LMFDB - Embedded newform 196.5.h.a.117.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,5,Mod(117,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("196.117");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	196.h (of order $6$, degree $2$, 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:	$20.2605127644$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	196.117
Dual form			196.5.h.a.129.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.00000 + 3.46410i) q^{3} +(18.0000 + 10.3923i) q^{5} +(-16.5000 + 28.5788i) q^{9} +O(q^{10})$	\(q+(-6.00000 + 3.46410i) q^{3} +(18.0000 + 10.3923i) q^{5} +(-16.5000 + 28.5788i) q^{9} +(-9.00000 - 15.5885i) q^{11} +131.636i q^{13} -144.000 q^{15} +(360.000 - 207.846i) q^{17} +(78.0000 + 45.0333i) q^{19} +(-369.000 + 639.127i) q^{23} +(-96.5000 - 167.143i) q^{25} -789.815i q^{27} -846.000 q^{29} +(-1008.00 + 581.969i) q^{31} +(108.000 + 62.3538i) q^{33} +(-1193.00 + 2066.34i) q^{37} +(-456.000 - 789.815i) q^{39} +1704.34i q^{41} -2510.00 q^{43} +(-594.000 + 342.946i) q^{45} +(-2952.00 - 1704.34i) q^{47} +(-1440.00 + 2494.15i) q^{51} +(135.000 + 233.827i) q^{53} -374.123i q^{55} -624.000 q^{57} +(2718.00 - 1569.24i) q^{59} +(5622.00 + 3245.86i) q^{61} +(-1368.00 + 2369.45i) q^{65} +(-1225.00 - 2121.76i) q^{67} -5113.01i q^{69} -3150.00 q^{71} +(-204.000 + 117.779i) q^{73} +(1158.00 + 668.572i) q^{75} +(1991.00 - 3448.51i) q^{79} +(1399.50 + 2424.01i) q^{81} +5009.09i q^{83} +8640.00 q^{85} +(5076.00 - 2930.63i) q^{87} +(-6588.00 - 3803.58i) q^{89} +(4032.00 - 6983.63i) q^{93} +(936.000 + 1621.20i) q^{95} +12581.6i q^{97} +594.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 12 q^{3} + 36 q^{5} - 33 q^{9}+O(q^{10}) $ 2 * q - 12 * q^3 + 36 * q^5 - 33 * q^9	$ 2 q - 12 q^{3} + 36 q^{5} - 33 q^{9} - 18 q^{11} - 288 q^{15} + 720 q^{17} + 156 q^{19} - 738 q^{23} - 193 q^{25} - 1692 q^{29} - 2016 q^{31} + 216 q^{33} - 2386 q^{37} - 912 q^{39} - 5020 q^{43} - 1188 q^{45} - 5904 q^{47} - 2880 q^{51} + 270 q^{53} - 1248 q^{57} + 5436 q^{59} + 11244 q^{61} - 2736 q^{65} - 2450 q^{67} - 6300 q^{71} - 408 q^{73} + 2316 q^{75} + 3982 q^{79} + 2799 q^{81} + 17280 q^{85} + 10152 q^{87} - 13176 q^{89} + 8064 q^{93} + 1872 q^{95} + 1188 q^{99}+O(q^{100}) $ 2 * q - 12 * q^3 + 36 * q^5 - 33 * q^9 - 18 * q^11 - 288 * q^15 + 720 * q^17 + 156 * q^19 - 738 * q^23 - 193 * q^25 - 1692 * q^29 - 2016 * q^31 + 216 * q^33 - 2386 * q^37 - 912 * q^39 - 5020 * q^43 - 1188 * q^45 - 5904 * q^47 - 2880 * q^51 + 270 * q^53 - 1248 * q^57 + 5436 * q^59 + 11244 * q^61 - 2736 * q^65 - 2450 * q^67 - 6300 * q^71 - 408 * q^73 + 2316 * q^75 + 3982 * q^79 + 2799 * q^81 + 17280 * q^85 + 10152 * q^87 - 13176 * q^89 + 8064 * q^93 + 1872 * q^95 + 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−6.00000	+	3.46410i	−0.666667	+	0.384900i	−0.794812	−	0.606855i	$-0.792431\pi$
$3$	−6.00000	+	3.46410i	−0.666667	+	0.384900i	0.128146	+	0.991755i	$0.459097\pi$
$4$		0			0
$5$	18.0000	+	10.3923i	0.720000	+	0.415692i	0.814753	−	0.579809i	$-0.196873\pi$
$5$	18.0000	+	10.3923i	0.720000	+	0.415692i	−0.0947527	+	0.995501i	$0.530206\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−16.5000	+	28.5788i	−0.203704	+	0.352825i
$10$		0			0
$11$	−9.00000	−	15.5885i	−0.0743802	−	0.128830i	0.826436	−	0.563030i	$-0.190364\pi$
$11$	−9.00000	−	15.5885i	−0.0743802	−	0.128830i	−0.900817	+	0.434200i	$0.857031\pi$
$12$		0			0
$13$			131.636i			0.778910i	0.921045	+	0.389455i	$0.127337\pi$
$13$			131.636i			0.778910i	−0.921045	+	0.389455i	$0.872663\pi$
$14$		0			0
$15$	−144.000			−0.640000
$16$		0			0
$17$	360.000	−	207.846i	1.24567	−	0.719191i	0.275431	−	0.961321i	$-0.411179\pi$
$17$	360.000	−	207.846i	1.24567	−	0.719191i	0.970244	+	0.242130i	$0.0778461\pi$
$18$		0			0
$19$	78.0000	+	45.0333i	0.216066	+	0.124746i	0.604128	−	0.796888i	$-0.293522\pi$
$19$	78.0000	+	45.0333i	0.216066	+	0.124746i	−0.388061	+	0.921634i	$0.626855\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−369.000	+	639.127i	−0.697543	+	1.20818i	0.271774	+	0.962361i	$0.412390\pi$
$23$	−369.000	+	639.127i	−0.697543	+	1.20818i	−0.969316	+	0.245818i	$0.920943\pi$
$24$		0			0
$25$	−96.5000	−	167.143i	−0.154400	−	0.267429i
$26$		0			0
$27$		−	789.815i		−	1.08342i
$28$		0			0
$29$	−846.000			−1.00595			−0.502973	−	0.864302i	$-0.667760\pi$
$29$	−846.000			−1.00595			−0.502973	+	0.864302i	$0.667760\pi$
$30$		0			0
$31$	−1008.00	+	581.969i	−1.04891	+	0.605587i	−0.922343	−	0.386371i	$-0.873728\pi$
$31$	−1008.00	+	581.969i	−1.04891	+	0.605587i	−0.126564	+	0.991958i	$0.540395\pi$
$32$		0			0
$33$	108.000	+	62.3538i	0.0991736	+	0.0572579i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1193.00	+	2066.34i	−0.871439	+	1.50938i	−0.0109307	+	0.999940i	$0.503479\pi$
$37$	−1193.00	+	2066.34i	−0.871439	+	1.50938i	−0.860508	+	0.509436i	$0.829854\pi$
$38$		0			0
$39$	−456.000	−	789.815i	−0.299803	−	0.519274i
$40$		0			0
$41$			1704.34i			1.01388i	0.861980	+	0.506942i	$0.169224\pi$
$41$			1704.34i			1.01388i	−0.861980	+	0.506942i	$0.830776\pi$
$42$		0			0
$43$	−2510.00			−1.35749			−0.678745	−	0.734374i	$-0.737476\pi$
$43$	−2510.00			−1.35749			−0.678745	+	0.734374i	$0.737476\pi$
$44$		0			0
$45$	−594.000	+	342.946i	−0.293333	+	0.169356i
$46$		0			0
$47$	−2952.00	−	1704.34i	−1.33635	−	0.771543i	−0.350087	−	0.936717i	$-0.613848\pi$
$47$	−2952.00	−	1704.34i	−1.33635	−	0.771543i	−0.986264	+	0.165174i	$0.947181\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1440.00	+	2494.15i	−0.553633	+	0.958921i
$52$		0			0
$53$	135.000	+	233.827i	0.0480598	+	0.0832420i	0.889055	−	0.457801i	$-0.151363\pi$
$53$	135.000	+	233.827i	0.0480598	+	0.0832420i	−0.840995	+	0.541043i	$0.818030\pi$
$54$		0			0
$55$		−	374.123i		−	0.123677i
$56$		0			0
$57$	−624.000			−0.192059
$58$		0			0
$59$	2718.00	−	1569.24i	0.780810	−	0.450801i	−0.0559072	−	0.998436i	$-0.517805\pi$
$59$	2718.00	−	1569.24i	0.780810	−	0.450801i	0.836717	+	0.547635i	$0.184472\pi$
$60$		0			0
$61$	5622.00	+	3245.86i	1.51088	+	0.872309i	0.999919	+	0.0127078i	$0.00404513\pi$
$61$	5622.00	+	3245.86i	1.51088	+	0.872309i	0.510965	+	0.859602i	$0.329288\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1368.00	+	2369.45i	−0.323787	+	0.560816i
$66$		0			0
$67$	−1225.00	−	2121.76i	−0.272889	−	0.472658i	0.696711	−	0.717352i	$-0.254646\pi$
$67$	−1225.00	−	2121.76i	−0.272889	−	0.472658i	−0.969600	+	0.244694i	$0.921313\pi$
$68$		0			0
$69$		−	5113.01i		−	1.07394i
