848$	20.4644	+	25.7396i	0.702752	+	0.883900i
$849$		0			0
$850$	−4.30644	+	11.5931i	−0.147710	+	0.397640i
$851$	−30.5188	+	8.17749i	−1.04617	+	0.280321i
$852$		0			0
$853$	−28.6500	−	28.6500i	−0.980956	−	0.980956i	0.0188661	−	0.999822i	$-0.493994\pi$
$853$	−28.6500	−	28.6500i	−0.980956	−	0.980956i	−0.999822	+	0.0188661i	$0.993994\pi$
$854$	4.76704	+	0.448798i	0.163125	+	0.0153575i
$855$		0			0
$856$	−24.6205	−	14.8725i	−0.841510	−	0.508332i
$857$			11.6602i			0.398306i	0.979968	+	0.199153i	$0.0638191\pi$
$857$			11.6602i			0.398306i	−0.979968	+	0.199153i	$0.936181\pi$
$858$		0			0
$859$	29.0257			0.990343			0.495172	−	0.868795i	$-0.335105\pi$
$859$	29.0257			0.990343			0.495172	+	0.868795i	$0.335105\pi$
$860$	35.4261	−	24.1148i	1.20802	−	0.822307i
$861$		0			0
$862$	−12.2589	−	1.15413i	−0.417540	−	0.0393098i
$863$	−8.05746	+	8.05746i	−0.274279	+	0.274279i	−0.830820	−	0.556541i	$-0.812128\pi$
$863$	−8.05746	+	8.05746i	−0.274279	+	0.274279i	0.556541	+	0.830820i	$0.312128\pi$
$864$		0			0
$865$	−7.24145	−	27.0255i	−0.246217	−	0.918894i
$866$	−13.3347	−	4.95339i	−0.453132	−	0.168323i
$867$		0			0
$868$	9.71718	−	51.1495i	0.329823	−	1.73613i
$869$	−5.31333	+	19.8296i	−0.180242	+	0.672673i
$870$		0			0
$871$	4.27243	+	17.0882i	0.144766	+	0.579011i
$872$	−5.63002	+	19.4611i	−0.190657	+	0.659036i
$873$		0			0
$874$	21.4179	+	15.2087i	0.724472	+	0.514443i
$875$	−33.8181	−	19.5249i	−1.14326	−	0.660062i
$876$		0			0
$877$	1.68176	+	6.27643i	0.0567891	+	0.211940i	0.988490	−	0.151287i	$-0.0483417\pi$
$877$	1.68176	+	6.27643i	0.0567891	+	0.211940i	−0.931701	+	0.363227i	$0.881675\pi$
$878$	6.92454	+	8.36389i	0.233692	+	0.282268i
$879$		0			0
$880$	−8.01559	+	20.3349i	−0.270205	+	0.685490i
$881$	−16.3109	+	9.41711i	−0.549528	+	0.317270i	−0.748932	−	0.662647i	$-0.769433\pi$
$881$	−16.3109	+	9.41711i	−0.549528	+	0.317270i	0.199403	+	0.979917i	$0.436100\pi$
$882$		0			0
$883$			7.15931i			0.240930i	0.992718	+	0.120465i	$0.0384385\pi$
$883$			7.15931i			0.240930i	−0.992718	+	0.120465i	$0.961561\pi$
$884$	30.4340	−	10.0538i	1.02361	−	0.338145i
$885$		0			0
$886$	8.50365	−	1.44160i	0.285686	−	0.0484314i
$887$	5.21027	−	3.00815i	0.174944	−	0.101004i	−0.409971	−	0.912098i	$-0.634461\pi$
$887$	5.21027	−	3.00815i	0.174944	−	0.101004i	0.584915	+	0.811095i	$0.301128\pi$
$888$		0			0
$889$	−55.6727	−	55.6727i	−1.86720	−	1.86720i
$890$	39.1626	−	32.4231i	1.31273	−	1.08682i
$891$		0			0
$892$	−50.4418	+	3.74260i	−1.68892	+	0.125312i
$893$	6.22906	+	3.59635i	0.208447	+	0.120347i
$894$		0			0
$895$	−10.8981	+	40.6721i	−0.364282	+	1.35952i
$896$	7.34559	−	54.7014i	0.245399	−	1.82744i
$897$		0			0
$898$	14.2247	+	31.0383i	0.474684	+	1.03576i
$899$	0.229045	−	0.854807i	0.00763907	−	0.0285094i
$900$		0			0
$901$	18.2699	−	31.6443i	0.608658	−	1.05423i
$902$	8.13868	−	21.9096i	0.270989	−	0.729511i
