LMFDB - Embedded newform 945.2.cj.e.577.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(208,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 10]))

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

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

chi := DirichletCharacter("945.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cj (of order $12$, degree $4$, not 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			577.16
Character	$\chi$	$=$	945.577
Dual form			945.2.cj.e.208.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.772339 + 0.206948i) q^{2} +(-1.17837 + 0.680332i) q^{4} +(-0.657057 - 2.13735i) q^{5} +(0.914904 + 2.48253i) q^{7} +(1.90009 - 1.90009i) q^{8} +O(q^{10})$	\(q+(-0.772339 + 0.206948i) q^{2} +(-1.17837 + 0.680332i) q^{4} +(-0.657057 - 2.13735i) q^{5} +(0.914904 + 2.48253i) q^{7} +(1.90009 - 1.90009i) q^{8} +(0.949791 + 1.51478i) q^{10} -1.89753 q^{11} +(0.343579 - 0.0920618i) q^{13} +(-1.22037 - 1.72802i) q^{14} +(0.286369 - 0.496007i) q^{16} +(0.521621 + 1.94672i) q^{17} +(-2.27028 - 3.93224i) q^{19} +(2.22837 + 2.07158i) q^{20} +(1.46554 - 0.392689i) q^{22} +(-0.952115 + 0.952115i) q^{23} +(-4.13655 + 2.80873i) q^{25} +(-0.246308 + 0.142206i) q^{26} +(-2.76704 - 2.30290i) q^{28} +(2.25903 - 1.30425i) q^{29} +(3.50326 - 2.02261i) q^{31} +(-1.50949 + 5.63349i) q^{32} +(-0.805736 - 1.39558i) q^{34} +(4.70490 - 3.58664i) q^{35} +(2.17042 - 8.10011i) q^{37} +(2.56719 + 2.56719i) q^{38} +(-5.30963 - 2.81270i) q^{40} +(0.370817 + 0.214091i) q^{41} +(-8.10338 - 2.17129i) q^{43} +(2.23599 - 1.29095i) q^{44} +(0.538318 - 0.932394i) q^{46} +(-2.10426 - 7.85320i) q^{47} +(-5.32590 + 4.54255i) q^{49} +(2.61356 - 3.02534i) q^{50} +(-0.342231 + 0.342231i) q^{52} +(-2.26746 - 8.46228i) q^{53} +(1.24678 + 4.05569i) q^{55} +(6.45543 + 2.97863i) q^{56} +(-1.47483 + 1.47483i) q^{58} +(-3.70997 - 6.42586i) q^{59} +(-4.06455 - 2.34667i) q^{61} +(-2.28713 + 2.28713i) q^{62} -3.51788i q^{64} +(-0.422520 - 0.673860i) q^{65} +(3.81975 - 14.2555i) q^{67} +(-1.93908 - 1.93908i) q^{68} +(-2.89153 + 3.74377i) q^{70} +3.22107 q^{71} +(9.02450 - 2.41811i) q^{73} +6.70519i q^{74} +(5.35046 + 3.08909i) q^{76} +(-1.73606 - 4.71067i) q^{77} +(-8.77792 - 5.06793i) q^{79} +(-1.24830 - 0.286168i) q^{80} +(-0.330702 - 0.0886114i) q^{82} +(4.50725 - 16.8213i) q^{83} +(3.81808 - 2.39399i) q^{85} +6.70790 q^{86} +(-3.60548 + 3.60548i) q^{88} +(0.865525 + 1.49913i) q^{89} +(0.542888 + 0.768718i) q^{91} +(0.474189 - 1.76970i) q^{92} +(3.25040 + 5.62987i) q^{94} +(-6.91288 + 7.43610i) q^{95} +(-6.33706 - 1.69801i) q^{97} +(3.17333 - 4.61057i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) $ 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8	$ 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8} - 24 q^{10} - 32 q^{11} + 76 q^{16} + 6 q^{17} + 60 q^{20} + 8 q^{22} + 16 q^{23} - 4 q^{25} + 36 q^{26} + 22 q^{28} + 48 q^{31} + 6 q^{32} + 36 q^{35} - 4 q^{37} - 12 q^{41} - 4 q^{43} - 16 q^{46} + 54 q^{47} + 44 q^{50} - 8 q^{53} + 92 q^{56} - 56 q^{58} - 24 q^{61} - 62 q^{65} + 12 q^{67} + 2 q^{70} + 40 q^{71} + 36 q^{73} - 96 q^{76} + 110 q^{77} - 36 q^{80} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 32 q^{86} - 92 q^{88} - 48 q^{91} + 26 q^{92} + 94 q^{95} - 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8 - 24 * q^10 - 32 * q^11 + 76 * q^16 + 6 * q^17 + 60 * q^20 + 8 * q^22 + 16 * q^23 - 4 * q^25 + 36 * q^26 + 22 * q^28 + 48 * q^31 + 6 * q^32 + 36 * q^35 - 4 * q^37 - 12 * q^41 - 4 * q^43 - 16 * q^46 + 54 * q^47 + 44 * q^50 - 8 * q^53 + 92 * q^56 - 56 * q^58 - 24 * q^61 - 62 * q^65 + 12 * q^67 + 2 * q^70 + 40 * q^71 + 36 * q^73 - 96 * q^76 + 110 * q^77 - 36 * q^80 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 32 * q^86 - 92 * q^88 - 48 * q^91 + 26 * q^92 + 94 * q^95 - 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.772339	+	0.206948i	−0.546126	+	0.146334i	−0.521325	−	0.853358i	$-0.674562\pi$
$2$	−0.772339	+	0.206948i	−0.546126	+	0.146334i	−0.0248014	+	0.999692i	$0.507895\pi$
$3$		0			0
$3$		0			0
$4$	−1.17837	+	0.680332i	−0.589185	+	0.340166i
$5$	−0.657057	−	2.13735i	−0.293845	−	0.955853i
$5$	−0.657057	−	2.13735i	−0.293845	−	0.955853i
$6$		0			0
$7$	0.914904	+	2.48253i	0.345801	+	0.938308i
$7$	0.914904	+	2.48253i	0.345801	+	0.938308i
$8$	1.90009	−	1.90009i	0.671784	−	0.671784i
$9$		0			0
$10$	0.949791	+	1.51478i	0.300350	+	0.479017i
$11$	−1.89753			−0.572126			−0.286063	−	0.958211i	$-0.592347\pi$
$11$	−1.89753			−0.572126			−0.286063	+	0.958211i	$0.592347\pi$
$12$		0			0
$13$	0.343579	−	0.0920618i	0.0952918	−	0.0255334i	−0.210858	−	0.977517i	$-0.567626\pi$
$13$	0.343579	−	0.0920618i	0.0952918	−	0.0255334i	0.306150	+	0.951983i	$0.400959\pi$
$14$	−1.22037	−	1.72802i	−0.326157	−	0.461832i
$15$		0			0
$16$	0.286369	−	0.496007i	0.0715924	−	0.124002i
$17$	0.521621	+	1.94672i	0.126512	+	0.472148i	0.999889	−	0.0148962i	$-0.00474179\pi$
$17$	0.521621	+	1.94672i	0.126512	+	0.472148i	−0.873377	+	0.487044i	$0.838075\pi$
$18$		0			0
$19$	−2.27028	−	3.93224i	−0.520838	−	0.902118i	−0.999706	−	0.0242311i	$-0.992286\pi$
$19$	−2.27028	−	3.93224i	−0.520838	−	0.902118i	0.478868	−	0.877887i	$-0.341047\pi$
$20$	2.22837	+	2.07158i	0.498278	+	0.463218i
$21$		0			0
$22$	1.46554	−	0.392689i	0.312453	−	0.0837216i
$23$	−0.952115	+	0.952115i	−0.198530	+	0.198530i	−0.799369	−	0.600840i	$-0.794833\pi$
$23$	−0.952115	+	0.952115i	−0.198530	+	0.198530i	0.600840	+	0.799369i	$0.294833\pi$
$24$		0			0
$25$	−4.13655	+	2.80873i	−0.827310	+	0.561745i
$26$	−0.246308	+	0.142206i	−0.0483049	+	0.0278889i
$27$		0			0
$28$	−2.76704	−	2.30290i	−0.522922	−	0.435207i
$29$	2.25903	−	1.30425i	0.419492	−	0.242194i	−0.275368	−	0.961339i	$-0.588800\pi$
$29$	2.25903	−	1.30425i	0.419492	−	0.242194i	0.694860	+	0.719145i	$0.255466\pi$
$30$		0			0
$31$	3.50326	−	2.02261i	0.629205	−	0.363271i	−0.151239	−	0.988497i	$-0.548326\pi$
$31$	3.50326	−	2.02261i	0.629205	−	0.363271i	0.780444	+	0.625226i	$0.214993\pi$
$32$	−1.50949	+	5.63349i	−0.266843	+	0.995871i
$33$		0			0
$34$	−0.805736	−	1.39558i	−0.138183	−	0.239339i
$35$	4.70490	−	3.58664i	0.795273	−	0.606252i
$36$		0			0
$37$	2.17042	−	8.10011i	0.356814	−	1.33165i	−0.521371	−	0.853330i	$-0.674579\pi$
$37$	2.17042	−	8.10011i	0.356814	−	1.33165i	0.878186	−	0.478320i	$-0.158754\pi$
$38$	2.56719	+	2.56719i	0.416454	+	0.416454i
$39$		0			0
$40$	−5.30963	−	2.81270i	−0.839527	−	0.444726i
$41$	0.370817	+	0.214091i	0.0579119	+	0.0334354i	0.528676	−	0.848823i	$-0.322689\pi$
$41$	0.370817	+	0.214091i	0.0579119	+	0.0334354i	−0.470764	+	0.882259i	$0.656022\pi$
$42$		0			0
$43$	−8.10338	−	2.17129i	−1.23575	−	0.331119i	−0.418937	−	0.908015i	$-0.637597\pi$
$43$	−8.10338	−	2.17129i	−1.23575	−	0.331119i	−0.816818	+	0.576896i	$0.804264\pi$
$44$	2.23599	−	1.29095i	0.337088	−	0.194618i
$45$		0			0
$46$	0.538318	−	0.932394i	0.0793706	−	0.137474i
$47$	−2.10426	−	7.85320i	−0.306938	−	1.14551i	−0.931264	−	0.364344i	$-0.881293\pi$
$47$	−2.10426	−	7.85320i	−0.306938	−	1.14551i	0.624327	−	0.781163i	$-0.285373\pi$
$48$		0			0
$49$	−5.32590	+	4.54255i	−0.760843	+	0.648936i
$50$	2.61356	−	3.02534i	0.369613	−	0.427847i
$51$		0			0
$52$	−0.342231	+	0.342231i	−0.0474589	+	0.0474589i
$53$	−2.26746	−	8.46228i	−0.311460	−	1.16238i	−0.927241	−	0.374466i	$-0.877826\pi$
$53$	−2.26746	−	8.46228i	−0.311460	−	1.16238i	0.615781	−	0.787917i	$-0.288841\pi$
$54$		0			0
$55$	1.24678	+	4.05569i	0.168116	+	0.546869i
$56$	6.45543	+	2.97863i	0.862643	+	0.398036i
$57$		0			0
$58$	−1.47483	+	1.47483i	−0.193654	+	0.193654i
$59$	−3.70997	−	6.42586i	−0.482997	−	0.836575i	0.516813	−	0.856099i	$-0.327118\pi$
$59$	−3.70997	−	6.42586i	−0.482997	−	0.836575i	−0.999809	+	0.0195235i	$0.993785\pi$
$60$		0			0
$61$	−4.06455	−	2.34667i	−0.520412	−	0.300460i	0.216691	−	0.976240i	$-0.430474\pi$
$61$	−4.06455	−	2.34667i	−0.520412	−	0.300460i	−0.737103	+	0.675780i	$0.763807\pi$
