LMFDB - Embedded newform 784.2.u.d.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(113,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("784.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.u (of order $7$, degree $6$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 37 x^{16} + 557 x^{14} + 4495 x^{12} + 21331 x^{10} + 60904 x^{8} + 101893 x^{6} + 91665 x^{4} + \cdots + 5103 $ x^18 + 37x^16 + 557x^14 + 4495x^12 + 21331x^10 + 60904x^8 + 101893x^6 + 91665x^4 + 36855x^2 + 5103
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			113.3
Root			$-3.48640i$ of defining polynomial
Character	$\chi$	$=$	784.113
Dual form			784.2.u.d.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91682 - 2.40361i) q^{3} +(-1.88629 + 2.36534i) q^{5} +(-2.31779 - 1.27588i) q^{7} +(-1.43560 - 6.28979i) q^{9} +O(q^{10})$	\(q+(1.91682 - 2.40361i) q^{3} +(-1.88629 + 2.36534i) q^{5} +(-2.31779 - 1.27588i) q^{7} +(-1.43560 - 6.28979i) q^{9} +(0.673210 - 2.94953i) q^{11} +(0.532118 - 2.33136i) q^{13} +(2.06968 + 9.06784i) q^{15} +(0.579338 - 0.278994i) q^{17} -0.629295 q^{19} +(-7.50949 + 3.12544i) q^{21} +(-8.46635 - 4.07718i) q^{23} +(-0.924113 - 4.04880i) q^{25} +(-9.56038 - 4.60404i) q^{27} +(-3.84228 + 1.85034i) q^{29} +2.51075 q^{31} +(-5.79910 - 7.27184i) q^{33} +(7.38991 - 3.07567i) q^{35} +(5.78775 - 2.78724i) q^{37} +(-4.58372 - 5.74780i) q^{39} +(1.29087 - 1.61870i) q^{41} +(-0.845798 - 1.06060i) q^{43} +(17.5855 + 8.46871i) q^{45} +(0.235928 - 1.03367i) q^{47} +(3.74427 + 5.91443i) q^{49} +(0.439890 - 1.92728i) q^{51} +(-4.22215 - 2.03328i) q^{53} +(5.70676 + 7.15605i) q^{55} +(-1.20624 + 1.51258i) q^{57} +(-1.96057 - 2.45848i) q^{59} +(4.86234 - 2.34158i) q^{61} +(-4.69759 + 16.4101i) q^{63} +(4.51073 + 5.65627i) q^{65} -6.32287 q^{67} +(-26.0284 + 12.5346i) q^{69} +(12.7586 + 6.14419i) q^{71} +(-0.925455 - 4.05468i) q^{73} +(-11.5031 - 5.53961i) q^{75} +(-5.32360 + 5.97744i) q^{77} +11.2211 q^{79} +(-11.9539 + 5.75669i) q^{81} +(1.69664 + 7.43348i) q^{83} +(-0.432885 + 1.89659i) q^{85} +(-2.91744 + 12.7821i) q^{87} +(-0.265089 - 1.16143i) q^{89} +(-4.20787 + 4.72468i) q^{91} +(4.81265 - 6.03488i) q^{93} +(1.18704 - 1.48850i) q^{95} +16.3992 q^{97} -19.5184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{3} + q^{7} - 10 q^{9}+O(q^{10}) $ 18 * q + 5 * q^3 + q^7 - 10 * q^9	$ 18 q + 5 q^{3} + q^{7} - 10 q^{9} - 7 q^{11} - 10 q^{13} - 7 q^{15} + q^{17} + 44 q^{19} - 5 q^{21} - 21 q^{23} + q^{25} - 10 q^{27} + 11 q^{29} + 24 q^{31} - 14 q^{33} + 21 q^{35} - 13 q^{37} + 3 q^{39} + 8 q^{41} + 24 q^{43} + 98 q^{45} - 40 q^{47} - 43 q^{49} - 36 q^{51} + 10 q^{53} - 49 q^{55} + 19 q^{57} - 13 q^{59} + 27 q^{61} - 41 q^{63} + 86 q^{67} - 91 q^{69} + 5 q^{73} + 3 q^{75} - 14 q^{77} + 66 q^{79} - 2 q^{81} - 55 q^{83} - 49 q^{85} + 110 q^{87} + 62 q^{89} - 39 q^{91} + 46 q^{93} + 7 q^{95} - 32 q^{97} - 14 q^{99}+O(q^{100}) $ 18 * q + 5 * q^3 + q^7 - 10 * q^9 - 7 * q^11 - 10 * q^13 - 7 * q^15 + q^17 + 44 * q^19 - 5 * q^21 - 21 * q^23 + q^25 - 10 * q^27 + 11 * q^29 + 24 * q^31 - 14 * q^33 + 21 * q^35 - 13 * q^37 + 3 * q^39 + 8 * q^41 + 24 * q^43 + 98 * q^45 - 40 * q^47 - 43 * q^49 - 36 * q^51 + 10 * q^53 - 49 * q^55 + 19 * q^57 - 13 * q^59 + 27 * q^61 - 41 * q^63 + 86 * q^67 - 91 * q^69 + 5 * q^73 + 3 * q^75 - 14 * q^77 + 66 * q^79 - 2 * q^81 - 55 * q^83 - 49 * q^85 + 110 * q^87 + 62 * q^89 - 39 * q^91 + 46 * q^93 + 7 * q^95 - 32 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{7}\right)$

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
$3$	1.91682	−	2.40361i	1.10668	−	1.38773i	0.193040	−	0.981191i	$-0.438165\pi$
$3$	1.91682	−	2.40361i	1.10668	−	1.38773i	0.913635	−	0.406536i	$-0.133263\pi$
$4$		0			0
$5$	−1.88629	+	2.36534i	−0.843576	+	1.05781i	0.153989	+	0.988073i	$0.450788\pi$
$5$	−1.88629	+	2.36534i	−0.843576	+	1.05781i	−0.997565	+	0.0697386i	$0.977783\pi$
$6$		0			0
$7$	−2.31779	−	1.27588i	−0.876041	−	0.482237i
$7$	−2.31779	−	1.27588i	−0.876041	−	0.482237i
$8$		0			0
$9$	−1.43560	−	6.28979i	−0.478535	−	2.09660i
$10$		0			0
$11$	0.673210	−	2.94953i	0.202981	−	0.889316i	−0.766129	−	0.642687i	$-0.777820\pi$
$11$	0.673210	−	2.94953i	0.202981	−	0.889316i	0.969110	−	0.246630i	$-0.0793231\pi$
$12$		0			0
$13$	0.532118	−	2.33136i	0.147583	−	0.646603i	−0.845970	−	0.533231i	$-0.820978\pi$
$13$	0.532118	−	2.33136i	0.147583	−	0.646603i	0.993553	−	0.113372i	$-0.0361653\pi$
$14$		0			0
$15$	2.06968	+	9.06784i	0.534388	+	2.34131i
$16$		0			0
$17$	0.579338	−	0.278994i	0.140510	−	0.0676661i	−0.362308	−	0.932059i	$-0.618011\pi$
$17$	0.579338	−	0.278994i	0.140510	−	0.0676661i	0.502818	+	0.864393i	$0.332297\pi$
$18$		0			0
$19$	−0.629295			−0.144370			−0.0721851	−	0.997391i	$-0.522997\pi$
$19$	−0.629295			−0.144370			−0.0721851	+	0.997391i	$0.522997\pi$
$20$		0			0
$21$	−7.50949	+	3.12544i	−1.63871	+	0.682026i
$22$		0			0
$23$	−8.46635	−	4.07718i	−1.76536	−	0.850150i	−0.969662	−	0.244451i	$-0.921392\pi$
$23$	−8.46635	−	4.07718i	−1.76536	−	0.850150i	−0.795694	−	0.605699i	$-0.792893\pi$
$24$		0			0
$25$	−0.924113	−	4.04880i	−0.184823	−	0.809761i
$26$		0			0
$27$	−9.56038	−	4.60404i	−1.83990	−	0.886047i
$28$		0			0
$29$	−3.84228	+	1.85034i	−0.713493	+	0.343600i	−0.755168	−	0.655531i	$-0.772445\pi$
$29$	−3.84228	+	1.85034i	−0.713493	+	0.343600i	0.0416749	+	0.999131i	$0.486731\pi$
$30$		0			0
$31$	2.51075			0.450944			0.225472	−	0.974250i	$-0.427608\pi$
$31$	2.51075			0.450944			0.225472	+	0.974250i	$0.427608\pi$
$32$		0			0
$33$	−5.79910	−	7.27184i	−1.00949	−	1.26587i
$34$		0			0
$35$	7.38991	−	3.07567i	1.24912	−	0.519883i
$36$		0			0
$37$	5.78775	−	2.78724i	0.951501	−	0.458219i	0.107289	−	0.994228i	$-0.465783\pi$
$37$	5.78775	−	2.78724i	0.951501	−	0.458219i	0.844212	+	0.536009i	$0.180069\pi$
$38$		0			0
$39$	−4.58372	−	5.74780i	−0.733982	−	0.920385i
$40$		0			0
$41$	1.29087	−	1.61870i	0.201600	−	0.252798i	−0.670747	−	0.741687i	$-0.734026\pi$
$41$	1.29087	−	1.61870i	0.201600	−	0.252798i	0.872346	+	0.488889i	$0.162598\pi$
$42$		0			0
$43$	−0.845798	−	1.06060i	−0.128983	−	0.161740i	0.713146	−	0.701015i	$-0.247270\pi$
$43$	−0.845798	−	1.06060i	−0.128983	−	0.161740i	−0.842129	+	0.539276i	$0.818698\pi$
$44$		0			0
$45$	17.5855	+	8.46871i	2.62149	+	1.26244i
$46$		0			0
$47$	0.235928	−	1.03367i	0.0344137	−	0.150776i	−0.954802	−	0.297243i	$-0.903933\pi$
$47$	0.235928	−	1.03367i	0.0344137	−	0.150776i	0.989216	+	0.146467i	$0.0467901\pi$
$48$		0			0
$49$	3.74427	+	5.91443i	0.534896	+	0.844918i
$50$		0			0
$51$	0.439890	−	1.92728i	0.0615969	−	0.269874i
$52$		0			0
$53$	−4.22215	−	2.03328i	−0.579957	−	0.279293i	0.120818	−	0.992675i	$-0.461448\pi$
$53$	−4.22215	−	2.03328i	−0.579957	−	0.279293i	−0.700775	+	0.713382i	$0.747162\pi$
$54$		0			0
$55$	5.70676	+	7.15605i	0.769499	+	0.964921i
$56$		0			0
$57$	−1.20624	+	1.51258i	−0.159771	+	0.200346i
$58$		0			0
$59$	−1.96057	−	2.45848i	−0.255245	−	0.320067i	0.637655	−	0.770322i	$-0.279905\pi$
$59$	−1.96057	−	2.45848i	−0.255245	−	0.320067i	−0.892900	+	0.450255i	$0.851333\pi$
$60$		0			0
