LMFDB - Embedded newform 756.2.bt.a.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41356 + 0.0430901i) q^{2} +(-1.54969 + 0.773606i) q^{3} +(1.99629 - 0.121821i) q^{4} +(-0.175857 - 0.0310083i) q^{5} +(2.15724 - 1.16031i) q^{6} +(-2.42990 + 1.04671i) q^{7} +(-2.81662 + 0.258221i) q^{8} +(1.80307 - 2.39770i) q^{9} +O(q^{10})$	\(q+(-1.41356 + 0.0430901i) q^{2} +(-1.54969 + 0.773606i) q^{3} +(1.99629 - 0.121821i) q^{4} +(-0.175857 - 0.0310083i) q^{5} +(2.15724 - 1.16031i) q^{6} +(-2.42990 + 1.04671i) q^{7} +(-2.81662 + 0.258221i) q^{8} +(1.80307 - 2.39770i) q^{9} +(0.249920 + 0.0362544i) q^{10} +(3.67538 - 0.648069i) q^{11} +(-2.99938 + 1.73312i) q^{12} +(-3.16634 + 3.77349i) q^{13} +(3.38969 - 1.58429i) q^{14} +(0.296512 - 0.0879908i) q^{15} +(3.97032 - 0.486378i) q^{16} +1.56508i q^{17} +(-2.44542 + 3.46697i) q^{18} -5.25693 q^{19} +(-0.354839 - 0.0404785i) q^{20} +(2.95584 - 3.50186i) q^{21} +(-5.16743 + 1.07445i) q^{22} +(4.69503 - 5.59532i) q^{23} +(4.16511 - 2.57911i) q^{24} +(-4.66850 - 1.69919i) q^{25} +(4.31320 - 5.47049i) q^{26} +(-0.939322 + 5.11055i) q^{27} +(-4.72326 + 2.38555i) q^{28} +(-1.61131 + 1.35205i) q^{29} +(-0.415345 + 0.137157i) q^{30} +(-2.14361 + 0.780211i) q^{31} +(-5.59131 + 0.858605i) q^{32} +(-5.19434 + 3.84760i) q^{33} +(-0.0674397 - 2.21234i) q^{34} +(0.459771 - 0.108725i) q^{35} +(3.30735 - 5.00614i) q^{36} +(2.92408 + 5.06465i) q^{37} +(7.43097 - 0.226522i) q^{38} +(1.98764 - 8.29724i) q^{39} +(0.503329 + 0.0419286i) q^{40} +(2.24813 - 2.67922i) q^{41} +(-4.02735 + 5.07745i) q^{42} +(2.95341 - 8.11442i) q^{43} +(7.25816 - 1.74147i) q^{44} +(-0.391431 + 0.365742i) q^{45} +(-6.39559 + 8.11161i) q^{46} +(2.30007 + 0.837157i) q^{47} +(-5.77649 + 3.82520i) q^{48} +(4.80878 - 5.08681i) q^{49} +(6.67241 + 2.20074i) q^{50} +(-1.21076 - 2.42539i) q^{51} +(-5.86123 + 7.91870i) q^{52} +(-3.89512 - 6.74654i) q^{53} +(1.10757 - 7.26452i) q^{54} -0.666437 q^{55} +(6.57380 - 3.57564i) q^{56} +(8.14660 - 4.06679i) q^{57} +(2.21941 - 1.98063i) q^{58} +(-6.65194 - 5.58164i) q^{59} +(0.581204 - 0.211776i) q^{60} +(3.70248 - 10.1725i) q^{61} +(2.99650 - 1.19524i) q^{62} +(-1.87157 + 7.71345i) q^{63} +(7.86664 - 1.45462i) q^{64} +(0.673833 - 0.565413i) q^{65} +(7.17671 - 5.66263i) q^{66} +(-12.6419 - 2.22911i) q^{67} +(0.190660 + 3.12436i) q^{68} +(-2.94726 + 12.3031i) q^{69} +(-0.645228 + 0.173500i) q^{70} +(-10.2273 - 5.90473i) q^{71} +(-4.45941 + 7.21898i) q^{72} +(-8.66167 - 5.00082i) q^{73} +(-4.35159 - 7.03317i) q^{74} +(8.54923 - 0.978356i) q^{75} +(-10.4943 + 0.640403i) q^{76} +(-8.25244 + 5.42181i) q^{77} +(-2.45211 + 11.8143i) q^{78} +(10.2468 - 1.80678i) q^{79} +(-0.713290 - 0.0375800i) q^{80} +(-2.49789 - 8.64642i) q^{81} +(-3.06242 + 3.88410i) q^{82} +(13.2854 - 11.1478i) q^{83} +(5.47410 - 7.35080i) q^{84} +(0.0485307 - 0.275231i) q^{85} +(-3.82516 + 11.5975i) q^{86} +(1.45107 - 3.34177i) q^{87} +(-10.1848 + 2.77442i) q^{88} -17.8944i q^{89} +(0.537550 - 0.533863i) q^{90} +(3.74410 - 12.4834i) q^{91} +(8.69100 - 11.7418i) q^{92} +(2.71835 - 2.86739i) q^{93} +(-3.28735 - 1.08426i) q^{94} +(0.924468 + 0.163009i) q^{95} +(8.00057 - 5.65604i) q^{96} +(1.08192 - 2.97255i) q^{97} +(-6.57830 + 7.39770i) q^{98} +(5.07309 - 9.98095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41356	+	0.0430901i	−0.999536	+	0.0304693i
$2$	−1.41356	+	0.0430901i	−0.999536	+	0.0304693i
$3$	−1.54969	+	0.773606i	−0.894713	+	0.446642i
$3$	−1.54969	+	0.773606i	−0.894713	+	0.446642i
$4$	1.99629	−	0.121821i	0.998143	−	0.0609104i
$5$	−0.175857	−	0.0310083i	−0.0786457	−	0.0138674i	0.134187	−	0.990956i	$-0.457158\pi$
$5$	−0.175857	−	0.0310083i	−0.0786457	−	0.0138674i	−0.212833	+	0.977089i	$0.568269\pi$
$6$	2.15724	−	1.16031i	0.880689	−	0.473695i
$7$	−2.42990	+	1.04671i	−0.918414	+	0.395620i
$7$	−2.42990	+	1.04671i	−0.918414	+	0.395620i
$8$	−2.81662	+	0.258221i	−0.995824	+	0.0912948i
$9$	1.80307	−	2.39770i	0.601023	−	0.799232i
$10$	0.249920	+	0.0362544i	0.0790317	+	0.0114646i
$11$	3.67538	−	0.648069i	1.10817	−	0.195400i	0.410528	−	0.911848i	$-0.365344\pi$
$11$	3.67538	−	0.648069i	1.10817	−	0.195400i	0.697641	+	0.716448i	$0.254233\pi$
$12$	−2.99938	+	1.73312i	−0.865847	+	0.500310i
$13$	−3.16634	+	3.77349i	−0.878184	+	1.04658i	0.120365	+	0.992730i	$0.461593\pi$
$13$	−3.16634	+	3.77349i	−0.878184	+	1.04658i	−0.998549	+	0.0538492i	$0.982851\pi$
$14$	3.38969	−	1.58429i	0.905933	−	0.423420i
$15$	0.296512	−	0.0879908i	0.0765590	−	0.0227191i
$16$	3.97032	−	0.486378i	0.992580	−	0.121595i
$17$			1.56508i			0.379589i	0.981824	+	0.189794i	$0.0607821\pi$
$17$			1.56508i			0.379589i	−0.981824	+	0.189794i	$0.939218\pi$
$18$	−2.44542	+	3.46697i	−0.576392	+	0.817174i
$19$	−5.25693			−1.20602			−0.603011	−	0.797733i	$-0.706033\pi$
$19$	−5.25693			−1.20602			−0.603011	+	0.797733i	$0.706033\pi$
$20$	−0.354839	−	0.0404785i	−0.0793443	−	0.00905127i
$21$	2.95584	−	3.50186i	0.645017	−	0.764169i
$22$	−5.16743	+	1.07445i	−1.10170	+	0.229074i
$23$	4.69503	−	5.59532i	0.978981	−	1.16670i	−0.00702144	−	0.999975i	$-0.502235\pi$
$23$	4.69503	−	5.59532i	0.978981	−	1.16670i	0.986003	−	0.166729i	$-0.0533205\pi$
$24$	4.16511	−	2.57911i	0.850201	−	0.526459i
$25$	−4.66850	−	1.69919i	−0.933700	−	0.339839i
$26$	4.31320	−	5.47049i	0.845888	−	1.07285i
$27$	−0.939322	+	5.11055i	−0.180773	+	0.983525i
$28$	−4.72326	+	2.38555i	−0.892611	+	0.450827i
$29$	−1.61131	+	1.35205i	−0.299212	+	0.251069i	−0.780016	−	0.625759i	$-0.784789\pi$
$29$	−1.61131	+	1.35205i	−0.299212	+	0.251069i	0.480804	+	0.876828i	$0.340345\pi$
$30$	−0.415345	+	0.137157i	−0.0758313	+	0.0250413i
$31$	−2.14361	+	0.780211i	−0.385004	+	0.140130i	−0.527269	−	0.849699i	$-0.676784\pi$
$31$	−2.14361	+	0.780211i	−0.385004	+	0.140130i	0.142265	+	0.989829i	$0.454562\pi$
$32$	−5.59131	+	0.858605i	−0.988414	+	0.151781i
$33$	−5.19434	+	3.84760i	−0.904219	+	0.669781i
$34$	−0.0674397	−	2.21234i	−0.0115658	−	0.379412i
$35$	0.459771	−	0.108725i	0.0777155	−	0.0183779i
$36$	3.30735	−	5.00614i	0.551225	−	0.834356i
$37$	2.92408	+	5.06465i	0.480715	+	0.832623i	0.999755	−	0.0221267i	$-0.00704371\pi$
$37$	2.92408	+	5.06465i	0.480715	+	0.832623i	−0.519040	+	0.854750i	$0.673710\pi$
$38$	7.43097	−	0.226522i	1.20546	−	0.0367467i
$39$	1.98764	−	8.29724i	0.318277	−	1.32862i
$40$	0.503329	+	0.0419286i	0.0795833	+	0.00662950i
$41$	2.24813	−	2.67922i	0.351099	−	0.418424i	−0.561373	−	0.827563i	$-0.689727\pi$
$41$	2.24813	−	2.67922i	0.351099	−	0.418424i	0.912472	+	0.409139i	$0.134171\pi$
$42$	−4.02735	+	5.07745i	−0.621433	+	0.783467i
$43$	2.95341	−	8.11442i	0.450390	−	1.23744i	−0.482060	−	0.876138i	$-0.660111\pi$
$43$	2.95341	−	8.11442i	0.450390	−	1.23744i	0.932450	−	0.361299i	$-0.117666\pi$
$44$	7.25816	−	1.74147i	1.09421	−	0.262536i
$45$	−0.391431	+	0.365742i	−0.0583511	+	0.0545215i
$46$	−6.39559	+	8.11161i	−0.942978	+	1.19599i
$47$	2.30007	+	0.837157i	0.335500	+	0.122112i	0.504276	−	0.863542i	$-0.331759\pi$
$47$	2.30007	+	0.837157i	0.335500	+	0.122112i	−0.168777	+	0.985654i	$0.553982\pi$
$48$	−5.77649	+	3.82520i	−0.833765	+	0.552120i
$49$	4.80878	−	5.08681i	0.686969	−	0.726687i
$50$	6.67241	+	2.20074i	0.943621	+	0.311232i
$51$	−1.21076	−	2.42539i	−0.169540	−	0.339623i
$52$	−5.86123	+	7.91870i	−0.812806	+	1.09813i
$53$	−3.89512	−	6.74654i	−0.535035	−	0.926708i	−0.999162	−	0.0409394i	$-0.986965\pi$
$53$	−3.89512	−	6.74654i	−0.535035	−	0.926708i	0.464126	−	0.885769i	$-0.346368\pi$
$54$	1.10757	−	7.26452i	0.150721	−	0.988576i
$55$	−0.666437			−0.0898623
$56$	6.57380	−	3.57564i	0.878461	−	0.477815i
$57$	8.14660	−	4.06679i	1.07904	−	0.538660i
$58$	2.21941	−	1.98063i	0.291423	−	0.260069i
$59$	−6.65194	−	5.58164i	−0.866009	−	0.726668i	0.0972450	−	0.995260i	$-0.468997\pi$
$59$	−6.65194	−	5.58164i	−0.866009	−	0.726668i	−0.963254	+	0.268593i	$0.913441\pi$
$60$	0.581204	−	0.211776i	0.0750331	−	0.0273402i
$61$	3.70248	−	10.1725i	0.474054	−	1.30245i	−0.440415	−	0.897794i	$-0.645169\pi$
$61$	3.70248	−	10.1725i	0.474054	−	1.30245i	0.914468	−	0.404657i	$-0.132609\pi$
$62$	2.99650	−	1.19524i	0.380556	−	0.151796i
$63$	−1.87157	+	7.71345i	−0.235795	+	0.971803i
$64$	7.86664	−	1.45462i	0.983331	−	0.181827i
$65$	0.673833	−	0.565413i	0.0835786	−	0.0701308i
$66$	7.17671	−	5.66263i	0.883391	−	0.697021i
$67$	−12.6419	−	2.22911i	−1.54445	−	0.272329i	−0.664462	−	0.747322i	$-0.731339\pi$
$67$	−12.6419	−	2.22911i	−1.54445	−	0.272329i	−0.879989	+	0.474993i	$0.842451\pi$
$68$	0.190660	+	3.12436i	0.0231209	+	0.378884i
$69$	−2.94726	+	12.3031i	−0.354809	+	1.48112i
$70$	−0.645228	+	0.173500i	−0.0771195	+	0.0207373i
$71$	−10.2273	−	5.90473i	−1.21376	−	0.700762i	−0.250180	−	0.968199i	$-0.580490\pi$
$71$	−10.2273	−	5.90473i	−1.21376	−	0.700762i	−0.963575	+	0.267437i	$0.913823\pi$
$72$	−4.45941	+	7.21898i	−0.525547	+	0.850765i
$73$	−8.66167	−	5.00082i	−1.01377	−	0.585302i	−0.101478	−	0.994838i	$-0.532357\pi$
$73$	−8.66167	−	5.00082i	−1.01377	−	0.585302i	−0.912294	+	0.409536i	$0.865691\pi$
$74$	−4.35159	−	7.03317i	−0.505862	−	0.817590i
$75$	8.54923	−	0.978356i	0.987180	−	0.112971i
$76$	−10.4943	+	0.640403i	−1.20378	+	0.0734593i
$77$	−8.25244	+	5.42181i	−0.940453	+	0.617872i
$78$	−2.45211	+	11.8143i	−0.277647	+	1.33770i
$79$	10.2468	−	1.80678i	1.15285	−	0.203279i	0.435632	−	0.900125i	$-0.356525\pi$
$79$	10.2468	−	1.80678i	1.15285	−	0.203279i	0.717221	+	0.696846i	$0.245414\pi$
