LMFDB - Embedded newform 945.2.cj.e.208.13

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			208.13
Character	$\chi$	$=$	945.208
Dual form			945.2.cj.e.577.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.943703 - 0.252864i) q^{2} +(-0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.85665 + 1.88490i) q^{7} +(2.10394 + 2.10394i) q^{8} +O(q^{10})$	\(q+(-0.943703 - 0.252864i) q^{2} +(-0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.85665 + 1.88490i) q^{7} +(2.10394 + 2.10394i) q^{8} +(-0.286383 + 2.16577i) q^{10} +1.63342 q^{11} +(0.513429 + 0.137573i) q^{13} +(2.22875 - 1.30930i) q^{14} +(-0.407995 - 0.706668i) q^{16} +(-0.265268 + 0.989992i) q^{17} +(-2.99374 + 5.18531i) q^{19} +(-0.895857 + 2.15931i) q^{20} +(-1.54146 - 0.413034i) q^{22} +(-5.24887 - 5.24887i) q^{23} +(-4.83110 + 1.28860i) q^{25} +(-0.449737 - 0.259656i) q^{26} +(2.66636 - 0.736068i) q^{28} +(5.82340 + 3.36214i) q^{29} +(7.23702 + 4.17830i) q^{31} +(-1.33385 - 4.97801i) q^{32} +(0.500668 - 0.867182i) q^{34} +(4.71857 + 3.56863i) q^{35} +(1.47305 + 5.49748i) q^{37} +(4.13638 - 4.13638i) q^{38} +(4.05324 - 5.27606i) q^{40} +(6.13816 - 3.54387i) q^{41} +(7.41230 - 1.98612i) q^{43} +(-1.47893 - 0.853858i) q^{44} +(3.62612 + 6.28062i) q^{46} +(-0.511176 + 1.90773i) q^{47} +(-0.105686 - 6.99920i) q^{49} +(4.88496 + 0.00555968i) q^{50} +(-0.392952 - 0.392952i) q^{52} +(-0.361997 + 1.35099i) q^{53} +(-0.474678 - 3.62146i) q^{55} +(-7.87199 + 0.0594290i) q^{56} +(-4.64539 - 4.64539i) q^{58} +(-0.552610 + 0.957148i) q^{59} +(11.8958 - 6.86804i) q^{61} +(-5.77305 - 5.77305i) q^{62} +6.66703i q^{64} +(0.155809 - 1.17830i) q^{65} +(1.44675 + 5.39935i) q^{67} +(0.757689 - 0.757689i) q^{68} +(-3.55054 - 4.56088i) q^{70} +6.35753 q^{71} +(6.07255 + 1.62714i) q^{73} -5.56047i q^{74} +(5.42116 - 3.12991i) q^{76} +(-3.03269 + 3.07883i) q^{77} +(-5.83478 + 3.36871i) q^{79} +(-1.44819 + 1.10993i) q^{80} +(-6.68871 + 1.79224i) q^{82} +(1.01416 + 3.78491i) q^{83} +(2.27200 + 0.300430i) q^{85} -7.49722 q^{86} +(3.43661 + 3.43661i) q^{88} +(9.04644 - 15.6689i) q^{89} +(-1.21257 + 0.712336i) q^{91} +(2.00861 + 7.49622i) q^{92} +(0.964796 - 1.67108i) q^{94} +(12.3664 + 5.13056i) q^{95} +(-0.148983 + 0.0399199i) q^{97} +(-1.67011 + 6.63189i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.943703	−	0.252864i	−0.667298	−	0.178802i	−0.0907609	−	0.995873i	$-0.528930\pi$
$2$	−0.943703	−	0.252864i	−0.667298	−	0.178802i	−0.576538	+	0.817071i	$0.695597\pi$
$3$		0			0
$3$		0			0
$4$	−0.905417	−	0.522743i	−0.452708	−	0.261371i
$5$	−0.290604	−	2.21710i	−0.129962	−	0.991519i
$5$	−0.290604	−	2.21710i	−0.129962	−	0.991519i
$6$		0			0
$7$	−1.85665	+	1.88490i	−0.701749	+	0.712425i
$7$	−1.85665	+	1.88490i	−0.701749	+	0.712425i
$8$	2.10394	+	2.10394i	0.743854	+	0.743854i
$9$		0			0
$10$	−0.286383	+	2.16577i	−0.0905622	+	0.684877i
$11$	1.63342			0.492495			0.246247	−	0.969207i	$-0.420802\pi$
$11$	1.63342			0.492495			0.246247	+	0.969207i	$0.420802\pi$
$12$		0			0
$13$	0.513429	+	0.137573i	0.142400	+	0.0381558i	0.329315	−	0.944220i	$-0.393182\pi$
$13$	0.513429	+	0.137573i	0.142400	+	0.0381558i	−0.186915	+	0.982376i	$0.559849\pi$
$14$	2.22875	−	1.30930i	0.595659	−	0.349926i
$15$		0			0
$16$	−0.407995	−	0.706668i	−0.101999	−	0.176667i
$17$	−0.265268	+	0.989992i	−0.0643369	+	0.240108i	−0.990604	−	0.136758i	$-0.956332\pi$
$17$	−0.265268	+	0.989992i	−0.0643369	+	0.240108i	0.926268	+	0.376866i	$0.122998\pi$
$18$		0			0
$19$	−2.99374	+	5.18531i	−0.686811	+	1.18959i	0.286053	+	0.958214i	$0.407657\pi$
$19$	−2.99374	+	5.18531i	−0.686811	+	1.18959i	−0.972864	+	0.231377i	$0.925677\pi$
$20$	−0.895857	+	2.15931i	−0.200320	+	0.482837i
$21$		0			0
$22$	−1.54146	−	0.413034i	−0.328641	−	0.0880591i
$23$	−5.24887	−	5.24887i	−1.09446	−	1.09446i	−0.995046	−	0.0994192i	$-0.968302\pi$
$23$	−5.24887	−	5.24887i	−1.09446	−	1.09446i	−0.0994192	−	0.995046i	$-0.531698\pi$
$24$		0			0
$25$	−4.83110	+	1.28860i	−0.966220	+	0.257720i
$26$	−0.449737	−	0.259656i	−0.0882006	−	0.0509227i
$27$		0			0
$28$	2.66636	−	0.736068i	0.503895	−	0.139104i
$29$	5.82340	+	3.36214i	1.08138	+	0.624334i	0.931268	−	0.364335i	$-0.118704\pi$
$29$	5.82340	+	3.36214i	1.08138	+	0.624334i	0.150110	+	0.988669i	$0.452037\pi$
$30$		0			0
$31$	7.23702	+	4.17830i	1.29981	+	0.750444i	0.980371	−	0.197164i	$-0.0631730\pi$
$31$	7.23702	+	4.17830i	1.29981	+	0.750444i	0.319437	+	0.947608i	$0.396506\pi$
$32$	−1.33385	−	4.97801i	−0.235794	−	0.879997i
$33$		0			0
$34$	0.500668	−	0.867182i	0.0858638	−	0.148720i
$35$	4.71857	+	3.56863i	0.797583	+	0.603209i
$36$		0			0
$37$	1.47305	+	5.49748i	0.242167	+	0.903780i	0.974786	+	0.223141i	$0.0716311\pi$
$37$	1.47305	+	5.49748i	0.242167	+	0.903780i	−0.732619	+	0.680639i	$0.761702\pi$
$38$	4.13638	−	4.13638i	0.671009	−	0.671009i
$39$		0			0
$40$	4.05324	−	5.27606i	0.640873	−	0.834218i
$41$	6.13816	−	3.54387i	0.958619	−	0.553459i	0.0628714	−	0.998022i	$-0.479974\pi$
$41$	6.13816	−	3.54387i	0.958619	−	0.553459i	0.895748	+	0.444563i	$0.146641\pi$
$42$		0			0
$43$	7.41230	−	1.98612i	1.13036	−	0.302880i	0.355294	−	0.934755i	$-0.384381\pi$
$43$	7.41230	−	1.98612i	1.13036	−	0.302880i	0.775071	+	0.631874i	$0.217714\pi$
$44$	−1.47893	−	0.853858i	−0.222956	−	0.128724i
$45$		0			0
$46$	3.62612	+	6.28062i	0.534642	+	0.926027i
$47$	−0.511176	+	1.90773i	−0.0745627	+	0.278272i	−0.993134	−	0.116984i	$-0.962677\pi$
$47$	−0.511176	+	1.90773i	−0.0745627	+	0.278272i	0.918571	+	0.395256i	$0.129344\pi$
$48$		0			0
$49$	−0.105686	−	6.99920i	−0.0150980	−	0.999886i
$50$	4.88496	+	0.00555968i	0.690838	+	0.000786257i
$51$		0			0
$52$	−0.392952	−	0.392952i	−0.0544926	−	0.0544926i
$53$	−0.361997	+	1.35099i	−0.0497241	+	0.185573i	−0.986321	−	0.164836i	$-0.947291\pi$
$53$	−0.361997	+	1.35099i	−0.0497241	+	0.185573i	0.936597	+	0.350409i	$0.113957\pi$
$54$		0			0
$55$	−0.474678	−	3.62146i	−0.0640056	−	0.488318i
$56$	−7.87199	+	0.0594290i	−1.05194	+	0.00794154i
$57$		0			0
$58$	−4.64539	−	4.64539i	−0.609970	−	0.609970i
$59$	−0.552610	+	0.957148i	−0.0719437	+	0.124610i	−0.899753	−	0.436399i	$-0.856254\pi$
$59$	−0.552610	+	0.957148i	−0.0719437	+	0.124610i	0.827809	+	0.561009i	$0.189587\pi$
$60$		0			0
$61$	11.8958	−	6.86804i	1.52310	−	0.879363i	0.523474	−	0.852042i	$-0.324636\pi$
$61$	11.8958	−	6.86804i	1.52310	−	0.879363i	0.999627	−	0.0273211i	$-0.00869765\pi$
$62$	−5.77305	−	5.77305i	−0.733178	−	0.733178i
$63$		0			0
$64$			6.66703i			0.833378i
$65$	0.155809	−	1.17830i	0.0193257	−	0.146151i
$66$		0			0
$67$	1.44675	+	5.39935i	0.176749	+	0.659635i	0.996247	+	0.0865538i	$0.0275854\pi$
$67$	1.44675	+	5.39935i	0.176749	+	0.659635i	−0.819498	+	0.573081i	$0.805748\pi$
$68$	0.757689	−	0.757689i	0.0918833	−	0.0918833i
$69$		0			0
$70$	−3.55054	−	4.56088i	−0.424371	−	0.545130i
$71$	6.35753			0.754500			0.377250	−	0.926112i	$-0.376870\pi$
$71$	6.35753			0.754500			0.377250	+	0.926112i	$0.376870\pi$
$72$		0			0
$73$	6.07255	+	1.62714i	0.710739	+	0.190442i	0.596036	−	0.802958i	$-0.296742\pi$
$73$	6.07255	+	1.62714i	0.710739	+	0.190442i	0.114703	+	0.993400i	$0.463408\pi$
$74$		−	5.56047i		−	0.646391i
$75$		0			0
$76$	5.42116	−	3.12991i	0.621850	−	0.359025i
$77$	−3.03269	+	3.07883i	−0.345607	+	0.350865i
$78$		0			0
$79$	−5.83478	+	3.36871i	−0.656465	+	0.379010i	−0.790929	−	0.611908i	$-0.790402\pi$
$79$	−5.83478	+	3.36871i	−0.656465	+	0.379010i	0.134464	+	0.990918i	$0.457069\pi$
$80$	−1.44819	+	1.10993i	−0.161913	+	0.124094i
$81$		0			0
$82$	−6.68871	+	1.79224i	−0.738645	+	0.197919i
$83$	1.01416	+	3.78491i	0.111319	+	0.415448i	0.998985	−	0.0450392i	$-0.0143413\pi$
