LMFDB - Embedded newform 825.2.m.b.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(16,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("825.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.m (of order $5$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			256.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.256
Dual form			825.2.m.b.796.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.736068 + 2.26538i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.736068 + 2.26538i) q^{7} +(0.309017 + 0.951057i) q^{9} +(3.30902 + 0.224514i) q^{11} +(-0.618034 + 1.90211i) q^{12} +(-0.736068 - 2.26538i) q^{13} +(-0.690983 - 2.12663i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(1.92705 + 5.93085i) q^{17} +(-0.454915 + 1.40008i) q^{19} +(1.38197 - 4.25325i) q^{20} +(1.92705 - 1.40008i) q^{21} +(1.42705 + 4.39201i) q^{23} +(1.54508 + 4.75528i) q^{25} +(0.309017 - 0.951057i) q^{27} +4.76393 q^{28} +(-2.38197 - 7.33094i) q^{29} -2.00000 q^{31} +(-2.54508 - 2.12663i) q^{33} +(-4.30902 + 3.13068i) q^{35} +(1.61803 - 1.17557i) q^{36} +(8.28115 + 6.01661i) q^{37} +(-0.736068 + 2.26538i) q^{39} +6.23607 q^{41} +6.23607 q^{43} +(-1.61803 - 6.43288i) q^{44} +(-0.690983 + 2.12663i) q^{45} +(-1.11803 - 0.812299i) q^{47} +4.00000 q^{48} +(1.07295 + 0.779543i) q^{49} +(1.92705 - 5.93085i) q^{51} +(-3.85410 + 2.80017i) q^{52} +(2.78115 - 8.55951i) q^{53} +(5.69098 + 4.75528i) q^{55} +(1.19098 - 0.865300i) q^{57} +(9.89919 + 7.19218i) q^{59} +(-3.61803 + 2.62866i) q^{60} +(4.30902 - 13.2618i) q^{61} -2.38197 q^{63} +(6.47214 + 4.70228i) q^{64} +(1.64590 - 5.06555i) q^{65} +(-1.80902 - 1.31433i) q^{67} +(10.0902 - 7.33094i) q^{68} +(1.42705 - 4.39201i) q^{69} -11.4721 q^{71} -7.70820 q^{73} +(1.54508 - 4.75528i) q^{75} +2.94427 q^{76} +(-2.94427 + 7.33094i) q^{77} +(-0.281153 + 0.865300i) q^{79} -8.94427 q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.281153 + 0.865300i) q^{83} +(-3.85410 - 2.80017i) q^{84} +(-4.30902 + 13.2618i) q^{85} +(-2.38197 + 7.33094i) q^{87} +(-0.218847 - 0.673542i) q^{89} +5.67376 q^{91} +(7.47214 - 5.42882i) q^{92} +(1.61803 + 1.17557i) q^{93} +(-2.66312 + 1.93487i) q^{95} +(-1.35410 + 4.16750i) q^{97} +(0.809017 + 3.21644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9	$ 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9} + 11 q^{11} + 2 q^{12} + 6 q^{13} - 5 q^{15} - 4 q^{16} + q^{17} - 13 q^{19} + 10 q^{20} + q^{21} - q^{23} - 5 q^{25} - q^{27} + 28 q^{28} - 14 q^{29} - 8 q^{31} + q^{33} - 15 q^{35} + 2 q^{36} + 13 q^{37} + 6 q^{39} + 16 q^{41} + 16 q^{43} - 2 q^{44} - 5 q^{45} + 16 q^{48} + 11 q^{49} + q^{51} - 2 q^{52} - 9 q^{53} + 25 q^{55} + 7 q^{57} + 15 q^{59} - 10 q^{60} + 15 q^{61} - 14 q^{63} + 8 q^{64} + 20 q^{65} - 5 q^{67} + 18 q^{68} - q^{69} - 28 q^{71} - 4 q^{73} - 5 q^{75} - 24 q^{76} + 24 q^{77} + 19 q^{79} - q^{81} - 19 q^{83} - 2 q^{84} - 15 q^{85} - 14 q^{87} - 21 q^{89} + 54 q^{91} + 12 q^{92} + 2 q^{93} + 5 q^{95} + 8 q^{97} + q^{99}+O(q^{100}) $ 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9 + 11 * q^11 + 2 * q^12 + 6 * q^13 - 5 * q^15 - 4 * q^16 + q^17 - 13 * q^19 + 10 * q^20 + q^21 - q^23 - 5 * q^25 - q^27 + 28 * q^28 - 14 * q^29 - 8 * q^31 + q^33 - 15 * q^35 + 2 * q^36 + 13 * q^37 + 6 * q^39 + 16 * q^41 + 16 * q^43 - 2 * q^44 - 5 * q^45 + 16 * q^48 + 11 * q^49 + q^51 - 2 * q^52 - 9 * q^53 + 25 * q^55 + 7 * q^57 + 15 * q^59 - 10 * q^60 + 15 * q^61 - 14 * q^63 + 8 * q^64 + 20 * q^65 - 5 * q^67 + 18 * q^68 - q^69 - 28 * q^71 - 4 * q^73 - 5 * q^75 - 24 * q^76 + 24 * q^77 + 19 * q^79 - q^81 - 19 * q^83 - 2 * q^84 - 15 * q^85 - 14 * q^87 - 21 * q^89 + 54 * q^91 + 12 * q^92 + 2 * q^93 + 5 * q^95 + 8 * q^97 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$2$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.618034	−	1.90211i	−0.309017	−	0.951057i
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$6$		0			0
$7$	−0.736068	+	2.26538i	−0.278208	+	0.856235i	0.710145	+	0.704055i	$0.248629\pi$
$7$	−0.736068	+	2.26538i	−0.278208	+	0.856235i	−0.988353	+	0.152180i	$0.951371\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	3.30902	+	0.224514i	0.997706	+	0.0676935i
$11$	3.30902	+	0.224514i	0.997706	+	0.0676935i
$12$	−0.618034	+	1.90211i	−0.178411	+	0.549093i
$13$	−0.736068	−	2.26538i	−0.204149	−	0.628305i	−0.999747	−	0.0224806i	$-0.992844\pi$
$13$	−0.736068	−	2.26538i	−0.204149	−	0.628305i	0.795599	−	0.605824i	$-0.207156\pi$
$14$		0			0
$15$	−0.690983	−	2.12663i	−0.178411	−	0.549093i
$16$	−3.23607	+	2.35114i	−0.809017	+	0.587785i
$17$	1.92705	+	5.93085i	0.467379	+	1.43844i	0.855966	+	0.517031i	$0.172963\pi$
$17$	1.92705	+	5.93085i	0.467379	+	1.43844i	−0.388588	+	0.921412i	$0.627037\pi$
$18$		0			0
$19$	−0.454915	+	1.40008i	−0.104365	+	0.321201i	−0.989581	−	0.143979i	$-0.954010\pi$
$19$	−0.454915	+	1.40008i	−0.104365	+	0.321201i	0.885216	+	0.465180i	$0.154010\pi$
$20$	1.38197	−	4.25325i	0.309017	−	0.951057i
$21$	1.92705	−	1.40008i	0.420517	−	0.305523i
$22$		0			0
$23$	1.42705	+	4.39201i	0.297561	+	0.915798i	0.982349	+	0.187056i	$0.0598945\pi$
$23$	1.42705	+	4.39201i	0.297561	+	0.915798i	−0.684789	+	0.728742i	$0.740105\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$		0			0
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	4.76393			0.900299
$29$	−2.38197	−	7.33094i	−0.442320	−	1.36132i	−0.885396	−	0.464837i	$-0.846113\pi$
$29$	−2.38197	−	7.33094i	−0.442320	−	1.36132i	0.443076	−	0.896484i	$-0.353887\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$		0			0
$33$	−2.54508	−	2.12663i	−0.443042	−	0.370198i
$34$		0			0
$35$	−4.30902	+	3.13068i	−0.728357	+	0.529182i
$36$	1.61803	−	1.17557i	0.269672	−	0.195928i
$37$	8.28115	+	6.01661i	1.36141	+	0.989125i	0.998354	+	0.0573586i	$0.0182678\pi$
$37$	8.28115	+	6.01661i	1.36141	+	0.989125i	0.363060	+	0.931766i	$0.381732\pi$
$38$		0			0
$39$	−0.736068	+	2.26538i	−0.117865	+	0.362752i
$40$		0			0
$41$	6.23607			0.973910			0.486955	−	0.873427i	$-0.338108\pi$
$41$	6.23607			0.973910			0.486955	+	0.873427i	$0.338108\pi$
$42$		0			0
$43$	6.23607			0.950991			0.475496	−	0.879718i	$-0.342269\pi$
$43$	6.23607			0.950991			0.475496	+	0.879718i	$0.342269\pi$
$44$	−1.61803	−	6.43288i	−0.243928	−	0.969793i
$45$	−0.690983	+	2.12663i	−0.103006	+	0.317019i
$46$		0			0
$47$	−1.11803	−	0.812299i	−0.163082	−	0.118486i	0.503251	−	0.864140i	$-0.332137\pi$
$47$	−1.11803	−	0.812299i	−0.163082	−	0.118486i	−0.666333	+	0.745654i	$0.732137\pi$
$48$	4.00000			0.577350
$49$	1.07295	+	0.779543i	0.153278	+	0.111363i
$50$		0			0
$51$	1.92705	−	5.93085i	0.269841	−	0.830486i
$52$	−3.85410	+	2.80017i	−0.534468	+	0.388314i
$53$	2.78115	−	8.55951i	0.382021	−	1.17574i	−0.556598	−	0.830782i	$-0.687894\pi$
$53$	2.78115	−	8.55951i	0.382021	−	1.17574i	0.938619	−	0.344957i	$-0.112106\pi$
$54$		0			0
$55$	5.69098	+	4.75528i	0.767372	+	0.641202i
$56$		0			0
$57$	1.19098	−	0.865300i	0.157750	−	0.114612i
$58$		0			0
$59$	9.89919	+	7.19218i	1.28876	+	0.936342i	0.999780	−	0.0209916i	$-0.00668232\pi$
$59$	9.89919	+	7.19218i	1.28876	+	0.936342i	0.288985	+	0.957334i	$0.406682\pi$
$60$	−3.61803	+	2.62866i	−0.467086	+	0.339358i
$61$	4.30902	−	13.2618i	0.551713	−	1.69800i	−0.152756	−	0.988264i	$-0.548815\pi$
$61$	4.30902	−	13.2618i	0.551713	−	1.69800i	0.704469	−	0.709734i	$-0.251185\pi$
$62$		0			0
$63$	−2.38197			−0.300100
$64$	6.47214	+	4.70228i	0.809017	+	0.587785i
$65$	1.64590	−	5.06555i	0.204149	−	0.628305i
$66$		0			0
$67$	−1.80902	−	1.31433i	−0.221007	−	0.160571i	0.471773	−	0.881720i	$-0.343614\pi$