$80$	−0.713290	−	0.0375800i	−0.0797483	−	0.00420157i
$81$	−2.49789	−	8.64642i	−0.277543	−	0.960713i
$82$	−3.06242	+	3.88410i	−0.338187	+	0.428927i
$83$	13.2854	−	11.1478i	1.45826	−	1.22363i	0.532002	−	0.846743i	$-0.321440\pi$
$83$	13.2854	−	11.1478i	1.45826	−	1.22363i	0.926260	−	0.376885i	$-0.123005\pi$
$84$	5.47410	−	7.35080i	0.597273	−	0.802038i
$85$	0.0485307	−	0.275231i	0.00526389	−	0.0298530i
$86$	−3.82516	+	11.5975i	−0.412477	+	1.25059i
$87$	1.45107	−	3.34177i	0.155571	−	0.358275i
$88$	−10.1848	+	2.77442i	−1.08570	+	0.295754i
$89$		−	17.8944i		−	1.89680i	−0.317075	−	0.948400i	$-0.602701\pi$
$89$		−	17.8944i		−	1.89680i	0.317075	−	0.948400i	$-0.397299\pi$
$90$	0.537550	−	0.533863i	0.0566627	−	0.0562741i
$91$	3.74410	−	12.4834i	0.392489	−	1.30862i
$92$	8.69100	−	11.7418i	0.906099	−	1.22417i
$93$	2.71835	−	2.86739i	0.281880	−	0.297335i
$94$	−3.28735	−	1.08426i	−0.339064	−	0.111833i
$95$	0.924468	+	0.163009i	0.0948485	+	0.0167243i
$96$	8.00057	−	5.65604i	0.816555	−	0.577267i
$97$	1.08192	−	2.97255i	0.109852	−	0.301817i	−0.872570	−	0.488489i	$-0.837548\pi$
$97$	1.08192	−	2.97255i	0.109852	−	0.301817i	0.982422	+	0.186672i	$0.0597703\pi$
$98$	−6.57830	+	7.39770i	−0.664508	+	0.747281i
$99$	5.07309	−	9.98095i	0.509865	−	1.00312i
$100$	−9.52666	−	2.82336i	−0.952666	−	0.282336i
$101$	6.13874	+	7.31587i	0.610828	+	0.727956i	0.979464	−	0.201617i	$-0.0646198\pi$
$101$	6.13874	+	7.31587i	0.610828	+	0.727956i	−0.368637	+	0.929574i	$0.620175\pi$
$102$	1.81599	+	3.37626i	0.179809	+	0.334299i
$103$	0.243480	−	1.38084i	0.0239908	−	0.136058i	−0.970460	−	0.241263i	$-0.922438\pi$
$103$	0.243480	−	1.38084i	0.0239908	−	0.136058i	0.994451	+	0.105204i	$0.0335496\pi$
$104$	7.94396	−	11.4461i	0.778969	−	1.12238i
$105$	−0.628392	+	0.524171i	−0.0613247	+	0.0511539i
$106$	5.79668	+	9.36878i	0.563023	+	0.909976i
$107$	8.20058	+	4.73461i	0.792780	+	0.457712i	0.840940	−	0.541128i	$-0.182002\pi$
$107$	8.20058	+	4.73461i	0.792780	+	0.457712i	−0.0481602	+	0.998840i	$0.515336\pi$
$108$	−1.25259	+	10.3165i	−0.120530	+	0.992710i
$109$	5.57977	+	9.66444i	0.534445	+	0.925685i	0.999190	+	0.0402408i	$0.0128125\pi$
$109$	5.57977	+	9.66444i	0.534445	+	0.925685i	−0.464745	+	0.885444i	$0.653854\pi$
$110$	0.942047	−	0.0287169i	0.0898206	−	0.00273804i
$111$	−8.44945	−	5.58655i	−0.801986	−	0.530252i
$112$	−9.13836	+	5.33763i	−0.863494	+	0.504359i
$113$	−14.6123	+	5.31846i	−1.37461	+	0.500318i	−0.920541	−	0.390647i	$-0.872251\pi$
$113$	−14.6123	+	5.31846i	−1.37461	+	0.500318i	−0.454072	+	0.890965i	$0.650029\pi$
$114$	−11.3405	+	6.09968i	−1.06213	+	0.571287i
$115$	−0.999156	+	0.838391i	−0.0931717	+	0.0781804i
$116$	−3.05192	+	2.89536i	−0.283364	+	0.268828i
$117$	3.33857	+	14.3958i	0.308651	+	1.33089i
$118$	9.64341	+	7.60333i	0.887748	+	0.699944i
$119$	−1.63819	−	3.80299i	−0.150173	−	0.348620i
$120$	−0.812439	+	0.324402i	−0.0741652	+	0.0296137i
$121$	2.75180	−	1.00157i	0.250164	−	0.0910522i
$122$	−4.79533	+	14.5389i	−0.434149	+	1.31629i
$123$	−1.41124	+	5.89112i	−0.127248	+	0.531185i
$124$	−4.18422	+	1.81866i	−0.375754	+	0.163321i
$125$	1.54153	+	0.890003i	0.137879	+	0.0796043i
$126$	2.31319	−	10.9840i	0.206076	−	0.978536i
$127$	1.44475	−	0.834129i	0.128201	−	0.0740170i	−0.434528	−	0.900658i	$-0.643085\pi$
$127$	1.44475	−	0.834129i	0.128201	−	0.0740170i	0.562729	+	0.826641i	$0.309751\pi$
$128$	−11.0573	+	2.39516i	−0.977334	+	0.211704i
$129$	1.70050	+	14.8596i	0.149721	+	1.30831i
$130$	−0.928137	+	0.828279i	−0.0814030	+	0.0726448i
$131$	−7.50439	−	6.29693i	−0.655661	−	0.550165i	0.253122	−	0.967434i	$-0.418543\pi$
$131$	−7.50439	−	6.29693i	−0.655661	−	0.550165i	−0.908783	+	0.417269i	$0.862987\pi$
$132$	−9.90068	+	8.31369i	−0.861744	+	0.723614i
$133$	12.7738	−	5.50250i	1.10763	−	0.477127i
$134$	17.9661	+	2.60623i	1.55203	+	0.225144i
$135$	0.323656	−	0.869599i	0.0278559	−	0.0748431i
$136$	−0.404137	−	4.40824i	−0.0346545	−	0.378003i
$137$	−5.14526	−	1.87272i	−0.439590	−	0.159998i	0.112738	−	0.993625i	$-0.464038\pi$
$137$	−5.14526	−	1.87272i	−0.439590	−	0.159998i	−0.552327	+	0.833627i	$0.686260\pi$
$138$	3.63598	−	17.5181i	0.309515	−	1.49124i
$139$	−3.25271	+	18.4470i	−0.275891	+	1.56466i	0.460226	+	0.887802i	$0.347768\pi$
$139$	−3.25271	+	18.4470i	−0.275891	+	1.56466i	−0.736117	+	0.676854i	$0.763343\pi$
$140$	0.904590	−	0.273056i	0.0764518	−	0.0230774i
$141$	−4.21202	+	0.482015i	−0.354716	+	0.0405930i
$142$	14.7113	+	7.90597i	1.23454	+	0.663454i
$143$	−9.19201	+	15.9210i	−0.768674	+	1.33138i
$144$	5.99257	−	10.3966i	0.499381	−	0.866383i
$145$	0.325284	−	0.187803i	0.0270134	−	0.0155962i
$146$	12.4593	+	6.69571i	1.03114	+	0.554141i
$147$	−3.51693	+	11.6031i	−0.290072	+	0.957005i
$148$	6.45427	+	9.75428i	0.530538	+	0.801797i
$149$	−7.24837	+	2.63819i	−0.593810	+	0.216129i	−0.621404	−	0.783490i	$-0.713438\pi$
$149$	−7.24837	+	2.63819i	−0.593810	+	0.216129i	0.0275944	+	0.999619i	$0.491215\pi$
$150$	−12.0427	+	1.75135i	−0.983279	+	0.142997i
$151$	−3.73128	+	0.657925i	−0.303647	+	0.0535412i	−0.323396	−	0.946264i	$-0.604824\pi$
$151$	−3.73128	+	0.657925i	−0.303647	+	0.0535412i	0.0197487	+	0.999805i	$0.493713\pi$
$152$	14.8068	−	1.35745i	1.20099	−	0.110104i
$153$	3.75260	+	2.82195i	0.303379	+	0.228141i
$154$	11.4317	−	8.01963i	0.921191	−	0.646240i
$155$	0.401162	−	0.0707357i	0.0322221	−	0.00568163i
$156$	2.95712	−	16.8058i	0.236759	−	1.34554i
$157$	−0.240044	+	0.286073i	−0.0191576	+	0.0228311i	−0.775538	−	0.631301i	$-0.782521\pi$
$157$	−0.240044	+	0.286073i	−0.0191576	+	0.0228311i	0.756381	+	0.654132i	$0.226966\pi$
$158$	−14.4066	+	2.99553i	−1.14612	+	0.238311i
$159$	11.2554	+	7.44175i	0.892610	+	0.590169i
$160$	1.00990	+	0.0223857i	0.0798393	+	0.00176975i
$161$	−5.55174	+	18.5104i	−0.437538	+	1.45882i
$162$	3.90349	+	12.1146i	0.306687	+	0.951810i
$163$	−10.2206	−	5.90089i	−0.800543	−	0.462194i	0.0431180	−	0.999070i	$-0.486271\pi$
$163$	−10.2206	−	5.90089i	−0.800543	−	0.462194i	−0.843661	+	0.536876i	$0.819604\pi$
$164$	4.16153	−	5.62236i	0.324961	−	0.439033i
$165$	1.03277	−	0.515559i	0.0804010	−	0.0401363i
$166$	−18.2993	+	16.3305i	−1.42030	+	1.26749i
$167$	−4.35663	+	1.58569i	−0.337127	+	0.122704i	−0.505036	−	0.863098i	$-0.668521\pi$
$167$	−4.35663	+	1.58569i	−0.337127	+	0.122704i	0.167909	+	0.985802i	$0.446298\pi$
$168$	−7.42120	+	10.6267i	−0.572558	+	0.819864i
$169$	−1.95614	−	11.0938i	−0.150472	−	0.853370i
$170$	−0.0567411	+	0.391146i	−0.00435185	+	0.0299995i
$171$	−9.47860	+	12.6045i	−0.724847	+	0.963892i
$172$	4.90734	−	16.5585i	0.374181	−	1.26257i
$173$	6.22068	+	7.41352i	0.472950	+	0.563640i	0.948796	−	0.315889i	$-0.102303\pi$
$173$	6.22068	+	7.41352i	0.472950	+	0.563640i	−0.475846	+	0.879528i	$0.657858\pi$
$174$	−1.90718	+	4.78631i	−0.144583	+	0.362849i
$175$	13.1225	−	0.757715i	0.991970	−	0.0572779i
$176$	14.2772	−	4.36066i	1.07619	−	0.328697i
$177$	14.6264	+	3.50382i	1.09939	+	0.263364i
$178$	0.771071	+	25.2947i	0.0577942	+	1.89592i
$179$			4.92915i			0.368422i	0.982887	+	0.184211i	$0.0589729\pi$
$179$			4.92915i			0.368422i	−0.982887	+	0.184211i	$0.941027\pi$
$180$	−0.736853	+	0.777809i	−0.0549218	+	0.0579745i
$181$	−10.0594	+	5.80781i	−0.747711	+	0.431691i	−0.824866	−	0.565328i	$-0.808750\pi$
$181$	−10.0594	+	5.80781i	−0.747711	+	0.431691i	0.0771555	+	0.997019i	$0.475416\pi$
$182$	−4.75459	+	17.8074i	−0.352434	+	1.31997i
$183$	2.13180	+	18.6284i	0.157587	+	1.37705i
$184$	−11.7793	+	16.9722i	−0.868379	+	1.25121i
$185$	−0.357173	−	0.981325i	−0.0262599	−	0.0721485i
$186$	−3.71899	+	4.17036i	−0.272690	+	0.305786i
$187$	1.01428	+	5.75228i	0.0741716	+	0.420648i
$188$	4.69358	+	1.39101i	0.342315	+	0.101450i
$189$	−3.06682	−	13.4013i	−0.223078	−	0.974800i
$190$	−1.31381	−	0.190587i	−0.0953140	−	0.0138266i
$191$	15.5071	−	2.73433i	1.12206	−	0.197849i	0.418313	−	0.908303i	$-0.362621\pi$
$191$	15.5071	−	2.73433i	1.12206	−	0.197849i	0.703744	+	0.710454i	$0.251510\pi$
$192$	−11.0655	+	8.33988i	−0.798587	+	0.601879i
$193$	2.69879	−	0.982281i	0.194263	−	0.0707061i	−0.243056	−	0.970012i	$-0.578150\pi$
$193$	2.69879	−	0.982281i	0.194263	−	0.0707061i	0.437320	+	0.899306i	$0.355928\pi$
$194$	−1.40127	+	4.24849i	−0.100605	+	0.305024i
$195$	−0.606824	+	1.39749i	−0.0434556	+	0.100077i
$196$	8.98003	−	10.7405i	0.641431	−	0.767181i
$197$	−4.99637	−	8.65396i	−0.355976	−	0.616569i	0.631308	−	0.775532i	$-0.282518\pi$
$197$	−4.99637	−	8.65396i	−0.355976	−	0.616569i	−0.987285	+	0.158963i	$0.949185\pi$
$198$	−6.74102	+	14.3272i	−0.479063	+	1.01819i
$199$	−20.6921			−1.46682			−0.733412	−	0.679784i	$-0.762073\pi$
$199$	−20.6921			−1.46682			−0.733412	+	0.679784i	$0.762073\pi$
$200$	13.5881	+	3.58047i	0.960826	+	0.253178i
$201$	21.3154	−	6.32542i	1.50347	−	0.446160i
$202$	−8.99270	−	10.0769i	−0.632724	−	0.709007i
$203$	2.50010	−	4.97191i	0.175473	−	0.348960i
$204$	−2.71248	−	4.69428i	−0.189912	−	0.328666i
$205$	−0.478428	+	0.401449i	−0.0334149	+	0.0280384i
$206$	−0.284672	+	1.96239i	−0.0198340	+	0.136726i
$207$	−4.95041	−	21.3460i	−0.344078	−	1.48365i
$208$	−10.7360	+	16.5220i	−0.744409	+	1.14560i
$209$	−19.3212	+	3.40685i	−1.33648	+	0.235657i
$210$	0.865681	−	0.768023i	0.0597377	−	0.0529987i
$211$	4.69351	+	12.8953i	0.323114	+	0.887750i	0.989807	+	0.142417i	$0.0454873\pi$
$211$	4.69351	+	12.8953i	0.323114	+	0.887750i	−0.666692	+	0.745333i	$0.732291\pi$
$212$	−8.59764	−	12.9935i	−0.590488	−	0.892399i