$61$	4.86234	−	2.34158i	0.622559	−	0.299809i	−0.0958862	−	0.995392i	$-0.530568\pi$
$61$	4.86234	−	2.34158i	0.622559	−	0.299809i	0.718445	+	0.695584i	$0.244854\pi$
$62$		0			0
$63$	−4.69759	+	16.4101i	−0.591840	+	2.06747i
$64$		0			0
$65$	4.51073	+	5.65627i	0.559487	+	0.701574i
$66$		0			0
$67$	−6.32287			−0.772462			−0.386231	−	0.922402i	$-0.626223\pi$
$67$	−6.32287			−0.772462			−0.386231	+	0.922402i	$0.626223\pi$
$68$		0			0
$69$	−26.0284	+	12.5346i	−3.13345	+	1.50899i
$70$		0			0
$71$	12.7586	+	6.14419i	1.51416	+	0.729182i	0.992301	−	0.123849i	$-0.0395239\pi$
$71$	12.7586	+	6.14419i	1.51416	+	0.729182i	0.521860	+	0.853031i	$0.325238\pi$
$72$		0			0
$73$	−0.925455	−	4.05468i	−0.108316	−	0.474565i	−0.999770	−	0.0214527i	$-0.993171\pi$
$73$	−0.925455	−	4.05468i	−0.108316	−	0.474565i	0.891454	−	0.453112i	$-0.149686\pi$
$74$		0			0
$75$	−11.5031	−	5.53961i	−1.32827	−	0.639659i
$76$		0			0
$77$	−5.32360	+	5.97744i	−0.606680	+	0.681193i
$78$		0			0
$79$	11.2211			1.26247			0.631236	−	0.775590i	$-0.282548\pi$
$79$	11.2211			1.26247			0.631236	+	0.775590i	$0.282548\pi$
$80$		0			0
$81$	−11.9539	+	5.75669i	−1.32821	+	0.639632i
$82$		0			0
$83$	1.69664	+	7.43348i	0.186231	+	0.815930i	0.978581	+	0.205864i	$0.0660003\pi$
$83$	1.69664	+	7.43348i	0.186231	+	0.815930i	−0.792350	+	0.610067i	$0.791143\pi$
$84$		0			0
$85$	−0.432885	+	1.89659i	−0.0469530	+	0.205715i
$86$		0			0
$87$	−2.91744	+	12.7821i	−0.312782	+	1.37039i
$88$		0			0
$89$	−0.265089	−	1.16143i	−0.0280994	−	0.123112i	0.958933	−	0.283633i	$-0.0915396\pi$
$89$	−0.265089	−	1.16143i	−0.0280994	−	0.123112i	−0.987032	+	0.160521i	$0.948683\pi$
$90$		0			0
$91$	−4.20787	+	4.72468i	−0.441105	+	0.495281i
$92$		0			0
$93$	4.81265	−	6.03488i	0.499049	−	0.625787i
$94$		0			0
$95$	1.18704	−	1.48850i	0.121787	−	0.152716i
$96$		0			0
$97$	16.3992			1.66509			0.832543	−	0.553961i	$-0.186884\pi$
$97$	16.3992			1.66509			0.832543	+	0.553961i	$0.186884\pi$
$98$		0			0
$99$	−19.5184			−1.96167
$100$		0			0
$101$	8.95938	−	11.2347i	0.891492	−	1.11790i	−0.100915	−	0.994895i	$-0.532177\pi$
$101$	8.95938	−	11.2347i	0.891492	−	1.11790i	0.992407	−	0.123000i	$-0.0392517\pi$
$102$		0			0
$103$	10.1830	−	12.7691i	1.00336	−	1.25817i	0.0374497	−	0.999299i	$-0.488077\pi$
$103$	10.1830	−	12.7691i	1.00336	−	1.25817i	0.965911	−	0.258876i	$-0.0833520\pi$
$104$		0			0
$105$	6.77240	−	23.6580i	0.660918	−	2.30878i
$106$		0			0
$107$	3.71249	+	16.2655i	0.358900	+	1.57244i	0.755939	+	0.654642i	$0.227180\pi$
$107$	3.71249	+	16.2655i	0.358900	+	1.57244i	−0.397039	+	0.917802i	$0.629962\pi$
$108$		0			0
$109$	−0.370529	+	1.62339i	−0.0354902	+	0.155493i	−0.989568	−	0.144066i	$-0.953982\pi$
$109$	−0.370529	+	1.62339i	−0.0354902	+	0.155493i	0.954078	+	0.299559i	$0.0968394\pi$
$110$		0			0
$111$	4.39463	−	19.2541i	0.417120	−	1.82752i
$112$		0			0
$113$	2.05961	+	9.02372i	0.193751	+	0.848880i	0.974563	+	0.224114i	$0.0719487\pi$
$113$	2.05961	+	9.02372i	0.193751	+	0.848880i	−0.780812	+	0.624767i	$0.785194\pi$
$114$		0			0
$115$	25.6139	−	12.3350i	2.38851	−	1.15025i
$116$		0			0
$117$	−15.4277			−1.42629
$118$		0			0
$119$	−1.69874	−	0.0925151i	−0.155724	−	0.00848085i
$120$		0			0
$121$	1.66416	+	0.801415i	0.151287	+	0.0728559i
$122$		0			0
$123$	−1.41636	−	6.20549i	−0.127709	−	0.559530i
$124$		0			0
$125$	−2.30893	−	1.11192i	−0.206517	−	0.0994533i
$126$		0			0
$127$	−12.0689	+	5.81208i	−1.07094	+	0.515739i	−0.884410	−	0.466710i	$-0.845439\pi$
$127$	−12.0689	+	5.81208i	−1.07094	+	0.515739i	−0.186532	+	0.982449i	$0.559725\pi$
$128$		0			0
$129$	−4.17051			−0.367193
$130$		0			0
$131$	−12.1193	−	15.1971i	−1.05887	−	1.32778i	−0.942364	−	0.334588i	$-0.891403\pi$
$131$	−12.1193	−	15.1971i	−1.05887	−	1.32778i	−0.116503	−	0.993190i	$-0.537169\pi$
$132$		0			0
$133$	1.45857	+	0.802904i	0.126474	+	0.0696206i
$134$		0			0
$135$	28.9238	−	13.9290i	2.48936	−	1.19881i
$136$		0			0
$137$	4.91692	+	6.16562i	0.420081	+	0.526764i	0.946172	−	0.323663i	$-0.104915\pi$
$137$	4.91692	+	6.16562i	0.420081	+	0.526764i	−0.526092	+	0.850428i	$0.676343\pi$
$138$		0			0
$139$	0.182803	−	0.229228i	0.0155052	−	0.0194428i	−0.774018	−	0.633163i	$-0.781756\pi$
$139$	0.182803	−	0.229228i	0.0155052	−	0.0194428i	0.789524	+	0.613720i	$0.210328\pi$
$140$		0			0
$141$	−2.03231	−	2.54844i	−0.171151	−	0.214617i
$142$		0			0
$143$	−6.51819	−	3.13899i	−0.545078	−	0.262496i
$144$		0			0
$145$	2.87098	−	12.5786i	0.238422	−	1.04459i
$146$		0			0
$147$	21.3931	+	2.33710i	1.76447	+	0.192761i
$148$		0			0
$149$	1.57842	−	6.91551i	0.129309	−	0.566540i	−0.868213	−	0.496191i	$-0.834732\pi$
$149$	1.57842	−	6.91551i	0.129309	−	0.566540i	0.997522	−	0.0703492i	$-0.0224114\pi$
$150$		0			0
$151$	10.6287	+	5.11852i	0.864953	+	0.416539i	0.813106	−	0.582116i	$-0.197775\pi$
$151$	10.6287	+	5.11852i	0.864953	+	0.416539i	0.0518469	+	0.998655i	$0.483489\pi$
$152$		0			0
$153$	−2.58652	−	3.24339i	−0.209107	−	0.262212i
$154$		0			0
$155$	−4.73601	+	5.93877i	−0.380406	+	0.477014i
$156$		0			0
$157$	−8.20330	−	10.2866i	−0.654695	−	0.820961i	0.338059	−	0.941125i	$-0.390230\pi$
$157$	−8.20330	−	10.2866i	−0.654695	−	0.820961i	−0.992754	+	0.120164i	$0.961658\pi$
$158$		0			0
$159$	−12.9803	+	6.25099i	−1.02941	+	0.495736i
$160$		0			0
$161$	14.4212	+	20.2521i	1.13655	+	1.59609i
$162$		0			0
$163$	−8.36144	−	10.4849i	−0.654918	−	0.821241i	0.337861	−	0.941196i	$-0.390297\pi$
$163$	−8.36144	−	10.4849i	−0.654918	−	0.821241i	−0.992779	+	0.119954i	$0.961725\pi$
$164$		0			0
$165$	28.1392			2.19063
$166$		0			0
$167$	−8.54332	+	4.11425i	−0.661102	+	0.318370i	−0.734179	−	0.678956i	$-0.762433\pi$
$167$	−8.54332	+	4.11425i	−0.661102	+	0.318370i	0.0730766	+	0.997326i	$0.476718\pi$
$168$		0			0
$169$	6.56050	+	3.15937i	0.504654	+	0.243028i
$170$		0			0
$171$	0.903419	+	3.95814i	0.0690861	+	0.302686i
$172$		0			0
$173$	0.948259	+	0.456658i	0.0720948	+	0.0347190i	0.469584	−	0.882888i	$-0.344404\pi$
$173$	0.948259	+	0.456658i	0.0720948	+	0.0347190i	−0.397489	+	0.917607i	$0.630118\pi$
$174$		0			0
$175$	−3.02388	+	10.5633i	−0.228584	+	0.798512i
$176$		0			0
$177$	−9.66730			−0.726639
$178$		0			0
$179$	−9.18269	+	4.42215i	−0.686347	+	0.330527i	−0.744350	−	0.667789i	$-0.767241\pi$
$179$	−9.18269	+	4.42215i	−0.686347	+	0.330527i	0.0580037	+	0.998316i	$0.481526\pi$
$180$		0			0
$181$	−3.08835	−	13.5309i	−0.229555	−	1.00575i	−0.950004	−	0.312238i	$-0.898921\pi$
$181$	−3.08835	−	13.5309i	−0.229555	−	1.00575i	0.720449	−	0.693508i	$-0.243936\pi$
$182$		0			0
$183$	3.69197	−	16.1756i	0.272918	−	1.19573i
$184$		0			0
$185$	−4.32465	+	18.9475i	−0.317955	+	1.39305i
$186$		0			0
$187$	−0.432885	−	1.89659i	−0.0316557	−	0.138693i
$188$		0			0
$189$	16.2847	+	22.8690i	1.18454	+	1.66348i
$190$		0			0
$191$	−4.19109	+	5.25546i	−0.303257	+	0.380272i	−0.909988	−	0.414635i	$-0.863909\pi$
$191$	−4.19109	+	5.25546i	−0.303257	+	0.380272i	0.606731	+	0.794907i	$0.292481\pi$
$192$		0			0
$193$	−1.44686	+	1.81431i	−0.104147	+	0.130597i	−0.831174	−	0.556013i	$-0.812330\pi$
$193$	−1.44686	+	1.81431i	−0.104147	+	0.130597i	0.727026	+	0.686610i	$0.240902\pi$
$194$		0			0
