LMFDB - Embedded newform 976.2.bw.c.849.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [976,2,Mod(225,976)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(976, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 28]))

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

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

chi := DirichletCharacter("976.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 976 = 2^{4} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	976.bw (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.79339923728$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			849.3
Character	$\chi$	$=$	976.849
Dual form			976.2.bw.c.561.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69101 + 1.22859i) q^{3} +(1.40283 + 0.298182i) q^{5} +(-0.125217 - 1.19136i) q^{7} +(0.423022 + 1.30193i) q^{9} +O(q^{10})$	\(q+(1.69101 + 1.22859i) q^{3} +(1.40283 + 0.298182i) q^{5} +(-0.125217 - 1.19136i) q^{7} +(0.423022 + 1.30193i) q^{9} +3.00395 q^{11} +(-1.72195 + 2.98250i) q^{13} +(2.00586 + 2.22773i) q^{15} +(4.87302 - 5.41204i) q^{17} +(-0.629830 + 5.99243i) q^{19} +(1.25194 - 2.16843i) q^{21} +(0.565515 + 1.74048i) q^{23} +(-2.68870 - 1.19708i) q^{25} +(1.05352 - 3.24240i) q^{27} +(2.62721 + 4.55046i) q^{29} +(5.21493 + 2.32184i) q^{31} +(5.07970 + 3.69062i) q^{33} +(0.179583 - 1.70861i) q^{35} +(-4.17017 + 3.02980i) q^{37} +(-6.57609 + 2.92786i) q^{39} +(7.17576 - 5.21349i) q^{41} +(-2.93465 - 3.25925i) q^{43} +(0.205219 + 1.95252i) q^{45} +(-4.25565 - 7.37101i) q^{47} +(5.44338 - 1.15703i) q^{49} +(14.8895 - 3.16486i) q^{51} +(-2.47558 + 7.61906i) q^{53} +(4.21405 + 0.895724i) q^{55} +(-8.42728 + 9.35944i) q^{57} +(-11.2943 + 5.02854i) q^{59} +(-6.78003 - 3.87700i) q^{61} +(1.49809 - 0.666993i) q^{63} +(-3.30493 + 3.67050i) q^{65} +(2.63158 + 0.559359i) q^{67} +(-1.18204 + 3.63794i) q^{69} +(-3.77191 + 0.801745i) q^{71} +(-8.52788 + 1.81266i) q^{73} +(-3.07588 - 5.32757i) q^{75} +(-0.376145 - 3.57878i) q^{77} +(1.10029 + 1.22199i) q^{79} +(9.08754 - 6.60249i) q^{81} +(-1.78051 + 0.792734i) q^{83} +(8.44982 - 6.13915i) q^{85} +(-1.14801 + 10.9226i) q^{87} +(-4.76070 - 3.45885i) q^{89} +(3.76884 + 1.67800i) q^{91} +(5.96589 + 10.3332i) q^{93} +(-2.67038 + 8.21859i) q^{95} +(5.09792 + 2.26974i) q^{97} +(1.27074 + 3.91093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9}+O(q^{10}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39} + 11 q^{41} - 40 q^{43} + 12 q^{45} - 40 q^{47} + q^{49} + 9 q^{51} + 17 q^{53} + 60 q^{55} - 38 q^{57} + 11 q^{59} - 55 q^{61} + 58 q^{63} + 59 q^{65} + 13 q^{67} - 32 q^{69} - 63 q^{71} - 46 q^{73} - q^{75} - 31 q^{77} + 49 q^{79} + 48 q^{81} - 39 q^{83} + 21 q^{85} - 17 q^{87} + 32 q^{89} - 70 q^{91} + 67 q^{93} - 47 q^{95} + 37 q^{97} + 31 q^{99}+O(q^{100}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/976\mathbb{Z}\right)^\times$.

$n$	$245$	$367$	$673$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{15}\right)$

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
$3$	1.69101	+	1.22859i	0.976303	+	0.709325i	0.956879	−	0.290486i	$-0.0938170\pi$
$3$	1.69101	+	1.22859i	0.976303	+	0.709325i	0.0194233	+	0.999811i	$0.493817\pi$
$4$		0			0
$5$	1.40283	+	0.298182i	0.627367	+	0.133351i	0.510614	−	0.859810i	$-0.329418\pi$
$5$	1.40283	+	0.298182i	0.627367	+	0.133351i	0.116753	+	0.993161i	$0.462752\pi$
$6$		0			0
$7$	−0.125217	−	1.19136i	−0.0473275	−	0.450291i	−0.992366	−	0.123331i	$-0.960642\pi$
$7$	−0.125217	−	1.19136i	−0.0473275	−	0.450291i	0.945038	−	0.326960i	$-0.106024\pi$
$8$		0			0
$9$	0.423022	+	1.30193i	0.141007	+	0.433976i
$10$		0			0
$11$	3.00395			0.905726			0.452863	−	0.891580i	$-0.350403\pi$
$11$	3.00395			0.905726			0.452863	+	0.891580i	$0.350403\pi$
$12$		0			0
$13$	−1.72195	+	2.98250i	−0.477582	+	0.827197i	−0.999670	−	0.0256950i	$-0.991820\pi$
$13$	−1.72195	+	2.98250i	−0.477582	+	0.827197i	0.522087	+	0.852892i	$0.325153\pi$
$14$		0			0
$15$	2.00586	+	2.22773i	0.517910	+	0.575198i
$16$		0			0
$17$	4.87302	−	5.41204i	1.18188	−	1.31261i	0.242335	−	0.970193i	$-0.422087\pi$
$17$	4.87302	−	5.41204i	1.18188	−	1.31261i	0.939547	−	0.342420i	$-0.111247\pi$
$18$		0			0
$19$	−0.629830	+	5.99243i	−0.144493	+	1.37476i	0.646491	+	0.762922i	$0.276236\pi$
$19$	−0.629830	+	5.99243i	−0.144493	+	1.37476i	−0.790984	+	0.611837i	$0.790431\pi$
$20$		0			0
$21$	1.25194	−	2.16843i	0.273197	−	0.473191i
$22$		0			0
$23$	0.565515	+	1.74048i	0.117918	+	0.362914i	0.992544	−	0.121883i	$-0.0388933\pi$
$23$	0.565515	+	1.74048i	0.117918	+	0.362914i	−0.874626	+	0.484797i	$0.838893\pi$
$24$		0			0
$25$	−2.68870	−	1.19708i	−0.537739	−	0.239417i
$26$		0			0
$27$	1.05352	−	3.24240i	0.202750	−	0.624001i
$28$		0			0
$29$	2.62721	+	4.55046i	0.487860	+	0.844999i	0.999903	−	0.0139612i	$-0.00444414\pi$
$29$	2.62721	+	4.55046i	0.487860	+	0.844999i	−0.512042	+	0.858960i	$0.671111\pi$
$30$		0			0
$31$	5.21493	+	2.32184i	0.936629	+	0.417014i	0.817541	−	0.575870i	$-0.195337\pi$
$31$	5.21493	+	2.32184i	0.936629	+	0.417014i	0.119087	+	0.992884i	$0.462003\pi$
$32$		0			0
$33$	5.07970	+	3.69062i	0.884263	+	0.642455i
$34$		0			0
$35$	0.179583	−	1.70861i	0.0303550	−	0.288809i
$36$		0			0
$37$	−4.17017	+	3.02980i	−0.685571	+	0.498097i	−0.875201	−	0.483759i	$-0.839271\pi$
$37$	−4.17017	+	3.02980i	−0.685571	+	0.498097i	0.189630	+	0.981856i	$0.439271\pi$
$38$		0			0
$39$	−6.57609	+	2.92786i	−1.05302	+	0.468833i
$40$		0			0
$41$	7.17576	−	5.21349i	1.12067	−	0.814211i	0.136355	−	0.990660i	$-0.456461\pi$
$41$	7.17576	−	5.21349i	1.12067	−	0.814211i	0.984310	+	0.176449i	$0.0564611\pi$
$42$		0			0
$43$	−2.93465	−	3.25925i	−0.447529	−	0.497032i	0.476595	−	0.879123i	$-0.341871\pi$
$43$	−2.93465	−	3.25925i	−0.447529	−	0.497032i	−0.924125	+	0.382091i	$0.875204\pi$
$44$		0			0
$45$	0.205219	+	1.95252i	0.0305922	+	0.291065i
$46$		0			0
$47$	−4.25565	−	7.37101i	−0.620751	−	1.07517i	−0.989346	−	0.145582i	$-0.953495\pi$
$47$	−4.25565	−	7.37101i	−0.620751	−	1.07517i	0.368595	−	0.929590i	$-0.379839\pi$
$48$		0			0
$49$	5.44338	−	1.15703i	0.777626	−	0.165289i
$50$		0			0
$51$	14.8895	−	3.16486i	2.08494	−	0.443168i
$52$		0			0
$53$	−2.47558	+	7.61906i	−0.340048	+	1.04656i	0.624134	+	0.781317i	$0.285452\pi$
$53$	−2.47558	+	7.61906i	−0.340048	+	1.04656i	−0.964182	+	0.265242i	$0.914548\pi$
$54$		0			0
$55$	4.21405	+	0.895724i	0.568222	+	0.120779i
$56$		0			0
$57$	−8.42728	+	9.35944i	−1.11622	+	1.23969i
$58$		0			0
$59$	−11.2943	+	5.02854i	−1.47039	+	0.654660i	−0.976628	−	0.214937i	$-0.931045\pi$
$59$	−11.2943	+	5.02854i	−1.47039	+	0.654660i	−0.493762	+	0.869597i	$0.664379\pi$
$60$		0			0
$61$	−6.78003	−	3.87700i	−0.868094	−	0.496399i
$61$	−6.78003	−	3.87700i	−0.868094	−	0.496399i
$62$		0			0
$63$	1.49809	−	0.666993i	0.188742	−	0.0840332i
$64$		0			0
$65$	−3.30493	+	3.67050i	−0.409927	+	0.455270i
$66$		0			0
$67$	2.63158	+	0.559359i	0.321498	+	0.0683366i	0.365834	−	0.930680i	$-0.380784\pi$
$67$	2.63158	+	0.559359i	0.321498	+	0.0683366i	−0.0443357	+	0.999017i	$0.514117\pi$