$213$	20.4170	+	1.23860i	1.39895	+	0.0848673i
$214$	−11.7960	−	6.33927i	−0.806358	−	0.433344i
$215$	−0.770992	+	1.33540i	−0.0525812	+	0.0910733i
$216$	1.32606	−	14.6370i	0.0902270	−	0.995921i
$217$	4.39210	−	4.13958i	0.298155	−	0.281013i
$218$	−8.30376	−	13.4208i	−0.562401	−	0.908971i
$219$	17.2916	+	1.04899i	1.16846	+	0.0708842i
$220$	−1.33040	+	0.0811858i	−0.0896955	+	0.00547355i
$221$	−5.90584	−	4.95558i	−0.397270	−	0.333349i
$222$	12.1845	+	7.53281i	0.817770	+	0.505569i
$223$	−3.02467	−	17.1537i	−0.202547	−	1.14870i	−0.901254	−	0.433291i	$-0.857352\pi$
$223$	−3.02467	−	17.1537i	−0.202547	−	1.14870i	0.698707	−	0.715408i	$-0.253759\pi$
$224$	12.6876	−	7.93882i	0.847726	−	0.530435i
$225$	−12.4918	+	8.12988i	−0.832785	+	0.541992i
$226$	20.4262	−	8.14759i	1.35873	−	0.541970i
$227$	0.649328	+	3.68252i	0.0430974	+	0.244418i	0.998744	−	0.0500971i	$-0.0159531\pi$
$227$	0.649328	+	3.68252i	0.0430974	+	0.244418i	−0.955647	+	0.294515i	$0.904842\pi$
$228$	15.7675	−	9.11091i	1.04423	−	0.603385i
$229$	3.26789	+	8.97847i	0.215949	+	0.593314i	0.999611	−	0.0278725i	$-0.00887324\pi$
$229$	3.26789	+	8.97847i	0.215949	+	0.593314i	−0.783663	+	0.621186i	$0.786651\pi$
$230$	1.37624	−	1.22817i	0.0907464	−	0.0809830i
$231$	8.59438	−	14.7863i	0.565468	−	0.972864i
$232$	4.18931	−	4.22427i	0.275041	−	0.277337i
$233$	3.13478	+	5.42960i	0.205366	+	0.355705i	0.950249	−	0.311490i	$-0.100828\pi$
$233$	3.13478	+	5.42960i	0.205366	+	0.355705i	−0.744883	+	0.667195i	$0.767495\pi$
$234$	−5.33957	−	20.2054i	−0.349059	−	1.32087i
$235$	−0.378525	−	0.218541i	−0.0246922	−	0.0142561i
$236$	−13.9591	−	10.3322i	−0.908662	−	0.672569i
$237$	−14.4816	+	10.7269i	−0.940680	+	0.696789i
$238$	2.47955	+	5.30515i	0.160726	+	0.343882i
$239$	14.2716	+	2.51647i	0.923154	+	0.162777i	0.614971	−	0.788550i	$-0.289168\pi$
$239$	14.2716	+	2.51647i	0.923154	+	0.162777i	0.308184	+	0.951327i	$0.400279\pi$
$240$	1.13445	−	0.493568i	0.0732284	−	0.0318597i
$241$	1.13151	−	3.10880i	0.0728871	−	0.200256i	−0.897899	−	0.440201i	$-0.854907\pi$
$241$	1.13151	−	3.10880i	0.0728871	−	0.200256i	0.970786	+	0.239945i	$0.0771295\pi$
$242$	−3.84667	+	1.53436i	−0.247273	+	0.0986322i
$243$	10.5599	+	11.4669i	0.677416	+	0.735600i
$244$	6.15199	−	20.7582i	0.393841	−	1.32891i
$245$	−1.00339	+	0.745439i	−0.0641044	+	0.0476243i
$246$	1.74103	−	8.38825i	0.111004	−	0.534815i
$247$	16.6452	−	19.8370i	1.05911	−	1.26220i
$248$	5.83626	−	2.75108i	0.370603	−	0.174694i
$249$	−11.9642	+	27.5532i	−0.758204	+	1.74612i
$250$	−2.21739	−	1.19164i	−0.140240	−	0.0753662i
$251$	2.41766	+	4.18751i	0.152601	+	0.264313i	0.932183	−	0.361987i	$-0.117902\pi$
$251$	2.41766	+	4.18751i	0.152601	+	0.264313i	−0.779582	+	0.626300i	$0.784568\pi$
$252$	−2.79653	+	15.6262i	−0.176165	+	0.984361i
$253$	13.6299	−	23.6076i	0.856902	−	1.48420i
$254$	−2.00630	+	1.24134i	−0.125886	+	0.0778888i
$255$	0.137713	+	0.464066i	0.00862392	+	0.0290609i
$256$	15.5269	−	3.86215i	0.970430	−	0.241385i
$257$	−5.70753	−	15.6813i	−0.356026	−	0.978174i	−0.980395	−	0.197044i	$-0.936866\pi$
$257$	−5.70753	−	15.6813i	−0.356026	−	0.978174i	0.624369	−	0.781130i	$-0.285356\pi$
$258$	−3.04406	−	20.9316i	−0.189515	−	1.30314i
$259$	−12.4064	−	9.24590i	−0.770899	−	0.574512i
$260$	1.27628	−	1.21081i	0.0791518	−	0.0750914i
$261$	0.336502	+	6.30126i	0.0208289	+	0.390038i
$262$	10.8792	+	8.57770i	0.672120	+	0.529932i
$263$	−6.94457	−	8.27621i	−0.428220	−	0.510333i	0.508188	−	0.861246i	$-0.330316\pi$
$263$	−6.94457	−	8.27621i	−0.428220	−	0.510333i	−0.936408	+	0.350913i	$0.885871\pi$
$264$	13.6369	−	12.1785i	0.839295	−	0.749534i
$265$	0.475785	+	1.30721i	0.0292272	+	0.0803011i
$266$	−17.8194	+	8.32852i	−1.09258	+	0.510654i
$267$	13.8432	+	27.7307i	0.847190	+	1.69709i
$268$	−25.5084	−	2.90989i	−1.55817	−	0.177750i
$269$	7.21956	−	4.16821i	0.440184	−	0.254140i	−0.263492	−	0.964662i	$-0.584874\pi$
$269$	7.21956	−	4.16821i	0.440184	−	0.254140i	0.703676	+	0.710521i	$0.251541\pi$
$270$	−0.420035	+	1.24317i	−0.0255625	+	0.0756571i
$271$	1.69405	−	2.93417i	0.102906	−	0.178238i	−0.809975	−	0.586465i	$-0.800519\pi$
$271$	1.69405	−	2.93417i	0.102906	−	0.178238i	0.912881	+	0.408226i	$0.133853\pi$
$272$	0.761223	+	6.21388i	0.0461559	+	0.376772i
$273$	3.85507	+	22.2419i	0.233320	+	1.34614i
$274$	7.35382	+	2.42549i	0.444260	+	0.146529i
$275$	−18.2597	−	3.21968i	−1.10110	−	0.194154i
$276$	−4.38481	+	24.9196i	−0.263934	+	1.49998i
$277$	4.53790	−	3.80775i	0.272656	−	0.228786i	−0.496199	−	0.868209i	$-0.665271\pi$
$277$	4.53790	−	3.80775i	0.272656	−	0.228786i	0.768855	+	0.639423i	$0.220827\pi$
$278$	3.80300	−	26.2161i	0.228089	−	1.57234i
$279$	−1.99437	+	6.54650i	−0.119400	+	0.391929i
$280$	−1.26692	+	0.424959i	−0.0757131	+	0.0253961i
$281$	−28.0194	−	10.1982i	−1.67150	−	0.608376i	−0.679393	−	0.733774i	$-0.737757\pi$
$281$	−28.0194	−	10.1982i	−1.67150	−	0.608376i	−0.992107	+	0.125398i	$0.959979\pi$
$282$	5.93316	−	0.862852i	0.353315	−	0.0513821i
$283$	−3.65779	+	20.7444i	−0.217433	+	1.23313i	0.659201	+	0.751967i	$0.270895\pi$
$283$	−3.65779	+	20.7444i	−0.217433	+	1.23313i	−0.876634	+	0.481158i	$0.840216\pi$
$284$	−21.1359	−	10.5416i	−1.25419	−	0.625531i
$285$	−1.55874	+	0.462561i	−0.0923319	+	0.0273998i
$286$	12.3074	−	22.9014i	0.727751	−	1.35419i
$287$	−2.65835	+	8.86337i	−0.156918	+	0.523188i
$288$	−8.02285	+	14.9544i	−0.472751	+	0.881196i
$289$	14.5505			0.855912
$290$	−0.451716	+	0.279487i	−0.0265257	+	0.0164120i
$291$	0.622944	+	5.44351i	0.0365176	+	0.319104i
$292$	−17.9004	−	8.92790i	−1.04754	−	0.522466i
$293$	−0.825044	−	0.145477i	−0.0481996	−	0.00849889i	0.149496	−	0.988762i	$-0.452235\pi$
$293$	−0.825044	−	0.145477i	−0.0481996	−	0.00849889i	−0.197696	+	0.980263i	$0.563346\pi$
$294$	4.47140	−	16.5531i	0.260778	−	0.965399i
$295$	0.996713	+	1.18784i	0.0580309	+	0.0691585i
$296$	−9.54380	−	13.5101i	−0.554722	−	0.785259i
$297$	−0.140382	+	19.3919i	−0.00814578	+	1.12523i
$298$	10.1323	−	4.04157i	0.586949	−	0.234122i
$299$	6.24785	+	35.4333i	0.361323	+	2.04916i
$300$	16.9475	−	2.99455i	0.978465	−	0.172890i
$301$	1.31700	+	22.8085i	0.0759106	+	1.31466i
$302$	5.24602	−	1.09080i	0.301875	−	0.0627682i
$303$	−15.1727	−	6.58835i	−0.871651	−	0.378491i
$304$	−20.8717	+	2.55686i	−1.19707	+	0.146646i
$305$	−0.966538	+	1.67409i	−0.0553438	+	0.0958583i
$306$	−5.42611	−	3.82729i	−0.310190	−	0.218792i
$307$	−4.72622	+	8.18605i	−0.269739	+	0.467202i	−0.968794	−	0.247865i	$-0.920271\pi$
$307$	−4.72622	+	8.18605i	−0.269739	+	0.467202i	0.699055	+	0.715068i	$0.253604\pi$
$308$	−15.8138	+	11.8288i	−0.901072	+	0.674008i
$309$	0.690910	+	2.32823i	0.0393045	+	0.132449i
$310$	−0.564018	+	0.117275i	−0.0320341	+	0.00666078i
$311$	1.01879	−	5.77782i	0.0577700	−	0.327630i	−0.942203	−	0.335044i	$-0.891249\pi$
$311$	1.01879	−	5.77782i	0.0577700	−	0.327630i	0.999973	+	0.00741394i	$0.00235995\pi$
$312$	−3.45590	+	23.8834i	−0.195652	+	1.35213i
$313$	−9.15427	−	10.9096i	−0.517430	−	0.616649i	0.442541	−	0.896748i	$-0.354077\pi$
$313$	−9.15427	−	10.9096i	−0.517430	−	0.616649i	−0.959971	+	0.280099i	$0.909633\pi$
$314$	0.326989	−	0.414724i	0.0184530	−	0.0234042i
$315$	0.568309	−	1.29843i	0.0320206	−	0.0731582i
$316$	20.2354	−	4.85513i	1.13833	−	0.273122i
$317$	0.200450	+	0.0729579i	0.0112584	+	0.00409773i	0.347643	−	0.937627i	$-0.386982\pi$
$317$	0.200450	+	0.0729579i	0.0112584	+	0.00409773i	−0.336385	+	0.941725i	$0.609204\pi$
$318$	−16.2308	−	10.0343i	−0.910177	−	0.562698i
$319$	−5.04595	+	6.01352i	−0.282519	+	0.336693i
$320$	−1.42851	+	0.0118731i	−0.0798561	+	0.000663725i
$321$	−16.3711	−	0.993149i	−0.913744	−	0.0554322i
$322$	7.05008	−	26.4047i	0.392886	−	1.47148i
$323$		−	8.22754i		−	0.457793i
$324$	−6.03982	−	16.9564i	−0.335545	−	0.942024i
$325$	21.1939	−	12.2363i	1.17563	−	0.678749i
$326$	14.7017	+	7.90084i	0.814254	+	0.437587i
$327$	−16.1234	−	10.6603i	−0.891624	−	0.589517i
$328$	−5.64029	+	8.12685i	−0.311433	+	0.448730i
$329$	−6.46519	+	0.373310i	−0.356438	+	0.0205812i
$330$	−1.43766	+	0.773275i	−0.0791407	+	0.0425674i
$331$	−7.50685	+	20.6249i	−0.412614	+	1.13365i	0.543182	+	0.839615i	$0.317219\pi$
$331$	−7.50685	+	20.6249i	−0.412614	+	1.13365i	−0.955796	+	0.294032i	$0.905003\pi$
$332$	25.1634	−	23.8726i	1.38102	−	1.31018i
$333$	17.4158	+	2.12086i	0.954380	+	0.116222i
$334$	6.09002	−	2.42918i	0.333231	−	0.132919i
$335$	2.15404	+	0.784008i	0.117688	+	0.0428349i
$336$	10.0324	−	15.3412i	0.547312	−	0.836929i
$337$	−17.3779	−	14.5818i	−0.946637	−	0.794322i	0.0320914	−	0.999485i	$-0.489783\pi$
$337$	−17.3779	−	14.5818i	−0.946637	−	0.794322i	−0.978728	+	0.205163i	$0.934228\pi$
$338$	3.24315	+	15.5974i	0.176404	+	0.848389i
$339$	18.5302	−	19.5461i	1.00642	−	1.06160i
$340$	0.0633523	−	0.555352i	0.00343576	−	0.0301182i
$341$	−7.37296	+	4.25678i	−0.399268	+	0.230517i
$342$	12.8554	−	18.2256i	0.695141	−	0.985530i
$343$	−6.36041	+	17.3938i	−0.343430	+	0.939178i
$344$	−6.22330	+	23.6178i	−0.335538	+	1.27339i
$345$	0.899796	−	2.07220i	0.0484434	−	0.111563i
$346$	−9.11274	−	10.2114i	−0.489904	−	0.548967i
$347$	7.32182	+	20.1165i	0.393056	+	1.07991i	0.965599	+	0.260037i	$0.0837348\pi$
$347$	7.32182	+	20.1165i	0.393056	+	1.07991i	−0.572543	+	0.819875i	$0.694043\pi$
$348$	2.48966	−	6.84790i	0.133460	−	0.367086i
$349$	−1.43845	−	1.71428i	−0.0769987	−	0.0917635i	0.726170	−	0.687515i	$-0.241299\pi$
$349$	−1.43845	−	1.71428i	−0.0769987	−	0.0917635i	−0.803169	+	0.595752i	$0.796854\pi$
