LMFDB - Embedded newform 84.12.k.b.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(5,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("84.5");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.k (of order $6$, degree $2$, 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:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	84.5
Dual form			84.12.k.b.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-416.405 + 61.2712i) q^{3} +(3914.60 - 6780.29i) q^{5} +(-44460.5 - 768.569i) q^{7} +(169639. - 51027.2i) q^{9} +O(q^{10})$	\(q+(-416.405 + 61.2712i) q^{3} +(3914.60 - 6780.29i) q^{5} +(-44460.5 - 768.569i) q^{7} +(169639. - 51027.2i) q^{9} +(650650. - 375653. i) q^{11} +1.53606e6i q^{13} +(-1.21462e6 + 3.06320e6i) q^{15} +(1.13310e6 + 1.96259e6i) q^{17} +(-1.29343e7 - 7.46761e6i) q^{19} +(1.85607e7 - 2.40411e6i) q^{21} +(4.98810e7 + 2.87988e7i) q^{23} +(-6.23417e6 - 1.07979e7i) q^{25} +(-6.75118e7 + 3.16420e7i) q^{27} -1.09792e8i q^{29} +(-1.32191e8 + 7.63203e7i) q^{31} +(-2.47917e8 + 1.96290e8i) q^{33} +(-1.79256e8 + 2.98446e8i) q^{35} +(-3.09464e8 + 5.36007e8i) q^{37} +(-9.41164e7 - 6.39623e8i) q^{39} +5.72560e8 q^{41} +4.55328e8 q^{43} +(3.18088e8 - 1.34995e9i) q^{45} +(-2.65090e8 + 4.59150e8i) q^{47} +(1.97615e9 + 6.83419e7i) q^{49} +(-5.92078e8 - 7.47803e8i) q^{51} +(3.33336e9 - 1.92452e9i) q^{53} -5.88213e9i q^{55} +(5.84344e9 + 2.31705e9i) q^{57} +(-3.62559e9 - 6.27971e9i) q^{59} +(3.36594e9 + 1.94333e9i) q^{61} +(-7.58144e9 + 2.13832e9i) q^{63} +(1.04149e10 + 6.01307e9i) q^{65} +(3.95833e8 + 6.85604e8i) q^{67} +(-2.25352e10 - 8.93569e9i) q^{69} -2.32309e10i q^{71} +(2.11716e10 - 1.22234e10i) q^{73} +(3.25754e9 + 4.11432e9i) q^{75} +(-2.92169e10 + 1.62017e10i) q^{77} +(1.91219e10 - 3.31201e10i) q^{79} +(2.61735e10 - 1.73124e10i) q^{81} +2.31403e10 q^{83} +1.77425e10 q^{85} +(6.72707e9 + 4.57178e10i) q^{87} +(5.17781e9 - 8.96823e9i) q^{89} +(1.18057e9 - 6.82941e10i) q^{91} +(5.03685e10 - 3.98796e10i) q^{93} +(-1.01265e11 + 5.84655e10i) q^{95} -2.68038e10i q^{97} +(9.12069e10 - 9.69262e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) $ 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9	$ 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) $ 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9 - 4853058 * q^15 + 28700520 * q^19 - 11325429 * q^21 - 316601194 * q^25 - 1368416388 * q^31 + 40874949 * q^33 - 87435712 * q^37 + 1177474410 * q^39 - 3055078348 * q^43 + 4109921793 * q^45 - 742582522 * q^49 - 694793715 * q^51 + 14605100370 * q^57 + 72584834058 * q^61 - 7310837811 * q^63 + 6131679148 * q^67 - 74402605464 * q^73 - 161115157854 * q^75 + 52181713528 * q^79 + 44948282337 * q^81 + 4658488716 * q^85 + 243101263104 * q^87 - 85311757146 * q^91 - 256628211777 * q^93 + 157345775874 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−416.405	+	61.2712i	−0.989347	+	0.145576i
$3$	−416.405	+	61.2712i	−0.989347	+	0.145576i
$4$		0			0
$5$	3914.60	−	6780.29i	0.560212	−	0.970316i	−0.437265	−	0.899333i	$-0.644053\pi$
$5$	3914.60	−	6780.29i	0.560212	−	0.970316i	0.997477	−	0.0709836i	$-0.0226138\pi$
$6$		0			0
$7$	−44460.5	−	768.569i	−0.999851	−	0.0172840i
$7$	−44460.5	−	768.569i	−0.999851	−	0.0172840i
$8$		0			0
$9$	169639.	−	51027.2i	0.957615	−	0.288050i
$10$		0			0
$11$	650650.	−	375653.i	1.21811	−	0.703278i	0.253599	−	0.967309i	$-0.418385\pi$
$11$	650650.	−	375653.i	1.21811	−	0.703278i	0.964514	+	0.264031i	$0.0850522\pi$
$12$		0			0
$13$			1.53606e6i			1.14741i	0.819060	+	0.573707i	$0.194495\pi$
$13$			1.53606e6i			1.14741i	−0.819060	+	0.573707i	$0.805505\pi$
$14$		0			0
$15$	−1.21462e6	+	3.06320e6i	−0.412990	+	1.04153i
$16$		0			0
$17$	1.13310e6	+	1.96259e6i	0.193553	+	0.335243i	0.946425	−	0.322924i	$-0.104666\pi$
$17$	1.13310e6	+	1.96259e6i	0.193553	+	0.335243i	−0.752872	+	0.658166i	$0.771332\pi$
$18$		0			0
$19$	−1.29343e7	−	7.46761e6i	−1.19839	−	0.691890i	−0.238192	−	0.971218i	$-0.576555\pi$
$19$	−1.29343e7	−	7.46761e6i	−1.19839	−	0.691890i	−0.960196	+	0.279328i	$0.909888\pi$
$20$		0			0
$21$	1.85607e7	−	2.40411e6i	0.991715	−	0.128454i
$22$		0			0
$23$	4.98810e7	+	2.87988e7i	1.61597	+	0.932978i	0.987949	+	0.154778i	$0.0494663\pi$
$23$	4.98810e7	+	2.87988e7i	1.61597	+	0.932978i	0.628016	+	0.778200i	$0.283867\pi$
$24$		0			0
$25$	−6.23417e6	−	1.07979e7i	−0.127676	−	0.221141i
$26$		0			0
$27$	−6.75118e7	+	3.16420e7i	−0.905481	+	0.424387i
$28$		0			0
$29$		−	1.09792e8i		−	0.993987i	−0.867754	−	0.496993i	$-0.834437\pi$
$29$		−	1.09792e8i		−	0.993987i	0.867754	−	0.496993i	$-0.165563\pi$
$30$		0			0
$31$	−1.32191e8	+	7.63203e7i	−0.829299	+	0.478796i	−0.853613	−	0.520908i	$-0.825593\pi$
$31$	−1.32191e8	+	7.63203e7i	−0.829299	+	0.478796i	0.0243135	+	0.999704i	$0.492260\pi$
$32$		0			0
$33$	−2.47917e8	+	1.96290e8i	−1.10276	+	0.873114i
$34$		0			0
$35$	−1.79256e8	+	2.98446e8i	−0.576900	+	0.960489i
$36$		0			0
$37$	−3.09464e8	+	5.36007e8i	−0.733670	+	1.27075i	0.221635	+	0.975130i	$0.428861\pi$
$37$	−3.09464e8	+	5.36007e8i	−0.733670	+	1.27075i	−0.955304	+	0.295624i	$0.904473\pi$
$38$		0			0
$39$	−9.41164e7	−	6.39623e8i	−0.167036	−	1.13519i
$40$		0			0
$41$	5.72560e8			0.771809			0.385905	−	0.922539i	$-0.373889\pi$
$41$	5.72560e8			0.771809			0.385905	+	0.922539i	$0.373889\pi$
$42$		0			0
$43$	4.55328e8			0.472333			0.236166	−	0.971713i	$-0.424109\pi$
$43$	4.55328e8			0.472333			0.236166	+	0.971713i	$0.424109\pi$
$44$		0			0
$45$	3.18088e8	−	1.34995e9i	0.256968	−	1.09056i
$46$		0			0
$47$	−2.65090e8	+	4.59150e8i	−0.168599	+	0.292022i	−0.937928	−	0.346831i	$-0.887258\pi$
$47$	−2.65090e8	+	4.59150e8i	−0.168599	+	0.292022i	0.769328	+	0.638854i	$0.220591\pi$
$48$		0			0
$49$	1.97615e9	+	6.83419e7i	0.999403	+	0.0345628i
$50$		0			0
$51$	−5.92078e8	−	7.47803e8i	−0.240294	−	0.303495i
$52$		0			0
$53$	3.33336e9	−	1.92452e9i	1.09488	−	0.632128i	0.160006	−	0.987116i	$-0.448849\pi$
$53$	3.33336e9	−	1.92452e9i	1.09488	−	0.632128i	0.934871	+	0.354988i	$0.115515\pi$
$54$		0			0
$55$		−	5.88213e9i		−	1.57594i
$56$		0			0
$57$	5.84344e9	+	2.31705e9i	1.28634	+	0.510063i
$58$		0			0
$59$	−3.62559e9	−	6.27971e9i	−0.660227	−	1.14355i	−0.980556	−	0.196240i	$-0.937127\pi$
$59$	−3.62559e9	−	6.27971e9i	−0.660227	−	1.14355i	0.320329	−	0.947306i	$-0.396206\pi$
$60$		0			0
$61$	3.36594e9	+	1.94333e9i	0.510261	+	0.294599i	0.732941	−	0.680292i	$-0.238147\pi$
$61$	3.36594e9	+	1.94333e9i	0.510261	+	0.294599i	−0.222680	+	0.974892i	$0.571480\pi$
$62$		0			0
$63$	−7.58144e9	+	2.13832e9i	−0.962451	+	0.271456i
$64$		0			0
$65$	1.04149e10	+	6.01307e9i	1.11335	+	0.642796i
$66$		0			0
$67$	3.95833e8	+	6.85604e8i	0.0358180	+	0.0620386i	0.883379	−	0.468660i	$-0.155263\pi$
$67$	3.95833e8	+	6.85604e8i	0.0358180	+	0.0620386i	−0.847561	+	0.530698i	$0.821930\pi$
$68$		0			0
$69$	−2.25352e10	−	8.93569e9i	−1.73457	−	0.687794i
$70$		0			0
$71$		−	2.32309e10i		−	1.52808i	−0.645171	−	0.764039i	$-0.723214\pi$
$71$		−	2.32309e10i		−	1.52808i	0.645171	−	0.764039i	$-0.276786\pi$
$72$		0			0
$73$	2.11716e10	−	1.22234e10i	1.19530	−	0.690109i	0.235799	−	0.971802i	$-0.424229\pi$