$83$	1.01416	+	3.78491i	0.111319	+	0.415448i	−0.887666	+	0.460488i	$0.847675\pi$
$84$		0			0
$85$	2.27200	+	0.300430i	0.246433	+	0.0325863i
$86$	−7.49722			−0.808446
$87$		0			0
$88$	3.43661	+	3.43661i	0.366344	+	0.366344i
$89$	9.04644	−	15.6689i	0.958921	−	1.66090i	0.233793	−	0.972286i	$-0.424886\pi$
$89$	9.04644	−	15.6689i	0.958921	−	1.66090i	0.725128	−	0.688614i	$-0.241780\pi$
$90$		0			0
$91$	−1.21257	+	0.712336i	−0.127112	+	0.0746731i
$92$	2.00861	+	7.49622i	0.209412	+	0.781535i
$93$		0			0
$94$	0.964796	−	1.67108i	0.0995111	−	0.172358i
$95$	12.3664	+	5.13056i	1.26876	+	0.526384i
$96$		0			0
$97$	−0.148983	+	0.0399199i	−0.0151270	+	0.00405325i	−0.266375	−	0.963870i	$-0.585826\pi$
$97$	−0.148983	+	0.0399199i	−0.0151270	+	0.00405325i	0.251248	+	0.967923i	$0.419159\pi$
$98$	−1.67011	+	6.63189i	−0.168707	+	0.669922i
$99$		0			0
$100$	5.04776	+	1.35870i	0.504776	+	0.135870i
$101$			8.14296i			0.810255i	0.914260	+	0.405127i	$0.132773\pi$
$101$			8.14296i			0.810255i	−0.914260	+	0.405127i	$0.867227\pi$
$102$		0			0
$103$	−7.26124	+	7.26124i	−0.715471	+	0.715471i	−0.967674	−	0.252203i	$-0.918845\pi$
$103$	−7.26124	+	7.26124i	−0.715471	+	0.715471i	0.252203	+	0.967674i	$0.418845\pi$
$104$	0.790777	+	1.36967i	0.0775421	+	0.134307i
$105$		0			0
$106$	0.683235	−	1.18340i	0.0663616	−	0.114942i
$107$	0.329306	+	1.22899i	0.0318352	+	0.118811i	0.980015	−	0.198924i	$-0.0637446\pi$
$107$	0.329306	+	1.22899i	0.0318352	+	0.118811i	−0.948180	+	0.317734i	$0.897078\pi$
$108$		0			0
$109$	10.0397	−	5.79643i	0.961630	−	0.555197i	0.0649556	−	0.997888i	$-0.479309\pi$
$109$	10.0397	−	5.79643i	0.961630	−	0.555197i	0.896674	+	0.442691i	$0.145976\pi$
$110$	−0.467784	+	3.53761i	−0.0446014	+	0.337298i
$111$		0			0
$112$	2.08950	+	0.543008i	0.197440	+	0.0513094i
$113$	−5.38592	+	20.1005i	−0.506664	+	1.89090i	−0.0554944	+	0.998459i	$0.517673\pi$
$113$	−5.38592	+	20.1005i	−0.506664	+	1.89090i	−0.451170	+	0.892438i	$0.648993\pi$
$114$		0			0
$115$	−10.1119	+	13.1626i	−0.942944	+	1.22742i
$116$	−3.51507	−	6.08828i	−0.326366	−	0.565282i
$117$		0			0
$118$	0.763528	−	0.763528i	0.0702884	−	0.0702884i
$119$	−1.37353	−	2.33807i	−0.125911	−	0.214331i
$120$		0			0
$121$	−8.33194			−0.757449
$122$	−12.9628	+	3.47337i	−1.17359	+	0.314464i
$123$		0			0
$124$	−4.36835	−	7.56620i	−0.392289	−	0.679465i
$125$	4.26089	+	10.3366i	0.381106	+	0.924531i
$126$		0			0
$127$	−1.86063	+	1.86063i	−0.165104	+	0.165104i	−0.784824	−	0.619719i	$-0.787246\pi$
$127$	−1.86063	+	1.86063i	−0.165104	+	0.165104i	0.619719	+	0.784824i	$0.287246\pi$
$128$	−0.981855	+	3.66433i	−0.0867846	+	0.323884i
$129$		0			0
$130$	−0.444988	+	1.07257i	−0.0390281	+	0.0940706i
$131$		−	2.10752i		−	0.184135i	−0.995753	−	0.0920674i	$-0.970652\pi$
$131$		−	2.10752i		−	0.184135i	0.995753	−	0.0920674i	$-0.0293475\pi$
$132$		0			0
$133$	−4.21545	−	15.2702i	−0.365526	−	1.32409i
$134$		−	5.46121i		−	0.471777i
$135$		0			0
$136$	−2.64099	+	1.52478i	−0.226463	+	0.130748i
$137$	9.56652	−	9.56652i	0.817323	−	0.817323i	−0.168396	−	0.985719i	$-0.553859\pi$
$137$	9.56652	−	9.56652i	0.817323	−	0.817323i	0.985719	+	0.168396i	$0.0538589\pi$
$138$		0			0
$139$	6.44269	+	11.1591i	0.546461	+	0.946499i	0.998513	+	0.0545074i	$0.0173588\pi$
$139$	6.44269	+	11.1591i	0.546461	+	0.946499i	−0.452052	+	0.891992i	$0.649308\pi$
$140$	−2.40679	−	5.69769i	−0.203411	−	0.481543i
$141$		0			0
$142$	−5.99961	−	1.60759i	−0.503476	−	0.134906i
$143$	0.838645	+	0.224714i	0.0701310	+	0.0187915i
$144$		0			0
$145$	5.76191	−	13.8881i	0.478501	−	1.15335i
$146$	−5.31924	−	3.07106i	−0.440223	−	0.254163i
$147$		0			0
$148$	1.54005	−	5.74753i	0.126591	−	0.472444i
$149$		−	3.66315i		−	0.300097i	−0.988679	−	0.150049i	$-0.952057\pi$
$149$		−	3.66315i		−	0.300097i	0.988679	−	0.150049i	$-0.0479430\pi$
$150$		0			0
$151$	1.99730			0.162538			0.0812691	−	0.996692i	$-0.474103\pi$
$151$	1.99730			0.162538			0.0812691	+	0.996692i	$0.474103\pi$
$152$	−17.2082	+	4.61092i	−1.39577	+	0.373995i
$153$		0			0
$154$	3.64049	−	2.13864i	0.293359	−	0.172337i
$155$	7.16061	−	17.2595i	0.575154	−	1.38631i
$156$		0			0
$157$	8.16051	−	2.18660i	0.651280	−	0.174510i	0.0819723	−	0.996635i	$-0.473878\pi$
$157$	8.16051	−	2.18660i	0.651280	−	0.174510i	0.569307	+	0.822125i	$0.307211\pi$
$158$	6.35813	−	1.70366i	0.505826	−	0.135536i
$159$		0			0
$160$	−10.6491	+	4.40392i	−0.841889	+	0.348161i
$161$	19.6389	−	0.148263i	1.54776	−	0.0116847i
$162$		0			0
$163$	−2.14187	+	0.573913i	−0.167764	+	0.0449523i	−0.341723	−	0.939801i	$-0.611011\pi$
$163$	−2.14187	+	0.573913i	−0.167764	+	0.0449523i	0.173959	+	0.984753i	$0.444344\pi$
$164$	−7.41012			−0.578633
$165$		0			0
$166$		−	3.82828i		−	0.297132i
$167$	0.351833	−	1.31306i	0.0272256	−	0.101607i	−0.950976	−	0.309265i	$-0.899917\pi$
$167$	0.351833	−	1.31306i	0.0272256	−	0.101607i	0.978202	+	0.207657i	$0.0665838\pi$
$168$		0			0
$169$	−11.0136	−	6.35873i	−0.847204	−	0.489133i
$170$	−2.06813	−	0.858026i	−0.158618	−	0.0658076i
$171$		0			0
$172$	−7.74945	−	2.07646i	−0.590890	−	0.158328i
$173$	1.98087	+	0.530773i	0.150603	+	0.0403539i	0.333333	−	0.942809i	$-0.391827\pi$
$173$	1.98087	+	0.530773i	0.150603	+	0.0403539i	−0.182730	+	0.983163i	$0.558493\pi$
$174$		0			0
$175$	6.54079	−	11.4986i	0.494438	−	0.869213i
$176$	−0.666427	−	1.15429i	−0.0502339	−	0.0870076i
$177$		0			0
$178$	−12.4993	+	12.4993i	−0.936859	+	0.936859i
$179$	−14.6028	+	8.43092i	−1.09146	+	0.630157i	−0.933966	−	0.357362i	$-0.883676\pi$
$179$	−14.6028	+	8.43092i	−1.09146	+	0.630157i	−0.157498	+	0.987519i	$0.550343\pi$
$180$		0			0
$181$			20.3678i			1.51392i	0.653459	+	0.756962i	$0.273317\pi$
$181$			20.3678i			1.51392i	−0.653459	+	0.756962i	$0.726683\pi$
$182$	1.32443	−	0.365618i	0.0981732	−	0.0271014i
$183$		0			0
$184$		−	22.0866i		−	1.62824i
$185$	11.7604	−	4.86348i	0.864643	−	0.357570i
$186$		0			0
$187$	−0.433294	+	1.61707i	−0.0316856	+	0.118252i
$188$	1.46008	−	1.46008i	0.106487	−	0.106487i
$189$		0			0
$190$	−10.3728	−	7.96873i	−0.752524	−	0.578113i
$191$	8.61703	+	14.9251i	0.623506	+	1.07994i	0.988828	+	0.149063i	$0.0476257\pi$
$191$	8.61703	+	14.9251i	0.623506	+	1.07994i	−0.365322	+	0.930881i	$0.619041\pi$
$192$		0			0
$193$	−10.4483	+	2.79962i	−0.752088	+	0.201521i	−0.614444	−	0.788960i	$-0.710620\pi$
$193$	−10.4483	+	2.79962i	−0.752088	+	0.201521i	−0.137644	+	0.990482i	$0.543953\pi$
$194$	0.150690			0.0108189
$195$		0			0
$196$	−3.56309	+	6.39244i	−0.254507	+	0.456603i
$197$	−4.66542	+	4.66542i	−0.332398	+	0.332398i	−0.853496	−	0.521099i	$-0.825522\pi$
$197$	−4.66542	+	4.66542i	−0.332398	+	0.332398i	0.521099	+	0.853496i	$0.325522\pi$
$198$		0			0
$199$	−2.58318	−	4.47420i	−0.183117	−	0.317168i	0.759823	−	0.650130i	$-0.225285\pi$
$199$	−2.58318	−	4.47420i	−0.183117	−	0.317168i	−0.942940	+	0.332962i	$0.891952\pi$
$200$	−12.8755	−	7.45320i	−0.910432	−	0.527021i
$201$		0			0
$202$	2.05906	−	7.68453i	0.144875	−	0.540682i
$203$	−17.1493	+	4.73419i	−1.20365	+	0.332275i
$204$		0			0
$205$	−9.64089	−	12.5791i	−0.673349	−	0.878560i
$206$	8.68856	−	5.01634i	0.605360	−	0.349505i
$207$		0			0
$208$	−0.112258	−	0.418953i	−0.00778370	−	0.0290492i
$209$	−4.89003	+	8.46978i	−0.338251	+	0.585867i
$210$		0			0
$211$	0.273339	+	0.473437i	0.0188174	+	0.0325927i	0.875281	−	0.483615i	$-0.160677\pi$
$211$	0.273339	+	0.473437i	0.0188174	+	0.0325927i	−0.856463	+	0.516208i	$0.827343\pi$
$212$	1.03398	−	1.03398i	0.0710139	−	0.0710139i
$213$		0			0
$214$		−	1.24307i		−	0.0849744i
$215$	−6.55747	−	15.8567i	−0.447216	−	1.08141i
$216$		0			0
$217$	−21.3123	+	5.88341i	−1.44677	+	0.399392i