$350$	−18.5168	+	1.63653i	−0.989764	+	0.0874759i
$351$	−16.3104	−	19.7262i	−0.870585	−	1.05291i
$352$	−19.9938	+	6.77925i	−1.06567	+	0.361335i
$353$	8.89163	−	24.4295i	0.473254	−	1.30025i	−0.441870	−	0.897079i	$-0.645685\pi$
$353$	8.89163	−	24.4295i	0.473254	−	1.30025i	0.915123	−	0.403174i	$-0.132093\pi$
$354$	−20.8263	−	4.32260i	−1.10690	−	0.229744i
$355$	1.61544	+	1.35552i	0.0857389	+	0.0719435i
$356$	−2.17991	−	35.7223i	−0.115535	−	1.89328i
$357$	5.48071	+	4.62613i	0.290070	+	0.244841i
$358$	−0.212398	−	6.96763i	−0.0112256	−	0.368251i
$359$			5.05013i			0.266536i	0.991080	+	0.133268i	$0.0425470\pi$
$359$			5.05013i			0.266536i	−0.991080	+	0.133268i	$0.957453\pi$
$360$	1.00807	−	1.13123i	0.0531298	−	0.0596210i
$361$	8.63532			0.454491
$362$	13.9693	−	8.64313i	0.734210	−	0.454273i
$363$	−3.48961	+	3.68094i	−0.183157	+	0.193199i
$364$	5.95356	−	25.3766i	0.312051	−	1.33010i
$365$	1.36815	+	1.14801i	0.0716122	+	0.0600898i
$366$	−3.81612	−	26.2405i	−0.199472	−	1.37161i
$367$	−4.23297	−	24.0064i	−0.220959	−	1.25312i	−0.870261	−	0.492591i	$-0.836050\pi$
$367$	−4.23297	−	24.0064i	−0.220959	−	1.25312i	0.649302	−	0.760531i	$-0.275061\pi$
$368$	15.9193	−	24.4988i	0.829852	−	1.27709i
$369$	−2.37042	−	10.2212i	−0.123399	−	0.532092i
$370$	0.547170	+	1.37177i	0.0284460	+	0.0713148i
$371$	16.5264	+	12.3163i	0.858009	+	0.639431i
$372$	5.07731	−	6.05529i	0.263246	−	0.313952i
$373$	5.39133	−	30.5757i	0.279152	−	1.58315i	−0.446303	−	0.894882i	$-0.647259\pi$
$373$	5.39133	−	30.5757i	0.279152	−	1.58315i	0.725455	−	0.688270i	$-0.241629\pi$
$374$	−1.68161	−	8.08747i	−0.0869541	−	0.418193i
$375$	−3.07740	−	0.186690i	−0.158916	−	0.00964065i
$376$	−6.69458	−	1.76402i	−0.345247	−	0.0909725i
$377$		−	10.3613i		−	0.533634i
$378$	4.91259	+	18.8113i	0.252676	+	0.967551i
$379$		−	0.493236i		−	0.0253358i	−0.999920	−	0.0126679i	$-0.995968\pi$
$379$		−	0.493236i		−	0.0253358i	0.999920	−	0.0126679i	$-0.00403243\pi$
$380$	1.86536	+	0.212793i	0.0956910	+	0.0109160i
$381$	−1.59363	+	2.41031i	−0.0816442	+	0.123484i
$382$	−21.8024	+	4.53333i	−1.11551	+	0.231945i
$383$	−1.33825	+	7.58962i	−0.0683816	+	0.387811i	0.931339	+	0.364155i	$0.118642\pi$
$383$	−1.33825	+	7.58962i	−0.0683816	+	0.387811i	−0.999720	+	0.0236568i	$0.992469\pi$
$384$	15.2824	−	12.2657i	0.779877	−	0.625932i
$385$	1.61937	−	0.697568i	0.0825308	−	0.0355514i
$386$	−3.77257	+	1.50480i	−0.192019	+	0.0765924i
$387$	−14.1307	−	21.7122i	−0.718304	−	1.10369i
$388$	1.79771	−	6.06587i	0.0912647	−	0.307948i
$389$	2.34925	+	13.3232i	0.119112	+	0.675515i	0.984632	+	0.174642i	$0.0558768\pi$
$389$	2.34925	+	13.3232i	0.119112	+	0.675515i	−0.865520	+	0.500874i	$0.833012\pi$
$390$	0.797562	−	2.00159i	0.0403861	−	0.101354i
$391$	8.75714	+	7.34812i	0.442868	+	0.371610i
$392$	−12.2310	+	15.5693i	−0.617757	+	0.786369i
$393$	16.5008	+	3.95284i	0.832355	+	0.199394i
$394$	7.43555	+	12.0176i	0.374598	+	0.605437i
$395$	−1.85799			−0.0934859
$396$	8.91145	−	20.5428i	0.447817	−	1.03232i
$397$			25.5528i			1.28246i	0.767349	+	0.641229i	$0.221575\pi$
$397$			25.5528i			1.28246i	−0.767349	+	0.641229i	$0.778425\pi$
$398$	29.2495	−	0.891625i	1.46614	−	0.0446931i
$399$	−15.5386	+	18.4090i	−0.777904	+	0.921605i
$400$	−19.3619	−	4.47569i	−0.968094	−	0.223785i
$401$	−6.81321	−	5.71696i	−0.340236	−	0.285492i	0.456619	−	0.889662i	$-0.349060\pi$
$401$	−6.81321	−	5.71696i	−0.340236	−	0.285492i	−0.796855	+	0.604171i	$0.793505\pi$
$402$	−29.8580	+	9.85982i	−1.48918	+	0.491763i
$403$	3.84328	−	10.5593i	0.191447	−	0.525997i
$404$	13.1459	+	13.8567i	0.654034	+	0.689399i
$405$	0.171161	+	1.59799i	0.00850504	+	0.0794047i
$406$	−3.31980	+	7.13581i	−0.164759	+	0.354144i
$407$	14.0293	+	16.7195i	0.695408	+	0.828755i
$408$	4.03653	+	6.51876i	0.199838	+	0.322727i
$409$	−3.20037	−	8.79295i	−0.158248	−	0.434783i	0.835077	−	0.550134i	$-0.185423\pi$
$409$	−3.20037	−	8.79295i	−0.158248	−	0.434783i	−0.993325	+	0.115350i	$0.963201\pi$
$410$	0.658987	−	0.588086i	0.0325450	−	0.0290435i
$411$	9.42230	−	1.07827i	0.464768	−	0.0531871i
$412$	0.317840	−	2.78622i	0.0156589	−	0.137267i
$413$	22.0059	+	6.60013i	1.08284	+	0.324771i
$414$	7.91749	+	29.9605i	0.389124	+	1.47248i
$415$	−2.68201	+	1.54846i	−0.131654	+	0.0760108i
$416$	14.4640	−	23.8174i	0.709158	−	1.16775i
$417$	−9.23004	−	31.1035i	−0.451997	−	1.52314i
$418$	27.1648	−	5.64833i	1.32868	−	0.276269i
$419$	−13.3164	−	11.1737i	−0.650547	−	0.545873i	0.256690	−	0.966494i	$-0.417368\pi$
$419$	−13.3164	−	11.1737i	−0.650547	−	0.545873i	−0.907237	+	0.420620i	$0.861812\pi$
$420$	−1.19059	+	1.12295i	−0.0580951	+	0.0547942i
$421$	−16.4193	−	5.97613i	−0.800227	−	0.291259i	−0.0906464	−	0.995883i	$-0.528893\pi$
$421$	−16.4193	−	5.97613i	−0.800227	−	0.291259i	−0.709581	+	0.704624i	$0.751116\pi$
$422$	−7.19020	−	18.0260i	−0.350014	−	0.877492i
$423$	6.15443	−	4.00542i	0.299239	−	0.194750i
$424$	12.7131	+	17.9966i	0.617405	+	0.873993i
$425$	2.65938	−	7.30659i	0.128999	−	0.354422i
$426$	−28.9140	−	0.871056i	−1.40089	−	0.0422028i
$427$	1.65103	+	28.5935i	0.0798990	+	1.38374i
$428$	16.9475	+	8.45263i	0.819188	+	0.408573i
$429$	1.92815	−	31.7836i	0.0930920	−	1.53453i
$430$	1.03230	−	1.92088i	0.0497818	−	0.0926331i
$431$	−30.9403	+	17.8634i	−1.49034	+	0.860450i	−0.999939	−	0.0110448i	$-0.996484\pi$
$431$	−30.9403	+	17.8634i	−1.49034	+	0.860450i	−0.490404	+	0.871495i	$0.663151\pi$
$432$	−1.24375	+	20.7474i	−0.0598401	+	0.998208i
$433$		−	6.67207i		−	0.320639i	−0.987065	−	0.160320i	$-0.948748\pi$
$433$		−	6.67207i		−	0.320639i	0.987065	−	0.160320i	$-0.0512525\pi$
$434$	−6.03010	+	6.04079i	−0.289454	+	0.289967i
$435$	−0.358804	+	0.542678i	−0.0172033	+	0.0260194i
$436$	12.3161	+	18.6133i	0.589836	+	0.891413i
$437$	−24.6814	+	29.4142i	−1.18067	+	1.40707i
$438$	−24.4878	−	0.737713i	−1.17007	−	0.0352493i
$439$	22.0352	+	8.02015i	1.05168	+	0.382781i	0.809297	−	0.587399i	$-0.199848\pi$
$439$	22.0352	+	8.02015i	1.05168	+	0.382781i	0.242385	+	0.970180i	$0.422070\pi$
$440$	1.87710	−	0.172088i	0.0894871	−	0.00820397i
$441$	−3.52606	−	20.7019i	−0.167907	−	0.985803i
$442$	8.56177	+	6.75052i	0.407242	+	0.321089i
$443$	−3.88130	−	4.62556i	−0.184406	−	0.219767i	0.665919	−	0.746024i	$-0.268039\pi$
$443$	−3.88130	−	4.62556i	−0.184406	−	0.219767i	−0.850326	+	0.526257i	$0.823595\pi$
$444$	−17.5481	−	10.1230i	−0.832795	−	0.480418i
$445$	−0.554875	+	3.14685i	−0.0263036	+	0.149175i
$446$	5.01469	+	24.1174i	0.237453	+	1.14199i
$447$	9.19180	−	9.69576i	0.434757	−	0.458594i
$448$	−17.5926	+	11.7687i	−0.831170	+	0.556018i
$449$	11.4089	−	19.7607i	0.538417	−	0.932566i	−0.460573	−	0.887622i	$-0.652356\pi$
$449$	11.4089	−	19.7607i	0.538417	−	0.932566i	0.998990	−	0.0449435i	$-0.0143108\pi$
$450$	17.3075	−	12.0303i	0.815884	−	0.567115i
$451$	6.52642	−	11.3041i	0.307317	−	0.532289i
$452$	−28.5225	+	12.3972i	−1.34159	+	0.583117i
$453$	5.27334	−	3.90612i	0.247763	−	0.183525i
$454$	−1.07654	−	5.17748i	−0.0505247	−	0.242991i
$455$	−1.04552	+	2.07920i	−0.0490146	+	0.0974745i
$456$	−21.8957	+	13.5582i	−1.02536	+	0.634921i
$457$	3.04268	+	17.2559i	0.142330	+	0.807196i	0.969472	+	0.245202i	$0.0788543\pi$
$457$	3.04268	+	17.2559i	0.142330	+	0.807196i	−0.827142	+	0.561993i	$0.810035\pi$
$458$	−5.00624	−	12.5508i	−0.233926	−	0.586459i
$459$	−7.99843	−	1.47012i	−0.373335	−	0.0686193i
$460$	−1.89247	+	1.79539i	−0.0882367	+	0.0837103i
$461$	12.1259	+	14.4511i	0.564760	+	0.673055i	0.970547	−	0.240913i	$-0.0774468\pi$
$461$	12.1259	+	14.4511i	0.564760	+	0.673055i	−0.405787	+	0.913968i	$0.633002\pi$
$462$	−11.5115	+	21.2715i	−0.535563	+	0.989642i
$463$	25.0674	+	4.42007i	1.16498	+	0.205418i	0.722508	−	0.691363i	$-0.242989\pi$
$463$	25.0674	+	4.42007i	1.16498	+	0.205418i	0.442475	+	0.896781i	$0.354100\pi$
$464$	−5.73980	+	6.15176i	−0.266463	+	0.285588i
$465$	−0.566955	+	0.419960i	−0.0262919	+	0.0194752i
$466$	−4.66515	−	7.53997i	−0.216109	−	0.349282i
$467$	−28.1152			−1.30102			−0.650509	−	0.759499i	$-0.725444\pi$
$467$	−28.1152			−1.30102			−0.650509	+	0.759499i	$0.725444\pi$
$468$	8.41844	+	28.3314i	0.389143	+	1.30962i
$469$	33.0517	−	7.81594i	1.52619	−	0.360906i
$470$	0.544483	+	0.292610i	0.0251151	+	0.0134971i
$471$	0.150685	−	0.629024i	0.00694322	−	0.0289839i
$472$	20.1773	+	14.0037i	0.928733	+	0.644571i
$473$	5.59619	−	31.7376i	0.257313	−	1.45929i
$474$	20.0083	−	15.7871i	0.919012	−	0.725127i
$475$	24.5420	+	8.93255i	1.12606	+	0.409853i
$476$	−3.73359	−	7.39229i	−0.171129	−	0.338825i
$477$	−23.1993	−	2.82517i	−1.06222	−	0.129355i
$478$	−20.2822	−	2.94221i	−0.927686	−	0.134574i
$479$	−13.6538	+	11.4569i	−0.623859	+	0.523480i	−0.899014	−	0.437920i	$-0.855715\pi$
$479$	−13.6538	+	11.4569i	−0.623859	+	0.523480i	0.275155	+	0.961400i	$0.411271\pi$
$480$	−1.58234	+	0.746571i	−0.0722237	+	0.0340761i
$481$	−28.3700	−	5.00240i	−1.29356	−	0.228090i
$482$	−1.46550	+	4.44323i	−0.0667516	+	0.202384i
$483$	−5.71628	−	32.9802i	−0.260100	−	1.50065i
$484$	5.37137	−	2.33465i	0.244153	−	0.106121i
$485$	−0.282437	+	0.489196i	−0.0128248	+	0.0222132i
$486$	−15.4211	−	15.7540i	−0.699515	−	0.714618i
$487$	−2.45267	+	1.41605i	−0.111141	+	0.0641672i	−0.554540	−	0.832157i	$-0.687106\pi$
$487$	−2.45267	+	1.41605i	−0.111141	+	0.0641672i	0.443399	+	0.896324i	$0.353772\pi$
$488$	−7.80171	+	29.6080i	−0.353167	+	1.34029i
$489$	20.4038	+	1.23779i	0.922691	+	0.0559750i
