LMFDB - Embedded newform 416.2.bd.a.83.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.5
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35152 + 0.416401i) q^{2} +(-2.25523 - 0.934148i) q^{3} +(1.65322 - 1.12555i) q^{4} +(0.261748 - 0.631915i) q^{5} +(3.43698 + 0.323439i) q^{6} -4.76655i q^{7} +(-1.76568 + 2.20961i) q^{8} +(2.09213 + 2.09213i) q^{9} +O(q^{10})$	\(q+(-1.35152 + 0.416401i) q^{2} +(-2.25523 - 0.934148i) q^{3} +(1.65322 - 1.12555i) q^{4} +(0.261748 - 0.631915i) q^{5} +(3.43698 + 0.323439i) q^{6} -4.76655i q^{7} +(-1.76568 + 2.20961i) q^{8} +(2.09213 + 2.09213i) q^{9} +(-0.0906275 + 0.963039i) q^{10} +(1.63978 + 0.679219i) q^{11} +(-4.77983 + 0.994027i) q^{12} +(3.28393 - 1.48856i) q^{13} +(1.98480 + 6.44209i) q^{14} +(-1.18061 + 1.18061i) q^{15} +(1.46627 - 3.72157i) q^{16} -2.74788 q^{17} +(-3.69872 - 1.95639i) q^{18} +(0.414355 + 1.00034i) q^{19} +(-0.278526 - 1.33931i) q^{20} +(-4.45266 + 10.7497i) q^{21} +(-2.49902 - 0.235173i) q^{22} +(-5.08603 - 5.08603i) q^{23} +(6.04613 - 3.33378i) q^{24} +(3.20473 + 3.20473i) q^{25} +(-3.81846 + 3.37925i) q^{26} +(0.0385689 + 0.0931135i) q^{27} +(-5.36499 - 7.88015i) q^{28} +(0.203632 - 0.491611i) q^{29} +(1.10401 - 2.08722i) q^{30} +(-5.24354 - 5.24354i) q^{31} +(-0.432033 + 5.64033i) q^{32} +(-3.06360 - 3.06360i) q^{33} +(3.71382 - 1.14422i) q^{34} +(-3.01206 - 1.24763i) q^{35} +(5.81354 + 1.10395i) q^{36} +(-4.94751 - 2.04933i) q^{37} +(-0.976552 - 1.17944i) q^{38} +(-8.79656 + 0.289375i) q^{39} +(0.934122 + 1.69412i) q^{40} -2.97903 q^{41} +(1.54169 - 16.3825i) q^{42} +(-2.44549 - 5.90392i) q^{43} +(3.47541 - 0.722757i) q^{44} +(1.86966 - 0.774437i) q^{45} +(8.99170 + 4.75604i) q^{46} +(-2.46927 - 2.46927i) q^{47} +(-6.78328 + 7.02328i) q^{48} -15.7200 q^{49} +(-5.66571 - 2.99681i) q^{50} +(6.19712 + 2.56693i) q^{51} +(3.75361 - 6.15715i) q^{52} +(1.10766 + 2.67412i) q^{53} +(-0.0908993 - 0.109785i) q^{54} +(0.858418 - 0.858418i) q^{55} +(10.5322 + 8.41621i) q^{56} -2.64307i q^{57} +(-0.0705055 + 0.749215i) q^{58} +(-3.75224 + 9.05870i) q^{59} +(-0.622969 + 3.28063i) q^{60} +(-4.09073 + 9.87589i) q^{61} +(9.27017 + 4.90334i) q^{62} +(9.97222 - 9.97222i) q^{63} +(-1.76474 - 7.80293i) q^{64} +(-0.0810828 - 2.46479i) q^{65} +(5.41620 + 2.86483i) q^{66} +(7.51832 - 3.11419i) q^{67} +(-4.54286 + 3.09288i) q^{68} +(6.71907 + 16.2213i) q^{69} +(4.59037 + 0.431980i) q^{70} +12.2690 q^{71} +(-8.31681 + 0.928752i) q^{72} -1.56983i q^{73} +(7.54001 + 0.709558i) q^{74} +(-4.23372 - 10.2211i) q^{75} +(1.81095 + 1.18741i) q^{76} +(3.23753 - 7.81609i) q^{77} +(11.7682 - 4.05400i) q^{78} -4.45846 q^{79} +(-1.96792 - 1.90067i) q^{80} -9.12216i q^{81} +(4.02623 - 1.24047i) q^{82} +(5.77758 + 13.9483i) q^{83} +(4.73808 + 22.7833i) q^{84} +(-0.719253 + 1.73643i) q^{85} +(5.76353 + 6.96098i) q^{86} +(-0.918475 + 0.918475i) q^{87} +(-4.39614 + 2.42399i) q^{88} +4.19672 q^{89} +(-2.20440 + 1.82520i) q^{90} +(-7.09530 - 15.6530i) q^{91} +(-14.1329 - 2.68374i) q^{92} +(6.92716 + 16.7236i) q^{93} +(4.36548 + 2.30906i) q^{94} +0.740587 q^{95} +(6.24324 - 12.3167i) q^{96} +(-0.245304 + 0.245304i) q^{97} +(21.2459 - 6.54582i) q^{98} +(2.00961 + 4.85164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.35152	+	0.416401i	−0.955670	+	0.294440i
$2$	−1.35152	+	0.416401i	−0.955670	+	0.294440i
$3$	−2.25523	−	0.934148i	−1.30206	−	0.539331i	−0.379502	−	0.925191i	$-0.623905\pi$
$3$	−2.25523	−	0.934148i	−1.30206	−	0.539331i	−0.922557	+	0.385860i	$0.873905\pi$
$4$	1.65322	−	1.12555i	0.826610	−	0.562775i
$5$	0.261748	−	0.631915i	0.117057	−	0.282601i	−0.854482	−	0.519482i	$-0.826125\pi$
$5$	0.261748	−	0.631915i	0.117057	−	0.282601i	0.971539	+	0.236881i	$0.0761250\pi$
$6$	3.43698	+	0.323439i	1.40314	+	0.132043i
$7$		−	4.76655i		−	1.80159i	−0.434249	−	0.900793i	$-0.642986\pi$
$7$		−	4.76655i		−	1.80159i	0.434249	−	0.900793i	$-0.357014\pi$
$8$	−1.76568	+	2.20961i	−0.624263	+	0.781215i
$9$	2.09213	+	2.09213i	0.697375	+	0.697375i
$10$	−0.0906275	+	0.963039i	−0.0286589	+	0.304540i
$11$	1.63978	+	0.679219i	0.494412	+	0.204792i	0.615936	−	0.787796i	$-0.288778\pi$
$11$	1.63978	+	0.679219i	0.494412	+	0.204792i	−0.121524	+	0.992589i	$0.538778\pi$
$12$	−4.77983	+	0.994027i	−1.37982	+	0.286951i
$13$	3.28393	−	1.48856i	0.910798	−	0.412852i
$13$	3.28393	−	1.48856i	0.910798	−	0.412852i
$14$	1.98480	+	6.44209i	0.530459	+	1.72172i
$15$	−1.18061	+	1.18061i	−0.304831	+	0.304831i
$16$	1.46627	−	3.72157i	0.366568	−	0.930391i
$17$	−2.74788			−0.666460			−0.333230	−	0.942846i	$-0.608138\pi$
$17$	−2.74788			−0.666460			−0.333230	+	0.942846i	$0.608138\pi$
$18$	−3.69872	−	1.95639i	−0.871796	−	0.461125i
$19$	0.414355	+	1.00034i	0.0950595	+	0.229494i	0.964256	−	0.264973i	$-0.0853632\pi$
$19$	0.414355	+	1.00034i	0.0950595	+	0.229494i	−0.869196	+	0.494467i	$0.835363\pi$
$20$	−0.278526	−	1.33931i	−0.0622803	−	0.299478i
$21$	−4.45266	+	10.7497i	−0.971651	+	2.34577i
$22$	−2.49902	−	0.235173i	−0.532794	−	0.0501390i
$23$	−5.08603	−	5.08603i	−1.06051	−	1.06051i	−0.998047	−	0.0624623i	$-0.980105\pi$
$23$	−5.08603	−	5.08603i	−1.06051	−	1.06051i	−0.0624623	−	0.998047i	$-0.519895\pi$
$24$	6.04613	−	3.33378i	1.23416	−	0.680504i
$25$	3.20473	+	3.20473i	0.640946	+	0.640946i
$26$	−3.81846	+	3.37925i	−0.748862	+	0.662726i
$27$	0.0385689	+	0.0931135i	0.00742259	+	0.0179197i
$28$	−5.36499	−	7.88015i	−1.01389	−	1.48921i
$29$	0.203632	−	0.491611i	0.0378135	−	0.0912899i	−0.903845	−	0.427861i	$-0.859267\pi$
$29$	0.203632	−	0.491611i	0.0378135	−	0.0912899i	0.941658	+	0.336571i	$0.109267\pi$
$30$	1.10401	−	2.08722i	0.201563	−	0.381072i
$31$	−5.24354	−	5.24354i	−0.941767	−	0.941767i	0.0566280	−	0.998395i	$-0.481965\pi$
$31$	−5.24354	−	5.24354i	−0.941767	−	0.941767i	−0.998395	+	0.0566280i	$0.981965\pi$
$32$	−0.432033	+	5.64033i	−0.0763734	+	0.997079i
$33$	−3.06360	−	3.06360i	−0.533303	−	0.533303i
$34$	3.71382	−	1.14422i	0.636915	−	0.196233i
$35$	−3.01206	−	1.24763i	−0.509130	−	0.210889i
$36$	5.81354	+	1.10395i	0.968923	+	0.183992i
$37$	−4.94751	−	2.04933i	−0.813366	−	0.336907i	−0.0630697	−	0.998009i	$-0.520089\pi$
$37$	−4.94751	−	2.04933i	−0.813366	−	0.336907i	−0.750296	+	0.661102i	$0.770089\pi$
$38$	−0.976552	−	1.17944i	−0.158418	−	0.191331i
$39$	−8.79656	+	0.289375i	−1.40858	+	0.0463371i
$40$	0.934122	+	1.69412i	0.147698	+	0.267864i
$41$	−2.97903			−0.465247			−0.232623	−	0.972567i	$-0.574731\pi$
$41$	−2.97903			−0.465247			−0.232623	+	0.972567i	$0.574731\pi$
$42$	1.54169	−	16.3825i	0.237888	−	2.52788i
$43$	−2.44549	−	5.90392i	−0.372933	−	0.900340i	−0.993250	−	0.115989i	$-0.962996\pi$
$43$	−2.44549	−	5.90392i	−0.372933	−	0.900340i	0.620317	−	0.784351i	$-0.287004\pi$
$44$	3.47541	−	0.722757i	0.523938	−	0.108960i
$45$	1.86966	−	0.774437i	0.278712	−	0.115446i
$46$	8.99170	+	4.75604i	1.32575	+	0.701240i
$47$	−2.46927	−	2.46927i	−0.360180	−	0.360180i	0.503699	−	0.863879i	$-0.331972\pi$
$47$	−2.46927	−	2.46927i	−0.360180	−	0.360180i	−0.863879	+	0.503699i	$0.831972\pi$
$48$	−6.78328	+	7.02328i	−0.979082	+	1.01372i
$49$	−15.7200			−2.24571
$50$	−5.66571	−	2.99681i	−0.801253	−	0.423812i
$51$	6.19712	+	2.56693i	0.867770	+	0.359442i
