LMFDB - Embedded newform 1008.2.t.l.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Character	$\chi$	$=$	1008.961
Dual form			1008.2.t.l.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72252 - 0.181425i) q^{3} +2.10440 q^{5} +(1.78475 + 1.95312i) q^{7} +(2.93417 + 0.625017i) q^{9} +O(q^{10})$	\(q+(-1.72252 - 0.181425i) q^{3} +2.10440 q^{5} +(1.78475 + 1.95312i) q^{7} +(2.93417 + 0.625017i) q^{9} -0.399064 q^{11} +(1.44292 + 2.49921i) q^{13} +(-3.62487 - 0.381790i) q^{15} +(-0.176596 - 0.305873i) q^{17} +(-2.84888 + 4.93440i) q^{19} +(-2.71993 - 3.68809i) q^{21} +0.877364 q^{23} -0.571513 q^{25} +(-4.94078 - 1.60894i) q^{27} +(0.874997 - 1.51554i) q^{29} +(4.56745 - 7.91106i) q^{31} +(0.687397 + 0.0724002i) q^{33} +(3.75582 + 4.11014i) q^{35} +(-3.39555 + 5.88127i) q^{37} +(-2.03205 - 4.56673i) q^{39} +(1.20377 + 2.08499i) q^{41} +(-0.276745 + 0.479336i) q^{43} +(6.17466 + 1.31528i) q^{45} +(5.86859 + 10.1647i) q^{47} +(-0.629343 + 6.97165i) q^{49} +(0.248697 + 0.558912i) q^{51} +(-2.07821 - 3.59956i) q^{53} -0.839790 q^{55} +(5.80248 - 7.98277i) q^{57} +(-4.66210 + 8.07500i) q^{59} +(5.03601 + 8.72262i) q^{61} +(4.01602 + 6.84628i) q^{63} +(3.03648 + 5.25934i) q^{65} +(0.601204 - 1.04132i) q^{67} +(-1.51128 - 0.159176i) q^{69} +14.6826 q^{71} +(0.315636 + 0.546697i) q^{73} +(0.984444 + 0.103687i) q^{75} +(-0.712229 - 0.779420i) q^{77} +(-1.24364 - 2.15406i) q^{79} +(8.21871 + 3.66781i) q^{81} +(4.59366 - 7.95645i) q^{83} +(-0.371628 - 0.643678i) q^{85} +(-1.78216 + 2.45180i) q^{87} +(7.29358 - 12.6328i) q^{89} +(-2.30601 + 7.27866i) q^{91} +(-9.30280 + 12.7983i) q^{93} +(-5.99517 + 10.3839i) q^{95} +(-7.84245 + 13.5835i) q^{97} +(-1.17092 - 0.249422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 2 q^{5} + q^{7}+O(q^{10}) $ 22 * q + 2 * q^3 - 2 * q^5 + q^7	$ 22 q + 2 q^{3} - 2 q^{5} + q^{7} + 6 q^{11} + 7 q^{13} + q^{15} - q^{17} - 13 q^{19} + 33 q^{21} + 44 q^{25} + 2 q^{27} - 7 q^{29} - 6 q^{31} + 9 q^{33} - 2 q^{35} + 6 q^{37} + 4 q^{39} + 4 q^{41} - 2 q^{43} - 17 q^{47} + 29 q^{49} + 25 q^{51} + q^{53} - 2 q^{55} - 21 q^{57} + 21 q^{59} + 31 q^{61} + 7 q^{63} - 3 q^{65} + 26 q^{67} - 40 q^{69} + 32 q^{71} + 17 q^{73} + 16 q^{75} - 4 q^{77} + 16 q^{79} + 36 q^{83} + 28 q^{85} - 7 q^{87} - 2 q^{89} - 15 q^{91} - 56 q^{93} + 24 q^{95} + 19 q^{97} - 24 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 2 * q^5 + q^7 + 6 * q^11 + 7 * q^13 + q^15 - q^17 - 13 * q^19 + 33 * q^21 + 44 * q^25 + 2 * q^27 - 7 * q^29 - 6 * q^31 + 9 * q^33 - 2 * q^35 + 6 * q^37 + 4 * q^39 + 4 * q^41 - 2 * q^43 - 17 * q^47 + 29 * q^49 + 25 * q^51 + q^53 - 2 * q^55 - 21 * q^57 + 21 * q^59 + 31 * q^61 + 7 * q^63 - 3 * q^65 + 26 * q^67 - 40 * q^69 + 32 * q^71 + 17 * q^73 + 16 * q^75 - 4 * q^77 + 16 * q^79 + 36 * q^83 + 28 * q^85 - 7 * q^87 - 2 * q^89 - 15 * q^91 - 56 * q^93 + 24 * q^95 + 19 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.72252	−	0.181425i	−0.994499	−	0.104746i
$3$	−1.72252	−	0.181425i	−0.994499	−	0.104746i
$4$		0			0
$5$	2.10440			0.941115			0.470558	−	0.882369i	$-0.344053\pi$
$5$	2.10440			0.941115			0.470558	+	0.882369i	$0.344053\pi$
$6$		0			0
$7$	1.78475	+	1.95312i	0.674572	+	0.738209i
$7$	1.78475	+	1.95312i	0.674572	+	0.738209i
$8$		0			0
$9$	2.93417	+	0.625017i	0.978057	+	0.208339i
$10$		0			0
$11$	−0.399064			−0.120322			−0.0601612	−	0.998189i	$-0.519161\pi$
$11$	−0.399064			−0.120322			−0.0601612	+	0.998189i	$0.519161\pi$
$12$		0			0
$13$	1.44292	+	2.49921i	0.400194	+	0.693157i	0.993749	−	0.111637i	$-0.0356093\pi$
$13$	1.44292	+	2.49921i	0.400194	+	0.693157i	−0.593555	+	0.804794i	$0.702276\pi$
$14$		0			0
$15$	−3.62487	−	0.381790i	−0.935938	−	0.0985778i
$16$		0			0
$17$	−0.176596	−	0.305873i	−0.0428308	−	0.0741851i	0.843815	−	0.536634i	$-0.180304\pi$
$17$	−0.176596	−	0.305873i	−0.0428308	−	0.0741851i	−0.886646	+	0.462449i	$0.846971\pi$
$18$		0			0
$19$	−2.84888	+	4.93440i	−0.653578	+	1.13203i	0.328670	+	0.944445i	$0.393399\pi$
$19$	−2.84888	+	4.93440i	−0.653578	+	1.13203i	−0.982248	+	0.187585i	$0.939934\pi$
$20$		0			0
$21$	−2.71993	−	3.68809i	−0.593537	−	0.804807i
$22$		0			0
$23$	0.877364			0.182943			0.0914716	−	0.995808i	$-0.470843\pi$
$23$	0.877364			0.182943			0.0914716	+	0.995808i	$0.470843\pi$
$24$		0			0
$25$	−0.571513			−0.114303
$26$		0			0
$27$	−4.94078	−	1.60894i	−0.950854	−	0.309640i
$28$		0			0
$29$	0.874997	−	1.51554i	0.162483	−	0.281429i	−0.773276	−	0.634070i	$-0.781383\pi$
$29$	0.874997	−	1.51554i	0.162483	−	0.281429i	0.935759	+	0.352641i	$0.114716\pi$
$30$		0			0
$31$	4.56745	−	7.91106i	0.820339	−	1.42087i	−0.0850916	−	0.996373i	$-0.527118\pi$
$31$	4.56745	−	7.91106i	0.820339	−	1.42087i	0.905430	−	0.424495i	$-0.139548\pi$
$32$		0			0
$33$	0.687397	+	0.0724002i	0.119661	+	0.0126033i
$34$		0			0
$35$	3.75582	+	4.11014i	0.634850	+	0.694740i