$62$	−2.28713	+	2.28713i	−0.290466	+	0.290466i
$63$		0			0
$64$		−	3.51788i		−	0.439734i
$65$	−0.422520	−	0.673860i	−0.0524072	−	0.0835821i
$66$		0			0
$67$	3.81975	−	14.2555i	0.466657	−	1.74159i	−0.184679	−	0.982799i	$-0.559124\pi$
$67$	3.81975	−	14.2555i	0.466657	−	1.74159i	0.651336	−	0.758789i	$-0.274209\pi$
$68$	−1.93908	−	1.93908i	−0.235148	−	0.235148i
$69$		0			0
$70$	−2.89153	+	3.74377i	−0.345604	+	0.447466i
$71$	3.22107			0.382270			0.191135	−	0.981564i	$-0.438783\pi$
$71$	3.22107			0.382270			0.191135	+	0.981564i	$0.438783\pi$
$72$		0			0
$73$	9.02450	−	2.41811i	1.05624	−	0.283018i	0.311411	−	0.950275i	$-0.399199\pi$
$73$	9.02450	−	2.41811i	1.05624	−	0.283018i	0.744827	+	0.667257i	$0.232532\pi$
$74$			6.70519i			0.779463i
$75$		0			0
$76$	5.35046	+	3.08909i	0.613740	+	0.354343i
$77$	−1.73606	−	4.71067i	−0.197842	−	0.536831i
$78$		0			0
$79$	−8.77792	−	5.06793i	−0.987593	−	0.570187i	−0.0830390	−	0.996546i	$-0.526463\pi$
$79$	−8.77792	−	5.06793i	−0.987593	−	0.570187i	−0.904554	+	0.426359i	$0.859796\pi$
$80$	−1.24830	−	0.286168i	−0.139564	−	0.0319945i
$81$		0			0
$82$	−0.330702	−	0.0886114i	−0.0365199	−	0.00978549i
$83$	4.50725	−	16.8213i	0.494735	−	1.84637i	−0.0367774	−	0.999323i	$-0.511709\pi$
$83$	4.50725	−	16.8213i	0.494735	−	1.84637i	0.531512	−	0.847051i	$-0.321624\pi$
$84$		0			0
$85$	3.81808	−	2.39399i	0.414129	−	0.259665i
$86$	6.70790			0.723332
$87$		0			0
$88$	−3.60548	+	3.60548i	−0.384345	+	0.384345i
$89$	0.865525	+	1.49913i	0.0917455	+	0.158908i	0.908246	−	0.418437i	$-0.137422\pi$
$89$	0.865525	+	1.49913i	0.0917455	+	0.158908i	−0.816500	+	0.577345i	$0.804089\pi$
$90$		0			0
$91$	0.542888	+	0.768718i	0.0569102	+	0.0805836i
$92$	0.474189	−	1.76970i	0.0494377	−	0.184504i
$93$		0			0
$94$	3.25040	+	5.62987i	0.335254	+	0.580676i
$95$	−6.91288	+	7.43610i	−0.709246	+	0.762927i
$96$		0			0
$97$	−6.33706	−	1.69801i	−0.643431	−	0.172407i	−0.0776741	−	0.996979i	$-0.524749\pi$
$97$	−6.33706	−	1.69801i	−0.643431	−	0.172407i	−0.565757	+	0.824572i	$0.691416\pi$
$98$	3.17333	−	4.61057i	0.320555	−	0.465738i
$99$		0			0
$100$	2.96352	−	6.12395i	0.296352	−	0.612395i
$101$			17.1328i			1.70478i	0.522908	+	0.852389i	$0.324847\pi$
$101$			17.1328i			1.70478i	−0.522908	+	0.852389i	$0.675153\pi$
$102$		0			0
$103$	11.2221	+	11.2221i	1.10574	+	1.10574i	0.993704	+	0.112037i	$0.0357377\pi$
$103$	11.2221	+	11.2221i	1.10574	+	1.10574i	0.112037	+	0.993704i	$0.464262\pi$
$104$	0.477906	−	0.827758i	0.0468626	−	0.0811684i
$105$		0			0
$106$	3.50250	+	6.06650i	0.340193	+	0.589231i
$107$	1.14381	−	4.26877i	0.110577	−	0.412677i	−0.888341	−	0.459183i	$-0.848142\pi$
$107$	1.14381	−	4.26877i	0.110577	−	0.412677i	0.998918	+	0.0465063i	$0.0148087\pi$
$108$		0			0
$109$	−5.17609	−	2.98842i	−0.495779	−	0.286238i	0.231190	−	0.972909i	$-0.425738\pi$
$109$	−5.17609	−	2.98842i	−0.495779	−	0.286238i	−0.726969	+	0.686670i	$0.759072\pi$
$110$	−1.80226	−	2.87435i	−0.171838	−	0.274058i
$111$		0			0
$112$	1.49335	+	0.257122i	0.141108	+	0.0242958i
$113$	4.91835	+	18.3555i	0.462679	+	1.72674i	0.664470	+	0.747315i	$0.268657\pi$
$113$	4.91835	+	18.3555i	0.462679	+	1.72674i	−0.201791	+	0.979429i	$0.564676\pi$
$114$		0			0
$115$	2.66060	+	1.40941i	0.248102	+	0.131428i
$116$	−1.77465	+	3.07379i	−0.164772	+	0.285394i
$117$		0			0
$118$	4.19517	+	4.19517i	0.386197	+	0.386197i
$119$	−4.35554	+	3.07600i	−0.399272	+	0.281976i
$120$		0			0
$121$	−7.39939			−0.672671
$122$	3.62485	+	0.971275i	0.328178	+	0.0879351i
$123$		0			0
$124$	−2.75209	+	4.76677i	−0.247145	+	0.428068i
$125$	8.72119	+	6.99577i	0.780047	+	0.625721i
$126$		0			0
$127$	−5.71266	−	5.71266i	−0.506917	−	0.506917i	0.406662	−	0.913579i	$-0.366693\pi$
$127$	−5.71266	−	5.71266i	−0.506917	−	0.506917i	−0.913579	+	0.406662i	$0.866693\pi$
$128$	−2.29096	−	8.55000i	−0.202495	−	0.755720i
$129$		0			0
$130$	0.465783	+	0.433009i	0.0408518	+	0.0379774i
$131$		−	9.76378i		−	0.853066i	−0.904472	−	0.426533i	$-0.859735\pi$
$131$		−	9.76378i		−	0.853066i	0.904472	−	0.426533i	$-0.140265\pi$
$132$		0			0
$133$	7.68481	−	9.23366i	0.666358	−	0.800660i
$134$			11.8006i			1.01941i
$135$		0			0
$136$	4.69006	+	2.70781i	0.402170	+	0.232193i
$137$	−13.2518	−	13.2518i	−1.13217	−	1.13217i	−0.989815	−	0.142360i	$-0.954531\pi$
$137$	−13.2518	−	13.2518i	−1.13217	−	1.13217i	−0.142360	−	0.989815i	$-0.545469\pi$
$138$		0			0
$139$	−1.20016	+	2.07873i	−0.101796	+	0.176316i	−0.912425	−	0.409245i	$-0.865792\pi$
$139$	−1.20016	+	2.07873i	−0.101796	+	0.176316i	0.810629	+	0.585561i	$0.199126\pi$
$140$	−3.10401	+	7.42728i	−0.262336	+	0.627720i
$141$		0			0
$142$	−2.48776	+	0.666592i	−0.208768	+	0.0559392i
$143$	−0.651952	+	0.174690i	−0.0545189	+	0.0146083i
$144$		0			0
$145$	−4.27196	−	3.97138i	−0.354767	−	0.329805i
$146$	−6.46955	+	3.73520i	−0.535424	+	0.309127i
$147$		0			0
$148$	2.95321	+	11.0215i	0.242752	+	0.905964i
$149$			4.14875i			0.339879i	0.985454	+	0.169940i	$0.0543572\pi$
$149$			4.14875i			0.339879i	−0.985454	+	0.169940i	$0.945643\pi$
$150$		0			0
$151$	15.5663			1.26677			0.633384	−	0.773838i	$-0.281665\pi$
$151$	15.5663			1.26677			0.633384	+	0.773838i	$0.281665\pi$
$152$	−11.7854	−	3.15788i	−0.955918	−	0.256138i
$153$		0			0
$154$	2.31569	+	3.27896i	0.186603	+	0.264226i
$155$	−6.62487	−	6.15874i	−0.532123	−	0.494682i
$156$		0			0
$157$	20.1571	+	5.40107i	1.60871	+	0.431052i	0.947658	−	0.319288i	$-0.103444\pi$
$157$	20.1571	+	5.40107i	1.60871	+	0.431052i	0.661051	+	0.750341i	$0.270110\pi$
$158$	7.82833	+	2.09759i	0.622788	+	0.166876i
$159$		0			0
$160$	13.0326	−	0.475216i	1.03032	−	0.0375691i
$161$	−3.23475	−	1.49256i	−0.254934	−	0.117630i
$162$		0			0
$163$	−12.4502	−	3.33601i	−0.975172	−	0.261296i	−0.264162	−	0.964478i	$-0.585095\pi$
$163$	−12.4502	−	3.33601i	−0.975172	−	0.261296i	−0.711010	+	0.703182i	$0.751762\pi$
$164$	−0.582613			−0.0454944
$165$		0			0
$166$			13.9245i			1.08075i
$167$	−2.28189	−	8.51613i	−0.176578	−	0.658998i	−0.996277	−	0.0862041i	$-0.972526\pi$
$167$	−2.28189	−	8.51613i	−0.176578	−	0.658998i	0.819700	−	0.572794i	$-0.194140\pi$
$168$		0			0
$169$	−11.1488	+	6.43674i	−0.857597	+	0.495134i
$170$	−2.45342	+	2.63912i	−0.188169	+	0.202411i
$171$		0			0
$172$	11.0260	−	2.95440i	0.840724	−	0.225271i
$173$	−22.1840	+	5.94419i	−1.68662	+	0.451928i	−0.969514	−	0.245037i	$-0.921200\pi$
$173$	−22.1840	+	5.94419i	−1.68662	+	0.451928i	−0.717105	+	0.696965i	$0.754533\pi$
$174$		0			0
$175$	−10.7573	−	7.69940i	−0.813175	−	0.582020i
$176$	−0.543394	+	0.941186i	−0.0409599	+	0.0709446i
$177$		0			0
$178$	−0.978721	−	0.978721i	−0.0733582	−	0.0733582i
$179$	5.47867	+	3.16311i	0.409495	+	0.236422i	0.690573	−	0.723263i	$-0.257359\pi$
$179$	5.47867	+	3.16311i	0.409495	+	0.236422i	−0.281078	+	0.959685i	$0.590692\pi$
$180$		0			0
$181$			19.4981i			1.44928i	0.689128	+	0.724640i	$0.257994\pi$
$181$			19.4981i			1.44928i	−0.689128	+	0.724640i	$0.742006\pi$
$182$	−0.578378	−	0.481362i	−0.0428723	−	0.0356809i
$183$		0			0
$184$			3.61821i			0.266738i
$185$	−18.7389	+	0.683288i	−1.37771	+	0.0502363i
$186$		0			0
$187$	−0.989790	−	3.69395i	−0.0723806	−	0.270128i
$188$	7.82239	+	7.82239i	0.570506	+	0.570506i
$189$		0			0
$190$	3.80020	−	7.17379i	0.275696	−	0.520442i
$191$	11.1365	−	19.2890i	0.805809	−	1.39570i	−0.109935	−	0.993939i	$-0.535064\pi$
$191$	11.1365	−	19.2890i	0.805809	−	1.39570i	0.915744	−	0.401763i	$-0.131602\pi$
$192$		0			0
$193$	9.14701	+	2.45093i	0.658416	+	0.176422i	0.572531	−	0.819883i	$-0.305962\pi$
$193$	9.14701	+	2.45093i	0.658416	+	0.176422i	0.0858851	+	0.996305i	$0.472628\pi$
$194$	5.24576			0.376624
$195$		0			0
$196$	3.18544	−	8.97619i	0.227532	−	0.641157i
$197$	−3.48413	−	3.48413i	−0.248234	−	0.248234i	0.572012	−	0.820245i	$-0.306163\pi$
$197$	−3.48413	−	3.48413i	−0.248234	−	0.248234i	−0.820245	+	0.572012i	$0.806163\pi$
$198$		0			0
$199$	0.232271	−	0.402305i	0.0164653	−	0.0285187i	−0.857675	−	0.514192i	$-0.828092\pi$