$52$	3.75361	−	6.15715i	0.520531	−	0.853842i
$53$	1.10766	+	2.67412i	0.152148	+	0.367318i	0.981515	−	0.191387i	$-0.0612984\pi$
$53$	1.10766	+	2.67412i	0.152148	+	0.367318i	−0.829367	+	0.558705i	$0.811298\pi$
$54$	−0.0908993	−	0.109785i	−0.0123698	−	0.0149398i
$55$	0.858418	−	0.858418i	0.115749	−	0.115749i
$56$	10.5322	+	8.41621i	1.40743	+	1.12466i
$57$		−	2.64307i		−	0.350083i
$58$	−0.0705055	+	0.749215i	−0.00925782	+	0.0983768i
$59$	−3.75224	+	9.05870i	−0.488499	+	1.17934i	0.466976	+	0.884270i	$0.345344\pi$
$59$	−3.75224	+	9.05870i	−0.488499	+	1.17934i	−0.955475	+	0.295072i	$0.904656\pi$
$60$	−0.622969	+	3.28063i	−0.0804250	+	0.423528i
$61$	−4.09073	+	9.87589i	−0.523764	+	1.26448i	0.411785	+	0.911281i	$0.364905\pi$
$61$	−4.09073	+	9.87589i	−0.523764	+	1.26448i	−0.935549	+	0.353197i	$0.885095\pi$
$62$	9.27017	+	4.90334i	1.17731	+	0.622725i
$63$	9.97222	−	9.97222i	1.25638	−	1.25638i
$64$	−1.76474	−	7.80293i	−0.220592	−	0.975366i
$65$	−0.0810828	−	2.46479i	−0.0100571	−	0.305720i
$66$	5.41620	+	2.86483i	0.666688	+	0.352636i
$67$	7.51832	−	3.11419i	0.918509	−	0.380459i	0.127201	−	0.991877i	$-0.459401\pi$
$67$	7.51832	−	3.11419i	0.918509	−	0.380459i	0.791308	+	0.611418i	$0.209401\pi$
$68$	−4.54286	+	3.09288i	−0.550902	+	0.375067i
$69$	6.71907	+	16.2213i	0.808881	+	1.95281i
$70$	4.59037	+	0.431980i	0.548655	+	0.0516315i
$71$	12.2690			1.45606			0.728028	−	0.685547i	$-0.240437\pi$
$71$	12.2690			1.45606			0.728028	+	0.685547i	$0.240437\pi$
$72$	−8.31681	+	0.928752i	−0.980145	+	0.109454i
$73$		−	1.56983i		−	0.183734i	−0.995771	−	0.0918672i	$-0.970716\pi$
$73$		−	1.56983i		−	0.183734i	0.995771	−	0.0918672i	$-0.0292835\pi$
$74$	7.54001	+	0.709558i	0.876508	+	0.0824844i
$75$	−4.23372	−	10.2211i	−0.488868	−	1.18023i
$76$	1.81095	+	1.18741i	0.207731	+	0.136205i
$77$	3.23753	−	7.81609i	0.368951	−	0.890726i
$78$	11.7682	−	4.05400i	1.33249	−	0.459025i
$79$	−4.45846			−0.501616			−0.250808	−	0.968037i	$-0.580696\pi$
$79$	−4.45846			−0.501616			−0.250808	+	0.968037i	$0.580696\pi$
$80$	−1.96792	−	1.90067i	−0.220020	−	0.212502i
$81$		−	9.12216i		−	1.01357i
$82$	4.02623	−	1.24047i	0.444622	−	0.136987i
$83$	5.77758	+	13.9483i	0.634172	+	1.53103i	0.834331	+	0.551263i	$0.185854\pi$
$83$	5.77758	+	13.9483i	0.634172	+	1.53103i	−0.200159	+	0.979763i	$0.564146\pi$
$84$	4.73808	+	22.7833i	0.516967	+	2.48586i
$85$	−0.719253	+	1.73643i	−0.0780139	+	0.188342i
$86$	5.76353	+	6.96098i	0.621497	+	0.750621i
$87$	−0.918475	+	0.918475i	−0.0984709	+	0.0984709i
$88$	−4.39614	+	2.42399i	−0.468630	+	0.258398i
$89$	4.19672			0.444851			0.222426	−	0.974950i	$-0.428603\pi$
$89$	4.19672			0.444851			0.222426	+	0.974950i	$0.428603\pi$
$90$	−2.20440	+	1.82520i	−0.232365	+	0.192392i
$91$	−7.09530	−	15.6530i	−0.743789	−	1.64088i
$92$	−14.1329	−	2.68374i	−1.47346	−	0.279799i
$93$	6.92716	+	16.7236i	0.718313	+	1.73416i
$94$	4.36548	+	2.30906i	0.450264	+	0.238162i
$95$	0.740587			0.0759826
$96$	6.24324	−	12.3167i	0.637198	−	1.25707i
$97$	−0.245304	+	0.245304i	−0.0249069	+	0.0249069i	−0.719451	−	0.694544i	$-0.755606\pi$
$97$	−0.245304	+	0.245304i	−0.0249069	+	0.0249069i	0.694544	+	0.719451i	$0.255606\pi$
$98$	21.2459	−	6.54582i	2.14616	−	0.661228i
$99$	2.00961	+	4.85164i	0.201974	+	0.487608i
$100$	8.90521	+	1.69104i	0.890521	+	0.169104i
$101$	−2.01267	−	4.85902i	−0.200268	−	0.483490i	0.791557	−	0.611096i	$-0.209271\pi$
$101$	−2.01267	−	4.85902i	−0.200268	−	0.483490i	−0.991825	+	0.127605i	$0.959271\pi$
$102$	−9.44441	−	0.888773i	−0.935136	−	0.0880017i
$103$	−8.16643	+	8.16643i	−0.804663	+	0.804663i	−0.983820	−	0.179158i	$-0.942663\pi$
$103$	−8.16643	+	8.16643i	−0.804663	+	0.804663i	0.179158	+	0.983820i	$0.442663\pi$
$104$	−2.50924	+	9.88452i	−0.246051	+	0.969257i
$105$	5.62741	+	5.62741i	0.549179	+	0.549179i
$106$	−2.61053	−	3.15290i	−0.253557	−	0.306236i
$107$	−0.342942	+	0.142051i	−0.0331534	+	0.0137326i	−0.399199	−	0.916865i	$-0.630712\pi$
$107$	−0.342942	+	0.142051i	−0.0331534	+	0.0137326i	0.366045	+	0.930597i	$0.380712\pi$
$108$	0.168567	+	0.110526i	0.0162204	+	0.0106354i
$109$	19.0153	−	7.87639i	1.82133	−	0.754421i	0.846178	−	0.532901i	$-0.178898\pi$
$109$	19.0153	−	7.87639i	1.82133	−	0.754421i	0.975156	−	0.221520i	$-0.0711019\pi$
$110$	−0.802724	+	1.51762i	−0.0765367	+	0.144699i
$111$	9.24342	+	9.24342i	0.877346	+	0.877346i
$112$	−17.7390	−	6.98906i	−1.67618	−	0.660404i
$113$			0.911688i			0.0857644i	0.999080	+	0.0428822i	$0.0136540\pi$
$113$			0.911688i			0.0857644i	−0.999080	+	0.0428822i	$0.986346\pi$
$114$	1.10058	+	3.57217i	0.103079	+	0.334564i
$115$	−4.54519	+	1.88268i	−0.423842	+	0.175561i
$116$	−0.216685	−	1.04194i	−0.0201187	−	0.0967416i
$117$	9.98465	+	3.75614i	0.923081	+	0.347255i
$118$	1.29917	−	13.8055i	0.119599	−	1.27090i
$119$			13.0979i			1.20068i
$120$	−0.524103	−	4.69325i	−0.0478438	−	0.428433i
$121$	−5.55064	−	5.55064i	−0.504603	−	0.504603i
$122$	1.41637	−	15.0509i	0.128232	−	1.36264i
$123$	6.71842	+	2.78286i	0.605779	+	0.250922i
$124$	−14.5706	−	2.76685i	−1.30848	−	0.248471i
$125$	6.02353	−	2.49503i	0.538761	−	0.223162i
$126$	−9.32522	+	17.6301i	−0.830757	+	1.57062i
$127$	−19.1141			−1.69611			−0.848053	−	0.529911i	$-0.822225\pi$
$127$	−19.1141			−1.69611			−0.848053	+	0.529911i	$0.822225\pi$
$128$	5.63423	+	9.81098i	0.498001	+	0.867177i
$129$			15.5992i			1.37343i
$130$	1.13593	+	3.29746i	0.0996275	+	0.289206i
$131$	−12.2119	−	5.05835i	−1.06696	−	0.441950i	−0.221044	−	0.975264i	$-0.570946\pi$
$131$	−12.2119	−	5.05835i	−1.06696	−	0.441950i	−0.845917	+	0.533314i	$0.820946\pi$
$132$	−8.51303	−	1.61657i	−0.740964	−	0.140704i
$133$	4.76817	−	1.97504i	0.413453	−	0.171258i
$134$	−8.86442	+	7.33953i	−0.765769	+	0.634039i
$135$	0.0689352			0.00593300
$136$	4.85189	−	6.07175i	0.416046	−	0.520648i
$137$		−	13.5356i		−	1.15642i	−0.815887	−	0.578212i	$-0.803751\pi$
$137$		−	13.5356i		−	1.15642i	0.815887	−	0.578212i	$-0.196249\pi$
$138$	−15.8355	−	19.1256i	−1.34801	−	1.62808i
$139$	−1.05909	+	0.438691i	−0.0898311	+	0.0372093i	−0.427146	−	0.904182i	$-0.640481\pi$
$139$	−1.05909	+	0.438691i	−0.0898311	+	0.0372093i	0.337315	+	0.941392i	$0.390481\pi$
$140$	−6.38387	+	1.32761i	−0.539535	+	0.112203i
$141$	3.26211	+	7.87544i	0.274720	+	0.663232i
$142$	−16.5818	+	5.10881i	−1.39151	+	0.428722i
$143$	6.39598	−	0.210405i	0.534859	−	0.0175949i
$144$	10.8536	−	4.71836i	0.904467	−	0.393196i
$145$	−0.257356	−	0.257356i	−0.0213723	−	0.0213723i
$146$	0.653678	+	2.12165i	0.0540988	+	0.175589i
$147$	35.4523	+	14.6848i	2.92405	+	1.21118i
$148$	−10.4859	+	2.18069i	−0.861939	+	0.179251i
$149$	−16.1546	−	6.69145i	−1.32344	−	0.548185i	−0.394660	−	0.918827i	$-0.629137\pi$
$149$	−16.1546	−	6.69145i	−1.32344	−	0.548185i	−0.928776	+	0.370643i	$0.879137\pi$
$150$	9.97804	+	12.0511i	0.814704	+	0.983969i
$151$	21.8089			1.77478			0.887392	−	0.461016i	$-0.152515\pi$
$151$	21.8089			1.77478			0.887392	+	0.461016i	$0.152515\pi$
$152$	−2.94198	−	0.850721i	−0.238626	−	0.0690026i
$153$	−5.74892	−	5.74892i	−0.464772	−	0.464772i
$154$	−1.12096	+	11.9117i	−0.0903296	+	0.959874i
$155$	−4.68596	+	1.94099i	−0.376385	+	0.155904i
$156$	−14.2169	+	10.3794i	−1.13827	+	0.831015i