$68$		0			0
$69$	−1.18204	+	3.63794i	−0.142301	+	0.437956i
$70$		0			0
$71$	−3.77191	+	0.801745i	−0.447644	+	0.0951496i	−0.426217	−	0.904621i	$-0.640154\pi$
$71$	−3.77191	+	0.801745i	−0.447644	+	0.0951496i	−0.0214264	+	0.999770i	$0.506821\pi$
$72$		0			0
$73$	−8.52788	+	1.81266i	−0.998113	+	0.212156i	−0.677872	−	0.735180i	$-0.737097\pi$
$73$	−8.52788	+	1.81266i	−0.998113	+	0.212156i	−0.320242	+	0.947336i	$0.603764\pi$
$74$		0			0
$75$	−3.07588	−	5.32757i	−0.355172	−	0.615175i
$76$		0			0
$77$	−0.376145	−	3.57878i	−0.0428657	−	0.407840i
$78$		0			0
$79$	1.10029	+	1.22199i	0.123792	+	0.137485i	0.801855	−	0.597519i	$-0.203847\pi$
$79$	1.10029	+	1.22199i	0.123792	+	0.137485i	−0.678063	+	0.735004i	$0.737180\pi$
$80$		0			0
$81$	9.08754	−	6.60249i	1.00973	−	0.733610i
$82$		0			0
$83$	−1.78051	+	0.792734i	−0.195436	+	0.0870139i	−0.502121	−	0.864797i	$-0.667447\pi$
$83$	−1.78051	+	0.792734i	−0.195436	+	0.0870139i	0.306685	+	0.951811i	$0.400780\pi$
$84$		0			0
$85$	8.44982	−	6.13915i	0.916511	−	0.665884i
$86$		0			0
$87$	−1.14801	+	10.9226i	−0.123080	+	1.17103i
$88$		0			0
$89$	−4.76070	−	3.45885i	−0.504633	−	0.366638i	0.306151	−	0.951983i	$-0.400959\pi$
$89$	−4.76070	−	3.45885i	−0.504633	−	0.366638i	−0.810784	+	0.585345i	$0.800959\pi$
$90$		0			0
$91$	3.76884	+	1.67800i	0.395082	+	0.175902i
$92$		0			0
$93$	5.96589	+	10.3332i	0.618634	+	1.07151i
$94$		0			0
$95$	−2.67038	+	8.21859i	−0.273975	+	0.843209i
$96$		0			0
$97$	5.09792	+	2.26974i	0.517616	+	0.230457i	0.648881	−	0.760890i	$-0.275237\pi$
$97$	5.09792	+	2.26974i	0.517616	+	0.230457i	−0.131265	+	0.991347i	$0.541904\pi$
$98$		0			0
$99$	1.27074	+	3.91093i	0.127714	+	0.393063i
$100$		0			0
$101$	−2.24288	+	3.88478i	−0.223175	+	0.386550i	−0.955770	−	0.294114i	$-0.904975\pi$
$101$	−2.24288	+	3.88478i	−0.223175	+	0.386550i	0.732595	+	0.680664i	$0.238309\pi$
$102$		0			0
$103$	1.31107	−	12.4740i	0.129183	−	1.22910i	−0.717331	−	0.696733i	$-0.754636\pi$
$103$	1.31107	−	12.4740i	0.129183	−	1.22910i	0.846514	−	0.532366i	$-0.178697\pi$
$104$		0			0
$105$	2.40286	−	2.66864i	0.234495	−	0.260433i
$106$		0			0
$107$	3.27204	+	3.63396i	0.316320	+	0.351308i	0.880247	−	0.474516i	$-0.157377\pi$
$107$	3.27204	+	3.63396i	0.316320	+	0.351308i	−0.563927	+	0.825824i	$0.690710\pi$
$108$		0			0
$109$	−0.00395012	+	0.00684180i	−0.000378353	+	0.000655326i	−0.866215	−	0.499672i	$-0.833454\pi$
$109$	−0.00395012	+	0.00684180i	−0.000378353	+	0.000655326i	0.865836	+	0.500328i	$0.166787\pi$
$110$		0			0
$111$	−10.7742			−1.02264
$112$		0			0
$113$	−4.39592	−	13.5293i	−0.413533	−	1.27272i	−0.913556	−	0.406713i	$-0.866675\pi$
$113$	−4.39592	−	13.5293i	−0.413533	−	1.27272i	0.500023	−	0.866012i	$-0.333325\pi$
$114$		0			0
$115$	0.274346	+	2.61022i	0.0255829	+	0.243405i
$116$		0			0
$117$	−4.61142	−	0.980187i	−0.426326	−	0.0906184i
$118$		0			0
$119$	−7.05786	−	5.12783i	−0.646993	−	0.470068i
$120$		0			0
$121$	−1.97626			−0.179660
$122$		0			0
$123$	18.5395			1.67165
$124$		0			0
$125$	−9.21620	−	6.69596i	−0.824322	−	0.598905i
$126$		0			0
$127$	−13.2169	−	2.80934i	−1.17281	−	0.249289i	−0.419999	−	0.907525i	$-0.637970\pi$
$127$	−13.2169	−	2.80934i	−1.17281	−	0.249289i	−0.752812	+	0.658236i	$0.771303\pi$
$128$		0			0
$129$	−0.958224	−	9.11689i	−0.0843669	−	0.802697i
$130$		0			0
$131$	2.12367	+	6.53600i	0.185546	+	0.571053i	0.999957	−	0.00923556i	$-0.00293981\pi$
$131$	2.12367	+	6.53600i	0.185546	+	0.571053i	−0.814411	+	0.580288i	$0.802940\pi$
$132$		0			0
$133$	7.21800			0.625880
$134$		0			0
$135$	2.44474	−	4.23442i	0.210410	−	0.364440i
$136$		0			0
$137$	9.35035	+	10.3846i	0.798855	+	0.887218i	0.995645	−	0.0932277i	$-0.0297184\pi$
$137$	9.35035	+	10.3846i	0.798855	+	0.887218i	−0.196790	+	0.980446i	$0.563052\pi$
$138$		0			0
$139$	14.1515	−	15.7168i	1.20031	−	1.33308i	0.271541	−	0.962427i	$-0.412467\pi$
$139$	14.1515	−	15.7168i	1.20031	−	1.33308i	0.928771	−	0.370654i	$-0.120867\pi$
$140$		0			0
$141$	1.85959	−	17.6929i	0.156606	−	1.49001i
$142$		0			0
$143$	−5.17265	+	8.95930i	−0.432559	+	0.749214i
$144$		0			0
$145$	2.32868	+	7.16693i	0.193386	+	0.595181i
$146$		0			0
$147$	10.6263	+	4.73113i	0.876442	+	0.390217i
$148$		0			0
$149$	−1.57127	+	4.83587i	−0.128723	+	0.396170i	−0.994561	−	0.104155i	$-0.966786\pi$
$149$	−1.57127	+	4.83587i	−0.128723	+	0.396170i	0.865838	+	0.500325i	$0.166786\pi$
$150$		0			0
$151$	−2.61117	−	4.52268i	−0.212494	−	0.368050i	0.740000	−	0.672606i	$-0.234825\pi$
$151$	−2.61117	−	4.52268i	−0.212494	−	0.368050i	−0.952494	+	0.304556i	$0.901492\pi$
$152$		0			0
$153$	9.10748	+	4.05491i	0.736296	+	0.327820i
$154$		0			0
$155$	6.62335	+	4.81215i	0.532000	+	0.386521i
$156$		0			0
$157$	0.719255	−	6.84326i	0.0574028	−	0.546151i	−0.927595	−	0.373587i	$-0.878128\pi$
$157$	0.719255	−	6.84326i	0.0574028	−	0.546151i	0.984998	−	0.172565i	$-0.0552054\pi$
$158$		0			0
$159$	−13.5469	+	9.84241i	−1.07434	+	0.780554i
$160$		0			0
$161$	2.00272	−	0.891667i	0.157836	−	0.0702732i
$162$		0			0
$163$	−1.71501	+	1.24603i	−0.134330	+	0.0975963i	−0.652921	−	0.757426i	$-0.726457\pi$
$163$	−1.71501	+	1.24603i	−0.134330	+	0.0975963i	0.518591	+	0.855022i	$0.326457\pi$
$164$		0			0
$165$	6.02551	+	6.69200i	0.469085	+	0.520972i
$166$		0			0
$167$	−0.955755	−	9.09340i	−0.0739585	−	0.703668i	−0.967187	−	0.254065i	$-0.918232\pi$
$167$	−0.955755	−	9.09340i	−0.0739585	−	0.703668i	0.893229	−	0.449603i	$-0.148435\pi$
$168$		0			0
$169$	0.569792	+	0.986909i	0.0438302	+	0.0759161i
$170$		0			0
$171$	−8.06814	+	1.71494i	−0.616986	+	0.131144i
$172$		0			0
$173$	−11.7941	+	2.50692i	−0.896689	+	0.190597i	−0.633130	−	0.774046i	$-0.718230\pi$
$173$	−11.7941	+	2.50692i	−0.896689	+	0.190597i	−0.263560	+	0.964643i	$0.584897\pi$
$174$		0			0
$175$	−1.08949	+	3.35309i	−0.0823574	+	0.253470i
$176$		0			0
$177$	−25.2767	−	5.37273i	−1.89991	−	0.403839i
$178$		0			0
$179$	8.24668	−	9.15887i	0.616386	−	0.684566i	−0.351433	−	0.936213i	$-0.614306\pi$
$179$	8.24668	−	9.15887i	0.616386	−	0.684566i	0.967819	+	0.251647i	$0.0809722\pi$
$180$		0			0
$181$	10.3685	−	4.61634i	0.770681	−	0.343130i	0.0165587	−	0.999863i	$-0.494729\pi$
$181$	10.3685	−	4.61634i	0.770681	−	0.343130i	0.754123	+	0.656733i	$0.228062\pi$
$182$		0			0
$183$	−6.70184	−	14.8859i	−0.495414	−	1.10040i
$184$		0			0
$185$	−6.75348	+	3.00685i	−0.496526	+	0.221068i
$186$		0			0
$187$	14.6383	−	16.2575i	1.07046	−	1.18887i
$188$		0			0
$189$	−3.99478	−	0.849117i	−0.290578	−	0.0617642i
$190$		0			0
$191$	−1.42798	+	4.39486i	−0.103325	+	0.318001i	−0.989334	−	0.145667i	$-0.953467\pi$
$191$	−1.42798	+	4.39486i	−0.103325	+	0.318001i	0.886009	+	0.463668i	$0.153467\pi$
$192$		0			0
$193$	−6.88275	+	1.46297i	−0.495431	+	0.105307i	−0.448850	−	0.893607i	$-0.648166\pi$
$193$	−6.88275	+	1.46297i	−0.495431	+	0.105307i	−0.0465817	+	0.998914i	$0.514833\pi$
$194$		0			0
$195$	−10.0982	+	2.14644i	−0.723147	+	0.153710i
$196$		0			0
$197$	−11.1084	−	19.2403i	−0.791440	−	1.37081i	−0.925075	−	0.379784i	$-0.875998\pi$