$36$		0			0
$37$	−3.39555	+	5.88127i	−0.558225	+	0.966874i	0.439420	+	0.898282i	$0.355184\pi$
$37$	−3.39555	+	5.88127i	−0.558225	+	0.966874i	−0.997645	+	0.0685922i	$0.978149\pi$
$38$		0			0
$39$	−2.03205	−	4.56673i	−0.325388	−	0.731263i
$40$		0			0
$41$	1.20377	+	2.08499i	0.187997	+	0.325621i	0.944582	−	0.328274i	$-0.106467\pi$
$41$	1.20377	+	2.08499i	0.187997	+	0.325621i	−0.756585	+	0.653895i	$0.773134\pi$
$42$		0			0
$43$	−0.276745	+	0.479336i	−0.0422032	+	0.0730981i	−0.886355	−	0.463005i	$-0.846771\pi$
$43$	−0.276745	+	0.479336i	−0.0422032	+	0.0730981i	0.844152	+	0.536104i	$0.180104\pi$
$44$		0			0
$45$	6.17466	+	1.31528i	0.920464	+	0.196071i
$46$		0			0
$47$	5.86859	+	10.1647i	0.856023	+	1.48267i	0.875693	+	0.482868i	$0.160405\pi$
$47$	5.86859	+	10.1647i	0.856023	+	1.48267i	−0.0196707	+	0.999807i	$0.506262\pi$
$48$		0			0
$49$	−0.629343	+	6.97165i	−0.0899061	+	0.995950i
$50$		0			0
$51$	0.248697	+	0.558912i	0.0348246	+	0.0782634i
$52$		0			0
$53$	−2.07821	−	3.59956i	−0.285464	−	0.494437i	0.687258	−	0.726413i	$-0.258814\pi$
$53$	−2.07821	−	3.59956i	−0.285464	−	0.494437i	−0.972721	+	0.231976i	$0.925481\pi$
$54$		0			0
$55$	−0.839790			−0.113237
$56$		0			0
$57$	5.80248	−	7.98277i	0.768558	−	1.05734i
$58$		0			0
$59$	−4.66210	+	8.07500i	−0.606954	+	1.05128i	0.384785	+	0.923006i	$0.374276\pi$
$59$	−4.66210	+	8.07500i	−0.606954	+	1.05128i	−0.991739	+	0.128269i	$0.959058\pi$
$60$		0			0
$61$	5.03601	+	8.72262i	0.644795	+	1.11682i	0.984349	+	0.176231i	$0.0563905\pi$
$61$	5.03601	+	8.72262i	0.644795	+	1.11682i	−0.339554	+	0.940586i	$0.610276\pi$
$62$		0			0
$63$	4.01602	+	6.84628i	0.505971	+	0.862550i
$64$		0			0
$65$	3.03648	+	5.25934i	0.376629	+	0.652340i
$66$		0			0
$67$	0.601204	−	1.04132i	0.0734488	−	0.127217i	−0.826962	−	0.562258i	$-0.809933\pi$
$67$	0.601204	−	1.04132i	0.0734488	−	0.127217i	0.900411	+	0.435041i	$0.143266\pi$
$68$		0			0
$69$	−1.51128	−	0.159176i	−0.181937	−	0.0191625i
$70$		0			0
$71$	14.6826			1.74250			0.871250	−	0.490840i	$-0.163310\pi$
$71$	14.6826			1.74250			0.871250	+	0.490840i	$0.163310\pi$
$72$		0			0
$73$	0.315636	+	0.546697i	0.0369423	+	0.0639860i	0.883905	−	0.467666i	$-0.154905\pi$
$73$	0.315636	+	0.546697i	0.0369423	+	0.0639860i	−0.846963	+	0.531652i	$0.821572\pi$
$74$		0			0
$75$	0.984444	+	0.103687i	0.113674	+	0.0119727i
$76$		0			0
$77$	−0.712229	−	0.779420i	−0.0811661	−	0.0888231i
$78$		0			0