$70$		0			0
$71$	−3150.00			−0.624876			−0.312438	−	0.949938i	$-0.601146\pi$
$71$	−3150.00			−0.624876			−0.312438	+	0.949938i	$0.601146\pi$
$72$		0			0
$73$	−204.000	+	117.779i	−0.0382811	+	0.0221016i	−0.519018	−	0.854763i	$-0.673702\pi$
$73$	−204.000	+	117.779i	−0.0382811	+	0.0221016i	0.480737	+	0.876865i	$0.340369\pi$
$74$		0			0
$75$	1158.00	+	668.572i	0.205867	+	0.118857i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1991.00	−	3448.51i	0.319019	−	0.552558i	−0.661264	−	0.750153i	$-0.729980\pi$
$79$	1991.00	−	3448.51i	0.319019	−	0.552558i	0.980284	+	0.197595i	$0.0633132\pi$
$80$		0			0
$81$	1399.50	+	2424.01i	0.213306	+	0.369457i
$82$		0			0
$83$			5009.09i			0.727114i	0.931572	+	0.363557i	$0.118438\pi$
$83$			5009.09i			0.727114i	−0.931572	+	0.363557i	$0.881562\pi$
$84$		0			0
$85$	8640.00			1.19585
$86$		0			0
$87$	5076.00	−	2930.63i	0.670630	−	0.387189i
$88$		0			0
$89$	−6588.00	−	3803.58i	−0.831713	−	0.480190i	0.0227257	−	0.999742i	$-0.492766\pi$
$89$	−6588.00	−	3803.58i	−0.831713	−	0.480190i	−0.854439	+	0.519552i	$0.826099\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4032.00	−	6983.63i	0.466181	−	0.807449i
$94$		0			0
$95$	936.000	+	1621.20i	0.103712	+	0.179634i
$96$		0			0
$97$			12581.6i			1.33719i	0.743627	+	0.668595i	$0.233104\pi$
$97$			12581.6i			1.33719i	−0.743627	+	0.668595i	$0.766896\pi$
$98$		0			0
$99$	594.000			0.0606061
$100$		0			0
$101$	−9666.00	+	5580.67i	−0.947554	+	0.547071i	−0.892320	−	0.451403i	$-0.850924\pi$
$101$	−9666.00	+	5580.67i	−0.947554	+	0.547071i	−0.0552339	+	0.998473i	$0.517590\pi$
$102$		0			0
$103$	−732.000	−	422.620i	−0.0689980	−	0.0398360i	0.465104	−	0.885256i	$-0.346017\pi$
$103$	−732.000	−	422.620i	−0.0689980	−	0.0398360i	−0.534102	+	0.845420i	$0.679350\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6471.00	−	11208.1i	0.565202	−	0.978959i	−0.431829	−	0.901956i	$-0.642131\pi$
$107$	6471.00	−	11208.1i	0.565202	−	0.978959i	0.997031	−	0.0770033i	$-0.0245352\pi$
$108$		0			0
$109$	3511.00	+	6081.23i	0.295514	+	0.511845i	0.975104	−	0.221747i	$-0.0711758\pi$
$109$	3511.00	+	6081.23i	0.295514	+	0.511845i	−0.679590	+	0.733592i	$0.737842\pi$
$110$		0			0
$111$		−	16530.7i		−	1.34167i
$112$		0			0
$113$	18738.0			1.46746			0.733730	−	0.679441i	$-0.237778\pi$
$113$	18738.0			1.46746			0.733730	+	0.679441i	$0.237778\pi$
$114$		0			0
$115$	−13284.0	+	7669.52i	−1.00446	+	0.579926i
$116$		0			0
$117$	−3762.00	−	2171.99i	−0.274819	−	0.158667i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	7158.50	−	12398.9i	0.488935	−	0.846861i
$122$		0			0
$123$	−5904.00	−	10226.0i	−0.390244	−	0.675922i
$124$		0			0
$125$		−	17001.8i		−	1.08812i
$126$		0			0
$127$	−2302.00			−0.142724			−0.0713621	−	0.997450i	$-0.522735\pi$
$127$	−2302.00			−0.142724			−0.0713621	+	0.997450i	$0.522735\pi$
$128$		0			0
$129$	15060.0	−	8694.90i	0.904994	−	0.522498i
$130$		0			0
$131$	16902.0	+	9758.37i	0.984908	+	0.568637i	0.903748	−	0.428064i	$-0.140804\pi$
$131$	16902.0	+	9758.37i	0.984908	+	0.568637i	0.0811594	+	0.996701i	$0.474138\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	8208.00	−	14216.7i	0.450370	−	0.780064i
$136$		0			0
$137$	13167.0	+	22805.9i	0.701529	+	1.21508i	0.967930	+	0.251222i	$0.0808323\pi$
$137$	13167.0	+	22805.9i	0.701529	+	1.21508i	−0.266400	+	0.963862i	$0.585834\pi$
$138$		0			0
$139$			15914.1i			0.823668i	0.911259	+	0.411834i	$0.135112\pi$
$139$			15914.1i			0.823668i	−0.911259	+	0.411834i	$0.864888\pi$
$140$		0			0
$141$	23616.0			1.18787
$142$		0			0
$143$	2052.00	−	1184.72i	0.100347	−	0.0579355i
$144$		0			0
$145$	−15228.0	−	8791.89i	−0.724281	−	0.418164i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5913.00	+	10241.6i	−0.266339	+	0.461313i	−0.967914	−	0.251283i	$-0.919148\pi$
$149$	−5913.00	+	10241.6i	−0.266339	+	0.461313i	0.701574	+	0.712596i	$0.252481\pi$
$150$		0			0
$151$	−7985.00	−	13830.4i	−0.350204	−	0.606571i	0.636081	−	0.771622i	$-0.280554\pi$
$151$	−7985.00	−	13830.4i	−0.350204	−	0.606571i	−0.986285	+	0.165051i	$0.947221\pi$
$152$		0			0
$153$			13717.8i			0.586007i
$154$		0			0
$155$	−24192.0			−1.00695
$156$		0			0
$157$	24858.0	−	14351.8i	1.00848	−	0.582246i	0.0977331	−	0.995213i	$-0.468841\pi$
$157$	24858.0	−	14351.8i	1.00848	−	0.582246i	0.910746	+	0.412967i	$0.135508\pi$
$158$		0			0
$159$	−1620.00	−	935.307i	−0.0640797	−	0.0369965i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	3911.00	−	6774.05i	0.147202	−	0.254961i	−0.782991	−	0.622034i	$-0.786307\pi$
$163$	3911.00	−	6774.05i	0.147202	−	0.254961i	0.930192	+	0.367073i	$0.119640\pi$
$164$		0			0
$165$	1296.00	+	2244.74i	0.0476033	+	0.0824513i
$166$		0			0
$167$			24234.9i			0.868975i	0.900678	+	0.434488i	$0.143071\pi$
$167$			24234.9i			0.868975i	−0.900678	+	0.434488i	$0.856929\pi$
$168$		0			0
$169$	11233.0			0.393299
$170$		0			0
$171$	−2574.00	+	1486.10i	−0.0880271	+	0.0508225i
$172$		0			0
$173$	24894.0	+	14372.6i	0.831769	+	0.480222i	0.854458	−	0.519521i	$-0.173890\pi$
$173$	24894.0	+	14372.6i	0.831769	+	0.480222i	−0.0226893	+	0.999743i	$0.507223\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10872.0	+	18830.9i	−0.347027	+	0.601068i
$178$		0			0
$179$	−4473.00	−	7747.46i	−0.139602	−	0.241798i	0.787744	−	0.616003i	$-0.211249\pi$
$179$	−4473.00	−	7747.46i	−0.139602	−	0.241798i	−0.927346	+	0.374205i	$0.877916\pi$
$180$		0			0
$181$		−	30920.6i		−	0.943823i	−0.881646	−	0.471911i	$-0.843564\pi$
$181$		−	30920.6i		−	0.943823i	0.881646	−	0.471911i	$-0.156436\pi$
$182$		0			0
$183$	−44976.0			−1.34301
$184$		0			0
$185$	−42948.0	+	24796.0i	−1.25487	+	0.724501i
$186$		0			0
$187$	−6480.00	−	3741.23i	−0.185307	−	0.106987i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−30393.0	+	52642.2i	−0.833119	+	1.44300i	0.0624345	+	0.998049i	$0.480114\pi$
$191$	−30393.0	+	52642.2i	−0.833119	+	1.44300i	−0.895553	+	0.444955i	$0.853220\pi$
$192$		0			0
$193$	−5273.00	−	9133.10i	−0.141561	−	0.245191i	0.786524	−	0.617560i	$-0.211879\pi$
$193$	−5273.00	−	9133.10i	−0.141561	−	0.245191i	−0.928085	+	0.372369i	$0.878545\pi$
$194$		0			0
$195$		−	18955.6i		−	0.498503i
$196$		0			0
$197$	18.0000			0.000463810			0.000231905	−	1.00000i	$-0.499926\pi$
$197$	18.0000			0.000463810			0.000231905		1.00000i	$0.499926\pi$
$198$		0			0
$199$	−84.0000	+	48.4974i	−0.00212116	+	0.00122465i	−0.501060	−	0.865412i	$-0.667056\pi$
$199$	−84.0000	+	48.4974i	−0.00212116	+	0.00122465i	0.498939	+	0.866637i	$0.333723\pi$