$73$	2.11716e10	−	1.22234e10i	1.19530	−	0.690109i	0.959504	+	0.281693i	$0.0908961\pi$
$74$		0			0
$75$	3.25754e9	+	4.11432e9i	0.158508	+	0.200199i
$76$		0			0
$77$	−2.92169e10	+	1.62017e10i	−1.23009	+	0.682119i
$78$		0			0
$79$	1.91219e10	−	3.31201e10i	0.699169	−	1.21100i	−0.269586	−	0.962976i	$-0.586887\pi$
$79$	1.91219e10	−	3.31201e10i	0.699169	−	1.21100i	0.968755	−	0.248020i	$-0.0797798\pi$
$80$		0			0
$81$	2.61735e10	−	1.73124e10i	0.834054	−	0.551683i
$82$		0			0
$83$	2.31403e10			0.644822			0.322411	−	0.946600i	$-0.395507\pi$
$83$	2.31403e10			0.644822			0.322411	+	0.946600i	$0.395507\pi$
$84$		0			0
$85$	1.77425e10			0.433722
$86$		0			0
$87$	6.72707e9	+	4.57178e10i	0.144701	+	0.983398i
$88$		0			0
$89$	5.17781e9	−	8.96823e9i	0.0982881	−	0.170240i	−0.812688	−	0.582699i	$-0.801997\pi$
$89$	5.17781e9	−	8.96823e9i	0.0982881	−	0.170240i	0.910976	+	0.412459i	$0.135330\pi$
$90$		0			0
$91$	1.18057e9	−	6.82941e10i	0.0198319	−	1.14724i
$92$		0			0
$93$	5.03685e10	−	3.98796e10i	0.750763	−	0.594421i
$94$		0			0
$95$	−1.01265e11	+	5.84655e10i	−1.34270	+	0.775210i
$96$		0			0
$97$		−	2.68038e10i		−	0.316922i	−0.987365	−	0.158461i	$-0.949347\pi$
$97$		−	2.68038e10i		−	0.316922i	0.987365	−	0.158461i	$-0.0506532\pi$
$98$		0			0
$99$	9.12069e10	−	9.69262e10i	0.963905	−	1.02435i
$100$		0			0
$101$	9.56936e9	+	1.65746e10i	0.0905974	+	0.156919i	0.907763	−	0.419484i	$-0.137789\pi$
$101$	9.56936e9	+	1.65746e10i	0.0905974	+	0.156919i	−0.817165	+	0.576403i	$0.804456\pi$
$102$		0			0
$103$	6.09296e10	+	3.51777e10i	0.517874	+	0.298994i	0.736064	−	0.676912i	$-0.236682\pi$
$103$	6.09296e10	+	3.51777e10i	0.517874	+	0.298994i	−0.218191	+	0.975906i	$0.570015\pi$
$104$		0			0
$105$	5.63570e10	−	1.35258e11i	0.430930	−	1.03424i
$106$		0			0
$107$	−2.24209e11	−	1.29447e11i	−1.54541	−	0.892241i	−0.998483	−	0.0550581i	$-0.982466\pi$
$107$	−2.24209e11	−	1.29447e11i	−1.54541	−	0.892241i	−0.546923	−	0.837183i	$-0.684201\pi$
$108$		0			0
$109$	7.10453e10	+	1.23054e11i	0.442272	+	0.766038i	0.997858	−	0.0654214i	$-0.0208391\pi$
$109$	7.10453e10	+	1.23054e11i	0.442272	+	0.766038i	−0.555585	+	0.831459i	$0.687506\pi$
$110$		0			0
$111$	9.60204e10	−	2.42157e11i	0.540863	−	1.36402i
$112$		0			0
$113$		−	2.71376e11i		−	1.38561i	−0.721126	−	0.692804i	$-0.756375\pi$
$113$		−	2.71376e11i		−	1.38561i	0.721126	−	0.692804i	$-0.243625\pi$
$114$		0			0
$115$	3.90529e11	−	2.25472e11i	1.81057	−	1.04533i
$116$		0			0
$117$	7.83810e10	+	2.60576e11i	0.330513	+	1.09878i
$118$		0			0
$119$	−4.88698e10	−	8.81284e10i	−0.187729	−	0.338538i
$120$		0			0
$121$	1.39575e11	−	2.41750e11i	0.489200	−	0.847320i
$122$		0			0
$123$	−2.38417e11	+	3.50815e10i	−0.763587	+	0.112357i
$124$		0			0
$125$	2.84668e11			0.834323
$126$		0			0
$127$	−6.47094e11			−1.73799			−0.868994	−	0.494823i	$-0.835233\pi$
$127$	−6.47094e11			−1.73799			−0.868994	+	0.494823i	$0.835233\pi$
$128$		0			0
$129$	−1.89601e11	+	2.78985e10i	−0.467301	+	0.0687603i
$130$		0			0
$131$	−2.04238e11	+	3.53751e11i	−0.462535	+	0.801135i	−0.999087	−	0.0427331i	$-0.986393\pi$
$131$	−2.04238e11	+	3.53751e11i	−0.462535	+	0.801135i	0.536551	+	0.843868i	$0.319727\pi$
$132$		0			0
$133$	5.69325e11	+	3.41955e11i	1.18625	+	0.712499i
$134$		0			0
$135$	−4.97404e10	+	5.81616e11i	−0.0954714	+	1.11635i
$136$		0			0
$137$	5.62000e11	−	3.24471e11i	0.994885	−	0.574397i	0.0881541	−	0.996107i	$-0.471903\pi$
$137$	5.62000e11	−	3.24471e11i	0.994885	−	0.574397i	0.906731	+	0.421710i	$0.138570\pi$
$138$		0			0
$139$		−	2.15022e11i		−	0.351480i	−0.984437	−	0.175740i	$-0.943768\pi$
$139$		−	2.15022e11i		−	0.351480i	0.984437	−	0.175740i	$-0.0562318\pi$
$140$		0			0
$141$	8.22521e10	−	2.07434e11i	0.124292	−	0.313455i
$142$		0			0
$143$	5.77026e11	+	9.99439e11i	0.806952	+	1.39768i
$144$		0			0
$145$	−7.44420e11	−	4.29791e11i	−0.964481	−	0.556844i
$146$		0			0
$147$	−8.27064e11	+	9.26230e10i	−0.993787	+	0.111294i
$148$		0			0
$149$	1.06652e11	+	6.15753e10i	0.118972	+	0.0686882i	0.558305	−	0.829636i	$-0.311452\pi$
$149$	1.06652e11	+	6.15753e10i	0.118972	+	0.0686882i	−0.439333	+	0.898324i	$0.644785\pi$
$150$		0			0
$151$	−5.05755e10	−	8.75993e10i	−0.0524284	−	0.0908087i	0.838620	−	0.544717i	$-0.183363\pi$
$151$	−5.05755e10	−	8.75993e10i	−0.0524284	−	0.0908087i	−0.891049	+	0.453908i	$0.850029\pi$
$152$		0			0
$153$	2.92363e11	+	2.75111e11i	0.281916	+	0.265281i
$154$		0			0
$155$			1.19505e12i			1.07291i
$156$		0			0
$157$	−1.87323e12	+	1.08151e12i	−1.56726	+	0.904861i	−0.570778	+	0.821104i	$0.693358\pi$
$157$	−1.87323e12	+	1.08151e12i	−1.56726	+	0.904861i	−0.996486	+	0.0837566i	$0.973308\pi$
$158$		0			0
$159$	−1.27011e12	+	1.00562e12i	−0.991191	+	0.784781i
$160$		0			0
$161$	−2.19560e12	−	1.31875e12i	−1.59960	−	0.960769i
$162$		0			0
$163$	1.53517e11	−	2.65900e11i	0.104502	−	0.181003i	−0.809032	−	0.587764i	$-0.800008\pi$
$163$	1.53517e11	−	2.65900e11i	0.104502	−	0.181003i	0.913535	+	0.406761i	$0.133342\pi$
$164$		0			0
$165$	3.60405e11	+	2.44935e12i	0.229419	+	1.55915i
$166$		0			0
$167$	1.44797e12			0.862620			0.431310	−	0.902204i	$-0.358052\pi$
$167$	1.44797e12			0.862620			0.431310	+	0.902204i	$0.358052\pi$
$168$		0			0
$169$	−5.67326e11			−0.316560
$170$		0			0
$171$	−2.57521e12	−	6.06795e11i	−1.34689	−	0.317368i
$172$		0			0
$173$	1.89441e11	−	3.28121e11i	0.0929436	−	0.160983i	−0.815805	−	0.578327i	$-0.803706\pi$
$173$	1.89441e11	−	3.28121e11i	0.0929436	−	0.160983i	0.908748	+	0.417344i	$0.137039\pi$
$174$		0			0
$175$	2.68875e11	+	4.84871e11i	0.123834	+	0.223315i
$176$		0			0
$177$	1.89448e12	+	2.39276e12i	0.819666	+	1.03525i
$178$		0			0
$179$	3.35250e12	−	1.93557e12i	1.36357	−	0.787258i	0.373473	−	0.927641i	$-0.378167\pi$
$179$	3.35250e12	−	1.93557e12i	1.36357	−	0.787258i	0.990097	+	0.140383i	$0.0448335\pi$
$180$		0			0
$181$			2.58201e11i			0.0987931i	0.998779	+	0.0493965i	$0.0157298\pi$
$181$			2.58201e11i			0.0987931i	−0.998779	+	0.0493965i	$0.984270\pi$
$182$		0			0
$183$	−1.52066e12	−	6.02975e11i	−0.547712	−	0.217179i
$184$		0			0
$185$	2.42286e12	+	4.19651e12i	0.822022	+	1.42378i
$186$		0			0
$187$	1.47450e12	+	8.51305e11i	0.471538	+	0.272243i
$188$		0			0
$189$	3.02593e12	−	1.35493e12i	0.912681	−	0.408674i
$190$		0			0
$191$	−3.10868e12	−	1.79480e12i	−0.884896	−	0.510895i	−0.0126261	−	0.999920i	$-0.504019\pi$
$191$	−3.10868e12	−	1.79480e12i	−0.884896	−	0.510895i	−0.872269	+	0.489026i	$0.837352\pi$
$192$		0			0
$193$	1.03325e10	+	1.78964e10i	0.00277742	+	0.00481063i	0.867411	−	0.497593i	$-0.165783\pi$
$193$	1.03325e10	+	1.78964e10i	0.00277742	+	0.00481063i	−0.864633	+	0.502403i	$0.832449\pi$
$194$		0			0
$195$	−4.70526e12	−	1.86573e12i	−1.19507	−	0.473870i
$196$		0			0
$197$		−	1.88985e12i		−	0.453799i	−0.973918	−	0.226900i	$-0.927141\pi$
$197$		−	1.88985e12i		−	0.453799i	0.973918	−	0.226900i	$-0.0728589\pi$
$198$		0			0
$199$	−3.13197e12	+	1.80825e12i	−0.711420	+	0.410739i	−0.811587	−	0.584232i	$-0.801396\pi$
$199$	−3.13197e12	+	1.80825e12i	−0.711420	+	0.410739i	0.100167	+	0.994971i	$0.468062\pi$
$200$		0			0
$201$	−2.06835e11	−	2.61235e11i	−0.0444677	−	0.0561634i
$202$		0			0