$79$	−1.24364	−	2.15406i	−0.139921	−	0.242350i	0.787546	−	0.616256i	$-0.211352\pi$
$79$	−1.24364	−	2.15406i	−0.139921	−	0.242350i	−0.927467	+	0.373906i	$0.878018\pi$
$80$		0			0
$81$	8.21871	+	3.66781i	0.913190	+	0.407535i
$82$		0			0
$83$	4.59366	−	7.95645i	0.504219	−	0.873333i	−0.495769	−	0.868455i	$-0.665114\pi$
$83$	4.59366	−	7.95645i	0.504219	−	0.873333i	0.999988	−	0.00487885i	$-0.00155299\pi$
$84$		0			0
$85$	−0.371628	−	0.643678i	−0.0403087	−	0.0698167i
$86$		0			0
$87$	−1.78216	+	2.45180i	−0.191068	+	0.262861i
$88$		0			0
$89$	7.29358	−	12.6328i	0.773118	−	1.33908i	−0.162729	−	0.986671i	$-0.552029\pi$
$89$	7.29358	−	12.6328i	0.773118	−	1.33908i	0.935846	−	0.352408i	$-0.114637\pi$
$90$		0			0
$91$	−2.30601	+	7.27866i	−0.241735	+	0.763011i
$92$		0			0
$93$	−9.30280	+	12.7983i	−0.964656	+	1.32713i
$94$		0			0
$95$	−5.99517	+	10.3839i	−0.615092	+	1.06537i
$96$		0			0
$97$	−7.84245	+	13.5835i	−0.796280	+	1.37920i	0.125744	+	0.992063i	$0.459868\pi$
$97$	−7.84245	+	13.5835i	−0.796280	+	1.37920i	−0.922023	+	0.387134i	$0.873465\pi$
$98$		0			0
$99$	−1.17092	−	0.249422i	−0.117682	−	0.0250679i
$100$		0			0
$101$	−0.0928571			−0.00923962			−0.00461981	−	0.999989i	$-0.501471\pi$
$101$	−0.0928571			−0.00923962			−0.00461981	+	0.999989i	$0.501471\pi$
$102$		0			0
$103$	19.9154			1.96232			0.981161	−	0.193193i	$-0.0618845\pi$
$103$	19.9154			1.96232			0.981161	+	0.193193i	$0.0618845\pi$
$104$		0			0
$105$	−5.72381	−	7.76120i	−0.558586	−	0.757416i
$106$		0			0
$107$	2.89225	−	5.00953i	0.279605	−	0.484290i	−0.691682	−	0.722202i	$-0.743130\pi$
$107$	2.89225	−	5.00953i	0.279605	−	0.484290i	0.971287	+	0.237913i	$0.0764633\pi$
$108$		0			0
$109$	−6.25516	−	10.8343i	−0.599136	−	1.03773i	−0.992949	−	0.118543i	$-0.962178\pi$
$109$	−6.25516	−	10.8343i	−0.599136	−	1.03773i	0.393813	−	0.919191i	$-0.371156\pi$
$110$		0			0
$111$	6.91592	−	9.51458i	0.656430	−	0.903084i
$112$		0			0
$113$	1.69411	+	2.93428i	0.159368	+	0.276034i	0.934641	−	0.355593i	$-0.115721\pi$
$113$	1.69411	+	2.93428i	0.159368	+	0.276034i	−0.775273	+	0.631627i	$0.782388\pi$
$114$		0			0
$115$	1.84632			0.172171
$116$		0			0
$117$	2.67172	+	8.23497i	0.247001	+	0.761323i
$118$		0			0
$119$	0.282227	−	0.890819i	0.0258717	−	0.0816613i
$120$		0			0
$121$	−10.8407			−0.985523
$122$		0			0
$123$	−1.69525	−	3.80984i	−0.152856	−	0.343522i
$124$		0			0
$125$	−11.7247			−1.04869
$126$		0			0