$200$		0			0
$201$	14700.0	+	8487.05i	0.363852	+	0.210070i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−17712.0	+	30678.1i	−0.421463	+	0.729996i
$206$		0			0
$207$	−12177.0	−	21091.2i	−0.284184	−	0.492221i
$208$		0			0
$209$		−	1621.20i		−	0.0371145i
$210$		0			0
$211$	−46190.0			−1.03749			−0.518744	−	0.854930i	$-0.673600\pi$
$211$	−46190.0			−1.03749			−0.518744	+	0.854930i	$0.673600\pi$
$212$		0			0
$213$	18900.0	−	10911.9i	0.416584	−	0.240515i
$214$		0			0
$215$	−45180.0	−	26084.7i	−0.977393	−	0.564298i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	816.000	−	1413.35i	0.0170138	−	0.0294688i
$220$		0			0
$221$	27360.0	+	47388.9i	0.560185	+	0.970269i
$222$		0			0
$223$		−	7815.01i		−	0.157152i	−0.996908	−	0.0785760i	$-0.974963\pi$
$223$		−	7815.01i		−	0.157152i	0.996908	−	0.0785760i	$-0.0250373\pi$
$224$		0			0
$225$	6369.00			0.125807
$226$		0			0
$227$	26730.0	−	15432.6i	0.518737	−	0.299493i	−0.217681	−	0.976020i	$-0.569849\pi$
$227$	26730.0	−	15432.6i	0.518737	−	0.299493i	0.736418	+	0.676527i	$0.236516\pi$
$228$		0			0
$229$	−49662.0	−	28672.4i	−0.947007	−	0.546755i	−0.0548572	−	0.998494i	$-0.517470\pi$
$229$	−49662.0	−	28672.4i	−0.947007	−	0.546755i	−0.892150	+	0.451739i	$0.850804\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−35217.0	+	60997.6i	−0.648695	+	1.12357i	0.334740	+	0.942311i	$0.391352\pi$
$233$	−35217.0	+	60997.6i	−0.648695	+	1.12357i	−0.983435	+	0.181262i	$0.941982\pi$
$234$		0			0
$235$	−35424.0	−	61356.2i	−0.641449	−	1.11102i
$236$		0			0
$237$			27588.1i			0.491162i
$238$		0			0
$239$	−76158.0			−1.33327			−0.666637	−	0.745382i	$-0.732267\pi$
$239$	−76158.0			−1.33327			−0.666637	+	0.745382i	$0.732267\pi$
$240$		0			0
$241$	−42792.0	+	24706.0i	−0.736764	+	0.425371i	−0.820892	−	0.571084i	$-0.806523\pi$
$241$	−42792.0	+	24706.0i	−0.736764	+	0.425371i	0.0841274	+	0.996455i	$0.473190\pi$
$242$		0			0
$243$	38610.0	+	22291.5i	0.653864	+	0.377508i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5928.00	+	10267.6i	−0.0971660	+	0.168296i
$248$		0			0
$249$	−17352.0	−	30054.5i	−0.279866	−	0.484743i
$250$		0			0
$251$			16440.6i			0.260958i	0.991451	+	0.130479i	$0.0416515\pi$
$251$			16440.6i			0.260958i	−0.991451	+	0.130479i	$0.958348\pi$
$252$		0			0
$253$	13284.0			0.207533
$254$		0			0
$255$	−51840.0	+	29929.8i	−0.797232	+	0.460282i
$256$		0			0
$257$	29376.0	+	16960.2i	0.444761	+	0.256783i	0.705615	−	0.708595i	$-0.250671\pi$
$257$	29376.0	+	16960.2i	0.444761	+	0.256783i	−0.260854	+	0.965378i	$0.584004\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	13959.0	−	24177.7i	0.204915	−	0.354923i
$262$		0			0
$263$	47367.0	+	82042.1i	0.684801	+	1.18611i	0.973499	+	0.228690i	$0.0734442\pi$
$263$	47367.0	+	82042.1i	0.684801	+	1.18611i	−0.288698	+	0.957420i	$0.593222\pi$
$264$		0			0
$265$			5611.84i			0.0799123i
$266$		0			0
$267$	52704.0			0.739301
$268$		0			0
$269$	56178.0	−	32434.4i	0.776357	−	0.448230i	−0.0587804	−	0.998271i	$-0.518721\pi$
$269$	56178.0	−	32434.4i	0.776357	−	0.448230i	0.835138	+	0.550041i	$0.185388\pi$
$270$		0			0
$271$	72264.0	+	41721.6i	0.983974	+	0.568097i	0.903467	−	0.428657i	$-0.141013\pi$
$271$	72264.0	+	41721.6i	0.983974	+	0.568097i	0.0805061	+	0.996754i	$0.474346\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1737.00	+	3008.57i	−0.0229686	+	0.0397828i
$276$		0			0
$277$	−3721.00	−	6444.96i	−0.0484954	−	0.0839964i	0.840759	−	0.541410i	$-0.182109\pi$
$277$	−3721.00	−	6444.96i	−0.0484954	−	0.0839964i	−0.889254	+	0.457413i	$0.848776\pi$
$278$		0			0
$279$		−	38410.0i		−	0.493441i
$280$		0			0
$281$	14562.0			0.184420			0.0922101	−	0.995740i	$-0.470607\pi$
$281$	14562.0			0.184420			0.0922101	+	0.995740i	$0.470607\pi$
$282$		0			0
$283$	37710.0	−	21771.9i	0.470851	−	0.271846i	−0.245745	−	0.969335i	$-0.579033\pi$
$283$	37710.0	−	21771.9i	0.470851	−	0.271846i	0.716596	+	0.697489i	$0.245699\pi$
$284$		0			0
$285$	−11232.0	−	6484.80i	−0.138283	−	0.0798375i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	44639.5	−	77317.9i	0.534470	−	0.925730i
$290$		0			0
$291$	−43584.0	−	75489.7i	−0.514685	−	0.891460i
$292$		0			0
$293$			51026.2i			0.594372i	0.954820	+	0.297186i	$0.0960481\pi$
$293$			51026.2i			0.594372i	−0.954820	+	0.297186i	$0.903952\pi$
$294$		0			0
$295$	65232.0			0.749578
$296$		0			0
$297$	−12312.0	+	7108.34i	−0.139578	+	0.0805852i
$298$		0			0
$299$	−84132.0	−	48573.6i	−0.941063	−	0.543323i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	38664.0	−	66968.0i	0.421135	−	0.729428i
$304$		0			0
$305$	67464.0	+	116851.i	0.725224	+	1.25613i
$306$		0			0
$307$		−	60670.3i		−	0.643723i	−0.946787	−	0.321862i	$-0.895691\pi$
$307$		−	60670.3i		−	0.643723i	0.946787	−	0.321862i	$-0.104309\pi$
$308$		0			0
$309$	5856.00			0.0613316
$310$		0			0
$311$	117972.	−	68111.2i	1.21971	−	0.704202i	0.254858	−	0.966979i	$-0.417971\pi$
$311$	117972.	−	68111.2i	1.21971	−	0.704202i	0.964857	+	0.262776i	$0.0846381\pi$
$312$		0			0
$313$	57972.0	+	33470.1i	0.591738	+	0.341640i	0.765785	−	0.643097i	$-0.222351\pi$
$313$	57972.0	+	33470.1i	0.591738	+	0.341640i	−0.174046	+	0.984737i	$0.555684\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13959.0	−	24177.7i	0.138911	−	0.240600i	−0.788174	−	0.615453i	$-0.788973\pi$
$317$	13959.0	−	24177.7i	0.138911	−	0.240600i	0.927085	+	0.374852i	$0.122307\pi$
$318$		0			0
$319$	7614.00	+	13187.8i	0.0748224	+	0.129596i
$320$		0			0
$321$			89664.8i			0.870186i
$322$		0			0
$323$	37440.0			0.358865
$324$		0			0
$325$	22002.0	−	12702.9i	0.208303	−	0.120264i
$326$		0			0
$327$	−42132.0	−	24324.9i	−0.394018	−	0.227487i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	90583.0	−	156894.i	0.826781	−	1.43203i	−0.0737688	−	0.997275i	$-0.523503\pi$
$331$	90583.0	−	156894.i	0.826781	−	1.43203i	0.900550	−	0.434752i	$-0.143164\pi$
$332$		0			0
$333$	−39369.0	−	68189.1i	−0.355031	−	0.614931i
$334$		0			0
$335$		−	50922.3i		−	0.453752i
$336$		0			0
$337$	92338.0			0.813056			0.406528	−	0.913638i	$-0.366739\pi$
$337$	92338.0			0.813056			0.406528	+	0.913638i	$0.366739\pi$
$338$		0			0
$339$	−112428.	+	64910.3i	−0.978307	+	0.564826i
$340$		0			0
$341$	18144.0	+	10475.4i	0.156036	+	0.0900873i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	53136.0	−	92034.3i	0.446427	−	0.773235i
$346$		0			0
$347$	73863.0	+	127934.i	0.613434	+	1.06250i	0.990657	+	0.136377i	$0.0435458\pi$
$347$	73863.0	+	127934.i	0.613434	+	1.06250i	−0.377223	+	0.926123i	$0.623121\pi$