$157$	4.63951	−	11.2008i	0.370273	−	0.893918i	−0.623431	−	0.781879i	$-0.714262\pi$
$157$	4.63951	−	11.2008i	0.370273	−	0.893918i	0.993704	−	0.112040i	$-0.0357384\pi$
$158$	6.02571	−	1.85651i	0.479380	−	0.147696i
$159$		−	7.06547i		−	0.560329i
$160$	3.45113	+	1.74935i	0.272836	+	0.138299i
$161$	−24.2428	+	24.2428i	−1.91060	+	1.91060i
$162$	3.79848	+	12.3288i	0.298437	+	0.968641i
$163$	1.91518	+	4.62366i	0.150009	+	0.362153i	0.980965	−	0.194185i	$-0.0622061\pi$
$163$	1.91518	+	4.62366i	0.150009	+	0.362153i	−0.830956	+	0.556338i	$0.812206\pi$
$164$	−4.92500	+	3.35305i	−0.384578	+	0.261829i
$165$	−2.73782	+	1.13404i	−0.213139	+	0.0882851i
$166$	−13.6166	−	16.4457i	−1.05685	−	1.27643i
$167$		−	20.0885i		−	1.55450i	−0.629195	−	0.777248i	$-0.716615\pi$
$167$		−	20.0885i		−	1.55450i	0.629195	−	0.777248i	$-0.283385\pi$
$168$	−15.8906	−	28.8192i	−1.22599	−	2.22345i
$169$	8.56837	−	9.77665i	0.659106	−	0.752050i
$170$	0.249034	−	2.64632i	0.0191000	−	0.202963i
$171$	−1.22596	+	2.95972i	−0.0937512	+	0.226335i
$172$	−10.6881	−	7.00797i	−0.814959	−	0.534353i
$173$	6.32717	−	15.2752i	0.481046	−	1.16135i	−0.478066	−	0.878324i	$-0.658662\pi$
$173$	6.32717	−	15.2752i	0.481046	−	1.16135i	0.959113	−	0.283025i	$-0.0913378\pi$
$174$	0.858885	−	1.62379i	0.0651119	−	0.123099i
$175$	15.2755	−	15.2755i	1.15472	−	1.15472i
$176$	4.93212	−	5.10663i	0.371773	−	0.384926i
$177$	16.9243	−	16.9243i	1.27211	−	1.27211i
$178$	−5.67195	+	1.74752i	−0.425131	+	0.130982i
$179$	−8.30332	−	3.43935i	−0.620619	−	0.257069i	0.0501422	−	0.998742i	$-0.484033\pi$
$179$	−8.30332	−	3.43935i	−0.620619	−	0.257069i	−0.670761	+	0.741673i	$0.734033\pi$
$180$	2.21928	−	3.38471i	0.165416	−	0.252281i
$181$	7.67585	−	3.17944i	0.570542	−	0.236326i	−0.0787128	−	0.996897i	$-0.525081\pi$
$181$	7.67585	−	3.17944i	0.570542	−	0.236326i	0.649254	+	0.760571i	$0.275081\pi$
$182$	16.1074	+	18.2009i	1.19396	+	1.34914i
$183$	18.4511	−	18.4511i	1.36394	−	1.36394i
$184$	20.2184	−	2.25783i	1.49052	−	0.166449i
$185$	−2.59000	+	2.59000i	−0.190421	+	0.190421i
$186$	−16.3260	−	19.7179i	−1.19708	−	1.44579i
$187$	−4.50592	−	1.86641i	−0.329506	−	0.136486i
$188$	−6.86153	−	1.30296i	−0.500429	−	0.0950279i
$189$	0.443830	−	0.183840i	0.0322839	−	0.0133724i
$190$	−1.00092	+	0.308381i	−0.0726143	+	0.0223723i
$191$			7.74904i			0.560701i	0.959898	+	0.280350i	$0.0904507\pi$
$191$			7.74904i			0.560701i	−0.959898	+	0.280350i	$0.909549\pi$
$192$	−3.30919	+	19.2460i	−0.238820	+	1.38896i
$193$	12.4434	+	12.4434i	0.895696	+	0.895696i	0.995052	−	0.0993562i	$-0.0316783\pi$
$193$	12.4434	+	12.4434i	0.895696	+	0.895696i	−0.0993562	+	0.995052i	$0.531678\pi$
$194$	0.229389	−	0.433679i	0.0164692	−	0.0311363i
$195$	−2.11962	+	5.63443i	−0.151789	+	0.403490i
$196$	−25.9886	+	17.6936i	−1.85633	+	1.26383i
$197$	2.23719	−	5.40104i	0.159393	−	0.384809i	−0.823926	−	0.566697i	$-0.808221\pi$
$197$	2.23719	−	5.40104i	0.159393	−	0.384809i	0.983319	+	0.181889i	$0.0582210\pi$
$198$	−4.73626	−	5.72028i	−0.336592	−	0.406523i
$199$	3.20031	−	3.20031i	0.226864	−	0.226864i	−0.584517	−	0.811381i	$-0.698716\pi$
$199$	3.20031	−	3.20031i	0.226864	−	0.226864i	0.811381	+	0.584517i	$0.198716\pi$
$200$	−12.7397	+	1.42267i	−0.900835	+	0.100598i
$201$	−19.8647			−1.40115
$202$	4.74347	+	5.72899i	0.333749	+	0.403090i
$203$	−2.34329	−	0.970622i	−0.164467	−	0.0681243i
$204$	13.1344	−	2.73147i	0.919593	−	0.191241i
$205$	−0.779756	+	1.88250i	−0.0544605	+	0.131479i
$206$	7.63660	−	14.4376i	0.532067	−	1.00592i
$207$		−	21.2812i		−	1.47915i
$208$	−0.724642	−	14.4040i	−0.0502449	−	0.998737i
$209$			1.92178i			0.132932i
$210$	−9.94883	−	5.26231i	−0.686535	−	0.363134i
$211$	−0.961172	+	2.32047i	−0.0661698	+	0.159748i	−0.953505	−	0.301377i	$-0.902554\pi$
$211$	−0.961172	+	2.32047i	−0.0661698	+	0.159748i	0.887335	+	0.461125i	$0.152554\pi$
$212$	4.84105	+	3.17418i	0.332485	+	0.218004i
$213$	−27.6694	−	11.4610i	−1.89587	−	0.785296i
$214$	0.404343	−	0.334787i	0.0276403	−	0.0228855i
$215$	−4.37088			−0.298092
$216$	−0.273845	−	0.0791867i	−0.0186328	−	0.00538797i
$217$	−24.9936	+	24.9936i	−1.69668	+	1.69668i
$218$	−22.4198	+	18.5631i	−1.51846	+	1.25725i
$219$	−1.46645	+	3.54033i	−0.0990936	+	0.239233i
$220$	0.452961	−	2.38535i	0.0305386	−	0.160820i
$221$	−9.02385	+	4.09039i	−0.607010	+	0.275149i
$222$	−16.3416	−	8.64371i	−1.09678	−	0.580128i
$223$	6.19432	+	6.19432i	0.414802	+	0.414802i	0.883408	−	0.468605i	$-0.155243\pi$
$223$	6.19432	+	6.19432i	0.414802	+	0.414802i	−0.468605	+	0.883408i	$0.655243\pi$
$224$	26.8849	+	2.05931i	1.79632	+	0.137593i
$225$			13.4094i			0.893959i
$226$	−0.379628	−	1.23217i	−0.0252525	−	0.0819624i
$227$	−19.9580	+	8.26686i	−1.32466	+	0.548690i	−0.929126	−	0.369763i	$-0.879439\pi$
$227$	−19.9580	+	8.26686i	−1.32466	+	0.548690i	−0.395530	+	0.918453i	$0.629439\pi$
$228$	−2.97491	−	4.36958i	−0.197018	−	0.289382i
$229$	19.3325	+	8.00780i	1.27753	+	0.529170i	0.915245	−	0.402897i	$-0.131997\pi$
$229$	19.3325	+	8.00780i	1.27753	+	0.529170i	0.362285	+	0.932068i	$0.381997\pi$
$230$	5.35898	−	4.43711i	0.353360	−	0.292574i
$231$	−14.6028	+	14.6028i	−0.960792	+	0.960792i
$232$	0.726719	+	1.31798i	0.0477114	+	0.0865293i
$233$	8.75627	−	8.75627i	0.573642	−	0.573642i	−0.359502	−	0.933144i	$-0.617053\pi$
$233$	8.75627	−	8.75627i	0.573642	−	0.573642i	0.933144	+	0.359502i	$0.117053\pi$
$234$	−15.0585	−	0.918877i	−0.984406	−	0.0600689i
$235$	−2.20669	+	0.914043i	−0.143949	+	0.0596256i
$236$	3.99275	+	19.1993i	0.259906	+	1.24977i
$237$	10.0549	+	4.16487i	0.653134	+	0.270537i
$238$	−5.45399	−	17.7021i	−0.353530	−	1.14746i
$239$	15.7148	−	15.7148i	1.01651	−	1.01651i	0.0166470	−	0.999861i	$-0.494701\pi$
$239$	15.7148	−	15.7148i	1.01651	−	1.01651i	0.999861	−	0.0166470i	$-0.00529915\pi$
$240$	2.66261	+	6.12479i	0.171871	+	0.395353i
$241$	3.57821	−	3.57821i	0.230493	−	0.230493i	−0.582405	−	0.812898i	$-0.697888\pi$
$241$	3.57821	−	3.57821i	0.230493	−	0.230493i	0.812898	+	0.582405i	$0.197888\pi$
$242$	9.81309	+	5.19051i	0.630810	+	0.333659i
$243$	−8.40574	+	20.2933i	−0.539229	+	1.30181i
$244$	4.35294	+	20.9313i	0.278668	+	1.33999i
$245$	−4.11467	+	9.93370i	−0.262877	+	0.634641i
$246$	−10.2389	−	0.963536i	−0.652806	−	0.0614328i
$247$	2.84978	+	2.66826i	0.181327	+	0.169777i
$248$	20.8446	−	2.32775i	1.32363	−	0.147812i
$249$		−	36.8538i		−	2.33552i
$250$	−7.10199	+	5.88028i	−0.449169	+	0.371902i
$251$	−9.20091	+	3.81114i	−0.580756	+	0.240557i	−0.653668	−	0.756781i	$-0.726771\pi$
$251$	−9.20091	+	3.81114i	−0.580756	+	0.240557i	0.0729119	+	0.997338i	$0.476771\pi$
$252$	5.26203	−	27.7105i	0.331477	−	1.74560i
$253$	−4.88544	−	11.7945i	−0.307145	−	0.741513i
$254$	25.8332	−	7.95916i	1.62092	−	0.499402i
$255$	3.24417	−	3.24417i	0.203158	−	0.203158i
$256$	−11.7001	−	10.9137i	−0.731256	−	0.682103i
$257$		−	15.4585i		−	0.964276i	−0.876095	−	0.482138i	$-0.839860\pi$
$257$		−	15.4585i		−	0.964276i	0.876095	−	0.482138i	$-0.160140\pi$
$258$	−6.49552	−	21.0826i	−0.404393	−	1.31255i
$259$	−9.76821	+	23.5826i	−0.606967	+	1.46535i
$260$	−2.90830	−	3.98358i	−0.180365	−	0.247051i
$261$	1.45454	−	0.602488i	0.0900335	−	0.0372931i
$262$	18.6110	+	1.75140i	1.14979	+	0.108202i