$67$	−1.80902	−	1.31433i	−0.221007	−	0.160571i	−0.692780	+	0.721149i	$0.743614\pi$
$68$	10.0902	−	7.33094i	1.22361	−	0.889007i
$69$	1.42705	−	4.39201i	0.171797	−	0.528736i
$70$		0			0
$71$	−11.4721			−1.36149			−0.680746	−	0.732520i	$-0.738344\pi$
$71$	−11.4721			−1.36149			−0.680746	+	0.732520i	$0.738344\pi$
$72$		0			0
$73$	−7.70820			−0.902177			−0.451089	−	0.892479i	$-0.648964\pi$
$73$	−7.70820			−0.902177			−0.451089	+	0.892479i	$0.648964\pi$
$74$		0			0
$75$	1.54508	−	4.75528i	0.178411	−	0.549093i
$76$	2.94427			0.337731
$77$	−2.94427	+	7.33094i	−0.335531	+	0.835438i
$78$		0			0
$79$	−0.281153	+	0.865300i	−0.0316322	+	0.0973538i	−0.965626	−	0.259935i	$-0.916299\pi$
$79$	−0.281153	+	0.865300i	−0.0316322	+	0.0973538i	0.933994	+	0.357289i	$0.116299\pi$
$80$	−8.94427			−1.00000
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	0.281153	+	0.865300i	0.0308605	+	0.0949790i	0.965300	−	0.261142i	$-0.0840991\pi$
$83$	0.281153	+	0.865300i	0.0308605	+	0.0949790i	−0.934440	+	0.356121i	$0.884099\pi$
$84$	−3.85410	−	2.80017i	−0.420517	−	0.305523i
$85$	−4.30902	+	13.2618i	−0.467379	+	1.43844i
$86$		0			0
$87$	−2.38197	+	7.33094i	−0.255374	+	0.785959i
$88$		0			0
$89$	−0.218847	−	0.673542i	−0.0231977	−	0.0713953i	0.938787	−	0.344497i	$-0.111950\pi$
$89$	−0.218847	−	0.673542i	−0.0231977	−	0.0713953i	−0.961985	+	0.273102i	$0.911950\pi$
$90$		0			0
$91$	5.67376			0.594772
$92$	7.47214	−	5.42882i	0.779024	−	0.565994i
$93$	1.61803	+	1.17557i	0.167782	+	0.121901i
$94$		0			0
$95$	−2.66312	+	1.93487i	−0.273230	+	0.198513i
$96$		0			0
$97$	−1.35410	+	4.16750i	−0.137488	+	0.423145i	−0.995969	−	0.0897009i	$-0.971409\pi$
$97$	−1.35410	+	4.16750i	−0.137488	+	0.423145i	0.858481	+	0.512846i	$0.171409\pi$
$98$		0			0
$99$	0.809017	+	3.21644i	0.0813093	+	0.323264i
$100$	8.09017	−	5.87785i	0.809017	−	0.587785i
$101$	−4.30902	+	3.13068i	−0.428763	+	0.311515i	−0.781154	−	0.624338i	$-0.785369\pi$
$101$	−4.30902	+	3.13068i	−0.428763	+	0.311515i	0.352391	+	0.935853i	$0.385369\pi$
$102$		0			0
$103$	5.13525	+	15.8047i	0.505992	+	1.55728i	0.799097	+	0.601202i	$0.205311\pi$
$103$	5.13525	+	15.8047i	0.505992	+	1.55728i	−0.293105	+	0.956080i	$0.594689\pi$
$104$		0			0
$105$	5.32624			0.519788
$106$		0			0
$107$	−3.39919	−	10.4616i	−0.328612	−	1.01136i	−0.969784	−	0.243966i	$-0.921551\pi$
$107$	−3.39919	−	10.4616i	−0.328612	−	1.01136i	0.641172	−	0.767397i	$-0.278449\pi$
$108$	−2.00000			−0.192450
$109$	−0.909830	+	2.80017i	−0.0871459	+	0.268208i	−0.985127	−	0.171826i	$-0.945033\pi$
$109$	−0.909830	+	2.80017i	−0.0871459	+	0.268208i	0.897981	+	0.440033i	$0.145033\pi$
$110$		0			0
$111$	−3.16312	−	9.73508i	−0.300230	−	0.924013i
$112$	−2.94427	−	9.06154i	−0.278208	−	0.856235i
$113$	10.6180			0.998861			0.499430	−	0.866354i	$-0.333543\pi$
$113$	10.6180			0.998861			0.499430	+	0.866354i	$0.333543\pi$
$114$		0			0
$115$	−3.19098	+	9.82084i	−0.297561	+	0.915798i
$116$	−12.4721	+	9.06154i	−1.15801	+	0.841343i
$117$	1.92705	−	1.40008i	0.178156	−	0.129438i
$118$		0			0
$119$	−14.8541			−1.36167
$120$		0			0
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$		0			0
$123$	−5.04508	−	3.66547i	−0.454900	−	0.330504i
$124$	1.23607	+	3.80423i	0.111002	+	0.341630i
$125$	−3.45492	+	10.6331i	−0.309017	+	0.951057i
$126$		0			0
$127$	−4.76393	+	14.6619i	−0.422731	+	1.30103i	0.482420	+	0.875940i	$0.339758\pi$
$127$	−4.76393	+	14.6619i	−0.422731	+	1.30103i	−0.905151	+	0.425091i	$0.860242\pi$
$128$		0			0
$129$	−5.04508	−	3.66547i	−0.444195	−	0.322727i
$130$		0			0
$131$	−12.7533	−	9.26581i	−1.11426	−	0.809557i	−0.130931	−	0.991392i	$-0.541797\pi$
$131$	−12.7533	−	9.26581i	−1.11426	−	0.809557i	−0.983329	+	0.181834i	$0.941797\pi$
$132$	−2.47214	+	6.15537i	−0.215172	+	0.535756i
$133$	−2.83688	−	2.06111i	−0.245989	−	0.178721i
$134$		0			0
$135$	1.80902	−	1.31433i	0.155695	−	0.113119i
$136$		0			0
$137$	−14.2082	+	10.3229i	−1.21389	+	0.881942i	−0.995578	−	0.0939375i	$-0.970055\pi$
$137$	−14.2082	+	10.3229i	−1.21389	+	0.881942i	−0.218311	+	0.975879i	$0.570055\pi$
$138$		0			0
$139$	−6.23607			−0.528936			−0.264468	−	0.964394i	$-0.585196\pi$
$139$	−6.23607			−0.528936			−0.264468	+	0.964394i	$0.585196\pi$
$140$	8.61803	+	6.26137i	0.728357	+	0.529182i
$141$	0.427051	+	1.31433i	0.0359642	+	0.110686i
$142$		0			0
$143$	−1.92705	−	7.66145i	−0.161148	−	0.640683i
$144$	−3.23607	−	2.35114i	−0.269672	−	0.195928i
$145$	5.32624	−	16.3925i	0.442320	−	1.36132i
$146$		0			0
$147$	−0.409830	−	1.26133i	−0.0338022	−	0.104033i
$148$	6.32624	−	19.4702i	0.520014	−	1.60044i
$149$	−16.3262	−	11.8617i	−1.33750	−	0.971749i	−0.999532	−	0.0305903i	$-0.990261\pi$
$149$	−16.3262	−	11.8617i	−1.33750	−	0.971749i	−0.337966	−	0.941158i	$-0.609739\pi$
$150$		0			0
$151$	2.20820	+	6.79615i	0.179701	+	0.553063i	0.999817	−	0.0191345i	$-0.00609106\pi$
$151$	2.20820	+	6.79615i	0.179701	+	0.553063i	−0.820116	+	0.572198i	$0.806091\pi$
$152$		0			0
$153$	−5.04508	+	3.66547i	−0.407871	+	0.296336i
$154$		0			0
$155$	−3.61803	−	2.62866i	−0.290607	−	0.211139i
$156$	4.76393			0.381420
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$		0			0
$159$	−7.28115	+	5.29007i	−0.577433	+	0.419530i
$160$		0			0
$161$	−11.0000			−0.866921
$162$		0			0
$163$	−0.336881	−	1.03681i	−0.0263866	−	0.0812095i	0.936996	−	0.349340i	$-0.113594\pi$
$163$	−0.336881	−	1.03681i	−0.0263866	−	0.0812095i	−0.963383	+	0.268130i	$0.913594\pi$
$164$	−3.85410	−	11.8617i	−0.300955	−	0.926244i
$165$	−1.80902	−	7.19218i	−0.140832	−	0.559910i
$166$		0			0
$167$	−10.6525			−0.824313			−0.412157	−	0.911113i	$-0.635224\pi$
$167$	−10.6525			−0.824313			−0.412157	+	0.911113i	$0.635224\pi$
$168$		0			0
$169$	5.92705	−	4.30625i	0.455927	−	0.331250i
$170$		0			0
$171$	−1.47214			−0.112577
$172$	−3.85410	−	11.8617i	−0.293873	−	0.904447i
$173$	13.6631	−	9.92684i	1.03879	−	0.754723i	0.0687392	−	0.997635i	$-0.478102\pi$
$173$	13.6631	−	9.92684i	1.03879	−	0.754723i	0.970049	+	0.242911i	$0.0781024\pi$
$174$		0			0
$175$	−11.9098			−0.900299
$176$	−11.2361	+	7.05342i	−0.846950	+	0.531672i
$177$	−3.78115	−	11.6372i	−0.284209	−	0.874705i
$178$		0			0
$179$	−5.19098	−	3.77147i	−0.387992	−	0.281893i	0.376640	−	0.926360i	$-0.377079\pi$
$179$	−5.19098	−	3.77147i	−0.387992	−	0.281893i	−0.764632	+	0.644467i	$0.777079\pi$
$180$	4.47214			0.333333
$181$	−5.06231	−	15.5802i	−0.376278	−	1.15807i	−0.942612	−	0.333889i	$-0.891639\pi$
$181$	−5.06231	−	15.5802i	−0.376278	−	1.15807i	0.566334	−	0.824176i	$-0.308361\pi$
$182$		0			0
$183$	−11.2812	+	8.19624i	−0.833927	+	0.605883i
$184$		0			0
$185$	7.07295	+	21.7683i	0.520014	+	1.60044i
$186$		0			0
$187$	5.04508	+	20.0579i	0.368933	+	1.46678i
$188$	−0.854102	+	2.62866i	−0.0622918	+	0.191714i
$189$	1.92705	+	1.40008i	0.140172	+	0.101841i
$190$		0			0
$191$	−10.7812	−	7.83297i	−0.780097	−	0.566774i	0.124911	−	0.992168i	$-0.460135\pi$
$191$	−10.7812	−	7.83297i	−0.780097	−	0.566774i	−0.905008	+	0.425394i	$0.860135\pi$
$192$	−2.47214	−	7.60845i	−0.178411	−	0.549093i
$193$	1.19098	+	0.865300i	0.0857288	+	0.0622856i	0.629824	−	0.776738i	$-0.283127\pi$
$193$	1.19098	+	0.865300i	0.0857288	+	0.0622856i	−0.544095	+	0.839023i	$0.683127\pi$
$194$		0			0
$195$	−4.30902	+	3.13068i	−0.308575	+	0.224193i
$196$	0.819660	−	2.52265i	0.0585472	−	0.180190i
$197$	15.8713	−	11.5312i	1.13078	−	0.821563i	0.144976	−	0.989435i	$-0.453689\pi$
$197$	15.8713	−	11.5312i	1.13078	−	0.821563i	0.985809	+	0.167872i	$0.0536895\pi$
$198$		0			0
$199$	−23.2705			−1.64960			−0.824801	−	0.565423i	$-0.808713\pi$
$199$	−23.2705			−1.64960			−0.824801	+	0.565423i	$0.808713\pi$