$195$	22.2417			1.59276
$196$		0			0
$197$	8.72306			0.621492			0.310746	−	0.950493i	$-0.399421\pi$
$197$	8.72306			0.621492			0.310746	+	0.950493i	$0.399421\pi$
$198$		0			0
$199$	6.65827	−	8.34921i	0.471992	−	0.591860i	−0.487665	−	0.873031i	$-0.662151\pi$
$199$	6.65827	−	8.34921i	0.471992	−	0.591860i	0.959658	+	0.281171i	$0.0907228\pi$
$200$		0			0
$201$	−12.1198	+	15.1977i	−0.854865	+	1.07197i
$202$		0			0
$203$	11.2664	+	0.613578i	0.790746	+	0.0430647i
$204$		0			0
$205$	1.39381	+	6.10667i	0.0973478	+	0.426509i
$206$		0			0
$207$	−13.4903	+	59.1048i	−0.937639	+	4.10807i
$208$		0			0
$209$	−0.423648	+	1.85612i	−0.0293043	+	0.128391i
$210$		0			0
$211$	−3.16480	−	13.8659i	−0.217874	−	0.954566i	−0.959046	−	0.283251i	$-0.908587\pi$
$211$	−3.16480	−	13.8659i	−0.217874	−	0.954566i	0.741172	−	0.671315i	$-0.234270\pi$
$212$		0			0
$213$	39.2241	−	18.8893i	2.68759	−	1.29428i
$214$		0			0
$215$	4.10410			0.279897
$216$		0			0
$217$	−5.81939	−	3.20341i	−0.395046	−	0.217462i
$218$		0			0
$219$	−11.5198	−	5.54765i	−0.778437	−	0.374876i
$220$		0			0
$221$	−0.342161	−	1.49910i	−0.0230162	−	0.100841i
$222$		0			0
$223$	−8.73560	−	4.20684i	−0.584979	−	0.281711i	0.117894	−	0.993026i	$-0.462386\pi$
$223$	−8.73560	−	4.20684i	−0.584979	−	0.281711i	−0.702873	+	0.711315i	$0.748100\pi$
$224$		0			0
$225$	−24.1395	+	11.6250i	−1.60930	+	0.774997i
$226$		0			0
$227$	6.19599			0.411242			0.205621	−	0.978632i	$-0.434079\pi$
$227$	6.19599			0.411242			0.205621	+	0.978632i	$0.434079\pi$
$228$		0			0
$229$	0.341248	+	0.427912i	0.0225503	+	0.0282772i	0.792979	−	0.609249i	$-0.208529\pi$
$229$	0.341248	+	0.427912i	0.0225503	+	0.0282772i	−0.770428	+	0.637526i	$0.779958\pi$
$230$		0			0
$231$	4.16309	+	24.2535i	0.273911	+	1.59577i
$232$		0			0
$233$	−6.10655	+	2.94076i	−0.400053	+	0.192656i	−0.623082	−	0.782156i	$-0.714120\pi$
$233$	−6.10655	+	2.94076i	−0.400053	+	0.192656i	0.223029	+	0.974812i	$0.428406\pi$
$234$		0			0
$235$	1.99995	+	2.50785i	0.130462	+	0.163594i
$236$		0			0
$237$	21.5088	−	26.9712i	1.39715	−	1.75197i
$238$		0			0
$239$	4.24070	+	5.31767i	0.274308	+	0.343971i	0.899834	−	0.436232i	$-0.143687\pi$
$239$	4.24070	+	5.31767i	0.274308	+	0.343971i	−0.625526	+	0.780203i	$0.715116\pi$
$240$		0			0
$241$	−23.4832	−	11.3089i	−1.51269	−	0.728471i	−0.520572	−	0.853818i	$-0.674281\pi$
$241$	−23.4832	−	11.3089i	−1.51269	−	0.728471i	−0.992113	+	0.125347i	$0.959996\pi$
$242$		0			0
$243$	−1.99292	+	8.73154i	−0.127846	+	0.560129i
$244$		0			0
$245$	−21.0524	−	2.29989i	−1.34499	−	0.146934i
$246$		0			0
$247$	−0.334859	+	1.46711i	−0.0213066	+	0.0933502i
$248$		0			0
$249$	21.1194	+	10.1706i	1.33839	+	0.644533i
$250$		0			0
$251$	16.3304	+	20.4777i	1.03077	+	1.29254i	0.955378	+	0.295386i	$0.0954484\pi$
$251$	16.3304	+	20.4777i	1.03077	+	1.29254i	0.0753889	+	0.997154i	$0.475980\pi$
$252$		0			0
$253$	−17.7254	+	22.2269i	−1.11439	+	1.39739i
$254$		0			0
$255$	3.72892	+	4.67591i	0.233514	+	0.292817i
$256$		0			0
$257$	−12.0796	+	5.81722i	−0.753504	+	0.362868i	−0.770880	−	0.636981i	$-0.780183\pi$
$257$	−12.0796	+	5.81722i	−0.753504	+	0.362868i	0.0173758	+	0.999849i	$0.494469\pi$
$258$		0			0
$259$	−16.9710	−	0.924253i	−1.05452	−	0.0574303i
$260$		0			0
$261$	17.1543	+	21.5108i	1.06182	+	1.33148i
$262$		0			0
$263$	10.5626			0.651320			0.325660	−	0.945487i	$-0.394414\pi$
$263$	10.5626			0.651320			0.325660	+	0.945487i	$0.394414\pi$
$264$		0			0
$265$	12.7736	−	6.15145i	0.784677	−	0.377880i
$266$		0			0
$267$	−3.29976	−	1.58908i	−0.201942	−	0.0972502i
$268$		0			0
$269$	2.65240	+	11.6209i	0.161720	+	0.708540i	0.989142	+	0.146960i	$0.0469489\pi$
$269$	2.65240	+	11.6209i	0.161720	+	0.708540i	−0.827423	+	0.561579i	$0.810194\pi$
$270$		0			0
$271$	22.4071	+	10.7907i	1.36114	+	0.655489i	0.964890	−	0.262656i	$-0.0845983\pi$
$271$	22.4071	+	10.7907i	1.36114	+	0.655489i	0.396246	+	0.918144i	$0.370313\pi$
$272$		0			0
$273$	3.29059	+	19.1704i	0.199155	+	1.16025i
$274$		0			0
$275$	−12.5642			−0.757649
$276$		0			0
$277$	−25.0286	+	12.0531i	−1.50382	+	0.724202i	−0.990946	−	0.134262i	$-0.957134\pi$
$277$	−25.0286	+	12.0531i	−1.50382	+	0.724202i	−0.512875	+	0.858464i	$0.671419\pi$
$278$		0			0
$279$	−3.60445	−	15.7921i	−0.215793	−	0.945449i
$280$		0			0
$281$	6.94033	−	30.4076i	0.414025	−	1.81396i	−0.150574	−	0.988599i	$-0.548112\pi$
$281$	6.94033	−	30.4076i	0.414025	−	1.81396i	0.564600	−	0.825365i	$-0.309031\pi$
$282$		0			0
$283$	−4.22408	+	18.5069i	−0.251096	+	1.10012i	0.679385	+	0.733782i	$0.262246\pi$
$283$	−4.22408	+	18.5069i	−0.251096	+	1.10012i	−0.930481	+	0.366340i	$0.880611\pi$
$284$		0			0
$285$	−1.30244	−	5.70635i	−0.0771497	−	0.338015i
$286$		0			0
$287$	−5.05721	+	2.10480i	−0.298518	+	0.124243i
$288$		0			0
$289$	−10.3415	+	12.9679i	−0.608325	+	0.762816i
$290$		0			0
$291$	31.4343	−	39.4173i	1.84271	−	2.31068i
$292$		0			0
$293$	19.6220			1.14633			0.573163	−	0.819441i	$-0.305716\pi$
$293$	19.6220			1.14633			0.573163	+	0.819441i	$0.305716\pi$
$294$		0			0
$295$	9.51336			0.553889
$296$		0			0
$297$	−20.0159	+	25.0991i	−1.16144	+	1.45640i
$298$		0			0
$299$	−14.0105	+	17.5686i	−0.810247	+	1.01602i
$300$		0			0
$301$	0.607187	+	3.53737i	0.0349977	+	0.203891i
$302$		0			0
$303$	−9.83040	−	43.0698i	−0.564742	−	2.47429i
$304$		0			0
$305$	−3.63318	+	15.9180i	−0.208035	+	0.911461i
$306$		0			0
$307$	4.68518	−	20.5271i	0.267397	−	1.17154i	−0.645632	−	0.763649i	$-0.723406\pi$
$307$	4.68518	−	20.5271i	0.267397	−	1.17154i	0.913029	−	0.407895i	$-0.133737\pi$
$308$		0			0
$309$	−11.1730	−	48.9520i	−0.635608	−	2.78478i
$310$		0			0
$311$	−10.6094	+	5.10920i	−0.601602	+	0.289716i	−0.709789	−	0.704414i	$-0.751210\pi$
$311$	−10.6094	+	5.10920i	−0.601602	+	0.289716i	0.108187	+	0.994131i	$0.465496\pi$
$312$		0			0
$313$	21.4522			1.21255			0.606275	−	0.795255i	$-0.292663\pi$
$313$	21.4522			1.21255			0.606275	+	0.795255i	$0.292663\pi$
$314$		0			0
$315$	−29.9543	−	42.0656i	−1.68773	−	2.37013i
$316$		0			0
$317$	−26.7438	−	12.8791i	−1.50208	−	0.723363i	−0.511370	−	0.859360i	$-0.670862\pi$
$317$	−26.7438	−	12.8791i	−1.50208	−	0.723363i	−0.990709	+	0.135997i	$0.956576\pi$
$318$		0			0
$319$	2.87098	+	12.5786i	0.160744	+	0.704265i
$320$		0			0
$321$	46.2121	+	22.2546i	2.57931	+	1.24213i
$322$		0			0
$323$	−0.364574	+	0.175570i	−0.0202855	+	0.00976896i
$324$		0			0
$325$	−9.93096			−0.550871
$326$		0			0
$327$	3.19177	+	4.00235i	0.176505	+	0.221331i
$328$		0			0
$329$	−1.86567	+	2.09481i	−0.102858	+	0.115491i
$330$		0			0
$331$	−0.739639	+	0.356191i	−0.0406542	+	0.0195780i	−0.454100	−	0.890951i	$-0.650039\pi$
$331$	−0.739639	+	0.356191i	−0.0406542	+	0.0195780i	0.413446	+	0.910529i	$0.364325\pi$
$332$		0			0
$333$	−25.8401	−	32.4024i	−1.41603	−	1.77564i
$334$		0			0
$335$	11.9268	−	14.9557i	0.651631	−	0.817119i
$336$		0			0
$337$	2.24830	+	2.81928i	0.122473	+	0.153576i	0.839288	−	0.543687i	$-0.182972\pi$
$337$	2.24830	+	2.81928i	0.122473	+	0.153576i	−0.716815	+	0.697263i	$0.754401\pi$
$338$		0			0
$339$	25.6374	+	12.3463i	1.39243	+	0.670561i
$340$		0			0
$341$	1.69026	−	7.40553i	0.0915329	−	0.401032i
