LMFDB - Embedded newform 945.2.cj.e.388.28

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			388.28
Character	$\chi$	$=$	945.388
Dual form			945.2.cj.e.397.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.252864 + 0.943703i) q^{2} +(0.905417 - 0.522743i) q^{4} +(0.290604 + 2.21710i) q^{5} +(-1.88490 + 1.85665i) q^{7} +(2.10394 + 2.10394i) q^{8} +O(q^{10})$	\(q+(0.252864 + 0.943703i) q^{2} +(0.905417 - 0.522743i) q^{4} +(0.290604 + 2.21710i) q^{5} +(-1.88490 + 1.85665i) q^{7} +(2.10394 + 2.10394i) q^{8} +(-2.01880 + 0.834870i) q^{10} +1.63342 q^{11} +(0.137573 + 0.513429i) q^{13} +(-2.22875 - 1.30930i) q^{14} +(-0.407995 + 0.706668i) q^{16} +(-0.989992 + 0.265268i) q^{17} +(2.99374 + 5.18531i) q^{19} +(1.42209 + 1.85549i) q^{20} +(0.413034 + 1.54146i) q^{22} +(-5.24887 - 5.24887i) q^{23} +(-4.83110 + 1.28860i) q^{25} +(-0.449737 + 0.259656i) q^{26} +(-0.736068 + 2.66636i) q^{28} +(-5.82340 + 3.36214i) q^{29} +(7.23702 - 4.17830i) q^{31} +(4.97801 + 1.33385i) q^{32} +(-0.500668 - 0.867182i) q^{34} +(-4.66415 - 3.63947i) q^{35} +(-5.49748 - 1.47305i) q^{37} +(-4.13638 + 4.13638i) q^{38} +(-4.05324 + 5.27606i) q^{40} +(6.13816 + 3.54387i) q^{41} +(-1.98612 + 7.41230i) q^{43} +(1.47893 - 0.853858i) q^{44} +(3.62612 - 6.28062i) q^{46} +(-1.90773 + 0.511176i) q^{47} +(0.105686 - 6.99920i) q^{49} +(-2.43767 - 4.23328i) q^{50} +(0.392952 + 0.392952i) q^{52} +(1.35099 - 0.361997i) q^{53} +(0.474678 + 3.62146i) q^{55} +(-7.87199 - 0.0594290i) q^{56} +(-4.64539 - 4.64539i) q^{58} +(0.552610 + 0.957148i) q^{59} +(11.8958 + 6.86804i) q^{61} +(5.77305 + 5.77305i) q^{62} +6.66703i q^{64} +(-1.09835 + 0.454218i) q^{65} +(-5.39935 - 1.44675i) q^{67} +(-0.757689 + 0.757689i) q^{68} +(2.25518 - 5.32186i) q^{70} +6.35753 q^{71} +(1.62714 + 6.07255i) q^{73} -5.56047i q^{74} +(5.42116 + 3.12991i) q^{76} +(-3.07883 + 3.03269i) q^{77} +(5.83478 + 3.36871i) q^{79} +(-1.68532 - 0.699207i) q^{80} +(-1.79224 + 6.68871i) q^{82} +(3.78491 + 1.01416i) q^{83} +(-0.875822 - 2.11783i) q^{85} -7.49722 q^{86} +(3.43661 + 3.43661i) q^{88} +(-9.04644 - 15.6689i) q^{89} +(-1.21257 - 0.712336i) q^{91} +(-7.49622 - 2.00861i) q^{92} +(-0.964796 - 1.67108i) q^{94} +(-10.6264 + 8.14430i) q^{95} +(-0.0399199 + 0.148983i) q^{97} +(6.63189 - 1.67011i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.252864	+	0.943703i	0.178802	+	0.667298i	0.995873	+	0.0907609i	$0.0289299\pi$
$2$	0.252864	+	0.943703i	0.178802	+	0.667298i	−0.817071	+	0.576538i	$0.804403\pi$
$3$		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
$7$	−1.88490	+	1.85665i	−0.712425	+	0.701749i
$7$	−1.88490	+	1.85665i	−0.712425	+	0.701749i
$8$	2.10394	+	2.10394i	0.743854	+	0.743854i
$9$		0			0
$10$	−2.01880	+	0.834870i	−0.638402	+	0.264009i
$11$	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
$13$	0.137573	+	0.513429i	0.0381558	+	0.142400i	0.982376	−	0.186915i	$-0.0598490\pi$
$13$	0.137573	+	0.513429i	0.0381558	+	0.142400i	−0.944220	+	0.329315i	$0.893182\pi$
$14$	−2.22875	−	1.30930i	−0.595659	−	0.349926i
$15$		0			0
$16$	−0.407995	+	0.706668i	−0.101999	+	0.176667i
$17$	−0.989992	+	0.265268i	−0.240108	+	0.0643369i	−0.376866	−	0.926268i	$-0.622998\pi$
$17$	−0.989992	+	0.265268i	−0.240108	+	0.0643369i	0.136758	+	0.990604i	$0.456332\pi$
$18$		0			0
$19$	2.99374	+	5.18531i	0.686811	+	1.18959i	0.972864	+	0.231377i	$0.0743232\pi$
$19$	2.99374	+	5.18531i	0.686811	+	1.18959i	−0.286053	+	0.958214i	$0.592343\pi$
$20$	1.42209	+	1.85549i	0.317989	+	0.414901i
$21$		0			0
$22$	0.413034	+	1.54146i	0.0880591	+	0.328641i
$23$	−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
$28$	−0.736068	+	2.66636i	−0.139104	+	0.503895i
$29$	−5.82340	+	3.36214i	−1.08138	+	0.624334i	−0.931268	−	0.364335i	$-0.881296\pi$
$29$	−5.82340	+	3.36214i	−1.08138	+	0.624334i	−0.150110	+	0.988669i	$0.547963\pi$
$30$		0			0
$31$	7.23702	−	4.17830i	1.29981	−	0.750444i	0.319437	−	0.947608i	$-0.396506\pi$
$31$	7.23702	−	4.17830i	1.29981	−	0.750444i	0.980371	+	0.197164i	$0.0631730\pi$
$32$	4.97801	+	1.33385i	0.879997	+	0.235794i
$33$		0			0
$34$	−0.500668	−	0.867182i	−0.0858638	−	0.148720i
$35$	−4.66415	−	3.63947i	−0.788385	−	0.615182i
$36$		0			0
$37$	−5.49748	−	1.47305i	−0.903780	−	0.242167i	−0.223141	−	0.974786i	$-0.571631\pi$
$37$	−5.49748	−	1.47305i	−0.903780	−	0.242167i	−0.680639	+	0.732619i	$0.738298\pi$
$38$	−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	0.895748	−	0.444563i	$-0.146641\pi$
$41$	6.13816	+	3.54387i	0.958619	+	0.553459i	0.0628714	+	0.998022i	$0.479974\pi$
$42$		0			0
$43$	−1.98612	+	7.41230i	−0.302880	+	1.13036i	0.631874	+	0.775071i	$0.282286\pi$
$43$	−1.98612	+	7.41230i	−0.302880	+	1.13036i	−0.934755	+	0.355294i	$0.884381\pi$
$44$	1.47893	−	0.853858i	0.222956	−	0.128724i
$45$		0			0
$46$	3.62612	−	6.28062i	0.534642	−	0.926027i
$47$	−1.90773	+	0.511176i	−0.278272	+	0.0745627i	−0.395256	−	0.918571i	$-0.629344\pi$
$47$	−1.90773	+	0.511176i	−0.278272	+	0.0745627i	0.116984	+	0.993134i	$0.462677\pi$
$48$		0			0
$49$	0.105686	−	6.99920i	0.0150980	−	0.999886i
$50$	−2.43767	−	4.23328i	−0.344738	−	0.598676i
$51$		0			0
$52$	0.392952	+	0.392952i	0.0544926	+	0.0544926i
$53$	1.35099	−	0.361997i	0.185573	−	0.0497241i	−0.164836	−	0.986321i	$-0.552709\pi$
$53$	1.35099	−	0.361997i	0.185573	−	0.0497241i	0.350409	+	0.936597i	$0.386043\pi$
$54$		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	$-0.143746\pi$
$59$	0.552610	+	0.957148i	0.0719437	+	0.124610i	−0.827809	+	0.561009i	$0.810413\pi$
$60$		0			0
$61$	11.8958	+	6.86804i	1.52310	+	0.879363i	0.999627	+	0.0273211i	$0.00869765\pi$
$61$	11.8958	+	6.86804i	1.52310	+	0.879363i	0.523474	+	0.852042i	$0.324636\pi$
$62$	5.77305	+	5.77305i	0.733178	+	0.733178i
$63$		0			0
$64$			6.66703i			0.833378i
$65$	−1.09835	+	0.454218i	−0.136233	+	0.0563388i
$66$		0			0
$67$	−5.39935	−	1.44675i	−0.659635	−	0.176749i	−0.0865538	−	0.996247i	$-0.527585\pi$
$67$	−5.39935	−	1.44675i	−0.659635	−	0.176749i	−0.573081	+	0.819498i	$0.694252\pi$
$68$	−0.757689	+	0.757689i	−0.0918833	+	0.0918833i
$69$		0			0
$70$	2.25518	−	5.32186i	0.269545	−	0.636084i
$71$	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
$73$	1.62714	+	6.07255i	0.190442	+	0.710739i	0.993400	+	0.114703i	$0.0365917\pi$
$73$	1.62714	+	6.07255i	0.190442	+	0.710739i	−0.802958	+	0.596036i	$0.796742\pi$
$74$		−	5.56047i		−	0.646391i
$75$		0			0
$76$	5.42116	+	3.12991i	0.621850	+	0.359025i
$77$	−3.07883	+	3.03269i	−0.350865	+	0.345607i
$78$		0			0
$79$	5.83478	+	3.36871i	0.656465	+	0.379010i	0.790929	−	0.611908i	$-0.209598\pi$