$127$	−14.7348			−1.30750			−0.653752	−	0.756709i	$-0.726806\pi$
$127$	−14.7348			−1.30750			−0.653752	+	0.756709i	$0.726806\pi$
$128$		0			0
$129$	0.563663	−	0.775460i	0.0496278	−	0.0682754i
$130$		0			0
$131$	13.9078			1.21513			0.607567	−	0.794268i	$-0.292146\pi$
$131$	13.9078			1.21513			0.607567	+	0.794268i	$0.292146\pi$
$132$		0			0
$133$	−14.7220	+	3.24247i	−1.27656	+	0.281158i
$134$		0			0
$135$	−10.3974	−	3.38585i	−0.894863	−	0.291407i
$136$		0			0
$137$	14.5575			1.24373			0.621865	−	0.783124i	$-0.286375\pi$
$137$	14.5575			1.24373			0.621865	+	0.783124i	$0.286375\pi$
$138$		0			0
$139$	3.63996	+	6.30460i	0.308737	+	0.534749i	0.978086	−	0.208199i	$-0.0667603\pi$
$139$	3.63996	+	6.30460i	0.308737	+	0.534749i	−0.669349	+	0.742948i	$0.733427\pi$
$140$		0			0
$141$	−8.26466	−	18.5736i	−0.696010	−	1.56418i
$142$		0			0
$143$	−0.575818	−	0.997347i	−0.0481523	−	0.0834023i
$144$		0			0
$145$	1.84134	−	3.18930i	0.152915	−	0.264857i
$146$		0			0
$147$	2.34889	−	11.8947i	0.193733	−	0.981054i
$148$		0			0
$149$	−0.721664			−0.0591210			−0.0295605	−	0.999563i	$-0.509411\pi$
$149$	−0.721664			−0.0591210			−0.0295605	+	0.999563i	$0.509411\pi$
$150$		0			0
$151$	−21.8044			−1.77441			−0.887207	−	0.461372i	$-0.847357\pi$
$151$	−21.8044			−1.77441			−0.887207	+	0.461372i	$0.847357\pi$
$152$		0			0
$153$	−0.326986	−	1.00786i	−0.0264353	−	0.0814806i
$154$		0			0
$155$	9.61173	−	16.6480i	0.772033	−	1.33720i
$156$		0			0
$157$	−2.58986	+	4.48577i	−0.206694	+	0.358004i	−0.950671	−	0.310201i	$-0.899604\pi$
$157$	−2.58986	+	4.48577i	−0.206694	+	0.358004i	0.743977	+	0.668205i	$0.232937\pi$
$158$		0			0
$159$	2.92671	+	6.57736i	0.232103	+	0.521619i
$160$		0			0
$161$	1.56588	+	1.71360i	0.123408	+	0.135050i
$162$		0			0
$163$	−2.63906	+	4.57098i	−0.206707	+	0.358027i	−0.950675	−	0.310188i	$-0.899608\pi$
$163$	−2.63906	+	4.57098i	−0.206707	+	0.358027i	0.743968	+	0.668215i	$0.232941\pi$
$164$		0			0
$165$	1.44656	+	0.152359i	0.112614	+	0.0118611i
$166$		0			0
$167$	6.83710	+	11.8422i	0.529071	+	0.916378i	0.999425	+	0.0339001i	$0.0107928\pi$
$167$	6.83710	+	11.8422i	0.529071	+	0.916378i	−0.470354	+	0.882478i	$0.655874\pi$
$168$		0			0
$169$	2.33596	−	4.04599i	0.179689	−	0.311230i
$170$		0			0
$171$	−11.4432	+	12.6978i	−0.875082	+	0.971024i
$172$		0			0
$173$	−10.0912	−	17.4784i	−0.767218	−	1.32886i	−0.939066	−	0.343738i	$-0.888307\pi$
$173$	−10.0912	−	17.4784i	−0.767218	−	1.32886i	0.171847	−	0.985124i	$-0.445026\pi$