$200$		0			0
$201$	0.690983	+	2.12663i	0.0487382	+	0.150001i
$202$		0			0
$203$	18.3607			1.28867
$204$	−12.4721			−0.873224
$205$	11.2812	+	8.19624i	0.787910	+	0.572450i
$206$		0			0
$207$	−3.73607	+	2.71441i	−0.259675	+	0.188665i
$208$	7.70820	+	5.60034i	0.534468	+	0.388314i
$209$	−1.81966	+	4.53077i	−0.125869	+	0.313400i
$210$		0			0
$211$	4.30902	+	3.13068i	0.296645	+	0.215525i	0.726145	−	0.687542i	$-0.241310\pi$
$211$	4.30902	+	3.13068i	0.296645	+	0.215525i	−0.429500	+	0.903067i	$0.641310\pi$
$212$	−18.0000			−1.23625
$213$	9.28115	+	6.74315i	0.635934	+	0.462033i
$214$		0			0
$215$	11.2812	+	8.19624i	0.769368	+	0.558979i
$216$		0			0
$217$	1.47214	−	4.53077i	0.0999351	−	0.307569i
$218$		0			0
$219$	6.23607	+	4.53077i	0.421394	+	0.306161i
$220$	5.52786	−	13.7638i	0.372689	−	0.927957i
$221$	12.0172	−	8.73102i	0.808366	−	0.587312i
$222$		0			0
$223$	3.45492	−	2.51014i	0.231358	−	0.168092i	−0.466066	−	0.884750i	$-0.654329\pi$
$223$	3.45492	−	2.51014i	0.231358	−	0.168092i	0.697425	+	0.716658i	$0.254329\pi$
$224$		0			0
$225$	−4.04508	+	2.93893i	−0.269672	+	0.195928i
$226$		0			0
$227$	5.67376			0.376581			0.188290	−	0.982113i	$-0.439705\pi$
$227$	5.67376			0.376581			0.188290	+	0.982113i	$0.439705\pi$
$228$	−2.38197	−	1.73060i	−0.157750	−	0.114612i
$229$	4.56231	−	14.0413i	0.301486	−	0.927877i	−0.679480	−	0.733694i	$-0.737794\pi$
$229$	4.56231	−	14.0413i	0.301486	−	0.927877i	0.980965	−	0.194183i	$-0.0622056\pi$
$230$		0			0
$231$	6.69098	−	4.20025i	0.440234	−	0.276356i
$232$		0			0
$233$	1.47214			0.0964428			0.0482214	−	0.998837i	$-0.484645\pi$
$233$	1.47214			0.0964428			0.0482214	+	0.998837i	$0.484645\pi$
$234$		0			0
$235$	−0.954915	−	2.93893i	−0.0622918	−	0.191714i
$236$	7.56231	−	23.2744i	0.492264	−	1.51503i
$237$	0.736068	−	0.534785i	0.0478128	−	0.0347380i
$238$		0			0
$239$	15.5902	−	11.3269i	1.00844	−	0.732678i	0.0445621	−	0.999007i	$-0.485811\pi$
$239$	15.5902	−	11.3269i	1.00844	−	0.732678i	0.963882	+	0.266329i	$0.0858108\pi$
$240$	7.23607	+	5.25731i	0.467086	+	0.339358i
$241$	3.74671	−	11.5312i	0.241347	−	0.742789i	−0.754869	−	0.655876i	$-0.772300\pi$
$241$	3.74671	−	11.5312i	0.241347	−	0.742789i	0.996216	−	0.0869137i	$-0.0277004\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−27.8885			−1.78538
$245$	0.916408	+	2.82041i	0.0585472	+	0.180190i
$246$		0			0
$247$	3.50658			0.223118
$248$		0			0
$249$	0.281153	−	0.865300i	0.0178173	−	0.0548361i
$250$		0			0
$251$	−6.09017	+	4.42477i	−0.384408	+	0.279289i	−0.763160	−	0.646209i	$-0.776353\pi$
$251$	−6.09017	+	4.42477i	−0.384408	+	0.279289i	0.378752	+	0.925498i	$0.376353\pi$
$252$	1.47214	+	4.53077i	0.0927358	+	0.285412i
$253$	3.73607	+	14.8536i	0.234885	+	0.933840i
$254$		0			0
$255$	11.2812	−	8.19624i	0.706453	−	0.513268i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	1.56231	−	4.80828i	0.0974540	−	0.299932i	−0.890431	−	0.455117i	$-0.849597\pi$
$257$	1.56231	−	4.80828i	0.0974540	−	0.299932i	0.987885	+	0.155185i	$0.0495973\pi$
$258$		0			0
$259$	−19.7254	+	14.3314i	−1.22568	+	0.890507i
$260$	−10.6525			−0.660639
$261$	6.23607	−	4.53077i	0.386003	−	0.280448i
$262$		0			0
$263$	5.78115	−	17.7926i	0.356481	−	1.09714i	−0.598665	−	0.801000i	$-0.704302\pi$
$263$	5.78115	−	17.7926i	0.356481	−	1.09714i	0.955146	−	0.296136i	$-0.0956983\pi$
$264$		0			0
$265$	16.2812	−	11.8290i	1.00014	−	0.726647i
$266$		0			0
$267$	−0.218847	+	0.673542i	−0.0133932	+	0.0412201i
$268$	−1.38197	+	4.25325i	−0.0844170	+	0.259809i
$269$	8.65248	+	26.6296i	0.527551	+	1.62363i	0.759216	+	0.650839i	$0.225583\pi$
$269$	8.65248	+	26.6296i	0.527551	+	1.62363i	−0.231665	+	0.972796i	$0.574417\pi$
$270$		0			0
$271$	−2.38197	−	7.33094i	−0.144694	−	0.445323i	0.852277	−	0.523090i	$-0.175221\pi$
$271$	−2.38197	−	7.33094i	−0.144694	−	0.445323i	−0.996972	+	0.0777673i	$0.975221\pi$
$272$	−20.1803	−	14.6619i	−1.22361	−	0.889007i
$273$	−4.59017	−	3.33495i	−0.277810	−	0.201841i
$274$		0			0
$275$	4.04508	+	16.0822i	0.243928	+	0.969793i
$276$	−9.23607			−0.555946
$277$	−8.16312	−	5.93085i	−0.490474	−	0.356350i	0.314892	−	0.949127i	$-0.398032\pi$
$277$	−8.16312	−	5.93085i	−0.490474	−	0.356350i	−0.805367	+	0.592777i	$0.798032\pi$
$278$		0			0
$279$	−0.618034	−	1.90211i	−0.0370007	−	0.113877i
$280$		0			0
$281$	4.76393	+	14.6619i	0.284192	+	0.874654i	0.986640	+	0.162918i	$0.0520907\pi$
$281$	4.76393	+	14.6619i	0.284192	+	0.874654i	−0.702447	+	0.711736i	$0.747909\pi$
$282$		0			0
$283$	−8.72542	+	26.8541i	−0.518673	+	1.59631i	0.257826	+	0.966191i	$0.416994\pi$
$283$	−8.72542	+	26.8541i	−0.518673	+	1.59631i	−0.776499	+	0.630119i	$0.783006\pi$
$284$	7.09017	+	21.8213i	0.420724	+	1.29486i
$285$	3.29180			0.194989
$286$		0			0
$287$	−4.59017	+	14.1271i	−0.270949	+	0.833896i
$288$		0			0
$289$	−17.7082	+	12.8658i	−1.04166	+	0.756810i
$290$		0			0
$291$	3.54508	−	2.57565i	0.207817	−	0.150988i
$292$	4.76393	+	14.6619i	0.278788	+	0.858021i
$293$	−1.47214	+	4.53077i	−0.0860031	+	0.264690i	−0.984805	−	0.173665i	$-0.944439\pi$
$293$	−1.47214	+	4.53077i	−0.0860031	+	0.264690i	0.898802	+	0.438356i	$0.144439\pi$
$294$		0			0
$295$	8.45492	+	26.0216i	0.492264	+	1.51503i
$296$		0			0
$297$	1.23607	−	3.07768i	0.0717239	−	0.178585i
$298$		0			0
$299$	8.89919	−	6.46564i	0.514653	−	0.373917i
$300$	−10.0000			−0.577350
$301$	−4.59017	+	14.1271i	−0.264573	+	0.814272i
$302$		0			0
$303$	5.32624			0.305984
$304$	−1.81966	−	5.60034i	−0.104365	−	0.321201i
$305$	25.2254	−	18.3273i	1.44440	−	1.04942i
$306$		0			0
$307$	−24.5967			−1.40381			−0.701905	−	0.712270i	$-0.747667\pi$
$307$	−24.5967			−1.40381			−0.701905	+	0.712270i	$0.747667\pi$
$308$	15.7639	+	1.06957i	0.898233	+	0.0609444i
$309$	5.13525	−	15.8047i	0.292134	−	0.899097i
$310$		0			0
$311$	−1.89919	+	1.37984i	−0.107693	+	0.0782436i	−0.640328	−	0.768101i	$-0.721202\pi$
$311$	−1.89919	+	1.37984i	−0.107693	+	0.0782436i	0.532635	+	0.846345i	$0.321202\pi$
$312$		0			0
$313$	−19.7082	+	14.3188i	−1.11397	+	0.809349i	−0.983285	−	0.182074i	$-0.941719\pi$
$313$	−19.7082	+	14.3188i	−1.11397	+	0.809349i	−0.130689	+	0.991423i	$0.541719\pi$
$314$		0			0
$315$	−4.30902	−	3.13068i	−0.242786	−	0.176394i
$316$	1.81966			0.102364
$317$	−0.527864			−0.0296478			−0.0148239	−	0.999890i	$-0.504719\pi$
$317$	−0.527864			−0.0296478			−0.0148239	+	0.999890i	$0.504719\pi$
$318$		0			0
$319$	−6.23607	−	24.7930i	−0.349153	−	1.38814i
$320$	5.52786	+	17.0130i	0.309017	+	0.951057i
$321$	−3.39919	+	10.4616i	−0.189724	+	0.583911i
$322$		0			0
$323$	−9.18034			−0.510808
$324$	1.61803	+	1.17557i	0.0898908	+	0.0653095i
$325$	9.63525	−	7.00042i	0.534468	−	0.388314i
$326$		0			0
$327$	2.38197	−	1.73060i	0.131723	−	0.0957024i
$328$		0			0
$329$	2.66312	−	1.93487i	0.146823	−	0.106673i
$330$		0			0
$331$	0.572949	+	0.416272i	0.0314921	+	0.0228804i	0.603420	−	0.797424i	$-0.293804\pi$
$331$	0.572949	+	0.416272i	0.0314921	+	0.0228804i	−0.571928	+	0.820304i	$0.693804\pi$
$332$	1.47214	−	1.06957i	0.0807940	−	0.0587002i
$333$	−3.16312	+	9.73508i	−0.173338	+	0.533479i
$334$		0			0
$335$	−1.54508	−	4.75528i	−0.0844170	−	0.259809i
$336$	−2.94427	+	9.06154i	−0.160623	+	0.494347i
$337$	−3.85410	−	2.80017i	−0.209946	−	0.152535i	0.477843	−	0.878445i	$-0.341419\pi$
$337$	−3.85410	−	2.80017i	−0.209946	−	0.152535i	−0.687789	+	0.725910i	$0.741419\pi$
$338$		0			0
$339$	−8.59017	−	6.24112i	−0.466554	−	0.338971i
$340$	27.8885			1.51247
$341$	−6.61803	−	0.449028i	−0.358387	−	0.0243162i
$342$		0			0
$343$	−16.0451	+	11.6574i	−0.866353	+	0.629442i
$344$		0			0
$345$	8.35410	−	6.06961i	0.449770	−	0.326777i