$79$	5.83478	+	3.36871i	0.656465	+	0.379010i	−0.134464	+	0.990918i	$0.542931\pi$
$80$	−1.68532	−	0.699207i	−0.188425	−	0.0781737i
$81$		0			0
$82$	−1.79224	+	6.68871i	−0.197919	+	0.738645i
$83$	3.78491	+	1.01416i	0.415448	+	0.111319i	0.460488	−	0.887666i	$-0.347675\pi$
$83$	3.78491	+	1.01416i	0.415448	+	0.111319i	−0.0450392	+	0.998985i	$0.514341\pi$
$84$		0			0
$85$	−0.875822	−	2.11783i	−0.0949962	−	0.229711i
$86$	−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	−0.725128	−	0.688614i	$-0.758220\pi$
$89$	−9.04644	−	15.6689i	−0.958921	−	1.66090i	−0.233793	−	0.972286i	$-0.575114\pi$
$90$		0			0
$91$	−1.21257	−	0.712336i	−0.127112	−	0.0746731i
$92$	−7.49622	−	2.00861i	−0.781535	−	0.209412i
$93$		0			0
$94$	−0.964796	−	1.67108i	−0.0995111	−	0.172358i
$95$	−10.6264	+	8.14430i	−1.09024	+	0.835587i
$96$		0			0
$97$	−0.0399199	+	0.148983i	−0.00405325	+	0.0151270i	−0.967923	−	0.251248i	$-0.919159\pi$
$97$	−0.0399199	+	0.148983i	−0.00405325	+	0.0151270i	0.963870	+	0.266375i	$0.0858258\pi$
$98$	6.63189	−	1.67011i	0.669922	−	0.168707i
$99$		0			0
$100$	−3.70055	+	3.69214i	−0.370055	+	0.369214i
$101$		−	8.14296i		−	0.810255i	−0.914260	−	0.405127i	$-0.867227\pi$
$101$		−	8.14296i		−	0.810255i	0.914260	−	0.405127i	$-0.132773\pi$
$102$		0			0
$103$	7.26124	−	7.26124i	0.715471	−	0.715471i	−0.252203	−	0.967674i	$-0.581155\pi$
$103$	7.26124	−	7.26124i	0.715471	−	0.715471i	0.967674	+	0.252203i	$0.0811551\pi$
$104$	−0.790777	+	1.36967i	−0.0775421	+	0.134307i
$105$		0			0
$106$	0.683235	+	1.18340i	0.0663616	+	0.114942i
$107$	−1.22899	−	0.329306i	−0.118811	−	0.0318352i	0.198924	−	0.980015i	$-0.436255\pi$
$107$	−1.22899	−	0.329306i	−0.118811	−	0.0318352i	−0.317734	+	0.948180i	$0.602922\pi$
$108$		0			0
$109$	−10.0397	−	5.79643i	−0.961630	−	0.555197i	−0.0649556	−	0.997888i	$-0.520691\pi$
$109$	−10.0397	−	5.79643i	−0.961630	−	0.555197i	−0.896674	+	0.442691i	$0.854024\pi$
$110$	−3.29755	+	1.36369i	−0.314409	+	0.130023i
$111$		0			0
$112$	−0.543008	−	2.08950i	−0.0513094	−	0.197440i
$113$	20.1005	−	5.38592i	1.89090	−	0.506664i	0.892438	−	0.451170i	$-0.148993\pi$
$113$	20.1005	−	5.38592i	1.89090	−	0.506664i	0.998459	−	0.0554944i	$-0.0176735\pi$
$114$		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
$122$	−3.47337	+	12.9628i	−0.314464	+	1.17359i
$123$		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	$0.287246\pi$
$128$	3.66433	−	0.981855i	0.323884	−	0.0867846i
$129$		0			0
$130$	−0.706379	−	0.921656i	−0.0619535	−	0.0808346i
$131$			2.10752i			0.184135i	0.995753	+	0.0920674i	$0.0293475\pi$
$131$			2.10752i			0.184135i	−0.995753	+	0.0920674i	$0.970652\pi$
$132$		0			0
$133$	−15.2702	−	4.21545i	−1.32409	−	0.365526i
$134$		−	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	0.452052	+	0.891992i	$0.350692\pi$
$139$	−6.44269	+	11.1591i	−0.546461	+	0.946499i	−0.998513	+	0.0545074i	$0.982641\pi$
$140$	−6.12550	−	0.857084i	−0.517699	−	0.0724368i
$141$		0			0
$142$	1.60759	+	5.99961i	0.134906	+	0.503476i
$143$	0.224714	+	0.838645i	0.0187915	+	0.0701310i
$144$		0			0
$145$	−9.14652	−	11.9340i	−0.759577	−	0.991067i
$146$	−5.31924	+	3.07106i	−0.440223	+	0.254163i
$147$		0			0
$148$	−5.74753	+	1.54005i	−0.472444	+	0.126591i
$149$		−	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	$0.474103\pi$
$152$	−4.61092	+	17.2082i	−0.373995	+	1.39577i
$153$		0			0
$154$	−3.64049	−	2.13864i	−0.293359	−	0.172337i
$155$	11.3668	+	14.8310i	0.913005	+	1.19125i
$156$		0			0
$157$	2.18660	−	8.16051i	0.174510	−	0.651280i	−0.822125	−	0.569307i	$-0.807211\pi$
$157$	2.18660	−	8.16051i	0.174510	−	0.651280i	0.996635	−	0.0819723i	$-0.0261219\pi$
$158$	−1.70366	+	6.35813i	−0.135536	+	0.505826i
$159$		0			0
$160$	−1.51066	+	11.4244i	−0.119428	+	0.903178i
$161$	19.6389	+	0.148263i	1.54776	+	0.0116847i
$162$		0			0
$163$	0.573913	−	2.14187i	0.0449523	−	0.167764i	−0.939801	−	0.341723i	$-0.888989\pi$
$163$	0.573913	−	2.14187i	0.0449523	−	0.167764i	0.984753	+	0.173959i	$0.0556561\pi$
$164$	7.41012			0.578633
$165$		0			0
$166$			3.82828i			0.297132i
$167$	1.31306	−	0.351833i	0.101607	−	0.0272256i	−0.207657	−	0.978202i	$-0.566584\pi$
$167$	1.31306	−	0.351833i	0.101607	−	0.0272256i	0.309265	+	0.950976i	$0.399917\pi$
$168$		0			0
$169$	11.0136	−	6.35873i	0.847204	−	0.489133i
$170$	1.77714	−	1.36204i	0.136300	−	0.104464i
$171$		0			0
$172$	2.07646	+	7.74945i	0.158328	+	0.590890i
$173$	0.530773	+	1.98087i	0.0403539	+	0.150603i	0.983163	−	0.182730i	$-0.0584934\pi$
$173$	0.530773	+	1.98087i	0.0403539	+	0.150603i	−0.942809	+	0.333333i	$0.891827\pi$
$174$		0			0
$175$	6.71365	−	11.3985i	0.507505	−	0.861649i
$176$	−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	$-0.116324\pi$
$179$	14.6028	+	8.43092i	1.09146	+	0.630157i	0.157498	+	0.987519i	$0.449657\pi$
$180$		0			0
$181$		−	20.3678i		−	1.51392i	−0.653459	−	0.756962i	$-0.726683\pi$
$181$		−	20.3678i		−	1.51392i	0.653459	−	0.756962i	$-0.273317\pi$
$182$	0.365618	−	1.32443i	0.0271014	−	0.0981732i
$183$		0			0
$184$		−	22.0866i		−	1.62824i
$185$	1.66831	−	12.6166i	0.122656	−	0.927588i
$186$		0			0
$187$	−1.61707	+	0.433294i	−0.118252	+	0.0316856i
$188$	−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	−0.365322	−	0.930881i	$-0.619041\pi$
$191$	8.61703	−	14.9251i	0.623506	−	1.07994i	0.988828	−	0.149063i	$-0.0476257\pi$
$192$		0			0
$193$	2.79962	−	10.4483i	0.201521	−	0.752088i	−0.788960	−	0.614444i	$-0.789380\pi$
$193$	2.79962	−	10.4483i	0.201521	−	0.752088i	0.990482	−	0.137644i	$-0.0439530\pi$
$194$	−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	$-0.774715\pi$
$199$	2.58318	−	4.47420i	0.183117	−	0.317168i	0.942940	+	0.332962i	$0.108048\pi$
$200$	−12.8755	−	7.45320i	−0.910432	−	0.527021i
$201$		0			0
$202$	7.68453	−	2.05906i	0.540682	−	0.144875i
$203$	4.73419	−	17.1493i	0.332275	−	1.20365i
$204$		0			0
$205$	−6.07335	+	14.6388i	−0.424181	+	1.02242i
$206$	8.68856	+	5.01634i	0.605360	+	0.349505i
$207$		0			0
$208$	−0.418953	−	0.112258i	−0.0290492	−	0.00778370i
$209$	4.89003	+	8.46978i	0.338251	+	0.585867i
$210$		0			0
$211$	0.273339	−	0.473437i	0.0188174	−	0.0325927i	−0.856463	−	0.516208i	$-0.827343\pi$
$211$	0.273339	−	0.473437i	0.0188174	−	0.0325927i	0.875281	+	0.483615i	$0.160677\pi$
$212$	1.03398	−	1.03398i	0.0710139	−	0.0710139i
$213$		0			0
$214$		−	1.24307i		−	0.0849744i
$215$	−17.0110	−	2.24939i	−1.16014	−	0.153407i
$216$		0			0
$217$	−5.88341	+	21.3123i	−0.399392	+	1.44677i
$218$	2.93142	−	10.9402i	0.198541	−	0.740965i
$219$		0			0
$220$	2.32287	+	3.03080i	0.156608	+	0.204336i
$221$	−0.272392	−	0.471797i	−0.0183231	−	0.0317365i