$218$	−10.9402	+	2.93142i	−0.740965	+	0.198541i
$219$		0			0
$220$	−1.46331	+	3.52707i	−0.0986564	+	0.237795i
$221$	−0.272392	+	0.471797i	−0.0183231	+	0.0317365i
$222$		0			0
$223$	6.86061	+	25.6042i	0.459421	+	1.71458i	0.674756	+	0.738041i	$0.264249\pi$
$223$	6.86061	+	25.6042i	0.459421	+	1.71458i	−0.215335	+	0.976540i	$0.569084\pi$
$224$	11.8596	+	6.72826i	0.792400	+	0.449551i
$225$		0			0
$226$	10.1654	−	17.6070i	0.676193	−	1.17120i
$227$	−12.0327	−	12.0327i	−0.798640	−	0.798640i	0.184241	−	0.982881i	$-0.441017\pi$
$227$	−12.0327	−	12.0327i	−0.798640	−	0.798640i	−0.982881	+	0.184241i	$0.941017\pi$
$228$		0			0
$229$	13.9913			0.924574			0.462287	−	0.886730i	$-0.347029\pi$
$229$	13.9913			0.924574			0.462287	+	0.886730i	$0.347029\pi$
$230$	12.8710	−	9.86466i	0.848690	−	0.650456i
$231$		0			0
$232$	5.17833	+	19.3258i	0.339974	+	1.26880i
$233$	−11.8929	+	3.18669i	−0.779130	+	0.208767i	−0.626401	−	0.779501i	$-0.715473\pi$
$233$	−11.8929	+	3.18669i	−0.779130	+	0.208767i	−0.152729	+	0.988268i	$0.548806\pi$
$234$		0			0
$235$	4.37819	+	0.578935i	0.285602	+	0.0377656i
$236$	1.00068	−	0.577745i	0.0651390	−	0.0376080i
$237$		0			0
$238$	0.704984	+	2.55376i	0.0456973	+	0.165536i
$239$	−6.57367	+	3.79531i	−0.425215	+	0.245498i	−0.697306	−	0.716773i	$-0.745618\pi$
$239$	−6.57367	+	3.79531i	−0.425215	+	0.245498i	0.272091	+	0.962272i	$0.412285\pi$
$240$		0			0
$241$		−	6.02593i		−	0.388164i	−0.980985	−	0.194082i	$-0.937827\pi$
$241$		−	6.02593i		−	0.388164i	0.980985	−	0.194082i	$-0.0621728\pi$
$242$	7.86287	+	2.10685i	0.505445	+	0.135433i
$243$		0			0
$244$	−14.3609			−0.919361
$245$	−15.4872	+	2.26831i	−0.989444	+	0.144917i
$246$		0			0
$247$	−2.25043	+	2.25043i	−0.143191	+	0.143191i
$248$	6.43537	+	24.0171i	0.408646	+	1.52509i
$249$		0			0
$250$	−1.40726	−	10.8321i	−0.0890031	−	0.685081i
$251$		−	4.81059i		−	0.303642i	−0.988408	−	0.151821i	$-0.951486\pi$
$251$		−	4.81059i		−	0.303642i	0.988408	−	0.151821i	$-0.0485137\pi$
$252$		0			0
$253$	−8.57361	−	8.57361i	−0.539018	−	0.539018i
$254$	2.22637	−	1.28540i	0.139695	−	0.0806529i
$255$		0			0
$256$	8.52019	−	14.7574i	0.532512	−	0.922337i
$257$	−11.5783	−	11.5783i	−0.722235	−	0.722235i	0.246825	−	0.969060i	$-0.420613\pi$
$257$	−11.5783	−	11.5783i	−0.722235	−	0.722235i	−0.969060	+	0.246825i	$0.920613\pi$
$258$		0			0
$259$	−13.0971	−	7.43037i	−0.813816	−	0.461701i
$260$	−0.757022	+	0.985408i	−0.0469485	+	0.0611124i
$261$		0			0
$262$	−0.532917	+	1.98887i	−0.0329237	+	0.122873i
$263$	−5.89707	−	5.89707i	−0.363629	−	0.363629i	0.501518	−	0.865147i	$-0.332775\pi$
$263$	−5.89707	−	5.89707i	−0.363629	−	0.363629i	−0.865147	+	0.501518i	$0.832775\pi$
$264$		0			0
$265$	3.10048	+	0.409982i	0.190461	+	0.0251850i
$266$	0.116839	+	15.4765i	0.00716383	+	0.948923i
$267$		0			0
$268$	1.51256	−	5.64494i	0.0923941	−	0.344819i
$269$	1.86662	+	3.23307i	0.113810	+	0.197124i	0.917303	−	0.398189i	$-0.130361\pi$
$269$	1.86662	+	3.23307i	0.113810	+	0.197124i	−0.803494	+	0.595313i	$0.797028\pi$
$270$		0			0
$271$	5.54325	+	3.20039i	0.336728	+	0.194410i	0.658824	−	0.752297i	$-0.271054\pi$
$271$	5.54325	+	3.20039i	0.336728	+	0.194410i	−0.322096	+	0.946707i	$0.604387\pi$
$272$	0.807824	−	0.216456i	0.0489815	−	0.0131246i
$273$		0			0
$274$	−11.4470	+	6.60892i	−0.691537	+	0.399259i
$275$	−7.89121	+	2.10482i	−0.475858	+	0.126925i
$276$		0			0
$277$	0.406069	−	0.406069i	0.0243983	−	0.0243983i	−0.694802	−	0.719201i	$-0.744508\pi$
$277$	0.406069	−	0.406069i	0.0243983	−	0.0243983i	0.719201	+	0.694802i	$0.244508\pi$
$278$	−3.25825	−	12.1600i	−0.195417	−	0.729306i
$279$		0			0
$280$	2.41939	+	17.4357i	0.144586	+	1.04199i
$281$	−2.21693	+	3.83984i	−0.132251	+	0.229065i	−0.924544	−	0.381075i	$-0.875554\pi$
$281$	−2.21693	+	3.83984i	−0.132251	+	0.229065i	0.792293	+	0.610141i	$0.208887\pi$
$282$		0			0
$283$	1.92756	+	7.19375i	0.114582	+	0.427624i	0.999255	−	0.0385865i	$-0.0122855\pi$
$283$	1.92756	+	7.19375i	0.114582	+	0.427624i	−0.884674	+	0.466211i	$0.845619\pi$
$284$	−5.75621	−	3.32335i	−0.341568	−	0.197205i
$285$		0			0
$286$	−0.734609	−	0.424127i	−0.0434383	−	0.0250791i
$287$	−4.71659	+	18.1495i	−0.278412	+	1.07133i
$288$		0			0
$289$	13.8127	+	7.97477i	0.812513	+	0.469104i
$290$	−8.94935	+	11.6493i	−0.525524	+	0.684069i
$291$		0			0
$292$	−4.64762	−	4.64762i	−0.271981	−	0.271981i
$293$	−18.6047	−	4.98512i	−1.08690	−	0.291234i	−0.329480	−	0.944163i	$-0.606873\pi$
$293$	−18.6047	−	4.98512i	−1.08690	−	0.291234i	−0.757419	+	0.652929i	$0.773540\pi$
$294$		0			0
$295$	2.28269	+	0.947042i	0.132903	+	0.0551389i
$296$	−8.46716	+	14.6656i	−0.492144	+	0.852418i
$297$		0			0
$298$	−0.926280	+	3.45692i	−0.0536580	+	0.200254i
$299$	−1.97282	−	3.41702i	−0.114091	−	0.197611i
$300$		0			0
$301$	−10.0184	+	17.6590i	−0.577452	+	1.01785i
$302$	−1.88486	−	0.505047i	−0.108462	−	0.0290622i
$303$		0			0
$304$	4.88572			0.280215
$305$	−18.6841	−	24.3783i	−1.06985	−	1.39590i
$306$		0			0
$307$	6.54479	+	6.54479i	0.373531	+	0.373531i	0.868761	−	0.495231i	$-0.164916\pi$
$307$	6.54479	+	6.54479i	0.373531	+	0.373531i	−0.495231	+	0.868761i	$0.664916\pi$
$308$	4.35529	−	1.20231i	0.248166	−	0.0685078i
$309$		0			0
$310$	−11.1218	+	14.4771i	−0.631675	+	0.822246i
$311$	21.3328	+	12.3165i	1.20967	+	0.698406i	0.962688	−	0.270613i	$-0.0872265\pi$
$311$	21.3328	+	12.3165i	1.20967	+	0.698406i	0.246986	+	0.969019i	$0.420560\pi$
$312$		0			0
$313$	24.5104	+	6.56755i	1.38541	+	0.371220i	0.873083	−	0.487571i	$-0.162117\pi$
$313$	24.5104	+	6.56755i	1.38541	+	0.371220i	0.512327	+	0.858790i	$0.328784\pi$
$314$	−8.25401			−0.465801
$315$		0			0
$316$	7.04388			0.396249
$317$	−10.2922	−	2.75779i	−0.578069	−	0.154893i	−0.0420744	−	0.999114i	$-0.513397\pi$
$317$	−10.2922	−	2.75779i	−0.578069	−	0.154893i	−0.535995	+	0.844221i	$0.680063\pi$
$318$		0			0
$319$	9.51206	+	5.49179i	0.532573	+	0.307481i
$320$	14.7815	−	1.93746i	0.826311	−	0.108308i
$321$		0			0
$322$	−18.5708	−	4.82606i	−1.03491	−	0.268946i
$323$	−4.33927	−	4.33927i	−0.241444	−	0.241444i
$324$		0			0
$325$	−2.65770	−	0.00302479i	−0.147423	−	0.000167785i
$326$	2.16641			0.119986
$327$		0			0
$328$	20.3704	+	5.45823i	1.12477	+	0.301380i
$329$	−2.64681	−	4.50551i	−0.145923	−	0.248397i
$330$		0			0
$331$	−3.12351	−	5.41009i	−0.171684	−	0.297365i	0.767325	−	0.641259i	$-0.221587\pi$
$331$	−3.12351	−	5.41009i	−0.171684	−	0.297365i	−0.939009	+	0.343893i	$0.888254\pi$
$332$	1.06029	−	3.95707i	0.0581912	−	0.217173i
$333$		0			0
$334$	−0.664051	+	1.15017i	−0.0363352	+	0.0629345i
$335$	11.5505	−	4.77667i	0.631070	−	0.260977i
$336$		0			0
$337$	12.3630	+	3.31266i	0.673457	+	0.180452i	0.579311	−	0.815106i	$-0.303322\pi$
$337$	12.3630	+	3.31266i	0.673457	+	0.180452i	0.0941452	+	0.995558i	$0.469988\pi$
$338$	8.78571	+	8.78571i	0.477880	+	0.477880i
$339$		0			0
$340$	−1.90006	−	1.45969i	−0.103045	−	0.0791627i
$341$	11.8211	+	6.82491i	0.640148	+	0.369590i
$342$		0			0
$343$	13.3890	+	12.7959i	0.722939	+	0.690912i
$344$	19.7737	+	11.4163i	1.06613	+	0.615528i
$345$		0			0
$346$	−1.73514	−	1.00178i	−0.0932817	−	0.0538562i
$347$	3.46816	+	12.9433i	0.186181	+	0.694835i	0.994375	+	0.105919i	$0.0337785\pi$
$347$	3.46816	+	12.9433i	0.186181	+	0.694835i	−0.808194	+	0.588916i	$0.799555\pi$
$348$		0			0
$349$	15.4350	−	26.7341i	0.826215	−	1.43105i	−0.0747724	−	0.997201i	$-0.523823\pi$
$349$	15.4350	−	26.7341i	0.826215	−	1.43105i	0.900987	−	0.433846i	$-0.142844\pi$
$350$	−9.08015	+	9.19733i	−0.485355	+	0.491618i
$351$		0			0
$352$	−2.17874	−	8.13118i	−0.116127	−	0.433394i
$353$	11.6226	−	11.6226i	0.618609	−	0.618609i	−0.326566	−	0.945174i	$-0.605891\pi$