$197$	−11.1084	−	19.2403i	−0.791440	−	1.37081i	0.133635	−	0.991031i	$-0.457335\pi$
$198$		0			0
$199$	2.23420	+	21.2570i	0.158378	+	1.50687i	0.728352	+	0.685203i	$0.240287\pi$
$199$	2.23420	+	21.2570i	0.158378	+	1.50687i	−0.569974	+	0.821663i	$0.693047\pi$
$200$		0			0
$201$	3.76279	+	4.17900i	0.265407	+	0.294764i
$202$		0			0
$203$	5.09225	−	3.69974i	0.357406	−	0.259671i
$204$		0			0
$205$	11.6210	−	5.17399i	0.811644	−	0.361367i
$206$		0			0
$207$	−2.02675	+	1.47252i	−0.140869	+	0.102347i
$208$		0			0
$209$	−1.89198	+	18.0010i	−0.130871	+	1.24516i
$210$		0			0
$211$	−18.5053	−	13.4449i	−1.27395	−	0.925582i	−0.274602	−	0.961558i	$-0.588546\pi$
$211$	−18.5053	−	13.4449i	−1.27395	−	0.925582i	−0.999353	+	0.0359760i	$0.988546\pi$
$212$		0			0
$213$	−7.36334	−	3.27837i	−0.504528	−	0.224630i
$214$		0			0
$215$	−3.14497	−	5.44725i	−0.214485	−	0.371500i
$216$		0			0
$217$	2.11314	−	6.50358i	0.143449	−	0.441491i
$218$		0			0
$219$	−16.6477	−	7.41204i	−1.12495	−	0.500859i
$220$		0			0
$221$	7.75033	+	23.8530i	0.521343	+	1.60453i
$222$		0			0
$223$	6.58329	−	11.4026i	0.440849	−	0.763574i	−0.556903	−	0.830577i	$-0.688011\pi$
$223$	6.58329	−	11.4026i	0.440849	−	0.763574i	0.997753	+	0.0670038i	$0.0213439\pi$
$224$		0			0
$225$	0.421140	−	4.00688i	0.0280760	−	0.267125i
$226$		0			0
$227$	−1.24364	+	1.38121i	−0.0825435	+	0.0916738i	−0.783002	−	0.622020i	$-0.786312\pi$
$227$	−1.24364	+	1.38121i	−0.0825435	+	0.0916738i	0.700458	+	0.713693i	$0.252979\pi$
$228$		0			0
$229$	−17.6132	−	19.5615i	−1.16392	−	1.29266i	−0.948731	−	0.316086i	$-0.897631\pi$
$229$	−17.6132	−	19.5615i	−1.16392	−	1.29266i	−0.215185	−	0.976573i	$-0.569035\pi$
$230$		0			0
$231$	3.76078	−	6.51387i	0.247441	−	0.428581i
$232$		0			0
$233$	10.9326			0.716219			0.358110	−	0.933680i	$-0.383421\pi$
$233$	10.9326			0.716219			0.358110	+	0.933680i	$0.383421\pi$
$234$		0			0
$235$	−3.77208	−	11.6093i	−0.246063	−	0.757305i
$236$		0			0
$237$	0.359266	+	3.41819i	0.0233369	+	0.222035i
$238$		0			0
$239$	−14.0110	−	2.97814i	−0.906298	−	0.192640i	−0.268894	−	0.963170i	$-0.586658\pi$
$239$	−14.0110	−	2.97814i	−0.906298	−	0.192640i	−0.637404	+	0.770530i	$0.719992\pi$
$240$		0			0
$241$	−7.01389	−	5.09589i	−0.451805	−	0.328255i	0.338503	−	0.940965i	$-0.390079\pi$
$241$	−7.01389	−	5.09589i	−0.451805	−	0.328255i	−0.790308	+	0.612710i	$0.790079\pi$
$242$		0			0
$243$	13.2510			0.850053
$244$		0			0
$245$	7.98116			0.509898
$246$		0			0
$247$	−16.7879	−	12.1971i	−1.06819	−	0.776085i
$248$		0			0
$249$	−3.98480	−	0.846994i	−0.252526	−	0.0536761i
$250$		0			0
$251$	1.03296	+	9.82794i	0.0651997	+	0.620334i	0.977518	+	0.210852i	$0.0676238\pi$
$251$	1.03296	+	9.82794i	0.0651997	+	0.620334i	−0.912318	+	0.409482i	$0.865710\pi$
$252$		0			0
$253$	1.69878	+	5.22831i	0.106801	+	0.328701i
$254$		0			0
$255$	21.8312			1.36712
$256$		0			0
$257$	2.60307	−	4.50864i	0.162375	−	0.281241i	−0.773345	−	0.633985i	$-0.781418\pi$
$257$	2.60307	−	4.50864i	0.162375	−	0.281241i	0.935720	+	0.352744i	$0.114751\pi$
$258$		0			0
$259$	4.13175	+	4.58878i	0.256735	+	0.285133i
$260$		0			0
$261$	−4.81300	+	5.34538i	−0.297917	+	0.330871i
$262$		0			0
$263$	−1.22820	+	11.6856i	−0.0757343	+	0.720564i	0.889101	+	0.457710i	$0.151330\pi$
$263$	−1.22820	+	11.6856i	−0.0757343	+	0.720564i	−0.964836	+	0.262854i	$0.915336\pi$
$264$		0			0
$265$	−5.74470	+	9.95011i	−0.352894	+	0.611230i
$266$		0			0
$267$	−3.80087	−	11.6979i	−0.232610	−	0.715899i
$268$		0			0
$269$	3.33020	+	1.48270i	0.203046	+	0.0904018i	0.505740	−	0.862686i	$-0.331219\pi$
$269$	3.33020	+	1.48270i	0.203046	+	0.0904018i	−0.302694	+	0.953088i	$0.597886\pi$
$270$		0			0
$271$	−6.82316	+	20.9995i	−0.414477	+	1.27563i	0.498240	+	0.867039i	$0.333980\pi$
$271$	−6.82316	+	20.9995i	−0.414477	+	1.27563i	−0.912717	+	0.408591i	$0.866020\pi$
$272$		0			0
$273$	4.31157	+	7.46785i	0.260948	+	0.451975i
$274$		0			0
$275$	−8.07672	−	3.59599i	−0.487044	−	0.216846i
$276$		0			0
$277$	−3.39311	−	2.46524i	−0.203872	−	0.148122i	0.481165	−	0.876630i	$-0.340214\pi$
$277$	−3.39311	−	2.46524i	−0.203872	−	0.148122i	−0.685037	+	0.728508i	$0.740214\pi$
$278$		0			0
$279$	−0.816832	+	7.77164i	−0.0489025	+	0.465276i
$280$		0			0
$281$	−23.0097	+	16.7175i	−1.37264	+	0.997283i	−0.375117	+	0.926977i	$0.622397\pi$
$281$	−23.0097	+	16.7175i	−1.37264	+	0.997283i	−0.997525	+	0.0703057i	$0.977603\pi$
$282$		0			0
$283$	8.46959	−	3.77090i	0.503465	−	0.224157i	−0.139257	−	0.990256i	$-0.544472\pi$
$283$	8.46959	−	3.77090i	0.503465	−	0.224157i	0.642722	+	0.766099i	$0.277805\pi$
$284$		0			0
$285$	−14.6129	+	10.6169i	−0.865593	+	0.628890i
$286$		0			0
$287$	−7.10966	−	7.89608i	−0.419670	−	0.466091i
$288$		0			0
$289$	−3.76684	−	35.8391i	−0.221579	−	2.10818i
$290$		0			0
$291$	5.83204	+	10.1014i	0.341880	+	0.592154i
$292$		0			0
$293$	10.7539	−	2.28581i	0.628248	−	0.133538i	0.117225	−	0.993105i	$-0.462600\pi$
$293$	10.7539	−	2.28581i	0.628248	−	0.133538i	0.511023	+	0.859567i	$0.329267\pi$
$294$		0			0
$295$	−17.3434	+	3.68646i	−1.00977	+	0.214634i
$296$		0			0
$297$	3.16473	−	9.74003i	0.183636	−	0.565174i
$298$		0			0
$299$	−6.16476	−	1.31036i	−0.356517	−	0.0757800i
$300$		0			0
$301$	−3.51547	+	3.90433i	−0.202628	+	0.225042i
$302$		0			0
$303$	−8.56552	+	3.81361i	−0.492076	+	0.219086i
$304$		0			0
$305$	−8.35521	−	7.46047i	−0.478418	−	0.427185i
$306$		0			0
$307$	−23.3187	+	10.3822i	−1.33087	+	0.592541i	−0.944107	−	0.329638i	$-0.893073\pi$
$307$	−23.3187	+	10.3822i	−1.33087	+	0.592541i	−0.386762	+	0.922180i	$0.626406\pi$
$308$		0			0
$309$	17.5424	−	19.4828i	0.997953	−	1.10834i
$310$		0			0
$311$	3.82370	+	0.812752i	0.216822	+	0.0460869i	0.315042	−	0.949078i	$-0.397981\pi$
$311$	3.82370	+	0.812752i	0.216822	+	0.0460869i	−0.0982198	+	0.995165i	$0.531315\pi$
$312$		0			0
$313$	−2.76404	+	8.50685i	−0.156233	+	0.480836i	−0.998284	−	0.0585626i	$-0.981348\pi$
$313$	−2.76404	+	8.50685i	−0.156233	+	0.480836i	0.842051	+	0.539398i	$0.181348\pi$
$314$		0			0
$315$	2.30046	−	0.488977i	0.129616	−	0.0275508i
$316$		0			0
$317$	29.5274	−	6.27625i	1.65843	−	0.352509i	0.718933	−	0.695079i	$-0.244631\pi$
$317$	29.5274	−	6.27625i	1.65843	−	0.352509i	0.939492	+	0.342570i	$0.111297\pi$
$318$		0			0
$319$	7.89202	+	13.6694i	0.441868	+	0.765338i
$320$		0			0
$321$	1.06839	+	10.1650i	0.0596316	+	0.567357i
$322$		0			0
$323$	29.3621	+	32.6099i	1.63375	+	1.81447i
$324$		0			0
$325$	8.20010	−	5.95772i	0.454860	−	0.330475i
$326$		0			0
$327$	−0.0150854	+	0.00671646i	−0.000834226	+	0.000371421i
$328$		0			0
$329$	−8.24862	+	5.99298i	−0.454761	+	0.330403i
$330$		0			0
$331$	1.88767	−	17.9600i	0.103756	−	0.987170i	−0.811515	−	0.584331i	$-0.801357\pi$
$331$	1.88767	−	17.9600i	0.103756	−	0.987170i	0.915271	−	0.402839i	$-0.131976\pi$
$332$		0			0
$333$	−5.70865	−	4.14758i	−0.312832	−	0.227286i
$334$		0			0
$335$	3.52488	+	1.56938i	0.192585	+	0.0857442i
$336$		0			0
$337$	−10.0162	−	17.3486i	−0.545618	−	0.945037i	−0.998568	−	0.0535015i	$-0.982962\pi$