$222$		0			0
$223$	25.6042	+	6.86061i	1.71458	+	0.459421i	0.976540	−	0.215335i	$-0.0690844\pi$
$223$	25.6042	+	6.86061i	1.71458	+	0.459421i	0.738041	+	0.674756i	$0.235751\pi$
$224$	−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	0.982881	−	0.184241i	$-0.0589827\pi$
$227$	12.0327	+	12.0327i	0.798640	+	0.798640i	−0.184241	+	0.982881i	$0.558983\pi$
$228$		0			0
$229$	−13.9913			−0.924574			−0.462287	−	0.886730i	$-0.652971\pi$
$229$	−13.9913			−0.924574			−0.462287	+	0.886730i	$0.652971\pi$
$230$	14.9786	+	6.21431i	0.987657	+	0.409759i
$231$		0			0
$232$	−19.3258	−	5.17833i	−1.26880	−	0.339974i
$233$	3.18669	−	11.8929i	0.208767	−	0.779130i	−0.779501	−	0.626401i	$-0.784527\pi$
$233$	3.18669	−	11.8929i	0.208767	−	0.779130i	0.988268	−	0.152729i	$-0.0488061\pi$
$234$		0			0
$235$	−1.68772	−	4.08110i	−0.110095	−	0.266221i
$236$	1.00068	+	0.577745i	0.0651390	+	0.0376080i
$237$		0			0
$238$	2.55376	+	0.704984i	0.165536	+	0.0456973i
$239$	6.57367	+	3.79531i	0.425215	+	0.245498i	0.697306	−	0.716773i	$-0.254382\pi$
$239$	6.57367	+	3.79531i	0.425215	+	0.245498i	−0.272091	+	0.962272i	$0.587715\pi$
$240$		0			0
$241$			6.02593i			0.388164i	0.980985	+	0.194082i	$0.0621728\pi$
$241$			6.02593i			0.388164i	−0.980985	+	0.194082i	$0.937827\pi$
$242$	−2.10685	−	7.86287i	−0.135433	−	0.505445i
$243$		0			0
$244$	14.3609			0.919361
$245$	15.5487	−	1.79968i	0.993368	−	0.114977i
$246$		0			0
$247$	−2.25043	+	2.25043i	−0.143191	+	0.143191i
$248$	24.0171	+	6.43537i	1.52509	+	0.408646i
$249$		0			0
$250$	8.67723	−	6.63476i	0.548796	−	0.419619i
$251$			4.81059i			0.303642i	0.988408	+	0.151821i	$0.0485137\pi$
$251$			4.81059i			0.303642i	−0.988408	+	0.151821i	$0.951486\pi$
$252$		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	0.969060	−	0.246825i	$-0.0793872\pi$
$257$	11.5783	+	11.5783i	0.722235	+	0.722235i	−0.246825	+	0.969060i	$0.579387\pi$
$258$		0			0
$259$	13.0971	−	7.43037i	0.813816	−	0.461701i
$260$	−0.757022	+	0.985408i	−0.0469485	+	0.0611124i
$261$		0			0
$262$	−1.98887	+	0.532917i	−0.122873	+	0.0329237i
$263$	−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
$265$	1.19519	+	2.89009i	0.0734198	+	0.177537i
$266$	0.116839	−	15.4765i	0.00716383	−	0.948923i
$267$		0			0
$268$	−5.64494	+	1.51256i	−0.344819	+	0.0923941i
$269$	−1.86662	+	3.23307i	−0.113810	+	0.197124i	−0.917303	−	0.398189i	$-0.869639\pi$
$269$	−1.86662	+	3.23307i	−0.113810	+	0.197124i	0.803494	+	0.595313i	$0.202972\pi$
$270$		0			0
$271$	5.54325	−	3.20039i	0.336728	−	0.194410i	−0.322096	−	0.946707i	$-0.604387\pi$
$271$	5.54325	−	3.20039i	0.336728	−	0.194410i	0.658824	+	0.752297i	$0.271054\pi$
$272$	0.216456	−	0.807824i	0.0131246	−	0.0489815i
$273$		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	$0.244508\pi$
$278$	−12.1600	−	3.25825i	−0.729306	−	0.195417i
$279$		0			0
$280$	−2.15587	−	17.4703i	−0.128838	−	1.04405i
$281$	−2.21693	−	3.83984i	−0.132251	−	0.229065i	0.792293	−	0.610141i	$-0.208887\pi$
$281$	−2.21693	−	3.83984i	−0.132251	−	0.229065i	−0.924544	+	0.381075i	$0.875554\pi$
$282$		0			0
$283$	7.19375	+	1.92756i	0.427624	+	0.114582i	0.466211	−	0.884674i	$-0.345619\pi$
$283$	7.19375	+	1.92756i	0.427624	+	0.114582i	−0.0385865	+	0.999255i	$0.512286\pi$
$284$	5.75621	−	3.32335i	0.341568	−	0.197205i
$285$		0			0
$286$	−0.734609	+	0.424127i	−0.0434383	+	0.0250791i
$287$	−18.1495	+	4.71659i	−1.07133	+	0.278412i
$288$		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
$293$	−4.98512	−	18.6047i	−0.291234	−	1.08690i	−0.944163	−	0.329480i	$-0.893127\pi$
$293$	−4.98512	−	18.6047i	−0.291234	−	1.08690i	0.652929	−	0.757419i	$-0.273540\pi$
$294$		0			0
$295$	−1.96151	+	1.50334i	−0.114203	+	0.0875281i
$296$	−8.46716	−	14.6656i	−0.492144	−	0.852418i
$297$		0			0
$298$	3.45692	−	0.926280i	0.200254	−	0.0536580i
$299$	1.97282	−	3.41702i	0.114091	−	0.197611i
$300$		0			0
$301$	−10.0184	−	17.6590i	−0.577452	−	1.01785i
$302$	0.505047	+	1.88486i	0.0290622	+	0.108462i
$303$		0			0
$304$	−4.88572			−0.280215
$305$	−11.7702	+	28.3701i	−0.673960	+	1.62447i
$306$		0			0
$307$	−6.54479	−	6.54479i	−0.373531	−	0.373531i	0.495231	−	0.868761i	$-0.335084\pi$
$307$	−6.54479	−	6.54479i	−0.373531	−	0.373531i	−0.868761	+	0.495231i	$0.835084\pi$
$308$	−1.20231	+	4.35529i	−0.0685078	+	0.248166i
$309$		0			0
$310$	−11.1218	+	14.4771i	−0.631675	+	0.822246i
$311$	21.3328	−	12.3165i	1.20967	−	0.698406i	0.246986	−	0.969019i	$-0.420560\pi$
$311$	21.3328	−	12.3165i	1.20967	−	0.698406i	0.962688	+	0.270613i	$0.0872265\pi$
$312$		0			0
$313$	6.56755	+	24.5104i	0.371220	+	1.38541i	0.858790	+	0.512327i	$0.171216\pi$
$313$	6.56755	+	24.5104i	0.371220	+	1.38541i	−0.487571	+	0.873083i	$0.662117\pi$
$314$	8.25401			0.465801
$315$		0			0
$316$	7.04388			0.396249
$317$	2.75779	+	10.2922i	0.154893	+	0.578069i	0.999114	+	0.0420744i	$0.0133966\pi$
$317$	2.75779	+	10.2922i	0.154893	+	0.578069i	−0.844221	+	0.535995i	$0.819937\pi$
$318$		0			0
$319$	−9.51206	+	5.49179i	−0.532573	+	0.307481i
$320$	−14.7815	+	1.93746i	−0.826311	+	0.108308i
$321$		0			0
$322$	4.82606	+	18.5708i	0.268946	+	1.03491i
$323$	−4.33927	−	4.33927i	−0.241444	−	0.241444i
$324$		0			0
$325$	−1.32623	−	2.30315i	−0.0735661	−	0.127756i
$326$	2.16641			0.119986
$327$		0			0
$328$	5.45823	+	20.3704i	0.301380	+	1.12477i
$329$	2.64681	−	4.50551i	0.145923	−	0.248397i
$330$		0			0
$331$	−3.12351	+	5.41009i	−0.171684	+	0.297365i	−0.939009	−	0.343893i	$-0.888254\pi$
$331$	−3.12351	+	5.41009i	−0.171684	+	0.297365i	0.767325	+	0.641259i	$0.221587\pi$
$332$	3.95707	−	1.06029i	0.217173	−	0.0581912i
$333$		0			0
$334$	0.664051	+	1.15017i	0.0363352	+	0.0629345i
$335$	1.63853	−	12.3913i	0.0895222	−	0.677011i
$336$		0			0
$337$	−3.31266	−	12.3630i	−0.180452	−	0.673457i	−0.995558	−	0.0941452i	$-0.969988\pi$
$337$	−3.31266	−	12.3630i	−0.180452	−	0.673457i	0.815106	−	0.579311i	$-0.196678\pi$
$338$	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
$343$	12.7959	+	13.3890i	0.690912	+	0.722939i
$344$	−19.7737	+	11.4163i	−1.06613	+	0.615528i
$345$		0			0
$346$	−1.73514	+	1.00178i	−0.0932817	+	0.0538562i
$347$	−12.9433	−	3.46816i	−0.694835	−	0.186181i	−0.105919	−	0.994375i	$-0.533778\pi$
$347$	−12.9433	−	3.46816i	−0.694835	−	0.186181i	−0.588916	+	0.808194i	$0.700445\pi$
$348$		0			0
$349$	−15.4350	−	26.7341i	−0.826215	−	1.43105i	−0.900987	−	0.433846i	$-0.857156\pi$
$349$	−15.4350	−	26.7341i	−0.826215	−	1.43105i	0.0747724	−	0.997201i	$-0.476177\pi$
$350$	12.4545	+	3.45341i	0.665720	+	0.184592i
$351$		0			0
$352$	8.13118	+	2.17874i	0.433394	+	0.116127i