$203$	−8.43825e10	+	4.88139e12i	−0.0171800	+	0.993838i
$204$		0			0
$205$	2.24135e12	−	3.88213e12i	0.432377	−	0.748899i
$206$		0			0
$207$	9.93127e12	+	2.34010e12i	1.81622	+	0.427955i
$208$		0			0
$209$	−1.12209e13			−1.94636
$210$		0			0
$211$	−9.86782e11			−0.162431			−0.0812153	−	0.996697i	$-0.525880\pi$
$211$	−9.86782e11			−0.162431			−0.0812153	+	0.996697i	$0.525880\pi$
$212$		0			0
$213$	1.42339e12	+	9.67346e12i	0.222451	+	1.51180i
$214$		0			0
$215$	1.78243e12	−	3.08726e12i	0.264607	−	0.458312i
$216$		0			0
$217$	5.93592e12	−	3.29164e12i	0.837451	−	0.464391i
$218$		0			0
$219$	−8.06701e12	+	6.38710e12i	−1.08211	+	0.856764i
$220$		0			0
$221$	−3.01465e12	+	1.74051e12i	−0.384663	+	0.222085i
$222$		0			0
$223$		−	1.51241e13i		−	1.83651i	−0.395995	−	0.918253i	$-0.629600\pi$
$223$		−	1.51241e13i		−	1.83651i	0.395995	−	0.918253i	$-0.370400\pi$
$224$		0			0
$225$	−1.60854e12	−	1.51363e12i	−0.185964	−	0.174991i
$226$		0			0
$227$	−7.95720e11	−	1.37823e12i	−0.0876230	−	0.151767i	0.818883	−	0.573961i	$-0.194594\pi$
$227$	−7.95720e11	−	1.37823e12i	−0.0876230	−	0.151767i	−0.906506	+	0.422193i	$0.861260\pi$
$228$		0			0
$229$	−1.17063e13	−	6.75866e12i	−1.22836	−	0.709194i	−0.261673	−	0.965156i	$-0.584274\pi$
$229$	−1.17063e13	−	6.75866e12i	−1.22836	−	0.709194i	−0.966687	+	0.255962i	$0.917608\pi$
$230$		0			0
$231$	1.11734e13	−	8.53660e12i	1.11768	−	0.853924i
$232$		0			0
$233$	−1.15987e12	−	6.69654e11i	−0.110651	−	0.0638841i	0.443653	−	0.896198i	$-0.353682\pi$
$233$	−1.15987e12	−	6.69654e11i	−0.110651	−	0.0638841i	−0.554304	+	0.832314i	$0.687015\pi$
$234$		0			0
$235$	2.07545e12	+	3.59478e12i	0.188903	+	0.327189i
$236$		0			0
$237$	−5.93314e12	+	1.49630e13i	−0.515429	+	1.29988i
$238$		0			0
$239$			1.95527e13i			1.62187i	0.585133	+	0.810937i	$0.301042\pi$
$239$			1.95527e13i			1.62187i	−0.585133	+	0.810937i	$0.698958\pi$
$240$		0			0
$241$	1.34554e13	−	7.76848e12i	1.06611	−	0.615520i	0.138996	−	0.990293i	$-0.455613\pi$
$241$	1.34554e13	−	7.76848e12i	1.06611	−	0.615520i	0.927117	+	0.374773i	$0.122279\pi$
$242$		0			0
$243$	−9.83802e12	+	8.81264e12i	−0.744857	+	0.667224i
$244$		0			0
$245$	8.19920e12	−	1.31313e13i	0.593414	−	0.950374i
$246$		0			0
$247$	1.14707e13	−	1.98679e13i	0.793884	−	1.37505i
$248$		0			0
$249$	−9.63574e12	+	1.41784e12i	−0.637953	+	0.0938706i
$250$		0			0
$251$	−7.50746e11			−0.0475650			−0.0237825	−	0.999717i	$-0.507571\pi$
$251$	−7.50746e11			−0.0475650			−0.0237825	+	0.999717i	$0.507571\pi$
$252$		0			0
$253$	4.32735e13			2.62457
$254$		0			0
$255$	−7.38807e12	+	1.08711e12i	−0.429102	+	0.0631395i
$256$		0			0
$257$	8.73516e12	−	1.51297e13i	0.486003	−	0.841782i	−0.513868	−	0.857869i	$-0.671788\pi$
$257$	8.73516e12	−	1.51297e13i	0.486003	−	0.841782i	0.999871	+	0.0160879i	$0.00512115\pi$
$258$		0			0
$259$	1.41709e13	−	2.35933e13i	0.755524	−	1.25788i
$260$		0			0
$261$	−5.60237e12	−	1.86249e13i	−0.286318	−	0.951857i
$262$		0			0
$263$	3.34132e13	−	1.92911e13i	1.63742	−	0.945367i	0.655708	−	0.755014i	$-0.272370\pi$
$263$	3.34132e13	−	1.92911e13i	1.63742	−	0.945367i	0.981716	−	0.190353i	$-0.0609633\pi$
$264$		0			0
$265$		−	3.01349e13i		−	1.41650i
$266$		0			0
$267$	−1.60657e12	+	4.05166e12i	−0.0724582	+	0.182735i
$268$		0			0
$269$	−1.63697e13	−	2.83532e13i	−0.708604	−	1.22734i	−0.965375	−	0.260866i	$-0.915992\pi$
$269$	−1.63697e13	−	2.83532e13i	−0.708604	−	1.22734i	0.256771	−	0.966472i	$-0.417342\pi$
$270$		0			0
$271$	−6.95405e12	−	4.01492e12i	−0.289006	−	0.166858i	0.348488	−	0.937313i	$-0.386695\pi$
$271$	−6.95405e12	−	4.01492e12i	−0.289006	−	0.166858i	−0.637493	+	0.770456i	$0.720029\pi$
$272$		0			0
$273$	3.69287e12	+	2.85103e13i	0.147390	+	1.13791i
$274$		0			0
$275$	−8.11252e12	−	4.68377e12i	−0.311047	−	0.179583i
$276$		0			0
$277$	1.06811e13	+	1.85002e13i	0.393529	+	0.681613i	0.992912	−	0.118850i	$-0.0379207\pi$
$277$	1.06811e13	+	1.85002e13i	0.393529	+	0.681613i	−0.599383	+	0.800462i	$0.704587\pi$
$278$		0			0
$279$	−1.85302e13	+	1.96922e13i	−0.656232	+	0.697382i
$280$		0			0
$281$			2.08162e13i			0.708789i	0.935096	+	0.354394i	$0.115313\pi$
$281$			2.08162e13i			0.708789i	−0.935096	+	0.354394i	$0.884687\pi$
$282$		0			0
$283$	7.91344e12	−	4.56883e12i	0.259143	−	0.149617i	−0.364800	−	0.931086i	$-0.618863\pi$
$283$	7.91344e12	−	4.56883e12i	0.259143	−	0.149617i	0.623944	+	0.781469i	$0.285529\pi$
$284$		0			0
$285$	3.85850e13	−	3.05499e13i	1.21555	−	0.962417i
$286$		0			0
$287$	−2.54563e13	−	4.40052e11i	−0.771694	−	0.0133399i
$288$		0			0
$289$	1.45681e13	−	2.52327e13i	0.425075	−	0.736251i
$290$		0			0
$291$	1.64230e12	+	1.11612e13i	0.0461362	+	0.313546i
$292$		0			0
$293$	−3.99193e12			−0.107997			−0.0539984	−	0.998541i	$-0.517197\pi$
$293$	−3.99193e12			−0.107997			−0.0539984	+	0.998541i	$0.517197\pi$
$294$		0			0
$295$	−5.67710e13			−1.47947
$296$		0			0
$297$	−3.20402e13	+	4.59489e13i	−0.804516	+	1.15376i
$298$		0			0
$299$	−4.42368e13	+	7.66203e13i	−1.07051	+	1.85418i
$300$		0			0
$301$	−2.02441e13	−	3.49951e11i	−0.472262	−	0.00816378i
$302$		0			0
$303$	−5.00028e12	−	6.31542e12i	−0.112476	−	0.142059i
$304$		0			0
$305$	2.63526e13	−	1.52147e13i	0.571709	−	0.330076i
$306$		0			0
$307$		−	1.76589e13i		−	0.369575i	−0.982779	−	0.184787i	$-0.940840\pi$
$307$		−	1.76589e13i		−	0.369575i	0.982779	−	0.184787i	$-0.0591597\pi$
$308$		0			0
$309$	−2.75268e13	−	1.09149e13i	−0.555883	−	0.220419i
$310$		0			0
$311$	6.93664e12	+	1.20146e13i	0.135197	+	0.234168i	0.925673	−	0.378325i	$-0.123500\pi$
$311$	6.93664e12	+	1.20146e13i	0.135197	+	0.234168i	−0.790476	+	0.612493i	$0.790167\pi$
$312$		0			0
$313$	3.92739e13	+	2.26748e13i	0.738941	+	0.426628i	0.821684	−	0.569943i	$-0.193035\pi$
$313$	3.92739e13	+	2.26748e13i	0.738941	+	0.426628i	−0.0827432	+	0.996571i	$0.526368\pi$
$314$		0			0
$315$	−1.51799e13	+	5.97750e13i	−0.275779	+	1.08595i
$316$		0			0
$317$	5.12138e13	+	2.95683e13i	0.898589	+	0.518801i	0.876742	−	0.480961i	$-0.159712\pi$
$317$	5.12138e13	+	2.95683e13i	0.898589	+	0.518801i	0.0218470	+	0.999761i	$0.493045\pi$
$318$		0			0
$319$	−4.12436e13	−	7.14360e13i	−0.699049	−	1.21079i
$320$		0			0
$321$	1.01293e14	+	4.01649e13i	1.65883	+	0.657762i
$322$		0			0
$323$		−	3.38462e13i		−	0.535668i
$324$		0			0
$325$	1.65862e13	−	9.57607e12i	0.253740	−	0.146497i
$326$		0			0
$327$	−3.71233e13	−	4.68873e13i	−0.549078	−	0.693493i
$328$		0			0
$329$	1.21389e13	−	2.02103e13i	0.173621	−	0.289065i
$330$		0			0
$331$	−3.21737e13	+	5.57265e13i	−0.445090	+	0.770918i	−0.998058	−	0.0622840i	$-0.980162\pi$
$331$	−3.21737e13	+	5.57265e13i	−0.445090	+	0.770918i	0.552969	+	0.833202i	$0.313495\pi$
$332$		0			0
$333$	−2.51461e13	+	1.06719e14i	−0.336533	+	1.42823i
$334$		0			0
$335$	6.19812e12			0.0802627
$336$		0			0
$337$	8.15966e13			1.02260			0.511302	−	0.859401i	$-0.329163\pi$
$337$	8.15966e13			1.02260			0.511302	+	0.859401i	$0.329163\pi$
$338$		0			0
$339$	1.66276e13	+	1.13002e14i	0.201711	+	1.37085i
$340$		0			0
$341$	−5.73399e13	+	9.93156e13i	−0.673454	+	1.16646i
$342$		0			0
$343$	−8.78079e13	−	4.55732e12i	−0.998656	−	0.0518313i
$344$		0			0