$346$		0			0
$347$	−4.41641			−0.237085			−0.118543	−	0.992949i	$-0.537822\pi$
$347$	−4.41641			−0.237085			−0.118543	+	0.992949i	$0.537822\pi$
$348$	15.4164			0.826406
$349$	−3.29180	−	10.1311i	−0.176206	−	0.542306i	0.823481	−	0.567344i	$-0.192029\pi$
$349$	−3.29180	−	10.1311i	−0.176206	−	0.542306i	−0.999686	+	0.0250386i	$0.992029\pi$
$350$		0			0
$351$	−2.38197			−0.127140
$352$		0			0
$353$	29.5623	−	21.4783i	1.57344	−	1.14317i	0.649680	−	0.760208i	$-0.274903\pi$
$353$	29.5623	−	21.4783i	1.57344	−	1.14317i	0.923763	−	0.382965i	$-0.125097\pi$
$354$		0			0
$355$	−20.7533	−	15.0781i	−1.10147	−	0.800265i
$356$	−1.14590	+	0.832544i	−0.0607325	+	0.0441247i
$357$	12.0172	+	8.73102i	0.636019	+	0.462095i
$358$		0			0
$359$	5.04508	+	3.66547i	0.266269	+	0.193456i	0.712906	−	0.701259i	$-0.247378\pi$
$359$	5.04508	+	3.66547i	0.266269	+	0.193456i	−0.446637	+	0.894715i	$0.647378\pi$
$360$		0			0
$361$	13.6180	+	9.89408i	0.716739	+	0.520741i
$362$		0			0
$363$	−7.94427	−	7.60845i	−0.416966	−	0.399340i
$364$	−3.50658	−	10.7921i	−0.183795	−	0.565662i
$365$	−13.9443	−	10.1311i	−0.729877	−	0.530286i
$366$		0			0
$367$	4.80902	−	3.49396i	0.251029	−	0.182383i	−0.455154	−	0.890413i	$-0.650416\pi$
$367$	4.80902	−	3.49396i	0.251029	−	0.182383i	0.706183	+	0.708030i	$0.250416\pi$
$368$	−14.9443	−	10.8576i	−0.779024	−	0.565994i
$369$	1.92705	+	5.93085i	0.100318	+	0.308748i
$370$		0			0
$371$	17.3435	+	12.6008i	0.900428	+	0.654199i
$372$	1.23607	−	3.80423i	0.0640871	−	0.197240i
$373$	−11.0000	−	33.8545i	−0.569558	−	1.75292i	−0.654003	−	0.756492i	$-0.726911\pi$
$373$	−11.0000	−	33.8545i	−0.569558	−	1.75292i	0.0844442	−	0.996428i	$-0.473089\pi$
$374$		0			0
$375$	9.04508	−	6.57164i	0.467086	−	0.339358i
$376$		0			0
$377$	−14.8541	+	10.7921i	−0.765025	+	0.555823i
$378$		0			0
$379$	17.1803			0.882495			0.441247	−	0.897386i	$-0.354536\pi$
$379$	17.1803			0.882495			0.441247	+	0.897386i	$0.354536\pi$
$380$	5.32624	+	3.86974i	0.273230	+	0.198513i
$381$	12.4721	−	9.06154i	0.638967	−	0.464237i
$382$		0			0
$383$	−15.5967			−0.796957			−0.398478	−	0.917178i	$-0.630462\pi$
$383$	−15.5967			−0.796957			−0.398478	+	0.917178i	$0.630462\pi$
$384$		0			0
$385$	−14.9615	+	9.39205i	−0.762508	+	0.478663i
$386$		0			0
$387$	1.92705	+	5.93085i	0.0979575	+	0.301482i
$388$	8.76393			0.444921
$389$	22.2361			1.12741			0.563707	−	0.825975i	$-0.309375\pi$
$389$	22.2361			1.12741			0.563707	+	0.825975i	$0.309375\pi$
$390$		0			0
$391$	−23.2984	+	16.9273i	−1.17825	+	0.856048i
$392$		0			0
$393$	4.87132	+	14.9924i	0.245726	+	0.756266i
$394$		0			0
$395$	−1.64590	+	1.19581i	−0.0828141	+	0.0601680i
$396$	5.61803	−	3.52671i	0.282317	−	0.177224i
$397$	9.47214	−	6.88191i	0.475393	−	0.345393i	−0.324146	−	0.946007i	$-0.605077\pi$
$397$	9.47214	−	6.88191i	0.475393	−	0.345393i	0.799539	+	0.600614i	$0.205077\pi$
$398$		0			0
$399$	1.08359	+	3.33495i	0.0542475	+	0.166957i
$400$	−16.1803	−	11.7557i	−0.809017	−	0.587785i
$401$	11.2082	+	8.14324i	0.559711	+	0.406654i	0.831353	−	0.555744i	$-0.187567\pi$
$401$	11.2082	+	8.14324i	0.559711	+	0.406654i	−0.271642	+	0.962398i	$0.587567\pi$
$402$		0			0
$403$	1.47214	+	4.53077i	0.0733323	+	0.225694i
$404$	8.61803	+	6.26137i	0.428763	+	0.311515i
$405$	−2.23607			−0.111111
$406$		0			0
$407$	26.0517	+	21.7683i	1.29133	+	1.07901i
$408$		0			0
$409$	8.05573	+	24.7930i	0.398330	+	1.22593i	0.926338	+	0.376694i	$0.122939\pi$
$409$	8.05573	+	24.7930i	0.398330	+	1.22593i	−0.528007	+	0.849240i	$0.677061\pi$
$410$		0			0
$411$	17.5623			0.866285
$412$	26.8885	−	19.5357i	1.32470	−	0.962453i
$413$	−23.5795	+	17.1315i	−1.16027	+	0.842987i
$414$		0			0
$415$	−0.628677	+	1.93487i	−0.0308605	+	0.0949790i
$416$		0			0
$417$	5.04508	+	3.66547i	0.247059	+	0.179499i
$418$		0			0
$419$	−1.69098	−	1.22857i	−0.0826099	−	0.0600196i	0.545714	−	0.837972i	$-0.316259\pi$
$419$	−1.69098	−	1.22857i	−0.0826099	−	0.0600196i	−0.628324	+	0.777952i	$0.716259\pi$
$420$	−3.29180	−	10.1311i	−0.160623	−	0.494347i
$421$	−24.6353	−	17.8986i	−1.20065	−	0.872322i	−0.206300	−	0.978489i	$-0.566142\pi$
$421$	−24.6353	−	17.8986i	−1.20065	−	0.872322i	−0.994348	+	0.106166i	$0.966142\pi$
$422$		0			0
$423$	0.427051	−	1.31433i	0.0207639	−	0.0639048i
$424$		0			0
$425$	−25.2254	+	18.3273i	−1.22361	+	0.889007i
$426$		0			0
$427$	26.8713	+	19.5232i	1.30039	+	0.944792i
$428$	−17.7984	+	12.9313i	−0.860317	+	0.625057i
$429$	−2.94427	+	7.33094i	−0.142151	+	0.353941i
$430$		0			0
$431$	25.8541			1.24535			0.622674	−	0.782481i	$-0.286046\pi$
$431$	25.8541			1.24535			0.622674	+	0.782481i	$0.286046\pi$
$432$	1.23607	+	3.80423i	0.0594703	+	0.183031i
$433$	5.89919	−	4.28601i	0.283497	−	0.205973i	−0.436944	−	0.899489i	$-0.643939\pi$
$433$	5.89919	−	4.28601i	0.283497	−	0.205973i	0.720441	+	0.693516i	$0.243939\pi$
$434$		0			0
$435$	−13.9443	+	10.1311i	−0.668577	+	0.485749i
$436$	5.88854			0.282010
$437$	−6.79837			−0.325210
$438$		0			0
$439$	9.63525	+	29.6543i	0.459866	+	1.41532i	0.865327	+	0.501208i	$0.167111\pi$
$439$	9.63525	+	29.6543i	0.459866	+	1.41532i	−0.405461	+	0.914112i	$0.632889\pi$
$440$		0			0
$441$	−0.409830	+	1.26133i	−0.0195157	+	0.0600632i
$442$		0			0
$443$	−11.9721	−	36.8464i	−0.568813	−	1.75063i	−0.656340	−	0.754465i	$-0.727896\pi$
$443$	−11.9721	−	36.8464i	−0.568813	−	1.75063i	0.0875266	−	0.996162i	$-0.472104\pi$
$444$	−16.5623	+	12.0332i	−0.786012	+	0.571071i
$445$	0.489357	−	1.50609i	0.0231977	−	0.0713953i
$446$		0			0
$447$	6.23607	+	19.1926i	0.294956	+	0.907781i
$448$	−15.4164	+	11.2007i	−0.728357	+	0.529182i
$449$	17.4164	−	12.6538i	0.821931	−	0.597168i	−0.0953339	−	0.995445i	$-0.530392\pi$
$449$	17.4164	−	12.6538i	0.821931	−	0.597168i	0.917265	+	0.398277i	$0.130392\pi$
$450$		0			0
$451$	20.6353	+	1.40008i	0.971676	+	0.0659274i
$452$	−6.56231	−	20.1967i	−0.308665	−	0.949973i
$453$	2.20820	−	6.79615i	0.103750	−	0.319311i
$454$		0			0
$455$	10.2639	+	7.45718i	0.481181	+	0.349598i
$456$		0			0
$457$	−24.4894	−	17.7926i	−1.14556	−	0.832301i	−0.157679	−	0.987490i	$-0.550401\pi$
$457$	−24.4894	−	17.7926i	−1.14556	−	0.832301i	−0.987885	+	0.155190i	$0.950401\pi$
$458$		0			0
$459$	6.23607			0.291075
$460$	20.6525			0.962927
$461$	−10.5451	−	32.4544i	−0.491134	−	1.51155i	−0.822897	−	0.568191i	$-0.807643\pi$
$461$	−10.5451	−	32.4544i	−0.491134	−	1.51155i	0.331763	−	0.943363i	$-0.392357\pi$
$462$		0			0
$463$	6.75329	−	20.7845i	0.313852	−	0.965937i	−0.662372	−	0.749175i	$-0.730450\pi$
$463$	6.75329	−	20.7845i	0.313852	−	0.965937i	0.976224	−	0.216762i	$-0.0695497\pi$
$464$	24.9443	+	18.1231i	1.15801	+	0.841343i
$465$	1.38197	+	4.25325i	0.0640871	+	0.197240i
$466$		0			0
$467$	4.01064	+	12.3435i	0.185590	+	0.571189i	0.999958	−	0.00916076i	$-0.00291600\pi$
$467$	4.01064	+	12.3435i	0.185590	+	0.571189i	−0.814368	+	0.580349i	$0.802916\pi$
$468$	−3.85410	−	2.80017i	−0.178156	−	0.129438i
$469$	4.30902	−	3.13068i	0.198972	−	0.144562i
$470$		0			0
$471$	3.00000	−	9.23305i	0.138233	−	0.425437i
$472$		0			0
$473$	20.6353	+	1.40008i	0.948810	+	0.0643760i
$474$		0			0
$475$	−7.36068			−0.337731
$476$	9.18034	+	28.2542i	0.420780	+	1.29503i
$477$	9.00000			0.412082
$478$		0			0
$479$	2.94427			0.134527			0.0672636	−	0.997735i	$-0.478573\pi$
$479$	2.94427			0.134527			0.0672636	+	0.997735i	$0.478573\pi$
$480$		0			0
$481$	7.53444	−	23.1886i	0.343541	−	1.05731i
$482$		0			0
$483$	8.89919	+	6.46564i	0.404927	+	0.294197i
$484$	−3.90983	−	21.6498i	−0.177720	−	0.984081i
$485$	−7.92705	+	5.75934i	−0.359949	+	0.261518i
$486$		0			0
$487$	9.43769			0.427663			0.213831	−	0.976871i	$-0.431406\pi$