$490$	1.38623	−	1.09696i	0.0626235	−	0.0495554i
$491$	−6.51931	−	17.9117i	−0.294212	−	0.808341i	−0.995439	−	0.0954029i	$-0.969586\pi$
$491$	−6.51931	−	17.9117i	−0.294212	−	0.808341i	0.701226	−	0.712939i	$-0.252636\pi$
$492$	−2.09959	+	11.9323i	−0.0946567	+	0.537949i
$493$	−2.11607	−	2.52183i	−0.0953029	−	0.113578i
$494$	−22.6742	+	28.7580i	−1.02016	+	1.29388i
$495$	−1.20163	+	1.59791i	−0.0540093	+	0.0718209i
$496$	−8.13135	+	4.14029i	−0.365108	+	0.185905i
$497$	31.0318	+	3.64283i	1.39197	+	0.163403i
$498$	15.7249	−	39.4636i	0.704649	−	1.76841i
$499$	7.72125	+	21.2139i	0.345650	+	0.949667i	0.983723	+	0.179691i	$0.0575097\pi$
$499$	7.72125	+	21.2139i	0.345650	+	0.949667i	−0.638073	+	0.769976i	$0.720268\pi$
$500$	3.18576	+	1.58891i	0.142471	+	0.0710582i
$501$	5.52473	−	5.82764i	0.246827	−	0.260360i
$502$	−3.59794	−	5.81510i	−0.160584	−	0.259541i
$503$	3.76551	−	6.52205i	0.167896	−	0.290804i	−0.769784	−	0.638304i	$-0.779636\pi$
$503$	3.76551	−	6.52205i	0.167896	−	0.290804i	0.937680	+	0.347500i	$0.112969\pi$
$504$	3.27971	−	22.2091i	0.146090	−	0.989271i
$505$	−0.852688	−	1.47690i	−0.0379441	−	0.0657212i
$506$	−18.2493	+	33.9580i	−0.811282	+	1.50962i
$507$	11.6136	+	15.6787i	0.515780	+	0.696314i
$508$	2.78253	−	1.84116i	0.123455	−	0.0816883i
$509$	−2.35667	+	2.80857i	−0.104458	+	0.124488i	−0.815740	−	0.578418i	$-0.803670\pi$
$509$	−2.35667	+	2.80857i	−0.104458	+	0.124488i	0.711283	+	0.702906i	$0.248115\pi$
$510$	−0.214662	−	0.650050i	−0.00950538	−	0.0287847i
$511$	26.2814	+	3.08518i	1.16262	+	0.136480i
$512$	−21.7817	+	6.12843i	−0.962624	+	0.270841i
$513$	4.93795	−	26.8658i	0.218016	−	1.18615i
$514$	8.74363	+	21.9205i	0.385665	+	0.966872i
$515$	−0.0856353	+	0.235281i	−0.00377354	+	0.0103677i
$516$	5.20489	+	29.4568i	0.229133	+	1.29676i
$517$	8.99616	+	1.58627i	0.395651	+	0.0697639i
$518$	17.9356	+	12.5350i	0.788046	+	0.550757i
$519$	−15.3753	−	6.67629i	−0.674899	−	0.293057i
$520$	−1.75193	+	1.76655i	−0.0768270	+	0.0774682i
$521$	30.1557	+	17.4104i	1.32115	+	0.762763i	0.983911	−	0.178657i	$-0.0571754\pi$
$521$	30.1557	+	17.4104i	1.32115	+	0.762763i	0.337234	+	0.941421i	$0.390509\pi$
$522$	−0.747186	−	8.89269i	−0.0327034	−	0.389222i
$523$	−16.2992	−	28.2310i	−0.712713	−	1.23446i	−0.963835	−	0.266500i	$-0.914133\pi$
$523$	−16.2992	−	28.2310i	−0.712713	−	1.23446i	0.251122	−	0.967956i	$-0.419201\pi$
$524$	−15.7480	−	11.6563i	−0.687955	−	0.509207i
$525$	−19.7497	+	11.3259i	−0.861946	+	0.494302i
$526$	10.1732	+	11.3997i	0.443571	+	0.497049i
$527$	−1.22110	−	3.35493i	−0.0531918	−	0.146143i
$528$	−18.7518	+	17.8026i	−0.816068	+	0.774759i
$529$	−5.27038	−	29.8898i	−0.229147	−	1.29956i
$530$	−0.728877	−	1.82731i	−0.0316604	−	0.0793733i
$531$	−25.3770	+	5.88525i	−1.10127	+	0.255398i
$532$	24.8298	−	12.5407i	1.07651	−	0.543707i
$533$	2.99167	+	16.9666i	0.129584	+	0.734906i
$534$	−20.7631	−	38.6024i	−0.898506	−	1.67049i
$535$	−1.29532	−	1.08690i	−0.0560015	−	0.0469908i
$536$	36.1829	+	3.01413i	1.56286	+	0.130191i
$537$	−3.81322	−	7.63864i	−0.164552	−	0.329632i
$538$	−10.0256	+	6.20310i	−0.432236	+	0.267435i
$539$	14.3775	−	21.8124i	0.619283	−	0.939525i
$540$	0.540175	−	1.77540i	0.0232454	−	0.0764009i
$541$	−5.63436	+	9.75900i	−0.242240	+	0.419572i	−0.961352	−	0.275322i	$-0.911216\pi$
$541$	−5.63436	+	9.75900i	−0.242240	+	0.419572i	0.719112	+	0.694894i	$0.244549\pi$
$542$	−2.26820	+	4.22062i	−0.0974274	+	0.181291i
$543$	11.0960	−	16.7823i	0.476175	−	0.720198i
$544$	−1.34379	−	8.75088i	−0.0576145	−	0.375191i
$545$	−0.681563	−	1.87258i	−0.0291949	−	0.0802125i
$546$	−6.40777	−	31.2741i	−0.274227	−	1.33841i
$547$	34.4728	−	6.07848i	1.47395	−	0.259897i	0.621792	−	0.783183i	$-0.286405\pi$
$547$	34.4728	−	6.07848i	1.47395	−	0.259897i	0.852157	+	0.523286i	$0.175294\pi$
$548$	−10.4996	−	3.11169i	−0.448519	−	0.132925i
$549$	−17.7147	−	27.2191i	−0.756044	−	1.16168i
$550$	25.9499	+	3.76438i	1.10651	+	0.160514i
$551$	8.47053	−	7.10762i	0.360857	−	0.302795i
$552$	5.12439	−	35.4141i	0.218108	−	1.50733i
$553$	−23.0074	+	15.1157i	−0.978375	+	0.642787i
$554$	−6.25051	+	5.57801i	−0.265559	+	0.236987i
$555$	1.31267	+	1.24444i	0.0557196	+	0.0528234i
$556$	−4.24611	+	37.2218i	−0.180075	+	1.57856i
$557$	25.2843			1.07133			0.535664	−	0.844431i	$-0.320061\pi$
$557$	25.2843			1.07133			0.535664	+	0.844431i	$0.320061\pi$
$558$	2.53707	−	9.33979i	0.107403	−	0.395385i
$559$	21.2682	+	36.8376i	0.899550	+	1.55807i
$560$	1.77256	−	0.655295i	0.0749042	−	0.0276913i
$561$	−6.02182	−	8.12958i	−0.254241	−	0.343231i
$562$	40.0465	+	13.2084i	1.68926	+	0.557164i
$563$	−15.5057	+	5.64361i	−0.653487	+	0.237850i	−0.647422	−	0.762132i	$-0.724153\pi$
$563$	−15.5057	+	5.64361i	−0.653487	+	0.237850i	−0.00606519	+	0.999982i	$0.501931\pi$
$564$	−8.34968	+	1.47535i	−0.351585	+	0.0621235i
$565$	2.73460	−	0.482184i	0.115045	−	0.0202856i
$566$	4.27662	−	29.4810i	0.179760	−	1.23918i
$567$	15.1199	+	18.3953i	0.634978	+	0.772531i
$568$	30.3311	+	13.9904i	1.27266	+	0.587026i
$569$	3.49968	+	19.8477i	0.146714	+	0.832058i	0.965975	+	0.258637i	$0.0832732\pi$
$569$	3.49968	+	19.8477i	0.146714	+	0.832058i	−0.819260	+	0.573422i	$0.805616\pi$
$570$	2.18344	−	0.721023i	0.0914542	−	0.0302003i
$571$	−11.2585	−	30.9324i	−0.471153	−	1.29448i	−0.916827	−	0.399286i	$-0.869258\pi$
$571$	−11.2585	−	30.9324i	−0.471153	−	1.29448i	0.445674	−	0.895195i	$-0.352964\pi$
$572$	−16.4104	+	32.9027i	−0.686152	+	1.37573i
$573$	−21.9159	+	16.2338i	−0.915551	+	0.678175i
$574$	3.37581	−	12.6434i	0.140903	−	0.527727i
$575$	−31.4263	+	18.1440i	−1.31057	+	0.756656i
$576$	10.6964	−	21.4846i	0.445682	−	0.895191i
$577$			7.01671i			0.292109i	0.989277	+	0.146055i	$0.0466575\pi$
$577$			7.01671i			0.292109i	−0.989277	+	0.146055i	$0.953342\pi$
$578$	−20.5680	+	0.626983i	−0.855515	+	0.0260791i
$579$	−3.42239	+	3.61003i	−0.142230	+	0.150028i
$580$	0.626483	−	0.414535i	0.0260133	−	0.0172126i
$581$	−20.6136	+	40.9939i	−0.855197	+	1.70072i
$582$	−1.11513	−	7.66787i	−0.0462236	−	0.317843i
$583$	−18.6883	−	22.2718i	−0.773988	−	0.922403i
$584$	25.6879	+	11.8488i	1.06297	+	0.490305i
$585$	−0.140722	−	2.63512i	−0.00581812	−	0.108949i
$586$	1.17252	+	0.170089i	0.0484362	+	0.00702633i
$587$	−5.61599	−	31.8498i	−0.231797	−	1.31458i	−0.849256	−	0.527981i	$-0.822949\pi$
$587$	−5.61599	−	31.8498i	−0.231797	−	1.31458i	0.617460	−	0.786602i	$-0.288162\pi$
$588$	−5.60731	+	23.5915i	−0.231241	+	0.972896i
$589$	11.2688	−	4.10151i	0.464324	−	0.169000i
$590$	−1.46009	−	1.63613i	−0.0601111	−	0.0673582i
$591$	14.4376	+	9.54572i	0.593882	+	0.392659i
$592$	14.0729	+	18.6861i	0.578391	+	0.767993i
$593$	−13.9880	−	8.07597i	−0.574418	−	0.331640i	0.184494	−	0.982834i	$-0.440935\pi$
$593$	−13.9880	−	8.07597i	−0.574418	−	0.331640i	−0.758912	+	0.651193i	$0.774269\pi$
$594$	−0.637163	−	27.4177i	−0.0261431	−	1.12496i
$595$	0.170164	+	0.719580i	0.00697603	+	0.0294999i
$596$	−14.1484	+	6.14959i	−0.579543	+	0.251897i
$597$	32.0663	−	16.0075i	1.31239	−	0.655145i
$598$	−10.3585	−	49.8178i	−0.423591	−	2.03720i
$599$	0.337755	−	0.402521i	0.0138003	−	0.0164466i	−0.759100	−	0.650974i	$-0.774361\pi$
$599$	0.337755	−	0.402521i	0.0138003	−	0.0164466i	0.772900	+	0.634527i	$0.218805\pi$
$600$	−23.8272	+	4.96324i	−0.972743	+	0.202623i
$601$	−11.1873	+	1.97263i	−0.456340	+	0.0804651i	−0.397093	−	0.917778i	$-0.629981\pi$
$601$	−11.1873	+	1.97263i	−0.456340	+	0.0804651i	−0.0592468	+	0.998243i	$0.518870\pi$
$602$	−2.84448	−	32.1844i	−0.115932	−	1.31174i
$603$	−28.1389	+	26.2922i	−1.14590	+	1.07070i
$604$	−7.36855	+	1.76795i	−0.299822	+	0.0719370i
$605$	−0.514981	+	0.0908050i	−0.0209369	+	0.00369175i
$606$	21.7314	+	8.65921i	0.882779	+	0.351756i
$607$	−7.98770	+	2.90729i	−0.324211	+	0.118003i	−0.498998	−	0.866603i	$-0.666298\pi$
$607$	−7.98770	+	2.90729i	−0.324211	+	0.118003i	0.174787	+	0.984606i	$0.444076\pi$
$608$	29.3932	−	4.51363i	1.19205	−	0.183052i
$609$	−0.0280803	+	9.63900i	−0.00113787	+	0.390592i
$610$	1.29412	−	2.40807i	0.0523974	−	0.0975001i
$611$	−10.4418	+	6.02858i	−0.422430	+	0.243890i
$612$	7.83503	+	5.17628i	0.316712	+	0.209239i
$613$	−14.4763	+	25.0737i	−0.584693	+	1.01272i	0.410221	+	0.911986i	$0.365452\pi$
$613$	−14.4763	+	25.0737i	−0.584693	+	1.01272i	−0.994914	+	0.100732i	$0.967882\pi$
$614$	6.32804	−	11.7751i	0.255379	−	0.475204i
$615$	0.430851	−	0.992235i	0.0173736	−	0.0400108i
$616$	21.8439	−	17.4021i	0.880117	−	0.701151i
$617$	−2.16572	+	12.2824i	−0.0871887	+	0.494472i	0.909674	+	0.415323i	$0.136331\pi$
$617$	−2.16572	+	12.2824i	−0.0871887	+	0.494472i	−0.996863	+	0.0791489i	$0.974780\pi$
$618$	−1.07696	−	3.26132i	−0.0433219	−	0.131189i
$619$	−27.3891	−	9.96882i	−1.10086	−	0.400681i	−0.273227	−	0.961950i	$-0.588091\pi$
$619$	−27.3891	−	9.96882i	−1.10086	−	0.400681i	−0.827633	+	0.561269i	$0.810313\pi$
$620$	0.792218	−	0.190079i	0.0318162	−	0.00763374i
$621$	24.1850	+	29.2500i	0.970510	+	1.17376i
$622$	−1.19114	+	8.21117i	−0.0477605	+	0.329238i
$623$	18.7303	+	43.4815i	0.750413	+	1.74205i
$624$	3.85597	−	33.9094i	0.154362	−	1.35746i
$625$	18.7855	+	15.7629i	0.751419	+	0.630516i
$626$	13.4102	+	15.0269i	0.535979	+	0.600597i
$627$	27.3063	−	20.2266i	1.09051	−	0.807771i
$628$	−0.444347	+	0.600326i	−0.0177314	+	0.0239556i
$629$	−7.92660	+	4.57643i	−0.316054	+	0.182474i
$630$	−0.747388	+	1.85989i	−0.0297767	+	0.0740999i
$631$	−24.8757	−	14.3620i	−0.990285	−	0.571741i	−0.0849255	−	0.996387i	$-0.527065\pi$