$903$		0			0
$904$	0.0418655	−	2.11321i	0.00139242	−	0.0702845i
$905$	13.7481	−	13.7481i	0.457002	−	0.457002i
$906$		0			0
$907$	7.90224	−	4.56236i	0.262390	−	0.151491i	−0.363035	−	0.931776i	$-0.618259\pi$
$907$	7.90224	−	4.56236i	0.262390	−	0.151491i	0.625424	+	0.780285i	$0.284926\pi$
$908$	36.4977	−	24.8442i	1.21122	−	0.824485i
$909$		0			0
$910$	−9.88541	−	64.9111i	−0.327698	−	2.15178i
$911$			33.8691i			1.12213i	0.827770	+	0.561067i	$0.189609\pi$
$911$			33.8691i			1.12213i	−0.827770	+	0.561067i	$0.810391\pi$
$912$		0			0
$913$	−5.68614	−	9.84868i	−0.188184	−	0.325944i
$914$	−2.63524	+	27.9910i	−0.0871660	+	0.925860i
$915$		0			0
$916$	−29.8560	−	14.4051i	−0.986469	−	0.475957i
$917$	−78.4941	+	21.0324i	−2.59210	+	0.694552i
$918$		0			0
$919$	15.7907	+	9.11677i	0.520887	+	0.300734i	0.737298	−	0.675568i	$-0.236102\pi$
$919$	15.7907	+	9.11677i	0.520887	+	0.300734i	−0.216410	+	0.976302i	$0.569435\pi$
$920$	−49.5117	+	12.2209i	−1.63235	+	0.402910i
$921$		0			0
$922$	7.26276	+	15.8474i	0.239186	+	0.521907i
$923$	23.8615	+	24.6770i	0.785411	+	0.812253i
$924$		0			0
$925$	8.79030	+	2.35535i	0.289023	+	0.0774436i
$926$	−9.60830	−	6.82279i	−0.315748	−	0.224211i
$927$		0			0
$928$	0.193311	−	0.917996i	0.00634576	−	0.0301347i
$929$	−41.6902	+	11.1709i	−1.36781	+	0.366504i	−0.866679	−	0.498866i	$-0.833750\pi$
$929$	−41.6902	+	11.1709i	−1.36781	+	0.366504i	−0.501133	+	0.865370i	$0.667083\pi$
$930$		0			0
$931$	32.3002	−	32.3002i	1.05860	−	1.05860i
$932$	−3.23730	−	9.27366i	−0.106041	−	0.303769i
$933$		0			0
$934$	−5.55814	−	32.7862i	−0.181868	−	1.07280i
$935$	24.2881			0.794305
$936$		0			0
$937$	12.5702			0.410650			0.205325	−	0.978694i	$-0.434175\pi$
$937$	12.5702			0.410650			0.205325	+	0.978694i	$0.434175\pi$
$938$	−5.63333	−	33.2297i	−0.183935	−	1.08499i
$939$		0			0
$940$	−13.1837	+	4.60224i	−0.430005	+	0.150108i
$941$	−19.4028	+	19.4028i	−0.632512	+	0.632512i	−0.948697	−	0.316185i	$-0.897598\pi$
$941$	−19.4028	+	19.4028i	−0.632512	+	0.632512i	0.316185	+	0.948697i	$0.397598\pi$
$942$		0			0
$943$	52.6736	−	14.1138i	1.71529	−	0.459610i
$944$	−4.37776	−	3.24094i	−0.142484	−	0.105484i
$945$		0			0
$946$	−19.3775	−	13.7598i	−0.630016	−	0.447370i
$947$	23.2132	+	6.21995i	0.754327	+	0.202121i	0.615437	−	0.788186i	$-0.288980\pi$
$947$	23.2132	+	6.21995i	0.754327	+	0.202121i	0.138890	+	0.990308i	$0.455646\pi$
$948$		0			0
$949$	15.7994	−	55.2354i	0.512871	−	1.79302i
$950$	−3.15222	−	6.87817i	−0.102271	−	0.223157i
$951$		0			0
$952$	−59.5423	+	14.6967i	−1.92978	+	0.476322i
$953$	7.54135	+	4.35400i	0.244288	+	0.141040i	0.617146	−	0.786849i	$-0.288289\pi$
$953$	7.54135	+	4.35400i	0.244288	+	0.141040i	−0.372858	+	0.927889i	$0.621622\pi$
$954$		0			0
$955$	14.8757	−	3.98592i	0.481365	−	0.128981i
$956$	−12.5477	+	26.0063i	−0.405821	+	0.841104i
$957$		0			0