$337$	−10.0162	−	17.3486i	−0.545618	−	0.945037i	0.452950	−	0.891536i	$-0.350372\pi$
$338$		0			0
$339$	9.18834	−	28.2788i	0.499042	−	1.53589i
$340$		0			0
$341$	15.6654	+	6.97469i	0.848329	+	0.377701i
$342$		0			0
$343$	−4.65128	−	14.3152i	−0.251145	−	0.772946i
$344$		0			0
$345$	−2.74297	+	4.75096i	−0.147676	+	0.255783i
$346$		0			0
$347$	−0.957961	+	9.11439i	−0.0514260	+	0.489286i	0.938249	+	0.345960i	$0.112447\pi$
$347$	−0.957961	+	9.11439i	−0.0514260	+	0.489286i	−0.989675	+	0.143326i	$0.954220\pi$
$348$		0			0
$349$	−11.8630	+	13.1752i	−0.635013	+	0.705253i	−0.971661	−	0.236377i	$-0.924040\pi$
$349$	−11.8630	+	13.1752i	−0.635013	+	0.705253i	0.336649	+	0.941630i	$0.390707\pi$
$350$		0			0
$351$	7.85637	+	8.72538i	0.419342	+	0.465726i
$352$		0			0
$353$	−3.34891	+	5.80049i	−0.178245	+	0.308729i	−0.941279	−	0.337629i	$-0.890375\pi$
$353$	−3.34891	+	5.80049i	−0.178245	+	0.308729i	0.763035	+	0.646358i	$0.223709\pi$
$354$		0			0
$355$	−5.53043			−0.293525
$356$		0			0
$357$	−5.63488	−	17.3424i	−0.298230	−	0.917857i
$358$		0			0
$359$	−2.88420	−	27.4413i	−0.152222	−	1.44830i	−0.757787	−	0.652502i	$-0.773719\pi$
$359$	−2.88420	−	27.4413i	−0.152222	−	1.44830i	0.605564	−	0.795796i	$-0.292947\pi$
$360$		0			0
$361$	−16.9278	−	3.59811i	−0.890936	−	0.189374i
$362$		0			0
$363$	−3.34186	−	2.42801i	−0.175402	−	0.127437i
$364$		0			0
$365$	−12.5037			−0.654474
$366$		0			0
$367$	−14.0141			−0.731532			−0.365766	−	0.930707i	$-0.619193\pi$
$367$	−14.0141			−0.731532			−0.365766	+	0.930707i	$0.619193\pi$
$368$		0			0
$369$	9.82309	+	7.13689i	0.511369	+	0.371532i
$370$		0			0
$371$	9.38701	+	1.99527i	0.487349	+	0.103589i
$372$		0			0
$373$	0.660105	+	6.28048i	0.0341790	+	0.325191i	0.998230	+	0.0594735i	$0.0189422\pi$
$373$	0.660105	+	6.28048i	0.0341790	+	0.325191i	−0.964051	+	0.265718i	$0.914391\pi$
$374$		0			0
$375$	−7.35807	−	22.6458i	−0.379969	−	1.16943i
$376$		0			0
$377$	−18.0957			−0.931974
$378$		0			0
$379$	−0.411458	+	0.712666i	−0.0211352	+	0.0366072i	−0.876400	−	0.481585i	$-0.840061\pi$
$379$	−0.411458	+	0.712666i	−0.0211352	+	0.0366072i	0.855264	+	0.518192i	$0.173395\pi$
$380$		0			0
$381$	−18.8983	−	20.9887i	−0.968191	−	1.07529i
$382$		0			0
$383$	12.0053	−	13.3332i	0.613442	−	0.681296i	−0.353751	−	0.935340i	$-0.615094\pi$
$383$	12.0053	−	13.3332i	0.613442	−	0.681296i	0.967193	+	0.254043i	$0.0817606\pi$
$384$		0			0
$385$	0.539458	−	5.13260i	0.0274933	−	0.261581i
$386$		0			0
$387$	3.00189	−	5.19943i	0.152595	−	0.264302i
$388$		0			0
$389$	−0.637490	−	1.96199i	−0.0323220	−	0.0994770i	0.933594	−	0.358333i	$-0.116655\pi$
$389$	−0.637490	−	1.96199i	−0.0323220	−	0.0994770i	−0.965916	+	0.258856i	$0.916655\pi$
$390$		0			0
$391$	12.1753	+	5.42079i	0.615731	+	0.274141i
$392$		0			0
$393$	−4.43890	+	13.6615i	−0.223913	+	0.689133i
$394$		0			0
$395$	1.17914	+	2.04234i	0.0593291	+	0.102761i
$396$		0			0
$397$	15.7251	+	7.00127i	0.789221	+	0.351384i	0.761444	−	0.648230i	$-0.224491\pi$
$397$	15.7251	+	7.00127i	0.789221	+	0.351384i	0.0277766	+	0.999614i	$0.491157\pi$
$398$		0			0
$399$	12.2057	+	8.86794i	0.611048	+	0.443952i
$400$		0			0
$401$	−0.730410	+	6.94938i	−0.0364749	+	0.347036i	0.961030	+	0.276443i	$0.0891557\pi$
$401$	−0.730410	+	6.94938i	−0.0364749	+	0.347036i	−0.997505	+	0.0705926i	$0.977511\pi$
$402$		0			0
$403$	−15.9047	+	11.5554i	−0.792270	+	0.575618i
$404$		0			0
$405$	14.7171	−	6.55246i	0.731296	−	0.325594i
$406$		0			0
$407$	−12.5270	+	9.10139i	−0.620940	+	0.451139i
$408$		0			0
$409$	12.1125	+	13.4522i	0.598922	+	0.665171i	0.964030	−	0.265795i	$-0.0856343\pi$
$409$	12.1125	+	13.4522i	0.598922	+	0.665171i	−0.365107	+	0.930965i	$0.618968\pi$
$410$		0			0
$411$	3.05309	+	29.0482i	0.150598	+	1.43284i
$412$		0			0
$413$	7.40502	+	12.8259i	0.364377	+	0.631120i
$414$		0			0
$415$	−2.73414	+	0.581159i	−0.134214	+	0.0285280i
$416$		0			0
$417$	43.2397	−	9.19087i	2.11746	−	0.450079i
$418$		0			0
$419$	−8.70426	+	26.7889i	−0.425231	+	1.30873i	0.477543	+	0.878609i	$0.341528\pi$
$419$	−8.70426	+	26.7889i	−0.425231	+	1.30873i	−0.902773	+	0.430117i	$0.858472\pi$
$420$		0			0
$421$	31.4668	+	6.68848i	1.53360	+	0.325977i	0.895882	−	0.444293i	$-0.146545\pi$
$421$	31.4668	+	6.68848i	1.53360	+	0.325977i	0.637718	+	0.770270i	$0.279878\pi$
$422$		0			0
$423$	7.79628	−	8.65864i	0.379068	−	0.420998i
$424$		0			0
$425$	−19.5807	+	8.71791i	−0.949806	+	0.422881i
$426$		0			0
$427$	−3.76992	+	8.56291i	−0.182439	+	0.414388i
$428$		0			0
$429$	−19.7543	+	8.79516i	−0.953745	+	0.424635i
$430$		0			0
$431$	−11.6269	+	12.9130i	−0.560048	+	0.621996i	−0.954964	−	0.296721i	$-0.904107\pi$
$431$	−11.6269	+	12.9130i	−0.560048	+	0.621996i	0.394916	+	0.918717i	$0.370774\pi$
$432$		0			0
$433$	21.0308	+	4.47024i	1.01068	+	0.214826i	0.683354	−	0.730087i	$-0.260520\pi$
$433$	21.0308	+	4.47024i	1.01068	+	0.214826i	0.327322	+	0.944913i	$0.393854\pi$
$434$		0			0
$435$	−4.86739	+	14.9803i	−0.233374	+	0.718250i
$436$		0			0
$437$	−10.7859	+	2.29261i	−0.515958	+	0.109670i
$438$		0			0
$439$	32.3740	−	6.88131i	1.54513	−	0.328427i	0.645044	−	0.764145i	$-0.276839\pi$
$439$	32.3740	−	6.88131i	1.54513	−	0.328427i	0.900083	+	0.435718i	$0.143506\pi$
$440$		0			0
$441$	3.80903	+	6.59744i	0.181382	+	0.314164i
$442$		0			0
$443$	1.48072	+	14.0881i	0.0703512	+	0.669347i	0.971694	+	0.236241i	$0.0759155\pi$
$443$	1.48072	+	14.0881i	0.0703512	+	0.669347i	−0.901343	+	0.433105i	$0.857418\pi$
$444$		0			0
$445$	−5.64711	−	6.27175i	−0.267699	−	0.297310i
$446$		0			0
$447$	−8.59831	+	6.24704i	−0.406686	+	0.295475i
$448$		0			0
$449$	−3.06190	+	1.36325i	−0.144500	+	0.0643356i	−0.477713	−	0.878516i	$-0.658534\pi$
$449$	−3.06190	+	1.36325i	−0.144500	+	0.0643356i	0.333213	+	0.942852i	$0.391867\pi$
$450$		0			0
$451$	21.5556	−	15.6611i	1.01502	−	0.737452i
$452$		0			0
$453$	1.14100	−	10.8559i	0.0536090	−	0.510056i
$454$		0			0
$455$	4.78671	+	3.47775i	0.224405	+	0.163039i
$456$		0			0
$457$	34.3209	+	15.2807i	1.60547	+	0.714799i	0.996898	−	0.0787024i	$-0.0250777\pi$
$457$	34.3209	+	15.2807i	1.60547	+	0.714799i	0.608568	+	0.793502i	$0.291744\pi$
$458$		0			0
$459$	−12.4142	−	21.5020i	−0.579445	−	1.00363i
$460$		0			0
$461$	2.07827	−	6.39627i	0.0967948	−	0.297904i	−0.890922	−	0.454155i	$-0.849941\pi$
$461$	2.07827	−	6.39627i	0.0967948	−	0.297904i	0.987717	+	0.156252i	$0.0499411\pi$
$462$		0			0
$463$	13.0810	+	5.82402i	0.607924	+	0.270665i	0.687524	−	0.726162i	$-0.258698\pi$
$463$	13.0810	+	5.82402i	0.607924	+	0.270665i	−0.0796000	+	0.996827i	$0.525364\pi$
$464$		0			0
$465$	5.28798	+	16.2747i	0.245224	+	0.754723i
$466$		0			0
$467$	−14.9623	+	25.9154i	−0.692372	+	1.19922i	0.278687	+	0.960382i	$0.410101\pi$
$467$	−14.9623	+	25.9154i	−0.692372	+	1.19922i	−0.971059	+	0.238841i	$0.923233\pi$
$468$		0			0
$469$	0.336879	−	3.20519i	0.0155556	−	0.148002i
$470$		0			0
$471$	9.62381	−	10.6883i	0.443442	−	0.492492i
$472$		0			0
$473$	−8.81554	−	9.79065i	−0.405339	−	0.450175i
$474$		0			0
$475$	8.86687	−	15.3579i	0.406840	−	0.704668i