$631$	−24.8757	−	14.3620i	−0.990285	−	0.571741i	−0.905359	+	0.424646i	$0.860399\pi$
$632$	−28.3947	+	7.73495i	−1.12948	+	0.307680i
$633$	−17.2494	−	16.3528i	−0.685601	−	0.649965i
$634$	−0.286492	−	0.0944928i	−0.0113780	−	0.00375279i
$635$	−0.279935	+	0.101888i	−0.0111089	+	0.00404330i
$636$	23.3755	+	13.4847i	0.926900	+	0.534704i
$637$	3.96881	+	34.2525i	0.157250	+	1.35713i
$638$	6.87361	−	8.71789i	0.272129	−	0.345145i
$639$	−32.5982	+	13.8753i	−1.28957	+	0.548898i
$640$	2.01877	−	0.0783380i	0.0797988	−	0.00309658i
$641$	11.0263	−	9.25221i	0.435515	−	0.365440i	−0.398513	−	0.917163i	$-0.630474\pi$
$641$	11.0263	−	9.25221i	0.435515	−	0.365440i	0.834028	+	0.551722i	$0.186029\pi$
$642$	23.1842	+	0.698442i	0.915009	+	0.0275653i
$643$	22.5803	−	8.21857i	0.890481	−	0.324109i	0.144049	−	0.989571i	$-0.453988\pi$
$643$	22.5803	−	8.21857i	0.890481	−	0.324109i	0.746432	+	0.665462i	$0.231765\pi$
$644$	−8.82791	+	37.6284i	−0.347868	+	1.48276i
$645$	0.161726	−	2.66589i	0.00636796	−	0.104969i
$646$	0.354526	+	11.6301i	0.0139486	+	0.457580i
$647$	21.0543	+	36.4671i	0.827729	+	1.43367i	0.899816	+	0.436270i	$0.143701\pi$
$647$	21.0543	+	36.4671i	0.827729	+	1.43367i	−0.0720869	+	0.997398i	$0.522966\pi$
$648$	9.26828	+	23.7086i	0.364093	+	0.931363i
$649$	−28.0657	−	16.2037i	−1.10167	−	0.636052i
$650$	−29.4316	+	18.2100i	−1.15440	+	0.714255i
$651$	−3.60398	+	9.81281i	−0.141251	+	0.384594i
$652$	−21.1222	−	10.5348i	−0.827209	−	0.412574i
$653$	7.21833	−	40.9372i	0.282475	−	1.60200i	−0.431693	−	0.902021i	$-0.642084\pi$
$653$	7.21833	−	40.9372i	0.282475	−	1.60200i	0.714168	−	0.699974i	$-0.246805\pi$
$654$	23.2506	+	14.3742i	0.909172	+	0.562077i
$655$	1.12444	+	1.34006i	0.0439356	+	0.0523604i
$656$	7.62269	−	11.7308i	0.297616	−	0.458011i
$657$	−27.6080	+	11.7512i	−1.07709	+	0.458460i
$658$	9.12283	−	0.806281i	0.355645	−	0.0314321i
$659$	12.7615	−	35.0620i	0.497118	−	1.36582i	−0.396929	−	0.917849i	$-0.629924\pi$
$659$	12.7615	−	35.0620i	0.497118	−	1.36582i	0.894048	−	0.447972i	$-0.147854\pi$
$660$	1.99890	−	1.15502i	0.0778070	−	0.0449590i
$661$	−19.8066	−	3.49244i	−0.770388	−	0.135840i	−0.225380	−	0.974271i	$-0.572362\pi$
$661$	−19.8066	−	3.49244i	−0.770388	−	0.135840i	−0.545008	+	0.838431i	$0.683473\pi$
$662$	9.72263	−	29.4779i	0.377881	−	1.14569i
$663$	12.9859	+	3.11082i	0.504330	+	0.120814i
$664$	−34.5413	+	34.8296i	−1.34046	+	1.35165i
$665$	−2.41698	+	0.571559i	−0.0937266	+	0.0221641i
$666$	−24.7096	−	2.24751i	−0.957478	−	0.0870892i
$667$			15.3637i			0.594884i
$668$	−8.50392	+	3.69621i	−0.329027	+	0.143011i
$669$	17.9575	+	24.2430i	0.694278	+	0.937290i
$670$	−3.07865	−	1.01542i	−0.118938	−	0.0392292i
$671$	7.01555	−	39.7872i	0.270832	−	1.53597i
$672$	−13.5203	+	22.1179i	−0.521557	+	0.853217i
$673$	18.1251	−	15.2088i	0.698672	−	0.586255i	−0.222724	−	0.974882i	$-0.571495\pi$
$673$	18.1251	−	15.2088i	0.698672	−	0.586255i	0.921395	+	0.388626i	$0.127050\pi$
$674$	25.1930	+	19.8634i	0.970399	+	0.765110i
$675$	13.0690	−	22.2625i	0.503027	−	0.856883i
$676$	−5.25647	−	21.9081i	−0.202172	−	0.842620i
$677$	32.9046	−	5.80196i	1.26462	−	0.222988i	0.499185	−	0.866495i	$-0.333633\pi$
$677$	32.9046	−	5.80196i	1.26462	−	0.222988i	0.765440	+	0.643508i	$0.222522\pi$
$678$	−25.3512	+	28.4280i	−0.973608	+	1.09177i
$679$	0.482457	+	8.35545i	0.0185150	+	0.320653i
$680$	−0.0656218	+	0.787752i	−0.00251648	+	0.0302089i
$681$	−3.85508	−	5.20444i	−0.147727	−	0.199435i
$682$	10.2387	−	6.33490i	0.392059	−	0.242576i
$683$	1.77040	+	1.02214i	0.0677424	+	0.0391111i	0.533489	−	0.845807i	$-0.320881\pi$
$683$	1.77040	+	1.02214i	0.0677424	+	0.0391111i	−0.465746	+	0.884918i	$0.654214\pi$
$684$	−17.3865	+	26.3169i	−0.664790	+	1.00625i
$685$	0.846761	+	0.488878i	0.0323531	+	0.0186791i
$686$	8.24130	−	24.8612i	0.314654	−	0.949206i
$687$	−12.0100	−	11.3858i	−0.458211	−	0.434394i
$688$	7.77929	−	33.6533i	0.296583	−	1.28302i
$689$	37.7913	+	6.66362i	1.43973	+	0.253864i
$690$	−1.18262	+	2.96794i	−0.0450216	+	0.112988i
$691$	17.8104	−	14.9447i	0.677541	−	0.568525i	−0.237746	−	0.971327i	$-0.576408\pi$
$691$	17.8104	−	14.9447i	0.677541	−	0.568525i	0.915287	+	0.402803i	$0.131964\pi$
$692$	13.3214	+	14.0417i	0.506403	+	0.533786i
$693$	−1.87988	+	29.5627i	−0.0714106	+	1.12300i
$694$	−11.2166	−	28.1204i	−0.425778	−	1.06743i
$695$	1.14402	−	3.14318i	0.0433953	−	0.119228i
$696$	−3.22420	+	9.78717i	−0.122213	+	0.370982i
$697$	4.19320	+	3.51852i	0.158829	+	0.133273i
$698$	2.10721	+	2.36125i	0.0797589	+	0.0893748i
$699$	−9.05830	−	5.98910i	−0.342616	−	0.226529i
$700$	26.1040	−	3.11121i	0.986640	−	0.117593i
$701$	6.92697			0.261628			0.130814	−	0.991407i	$-0.458241\pi$
$701$	6.92697			0.261628			0.130814	+	0.991407i	$0.458241\pi$
$702$	23.9057	+	27.1813i	0.902262	+	1.02589i
$703$	−15.3717	−	26.6245i	−0.579754	−	1.00416i
$704$	27.9702	−	10.4444i	1.05417	−	0.393638i
$705$	0.755660	+	0.0458420i	0.0284598	+	0.00172651i
$706$	−11.5162	+	34.9157i	−0.433416	+	1.31407i
$707$	−22.5741	−	11.3513i	−0.848987	−	0.426909i
$708$	29.6254	+	5.21283i	1.11339	+	0.195910i
$709$	28.8656	+	10.5062i	1.08407	+	0.394569i	0.821421	−	0.570323i	$-0.193182\pi$
$709$	28.8656	+	10.5062i	1.08407	+	0.394569i	0.262648	+	0.964892i	$0.415404\pi$
$710$	−2.34193	−	1.84649i	−0.0878912	−	0.0692977i
$711$	14.1435	−	27.8264i	0.530424	−	1.04357i
$712$	4.62070	+	50.4016i	0.173168	+	1.88888i
$713$	−5.69879	+	15.6573i	−0.213421	+	0.586371i
$714$	−7.94663	−	6.30314i	−0.297395	−	0.235889i
$715$	2.11016	−	2.51480i	0.0789157	−	0.0940480i
$716$	0.600472	+	9.83999i	0.0224407	+	0.367738i
$717$	−24.0633	+	7.14086i	−0.898661	+	0.266680i
$718$	−0.217611	−	7.13864i	−0.00812116	−	0.266412i
$719$	−9.10352	−	15.7678i	−0.339504	−	0.588038i	0.644836	−	0.764321i	$-0.276926\pi$
$719$	−9.10352	−	15.7678i	−0.339504	−	0.588038i	−0.984339	+	0.176283i	$0.943592\pi$
$720$	−1.37622	+	1.64249i	−0.0512886	+	0.0612121i
$721$	0.853716	+	3.61016i	0.0317940	+	0.134449i
$722$	−12.2065	+	0.372097i	−0.454279	+	0.0138480i
$723$	0.651498	+	5.69302i	0.0242295	+	0.211726i
$724$	−19.3740	+	12.8195i	−0.720028	+	0.476433i
$725$	9.81978	−	3.57411i	0.364697	−	0.132739i
$726$	4.77415	−	5.35358i	0.177185	−	0.198690i
$727$	−29.2647	+	24.5560i	−1.08537	+	0.910733i	−0.996356	−	0.0852976i	$-0.972816\pi$
$727$	−29.2647	+	24.5560i	−1.08537	+	0.910733i	−0.0890136	+	0.996030i	$0.528371\pi$
$728$	−7.32221	+	36.1279i	−0.271379	+	1.33899i
$729$	−25.2353	−	9.60090i	−0.934643	−	0.355589i
$730$	−1.98342	−	1.56383i	−0.0734099	−	0.0578799i
$731$	12.6997	+	4.62233i	0.469717	+	0.170963i
$732$	6.52501	+	36.9280i	0.241171	+	1.36490i
$733$	−32.5548	+	38.7973i	−1.20244	+	1.43301i	−0.330217	+	0.943905i	$0.607122\pi$
$733$	−32.5548	+	38.7973i	−1.20244	+	1.43301i	−0.872224	+	0.489107i	$0.837323\pi$
$734$	7.01798	+	33.7520i	0.259038	+	1.24581i
$735$	0.978269	−	1.93143i	0.0360840	−	0.0712418i
$736$	−21.4472	+	35.3164i	−0.790555	+	1.30178i
$737$	−47.9083			−1.76473
$738$	3.79115	+	14.3460i	0.139554	+	0.528085i
$739$			19.7365i			0.726019i	0.931785	+	0.363010i	$0.118251\pi$
$739$			19.7365i			0.726019i	−0.931785	+	0.363010i	$0.881749\pi$
$740$	−0.832566	−	1.91550i	−0.0306057	−	0.0704150i
$741$	−10.4489	+	43.6180i	−0.383849	+	1.60235i
$742$	−23.8917	−	16.6977i	−0.877094	−	0.612991i
$743$	20.1151	−	23.9722i	0.737952	−	0.879456i	−0.258291	−	0.966067i	$-0.583159\pi$
$743$	20.1151	−	23.9722i	0.737952	−	0.879456i	0.996242	+	0.0866108i	$0.0276037\pi$
$744$	−6.91614	+	8.77828i	−0.253558	+	0.321827i
$745$	1.35648	−	0.239185i	0.0496977	−	0.00876305i
$746$	−6.30344	+	43.4529i	−0.230785	+	1.59092i
$747$	−2.77449	−	51.9546i	−0.101513	−	1.90092i
$748$	2.72554	+	11.3596i	0.0996557	+	0.415349i
$749$	−24.8823	−	2.92094i	−0.909181	−	0.106729i
$750$	4.35813	+	0.131292i	0.159136	+	0.00479410i
$751$	53.7593	+	9.47921i	1.96170	+	0.345901i	0.996401	+	0.0847679i	$0.0270149\pi$
$751$	53.7593	+	9.47921i	1.96170	+	0.345901i	0.965303	+	0.261133i	$0.0840962\pi$
$752$	9.53918	+	2.20508i	0.347858	+	0.0804109i
$753$	−6.98610	−	4.61902i	−0.254587	−	0.168326i
$754$	0.446470	+	14.6463i	0.0162595	+	0.533386i
$755$	0.676573			0.0246230
$756$	−7.75481	−	26.3792i	−0.282040	−	0.959403i
$757$	−48.5039			−1.76291			−0.881453	−	0.472272i	$-0.843434\pi$
$757$	−48.5039			−1.76291			−0.881453	+	0.472272i	$0.843434\pi$
$758$	0.0212536	+	0.697217i	0.000771966	+	0.0253241i
$759$	−2.85905	+	47.1286i	−0.103777	+	1.71066i
$760$	−2.64596	−	0.220416i	−0.0959792	−	0.00799533i
$761$	0.695809	+	0.122690i	0.0252230	+	0.00444750i	0.186245	−	0.982503i	$-0.440368\pi$
$761$	0.695809	+	0.122690i	0.0252230	+	0.00444750i	−0.161022	+	0.986951i	$0.551479\pi$
$762$	2.14883	−	3.47578i	0.0778438	−	0.125914i
$763$	−23.6741	−	17.6432i	−0.857061	−	0.638725i
$764$	30.6236	−	7.34759i	1.10792	−	0.265826i
$765$	−0.572416	−	0.612622i	−0.0206958	−	0.0221494i
$766$	1.56466	−	10.7860i	0.0565335	−	0.389715i
$767$	42.1246	−	7.42770i	1.52103	−	0.268199i
$768$	−21.0740	+	17.9968i	−0.760444	+	0.649404i
$769$	−15.8425	+	18.8804i	−0.571296	+	0.680845i	−0.971897	−	0.235408i	$-0.924357\pi$
$769$	−15.8425	+	18.8804i	−0.571296	+	0.680845i	0.400600	+	0.916253i	$0.368802\pi$
$770$	−2.25902	+	1.05583i	−0.0814093	+	0.0380495i
$771$	20.9761	+	19.8858i	0.755434	+	0.716169i
$772$	5.26790	−	2.28968i	0.189596	−	0.0824075i
$773$			2.88281i			0.103687i	0.998655	+	0.0518437i	$0.0165098\pi$