$353$	−11.6226	+	11.6226i	−0.618609	+	0.618609i	−0.945174	−	0.326566i	$-0.894109\pi$
$353$	−11.6226	+	11.6226i	−0.618609	+	0.618609i	0.326566	+	0.945174i	$0.394109\pi$
$354$		0			0
$355$	1.84752	+	14.0953i	0.0980563	+	0.748101i
$356$	−16.3816	−	9.45792i	−0.868223	−	0.501269i
$357$		0			0
$358$	−4.26376	+	15.9126i	−0.225347	+	0.841005i
$359$	1.40486	−	0.811094i	0.0741455	−	0.0428079i	−0.462469	−	0.886635i	$-0.653036\pi$
$359$	1.40486	−	0.811094i	0.0741455	−	0.0428079i	0.536614	+	0.843828i	$0.319703\pi$
$360$		0			0
$361$	−8.42494	+	14.5924i	−0.443418	+	0.768022i
$362$	19.2211	−	5.15028i	1.01024	−	0.270693i
$363$		0			0
$364$	−1.47025	−	0.0110995i	−0.0770620	−	0.000581774i
$365$	−12.9906	+	5.37224i	−0.679961	+	0.281196i
$366$		0			0
$367$	1.71374	+	1.71374i	0.0894563	+	0.0894563i	0.750419	−	0.660963i	$-0.229852\pi$
$367$	1.71374	+	1.71374i	0.0894563	+	0.0894563i	−0.660963	+	0.750419i	$0.729852\pi$
$368$	5.85072	−	1.56770i	0.304990	−	0.0817218i
$369$		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	$-0.292715\pi$
$380$	−5.36392	+	12.9288i	−0.275163	+	0.663236i
$381$		0			0
$382$	16.2638	+	4.35788i	0.832129	+	0.222968i
$383$	−13.3140	+	13.3140i	−0.680313	+	0.680313i	−0.960071	−	0.279758i	$-0.909746\pi$
$383$	−13.3140	+	13.3140i	−0.680313	+	0.680313i	0.279758	+	0.960071i	$0.409746\pi$
$384$		0			0
$385$	−7.61851	−	5.94478i	−0.388275	−	0.302974i
$386$	10.5681			0.537900
$387$		0			0
$388$	0.0417357	+	0.155760i	0.00211881	+	0.00790750i
$389$			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
$392$	14.9482	−	14.5035i	0.755000	−	0.732539i
$393$		0			0
$394$	−5.58249	−	3.22305i	−0.281242	−	0.162375i
$395$	−5.77318	+	13.9153i	−0.290480	+	0.700154i
$396$		0			0
$397$	−6.22065	+	23.2158i	−0.312205	+	1.16517i	0.614358	+	0.789027i	$0.289415\pi$
$397$	−6.22065	+	23.2158i	−0.312205	+	1.16517i	−0.926563	+	0.376139i	$0.877252\pi$
$398$	4.87551	+	1.30639i	0.244387	+	0.0654834i
$399$		0			0
$400$	1.06045	−	3.93973i	0.0530227	−	0.196986i
$401$	−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
$407$	−8.97969	−	2.40610i	−0.445107	−	0.119266i
$408$		0			0
$409$	0.0455144	+	0.0788332i	0.00225054	+	0.00389805i	0.867148	−	0.498050i	$-0.165950\pi$
$409$	0.0455144	+	0.0788332i	0.00225054	+	0.00389805i	−0.864898	+	0.501948i	$0.832617\pi$
$410$	−15.3504	−	2.02981i	−0.758102	−	0.100245i
$411$		0			0
$412$	2.77869	−	10.3702i	0.136896	−	0.510903i
$413$	−2.81870	−	0.778123i	−0.138699	−	0.0382889i
$414$		0			0
$415$	−1.14860	+	8.68627i	−0.0563825	+	0.426392i
$416$			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	0.307464	+	0.951560i	$0.400520\pi$
$419$	−13.7216	+	23.7665i	−0.670343	+	1.16107i	−0.977807	+	0.209508i	$0.932814\pi$
$420$		0			0
$421$	−5.94319	−	10.2939i	−0.289653	−	0.501695i	0.684074	−	0.729413i	$-0.260207\pi$
$421$	−5.94319	−	10.2939i	−0.289653	−	0.501695i	−0.973727	+	0.227719i	$0.926873\pi$
$422$	0.515901	+	0.138235i	0.0251137	+	0.00672919i
$423$		0			0
$424$	3.60402	+	2.08078i	0.175027	+	0.101052i
$425$	4.44093	−	2.55724i	0.215417	−	0.124044i
$426$		0			0
$427$	−35.1739	+	9.14079i	−1.70219	+	0.442354i
$428$	−1.28489	+	0.344285i	−0.0621074	+	0.0166416i
$429$		0			0
$430$	−2.17872	−	16.6221i	−0.105067	−	0.801590i
$431$	11.1221	−	19.2640i	0.535732	−	0.927915i	−0.463396	−	0.886152i	$-0.653369\pi$
$431$	11.1221	−	19.2640i	0.535732	−	0.927915i	0.999128	−	0.0417634i	$-0.0132976\pi$
$432$		0			0
$433$	5.23695	−	5.23695i	0.251672	−	0.251672i	−0.569984	−	0.821656i	$-0.693051\pi$
$433$	5.23695	−	5.23695i	0.251672	−	0.251672i	0.821656	+	0.569984i	$0.193051\pi$
$434$	−21.6002	−	0.163069i	−1.03684	−	0.00782756i
$435$		0			0
$436$	−12.1202			−0.580450
$437$	11.5033	−	42.9307i	0.550275	−	2.05366i
$438$		0			0
$439$	−9.77505	+	16.9309i	−0.466538	+	0.808067i	−0.999269	−	0.0382173i	$-0.987832\pi$
$439$	−9.77505	+	16.9309i	−0.466538	+	0.808067i	0.532732	+	0.846284i	$0.321165\pi$
$440$	−6.62064	+	8.61802i	−0.315626	+	0.410848i
$441$		0			0
$442$	0.376358	−	0.376358i	0.0179015	−	0.0179015i
$443$	−36.2031	+	9.70060i	−1.72006	+	0.460889i	−0.977856	−	0.209281i	$-0.932888\pi$
$443$	−36.2031	+	9.70060i	−1.72006	+	0.460889i	−0.742207	+	0.670170i	$0.766221\pi$
$444$		0			0
$445$	32.1107	−	24.6103i	1.52219	−	1.16664i
$446$			25.8975i			1.22628i
$447$		0			0
$448$	−12.3784	−	12.5667i	−0.584822	−	0.593719i
$449$		−	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
$455$	1.22695	−	2.89540i	0.0575201	−	0.135738i
$456$		0			0
$457$	−7.55435	−	28.1932i	−0.353378	−	1.31882i	−0.882514	−	0.470286i	$-0.844151\pi$
$457$	−7.55435	−	28.1932i	−0.353378	−	1.31882i	0.529136	−	0.848537i	$-0.322516\pi$
$458$	−3.53791	−	13.2037i	−0.165316	−	0.616967i
$459$		0			0
$460$	2.27486	−	17.2036i	0.106066	−	0.802122i
$461$	13.2237	−	7.63473i	0.615891	−	0.355585i	−0.159377	−	0.987218i	$-0.550948\pi$
$461$	13.2237	−	7.63473i	0.615891	−	0.355585i	0.775267	+	0.631633i	$0.217615\pi$
$462$		0			0
$463$	39.9841	−	10.7137i	1.85822	−	0.497908i	0.858333	−	0.513092i	$-0.171500\pi$
$463$	39.9841	−	10.7137i	1.85822	−	0.497908i	0.999885	+	0.0151842i	$0.00483345\pi$
$464$		−	5.48695i		−	0.254725i
$465$		0			0
$466$	12.0292			0.557240
$467$	−4.67993	+	17.4657i	−0.216561	+	0.808217i	0.769050	+	0.639189i	$0.220730\pi$
$467$	−4.67993	+	17.4657i	−0.216561	+	0.808217i	−0.985611	+	0.169029i	$0.945937\pi$
$468$		0			0
$469$	12.8633	−	7.29773i	0.593973	−	0.336978i
$470$	3.42457	−	2.62467i	0.157964	−	0.121067i
$471$		0			0
$472$	−0.851123	+	3.17644i	−0.0391761	+	0.146207i
$473$	−3.24417	+	12.1074i	−0.149167	+	0.556698i
$474$		0			0
$475$	−21.1448	−	21.1930i	−0.970191	−	0.972402i
$476$	0.0214021	−	2.83493i	0.000980965	−	0.129939i
$477$		0			0
$478$	−1.91940	+	7.16329i	−0.0877912	+	0.327641i
$479$	−8.15139			−0.372447			−0.186223	−	0.982507i	$-0.559625\pi$
$479$	−8.15139			−0.372447			−0.186223	+	0.982507i	$0.559625\pi$
$480$		0			0
$481$		−	3.02522i		−	0.137938i
$482$	−5.68668	+	1.52374i	−0.259021	+	0.0694045i
$483$		0			0
$484$	−7.54388	+	4.35546i	−0.342903	+	0.197975i
$485$	−0.341912	−	0.0452115i	−0.0155254	−	0.00205295i
$486$		0			0
$487$	−1.05326	−	3.93080i	−0.0477276	−	0.178122i	0.937947	−	0.346777i	$-0.112724\pi$
$487$	−1.05326	−	3.93080i	−0.0477276	−	0.178122i	−0.985675	+	0.168656i	$0.946057\pi$
$488$	10.5781	+	39.4779i	0.478847	+	1.78708i
$489$		0			0
$490$	5.63006	+	14.2182i	0.254340	+	0.642315i
$491$	−14.1237	+	24.4629i	−0.637392	+	1.10399i	0.348612	+	0.937267i	$0.386653\pi$
$491$	−14.1237	+	24.4629i	−0.637392	+	1.10399i	−0.986003	+	0.166727i	$0.946680\pi$
$492$		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