$476$		0			0
$477$	−10.9667			−0.502130
$478$		0			0
$479$	4.30299	+	13.2432i	0.196609	+	0.605099i	0.999954	+	0.00958585i	$0.00305132\pi$
$479$	4.30299	+	13.2432i	0.196609	+	0.605099i	−0.803345	+	0.595513i	$0.796949\pi$
$480$		0			0
$481$	−1.85558	−	17.6547i	−0.0846073	−	0.804985i
$482$		0			0
$483$	4.48209	+	0.952698i	0.203942	+	0.0433493i
$484$		0			0
$485$	6.47475	+	4.70418i	0.294003	+	0.213606i
$486$		0			0
$487$	41.7968			1.89399			0.946996	−	0.321244i	$-0.104101\pi$
$487$	41.7968			1.89399			0.946996	+	0.321244i	$0.104101\pi$
$488$		0			0
$489$	−4.43094			−0.200374
$490$		0			0
$491$	9.01346	+	6.54866i	0.406772	+	0.295537i	0.772294	−	0.635266i	$-0.219109\pi$
$491$	9.01346	+	6.54866i	0.406772	+	0.295537i	−0.365522	+	0.930803i	$0.619109\pi$
$492$		0			0
$493$	37.4297	+	7.95593i	1.68575	+	0.358317i
$494$		0			0
$495$	0.616467	+	5.86530i	0.0277081	+	0.263625i
$496$		0			0
$497$	1.42747	+	4.39330i	0.0640308	+	0.197067i
$498$		0			0
$499$	−7.81559			−0.349874			−0.174937	−	0.984580i	$-0.555972\pi$
$499$	−7.81559			−0.349874			−0.174937	+	0.984580i	$0.555972\pi$
$500$		0			0
$501$	9.55585	−	16.5512i	0.426924	−	0.739454i
$502$		0			0
$503$	5.23989	+	5.81949i	0.233635	+	0.259478i	0.848550	−	0.529115i	$-0.177476\pi$
$503$	5.23989	+	5.81949i	0.233635	+	0.259478i	−0.614915	+	0.788594i	$0.710810\pi$
$504$		0			0
$505$	−4.30476	+	4.78092i	−0.191559	+	0.212748i
$506$		0			0
$507$	−0.248982	+	2.36891i	−0.0110577	+	0.105207i
$508$		0			0
$509$	−11.9730	+	20.7379i	−0.530695	+	0.919191i	0.468663	+	0.883377i	$0.344736\pi$
$509$	−11.9730	+	20.7379i	−0.530695	+	0.919191i	−0.999358	+	0.0358144i	$0.988597\pi$
$510$		0			0
$511$	3.22736	+	9.93278i	0.142770	+	0.439400i
$512$		0			0
$513$	18.7664	+	8.35532i	0.828555	+	0.368896i
$514$		0			0
$515$	5.55873	−	17.1080i	0.244947	−	0.753869i
$516$		0			0
$517$	−12.7838	−	22.1422i	−0.562230	−	0.973811i
$518$		0			0
$519$	−23.0239	−	10.2509i	−1.01064	−	0.449964i
$520$		0			0
$521$	−5.15668	−	3.74655i	−0.225918	−	0.164139i	0.469068	−	0.883162i	$-0.344590\pi$
$521$	−5.15668	−	3.74655i	−0.225918	−	0.164139i	−0.694987	+	0.719023i	$0.744590\pi$
$522$		0			0
$523$	0.862291	−	8.20415i	0.0377054	−	0.358743i	−0.959360	−	0.282186i	$-0.908941\pi$
$523$	0.862291	−	8.20415i	0.0377054	−	0.358743i	0.997065	−	0.0765570i	$-0.0243927\pi$
$524$		0			0
$525$	−5.96189	+	4.33157i	−0.260198	+	0.189045i
$526$		0			0
$527$	37.9783	−	16.9090i	1.65436	−	0.736569i
$528$		0			0
$529$	15.8979	−	11.5505i	0.691215	−	0.502197i
$530$		0			0
$531$	−11.3245	−	12.5771i	−0.491442	−	0.545802i
$532$		0			0
$533$	3.19297	+	30.3791i	0.138303	+	1.31586i
$534$		0			0
$535$	3.50654	+	6.07351i	0.151601	+	0.262581i
$536$		0			0
$537$	25.1977	−	5.35593i	1.08736	−	0.231125i
$538$		0			0
$539$	16.3517	−	3.47565i	0.704316	−	0.149707i
$540$		0			0
$541$	−9.68894	+	29.8195i	−0.416560	+	1.28204i	0.494288	+	0.869298i	$0.335429\pi$
$541$	−9.68894	+	29.8195i	−0.416560	+	1.28204i	−0.910848	+	0.412742i	$0.864571\pi$
$542$		0			0
$543$	23.2047	+	4.93231i	0.995809	+	0.211666i
$544$		0			0
$545$	−0.00758146	+	0.00842006i	−0.000324754	+	0.000360676i
$546$		0			0
$547$	32.7420	−	14.5777i	1.39995	−	0.623296i	0.438611	−	0.898677i	$-0.355470\pi$
$547$	32.7420	−	14.5777i	1.39995	−	0.623296i	0.961335	+	0.275380i	$0.0888038\pi$
$548$		0			0
$549$	2.17947	−	10.4672i	0.0930175	−	0.446728i
$550$		0			0
$551$	−28.9230	+	12.8774i	−1.23216	+	0.548594i
$552$		0			0
$553$	1.31805	−	1.46385i	0.0560494	−	0.0622491i
$554$		0			0
$555$	−15.1144	−	3.21265i	−0.641569	−	0.136370i
$556$		0			0
$557$	−0.940299	+	2.89394i	−0.0398418	+	0.122620i	−0.968999	−	0.247064i	$-0.920534\pi$
$557$	−0.940299	+	2.89394i	−0.0398418	+	0.122620i	0.929157	+	0.369684i	$0.120534\pi$
$558$		0			0
$559$	14.7740	−	3.14032i	0.624875	−	0.132821i
$560$		0			0
$561$	44.7273	−	9.50708i	1.88839	−	0.401389i
$562$		0			0
$563$	−9.02183	−	15.6263i	−0.380225	−	0.658569i	0.610869	−	0.791731i	$-0.290820\pi$
$563$	−9.02183	−	15.6263i	−0.380225	−	0.658569i	−0.991094	+	0.133163i	$0.957487\pi$
$564$		0			0
$565$	−2.13257	−	20.2901i	−0.0897180	−	0.853610i
$566$		0			0
$567$	−9.00383	−	9.99977i	−0.378125	−	0.419951i
$568$		0			0
$569$	20.7813	−	15.0985i	0.871197	−	0.632961i	−0.0597112	−	0.998216i	$-0.519018\pi$
$569$	20.7813	−	15.0985i	0.871197	−	0.632961i	0.930908	+	0.365254i	$0.119018\pi$
$570$		0			0
$571$	−12.3806	+	5.51218i	−0.518110	+	0.230677i	−0.649096	−	0.760707i	$-0.724853\pi$
$571$	−12.3806	+	5.51218i	−0.518110	+	0.230677i	0.130986	+	0.991384i	$0.458186\pi$
$572$		0			0
$573$	−7.81419	+	5.67734i	−0.326442	+	0.237174i
$574$		0			0
$575$	0.562999	−	5.35658i	0.0234787	−	0.223385i
$576$		0			0
$577$	−17.5073	−	12.7198i	−0.728840	−	0.529533i	0.160357	−	0.987059i	$-0.448736\pi$
$577$	−17.5073	−	12.7198i	−0.728840	−	0.529533i	−0.889196	+	0.457526i	$0.848736\pi$
$578$		0			0
$579$	−13.4362	−	5.98216i	−0.558388	−	0.248610i
$580$		0			0
$581$	1.16738	+	2.02196i	0.0484311	+	0.0838850i
$582$		0			0
$583$	−7.43654	+	22.8873i	−0.307990	+	0.947896i
$584$		0			0
$585$	−6.17678	−	2.75008i	−0.255379	−	0.113702i
$586$		0			0
$587$	3.13370	+	9.64455i	0.129342	+	0.398073i	0.994667	−	0.103138i	$-0.0328882\pi$
$587$	3.13370	+	9.64455i	0.129342	+	0.398073i	−0.865325	+	0.501211i	$0.832888\pi$
$588$		0			0
$589$	−17.1980	+	29.7878i	−0.708630	+	1.22738i
$590$		0			0
$591$	4.85404	−	46.1831i	0.199668	−	1.89972i
$592$		0			0
$593$	−3.64615	+	4.04946i	−0.149730	+	0.166291i	−0.813344	−	0.581784i	$-0.802355\pi$
$593$	−3.64615	+	4.04946i	−0.149730	+	0.166291i	0.663614	+	0.748075i	$0.269022\pi$
$594$		0			0
$595$	−8.37198	−	9.29803i	−0.343218	−	0.381182i
$596$		0			0
$597$	−22.3380	+	38.6906i	−0.914234	+	1.58350i
$598$		0			0
$599$	16.6779			0.681442			0.340721	−	0.940164i	$-0.389329\pi$
$599$	16.6779			0.681442			0.340721	+	0.940164i	$0.389329\pi$
$600$		0			0
$601$	5.93270	+	18.2590i	0.242000	+	0.744799i	0.996115	+	0.0880574i	$0.0280659\pi$
$601$	5.93270	+	18.2590i	0.242000	+	0.744799i	−0.754115	+	0.656742i	$0.771934\pi$
$602$		0			0
$603$	0.384970	+	3.66274i	0.0156772	+	0.149158i
$604$		0			0
$605$	−2.77236	−	0.589284i	−0.112713	−	0.0239578i
$606$		0			0
$607$	15.4012	+	11.1896i	0.625116	+	0.454174i	0.854705	−	0.519114i	$-0.173738\pi$
$607$	15.4012	+	11.1896i	0.625116	+	0.454174i	−0.229589	+	0.973288i	$0.573738\pi$
$608$		0			0
$609$	13.1565			0.533127
$610$		0			0
$611$	29.3120			1.18584
$612$		0			0
$613$	6.30542	+	4.58116i	0.254674	+	0.185031i	0.707796	−	0.706417i	$-0.249690\pi$
$613$	6.30542	+	4.58116i	0.254674	+	0.185031i	−0.453122	+	0.891449i	$0.649690\pi$
$614$		0			0
$615$	26.0078	+	5.52813i	1.04874	+	0.222916i
$616$		0			0
$617$	3.88060	+	36.9214i	0.156227	+	1.48640i	0.738967	+	0.673741i	$0.235314\pi$
$617$	3.88060	+	36.9214i	0.156227	+	1.48640i	−0.582740	+	0.812658i	$0.698020\pi$
$618$		0			0
$619$	2.07910	+	6.39880i	0.0835659	+	0.257189i	0.984106	−	0.177584i	$-0.0568283\pi$
$619$	2.07910	+	6.39880i	0.0835659	+	0.257189i	−0.900540	+	0.434774i	$0.856828\pi$