$353$	11.6226	−	11.6226i	0.618609	−	0.618609i	0.945174	+	0.326566i	$0.105891\pi$
$354$		0			0
$355$	−1.84752	−	14.0953i	−0.0980563	−	0.748101i
$356$	−16.3816	+	9.45792i	−0.868223	+	0.501269i
$357$		0			0
$358$	15.9126	−	4.26376i	0.841005	−	0.225347i
$359$	−1.40486	−	0.811094i	−0.0741455	−	0.0428079i	0.462469	−	0.886635i	$-0.346964\pi$
$359$	−1.40486	−	0.811094i	−0.0741455	−	0.0428079i	−0.536614	+	0.843828i	$0.680297\pi$
$360$		0			0
$361$	−8.42494	−	14.5924i	−0.443418	−	0.768022i
$362$	5.15028	−	19.2211i	0.270693	−	1.01024i
$363$		0			0
$364$	1.47025	−	0.0110995i	0.0770620	−	0.000581774i
$365$	1.84282	−	13.9363i	0.0964577	−	0.729461i
$366$		0			0
$367$	−1.71374	−	1.71374i	−0.0894563	−	0.0894563i	0.660963	−	0.750419i	$-0.270148\pi$
$367$	−1.71374	−	1.71374i	−0.0894563	−	0.0894563i	−0.750419	+	0.660963i	$0.770148\pi$
$368$	−1.56770	+	5.85072i	−0.0817218	+	0.304990i
$369$		0			0
$370$	−12.3281	+	1.61589i	−0.640909	+	0.0840063i
$371$	−1.87438	−	3.19065i	−0.0973129	−	0.165650i
$372$		0			0
$373$	−22.6169	−	22.6169i	−1.17106	−	1.17106i	−0.981958	−	0.189099i	$-0.939443\pi$
$373$	−22.6169	−	22.6169i	−1.17106	−	1.17106i	−0.189099	−	0.981958i	$-0.560557\pi$
$374$	0.817800	−	1.41647i	0.0422875	−	0.0732440i
$375$		0			0
$376$	−5.08924	+	2.93827i	−0.262457	+	0.151530i
$377$	2.52736	+	2.52736i	0.130166	+	0.130166i
$378$		0			0
$379$		−	30.9678i		−	1.59071i	−0.606146	−	0.795353i	$-0.707285\pi$
$379$		−	30.9678i		−	1.59071i	0.606146	−	0.795353i	$-0.292715\pi$
$380$	−8.51474	−	11.1097i	−0.436797	−	0.569916i
$381$		0			0
$382$	−4.35788	−	16.2638i	−0.222968	−	0.832129i
$383$	13.3140	−	13.3140i	0.680313	−	0.680313i	−0.279758	−	0.960071i	$-0.590254\pi$
$383$	13.3140	−	13.3140i	0.680313	−	0.680313i	0.960071	+	0.279758i	$0.0902542\pi$
$384$		0			0
$385$	7.70740	+	5.82907i	0.392806	+	0.297077i
$386$	10.5681			0.537900
$387$		0			0
$388$	0.155760	+	0.0417357i	0.00790750	+	0.00211881i
$389$			23.6875i			1.20101i	0.799622	+	0.600503i	$0.205033\pi$
$389$			23.6875i			1.20101i	−0.799622	+	0.600503i	$0.794967\pi$
$390$		0			0
$391$	6.58870	−	3.80399i	0.333205	−	0.192376i
$392$	14.5035	−	14.9482i	0.732539	−	0.755000i
$393$		0			0
$394$	5.58249	−	3.22305i	0.281242	−	0.162375i
$395$	9.16440	+	11.9574i	0.461111	+	0.601640i
$396$		0			0
$397$	−23.2158	+	6.22065i	−1.16517	+	0.312205i	−0.789027	−	0.614358i	$-0.789415\pi$
$397$	−23.2158	+	6.22065i	−1.16517	+	0.312205i	−0.376139	+	0.926563i	$0.622748\pi$
$398$	1.30639	+	4.87551i	0.0654834	+	0.244387i
$399$		0			0
$400$	2.88168	+	2.88824i	0.144084	+	0.144412i
$401$	−34.2145			−1.70859			−0.854295	−	0.519789i	$-0.826011\pi$
$401$	−34.2145			−1.70859			−0.854295	+	0.519789i	$0.826011\pi$
$402$		0			0
$403$	3.14087	+	3.14087i	0.156458	+	0.156458i
$404$	4.25667	−	7.37277i	0.211777	−	0.366809i
$405$		0			0
$406$	17.3810	−	0.131216i	0.862603	−	0.00651216i
$407$	2.40610	+	8.97969i	0.119266	+	0.445107i
$408$		0			0
$409$	−0.0455144	+	0.0788332i	−0.00225054	+	0.00389805i	−0.867148	−	0.498050i	$-0.834050\pi$
$409$	−0.0455144	+	0.0788332i	−0.00225054	+	0.00389805i	0.864898	+	0.501948i	$0.167383\pi$
$410$	5.91734	+	14.3087i	0.292236	+	0.706658i
$411$		0			0
$412$	10.3702	−	2.77869i	0.510903	−	0.136896i
$413$	−0.778123	−	2.81870i	−0.0382889	−	0.138699i
$414$		0			0
$415$	8.09683	−	3.34842i	0.397458	−	0.164367i
$416$		−	2.73936i		−	0.134308i
$417$		0			0
$418$	6.75644	−	6.75644i	0.330468	−	0.330468i
$419$	13.7216	+	23.7665i	0.670343	+	1.16107i	0.977807	+	0.209508i	$0.0671862\pi$
$419$	13.7216	+	23.7665i	0.670343	+	1.16107i	−0.307464	+	0.951560i	$0.599480\pi$
$420$		0			0
$421$	−5.94319	+	10.2939i	−0.289653	+	0.501695i	−0.973727	−	0.227719i	$-0.926873\pi$
$421$	−5.94319	+	10.2939i	−0.289653	+	0.501695i	0.684074	+	0.729413i	$0.260207\pi$
$422$	−0.138235	−	0.515901i	−0.00672919	−	0.0251137i
$423$		0			0
$424$	−3.60402	+	2.08078i	−0.175027	+	0.101052i
$425$	0.00583239	−	5.12457i	0.000282912	−	0.248578i
$426$		0			0
$427$	−9.14079	+	35.1739i	−0.442354	+	1.70219i
$428$	0.344285	−	1.28489i	0.0166416	−	0.0621074i
$429$		0			0
$430$	2.17872	+	16.6221i	0.105067	+	0.801590i
$431$	11.1221	+	19.2640i	0.535732	+	0.927915i	0.999128	+	0.0417634i	$0.0132976\pi$
$431$	11.1221	+	19.2640i	0.535732	+	0.927915i	−0.463396	+	0.886152i	$0.653369\pi$
$432$		0			0
$433$	−5.23695	+	5.23695i	−0.251672	+	0.251672i	−0.821656	−	0.569984i	$-0.806949\pi$
$433$	−5.23695	+	5.23695i	−0.251672	+	0.251672i	0.569984	+	0.821656i	$0.306949\pi$
$434$	21.6002	−	0.163069i	1.03684	−	0.00782756i
$435$		0			0
$436$	−12.1202			−0.580450
$437$	42.9307	−	11.5033i	2.05366	−	0.550275i
$438$		0			0
$439$	9.77505	+	16.9309i	0.466538	+	0.808067i	0.999269	−	0.0382173i	$-0.0121679\pi$
$439$	9.77505	+	16.9309i	0.466538	+	0.808067i	−0.532732	+	0.846284i	$0.678835\pi$
$440$	6.62064	−	8.61802i	0.315626	−	0.410848i
$441$		0			0
$442$	0.376358	−	0.376358i	0.0179015	−	0.0179015i
$443$	9.70060	−	36.2031i	0.460889	−	1.72006i	−0.209281	−	0.977856i	$-0.567112\pi$
$443$	9.70060	−	36.2031i	0.460889	−	1.72006i	0.670170	−	0.742207i	$-0.266221\pi$
$444$		0			0
$445$	−37.3685	−	15.5035i	−1.77144	−	0.734935i
$446$		−	25.8975i		−	1.22628i
$447$		0			0
$448$	−12.5667	−	12.3784i	−0.593719	−	0.584822i
$449$		−	18.6203i		−	0.878748i	−0.898304	−	0.439374i	$-0.855200\pi$
$449$		−	18.6203i		−	0.878748i	0.898304	−	0.439374i	$-0.144800\pi$
$450$		0			0
$451$	10.0262	−	5.78862i	0.472115	−	0.272576i
$452$	15.3839	−	15.3839i	0.723597	−	0.723597i
$453$		0			0
$454$	8.31267	+	14.3980i	0.390133	+	0.675730i
$455$	1.93170	+	2.48138i	0.0905595	+	0.116329i
$456$		0			0
$457$	28.1932	+	7.55435i	1.31882	+	0.353378i	0.848537	−	0.529136i	$-0.177484\pi$
$457$	28.1932	+	7.55435i	1.31882	+	0.353378i	0.470286	+	0.882514i	$0.344151\pi$
$458$	−13.2037	−	3.53791i	−0.616967	−	0.165316i
$459$		0			0
$460$	16.0362	−	6.63172i	0.747691	−	0.309206i
$461$	13.2237	+	7.63473i	0.615891	+	0.355585i	0.775267	−	0.631633i	$-0.217615\pi$
$461$	13.2237	+	7.63473i	0.615891	+	0.355585i	−0.159377	+	0.987218i	$0.550948\pi$
$462$		0			0
$463$	−10.7137	+	39.9841i	−0.497908	+	1.85822i	0.0151842	+	0.999885i	$0.495167\pi$
$463$	−10.7137	+	39.9841i	−0.497908	+	1.85822i	−0.513092	+	0.858333i	$0.671500\pi$
$464$		−	5.48695i		−	0.254725i
$465$		0			0
$466$	12.0292			0.557240
$467$	−17.4657	+	4.67993i	−0.808217	+	0.216561i	−0.639189	−	0.769050i	$-0.720730\pi$
$467$	−17.4657	+	4.67993i	−0.808217	+	0.216561i	−0.169029	+	0.985611i	$0.554063\pi$
$468$		0			0
$469$	−12.8633	−	7.29773i	−0.593973	−	0.336978i
$470$	−3.98532	−	1.65343i	−0.183829	−	0.0762671i
$471$		0			0
$472$	−3.17644	+	0.851123i	−0.146207	+	0.0391761i
$473$	12.1074	−	3.24417i	0.556698	−	0.149167i
$474$		0			0
$475$	7.78127	−	28.9085i	0.357029	−	1.32641i
$476$	0.0214021	+	2.83493i	0.000980965	+	0.129939i
$477$		0			0
$478$	7.16329	−	1.91940i	0.327641	−	0.0877912i
$479$	8.15139			0.372447			0.186223	−	0.982507i	$-0.440375\pi$
$479$	8.15139			0.372447			0.186223	+	0.982507i	$0.440375\pi$
$480$		0			0
$481$			3.02522i			0.137938i
$482$	−1.52374	+	5.68668i	−0.0694045	+	0.259021i
$483$		0			0
$484$	7.54388	+	4.35546i	0.342903	+	0.197975i
$485$	0.131802	+	0.318710i	0.00598481	+	0.0144719i
$486$		0			0
$487$	3.93080	+	1.05326i	0.178122	+	0.0477276i	0.346777	−	0.937947i	$-0.387276\pi$
$487$	3.93080	+	1.05326i	0.178122	+	0.0477276i	−0.168656	+	0.985675i	$0.553943\pi$
$488$	39.4779	+	10.5781i	1.78708	+	0.478847i
$489$		0			0
$490$	15.1889	+	1.77556i	0.686166	+	0.0802116i
$491$	−14.1237	−	24.4629i	−0.637392	−	1.10399i	−0.986003	−	0.166727i	$-0.946680\pi$