$342$		0			0
$343$	−1.13233	−	18.4856i	−0.0611399	−	0.998129i
$344$		0			0
$345$	19.4486	−	85.2099i	1.04708	−	4.58755i
$346$		0			0
$347$	−14.9046	−	7.17767i	−0.800120	−	0.385317i	−0.0112956	−	0.999936i	$-0.503596\pi$
$347$	−14.9046	−	7.17767i	−0.800120	−	0.385317i	−0.788824	+	0.614619i	$0.789310\pi$
$348$		0			0
$349$	1.47185	+	1.84565i	0.0787865	+	0.0987951i	0.819663	−	0.572847i	$-0.194161\pi$
$349$	1.47185	+	1.84565i	0.0787865	+	0.0987951i	−0.740876	+	0.671642i	$0.765589\pi$
$350$		0			0
$351$	−15.8209	+	19.8388i	−0.844458	+	1.05892i
$352$		0			0
$353$	−2.36737	−	2.96859i	−0.126003	−	0.158002i	0.714829	−	0.699300i	$-0.246505\pi$
$353$	−2.36737	−	2.96859i	−0.126003	−	0.158002i	−0.840831	+	0.541297i	$0.817933\pi$
$354$		0			0
$355$	−38.5995	+	18.5885i	−2.04865	+	0.986577i
$356$		0			0
$357$	−3.47855	+	3.90579i	−0.184105	+	0.206716i
$358$		0			0
$359$	17.4182	+	21.8418i	0.919299	+	1.15276i	0.987896	+	0.155120i	$0.0495764\pi$
$359$	17.4182	+	21.8418i	0.919299	+	1.15276i	−0.0685967	+	0.997644i	$0.521852\pi$
$360$		0			0
$361$	−18.6040			−0.979157
$362$		0			0
$363$	5.11617	−	2.46382i	0.268530	−	0.129317i
$364$		0			0
$365$	11.3364	+	5.45931i	0.593373	+	0.285753i
$366$		0			0
$367$	−6.93948	−	30.4038i	−0.362238	−	1.58707i	−0.747501	−	0.664260i	$-0.768747\pi$
$367$	−6.93948	−	30.4038i	−0.362238	−	1.58707i	0.385264	−	0.922807i	$-0.374110\pi$
$368$		0			0
$369$	−12.0344	−	5.79548i	−0.626488	−	0.301701i
$370$		0			0
$371$	7.19183	+	10.0997i	0.373381	+	0.524348i
$372$		0			0
$373$	−16.2454			−0.841155			−0.420578	−	0.907257i	$-0.638173\pi$
$373$	−16.2454			−0.841155			−0.420578	+	0.907257i	$0.638173\pi$
$374$		0			0
$375$	−7.09843	+	3.41842i	−0.366561	+	0.176527i
$376$		0			0
$377$	2.26928	+	9.94235i	0.116874	+	0.512057i
$378$		0			0
$379$	6.55969	−	28.7399i	0.336949	−	1.47627i	−0.468426	−	0.883503i	$-0.655179\pi$
$379$	6.55969	−	28.7399i	0.336949	−	1.47627i	0.805375	−	0.592766i	$-0.201964\pi$
$380$		0			0
$381$	−9.16390	+	40.1497i	−0.469481	+	2.05693i
$382$		0			0
$383$	−3.73776	−	16.3762i	−0.190991	−	0.836784i	−0.976082	−	0.217404i	$-0.930241\pi$
$383$	−3.73776	−	16.3762i	−0.190991	−	0.836784i	0.785091	−	0.619380i	$-0.212616\pi$
$384$		0			0
$385$	−4.09680	−	23.8673i	−0.208792	−	1.21639i
$386$		0			0
$387$	−5.45671	+	6.84250i	−0.277380	+	0.347824i
$388$		0			0
$389$	−7.22891	+	9.06477i	−0.366520	+	0.459602i	−0.930557	−	0.366148i	$-0.880676\pi$
$389$	−7.22891	+	9.06477i	−0.366520	+	0.459602i	0.564036	+	0.825750i	$0.309248\pi$
$390$		0			0
$391$	−6.04238			−0.305576
$392$		0			0
$393$	−59.7585			−3.01442
$394$		0			0
$395$	−21.1663	+	26.5417i	−1.06499	+	1.33546i
$396$		0			0
$397$	8.51285	−	10.6748i	0.427247	−	0.535751i	−0.520885	−	0.853627i	$-0.674398\pi$
$397$	8.51285	−	10.6748i	0.427247	−	0.535751i	0.948132	+	0.317875i	$0.102969\pi$
$398$		0			0
$399$	4.72569	−	1.96682i	0.236580	−	0.0984642i
$400$		0			0
$401$	−2.68854	−	11.7792i	−0.134259	−	0.588228i	−0.996636	−	0.0819601i	$-0.973882\pi$
$401$	−2.68854	−	11.7792i	−0.134259	−	0.588228i	0.862377	−	0.506267i	$-0.168975\pi$
$402$		0			0
$403$	1.33602	−	5.85347i	0.0665517	−	0.291582i
$404$		0			0
$405$	8.93203	−	39.1338i	0.443836	−	1.94457i
$406$		0			0
$407$	−4.32465	−	18.9475i	−0.214365	−	0.939195i
$408$		0			0
$409$	22.6745	−	10.9195i	1.12118	−	0.539933i	0.220924	−	0.975291i	$-0.429093\pi$
$409$	22.6745	−	10.9195i	1.12118	−	0.539933i	0.900257	+	0.435358i	$0.143378\pi$
$410$		0			0
$411$	24.2446			1.19590
$412$		0			0
$413$	1.40747	+	8.19969i	0.0692570	+	0.403480i
$414$		0			0
$415$	−20.7831	−	10.0086i	−1.02020	−	0.491303i
$416$		0			0
$417$	−0.200575	−	0.878776i	−0.00982219	−	0.0430338i
$418$		0			0
$419$	19.3992	+	9.34214i	0.947711	+	0.456393i	0.842883	−	0.538097i	$-0.180857\pi$
$419$	19.3992	+	9.34214i	0.947711	+	0.456393i	0.104828	+	0.994490i	$0.466571\pi$
$420$		0			0
$421$	25.2231	−	12.1468i	1.22930	−	0.591998i	0.297411	−	0.954750i	$-0.403877\pi$
$421$	25.2231	−	12.1468i	1.22930	−	0.591998i	0.931886	+	0.362751i	$0.118163\pi$
$422$		0			0
$423$	−6.84026			−0.332585
$424$		0			0
$425$	−1.66497	−	2.08780i	−0.0807628	−	0.101273i
$426$		0			0
$427$	−14.2574	−	0.776473i	−0.689966	−	0.0375761i
$428$		0			0
$429$	−20.0391	+	9.65033i	−0.967497	+	0.465922i
$430$		0			0
$431$	11.0229	+	13.8223i	0.530956	+	0.665798i	0.972895	−	0.231247i	$-0.0742806\pi$
$431$	11.0229	+	13.8223i	0.530956	+	0.665798i	−0.441939	+	0.897045i	$0.645709\pi$
$432$		0			0
$433$	−0.735843	+	0.922718i	−0.0353624	+	0.0443430i	−0.799198	−	0.601068i	$-0.794742\pi$
$433$	−0.735843	+	0.922718i	−0.0353624	+	0.0443430i	0.763836	+	0.645411i	$0.223314\pi$
$434$		0			0
$435$	−24.7309	−	31.0116i	−1.18576	−	1.48689i
$436$		0			0
$437$	5.32783	+	2.56575i	0.254865	+	0.122736i
$438$		0			0
$439$	−4.75079	+	20.8146i	−0.226743	+	0.993424i	0.725534	+	0.688187i	$0.241593\pi$
$439$	−4.75079	+	20.8146i	−0.226743	+	0.993424i	−0.952276	+	0.305238i	$0.901264\pi$
$440$		0			0
$441$	31.8252	−	32.0415i	1.51549	−	1.52578i
$442$		0			0
$443$	1.91875	−	8.40661i	0.0911627	−	0.399410i	−0.908673	−	0.417507i	$-0.862904\pi$
$443$	1.91875	−	8.40661i	0.0911627	−	0.399410i	0.999836	+	0.0180974i	$0.00576091\pi$
$444$		0			0
$445$	3.24721	+	1.56378i	0.153933	+	0.0741301i
$446$		0			0
$447$	−13.5967	−	17.0497i	−0.643100	−	0.806422i
$448$		0			0
$449$	10.4421	−	13.0940i	0.492794	−	0.617944i	−0.471793	−	0.881710i	$-0.656393\pi$
$449$	10.4421	−	13.0940i	0.492794	−	0.617944i	0.964587	+	0.263765i	$0.0849644\pi$
$450$		0			0
$451$	−3.90536	−	4.89717i	−0.183896	−	0.230599i
$452$		0			0
$453$	32.6763	−	15.7361i	1.53526	−	0.739345i
$454$		0			0
$455$	−3.23819	−	18.8652i	−0.151809	−	0.884413i
$456$		0			0
$457$	4.99775	+	6.26698i	0.233785	+	0.293157i	0.884861	−	0.465856i	$-0.154253\pi$
$457$	4.99775	+	6.26698i	0.233785	+	0.293157i	−0.651076	+	0.759013i	$0.725682\pi$
$458$		0			0
$459$	−6.82319			−0.318479
$460$		0			0
$461$	−16.3204	+	7.85951i	−0.760118	+	0.366054i	−0.773450	−	0.633857i	$-0.781471\pi$
$461$	−16.3204	+	7.85951i	−0.760118	+	0.366054i	0.0133316	+	0.999911i	$0.495756\pi$
$462$		0			0
$463$	4.79374	+	2.30855i	0.222784	+	0.107287i	0.541947	−	0.840413i	$-0.317687\pi$
$463$	4.79374	+	2.30855i	0.222784	+	0.107287i	−0.319163	+	0.947700i	$0.603402\pi$
$464$		0			0
$465$	5.19644	+	22.7671i	0.240979	+	1.05580i
$466$		0			0
$467$	−30.2327	−	14.5593i	−1.39900	−	0.673724i	−0.426043	−	0.904703i	$-0.640093\pi$
$467$	−30.2327	−	14.5593i	−1.39900	−	0.673724i	−0.972959	+	0.230979i	$0.925807\pi$
$468$		0			0
$469$	14.6551	+	8.06722i	0.676708	+	0.372510i
$470$		0			0
$471$	−40.4493			−1.86380
$472$		0			0
$473$	−3.69766	+	1.78070i	−0.170019	+	0.0818767i
$474$		0			0
$475$	0.581540	+	2.54789i	0.0266829	+	0.116905i
$476$		0			0
$477$	−6.72758	+	29.4754i	−0.308035	+	1.34959i
$478$		0			0
$479$	−3.72555	+	16.3227i	−0.170225	+	0.745804i	0.815681	+	0.578502i	$0.196363\pi$
$479$	−3.72555	+	16.3227i	−0.170225	+	0.745804i	−0.985906	+	0.167302i	$0.946495\pi$
$480$		0			0
$481$	−3.41829	−	14.9765i	−0.155860	−	0.682869i
$482$		0			0
$483$	76.3209	+	4.15651i	3.47272	+	0.189128i