$497$	−11.9833	+	11.8037i	−0.537524	+	0.529469i
$498$		0			0
$499$			24.7679i			1.10876i	0.832262	+	0.554382i	$0.187045\pi$
$499$			24.7679i			1.10876i	−0.832262	+	0.554382i	$0.812955\pi$
$500$	−9.26125	−	7.13156i	−0.414176	−	0.318933i
$501$		0			0
$502$	−4.53977	+	1.21643i	−0.202620	+	0.0542918i
$503$	−22.1184	+	22.1184i	−0.986211	+	0.986211i	−0.999906	−	0.0136949i	$-0.995641\pi$
$503$	−22.1184	+	22.1184i	−0.986211	+	0.986211i	0.0136949	+	0.999906i	$0.495641\pi$
$504$		0			0
$505$	18.0538	−	2.36638i	0.803383	−	0.105302i
$506$	5.92298	−	10.2589i	0.263308	−	0.456064i
$507$		0			0
$508$	−0.712015	+	2.65728i	−0.0315906	+	0.117898i
$509$	1.37539			0.0609630			0.0304815	−	0.999535i	$-0.490296\pi$
$509$	1.37539			0.0609630			0.0304815	+	0.999535i	$0.490296\pi$
$510$		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
$517$	−3.11613	+	0.834965i	−0.137047	+	0.0367217i
$518$	10.3239	+	10.4809i	0.453604	+	0.460505i
$519$		0			0
$520$	−3.26650	−	1.35521i	−0.143245	−	0.0594297i
$521$	22.4862	+	12.9824i	0.985140	+	0.568771i	0.903818	−	0.427917i	$-0.140752\pi$
$521$	22.4862	+	12.9824i	0.985140	+	0.568771i	0.0813222	+	0.996688i	$0.474086\pi$
$522$		0			0
$523$	2.60320	+	0.697525i	0.113830	+	0.0305006i	0.315284	−	0.948997i	$-0.397900\pi$
$523$	2.60320	+	0.697525i	0.113830	+	0.0305006i	−0.201454	+	0.979498i	$0.564567\pi$
$524$	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
$530$	−2.42516	+	1.85870i	−0.105342	+	0.0807368i
$531$		0			0
$532$	−16.0295	+	4.16565i	−0.694967	+	0.180604i
$533$	−0.975080	+	3.63905i	−0.0422354	+	0.157625i
$534$		0			0
$535$	0.372958	−	2.82049i	0.0161244	−	0.121940i
$536$	−8.31601	−	14.4038i	−0.359197	−	0.622148i
$537$		0			0
$538$	−3.52306	−	0.944001i	−0.151890	−	0.0406988i
$539$	0.172630	−	11.4326i	0.00743569	−	0.492439i
$540$		0			0
$541$	−10.0369	−	17.3845i	−0.431522	−	0.747418i	0.565482	−	0.824760i	$-0.308690\pi$
$541$	−10.0369	−	17.3845i	−0.431522	−	0.747418i	−0.997005	+	0.0773420i	$0.975357\pi$
$542$	4.42191	+	4.42191i	0.189937	+	0.189937i
$543$		0			0
$544$	−5.28202			−0.226465
$545$	9.93371	−	23.9435i	0.425513	−	1.02563i
$546$		0			0
$547$	14.4892	+	3.88238i	0.619515	+	0.165999i	0.554907	−	0.831912i	$-0.312754\pi$
$547$	14.4892	+	3.88238i	0.619515	+	0.165999i	0.0646077	+	0.997911i	$0.479420\pi$
$548$	3.66086	−	13.6625i	0.156384	−	0.583634i
$549$		0			0
$550$	−3.98173	−	6.91472i	−0.169782	−	0.294845i
$551$	−34.8675	−	20.1307i	−1.48540	−	0.857598i
$552$		0			0
$553$	−17.2525	+	4.48348i	−0.733651	+	0.190657i
$554$	0.485889	+	0.280528i	0.0206434	+	0.0119185i
$555$		0			0
$556$			13.4715i			0.571317i
$557$	0.0632745	+	0.236144i	0.00268103	+	0.0100057i	0.967253	−	0.253813i	$-0.0816847\pi$
$557$	0.0632745	+	0.236144i	0.00268103	+	0.0100057i	−0.964572	+	0.263818i	$0.915018\pi$
$558$		0			0
$559$	−4.07892			−0.172520
$560$	4.47485	−	1.81112i	0.189097	−	0.0765339i
$561$		0			0
$562$	3.06308	−	3.06308i	0.129208	−	0.129208i
$563$	−0.0758206	−	0.0203161i	−0.00319546	−	0.000856220i	0.257221	−	0.966353i	$-0.417193\pi$
$563$	−0.0758206	−	0.0203161i	−0.00319546	−	0.000856220i	−0.260416	+	0.965496i	$0.583860\pi$
$564$		0			0
$565$	17.7824	+	42.9998i	0.748112	+	1.80901i
$566$			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	$-0.433421\pi$
$569$	−12.7781	−	7.37743i	−0.535685	−	0.309278i	−0.743328	+	0.668927i	$0.766754\pi$
$570$		0			0
$571$	14.7758	+	25.5924i	0.618347	+	1.07101i	0.989787	+	0.142552i	$0.0455308\pi$
$571$	14.7758	+	25.5924i	0.618347	+	1.07101i	−0.371440	+	0.928457i	$0.621136\pi$
$572$	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
$577$	−8.07441	+	2.16353i	−0.336142	+	0.0900690i	−0.422942	−	0.906157i	$-0.639003\pi$
$577$	−8.07441	+	2.16353i	−0.336142	+	0.0900690i	0.0867998	+	0.996226i	$0.472336\pi$
$578$	−11.0186	−	11.0186i	−0.458312	−	0.458312i
$579$		0			0
$580$	−14.5198	−	6.02400i	−0.602903	−	0.250133i
$581$	−9.01713	+	5.11567i	−0.374094	+	0.212234i
$582$		0			0
$583$	2.20673	−	0.591293i	0.0913936	−	0.0244888i
$584$	−9.35288	+	16.1997i	−0.387025	+	0.670347i
$585$		0			0
$586$	16.2968	−	9.40894i	0.673213	−	0.388680i
$587$	2.34352	−	8.74614i	0.0967275	−	0.360992i	−0.900548	−	0.434756i	$-0.856835\pi$
$587$	2.34352	−	8.74614i	0.0967275	−	0.360992i	0.997276	+	0.0737643i	$0.0235013\pi$
$588$		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
$593$	27.9474	+	7.48847i	1.14766	+	0.307515i	0.782027	−	0.623244i	$-0.214186\pi$
$593$	27.9474	+	7.48847i	1.14766	+	0.307515i	0.365633	+	0.930759i	$0.380852\pi$
$594$		0			0
$595$	5.58291	+	2.36580i	0.228877	+	0.0969882i
$596$	−1.91489	−	3.31668i	−0.0784367	−	0.135856i
$597$		0			0
$598$	3.72351	+	0.997711i	0.152266	+	0.0407994i
$599$	−8.70341	+	5.02492i	−0.355612	+	0.205313i	−0.667154	−	0.744920i	$-0.732488\pi$
$599$	−8.70341	+	5.02492i	−0.355612	+	0.205313i	0.311542	+	0.950232i	$0.399154\pi$
$600$		0			0
$601$	−27.4153	+	15.8282i	−1.11829	+	0.645647i	−0.940965	−	0.338505i	$-0.890079\pi$
$601$	−27.4153	+	15.8282i	−1.11829	+	0.645647i	−0.177329	+	0.984152i	$0.556746\pi$
$602$	14.1315	−	13.9197i	0.575957	−	0.567326i
$603$		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	0.847718	−	0.530448i	$-0.177976\pi$
$607$	7.81669	+	7.81669i	0.317270	+	0.317270i	−0.530448	+	0.847718i	$0.677976\pi$
$608$	7.98642	+	29.8057i	0.323892	+	1.20878i
$609$		0			0
$610$	−29.7492	−	3.93378i	−1.20451	−	0.159274i
$611$	−0.524905	−	0.909162i	−0.0212354	−	0.0367807i
$612$		0			0
$613$	−23.0984	+	6.18919i	−0.932934	+	0.249979i	−0.693105	−	0.720836i	$-0.743758\pi$
$613$	−23.0984	+	6.18919i	−0.932934	+	0.249979i	−0.239829	+	0.970815i	$0.577091\pi$
$614$	4.52139	−	7.83128i	0.182468	−	0.316045i
$615$		0			0
$616$	−12.8583	−	0.0970726i	−0.518074	−	0.00391117i
$617$	1.79766	+	6.70895i	0.0723709	+	0.270092i	0.992624	−	0.121231i	$-0.0386842\pi$
$617$	1.79766	+	6.70895i	0.0723709	+	0.270092i	−0.920253	+	0.391323i	$0.872018\pi$
$618$		0			0
$619$	−31.3954			−1.26189			−0.630945	−	0.775828i	$-0.717333\pi$
$619$	−31.3954			−1.26189			−0.630945	+	0.775828i	$0.717333\pi$
$620$	18.0445	+	7.48631i	0.724685	+	0.300658i
$621$		0			0
$622$	17.0174	+	17.0174i	0.682337	+	0.682337i
$623$	46.1433	+	12.7382i	1.84869	+	0.510345i
$624$		0			0
$625$	21.6790	−	12.4507i	0.867161	−	0.498027i
$626$	−21.4698	+	12.3956i	−0.858107	+	0.495429i
$627$		0			0
$628$	−2.28606	−	8.53169i	−0.0912237	−	0.340452i
$629$	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	$0.762222\pi$
$632$	5.18846	+	19.3636i	0.206386	+	0.770242i
$633$		0			0
$634$	−9.01545	+	5.20507i	−0.358049	+	0.206720i
$635$	−4.66592	−	3.58451i	−0.185161	−	0.142247i