$199$	0.232271	−	0.402305i	0.0164653	−	0.0285187i	0.874141	+	0.485673i	$0.161425\pi$
$200$	−2.52299	+	13.1967i	−0.178402	+	0.933145i
$201$		0			0
$202$	−3.54559	−	13.2323i	−0.249467	−	0.931024i
$203$	5.30465	+	4.41485i	0.372313	+	0.309862i
$204$		0			0
$205$	0.213941	−	0.933237i	0.0149423	−	0.0651801i
$206$	−10.9896	−	6.34485i	−0.765682	−	0.442067i
$207$		0			0
$208$	0.0527274	−	0.196781i	0.00365599	−	0.0136443i
$209$	4.30792	+	7.46154i	0.297985	+	0.516125i
$210$		0			0
$211$	−11.0638	+	19.1630i	−0.761663	+	1.31924i	0.180331	+	0.983606i	$0.442283\pi$
$211$	−11.0638	+	19.1630i	−0.761663	+	1.31924i	−0.941993	+	0.335632i	$0.891050\pi$
$212$	8.42907	+	8.42907i	0.578911	+	0.578911i
$213$		0			0
$214$			3.53364i			0.241555i
$215$	0.683564	+	18.7465i	0.0466187	+	1.27850i
$216$		0			0
$217$	8.22634	+	6.84646i	0.558440	+	0.464768i
$218$	4.61614	+	1.23689i	0.312644	+	0.0837728i
$219$		0			0
$220$	−4.22839	−	3.93087i	−0.285078	−	0.265019i
$221$	0.358436	+	0.620830i	0.0241110	+	0.0417615i
$222$		0			0
$223$	0.546729	−	2.04042i	0.0366116	−	0.136637i	−0.945201	−	0.326489i	$-0.894134\pi$
$223$	0.546729	−	2.04042i	0.0366116	−	0.136637i	0.981813	+	0.189853i	$0.0608010\pi$
$224$	−15.3664	+	1.40675i	−1.02671	+	0.0939925i
$225$		0			0
$226$	−7.59727	−	13.1589i	−0.505363	−	0.875314i
$227$	−1.61863	+	1.61863i	−0.107432	+	0.107432i	−0.758780	−	0.651347i	$-0.774204\pi$
$227$	−1.61863	+	1.61863i	−0.107432	+	0.107432i	0.651347	+	0.758780i	$0.274204\pi$
$228$		0			0
$229$	−0.131734			−0.00870523			−0.00435262	−	0.999991i	$-0.501385\pi$
$229$	−0.131734			−0.00870523			−0.00435262	+	0.999991i	$0.501385\pi$
$230$	−2.34656	−	0.537939i	−0.154728	−	0.0354706i
$231$		0			0
$232$	1.81417	−	6.77057i	0.119106	−	0.444510i
$233$	−7.31550	−	1.96018i	−0.479254	−	0.128416i	0.0111012	−	0.999938i	$-0.496466\pi$
$233$	−7.31550	−	1.96018i	−0.479254	−	0.128416i	−0.490355	+	0.871523i	$0.663133\pi$
$234$		0			0
$235$	−15.4024	+	9.65755i	−1.00474	+	0.629989i
$236$	8.74344	+	5.04802i	0.569149	+	0.328598i
$237$		0			0
$238$	2.72739	−	3.27708i	0.176790	−	0.212422i
$239$	7.82313	+	4.51669i	0.506036	+	0.292160i	0.731203	−	0.682160i	$-0.238959\pi$
$239$	7.82313	+	4.51669i	0.506036	+	0.292160i	−0.225167	+	0.974320i	$0.572293\pi$
$240$		0			0
$241$			16.0799i			1.03580i	0.855441	+	0.517900i	$0.173286\pi$
$241$			16.0799i			1.03580i	−0.855441	+	0.517900i	$0.826714\pi$
$242$	5.71484	−	1.53129i	0.367364	−	0.0984348i
$243$		0			0
$244$	6.38606			0.408826
$245$	13.2085	+	8.39862i	0.843857	+	0.536568i
$246$		0			0
$247$	−1.14203	−	1.14203i	−0.0726657	−	0.0726657i
$248$	2.81338	−	10.4997i	0.178650	−	0.666729i
$249$		0			0
$250$	−8.18347	−	3.59828i	−0.517568	−	0.227575i
$251$			11.2568i			0.710521i	0.934767	+	0.355260i	$0.115608\pi$
$251$			11.2568i			0.710521i	−0.934767	+	0.355260i	$0.884392\pi$
$252$		0			0
$253$	1.80667	−	1.80667i	0.113584	−	0.113584i
$254$	5.59434	+	3.22989i	0.351020	+	0.202661i
$255$		0			0
$256$	7.05668	+	12.2225i	0.441042	+	0.763908i
$257$	4.00109	−	4.00109i	0.249581	−	0.249581i	−0.571217	−	0.820799i	$-0.693529\pi$
$257$	4.00109	−	4.00109i	0.249581	−	0.249581i	0.820799	+	0.571217i	$0.193529\pi$
$258$		0			0
$259$	22.0945	−	2.02269i	1.37288	−	0.125684i
$260$	0.956334	+	0.506603i	0.0593093	+	0.0314182i
$261$		0			0
$262$	2.02059	+	7.54095i	0.124833	+	0.465882i
$263$	1.72403	−	1.72403i	0.106308	−	0.106308i	−0.651952	−	0.758260i	$-0.726050\pi$
$263$	1.72403	−	1.72403i	0.106308	−	0.106308i	0.758260	+	0.651952i	$0.226050\pi$
$264$		0			0
$265$	−16.5970	+	10.4066i	−1.01955	+	0.639270i
$266$	−4.02440	+	8.72187i	−0.246752	+	0.534772i
$267$		0			0
$268$	5.19741	+	19.3970i	0.317482	+	1.18486i
$269$	2.87950	−	4.98744i	0.175566	−	0.304090i	−0.764791	−	0.644279i	$-0.777158\pi$
$269$	2.87950	−	4.98744i	0.175566	−	0.304090i	0.940357	+	0.340189i	$0.110491\pi$
$270$		0			0
$271$	−22.3773	+	12.9196i	−1.35933	+	0.784808i	−0.989533	−	0.144306i	$-0.953905\pi$
$271$	−22.3773	+	12.9196i	−1.35933	+	0.784808i	−0.369793	+	0.929114i	$0.620572\pi$
$272$	1.11496	+	0.298753i	0.0676044	+	0.0181145i
$273$		0			0
$274$	12.9773	+	7.49244i	0.783986	+	0.452635i
$275$	7.84922	−	5.32964i	0.473326	−	0.321389i
$276$		0			0
$277$	−12.0321	−	12.0321i	−0.722937	−	0.722937i	0.246266	−	0.969202i	$-0.420796\pi$
$277$	−12.0321	−	12.0321i	−0.722937	−	0.722937i	−0.969202	+	0.246266i	$0.920796\pi$
$278$	0.496739	−	1.85386i	0.0297924	−	0.111187i
$279$		0			0
$280$	2.12480	−	15.7547i	0.126981	−	0.941521i
$281$	16.1409	+	27.9568i	0.962884	+	1.66776i	0.715196	+	0.698924i	$0.246337\pi$
$281$	16.1409	+	27.9568i	0.962884	+	1.66776i	0.247688	+	0.968840i	$0.420329\pi$
$282$		0			0
$283$	−0.317296	+	1.18417i	−0.0188613	+	0.0703914i	−0.974715	−	0.223451i	$-0.928268\pi$
$283$	−0.317296	+	1.18417i	−0.0188613	+	0.0703914i	0.955854	+	0.293843i	$0.0949342\pi$
$284$	−3.79561	+	2.19140i	−0.225228	+	0.130035i
$285$		0			0
$286$	0.467376	−	0.269840i	0.0276365	−	0.0159560i
$287$	−0.192226	+	1.11644i	−0.0113467	+	0.0659012i
$288$		0			0
$289$	11.2048	−	6.46911i	0.659107	−	0.380536i
$290$	4.12127	+	2.18318i	0.242010	+	0.128201i
$291$		0			0
$292$	−8.98909	+	8.98909i	−0.526047	+	0.526047i
$293$	−5.65776	+	1.51599i	−0.330530	+	0.0885653i	−0.420268	−	0.907400i	$-0.638064\pi$
$293$	−5.65776	+	1.51599i	−0.330530	+	0.0885653i	0.0897376	+	0.995965i	$0.471397\pi$
$294$		0			0
$295$	−11.2967	+	12.1517i	−0.657717	+	0.707497i
$296$	−11.2670	−	19.5149i	−0.654878	−	1.13428i
$297$		0			0
$298$	−0.858575	−	3.20424i	−0.0497359	−	0.185617i
$299$	−0.239474	+	0.414781i	−0.0138491	+	0.0239874i
$300$		0			0
$301$	−2.02351	−	22.1034i	−0.116633	−	1.27402i
$302$	−12.0225	+	3.22141i	−0.691815	+	0.185371i
$303$		0			0
$304$	−2.60056			−0.149152
$305$	−2.34502	+	10.2293i	−0.134275	+	0.585726i
$306$		0			0
$307$	−3.77724	+	3.77724i	−0.215578	+	0.215578i	−0.806632	−	0.591054i	$-0.798712\pi$
$307$	−3.77724	+	3.77724i	−0.215578	+	0.215578i	0.591054	+	0.806632i	$0.298712\pi$
$308$	5.25054	+	4.36982i	0.299177	+	0.248994i
$309$		0			0
$310$	6.39119	+	3.38563i	0.362995	+	0.192291i
$311$	18.1547	−	10.4816i	1.02946	−	0.594359i	0.112630	−	0.993637i	$-0.464073\pi$
$311$	18.1547	−	10.4816i	1.02946	−	0.594359i	0.916830	+	0.399278i	$0.130739\pi$
$312$		0			0
$313$	12.0347	−	3.22468i	0.680240	−	0.182270i	0.0978768	−	0.995199i	$-0.468795\pi$
$313$	12.0347	−	3.22468i	0.680240	−	0.182270i	0.582363	+	0.812929i	$0.302128\pi$
$314$	−16.6858			−0.941636
$315$		0			0
$316$	13.7915			0.775834
$317$	14.2760	−	3.82525i	0.801822	−	0.214848i	0.165438	−	0.986220i	$-0.447096\pi$
$317$	14.2760	−	3.82525i	0.801822	−	0.214848i	0.636384	+	0.771373i	$0.280429\pi$
$318$		0			0
$319$	−4.28658	+	2.47486i	−0.240002	+	0.138565i
$320$	−7.51894	+	2.31145i	−0.420322	+	0.129214i
$321$		0			0
$322$	2.80720	+	0.483339i	0.156439	+	0.0269354i
$323$	6.47073	−	6.47073i	0.360041	−	0.360041i
$324$		0			0
$325$	−1.16266	+	1.34584i	−0.0644926	+	0.0746537i
$326$	10.3061			0.570803
$327$		0			0
$328$	1.11138	−	0.297793i	0.0613656	−	0.0164429i
$329$	17.5706	−	12.4088i	0.968699	−	0.684120i
$330$		0			0
$331$	3.28364	−	5.68743i	0.180485	−	0.312610i	−0.761561	−	0.648094i	$-0.775567\pi$
$331$	3.28364	−	5.68743i	0.180485	−	0.312610i	0.942046	+	0.335484i	$0.108900\pi$
$332$	6.13285	+	22.8881i	0.336584	+	1.25615i
$333$		0			0
$334$	3.52479	+	6.10511i	0.192868	+	0.334057i
$335$	−32.9789	+	1.20253i	−1.80183	+	0.0657012i
$336$		0			0
$337$	13.6413	−	3.65517i	0.743087	−	0.199110i	0.132638	−	0.991165i	$-0.457655\pi$
$337$	13.6413	−	3.65517i	0.743087	−	0.199110i	0.610450	+	0.792055i	$0.290989\pi$
$338$	7.27855	−	7.27855i	0.395901	−	0.395901i
$339$		0			0
$340$	−2.87041	+	5.41857i	−0.155670	+	0.293863i
$341$	−6.64754	+	3.83796i	−0.359985	+	0.207837i
$342$		0			0
$343$	−16.1497	−	9.06571i	−0.872002	−	0.489503i
$344$	−19.5228	+	11.2715i	−1.05260	+	0.607719i
$345$		0			0
$346$	15.9034	−	9.18185i	0.854974	−	0.493620i