$484$		0			0
$485$	−30.9337	+	38.7896i	−1.40463	+	1.76135i
$486$		0			0
$487$	−16.6150	+	20.8346i	−0.752899	+	0.944105i	−0.999688	−	0.0249638i	$-0.992053\pi$
$487$	−16.6150	+	20.8346i	−0.752899	+	0.944105i	0.246789	+	0.969069i	$0.420624\pi$
$488$		0			0
$489$	−41.2290			−1.86444
$490$		0			0
$491$	−7.56655			−0.341474			−0.170737	−	0.985317i	$-0.554615\pi$
$491$	−7.56655			−0.341474			−0.170737	+	0.985317i	$0.554615\pi$
$492$		0			0
$493$	−1.70974	+	2.14395i	−0.0770029	+	0.0965586i
$494$		0			0
$495$	36.8174	−	46.1676i	1.65482	−	2.07508i
$496$		0			0
$497$	−21.7324	−	30.5193i	−0.974829	−	1.36898i
$498$		0			0
$499$	−2.33363	−	10.2243i	−0.104468	−	0.457702i	−0.999921	−	0.0125476i	$-0.996006\pi$
$499$	−2.33363	−	10.2243i	−0.104468	−	0.457702i	0.895454	−	0.445155i	$-0.146851\pi$
$500$		0			0
$501$	−6.48693	+	28.4211i	−0.289815	+	1.26976i
$502$		0			0
$503$	−0.109148	+	0.478210i	−0.00486668	+	0.0213223i	−0.977303	−	0.211846i	$-0.932052\pi$
$503$	−0.109148	+	0.478210i	−0.00486668	+	0.0213223i	0.972436	+	0.233169i	$0.0749095\pi$
$504$		0			0
$505$	9.67386	+	42.3839i	0.430481	+	1.88606i
$506$		0			0
$507$	20.1692	−	9.71296i	0.895745	−	0.431368i
$508$		0			0
$509$	−15.9439			−0.706703			−0.353351	−	0.935491i	$-0.614958\pi$
$509$	−15.9439			−0.706703			−0.353351	+	0.935491i	$0.614958\pi$
$510$		0			0
$511$	−3.02828	+	10.5787i	−0.133963	+	0.467972i
$512$		0			0
$513$	6.01630	+	2.89730i	0.265626	+	0.127919i
$514$		0			0
$515$	10.9950	+	48.1724i	0.484500	+	2.12273i
$516$		0			0
$517$	−2.89001	−	1.39175i	−0.127102	−	0.0612093i
$518$		0			0
$519$	2.91527	−	1.40392i	0.127966	−	0.0616252i
$520$		0			0
$521$	31.8495			1.39535			0.697677	−	0.716413i	$-0.254217\pi$
$521$	31.8495			1.39535			0.697677	+	0.716413i	$0.254217\pi$
$522$		0			0
$523$	26.4558	+	33.1745i	1.15683	+	1.45062i	0.870282	+	0.492554i	$0.163937\pi$
$523$	26.4558	+	33.1745i	1.15683	+	1.45062i	0.286549	+	0.958066i	$0.407492\pi$
$524$		0			0
$525$	19.5939	+	27.5162i	0.855148	+	1.20091i
$526$		0			0
$527$	1.45457	−	0.700485i	0.0633622	−	0.0305136i
$528$		0			0
$529$	40.7154	+	51.0555i	1.77023	+	2.21980i
$530$		0			0
$531$	−12.6487	+	15.8610i	−0.548908	+	0.688309i
$532$		0			0
$533$	−3.08687	−	3.87082i	−0.133707	−	0.167664i
$534$		0			0
$535$	−45.4762	−	21.9002i	−1.96611	−	0.946827i
$536$		0			0
$537$	−6.97241	+	30.5481i	−0.300881	+	1.31825i
$538$		0			0
$539$	19.9654	−	7.06217i	0.859973	−	0.304189i
$540$		0			0
$541$	−1.45562	+	6.37750i	−0.0625821	+	0.274190i	−0.996532	−	0.0832148i	$-0.973481\pi$
$541$	−1.45562	+	6.37750i	−0.0625821	+	0.274190i	0.933950	+	0.357405i	$0.116338\pi$
$542$		0			0
$543$	−38.4429	−	18.5131i	−1.64974	−	0.794475i
$544$		0			0
$545$	−3.14094	−	3.93862i	−0.134543	−	0.168712i
$546$		0			0
$547$	−11.3933	+	14.2867i	−0.487141	+	0.610856i	−0.963275	−	0.268517i	$-0.913466\pi$
$547$	−11.3933	+	14.2867i	−0.487141	+	0.610856i	0.476134	+	0.879373i	$0.342038\pi$
$548$		0			0
$549$	−21.7084	−	27.2215i	−0.926494	−	1.16179i
$550$		0			0
$551$	2.41793	−	1.16441i	0.103007	−	0.0496056i
$552$		0			0
$553$	−26.0081	−	14.3168i	−1.10598	−	0.608811i
$554$		0			0
$555$	37.2530	+	46.7138i	1.58130	+	1.98289i
$556$		0			0
$557$	−36.4469			−1.54431			−0.772153	−	0.635436i	$-0.780820\pi$
$557$	−36.4469			−1.54431			−0.772153	+	0.635436i	$0.780820\pi$
$558$		0			0
$559$	−2.92270	+	1.40750i	−0.123617	+	0.0595309i
$560$		0			0
$561$	−5.38844	−	2.59494i	−0.227500	−	0.109558i
$562$		0			0
$563$	1.36966	+	6.00086i	0.0577242	+	0.252906i	0.995554	−	0.0941881i	$-0.0300255\pi$
$563$	1.36966	+	6.00086i	0.0577242	+	0.252906i	−0.937830	+	0.347094i	$0.887168\pi$
$564$		0			0
$565$	−25.2292	−	12.1497i	−1.06140	−	0.511143i
$566$		0			0
$567$	35.0514	+	1.90893i	1.47202	+	0.0801676i
$568$		0			0
$569$	8.41931			0.352956			0.176478	−	0.984305i	$-0.443530\pi$
$569$	8.41931			0.352956			0.176478	+	0.984305i	$0.443530\pi$
$570$		0			0
$571$	−31.5658	+	15.2013i	−1.32099	+	0.636155i	−0.955591	−	0.294696i	$-0.904781\pi$
$571$	−31.5658	+	15.2013i	−1.32099	+	0.636155i	−0.365398	+	0.930851i	$0.619067\pi$
$572$		0			0
$573$	4.59854	+	20.1475i	0.192107	+	0.841675i
$574$		0			0
$575$	−8.68383	+	38.0464i	−0.362141	+	1.58664i
$576$		0			0
$577$	7.74498	−	33.9330i	0.322428	−	1.41265i	−0.510791	−	0.859705i	$-0.670648\pi$
$577$	7.74498	−	33.9330i	0.322428	−	1.41265i	0.833219	−	0.552943i	$-0.186495\pi$
$578$		0			0
$579$	1.58752	+	6.95539i	0.0659752	+	0.289056i
$580$		0			0
$581$	5.55176	−	19.3939i	0.230326	−	0.804596i
$582$		0			0
$583$	−8.83961	+	11.0845i	−0.366099	+	0.459074i
$584$		0			0
$585$	29.1012	−	36.4917i	1.20319	−	1.50875i
$586$		0			0
$587$	−19.8051			−0.817443			−0.408722	−	0.912659i	$-0.634025\pi$
$587$	−19.8051			−0.817443			−0.408722	+	0.912659i	$0.634025\pi$
$588$		0			0
$589$	−1.58000			−0.0651029
$590$		0			0
$591$	16.7205	−	20.9669i	0.687790	−	0.862461i
$592$		0			0
$593$	6.57004	−	8.23857i	0.269799	−	0.338317i	−0.628413	−	0.777880i	$-0.716295\pi$
$593$	6.57004	−	8.23857i	0.269799	−	0.338317i	0.898212	+	0.439563i	$0.144867\pi$
$594$		0			0
$595$	3.42316	−	3.84359i	0.140336	−	0.157572i
$596$		0			0
$597$	−7.30558	−	32.0078i	−0.298997	−	1.30999i
$598$		0			0
$599$	−0.828100	+	3.62814i	−0.0338352	+	0.148242i	−0.989024	−	0.147756i	$-0.952795\pi$
$599$	−0.828100	+	3.62814i	−0.0338352	+	0.148242i	0.955189	+	0.295998i	$0.0956521\pi$
$600$		0			0
$601$	−0.0432317	+	0.189411i	−0.00176346	+	0.00772622i	−0.975802	−	0.218656i	$-0.929833\pi$
$601$	−0.0432317	+	0.189411i	−0.00176346	+	0.00772622i	0.974039	+	0.226382i	$0.0726899\pi$
$602$		0			0
$603$	9.07715	+	39.7696i	0.369650	+	1.61954i
$604$		0			0
$605$	−5.03470	+	2.42459i	−0.204690	+	0.0985734i
$606$		0			0
$607$	20.2928			0.823658			0.411829	−	0.911261i	$-0.364890\pi$
$607$	20.2928			0.823658			0.411829	+	0.911261i	$0.364890\pi$
$608$		0			0
$609$	23.0704	−	25.9039i	0.934861	−	1.04968i
$610$		0			0
$611$	−2.28431	−	1.10007i	−0.0924135	−	0.0445040i
$612$		0			0
$613$	−3.25039	−	14.2409i	−0.131282	−	0.575185i	−0.997186	−	0.0749735i	$-0.976113\pi$
$613$	−3.25039	−	14.2409i	−0.131282	−	0.575185i	0.865903	−	0.500211i	$-0.166744\pi$
$614$		0			0
$615$	17.3498	+	8.35520i	0.699610	+	0.336914i
$616$		0			0
$617$	−10.5371	+	5.07442i	−0.424209	+	0.204288i	−0.633794	−	0.773502i	$-0.718503\pi$
$617$	−10.5371	+	5.07442i	−0.424209	+	0.204288i	0.209584	+	0.977791i	$0.432789\pi$
$618$		0			0
$619$	37.4631			1.50577			0.752885	−	0.658152i	$-0.228662\pi$
$619$	37.4631			1.50577			0.752885	+	0.658152i	$0.228662\pi$
$620$		0			0
$621$	62.1700	+	77.9587i	2.49480	+	3.12838i
$622$		0			0
$623$	−0.867425	+	3.03017i	−0.0347527	+	0.121401i
$624$		0			0
$625$	25.6937	−	12.3734i	1.02775	−	0.494937i
$626$		0			0
$627$	3.64935	+	4.57614i	0.145741	+	0.182753i
$628$		0			0
$629$	2.57544	−	3.22950i	0.102690	−	0.128769i
$630$		0			0
$631$	8.17143	+	10.2467i	0.325300	+	0.407913i	0.917410	−	0.397944i	$-0.130276\pi$
$631$	8.17143	+	10.2467i	0.325300	+	0.407913i	−0.592110	+	0.805857i	$0.701705\pi$
$632$		0			0
$633$	−39.3945	−	18.9714i	−1.56579	−	0.754046i
$634$		0			0
$635$	9.01798	−	39.5103i	0.357867	−	1.56792i