$636$		0			0
$637$	3.60813	−	0.908638i	0.142959	−	0.0360015i
$638$	−7.58787	−	7.58787i	−0.300407	−	0.300407i
$639$		0			0
$640$	3.24174	+	7.83888i	0.128141	+	0.309859i
$641$	−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
$643$	4.70433	+	17.5568i	0.185521	+	0.692372i	0.994518	+	0.104561i	$0.0333437\pi$
$643$	4.70433	+	17.5568i	0.185521	+	0.692372i	−0.808998	+	0.587812i	$0.799990\pi$
$644$	17.8589	−	10.1319i	0.703739	−	0.399251i
$645$		0			0
$646$	2.99774	−	5.19223i	0.117944	−	0.204286i
$647$	3.91026	−	1.04775i	0.153728	−	0.0411913i	−0.181134	−	0.983458i	$-0.557977\pi$
$647$	3.91026	−	1.04775i	0.153728	−	0.0411913i	0.334862	+	0.942267i	$0.391310\pi$
$648$		0			0
$649$	0.902644	+	1.56342i	0.0354319	+	0.0613698i
$650$	1.83813	−	1.83395i	0.0720974	−	0.0719335i
$651$		0			0
$652$	−0.600017	−	2.23930i	−0.0234985	−	0.0876976i
$653$	−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
$658$	4.92115	+	1.35852i	0.191846	+	0.0529605i
$659$	38.7647	−	22.3808i	1.51006	−	0.871834i	0.510129	−	0.860098i	$-0.329598\pi$
$659$	38.7647	−	22.3808i	1.51006	−	0.871834i	0.999931	−	0.0117356i	$-0.00373563\pi$
$660$		0			0
$661$	−15.1919	+	8.77106i	−0.590897	+	0.341155i	−0.765452	−	0.643493i	$-0.777485\pi$
$661$	−15.1919	+	8.77106i	−0.590897	+	0.341155i	0.174555	+	0.984647i	$0.444151\pi$
$662$	−5.89534	−	1.57965i	−0.229129	−	0.0613949i
$663$		0			0
$664$	5.82948	+	10.0970i	0.226228	+	0.391838i
$665$	4.90851	−	35.0807i	0.190344	−	1.36037i
$666$		0			0
$667$	48.2137	+	12.9188i	1.86684	+	0.500219i
$668$	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
$673$	−12.8090	+	47.8039i	−0.493751	+	1.84270i	0.0431629	+	0.999068i	$0.486257\pi$
$673$	−12.8090	+	47.8039i	−0.493751	+	1.84270i	−0.536914	+	0.843637i	$0.680410\pi$
$674$	10.8294	−	6.25233i	0.417131	−	0.240831i
$675$		0			0
$676$	6.64796	−	11.5146i	0.255691	−	0.442869i
$677$	−36.1964	+	9.69880i	−1.39114	+	0.372755i	−0.875155	−	0.483842i	$-0.839241\pi$
$677$	−36.1964	+	9.69880i	−1.39114	+	0.372755i	−0.515986	+	0.856597i	$0.672574\pi$
$678$		0			0
$679$	−0.201365	−	0.354936i	−0.00772768	−	0.0136212i
$680$	2.61310	−	6.29845i	0.100208	−	0.241535i
$681$		0			0
$682$	9.42982	+	9.42982i	0.361086	+	0.361086i
$683$	−25.2542	+	6.76683i	−0.966324	+	0.258926i	−0.707275	−	0.706939i	$-0.750076\pi$
$683$	−25.2542	+	6.76683i	−0.966324	+	0.258926i	−0.259049	+	0.965864i	$0.583409\pi$
$684$		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	0.805949	−	0.591984i	$-0.201655\pi$
$691$	18.3023	+	10.5668i	0.696251	+	0.401980i	−0.109699	+	0.993965i	$0.534989\pi$
$692$	1.51606	+	1.51606i	0.0576318	+	0.0576318i
$693$		0			0
$694$		−	13.0916i		−	0.496952i
$695$	−26.6131	−	11.0412i	−1.00949	−	0.418818i
$696$		0			0
$697$	−7.01680	−	1.88015i	−0.265780	−	0.0712156i
$698$	21.3261	−	21.3261i	0.807206	−	0.807206i
$699$		0			0
$700$	0.120149	−	13.8299i	0.00454122	−	0.522723i
$701$	−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
$703$	−8.81983	−	32.9160i	−0.332646	−	1.24145i
$704$			10.8901i			0.410434i
$705$		0			0
$706$	−13.9072	−	8.02934i	−0.523405	−	0.302188i
$707$	15.1186	+	15.3487i	0.568595	+	0.577246i
$708$		0			0
$709$	37.8779	+	21.8688i	1.42254	+	0.821302i	0.996515	−	0.0834117i	$-0.0265817\pi$
$709$	37.8779	+	21.8688i	1.42254	+	0.821302i	0.426021	+	0.904713i	$0.359915\pi$
$710$	−12.8346	+	5.30771i	−0.481674	+	0.199195i
$711$		0			0
$712$	13.9332	−	51.9995i	0.522170	−	1.94877i
$713$	−59.9175	−	16.0548i	−2.24393	−	0.601259i
$714$		0			0
$715$	−1.79406	+	0.741928i	−0.0670940	+	0.0277465i
$716$	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	$-0.276894\pi$
$719$	−9.10099	−	15.7634i	−0.339410	−	0.587875i	−0.984322	+	0.176382i	$0.943561\pi$
$720$		0			0
$721$	−0.205105	+	27.1683i	−0.00763851	+	1.01180i
$722$	−15.9013	−	4.26073i	−0.591784	−	0.158568i
$723$		0			0
$724$	−10.6471	−	18.4413i	−0.395696	−	0.685366i
$725$	23.8010	−	23.7469i	0.883946	−	0.881936i
$726$		0			0
$727$	12.6674	−	47.2752i	0.469806	−	1.75334i	−0.170635	−	0.985334i	$-0.554582\pi$
$727$	12.6674	−	47.2752i	0.469806	−	1.75334i	0.640441	−	0.768007i	$-0.278752\pi$
$728$	−1.05246	−	4.04988i	−0.0390067	−	0.150099i
$729$		0			0
$730$	−8.35466	−	10.9008i	−0.309220	−	0.403458i
$731$		−	7.86497i		−	0.290896i
$732$		0			0
$733$	14.0880	−	14.0880i	0.520350	−	0.520350i	−0.397327	−	0.917677i	$-0.630062\pi$
$733$	14.0880	−	14.0880i	0.520350	−	0.520350i	0.917677	+	0.397327i	$0.130062\pi$
$734$	−1.18391	+	2.05060i	−0.0436991	+	0.0756890i
$735$		0			0
$736$	−19.1277	−	33.1302i	−0.705057	−	1.22119i
$737$	−8.81940	−	2.36315i	−0.324867	−	0.0870478i
$738$		0			0
$739$	41.8852	+	24.1825i	1.54077	+	0.889566i	0.998790	+	0.0491770i	$0.0156598\pi$
$739$	41.8852	+	24.1825i	1.54077	+	0.889566i	0.541984	+	0.840389i	$0.317673\pi$
$740$	−5.08470	−	12.2953i	−0.186917	−	0.451986i
$741$		0			0
$742$	−3.48498	−	0.962055i	−0.127938	−	0.0353181i
$743$	31.7951	−	8.51948i	1.16645	−	0.312549i	0.376911	−	0.926250i	$-0.376986\pi$
$743$	31.7951	−	8.51948i	1.16645	−	0.312549i	0.789539	+	0.613700i	$0.210320\pi$
$744$		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	$0.579340\pi$
$752$	0.417115	−	1.55669i	0.0152106	−	0.0567667i
$753$		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	$-0.0105522\pi$
$758$	29.2244	−	7.83064i	1.06148	−	0.284422i
$759$		0			0
$760$	−39.4923	−	5.22213i	−1.43254	−	0.189426i
$761$			15.8150i			0.573292i	0.958037	+	0.286646i	$0.0925404\pi$
$761$			15.8150i			0.573292i	−0.958037	+	0.286646i	$0.907460\pi$
$762$		0			0
$763$	29.6858	−	7.71457i	1.07470	−	0.279286i
$764$		−	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	$-0.707238\pi$
$769$	10.7002	−	18.5333i	0.385860	−	0.668328i	0.991888	+	0.127115i	$0.0405716\pi$
$770$	3.68365	−	8.69283i	0.132750	−	0.313268i
$771$		0			0
$772$	−2.92697	−	10.9236i	−0.105344	−	0.393148i
$773$	−2.38488	−	8.90050i	−0.0857782	−	0.320129i	0.909682	−	0.415305i	$-0.136325\pi$
$773$	−2.38488	−	8.90050i	−0.0857782	−	0.320129i	−0.995460	+	0.0951763i	$0.969659\pi$
$774$		0			0
$775$	−29.5786	+	29.5114i	−1.06250	+	1.06008i
$776$	−0.397440	+	0.229462i	−0.0142673	+	0.00823722i
$777$		0			0
$778$	−22.3540	+	5.98973i	−0.801430	+	0.214742i
$779$			42.4376i			1.52049i
$780$		0			0
$781$	10.3845			0.371587
$782$	−1.92378	+	7.17966i	−0.0687944	+	0.256744i
$783$		0			0
$784$	4.90300	+	2.93033i	0.175107	+	0.104654i
$785$	18.7281	+	2.47645i	0.668436	+	0.0883882i
$786$		0			0
$787$	−13.4497	+	50.1948i	−0.479428	+	1.78925i	0.124509	+	0.992219i	$0.460265\pi$
$787$	−13.4497	+	50.1948i	−0.479428	+	1.78925i	−0.603937	+	0.797032i	$0.706402\pi$