$347$	7.09254	−	26.4697i	0.380747	−	1.42097i	−0.464015	−	0.885827i	$-0.653592\pi$
$347$	7.09254	−	26.4697i	0.380747	−	1.42097i	0.844763	−	0.535141i	$-0.179742\pi$
$348$		0			0
$349$	−5.35414	−	9.27365i	−0.286601	−	0.496407i	0.686395	−	0.727229i	$-0.259192\pi$
$349$	−5.35414	−	9.27365i	−0.286601	−	0.496407i	−0.972996	+	0.230822i	$0.925859\pi$
$350$	9.90165	+	3.72035i	0.529265	+	0.198861i
$351$		0			0
$352$	2.86430	−	10.6897i	0.152668	−	0.569764i
$353$	12.9115	+	12.9115i	0.687207	+	0.687207i	0.961614	−	0.274407i	$-0.0884814\pi$
$353$	12.9115	+	12.9115i	0.687207	+	0.687207i	−0.274407	+	0.961614i	$0.588481\pi$
$354$		0			0
$355$	−2.11643	−	6.88455i	−0.112328	−	0.365394i
$356$	−2.03982	−	1.17769i	−0.108110	−	0.0624174i
$357$		0			0
$358$	−4.88599	−	1.30920i	−0.258233	−	0.0691932i
$359$	6.12023	−	3.53352i	0.323013	−	0.186492i	−0.329722	−	0.944078i	$-0.606955\pi$
$359$	6.12023	−	3.53352i	0.323013	−	0.186492i	0.652735	+	0.757586i	$0.273622\pi$
$360$		0			0
$361$	−0.808341	+	1.40009i	−0.0425442	+	0.0736888i
$362$	−4.03508	−	15.0591i	−0.212079	−	0.791490i
$363$		0			0
$364$	−1.16271	−	0.536490i	−0.0609424	−	0.0281197i
$365$	−11.0980	−	17.6997i	−0.580894	−	0.926445i
$366$		0			0
$367$	−15.4582	+	15.4582i	−0.806912	+	0.806912i	−0.984165	−	0.177253i	$-0.943279\pi$
$367$	−15.4582	+	15.4582i	−0.806912	+	0.806912i	0.177253	+	0.984165i	$0.443279\pi$
$368$	0.199599	+	0.744912i	0.0104048	+	0.0388312i
$369$		0			0
$370$	14.3314	−	4.40570i	0.745052	−	0.229041i
$371$	18.9333	−	13.3712i	0.982970	−	0.694198i
$372$		0			0
$373$	13.2315	−	13.2315i	0.685103	−	0.685103i	−0.276042	−	0.961145i	$-0.589023\pi$
$373$	13.2315	−	13.2315i	0.685103	−	0.685103i	0.961145	+	0.276042i	$0.0890230\pi$
$374$	1.52891	+	2.64815i	0.0790579	+	0.136932i
$375$		0			0
$376$	−18.9201	−	10.9235i	−0.975729	−	0.563338i
$377$	0.656086	−	0.656086i	0.0337901	−	0.0337901i
$378$		0			0
$379$			14.4563i			0.742571i	0.928519	+	0.371285i	$0.121083\pi$
$379$			14.4563i			0.742571i	−0.928519	+	0.371285i	$0.878917\pi$
$380$	3.08692	−	13.4655i	0.158355	−	0.690767i
$381$		0			0
$382$	−4.60934	+	17.2023i	−0.235835	+	0.880147i
$383$	−6.79699	−	6.79699i	−0.347310	−	0.347310i	0.511797	−	0.859107i	$-0.328980\pi$
$383$	−6.79699	−	6.79699i	−0.347310	−	0.347310i	−0.859107	+	0.511797i	$0.828980\pi$
$384$		0			0
$385$	−8.92767	+	6.80574i	−0.454996	+	0.346853i
$386$	−7.57181			−0.385395
$387$		0			0
$388$	8.62262	−	2.31042i	0.437747	−	0.117294i
$389$		−	4.44912i		−	0.225579i	−0.993619	−	0.112790i	$-0.964021\pi$
$389$		−	4.44912i		−	0.225579i	0.993619	−	0.112790i	$-0.0359786\pi$
$390$		0			0
$391$	−2.35014	−	1.35685i	−0.118852	−	0.0686191i
$392$	−1.48844	+	18.7510i	−0.0751777	+	0.947067i
$393$		0			0
$394$	3.41196	+	1.96989i	0.171892	+	0.0992419i
$395$	−5.06437	+	22.0914i	−0.254816	+	1.11154i
$396$		0			0
$397$	6.67418	+	1.78834i	0.334967	+	0.0897542i	0.422382	−	0.906418i	$-0.361194\pi$
$397$	6.67418	+	1.78834i	0.334967	+	0.0897542i	−0.0874150	+	0.996172i	$0.527861\pi$
$398$	−0.0961359	+	0.358784i	−0.00481886	+	0.0179842i
$399$		0			0
$400$	0.208564	+	2.85609i	0.0104282	+	0.142804i
$401$	−27.5158			−1.37407			−0.687037	−	0.726622i	$-0.741089\pi$
$401$	−27.5158			−1.37407			−0.687037	+	0.726622i	$0.741089\pi$
$402$		0			0
$403$	1.01744	−	1.01744i	0.0506825	−	0.0506825i
$404$	−11.6560	−	20.1888i	−0.579908	−	1.00443i
$405$		0			0
$406$	−5.01063	−	2.31198i	−0.248673	−	0.114742i
$407$	−4.11843	+	15.3702i	−0.204143	+	0.761872i
$408$		0			0
$409$	−16.9076	−	29.2848i	−0.836026	−	1.44804i	−0.893192	−	0.449675i	$-0.851540\pi$
$409$	−16.9076	−	29.2848i	−0.836026	−	1.44804i	0.0571656	−	0.998365i	$-0.481794\pi$
$410$	0.0278965	+	0.765050i	0.00137771	+	0.0377831i
$411$		0			0
$412$	−20.8585	−	5.58901i	−1.02762	−	0.275351i
$413$	12.5581	−	15.0891i	0.617944	−	0.742488i
$414$		0			0
$415$	−38.9145	+	1.41896i	−1.91024	+	0.0696542i
$416$			2.07452i			0.101712i
$417$		0			0
$418$	−4.87132	−	4.87132i	−0.238264	−	0.238264i
$419$	−12.1462	+	21.0378i	−0.593380	+	1.02776i	0.400393	+	0.916343i	$0.368873\pi$
$419$	−12.1462	+	21.0378i	−0.593380	+	1.02776i	−0.993773	+	0.111421i	$0.964460\pi$
$420$		0			0
$421$	−2.49624	−	4.32361i	−0.121659	−	0.210720i	0.798763	−	0.601646i	$-0.205488\pi$
$421$	−2.49624	−	4.32361i	−0.121659	−	0.210720i	−0.920422	+	0.390926i	$0.872155\pi$
$422$	4.57925	−	17.0900i	0.222914	−	0.831928i
$423$		0			0
$424$	−20.3875	−	11.7707i	−0.990104	−	0.571637i
$425$	−7.62550	−	6.58760i	−0.369891	−	0.319545i
$426$		0			0
$427$	2.10700	−	12.2373i	0.101965	−	0.592206i
$428$	1.55635	+	5.80836i	0.0752288	+	0.280758i
$429$		0			0
$430$	−4.40748	−	14.3372i	−0.212547	−	0.691399i
$431$	2.71752	−	4.70688i	0.130898	−	0.226723i	−0.793125	−	0.609059i	$-0.791547\pi$
$431$	2.71752	−	4.70688i	0.130898	−	0.226723i	0.924023	+	0.382337i	$0.124881\pi$
$432$		0			0
$433$	12.6985	+	12.6985i	0.610249	+	0.610249i	0.943011	−	0.332762i	$-0.107981\pi$
$433$	12.6985	+	12.6985i	0.610249	+	0.610249i	−0.332762	+	0.943011i	$0.607981\pi$
$434$	−7.77038	−	3.58537i	−0.372990	−	0.172103i
$435$		0			0
$436$	8.13246			0.389474
$437$	5.90551	+	1.58238i	0.282499	+	0.0756954i
$438$		0			0
$439$	−5.08944	+	8.81517i	−0.242906	+	0.420725i	−0.961541	−	0.274662i	$-0.911434\pi$
$439$	−5.08944	+	8.81517i	−0.242906	+	0.420725i	0.718635	+	0.695388i	$0.244767\pi$
$440$	10.0752	+	5.33717i	0.480315	+	0.254440i
$441$		0			0
$442$	−0.405314	−	0.405314i	−0.0192788	−	0.0192788i
$443$	−1.20215	−	4.48649i	−0.0571159	−	0.213159i	0.931470	−	0.363818i	$-0.118527\pi$
$443$	−1.20215	−	4.48649i	−0.0571159	−	0.213159i	−0.988586	+	0.150659i	$0.951860\pi$
$444$		0			0
$445$	2.63548	−	2.83495i	0.124934	−	0.134389i
$446$			1.68904i			0.0799783i
$447$		0			0
$448$	8.73323	−	3.21852i	0.412606	−	0.152061i
$449$		−	36.0848i		−	1.70295i	−0.524398	−	0.851474i	$-0.675709\pi$
$449$		−	36.0848i		−	1.70295i	0.524398	−	0.851474i	$-0.324291\pi$
$450$		0			0
$451$	−0.703636	−	0.406244i	−0.0331329	−	0.0191293i
$452$	−18.2835	−	18.2835i	−0.859984	−	0.859984i
$453$		0			0
$454$	0.915160	−	1.58510i	0.0429506	−	0.0743926i
$455$	1.28631	−	1.66544i	0.0603033	−	0.0780768i
$456$		0			0
$457$	26.3908	−	7.07140i	1.23451	−	0.330786i	0.418176	−	0.908366i	$-0.362669\pi$
$457$	26.3908	−	7.07140i	1.23451	−	0.330786i	0.816334	+	0.577580i	$0.196003\pi$
$458$	0.101743	−	0.0272621i	0.00475415	−	0.00127387i
$459$		0			0
$460$	−4.09404	+	0.149284i	−0.190886	+	0.00696039i
$461$	2.22321	−	1.28357i	0.103545	−	0.0597819i	−0.447333	−	0.894367i	$-0.647626\pi$
$461$	2.22321	−	1.28357i	0.103545	−	0.0597819i	0.550878	+	0.834586i	$0.314293\pi$
$462$		0			0
$463$	−6.43065	−	23.9995i	−0.298858	−	1.11535i	−0.938105	−	0.346351i	$-0.887421\pi$
$463$	−6.43065	−	23.9995i	−0.298858	−	1.11535i	0.639247	−	0.769001i	$-0.279246\pi$
$464$		−	1.49399i		−	0.0693569i
$465$		0			0
$466$	6.05570			0.280525
$467$	−19.2509	−	5.15827i	−0.890827	−	0.238696i	−0.215755	−	0.976448i	$-0.569221\pi$
$467$	−19.2509	−	5.15827i	−0.890827	−	0.238696i	−0.675073	+	0.737751i	$0.735888\pi$
$468$		0			0
$469$	38.8844	−	3.55977i	1.79552	−	0.164375i
$470$	9.89731	−	10.6464i	0.456529	−	0.491082i
$471$		0			0
$472$	−19.2590	−	5.16043i	−0.886467	−	0.237528i
$473$	15.3764	+	4.12009i	0.707008	+	0.189442i
$474$		0			0
$475$	20.4357	+	9.88932i	0.937655	+	0.453753i
$476$	3.03975	−	6.58788i	0.139327	−	0.301955i
$477$		0			0
$478$	−6.97683	−	1.86944i	−0.319113	−	0.0855060i
$479$	−13.6387			−0.623167			−0.311584	−	0.950219i	$-0.600859\pi$
$479$	−13.6387			−0.623167			−0.311584	+	0.950219i	$0.600859\pi$
$480$		0			0
$481$		−	2.98284i		−	0.136006i
$482$	−3.32771	−	12.4192i	−0.151573	−	0.565678i
$483$		0			0
$484$	8.71922	−	5.03404i	0.396328	−	0.228820i
$485$	0.534565	+	14.6602i	0.0242734	+	0.665687i
$486$		0			0
$487$	0.813737	−	0.218040i	0.0368739	−	0.00988034i	−0.240335	−	0.970690i	$-0.577257\pi$
$487$	0.813737	−	0.218040i	0.0368739	−	0.00988034i	0.277209	+	0.960810i	$0.410591\pi$
$488$	−12.1819	+	3.26413i	−0.551449	+	0.147760i