$958$	0.422409	−	4.48674i	0.0136474	−	0.144960i
$959$	7.16303	+	12.4067i	0.231306	+	0.400634i
$960$		0			0
$961$			2.52438i			0.0814317i
$962$	−9.46468	−	21.6030i	−0.305154	−	0.696509i
$963$		0			0
$964$	3.02295	+	4.44090i	0.0973626	+	0.143032i
$965$	−41.5070	+	23.9641i	−1.33616	+	0.771430i
$966$		0			0
$967$	−32.8150	+	32.8150i	−1.05526	+	1.05526i	−0.0568771	+	0.998381i	$0.518114\pi$
$967$	−32.8150	+	32.8150i	−1.05526	+	1.05526i	−0.998381	+	0.0568771i	$0.981886\pi$
$968$	−18.9874	−	0.376164i	−0.610277	−	0.0120904i
$969$		0			0
$970$	2.05118	−	5.52184i	0.0658593	−	0.177296i
$971$	−0.777271	+	1.34627i	−0.0249438	+	0.0432040i	−0.878228	−	0.478242i	$-0.841274\pi$
$971$	−0.777271	+	1.34627i	−0.0249438	+	0.0432040i	0.853284	+	0.521446i	$0.174607\pi$
$972$		0			0
$973$	4.77670	−	17.8269i	0.153134	−	0.571504i
$974$	10.0380	+	21.9029i	0.321638	+	0.701816i
$975$		0			0
$976$	2.74571	−	0.409699i	0.0878880	−	0.0131141i
$977$	−10.8059	+	40.3282i	−0.345712	+	1.29021i	0.546067	+	0.837742i	$0.316125\pi$
$977$	−10.8059	+	40.3282i	−0.345712	+	1.29021i	−0.891778	+	0.452472i	$0.850542\pi$
$978$		0			0
$979$	−24.4182	−	14.0979i	−0.780409	−	0.450569i
$980$	6.56184	+	88.4388i	0.209610	+	2.82508i
$981$		0			0
$982$	−13.2539	+	10.9730i	−0.422950	+	0.350164i
$983$	18.5465	+	18.5465i	0.591540	+	0.591540i	0.938047	−	0.346507i	$-0.112632\pi$
$983$	18.5465	+	18.5465i	0.591540	+	0.591540i	−0.346507	+	0.938047i	$0.612632\pi$
$984$		0			0
$985$	−18.3907	+	10.6179i	−0.585976	+	0.338313i
$986$	−1.02778	+	0.174235i	−0.0327311	+	0.00554879i
$987$		0			0
$988$	−8.81653	+	17.5151i	−0.280491	+	0.557230i
$989$		−	55.4498i		−	1.76320i
$990$		0			0
$991$	−38.3423	+	22.1369i	−1.21798	+	0.703203i	−0.964486	−	0.264133i	$-0.914914\pi$
$991$	−38.3423	+	22.1369i	−1.21798	+	0.703203i	−0.253497	+	0.967336i	$0.581581\pi$
$992$	−1.63687	−	30.1420i	−0.0519707	−	0.957010i
$993$		0			0
$994$	−41.8868	−	50.5934i	−1.32857	−	1.60473i
$995$	−2.24191	−	8.36691i	−0.0710733	−	0.265249i
$996$		0			0
$997$	11.1621	+	6.44442i	0.353506	+	0.204097i	0.666228	−	0.745748i	$-0.267908\pi$
$997$	11.1621	+	6.44442i	0.353506	+	0.204097i	−0.312722	+	0.949845i	$0.601241\pi$
$998$	−47.1880	−	33.5079i	−1.49371	−	1.06067i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.c.739.12		48
3.2	odd	2		312.2.bt.c.115.1	yes	48
8.3	odd	2	inner	936.2.ed.c.739.3		48
13.6	odd	12	inner	936.2.ed.c.19.3		48
24.11	even	2		312.2.bt.c.115.10	yes	48
39.32	even	12		312.2.bt.c.19.10	yes	48
104.19	even	12	inner	936.2.ed.c.19.12		48
312.227	odd	12		312.2.bt.c.19.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.c.19.1	✓	48	312.227	odd	12
312.2.bt.c.19.10	yes	48	39.32	even	12
312.2.bt.c.115.1	yes	48	3.2	odd	2
312.2.bt.c.115.10	yes	48	24.11	even	2
936.2.ed.c.19.3		48	13.6	odd	12	inner
936.2.ed.c.19.12		48	104.19	even	12	inner
936.2.ed.c.739.3		48	8.3	odd	2	inner