$620$		0			0
$621$	6.23911			0.250367
$622$		0			0
$623$	−3.52461	+	6.10480i	−0.141211	+	0.244584i
$624$		0			0
$625$	−1.08546	−	1.20552i	−0.0434182	−	0.0482208i
$626$		0			0
$627$	−25.3152	+	28.1153i	−1.01099	+	1.12282i
$628$		0			0
$629$	−3.92390	+	37.3334i	−0.156456	+	1.48858i
$630$		0			0
$631$	−20.0257	+	34.6855i	−0.797210	+	1.38081i	0.124216	+	0.992255i	$0.460358\pi$
$631$	−20.0257	+	34.6855i	−0.797210	+	1.38081i	−0.921426	+	0.388553i	$0.872975\pi$
$632$		0			0
$633$	−14.7743	−	45.4707i	−0.587226	−	1.80730i
$634$		0			0
$635$	−17.7034	−	7.88208i	−0.702539	−	0.312791i
$636$		0			0
$637$	−5.92238	+	18.2272i	−0.234653	+	0.722189i
$638$		0			0
$639$	−2.63941	−	4.57160i	−0.104414	−	0.180850i
$640$		0			0
$641$	5.54423	+	2.46845i	0.218984	+	0.0974980i	0.513297	−	0.858211i	$-0.328424\pi$
$641$	5.54423	+	2.46845i	0.218984	+	0.0974980i	−0.294313	+	0.955709i	$0.595091\pi$
$642$		0			0
$643$	−3.45737	−	2.51193i	−0.136345	−	0.0990608i	0.517522	−	0.855670i	$-0.326855\pi$
$643$	−3.45737	−	2.51193i	−0.136345	−	0.0990608i	−0.653867	+	0.756609i	$0.726855\pi$
$644$		0			0
$645$	1.37426	−	13.0752i	0.0541114	−	0.514836i
$646$		0			0
$647$	−16.1915	+	11.7638i	−0.636555	+	0.462484i	−0.858665	−	0.512537i	$-0.828706\pi$
$647$	−16.1915	+	11.7638i	−0.636555	+	0.462484i	0.222110	+	0.975022i	$0.428706\pi$
$648$		0			0
$649$	−33.9275	+	15.1055i	−1.33177	+	0.592943i
$650$		0			0
$651$	11.5635	−	8.40140i	0.453211	−	0.329277i
$652$		0			0
$653$	6.50424	+	7.22369i	0.254531	+	0.282685i	0.856845	−	0.515574i	$-0.172421\pi$
$653$	6.50424	+	7.22369i	0.254531	+	0.282685i	−0.602314	+	0.798259i	$0.705755\pi$
$654$		0			0
$655$	1.03025	+	9.80216i	0.0402552	+	0.383002i
$656$		0			0
$657$	−5.96743	−	10.3359i	−0.232811	−	0.403241i
$658$		0			0
$659$	−4.60609	+	0.979054i	−0.179428	+	0.0381385i	−0.296749	−	0.954955i	$-0.595903\pi$
$659$	−4.60609	+	0.979054i	−0.179428	+	0.0381385i	0.117322	+	0.993094i	$0.462569\pi$
$660$		0			0
$661$	42.4993	−	9.03351i	1.65303	−	0.351363i	0.715326	−	0.698791i	$-0.246278\pi$
$661$	42.4993	−	9.03351i	1.65303	−	0.351363i	0.937707	+	0.347428i	$0.112945\pi$
$662$		0			0
$663$	−16.1997	+	49.8576i	−0.629145	+	1.93631i
$664$		0			0
$665$	10.1257	+	2.15227i	0.392656	+	0.0834616i
$666$		0			0
$667$	−6.43424	+	7.14594i	−0.249135	+	0.276692i
$668$		0			0
$669$	25.1414	−	11.1937i	0.972024	−	0.432773i
$670$		0			0
$671$	−20.3669	−	11.6463i	−0.786256	−	0.449602i
$672$		0			0
$673$	−21.4708	+	9.55943i	−0.827640	+	0.368489i	−0.776434	−	0.630199i	$-0.782973\pi$
$673$	−21.4708	+	9.55943i	−0.827640	+	0.368489i	−0.0512064	+	0.998688i	$0.516307\pi$
$674$		0			0
$675$	−6.71403	+	7.45668i	−0.258423	+	0.287008i
$676$		0			0
$677$	−32.3540	−	6.87706i	−1.24347	−	0.264307i	−0.461225	−	0.887283i	$-0.652590\pi$
$677$	−32.3540	−	6.87706i	−1.24347	−	0.264307i	−0.782241	+	0.622976i	$0.785923\pi$
$678$		0			0
$679$	2.06573	−	6.35766i	0.0792754	−	0.243985i
$680$		0			0
$681$	−3.79994	+	0.807702i	−0.145614	+	0.0309512i
$682$		0			0
$683$	−8.60480	+	1.82901i	−0.329253	+	0.0699850i	−0.369573	−	0.929202i	$-0.620496\pi$
$683$	−8.60480	+	1.82901i	−0.329253	+	0.0699850i	0.0403191	+	0.999187i	$0.487163\pi$
$684$		0			0
$685$	10.0205	+	17.3560i	0.382863	+	0.663139i
$686$		0			0
$687$	−5.75109	−	54.7180i	−0.219418	−	2.08762i
$688$		0			0
$689$	−18.4610	−	20.5031i	−0.703309	−	0.781104i
$690$		0			0
$691$	−12.9260	+	9.39132i	−0.491730	+	0.357263i	−0.805849	−	0.592121i	$-0.798291\pi$
$691$	−12.9260	+	9.39132i	−0.491730	+	0.357263i	0.314119	+	0.949384i	$0.398291\pi$
$692$		0			0
$693$	4.50020	−	2.00362i	0.170948	−	0.0761111i
$694$		0			0
$695$	24.5386	−	17.8284i	0.930803	−	0.676268i
$696$		0			0
$697$	6.75200	−	64.2410i	0.255750	−	2.43330i
$698$		0			0
$699$	18.4871	+	13.4317i	0.699246	+	0.508032i
$700$		0			0
$701$	−20.3073	−	9.04140i	−0.766996	−	0.341489i	−0.0143356	−	0.999897i	$-0.504563\pi$
$701$	−20.3073	−	9.04140i	−0.766996	−	0.341489i	−0.752661	+	0.658408i	$0.771230\pi$
$702$		0			0
$703$	−15.5294	−	26.8977i	−0.585703	−	1.01447i
$704$		0			0
$705$	7.88439	−	24.2656i	0.296943	−	0.913897i
$706$		0			0
$707$	4.90901	+	2.18563i	0.184622	+	0.0821991i
$708$		0			0
$709$	−4.93933	−	15.2017i	−0.185500	−	0.570911i	0.814456	−	0.580225i	$-0.197035\pi$
$709$	−4.93933	−	15.2017i	−0.185500	−	0.570911i	−0.999957	+	0.00931352i	$0.997035\pi$
$710$		0			0
$711$	−1.12550	+	1.94942i	−0.0422095	+	0.0731090i
$712$		0			0
$713$	−1.09198	+	10.3895i	−0.0408949	+	0.389089i
$714$		0			0
$715$	−9.92787	+	11.0260i	−0.371281	+	0.412350i
$716$		0			0
$717$	−20.0338	−	22.2498i	−0.748177	−	0.830934i
$718$		0			0
$719$	−25.7291	+	44.5642i	−0.959535	+	1.66196i	−0.235902	+	0.971777i	$0.575805\pi$
$719$	−25.7291	+	44.5642i	−0.959535	+	1.66196i	−0.723632	+	0.690186i	$0.757529\pi$
$720$		0			0
$721$	−15.0251			−0.559566
$722$		0			0
$723$	−5.59978	−	17.2344i	−0.208258	−	0.640953i
$724$		0			0
$725$	−1.61648	−	15.3798i	−0.0600346	−	0.571191i
$726$		0			0
$727$	28.1676	+	5.98721i	1.04468	+	0.222053i	0.698124	−	0.715976i	$-0.254018\pi$
$727$	28.1676	+	5.98721i	1.04468	+	0.222053i	0.346555	+	0.938030i	$0.387352\pi$
$728$		0			0
$729$	−4.85508	−	3.52742i	−0.179818	−	0.130645i
$730$		0			0
$731$	−31.9398			−1.18134
$732$		0			0
$733$	−32.0787			−1.18485			−0.592427	−	0.805624i	$-0.701830\pi$
$733$	−32.0787			−1.18485			−0.592427	+	0.805624i	$0.701830\pi$
$734$		0			0
$735$	13.4962	+	9.80556i	0.497815	+	0.361683i
$736$		0			0
$737$	7.90514	+	1.68029i	0.291189	+	0.0618942i
$738$		0			0
$739$	0.232406	+	2.21120i	0.00854920	+	0.0813402i	0.997965	−	0.0637709i	$-0.0203127\pi$
$739$	0.232406	+	2.21120i	0.00854920	+	0.0813402i	−0.989415	+	0.145111i	$0.953646\pi$
$740$		0			0
$741$	−13.4032	−	41.2508i	−0.492379	−	1.51539i
$742$		0			0
$743$	22.3986			0.821724			0.410862	−	0.911698i	$-0.365228\pi$
$743$	22.3986			0.821724			0.410862	+	0.911698i	$0.365228\pi$
$744$		0			0
$745$	−3.64620	+	6.31540i	−0.133586	+	0.231378i
$746$		0			0
$747$	−1.78528	−	1.98275i	−0.0653198	−	0.0725450i
$748$		0			0
$749$	3.91964	−	4.35320i	0.143220	−	0.159062i
$750$		0			0
$751$	1.98895	−	18.9236i	0.0725777	−	0.690530i	−0.896377	−	0.443292i	$-0.853810\pi$
$751$	1.98895	−	18.9236i	0.0725777	−	0.690530i	0.968955	−	0.247238i	$-0.0795230\pi$
$752$		0			0
$753$	−10.3277	+	17.8882i	−0.376364	+	0.651881i
$754$		0			0
$755$	−2.31446	−	7.12317i	−0.0842318	−	0.259239i
$756$		0			0
$757$	−46.9153	−	20.8880i	−1.70517	−	0.759189i	−0.998675	−	0.0514679i	$-0.983610\pi$
$757$	−46.9153	−	20.8880i	−1.70517	−	0.759189i	−0.706492	−	0.707721i	$-0.749723\pi$
$758$		0			0
$759$	−3.55079	+	10.9282i	−0.128885	+	0.396668i
$760$		0			0
$761$	5.49231	+	9.51296i	0.199096	+	0.344845i	0.948236	−	0.317568i	$-0.102866\pi$
$761$	5.49231	+	9.51296i	0.199096	+	0.344845i	−0.749140	+	0.662412i	$0.769533\pi$
$762$		0			0
$763$	0.00864565	+	0.00384929i	0.000312994	+	0.000139354i
$764$		0			0
$765$	11.5672	+	8.40405i	0.418212	+	0.303849i
$766$		0			0
$767$	4.45054	−	42.3441i	0.160700	−	1.52896i