$487$	9.43769			0.427663			0.213831	+	0.976871i	$0.431406\pi$
$488$		0			0
$489$	−0.336881	+	1.03681i	−0.0152343	+	0.0468863i
$490$		0			0
$491$	−34.2984	−	24.9192i	−1.54786	−	1.12459i	−0.945152	−	0.326630i	$-0.894087\pi$
$491$	−34.2984	−	24.9192i	−1.54786	−	1.12459i	−0.602712	−	0.797959i	$-0.705913\pi$
$492$	−3.85410	+	11.8617i	−0.173756	+	0.534767i
$493$	38.8885	−	28.2542i	1.75145	−	1.27250i
$494$		0			0
$495$	−2.76393	+	6.88191i	−0.124230	+	0.309319i
$496$	6.47214	−	4.70228i	0.290607	−	0.211139i
$497$	8.44427	−	25.9888i	0.378777	−	1.16576i
$498$		0			0
$499$	8.58359	−	26.4176i	0.384254	−	1.18261i	−0.552765	−	0.833337i	$-0.686427\pi$
$499$	8.58359	−	26.4176i	0.384254	−	1.18261i	0.937020	−	0.349276i	$-0.113573\pi$
$500$	22.3607			1.00000
$501$	8.61803	+	6.26137i	0.385025	+	0.279737i
$502$		0			0
$503$	−7.25329	−	5.26982i	−0.323408	−	0.234970i	0.414220	−	0.910177i	$-0.364054\pi$
$503$	−7.25329	−	5.26982i	−0.323408	−	0.234970i	−0.737628	+	0.675207i	$0.764054\pi$
$504$		0			0
$505$	−11.9098			−0.529980
$506$		0			0
$507$	−7.32624			−0.325370
$508$	30.8328			1.36798
$509$	10.2705			0.455232			0.227616	−	0.973751i	$-0.426907\pi$
$509$	10.2705			0.455232			0.227616	+	0.973751i	$0.426907\pi$
$510$		0			0
$511$	5.67376	−	17.4620i	0.250992	−	0.772475i
$512$		0			0
$513$	1.19098	+	0.865300i	0.0525832	+	0.0382039i
$514$		0			0
$515$	−11.4828	+	35.3404i	−0.505992	+	1.55728i
$516$	−3.85410	+	11.8617i	−0.169667	+	0.522182i
$517$	−3.51722	−	2.93893i	−0.154687	−	0.129254i
$518$		0			0
$519$	−16.8885			−0.741325
$520$		0			0
$521$	−7.16312	−	22.0458i	−0.313822	−	0.965845i	−0.976237	−	0.216707i	$-0.930468\pi$
$521$	−7.16312	−	22.0458i	−0.313822	−	0.965845i	0.662415	−	0.749137i	$-0.269532\pi$
$522$		0			0
$523$	−11.8435	+	36.4504i	−0.517878	+	1.59387i	0.260105	+	0.965580i	$0.416243\pi$
$523$	−11.8435	+	36.4504i	−0.517878	+	1.59387i	−0.777983	+	0.628285i	$0.783757\pi$
$524$	−9.74265	+	29.9848i	−0.425609	+	1.30989i
$525$	9.63525	+	7.00042i	0.420517	+	0.305523i
$526$		0			0
$527$	−3.85410	−	11.8617i	−0.167887	−	0.516704i
$528$	13.2361	+	0.898056i	0.576026	+	0.0390829i
$529$	1.35410	−	0.983813i	0.0588740	−	0.0427745i
$530$		0			0
$531$	−3.78115	+	11.6372i	−0.164088	+	0.505011i
$532$	−2.16718	+	6.66991i	−0.0939594	+	0.289177i
$533$	−4.59017	−	14.1271i	−0.198822	−	0.611912i
$534$		0			0
$535$	7.60081	−	23.3929i	0.328612	−	1.01136i
$536$		0			0
$537$	1.98278	+	6.10237i	0.0855632	+	0.263337i
$538$		0			0
$539$	3.37539	+	2.82041i	0.145388	+	0.121484i
$540$	−3.61803	−	2.62866i	−0.155695	−	0.113119i
$541$	0.562306	+	1.73060i	0.0241754	+	0.0744043i	0.962416	−	0.271578i	$-0.0875456\pi$
$541$	0.562306	+	1.73060i	0.0241754	+	0.0744043i	−0.938241	+	0.345983i	$0.887546\pi$
$542$		0			0
$543$	−5.06231	+	15.5802i	−0.217244	+	0.668609i
$544$		0			0
$545$	−5.32624	+	3.86974i	−0.228151	+	0.165761i
$546$		0			0
$547$	1.47214	+	1.06957i	0.0629440	+	0.0457315i	0.618812	−	0.785539i	$-0.287614\pi$
$547$	1.47214	+	1.06957i	0.0629440	+	0.0457315i	−0.555868	+	0.831270i	$0.687614\pi$
$548$	28.4164	+	20.6457i	1.21389	+	0.881942i
$549$	13.9443			0.595127
$550$		0			0
$551$	11.3475			0.483421
$552$		0			0
$553$	−1.75329	−	1.27384i	−0.0745574	−	0.0541691i
$554$		0			0
$555$	7.07295	−	21.7683i	0.300230	−	0.924013i
$556$	3.85410	+	11.8617i	0.163450	+	0.503048i
$557$	1.19098	−	3.66547i	0.0504636	−	0.155311i	−0.922649	−	0.385641i	$-0.873980\pi$
$557$	1.19098	−	3.66547i	0.0504636	−	0.155311i	0.973113	+	0.230330i	$0.0739805\pi$
$558$		0			0
$559$	−4.59017	−	14.1271i	−0.194144	−	0.597512i
$560$	6.58359	−	20.2622i	0.278208	−	0.856235i
$561$	7.70820	−	19.1926i	0.325441	−	0.810314i
$562$		0			0
$563$	−1.01722	−	3.13068i	−0.0428708	−	0.131943i	0.927330	−	0.374244i	$-0.122098\pi$
$563$	−1.01722	−	3.13068i	−0.0428708	−	0.131943i	−0.970201	+	0.242301i	$0.922098\pi$
$564$	2.23607	−	1.62460i	0.0941554	−	0.0684079i
$565$	19.2082	+	13.9556i	0.808095	+	0.587116i
$566$		0			0
$567$	−0.736068	−	2.26538i	−0.0309119	−	0.0951372i
$568$		0			0
$569$	8.61803	−	26.5236i	0.361287	−	1.11193i	−0.590987	−	0.806681i	$-0.701262\pi$
$569$	8.61803	−	26.5236i	0.361287	−	1.11193i	0.952274	−	0.305245i	$-0.0987385\pi$
$570$		0			0
$571$	−23.2984	+	16.9273i	−0.975007	+	0.708384i	−0.956587	−	0.291447i	$-0.905863\pi$
$571$	−23.2984	+	16.9273i	−0.975007	+	0.708384i	−0.0184195	+	0.999830i	$0.505863\pi$
$572$	−13.3820	+	8.40051i	−0.559528	+	0.351243i
$573$	4.11803	+	12.6740i	0.172033	+	0.529464i
$574$		0			0
$575$	−18.6803	+	13.5721i	−0.779024	+	0.565994i
$576$	−2.47214	+	7.60845i	−0.103006	+	0.317019i
$577$	−11.4271	+	35.1688i	−0.475714	+	1.46410i	0.369278	+	0.929319i	$0.379605\pi$
$577$	−11.4271	+	35.1688i	−0.475714	+	1.46410i	−0.844992	+	0.534779i	$0.820395\pi$
$578$		0			0
$579$	−0.454915	−	1.40008i	−0.0189056	−	0.0581855i
$580$	−34.4721			−1.43138
$581$	−2.16718			−0.0899100
$582$		0			0
$583$	11.1246	−	27.6992i	0.460734	−	1.14718i
$584$		0			0
$585$	5.32624			0.220213
$586$		0			0
$587$	3.38197	+	2.45714i	0.139589	+	0.101417i	0.655388	−	0.755292i	$-0.272505\pi$
$587$	3.38197	+	2.45714i	0.139589	+	0.101417i	−0.515800	+	0.856709i	$0.672505\pi$
$588$	−2.14590	+	1.55909i	−0.0884953	+	0.0642956i
$589$	0.909830	−	2.80017i	0.0374889	−	0.115379i
$590$		0			0
$591$	−19.6180			−0.806978
$592$	−40.9443			−1.68280
$593$	−9.52786			−0.391262			−0.195631	−	0.980678i	$-0.562676\pi$
$593$	−9.52786			−0.391262			−0.195631	+	0.980678i	$0.562676\pi$
$594$		0			0
$595$	−26.8713	−	19.5232i	−1.10162	−	0.800371i
$596$	−12.4721	+	38.3853i	−0.510879	+	1.57232i
$597$	18.8262	+	13.6781i	0.770507	+	0.559806i
$598$		0			0
$599$	4.23607	+	3.07768i	0.173081	+	0.125751i	0.670953	−	0.741500i	$-0.265885\pi$
$599$	4.23607	+	3.07768i	0.173081	+	0.125751i	−0.497872	+	0.867250i	$0.665885\pi$
$600$		0			0
$601$	−2.83688	+	8.73102i	−0.115719	+	0.356146i	−0.992096	−	0.125479i	$-0.959953\pi$
$601$	−2.83688	+	8.73102i	−0.115719	+	0.356146i	0.876377	+	0.481625i	$0.159953\pi$
$602$		0			0
$603$	0.690983	−	2.12663i	0.0281390	−	0.0866029i
$604$	11.5623	−	8.40051i	0.470464	−	0.341812i
$605$	17.7639	+	17.0130i	0.722207	+	0.691677i
$606$		0			0
$607$	32.1976	−	23.3929i	1.30686	−	0.949488i	0.306861	−	0.951754i	$-0.400721\pi$
$607$	32.1976	−	23.3929i	1.30686	−	0.949488i	0.999997	+	0.00226585i	$0.000721244\pi$
$608$		0			0
$609$	−14.8541	−	10.7921i	−0.601919	−	0.437319i
$610$		0			0
$611$	−1.01722	+	3.13068i	−0.0411524	+	0.126654i
$612$	10.0902	+	7.33094i	0.407871	+	0.296336i
$613$	−21.6525			−0.874535			−0.437268	−	0.899331i	$-0.644054\pi$
$613$	−21.6525			−0.874535			−0.437268	+	0.899331i	$0.644054\pi$
$614$		0			0
$615$	−4.30902	−	13.2618i	−0.173756	−	0.534767i
$616$		0			0
$617$	−10.1353	−	7.36369i	−0.408030	−	0.296451i	0.364774	−	0.931096i	$-0.381146\pi$
$617$	−10.1353	−	7.36369i	−0.408030	−	0.296451i	−0.772804	+	0.634645i	$0.781146\pi$
$618$		0			0
$619$	−0.864745	+	2.66141i	−0.0347570	+	0.106971i	−0.966930	−	0.255042i	$-0.917911\pi$
$619$	−0.864745	+	2.66141i	−0.0347570	+	0.106971i	0.932173	+	0.362014i	$0.117911\pi$
$620$	−2.76393	+	8.50651i	−0.111002	+	0.341630i
$621$	4.61803			0.185315
$622$		0			0
$623$	1.68692			0.0675849
$624$	−2.94427	−	9.06154i	−0.117865	−	0.362752i
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$	4.13525	−	2.59590i	0.165146	−	0.103670i
$628$	15.7082	−	11.4127i	0.626826	−	0.455415i
$629$	−19.7254	+	60.7086i	−0.786504	+	2.42061i
$630$		0			0
$631$	32.2426	−	23.4257i	1.28356	−	0.932561i	0.283905	−	0.958852i	$-0.408370\pi$
$631$	32.2426	−	23.4257i	1.28356	−	0.932561i	0.999654	+	0.0262918i	$0.00836991\pi$