$348$		0			0
$349$		−	149989.i		−	1.23142i	−0.787971	−	0.615712i	$-0.788868\pi$
$349$		−	149989.i		−	1.23142i	0.787971	−	0.615712i	$-0.211132\pi$
$350$		0			0
$351$	103968.			0.843889
$352$		0			0
$353$	−156240.	+	90205.2i	−1.25384	+	0.723906i	−0.971870	−	0.235517i	$-0.924322\pi$
$353$	−156240.	+	90205.2i	−1.25384	+	0.723906i	−0.281972	+	0.959423i	$0.590988\pi$
$354$		0			0
$355$	−56700.0	−	32735.8i	−0.449911	−	0.259756i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−56529.0	+	97911.1i	−0.438614	+	0.759702i	−0.997583	−	0.0694870i	$-0.977864\pi$
$359$	−56529.0	+	97911.1i	−0.438614	+	0.759702i	0.558969	+	0.829189i	$0.311197\pi$
$360$		0			0
$361$	−61104.5	−	105836.i	−0.468877	−	0.812119i
$362$		0			0
$363$			99191.1i			0.752765i
$364$		0			0
$365$	−4896.00			−0.0367499
$366$		0			0
$367$	−123384.	+	71235.8i	−0.916066	+	0.528891i	−0.882378	−	0.470542i	$-0.844059\pi$
$367$	−123384.	+	71235.8i	−0.916066	+	0.528891i	−0.0336880	+	0.999432i	$0.510725\pi$
$368$		0			0
$369$	−48708.0	−	28121.6i	−0.357724	−	0.206532i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	49751.0	−	86171.3i	0.357589	−	0.619362i	−0.629968	−	0.776621i	$-0.716932\pi$
$373$	49751.0	−	86171.3i	0.357589	−	0.619362i	0.987557	+	0.157258i	$0.0502655\pi$
$374$		0			0
$375$	58896.0	+	102011.i	0.418816	+	0.725411i
$376$		0			0
$377$		−	111364.i		−	0.783541i
$378$		0			0
$379$	75538.0			0.525880			0.262940	−	0.964812i	$-0.415308\pi$
$379$	75538.0			0.525880			0.262940	+	0.964812i	$0.415308\pi$
$380$		0			0
$381$	13812.0	−	7974.36i	0.0951495	−	0.0549346i
$382$		0			0
$383$	86112.0	+	49716.8i	0.587038	+	0.338926i	0.763925	−	0.645305i	$-0.223270\pi$
$383$	86112.0	+	49716.8i	0.587038	+	0.338926i	−0.176887	+	0.984231i	$0.556603\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	41415.0	−	71732.9i	0.276526	−	0.478957i
$388$		0			0
$389$	15543.0	+	26921.3i	0.102715	+	0.177908i	0.912803	−	0.408401i	$-0.133914\pi$
$389$	15543.0	+	26921.3i	0.102715	+	0.177908i	−0.810087	+	0.586310i	$0.800580\pi$
$390$		0			0
$391$			306781.i			2.00666i
$392$		0			0
$393$	−135216.			−0.875473
$394$		0			0
$395$	71676.0	−	41382.2i	0.459388	−	0.265228i
$396$		0			0
$397$	78318.0	+	45216.9i	0.496913	+	0.286893i	0.727438	−	0.686173i	$-0.240711\pi$
$397$	78318.0	+	45216.9i	0.496913	+	0.286893i	−0.230525	+	0.973066i	$0.574044\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−50265.0	+	87061.5i	−0.312591	+	0.541424i	−0.978923	−	0.204232i	$-0.934530\pi$
$401$	−50265.0	+	87061.5i	−0.312591	+	0.541424i	0.666331	+	0.745656i	$0.267864\pi$
$402$		0			0
$403$	−76608.0	−	132689.i	−0.471698	−	0.817005i
$404$		0			0
$405$			58176.1i			0.354678i
$406$		0			0
$407$	42948.0			0.259271
$408$		0			0
$409$	264828.	−	152899.i	1.58313	−	0.914022i	0.588734	−	0.808327i	$-0.299627\pi$
$409$	264828.	−	152899.i	1.58313	−	0.914022i	0.994399	−	0.105695i	$-0.0337068\pi$
$410$		0			0
$411$	−158004.	−	91223.7i	−0.935372	−	0.540037i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−52056.0	+	90163.6i	−0.302256	+	0.523522i
$416$		0			0
$417$	−55128.0	−	95484.5i	−0.317030	−	0.549112i
$418$		0			0
$419$		−	239834.i		−	1.36610i	−0.730372	−	0.683049i	$-0.760653\pi$
$419$		−	239834.i		−	1.36610i	0.730372	−	0.683049i	$-0.239347\pi$
$420$		0			0
$421$	−214222.			−1.20865			−0.604324	−	0.796739i	$-0.706557\pi$
$421$	−214222.			−1.20865			−0.604324	+	0.796739i	$0.706557\pi$
$422$		0			0
$423$	97416.0	−	56243.2i	0.544439	−	0.314332i
$424$		0			0
$425$	−69480.0	−	40114.3i	−0.384664	−	0.222086i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−8208.00	+	14216.7i	−0.0445988	+	0.0772473i
$430$		0			0
$431$	172575.	+	298909.i	0.929016	+	1.60910i	0.784971	+	0.619532i	$0.212678\pi$
$431$	172575.	+	298909.i	0.929016	+	1.60910i	0.144045	+	0.989571i	$0.453989\pi$
$432$		0			0
$433$			48469.7i			0.258520i	0.991611	+	0.129260i	$0.0412602\pi$
$433$			48469.7i			0.258520i	−0.991611	+	0.129260i	$0.958740\pi$
$434$		0			0
$435$	121824.			0.643805
$436$		0			0
$437$	−57564.0	+	33234.6i	−0.301431	+	0.174031i
$438$		0			0
$439$	160812.	+	92844.9i	0.834429	+	0.481758i	0.855367	−	0.518023i	$-0.173332\pi$
$439$	160812.	+	92844.9i	0.834429	+	0.481758i	−0.0209377	+	0.999781i	$0.506665\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−128169.	+	221995.i	−0.653094	+	1.13119i	0.329274	+	0.944234i	$0.393196\pi$
$443$	−128169.	+	221995.i	−0.653094	+	1.13119i	−0.982368	+	0.186957i	$0.940137\pi$
$444$		0			0
$445$	−79056.0	−	136929.i	−0.399222	−	0.691473i
$446$		0			0
$447$		−	81932.9i		−	0.410056i
$448$		0			0
$449$	−319806.			−1.58633			−0.793166	−	0.609006i	$-0.791569\pi$
$449$	−319806.			−1.58633			−0.793166	+	0.609006i	$0.791569\pi$
$450$		0			0
$451$	26568.0	−	15339.0i	0.130619	−	0.0754128i
$452$		0			0
$453$	95820.0	+	55321.7i	0.466939	+	0.269587i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−70169.0	+	121536.i	−0.335980	+	0.581934i	−0.983673	−	0.179968i	$-0.942401\pi$
$457$	−70169.0	+	121536.i	−0.335980	+	0.581934i	0.647693	+	0.761901i	$0.275734\pi$
$458$		0			0
$459$	−164160.	−	284333.i	−0.779187	−	1.34959i
$460$		0			0
$461$		−	70813.2i		−	0.333205i	−0.986024	−	0.166603i	$-0.946720\pi$
$461$		−	70813.2i		−	0.333205i	0.986024	−	0.166603i	$-0.0532797\pi$
$462$		0			0
$463$	−8206.00			−0.0382798			−0.0191399	−	0.999817i	$-0.506093\pi$
$463$	−8206.00			−0.0382798			−0.0191399	+	0.999817i	$0.506093\pi$
$464$		0			0
$465$	145152.	−	83803.5i	0.671301	−	0.387576i
$466$		0			0
$467$	351918.	+	203180.i	1.61364	+	0.931638i	0.988516	+	0.151115i	$0.0482865\pi$
$467$	351918.	+	203180.i	1.61364	+	0.931638i	0.625128	+	0.780522i	$0.285047\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−99432.0	+	172221.i	−0.448213	+	0.776328i
$472$		0			0
$473$	22590.0	+	39127.0i	0.100970	+	0.174886i
$474$		0			0
$475$		−	17382.9i		−	0.0770432i
$476$		0			0
$477$	−8910.00			−0.0391598
$478$		0			0
$479$	−243792.	+	140753.i	−1.06255	+	0.613462i	−0.926136	−	0.377190i	$-0.876890\pi$
$479$	−243792.	+	140753.i	−1.06255	+	0.613462i	−0.136412	+	0.990652i	$0.543557\pi$
$480$		0			0
$481$	−272004.	−	157042.i	−1.17567	−	0.678773i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−130752.	+	226469.i	−0.555859	+	0.962777i
$486$		0			0
$487$	114799.	+	198838.i	0.484039	+	0.838380i	0.999832	−	0.0183334i	$-0.00583602\pi$
$487$	114799.	+	198838.i	0.484039	+	0.838380i	−0.515793	+	0.856713i	$0.672503\pi$
$488$		0			0
$489$			54192.4i			0.226632i
$490$		0			0