$768$		0			0
$769$	−17.5621	+	12.7596i	−0.633306	+	0.460124i	−0.857544	−	0.514410i	$-0.828011\pi$
$769$	−17.5621	+	12.7596i	−0.633306	+	0.460124i	0.224238	+	0.974534i	$0.428011\pi$
$770$		0			0
$771$	9.94106	−	4.42605i	0.358019	−	0.159400i
$772$		0			0
$773$	29.1573	−	21.1841i	1.04872	−	0.761937i	0.0767489	−	0.997050i	$-0.475546\pi$
$773$	29.1573	−	21.1841i	1.04872	−	0.761937i	0.971968	+	0.235113i	$0.0755460\pi$
$774$		0			0
$775$	−11.2419	−	12.4854i	−0.403822	−	0.448489i
$776$		0			0
$777$	1.34910	+	12.8359i	0.0483988	+	0.460484i
$778$		0			0
$779$	26.7220	+	46.2839i	0.957415	+	1.65829i
$780$		0			0
$781$	−11.3307	+	2.40840i	−0.405443	+	0.0861795i
$782$		0			0
$783$	17.5222	−	3.72447i	0.626194	−	0.133102i
$784$		0			0
$785$	3.04953	−	9.38549i	0.108842	−	0.334982i
$786$		0			0
$787$	−36.1443	−	7.68270i	−1.28840	−	0.273859i	−0.487749	−	0.872984i	$-0.662182\pi$
$787$	−36.1443	−	7.68270i	−1.28840	−	0.273859i	−0.800655	+	0.599125i	$0.795515\pi$
$788$		0			0
$789$	−16.4337	+	18.2514i	−0.585054	+	0.649768i
$790$		0			0
$791$	−15.5677	+	6.93120i	−0.553525	+	0.246445i
$792$		0			0
$793$	23.2380	−	13.5455i	0.825206	−	0.481014i
$794$		0			0
$795$	−21.9389	+	9.76783i	−0.778092	+	0.346429i
$796$		0			0
$797$	−19.2600	+	21.3904i	−0.682225	+	0.757687i	−0.980441	−	0.196811i	$-0.936942\pi$
$797$	−19.2600	+	21.3904i	−0.682225	+	0.757687i	0.298217	+	0.954498i	$0.403608\pi$
$798$		0			0
$799$	−60.6301	−	12.8873i	−2.14494	−	0.455921i
$800$		0			0
$801$	2.48929	−	7.66126i	0.0879548	−	0.270697i
$802$		0			0
$803$	−25.6174	+	5.44514i	−0.904017	+	0.192155i
$804$		0			0
$805$	3.07536	−	0.653687i	0.108392	−	0.0230395i
$806$		0			0
$807$	3.80976	+	6.59869i	0.134110	+	0.232285i
$808$		0			0
$809$	4.14148	+	39.4035i	0.145607	+	1.38535i	0.786436	+	0.617672i	$0.211924\pi$
$809$	4.14148	+	39.4035i	0.145607	+	1.38535i	−0.640829	+	0.767683i	$0.721409\pi$
$810$		0			0
$811$	−18.3137	−	20.3394i	−0.643081	−	0.714213i	0.330180	−	0.943918i	$-0.392891\pi$
$811$	−18.3137	−	20.3394i	−0.643081	−	0.714213i	−0.973260	+	0.229705i	$0.926224\pi$
$812$		0			0
$813$	−37.3378	+	27.1275i	−1.30949	+	0.951402i
$814$		0			0
$815$	−2.77741	+	1.23658i	−0.0972885	+	0.0433156i
$816$		0			0
$817$	21.3792	−	15.5329i	0.747964	−	0.543427i
$818$		0			0
$819$	−0.590327	+	5.61658i	−0.0206277	+	0.196259i
$820$		0			0
$821$	−5.86531	−	4.26140i	−0.204701	−	0.148724i	0.480712	−	0.876879i	$-0.340378\pi$
$821$	−5.86531	−	4.26140i	−0.204701	−	0.148724i	−0.685413	+	0.728155i	$0.740378\pi$
$822$		0			0
$823$	47.2969	+	21.0579i	1.64867	+	0.734033i	0.999643	−	0.0267358i	$-0.00851130\pi$
$823$	47.2969	+	21.0579i	1.64867	+	0.734033i	0.649023	+	0.760769i	$0.275178\pi$
$824$		0			0
$825$	−9.23979	−	16.0038i	−0.321688	−	0.557180i
$826$		0			0
$827$	2.75281	−	8.47228i	0.0957246	−	0.294610i	−0.891717	−	0.452593i	$-0.850499\pi$
$827$	2.75281	−	8.47228i	0.0957246	−	0.294610i	0.987442	+	0.157983i	$0.0504991\pi$
$828$		0			0
$829$	19.7872	+	8.80981i	0.687236	+	0.305977i	0.720486	−	0.693470i	$-0.243919\pi$
$829$	19.7872	+	8.80981i	0.687236	+	0.305977i	−0.0332494	+	0.999447i	$0.510586\pi$
$830$		0			0
$831$	−2.70900	−	8.33746i	−0.0939743	−	0.289223i
$832$		0			0
$833$	20.2638	−	35.0980i	0.702101	−	1.21607i
$834$		0			0
$835$	1.37072	−	13.0415i	0.0474357	−	0.451320i
$836$		0			0
$837$	13.0224	−	14.4628i	0.450119	−	0.499908i
$838$		0			0
$839$	−23.8292	−	26.4650i	−0.822675	−	0.913673i	0.174807	−	0.984603i	$-0.444070\pi$
$839$	−23.8292	−	26.4650i	−0.822675	−	0.913673i	−0.997481	+	0.0709300i	$0.977403\pi$
$840$		0			0
$841$	0.695545	−	1.20472i	0.0239843	−	0.0415420i
$842$		0			0
$843$	−59.4484			−2.04751
$844$		0			0
$845$	0.505046	+	1.55437i	0.0173741	+	0.0534720i
$846$		0			0
$847$	0.247461	+	2.35443i	0.00850284	+	0.0808992i
$848$		0			0
$849$	18.9550	+	4.02901i	0.650534	+	0.138275i
$850$		0			0
$851$	−7.63159	−	5.54467i	−0.261607	−	0.190069i
$852$		0			0
$853$	40.1774			1.37565			0.687823	−	0.725878i	$-0.258566\pi$
$853$	40.1774			1.37565			0.687823	+	0.725878i	$0.258566\pi$
$854$		0			0
$855$	−11.8296			−0.404565
$856$		0			0
$857$	−38.5704	−	28.0230i	−1.31754	−	0.957249i	−0.999959	−	0.00901774i	$-0.997130\pi$
$857$	−38.5704	−	28.0230i	−1.31754	−	0.957249i	−0.317581	−	0.948231i	$-0.602870\pi$
$858$		0			0
$859$	36.8929	+	7.84183i	1.25877	+	0.267560i	0.788540	−	0.614984i	$-0.210838\pi$
$859$	36.8929	+	7.84183i	1.25877	+	0.267560i	0.470230	+	0.882544i	$0.344171\pi$
$860$		0			0
$861$	−2.32145	−	22.0871i	−0.0791149	−	0.752728i
$862$		0			0
$863$	11.9273	+	36.7084i	0.406009	+	1.24957i	0.920050	+	0.391801i	$0.128148\pi$
$863$	11.9273	+	36.7084i	0.406009	+	1.24957i	−0.514041	+	0.857766i	$0.671852\pi$
$864$		0			0
$865$	−17.2927			−0.587969
$866$		0			0
$867$	37.6617	−	65.2321i	1.27906	−	2.21540i
$868$		0			0
$869$	3.30521	+	3.67081i	0.112122	+	0.124524i
$870$		0			0
$871$	−6.19973	+	6.88549i	−0.210070	+	0.233306i
$872$		0			0
$873$	−0.798505	+	7.59727i	−0.0270253	+	0.257129i
$874$		0			0
$875$	−6.82326	+	11.8182i	−0.230668	+	0.399529i
$876$		0			0
$877$	7.34791	+	22.6145i	0.248121	+	0.763639i	0.995107	+	0.0987991i	$0.0315001\pi$
$877$	7.34791	+	22.6145i	0.248121	+	0.763639i	−0.746986	+	0.664840i	$0.768500\pi$
$878$		0			0
$879$	20.9932	+	9.34676i	0.708082	+	0.315259i
$880$		0			0
$881$	−4.75213	+	14.6256i	−0.160103	+	0.492748i	−0.998642	−	0.0520944i	$-0.983410\pi$
$881$	−4.75213	+	14.6256i	−0.160103	+	0.492748i	0.838539	+	0.544842i	$0.183410\pi$
$882$		0			0
$883$	−23.4125	−	40.5517i	−0.787895	−	1.36467i	−0.927255	−	0.374432i	$-0.877838\pi$
$883$	−23.4125	−	40.5517i	−0.787895	−	1.36467i	0.139360	−	0.990242i	$-0.455495\pi$
$884$		0			0
$885$	−33.8570	−	15.0741i	−1.13809	−	0.506710i
$886$		0			0
$887$	−0.598216	−	0.434630i	−0.0200861	−	0.0145934i	0.577697	−	0.816251i	$-0.303952\pi$
$887$	−0.598216	−	0.434630i	−0.0200861	−	0.0145934i	−0.597783	+	0.801658i	$0.703952\pi$
$888$		0			0
$889$	−1.69195	+	16.0978i	−0.0567462	+	0.539904i
$890$		0			0
$891$	27.2986	−	19.8336i	0.914536	−	0.664449i
$892$		0			0
$893$	46.8506	−	20.8592i	1.56780	−	0.698028i
$894$		0			0
$895$	14.2997	−	10.3894i	0.477987	−	0.347278i
$896$		0			0
$897$	−8.81474	−	9.78977i	−0.294316	−	0.326871i
$898$		0			0
$899$	3.13529	+	29.8303i	0.104568	+	0.994895i
$900$		0			0
$901$	29.1711	+	50.5258i	0.971830	+	1.68326i
$902$		0			0
$903$	−10.7415	+	2.28317i	−0.357454	+	0.0759793i
$904$		0			0
$905$	15.9217	−	3.38427i	0.529256	−	0.112497i
$906$		0			0
$907$	−0.633663	+	1.95021i	−0.0210404	+	0.0647558i	−0.961025	−	0.276460i	$-0.910839\pi$
$907$	−0.633663	+	1.95021i	−0.0210404	+	0.0647558i	0.939985	+	0.341216i	$0.110839\pi$
$908$		0			0
$909$	−6.00649	−	1.27672i	−0.199223	−	0.0423461i
$910$		0			0
$911$	16.7541	−	18.6073i	0.555088	−	0.616487i	−0.398659	−	0.917099i	$-0.630524\pi$
$911$	16.7541	−	18.6073i	0.555088	−	0.616487i	0.953747	+	0.300612i	$0.0971909\pi$
$912$		0			0
$913$	−5.34857	+	2.38134i	−0.177012	+	0.0788108i
$914$		0			0
$915$	−4.96287	−	22.8808i	−0.164067	−	0.756416i