$632$		0			0
$633$	−1.64590	−	5.06555i	−0.0654186	−	0.201338i
$634$		0			0
$635$	−27.8885	+	20.2622i	−1.10672	+	0.804081i
$636$	14.5623	+	10.5801i	0.577433	+	0.419530i
$637$	0.976201	−	3.00444i	0.0386785	−	0.119040i
$638$		0			0
$639$	−3.54508	−	10.9106i	−0.140241	−	0.431619i
$640$		0			0
$641$	−29.9098			−1.18137			−0.590684	−	0.806903i	$-0.701142\pi$
$641$	−29.9098			−1.18137			−0.590684	+	0.806903i	$0.701142\pi$
$642$		0			0
$643$	−32.2705	−	23.4459i	−1.27262	−	0.924616i	−0.273321	−	0.961923i	$-0.588122\pi$
$643$	−32.2705	−	23.4459i	−1.27262	−	0.924616i	−0.999304	+	0.0373070i	$0.988122\pi$
$644$	6.79837	+	20.9232i	0.267893	+	0.824491i
$645$	−4.30902	−	13.2618i	−0.169667	−	0.522182i
$646$		0			0
$647$	−0.871323	+	2.68166i	−0.0342552	+	0.105427i	−0.966722	−	0.255829i	$-0.917652\pi$
$647$	−0.871323	+	2.68166i	−0.0342552	+	0.105427i	0.932467	+	0.361255i	$0.117652\pi$
$648$		0			0
$649$	31.1418	+	26.0216i	1.22242	+	1.02144i
$650$		0			0
$651$	−3.85410	+	2.80017i	−0.151054	+	0.109747i
$652$	−1.76393	+	1.28157i	−0.0690809	+	0.0501902i
$653$	4.94427	+	15.2169i	0.193484	+	0.595483i	0.999991	+	0.00425842i	$0.00135550\pi$
$653$	4.94427	+	15.2169i	0.193484	+	0.595483i	−0.806507	+	0.591225i	$0.798644\pi$
$654$		0			0
$655$	−10.8926	−	33.5240i	−0.425609	−	1.30989i
$656$	−20.1803	+	14.6619i	−0.787910	+	0.572450i
$657$	−2.38197	−	7.33094i	−0.0929293	−	0.286007i
$658$		0			0
$659$	9.74265	−	29.9848i	0.379520	−	1.16804i	−0.560859	−	0.827911i	$-0.689529\pi$
$659$	9.74265	−	29.9848i	0.379520	−	1.16804i	0.940378	−	0.340130i	$-0.110471\pi$
$660$	−12.5623	+	7.88597i	−0.488987	+	0.306961i
$661$	5.73607	+	17.6538i	0.223107	+	0.686653i	0.998478	+	0.0551474i	$0.0175629\pi$
$661$	5.73607	+	17.6538i	0.223107	+	0.686653i	−0.775371	+	0.631506i	$0.782437\pi$
$662$		0			0
$663$	−14.8541			−0.576886
$664$		0			0
$665$	−2.42299	−	7.45718i	−0.0939594	−	0.289177i
$666$		0			0
$667$	28.7984	−	20.9232i	1.11508	−	0.810151i
$668$	6.58359	+	20.2622i	0.254727	+	0.783969i
$669$	−4.27051			−0.165107
$670$		0			0
$671$	17.2361	−	42.9161i	0.665391	−	1.65676i
$672$		0			0
$673$	−19.7254	−	14.3314i	−0.760359	−	0.552433i	0.138661	−	0.990340i	$-0.455720\pi$
$673$	−19.7254	−	14.3314i	−0.760359	−	0.552433i	−0.899021	+	0.437907i	$0.855720\pi$
$674$		0			0
$675$	5.00000			0.192450
$676$	−11.8541	−	8.61251i	−0.455927	−	0.331250i
$677$	11.2812	−	34.7198i	0.433570	−	1.33439i	−0.460975	−	0.887413i	$-0.652500\pi$
$677$	11.2812	−	34.7198i	0.433570	−	1.33439i	0.894545	−	0.446978i	$-0.147500\pi$
$678$		0			0
$679$	−8.44427	−	6.13512i	−0.324061	−	0.235444i
$680$		0			0
$681$	−4.59017	−	3.33495i	−0.175896	−	0.127796i
$682$		0			0
$683$	6.80902	+	4.94704i	0.260540	+	0.189293i	0.710385	−	0.703813i	$-0.248521\pi$
$683$	6.80902	+	4.94704i	0.260540	+	0.189293i	−0.449845	+	0.893107i	$0.648521\pi$
$684$	0.909830	+	2.80017i	0.0347882	+	0.107067i
$685$	−39.2705			−1.50045
$686$		0			0
$687$	−11.9443	+	8.67802i	−0.455702	+	0.331087i
$688$	−20.1803	+	14.6619i	−0.769368	+	0.558979i
$689$	−21.4377			−0.816711
$690$		0			0
$691$	0.774575	+	2.38390i	0.0294662	+	0.0906877i	0.964708	−	0.263322i	$-0.0848181\pi$
$691$	0.774575	+	2.38390i	0.0294662	+	0.0906877i	−0.935242	+	0.354009i	$0.884818\pi$
$692$	−27.3262	−	19.8537i	−1.03879	−	0.754723i
$693$	−7.88197	−	0.534785i	−0.299411	−	0.0203148i
$694$		0			0
$695$	−11.2812	−	8.19624i	−0.427919	−	0.310901i
$696$		0			0
$697$	12.0172	+	36.9852i	0.455185	+	1.40091i
$698$		0			0
$699$	−1.19098	−	0.865300i	−0.0450471	−	0.0327286i
$700$	7.36068	+	22.6538i	0.278208	+	0.856235i
$701$	6.23607	+	19.1926i	0.235533	+	0.724896i	0.997050	+	0.0767515i	$0.0244548\pi$
$701$	6.23607	+	19.1926i	0.235533	+	0.724896i	−0.761517	+	0.648145i	$0.775545\pi$
$702$		0			0
$703$	−12.1910	+	8.85727i	−0.459792	+	0.334058i
$704$	20.3607	+	17.0130i	0.767372	+	0.641202i
$705$	−0.954915	+	2.93893i	−0.0359642	+	0.110686i
$706$		0			0
$707$	−3.92047	−	12.0660i	−0.147445	−	0.453788i
$708$	−19.7984	+	14.3844i	−0.744068	+	0.540597i
$709$	26.7984	−	19.4702i	1.00643	−	0.731217i	0.0429759	−	0.999076i	$-0.486316\pi$
$709$	26.7984	−	19.4702i	1.00643	−	0.731217i	0.963458	+	0.267859i	$0.0863161\pi$
$710$		0			0
$711$	−0.909830			−0.0341213
$712$		0			0
$713$	−2.85410	−	8.78402i	−0.106887	−	0.328964i
$714$		0			0
$715$	6.58359	−	16.3925i	0.246212	−	0.613044i
$716$	−3.96556	+	12.2047i	−0.148200	+	0.456112i
$717$	−19.2705			−0.719670
$718$		0			0
$719$	37.7426	−	27.4216i	1.40756	−	1.02265i	0.413892	−	0.910326i	$-0.364169\pi$
$719$	37.7426	−	27.4216i	1.40756	−	1.02265i	0.993671	−	0.112329i	$-0.0358309\pi$
$720$	−2.76393	−	8.50651i	−0.103006	−	0.317019i
$721$	−39.5836			−1.47417
$722$		0			0
$723$	−9.80902	+	7.12667i	−0.364801	+	0.265044i
$724$	−26.5066	+	19.2582i	−0.985109	+	0.715724i
$725$	31.1803	−	22.6538i	1.15801	−	0.841343i
$726$		0			0
$727$	−0.892609	−	2.74717i	−0.0331050	−	0.101887i	0.933139	−	0.359517i	$-0.117058\pi$
$727$	−0.892609	−	2.74717i	−0.0331050	−	0.101887i	−0.966244	+	0.257630i	$0.917058\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	12.0172	+	36.9852i	0.444473	+	1.36795i
$732$	22.5623	+	16.3925i	0.833927	+	0.605883i
$733$	−29.2533	+	21.2538i	−1.08049	+	0.785025i	−0.977769	−	0.209684i	$-0.932756\pi$
$733$	−29.2533	+	21.2538i	−1.08049	+	0.785025i	−0.102726	+	0.994710i	$0.532756\pi$
$734$		0			0
$735$	0.916408	−	2.82041i	0.0338022	−	0.104033i
$736$		0			0
$737$	−5.69098	−	4.75528i	−0.209630	−	0.175163i
$738$		0			0
$739$	−35.0344	−	25.4540i	−1.28876	−	0.936341i	−0.288983	−	0.957334i	$-0.593317\pi$
$739$	−35.0344	−	25.4540i	−1.28876	−	0.936341i	−0.999780	+	0.0209932i	$0.993317\pi$
$740$	37.0344	−	26.9071i	1.36141	−	0.989125i
$741$	−2.83688	−	2.06111i	−0.104215	−	0.0757169i
$742$		0			0
$743$	−22.2812	−	16.1882i	−0.817416	−	0.593888i	0.0985550	−	0.995132i	$-0.468578\pi$
$743$	−22.2812	−	16.1882i	−0.817416	−	0.593888i	−0.915971	+	0.401244i	$0.868578\pi$
$744$		0			0
$745$	−13.9443	−	42.9161i	−0.510879	−	1.57232i
$746$		0			0
$747$	−0.736068	+	0.534785i	−0.0269313	+	0.0195667i
$748$	35.0344	−	21.9928i	1.28099	−	0.804137i
$749$	26.2016			0.957387
$750$		0			0
$751$	11.2705	+	34.6871i	0.411267	+	1.26575i	0.915548	+	0.402209i	$0.131758\pi$
$751$	11.2705	+	34.6871i	0.411267	+	1.26575i	−0.504281	+	0.863540i	$0.668242\pi$
$752$	5.52786			0.201580
$753$	7.52786			0.274331
$754$		0			0
$755$	−4.93769	+	15.1967i	−0.179701	+	0.553063i
$756$	1.47214	−	4.53077i	0.0535411	−	0.164782i
$757$	−29.8435	+	21.6825i	−1.08468	+	0.788065i	−0.978493	−	0.206281i	$-0.933864\pi$
$757$	−29.8435	+	21.6825i	−1.08468	+	0.788065i	−0.106186	+	0.994346i	$0.533864\pi$
$758$		0			0
$759$	5.70820	−	14.2128i	0.207195	−	0.515894i
$760$		0			0
$761$	2.66312	+	1.93487i	0.0965380	+	0.0701390i	0.635007	−	0.772506i	$-0.280997\pi$
$761$	2.66312	+	1.93487i	0.0965380	+	0.0701390i	−0.538469	+	0.842645i	$0.680997\pi$
$762$		0			0
$763$	−5.67376	−	4.12223i	−0.205404	−	0.149235i
$764$	−8.23607	+	25.3480i	−0.297970	+	0.917059i
$765$	−13.9443			−0.504156
$766$		0			0
$767$	9.00658	−	27.7194i	0.325209	−	1.00089i
$768$	−12.9443	+	9.40456i	−0.467086	+	0.339358i
$769$	29.8156	+	21.6623i	1.07518	+	0.781162i	0.976836	−	0.213990i	$-0.0686461\pi$
$769$	29.8156	+	21.6623i	1.07518	+	0.781162i	0.0983420	+	0.995153i	$0.468646\pi$
$770$		0			0
$771$	−4.09017	+	2.97168i	−0.147304	+	0.107023i
$772$	0.909830	−	2.80017i	0.0327455	−	0.100780i
$773$	37.1246	−	26.9726i	1.33528	−	0.970137i	0.335676	−	0.941977i	$-0.391035\pi$
$773$	37.1246	−	26.9726i	1.33528	−	0.970137i	0.999603	−	0.0281598i	$-0.00896474\pi$
$774$		0			0