$263$	22.1324	+	22.1324i	1.36474	+	1.36474i	0.867761	+	0.496981i	$0.165558\pi$
$263$	22.1324	+	22.1324i	1.36474	+	1.36474i	0.496981	+	0.867761i	$0.334442\pi$
$264$	12.1787	−	1.36001i	0.749546	−	0.0837030i
$265$	1.97974			0.121615
$266$	−5.62188	+	4.65478i	−0.344699	+	0.285403i
$267$	−9.46458	−	3.92036i	−0.579223	−	0.239922i
$268$	8.92426	−	13.6107i	0.545136	−	0.831405i
$269$	21.4569	+	8.88775i	1.30825	+	0.541896i	0.924374	−	0.381488i	$-0.124588\pi$
$269$	21.4569	+	8.88775i	1.30825	+	0.541896i	0.383878	+	0.923384i	$0.374588\pi$
$270$	−0.0931674	+	0.0287047i	−0.00566999	+	0.00174691i
$271$	−15.0473	−	15.0473i	−0.914058	−	0.914058i	0.0825308	−	0.996589i	$-0.473700\pi$
$271$	−15.0473	−	15.0473i	−0.914058	−	0.914058i	−0.996589	+	0.0825308i	$0.973700\pi$
$272$	−4.02914	+	10.2264i	−0.244303	+	0.620068i
$273$	1.37932	+	41.9292i	0.0834804	+	2.53767i
$274$	5.63624	+	18.2936i	0.340498	+	1.10516i
$275$	3.07834	+	7.43176i	0.185631	+	0.448152i
$276$	29.3660	+	19.2547i	1.76762	+	1.15900i
$277$	−12.0846	+	5.00560i	−0.726092	+	0.300757i	−0.714945	−	0.699181i	$-0.753548\pi$
$277$	−12.0846	+	5.00560i	−0.726092	+	0.300757i	−0.0111473	+	0.999938i	$0.503548\pi$
$278$	1.24872	−	1.03391i	0.0748930	−	0.0620097i
$279$		−	21.9403i		−	1.31353i
$280$	8.07511	−	4.45254i	0.482580	−	0.266090i
$281$	18.2366			1.08791			0.543953	−	0.839116i	$-0.316927\pi$
$281$	18.2366			1.08791			0.543953	+	0.839116i	$0.316927\pi$
$282$	−7.68816	−	9.28548i	−0.457823	−	0.552942i
$283$	5.24389	−	2.17209i	0.311717	−	0.129117i	−0.221340	−	0.975197i	$-0.571043\pi$
$283$	5.24389	−	2.17209i	0.311717	−	0.129117i	0.533057	+	0.846079i	$0.321043\pi$
$284$	20.2833	−	13.8093i	1.20359	−	0.819433i
$285$	−1.67020	−	0.691818i	−0.0989339	−	0.0409798i
$286$	−8.55669	+	2.94766i	−0.505968	+	0.174299i
$287$			14.1997i			0.838182i
$288$	−12.7042	+	10.8964i	−0.748599	+	0.642077i
$289$	−9.44914			−0.555832
$290$	0.454986	+	0.240659i	0.0267177	+	0.0141320i
$291$	0.782369	−	0.324068i	0.0458633	−	0.0189972i
$292$	−1.76692	−	2.59527i	−0.103401	−	0.151877i
$293$	−27.8685	−	11.5435i	−1.62809	−	0.674379i	−0.633077	−	0.774089i	$-0.718208\pi$
$293$	−27.8685	−	11.5435i	−1.62809	−	0.674379i	−0.995017	+	0.0997101i	$0.968208\pi$
$294$	−54.0292	−	5.08446i	−3.15105	−	0.296532i
$295$	4.74219	+	4.74219i	0.276101	+	0.276101i
$296$	13.2639	−	7.31361i	0.770951	−	0.425095i
$297$			0.178882i			0.0103798i
$298$	24.6196	+	2.31684i	1.42617	+	0.134211i
$299$	−24.2730	−	9.13129i	−1.40374	−	0.528076i
$300$	−18.5036	−	12.1325i	−1.06831	−	0.700468i
$301$	−28.1413	+	11.6565i	−1.62204	+	0.671871i
$302$	−29.4752	+	9.08126i	−1.69611	+	0.522568i
$303$			12.8384i			0.737544i
$304$	4.33039	−	0.0752764i	0.248365	−	0.00431740i
$305$	5.16999	+	5.16999i	0.296033	+	0.296033i
$306$	10.1636	+	5.37593i	0.581017	+	0.307321i
$307$	13.0113	−	5.38945i	0.742593	−	0.307592i	0.0208779	−	0.999782i	$-0.493354\pi$
$307$	13.0113	−	5.38945i	0.742593	−	0.307592i	0.721716	+	0.692190i	$0.243354\pi$
$308$	−3.44505	−	16.5657i	−0.196300	−	0.943920i
$309$	26.0459	−	10.7886i	1.48170	−	0.613739i
$310$	5.52494	−	4.57453i	0.313796	−	0.259816i
$311$	−14.0691	−	14.0691i	−0.797786	−	0.797786i	0.184960	−	0.982746i	$-0.440784\pi$
$311$	−14.0691	−	14.0691i	−0.797786	−	0.797786i	−0.982746	+	0.184960i	$0.940784\pi$
$312$	14.8925	−	19.9479i	0.843123	−	1.12933i
$313$	0.452439	−	0.452439i	0.0255734	−	0.0255734i	−0.694204	−	0.719778i	$-0.744244\pi$
$313$	0.452439	−	0.452439i	0.0255734	−	0.0255734i	0.719778	+	0.694204i	$0.244244\pi$
$314$	−1.60638	+	17.0700i	−0.0906534	+	0.963314i
$315$	−3.69139	−	8.91181i	−0.207986	−	0.502123i
$316$	−7.37082	+	5.01823i	−0.414641	+	0.282297i
$317$	−5.13543	−	12.3980i	−0.288435	−	0.696343i	0.711546	−	0.702640i	$-0.247996\pi$
$317$	−5.13543	−	12.3980i	−0.288435	−	0.696343i	−0.999980	+	0.00629718i	$0.997996\pi$
$318$	2.94207	+	9.54914i	0.164983	+	0.535489i
$319$	0.667823	−	0.667823i	0.0373909	−	0.0373909i
$320$	−5.39271	−	0.927234i	−0.301462	−	0.0518340i
$321$	0.906111			0.0505742
$322$	22.6699	−	42.8594i	1.26335	−	2.38846i
$323$	−1.13860	−	2.74882i	−0.0633533	−	0.152948i
$324$	−10.2675	−	15.0809i	−0.570414	−	0.837830i
$325$	15.2945	+	5.75367i	0.848388	+	0.319156i
$326$	−4.51371	−	5.45149i	−0.249991	−	0.301930i
$327$	−50.2416			−2.77837
$328$	5.26002	−	6.58250i	0.290436	−	0.363458i
$329$	−11.7699	+	11.7699i	−0.648895	+	0.648895i
$330$	3.22801	−	2.67272i	0.177696	−	0.147128i
$331$	6.46992	−	15.6198i	0.355619	−	0.858540i	−0.640286	−	0.768136i	$-0.721184\pi$
$331$	6.46992	−	15.6198i	0.355619	−	0.858540i	0.995905	−	0.0904037i	$-0.0288157\pi$
$332$	25.2511	+	16.5567i	1.38584	+	0.908665i
$333$	−6.06337	−	14.6383i	−0.332270	−	0.802172i
$334$	8.36488	+	27.1500i	0.457706	+	1.48558i
$335$		−	5.56608i		−	0.304107i
$336$	33.4768	+	32.3328i	1.82631	+	1.76390i
$337$	19.8195			1.07964			0.539819	−	0.841781i	$-0.318493\pi$
$337$	19.8195			1.07964			0.539819	+	0.841781i	$0.318493\pi$
$338$	−7.50933	+	16.7812i	−0.408454	+	0.912779i
$339$	0.851652	−	2.05607i	0.0462554	−	0.111670i
$340$	0.765357	+	3.68026i	0.0415073	+	0.199590i
$341$	−5.03674	−	12.1598i	−0.272755	−	0.658488i
$342$	0.424475	−	4.51061i	0.0229530	−	0.243906i
$343$			41.5643i			2.24426i
$344$	17.3633	+	5.02088i	0.936167	+	0.270708i
$345$	12.0092			0.646552
$346$	−2.19072	+	23.2793i	−0.117774	+	1.25150i
$347$	−7.82618	−	18.8941i	−0.420131	−	1.01429i	−0.982308	−	0.187270i	$-0.940036\pi$
$347$	−7.82618	−	18.8941i	−0.420131	−	1.01429i	0.562177	−	0.827017i	$-0.309964\pi$
$348$	−0.484651	+	2.55223i	−0.0259800	+	0.136814i
$349$	−9.16581	+	3.79660i	−0.490634	+	0.203227i	−0.614263	−	0.789101i	$-0.710547\pi$
$349$	−9.16581	+	3.79660i	−0.490634	+	0.203227i	0.123629	+	0.992329i	$0.460547\pi$
$350$	−14.2844	+	27.0059i	−0.763535	+	1.44353i
$351$	0.265263	+	0.248366i	0.0141587	+	0.0132568i
$352$	−4.53946	+	8.95546i	−0.241954	+	0.477327i
$353$	−2.03374	+	2.03374i	−0.108245	+	0.108245i	−0.759155	−	0.650910i	$-0.774388\pi$
$353$	−2.03374	+	2.03374i	−0.108245	+	0.108245i	0.650910	+	0.759155i	$0.274388\pi$
$354$	−15.8263	+	29.9209i	−0.841158	+	1.59028i
$355$	3.21137	−	7.75294i	0.170442	−	0.411483i
$356$	6.93810	−	4.72362i	0.367718	−	0.250351i
$357$	12.2354	−	29.5389i	0.647566	−	1.56336i
$358$	12.6543	+	1.19084i	0.668799	+	0.0629378i
$359$			5.77186i			0.304627i	0.988332	+	0.152314i	$0.0486724\pi$
$359$			5.77186i			0.304627i	−0.988332	+	0.152314i	$0.951328\pi$
$360$	−1.59001	+	5.49862i	−0.0838011	+	0.289803i
$361$	12.6060	−	12.6060i	0.663476	−	0.663476i
$362$	−9.05016	+	7.49332i	−0.475666	+	0.393840i
$363$	7.33286	+	17.7031i	0.384876	+	0.929172i
$364$	−29.3483	−	17.8917i	−1.53827	−	0.937782i
$365$	−0.991998	−	0.410899i	−0.0519235	−	0.0215074i
$366$	−17.2540	+	32.6201i	−0.901880	+	1.70508i
$367$	5.52161			0.288226			0.144113	−	0.989561i	$-0.453967\pi$
$367$	5.52161			0.288226			0.144113	+	0.989561i	$0.453967\pi$
$368$	−26.3855	+	11.4705i	−1.37544	+	0.597940i
$369$	−6.23251	−	6.23251i	−0.324452	−	0.324452i
$370$	2.42196	−	4.57892i	0.125912	−	0.238047i
$371$	12.7463	−	5.27969i	0.661755	−	0.274108i
$372$	30.2754	+	19.8510i	1.56971	+	1.02923i
$373$	5.04449	+	12.1785i	0.261194	+	0.630577i	0.999013	−	0.0444210i	$-0.0141443\pi$