$491$	−14.1237	−	24.4629i	−0.637392	−	1.10399i	0.348612	−	0.937267i	$-0.386653\pi$
$492$		0			0
$493$	−4.87325	+	4.87325i	−0.219480	+	0.219480i
$494$	2.69279	−	1.55468i	0.121154	−	0.0699485i
$495$		0			0
$496$		−	6.81890i		−	0.306178i
$497$	−11.8037	+	11.9833i	−0.529469	+	0.537524i
$498$		0			0
$499$			24.7679i			1.10876i	0.832262	+	0.554382i	$0.187045\pi$
$499$			24.7679i			1.10876i	−0.832262	+	0.554382i	$0.812955\pi$
$500$	1.54549	−	11.5863i	0.0691163	−	0.518153i
$501$		0			0
$502$	−1.21643	+	4.53977i	−0.0542918	+	0.202620i
$503$	22.1184	−	22.1184i	0.986211	−	0.986211i	−0.0136949	−	0.999906i	$-0.504359\pi$
$503$	22.1184	−	22.1184i	0.986211	−	0.986211i	0.999906	+	0.0136949i	$0.00435937\pi$
$504$		0			0
$505$	18.0538	−	2.36638i	0.803383	−	0.105302i
$506$	5.92298	+	10.2589i	0.263308	+	0.456064i
$507$		0			0
$508$	2.65728	−	0.712015i	0.117898	−	0.0315906i
$509$	−1.37539			−0.0609630			−0.0304815	−	0.999535i	$-0.509704\pi$
$509$	−1.37539			−0.0609630			−0.0304815	+	0.999535i	$0.509704\pi$
$510$		0			0
$511$	−14.3416	+	8.42512i	−0.634435	+	0.372706i
$512$	−6.40718	+	6.40718i	−0.283160	+	0.283160i
$513$		0			0
$514$	7.99874	+	13.8542i	0.352809	+	0.611084i
$515$	18.2091	+	13.9888i	0.802387	+	0.616419i
$516$		0			0
$517$	−0.834965	+	3.11613i	−0.0367217	+	0.137047i
$518$	10.4809	+	10.3239i	0.460505	+	0.453604i
$519$		0			0
$520$	2.80689	−	2.15127i	0.123090	−	0.0943393i
$521$	22.4862	−	12.9824i	0.985140	−	0.568771i	0.0813222	−	0.996688i	$-0.474086\pi$
$521$	22.4862	−	12.9824i	0.985140	−	0.568771i	0.903818	+	0.427917i	$0.140752\pi$
$522$		0			0
$523$	0.697525	+	2.60320i	0.0305006	+	0.113830i	0.979498	−	0.201454i	$-0.0645668\pi$
$523$	0.697525	+	2.60320i	0.0305006	+	0.113830i	−0.948997	+	0.315284i	$0.897900\pi$
$524$	−1.10169	+	1.90818i	−0.0481276	+	0.0833594i
$525$		0			0
$526$	4.07392	+	7.05624i	0.177631	+	0.307667i
$527$	−6.05623	+	6.05623i	−0.263813	+	0.263813i
$528$		0			0
$529$			32.1013i			1.39571i
$530$	−2.82226	−	1.17090i	−0.122591	−	0.0508607i
$531$		0			0
$532$	−4.16565	+	16.0295i	−0.180604	+	0.694967i
$533$	3.63905	−	0.975080i	0.157625	−	0.0422354i
$534$		0			0
$535$	2.62910	−	1.08725i	0.113666	−	0.0470061i
$536$	−8.31601	+	14.4038i	−0.359197	+	0.622148i
$537$		0			0
$538$	−0.944001	−	3.52306i	−0.0406988	−	0.151890i
$539$	−0.172630	−	11.4326i	−0.00743569	−	0.492439i
$540$		0			0
$541$	−10.0369	+	17.3845i	−0.431522	+	0.747418i	−0.997005	−	0.0773420i	$-0.975357\pi$
$541$	−10.0369	+	17.3845i	−0.431522	+	0.747418i	0.565482	+	0.824760i	$0.308690\pi$
$542$	−4.42191	−	4.42191i	−0.189937	−	0.189937i
$543$		0			0
$544$	5.28202			0.226465
$545$	−15.7689	−	20.5746i	−0.675464	−	0.881320i
$546$		0			0
$547$	−3.88238	−	14.4892i	−0.165999	−	0.619515i	−0.997911	−	0.0646077i	$-0.979420\pi$
$547$	−3.88238	−	14.4892i	−0.165999	−	0.619515i	0.831912	−	0.554907i	$-0.187246\pi$
$548$	−13.6625	+	3.66086i	−0.583634	+	0.156384i
$549$		0			0
$550$	7.97919	+	0.00908129i	0.340234	+	0.000387228i
$551$	−34.8675	+	20.1307i	−1.48540	+	0.857598i
$552$		0			0
$553$	4.48348	−	17.2525i	0.190657	−	0.733651i
$554$	−0.485889	+	0.280528i	−0.0206434	+	0.0119185i
$555$		0			0
$556$		−	13.4715i		−	0.571317i
$557$	−0.236144	−	0.0632745i	−0.0100057	−	0.00268103i	0.253813	−	0.967253i	$-0.418315\pi$
$557$	−0.236144	−	0.0632745i	−0.0100057	−	0.00268103i	−0.263818	+	0.964572i	$0.584982\pi$
$558$		0			0
$559$	4.07892			0.172520
$560$	0.596687	−	4.79045i	0.0252146	−	0.202433i
$561$		0			0
$562$	3.06308	−	3.06308i	0.129208	−	0.129208i
$563$	−0.0203161	−	0.0758206i	−0.000856220	−	0.00319546i	0.965496	−	0.260416i	$-0.0838598\pi$
$563$	−0.0203161	−	0.0758206i	−0.000856220	−	0.00319546i	−0.966353	+	0.257221i	$0.917193\pi$
$564$		0			0
$565$	46.1301	+	6.09985i	1.94071	+	0.256623i
$566$		−	7.27618i		−	0.305840i
$567$		0			0
$568$	13.3758	+	13.3758i	0.561238	+	0.561238i
$569$	12.7781	−	7.37743i	0.535685	−	0.309278i	−0.207643	−	0.978205i	$-0.566579\pi$
$569$	12.7781	−	7.37743i	0.535685	−	0.309278i	0.743328	+	0.668927i	$0.233246\pi$
$570$		0			0
$571$	14.7758	−	25.5924i	0.618347	−	1.07101i	−0.371440	−	0.928457i	$-0.621136\pi$
$571$	14.7758	−	25.5924i	0.618347	−	1.07101i	0.989787	−	0.142552i	$-0.0455308\pi$
$572$	−0.641855	−	0.641855i	−0.0268373	−	0.0268373i
$573$		0			0
$574$	9.04043	−	15.9351i	0.377340	−	0.665118i
$575$	32.1215	+	18.5941i	1.33956	+	0.775429i
$576$		0			0
$577$	−2.16353	+	8.07441i	−0.0900690	+	0.336142i	−0.996226	−	0.0867998i	$-0.972336\pi$
$577$	−2.16353	+	8.07441i	−0.0900690	+	0.336142i	0.906157	+	0.422942i	$0.139003\pi$
$578$	−11.0186	−	11.0186i	−0.458312	−	0.458312i
$579$		0			0
$580$	−12.4769	+	9.56255i	−0.518073	+	0.397063i
$581$	−9.01713	−	5.11567i	−0.374094	−	0.212234i
$582$		0			0
$583$	−0.591293	+	2.20673i	−0.0244888	+	0.0913936i
$584$	9.35288	+	16.1997i	0.387025	+	0.670347i
$585$		0			0
$586$	16.2968	+	9.40894i	0.673213	+	0.388680i
$587$	8.74614	−	2.34352i	0.360992	−	0.0967275i	−0.0737643	−	0.997276i	$-0.523501\pi$
$587$	8.74614	−	2.34352i	0.360992	−	0.0967275i	0.434756	+	0.900548i	$0.356835\pi$
$588$		0			0
$589$	−43.3315	+	25.0175i	−1.78544	+	1.03083i
$590$	−1.91470	−	1.47094i	−0.0788271	−	0.0605575i
$591$		0			0
$592$	3.28390	−	3.28390i	0.134967	−	0.134967i
$593$	7.48847	+	27.9474i	0.307515	+	1.14766i	0.930759	+	0.365633i	$0.119148\pi$
$593$	7.48847	+	27.9474i	0.307515	+	1.14766i	−0.623244	+	0.782027i	$0.714186\pi$
$594$		0			0
$595$	−4.78460	+	3.72470i	−0.196150	+	0.152698i
$596$	−1.91489	+	3.31668i	−0.0784367	+	0.135856i
$597$		0			0
$598$	0.997711	+	3.72351i	0.0407994	+	0.152266i
$599$	8.70341	+	5.02492i	0.355612	+	0.205313i	0.667154	−	0.744920i	$-0.267512\pi$
$599$	8.70341	+	5.02492i	0.355612	+	0.205313i	−0.311542	+	0.950232i	$0.600846\pi$
$600$		0			0
$601$	−27.4153	−	15.8282i	−1.11829	−	0.645647i	−0.177329	−	0.984152i	$-0.556746\pi$
$601$	−27.4153	−	15.8282i	−1.11829	−	0.645647i	−0.940965	+	0.338505i	$0.890079\pi$
$602$	13.9197	−	14.1315i	0.567326	−	0.575957i
$603$		0			0
$604$	−1.80839	−	1.04408i	−0.0735824	−	0.0424828i
$605$	2.42129	+	18.4728i	0.0984396	+	0.751025i
$606$		0			0
$607$	−7.81669	−	7.81669i	−0.317270	−	0.317270i	0.530448	−	0.847718i	$-0.322024\pi$
$607$	−7.81669	−	7.81669i	−0.317270	−	0.317270i	−0.847718	+	0.530448i	$0.822024\pi$
$608$	29.8057	+	7.98642i	1.20878	+	0.323892i
$609$		0			0
$610$	11.4678	+	27.7304i	0.464319	+	1.12277i
$611$	−0.524905	+	0.909162i	−0.0212354	+	0.0367807i
$612$		0			0
$613$	6.18919	−	23.0984i	0.249979	−	0.932934i	−0.720836	−	0.693105i	$-0.756242\pi$
$613$	6.18919	−	23.0984i	0.249979	−	0.932934i	0.970815	−	0.239829i	$-0.0770913\pi$
$614$	−4.52139	−	7.83128i	−0.182468	−	0.316045i
$615$		0			0
$616$	−12.8583	+	0.0970726i	−0.518074	+	0.00391117i
$617$	−6.70895	−	1.79766i	−0.270092	−	0.0723709i	0.121231	−	0.992624i	$-0.461316\pi$
$617$	−6.70895	−	1.79766i	−0.270092	−	0.0723709i	−0.391323	+	0.920253i	$0.627982\pi$
$618$		0			0
$619$	31.3954			1.26189			0.630945	−	0.775828i	$-0.282667\pi$
$619$	31.3954			1.26189			0.630945	+	0.775828i	$0.282667\pi$
$620$	−15.5056	+	11.8838i	−0.622719	+	0.477267i
$621$		0			0
$622$	−17.0174	−	17.0174i	−0.682337	−	0.682337i
$623$	12.7382	+	46.1433i	0.510345	+	1.84869i
$624$		0			0
$625$	21.6790	−	12.4507i	0.867161	−	0.498027i
$626$	−21.4698	−	12.3956i	−0.858107	−	0.495429i
$627$		0			0
$628$	−8.53169	−	2.28606i	−0.340452	−	0.0912237i
$629$	−5.83322			−0.232586
$630$		0			0
$631$	−36.8622			−1.46746			−0.733730	−	0.679441i	$-0.762222\pi$
$631$	−36.8622			−1.46746			−0.733730	+	0.679441i	$0.762222\pi$
$632$	−19.3636	−	5.18846i	−0.770242	−	0.206386i
$633$		0			0
$634$	9.01545	+	5.20507i	0.358049	+	0.206720i