$775$	−3.09017	−	9.51057i	−0.111002	−	0.341630i
$776$		0			0
$777$	24.3820			0.874698
$778$		0			0
$779$	−2.83688	+	8.73102i	−0.101642	+	0.312821i
$780$	8.61803	+	6.26137i	0.308575	+	0.224193i
$781$	−37.9615	−	2.57565i	−1.35837	−	0.0921642i
$782$		0			0
$783$	−7.70820			−0.275469
$784$	−5.30495			−0.189463
$785$	−6.70820	+	20.6457i	−0.239426	+	0.736878i
$786$		0			0
$787$	20.9164	−	15.1967i	0.745589	−	0.541702i	−0.148867	−	0.988857i	$-0.547563\pi$
$787$	20.9164	−	15.1967i	0.745589	−	0.541702i	0.894457	+	0.447155i	$0.147563\pi$
$788$	−31.7426	−	23.0624i	−1.13078	−	0.821563i
$789$	−15.1353	+	10.9964i	−0.538829	+	0.391482i
$790$		0			0
$791$	−7.81559	+	24.0539i	−0.277891	+	0.855259i
$792$		0			0
$793$	−33.2148			−1.17949
$794$		0			0
$795$	−20.1246			−0.713746
$796$	14.3820	+	44.2631i	0.509755	+	1.56887i
$797$	33.5410			1.18808			0.594042	−	0.804434i	$-0.297531\pi$
$797$	33.5410			1.18808			0.594042	+	0.804434i	$0.297531\pi$
$798$		0			0
$799$	2.66312	−	8.19624i	0.0942144	−	0.289962i
$800$		0			0
$801$	0.572949	−	0.416272i	0.0202442	−	0.0147082i
$802$		0			0
$803$	−25.5066	−	1.73060i	−0.900108	−	0.0610715i
$804$	3.61803	−	2.62866i	0.127598	−	0.0927055i
$805$	−19.8992	−	14.4576i	−0.701354	−	0.509564i
$806$		0			0
$807$	8.65248	−	26.6296i	0.304582	−	0.937406i
$808$		0			0
$809$	−4.87132	+	3.53922i	−0.171267	+	0.124432i	−0.670117	−	0.742256i	$-0.733756\pi$
$809$	−4.87132	+	3.53922i	−0.171267	+	0.124432i	0.498850	+	0.866688i	$0.333756\pi$
$810$		0			0
$811$	23.7533	−	17.2578i	0.834091	−	0.606002i	−0.0866229	−	0.996241i	$-0.527608\pi$
$811$	23.7533	−	17.2578i	0.834091	−	0.606002i	0.920714	+	0.390239i	$0.127608\pi$
$812$	−11.3475	−	34.9241i	−0.398220	−	1.22560i
$813$	−2.38197	+	7.33094i	−0.0835392	+	0.257107i
$814$		0			0
$815$	0.753289	−	2.31838i	0.0263866	−	0.0812095i
$816$	7.70820	+	23.7234i	0.269841	+	0.830486i
$817$	−2.83688	+	8.73102i	−0.0992499	+	0.305460i
$818$		0			0
$819$	1.75329	+	5.39607i	0.0612649	+	0.188554i
$820$	8.61803	−	26.5236i	0.300955	−	0.926244i
$821$	−1.01722	−	3.13068i	−0.0355013	−	0.109262i	0.931736	−	0.363138i	$-0.118295\pi$
$821$	−1.01722	−	3.13068i	−0.0355013	−	0.109262i	−0.967237	+	0.253876i	$0.918295\pi$
$822$		0			0
$823$	10.9721	+	7.97172i	0.382465	+	0.277877i	0.762361	−	0.647152i	$-0.224040\pi$
$823$	10.9721	+	7.97172i	0.382465	+	0.277877i	−0.379896	+	0.925029i	$0.624040\pi$
$824$		0			0
$825$	6.18034	−	15.3884i	0.215172	−	0.535756i
$826$		0			0
$827$	−6.51722	−	4.73504i	−0.226626	−	0.164653i	0.468678	−	0.883369i	$-0.344730\pi$
$827$	−6.51722	−	4.73504i	−0.226626	−	0.164653i	−0.695304	+	0.718716i	$0.744730\pi$
$828$	7.47214	+	5.42882i	0.259675	+	0.188665i
$829$	−10.4721	−	32.2299i	−0.363712	−	1.11939i	−0.950783	−	0.309856i	$-0.899719\pi$
$829$	−10.4721	−	32.2299i	−0.363712	−	1.11939i	0.587071	−	0.809535i	$-0.300281\pi$
$830$		0			0
$831$	3.11803	+	9.59632i	0.108163	+	0.332893i
$832$	5.88854	−	18.1231i	0.204149	−	0.628305i
$833$	−2.55573	+	7.86572i	−0.0885507	+	0.272531i
$834$		0			0
$835$	−19.2705	−	14.0008i	−0.666883	−	0.484519i
$836$	9.74265	+	0.661030i	0.336956	+	0.0228622i
$837$	−0.618034	+	1.90211i	−0.0213624	+	0.0657466i
$838$		0			0
$839$	37.7254	−	27.4091i	1.30243	−	0.946268i	0.302450	−	0.953165i	$-0.402195\pi$
$839$	37.7254	−	27.4091i	1.30243	−	0.946268i	0.999976	+	0.00689712i	$0.00219544\pi$
$840$		0			0
$841$	−24.6074	+	17.8783i	−0.848531	+	0.616494i
$842$		0			0
$843$	4.76393	−	14.6619i	0.164079	−	0.504982i
$844$	3.29180	−	10.1311i	0.113308	−	0.348727i
$845$	16.3820			0.563557
$846$		0			0
$847$	−11.3885	+	23.5972i	−0.391315	+	0.810808i
$848$	11.1246	+	34.2380i	0.382021	+	1.17574i
$849$	22.8435	−	16.5967i	0.783985	−	0.569599i
$850$		0			0
$851$	−14.6074	+	44.9569i	−0.500735	+	1.54110i
$852$	7.09017	−	21.8213i	0.242905	−	0.747585i
$853$	−4.97871			−0.170468			−0.0852340	−	0.996361i	$-0.527164\pi$
$853$	−4.97871			−0.170468			−0.0852340	+	0.996361i	$0.527164\pi$
$854$		0			0
$855$	−2.66312	−	1.93487i	−0.0910767	−	0.0661711i
$856$		0			0
$857$	−13.9443			−0.476327			−0.238164	−	0.971225i	$-0.576545\pi$
$857$	−13.9443			−0.476327			−0.238164	+	0.971225i	$0.576545\pi$
$858$		0			0
$859$	−4.22542	+	13.0045i	−0.144170	+	0.443709i	−0.996903	−	0.0786375i	$-0.974943\pi$
$859$	−4.22542	+	13.0045i	−0.144170	+	0.443709i	0.852734	+	0.522346i	$0.174943\pi$
$860$	8.61803	−	26.5236i	0.293873	−	0.904447i
$861$	12.0172	−	8.73102i	0.409546	−	0.297552i
$862$		0			0
$863$	−18.6074	+	13.5191i	−0.633403	+	0.460194i	−0.857577	−	0.514355i	$-0.828031\pi$
$863$	−18.6074	+	13.5191i	−0.633403	+	0.460194i	0.224175	+	0.974549i	$0.428031\pi$
$864$		0			0
$865$	37.7639			1.28401
$866$		0			0
$867$	21.8885			0.743374
$868$	−9.52786			−0.323397
$869$	−1.12461	+	2.80017i	−0.0381498	+	0.0949892i
$870$		0			0
$871$	−1.64590	+	5.06555i	−0.0557691	+	0.171640i
$872$		0			0
$873$	−4.38197			−0.148307
$874$		0			0
$875$	−21.5451	−	15.6534i	−0.728357	−	0.529182i
$876$	4.76393	−	14.6619i	0.160958	−	0.495379i
$877$	22.1074	−	16.0620i	0.746514	−	0.542374i	−0.148231	−	0.988953i	$-0.547358\pi$
$877$	22.1074	−	16.0620i	0.746514	−	0.542374i	0.894744	+	0.446579i	$0.147358\pi$
$878$		0			0
$879$	3.85410	−	2.80017i	0.129996	−	0.0944474i
$880$	−29.5967	−	2.00811i	−0.997706	−	0.0676935i
$881$	−30.4894	−	22.1518i	−1.02721	−	0.746314i	−0.0594637	−	0.998230i	$-0.518939\pi$
$881$	−30.4894	−	22.1518i	−1.02721	−	0.746314i	−0.967749	+	0.251917i	$0.918939\pi$
$882$		0			0
$883$	−13.8328	+	42.5730i	−0.465511	+	1.43270i	0.392827	+	0.919612i	$0.371497\pi$
$883$	−13.8328	+	42.5730i	−0.465511	+	1.43270i	−0.858338	+	0.513084i	$0.828503\pi$
$884$	−24.0344	−	17.4620i	−0.808366	−	0.587312i
$885$	8.45492	−	26.0216i	0.284209	−	0.874705i
$886$		0			0
$887$	−32.9336	−	23.9277i	−1.10580	−	0.803413i	−0.123805	−	0.992307i	$-0.539510\pi$
$887$	−32.9336	−	23.9277i	−1.10580	−	0.803413i	−0.981998	+	0.188894i	$0.939510\pi$
$888$		0			0
$889$	−29.7082	−	21.5843i	−0.996381	−	0.723913i
$890$		0			0
$891$	−2.80902	+	1.76336i	−0.0941056	+	0.0590746i
$892$	−6.90983	−	5.02029i	−0.231358	−	0.168092i
$893$	1.64590	−	1.19581i	0.0550779	−	0.0400164i
$894$		0			0
$895$	−4.43363	−	13.6453i	−0.148200	−	0.456112i
$896$		0			0
$897$	−11.0000			−0.367279
$898$		0			0
$899$	4.76393	+	14.6619i	0.158886	+	0.489001i
$900$	8.09017	+	5.87785i	0.269672	+	0.195928i
$901$	56.1246			1.86978
$902$		0			0
$903$	12.0172	−	8.73102i	0.399908	−	0.290550i
$904$		0			0
$905$	11.3197	−	34.8383i	0.376278	−	1.15807i
$906$		0			0
$907$	13.2533	+	9.62908i	0.440068	+	0.319728i	0.785662	−	0.618656i	$-0.212322\pi$
$907$	13.2533	+	9.62908i	0.440068	+	0.319728i	−0.345594	+	0.938384i	$0.612322\pi$
$908$	−3.50658	−	10.7921i	−0.116370	−	0.358150i
$909$	−4.30902	−	3.13068i	−0.142921	−	0.103838i
$910$		0			0
$911$	−25.3262	−	18.4006i	−0.839096	−	0.609639i	0.0830222	−	0.996548i	$-0.473543\pi$
$911$	−25.3262	−	18.4006i	−0.839096	−	0.609639i	−0.922118	+	0.386909i	$0.873543\pi$
$912$	−1.81966	+	5.60034i	−0.0602550	+	0.185446i
$913$	0.736068	+	2.92641i	0.0243603	+	0.0968502i
$914$		0			0
$915$	−31.1803			−1.03079
$916$	−29.5279			−0.975628
$917$	30.3779	−	22.0708i	1.00317	−	0.728843i
$918$		0			0
$919$	11.1074	+	34.1850i	0.366399	+	1.12766i	0.949100	+	0.314974i	$0.101996\pi$
$919$	11.1074	+	34.1850i	0.366399	+	1.12766i	−0.582701	+	0.812686i	$0.698004\pi$
$920$		0			0
$921$	19.8992	+	14.4576i	0.655701	+	0.476394i
$922$		0			0
$923$	8.44427	+	25.9888i	0.277947	+	0.855432i
$924$	−12.1246	−	10.1311i	−0.398870	−	0.333289i
$925$	−15.8156	+	48.6754i	−0.520014	+	1.60044i
$926$		0			0