$788$	−1.78534	+	6.66297i	−0.0636000	+	0.237358i
$789$		0			0
$790$	−14.5917	−	1.92948i	−0.519150	−	0.0686480i
$791$	−27.8877	+	47.4716i	−0.991571	+	1.68789i
$792$		0			0
$793$	−1.88971	+	7.05250i	−0.0671056	+	0.250442i
$794$	−23.4818			−0.833336
$795$		0			0
$796$		−	5.40136i		−	0.191446i
$797$	−4.61563	+	1.23676i	−0.163494	+	0.0438081i	−0.339638	−	0.940556i	$-0.610304\pi$
$797$	−4.61563	+	1.23676i	−0.163494	+	0.0438081i	0.176143	+	0.984365i	$0.443638\pi$
$798$		0			0
$799$	1.75304	−	1.01212i	0.0620182	−	0.0358062i
$800$	−25.7681	−	0.0293272i	−0.911039	−	0.00103687i
$801$		0			0
$802$	−8.65162	−	32.2883i	−0.305499	−	1.14014i
$803$	2.65780	+	9.91903i	0.0937916	+	0.350035i
$804$		0			0
$805$	5.37843	+	43.5846i	0.189565	+	1.53615i
$806$	−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	$-0.223229\pi$
$809$	16.7030	+	9.64348i	0.587246	+	0.339047i	−0.176762	+	0.984254i	$0.556562\pi$
$810$		0			0
$811$		−	7.57899i		−	0.266134i	−0.991107	−	0.133067i	$-0.957517\pi$
$811$		−	7.57899i		−	0.266134i	0.991107	−	0.133067i	$-0.0424826\pi$
$812$	−4.67826	−	18.0020i	−0.164175	−	0.631748i
$813$		0			0
$814$		−	9.08258i		−	0.318344i
$815$	4.91553	+	0.649988i	0.172184	+	0.0227681i
$816$		0			0
$817$	−44.3810	+	11.8918i	−1.55269	+	0.416043i
$818$	−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	−0.595383	−	0.803442i	$-0.703000\pi$
$821$	11.4071	−	19.7576i	0.398110	−	0.689547i	0.993493	+	0.113895i	$0.0363329\pi$
$822$		0			0
$823$	1.93083	−	7.20595i	0.0673044	−	0.251183i	−0.924074	−	0.382214i	$-0.875162\pi$
$823$	1.93083	−	7.20595i	0.0673044	−	0.251183i	0.991378	+	0.131030i	$0.0418285\pi$
$824$	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	$-0.880417\pi$
$829$	−4.24336	+	7.34971i	−0.147378	+	0.255266i	0.782880	+	0.622173i	$0.213750\pi$
$830$	−8.48769	+	1.11251i	−0.294612	+	0.0386159i
$831$		0			0
$832$	−3.42304	+	0.917202i	−0.118673	+	0.0317983i
$833$	1.75203	+	6.95719i	0.0607044	+	0.241052i
$834$		0			0
$835$	1.16163	+	2.80894i	0.0401998	+	0.0972074i
$836$	8.85503	+	5.11246i	0.306258	+	0.176818i
$837$		0			0
$838$	−25.8982	−	6.93939i	−0.894637	−	0.239717i
$839$	0.839410	+	1.45390i	0.0289797	+	0.0501942i	0.880152	−	0.474693i	$-0.157441\pi$
$839$	0.839410	+	1.45390i	0.0289797	+	0.0501942i	−0.851172	+	0.524887i	$0.824108\pi$
$840$		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
$845$	17.2986	+	22.5705i	0.595089	+	0.776450i
$846$		0			0
$847$	15.7049	−	15.4695i	0.539625	−	0.531539i
$848$	−0.295386	+	1.10240i	−0.0101436	+	0.0378564i
$849$		0			0
$850$	3.53622	+	3.54428i	0.121291	+	0.121568i
$851$	21.1237	+	36.5874i	0.724112	+	1.25420i
$852$		0			0
$853$	−41.0407	−	10.9968i	−1.40521	−	0.376524i	−0.524995	−	0.851105i	$-0.675933\pi$
$853$	−41.0407	−	10.9968i	−1.40521	−	0.376524i	−0.880212	+	0.474581i	$0.842599\pi$
$854$	−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	$0.0928616\pi$
$857$	36.4574	+	36.4574i	1.24536	+	1.24536i	0.287613	+	0.957747i	$0.407138\pi$
$858$		0			0
$859$	−19.3844			−0.661387			−0.330694	−	0.943738i	$-0.607283\pi$
$859$	−19.3844			−0.661387			−0.330694	+	0.943738i	$0.607283\pi$
$860$	−16.5779	+	6.85574i	−0.565302	+	0.233779i
$861$		0			0
$862$	20.9919	+	5.62476i	0.714986	+	0.191580i
$863$	0.109624	−	0.409122i	0.00373165	−	0.0139267i	−0.964035	−	0.265776i	$-0.914372\pi$
$863$	0.109624	−	0.409122i	0.00373165	−	0.0139267i	0.967767	+	0.251849i	$0.0810386\pi$
$864$		0			0
$865$	−4.23755	+	1.75243i	−0.144081	+	0.0595843i
$866$	6.26636	+	3.61788i	0.212939	+	0.122941i
$867$		0			0
$868$	5.81391	+	22.3720i	0.197337	+	0.759356i
$869$	9.53065	+	5.50253i	0.323305	+	0.186660i
$870$		0			0
$871$		−	2.97121i		−	0.100676i
$872$	−8.92760	−	33.3182i	−0.302327	−	1.12830i
$873$		0			0
$874$	43.4226			1.46879
$875$	27.2228	+	11.5724i	0.920298	+	0.391219i
$876$		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	$0.0203970\pi$
$878$	−18.4495	−	4.94352i	−0.622640	−	0.166836i
$879$		0			0
$880$	−2.75284	−	1.14210i	−0.0927982	−	0.0385001i
$881$		−	34.8974i		−	1.17572i	−0.808961	−	0.587862i	$-0.799970\pi$
$881$		−	34.8974i		−	1.17572i	0.808961	−	0.587862i	$-0.200030\pi$
$882$		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	$-0.958949\pi$
$887$	−33.3655	−	33.3655i	−1.12030	−	1.12030i	−0.128609	−	0.991695i	$-0.541051\pi$
$888$		0			0
$889$	0.0525565	−	6.96165i	0.00176269	−	0.233486i
$890$	31.3445	+	24.0798i	1.05067	+	0.807157i
$891$		0			0
$892$	26.7688	−	7.17267i	0.896285	−	0.240159i
$893$	−8.36186	−	8.36186i	−0.279819	−	0.279819i
$894$		0			0
$895$	−14.4486	+	34.8260i	−0.482964	+	1.16410i
$896$	−5.08393	+	8.65409i	−0.169842	+	0.289113i
$897$		0			0
$898$	17.5721	−	4.70842i	0.586387	−	0.157122i
$899$	−28.0960	+	48.6638i	−0.937055	+	1.62303i
$900$		0			0
$901$	−1.24144	+	0.716748i	−0.0413585	+	0.0238783i
$902$	−2.92747	+	10.9255i	−0.0974742	+	0.363779i
$903$		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	$0.113154\pi$
$908$	17.1846	+	4.60461i	0.570293	+	0.152809i
$909$		0			0
$910$	3.04265	+	0.425729i	0.100863	+	0.0141128i
$911$	−18.7147	−	32.4148i	−0.620045	−	1.07395i	−0.989477	−	0.144692i	$-0.953781\pi$
$911$	−18.7147	−	32.4148i	−0.620045	−	1.07395i	0.369431	−	0.929258i	$-0.379552\pi$
$912$		0			0
$913$	6.18235	+	1.65656i	0.204606	+	0.0548240i
$914$	24.6958	−	14.2581i	0.816864	−	0.471617i
$915$		0			0
$916$	−12.6680	+	7.31387i	−0.418562	+	0.241657i
$917$	−3.91293	−	3.97246i	−0.129216	−	0.131182i
$918$		0			0
$919$	−31.8867	+	18.4098i	−1.05184	+	0.607283i	−0.923165	−	0.384403i	$-0.874407\pi$
$919$	−31.8867	+	18.4098i	−1.05184	+	0.607283i	−0.128680	+	0.991686i	$0.541074\pi$
$920$	48.9683	−	6.41845i	1.61444	−	0.211610i
$921$		0			0
$922$	10.5487	+	10.5487i	0.347404	+	0.347404i
$923$	0.874623	+	3.26414i	0.0287886	+	0.107440i
$924$		0			0
$925$	28.4570	+	0.0323876i	0.935662	+	0.00106490i
$926$	20.2211	+	35.0240i	0.664507	+	1.15096i
$927$		0			0
$928$	−33.4736	+	8.96921i	−1.09882	+	0.294429i
$929$	−5.43502	+	9.41374i	−0.178317	+	0.308855i	−0.941304	−	0.337559i	$-0.890399\pi$
$929$	−5.43502	+	9.41374i	−0.178317	+	0.308855i	0.762987	+	0.646414i	$0.223732\pi$
$930$		0			0
$931$	36.6094	−	20.4058i	1.19982	−	0.668772i
$932$	−3.33164	−	12.4339i	−0.109132	−	0.407284i
$933$		0			0
$934$	−17.6658			−0.578044
$935$	−1.43058	−	3.45930i	−0.0467851	−	0.113131i
$936$		0			0
$937$	−22.9760	−	22.9760i	−0.750592	−	0.750592i	0.223998	−	0.974590i	$-0.428089\pi$
$937$	−22.9760	−	22.9760i	−0.750592	−	0.750592i	−0.974590	+	0.223998i	$0.928089\pi$
$938$	10.1396	+	10.2938i	0.331068	+	0.336105i
$939$		0			0
$940$	−3.66146	−	2.81285i	−0.119424	−	0.0917449i