$635$	4.66592	+	3.58451i	0.185161	+	0.142247i
$636$		0			0
$637$	0.908638	−	3.60813i	0.0360015	−	0.142959i
$638$	−7.58787	−	7.58787i	−0.300407	−	0.300407i
$639$		0			0
$640$	8.40954	+	1.11201i	0.332416	+	0.0439559i
$641$	−15.0643			−0.595004			−0.297502	−	0.954721i	$-0.596154\pi$
$641$	−15.0643			−0.595004			−0.297502	+	0.954721i	$0.596154\pi$
$642$		0			0
$643$	17.5568	+	4.70433i	0.692372	+	0.185521i	0.587812	−	0.808998i	$-0.299990\pi$
$643$	17.5568	+	4.70433i	0.692372	+	0.185521i	0.104561	+	0.994518i	$0.466656\pi$
$644$	−17.8589	−	10.1319i	−0.703739	−	0.399251i
$645$		0			0
$646$	2.99774	+	5.19223i	0.117944	+	0.204286i
$647$	1.04775	−	3.91026i	0.0411913	−	0.153728i	−0.942267	−	0.334862i	$-0.891310\pi$
$647$	1.04775	−	3.91026i	0.0411913	−	0.153728i	0.983458	+	0.181134i	$0.0579769\pi$
$648$		0			0
$649$	−0.902644	+	1.56342i	−0.0354319	+	0.0613698i
$650$	2.50731	+	0.674892i	0.0983450	+	0.0264715i
$651$		0			0
$652$	2.23930	+	0.600017i	0.0876976	+	0.0234985i
$653$	−16.3529	−	16.3529i	−0.639940	−	0.639940i	0.310601	−	0.950540i	$-0.399470\pi$
$653$	−16.3529	−	16.3529i	−0.639940	−	0.639940i	−0.950540	+	0.310601i	$0.899470\pi$
$654$		0			0
$655$	−4.67259	+	0.612453i	−0.182573	+	0.0239305i
$656$	−5.00868	−	2.89176i	−0.195556	−	0.112904i
$657$		0			0
$658$	1.35852	+	4.92115i	0.0529605	+	0.191846i
$659$	−38.7647	−	22.3808i	−1.51006	−	0.871834i	−0.999931	−	0.0117356i	$-0.996264\pi$
$659$	−38.7647	−	22.3808i	−1.51006	−	0.871834i	−0.510129	−	0.860098i	$-0.670402\pi$
$660$		0			0
$661$	−15.1919	−	8.77106i	−0.590897	−	0.341155i	0.174555	−	0.984647i	$-0.444151\pi$
$661$	−15.1919	−	8.77106i	−0.590897	−	0.341155i	−0.765452	+	0.643493i	$0.777485\pi$
$662$	1.57965	+	5.89534i	0.0613949	+	0.229129i
$663$		0			0
$664$	−5.82948	+	10.0970i	−0.226228	+	0.391838i
$665$	−32.6306	+	13.7837i	−1.26536	+	0.534508i
$666$		0			0
$667$	−12.9188	−	48.2137i	−0.500219	−	1.86684i
$668$	−1.00495	+	1.00495i	−0.0388825	+	0.0388825i
$669$		0			0
$670$	−12.1081	+	1.58705i	−0.467775	+	0.0613130i
$671$	19.4308	−	11.2184i	0.750119	−	0.433081i
$672$		0			0
$673$	47.8039	−	12.8090i	1.84270	−	0.493751i	0.843637	−	0.536914i	$-0.180410\pi$
$673$	47.8039	−	12.8090i	1.84270	−	0.493751i	0.999068	+	0.0431629i	$0.0137434\pi$
$674$	−10.8294	−	6.25233i	−0.417131	−	0.240831i
$675$		0			0
$676$	6.64796	+	11.5146i	0.255691	+	0.442869i
$677$	−9.69880	+	36.1964i	−0.372755	+	1.39114i	0.483842	+	0.875155i	$0.339241\pi$
$677$	−9.69880	+	36.1964i	−0.372755	+	1.39114i	−0.856597	+	0.515986i	$0.827426\pi$
$678$		0			0
$679$	0.201365	−	0.354936i	0.00772768	−	0.0136212i
$680$	4.14807	+	5.41224i	0.159071	+	0.207550i
$681$		0			0
$682$	−9.42982	−	9.42982i	−0.361086	−	0.361086i
$683$	6.76683	−	25.2542i	0.258926	−	0.966324i	−0.706939	−	0.707275i	$-0.749924\pi$
$683$	6.76683	−	25.2542i	0.258926	−	0.966324i	0.965864	−	0.259049i	$-0.0834090\pi$
$684$		0			0
$685$	−23.9900	−	18.4299i	−0.916612	−	0.704170i
$686$	−9.39962	−	15.4611i	−0.358879	−	0.590308i
$687$		0			0
$688$	−4.42771	−	4.42771i	−0.168805	−	0.168805i
$689$	−0.371719	+	0.643836i	−0.0141614	+	0.0245282i
$690$		0			0
$691$	18.3023	−	10.5668i	0.696251	−	0.401980i	−0.109699	−	0.993965i	$-0.534989\pi$
$691$	18.3023	−	10.5668i	0.696251	−	0.401980i	0.805949	+	0.591984i	$0.201655\pi$
$692$	−1.51606	−	1.51606i	−0.0576318	−	0.0576318i
$693$		0			0
$694$		−	13.0916i		−	0.496952i
$695$	22.8685	−	17.5270i	0.867453	−	0.664836i
$696$		0			0
$697$	1.88015	+	7.01680i	0.0712156	+	0.265780i
$698$	−21.3261	+	21.3261i	−0.807206	+	0.807206i
$699$		0			0
$700$	−11.9330	+	6.99188i	−0.451023	+	0.264268i
$701$	−17.0822			−0.645186			−0.322593	−	0.946538i	$-0.604554\pi$
$701$	−17.0822			−0.645186			−0.322593	+	0.946538i	$0.604554\pi$
$702$		0			0
$703$	−32.9160	−	8.81983i	−1.24145	−	0.332646i
$704$			10.8901i			0.410434i
$705$		0			0
$706$	−13.9072	+	8.02934i	−0.523405	+	0.302188i
$707$	−15.3487	−	15.1186i	−0.577246	−	0.568595i
$708$		0			0
$709$	−37.8779	+	21.8688i	−1.42254	+	0.821302i	−0.996515	−	0.0834117i	$-0.973418\pi$
$709$	−37.8779	+	21.8688i	−1.42254	+	0.821302i	−0.426021	+	0.904713i	$0.640085\pi$
$710$	−1.82069	+	13.7689i	−0.0683292	+	0.516739i
$711$		0			0
$712$	51.9995	−	13.9332i	1.94877	−	0.522170i
$713$	−16.0548	−	59.9175i	−0.601259	−	2.24393i
$714$		0			0
$715$	0.254501	−	1.92467i	0.00951781	−	0.0719784i
$716$	17.6288			0.658820
$717$		0			0
$718$	1.12067	+	1.12067i	0.0418230	+	0.0418230i
$719$	9.10099	−	15.7634i	0.339410	−	0.587875i	−0.644912	−	0.764257i	$-0.723106\pi$
$719$	9.10099	−	15.7634i	0.339410	−	0.587875i	0.984322	+	0.176382i	$0.0564394\pi$
$720$		0			0
$721$	−0.205105	−	27.1683i	−0.00763851	−	1.01180i
$722$	4.26073	+	15.9013i	0.158568	+	0.591784i
$723$		0			0
$724$	10.6471	−	18.4413i	0.395696	−	0.685366i
$725$	−32.4659	−	8.73882i	−1.20575	−	0.324552i
$726$		0			0
$727$	47.2752	−	12.6674i	1.75334	−	0.469806i	0.768007	−	0.640441i	$-0.221248\pi$
$727$	47.2752	−	12.6674i	1.75334	−	0.469806i	0.985334	+	0.170635i	$0.0545818\pi$
$728$	−4.04988	−	1.05246i	−0.150099	−	0.0390067i
$729$		0			0
$730$	−5.26308	+	12.6858i	−0.194795	+	0.469521i
$731$			7.86497i			0.290896i
$732$		0			0
$733$	−14.0880	+	14.0880i	−0.520350	+	0.520350i	−0.917677	−	0.397327i	$-0.869938\pi$
$733$	−14.0880	+	14.0880i	−0.520350	+	0.520350i	0.397327	+	0.917677i	$0.369938\pi$
$734$	1.18391	+	2.05060i	0.0436991	+	0.0756890i
$735$		0			0
$736$	−19.1277	+	33.1302i	−0.705057	+	1.22119i
$737$	2.36315	+	8.81940i	0.0870478	+	0.324867i
$738$		0			0
$739$	−41.8852	+	24.1825i	−1.54077	+	0.889566i	−0.541984	+	0.840389i	$0.682327\pi$
$739$	−41.8852	+	24.1825i	−1.54077	+	0.889566i	−0.998790	+	0.0491770i	$0.984340\pi$
$740$	−13.1904	−	1.74419i	−0.484890	−	0.0641177i
$741$		0			0
$742$	0.962055	+	3.48498i	0.0353181	+	0.127938i
$743$	−8.51948	+	31.7951i	−0.312549	+	1.16645i	0.613700	+	0.789539i	$0.289680\pi$
$743$	−8.51948	+	31.7951i	−0.312549	+	1.16645i	−0.926250	+	0.376911i	$0.876986\pi$
$744$		0			0
$745$	−8.12159	+	1.06453i	−0.297552	+	0.0390012i
$746$	15.6246	+	27.0626i	0.572057	+	0.990832i
$747$		0			0
$748$	1.23762	−	1.23762i	0.0452520	−	0.0452520i
$749$	−2.92792	−	1.66109i	−0.106984	−	0.0606950i
$750$		0			0
$751$	−13.5203			−0.493364			−0.246682	−	0.969096i	$-0.579340\pi$
$751$	−13.5203			−0.493364			−0.246682	+	0.969096i	$0.579340\pi$
$752$	1.55669	−	0.417115i	0.0567667	−	0.0152106i
$753$		0			0
$754$	−1.74600	−	3.02416i	−0.0635855	−	0.110133i
$755$	−0.580424	−	4.42823i	−0.0211238	−	0.161160i
$756$		0			0
$757$	28.4104	−	28.4104i	1.03260	−	1.03260i	0.0331447	−	0.999451i	$-0.489448\pi$
$757$	28.4104	−	28.4104i	1.03260	−	1.03260i	0.999451	−	0.0331447i	$-0.0105522\pi$
$758$	−7.83064	+	29.2244i	−0.284422	+	1.06148i
$759$		0			0
$760$	15.2237	+	36.8124i	0.552220	+	1.33533i
$761$		−	15.8150i		−	0.573292i	−0.958037	−	0.286646i	$-0.907460\pi$
$761$		−	15.8150i		−	0.573292i	0.958037	−	0.286646i	$-0.0925404\pi$
$762$		0			0
$763$	−7.71457	+	29.6858i	−0.279286	+	1.07470i
$764$		−	18.0179i		−	0.651866i
$765$		0			0
$766$	−15.9311	+	9.19781i	−0.575613	+	0.332330i
$767$	−0.415403	+	0.415403i	−0.0149993	+	0.0149993i
$768$		0			0
$769$	−10.7002	−	18.5333i	−0.385860	−	0.668328i	0.606028	−	0.795443i	$-0.292762\pi$
$769$	−10.7002	−	18.5333i	−0.385860	−	0.668328i	−0.991888	+	0.127115i	$0.959428\pi$
$770$	−5.79953	−	7.44984i	−0.209000	−	0.268474i
$771$		0			0
$772$	10.9236	+	2.92697i	0.393148	+	0.105344i
$773$	−8.90050	−	2.38488i	−0.320129	−	0.0857782i	0.0951763	−	0.995460i	$-0.469659\pi$
$773$	−8.90050	−	2.38488i	−0.320129	−	0.0857782i	−0.415305	+	0.909682i	$0.636325\pi$
$774$		0			0