$345$	−1.48803e14	+	1.17816e14i	−1.63910	+	1.29777i
$346$		0			0
$347$	−2.00571e13	+	1.15800e13i	−0.214021	+	0.123565i	−0.603179	−	0.797606i	$-0.706099\pi$
$347$	−2.00571e13	+	1.15800e13i	−0.214021	+	0.123565i	0.389158	+	0.921171i	$0.372766\pi$
$348$		0			0
$349$		−	3.68983e12i		−	0.0381475i	−0.999818	−	0.0190738i	$-0.993928\pi$
$349$		−	3.68983e12i		−	0.0381475i	0.999818	−	0.0190738i	$-0.00607173\pi$
$350$		0			0
$351$	−4.86040e13	−	1.03702e14i	−0.486948	−	1.03896i
$352$		0			0
$353$	−2.76110e13	−	4.78237e13i	−0.268115	−	0.464389i	0.700260	−	0.713888i	$-0.253067\pi$
$353$	−2.76110e13	−	4.78237e13i	−0.268115	−	0.464389i	−0.968375	+	0.249499i	$0.919734\pi$
$354$		0			0
$355$	−1.57512e14	−	9.09398e13i	−1.48272	−	0.856048i
$356$		0			0
$357$	2.57493e13	+	3.37028e13i	0.235012	+	0.307603i
$358$		0			0
$359$	8.88317e13	+	5.12870e13i	0.786228	+	0.453929i	0.838633	−	0.544697i	$-0.183355\pi$
$359$	8.88317e13	+	5.12870e13i	0.786228	+	0.453929i	−0.0524051	+	0.998626i	$0.516689\pi$
$360$		0			0
$361$	5.32853e13	+	9.22928e13i	0.457423	+	0.792279i
$362$		0			0
$363$	−4.33072e13	+	1.09218e14i	−0.360640	+	0.909509i
$364$		0			0
$365$		−	1.91400e14i		−	1.54643i
$366$		0			0
$367$	5.58521e13	−	3.22462e13i	0.437901	−	0.252822i	−0.264806	−	0.964302i	$-0.585308\pi$
$367$	5.58521e13	−	3.22462e13i	0.437901	−	0.252822i	0.702707	+	0.711480i	$0.251975\pi$
$368$		0			0
$369$	9.71284e13	−	2.92162e13i	0.739096	−	0.222320i
$370$		0			0
$371$	−1.49682e14	+	8.30031e13i	−1.10564	+	0.613109i
$372$		0			0
$373$	1.05428e14	−	1.82606e14i	0.756060	−	1.30953i	−0.188785	−	0.982018i	$-0.560455\pi$
$373$	1.05428e14	−	1.82606e14i	0.756060	−	1.30953i	0.944845	−	0.327516i	$-0.106212\pi$
$374$		0			0
$375$	−1.18537e14	+	1.74420e13i	−0.825435	+	0.121457i
$376$		0			0
$377$	1.68647e14			1.14051
$378$		0			0
$379$	−6.35546e13			−0.417476			−0.208738	−	0.977972i	$-0.566936\pi$
$379$	−6.35546e13			−0.417476			−0.208738	+	0.977972i	$0.566936\pi$
$380$		0			0
$381$	2.69453e14	−	3.96482e13i	1.71947	−	0.253009i
$382$		0			0
$383$	4.87687e13	−	8.44699e13i	0.302377	−	0.523732i	−0.674297	−	0.738460i	$-0.735553\pi$
$383$	4.87687e13	−	8.44699e13i	0.302377	−	0.523732i	0.976674	+	0.214729i	$0.0688867\pi$
$384$		0			0
$385$	−4.52082e12	+	2.61522e14i	−0.0272385	+	1.57571i
$386$		0			0
$387$	7.72413e13	−	2.32341e13i	0.452313	−	0.136056i
$388$		0			0
$389$	−6.76559e13	+	3.90612e13i	−0.385109	+	0.222343i	−0.680039	−	0.733176i	$-0.738037\pi$
$389$	−6.76559e13	+	3.90612e13i	−0.385109	+	0.222343i	0.294930	+	0.955519i	$0.404704\pi$
$390$		0			0
$391$			1.30528e14i			0.722321i
$392$		0			0
$393$	6.33710e13	−	1.59817e14i	0.340982	−	0.859934i
$394$		0			0
$395$	−1.49709e14	−	2.59304e14i	−0.783366	−	1.35683i
$396$		0			0
$397$	7.05457e13	+	4.07296e13i	0.359023	+	0.207282i	0.668652	−	0.743575i	$-0.266871\pi$
$397$	7.05457e13	+	4.07296e13i	0.359023	+	0.207282i	−0.309629	+	0.950857i	$0.600205\pi$
$398$		0			0
$399$	−2.58022e14	−	1.07508e14i	−1.27734	−	0.532219i
$400$		0			0
$401$	1.30748e14	+	7.54872e13i	0.629709	+	0.363563i	0.780639	−	0.624982i	$-0.214894\pi$
$401$	1.30748e14	+	7.54872e13i	0.629709	+	0.363563i	−0.150930	+	0.988544i	$0.548227\pi$
$402$		0			0
$403$	−1.17233e14	−	2.03053e14i	−0.549378	−	0.951550i
$404$		0			0
$405$	−1.49242e13	−	2.45235e14i	−0.0680594	−	1.11836i
$406$		0			0
$407$			4.65004e14i			2.06390i
$408$		0			0
$409$	3.98507e13	−	2.30078e13i	0.172170	−	0.0994024i	−0.411439	−	0.911437i	$-0.634974\pi$
$409$	3.98507e13	−	2.30078e13i	0.172170	−	0.0994024i	0.583609	+	0.812035i	$0.301640\pi$
$410$		0			0
$411$	−2.14139e14	+	1.69545e14i	−0.900668	+	0.713109i
$412$		0			0
$413$	1.56369e14	+	2.81986e14i	0.640363	+	1.15479i
$414$		0			0
$415$	9.05852e13	−	1.56898e14i	0.361237	−	0.625682i
$416$		0			0
$417$	1.31746e13	+	8.95360e13i	0.0511670	+	0.347736i
$418$		0			0
$419$	3.64676e14			1.37953			0.689763	−	0.724035i	$-0.257715\pi$
$419$	3.64676e14			1.37953			0.689763	+	0.724035i	$0.257715\pi$
$420$		0			0
$421$	4.46037e13			0.164369			0.0821844	−	0.996617i	$-0.473810\pi$
$421$	4.46037e13			0.164369			0.0821844	+	0.996617i	$0.473810\pi$
$422$		0			0
$423$	−2.15404e13	+	9.14164e13i	−0.0773360	+	0.328210i
$424$		0			0
$425$	1.41279e13	−	2.44702e13i	0.0494239	−	0.0856048i
$426$		0			0
$427$	−1.48158e14	−	8.89882e13i	−0.505093	−	0.303375i
$428$		0			0
$429$	−3.01513e14	−	3.80816e14i	−1.00182	−	1.26532i
$430$		0			0
$431$	2.45964e14	−	1.42007e14i	0.796610	−	0.459923i	−0.0456743	−	0.998956i	$-0.514544\pi$
$431$	2.45964e14	−	1.42007e14i	0.796610	−	0.459923i	0.842284	+	0.539033i	$0.181210\pi$
$432$		0			0
$433$			4.58726e14i			1.44834i	0.689623	+	0.724169i	$0.257776\pi$
$433$			4.58726e14i			1.44834i	−0.689623	+	0.724169i	$0.742224\pi$
$434$		0			0
$435$	3.36314e14	+	1.33355e14i	1.03527	+	0.410506i
$436$		0			0
$437$	−4.30117e14	−	7.44984e14i	−1.29104	−	2.23614i
$438$		0			0
$439$	1.20636e14	+	6.96493e13i	0.353120	+	0.203874i	0.666059	−	0.745899i	$-0.267980\pi$
$439$	1.20636e14	+	6.96493e13i	0.353120	+	0.203874i	−0.312938	+	0.949773i	$0.601313\pi$
$440$		0			0
$441$	3.38718e14	−	8.92438e13i	0.966999	−	0.254780i
$442$		0			0
$443$	−5.37215e14	−	3.10161e14i	−1.49599	−	0.863708i	−0.495997	−	0.868324i	$-0.665197\pi$
$443$	−5.37215e14	−	3.10161e14i	−1.49599	−	0.863708i	−0.999989	+	0.00461656i	$0.998530\pi$
$444$		0			0
$445$	−4.05381e13	−	7.02141e13i	−0.110124	−	0.190741i
$446$		0			0
$447$	−4.81830e13	−	1.91056e13i	−0.127703	−	0.0506371i
$448$		0			0
$449$			2.84911e14i			0.736807i	0.929666	+	0.368404i	$0.120096\pi$
$449$			2.84911e14i			0.736807i	−0.929666	+	0.368404i	$0.879904\pi$
$450$		0			0
$451$	3.72536e14	−	2.15084e14i	0.940151	−	0.542797i
$452$		0			0
$453$	2.64272e13	+	3.33779e13i	0.0650895	+	0.0822090i
$454$		0			0
$455$	−4.58432e14	−	2.75349e14i	−1.10208	−	0.661943i
$456$		0			0
$457$	1.73713e14	−	3.00879e14i	0.407654	−	0.706078i	−0.586972	−	0.809607i	$-0.699680\pi$
$457$	1.73713e14	−	3.00879e14i	0.407654	−	0.706078i	0.994626	+	0.103529i	$0.0330135\pi$
$458$		0			0
$459$	−1.38598e14	−	9.66443e13i	−0.317531	−	0.221415i
$460$		0			0
$461$	−1.60458e14			−0.358928			−0.179464	−	0.983765i	$-0.557436\pi$
$461$	−1.60458e14			−0.358928			−0.179464	+	0.983765i	$0.557436\pi$
$462$		0			0
$463$	4.22098e14			0.921972			0.460986	−	0.887408i	$-0.347496\pi$
$463$	4.22098e14			0.921972			0.460986	+	0.887408i	$0.347496\pi$
$464$		0			0
$465$	−7.32224e13	−	4.97626e14i	−0.156190	−	1.06148i
$466$		0			0
$467$	4.32028e13	−	7.48294e13i	0.0900055	−	0.155894i	−0.817508	−	0.575918i	$-0.804645\pi$
$467$	4.32028e13	−	7.48294e13i	0.0900055	−	0.155894i	0.907513	+	0.420024i	$0.137978\pi$
$468$		0			0
$469$	−1.70720e13	−	3.07865e13i	−0.0347404	−	0.0626484i
$470$		0			0
$471$	7.13755e14	−	5.65120e14i	1.41884	−	1.12338i
$472$		0			0
$473$	2.96259e14	−	1.71045e14i	0.575355	−	0.332181i
$474$		0			0
$475$			1.86217e14i			0.353350i
$476$		0			0
$477$	4.67264e14	−	4.96565e14i	0.866386	−	0.920715i
$478$		0			0
$479$	5.38068e14	+	9.31961e14i	0.974971	+	1.68870i	0.680031	+	0.733184i	$0.261967\pi$
$479$	5.38068e14	+	9.31961e14i	0.974971	+	1.68870i	0.294941	+	0.955516i	$0.404700\pi$