$373$	5.04449	+	12.1785i	0.261194	+	0.630577i	−0.737819	+	0.674998i	$0.764144\pi$
$374$	6.86703	+	0.646227i	0.355086	+	0.0334156i
$375$	−15.9152			−0.821856
$376$	9.81606	−	1.09618i	0.506225	−	0.0565309i
$377$	−0.0630800	−	1.91753i	−0.00324878	−	0.0987580i
$378$	−0.523295	+	0.433276i	−0.0269154	+	0.0222853i
$379$	25.0950	+	10.3947i	1.28904	+	0.533939i	0.918700	−	0.394957i	$-0.129240\pi$
$379$	25.0950	+	10.3947i	1.28904	+	0.533939i	0.370342	+	0.928895i	$0.379240\pi$
$380$	1.22435	−	0.833568i	0.0628080	−	0.0427612i
$381$	43.1069	+	17.8555i	2.20843	+	0.914762i
$382$	−3.22671	−	10.4730i	−0.165093	−	0.535845i
$383$	18.8204	+	18.8204i	0.961679	+	0.961679i	0.999292	−	0.0376130i	$-0.0119754\pi$
$383$	18.8204	+	18.8204i	0.961679	+	0.961679i	−0.0376130	+	0.999292i	$0.511975\pi$
$384$	−3.54160	−	27.3893i	−0.180731	−	1.39770i
$385$	−4.09169	−	4.09169i	−0.208532	−	0.208532i
$386$	−21.9990	−	11.6361i	−1.11972	−	0.592261i
$387$	7.23549	−	17.4680i	0.367801	−	0.887949i
$388$	−0.129439	+	0.681644i	−0.00657129	+	0.0346052i
$389$	−1.64741	−	3.97720i	−0.0835269	−	0.201652i	0.876598	−	0.481224i	$-0.159808\pi$
$389$	−1.64741	−	3.97720i	−0.0835269	−	0.201652i	−0.960125	+	0.279572i	$0.909808\pi$
$390$	0.518531	−	8.49766i	0.0262568	−	0.430296i
$391$	13.9758	+	13.9758i	0.706787	+	0.706787i
$392$	27.7565	−	34.7350i	1.40191	−	1.75438i
$393$	22.8155	+	22.8155i	1.15089	+	1.15089i
$394$	−0.774602	+	8.23119i	−0.0390239	+	0.414682i
$395$	−1.16699	+	2.81737i	−0.0587178	+	0.141757i
$396$	8.78309	+	5.75890i	0.441367	+	0.289396i
$397$	−6.18853	−	14.9404i	−0.310593	−	0.749838i	−0.999683	−	0.0251627i	$-0.991990\pi$
$397$	−6.18853	−	14.9404i	−0.310593	−	0.749838i	0.689090	−	0.724676i	$-0.258010\pi$
$398$	−2.99267	+	5.65790i	−0.150009	+	0.283605i
$399$	−12.5983			−0.630705
$400$	16.6256	−	7.22760i	0.831281	−	0.361380i
$401$	10.4619	−	10.4619i	0.522441	−	0.522441i	−0.395867	−	0.918308i	$-0.629556\pi$
$401$	10.4619	−	10.4619i	0.522441	−	0.522441i	0.918308	+	0.395867i	$0.129556\pi$
$402$	26.8475	−	8.27168i	1.33903	−	0.412554i
$403$	−25.0247	−	9.41408i	−1.24657	−	0.468949i
$404$	−8.79646	−	5.76766i	−0.437640	−	0.286952i
$405$	−5.76443	−	2.38771i	−0.286437	−	0.118646i
$406$	3.57117	+	0.336068i	0.177234	+	0.0166788i
$407$	−6.72089	−	6.72089i	−0.333142	−	0.333142i
$408$	−16.6140	+	9.16083i	−0.822518	+	0.453528i
$409$		−	6.51944i		−	0.322366i	−0.986925	−	0.161183i	$-0.948469\pi$
$409$		−	6.51944i		−	0.322366i	0.986925	−	0.161183i	$-0.0515309\pi$
$410$	0.269982	−	2.86893i	0.0133335	−	0.141686i
$411$	−12.6443	+	30.5259i	−0.623695	+	1.50573i
$412$	−4.30918	+	22.6926i	−0.212298	+	1.11799i
$413$	43.1787	+	17.8852i	2.12469	+	0.880074i
$414$	8.86152	+	28.7620i	0.435520	+	1.41358i
$415$	10.3264			0.506904
$416$	6.97721	+	19.1656i	0.342086	+	0.939669i
$417$	2.79831			0.137034
$418$	−0.800230	−	2.59732i	−0.0391405	−	0.127039i
$419$	0.805740	+	0.333748i	0.0393630	+	0.0163047i	0.402278	−	0.915518i	$-0.368219\pi$
$419$	0.805740	+	0.333748i	0.0393630	+	0.0163047i	−0.362915	+	0.931822i	$0.618219\pi$
$420$	15.6373	+	2.96941i	0.763022	+	0.144893i
$421$	−6.16886	+	14.8930i	−0.300652	+	0.725838i	0.699287	+	0.714841i	$0.253501\pi$
$421$	−6.16886	+	14.8930i	−0.300652	+	0.725838i	−0.999940	+	0.0109977i	$0.996499\pi$
$422$	0.332796	−	3.53640i	0.0162002	−	0.172149i
$423$		−	10.3320i		−	0.502361i
$424$	−7.86452	−	2.27415i	−0.381935	−	0.110443i
$425$	−8.80622	−	8.80622i	−0.427164	−	0.427164i
$426$	42.1681	+	3.96826i	2.04305	+	0.192263i
$427$	47.0739	+	19.4986i	2.27807	+	0.943606i
$428$	−0.407073	+	0.620840i	−0.0196766	+	0.0300094i
$429$	−14.6210	−	5.50028i	−0.705907	−	0.265556i
$430$	5.90734	−	1.82004i	0.284877	−	0.0877702i
$431$	1.57232	−	1.57232i	0.0757361	−	0.0757361i	−0.668224	−	0.743960i	$-0.732945\pi$
$431$	1.57232	−	1.57232i	0.0757361	−	0.0757361i	0.743960	+	0.668224i	$0.232945\pi$
$432$	0.403081	−	0.00700686i	0.0193932	−	0.000337118i
$433$	−27.0551			−1.30019			−0.650094	−	0.759854i	$-0.725270\pi$
$433$	−27.0551			−1.30019			−0.650094	+	0.759854i	$0.725270\pi$
$434$	23.3720	−	44.1867i	1.12189	−	2.12103i
$435$	0.339990	+	0.820808i	0.0163013	+	0.0393547i
$436$	22.5712	−	34.4241i	1.08096	−	1.64861i
$437$	2.98034	−	7.19518i	0.142569	−	0.344192i
$438$	0.507743	−	5.39546i	0.0242609	−	0.257805i
$439$	7.17594	+	7.17594i	0.342489	+	0.342489i	0.857302	−	0.514813i	$-0.172139\pi$
$439$	7.17594	+	7.17594i	0.342489	+	0.342489i	−0.514813	+	0.857302i	$0.672139\pi$
$440$	0.381075	+	3.41246i	0.0181670	+	0.162683i
$441$	−32.8882	−	32.8882i	−1.56610	−	1.56610i
$442$	10.4927	−	9.28580i	0.499086	−	0.441680i
$443$	9.17145	+	22.1418i	0.435749	+	1.05199i	0.977402	+	0.211388i	$0.0677985\pi$
$443$	9.17145	+	22.1418i	0.435749	+	1.05199i	−0.541653	+	0.840602i	$0.682201\pi$
$444$	25.6853	+	4.87747i	1.21897	+	0.231474i
$445$	1.09848	−	2.65197i	0.0520730	−	0.125715i
$446$	−10.9511	−	5.79243i	−0.518549	−	0.274280i
$447$	30.1816	+	30.1816i	1.42754	+	1.42754i
$448$	−37.1930	+	8.41172i	−1.75721	+	0.397416i
$449$	1.55890	+	1.55890i	0.0735689	+	0.0735689i	0.742934	−	0.669365i	$-0.233434\pi$
$449$	1.55890	+	1.55890i	0.0735689	+	0.0735689i	−0.669365	+	0.742934i	$0.733434\pi$
$450$	−5.58369	−	18.1231i	−0.263218	−	0.854330i
$451$	−4.88496	−	2.02342i	−0.230024	−	0.0952789i
$452$	1.02615	+	1.50722i	0.0482661	+	0.0708937i
$453$	−49.1842	−	20.3728i	−2.31087	−	0.957196i
$454$	23.5313	−	19.4834i	1.10438	−	0.914399i
$455$	−11.7486	+	0.386485i	−0.550781	+	0.0181187i
$456$	5.84015	+	4.66682i	0.273490	+	0.218544i
$457$	−29.0570			−1.35923			−0.679614	−	0.733570i	$-0.737853\pi$
$457$	−29.0570			−1.35923			−0.679614	+	0.733570i	$0.737853\pi$
$458$	−29.4628	−	2.77262i	−1.37671	−	0.129556i
$459$	−0.105983	−	0.255865i	−0.00494685	−	0.0119428i
$460$	−5.39515	+	8.22833i	−0.251550	+	0.383648i
$461$	8.58483	−	3.55595i	0.399835	−	0.165617i	−0.173699	−	0.984799i	$-0.555572\pi$
$461$	8.58483	−	3.55595i	0.399835	−	0.165617i	0.573534	+	0.819182i	$0.305572\pi$
$462$	13.6553	−	25.8166i	0.635304	−	1.20110i
$463$	16.3647	+	16.3647i	0.760534	+	0.760534i	0.976419	−	0.215885i	$-0.0692635\pi$
$463$	16.3647	+	16.3647i	0.760534	+	0.760534i	−0.215885	+	0.976419i	$0.569263\pi$
$464$	−1.53098	−	1.47867i	−0.0710741	−	0.0686453i
$465$	12.3811			0.574160
$466$	−8.18816	+	15.4804i	−0.379309	+	0.717116i
$467$	−31.2231	−	12.9330i	−1.44483	−	0.598469i	−0.483869	−	0.875141i	$-0.660769\pi$
$467$	−31.2231	−	12.9330i	−1.44483	−	0.598469i	−0.960965	+	0.276671i	$0.910769\pi$
$468$	20.7345	−	5.02851i	0.958454	−	0.232443i
$469$	−14.8439	−	35.8364i	−0.685430	−	1.65477i
$470$	2.60179	−	2.15422i	0.120011	−	0.0993667i
$471$	−20.9264	+	20.9264i	−0.964235	+	0.964235i
$472$	−13.3909	−	24.2857i	−0.616367	−	1.11784i
$473$		−	11.3422i		−	0.521513i
$474$	−15.3236	−	1.44204i	−0.703838	−	0.0662352i
$475$	−1.87793	+	4.53372i	−0.0861652	+	0.208021i
$476$	14.7424	+	21.6537i	0.675716	+	0.992498i
$477$	−3.27723	+	7.91194i	−0.150054	+	0.362263i
$478$	−14.6953	+	27.7826i	−0.672146	+	1.27075i
$479$	10.5792	−	10.5792i	0.483375	−	0.483375i	−0.422832	−	0.906208i	$-0.638964\pi$
$479$	10.5792	−	10.5792i	0.483375	−	0.483375i	0.906208	+	0.422832i	$0.138964\pi$
$480$	−6.14895	−	7.16907i	−0.280660	−	0.327222i