$775$	−40.3469	−	10.8602i	−1.44930	−	0.390108i
$776$	−0.397440	−	0.229462i	−0.0142673	−	0.00823722i
$777$		0			0
$778$	5.98973	−	22.3540i	0.214742	−	0.801430i
$779$			42.4376i			1.52049i
$780$		0			0
$781$	10.3845			0.371587
$782$	−7.17966	+	1.92378i	−0.256744	+	0.0687944i
$783$		0			0
$784$	−4.90300	+	2.93033i	−0.175107	+	0.104654i
$785$	−7.21940	−	17.4573i	−0.257671	−	0.623077i
$786$		0			0
$787$	−50.1948	+	13.4497i	−1.78925	+	0.479428i	−0.992219	−	0.124509i	$-0.960265\pi$
$787$	−50.1948	+	13.4497i	−1.78925	+	0.479428i	−0.797032	+	0.603937i	$0.793598\pi$
$788$	6.66297	−	1.78534i	0.237358	−	0.0636000i
$789$		0			0
$790$	−5.62488	−	13.6015i	−0.200124	−	0.483921i
$791$	−27.8877	−	47.4716i	−0.991571	−	1.68789i
$792$		0			0
$793$	7.05250	−	1.88971i	0.250442	−	0.0671056i
$794$	23.4818			0.833336
$795$		0			0
$796$			5.40136i			0.191446i
$797$	−1.23676	+	4.61563i	−0.0438081	+	0.163494i	−0.984365	−	0.176143i	$-0.943638\pi$
$797$	−1.23676	+	4.61563i	−0.0438081	+	0.163494i	0.940556	+	0.339638i	$0.110304\pi$
$798$		0			0
$799$	−1.75304	−	1.01212i	−0.0620182	−	0.0358062i
$800$	12.8586	+	22.3305i	0.454621	+	0.789501i
$801$		0			0
$802$	32.2883	+	8.65162i	1.14014	+	0.305499i
$803$	9.91903	+	2.65780i	0.350035	+	0.0937916i
$804$		0			0
$805$	−6.03586	−	43.4984i	−0.212736	−	1.53312i
$806$	−2.16984	−	3.75827i	−0.0764292	−	0.132379i
$807$		0			0
$808$	−17.1323	+	17.1323i	−0.602711	+	0.602711i
$809$	−16.7030	+	9.64348i	−0.587246	+	0.339047i	−0.764008	−	0.645207i	$-0.776771\pi$
$809$	−16.7030	+	9.64348i	−0.587246	+	0.339047i	0.176762	+	0.984254i	$0.443438\pi$
$810$		0			0
$811$			7.57899i			0.266134i	0.991107	+	0.133067i	$0.0424826\pi$
$811$			7.57899i			0.266134i	−0.991107	+	0.133067i	$0.957517\pi$
$812$	18.0020	+	4.67826i	0.631748	+	0.164175i
$813$		0			0
$814$		−	9.08258i		−	0.318344i
$815$	1.89486	+	4.58197i	0.0663741	+	0.160499i
$816$		0			0
$817$	−11.8918	+	44.3810i	−0.416043	+	1.55269i
$818$	0.0628861	−	0.0628861i	0.00219876	−	0.00219876i
$819$		0			0
$820$	2.15341	+	16.4290i	0.0752003	+	0.573726i
$821$	11.4071	+	19.7576i	0.398110	+	0.689547i	0.993493	−	0.113895i	$-0.0363329\pi$
$821$	11.4071	+	19.7576i	0.398110	+	0.689547i	−0.595383	+	0.803442i	$0.703000\pi$
$822$		0			0
$823$	−7.20595	+	1.93083i	−0.251183	+	0.0673044i	−0.382214	−	0.924074i	$-0.624838\pi$
$823$	−7.20595	+	1.93083i	−0.251183	+	0.0673044i	0.131030	+	0.991378i	$0.458172\pi$
$824$	−30.5544			−1.06441
$825$		0			0
$826$	0.0215670	+	2.85678i	0.000750414	+	0.0994000i
$827$	21.2830	−	21.2830i	0.740083	−	0.740083i	−0.232511	−	0.972594i	$-0.574694\pi$
$827$	21.2830	−	21.2830i	0.740083	−	0.740083i	0.972594	+	0.232511i	$0.0746942\pi$
$828$		0			0
$829$	4.24336	+	7.34971i	0.147378	+	0.255266i	0.930258	−	0.366907i	$-0.119583\pi$
$829$	4.24336	+	7.34971i	0.147378	+	0.255266i	−0.782880	+	0.622173i	$0.786250\pi$
$830$	−8.48769	+	1.11251i	−0.294612	+	0.0386159i
$831$		0			0
$832$	−0.917202	+	3.42304i	−0.0317983	+	0.118673i
$833$	6.95719	+	1.75203i	0.241052	+	0.0607044i
$834$		0			0
$835$	−3.01343	−	0.398470i	−0.104284	−	0.0137896i
$836$	8.85503	−	5.11246i	0.306258	−	0.176818i
$837$		0			0
$838$	−6.93939	−	25.8982i	−0.239717	−	0.894637i
$839$	−0.839410	+	1.45390i	−0.0289797	+	0.0501942i	−0.880152	−	0.474693i	$-0.842559\pi$
$839$	−0.839410	+	1.45390i	−0.0289797	+	0.0501942i	0.851172	+	0.524887i	$0.175892\pi$
$840$		0			0
$841$	8.10798	+	14.0434i	0.279586	+	0.484256i
$842$	8.21157	−	8.21157i	0.282989	−	0.282989i
$843$		0			0
$844$		−	0.571544i		−	0.0196733i
$845$	−10.8974	+	26.2663i	−0.374881	+	0.903587i
$846$		0			0
$847$	15.4695	−	15.7049i	0.531539	−	0.539625i
$848$	1.10240	−	0.295386i	0.0378564	−	0.0101436i
$849$		0			0
$850$	−1.30133	+	4.83460i	−0.0446351	+	0.165825i
$851$	21.1237	−	36.5874i	0.724112	−	1.25420i
$852$		0			0
$853$	−10.9968	−	41.0407i	−0.376524	−	1.40521i	−0.851105	−	0.524995i	$-0.824067\pi$
$853$	−10.9968	−	41.0407i	−0.376524	−	1.40521i	0.474581	−	0.880212i	$-0.342599\pi$
$854$	17.5204	−	30.8824i	0.599537	−	1.05677i
$855$		0			0
$856$	−1.89287	+	3.27855i	−0.0646971	+	0.112059i
$857$	−36.4574	−	36.4574i	−1.24536	−	1.24536i	−0.957747	−	0.287613i	$-0.907138\pi$
$857$	−36.4574	−	36.4574i	−1.24536	−	1.24536i	−0.287613	−	0.957747i	$-0.592862\pi$
$858$		0			0
$859$	19.3844			0.661387			0.330694	−	0.943738i	$-0.392717\pi$
$859$	19.3844			0.661387			0.330694	+	0.943738i	$0.392717\pi$
$860$	−2.35170	+	17.7848i	−0.0801924	+	0.606455i
$861$		0			0
$862$	−5.62476	−	20.9919i	−0.191580	−	0.714986i
$863$	−0.409122	+	0.109624i	−0.0139267	+	0.00373165i	−0.265776	−	0.964035i	$-0.585628\pi$
$863$	−0.409122	+	0.109624i	−0.0139267	+	0.00373165i	0.251849	+	0.967767i	$0.418961\pi$
$864$		0			0
$865$	0.601130	−	4.54604i	0.0204390	−	0.154570i
$866$	6.26636	−	3.61788i	0.212939	−	0.122941i
$867$		0			0
$868$	22.3720	+	5.81391i	0.759356	+	0.197337i
$869$	−9.53065	+	5.50253i	−0.323305	+	0.186660i
$870$		0			0
$871$			2.97121i			0.100676i
$872$	33.3182	+	8.92760i	1.12830	+	0.302327i
$873$		0			0
$874$	−43.4226			−1.46879
$875$	−27.3944	−	11.1601i	−0.926099	−	0.377280i
$876$		0			0
$877$	27.6571	−	27.6571i	0.933913	−	0.933913i	−0.0640351	−	0.997948i	$-0.520397\pi$
$877$	27.6571	−	27.6571i	0.933913	−	0.933913i	0.997948	+	0.0640351i	$0.0203970\pi$
$878$	−4.94352	−	18.4495i	−0.166836	−	0.622640i
$879$		0			0
$880$	−2.36551	+	1.81298i	−0.0797412	+	0.0611155i
$881$			34.8974i			1.17572i	0.808961	+	0.587862i	$0.200030\pi$
$881$			34.8974i			1.17572i	−0.808961	+	0.587862i	$0.799970\pi$
$882$		0			0
$883$	−38.1289	−	38.1289i	−1.28314	−	1.28314i	−0.938872	−	0.344268i	$-0.888127\pi$
$883$	−38.1289	−	38.1289i	−1.28314	−	1.28314i	−0.344268	−	0.938872i	$-0.611873\pi$
$884$	0.493257	−	0.284782i	0.0165900	−	0.00957825i
$885$		0			0
$886$	−18.3090	+	31.7121i	−0.615102	+	1.06539i
$887$	33.3655	+	33.3655i	1.12030	+	1.12030i	0.991695	+	0.128609i	$0.0410511\pi$
$887$	33.3655	+	33.3655i	1.12030	+	1.12030i	0.128609	+	0.991695i	$0.458949\pi$
$888$		0			0
$889$	−0.0525565	−	6.96165i	−0.00176269	−	0.233486i
$890$	31.3445	+	24.0798i	1.05067	+	0.807157i
$891$		0			0
$892$	7.17267	−	26.7688i	0.240159	−	0.896285i
$893$	−8.36186	−	8.36186i	−0.279819	−	0.279819i
$894$		0			0
$895$	22.9359	+	29.9258i	0.766661	+	1.00031i
$896$	−5.08393	−	8.65409i	−0.169842	−	0.289113i
$897$		0			0
$898$	−4.70842	+	17.5721i	−0.157122	+	0.586387i
$899$	28.0960	+	48.6638i	0.937055	+	1.62303i
$900$		0			0
$901$	−1.24144	−	0.716748i	−0.0413585	−	0.0238783i
$902$	−10.9255	+	2.92747i	−0.363779	+	0.0974742i
$903$		0			0
$904$	−53.6218	+	30.9586i	−1.78344	+	1.02967i
$905$	45.1574	−	5.91895i	1.50108	−	0.196753i
$906$		0			0
$907$	17.7517	−	17.7517i	0.589436	−	0.589436i	−0.348043	−	0.937479i	$-0.613154\pi$
$907$	17.7517	−	17.7517i	0.589436	−	0.589436i	0.937479	+	0.348043i	$0.113154\pi$
$908$	4.60461	+	17.1846i	0.152809	+	0.570293i
$909$		0			0
$910$	−1.19550	−	2.83015i	−0.0396304	−	0.0938185i
$911$	−18.7147	+	32.4148i	−0.620045	+	1.07395i	0.369431	+	0.929258i	$0.379552\pi$
$911$	−18.7147	+	32.4148i	−0.620045	+	1.07395i	−0.989477	+	0.144692i	$0.953781\pi$
$912$		0			0
$913$	1.65656	+	6.18235i	0.0548240	+	0.204606i
$914$	−24.6958	−	14.2581i	−0.816864	−	0.471617i
$915$		0			0
$916$	−12.6680	−	7.31387i	−0.418562	−	0.241657i
$917$	3.97246	+	3.91293i	0.131182	+	0.129216i
$918$		0			0
$919$	31.8867	+	18.4098i	1.05184	+	0.607283i	0.923165	−	0.384403i	$-0.125593\pi$
$919$	31.8867	+	18.4098i	1.05184	+	0.607283i	0.128680	+	0.991686i	$0.458926\pi$
$920$	−48.9683	+	6.41845i	−1.61444	+	0.211610i
$921$		0			0
$922$	−10.5487	−	10.5487i	−0.347404	−	0.347404i
$923$	3.26414	+	0.874623i	0.107440	+	0.0287886i