$480$		0			0
$481$	−8.23341e14	−	4.75356e14i	−1.45808	−	0.841824i
$482$		0			0
$483$	9.95060e14	+	4.14605e14i	1.72242	+	0.717671i
$484$		0			0
$485$	−1.81738e14	−	1.04926e14i	−0.307514	−	0.177544i
$486$		0			0
$487$	5.41751e14	+	9.38341e14i	0.896171	+	1.55221i	0.832349	+	0.554252i	$0.186996\pi$
$487$	5.41751e14	+	9.38341e14i	0.896171	+	1.55221i	0.0638218	+	0.997961i	$0.479671\pi$
$488$		0			0
$489$	−4.76333e13	+	1.20128e14i	−0.0770393	+	0.194288i
$490$		0			0
$491$		−	4.73703e14i		−	0.749131i	−0.927200	−	0.374565i	$-0.877792\pi$
$491$		−	4.73703e14i		−	0.749131i	0.927200	−	0.374565i	$-0.122208\pi$
$492$		0			0
$493$	2.15476e14	−	1.24405e14i	0.333227	−	0.192389i
$494$		0			0
$495$	−3.00149e14	−	9.97837e14i	−0.453950	−	1.50914i
$496$		0			0
$497$	−1.78545e13	+	1.03286e15i	−0.0264112	+	1.52785i
$498$		0			0
$499$	−2.91573e14	+	5.05019e14i	−0.421885	+	0.730726i	−0.996124	−	0.0879620i	$-0.971965\pi$
$499$	−2.91573e14	+	5.05019e14i	−0.421885	+	0.730726i	0.574239	+	0.818688i	$0.305298\pi$
$500$		0			0
$501$	−6.02942e14	+	8.87190e13i	−0.853431	+	0.125577i
$502$		0			0
$503$	−1.37096e15			−1.89845			−0.949227	−	0.314592i	$-0.898132\pi$
$503$	−1.37096e15			−1.89845			−0.949227	+	0.314592i	$0.898132\pi$
$504$		0			0
$505$	1.49841e14			0.203015
$506$		0			0
$507$	2.36237e14	−	3.47608e13i	0.313188	−	0.0460835i
$508$		0			0
$509$	1.55389e14	−	2.69141e14i	0.201591	−	0.349166i	−0.747450	−	0.664318i	$-0.768722\pi$
$509$	1.55389e14	−	2.69141e14i	0.201591	−	0.349166i	0.949041	+	0.315152i	$0.102055\pi$
$510$		0			0
$511$	−9.50695e14	+	5.27188e14i	−1.20705	+	0.669346i
$512$		0			0
$513$	1.10951e15	+	9.48862e13i	1.37875	+	0.117912i
$514$		0			0
$515$	4.77031e14	−	2.75414e14i	0.580238	−	0.335001i
$516$		0			0
$517$			3.98328e14i			0.474288i
$518$		0			0
$519$	−5.87796e13	+	1.48238e14i	−0.0685182	+	0.172798i
$520$		0			0
$521$	−1.38465e14	−	2.39828e14i	−0.158027	−	0.273711i	0.776130	−	0.630573i	$-0.217180\pi$
$521$	−1.38465e14	−	2.39828e14i	−0.158027	−	0.273711i	−0.934157	+	0.356862i	$0.883847\pi$
$522$		0			0
$523$	−9.74025e14	−	5.62353e14i	−1.08846	−	0.628420i	−0.155291	−	0.987869i	$-0.549631\pi$
$523$	−9.74025e14	−	5.62353e14i	−1.08846	−	0.628420i	−0.933165	+	0.359449i	$0.882965\pi$
$524$		0			0
$525$	−1.41670e14	−	1.85428e14i	−0.155025	−	0.202908i
$526$		0			0
$527$	−2.99570e14	−	1.72957e14i	−0.321026	−	0.185344i
$528$		0			0
$529$	1.18234e15	+	2.04787e15i	1.24090	+	2.14930i
$530$		0			0
$531$	−9.35477e14	−	8.80278e14i	−0.961642	−	0.904899i
$532$		0			0
$533$			8.79488e14i			0.885585i
$534$		0			0
$535$	−1.75538e15	+	1.01347e15i	−1.73151	+	0.999689i
$536$		0			0
$537$	−1.27740e15	+	1.01139e15i	−1.23444	+	0.977374i
$538$		0			0
$539$	1.31145e15	−	6.97878e14i	1.24169	−	0.660757i
$540$		0			0
$541$	−3.40956e14	+	5.90554e14i	−0.316311	+	0.547866i	−0.979715	−	0.200395i	$-0.935778\pi$
$541$	−3.40956e14	+	5.90554e14i	−0.316311	+	0.547866i	0.663405	+	0.748261i	$0.269111\pi$
$542$		0			0
$543$	−1.58203e13	−	1.07516e14i	−0.0143819	−	0.0977406i
$544$		0			0
$545$	1.11246e15			0.991066
$546$		0			0
$547$	−1.13043e15			−0.986992			−0.493496	−	0.869748i	$-0.664281\pi$
$547$	−1.13043e15			−0.986992			−0.493496	+	0.869748i	$0.664281\pi$
$548$		0			0
$549$	6.70156e14	+	1.57909e14i	0.573493	+	0.135132i
$550$		0			0
$551$	−8.19882e14	+	1.42008e15i	−0.687729	+	1.19118i
$552$		0			0
$553$	−8.75624e14	+	1.45784e15i	−0.719995	+	1.19873i
$554$		0			0
$555$	−1.26601e15	−	1.59900e15i	−1.02053	−	1.28895i
$556$		0			0
$557$	1.14154e15	−	6.59067e14i	0.902167	−	0.520866i	0.0242644	−	0.999706i	$-0.492276\pi$
$557$	1.14154e15	−	6.59067e14i	0.902167	−	0.520866i	0.877903	+	0.478839i	$0.158942\pi$
$558$		0			0
$559$			6.99412e14i			0.541961i
$560$		0			0
$561$	−6.66150e14	−	2.64143e14i	−0.506147	−	0.200698i
$562$		0			0
$563$	1.07279e15	+	1.85812e15i	0.799313	+	1.38445i	0.920064	+	0.391767i	$0.128136\pi$
$563$	1.07279e15	+	1.85812e15i	0.799313	+	1.38445i	−0.120752	+	0.992683i	$0.538531\pi$
$564$		0			0
$565$	−1.84001e15	−	1.06233e15i	−1.34448	−	0.776235i
$566$		0			0
$567$	−1.17699e15	+	7.49601e14i	−0.843465	+	0.537185i
$568$		0			0
$569$	−1.09271e14	−	6.30877e13i	−0.0768047	−	0.0443432i	0.461106	−	0.887345i	$-0.347453\pi$
$569$	−1.09271e14	−	6.30877e13i	−0.0768047	−	0.0443432i	−0.537911	+	0.843002i	$0.680786\pi$
$570$		0			0
$571$	8.35236e14	+	1.44667e15i	0.575851	+	0.997404i	0.995949	+	0.0899247i	$0.0286626\pi$
$571$	8.35236e14	+	1.44667e15i	0.575851	+	0.997404i	−0.420097	+	0.907479i	$0.638004\pi$
$572$		0			0
$573$	1.40444e15	+	5.56889e14i	0.949843	+	0.376633i
$574$		0			0
$575$		−	7.18147e14i		−	0.476475i
$576$		0			0
$577$	−2.56393e15	+	1.48029e15i	−1.66893	+	0.963560i	−0.700720	+	0.713436i	$0.747138\pi$
$577$	−2.56393e15	+	1.48029e15i	−1.66893	+	0.963560i	−0.968214	+	0.250124i	$0.919529\pi$
$578$		0			0
$579$	−5.39905e12	−	6.81908e12i	−0.00344814	−	0.00435505i
$580$		0			0
$581$	−1.02883e15	−	1.77849e13i	−0.644726	−	0.0111451i
$582$		0			0
$583$	1.44590e15	−	2.50438e15i	0.889123	−	1.54001i
$584$		0			0
$585$	2.07361e15	+	4.88604e14i	1.25132	+	0.294849i
$586$		0			0
$587$	1.56255e15			0.925386			0.462693	−	0.886519i	$-0.346883\pi$
$587$	1.56255e15			0.925386			0.462693	+	0.886519i	$0.346883\pi$
$588$		0			0
$589$	2.27972e15			1.32510
$590$		0			0
$591$	1.15794e14	+	7.86944e14i	0.0660623	+	0.448965i
$592$		0			0
$593$	−3.24512e14	+	5.62072e14i	−0.181731	+	0.314768i	−0.942470	−	0.334290i	$-0.891504\pi$
$593$	−3.24512e14	+	5.62072e14i	−0.181731	+	0.314768i	0.760739	+	0.649058i	$0.224837\pi$
$594$		0			0
$595$	−7.88842e14	−	1.36364e13i	−0.433657	−	0.00749644i
$596$		0			0
$597$	1.19337e15	−	9.44862e14i	0.644048	−	0.509929i
$598$		0			0
$599$	1.60010e15	−	9.23818e14i	0.847812	−	0.489485i	−0.0120998	−	0.999927i	$-0.503852\pi$
$599$	1.60010e15	−	9.23818e14i	0.847812	−	0.489485i	0.859912	+	0.510442i	$0.170518\pi$
$600$		0			0
$601$		−	9.66604e14i		−	0.502851i	−0.967877	−	0.251425i	$-0.919101\pi$
$601$		−	9.66604e14i		−	0.502851i	0.967877	−	0.251425i	$-0.0808993\pi$
$602$		0			0
$603$	1.02133e14	+	9.61066e13i	0.0521701	+	0.0490917i
$604$		0			0
$605$	−1.09276e15	−	1.89271e15i	−0.548112	−	0.949358i
$606$		0			0
$607$	1.62928e15	+	9.40663e14i	0.802522	+	0.463336i	0.844352	−	0.535788i	$-0.179986\pi$
$607$	1.62928e15	+	9.40663e14i	0.802522	+	0.463336i	−0.0418303	+	0.999125i	$0.513319\pi$
$608$		0			0
$609$	−2.63952e14	−	2.03781e15i	−0.127682	−	0.985752i
$610$		0			0
$611$	−7.05282e14	−	4.07195e14i	−0.335071	−	0.193453i
$612$		0			0
$613$	−1.18489e14	−	2.05229e14i	−0.0552898	−	0.0957647i	0.837056	−	0.547118i	$-0.184275\pi$
$613$	−1.18489e14	−	2.05229e14i	−0.0552898	−	0.0957647i	−0.892346	+	0.451353i	$0.850942\pi$
$614$		0			0
$615$	−6.95444e14	+	1.75387e15i	−0.318749	+	0.803865i
$616$		0			0
$617$		−	1.98091e15i		−	0.891859i	−0.895068	−	0.445929i	$-0.852873\pi$
$617$		−	1.98091e15i		−	0.891859i	0.895068	−	0.445929i	$-0.147127\pi$
$618$		0			0
$619$	2.51866e15	−	1.45415e15i	1.11396	−	0.643146i	0.174109	−	0.984726i	$-0.444295\pi$
$619$	2.51866e15	−	1.45415e15i	1.11396	−	0.643146i	0.939853	+	0.341580i	$0.110962\pi$