$481$	−19.2978	+	0.634829i	−0.879905	+	0.0289457i
$482$	−3.34606	+	6.32601i	−0.152409	+	0.288142i
$483$	77.3195	−	32.0268i	3.51816	−	1.45727i
$484$	−15.4239	−	2.92890i	−0.701088	−	0.133132i
$485$	0.0908036	+	0.219219i	0.00412318	+	0.00995423i
$486$	2.91040	−	30.9269i	0.132018	−	1.40287i
$487$	−22.1275			−1.00269			−0.501346	−	0.865247i	$-0.667162\pi$
$487$	−22.1275			−1.00269			−0.501346	+	0.865247i	$0.667162\pi$
$488$	−14.5989	−	26.4766i	−0.660862	−	1.19854i
$489$		−	12.2165i		−	0.552449i
$490$	1.42466	−	15.1390i	0.0643597	−	0.683909i
$491$	−10.8369	−	26.1627i	−0.489064	−	1.18071i	−0.955192	−	0.295988i	$-0.904351\pi$
$491$	−10.8369	−	26.1627i	−0.489064	−	1.18071i	0.466127	−	0.884718i	$-0.345649\pi$
$492$	14.2393	−	2.96124i	0.641956	−	0.133503i
$493$	−0.559557	+	1.35089i	−0.0252012	+	0.0608410i
$494$	−4.96260	−	2.41955i	−0.223278	−	0.108861i
$495$	3.59184			0.161441
$496$	−27.2026	+	11.8257i	−1.22143	+	0.530990i
$497$		−	58.4806i		−	2.62321i
$498$	15.3460	+	49.8087i	0.687670	+	2.23198i
$499$	−6.86454	−	16.5725i	−0.307299	−	0.741886i	−0.999791	−	0.0204597i	$-0.993487\pi$
$499$	−6.86454	−	16.5725i	−0.307299	−	0.741886i	0.692492	−	0.721426i	$-0.256513\pi$
$500$	7.14993	−	10.9046i	0.319755	−	0.487669i
$501$	−18.7656	+	45.3043i	−0.838387	+	2.02405i
$502$	10.8483	−	8.98211i	0.484182	−	0.400891i
$503$	14.1124	−	14.1124i	0.629242	−	0.629242i	−0.318636	−	0.947877i	$-0.603225\pi$
$503$	14.1124	−	14.1124i	0.629242	−	0.629242i	0.947877	+	0.318636i	$0.103225\pi$
$504$	4.42694	+	39.6425i	0.197192	+	1.76582i
$505$	−3.59730			−0.160078
$506$	11.5140	+	13.9062i	0.511860	+	0.618206i
$507$	−28.4565	+	14.0445i	−1.26380	+	0.623738i
$508$	−31.5999	+	21.5139i	−1.40202	+	0.954527i
$509$	8.34879	+	20.1558i	0.370054	+	0.893388i	0.993740	+	0.111714i	$0.0356341\pi$
$509$	8.34879	+	20.1558i	0.370054	+	0.893388i	−0.623687	+	0.781674i	$0.714366\pi$
$510$	−3.03368	+	5.73544i	−0.134334	+	0.253969i
$511$	−7.48266			−0.331013
$512$	20.3574	+	9.87810i	0.899678	+	0.436555i
$513$	−0.0771641	+	0.0771641i	−0.00340688	+	0.00340688i
$514$	6.43695	+	20.8925i	0.283922	+	0.921530i
$515$	3.02295	+	7.29804i	0.133207	+	0.321590i
$516$	17.5577	+	25.7889i	0.772933	+	1.13529i
$517$	−2.37188	−	5.72623i	−0.104315	−	0.251839i
$518$	3.38214	−	35.9398i	0.148603	−	1.57911i
$519$	−28.5385	+	28.5385i	−1.25270	+	1.25270i
$520$	5.58939	+	4.17288i	0.245111	+	0.182993i
$521$	−12.6505	−	12.6505i	−0.554227	−	0.554227i	0.373431	−	0.927658i	$-0.378181\pi$
$521$	−12.6505	−	12.6505i	−0.554227	−	0.554227i	−0.927658	+	0.373431i	$0.878181\pi$
$522$	−1.71496	+	1.41995i	−0.0750617	+	0.0621494i
$523$	−4.54778	+	1.88375i	−0.198860	+	0.0823707i	−0.479891	−	0.877328i	$-0.659324\pi$
$523$	−4.54778	+	1.88375i	−0.198860	+	0.0823707i	0.281031	+	0.959699i	$0.409324\pi$
$524$	−25.8824	+	5.38259i	−1.13068	+	0.235139i
$525$	−48.7194	+	20.1802i	−2.12629	+	0.880738i
$526$	−39.1284	−	20.6965i	−1.70608	−	0.902408i
$527$	14.4086	+	14.4086i	0.627650	+	0.627650i
$528$	−15.8934	+	6.90930i	−0.691673	+	0.300689i
$529$			28.7353i			1.24936i
$530$	−2.67566	+	0.824367i	−0.116223	+	0.0358082i
$531$	−26.8021	+	11.1018i	−1.16311	+	0.481776i
$532$	5.65983	−	8.63200i	0.245385	−	0.374245i
$533$	−9.78293	+	4.43447i	−0.423746	+	0.192078i
$534$	14.4240	+	1.35738i	0.624188	+	0.0587397i
$535$			0.253892i			0.0109767i
$536$	−6.39382	+	22.1112i	−0.276171	+	0.955059i
$537$	15.5131	+	15.5131i	0.669438	+	0.669438i
$538$	−32.7004	−	3.07729i	−1.40981	−	0.132671i
$539$	−25.7773	−	10.6773i	−1.11031	−	0.459905i
$540$	0.113965	−	0.0775901i	0.00490427	−	0.00333894i
$541$	1.16123	−	0.480999i	0.0499253	−	0.0206797i	−0.357581	−	0.933882i	$-0.616398\pi$
$541$	1.16123	−	0.480999i	0.0499253	−	0.0206797i	0.407506	+	0.913202i	$0.366398\pi$
$542$	26.6024	+	14.0710i	1.14267	+	0.604402i
$543$	−20.2809			−0.870337
$544$	1.18718	−	15.4990i	0.0508998	−	0.664513i
$545$		−	14.0777i		−	0.603021i
$546$	−19.3236	−	56.0939i	−0.826973	−	2.40060i
$547$	35.9252	+	14.8807i	1.53605	+	0.636253i	0.980727	−	0.195381i	$-0.0625944\pi$
$547$	35.9252	+	14.8807i	1.53605	+	0.636253i	0.555324	+	0.831634i	$0.312594\pi$
$548$	−15.2350	−	22.3773i	−0.650807	−	0.955911i
$549$	−29.2199	+	12.1033i	−1.24708	+	0.516555i
$550$	−7.25503	−	8.76236i	−0.309356	−	0.373628i
$551$	0.576154			0.0245450
$552$	−47.7064	−	13.7951i	−2.03052	−	0.587158i
$553$			21.2515i			0.903705i
$554$	14.2482	−	11.7972i	0.605350	−	0.501216i
$555$	8.26050	−	3.42161i	0.350639	−	0.145239i
$556$	−1.25715	+	1.91732i	−0.0533149	+	0.0813123i
$557$	−4.64040	−	11.2029i	−0.196620	−	0.474683i	0.794563	−	0.607182i	$-0.207700\pi$
$557$	−4.64040	−	11.2029i	−0.196620	−	0.474683i	−0.991183	+	0.132498i	$0.957700\pi$
$558$	9.13596	+	29.6528i	0.386756	+	1.25530i
$559$	−16.8192	−	15.7478i	−0.711374	−	0.666062i
$560$	−9.05965	+	9.38019i	−0.382840	+	0.396385i
$561$	8.41840	+	8.41840i	0.355425	+	0.355425i
$562$	−24.6472	+	7.59375i	−1.03968	+	0.320323i
$563$	25.1805	+	10.4301i	1.06123	+	0.439577i	0.843889	−	0.536518i	$-0.180261\pi$
$563$	25.1805	+	10.4301i	1.06123	+	0.439577i	0.217344	+	0.976095i	$0.430261\pi$
$564$	14.2572	+	9.34816i	0.600336	+	0.393629i
$565$	0.576110	+	0.238632i	0.0242371	+	0.0100393i
$566$	−6.18277	+	5.11919i	−0.259881	+	0.215176i
$567$	−43.4812			−1.82604
$568$	−21.6631	+	27.1096i	−0.908962	+	1.13749i
$569$	−19.1179	−	19.1179i	−0.801463	−	0.801463i	0.181861	−	0.983324i	$-0.441788\pi$
$569$	−19.1179	−	19.1179i	−0.801463	−	0.801463i	−0.983324	+	0.181861i	$0.941788\pi$
$570$	2.54538	+	0.239535i	0.106614	+	0.0100330i
$571$	34.0120	−	14.0882i	1.42336	−	0.589574i	0.467656	−	0.883911i	$-0.345099\pi$
$571$	34.0120	−	14.0882i	1.42336	−	0.589574i	0.955702	+	0.294337i	$0.0950987\pi$
$572$	10.3371	−	7.54684i	0.432217	−	0.315549i
$573$	7.23875	−	17.4759i	0.302403	−	0.730066i
$574$	−5.91278	−	19.1912i	−0.246795	−	0.801026i
$575$		−	32.5987i		−	1.35946i
$576$	12.6326	−	20.0168i	0.526360	−	0.834032i
$577$	1.11287	−	1.11287i	0.0463293	−	0.0463293i	−0.683563	−	0.729892i	$-0.739570\pi$
$577$	1.11287	−	1.11287i	0.0463293	−	0.0463293i	0.729892	+	0.683563i	$0.239570\pi$
$578$	12.7707	−	3.93463i	0.531191	−	0.163659i
$579$	−16.4388	−	39.6868i	−0.683173	−	1.64933i
$580$	−0.715134	−	0.135799i	−0.0296943	−	0.00563875i
$581$	66.4853	−	27.5391i	2.75828	−	1.14252i
$582$	−0.922446	+	0.763764i	−0.0382366	+	0.0316590i
$583$			5.13730i			0.212765i
$584$	3.46870	+	2.77181i	0.143536	+	0.114698i
$585$	4.98702	−	5.32629i	0.206188	−	0.220215i
$586$	42.4716	+	3.99682i	1.75448	+	0.165107i
$587$	−10.0510	+	24.2652i	−0.414848	+	1.00153i	0.568969	+	0.822359i	$0.307342\pi$
$587$	−10.0510	+	24.2652i	−0.414848	+	1.00153i	−0.983818	+	0.179173i	$0.942658\pi$
$588$	75.1389	−	15.6261i	3.09867	−	0.644409i
$589$	3.07264	−	7.41801i	0.126606	−	0.305654i
$590$	−8.38383	−	4.43452i	−0.345157	−	0.182566i
$591$	−10.0908	+	10.0908i	−0.415078	+	0.415078i
$592$	−14.8811	+	15.4076i	−0.611609	+	0.633249i
$593$	0.990617	−	0.990617i	0.0406798	−	0.0406798i	−0.686474	−	0.727154i	$-0.740843\pi$
$593$	0.990617	−	0.990617i	0.0406798	−	0.0406798i	0.727154	+	0.686474i	$0.240843\pi$
$594$	−0.0744869	−	0.241763i	−0.00305623	−	0.00991967i
$595$	8.27678	+	3.42835i	0.339315	+	0.140549i