$927$	−13.4443	+	9.76784i	−0.441568	+	0.320818i
$928$		0			0
$929$	−0.583592			−0.0191470			−0.00957352	−	0.999954i	$-0.503047\pi$
$929$	−0.583592			−0.0191470			−0.00957352	+	0.999954i	$0.503047\pi$
$930$		0			0
$931$	−1.57953	+	1.14759i	−0.0517669	+	0.0376109i
$932$	−0.909830	−	2.80017i	−0.0298025	−	0.0917226i
$933$	2.34752			0.0768545
$934$		0			0
$935$	−17.2361	+	42.9161i	−0.563680	+	1.40351i
$936$		0			0
$937$	−2.10081	−	6.46564i	−0.0686306	−	0.211223i	0.910859	−	0.412717i	$-0.135420\pi$
$937$	−2.10081	−	6.46564i	−0.0686306	−	0.211223i	−0.979490	+	0.201494i	$0.935420\pi$
$938$		0			0
$939$	24.3607			0.794981
$940$	−5.00000	+	3.63271i	−0.163082	+	0.118486i
$941$	−31.4615	+	22.8581i	−1.02562	+	0.745153i	−0.967426	−	0.253152i	$-0.918533\pi$
$941$	−31.4615	+	22.8581i	−1.02562	+	0.745153i	−0.0581889	+	0.998306i	$0.518533\pi$
$942$		0			0
$943$	8.89919	+	27.3889i	0.289797	+	0.891905i
$944$	−48.9443			−1.59300
$945$	1.64590	+	5.06555i	0.0535411	+	0.164782i
$946$		0			0
$947$	−0.673762	+	0.489517i	−0.0218943	+	0.0159072i	−0.598679	−	0.800989i	$-0.704307\pi$
$947$	−0.673762	+	0.489517i	−0.0218943	+	0.0159072i	0.576784	+	0.816897i	$0.304307\pi$
$948$	−1.47214	−	1.06957i	−0.0478128	−	0.0347380i
$949$	5.67376	+	17.4620i	0.184178	+	0.566842i
$950$		0			0
$951$	0.427051	+	0.310271i	0.0138481	+	0.0100612i
$952$		0			0
$953$	−1.19098	−	3.66547i	−0.0385797	−	0.118736i	0.929912	−	0.367782i	$-0.119883\pi$
$953$	−1.19098	−	3.66547i	−0.0385797	−	0.118736i	−0.968492	+	0.249046i	$0.919883\pi$
$954$		0			0
$955$	−9.20820	−	28.3399i	−0.297970	−	0.917059i
$956$	−31.1803	−	22.6538i	−1.00844	−	0.732678i
$957$	−9.52786	+	23.7234i	−0.307992	+	0.766869i
$958$		0			0
$959$	−12.9271	−	39.7854i	−0.417436	−	1.28474i
$960$	5.52786	−	17.0130i	0.178411	−	0.549093i
$961$	−27.0000			−0.870968
$962$		0			0
$963$	8.89919	−	6.46564i	0.286772	−	0.208352i
$964$	−24.2492			−0.781015
$965$	1.01722	+	3.13068i	0.0327455	+	0.100780i
$966$		0			0
$967$	−0.454915	−	0.330515i	−0.0146291	−	0.0106286i	0.580447	−	0.814298i	$-0.302878\pi$
$967$	−0.454915	−	0.330515i	−0.0146291	−	0.0106286i	−0.595076	+	0.803670i	$0.702878\pi$
$968$		0			0
$969$	7.42705	+	5.39607i	0.238591	+	0.173347i
$970$		0			0
$971$	13.3713	+	9.71483i	0.429106	+	0.311764i	0.781291	−	0.624166i	$-0.214561\pi$
$971$	13.3713	+	9.71483i	0.429106	+	0.311764i	−0.352185	+	0.935930i	$0.614561\pi$
$972$	−0.618034	−	1.90211i	−0.0198234	−	0.0610103i
$973$	4.59017	−	14.1271i	0.147154	−	0.452894i
$974$		0			0
$975$	−11.9098			−0.381420
$976$	17.2361	+	53.0472i	0.551713	+	1.69800i
$977$	−14.0344	−	10.1966i	−0.449002	−	0.326219i	0.340200	−	0.940353i	$-0.389505\pi$
$977$	−14.0344	−	10.1966i	−0.449002	−	0.326219i	−0.789201	+	0.614134i	$0.789505\pi$
$978$		0			0
$979$	−0.572949	−	2.27790i	−0.0183115	−	0.0728019i
$980$	4.79837	−	3.48622i	0.153278	−	0.111363i
$981$	−2.94427			−0.0940034
$982$		0			0
$983$	−2.33688	+	1.69784i	−0.0745349	+	0.0541528i	−0.624429	−	0.781082i	$-0.714668\pi$
$983$	−2.33688	+	1.69784i	−0.0745349	+	0.0541528i	0.549894	+	0.835235i	$0.314668\pi$
$984$		0			0
$985$	43.8673			1.39773
$986$		0			0
$987$	−3.29180			−0.104779
$988$	−2.16718	−	6.66991i	−0.0689473	−	0.212198i
$989$	8.89919	+	27.3889i	0.282978	+	0.870916i
$990$		0			0
$991$	14.3090	−	44.0386i	0.454541	−	1.39893i	−0.417132	−	0.908846i	$-0.636965\pi$
$991$	14.3090	−	44.0386i	0.454541	−	1.39893i	0.871673	−	0.490087i	$-0.163035\pi$
$992$		0			0
$993$	−0.218847	−	0.673542i	−0.00694490	−	0.0213742i
$994$		0			0
$995$	−42.0967	−	30.5851i	−1.33456	−	0.969612i
$996$	−1.81966			−0.0576581
$997$	1.01722	+	3.13068i	0.0322157	+	0.0991498i	0.965871	−	0.259022i	$-0.0834002\pi$
$997$	1.01722	+	3.13068i	0.0322157	+	0.0991498i	−0.933656	+	0.358172i	$0.883400\pi$
$998$		0			0
$999$	8.28115	−	6.01661i	0.262004	−	0.190357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.m.b.256.1	✓	4
11.4	even	5		825.2.o.a.631.1	yes	4
25.21	even	5		825.2.o.a.421.1	yes	4
275.246	even	5	inner	825.2.m.b.796.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.b.256.1	✓	4	1.1	even	1	trivial
825.2.m.b.796.1	yes	4	275.246	even	5	inner
825.2.o.a.421.1	yes	4	25.21	even	5
825.2.o.a.631.1	yes	4	11.4	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.736068 + 2.26538i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.736068 + 2.26538i) q^{7} +(0.309017 + 0.951057i) q^{9} +(3.30902 + 0.224514i) q^{11} +(-0.618034 + 1.90211i) q^{12} +(-0.736068 - 2.26538i) q^{13} +(-0.690983 - 2.12663i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(1.92705 + 5.93085i) q^{17} +(-0.454915 + 1.40008i) q^{19} +(1.38197 - 4.25325i) q^{20} +(1.92705 - 1.40008i) q^{21} +(1.42705 + 4.39201i) q^{23} +(1.54508 + 4.75528i) q^{25} +(0.309017 - 0.951057i) q^{27} +4.76393 q^{28} +(-2.38197 - 7.33094i) q^{29} -2.00000 q^{31} +(-2.54508 - 2.12663i) q^{33} +(-4.30902 + 3.13068i) q^{35} +(1.61803 - 1.17557i) q^{36} +(8.28115 + 6.01661i) q^{37} +(-0.736068 + 2.26538i) q^{39} +6.23607 q^{41} +6.23607 q^{43} +(-1.61803 - 6.43288i) q^{44} +(-0.690983 + 2.12663i) q^{45} +(-1.11803 - 0.812299i) q^{47} +4.00000 q^{48} +(1.07295 + 0.779543i) q^{49} +(1.92705 - 5.93085i) q^{51} +(-3.85410 + 2.80017i) q^{52} +(2.78115 - 8.55951i) q^{53} +(5.69098 + 4.75528i) q^{55} +(1.19098 - 0.865300i) q^{57} +(9.89919 + 7.19218i) q^{59} +(-3.61803 + 2.62866i) q^{60} +(4.30902 - 13.2618i) q^{61} -2.38197 q^{63} +(6.47214 + 4.70228i) q^{64} +(1.64590 - 5.06555i) q^{65} +(-1.80902 - 1.31433i) q^{67} +(10.0902 - 7.33094i) q^{68} +(1.42705 - 4.39201i) q^{69} -11.4721 q^{71} -7.70820 q^{73} +(1.54508 - 4.75528i) q^{75} +2.94427 q^{76} +(-2.94427 + 7.33094i) q^{77} +(-0.281153 + 0.865300i) q^{79} -8.94427 q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.281153 + 0.865300i) q^{83} +(-3.85410 - 2.80017i) q^{84} +(-4.30902 + 13.2618i) q^{85} +(-2.38197 + 7.33094i) q^{87} +(-0.218847 - 0.673542i) q^{89} +5.67376 q^{91} +(7.47214 - 5.42882i) q^{92} +(1.61803 + 1.17557i) q^{93} +(-2.66312 + 1.93487i) q^{95} +(-1.35410 + 4.16750i) q^{97} +(0.809017 + 3.21644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9	\( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9} + 11 q^{11} + 2 q^{12} + 6 q^{13} - 5 q^{15} - 4 q^{16} + q^{17} - 13 q^{19} + 10 q^{20} + q^{21} - q^{23} - 5 q^{25} - q^{27} + 28 q^{28} - 14 q^{29} - 8 q^{31} + q^{33} - 15 q^{35} + 2 q^{36} + 13 q^{37} + 6 q^{39} + 16 q^{41} + 16 q^{43} - 2 q^{44} - 5 q^{45} + 16 q^{48} + 11 q^{49} + q^{51} - 2 q^{52} - 9 q^{53} + 25 q^{55} + 7 q^{57} + 15 q^{59} - 10 q^{60} + 15 q^{61} - 14 q^{63} + 8 q^{64} + 20 q^{65} - 5 q^{67} + 18 q^{68} - q^{69} - 28 q^{71} - 4 q^{73} - 5 q^{75} - 24 q^{76} + 24 q^{77} + 19 q^{79} - q^{81} - 19 q^{83} - 2 q^{84} - 15 q^{85} - 14 q^{87} - 21 q^{89} + 54 q^{91} + 12 q^{92} + 2 q^{93} + 5 q^{95} + 8 q^{97} + q^{99}+O(q^{100}) \) 4 * q - q^3 + 2 * q^4 + 5 * q^5 + 6 * q^7 - q^9 + 11 * q^11 + 2 * q^12 + 6 * q^13 - 5 * q^15 - 4 * q^16 + q^17 - 13 * q^19 + 10 * q^20 + q^21 - q^23 - 5 * q^25 - q^27 + 28 * q^28 - 14 * q^29 - 8 * q^31 + q^33 - 15 * q^35 + 2 * q^36 + 13 * q^37 + 6 * q^39 + 16 * q^41 + 16 * q^43 - 2 * q^44 - 5 * q^45 + 16 * q^48 + 11 * q^49 + q^51 - 2 * q^52 - 9 * q^53 + 25 * q^55 + 7 * q^57 + 15 * q^59 - 10 * q^60 + 15 * q^61 - 14 * q^63 + 8 * q^64 + 20 * q^65 - 5 * q^67 + 18 * q^68 - q^69 - 28 * q^71 - 4 * q^73 - 5 * q^75 - 24 * q^76 + 24 * q^77 + 19 * q^79 - q^81 - 19 * q^83 - 2 * q^84 - 15 * q^85 - 14 * q^87 - 21 * q^89 + 54 * q^91 + 12 * q^92 + 2 * q^93 + 5 * q^95 + 8 * q^97 + q^99

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