$620$		0			0
$621$	−4.27881e15	−	3.65928e14i	−1.85917	−	0.158998i
$622$		0			0
$623$	−2.37101e14	+	3.94752e14i	−0.101216	+	0.168516i
$624$		0			0
$625$	1.41877e15	−	2.45737e15i	0.595074	−	1.03070i
$626$		0			0
$627$	4.67244e15	−	6.87520e14i	1.92563	−	0.283344i
$628$		0			0
$629$	−1.40261e15			−0.568015
$630$		0			0
$631$	1.45914e15			0.580678			0.290339	−	0.956924i	$-0.406232\pi$
$631$	1.45914e15			0.580678			0.290339	+	0.956924i	$0.406232\pi$
$632$		0			0
$633$	4.10901e14	−	6.04614e13i	0.160700	−	0.0236460i
$634$		0			0
$635$	−2.53311e15	+	4.38748e15i	−0.973642	+	1.68640i
$636$		0			0
$637$	−1.04977e14	+	3.03548e15i	−0.0396578	+	1.14673i
$638$		0			0
$639$	−1.18541e15	−	3.94086e15i	−0.440163	−	1.46331i
$640$		0			0
$641$	−4.05736e15	+	2.34252e15i	−1.48090	+	0.854995i	−0.999766	−	0.0216541i	$-0.993107\pi$
$641$	−4.05736e15	+	2.34252e15i	−1.48090	+	0.854995i	−0.481130	+	0.876649i	$0.659773\pi$
$642$		0			0
$643$			1.55663e14i			0.0558503i	0.999610	+	0.0279252i	$0.00889001\pi$
$643$			1.55663e14i			0.0558503i	−0.999610	+	0.0279252i	$0.991110\pi$
$644$		0			0
$645$	−5.53052e14	+	1.39476e15i	−0.195069	+	0.491950i
$646$		0			0
$647$	−5.82203e14	−	1.00841e15i	−0.201884	−	0.349673i	0.747252	−	0.664541i	$-0.231373\pi$
$647$	−5.82203e14	−	1.00841e15i	−0.201884	−	0.349673i	−0.949135	+	0.314868i	$0.898040\pi$
$648$		0			0
$649$	−4.71799e15	−	2.72393e15i	−1.60846	−	0.928646i
$650$		0			0
$651$	−2.27006e15	+	1.73435e15i	−0.760925	+	0.581357i
$652$		0			0
$653$	−1.02620e15	−	5.92478e14i	−0.338229	−	0.195276i	0.321260	−	0.946991i	$-0.395894\pi$
$653$	−1.02620e15	−	5.92478e14i	−0.338229	−	0.195276i	−0.659488	+	0.751715i	$0.729227\pi$
$654$		0			0
$655$	1.59902e15	+	2.76959e15i	0.518236	+	0.897611i
$656$		0			0
$657$	2.96779e15	−	3.15390e15i	0.945854	−	1.00517i
$658$		0			0
$659$		−	3.09117e15i		−	0.968843i	−0.874835	−	0.484422i	$-0.839030\pi$
$659$		−	3.09117e15i		−	0.968843i	0.874835	−	0.484422i	$-0.160970\pi$
$660$		0			0
$661$	1.36474e15	−	7.87932e14i	0.420670	−	0.242874i	−0.274694	−	0.961532i	$-0.588577\pi$
$661$	1.36474e15	−	7.87932e14i	0.420670	−	0.242874i	0.695364	+	0.718658i	$0.255243\pi$
$662$		0			0
$663$	1.14867e15	−	9.09468e14i	0.348235	−	0.275717i
$664$		0			0
$665$	4.54723e15	−	2.52157e15i	1.35590	−	0.751887i
$666$		0			0
$667$	3.16187e15	−	5.47652e15i	0.927368	−	1.60625i
$668$		0			0
$669$	9.26671e14	+	6.29774e15i	0.267351	+	1.81694i
$670$		0			0
$671$	2.92007e15			0.828741
$672$		0			0
$673$	−2.57612e15			−0.719256			−0.359628	−	0.933096i	$-0.617096\pi$
$673$	−2.57612e15			−0.719256			−0.359628	+	0.933096i	$0.617096\pi$
$674$		0			0
$675$	7.62547e14	+	5.31724e14i	0.209457	+	0.146055i
$676$		0			0
$677$	3.50799e14	−	6.07601e14i	0.0948026	−	0.164203i	−0.814724	−	0.579849i	$-0.803111\pi$
$677$	3.50799e14	−	6.07601e14i	0.0948026	−	0.164203i	0.909526	+	0.415647i	$0.136445\pi$
$678$		0			0
$679$	−2.06006e13	+	1.19171e15i	−0.00547767	+	0.316874i
$680$		0			0
$681$	4.15787e14	+	5.25145e14i	0.108783	+	0.137395i
$682$		0			0
$683$	−1.03080e15	+	5.95135e14i	−0.265377	+	0.153215i	−0.626785	−	0.779193i	$-0.715629\pi$
$683$	−1.03080e15	+	5.95135e14i	−0.265377	+	0.153215i	0.361408	+	0.932408i	$0.382296\pi$
$684$		0			0
$685$		−	5.08069e15i		−	1.28714i
$686$		0			0
$687$	5.28868e15	+	2.09707e15i	1.31852	+	0.522819i
$688$		0			0
$689$	2.95618e15	+	5.12025e15i	0.725312	+	1.25628i
$690$		0			0
$691$	−4.26662e15	−	2.46334e15i	−1.03028	−	0.594832i	−0.113215	−	0.993571i	$-0.536115\pi$
$691$	−4.26662e15	−	2.46334e15i	−1.03028	−	0.594832i	−0.917065	+	0.398738i	$0.869448\pi$
$692$		0			0
$693$	−4.12960e15	+	4.23929e15i	−0.981465	+	1.00753i
$694$		0			0
$695$	−1.45791e15	−	8.41724e14i	−0.341047	−	0.196903i
$696$		0			0
$697$	6.48768e14	+	1.12370e15i	0.149386	+	0.258744i
$698$		0			0
$699$	5.24008e14	+	2.07780e14i	0.118772	+	0.0470955i
$700$		0			0
$701$		−	1.31638e15i		−	0.293719i	−0.989157	−	0.146860i	$-0.953083\pi$
$701$		−	1.31638e15i		−	0.293719i	0.989157	−	0.146860i	$-0.0469166\pi$
$702$		0			0
$703$	8.00539e15	−	4.62191e15i	1.75844	−	1.01524i
$704$		0			0
$705$	−1.08448e15	−	1.36972e15i	−0.234521	−	0.296204i
$706$		0			0
$707$	−4.12720e14	−	7.44271e14i	−0.0878716	−	0.158462i
$708$		0			0
$709$	2.86327e15	−	4.95932e15i	0.600216	−	1.03960i	−0.392572	−	0.919721i	$-0.628415\pi$
$709$	2.86327e15	−	4.95932e15i	0.600216	−	1.03960i	0.992788	−	0.119883i	$-0.0382520\pi$
$710$		0			0
$711$	1.55379e15	−	6.59419e15i	0.320707	−	1.36106i
$712$		0			0
$713$	−8.79173e15			−1.78683
$714$		0			0
$715$	9.03532e15			1.80826
$716$		0			0
$717$	−1.19802e15	−	8.14182e15i	−0.236106	−	1.60460i
$718$		0			0
$719$	3.94175e14	−	6.82732e14i	0.0765034	−	0.132508i	−0.825236	−	0.564789i	$-0.808958\pi$
$719$	3.94175e14	−	6.82732e14i	0.0765034	−	0.132508i	0.901739	+	0.432281i	$0.142291\pi$
$720$		0			0
$721$	−2.68193e15	−	1.61085e15i	−0.512628	−	0.307901i
$722$		0			0
$723$	−5.12691e15	+	4.05926e15i	−0.965150	+	0.764164i
$724$		0			0
$725$	−1.18552e15	+	6.84460e14i	−0.219811	+	0.126908i
$726$		0			0
$727$			1.07902e16i			1.97056i	0.170952	+	0.985279i	$0.445316\pi$
$727$			1.07902e16i			1.97056i	−0.170952	+	0.985279i	$0.554684\pi$
$728$		0			0
$729$	3.55663e15	−	4.27241e15i	0.639791	−	0.768549i
$730$		0			0
$731$	5.15932e14	+	8.93621e14i	0.0914212	+	0.158346i
$732$		0			0
$733$	−5.87209e15	−	3.39025e15i	−1.02499	−	0.591779i	−0.109446	−	0.993993i	$-0.534908\pi$
$733$	−5.87209e15	−	3.39025e15i	−1.02499	−	0.591779i	−0.915546	+	0.402213i	$0.868241\pi$
$734$		0			0
$735$	−2.60961e15	+	5.97031e15i	−0.448741	+	1.02664i
$736$		0			0
$737$	5.15098e14	+	2.97392e14i	0.0872607	+	0.0503800i
$738$		0			0
$739$	4.13087e15	+	7.15488e15i	0.689441	+	1.19415i	0.972019	+	0.234903i	$0.0754771\pi$
$739$	4.13087e15	+	7.15488e15i	0.689441	+	1.19415i	−0.282578	+	0.959244i	$0.591190\pi$
$740$		0			0
$741$	−3.55913e15	+	8.97589e15i	−0.585253	+	1.47597i
$742$		0			0
$743$		−	1.13253e16i		−	1.83489i	−0.397861	−	0.917446i	$-0.630247\pi$
$743$		−	1.13253e16i		−	1.83489i	0.397861	−	0.917446i	$-0.369753\pi$
$744$		0			0
$745$	8.34997e14	−	4.82086e14i	0.133299	−	0.0769600i
$746$		0			0
$747$	3.92549e15	−	1.18079e15i	0.617492	−	0.185741i
$748$		0			0
$749$	9.86897e15	+	5.92761e15i	1.52975	+	0.918818i
$750$		0			0
$751$	5.24618e15	−	9.08665e15i	0.801353	−	1.38798i	−0.117373	−	0.993088i	$-0.537447\pi$
$751$	5.24618e15	−	9.08665e15i	0.801353	−	1.38798i	0.918726	−	0.394896i	$-0.129219\pi$
$752$		0			0
$753$	3.12614e14	−	4.59991e13i	0.0470583	−	0.00692432i
$754$		0			0
$755$	−7.91932e14			−0.117484
$756$		0			0
$757$	−1.94582e15			−0.284495			−0.142248	−	0.989831i	$-0.545433\pi$
$757$	−1.94582e15			−0.284495			−0.142248	+	0.989831i	$0.545433\pi$
$758$		0			0
$759$	−1.80193e16	+	2.65142e15i	−2.59661	+	0.382075i
$760$		0			0
$761$	−1.28327e15	+	2.22269e15i	−0.182265	+	0.315692i	−0.942652	−	0.333779i	$-0.891676\pi$
$761$	−1.28327e15	+	2.22269e15i	−0.182265	+	0.315692i	0.760386	+	0.649471i	$0.225010\pi$
$762$		0			0
$763$	−3.06413e15	−	5.52565e15i	−0.428966	−	0.773568i
$764$		0			0
$765$	3.00982e15	−	9.05353e14i	0.415339	−	0.124934i