$596$	−34.2386	+	7.12037i	−1.40247	+	0.291662i
$597$	−10.2070	+	4.22788i	−0.417745	+	0.173036i
$598$	36.6078	+	2.23382i	1.49700	+	0.0913477i
$599$	−12.7082	+	12.7082i	−0.519242	+	0.519242i	−0.917342	−	0.398100i	$-0.869670\pi$
$599$	−12.7082	+	12.7082i	−0.519242	+	0.519242i	0.398100	+	0.917342i	$0.369670\pi$
$600$	30.0600	+	8.69235i	1.22720	+	0.354864i
$601$	10.1980	−	10.1980i	0.415983	−	0.415983i	−0.467833	−	0.883817i	$-0.654965\pi$
$601$	10.1980	−	10.1980i	0.415983	−	0.415983i	0.883817	+	0.467833i	$0.154965\pi$
$602$	33.1798	−	27.4721i	1.35231	−	1.11968i
$603$	22.2445	+	9.21399i	0.905868	+	0.375223i
$604$	36.0549	−	24.5470i	1.46705	−	0.998805i
$605$	−4.96040	+	2.05466i	−0.201669	+	0.0835340i
$606$	−5.34591	−	17.3513i	−0.217163	−	0.704849i
$607$		−	27.2432i		−	1.10577i	−0.833259	−	0.552883i	$-0.813528\pi$
$607$		−	27.2432i		−	1.10577i	0.833259	−	0.552883i	$-0.186472\pi$
$608$	−5.82127	+	1.90492i	−0.236084	+	0.0772546i
$609$	4.37796	+	4.37796i	0.177404	+	0.177404i
$610$	−9.14013	−	4.83456i	−0.370073	−	0.195745i
$611$	−11.7846	−	4.43325i	−0.476752	−	0.179350i
$612$	−15.9749	−	3.03353i	−0.645748	−	0.122623i
$613$	−1.02866	+	2.48341i	−0.0415473	+	0.100304i	−0.943291	−	0.331967i	$-0.892288\pi$
$613$	−1.02866	+	2.48341i	−0.0415473	+	0.100304i	0.901744	+	0.432271i	$0.142288\pi$
$614$	−15.3409	+	12.7019i	−0.619107	+	0.512606i
$615$	3.51706	−	3.51706i	0.141822	−	0.141822i
$616$	11.5541	+	20.9544i	0.465526	+	0.844277i
$617$	0.0166708			0.000671140			0.000335570	−	1.00000i	$-0.499893\pi$
$617$	0.0166708			0.000671140			0.000335570		1.00000i	$0.499893\pi$
$618$	−30.7092	+	25.4265i	−1.23530	+	1.02280i
$619$	−0.177010	−	0.0733199i	−0.00711463	−	0.00294698i	0.379123	−	0.925346i	$-0.376226\pi$
$619$	−0.177010	−	0.0733199i	−0.00711463	−	0.00294698i	−0.386238	+	0.922399i	$0.626226\pi$
$620$	−5.56224	+	8.48316i	−0.223385	+	0.340692i
$621$	0.277415	−	0.669740i	0.0111323	−	0.0268757i
$622$	24.8731	+	13.1563i	0.997320	+	0.527520i
$623$		−	20.0039i		−	0.801438i
$624$	−11.8212	+	33.1613i	−0.473228	+	1.32751i
$625$			18.2014i			0.728057i
$626$	−0.423085	+	0.799877i	−0.0169099	+	0.0319695i
$627$	1.79522	−	4.33405i	0.0716943	−	0.173085i
$628$	−4.93690	−	23.7393i	−0.197004	−	0.947302i
$629$	13.5952	+	5.63131i	0.542075	+	0.224535i
$630$	8.69988	+	10.5074i	0.346612	+	0.418625i
$631$	3.70486			0.147488			0.0737440	−	0.997277i	$-0.476505\pi$
$631$	3.70486			0.147488			0.0737440	+	0.997277i	$0.476505\pi$
$632$	7.87222	−	9.85146i	0.313140	−	0.391870i
$633$	4.33534	−	4.33534i	0.172314	−	0.172314i
$634$	12.1032	+	14.6178i	0.480680	+	0.580547i
$635$	−5.00309	+	12.0785i	−0.198542	+	0.479322i
$636$	−7.95255	−	11.6808i	−0.315339	−	0.463173i
$637$	−51.6233	+	23.4002i	−2.04539	+	0.927148i
$638$	−0.624495	+	1.18066i	−0.0247240	+	0.0467428i
$639$	25.6682	+	25.6682i	1.01542	+	1.01542i
$640$	7.67446	−	0.992354i	0.303360	−	0.0392262i
$641$		−	22.9808i		−	0.907685i	−0.891082	−	0.453843i	$-0.850053\pi$
$641$		−	22.9808i		−	0.907685i	0.891082	−	0.453843i	$-0.149947\pi$
$642$	−1.22463	+	0.377306i	−0.0483322	+	0.0148911i
$643$	−10.5208	+	4.35785i	−0.414899	+	0.171857i	−0.580361	−	0.814359i	$-0.697089\pi$
$643$	−10.5208	+	4.35785i	−0.414899	+	0.171857i	0.165462	+	0.986216i	$0.447089\pi$
$644$	−12.7922	+	67.3651i	−0.504082	+	2.65456i
$645$	9.85736	+	4.08305i	0.388133	+	0.160770i
$646$	2.68345	+	3.24097i	0.105579	+	0.127514i
$647$	−33.8281	+	33.8281i	−1.32992	+	1.32992i	−0.424483	+	0.905436i	$0.639544\pi$
$647$	−33.8281	+	33.8281i	−1.32992	+	1.32992i	−0.905436	+	0.424483i	$0.860456\pi$
$648$	20.1564	+	16.1068i	0.791818	+	0.632736i
$649$	−12.3057	+	12.3057i	−0.483040	+	0.483040i
$650$	−23.0667	−	1.40754i	−0.904751	−	0.0552083i
$651$	79.7141	−	33.0187i	3.12424	−	1.29410i
$652$	8.37038	+	5.48829i	0.327810	+	0.214938i
$653$	26.2471	+	10.8719i	1.02713	+	0.425451i	0.831675	−	0.555263i	$-0.187382\pi$
$653$	26.2471	+	10.8719i	1.02713	+	0.425451i	0.195453	+	0.980713i	$0.437382\pi$
$654$	67.9026	−	20.9207i	2.65520	−	0.818063i
$655$	−6.39290	+	6.39290i	−0.249791	+	0.249791i
$656$	−4.36807	+	11.0867i	−0.170545	+	0.432862i
$657$	3.28427	−	3.28427i	0.128132	−	0.128132i
$658$	11.0063	−	20.8083i	0.429069	−	0.811190i
$659$	10.8417	−	26.1741i	0.422332	−	1.01960i	−0.559326	−	0.828948i	$-0.688940\pi$
$659$	10.8417	−	26.1741i	0.422332	−	1.01960i	0.981658	−	0.190651i	$-0.0610599\pi$
$660$	−3.24980	+	4.95638i	−0.126498	+	0.192927i
$661$	−3.39761	+	8.20256i	−0.132152	+	0.319043i	−0.976079	−	0.217414i	$-0.930238\pi$
$661$	−3.39761	+	8.20256i	−0.132152	+	0.319043i	0.843928	+	0.536457i	$0.180238\pi$
$662$	−2.24014	+	23.8045i	−0.0870656	+	0.925189i
$663$	24.1719	−	0.795170i	0.938760	−	0.0308818i
$664$	−41.0217	−	11.8621i	−1.59195	−	0.460338i
$665$		−	3.53005i		−	0.136889i
$666$	14.2902	+	17.2591i	0.553732	+	0.668778i
$667$	−3.53602	+	1.46467i	−0.136915	+	0.0567122i
$668$	−22.6106	−	33.2107i	−0.874832	−	1.28496i
$669$	−8.18323	−	19.7561i	−0.316382	−	0.763813i
$670$	2.31772	+	7.52267i	0.0895414	+	0.290626i
$671$	−13.4158	+	13.4158i	−0.517910	+	0.517910i
$672$	−58.7081	−	29.7587i	−2.26471	−	1.14797i
$673$			32.8253i			1.26532i	0.774429	+	0.632661i	$0.218037\pi$
$673$			32.8253i			1.26532i	−0.774429	+	0.632661i	$0.781963\pi$
$674$	−26.7865	+	8.25288i	−1.03178	+	0.317889i
$675$	−0.174801	+	0.422006i	−0.00672809	+	0.0162430i
$676$	3.16129	−	25.8071i	0.121588	−	0.992581i
$677$	−29.4862	+	12.2136i	−1.13325	+	0.469406i	−0.868883	−	0.495017i	$-0.835162\pi$
$677$	−29.4862	+	12.2136i	−1.13325	+	0.469406i	−0.264363	+	0.964423i	$0.585162\pi$
$678$	−0.294876	+	3.13345i	−0.0113246	+	0.120339i
$679$	1.16925	+	1.16925i	0.0448719	+	0.0448719i
$680$	−2.56686	−	4.65525i	−0.0984346	−	0.178521i
$681$	52.7323			2.02071
$682$	11.8706	+	14.3369i	0.454549	+	0.548987i
$683$	−22.7829	−	9.43698i	−0.871763	−	0.361096i	−0.0984662	−	0.995140i	$-0.531394\pi$
$683$	−22.7829	−	9.43698i	−0.871763	−	0.361096i	−0.773297	+	0.634044i	$0.781394\pi$
$684$	1.30454	+	6.27294i	0.0498803	+	0.239852i
$685$	−8.55335	−	3.54291i	−0.326807	−	0.135368i
$686$	−17.3074	−	56.1750i	−0.660800	−	2.14477i
$687$	−36.1189	−	36.1189i	−1.37802	−	1.37802i
$688$	−25.5576	+	0.444275i	−0.974374	+	0.0169378i
$689$	7.61805	+	7.13280i	0.290224	+	0.271738i
$690$	−16.2307	+	5.00064i	−0.617891	+	0.190371i
$691$	3.99662	+	9.64869i	0.152039	+	0.367054i	0.981487	−	0.191530i	$-0.0613450\pi$
$691$	3.99662	+	9.64869i	0.152039	+	0.367054i	−0.829448	+	0.558584i	$0.811345\pi$
$692$	−6.73274	−	32.3747i	−0.255941	−	1.23070i
$693$	23.1256	−	9.57892i	0.878467	−	0.363873i
$694$	18.4448	+	22.2769i	0.700154	+	0.845620i
$695$			0.784084i			0.0297420i
$696$	−0.407736	−	3.65121i	−0.0154552	−	0.138399i
$697$	8.18604			0.310068
$698$	10.8069	−	8.94784i	0.409046	−	0.338681i
$699$	−27.9271	+	11.5678i	−1.05630	+	0.437534i
$700$	8.06041	−	42.4471i	0.304655	−	1.60435i
$701$	2.60641	+	1.07961i	0.0984428	+	0.0407763i	0.431361	−	0.902179i	$-0.358033\pi$
$701$	2.60641	+	1.07961i	0.0984428	+	0.0407763i	−0.332919	+	0.942956i	$0.608033\pi$
$702$	−0.461928	−	0.225216i	−0.0174343	−	0.00850024i
$703$		−	5.79834i		−	0.218689i
$704$	2.40611	−	13.9937i	0.0906838	−	0.527408i
$705$	5.83046			0.219588