$924$		0			0
$925$	−14.2005	−	24.6607i	−0.466909	−	0.810839i
$926$	20.2211	−	35.0240i	0.664507	−	1.15096i
$927$		0			0
$928$	8.96921	−	33.4736i	0.294429	−	1.09882i
$929$	5.43502	+	9.41374i	0.178317	+	0.308855i	0.941304	−	0.337559i	$-0.109601\pi$
$929$	5.43502	+	9.41374i	0.178317	+	0.308855i	−0.762987	+	0.646414i	$0.776268\pi$
$930$		0			0
$931$	36.6094	+	20.4058i	1.19982	+	0.668772i
$932$	12.4339	+	3.33164i	0.407284	+	0.109132i
$933$		0			0
$934$	17.6658			0.578044
$935$	3.71114	+	0.490729i	0.121367	+	0.0160486i
$936$		0			0
$937$	22.9760	+	22.9760i	0.750592	+	0.750592i	0.974590	−	0.223998i	$-0.0719108\pi$
$937$	22.9760	+	22.9760i	0.750592	+	0.750592i	−0.223998	+	0.974590i	$0.571911\pi$
$938$	10.2938	+	10.1396i	0.336105	+	0.331068i
$939$		0			0
$940$	−3.66146	−	2.81285i	−0.119424	−	0.0917449i
$941$	−31.4547	−	18.1604i	−1.02539	−	0.592012i	−0.109732	−	0.993961i	$-0.534999\pi$
$941$	−31.4547	−	18.1604i	−1.02539	−	0.592012i	−0.915662	+	0.401949i	$0.868333\pi$
$942$		0			0
$943$	−50.8197	−	13.6171i	−1.65492	−	0.443434i
$944$	0.901848			0.0293527
$945$		0			0
$946$	−12.2461			−0.398155
$947$	−11.1715	−	2.99339i	−0.363025	−	0.0972723i	0.0726957	−	0.997354i	$-0.476840\pi$
$947$	−11.1715	−	2.99339i	−0.363025	−	0.0972723i	−0.435721	+	0.900082i	$0.643506\pi$
$948$		0			0
$949$	2.89397	+	1.67084i	0.0939424	+	0.0542377i
$950$	−14.6531	+	25.3134i	−0.475410	+	0.821274i
$951$		0			0
$952$	2.02935	−	7.80897i	0.0657716	−	0.253090i
$953$	−39.2129	−	39.2129i	−1.27023	−	1.27023i	−0.945967	−	0.324263i	$-0.894884\pi$
$953$	−39.2129	−	39.2129i	−1.27023	−	1.27023i	−0.324263	−	0.945967i	$-0.605116\pi$
$954$		0			0
$955$	30.5864	−	23.4421i	0.989753	−	0.758570i
$956$	7.93588			0.256665
$957$		0			0
$958$	−7.69249	−	2.06120i	−0.248533	−	0.0665942i
$959$	0.270221	+	35.7936i	0.00872591	+	1.15584i
$960$		0			0
$961$	19.4163	+	33.6300i	0.626333	+	1.08484i
$962$	0.764969	−	2.85490i	0.0246636	−	0.0920458i
$963$		0			0
$964$	−3.15001	+	5.45598i	−0.101455	+	0.175725i
$965$	9.24339	+	22.3515i	0.297555	+	0.719520i
$966$		0			0
$967$	1.19560	+	0.320359i	0.0384478	+	0.0103021i	0.277992	−	0.960583i	$-0.410331\pi$
$967$	1.19560	+	0.320359i	0.0384478	+	0.0103021i	−0.239544	+	0.970886i	$0.576998\pi$
$968$	−17.5299	−	17.5299i	−0.563432	−	0.563432i
$969$		0			0
$970$	−0.0437911	−	0.334096i	−0.00140605	−	0.0107272i
$971$	36.8435	+	21.2716i	1.18237	+	0.682639i	0.956561	−	0.291533i	$-0.0941654\pi$
$971$	36.8435	+	21.2716i	1.18237	+	0.682639i	0.225805	+	0.974173i	$0.427499\pi$
$972$		0			0
$973$	−32.9955	−	8.57468i	−1.05779	−	0.274892i
$974$	−3.44318	−	1.98792i	−0.110327	−	0.0636971i
$975$		0			0
$976$	−9.70686	−	5.60426i	−0.310709	−	0.179388i
$977$	1.89952	+	7.08909i	0.0607709	+	0.226800i	0.989632	−	0.143629i	$-0.0458773\pi$
$977$	1.89952	+	7.08909i	0.0607709	+	0.226800i	−0.928861	+	0.370429i	$0.879211\pi$
$978$		0			0
$979$	14.7766	−	25.5939i	0.472264	−	0.817985i
$980$	15.2082	+	6.04208i	0.485807	+	0.193007i
$981$		0			0
$982$	7.14274	+	26.6571i	0.227934	+	0.850661i
$983$	−21.3401	+	21.3401i	−0.680645	+	0.680645i	−0.960146	−	0.279500i	$-0.909831\pi$
$983$	−21.3401	+	21.3401i	−0.680645	+	0.680645i	0.279500	+	0.960146i	$0.409831\pi$
$984$		0			0
$985$	11.6995	+	8.98794i	0.372778	+	0.286380i
$986$	5.83117	−	3.36663i	0.185702	−	0.107215i
$987$		0			0
$988$	3.21397	−	0.861181i	0.102250	−	0.0273978i
$989$	−49.3310	−	28.4813i	−1.56864	−	0.905652i
$990$		0			0
$991$	−25.4329	−	44.0511i	−0.807903	−	1.39933i	−0.914314	−	0.405007i	$-0.867269\pi$
$991$	−25.4329	−	44.0511i	−0.807903	−	1.39933i	0.106411	−	0.994322i	$-0.466064\pi$
$992$	11.1465	−	41.5992i	0.353901	−	1.32078i
$993$		0			0
$994$	14.1693	−	8.32393i	0.449424	−	0.264019i
$995$	−9.16909	+	7.02740i	−0.290680	+	0.222784i
$996$		0			0
$997$	4.43771	+	4.43771i	0.140544	+	0.140544i	0.773878	−	0.633334i	$-0.218314\pi$
$997$	4.43771	+	4.43771i	0.140544	+	0.140544i	−0.633334	+	0.773878i	$0.718314\pi$
$998$	6.26292	−	23.3735i	0.198249	−	0.739876i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cj.e.208.13		160
3.2	odd	2		315.2.cg.e.313.28	yes	160
5.2	odd	4	inner	945.2.cj.e.397.28		160
7.3	odd	6		945.2.bv.e.73.28		160
9.4	even	3		945.2.bv.e.523.28		160
9.5	odd	6		315.2.bs.e.103.13	yes	160
15.2	even	4		315.2.cg.e.187.13	yes	160
21.17	even	6		315.2.bs.e.178.13	yes	160
35.17	even	12		945.2.bv.e.262.28		160
45.22	odd	12		945.2.bv.e.712.28		160
45.32	even	12		315.2.bs.e.292.13	yes	160
63.31	odd	6	inner	945.2.cj.e.388.28		160
63.59	even	6		315.2.cg.e.283.13	yes	160
105.17	odd	12		315.2.bs.e.52.13	✓	160
315.122	odd	12		315.2.cg.e.157.28	yes	160
315.157	even	12	inner	945.2.cj.e.577.13		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.13	✓	160	105.17	odd	12
315.2.bs.e.103.13	yes	160	9.5	odd	6
315.2.bs.e.178.13	yes	160	21.17	even	6
315.2.bs.e.292.13	yes	160	45.32	even	12
315.2.cg.e.157.28	yes	160	315.122	odd	12
315.2.cg.e.187.13	yes	160	15.2	even	4
315.2.cg.e.283.13	yes	160	63.59	even	6
315.2.cg.e.313.28	yes	160	3.2	odd	2
945.2.bv.e.73.28		160	7.3	odd	6
945.2.bv.e.262.28		160	35.17	even	12
945.2.bv.e.523.28		160	9.4	even	3
945.2.bv.e.712.28		160	45.22	odd	12
945.2.cj.e.208.13		160	1.1	even	1	trivial
945.2.cj.e.388.28		160	63.31	odd	6	inner
945.2.cj.e.397.28		160	5.2	odd	4	inner
945.2.cj.e.577.13		160	315.157	even	12	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.943703 - 0.252864i) q^{2} +(-0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.85665 + 1.88490i) q^{7} +(2.10394 + 2.10394i) q^{8} +O(q^{10})\)	\(q+(-0.943703 - 0.252864i) q^{2} +(-0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.85665 + 1.88490i) q^{7} +(2.10394 + 2.10394i) q^{8} +(-0.286383 + 2.16577i) q^{10} +1.63342 q^{11} +(0.513429 + 0.137573i) q^{13} +(2.22875 - 1.30930i) q^{14} +(-0.407995 - 0.706668i) q^{16} +(-0.265268 + 0.989992i) q^{17} +(-2.99374 + 5.18531i) q^{19} +(-0.895857 + 2.15931i) q^{20} +(-1.54146 - 0.413034i) q^{22} +(-5.24887 - 5.24887i) q^{23} +(-4.83110 + 1.28860i) q^{25} +(-0.449737 - 0.259656i) q^{26} +(2.66636 - 0.736068i) q^{28} +(5.82340 + 3.36214i) q^{29} +(7.23702 + 4.17830i) q^{31} +(-1.33385 - 4.97801i) q^{32} +(0.500668 - 0.867182i) q^{34} +(4.71857 + 3.56863i) q^{35} +(1.47305 + 5.49748i) q^{37} +(4.13638 - 4.13638i) q^{38} +(4.05324 - 5.27606i) q^{40} +(6.13816 - 3.54387i) q^{41} +(7.41230 - 1.98612i) q^{43} +(-1.47893 - 0.853858i) q^{44} +(3.62612 + 6.28062i) q^{46} +(-0.511176 + 1.90773i) q^{47} +(-0.105686 - 6.99920i) q^{49} +(4.88496 + 0.00555968i) q^{50} +(-0.392952 - 0.392952i) q^{52} +(-0.361997 + 1.35099i) q^{53} +(-0.474678 - 3.62146i) q^{55} +(-7.87199 + 0.0594290i) q^{56} +(-4.64539 - 4.64539i) q^{58} +(-0.552610 + 0.957148i) q^{59} +(11.8958 - 6.86804i) q^{61} +(-5.77305 - 5.77305i) q^{62} +6.66703i q^{64} +(0.155809 - 1.17830i) q^{65} +(1.44675 + 5.39935i) q^{67} +(0.757689 - 0.757689i) q^{68} +(-3.55054 - 4.56088i) q^{70} +6.35753 q^{71} +(6.07255 + 1.62714i) q^{73} -5.56047i q^{74} +(5.42116 - 3.12991i) q^{76} +(-3.03269 + 3.07883i) q^{77} +(-5.83478 + 3.36871i) q^{79} +(-1.44819 + 1.10993i) q^{80} +(-6.68871 + 1.79224i) q^{82} +(1.01416 + 3.78491i) q^{83} +(2.27200 + 0.300430i) q^{85} -7.49722 q^{86} +(3.43661 + 3.43661i) q^{88} +(9.04644 - 15.6689i) q^{89} +(-1.21257 + 0.712336i) q^{91} +(2.00861 + 7.49622i) q^{92} +(0.964796 - 1.67108i) q^{94} +(12.3664 + 5.13056i) q^{95} +(-0.148983 + 0.0399199i) q^{97} +(-1.67011 + 6.63189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) \) 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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