$766$		0			0
$767$	9.64603e15	−	5.56914e15i	1.31212	−	0.757554i
$768$		0			0
$769$		−	9.14883e14i		−	0.122679i	−0.998117	−	0.0613396i	$-0.980463\pi$
$769$		−	9.14883e14i		−	0.122679i	0.998117	−	0.0613396i	$-0.0195373\pi$
$770$		0			0
$771$	−2.71034e15	+	6.83531e15i	−0.358282	+	0.903564i
$772$		0			0
$773$	−1.12136e15	−	1.94225e15i	−0.146136	−	0.253115i	0.783660	−	0.621190i	$-0.213350\pi$
$773$	−1.12136e15	−	1.94225e15i	−0.146136	−	0.253115i	−0.929796	+	0.368075i	$0.880017\pi$
$774$		0			0
$775$	1.64820e15	+	9.51587e14i	0.211763	+	0.122261i
$776$		0			0
$777$	−4.45523e15	+	1.06926e16i	−0.564358	+	1.35447i
$778$		0			0
$779$	−7.40566e15	−	4.27566e15i	−0.924927	−	0.534007i
$780$		0			0
$781$	−8.72676e15	−	1.51152e16i	−1.07466	−	1.86137i
$782$		0			0
$783$	3.47402e15	+	7.41224e15i	0.421836	+	0.900036i
$784$		0			0
$785$			1.69347e16i			2.02766i
$786$		0			0
$787$	2.84798e15	−	1.64428e15i	0.336260	−	0.194140i	−0.322357	−	0.946618i	$-0.604475\pi$
$787$	2.84798e15	−	1.64428e15i	0.336260	−	0.194140i	0.658617	+	0.752478i	$0.271142\pi$
$788$		0			0
$789$	−1.27314e16	+	1.00802e16i	−1.48236	+	1.17367i
$790$		0			0
$791$	−2.08571e14	+	1.20655e16i	−0.0239488	+	1.38540i
$792$		0			0
$793$	−2.98507e15	+	5.17029e15i	−0.338028	+	0.585481i
$794$		0			0
$795$	1.84640e15	+	1.25483e16i	0.206209	+	1.40141i
$796$		0			0
$797$	9.63390e15			1.06116			0.530580	−	0.847635i	$-0.321974\pi$
$797$	9.63390e15			1.06116			0.530580	+	0.847635i	$0.321974\pi$
$798$		0			0
$799$	−1.20149e15			−0.130531
$800$		0			0
$801$	4.20733e14	−	1.78557e15i	0.0450845	−	0.191336i
$802$		0			0
$803$	9.18354e15	−	1.59064e16i	0.970677	−	1.68126i
$804$		0			0
$805$	−1.75364e16	+	9.72444e15i	−1.82836	+	1.01388i
$806$		0			0
$807$	8.55366e15	+	1.08034e16i	0.879727	+	1.11111i
$808$		0			0
$809$	2.02037e14	−	1.16646e14i	0.0204981	−	0.0118346i	−0.489716	−	0.871882i	$-0.662900\pi$
$809$	2.02037e14	−	1.16646e14i	0.0204981	−	0.0118346i	0.510214	+	0.860047i	$0.329566\pi$
$810$		0			0
$811$		−	2.17182e15i		−	0.217375i	−0.994076	−	0.108688i	$-0.965335\pi$
$811$		−	2.17182e15i		−	0.217375i	0.994076	−	0.108688i	$-0.0346648\pi$
$812$		0			0
$813$	3.14170e15	+	1.24575e15i	0.310218	+	0.123008i
$814$		0			0
$815$	−1.20192e15	−	2.08179e15i	−0.117087	−	0.202801i
$816$		0			0
$817$	−5.88934e15	−	3.40021e15i	−0.566038	−	0.326802i
$818$		0			0
$819$	−3.28459e15	−	1.16456e16i	−0.311472	−	1.10433i
$820$		0			0
$821$	−1.15578e15	−	6.67291e14i	−0.108141	−	0.0624350i	0.444954	−	0.895553i	$-0.353220\pi$
$821$	−1.15578e15	−	6.67291e14i	−0.108141	−	0.0624350i	−0.553095	+	0.833118i	$0.686553\pi$
$822$		0			0
$823$	4.66232e15	+	8.07538e15i	0.430431	+	0.745528i	0.996910	−	0.0785478i	$-0.0250283\pi$
$823$	4.66232e15	+	8.07538e15i	0.430431	+	0.745528i	−0.566480	+	0.824076i	$0.691695\pi$
$824$		0			0
$825$	3.66507e15	+	1.45328e15i	0.333877	+	0.132389i
$826$		0			0
$827$			1.85920e16i			1.67127i	0.549286	+	0.835634i	$0.314900\pi$
$827$			1.85920e16i			1.67127i	−0.549286	+	0.835634i	$0.685100\pi$
$828$		0			0
$829$	2.07899e14	−	1.20030e14i	0.0184417	−	0.0106473i	−0.490751	−	0.871300i	$-0.663277\pi$
$829$	2.07899e14	−	1.20030e14i	0.0184417	−	0.0106473i	0.509193	+	0.860653i	$0.329944\pi$
$830$		0			0
$831$	−5.58119e15	−	7.04912e15i	−0.488563	−	0.617063i
$832$		0			0
$833$	2.10504e15	+	3.95579e15i	0.181850	+	0.341732i
$834$		0			0
$835$	5.66824e15	−	9.81767e15i	0.483250	−	0.837014i
$836$		0			0
$837$	6.50951e15	−	9.33529e15i	0.547719	−	0.785485i
$838$		0			0
$839$	1.34331e16			1.11554			0.557770	−	0.829996i	$-0.311657\pi$
$839$	1.34331e16			1.11554			0.557770	+	0.829996i	$0.311657\pi$
$840$		0			0
$841$	1.46290e14			0.0119905
$842$		0			0
$843$	−1.27543e15	−	8.66796e15i	−0.103183	−	0.701238i
$844$		0			0
$845$	−2.22086e15	+	3.84664e15i	−0.177341	+	0.307163i
$846$		0			0
$847$	−6.39136e15	+	1.06411e16i	−0.503772	+	0.838738i
$848$		0			0
$849$	−3.01526e15	+	2.38735e15i	−0.234602	+	0.185748i
$850$		0			0
$851$	−3.08728e16	+	1.78244e16i	−2.37117	+	1.36900i
$852$		0			0
$853$			2.09188e16i			1.58605i	0.609190	+	0.793025i	$0.291495\pi$
$853$			2.09188e16i			1.58605i	−0.609190	+	0.793025i	$0.708505\pi$
$854$		0			0
$855$	−1.41952e16	+	1.50853e16i	−1.06249	+	1.12912i
$856$		0			0
$857$	−6.09388e15	−	1.05549e16i	−0.450297	−	0.779938i	0.548107	−	0.836408i	$-0.315349\pi$
$857$	−6.09388e15	−	1.05549e16i	−0.450297	−	0.779938i	−0.998404	+	0.0564703i	$0.982015\pi$
$858$		0			0
$859$	−7.03889e15	−	4.06391e15i	−0.513502	−	0.296470i	0.220770	−	0.975326i	$-0.429143\pi$
$859$	−7.03889e15	−	4.06391e15i	−0.513502	−	0.296470i	−0.734272	+	0.678856i	$0.762476\pi$
$860$		0			0
$861$	1.06271e16	−	1.37650e15i	0.765415	−	0.0991423i
$862$		0			0
$863$	−6.06283e15	−	3.50038e15i	−0.431138	−	0.248917i	0.268694	−	0.963226i	$-0.413408\pi$
$863$	−6.06283e15	−	3.50038e15i	−0.431138	−	0.248917i	−0.699831	+	0.714308i	$0.746741\pi$
$864$		0			0
$865$	−1.48317e15	−	2.56892e15i	−0.104136	−	0.180369i
$866$		0			0
$867$	−4.52019e15	+	1.13996e16i	−0.313366	+	0.790289i
$868$		0			0
$869$		−	2.87328e16i		−	1.96684i
$870$		0			0
$871$	−1.05313e15	+	6.08025e14i	−0.0711839	+	0.0410981i
$872$		0			0
$873$	−1.36773e15	−	4.54696e15i	−0.0912894	−	0.303489i
$874$		0			0
$875$	−1.26565e16	−	2.18787e14i	−0.834198	−	0.0144204i
$876$		0			0
$877$	−5.35218e15	+	9.27025e15i	−0.348364	+	0.603384i	−0.985959	−	0.166988i	$-0.946596\pi$
$877$	−5.35218e15	+	9.27025e15i	−0.348364	+	0.603384i	0.637595	+	0.770372i	$0.279929\pi$
$878$		0			0
$879$	1.66226e15	−	2.44591e14i	0.106846	−	0.0157218i
$880$		0			0
$881$	−1.55605e16			−0.987772			−0.493886	−	0.869527i	$-0.664424\pi$
$881$	−1.55605e16			−0.987772			−0.493886	+	0.869527i	$0.664424\pi$
$882$		0			0
$883$	1.61350e16			1.01155			0.505773	−	0.862667i	$-0.331208\pi$
$883$	1.61350e16			1.01155			0.505773	+	0.862667i	$0.331208\pi$
$884$		0			0
$885$	2.36397e16	−	3.47843e15i	1.46371	−	0.215375i
$886$		0			0
$887$	−5.60498e15	+	9.70811e15i	−0.342763	+	0.593683i	−0.984945	−	0.172869i	$-0.944696\pi$
$887$	−5.60498e15	+	9.70811e15i	−0.342763	+	0.593683i	0.642182	+	0.766552i	$0.278029\pi$
$888$		0			0
$889$	2.87701e16	+	4.97336e14i	1.73773	+	0.0300393i
$890$		0			0
$891$	1.05263e16	−	2.10965e16i	0.627986	−	1.25858i
$892$		0			0
$893$	6.85750e15	−	3.95918e15i	0.404094	−	0.233304i
$894$		0			0
$895$		−	3.03079e16i		−	1.76413i
$896$		0			0
$897$	1.37258e16	−	3.46155e16i	0.789184	−	1.99027i
$898$		0			0
$899$	8.37933e15	+	1.45134e16i	0.475917	+	0.824312i
$900$		0			0
$901$	7.55406e15	+	4.36134e15i	0.423833	+	0.244700i
$902$		0			0
$903$	8.45119e15	−	1.09466e15i	0.468420	−	0.0606732i
$904$		0			0
$905$	1.75068e15	+	1.01076e15i	0.0958605	+	0.0553451i
$906$		0			0
$907$	−4.28904e15	−	7.42884e15i	−0.232017	−	0.401866i	0.726384	−	0.687289i	$-0.241199\pi$
$907$	−4.28904e15	−	7.42884e15i	−0.232017	−	0.401866i	−0.958402	+	0.285423i	$0.907866\pi$
$908$		0			0
$909$	2.46909e15	+	2.32340e15i	0.131958	+	0.124172i
$910$		0			0
$911$		−	2.86298e16i		−	1.51171i	−0.654741	−	0.755854i	$-0.727222\pi$
$911$		−	2.86298e16i		−	1.51171i	0.654741	−	0.755854i	$-0.272778\pi$