$489$		0			0
$490$	−11.9395	−	3.75312i	−0.539371	−	0.169549i
$491$	12.3106	−	21.3225i	0.555568	−	0.962271i	−0.442292	−	0.896871i	$-0.645834\pi$
$491$	12.3106	−	21.3225i	0.555568	−	0.962271i	0.997859	−	0.0653999i	$-0.0208323\pi$
$492$		0			0
$493$	3.71737	+	3.71737i	0.167422	+	0.167422i
$494$	1.11838	+	0.645694i	0.0503181	+	0.0290512i
$495$		0			0
$496$		−	2.31686i		−	0.104030i
$497$	2.94697	+	7.99639i	0.132189	+	0.358687i
$498$		0			0
$499$			7.38528i			0.330610i	0.986242	+	0.165305i	$0.0528609\pi$
$499$			7.38528i			0.330610i	−0.986242	+	0.165305i	$0.947139\pi$
$500$	−15.0362	−	2.31031i	−0.672441	−	0.103320i
$501$		0			0
$502$	−2.32956	−	8.69404i	−0.103973	−	0.388034i
$503$	−28.2531	−	28.2531i	−1.25974	−	1.25974i	−0.951215	−	0.308530i	$-0.900163\pi$
$503$	−28.2531	−	28.2531i	−1.25974	−	1.25974i	−0.308530	−	0.951215i	$-0.599837\pi$
$504$		0			0
$505$	36.6189	−	11.2572i	1.62952	−	0.500940i
$506$	−1.02147	+	1.76924i	−0.0454100	+	0.0786525i
$507$		0			0
$508$	10.6181	+	2.84512i	0.471104	+	0.126232i
$509$	12.3062			0.545463			0.272732	−	0.962090i	$-0.412073\pi$
$509$	12.3062			0.545463			0.272732	+	0.962090i	$0.412073\pi$
$510$		0			0
$511$	14.2596	+	20.1913i	0.630806	+	0.893208i
$512$	4.53849	+	4.53849i	0.200575	+	0.200575i
$513$		0			0
$514$	−2.26218	+	3.91822i	−0.0997807	+	0.172825i
$515$	16.6119	−	31.3590i	0.732010	−	1.38184i
$516$		0			0
$517$	3.99289	+	14.9017i	0.175607	+	0.655375i
$518$	−16.6458	+	6.13461i	−0.731376	+	0.269539i
$519$		0			0
$520$	−2.08322	−	0.477570i	−0.0913554	−	0.0209428i
$521$	30.8984	+	17.8392i	1.35368	+	0.781550i	0.988763	−	0.149489i	$-0.0477629\pi$
$521$	30.8984	+	17.8392i	1.35368	+	0.781550i	0.364920	+	0.931039i	$0.381096\pi$
$522$		0			0
$523$	−3.40911	+	12.7230i	−0.149070	+	0.556336i	0.850471	+	0.526023i	$0.176317\pi$
$523$	−3.40911	+	12.7230i	−0.149070	+	0.556336i	−0.999540	+	0.0303136i	$0.990349\pi$
$524$	6.64262	+	11.5054i	0.290184	+	0.502614i
$525$		0			0
$526$	−0.974751	+	1.68832i	−0.0425012	+	0.0736142i
$527$	5.76482	+	5.76482i	0.251120	+	0.251120i
$528$		0			0
$529$			21.1870i			0.921172i
$530$	10.6649	−	11.4721i	0.463254	−	0.498317i
$531$		0			0
$532$	−2.77360	+	16.1089i	−0.120251	+	0.698409i
$533$	0.147115	+	0.0394193i	0.00637225	+	0.00170744i
$534$		0			0
$535$	−9.87541	+	0.360093i	−0.426951	+	0.0155682i
$536$	−19.8289	−	34.3447i	−0.856478	−	1.48346i
$537$		0			0
$538$	−1.19181	+	4.44790i	−0.0513826	+	0.191763i
$539$	10.1061	−	8.61962i	0.435298	−	0.371273i
$540$		0			0
$541$	−10.4309	−	18.0669i	−0.448460	−	0.776756i	0.549826	−	0.835279i	$-0.314694\pi$
$541$	−10.4309	−	18.0669i	−0.448460	−	0.776756i	−0.998286	+	0.0585236i	$0.981361\pi$
$542$	14.6092	−	14.6092i	0.627520	−	0.627520i
$543$		0			0
$544$	−11.7542			−0.503957
$545$	−2.98631	+	13.0267i	−0.127920	+	0.558002i
$546$		0			0
$547$	7.30369	−	27.2577i	0.312283	−	1.16546i	−0.614209	−	0.789143i	$-0.710525\pi$
$547$	7.30369	−	27.2577i	0.312283	−	1.16546i	0.926492	−	0.376314i	$-0.122808\pi$
$548$	24.6311	+	6.59988i	1.05219	+	0.281933i
$549$		0			0
$550$	−4.95931	+	5.74067i	−0.211466	+	0.244783i
$551$	−10.2573	−	5.92204i	−0.436975	−	0.252287i
$552$		0			0
$553$	4.55034	−	26.4281i	0.193500	−	1.12384i
$554$	11.7828	+	6.80283i	0.500605	+	0.289024i
$555$		0			0
$556$		−	3.26602i		−	0.138510i
$557$	15.9512	−	4.27411i	0.675875	−	0.181100i	0.0954749	−	0.995432i	$-0.469563\pi$
$557$	15.9512	−	4.27411i	0.675875	−	0.181100i	0.580400	+	0.814332i	$0.302896\pi$
$558$		0			0
$559$	−2.98405			−0.126212
$560$	−0.431656	−	3.36076i	−0.0182408	−	0.142018i
$561$		0			0
$562$	−18.2518	−	18.2518i	−0.769907	−	0.769907i
$563$	−4.15415	+	15.5035i	−0.175076	+	0.653394i	0.821462	+	0.570263i	$0.193159\pi$
$563$	−4.15415	+	15.5035i	−0.175076	+	0.653394i	−0.996539	+	0.0831312i	$0.973508\pi$
$564$		0			0
$565$	36.0006	−	22.5729i	1.51456	−	0.949648i
$566$		−	0.980241i		−	0.0412026i
$567$		0			0
$568$	6.12032	−	6.12032i	0.256803	−	0.256803i
$569$	−0.476743	−	0.275248i	−0.0199861	−	0.0115390i	0.489974	−	0.871737i	$-0.337006\pi$
$569$	−0.476743	−	0.275248i	−0.0199861	−	0.0115390i	−0.509960	+	0.860198i	$0.670340\pi$
$570$		0			0
$571$	−16.3710	−	28.3554i	−0.685105	−	1.18664i	−0.973404	−	0.229096i	$-0.926423\pi$
$571$	−16.3710	−	28.3554i	−0.685105	−	1.18664i	0.288299	−	0.957540i	$-0.406910\pi$
$572$	0.649393	−	0.649393i	0.0271525	−	0.0271525i
$573$		0			0
$574$	−0.0825803	−	0.902049i	−0.00344683	−	0.0376508i
$575$	1.26424	−	6.61270i	0.0527226	−	0.275769i
$576$		0			0
$577$	3.43734	+	12.8283i	0.143098	+	0.534050i	0.999833	+	0.0182920i	$0.00582285\pi$
$577$	3.43734	+	12.8283i	0.143098	+	0.534050i	−0.856735	+	0.515758i	$0.827510\pi$
$578$	−7.31515	+	7.31515i	−0.304270	+	0.304270i
$579$		0			0
$580$	7.73582	+	1.77340i	0.321212	+	0.0736366i
$581$	45.8830	−	4.20047i	1.90355	−	0.174265i
$582$		0			0
$583$	4.30257	+	16.0574i	0.178194	+	0.665030i
$584$	12.5528	−	21.7420i	0.519437	−	0.899690i
$585$		0			0
$586$	4.05598	−	2.34172i	0.167551	−	0.0967356i
$587$	5.88487	+	1.57685i	0.242895	+	0.0650834i	0.378212	−	0.925719i	$-0.376539\pi$
$587$	5.88487	+	1.57685i	0.242895	+	0.0650834i	−0.135318	+	0.990802i	$0.543206\pi$
$588$		0			0
$589$	−15.9068	−	9.18378i	−0.655427	−	0.378411i
$590$	6.21009	−	11.7230i	0.255665	−	0.482629i
$591$		0			0
$592$	−3.39616	−	3.39616i	−0.139582	−	0.139582i
$593$	0.196420	−	0.733049i	0.00806599	−	0.0301027i	−0.961776	−	0.273839i	$-0.911706\pi$
$593$	0.196420	−	0.733049i	0.00806599	−	0.0301027i	0.969842	+	0.243736i	$0.0783731\pi$
$594$		0			0
$595$	9.43633	+	7.28823i	0.386852	+	0.298788i
$596$	−2.82253	−	4.88877i	−0.115615	−	0.200252i
$597$		0			0
$598$	0.0991170	−	0.369910i	0.00405320	−	0.0151267i
$599$	−28.4089	+	16.4019i	−1.16076	+	0.670163i	−0.951485	−	0.307695i	$-0.900442\pi$
$599$	−28.4089	+	16.4019i	−1.16076	+	0.670163i	−0.209271	+	0.977858i	$0.567109\pi$
$600$		0			0
$601$	15.5085	−	8.95386i	0.632607	−	0.365236i	−0.149154	−	0.988814i	$-0.547655\pi$
$601$	15.5085	−	8.95386i	0.632607	−	0.365236i	0.781761	+	0.623578i	$0.214322\pi$
$602$	6.13709	+	16.6526i	0.250129	+	0.678708i
$603$		0			0
$604$	−18.3429	+	10.5903i	−0.746361	+	0.430912i
$605$	4.86182	+	15.8151i	0.197661	+	0.642975i
$606$		0			0
$607$	−22.6668	+	22.6668i	−0.920015	+	0.920015i	−0.997030	−	0.0770149i	$-0.975461\pi$
$607$	−22.6668	+	22.6668i	−0.920015	+	0.920015i	0.0770149	+	0.997030i	$0.475461\pi$
$608$	25.5792	−	6.85393i	1.03737	−	0.277964i
$609$		0			0
$610$	−0.305775	−	8.38576i	−0.0123805	−	0.339530i
$611$	−1.44596	−	2.50448i	−0.0584973	−	0.101320i
$612$		0			0
$613$	0.479975	+	1.79129i	0.0193860	+	0.0723495i	0.974941	−	0.222463i	$-0.0714096\pi$
$613$	0.479975	+	1.79129i	0.0193860	+	0.0723495i	−0.955555	+	0.294812i	$0.904743\pi$
$614$	2.13562	−	3.69900i	0.0861865	−	0.149279i
$615$		0			0
$616$	−12.2494	−	5.65204i	−0.493541	−	0.227727i
$617$	−22.6208	+	6.06122i	−0.910679	+	0.244016i	−0.683597	−	0.729860i	$-0.739585\pi$
$617$	−22.6208	+	6.06122i	−0.910679	+	0.244016i	−0.227082	+	0.973876i	$0.572919\pi$
$618$		0			0
$619$	27.2421			1.09495			0.547476	−	0.836821i	$-0.315589\pi$
$619$	27.2421			1.09495			0.547476	+	0.836821i	$0.315589\pi$
$620$	11.9965	+	2.75016i	0.481793	+	0.110449i
$621$		0			0
$622$	−11.8524	+	11.8524i	−0.475240	+	0.475240i
$623$	−2.92977	+	3.52025i	−0.117379	+	0.141036i
$624$		0			0
$625$	9.22212	−	23.2369i	0.368885	−	0.929475i
$626$	−8.62751	+	4.98109i	−0.344825	+	0.199085i
$627$		0			0
$628$	−27.4270	+	7.34905i	−1.09446	+	0.293259i
$629$	16.9007			0.673877
$630$		0			0
$631$	22.8338			0.908998			0.454499	−	0.890747i	$-0.349818\pi$
$631$	22.8338			0.908998			0.454499	+	0.890747i	$0.349818\pi$
$632$	−26.3084	+	7.04931i	−1.04649	+	0.280406i
$633$		0			0
$634$	−10.2343	+	5.90878i	−0.406457	+	0.234668i
$635$	−8.45643	+	15.9635i	−0.335583	+	0.633493i
$636$		0			0
$637$	−1.41168	+	2.05104i	−0.0559326	+	0.0812651i
$638$	2.79853	−	2.79853i	0.110795	−	0.110795i
$639$		0			0