$491$	−48654.0			−0.201816			−0.100908	−	0.994896i	$-0.532175\pi$
$491$	−48654.0			−0.201816			−0.100908	+	0.994896i	$0.532175\pi$
$492$		0			0
$493$	−304560.	+	175838.i	−1.25308	+	0.723466i
$494$		0			0
$495$	10692.0	+	6173.03i	0.0436364	+	0.0251935i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	45799.0	−	79326.2i	0.183931	−	0.318578i	−0.759285	−	0.650758i	$-0.774451\pi$
$499$	45799.0	−	79326.2i	0.183931	−	0.318578i	0.943216	+	0.332181i	$0.107784\pi$
$500$		0			0
$501$	−83952.0	−	145409.i	−0.334469	−	0.579317i
$502$		0			0
$503$			163824.i			0.647504i	0.946142	+	0.323752i	$0.104944\pi$
$503$			163824.i			0.647504i	−0.946142	+	0.323752i	$0.895056\pi$
$504$		0			0
$505$	−231984.			−0.909652
$506$		0			0
$507$	−67398.0	+	38912.3i	−0.262199	+	0.151381i
$508$		0			0
$509$	−399402.	−	230595.i	−1.54161	−	0.890049i	−0.998737	−	0.0502345i	$-0.984003\pi$
$509$	−399402.	−	230595.i	−1.54161	−	0.890049i	−0.542873	−	0.839815i	$-0.682664\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	35568.0	−	61605.6i	0.135153	−	0.234091i
$514$		0			0
$515$	−8784.00	−	15214.3i	−0.0331190	−	0.0573639i
$516$		0			0
$517$			61356.2i			0.229550i
$518$		0			0
$519$	−199152.			−0.739350
$520$		0			0
$521$	110772.	−	63954.2i	0.408089	−	0.235610i	−0.281879	−	0.959450i	$-0.590958\pi$
$521$	110772.	−	63954.2i	0.408089	−	0.235610i	0.689968	+	0.723840i	$0.257625\pi$
$522$		0			0
$523$	−152214.	−	87880.8i	−0.556482	−	0.321285i	0.195250	−	0.980753i	$-0.437448\pi$
$523$	−152214.	−	87880.8i	−0.556482	−	0.321285i	−0.751732	+	0.659468i	$0.770781\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−241920.	+	419018.i	−0.871065	+	1.50873i
$528$		0			0
$529$	−132402.	−	229326.i	−0.473131	−	0.819487i
$530$		0			0
$531$			103570.i			0.367319i
$532$		0			0
$533$	−224352.			−0.789724
$534$		0			0
$535$	232956.	−	134497.i	0.813891	−	0.469900i
$536$		0			0
$537$	53676.0	+	30989.9i	0.186137	+	0.107466i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	9527.00	−	16501.2i	0.0325508	−	0.0563796i	−0.849291	−	0.527925i	$-0.822970\pi$
$541$	9527.00	−	16501.2i	0.0325508	−	0.0563796i	0.881842	+	0.471545i	$0.156304\pi$
$542$		0			0
$543$	107112.	+	185523.i	0.363277	+	0.629215i
$544$		0			0
$545$			145950.i			0.491371i
$546$		0			0
$547$	536306.			1.79241			0.896206	−	0.443637i	$-0.146312\pi$
$547$	536306.			1.79241			0.896206	+	0.443637i	$0.146312\pi$
$548$		0			0
$549$	−185526.	+	107113.i	−0.615545	+	0.355385i
$550$		0			0
$551$	−65988.0	−	38098.2i	−0.217351	−	0.125488i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	171792.	−	297552.i	0.557721	−	0.966001i
$556$		0			0
$557$	131319.	+	227451.i	0.423270	+	0.733125i	0.996257	−	0.0864396i	$-0.0275489\pi$
$557$	131319.	+	227451.i	0.423270	+	0.733125i	−0.572987	+	0.819564i	$0.694216\pi$
$558$		0			0
$559$		−	330406.i		−	1.05736i
$560$		0			0
$561$	51840.0			0.164717
$562$		0			0
$563$	95202.0	−	54964.9i	0.300351	−	0.173408i	−0.342249	−	0.939609i	$-0.611189\pi$
$563$	95202.0	−	54964.9i	0.300351	−	0.173408i	0.642601	+	0.766201i	$0.277855\pi$
$564$		0			0
$565$	337284.	+	194731.i	1.05657	+	0.610012i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	126855.	−	219719.i	0.391817	−	0.678647i	−0.600872	−	0.799345i	$-0.705180\pi$
$569$	126855.	−	219719.i	0.391817	−	0.678647i	0.992689	+	0.120698i	$0.0385134\pi$
$570$		0			0
$571$	−82009.0	−	142044.i	−0.251530	−	0.435662i	0.712417	−	0.701756i	$-0.247600\pi$
$571$	−82009.0	−	142044.i	−0.251530	−	0.435662i	−0.963947	+	0.266094i	$0.914267\pi$
$572$		0			0
$573$		−	421138.i		−	1.28267i
$574$		0			0
$575$	142434.			0.430802
$576$		0			0
$577$	−188448.	+	108801.i	−0.566031	+	0.326798i	−0.755562	−	0.655077i	$-0.772636\pi$
$577$	−188448.	+	108801.i	−0.566031	+	0.326798i	0.189532	+	0.981875i	$0.439303\pi$
$578$		0			0
$579$	63276.0	+	36532.4i	0.188748	+	0.108974i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2430.00	−	4208.88i	0.00714939	−	0.0123831i
$584$		0			0
$585$	−45144.0	−	78191.7i	−0.131913	−	0.228480i
$586$		0			0
$587$			251473.i			0.729819i	0.931043	+	0.364909i	$0.118900\pi$
$587$			251473.i			0.729819i	−0.931043	+	0.364909i	$0.881100\pi$
$588$		0			0
$589$	−104832.			−0.302178
$590$		0			0
$591$	−108.000	+	62.3538i	−0.000309207	+	0.000178521i
$592$		0			0
$593$	329112.	+	190013.i	0.935911	+	0.540348i	0.888676	−	0.458536i	$-0.151626\pi$
$593$	329112.	+	190013.i	0.935911	+	0.540348i	0.0472345	+	0.998884i	$0.484959\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	336.000	−	581.969i	0.000942737	−	0.00163287i
$598$		0			0
$599$	157671.	+	273094.i	0.439439	+	0.761130i	0.997646	−	0.0685714i	$-0.0218441\pi$
$599$	157671.	+	273094.i	0.439439	+	0.761130i	−0.558208	+	0.829701i	$0.688511\pi$
$600$		0			0
$601$		−	483907.i		−	1.33972i	−0.742489	−	0.669859i	$-0.766355\pi$
$601$		−	483907.i		−	1.33972i	0.742489	−	0.669859i	$-0.233645\pi$
$602$		0			0
$603$	80850.0			0.222354
$604$		0			0
$605$	257706.	−	148787.i	0.704067	−	0.406493i
$606$		0			0
$607$	−444624.	−	256704.i	−1.20675	−	0.696715i	−0.244698	−	0.969599i	$-0.578689\pi$
$607$	−444624.	−	256704.i	−1.20675	−	0.696715i	−0.962047	+	0.272885i	$0.912022\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	224352.	−	388589.i	0.600963	−	1.04090i
$612$		0			0
$613$	−113881.	−	197248.i	−0.303061	−	0.524917i	0.673767	−	0.738944i	$-0.264675\pi$
$613$	−113881.	−	197248.i	−0.303061	−	0.524917i	−0.976828	+	0.214027i	$0.931342\pi$
$614$		0			0
$615$		−	245425.i		−	0.648885i
$616$		0			0
$617$	502578.			1.32018			0.660090	−	0.751187i	$-0.270518\pi$
$617$	502578.			1.32018			0.660090	+	0.751187i	$0.270518\pi$
$618$		0			0
$619$	148614.	−	85802.3i	0.387863	−	0.223933i	−0.293371	−	0.955999i	$-0.594777\pi$
$619$	148614.	−	85802.3i	0.387863	−	0.223933i	0.681234	+	0.732066i	$0.261444\pi$
$620$		0			0
$621$	504792.	+	291442.i	1.30897	+	0.755733i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	116376.	−	201568.i	0.297921	−	0.516015i
$626$		0			0
$627$	5616.00	+	9727.20i	0.0142854	+	0.0247430i
$628$		0			0
$629$			991842.i			2.50692i
$630$		0			0
$631$	−29710.0			−0.0746181			−0.0373090	−	0.999304i	$-0.511879\pi$
$631$	−29710.0			−0.0746181			−0.0373090	+	0.999304i	$0.511879\pi$
$632$		0			0
$633$	277140.	−	160007.i	0.691659	−	0.399329i
$634$		0			0
$635$	−41436.0	−	23923.1i	−0.102761	−	0.0593294i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	51975.0	−	90023.3i	0.127290	−	0.220472i
$640$		0			0
$641$	109287.	+	189291.i	0.265982	+	0.460695i	0.967820	−	0.251642i	$-0.0809705\pi$