936.2.ed.c.739.12		48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39432 - 0.236374i) q^{2} +(1.88825 - 0.659163i) q^{4} +(-1.86647 + 1.86647i) q^{5} +(4.71214 - 1.26261i) q^{7} +(2.47702 - 1.36542i) q^{8} +(-2.16128 + 3.04365i) q^{10} +(1.99964 + 0.535801i) q^{11} +(-3.15234 + 1.75007i) q^{13} +(6.27177 - 2.87431i) q^{14} +(3.13101 - 2.48933i) q^{16} +(-3.84928 - 2.22238i) q^{17} +(2.62661 - 0.703799i) q^{19} +(-2.29407 + 4.75469i) q^{20} +(2.91478 + 0.274415i) q^{22} +(3.41537 + 5.91559i) q^{23} -1.96745i q^{25} +(-3.98170 + 3.18529i) q^{26} +(8.06544 - 5.49020i) q^{28} +(0.143621 - 0.0829197i) q^{29} +(3.77330 - 3.77330i) q^{31} +(3.77721 - 4.21102i) q^{32} +(-5.89244 - 2.18884i) q^{34} +(-6.43844 + 11.1517i) q^{35} +(-1.19716 + 4.46786i) q^{37} +(3.49598 - 1.60218i) q^{38} +(-2.07478 + 7.17181i) q^{40} +(2.06622 - 7.71126i) q^{41} +(-7.03012 - 4.05884i) q^{43} +(4.12900 - 0.306357i) q^{44} +(6.16041 + 7.44092i) q^{46} +(1.87036 + 1.87036i) q^{47} +(14.5479 - 8.39921i) q^{49} +(-0.465055 - 2.74326i) q^{50} +(-4.79885 + 5.38248i) q^{52} +8.22085i q^{53} +(-4.73233 + 2.73221i) q^{55} +(9.94806 - 9.56155i) q^{56} +(0.180654 - 0.149565i) q^{58} +(-0.352439 - 1.31532i) q^{59} +(0.601045 + 0.347013i) q^{61} +(4.36928 - 6.15310i) q^{62} +(4.27127 - 6.76434i) q^{64} +(2.61731 - 9.15022i) q^{65} +(1.26441 - 4.71883i) q^{67} +(-8.73333 - 1.65912i) q^{68} +(-6.34127 + 17.0709i) q^{70} +(-2.46409 - 9.19612i) q^{71} +(-11.2670 + 11.2670i) q^{73} +(-0.613136 + 6.51261i) q^{74} +(4.49579 - 3.06032i) q^{76} +10.0991 q^{77} +9.91660i q^{79} +(-1.19767 + 10.4902i) q^{80} +(1.05824 - 11.2404i) q^{82} +(-3.88441 - 3.88441i) q^{83} +(11.3326 - 3.03656i) q^{85} +(-10.7616 - 3.99758i) q^{86} +(5.68474 - 1.40315i) q^{88} +(-13.1559 - 3.52510i) q^{89} +(-12.6446 + 12.2267i) q^{91} +(10.3484 + 8.91886i) q^{92} +(3.04998 + 2.16577i) q^{94} +(-3.58888 + 6.21613i) q^{95} +(-1.52421 + 0.408410i) q^{97} +(18.2990 - 15.1499i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 4 q^{8} - 6 q^{10} - 20 q^{11} + 28 q^{14} + 4 q^{16} - 12 q^{17} + 20 q^{19} - 4 q^{20} + 14 q^{22} + 12 q^{26} - 2 q^{28} + 18 q^{32} - 12 q^{35} + 52 q^{40} + 36 q^{41} + 12 q^{43} - 12 q^{44}+ \cdots + 6 q^{98}+O(q^{100}) \) 48 * q - 2 * q^2 + 4 * q^8 - 6 * q^10 - 20 * q^11 + 28 * q^14 + 4 * q^16 - 12 * q^17 + 20 * q^19 - 4 * q^20 + 14 * q^22 + 12 * q^26 - 2 * q^28 + 18 * q^32 - 12 * q^35 + 52 * q^40 + 36 * q^41 + 12 * q^43 - 12 * q^44 - 14 * q^46 + 24 * q^49 + 32 * q^50 + 24 * q^52 + 54 * q^56 - 22 * q^58 - 96 * q^59 + 108 * q^62 + 52 * q^65 - 12 * q^67 + 6 * q^68 - 52 * q^70 - 48 * q^73 + 114 * q^76 + 16 * q^80 - 60 * q^82 - 48 * q^83 - 24 * q^86 + 102 * q^88 - 80 * q^89 - 152 * q^91 + 100 * q^92 - 10 * q^94 - 64 * q^97 + 6 * q^98

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