$706$	1.90179	−	3.59550i	0.0715750	−	0.135318i
$707$	−23.1608	+	9.59350i	−0.871050	+	0.360801i
$708$	8.93045	−	47.0288i	0.335627	−	1.76745i
$709$	15.7303	+	6.51571i	0.590764	+	0.244703i	0.657979	−	0.753036i	$-0.271411\pi$
$709$	15.7303	+	6.51571i	0.590764	+	0.244703i	−0.0672152	+	0.997739i	$0.521411\pi$
$710$	−1.11190	+	11.8155i	−0.0417290	+	0.443427i
$711$	−9.32766	−	9.32766i	−0.349815	−	0.349815i
$712$	−7.41006	+	9.27310i	−0.277704	+	0.347524i
$713$			53.3375i			1.99751i
$714$	−4.23638	+	45.0173i	−0.158543	+	1.68473i
$715$	1.54118	−	4.09679i	0.0576367	−	0.153211i
$716$	−17.5984	+	3.65981i	−0.657682	+	0.136773i
$717$	−50.1206	+	20.7606i	−1.87179	+	0.775320i
$718$	−2.40341	−	7.80080i	−0.0896945	−	0.291123i
$719$			7.89011i			0.294252i	0.989118	+	0.147126i	$0.0470022\pi$
$719$			7.89011i			0.294252i	−0.989118	+	0.147126i	$0.952998\pi$
$720$	−0.140693	−	8.09358i	−0.00524332	−	0.301630i
$721$	38.9257	+	38.9257i	1.44967	+	1.44967i
$722$	−11.7882	+	22.2865i	−0.438710	+	0.829418i
$723$	−11.4123	+	4.72713i	−0.424428	+	0.175804i
$724$	9.11125	−	13.8959i	0.338617	−	0.516436i
$725$	2.22807	−	0.922895i	0.0827483	−	0.0342755i
$726$	−17.2821	−	20.8727i	−0.641399	−	0.774659i
$727$	25.8773	+	25.8773i	0.959735	+	0.959735i	0.999220	−	0.0394856i	$-0.0125719\pi$
$727$	25.8773	+	25.8773i	0.959735	+	0.959735i	−0.0394856	+	0.999220i	$0.512572\pi$
$728$	47.1151	+	11.9604i	1.74620	+	0.443282i
$729$	18.5628	−	18.5628i	0.687511	−	0.687511i
$730$	1.51180	+	0.142269i	0.0559544	+	0.00526563i
$731$	6.71991	+	16.2233i	0.248545	+	0.600040i
$732$	9.73607	−	51.2713i	0.359856	−	1.89504i
$733$	−5.72801	−	13.8286i	−0.211569	−	0.510773i	0.782096	−	0.623158i	$-0.214151\pi$
$733$	−5.72801	−	13.8286i	−0.211569	−	0.510773i	−0.993665	+	0.112386i	$0.964151\pi$
$734$	−7.46257	+	2.29921i	−0.275449	+	0.0848652i
$735$	18.5591	−	18.5591i	0.684563	−	0.684563i
$736$	30.8842	−	26.4895i	1.13841	−	0.976417i
$737$	14.4436			0.532037
$738$	11.0186	+	5.82815i	0.405600	+	0.214537i
$739$	4.11332	+	9.93043i	0.151311	+	0.365297i	0.981300	−	0.192482i	$-0.0616537\pi$
$739$	4.11332	+	9.93043i	0.151311	+	0.365297i	−0.829990	+	0.557779i	$0.811654\pi$
$740$	−1.36666	+	7.19702i	−0.0502396	+	0.264568i
$741$	−3.93437	−	8.67966i	−0.144533	−	0.318855i
$742$	−15.0284	+	12.4432i	−0.551711	+	0.456804i
$743$	34.0245			1.24824			0.624118	−	0.781330i	$-0.285458\pi$
$743$	34.0245			1.24824			0.624118	+	0.781330i	$0.285458\pi$
$744$	−49.1839	−	14.2223i	−1.80317	−	0.521415i
$745$	−8.45686	+	8.45686i	−0.309835	+	0.309835i
$746$	−11.8889	−	14.3589i	−0.435282	−	0.525718i
$747$	−17.0942	+	41.2691i	−0.625444	+	1.50996i
$748$	−9.55003	+	1.98605i	−0.349184	+	0.0726172i
$749$	0.677094	+	1.63465i	0.0247405	+	0.0597288i
$750$	21.5097	−	6.62710i	0.785424	−	0.241988i
$751$		−	28.2172i		−	1.02966i	−0.857292	−	0.514830i	$-0.827855\pi$
$751$		−	28.2172i		−	1.02966i	0.857292	−	0.514830i	$-0.172145\pi$
$752$	−12.8102	+	5.56892i	−0.467139	+	0.203078i
$753$	24.3104			0.885919
$754$	0.883718	+	2.56532i	0.0321831	+	0.0934235i
$755$	5.70844	−	13.7814i	0.207751	−	0.501556i
$756$	0.526827	−	0.803482i	0.0191605	−	0.0292224i
$757$	8.60430	+	20.7726i	0.312729	+	0.754994i	0.999602	+	0.0282165i	$0.00898279\pi$
$757$	8.60430	+	20.7726i	0.312729	+	0.754994i	−0.686873	+	0.726777i	$0.741017\pi$
$758$	−38.2447	−	3.59905i	−1.38911	−	0.130723i
$759$			31.1630i			1.13115i
$760$	−1.30764	+	1.63641i	−0.0474331	+	0.0593587i
$761$	−6.99161			−0.253446			−0.126723	−	0.991938i	$-0.540446\pi$
$761$	−6.99161			−0.253446			−0.126723	+	0.991938i	$0.540446\pi$
$762$	−65.6949	−	6.18226i	−2.37987	−	0.223960i
$763$	−37.5432	−	90.6373i	−1.35915	−	3.28129i
$764$	8.72194	+	12.8109i	0.315549	+	0.463481i
$765$	−5.13760	+	2.12806i	−0.185750	+	0.0769402i
$766$	−33.2731	−	17.5994i	−1.20221	−	0.635891i
$767$	1.16235	+	35.3335i	0.0419699	+	1.27582i
$768$	16.1915	+	35.5425i	0.584259	+	1.28253i
$769$	38.7943	−	38.7943i	1.39896	−	1.39896i

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35152 + 0.416401i) q^{2} +(-2.25523 - 0.934148i) q^{3} +(1.65322 - 1.12555i) q^{4} +(0.261748 - 0.631915i) q^{5} +(3.43698 + 0.323439i) q^{6} -4.76655i q^{7} +(-1.76568 + 2.20961i) q^{8} +(2.09213 + 2.09213i) q^{9} +O(q^{10})\)	\(q+(-1.35152 + 0.416401i) q^{2} +(-2.25523 - 0.934148i) q^{3} +(1.65322 - 1.12555i) q^{4} +(0.261748 - 0.631915i) q^{5} +(3.43698 + 0.323439i) q^{6} -4.76655i q^{7} +(-1.76568 + 2.20961i) q^{8} +(2.09213 + 2.09213i) q^{9} +(-0.0906275 + 0.963039i) q^{10} +(1.63978 + 0.679219i) q^{11} +(-4.77983 + 0.994027i) q^{12} +(3.28393 - 1.48856i) q^{13} +(1.98480 + 6.44209i) q^{14} +(-1.18061 + 1.18061i) q^{15} +(1.46627 - 3.72157i) q^{16} -2.74788 q^{17} +(-3.69872 - 1.95639i) q^{18} +(0.414355 + 1.00034i) q^{19} +(-0.278526 - 1.33931i) q^{20} +(-4.45266 + 10.7497i) q^{21} +(-2.49902 - 0.235173i) q^{22} +(-5.08603 - 5.08603i) q^{23} +(6.04613 - 3.33378i) q^{24} +(3.20473 + 3.20473i) q^{25} +(-3.81846 + 3.37925i) q^{26} +(0.0385689 + 0.0931135i) q^{27} +(-5.36499 - 7.88015i) q^{28} +(0.203632 - 0.491611i) q^{29} +(1.10401 - 2.08722i) q^{30} +(-5.24354 - 5.24354i) q^{31} +(-0.432033 + 5.64033i) q^{32} +(-3.06360 - 3.06360i) q^{33} +(3.71382 - 1.14422i) q^{34} +(-3.01206 - 1.24763i) q^{35} +(5.81354 + 1.10395i) q^{36} +(-4.94751 - 2.04933i) q^{37} +(-0.976552 - 1.17944i) q^{38} +(-8.79656 + 0.289375i) q^{39} +(0.934122 + 1.69412i) q^{40} -2.97903 q^{41} +(1.54169 - 16.3825i) q^{42} +(-2.44549 - 5.90392i) q^{43} +(3.47541 - 0.722757i) q^{44} +(1.86966 - 0.774437i) q^{45} +(8.99170 + 4.75604i) q^{46} +(-2.46927 - 2.46927i) q^{47} +(-6.78328 + 7.02328i) q^{48} -15.7200 q^{49} +(-5.66571 - 2.99681i) q^{50} +(6.19712 + 2.56693i) q^{51} +(3.75361 - 6.15715i) q^{52} +(1.10766 + 2.67412i) q^{53} +(-0.0908993 - 0.109785i) q^{54} +(0.858418 - 0.858418i) q^{55} +(10.5322 + 8.41621i) q^{56} -2.64307i q^{57} +(-0.0705055 + 0.749215i) q^{58} +(-3.75224 + 9.05870i) q^{59} +(-0.622969 + 3.28063i) q^{60} +(-4.09073 + 9.87589i) q^{61} +(9.27017 + 4.90334i) q^{62} +(9.97222 - 9.97222i) q^{63} +(-1.76474 - 7.80293i) q^{64} +(-0.0810828 - 2.46479i) q^{65} +(5.41620 + 2.86483i) q^{66} +(7.51832 - 3.11419i) q^{67} +(-4.54286 + 3.09288i) q^{68} +(6.71907 + 16.2213i) q^{69} +(4.59037 + 0.431980i) q^{70} +12.2690 q^{71} +(-8.31681 + 0.928752i) q^{72} -1.56983i q^{73} +(7.54001 + 0.709558i) q^{74} +(-4.23372 - 10.2211i) q^{75} +(1.81095 + 1.18741i) q^{76} +(3.23753 - 7.81609i) q^{77} +(11.7682 - 4.05400i) q^{78} -4.45846 q^{79} +(-1.96792 - 1.90067i) q^{80} -9.12216i q^{81} +(4.02623 - 1.24047i) q^{82} +(5.77758 + 13.9483i) q^{83} +(4.73808 + 22.7833i) q^{84} +(-0.719253 + 1.73643i) q^{85} +(5.76353 + 6.96098i) q^{86} +(-0.918475 + 0.918475i) q^{87} +(-4.39614 + 2.42399i) q^{88} +4.19672 q^{89} +(-2.20440 + 1.82520i) q^{90} +(-7.09530 - 15.6530i) q^{91} +(-14.1329 - 2.68374i) q^{92} +(6.92716 + 16.7236i) q^{93} +(4.36548 + 2.30906i) q^{94} +0.740587 q^{95} +(6.24324 - 12.3167i) q^{96} +(-0.245304 + 0.245304i) q^{97} +(21.2459 - 6.54582i) q^{98} +(2.00961 + 4.85164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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