$636$		0			0
$637$	15.7811	−	5.58207i	0.625268	−	0.221170i
$638$		0			0
$639$	20.3295	−	89.0693i	0.804222	−	3.52353i
$640$		0			0
$641$	10.3864	+	5.00184i	0.410239	+	0.197561i	0.627609	−	0.778528i	$-0.284034\pi$
$641$	10.3864	+	5.00184i	0.410239	+	0.197561i	−0.217370	+	0.976089i	$0.569748\pi$
$642$		0			0
$643$	14.3138	+	17.9489i	0.564481	+	0.707836i	0.979379	−	0.202031i	$-0.0647543\pi$
$643$	14.3138	+	17.9489i	0.564481	+	0.707836i	−0.414898	+	0.909868i	$0.636183\pi$
$644$		0			0
$645$	7.86680	−	9.86466i	0.309755	−	0.388421i
$646$		0			0
$647$	−1.62204	−	2.03397i	−0.0637689	−	0.0799636i	0.748924	−	0.662656i	$-0.230571\pi$
$647$	−1.62204	−	2.03397i	−0.0637689	−	0.0799636i	−0.812693	+	0.582692i	$0.801999\pi$
$648$		0			0
$649$	−8.57124	+	4.12769i	−0.336451	+	0.162026i
$650$		0			0
$651$	−18.8545	+	7.84719i	−0.738965	+	0.307556i
$652$		0			0
$653$	22.0743	+	27.6803i	0.863835	+	1.08321i	0.995763	+	0.0919555i	$0.0293117\pi$
$653$	22.0743	+	27.6803i	0.863835	+	1.08321i	−0.131928	+	0.991259i	$0.542117\pi$
$654$		0			0
$655$	58.8069			2.29777
$656$		0			0
$657$	−24.1745	+	11.6418i	−0.943139	+	0.454192i
$658$		0			0
$659$	−24.6402	−	11.8661i	−0.959847	−	0.462238i	−0.112719	−	0.993627i	$-0.535956\pi$
$659$	−24.6402	−	11.8661i	−0.959847	−	0.462238i	−0.847128	+	0.531389i	$0.821670\pi$
$660$		0			0
$661$	−0.769109	−	3.36968i	−0.0299149	−	0.131066i	0.957765	−	0.287550i	$-0.0928409\pi$
$661$	−0.769109	−	3.36968i	−0.0299149	−	0.131066i	−0.987680	+	0.156485i	$0.949984\pi$
$662$		0			0
$663$	−4.25912	−	2.05109i	−0.165411	−	0.0796576i
$664$		0			0
$665$	−4.65043	+	1.93550i	−0.180336	+	0.0750555i
$666$		0			0
$667$	40.0743			1.55168
$668$		0			0
$669$	−26.8562	+	12.9332i	−1.03832	+	0.500028i
$670$		0			0
$671$	−3.63318	−	15.9180i	−0.140257	−	0.614507i
$672$		0			0
$673$	4.76589	−	20.8807i	0.183712	−	0.804893i	−0.796131	−	0.605124i	$-0.793124\pi$
$673$	4.76589	−	20.8807i	0.183712	−	0.804893i	0.979843	−	0.199769i	$-0.0640192\pi$
$674$		0			0
$675$	−9.80597	+	42.9627i	−0.377432	+	1.65364i
$676$		0			0
$677$	4.14397	+	18.1559i	0.159266	+	0.697789i	0.989994	+	0.141111i	$0.0450673\pi$
$677$	4.14397	+	18.1559i	0.159266	+	0.697789i	−0.830728	+	0.556679i	$0.812076\pi$
$678$		0			0
$679$	−38.0098	−	20.9234i	−1.45868	−	0.802965i
$680$		0			0
$681$	11.8766	−	14.8928i	0.455111	−	0.570692i
$682$		0			0
$683$	3.88430	−	4.87076i	0.148629	−	0.186374i	−0.701944	−	0.712232i	$-0.747684\pi$
$683$	3.88430	−	4.87076i	0.148629	−	0.186374i	0.850572	+	0.525858i	$0.176256\pi$
$684$		0			0
$685$	−23.8585			−0.911587
$686$		0			0
$687$	1.68264			0.0641969
$688$		0			0
$689$	−6.98700	+	8.76142i	−0.266183	+	0.333783i
$690$		0			0
$691$	14.0148	−	17.5739i	0.533146	−	0.668544i	−0.440196	−	0.897902i	$-0.645091\pi$
$691$	14.0148	−	17.5739i	0.533146	−	0.668544i	0.973342	+	0.229357i	$0.0736625\pi$
$692$		0			0
$693$	45.2394	+	24.9031i	1.71850	+	0.945990i
$694$		0			0
$695$	0.197381	+	0.864782i	0.00748708	+	0.0328030i
$696$		0			0
$697$	0.296241	−	1.29792i	0.0112209	−	0.0491621i
$698$		0			0
$699$	−4.63669	+	20.3147i	−0.175376	+	0.768372i
$700$		0			0
$701$	5.47281	+	23.9779i	0.206705	+	0.905634i	0.966742	+	0.255754i	$0.0823237\pi$
$701$	5.47281	+	23.9779i	0.206705	+	0.905634i	−0.760037	+	0.649880i	$0.774819\pi$
$702$		0			0
$703$	−3.64220	+	1.75399i	−0.137368	+	0.0661531i
$704$		0			0
$705$	9.86144			0.371403
$706$		0			0
$707$	−35.1001	+	14.6086i	−1.32007	+	0.549412i
$708$		0			0
$709$	−3.78492	−	1.82272i	−0.142146	−	0.0684538i	0.361459	−	0.932388i	$-0.382279\pi$
$709$	−3.78492	−	1.82272i	−0.142146	−	0.0684538i	−0.503605	+	0.863934i	$0.667993\pi$
$710$		0			0
$711$	−16.1091	−	70.5784i	−0.604137	−	2.64690i
$712$		0			0
$713$	−21.2569	−	10.2368i	−0.796077	−	0.383370i
$714$		0			0
$715$	19.7200	−	9.49665i	0.737486	−	0.355155i
$716$		0			0
$717$	20.9103			0.780908
$718$		0			0
$719$	−28.8282	−	36.1494i	−1.07511	−	1.34815i	−0.933644	−	0.358203i	$-0.883390\pi$
$719$	−28.8282	−	36.1494i	−1.07511	−	1.34815i	−0.141467	−	0.989943i	$-0.545182\pi$
$720$		0			0
$721$	−39.8938	+	16.6037i	−1.48572	+	0.618355i
$722$		0			0
$723$	−72.1952	+	34.7674i	−2.68497	+	1.29301i
$724$		0			0
$725$	11.0424	+	13.8467i	0.410104	+	0.514254i
$726$		0			0
$727$	−0.337641	+	0.423389i	−0.0125224	+	0.0157026i	−0.788053	−	0.615607i	$-0.788911\pi$
$727$	−0.337641	+	0.423389i	−0.0125224	+	0.0157026i	0.775531	+	0.631310i	$0.217482\pi$
$728$		0			0
$729$	−7.64986	−	9.59262i	−0.283328	−	0.355282i
$730$		0			0
$731$	−0.785903	−	0.378471i	−0.0290677	−	0.0139983i
$732$		0			0
$733$	−3.74578	+	16.4114i	−0.138354	+	0.606167i	0.857443	+	0.514579i	$0.172052\pi$
$733$	−3.74578	+	16.4114i	−0.138354	+	0.606167i	−0.995797	+	0.0915886i	$0.970806\pi$
$734$		0			0
$735$	−45.8817	+	46.1934i	−1.69237	+	1.70387i
$736$		0			0
$737$	−4.25663	+	18.6495i	−0.156795	+	0.686963i
$738$		0			0
$739$	−12.0260	−	5.79140i	−0.442382	−	0.213040i	0.199414	−	0.979915i	$-0.436096\pi$
$739$	−12.0260	−	5.79140i	−0.442382	−	0.213040i	−0.641796	+	0.766875i	$0.721811\pi$
$740$		0			0
$741$	2.88451	+	3.61706i	0.105965	+	0.132876i
$742$		0			0
$743$	25.2863	−	31.7080i	0.927663	−	1.16325i	−0.0586353	−	0.998279i	$-0.518675\pi$
$743$	25.2863	−	31.7080i	0.927663	−	1.16325i	0.986298	−	0.164973i	$-0.0527537\pi$
$744$		0			0
$745$	13.3801	+	16.7782i	0.490211	+	0.614705i
$746$		0			0
$747$	44.3193	−	21.3431i	1.62156	−	0.780902i
$748$		0			0
$749$	12.1480	−	42.4366i	0.443879	−	1.55060i
$750$		0			0
$751$	13.8236	+	17.3343i	0.504431	+	0.632536i	0.967222	−	0.253931i	$-0.0817236\pi$
$751$	13.8236	+	17.3343i	0.504431	+	0.632536i	−0.462792	+	0.886467i	$0.653152\pi$
$752$		0			0
$753$	80.5229			2.93442
$754$		0			0
$755$	−32.1559	+	15.4855i	−1.17027	+	0.563574i
$756$		0			0
$757$	−16.4965	−	7.94430i	−0.599576	−	0.288740i	0.109373	−	0.994001i	$-0.465116\pi$
$757$	−16.4965	−	7.94430i	−0.599576	−	0.288740i	−0.708948	+	0.705260i	$0.750830\pi$
$758$		0			0
$759$	19.4486	+	85.2099i	0.705940	+	3.09292i
$760$		0			0
$761$	−23.8595	−	11.4902i	−0.864908	−	0.416518i	−0.0518185	−	0.998657i	$-0.516502\pi$
$761$	−23.8595	−	11.4902i	−0.864908	−	0.416518i	−0.813089	+	0.582139i	$0.802216\pi$
$762$		0			0
$763$	2.93006	−	3.28993i	0.106075	−	0.119103i
$764$		0			0
$765$	12.5506			0.453769
$766$		0			0
$767$	−6.77487	+	3.26260i	−0.244626	+	0.117806i
$768$		0			0
$769$	11.1387	+	48.8018i	0.401671	+	1.75984i	0.620631	+	0.784103i	$0.286877\pi$
$769$	11.1387	+	48.8018i	0.401671	+	1.75984i	−0.218960	+	0.975734i	$0.570266\pi$
$770$		0			0
$771$	−9.17201	+	40.1852i	−0.330322	+	1.44724i
$772$		0			0
$773$	2.10947	−	9.24219i	0.0758723	−	0.332418i	−0.922719	−	0.385473i	$-0.874038\pi$
$773$	2.10947	−	9.24219i	0.0758723	−	0.332418i	0.998592	+	0.0530541i	$0.0168956\pi$
$774$		0			0
$775$	−2.32022	−	10.1655i	−0.0833447	−	0.365157i
$776$		0			0
$777$	−34.7518	+	39.0200i	−1.24671	+	1.39983i
$778$		0			0
$779$	−0.812336	+	1.01864i	−0.0291050	+	0.0364965i
$780$		0			0
$781$	26.7117	−	33.4954i	0.955819	−	1.19856i
$782$		0			0
$783$	45.2527			1.61720
$784$		0			0
$785$	39.8052			1.42071
$786$		0			0