$916$		0			0
$917$	7.52079	−	3.34847i	0.248358	−	0.110576i
$918$		0			0
$919$	26.5136	−	29.4463i	0.874601	−	0.971343i	−0.125183	−	0.992134i	$-0.539952\pi$
$919$	26.5136	−	29.4463i	0.874601	−	0.971343i	0.999784	+	0.0207906i	$0.00661832\pi$
$920$		0			0
$921$	−52.1875	−	11.0928i	−1.71964	−	0.365520i
$922$		0			0
$923$	4.10383	−	12.6303i	0.135079	−	0.415731i
$924$		0			0
$925$	14.8392	−	3.15418i	0.487911	−	0.103709i
$926$		0			0
$927$	16.7948	−	3.56985i	0.551615	−	0.117249i
$928$		0			0
$929$	7.28884	+	12.6246i	0.239139	+	0.414201i	0.960468	−	0.278392i	$-0.0898015\pi$
$929$	7.28884	+	12.6246i	0.239139	+	0.414201i	−0.721328	+	0.692593i	$0.756468\pi$
$930$		0			0
$931$	3.50500	+	33.3478i	0.114872	+	1.09293i
$932$		0			0
$933$	5.46736	+	6.07211i	0.178993	+	0.198792i
$934$		0			0
$935$	25.3829	−	18.4417i	0.830108	−	0.603109i
$936$		0			0
$937$	−20.1482	+	8.97055i	−0.658213	+	0.293055i	−0.708533	−	0.705678i	$-0.750643\pi$
$937$	−20.1482	+	8.97055i	−0.658213	+	0.293055i	0.0503201	+	0.998733i	$0.483976\pi$
$938$		0			0
$939$	−15.1254	+	10.9893i	−0.493600	+	0.358621i
$940$		0			0
$941$	−0.583472	+	5.55137i	−0.0190206	+	0.180969i	−0.999907	−	0.0136103i	$-0.995668\pi$
$941$	−0.583472	+	5.55137i	−0.0190206	+	0.180969i	0.980887	+	0.194580i	$0.0623343\pi$
$942$		0			0
$943$	13.1320	+	9.54092i	0.427635	+	0.310695i
$944$		0			0
$945$	−5.35082	−	2.38234i	−0.174062	−	0.0774975i
$946$		0			0
$947$	−24.8202	−	42.9899i	−0.806549	−	1.39698i	−0.915241	−	0.402908i	$-0.868000\pi$
$947$	−24.8202	−	42.9899i	−0.806549	−	1.39698i	0.108692	−	0.994075i	$-0.465334\pi$
$948$		0			0
$949$	9.27832	−	28.5557i	0.301187	−	0.926958i
$950$		0			0
$951$	57.6420	+	25.6639i	1.86917	+	0.832207i
$952$		0			0
$953$	−8.69025	−	26.7459i	−0.281505	−	0.866383i	−0.987425	−	0.158091i	$-0.949466\pi$
$953$	−8.69025	−	26.7459i	−0.281505	−	0.866383i	0.705920	−	0.708292i	$-0.250534\pi$
$954$		0			0
$955$	−3.31368	+	5.73946i	−0.107228	+	0.185725i
$956$		0			0
$957$	−3.44858	+	32.8110i	−0.111477	+	1.06063i
$958$		0			0
$959$	11.2010	−	12.4399i	0.361698	−	0.401707i
$960$		0			0
$961$	1.06150	+	1.17892i	0.0342420	+	0.0380296i
$962$		0			0
$963$	−3.34701	+	5.79720i	−0.107856	+	0.186812i
$964$		0			0
$965$	−10.0916			−0.324860
$966$		0			0
$967$	−9.39402	−	28.9118i	−0.302091	−	0.929742i	−0.980747	−	0.195285i	$-0.937437\pi$
$967$	−9.39402	−	28.9118i	−0.302091	−	0.929742i	0.678655	−	0.734457i	$-0.262563\pi$
$968$		0			0
$969$	9.58735	+	91.2175i	0.307990	+	2.93033i
$970$		0			0
$971$	0.184021	+	0.0391150i	0.00590553	+	0.00125526i	0.210864	−	0.977516i	$-0.432372\pi$
$971$	0.184021	+	0.0391150i	0.00590553	+	0.00125526i	−0.204958	+	0.978771i	$0.565706\pi$
$972$		0			0
$973$	−20.4963	−	14.8914i	−0.657082	−	0.477398i
$974$		0			0
$975$	21.1860			0.678495
$976$		0			0
$977$	30.0141			0.960236			0.480118	−	0.877204i	$-0.340594\pi$
$977$	30.0141			0.960236			0.480118	+	0.877204i	$0.340594\pi$
$978$		0			0
$979$	−14.3009	−	10.3902i	−0.457060	−	0.332073i
$980$		0			0
$981$	−0.0105785	−	0.00224853i	−0.000337746	−	7.17901e-5i
$982$		0			0
$983$	−3.74751	−	35.6552i	−0.119527	−	1.13722i	−0.875702	−	0.482853i	$-0.839601\pi$
$983$	−3.74751	−	35.6552i	−0.119527	−	1.13722i	0.756175	−	0.654370i	$-0.227066\pi$
$984$		0			0
$985$	−9.84613	−	30.3033i	−0.313724	−	0.965542i
$986$		0			0
$987$	−21.3114			−0.678348
$988$		0			0
$989$	4.01307	−	6.95084i	0.127608	−	0.221024i
$990$		0			0
$991$	−7.17386	−	7.96738i	−0.227885	−	0.253092i	0.618349	−	0.785904i	$-0.287802\pi$
$991$	−7.17386	−	7.96738i	−0.227885	−	0.253092i	−0.846234	+	0.532812i	$0.821135\pi$
$992$		0			0
$993$	25.2575	−	28.0513i	0.801522	−	0.890180i
$994$		0			0
$995$	−3.20423	+	30.4862i	−0.101581	+	0.966478i
$996$		0			0
$997$	−18.8770	+	32.6960i	−0.597841	+	1.03549i	0.395298	+	0.918553i	$0.370641\pi$
$997$	−18.8770	+	32.6960i	−0.597841	+	1.03549i	−0.993139	+	0.116939i	$0.962692\pi$
$998$		0			0
$999$	5.43049	+	16.7133i	0.171813	+	0.528786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	976.2.bw.c.849.3		32
4.3	odd	2		61.2.i.a.56.4	yes	32
12.11	even	2		549.2.bl.b.361.1		32
61.12	even	15	inner	976.2.bw.c.561.3		32
244.167	odd	30		3721.2.a.l.1.3		16
244.195	odd	30		61.2.i.a.12.4	✓	32
244.199	odd	30		3721.2.a.j.1.14		16
732.683	even	30		549.2.bl.b.73.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.12.4	✓	32	244.195	odd	30
61.2.i.a.56.4	yes	32	4.3	odd	2
549.2.bl.b.73.1		32	732.683	even	30
549.2.bl.b.361.1		32	12.11	even	2
976.2.bw.c.561.3		32	61.12	even	15	inner
976.2.bw.c.849.3		32	1.1	even	1	trivial
3721.2.a.j.1.14		16	244.199	odd	30
3721.2.a.l.1.3		16	244.167	odd	30

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:	\( N \)	\(=\)	\( 976 = 2^{4} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	976.bw (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.69101 + 1.22859i) q^{3} +(1.40283 + 0.298182i) q^{5} +(-0.125217 - 1.19136i) q^{7} +(0.423022 + 1.30193i) q^{9} +O(q^{10})\)	\(q+(1.69101 + 1.22859i) q^{3} +(1.40283 + 0.298182i) q^{5} +(-0.125217 - 1.19136i) q^{7} +(0.423022 + 1.30193i) q^{9} +3.00395 q^{11} +(-1.72195 + 2.98250i) q^{13} +(2.00586 + 2.22773i) q^{15} +(4.87302 - 5.41204i) q^{17} +(-0.629830 + 5.99243i) q^{19} +(1.25194 - 2.16843i) q^{21} +(0.565515 + 1.74048i) q^{23} +(-2.68870 - 1.19708i) q^{25} +(1.05352 - 3.24240i) q^{27} +(2.62721 + 4.55046i) q^{29} +(5.21493 + 2.32184i) q^{31} +(5.07970 + 3.69062i) q^{33} +(0.179583 - 1.70861i) q^{35} +(-4.17017 + 3.02980i) q^{37} +(-6.57609 + 2.92786i) q^{39} +(7.17576 - 5.21349i) q^{41} +(-2.93465 - 3.25925i) q^{43} +(0.205219 + 1.95252i) q^{45} +(-4.25565 - 7.37101i) q^{47} +(5.44338 - 1.15703i) q^{49} +(14.8895 - 3.16486i) q^{51} +(-2.47558 + 7.61906i) q^{53} +(4.21405 + 0.895724i) q^{55} +(-8.42728 + 9.35944i) q^{57} +(-11.2943 + 5.02854i) q^{59} +(-6.78003 - 3.87700i) q^{61} +(1.49809 - 0.666993i) q^{63} +(-3.30493 + 3.67050i) q^{65} +(2.63158 + 0.559359i) q^{67} +(-1.18204 + 3.63794i) q^{69} +(-3.77191 + 0.801745i) q^{71} +(-8.52788 + 1.81266i) q^{73} +(-3.07588 - 5.32757i) q^{75} +(-0.376145 - 3.57878i) q^{77} +(1.10029 + 1.22199i) q^{79} +(9.08754 - 6.60249i) q^{81} +(-1.78051 + 0.792734i) q^{83} +(8.44982 - 6.13915i) q^{85} +(-1.14801 + 10.9226i) q^{87} +(-4.76070 - 3.45885i) q^{89} +(3.76884 + 1.67800i) q^{91} +(5.96589 + 10.3332i) q^{93} +(-2.67038 + 8.21859i) q^{95} +(5.09792 + 2.26974i) q^{97} +(1.27074 + 3.91093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9}+O(q^{10}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39} + 11 q^{41} - 40 q^{43} + 12 q^{45} - 40 q^{47} + q^{49} + 9 q^{51} + 17 q^{53} + 60 q^{55} - 38 q^{57} + 11 q^{59} - 55 q^{61} + 58 q^{63} + 59 q^{65} + 13 q^{67} - 32 q^{69} - 63 q^{71} - 46 q^{73} - q^{75} - 31 q^{77} + 49 q^{79} + 48 q^{81} - 39 q^{83} + 21 q^{85} - 17 q^{87} + 32 q^{89} - 70 q^{91} + 67 q^{93} - 47 q^{95} + 37 q^{97} + 31 q^{99}+O(q^{100}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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