$640$	−16.7691	+	10.5144i	−0.662855	+	0.415620i
$641$	18.4180			0.727466			0.363733	−	0.931503i	$-0.381502\pi$
$641$	18.4180			0.727466			0.363733	+	0.931503i	$0.381502\pi$
$642$		0			0
$643$	−45.7457	+	12.2575i	−1.80403	+	0.483389i	−0.994596	−	0.103819i	$-0.966894\pi$
$643$	−45.7457	+	12.2575i	−1.80403	+	0.483389i	−0.809436	+	0.587208i	$0.800227\pi$
$644$	4.82717	−	0.441915i	0.190217	−	0.0174139i
$645$		0			0
$646$	−3.65849	+	6.33670i	−0.143942	+	0.249314i
$647$	0.633107	+	2.36279i	0.0248900	+	0.0928907i	0.977254	−	0.212074i	$-0.0680219\pi$
$647$	0.633107	+	2.36279i	0.0248900	+	0.0928907i	−0.952364	+	0.304965i	$0.901355\pi$
$648$		0			0
$649$	7.03977	+	12.1932i	0.276335	+	0.478627i
$650$	0.619448	−	1.28005i	0.0242967	−	0.0502078i
$651$		0			0
$652$	16.9405	−	4.53919i	0.663441	−	0.177768i
$653$	−16.5927	+	16.5927i	−0.649322	+	0.649322i	−0.952829	−	0.303507i	$-0.901842\pi$
$653$	−16.5927	+	16.5927i	−0.649322	+	0.649322i	0.303507	+	0.952829i	$0.401842\pi$
$654$		0			0
$655$	−20.8687	+	6.41537i	−0.815406	+	0.250669i
$656$	0.212381	−	0.122618i	0.00829210	−	0.00478745i
$657$		0			0
$658$	−11.0025	+	13.2200i	−0.428922	+	0.515370i
$659$	−17.3437	+	10.0134i	−0.675615	+	0.390067i	−0.798201	−	0.602391i	$-0.794215\pi$
$659$	−17.3437	+	10.0134i	−0.675615	+	0.390067i	0.122586	+	0.992458i	$0.460881\pi$
$660$		0			0
$661$	−0.625471	+	0.361116i	−0.0243280	+	0.0140458i	−0.512115	−	0.858917i	$-0.671138\pi$
$661$	−0.625471	+	0.361116i	−0.0243280	+	0.0140458i	0.487787	+	0.872963i	$0.337804\pi$
$662$	−1.35908	+	5.07217i	−0.0528223	+	0.197135i
$663$		0			0
$664$	−23.3978	−	40.5261i	−0.908010	−	1.57272i
$665$	−24.7849	−	10.3581i	−0.961119	−	0.401670i
$666$		0			0
$667$	−0.909061	+	3.39266i	−0.0351990	+	0.131364i
$668$	8.48271	+	8.48271i	0.328206	+	0.328206i
$669$		0			0
$670$	25.2220	−	7.75366i	0.974411	−	0.299550i
$671$	7.71260	+	4.45287i	0.297742	+	0.171901i
$672$		0			0
$673$	−26.4663	−	7.09161i	−1.02020	−	0.273362i	−0.290314	−	0.956931i	$-0.593760\pi$
$673$	−26.4663	−	7.09161i	−1.02020	−	0.273362i	−0.729885	+	0.683570i	$0.760426\pi$
$674$	−9.77926	+	5.64606i	−0.376683	+	0.217478i
$675$		0			0
$676$	8.75824	−	15.1697i	0.336856	−	0.583451i
$677$	8.20765	+	30.6314i	0.315446	+	1.17726i	0.923574	+	0.383421i	$0.125254\pi$
$677$	8.20765	+	30.6314i	0.315446	+	1.17726i	−0.608128	+	0.793839i	$0.708079\pi$
$678$		0			0
$679$	−1.58244	−	17.2855i	−0.0607285	−	0.663355i
$680$	2.70590	−	11.8035i	0.103767	−	0.452644i
$681$		0			0
$682$	4.33990	−	4.33990i	0.166183	−	0.166183i
$683$	5.84528	+	21.8149i	0.223663	+	0.834724i	0.982936	+	0.183950i	$0.0588885\pi$
$683$	5.84528	+	21.8149i	0.223663	+	0.834724i	−0.759272	+	0.650773i	$0.774445\pi$
$684$		0			0
$685$	−19.6165	+	37.0309i	−0.749509	+	1.41488i
$686$	14.3492	+	3.65966i	0.547854	+	0.139727i
$687$		0			0
$688$	−3.39754	+	3.39754i	−0.129530	+	0.129530i
$689$	−1.55811	−	2.69872i	−0.0593591	−	0.102813i
$690$		0			0
$691$	−7.75267	−	4.47600i	−0.294925	−	0.170275i	0.345236	−	0.938516i	$-0.387799\pi$
$691$	−7.75267	−	4.47600i	−0.294925	−	0.170275i	−0.640161	+	0.768241i	$0.721132\pi$
$692$	22.0969	−	22.0969i	0.840000	−	0.840000i
$693$		0			0
$694$			21.9114i			0.831744i
$695$	5.23156	+	1.19931i	0.198444	+	0.0454925i
$696$		0			0
$697$	−0.223349	+	0.833550i	−0.00845994	+	0.0315729i
$698$	6.05437	+	6.05437i	0.229161	+	0.229161i
$699$		0			0
$700$	17.9142	+	1.75421i	0.677094	+	0.0663028i
$701$	−28.2460			−1.06684			−0.533419	−	0.845851i	$-0.679093\pi$
$701$	−28.2460			−1.06684			−0.533419	+	0.845851i	$0.679093\pi$
$702$		0			0
$703$	−36.7790	+	9.85491i	−1.38715	+	0.371685i
$704$			6.67527i			0.251584i
$705$		0			0
$706$	−12.6440	−	7.30002i	−0.475864	−	0.274740i
$707$	−42.5327	+	15.6749i	−1.59961	+	0.589514i
$708$		0			0
$709$	16.6092	+	9.58931i	0.623770	+	0.360134i	0.778335	−	0.627849i	$-0.216064\pi$
$709$	16.6092	+	9.58931i	0.623770	+	0.360134i	−0.154565	+	0.987983i	$0.549398\pi$
$710$	3.05934	+	4.87922i	0.114815	+	0.183114i
$711$		0			0
$712$	4.49307	+	1.20391i	0.168385	+	0.0451186i
$713$	−1.40975	+	5.26127i	−0.0527956	+	0.197036i
$714$		0			0
$715$	0.801744	+	1.27867i	0.0299835	+	0.0478195i
$716$	−8.60787			−0.321691
$717$		0			0
$718$	−3.99564	+	3.99564i	−0.149116	+	0.149116i
$719$	13.9884	+	24.2287i	0.521681	+	0.903578i	0.999682	+	0.0252186i	$0.00802817\pi$
$719$	13.9884	+	24.2287i	0.521681	+	0.903578i	−0.478001	+	0.878359i	$0.658638\pi$
$720$		0			0
$721$	−17.5920	+	38.1262i	−0.655159	+	1.41989i
$722$	0.334568	−	1.24863i	0.0124513	−	0.0464691i
$723$		0			0
$724$	−13.2652	−	22.9759i	−0.492996	−	0.853894i
$725$	−5.68132	+	11.7401i	−0.210999	+	0.436017i
$726$		0			0
$727$	48.8362	+	13.0856i	1.81123	+	0.485319i	0.995638	−	0.0933035i	$-0.0297427\pi$
$727$	48.8362	+	13.0856i	1.81123	+	0.485319i	0.815596	+	0.578622i	$0.196409\pi$
$728$	2.49217	+	0.429098i	0.0923660	+	0.0159034i
$729$		0			0
$730$	12.2343	+	11.3735i	0.452812	+	0.420951i
$731$		−	16.9076i		−	0.625349i
$732$		0			0
$733$	8.77240	+	8.77240i	0.324016	+	0.324016i	0.850305	−	0.526289i	$-0.176417\pi$
$733$	8.77240	+	8.77240i	0.324016	+	0.324016i	−0.526289	+	0.850305i	$0.676417\pi$
$734$	8.73994	−	15.1380i	0.322597	−	0.558755i
$735$		0			0
$736$	−3.92653	−	6.80094i	−0.144734	−	0.250686i
$737$	−7.24809	+	27.0502i	−0.266987	+	0.996409i
$738$		0			0
$739$	−6.03461	−	3.48408i	−0.221987	−	0.128164i	0.384883	−	0.922965i	$-0.374242\pi$
$739$	−6.03461	−	3.48408i	−0.221987	−	0.128164i	−0.606870	+	0.794801i	$0.707575\pi$
$740$	21.6165	−	13.5538i	0.794637	−	0.498249i
$741$		0			0
$742$	−11.8558	+	14.2453i	−0.435241	+	0.522962i
$743$	−0.714284	−	2.66574i	−0.0262045	−	0.0977966i	0.951585	−	0.307385i	$-0.0994541\pi$
$743$	−0.714284	−	2.66574i	−0.0262045	−	0.0977966i	−0.977790	+	0.209589i	$0.932787\pi$
$744$		0			0
$745$	8.86735	−	2.72597i	0.324874	−	0.0998717i
$746$	−7.48100	+	12.9575i	−0.273899	+	0.474407i
$747$		0			0
$748$	3.67945	+	3.67945i	0.134534	+	0.134534i
$749$	11.6438	−	1.06596i	0.425456	−	0.0389494i
$750$		0			0
$751$	1.61214			0.0588277			0.0294138	−	0.999567i	$-0.490636\pi$
$751$	1.61214			0.0588277			0.0294138	+	0.999567i	$0.490636\pi$
$752$	−4.49784	−	1.20519i	−0.164019	−	0.0439488i
$753$		0			0
$754$	−0.370945	+	0.642496i	−0.0135090	+	0.0233983i
$755$	−10.2280	−	33.2707i	−0.372233	−	1.21084i
$756$		0			0
$757$	−20.4552	−	20.4552i	−0.743458	−	0.743458i	0.229784	−	0.973242i	$-0.426198\pi$
$757$	−20.4552	−	20.4552i	−0.743458	−	0.743458i	−0.973242	+	0.229784i	$0.926198\pi$
$758$	−2.99170	−	11.1652i	−0.108663	−	0.405537i
$759$		0			0
$760$	0.994158	+	27.2644i	0.0360619	+	0.988982i
$761$		−	9.49362i		−	0.344143i	−0.985084	−	0.172072i	$-0.944954\pi$
$761$		−	9.49362i		−	0.344143i	0.985084	−	0.172072i	$-0.0550461\pi$
$762$		0			0
$763$	2.68321	−	15.5839i	0.0971386	−	0.564175i
$764$			30.3061i			1.09644i
$765$		0			0
$766$	6.65620	+	3.84296i	0.240498	+	0.138852i
$767$	−1.86625	−	1.86625i	−0.0673862	−	0.0673862i
$768$		0			0
$769$	−17.6473	+	30.5659i	−0.636376	+	1.10224i	0.349846	+	0.936807i	$0.386234\pi$
$769$	−17.6473	+	30.5659i	−0.636376	+	1.10224i	−0.986222	+	0.165429i	$0.947099\pi$
$770$	5.48676	−	7.10390i	0.197729	−	0.256007i
$771$		0			0
$772$	−12.4460	+	3.33490i	−0.447942	+	0.120026i
$773$	−40.0084	+	10.7202i	−1.43900	+	0.385579i	−0.892184	−	0.451673i	$-0.850827\pi$
$773$	−40.0084	+	10.7202i	−1.43900	+	0.385579i	−0.546817	+	0.837252i	$0.684161\pi$
$774$		0			0
$775$	−8.81047	+	18.2063i	−0.316481	+	0.653991i
$776$	−15.2674	+	8.81462i	−0.548067	+	0.316427i
$777$		0			0
$778$	0.920735	+	3.43623i	0.0330099	+	0.123195i
$779$		−	1.94419i		−	0.0696578i
$780$		0			0
$781$	−6.11206			−0.218707
$782$	2.09590	+	0.561595i	0.0749493	+	0.0200826i
$783$		0			0
$784$	0.727958	+	3.94253i	0.0259985	+	0.140805i
$785$	−1.70036	−	46.6316i	−0.0606884	−	1.66435i
$786$		0			0
$787$	23.7719	+	6.36966i	0.847377	+	0.227054i	0.656280	−	0.754517i	$-0.272129\pi$
$787$	23.7719	+	6.36966i	0.847377	+	0.227054i	0.191097	+	0.981571i	$0.438796\pi$