$787$	27.1997	−	34.1074i	0.969565	−	1.21580i	−0.00686820	−	0.999976i	$-0.502186\pi$
$787$	27.1997	−	34.1074i	0.969565	−	1.21580i	0.976433	−	0.215820i	$-0.0692423\pi$
$788$		0			0
$789$	20.2466	−	25.3885i	0.720800	−	0.903854i
$790$		0			0
$791$	6.73944	−	23.5429i	0.239627	−	0.837088i
$792$		0			0
$793$	−2.87173	−	12.5819i	−0.101978	−	0.446795i
$794$		0			0
$795$	9.69898	−	42.4940i	0.343988	−	1.50711i
$796$		0			0
$797$	1.46387	−	6.41362i	0.0518528	−	0.227182i	−0.942362	−	0.334596i	$-0.891400\pi$
$797$	1.46387	−	6.41362i	0.0518528	−	0.227182i	0.994214	+	0.107414i	$0.0342572\pi$
$798$		0			0
$799$	−0.151706	−	0.664666i	−0.00536696	−	0.0235142i
$800$		0			0
$801$	−6.92460	+	3.33471i	−0.244669	+	0.117826i
$802$		0			0
$803$	−12.5824			−0.444024
$804$		0			0
$805$	−75.1056	−	4.09032i	−2.64712	−	0.144165i
$806$		0			0
$807$	33.0163	+	15.8998i	1.16223	+	0.559701i
$808$		0			0
$809$	−7.97579	−	34.9442i	−0.280414	−	1.22857i	−0.897265	−	0.441493i	$-0.854449\pi$
$809$	−7.97579	−	34.9442i	−0.280414	−	1.22857i	0.616851	−	0.787080i	$-0.288408\pi$
$810$		0			0
$811$	23.6835	+	11.4054i	0.831642	+	0.400498i	0.800731	−	0.599025i	$-0.204445\pi$
$811$	23.6835	+	11.4054i	0.831642	+	0.400498i	0.0309111	+	0.999522i	$0.490159\pi$
$812$		0			0
$813$	68.8871	−	33.1743i	2.41597	−	1.16347i
$814$		0			0
$815$	40.5725			1.42119
$816$		0			0
$817$	0.532257	+	0.667429i	0.0186213	+	0.0233504i
$818$		0			0
$819$	35.7581	+	19.6839i	1.24949	+	0.687810i
$820$		0			0
$821$	−31.5369	+	15.1874i	−1.10065	+	0.530043i	−0.893861	−	0.448344i	$-0.852014\pi$
$821$	−31.5369	+	15.1874i	−1.10065	+	0.530043i	−0.206784	+	0.978387i	$0.566300\pi$
$822$		0			0
$823$	−16.8693	−	21.1534i	−0.588026	−	0.737361i	0.395433	−	0.918495i	$-0.370595\pi$
$823$	−16.8693	−	21.1534i	−0.588026	−	0.737361i	−0.983458	+	0.181134i	$0.942023\pi$
$824$		0			0
$825$	−24.0832	+	30.1994i	−0.838471	+	1.05141i
$826$		0			0
$827$	19.5888	+	24.5635i	0.681168	+	0.854157i	0.995461	−	0.0951686i	$-0.0303390\pi$
$827$	19.5888	+	24.5635i	0.681168	+	0.854157i	−0.314293	+	0.949326i	$0.601768\pi$
$828$		0			0
$829$	17.2214	+	8.29339i	0.598124	+	0.288041i	0.708346	−	0.705866i	$-0.249442\pi$
$829$	17.2214	+	8.29339i	0.598124	+	0.288041i	−0.110222	+	0.993907i	$0.535156\pi$
$830$		0			0
$831$	−19.0041	+	83.2626i	−0.659247	+	2.88835i
$832$		0			0
$833$	3.81929	+	2.38182i	0.132330	+	0.0825252i
$834$		0			0
$835$	6.38363	−	27.9685i	0.220915	−	0.967890i
$836$		0			0
$837$	−24.0037	−	11.5596i	−0.829690	−	0.399558i
$838$		0			0
$839$	−6.82417	−	8.55724i	−0.235597	−	0.295429i	0.649952	−	0.759975i	$-0.274789\pi$
$839$	−6.82417	−	8.55724i	−0.235597	−	0.295429i	−0.885549	+	0.464546i	$0.846217\pi$
$840$		0			0
$841$	−6.74187	+	8.45403i	−0.232478	+	0.291518i
$842$		0			0
$843$	−59.7847	−	74.9676i	−2.05909	−	2.58202i
$844$		0			0
$845$	−19.8480	+	9.55829i	−0.682792	+	0.328815i
$846$		0			0
$847$	−2.83465	−	3.98077i	−0.0973997	−	0.136781i
$848$		0			0
$849$	36.3867	+	45.6274i	1.24879	+	1.56593i
$850$		0			0
$851$	−60.3652			−2.06929
$852$		0			0
$853$	44.1593	−	21.2660i	1.51199	−	0.728134i	0.519962	−	0.854189i	$-0.325946\pi$
$853$	44.1593	−	21.2660i	1.51199	−	0.728134i	0.992023	+	0.126056i	$0.0402318\pi$
$854$		0			0
$855$	−11.0664	−	5.32932i	−0.378464	−	0.182259i
$856$		0			0
$857$	2.46292	+	10.7908i	0.0841317	+	0.368605i	0.999415	−	0.0342061i	$-0.0108903\pi$
$857$	2.46292	+	10.7908i	0.0841317	+	0.368605i	−0.915283	+	0.402811i	$0.868033\pi$
$858$		0			0
$859$	−13.3149	−	6.41211i	−0.454298	−	0.218778i	0.192719	−	0.981254i	$-0.438269\pi$
$859$	−13.3149	−	6.41211i	−0.454298	−	0.218778i	−0.647017	+	0.762476i	$0.723984\pi$
$860$		0			0
$861$	−4.63462	+	16.1901i	−0.157948	+	0.551757i
$862$		0			0
$863$	7.06992			0.240663			0.120331	−	0.992734i	$-0.461604\pi$
$863$	7.06992			0.240663			0.120331	+	0.992734i	$0.461604\pi$
$864$		0			0
$865$	−2.86885	+	1.38156i	−0.0975437	+	0.0469745i
$866$		0			0
$867$	11.3469	+	49.7141i	0.385361	+	1.68838i
$868$		0			0
$869$	7.55417	−	33.0970i	0.256258	−	1.12274i
$870$		0			0
$871$	−3.36452	+	14.7409i	−0.114002	+	0.499477i
$872$		0			0
$873$	−23.5427	−	103.148i	−0.796801	−	3.49101i
$874$		0			0
$875$	3.93293	+	5.52311i	0.132957	+	0.186715i
$876$		0			0
$877$	30.0485	−	37.6796i	1.01467	−	1.27235i	0.0528650	−	0.998602i	$-0.483165\pi$
$877$	30.0485	−	37.6796i	1.01467	−	1.27235i	0.961801	−	0.273749i	$-0.0882639\pi$
$878$		0			0
$879$	37.6117	−	47.1636i	1.26861	−	1.59079i
$880$		0			0
$881$	5.91801			0.199383			0.0996915	−	0.995018i	$-0.468214\pi$
$881$	5.91801			0.199383			0.0996915	+	0.995018i	$0.468214\pi$
$882$		0			0
$883$	29.4616			0.991461			0.495730	−	0.868477i	$-0.334900\pi$
$883$	29.4616			0.991461			0.495730	+	0.868477i	$0.334900\pi$
$884$		0			0
$885$	18.2354	−	22.8664i	0.612975	−	0.768647i
$886$		0			0
$887$	−14.4965	+	18.1781i	−0.486746	+	0.610360i	−0.963182	−	0.268849i	$-0.913357\pi$
$887$	−14.4965	+	18.1781i	−0.486746	+	0.610360i	0.476437	+	0.879209i	$0.341928\pi$
$888$		0			0
$889$	35.3887	+	1.92730i	1.18690	+	0.0646395i
$890$		0			0
$891$	8.93203	+	39.1338i	0.299234	+	1.31103i
$892$		0			0
$893$	−0.148468	+	0.650483i	−0.00496831	+	0.0217676i
$894$		0			0
$895$	6.86137	−	30.0616i	0.229350	−	1.00485i
$896$		0			0
$897$	15.3725	+	67.3515i	0.513274	+	2.24880i
$898$		0			0
$899$	−9.64701	+	4.64575i	−0.321746	+	0.154945i
$900$		0			0
$901$	−3.01332			−0.100388
$902$		0			0
$903$	9.66635	+	5.32106i	0.321676	+	0.177074i
$904$		0			0
$905$	37.8308	+	18.2183i	1.25754	+	0.605598i
$906$		0			0
$907$	3.76041	+	16.4754i	0.124862	+	0.547057i	0.998202	+	0.0599450i	$0.0190925\pi$
$907$	3.76041	+	16.4754i	0.124862	+	0.547057i	−0.873339	+	0.487112i	$0.838050\pi$
$908$		0			0
$909$	−83.5261	−	40.2241i	−2.77039	−	1.33415i
$910$		0			0
$911$	43.4454	−	20.9222i	1.43941	−	0.693183i	0.458688	−	0.888597i	$-0.348320\pi$
$911$	43.4454	−	20.9222i	1.43941	−	0.693183i	0.980721	+	0.195415i	$0.0626052\pi$
$912$		0			0
$913$	23.0675			0.763421
$914$		0			0
$915$	31.2965	+	39.2446i	1.03463	+	1.29739i
$916$		0			0
$917$	8.70027	+	50.6864i	0.287308	+	1.67381i
$918$		0			0
$919$	−9.46409	+	4.55767i	−0.312192	+	0.150344i	−0.583418	−	0.812172i	$-0.698285\pi$
$919$	−9.46409	+	4.55767i	−0.312192	+	0.150344i	0.271226	+	0.962516i	$0.412571\pi$
$920$		0			0
$921$	−40.3586	−	50.6081i	−1.32986	−	1.66759i
$922$		0			0
$923$	21.1134	−	26.4754i	0.694956	−	0.871447i
$924$		0			0
$925$	−16.6335	−	20.8578i	−0.546906	−	0.685799i
$926$		0			0
$927$	−94.9336	−	45.7176i	−3.11803	−	1.50156i
$928$		0			0
$929$	−7.82533	+	34.2850i	−0.256741	+	1.12485i	0.667971	+	0.744187i	$0.267163\pi$
$929$	−7.82533	+	34.2850i	−0.256741	+	1.12485i	−0.924712	+	0.380668i	$0.875694\pi$
$930$		0			0
$931$	−2.35625	−	3.72192i	−0.0772230	−	0.121981i
$932$		0			0
$933$	−8.05568	+	35.2942i	−0.263731	+	1.15548i
$934$		0			0
$935$	5.30263	+	2.55361i	0.173415	+	0.0835121i
$936$		0			0
$937$	16.0560	+	20.1336i	0.524527	+	0.657736i	0.971563	−	0.236779i	$-0.0760919\pi$
$937$	16.0560	+	20.1336i	0.524527	+	0.657736i	−0.447036	+	0.894516i	$0.647520\pi$
$938$		0			0
$939$	41.1200	−	51.5628i	1.34190	−	1.68269i