$773$			2.88281i			0.103687i	−0.998655	+	0.0518437i	$0.983490\pi$
$774$	20.9101	+	30.0826i	0.751600	+	1.08130i
$775$	11.3332			0.407100
$776$	−2.27978	+	8.65191i	−0.0818393	+	0.310586i
$777$	26.3788	+	4.73057i	0.946334	+	0.169708i
$778$	−3.89490	−	18.7319i	−0.139639	−	0.671573i
$779$	−11.8183	+	14.0845i	−0.423434	+	0.504629i
$780$	−1.04115	+	2.86372i	−0.0372792	+	0.102538i
$781$	−41.4158	−	15.0741i	−1.48197	−	0.539395i
$782$	−12.6954	−	10.0096i	−0.453985	−	0.357944i
$783$	−5.39616	−	9.50467i	−0.192843	−	0.339669i
$784$	16.6183	−	22.5351i	0.593510	−	0.804826i
$785$	0.0510841	−	0.0428646i	0.00182327	−	0.00152990i
$786$	−23.4951	−	4.87654i	−0.838044	−	0.173940i
$787$	3.35716	−	1.22191i	0.119670	−	0.0435563i	−0.281491	−	0.959564i	$-0.590829\pi$
$787$	3.35716	−	1.22191i	0.119670	−	0.0435563i	0.401161	+	0.916008i	$0.368607\pi$
$788$	−11.0284	−	16.6671i	−0.392871	−	0.593742i
$789$	17.1644	+	7.45319i	0.611070	+	0.265341i
$790$	2.62638	−	0.0800612i	0.0934424	−	0.00284845i
$791$	29.9396	−	28.2182i	1.06453	−	1.00332i
$792$	−11.7116	+	29.4225i	−0.416155	+	1.04548i
$793$	26.6625	+	46.1808i	0.946812	+	1.63993i
$794$	−1.10107	−	36.1204i	−0.0390757	−	1.28186i
$795$	−1.74858	−	1.65769i	−0.0620158	−	0.0587924i
$796$	−41.3074	+	2.52073i	−1.46410	+	0.0893448i
$797$	−9.04307	+	10.7771i	−0.320322	+	0.381745i	−0.902045	−	0.431642i	$-0.857934\pi$
$797$	−9.04307	+	10.7771i	−0.320322	+	0.381745i	0.581723	+	0.813387i	$0.302379\pi$
$798$	21.1715	−	26.6918i	0.749463	−	0.944879i
$799$	−1.31022	+	3.59980i	−0.0463523	+	0.127352i
$800$	27.5620	+	5.49234i	0.974463	+	0.194183i
$801$	−42.9053	−	32.2648i	−1.51598	−	1.14002i
$802$	9.87721	+	7.78767i	0.348776	+	0.274992i
$803$	−35.0758	−	12.7666i	−1.23780	−	0.450522i
$804$	41.7811	−	15.2240i	1.47351	−	0.536909i
$805$	1.55029	−	3.08303i	0.0546405	−	0.108663i
$806$	−4.97769	+	15.0918i	−0.175332	+	0.531586i
$807$	−7.96351	+	12.0445i	−0.280329	+	0.423987i
$808$	−19.1796	−	19.0208i	−0.674736	−	0.669151i
$809$	1.90415	+	3.29809i	0.0669464	+	0.115955i	0.897556	−	0.440901i	$-0.145341\pi$
$809$	1.90415	+	3.29809i	0.0669464	+	0.115955i	−0.830609	+	0.556856i	$0.812008\pi$
$810$	−0.310803	−	2.25147i	−0.0109205	−	0.0791087i
$811$	52.9733			1.86015			0.930073	−	0.367375i	$-0.119743\pi$
$811$	52.9733			1.86015			0.930073	+	0.367375i	$0.119743\pi$
$812$	4.38524	−	10.2299i	0.153892	−	0.359000i
$813$	−0.355349	+	5.85758i	−0.0124626	+	0.205434i
$814$	−20.5517	−	23.0295i	−0.720337	−	0.807182i
$815$	1.61440	+	1.35464i	0.0565498	+	0.0474509i
$816$	−5.98675	−	9.04070i	−0.209578	−	0.316488i
$817$	−15.5258	+	42.6569i	−0.543181	+	1.49238i
$818$	4.90280	+	12.2914i	0.171422	+	0.429760i
$819$	−23.1806	−	31.4857i	−0.809997	−	1.10020i
$820$	−0.906175	+	0.859689i	−0.0316450	+	0.0300217i
$821$	1.10611	−	0.928136i	0.0386035	−	0.0323922i	−0.623282	−	0.781997i	$-0.714201\pi$
$821$	1.10611	−	0.928136i	0.0386035	−	0.0323922i	0.661885	+	0.749605i	$0.269757\pi$
$822$	−13.2725	+	1.93020i	−0.462932	+	0.0673236i
$823$	−0.944713	−	0.166578i	−0.0329306	−	0.00580655i	0.157159	−	0.987573i	$-0.449767\pi$
$823$	−0.944713	−	0.166578i	−0.0329306	−	0.00580655i	−0.190089	+	0.981767i	$0.560878\pi$
$824$	−0.329227	+	3.95217i	−0.0114692	+	0.137681i
$825$	30.7876	−	9.13631i	1.07189	−	0.318086i
$826$	−31.3910	−	8.38142i	−1.09223	−	0.291627i
$827$	−34.4380	−	19.8828i	−1.19753	−	0.691393i	−0.237525	−	0.971382i	$-0.576336\pi$
$827$	−34.4380	−	19.8828i	−1.19753	−	0.691393i	−0.960003	+	0.279988i	$0.909669\pi$
$828$	−12.4828	−	42.0097i	−0.433808	−	1.45994i
$829$	16.7131	+	9.64932i	0.580470	+	0.335135i	0.761320	−	0.648376i	$-0.224552\pi$
$829$	16.7131	+	9.64932i	0.580470	+	0.335135i	−0.180850	+	0.983511i	$0.557885\pi$
$830$	3.72445	−	2.30440i	0.129277	−	0.0799869i
$831$	−4.08663	+	9.41138i	−0.141764	+	0.326477i
$832$	−19.4195	+	34.2905i	−0.673249	+	1.18881i
$833$	7.96128	+	7.52615i	0.275842	+	0.260766i
$834$	14.3874	+	43.5688i	0.498196	+	1.50866i
$835$	0.815314	−	0.143762i	0.0282151	−	0.00497509i
$836$	−38.1557	+	9.15478i	−1.31964	+	0.316625i
$837$	−1.97376	−	11.6879i	−0.0682232	−	0.403993i
$838$	19.3049	+	15.2209i	0.666877	+	0.525798i
$839$	−35.4468	+	29.7434i	−1.22376	+	1.02685i	−0.225139	+	0.974327i	$0.572283\pi$
$839$	−35.4468	+	29.7434i	−1.22376	+	1.02685i	−0.998619	+	0.0525281i	$0.983272\pi$
$840$	1.63459	−	1.63865i	0.0563986	−	0.0565389i
$841$	−4.26752	+	24.2023i	−0.147156	+	0.834562i
$842$	23.4671	+	7.74009i	0.808730	+	0.266741i
$843$	51.3108	−	5.87191i	1.76724	−	0.202239i
$844$	10.9405	+	25.1710i	0.376588	+	0.866420i
$845$			2.01158i			0.0692005i
$846$	−8.52704	+	5.92708i	−0.293166	+	0.203777i
$847$	−5.63823	+	5.31407i	−0.193732	+	0.182593i
$848$	−18.7462	−	24.8914i	−0.643748	−	0.854775i
$849$	−10.3795	−	34.9770i	−0.356225	−	1.20041i
$850$	−3.44435	+	10.4429i	−0.118140	+	0.358188i
$851$	42.0670	+	7.41754i	1.44204	+	0.254270i
$852$	40.9091	−	0.0146217i	1.40152	−	0.000500933i
$853$	−0.270263	+	0.742540i	−0.00925362	+	0.0254241i	−0.944233	−	0.329277i	$-0.893195\pi$
$853$	−0.270263	+	0.742540i	−0.00925362	+	0.0254241i	0.934980	+	0.354701i	$0.115417\pi$
$854$	−3.56592	−	40.3474i	−0.122023	−	1.38066i
$855$	2.05772	−	1.92268i	0.0703727	−	0.0657542i
$856$	−24.3205	−	11.2180i	−0.831256	−	0.383424i
$857$	30.5214	+	36.3740i	1.04259	+	1.24251i	0.969475	+	0.245190i	$0.0788504\pi$
$857$	30.5214	+	36.3740i	1.04259	+	1.24251i	0.0731177	+	0.997323i	$0.476705\pi$
$858$	−1.35599	+	45.0110i	−0.0462927	+	1.53665i
$859$	4.42279	−	25.0829i	0.150904	−	0.855816i	−0.811532	−	0.584307i	$-0.801366\pi$
$859$	4.42279	−	25.0829i	0.150904	−	0.855816i	0.962436	−	0.271509i	$-0.0875226\pi$
$860$	−1.37644	+	2.75976i	−0.0469363	+	0.0941070i
$861$	−2.73714	−	15.7920i	−0.0932815	−	0.538189i
$862$	42.9662	−	26.5842i	1.46343	−	0.905460i
$863$	−14.9227	−	8.61561i	−0.507974	−	0.293279i	0.224026	−	0.974583i	$-0.428080\pi$
$863$	−14.9227	−	8.61561i	−0.507974	−	0.293279i	−0.732000	+	0.681304i	$0.761413\pi$
$864$	0.864108	−	29.3812i	0.0293975	−	0.999568i
$865$	−0.864070	−	1.49661i	−0.0293793	−	0.0508864i
$866$	0.287500	+	9.43135i	0.00976966	+	0.320490i
$867$	−22.5488	+	11.2564i	−0.765796	+	0.382286i
$868$	8.26359	−	8.79883i	0.280485	−	0.298652i
$869$	36.4899	−	13.2812i	1.23783	−	0.450535i
$870$	0.483806	−	0.782567i	0.0164026	−	0.0265315i
$871$	48.4400	−	40.6460i	1.64133	−	1.37724i
$872$	−18.2116	−	25.7802i	−0.616723	−	0.873027i
$873$	−5.17650	−	7.95383i	−0.175198	−	0.269196i
$874$	33.6212	−	42.6422i	1.13725	−	1.44239i
$875$	−4.67733	−	0.549073i	−0.158123	−	0.0185621i
$876$	34.6467	−	0.0123834i	1.17060	−	0.000418397i
$877$	−3.11902	+	1.13523i	−0.105322	+	0.0383340i	−0.394144	−	0.919049i	$-0.628959\pi$
$877$	−3.11902	+	1.13523i	−0.105322	+	0.0383340i	0.288822	+	0.957383i	$0.406737\pi$
$878$	−31.4936	−	10.3874i	−1.06286	−	0.350559i
$879$	1.39110	−	0.412814i	0.0469207	−	0.0139239i
$880$	−2.64597	+	0.324140i	−0.0891955	+	0.0109268i
$881$	15.0795	+	8.70617i	0.508042	+	0.293318i	0.732028	−	0.681274i	$-0.238574\pi$
$881$	15.0795	+	8.70617i	0.508042	+	0.293318i	−0.223986	+	0.974592i	$0.571907\pi$
$882$	5.87633	+	29.1113i	0.197866	+	0.980229i
$883$	−44.7196	+	25.8189i	−1.50493	+	0.868874i	−0.504950	+	0.863149i	$0.668489\pi$
$883$	−44.7196	+	25.8189i	−1.50493	+	0.868874i	−0.999984	+	0.00572526i	$0.998178\pi$
$884$	−12.3934	−	9.17331i	−0.416836	−	0.308532i
$885$	−2.46351	−	1.06971i	−0.0828100	−	0.0359580i
$886$	5.68576	+	6.37124i	0.191017	+	0.214046i
$887$	−6.21711	−	5.21677i	−0.208750	−	0.175162i	0.532418	−	0.846482i	$-0.321283\pi$
$887$	−6.21711	−	5.21677i	−0.208750	−	0.175162i	−0.741168	+	0.671319i	$0.765728\pi$
$888$	25.2414	+	13.5533i	0.847046	+	0.454820i
$889$	−2.63751	+	3.53909i	−0.0884591	+	0.118697i
$890$	0.648749	−	4.47217i	0.0217461	−	0.149907i
$891$	−14.7842	−	30.1601i	−0.495288	−	1.01040i
$892$	−8.12778	−	33.8753i	−0.272138	−	1.13423i
$893$	−12.0913	−	4.40088i	−0.404620	−	0.147270i
$894$	−12.5753	+	14.1016i	−0.420582	+	0.471628i
$895$	0.152845	−	0.866825i	0.00510903	−	0.0289748i
$896$	24.3610	−	17.3938i	0.813843	−	0.581085i
$897$	−37.0937	−	50.0772i	−1.23852	−	1.67203i
$898$	−15.2756	+	28.4245i	−0.509752	+	0.948538i
$899$	2.39914	−	4.15542i	0.0800156	−	0.138591i
$900$	−23.9468	+	17.7513i	−0.798226	+	0.591711i
$901$	10.5589	−	6.09619i	0.351768	−	0.203093i
$902$	−8.73837	+	16.2602i	−0.290956	+	0.541406i
$903$	−19.6858	−	34.3273i	−0.655101	−	1.14234i
$904$	39.7840	−	18.7533i	1.32320	−	0.623724i
$905$	1.94911	−	0.709418i	0.0647906	−	0.0235819i
$906$	−7.28586	+	5.74875i	−0.242056	+	0.190989i
$907$	−51.9682	+	9.16340i	−1.72558	+	0.304266i	−0.946510	−	0.322676i	$-0.895418\pi$
$907$	−51.9682	+	9.16340i	−1.72558	+	0.304266i	−0.779066	+	0.626941i	$0.784307\pi$
$908$	1.74485	+	7.27227i	0.0579050	+	0.241339i
$909$	28.6098	−	1.52783i	0.948927	−	0.0506749i
$910$	1.38831	−	2.98412i	0.0460219	−	0.0989227i
$911$	−29.6452	+	5.22724i	−0.982188	+	0.173186i	−0.641611	−	0.767030i	$-0.721734\pi$
$911$	−29.6452	+	5.22724i	−0.982188	+	0.173186i	−0.340577	+	0.940217i	$0.610622\pi$
$912$	30.3666	−	20.1088i	1.00554	−	0.665869i
$913$	41.6044	−	49.5822i	1.37690	−	1.64093i
$914$	−5.04455	−	24.2610i	−0.166859	−	0.802484i
$915$	0.202745	−	3.34204i	0.00670253	−	0.110485i
$916$	7.61742	+	17.5255i	0.251687	+	0.579059i
$917$	24.8260	+	7.44593i	0.819825	+	0.245886i
$918$	11.3696	+	1.73344i	0.375252	+	0.0572121i
$919$	−19.2235	−	11.0987i	−0.634124	−	0.366112i	0.148223	−	0.988954i	$-0.452645\pi$