$641$	109287.	+	189291.i	0.265982	+	0.460695i	−0.701838	+	0.712336i	$0.747637\pi$
$642$		0			0
$643$			414466.i			1.00246i	0.865314	+	0.501230i	$0.167119\pi$
$643$			414466.i			1.00246i	−0.865314	+	0.501230i	$0.832881\pi$
$644$		0			0
$645$	361440.			0.868794
$646$		0			0
$647$	132300.	−	76383.4i	0.316047	−	0.182470i	−0.333582	−	0.942721i	$-0.608258\pi$
$647$	132300.	−	76383.4i	0.316047	−	0.182470i	0.649629	+	0.760251i	$0.274924\pi$
$648$		0			0
$649$	−48924.0	−	28246.3i	−0.116154	−	0.0670613i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	320535.	−	555183.i	0.751708	−	1.30200i	−0.195287	−	0.980746i	$-0.562564\pi$
$653$	320535.	−	555183.i	0.751708	−	1.30200i	0.946994	−	0.321250i	$-0.104103\pi$
$654$		0			0
$655$	202824.	+	351301.i	0.472756	+	0.818837i
$656$		0			0
$657$		−	7773.44i		−	0.0180087i
$658$		0			0
$659$	−162990.			−0.375310			−0.187655	−	0.982235i	$-0.560089\pi$
$659$	−162990.			−0.375310			−0.187655	+	0.982235i	$0.560089\pi$
$660$		0			0
$661$	−366474.	+	211584.i	−0.838765	+	0.484261i	−0.856844	−	0.515575i	$-0.827578\pi$
$661$	−366474.	+	211584.i	−0.838765	+	0.484261i	0.0180793	+	0.999837i	$0.494245\pi$
$662$		0			0
$663$	−328320.	−	189556.i	−0.746913	−	0.431231i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	312174.	−	540701.i	0.701690	−	1.21536i
$668$		0			0
$669$	27072.0	+	46890.1i	0.0604878	+	0.104768i
$670$		0			0
$671$		−	116851.i		−	0.259530i
$672$		0			0
$673$	220738.			0.487357			0.243678	−	0.969856i	$-0.421646\pi$
$673$	220738.			0.487357			0.243678	+	0.969856i	$0.421646\pi$
$674$		0			0
$675$	−132012.	+	76217.2i	−0.289738	+	0.167280i
$676$		0			0
$677$	−598590.	−	345596.i	−1.30603	−	0.754035i	−0.324596	−	0.945853i	$-0.605228\pi$
$677$	−598590.	−	345596.i	−1.30603	−	0.754035i	−0.981431	+	0.191818i	$0.938562\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−106920.	+	185191.i	−0.230550	+	0.399324i
$682$		0			0
$683$	−401625.	−	695635.i	−0.860953	−	1.49121i	−0.871010	−	0.491265i	$-0.836535\pi$
$683$	−401625.	−	695635.i	−0.860953	−	1.49121i	0.0100576	−	0.999949i	$-0.496798\pi$
$684$		0			0
$685$			547342.i			1.16648i
$686$		0			0
$687$	397296.			0.841784
$688$		0			0
$689$	−30780.0	+	17770.8i	−0.0648381	+	0.0374343i
$690$		0			0
$691$	312318.	+	180317.i	0.654095	+	0.377642i	0.790023	−	0.613077i	$-0.210068\pi$
$691$	312318.	+	180317.i	0.654095	+	0.377642i	−0.135928	+	0.990719i	$0.543402\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−165384.	+	286453.i	−0.342392	+	0.593041i
$696$		0			0
$697$	354240.	+	613562.i	0.729175	+	1.26297i
$698$		0			0
$699$		−	487981.i		−	0.998731i
$700$		0			0
$701$	247698.			0.504065			0.252032	−	0.967719i	$-0.418901\pi$
$701$	247698.			0.504065			0.252032	+	0.967719i	$0.418901\pi$
$702$		0			0
$703$	−186108.	+	107450.i	−0.376578	+	0.217417i
$704$		0			0
$705$	425088.	+	245425.i	0.855265	+	0.493787i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7207.00	−	12482.9i	0.0143371	−	0.0248326i	−0.858768	−	0.512365i	$-0.828770\pi$
$709$	7207.00	−	12482.9i	0.0143371	−	0.0248326i	0.873105	+	0.487532i	$0.162103\pi$
$710$		0			0
$711$	65703.0	+	113801.i	0.129971	+	0.225116i
$712$		0			0
$713$		−	858986.i		−	1.68969i
$714$		0			0
$715$	49248.0			0.0963333
$716$		0			0
$717$	456948.	−	263819.i	0.888850	−	0.513178i
$718$		0			0
$719$	132552.	+	76528.9i	0.256406	+	0.148036i	0.622694	−	0.782465i	$-0.286038\pi$
$719$	132552.	+	76528.9i	0.256406	+	0.148036i	−0.366288	+	0.930502i	$0.619371\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	171168.	−	296472.i	0.327451	−	0.567161i
$724$		0			0
$725$	81639.0	+	141403.i	0.155318	+	0.269019i
$726$		0			0
$727$		−	359782.i		−	0.680723i	−0.940295	−	0.340361i	$-0.889451\pi$
$727$		−	359782.i		−	0.680723i	0.940295	−	0.340361i	$-0.110549\pi$
$728$		0			0
$729$	−535599.			−1.00782
$730$		0			0
$731$	−903600.	+	521694.i	−1.69099	+	0.976294i
$732$		0			0
$733$	−331866.	−	191603.i	−0.617668	−	0.356611i	0.158293	−	0.987392i	$-0.449401\pi$
$733$	−331866.	−	191603.i	−0.617668	−	0.356611i	−0.775960	+	0.630782i	$0.782734\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−22050.0	+	38191.7i	−0.0405951	+	0.0703128i
$738$		0			0
$739$	−429913.	−	744631.i	−0.787212	−	1.36349i	−0.927669	−	0.373404i	$-0.878190\pi$
$739$	−429913.	−	744631.i	−0.787212	−	1.36349i	0.140457	−	0.990087i	$-0.455143\pi$
$740$		0			0
$741$		−	82140.8i		−	0.149597i
$742$		0			0
$743$	−669150.			−1.21212			−0.606060	−	0.795419i	$-0.707251\pi$
$743$	−669150.			−1.21212			−0.606060	+	0.795419i	$0.707251\pi$
$744$		0			0
$745$	−212868.	+	122899.i	−0.383529	+	0.221430i
$746$		0			0
$747$	−143154.	−	82650.0i	−0.256544	−	0.148116i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−146753.	+	254184.i	−0.260200	+	0.450679i	−0.966295	−	0.257438i	$-0.917122\pi$
$751$	−146753.	+	254184.i	−0.260200	+	0.450679i	0.706095	+	0.708117i	$0.250455\pi$
$752$		0			0
$753$	−56952.0	−	98643.8i	−0.100443	−	0.173972i
$754$		0			0
$755$		−	331930.i		−	0.582308i
$756$		0			0
$757$	555634.			0.969610			0.484805	−	0.874622i	$-0.338891\pi$
$757$	555634.			0.969610			0.484805	+	0.874622i	$0.338891\pi$
$758$		0			0
$759$	−79704.0	+	46017.1i	−0.138356	+	0.0798796i
$760$		0			0
$761$	221652.	+	127971.i	0.382739	+	0.220974i	0.679009	−	0.734130i	$-0.262410\pi$
$761$	221652.	+	127971.i	0.382739	+	0.220974i	−0.296270	+	0.955104i	$0.595743\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−142560.	+	246921.i	−0.243599	+	0.421925i
$766$		0			0
$767$	206568.	+	357786.i	0.351134	+	0.608181i
$768$		0			0
$769$			481427.i			0.814100i	0.913406	+	0.407050i	$0.133443\pi$
$769$			481427.i			0.814100i	−0.913406	+	0.407050i	$0.866557\pi$
$770$		0			0
$771$	−235008.			−0.395343
$772$		0			0
$773$	183150.	−	105742.i	0.306512	−	0.176965i	−0.338852	−	0.940840i	$-0.610039\pi$
$773$	183150.	−	105742.i	0.306512	−	0.176965i	0.645365	+	0.763875i	$0.276705\pi$
$774$		0			0
$775$	194544.	+	112320.i	0.323903	+	0.187005i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−76752.0	+	132938.i	−0.126478	+	0.219066i
$780$		0			0
$781$	28350.0	+	49103.6i	0.0464784	+	0.0805029i
$782$		0			0
$783$			668184.i			1.08986i
$784$		0			0
$785$	596592.			0.968140
$786$		0			0
$787$	863538.	−	498564.i	1.39422	−	0.804955i	0.400443	−	0.916322i	$-0.368856\pi$
$787$	863538.	−	498564.i	1.39422	−	0.804955i	0.993779	+	0.111367i	$0.0355230\pi$
$788$		0			0