$941$	−31.4547	+	18.1604i	−1.02539	+	0.592012i	−0.915662	−	0.401949i	$-0.868333\pi$
$941$	−31.4547	+	18.1604i	−1.02539	+	0.592012i	−0.109732	+	0.993961i	$0.534999\pi$
$942$		0			0
$943$	−13.6171	−	50.8197i	−0.443434	−	1.65492i
$944$	−0.901848			−0.0293527
$945$		0			0
$946$	−12.2461			−0.398155
$947$	2.99339	+	11.1715i	0.0972723	+	0.363025i	0.997354	−	0.0726957i	$-0.0231602\pi$
$947$	2.99339	+	11.1715i	0.0972723	+	0.363025i	−0.900082	+	0.435721i	$0.856494\pi$
$948$		0			0
$949$	−2.89397	+	1.67084i	−0.0939424	+	0.0542377i
$950$	14.6531	−	25.3134i	0.475410	−	0.821274i
$951$		0			0
$952$	7.80897	−	2.02935i	0.253090	−	0.0657716i
$953$	−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
$955$	35.5947	+	14.7675i	1.15182	+	0.477866i
$956$	7.93588			0.256665
$957$		0			0
$958$	−2.06120	−	7.69249i	−0.0665942	−	0.248533i
$959$	−0.270221	+	35.7936i	−0.00872591	+	1.15584i
$960$		0			0
$961$	19.4163	−	33.6300i	0.626333	−	1.08484i
$962$	2.85490	−	0.764969i	0.0920458	−	0.0246636i
$963$		0			0
$964$	3.15001	+	5.45598i	0.101455	+	0.175725i
$965$	23.9786	+	3.17073i	0.771900	+	0.102069i
$966$		0			0
$967$	−0.320359	−	1.19560i	−0.0103021	−	0.0384478i	0.960583	−	0.277992i	$-0.0896688\pi$
$967$	−0.320359	−	1.19560i	−0.0103021	−	0.0384478i	−0.970886	+	0.239544i	$0.923002\pi$
$968$	−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	0.225805	−	0.974173i	$-0.427499\pi$
$971$	36.8435	−	21.2716i	1.18237	−	0.682639i	0.956561	+	0.291533i	$0.0941654\pi$
$972$		0			0
$973$	−8.57468	−	32.9955i	−0.274892	−	1.05779i
$974$	3.44318	−	1.98792i	0.110327	−	0.0636971i
$975$		0			0
$976$	−9.70686	+	5.60426i	−0.310709	+	0.179388i
$977$	−7.08909	−	1.89952i	−0.226800	−	0.0607709i	0.143629	−	0.989632i	$-0.454123\pi$
$977$	−7.08909	−	1.89952i	−0.226800	−	0.0607709i	−0.370429	+	0.928861i	$0.620789\pi$
$978$		0			0
$979$	−14.7766	−	25.5939i	−0.472264	−	0.817985i
$980$	13.1373	−	9.75741i	0.419654	−	0.311689i
$981$		0			0
$982$	−26.6571	−	7.14274i	−0.850661	−	0.227934i
$983$	21.3401	−	21.3401i	0.680645	−	0.680645i	−0.279500	−	0.960146i	$-0.590169\pi$
$983$	21.3401	−	21.3401i	0.680645	−	0.680645i	0.960146	+	0.279500i	$0.0901689\pi$
$984$		0			0
$985$	−11.6995	−	8.98794i	−0.372778	−	0.286380i
$986$	5.83117	+	3.36663i	0.185702	+	0.107215i
$987$		0			0
$988$	−0.861181	+	3.21397i	−0.0273978	+	0.102250i
$989$	49.3310	−	28.4813i	1.56864	−	0.905652i
$990$		0			0
$991$	−25.4329	+	44.0511i	−0.807903	+	1.39933i	0.106411	+	0.994322i	$0.466064\pi$
$991$	−25.4329	+	44.0511i	−0.807903	+	1.39933i	−0.914314	+	0.405007i	$0.867269\pi$
$992$	41.5992	−	11.1465i	1.32078	−	0.353901i
$993$		0			0
$994$	−14.1693	−	8.32393i	−0.449424	−	0.264019i
$995$	10.6705	+	4.42696i	0.338276	+	0.140344i
$996$		0			0
$997$	−4.43771	−	4.43771i	−0.140544	−	0.140544i	0.633334	−	0.773878i	$-0.281686\pi$
$997$	−4.43771	−	4.43771i	−0.140544	−	0.140544i	−0.773878	+	0.633334i	$0.781686\pi$
$998$	−23.3735	+	6.26292i	−0.739876	+	0.198249i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cj.e.388.28		160
3.2	odd	2		315.2.cg.e.283.13	yes	160
5.2	odd	4	inner	945.2.cj.e.577.13		160
7.5	odd	6		945.2.bv.e.523.28		160
9.2	odd	6		315.2.bs.e.178.13	yes	160
9.7	even	3		945.2.bv.e.73.28		160
15.2	even	4		315.2.cg.e.157.28	yes	160
21.5	even	6		315.2.bs.e.103.13	yes	160
35.12	even	12		945.2.bv.e.712.28		160
45.2	even	12		315.2.bs.e.52.13	✓	160
45.7	odd	12		945.2.bv.e.262.28		160
63.47	even	6		315.2.cg.e.313.28	yes	160
63.61	odd	6	inner	945.2.cj.e.208.13		160
105.47	odd	12		315.2.bs.e.292.13	yes	160
315.47	odd	12		315.2.cg.e.187.13	yes	160
315.187	even	12	inner	945.2.cj.e.397.28		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.13	✓	160	45.2	even	12
315.2.bs.e.103.13	yes	160	21.5	even	6
315.2.bs.e.178.13	yes	160	9.2	odd	6
315.2.bs.e.292.13	yes	160	105.47	odd	12
315.2.cg.e.157.28	yes	160	15.2	even	4
315.2.cg.e.187.13	yes	160	315.47	odd	12
315.2.cg.e.283.13	yes	160	3.2	odd	2
315.2.cg.e.313.28	yes	160	63.47	even	6
945.2.bv.e.73.28		160	9.7	even	3
945.2.bv.e.262.28		160	45.7	odd	12
945.2.bv.e.523.28		160	7.5	odd	6
945.2.bv.e.712.28		160	35.12	even	12
945.2.cj.e.208.13		160	63.61	odd	6	inner
945.2.cj.e.388.28		160	1.1	even	1	trivial
945.2.cj.e.397.28		160	315.187	even	12	inner
945.2.cj.e.577.13		160	5.2	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.252864 + 0.943703i) q^{2} +(0.905417 - 0.522743i) q^{4} +(0.290604 + 2.21710i) q^{5} +(-1.88490 + 1.85665i) q^{7} +(2.10394 + 2.10394i) q^{8} +O(q^{10})\)	\(q+(0.252864 + 0.943703i) q^{2} +(0.905417 - 0.522743i) q^{4} +(0.290604 + 2.21710i) q^{5} +(-1.88490 + 1.85665i) q^{7} +(2.10394 + 2.10394i) q^{8} +(-2.01880 + 0.834870i) q^{10} +1.63342 q^{11} +(0.137573 + 0.513429i) q^{13} +(-2.22875 - 1.30930i) q^{14} +(-0.407995 + 0.706668i) q^{16} +(-0.989992 + 0.265268i) q^{17} +(2.99374 + 5.18531i) q^{19} +(1.42209 + 1.85549i) q^{20} +(0.413034 + 1.54146i) q^{22} +(-5.24887 - 5.24887i) q^{23} +(-4.83110 + 1.28860i) q^{25} +(-0.449737 + 0.259656i) q^{26} +(-0.736068 + 2.66636i) q^{28} +(-5.82340 + 3.36214i) q^{29} +(7.23702 - 4.17830i) q^{31} +(4.97801 + 1.33385i) q^{32} +(-0.500668 - 0.867182i) q^{34} +(-4.66415 - 3.63947i) q^{35} +(-5.49748 - 1.47305i) q^{37} +(-4.13638 + 4.13638i) q^{38} +(-4.05324 + 5.27606i) q^{40} +(6.13816 + 3.54387i) q^{41} +(-1.98612 + 7.41230i) q^{43} +(1.47893 - 0.853858i) q^{44} +(3.62612 - 6.28062i) q^{46} +(-1.90773 + 0.511176i) q^{47} +(0.105686 - 6.99920i) q^{49} +(-2.43767 - 4.23328i) q^{50} +(0.392952 + 0.392952i) q^{52} +(1.35099 - 0.361997i) q^{53} +(0.474678 + 3.62146i) q^{55} +(-7.87199 - 0.0594290i) q^{56} +(-4.64539 - 4.64539i) q^{58} +(0.552610 + 0.957148i) q^{59} +(11.8958 + 6.86804i) q^{61} +(5.77305 + 5.77305i) q^{62} +6.66703i q^{64} +(-1.09835 + 0.454218i) q^{65} +(-5.39935 - 1.44675i) q^{67} +(-0.757689 + 0.757689i) q^{68} +(2.25518 - 5.32186i) q^{70} +6.35753 q^{71} +(1.62714 + 6.07255i) q^{73} -5.56047i q^{74} +(5.42116 + 3.12991i) q^{76} +(-3.07883 + 3.03269i) q^{77} +(5.83478 + 3.36871i) q^{79} +(-1.68532 - 0.699207i) q^{80} +(-1.79224 + 6.68871i) q^{82} +(3.78491 + 1.01416i) q^{83} +(-0.875822 - 2.11783i) q^{85} -7.49722 q^{86} +(3.43661 + 3.43661i) q^{88} +(-9.04644 - 15.6689i) q^{89} +(-1.21257 - 0.712336i) q^{91} +(-7.49622 - 2.00861i) q^{92} +(-0.964796 - 1.67108i) q^{94} +(-10.6264 + 8.14430i) q^{95} +(-0.0399199 + 0.148983i) q^{97} +(6.63189 - 1.67011i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) \) 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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