$919$	−19.2235	−	11.0987i	−0.634124	−	0.366112i	−0.782348	+	0.622842i	$0.785978\pi$
$920$	2.59775	−	2.61943i	0.0856452	−	0.0863600i
$921$	0.991389	−	16.3421i	0.0326674	−	0.538489i
$922$	−17.7634	−	19.9049i	−0.585005	−	0.655534i
$923$	54.6645	−	19.8962i	1.79930	−	0.654893i
$924$	15.3556	−	30.5646i	0.505161	−	1.00550i
$925$	−5.04522	−	28.6129i	−0.165886	−	0.940786i
$926$	−35.6247	−	5.16786i	−1.17070	−	0.169826i
$927$	−2.87183	−	3.07354i	−0.0943233	−	0.100948i
$928$	7.84845	−	8.94320i	0.257638	−	0.293575i
$929$	−27.4623	−	32.7284i	−0.901010	−	1.07378i	−0.996923	−	0.0783926i	$-0.975021\pi$
$929$	−27.4623	−	32.7284i	−0.901010	−	1.07378i	0.0959121	−	0.995390i	$-0.469423\pi$
$930$	0.783327	−	0.618067i	0.0256863	−	0.0202672i
$931$	−25.2794	+	26.7410i	−0.828500	+	0.876401i
$932$	6.91936	+	10.4572i	0.226651	+	0.342535i
$933$	2.89095	+	9.74195i	0.0946456	+	0.318937i
$934$	39.7425	−	1.21149i	1.30041	−	0.0396411i
$935$		−	1.04303i		−	0.0341107i
$936$	−13.1208	−	39.6853i	−0.428865	−	1.29715i
$937$	−17.4299	+	10.0632i	−0.569411	+	0.328750i	−0.756914	−	0.653514i	$-0.773294\pi$
$937$	−17.4299	+	10.0632i	−0.569411	+	0.328750i	0.187503	+	0.982264i	$0.439961\pi$
$938$	−46.3837	+	12.4725i	−1.51448	+	0.407241i
$939$	22.6260	+	9.82474i	0.738373	+	0.320618i
$940$	−0.782266	−	0.390159i	−0.0255147	−	0.0127256i
$941$	−11.8431	−	32.5386i	−0.386073	−	1.06073i	−0.968753	−	0.248026i	$-0.920218\pi$
$941$	−11.8431	−	32.5386i	−0.386073	−	1.06073i	0.582680	−	0.812701i	$-0.302004\pi$
$942$	−0.185898	+	0.895654i	−0.00605687	+	0.0291820i
$943$	−4.43604	−	25.1580i	−0.144457	−	0.819258i
$944$	−29.1251	−	18.9255i	−0.947942	−	0.615974i
$945$	0.123770	+	2.45181i	0.00402625	+	0.0797573i
$946$	−6.54296	+	45.1040i	−0.212730	+	1.46646i
$947$	33.1692	−	5.84862i	1.07785	−	0.190055i	0.393588	−	0.919287i	$-0.371234\pi$
$947$	33.1692	−	5.84862i	1.07785	−	0.190055i	0.684266	+	0.729232i	$0.260123\pi$
$948$	−27.6026	+	23.1782i	−0.896492	+	0.752792i
$949$	46.2963	−	16.8505i	1.50284	−	0.546990i
$950$	−35.0764	−	11.5691i	−1.13803	−	0.375353i
$951$	−0.367076	+	0.0420074i	−0.0119033	+	0.00136218i
$952$	5.59618	+	10.2885i	0.181373	+	0.333454i
$953$	2.20869	+	3.82557i	0.0715466	+	0.123922i	0.899579	−	0.436757i	$-0.143873\pi$
$953$	2.20869	+	3.82557i	0.0715466	+	0.123922i	−0.828033	+	0.560680i	$0.810540\pi$
$954$	32.9153	+	2.99387i	1.06567	+	0.0969302i
$955$	−2.81183			−0.0909885
$956$	28.7968	+	3.28502i	0.931355	+	0.106245i
$957$	3.16755	−	13.2227i	0.102392	−	0.427428i
$958$	18.8068	−	16.7833i	0.607619	−	0.542245i
$959$	14.4627	−	0.835096i	0.467024	−	0.0269666i
$960$	2.20456	−	1.12350i	0.0711519	−	0.0362609i
$961$	−19.7610	+	16.5815i	−0.637453	+	0.534886i
$962$	40.3182	+	5.84871i	1.29991	+	0.188570i
$963$	26.1384	−	11.1257i	0.842297	−	0.358520i
$964$	1.88011	−	6.34391i	0.0605541	−	0.204323i
$965$	−0.505061	+	0.0890559i	−0.0162585	+	0.00286681i
$966$	9.50141	+	46.3731i	0.305703	+	1.49203i
$967$	−10.1504	−	27.8881i	−0.326416	−	0.896820i	−0.989011	−	0.147842i	$-0.952767\pi$
$967$	−10.1504	−	27.8881i	−0.326416	−	0.896820i	0.662595	−	0.748978i	$-0.269455\pi$
$968$	−7.49214	+	3.53162i	−0.240806	+	0.113511i
$969$	6.36487	+	12.7501i	0.204469	+	0.409593i
$970$	0.378162	−	0.703677i	0.0121420	−	0.0225937i
$971$	15.6955	−	27.1853i	0.503691	−	0.872419i	−0.496300	−	0.868151i	$-0.665308\pi$
$971$	15.6955	−	27.1853i	0.503691	−	0.872419i	0.999991	−	0.00426755i	$-0.00135841\pi$
$972$	22.4774	+	21.6047i	0.720964	+	0.692973i
$973$	−11.4050	−	48.2290i	−0.365628	−	1.54615i
$974$	3.40597	−	2.10735i	0.109134	−	0.0675238i
$975$	−23.3779	+	35.3583i	−0.748692	+	1.13237i
$976$	9.75235	−	42.1888i	0.312165	−	1.35043i
$977$	42.7913	+	35.9062i	1.36902	+	1.14874i	0.973081	+	0.230463i	$0.0740240\pi$
$977$	42.7913	+	35.9062i	1.36902	+	1.14874i	0.395935	+	0.918278i	$0.370420\pi$
$978$	−28.8953	−	0.870491i	−0.923968	−	0.0278352i
$979$	−11.5968	−	65.7687i	−0.370635	−	2.10198i
$980$	−1.91225	+	1.61034i	−0.0610845	+	0.0514405i
$981$	33.2331	+	4.04706i	1.06105	+	0.129213i
$982$	9.98723	+	25.0382i	0.318705	+	0.799002i
$983$	−1.98916	−	11.2811i	−0.0634443	−	0.359811i	−0.999958	−	0.00917929i	$-0.997078\pi$
$983$	−1.98916	−	11.2811i	−0.0634443	−	0.359811i	0.936514	−	0.350631i	$-0.114033\pi$
$984$	2.45372	−	16.9574i	0.0782218	−	0.540584i
$985$	0.610301	+	1.67679i	0.0194458	+	0.0534269i
$986$	3.09985	+	3.47357i	0.0987193	+	0.110621i
$987$	9.73024	−	5.58002i	0.309717	−	0.177614i
$988$	30.8121	−	41.6281i	0.980262	−	1.32436i
$989$	−31.5364	−	54.6227i	−1.00280	−	1.73690i
$990$	1.62972	−	2.31052i	0.0517959	−	0.0734331i
$991$	−6.45091	−	3.72444i	−0.204920	−	0.118311i	0.394028	−	0.919098i	$-0.371081\pi$
$991$	−6.45091	−	3.72444i	−0.204920	−	0.118311i	−0.598948	+	0.800788i	$0.704415\pi$
$992$	11.3157	−	6.20292i	0.359274	−	0.196943i
$993$	−4.32226	−	37.7695i	−0.137163	−	1.19858i
$994$	−44.0222	−	3.81218i	−1.39630	−	0.120915i
$995$	3.63885	+	0.641628i	0.115359	+	0.0203410i
$996$	−20.5275	+	56.4617i	−0.650439	+	1.78906i
$997$	−20.9439	+	57.5428i	−0.663299	+	1.82240i	−0.102004	+	0.994784i	$0.532525\pi$
$997$	−20.9439	+	57.5428i	−0.663299	+	1.82240i	−0.561296	+	0.827615i	$0.689697\pi$
$998$	−11.8285	−	29.6544i	−0.374426	−	0.938694i
$999$	−28.6298	+	10.1863i	−0.905806	+	0.322280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.4	✓	840
4.3	odd	2	inner	756.2.bt.a.103.127	yes	840
7.3	odd	6		756.2.cd.a.535.94	yes	840
27.16	even	9		756.2.cd.a.691.61	yes	840
28.3	even	6		756.2.cd.a.535.61	yes	840
108.43	odd	18		756.2.cd.a.691.94	yes	840
189.178	odd	18	inner	756.2.bt.a.367.127	yes	840
756.367	even	18	inner	756.2.bt.a.367.4	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.4	✓	840	1.1	even	1	trivial
756.2.bt.a.103.127	yes	840	4.3	odd	2	inner
756.2.bt.a.367.4	yes	840	756.367	even	18	inner
756.2.bt.a.367.127	yes	840	189.178	odd	18	inner
756.2.cd.a.535.61	yes	840	28.3	even	6
756.2.cd.a.535.94	yes	840	7.3	odd	6
756.2.cd.a.691.61	yes	840	27.16	even	9
756.2.cd.a.691.94	yes	840	108.43	odd	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41356 + 0.0430901i) q^{2} +(-1.54969 + 0.773606i) q^{3} +(1.99629 - 0.121821i) q^{4} +(-0.175857 - 0.0310083i) q^{5} +(2.15724 - 1.16031i) q^{6} +(-2.42990 + 1.04671i) q^{7} +(-2.81662 + 0.258221i) q^{8} +(1.80307 - 2.39770i) q^{9} +O(q^{10})\)	\(q+(-1.41356 + 0.0430901i) q^{2} +(-1.54969 + 0.773606i) q^{3} +(1.99629 - 0.121821i) q^{4} +(-0.175857 - 0.0310083i) q^{5} +(2.15724 - 1.16031i) q^{6} +(-2.42990 + 1.04671i) q^{7} +(-2.81662 + 0.258221i) q^{8} +(1.80307 - 2.39770i) q^{9} +(0.249920 + 0.0362544i) q^{10} +(3.67538 - 0.648069i) q^{11} +(-2.99938 + 1.73312i) q^{12} +(-3.16634 + 3.77349i) q^{13} +(3.38969 - 1.58429i) q^{14} +(0.296512 - 0.0879908i) q^{15} +(3.97032 - 0.486378i) q^{16} +1.56508i q^{17} +(-2.44542 + 3.46697i) q^{18} -5.25693 q^{19} +(-0.354839 - 0.0404785i) q^{20} +(2.95584 - 3.50186i) q^{21} +(-5.16743 + 1.07445i) q^{22} +(4.69503 - 5.59532i) q^{23} +(4.16511 - 2.57911i) q^{24} +(-4.66850 - 1.69919i) q^{25} +(4.31320 - 5.47049i) q^{26} +(-0.939322 + 5.11055i) q^{27} +(-4.72326 + 2.38555i) q^{28} +(-1.61131 + 1.35205i) q^{29} +(-0.415345 + 0.137157i) q^{30} +(-2.14361 + 0.780211i) q^{31} +(-5.59131 + 0.858605i) q^{32} +(-5.19434 + 3.84760i) q^{33} +(-0.0674397 - 2.21234i) q^{34} +(0.459771 - 0.108725i) q^{35} +(3.30735 - 5.00614i) q^{36} +(2.92408 + 5.06465i) q^{37} +(7.43097 - 0.226522i) q^{38} +(1.98764 - 8.29724i) q^{39} +(0.503329 + 0.0419286i) q^{40} +(2.24813 - 2.67922i) q^{41} +(-4.02735 + 5.07745i) q^{42} +(2.95341 - 8.11442i) q^{43} +(7.25816 - 1.74147i) q^{44} +(-0.391431 + 0.365742i) q^{45} +(-6.39559 + 8.11161i) q^{46} +(2.30007 + 0.837157i) q^{47} +(-5.77649 + 3.82520i) q^{48} +(4.80878 - 5.08681i) q^{49} +(6.67241 + 2.20074i) q^{50} +(-1.21076 - 2.42539i) q^{51} +(-5.86123 + 7.91870i) q^{52} +(-3.89512 - 6.74654i) q^{53} +(1.10757 - 7.26452i) q^{54} -0.666437 q^{55} +(6.57380 - 3.57564i) q^{56} +(8.14660 - 4.06679i) q^{57} +(2.21941 - 1.98063i) q^{58} +(-6.65194 - 5.58164i) q^{59} +(0.581204 - 0.211776i) q^{60} +(3.70248 - 10.1725i) q^{61} +(2.99650 - 1.19524i) q^{62} +(-1.87157 + 7.71345i) q^{63} +(7.86664 - 1.45462i) q^{64} +(0.673833 - 0.565413i) q^{65} +(7.17671 - 5.66263i) q^{66} +(-12.6419 - 2.22911i) q^{67} +(0.190660 + 3.12436i) q^{68} +(-2.94726 + 12.3031i) q^{69} +(-0.645228 + 0.173500i) q^{70} +(-10.2273 - 5.90473i) q^{71} +(-4.45941 + 7.21898i) q^{72} +(-8.66167 - 5.00082i) q^{73} +(-4.35159 - 7.03317i) q^{74} +(8.54923 - 0.978356i) q^{75} +(-10.4943 + 0.640403i) q^{76} +(-8.25244 + 5.42181i) q^{77} +(-2.45211 + 11.8143i) q^{78} +(10.2468 - 1.80678i) q^{79} +(-0.713290 - 0.0375800i) q^{80} +(-2.49789 - 8.64642i) q^{81} +(-3.06242 + 3.88410i) q^{82} +(13.2854 - 11.1478i) q^{83} +(5.47410 - 7.35080i) q^{84} +(0.0485307 - 0.275231i) q^{85} +(-3.82516 + 11.5975i) q^{86} +(1.45107 - 3.34177i) q^{87} +(-10.1848 + 2.77442i) q^{88} -17.8944i q^{89} +(0.537550 - 0.533863i) q^{90} +(3.74410 - 12.4834i) q^{91} +(8.69100 - 11.7418i) q^{92} +(2.71835 - 2.86739i) q^{93} +(-3.28735 - 1.08426i) q^{94} +(0.924468 + 0.163009i) q^{95} +(8.00057 - 5.65604i) q^{96} +(1.08192 - 2.97255i) q^{97} +(-6.57830 + 7.39770i) q^{98} +(5.07309 - 9.98095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

L-functions

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