$788$	6.47595	+	1.73523i	0.230696	+	0.0618149i
$789$		0			0
$790$	−0.660361	−	18.1101i	−0.0234946	−	0.644330i
$791$	−41.0683	+	29.0035i	−1.46022	+	1.03125i
$792$		0			0
$793$	−1.61253	−	0.432077i	−0.0572628	−	0.0153435i
$794$	−5.52482			−0.196069
$795$		0			0
$796$			0.632086i			0.0224037i
$797$	6.22974	+	23.2497i	0.220669	+	0.823547i	0.984094	+	0.177651i	$0.0568497\pi$
$797$	6.22974	+	23.2497i	0.220669	+	0.823547i	−0.763425	+	0.645897i	$0.776484\pi$
$798$		0			0
$799$	14.1903	−	8.19279i	0.502018	−	0.289840i
$800$	−9.57886	−	27.5430i	−0.338664	−	0.973792i
$801$		0			0
$802$	21.2515	−	5.69433i	0.750418	−	0.201074i
$803$	−17.1242	+	4.58843i	−0.604302	+	0.161922i
$804$		0			0
$805$	−1.06471	+	7.89449i	−0.0375262	+	0.278244i
$806$	−0.575254	+	0.996369i	−0.0202625	+	0.0350956i
$807$		0			0
$808$	32.5539	+	32.5539i	1.14524	+	1.14524i
$809$	−4.30673	−	2.48649i	−0.151417	−	0.0874204i	0.422377	−	0.906420i	$-0.361196\pi$
$809$	−4.30673	−	2.48649i	−0.151417	−	0.0874204i	−0.573794	+	0.819000i	$0.694529\pi$
$810$		0			0
$811$		−	36.7094i		−	1.28904i	−0.764586	−	0.644521i	$-0.777057\pi$
$811$		−	36.7094i		−	1.28904i	0.764586	−	0.644521i	$-0.222943\pi$
$812$	−9.25441	−	1.59341i	−0.324766	−	0.0559176i
$813$		0			0
$814$		−	12.7233i		−	0.445951i
$815$	1.05024	+	28.8023i	0.0367882	+	1.00890i
$816$		0			0
$817$	9.85889	+	36.7939i	0.344919	+	1.28726i
$818$	19.1188	+	19.1188i	0.668474	+	0.668474i
$819$		0			0
$820$	0.382810	+	1.24525i	0.0133683	+	0.0434860i
$821$	−24.9798	+	43.2663i	−0.871801	+	1.51000i	−0.0116684	+	0.999932i	$0.503714\pi$
$821$	−24.9798	+	43.2663i	−0.871801	+	1.51000i	−0.860132	+	0.510071i	$0.829619\pi$
$822$		0			0
$823$	28.2064	+	7.55789i	0.983215	+	0.263452i	0.714398	−	0.699740i	$-0.246701\pi$
$823$	28.2064	+	7.55789i	0.983215	+	0.263452i	0.268817	+	0.963191i	$0.413367\pi$
$824$	42.6458			1.48564
$825$		0			0
$826$	−6.57646	+	14.2528i	−0.228824	+	0.495919i
$827$	9.28844	+	9.28844i	0.322991	+	0.322991i	0.849913	−	0.526923i	$-0.176654\pi$
$827$	9.28844	+	9.28844i	0.322991	+	0.322991i	−0.526923	+	0.849913i	$0.676654\pi$
$828$		0			0
$829$	19.5190	−	33.8079i	0.677923	−	1.17420i	−0.297683	−	0.954665i	$-0.596214\pi$
$829$	19.5190	−	33.8079i	0.677923	−	1.17420i	0.975605	−	0.219532i	$-0.0704529\pi$
$830$	29.7615	−	9.14919i	1.03304	−	0.317573i
$831$		0			0
$832$	−0.323862	−	1.20867i	−0.0112279	−	0.0419031i
$833$	−11.6212	−	7.99853i	−0.402649	−	0.277133i
$834$		0			0
$835$	−16.7026	+	10.4728i	−0.578019	+	0.362426i
$836$	−10.1527	−	5.86164i	−0.351137	−	0.202729i
$837$		0			0
$838$	5.02725	−	18.7619i	0.173663	−	0.648121i
$839$	3.93769	+	6.82027i	0.135944	+	0.235462i	0.925958	−	0.377627i	$-0.123260\pi$
$839$	3.93769	+	6.82027i	0.135944	+	0.235462i	−0.790014	+	0.613089i	$0.789927\pi$
$840$		0			0
$841$	−11.0978	+	19.2220i	−0.382684	+	0.662829i
$842$	2.82270	+	2.82270i	0.0972768	+	0.0972768i
$843$		0			0
$844$		−	30.1082i		−	1.03637i
$845$	21.0830	+	19.5995i	0.725276	+	0.674244i
$846$		0			0
$847$	−6.76973	−	18.3692i	−0.232611	−	0.631173i
$848$	−4.84668	−	1.29866i	−0.166436	−	0.0445963i
$849$		0			0
$850$	7.25276	+	3.50978i	0.248768	+	0.120384i
$851$	5.64575	+	9.77872i	0.193534	+	0.335210i
$852$		0			0
$853$	9.44853	−	35.2624i	0.323512	−	1.20736i	−0.592288	−	0.805726i	$-0.701775\pi$
$853$	9.44853	−	35.2624i	0.323512	−	1.20736i	0.915800	−	0.401635i	$-0.131558\pi$
$854$	0.905168	+	9.88742i	0.0309742	+	0.338340i
$855$		0			0
$856$	−5.93770	−	10.2844i	−0.202946	−	0.351513i
$857$	22.3925	−	22.3925i	0.764914	−	0.764914i	−0.212292	−	0.977206i	$-0.568093\pi$
$857$	22.3925	−	22.3925i	0.764914	−	0.764914i	0.977206	+	0.212292i	$0.0680927\pi$
$858$		0			0
$859$	58.2018			1.98582			0.992910	−	0.118871i	$-0.0379275\pi$
$859$	58.2018			1.98582			0.992910	+	0.118871i	$0.0379275\pi$
$860$	−13.5593	−	21.6252i	−0.462369	−	0.737414i
$861$		0			0
$862$	−1.12477	+	4.19769i	−0.0383098	+	0.142974i
$863$	−3.39357	−	0.909305i	−0.115519	−	0.0309531i	0.200597	−	0.979674i	$-0.435712\pi$
$863$	−3.39357	−	0.909305i	−0.115519	−	0.0309531i	−0.316115	+	0.948721i	$0.602379\pi$
$864$		0			0
$865$	27.2810	+	43.5094i	0.927581	+	1.47936i
$866$	−12.4354	−	7.17960i	−0.422573	−	0.243973i
$867$		0			0
$868$	−14.3515	−	2.47102i	−0.487123	−	0.0838719i
$869$	16.6563	+	9.61655i	0.565028	+	0.326219i
$870$		0			0
$871$		−	5.24956i		−	0.177874i
$872$	−15.5133	+	4.15678i	−0.525347	+	0.140766i
$873$		0			0
$874$	−4.88853			−0.165357
$875$	−9.38817	+	28.0511i	−0.317378	+	0.948299i
$876$		0			0
$877$	1.37958	+	1.37958i	0.0465852	+	0.0465852i	0.730016	−	0.683430i	$-0.239513\pi$
$877$	1.37958	+	1.37958i	0.0465852	+	0.0465852i	−0.683430	+	0.730016i	$0.739513\pi$
$878$	2.10650	−	7.86155i	0.0710908	−	0.265314i
$879$		0			0
$880$	2.36869	+	0.543012i	0.0798485	+	0.0183049i
$881$		−	1.32904i		−	0.0447765i	−0.999749	−	0.0223883i	$-0.992873\pi$
$881$		−	1.32904i		−	0.0447765i	0.999749	−	0.0223883i	$-0.00712700\pi$
$882$		0			0
$883$	24.9117	−	24.9117i	0.838347	−	0.838347i	−0.150295	−	0.988641i	$-0.548022\pi$
$883$	24.9117	−	24.9117i	0.838347	−	0.838347i	0.988641	+	0.150295i	$0.0480222\pi$
$884$	−0.844742	−	0.487712i	−0.0284117	−	0.0164035i
$885$		0			0
$886$	1.85694	+	3.21631i	0.0623850	+	0.108054i
$887$	−20.3728	+	20.3728i	−0.684052	+	0.684052i	−0.960911	−	0.276859i	$-0.910707\pi$
$887$	−20.3728	+	20.3728i	−0.684052	+	0.684052i	0.276859	+	0.960911i	$0.410707\pi$
$888$		0			0
$889$	8.95532	−	19.4084i	0.300352	−	0.650936i
$890$	−1.44880	+	2.73495i	−0.0485638	+	0.0916756i
$891$		0			0
$892$	0.743914	+	2.77633i	0.0249081	+	0.0929583i
$893$	−26.1034	+	26.1034i	−0.873518	+	0.873518i
$894$		0			0
$895$	3.16088	−	13.7882i	0.105657	−	0.460889i
$896$	19.1296	−	13.5098i	0.639075	−	0.451331i
$897$		0			0
$898$	7.46766	+	27.8697i	0.249199	+	0.930024i
$899$	5.27599	−	9.13829i	0.175964	−	0.304779i
$900$		0			0
$901$	15.2909	−	8.82820i	0.509413	−	0.294110i
$902$	0.627517	+	0.168143i	0.0208940	+	0.00559854i
$903$		0			0
$904$	44.2225	+	25.5319i	1.47082	+	0.849177i
$905$	41.6742	−	12.8113i	1.38530	−	0.425863i
$906$		0			0
$907$	23.9657	+	23.9657i	0.795767	+	0.795767i	0.982425	−	0.186658i	$-0.0597657\pi$
$907$	23.9657	+	23.9657i	0.795767	+	0.795767i	−0.186658	+	0.982425i	$0.559766\pi$
$908$	0.806139	−	3.00855i	0.0267527	−	0.0998423i
$909$		0			0
$910$	−0.648812	+	1.55248i	−0.0215079	+	0.0514642i
$911$	−3.92417	−	6.79686i	−0.130013	−	0.225190i	0.793668	−	0.608351i	$-0.208169\pi$
$911$	−3.92417	−	6.79686i	−0.130013	−	0.225190i	−0.923681	+	0.383161i	$0.874835\pi$
$912$		0			0
$913$	−8.55263	+	31.9188i	−0.283051	+	1.05636i
$914$	−18.9193	+	10.9230i	−0.625793	+	0.361302i
$915$		0			0
$916$	0.155232	−	0.0896229i	0.00512899	−	0.00296123i
$917$	24.2389	−	8.93292i	0.800438	−	0.294991i
$918$		0			0
$919$	−45.5357	+	26.2901i	−1.50208	+	0.867229i	−0.502088	+	0.864817i	$0.667435\pi$
$919$	−45.5357	+	26.2901i	−1.50208	+	0.867229i	−0.999997	+	0.00241227i	$0.999232\pi$
$920$	7.73339	−	2.37737i	0.254962	−	0.0783796i
$921$		0			0
$922$	−1.45144	+	1.45144i	−0.0478007	+	0.0478007i
$923$	1.10669	−	0.296537i	0.0364272	−	0.00976064i
$924$		0			0
$925$	13.7729	+	39.6026i	0.452851	+	1.30213i
$926$	9.93329	+	17.2050i	0.326428	+	0.565390i
$927$		0			0
$928$	3.93752	+	14.6950i	0.129255	+	0.482387i
$929$	19.4597	−	33.7052i	0.638452	−	1.10583i	−0.347320	−	0.937747i	$-0.612908\pi$
$929$	19.4597	−	33.7052i	0.638452	−	1.10583i	0.985772	−	0.168085i	$-0.0537584\pi$
$930$		0			0
$931$	29.9537	+	10.6299i	0.981692	+	0.348380i
$932$	9.95394	−	2.66715i	0.326052	−	0.0873654i
$933$		0			0
$934$	15.9357			0.521434
$935$	−7.24492	+	4.54267i	−0.236934	+	0.148561i
$936$		0			0
$937$	20.1650	−	20.1650i	0.658760	−	0.658760i	−0.296326	−	0.955087i	$-0.595762\pi$
$937$	20.1650	−	20.1650i	0.658760	−	0.658760i	0.955087	+	0.296326i	$0.0957616\pi$
$938$	−29.2953	+	10.7964i	−0.956525	+	0.352515i
$939$		0			0
$940$	11.5794	−	21.8590i	0.377680	−	0.712961i