$789$	−568404.	−	328168.i	−0.913068	−	0.527160i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−427272.	+	740057.i	−0.679451	+	1.17684i
$794$		0			0
$795$	−19440.0	−	33671.1i	−0.0307583	−	0.0532749i
$796$		0			0
$797$			258831.i			0.407473i	0.979026	+	0.203737i	$0.0653086\pi$
$797$			258831.i			0.407473i	−0.979026	+	0.203737i	$0.934691\pi$
$798$		0			0
$799$	−1.41696e6			−2.21955
$800$		0			0
$801$	217404.	−	125518.i	0.338846	−	0.195633i
$802$		0			0
$803$	3672.00	+	2120.03i	0.00569471	+	0.00328784i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−224712.	+	389213.i	−0.345048	+	0.597640i
$808$		0			0
$809$	−399897.	−	692642.i	−0.611014	−	1.05831i	−0.991070	−	0.133344i	$-0.957429\pi$
$809$	−399897.	−	692642.i	−0.611014	−	1.05831i	0.380056	−	0.924964i	$-0.375905\pi$
$810$		0			0
$811$			254632.i			0.387143i	0.981086	+	0.193572i	$0.0620072\pi$
$811$			254632.i			0.387143i	−0.981086	+	0.193572i	$0.937993\pi$
$812$		0			0
$813$	−578112.			−0.874643
$814$		0			0
$815$	140796.	−	81288.6i	0.211970	−	0.122381i
$816$		0			0
$817$	−195780.	−	113034.i	−0.293308	−	0.169342i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−54729.0	+	94793.4i	−0.0811954	+	0.140634i	−0.903764	−	0.428032i	$-0.859207\pi$
$821$	−54729.0	+	94793.4i	−0.0811954	+	0.140634i	0.822568	+	0.568666i	$0.192540\pi$
$822$		0			0
$823$	207719.	+	359780.i	0.306674	+	0.531174i	0.977633	−	0.210320i	$-0.0674506\pi$
$823$	207719.	+	359780.i	0.306674	+	0.531174i	−0.670959	+	0.741495i	$0.734117\pi$
$824$		0			0
$825$		−	24068.6i		−	0.0353625i
$826$		0			0
$827$	−23598.0			−0.0345036			−0.0172518	−	0.999851i	$-0.505492\pi$
$827$	−23598.0			−0.0345036			−0.0172518	+	0.999851i	$0.505492\pi$
$828$		0			0
$829$	96522.0	−	55727.0i	0.140449	−	0.0810880i	−0.428129	−	0.903718i	$-0.640827\pi$
$829$	96522.0	−	55727.0i	0.140449	−	0.0810880i	0.568578	+	0.822630i	$0.307494\pi$
$830$		0			0
$831$	44652.0	+	25779.8i	0.0646605	+	0.0373317i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−251856.	+	436227.i	−0.361226	+	0.625662i
$836$		0			0
$837$	459648.	+	796134.i	0.656107	+	1.13641i
$838$		0			0
$839$			477672.i			0.678587i	0.940680	+	0.339294i	$0.110188\pi$
$839$			477672.i			0.678587i	−0.940680	+	0.339294i	$0.889812\pi$
$840$		0			0
$841$	8435.00			0.0119260
$842$		0			0
$843$	−87372.0	+	50444.2i	−0.122947	+	0.0709834i
$844$		0			0
$845$	202194.	+	116737.i	0.283175	+	0.163491i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−150840.	+	261263.i	−0.209267	+	0.362461i
$850$		0			0
$851$	−880434.	−	1.52496e6i	−1.21573	−	2.10571i
$852$		0			0
$853$		−	415519.i		−	0.571075i	−0.958368	−	0.285537i	$-0.907828\pi$
$853$		−	415519.i		−	0.571075i	0.958368	−	0.285537i	$-0.0921720\pi$
$854$		0			0
$855$	−61776.0			−0.0845060
$856$		0			0
$857$	−830052.	+	479231.i	−1.13017	+	0.652504i	−0.943978	−	0.330010i	$-0.892948\pi$
$857$	−830052.	+	479231.i	−1.13017	+	0.652504i	−0.186192	+	0.982513i	$0.559615\pi$
$858$		0			0
$859$	1.14875e6	+	663233.i	1.55683	+	0.898835i	0.997557	+	0.0698502i	$0.0222521\pi$
$859$	1.14875e6	+	663233.i	1.55683	+	0.898835i	0.559271	+	0.828985i	$0.311081\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−159993.	+	277116.i	−0.214822	+	0.372083i	−0.953218	−	0.302285i	$-0.902251\pi$
$863$	−159993.	+	277116.i	−0.214822	+	0.372083i	0.738395	+	0.674368i	$0.235584\pi$
$864$		0			0
$865$	298728.	+	517412.i	0.399249	+	0.691519i
$866$		0			0
$867$			618543.i			0.822871i
$868$		0			0
$869$	−71676.0			−0.0949149
$870$		0			0
$871$	279300.	−	161254.i	0.368158	−	0.212556i
$872$		0			0
$873$	−359568.	−	207597.i	−0.471794	−	0.272390i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−543673.	+	941669.i	−0.706868	+	1.22433i	0.259145	+	0.965839i	$0.416559\pi$
$877$	−543673.	+	941669.i	−0.706868	+	1.22433i	−0.966013	+	0.258493i	$0.916774\pi$
$878$		0			0
$879$	−176760.	−	306157.i	−0.228774	−	0.396248i
$880$		0			0
$881$		−	1.41344e6i		−	1.82106i	−0.413442	−	0.910531i	$-0.635673\pi$
$881$		−	1.41344e6i		−	1.82106i	0.413442	−	0.910531i	$-0.364327\pi$
$882$		0			0
$883$	−1.03902e6			−1.33261			−0.666305	−	0.745679i	$-0.732125\pi$
$883$	−1.03902e6			−1.33261			−0.666305	+	0.745679i	$0.732125\pi$
$884$		0			0
$885$	−391392.	+	225970.i	−0.499718	+	0.288513i
$886$		0			0
$887$	733932.	+	423736.i	0.932843	+	0.538577i	0.887710	−	0.460404i	$-0.152295\pi$
$887$	733932.	+	423736.i	0.932843	+	0.538577i	0.0451334	+	0.998981i	$0.485629\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	25191.0	−	43632.1i	0.0317315	−	0.0549605i
$892$		0			0
$893$	−153504.	−	265877.i	−0.192494	−	0.333409i
$894$		0			0
$895$		−	185939.i		−	0.232126i
$896$		0			0
$897$	673056.			0.836501
$898$		0			0
$899$	852768.	−	492346.i	1.05514	−	0.609187i
$900$		0			0
$901$	97200.0	+	56118.4i	0.119734	+	0.0691283i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	321336.	−	556570.i	0.392340	−	0.679552i
$906$		0			0
$907$	78775.0	+	136442.i	0.0957577	+	0.165857i	0.909925	−	0.414774i	$-0.136139\pi$
$907$	78775.0	+	136442.i	0.0957577	+	0.165857i	−0.814167	+	0.580631i	$0.802806\pi$
$908$		0			0
$909$		−	368324.i		−	0.445761i
$910$		0			0
$911$	−962046.			−1.15920			−0.579601	−	0.814900i	$-0.696792\pi$
$911$	−962046.			−1.15920			−0.579601	+	0.814900i	$0.696792\pi$
$912$		0			0
$913$	78084.0	−	45081.8i	0.0936743	−	0.0540829i
$914$		0			0
$915$	−809568.	−	467404.i	−0.966966	−	0.558278i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	54919.0	−	95122.5i	0.0650267	−	0.112630i	−0.831679	−	0.555257i	$-0.812620\pi$
$919$	54919.0	−	95122.5i	0.0650267	−	0.112630i	0.896706	+	0.442627i	$0.145953\pi$
$920$		0			0
$921$	210168.	+	364022.i	0.247769	+	0.429149i
$922$		0			0
$923$		−	414653.i		−	0.486722i
$924$		0			0
$925$	460498.			0.538201
$926$		0			0
$927$	24156.0	−	13946.5i	0.0281103	−	0.0162295i
$928$		0			0
$929$	116496.	+	67259.0i	0.134983	+	0.0779326i	0.565971	−	0.824425i	$-0.308501\pi$
$929$	116496.	+	67259.0i	0.134983	+	0.0779326i	−0.430988	+	0.902358i	$0.641835\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−471888.	+	817334.i	−0.542095	+	0.938937i
$934$		0			0
$935$	−77760.0	−	134684.i	−0.0889474	−	0.154061i
$936$		0			0
$937$			799057.i			0.910120i	0.890461	+	0.455060i	$0.150382\pi$
$937$			799057.i			0.910120i	−0.890461	+	0.455060i	$0.849618\pi$
$938$		0			0
$939$	−463776.			−0.525990
$940$		0			0
$941$	295938.	−	170860.i	0.334212	−	0.192957i	−0.323498	−	0.946229i	$-0.604859\pi$
$941$	295938.	−	170860.i	0.334212	−	0.192957i	0.657709	+	0.753272i	$0.271525\pi$
$942$		0			0