$912$		0			0
$913$	1.50563e16	−	8.69274e15i	0.785467	−	0.453489i
$914$		0			0
$915$	−1.00411e16	+	7.95013e15i	−0.517567	+	0.409787i
$916$		0			0
$917$	9.35241e15	−	1.55710e16i	0.476313	−	0.793020i
$918$		0			0
$919$	2.45902e15	−	4.25915e15i	0.123745	−	0.214332i	−0.797497	−	0.603323i	$-0.793843\pi$
$919$	2.45902e15	−	4.25915e15i	0.123745	−	0.214332i	0.921242	+	0.388991i	$0.127176\pi$
$920$		0			0
$921$	1.08198e15	+	7.35325e15i	0.0538012	+	0.365638i
$922$		0			0
$923$	3.56841e16			1.75334
$924$		0			0
$925$	7.71700e15			0.374687
$926$		0			0
$927$	1.21310e16	+	2.85843e15i	0.582049	+	0.137148i
$928$		0			0
$929$	−2.72223e15	+	4.71505e15i	−0.129074	+	0.223563i	−0.923318	−	0.384036i	$-0.874534\pi$
$929$	−2.72223e15	+	4.71505e15i	−0.129074	+	0.223563i	0.794244	+	0.607599i	$0.207867\pi$
$930$		0			0
$931$	−2.50497e16	−	1.56410e16i	−1.17376	−	0.732896i
$932$		0			0
$933$	−3.62460e15	−	4.57793e15i	−0.167846	−	0.211992i
$934$		0			0
$935$	1.15442e16	−	6.66504e15i	0.528323	−	0.305027i
$936$		0			0
$937$		−	2.60283e16i		−	1.17728i	−0.808397	−	0.588638i	$-0.799664\pi$
$937$		−	2.60283e16i		−	1.17728i	0.808397	−	0.588638i	$-0.200336\pi$
$938$		0			0
$939$	−1.77431e16	−	7.03552e15i	−0.793176	−	0.314511i
$940$		0			0
$941$	5.09386e15	+	8.82283e15i	0.225063	+	0.389821i	0.956338	−	0.292262i	$-0.0944078\pi$
$941$	5.09386e15	+	8.82283e15i	0.225063	+	0.389821i	−0.731275	+	0.682082i	$0.761075\pi$
$942$		0			0
$943$	2.85599e16	+	1.64891e16i	1.24722	+	0.720081i
$944$		0			0
$945$	2.65849e15	−	2.58207e16i	0.114752	−	1.11453i
$946$		0			0
$947$	−1.34755e16	−	7.78009e15i	−0.574937	−	0.331940i	0.184182	−	0.982892i	$-0.441037\pi$
$947$	−1.34755e16	−	7.78009e15i	−0.574937	−	0.331940i	−0.759119	+	0.650952i	$0.774370\pi$
$948$		0			0
$949$	1.87759e16	+	3.25209e16i	0.791841	+	1.37151i
$950$		0			0
$951$	−2.31374e16	−	9.17445e15i	−0.964541	−	0.382461i
$952$		0			0
$953$			1.14850e16i			0.473281i	0.971597	+	0.236641i	$0.0760464\pi$
$953$			1.14850e16i			0.473281i	−0.971597	+	0.236641i	$0.923954\pi$
$954$		0			0
$955$	−2.43385e16	+	1.40518e16i	−0.991459	+	0.572419i
$956$		0			0
$957$	2.15510e16	+	2.72192e16i	0.867864	+	1.09613i
$958$		0			0
$959$	−2.52362e16	+	1.39942e16i	−1.00466	+	0.557116i
$960$		0			0
$961$	−1.05467e15	+	1.82675e15i	−0.0415087	+	0.0718951i
$962$		0			0
$963$	−4.46399e16	−	1.05185e16i	−1.73692	−	0.409269i
$964$		0			0
$965$	1.61791e14			0.00622377
$966$		0			0
$967$	−2.18286e16			−0.830194			−0.415097	−	0.909777i	$-0.636252\pi$
$967$	−2.18286e16			−0.830194			−0.415097	+	0.909777i	$0.636252\pi$
$968$		0			0
$969$	2.07380e15	+	1.40937e16i	0.0779804	+	0.529962i
$970$		0			0
$971$	6.93013e15	−	1.20033e16i	0.257653	−	0.446268i	−0.707960	−	0.706253i	$-0.750384\pi$
$971$	6.93013e15	−	1.20033e16i	0.257653	−	0.446268i	0.965613	+	0.259985i	$0.0837175\pi$
$972$		0			0
$973$	−1.65259e14	+	9.55997e15i	−0.00607497	+	0.351428i
$974$		0			0
$975$	−6.31985e15	+	5.00378e15i	−0.229711	+	0.181875i
$976$		0			0
$977$	2.38113e16	−	1.37474e16i	0.855781	−	0.494085i	−0.00681620	−	0.999977i	$-0.502170\pi$
$977$	2.38113e16	−	1.37474e16i	0.855781	−	0.494085i	0.862597	+	0.505891i	$0.168836\pi$
$978$		0			0
$979$		−	7.78024e15i		−	0.276496i
$980$		0			0
$981$	1.83311e16	+	1.72495e16i	0.644184	+	0.606173i
$982$		0			0
$983$	−2.23017e15	−	3.86277e15i	−0.0774987	−	0.134232i	0.824671	−	0.565612i	$-0.191360\pi$
$983$	−2.23017e15	−	3.86277e15i	−0.0774987	−	0.134232i	−0.902170	+	0.431380i	$0.858027\pi$
$984$		0			0
$985$	−1.28138e16	−	7.39802e15i	−0.440329	−	0.254224i
$986$		0			0
$987$	−3.81640e15	+	9.15942e15i	−0.129691	+	0.311260i
$988$		0			0
$989$	2.27122e16	+	1.31129e16i	0.763273	+	0.440676i
$990$		0			0
$991$	4.26211e15	+	7.38220e15i	0.141651	+	0.245347i	0.928119	−	0.372285i	$-0.121426\pi$
$991$	4.26211e15	+	7.38220e15i	0.141651	+	0.245347i	−0.786467	+	0.617632i	$0.788092\pi$
$992$		0			0
$993$	9.98286e15	−	2.51761e16i	0.328121	−	0.827500i
$994$		0			0
$995$			2.83142e16i			0.920403i
$996$		0			0
$997$	1.07346e15	−	6.19763e14i	0.0345114	−	0.0199252i	−0.482645	−	0.875816i	$-0.660324\pi$
$997$	1.07346e15	−	6.19763e14i	0.0345114	−	0.0199252i	0.517156	+	0.855891i	$0.326991\pi$
$998$		0			0
$999$	3.93216e15	−	4.59789e16i	0.125032	−	1.46200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.k.b.5.2	✓	56
3.2	odd	2	inner	84.12.k.b.5.9	yes	56
7.3	odd	6	inner	84.12.k.b.17.9	yes	56
21.17	even	6	inner	84.12.k.b.17.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.k.b.5.2	✓	56	1.1	even	1	trivial
84.12.k.b.5.9	yes	56	3.2	odd	2	inner
84.12.k.b.17.2	yes	56	21.17	even	6	inner
84.12.k.b.17.9	yes	56	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-416.405 + 61.2712i) q^{3} +(3914.60 - 6780.29i) q^{5} +(-44460.5 - 768.569i) q^{7} +(169639. - 51027.2i) q^{9} +O(q^{10})\)	\(q+(-416.405 + 61.2712i) q^{3} +(3914.60 - 6780.29i) q^{5} +(-44460.5 - 768.569i) q^{7} +(169639. - 51027.2i) q^{9} +(650650. - 375653. i) q^{11} +1.53606e6i q^{13} +(-1.21462e6 + 3.06320e6i) q^{15} +(1.13310e6 + 1.96259e6i) q^{17} +(-1.29343e7 - 7.46761e6i) q^{19} +(1.85607e7 - 2.40411e6i) q^{21} +(4.98810e7 + 2.87988e7i) q^{23} +(-6.23417e6 - 1.07979e7i) q^{25} +(-6.75118e7 + 3.16420e7i) q^{27} -1.09792e8i q^{29} +(-1.32191e8 + 7.63203e7i) q^{31} +(-2.47917e8 + 1.96290e8i) q^{33} +(-1.79256e8 + 2.98446e8i) q^{35} +(-3.09464e8 + 5.36007e8i) q^{37} +(-9.41164e7 - 6.39623e8i) q^{39} +5.72560e8 q^{41} +4.55328e8 q^{43} +(3.18088e8 - 1.34995e9i) q^{45} +(-2.65090e8 + 4.59150e8i) q^{47} +(1.97615e9 + 6.83419e7i) q^{49} +(-5.92078e8 - 7.47803e8i) q^{51} +(3.33336e9 - 1.92452e9i) q^{53} -5.88213e9i q^{55} +(5.84344e9 + 2.31705e9i) q^{57} +(-3.62559e9 - 6.27971e9i) q^{59} +(3.36594e9 + 1.94333e9i) q^{61} +(-7.58144e9 + 2.13832e9i) q^{63} +(1.04149e10 + 6.01307e9i) q^{65} +(3.95833e8 + 6.85604e8i) q^{67} +(-2.25352e10 - 8.93569e9i) q^{69} -2.32309e10i q^{71} +(2.11716e10 - 1.22234e10i) q^{73} +(3.25754e9 + 4.11432e9i) q^{75} +(-2.92169e10 + 1.62017e10i) q^{77} +(1.91219e10 - 3.31201e10i) q^{79} +(2.61735e10 - 1.73124e10i) q^{81} +2.31403e10 q^{83} +1.77425e10 q^{85} +(6.72707e9 + 4.57178e10i) q^{87} +(5.17781e9 - 8.96823e9i) q^{89} +(1.18057e9 - 6.82941e10i) q^{91} +(5.03685e10 - 3.98796e10i) q^{93} +(-1.01265e11 + 5.84655e10i) q^{95} -2.68038e10i q^{97} +(9.12069e10 - 9.69262e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) \) 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9	\( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) \) 56 * q - 729 * q^3 - 27194 * q^7 - 172347 * q^9 - 4853058 * q^15 + 28700520 * q^19 - 11325429 * q^21 - 316601194 * q^25 - 1368416388 * q^31 + 40874949 * q^33 - 87435712 * q^37 + 1177474410 * q^39 - 3055078348 * q^43 + 4109921793 * q^45 - 742582522 * q^49 - 694793715 * q^51 + 14605100370 * q^57 + 72584834058 * q^61 - 7310837811 * q^63 + 6131679148 * q^67 - 74402605464 * q^73 - 161115157854 * q^75 + 52181713528 * q^79 + 44948282337 * q^81 + 4658488716 * q^85 + 243101263104 * q^87 - 85311757146 * q^91 - 256628211777 * q^93 + 157345775874 * q^99

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