$941$	−6.25212	+	3.60966i	−0.203813	+	0.117672i	−0.598433	−	0.801173i	$-0.704210\pi$
$941$	−6.25212	+	3.60966i	−0.203813	+	0.117672i	0.394620	+	0.918845i	$0.370876\pi$
$942$		0			0
$943$	−0.556900	+	0.149221i	−0.0181352	+	0.00485930i
$944$	−4.24969			−0.138316
$945$		0			0
$946$	−12.7284			−0.413837
$947$	35.3046	−	9.45984i	1.14725	−	0.307403i	0.365384	−	0.930857i	$-0.380938\pi$
$947$	35.3046	−	9.45984i	1.14725	−	0.307403i	0.781861	+	0.623453i	$0.214271\pi$
$948$		0			0
$949$	2.87802	−	1.66162i	0.0934244	−	0.0539386i
$950$	−17.8299	−	3.40879i	−0.578477	−	0.110596i
$951$		0			0
$952$	−2.43126	+	14.1206i	−0.0787976	+	0.457651i
$953$	22.4458	−	22.4458i	0.727090	−	0.727090i	−0.242949	−	0.970039i	$-0.578115\pi$
$953$	22.4458	−	22.4458i	0.727090	−	0.727090i	0.970039	+	0.242949i	$0.0781147\pi$
$954$		0			0
$955$	−48.5447	−	11.1287i	−1.57087	−	0.360115i
$956$	−12.2914			−0.397532
$957$		0			0
$958$	10.5337	−	2.82249i	0.340328	−	0.0911906i
$959$	20.7738	−	45.0220i	0.670821	−	1.45384i
$960$		0			0
$961$	−7.31810	+	12.6753i	−0.236068	+	0.408881i
$962$	0.617292	+	2.30377i	0.0199023	+	0.0742764i
$963$		0			0
$964$	−10.9397	−	18.9481i	−0.352344	−	0.610278i
$965$	−0.771600	−	21.1608i	−0.0248387	−	0.681190i
$966$		0			0
$967$	−54.9695	+	14.7290i	−1.76770	+	0.473654i	−0.988255	−	0.152816i	$-0.951166\pi$
$967$	−54.9695	+	14.7290i	−1.76770	+	0.473654i	−0.779446	+	0.626470i	$0.784499\pi$
$968$	−14.0595	+	14.0595i	−0.451890	+	0.451890i
$969$		0			0
$970$	−3.44677	−	11.2120i	−0.110669	−	0.359997i
$971$	−16.7190	+	9.65271i	−0.536538	+	0.309770i	−0.743675	−	0.668542i	$-0.766919\pi$
$971$	−16.7190	+	9.65271i	−0.536538	+	0.309770i	0.207137	+	0.978312i	$0.433585\pi$
$972$		0			0
$973$	−6.25854	−	1.07758i	−0.200640	−	0.0345458i
$974$	−0.583358	+	0.336802i	−0.0186920	+	0.0107918i
$975$		0			0
$976$	−2.32793	+	1.34403i	−0.0745151	+	0.0430213i
$977$	4.87607	−	18.1977i	0.155999	−	0.582198i	−0.843018	−	0.537885i	$-0.819224\pi$
$977$	4.87607	−	18.1977i	0.155999	−	0.582198i	0.999018	−	0.0443127i	$-0.0141098\pi$
$978$		0			0
$979$	−1.64236	−	2.84465i	−0.0524900	−	0.0909153i
$980$	−21.2783	−	0.910541i	−0.679710	−	0.0290862i
$981$		0			0
$982$	−5.09528	+	19.0158i	−0.162597	+	0.606820i
$983$	−28.0864	−	28.0864i	−0.895818	−	0.895818i	0.0992448	−	0.995063i	$-0.468357\pi$
$983$	−28.0864	−	28.0864i	−0.895818	−	0.895818i	−0.995063	+	0.0992448i	$0.968357\pi$
$984$		0			0
$985$	−5.15753	+	9.73607i	−0.164333	+	0.310217i
$986$	−3.64037	−	2.10177i	−0.115933	−	0.0669340i
$987$		0			0
$988$	2.12270	+	0.568775i	0.0675319	+	0.0180951i
$989$	9.78268	−	5.64803i	0.311071	−	0.179597i
$990$		0			0
$991$	23.0121	−	39.8581i	0.731003	−	1.26613i	−0.225452	−	0.974254i	$-0.572386\pi$
$991$	23.0121	−	39.8581i	0.731003	−	1.26613i	0.956455	−	0.291880i	$-0.0942809\pi$
$992$	6.10622	+	22.7887i	0.193873	+	0.723543i
$993$		0			0
$994$	−3.93089	−	5.56606i	−0.124680	−	0.176545i
$995$	−1.01248	−	0.232107i	−0.0320979	−	0.00735830i
$996$		0			0
$997$	−13.7662	+	13.7662i	−0.435981	+	0.435981i	−0.890657	−	0.454676i	$-0.849755\pi$
$997$	−13.7662	+	13.7662i	−0.435981	+	0.435981i	0.454676	+	0.890657i	$0.349755\pi$
$998$	−1.52837	−	5.70394i	−0.0483796	−	0.180555i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cj.e.577.16		160
3.2	odd	2		315.2.cg.e.157.25	yes	160
5.3	odd	4	inner	945.2.cj.e.388.25		160
7.5	odd	6		945.2.bv.e.712.25		160
9.2	odd	6		315.2.bs.e.52.16	✓	160
9.7	even	3		945.2.bv.e.262.25		160
15.8	even	4		315.2.cg.e.283.16	yes	160
21.5	even	6		315.2.bs.e.292.16	yes	160
35.33	even	12		945.2.bv.e.523.25		160
45.38	even	12		315.2.bs.e.178.16	yes	160
45.43	odd	12		945.2.bv.e.73.25		160
63.47	even	6		315.2.cg.e.187.16	yes	160
63.61	odd	6	inner	945.2.cj.e.397.25		160
105.68	odd	12		315.2.bs.e.103.16	yes	160
315.173	odd	12		315.2.cg.e.313.25	yes	160
315.313	even	12	inner	945.2.cj.e.208.16		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.16	✓	160	9.2	odd	6
315.2.bs.e.103.16	yes	160	105.68	odd	12
315.2.bs.e.178.16	yes	160	45.38	even	12
315.2.bs.e.292.16	yes	160	21.5	even	6
315.2.cg.e.157.25	yes	160	3.2	odd	2
315.2.cg.e.187.16	yes	160	63.47	even	6
315.2.cg.e.283.16	yes	160	15.8	even	4
315.2.cg.e.313.25	yes	160	315.173	odd	12
945.2.bv.e.73.25		160	45.43	odd	12
945.2.bv.e.262.25		160	9.7	even	3
945.2.bv.e.523.25		160	35.33	even	12
945.2.bv.e.712.25		160	7.5	odd	6
945.2.cj.e.208.16		160	315.313	even	12	inner
945.2.cj.e.388.25		160	5.3	odd	4	inner
945.2.cj.e.397.25		160	63.61	odd	6	inner
945.2.cj.e.577.16		160	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cj (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.772339 + 0.206948i) q^{2} +(-1.17837 + 0.680332i) q^{4} +(-0.657057 - 2.13735i) q^{5} +(0.914904 + 2.48253i) q^{7} +(1.90009 - 1.90009i) q^{8} +O(q^{10})\)	\(q+(-0.772339 + 0.206948i) q^{2} +(-1.17837 + 0.680332i) q^{4} +(-0.657057 - 2.13735i) q^{5} +(0.914904 + 2.48253i) q^{7} +(1.90009 - 1.90009i) q^{8} +(0.949791 + 1.51478i) q^{10} -1.89753 q^{11} +(0.343579 - 0.0920618i) q^{13} +(-1.22037 - 1.72802i) q^{14} +(0.286369 - 0.496007i) q^{16} +(0.521621 + 1.94672i) q^{17} +(-2.27028 - 3.93224i) q^{19} +(2.22837 + 2.07158i) q^{20} +(1.46554 - 0.392689i) q^{22} +(-0.952115 + 0.952115i) q^{23} +(-4.13655 + 2.80873i) q^{25} +(-0.246308 + 0.142206i) q^{26} +(-2.76704 - 2.30290i) q^{28} +(2.25903 - 1.30425i) q^{29} +(3.50326 - 2.02261i) q^{31} +(-1.50949 + 5.63349i) q^{32} +(-0.805736 - 1.39558i) q^{34} +(4.70490 - 3.58664i) q^{35} +(2.17042 - 8.10011i) q^{37} +(2.56719 + 2.56719i) q^{38} +(-5.30963 - 2.81270i) q^{40} +(0.370817 + 0.214091i) q^{41} +(-8.10338 - 2.17129i) q^{43} +(2.23599 - 1.29095i) q^{44} +(0.538318 - 0.932394i) q^{46} +(-2.10426 - 7.85320i) q^{47} +(-5.32590 + 4.54255i) q^{49} +(2.61356 - 3.02534i) q^{50} +(-0.342231 + 0.342231i) q^{52} +(-2.26746 - 8.46228i) q^{53} +(1.24678 + 4.05569i) q^{55} +(6.45543 + 2.97863i) q^{56} +(-1.47483 + 1.47483i) q^{58} +(-3.70997 - 6.42586i) q^{59} +(-4.06455 - 2.34667i) q^{61} +(-2.28713 + 2.28713i) q^{62} -3.51788i q^{64} +(-0.422520 - 0.673860i) q^{65} +(3.81975 - 14.2555i) q^{67} +(-1.93908 - 1.93908i) q^{68} +(-2.89153 + 3.74377i) q^{70} +3.22107 q^{71} +(9.02450 - 2.41811i) q^{73} +6.70519i q^{74} +(5.35046 + 3.08909i) q^{76} +(-1.73606 - 4.71067i) q^{77} +(-8.77792 - 5.06793i) q^{79} +(-1.24830 - 0.286168i) q^{80} +(-0.330702 - 0.0886114i) q^{82} +(4.50725 - 16.8213i) q^{83} +(3.81808 - 2.39399i) q^{85} +6.70790 q^{86} +(-3.60548 + 3.60548i) q^{88} +(0.865525 + 1.49913i) q^{89} +(0.542888 + 0.768718i) q^{91} +(0.474189 - 1.76970i) q^{92} +(3.25040 + 5.62987i) q^{94} +(-6.91288 + 7.43610i) q^{95} +(-6.33706 - 1.69801i) q^{97} +(3.17333 - 4.61057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) \) 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8} - 24 q^{10} - 32 q^{11} + 76 q^{16} + 6 q^{17} + 60 q^{20} + 8 q^{22} + 16 q^{23} - 4 q^{25} + 36 q^{26} + 22 q^{28} + 48 q^{31} + 6 q^{32} + 36 q^{35} - 4 q^{37} - 12 q^{41} - 4 q^{43} - 16 q^{46} + 54 q^{47} + 44 q^{50} - 8 q^{53} + 92 q^{56} - 56 q^{58} - 24 q^{61} - 62 q^{65} + 12 q^{67} + 2 q^{70} + 40 q^{71} + 36 q^{73} - 96 q^{76} + 110 q^{77} - 36 q^{80} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 32 q^{86} - 92 q^{88} - 48 q^{91} + 26 q^{92} + 94 q^{95} - 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8 - 24 * q^10 - 32 * q^11 + 76 * q^16 + 6 * q^17 + 60 * q^20 + 8 * q^22 + 16 * q^23 - 4 * q^25 + 36 * q^26 + 22 * q^28 + 48 * q^31 + 6 * q^32 + 36 * q^35 - 4 * q^37 - 12 * q^41 - 4 * q^43 - 16 * q^46 + 54 * q^47 + 44 * q^50 - 8 * q^53 + 92 * q^56 - 56 * q^58 - 24 * q^61 - 62 * q^65 + 12 * q^67 + 2 * q^70 + 40 * q^71 + 36 * q^73 - 96 * q^76 + 110 * q^77 - 36 * q^80 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 32 * q^86 - 92 * q^88 - 48 * q^91 + 26 * q^92 + 94 * q^95 - 48 * q^97 - 102 * q^98

Introduction

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