$943$	−1.08929e6	−	628901.i	−1.22495	−	0.707227i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	310455.	−	537724.i	0.346177	−	0.599597i	−0.639390	−	0.768883i	$-0.720813\pi$
$947$	310455.	−	537724.i	0.346177	−	0.599597i	0.985567	+	0.169286i	$0.0541462\pi$
$948$		0			0
$949$	−15504.0	−	26853.7i	−0.0172152	−	0.0298176i
$950$		0			0
$951$			193422.i			0.213867i
$952$		0			0
$953$	855522.			0.941988			0.470994	−	0.882136i	$-0.343895\pi$
$953$	855522.			0.941988			0.470994	+	0.882136i	$0.343895\pi$
$954$		0			0
$955$	−1.09415e6	+	631707.i	−1.19969	+	0.692642i
$956$		0			0
$957$	−91368.0	−	52751.3i	−0.0997632	−	0.0575983i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	215616.	−	373457.i	0.233471	−	0.404384i
$962$		0			0
$963$	213543.	+	369867.i	0.230268	+	0.398835i
$964$		0			0
$965$		−	219194.i		−	0.235383i
$966$		0			0
$967$	1.68221e6			1.79898			0.899492	−	0.436937i	$-0.143937\pi$
$967$	1.68221e6			1.79898			0.899492	+	0.436937i	$0.143937\pi$
$968$		0			0
$969$	−224640.	+	129696.i	−0.239243	+	0.138127i
$970$		0			0
$971$	−1.44063e6	−	831748.i	−1.52797	−	0.882172i	−0.999447	−	0.0332514i	$-0.989414\pi$
$971$	−1.44063e6	−	831748.i	−1.52797	−	0.882172i	−0.528520	−	0.848921i	$-0.677253\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−88008.0	+	152434.i	−0.0925791	+	0.160352i
$976$		0			0
$977$	−801.000	−	1387.37i	−0.000839157	−	0.00145346i	0.865606	−	0.500727i	$-0.166934\pi$
$977$	−801.000	−	1387.37i	−0.000839157	−	0.00145346i	−0.866445	+	0.499273i	$0.833600\pi$
$978$		0			0
$979$			136929.i			0.142866i
$980$		0			0
$981$	−231726.			−0.240789
$982$		0			0
$983$	142308.	−	82161.6i	0.147273	−	0.0850279i	−0.424553	−	0.905403i	$-0.639569\pi$
$983$	142308.	−	82161.6i	0.147273	−	0.0850279i	0.571826	+	0.820375i	$0.306235\pi$
$984$		0			0
$985$	324.000	+	187.061i	0.000333943	+	0.000192802i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	926190.	−	1.60421e6i	0.946907	−	1.64009i
$990$		0			0
$991$	367303.	+	636187.i	0.374005	+	0.647795i	0.990178	−	0.139816i	$-0.0446510\pi$
$991$	367303.	+	636187.i	0.374005	+	0.647795i	−0.616173	+	0.787611i	$0.711318\pi$
$992$		0			0
$993$			1.25515e6i			1.27291i
$994$		0			0
$995$	−2016.00			−0.00203631
$996$		0			0
$997$	138078.	−	79719.4i	0.138910	−	0.0801998i	−0.428934	−	0.903336i	$-0.641111\pi$
$997$	138078.	−	79719.4i	0.138910	−	0.0801998i	0.567845	+	0.823136i	$0.307777\pi$
$998$		0			0
$999$	1.63202e6	+	942249.i	1.63529	+	0.944137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.5.h.a.117.1		2
7.2	even	3		28.5.b.a.13.1	✓	2
7.3	odd	6	inner	196.5.h.a.129.1		2
7.4	even	3		196.5.h.b.129.1		2
7.5	odd	6		28.5.b.a.13.2	yes	2
7.6	odd	2		196.5.h.b.117.1		2
21.2	odd	6		252.5.d.a.181.2		2
21.5	even	6		252.5.d.a.181.1		2
28.19	even	6		112.5.c.b.97.1		2
28.23	odd	6		112.5.c.b.97.2		2
35.2	odd	12		700.5.h.a.349.1		4
35.9	even	6		700.5.d.a.601.2		2
35.12	even	12		700.5.h.a.349.3		4
35.19	odd	6		700.5.d.a.601.1		2
35.23	odd	12		700.5.h.a.349.4		4
35.33	even	12		700.5.h.a.349.2		4
56.5	odd	6		448.5.c.c.321.1		2
56.19	even	6		448.5.c.d.321.2		2
56.37	even	6		448.5.c.c.321.2		2
56.51	odd	6		448.5.c.d.321.1		2
84.23	even	6		1008.5.f.c.433.2		2
84.47	odd	6		1008.5.f.c.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.5.b.a.13.1	✓	2	7.2	even	3
28.5.b.a.13.2	yes	2	7.5	odd	6
112.5.c.b.97.1		2	28.19	even	6
112.5.c.b.97.2		2	28.23	odd	6
196.5.h.a.117.1		2	1.1	even	1	trivial
196.5.h.a.129.1		2	7.3	odd	6	inner
196.5.h.b.117.1		2	7.6	odd	2
196.5.h.b.129.1		2	7.4	even	3
252.5.d.a.181.1		2	21.5	even	6
252.5.d.a.181.2		2	21.2	odd	6
448.5.c.c.321.1		2	56.5	odd	6
448.5.c.c.321.2		2	56.37	even	6
448.5.c.d.321.1		2	56.51	odd	6
448.5.c.d.321.2		2	56.19	even	6
700.5.d.a.601.1		2	35.19	odd	6
700.5.d.a.601.2		2	35.9	even	6
700.5.h.a.349.1		4	35.2	odd	12
700.5.h.a.349.2		4	35.33	even	12
700.5.h.a.349.3		4	35.12	even	12
700.5.h.a.349.4		4	35.23	odd	12
1008.5.f.c.433.1		2	84.47	odd	6
1008.5.f.c.433.2		2	84.23	even	6

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	196.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.00000 + 3.46410i) q^{3} +(18.0000 + 10.3923i) q^{5} +(-16.5000 + 28.5788i) q^{9} +O(q^{10})\)	\(q+(-6.00000 + 3.46410i) q^{3} +(18.0000 + 10.3923i) q^{5} +(-16.5000 + 28.5788i) q^{9} +(-9.00000 - 15.5885i) q^{11} +131.636i q^{13} -144.000 q^{15} +(360.000 - 207.846i) q^{17} +(78.0000 + 45.0333i) q^{19} +(-369.000 + 639.127i) q^{23} +(-96.5000 - 167.143i) q^{25} -789.815i q^{27} -846.000 q^{29} +(-1008.00 + 581.969i) q^{31} +(108.000 + 62.3538i) q^{33} +(-1193.00 + 2066.34i) q^{37} +(-456.000 - 789.815i) q^{39} +1704.34i q^{41} -2510.00 q^{43} +(-594.000 + 342.946i) q^{45} +(-2952.00 - 1704.34i) q^{47} +(-1440.00 + 2494.15i) q^{51} +(135.000 + 233.827i) q^{53} -374.123i q^{55} -624.000 q^{57} +(2718.00 - 1569.24i) q^{59} +(5622.00 + 3245.86i) q^{61} +(-1368.00 + 2369.45i) q^{65} +(-1225.00 - 2121.76i) q^{67} -5113.01i q^{69} -3150.00 q^{71} +(-204.000 + 117.779i) q^{73} +(1158.00 + 668.572i) q^{75} +(1991.00 - 3448.51i) q^{79} +(1399.50 + 2424.01i) q^{81} +5009.09i q^{83} +8640.00 q^{85} +(5076.00 - 2930.63i) q^{87} +(-6588.00 - 3803.58i) q^{89} +(4032.00 - 6983.63i) q^{93} +(936.000 + 1621.20i) q^{95} +12581.6i q^{97} +594.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 12 q^{3} + 36 q^{5} - 33 q^{9}+O(q^{10}) \) 2 * q - 12 * q^3 + 36 * q^5 - 33 * q^9	\( 2 q - 12 q^{3} + 36 q^{5} - 33 q^{9} - 18 q^{11} - 288 q^{15} + 720 q^{17} + 156 q^{19} - 738 q^{23} - 193 q^{25} - 1692 q^{29} - 2016 q^{31} + 216 q^{33} - 2386 q^{37} - 912 q^{39} - 5020 q^{43} - 1188 q^{45} - 5904 q^{47} - 2880 q^{51} + 270 q^{53} - 1248 q^{57} + 5436 q^{59} + 11244 q^{61} - 2736 q^{65} - 2450 q^{67} - 6300 q^{71} - 408 q^{73} + 2316 q^{75} + 3982 q^{79} + 2799 q^{81} + 17280 q^{85} + 10152 q^{87} - 13176 q^{89} + 8064 q^{93} + 1872 q^{95} + 1188 q^{99}+O(q^{100}) \) 2 * q - 12 * q^3 + 36 * q^5 - 33 * q^9 - 18 * q^11 - 288 * q^15 + 720 * q^17 + 156 * q^19 - 738 * q^23 - 193 * q^25 - 1692 * q^29 - 2016 * q^31 + 216 * q^33 - 2386 * q^37 - 912 * q^39 - 5020 * q^43 - 1188 * q^45 - 5904 * q^47 - 2880 * q^51 + 270 * q^53 - 1248 * q^57 + 5436 * q^59 + 11244 * q^61 - 2736 * q^65 - 2450 * q^67 - 6300 * q^71 - 408 * q^73 + 2316 * q^75 + 3982 * q^79 + 2799 * q^81 + 17280 * q^85 + 10152 * q^87 - 13176 * q^89 + 8064 * q^93 + 1872 * q^95 + 1188 * q^99

Introduction

L-functions

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