$940$		0			0
$941$	−0.647819	−	0.812339i	−0.0211183	−	0.0264815i	0.771160	−	0.636641i	$-0.219677\pi$
$941$	−0.647819	−	0.812339i	−0.0211183	−	0.0264815i	−0.792278	+	0.610160i	$0.791105\pi$
$942$		0			0
$943$	−17.5286	+	8.44135i	−0.570811	+	0.274888i
$944$		0			0
$945$	−84.8108	−	4.61887i	−2.75890	−	0.150252i
$946$		0			0
$947$	21.3235	+	26.7389i	0.692922	+	0.868897i	0.996473	−	0.0839185i	$-0.0267436\pi$
$947$	21.3235	+	26.7389i	0.692922	+	0.868897i	−0.303551	+	0.952815i	$0.598172\pi$
$948$		0			0
$949$	−9.94539			−0.322841
$950$		0			0
$951$	−82.2194	+	39.5948i	−2.66615	+	1.28395i
$952$		0			0
$953$	19.4727	+	9.37756i	0.630783	+	0.303769i	0.721822	−	0.692078i	$-0.243305\pi$
$953$	19.4727	+	9.37756i	0.630783	+	0.303769i	−0.0910396	+	0.995847i	$0.529019\pi$
$954$		0			0
$955$	−4.52531	−	19.8267i	−0.146436	−	0.641577i
$956$		0			0
$957$	35.7372	+	17.2101i	1.15522	+	0.556324i
$958$		0			0
$959$	−3.52979	−	20.5640i	−0.113983	−	0.664046i
$960$		0			0
$961$	−24.6961			−0.796649
$962$		0			0
$963$	96.9768	−	46.7016i	3.12503	−	1.50494i
$964$		0			0
$965$	−1.56224	−	6.84463i	−0.0502904	−	0.220336i
$966$		0			0
$967$	−6.95133	+	30.4558i	−0.223540	+	0.979392i	0.731250	+	0.682110i	$0.238937\pi$
$967$	−6.95133	+	30.4558i	−0.223540	+	0.979392i	−0.954790	+	0.297282i	$0.903920\pi$
$968$		0			0
$969$	−0.276821	+	1.21283i	−0.00889276	+	0.0389617i
$970$		0			0
$971$	1.89102	+	8.28509i	0.0606857	+	0.265881i	0.996164	−	0.0875019i	$-0.0278884\pi$
$971$	1.89102	+	8.28509i	0.0606857	+	0.265881i	−0.935479	+	0.353383i	$0.885031\pi$
$972$		0			0
$973$	−0.716165	+	0.298067i	−0.0229592	+	0.00955558i
$974$		0			0
$975$	−19.0358	+	23.8702i	−0.609635	+	0.764458i
$976$		0			0
$977$	1.35686	−	1.70145i	0.0434097	−	0.0544341i	−0.759653	−	0.650329i	$-0.774631\pi$
$977$	1.35686	−	1.70145i	0.0434097	−	0.0544341i	0.803062	+	0.595895i	$0.203203\pi$
$978$		0			0
$979$	−3.60414			−0.115189
$980$		0			0
$981$	10.7427			0.342989
$982$		0			0
$983$	17.1419	−	21.4952i	0.546741	−	0.685591i	−0.429304	−	0.903160i	$-0.641241\pi$
$983$	17.1419	−	21.4952i	0.546741	−	0.685591i	0.976045	+	0.217569i	$0.0698126\pi$
$984$		0			0
$985$	−16.4542	+	20.6330i	−0.524276	+	0.657421i
$986$		0			0
$987$	1.45897	+	8.49971i	0.0464394	+	0.270549i
$988$		0			0
$989$	2.83658	+	12.4279i	0.0901979	+	0.395183i
$990$		0			0
$991$	−0.140427	+	0.615250i	−0.00446080	+	0.0195440i	−0.977109	−	0.212738i	$-0.931762\pi$
$991$	−0.140427	+	0.615250i	−0.00446080	+	0.0195440i	0.972649	+	0.232282i	$0.0746191\pi$
$992$		0			0
$993$	−0.561607	+	2.46056i	−0.0178220	+	0.0780835i
$994$		0			0
$995$	7.18924	+	31.4981i	0.227914	+	0.998558i
$996$		0			0
$997$	−18.4649	+	8.89223i	−0.584789	+	0.281620i	−0.702794	−	0.711393i	$-0.748064\pi$
$997$	−18.4649	+	8.89223i	−0.584789	+	0.281620i	0.118005	+	0.993013i	$0.462350\pi$
$998$		0			0
$999$	−68.1657			−2.15667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.u.d.113.3		18
4.3	odd	2		98.2.e.b.15.1	✓	18
12.11	even	2		882.2.u.g.505.3		18
28.3	even	6		686.2.g.g.177.1		36
28.11	odd	6		686.2.g.h.177.3		36
28.19	even	6		686.2.g.g.67.3		36
28.23	odd	6		686.2.g.h.67.1		36
28.27	even	2		686.2.e.b.99.3		18
49.36	even	7	inner	784.2.u.d.673.3		18
196.11	odd	42		686.2.g.h.471.1		36
196.43	odd	14		4802.2.a.d.1.1		9
196.47	even	42		686.2.g.g.655.1		36
196.51	odd	42		686.2.g.h.655.3		36
196.55	even	14		4802.2.a.c.1.9		9
196.87	even	42		686.2.g.g.471.3		36
196.111	even	14		686.2.e.b.589.3		18
196.183	odd	14		98.2.e.b.85.1	yes	18
588.575	even	14		882.2.u.g.379.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.15.1	✓	18	4.3	odd	2
98.2.e.b.85.1	yes	18	196.183	odd	14
686.2.e.b.99.3		18	28.27	even	2
686.2.e.b.589.3		18	196.111	even	14
686.2.g.g.67.3		36	28.19	even	6
686.2.g.g.177.1		36	28.3	even	6
686.2.g.g.471.3		36	196.87	even	42
686.2.g.g.655.1		36	196.47	even	42
686.2.g.h.67.1		36	28.23	odd	6
686.2.g.h.177.3		36	28.11	odd	6
686.2.g.h.471.1		36	196.11	odd	42
686.2.g.h.655.3		36	196.51	odd	42
784.2.u.d.113.3		18	1.1	even	1	trivial
784.2.u.d.673.3		18	49.36	even	7	inner
882.2.u.g.379.3		18	588.575	even	14
882.2.u.g.505.3		18	12.11	even	2
4802.2.a.c.1.9		9	196.55	even	14
4802.2.a.d.1.1		9	196.43	odd	14

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.91682 - 2.40361i) q^{3} +(-1.88629 + 2.36534i) q^{5} +(-2.31779 - 1.27588i) q^{7} +(-1.43560 - 6.28979i) q^{9} +O(q^{10})\)	\(q+(1.91682 - 2.40361i) q^{3} +(-1.88629 + 2.36534i) q^{5} +(-2.31779 - 1.27588i) q^{7} +(-1.43560 - 6.28979i) q^{9} +(0.673210 - 2.94953i) q^{11} +(0.532118 - 2.33136i) q^{13} +(2.06968 + 9.06784i) q^{15} +(0.579338 - 0.278994i) q^{17} -0.629295 q^{19} +(-7.50949 + 3.12544i) q^{21} +(-8.46635 - 4.07718i) q^{23} +(-0.924113 - 4.04880i) q^{25} +(-9.56038 - 4.60404i) q^{27} +(-3.84228 + 1.85034i) q^{29} +2.51075 q^{31} +(-5.79910 - 7.27184i) q^{33} +(7.38991 - 3.07567i) q^{35} +(5.78775 - 2.78724i) q^{37} +(-4.58372 - 5.74780i) q^{39} +(1.29087 - 1.61870i) q^{41} +(-0.845798 - 1.06060i) q^{43} +(17.5855 + 8.46871i) q^{45} +(0.235928 - 1.03367i) q^{47} +(3.74427 + 5.91443i) q^{49} +(0.439890 - 1.92728i) q^{51} +(-4.22215 - 2.03328i) q^{53} +(5.70676 + 7.15605i) q^{55} +(-1.20624 + 1.51258i) q^{57} +(-1.96057 - 2.45848i) q^{59} +(4.86234 - 2.34158i) q^{61} +(-4.69759 + 16.4101i) q^{63} +(4.51073 + 5.65627i) q^{65} -6.32287 q^{67} +(-26.0284 + 12.5346i) q^{69} +(12.7586 + 6.14419i) q^{71} +(-0.925455 - 4.05468i) q^{73} +(-11.5031 - 5.53961i) q^{75} +(-5.32360 + 5.97744i) q^{77} +11.2211 q^{79} +(-11.9539 + 5.75669i) q^{81} +(1.69664 + 7.43348i) q^{83} +(-0.432885 + 1.89659i) q^{85} +(-2.91744 + 12.7821i) q^{87} +(-0.265089 - 1.16143i) q^{89} +(-4.20787 + 4.72468i) q^{91} +(4.81265 - 6.03488i) q^{93} +(1.18704 - 1.48850i) q^{95} +16.3992 q^{97} -19.5184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{3} + q^{7} - 10 q^{9}+O(q^{10}) \) 18 * q + 5 * q^3 + q^7 - 10 * q^9	\( 18 q + 5 q^{3} + q^{7} - 10 q^{9} - 7 q^{11} - 10 q^{13} - 7 q^{15} + q^{17} + 44 q^{19} - 5 q^{21} - 21 q^{23} + q^{25} - 10 q^{27} + 11 q^{29} + 24 q^{31} - 14 q^{33} + 21 q^{35} - 13 q^{37} + 3 q^{39} + 8 q^{41} + 24 q^{43} + 98 q^{45} - 40 q^{47} - 43 q^{49} - 36 q^{51} + 10 q^{53} - 49 q^{55} + 19 q^{57} - 13 q^{59} + 27 q^{61} - 41 q^{63} + 86 q^{67} - 91 q^{69} + 5 q^{73} + 3 q^{75} - 14 q^{77} + 66 q^{79} - 2 q^{81} - 55 q^{83} - 49 q^{85} + 110 q^{87} + 62 q^{89} - 39 q^{91} + 46 q^{93} + 7 q^{95} - 32 q^{97} - 14 q^{99}+O(q^{100}) \) 18 * q + 5 * q^3 + q^7 - 10 * q^9 - 7 * q^11 - 10 * q^13 - 7 * q^15 + q^17 + 44 * q^19 - 5 * q^21 - 21 * q^23 + q^25 - 10 * q^27 + 11 * q^29 + 24 * q^31 - 14 * q^33 + 21 * q^35 - 13 * q^37 + 3 * q^39 + 8 * q^41 + 24 * q^43 + 98 * q^45 - 40 * q^47 - 43 * q^49 - 36 * q^51 + 10 * q^53 - 49 * q^55 + 19 * q^57 - 13 * q^59 + 27 * q^61 - 41 * q^63 + 86 * q^67 - 91 * q^69 + 5 * q^73 + 3 * q^75 - 14 * q^77 + 66 * q^79 - 2 * q^81 - 55 * q^83 - 49 * q^85 + 110 * q^87 + 62 * q^89 - 39 * q^91 + 46 * q^93 + 7 * q^95 - 32 * q^97 - 14 * q^99

Introduction

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