$174$		0			0
$175$	−1.02001	−	1.11623i	−0.0771053	−	0.0843792i
$176$		0			0
$177$	9.49559	−	13.0636i	0.713732	−	0.981917i
$178$		0			0
$179$	−12.5968	−	21.8183i	−0.941528	−	1.63077i	−0.762557	−	0.646921i	$-0.776056\pi$
$179$	−12.5968	−	21.8183i	−0.941528	−	1.63077i	−0.178971	−	0.983854i	$-0.557277\pi$
$180$		0			0
$181$	−17.2815			−1.28453			−0.642263	−	0.766485i	$-0.722004\pi$
$181$	−17.2815			−1.28453			−0.642263	+	0.766485i	$0.722004\pi$
$182$		0			0
$183$	−7.09214	−	15.9386i	−0.524266	−	1.17821i
$184$		0			0
$185$	−7.14559	+	12.3765i	−0.525354	+	0.909940i
$186$		0			0
$187$	0.0704731	+	0.122063i	0.00515350	+	0.00892613i
$188$		0			0
$189$	−5.67561	−	12.5215i	−0.412840	−	0.910804i
$190$		0			0
$191$	−2.50949	−	4.34657i	−0.181580	−	0.314506i	0.760839	−	0.648941i	$-0.224788\pi$
$191$	−2.50949	−	4.34657i	−0.181580	−	0.314506i	−0.942419	+	0.334435i	$0.891455\pi$
$192$		0			0
$193$	2.71882	−	4.70914i	0.195705	−	0.338971i	−0.751426	−	0.659817i	$-0.770634\pi$
$193$	2.71882	−	4.70914i	0.195705	−	0.338971i	0.947131	+	0.320846i	$0.103967\pi$
$194$		0			0
$195$	−4.27623	−	9.61022i	−0.306227	−	0.688202i
$196$		0			0
$197$	5.95839			0.424517			0.212259	−	0.977214i	$-0.431918\pi$
$197$	5.95839			0.424517			0.212259	+	0.977214i	$0.431918\pi$
$198$		0			0
$199$	−5.62062	−	9.73520i	−0.398435	−	0.690110i	0.595098	−	0.803653i	$-0.297113\pi$
$199$	−5.62062	−	9.73520i	−0.398435	−	0.690110i	−0.993533	+	0.113543i	$0.963780\pi$
$200$		0			0
$201$	−1.22451	+	1.68462i	−0.0863702	+	0.118824i
$202$		0			0
$203$	4.52168	−	0.995884i	0.317360	−	0.0698974i
$204$		0			0
$205$	2.53321	+	4.38765i	0.176927	+	0.306447i
$206$		0			0
$207$	2.57434	+	0.548368i	0.178929	+	0.0381142i
$208$		0			0
$209$	1.13689	−	1.96914i	0.0786401	−	0.136209i
$210$		0			0
$211$	−0.381084	−	0.660057i	−0.0262349	−	0.0454402i	0.852610	−	0.522548i	$-0.175018\pi$
$211$	−0.381084	−	0.660057i	−0.0262349	−	0.0454402i	−0.878845	+	0.477108i	$0.841685\pi$
$212$		0			0
$213$	−25.2911	−	2.66378i	−1.73291	−	0.182519i
$214$		0			0
$215$	−0.582381	+	1.00871i	−0.0397181	+	0.0687937i
$216$		0			0
$217$	23.6030	−	5.19848i	1.60228	−	0.352896i
$218$		0			0
$219$	−0.444505	−	0.998962i	−0.0300369	−	0.0675036i
$220$		0			0
$221$	0.509628	−	0.882702i	0.0342813	−	0.0593769i
$222$		0			0
$223$	5.80556	−	10.0555i	0.388769	−	0.673368i	−0.603515	−	0.797352i	$-0.706234\pi$
$223$	5.80556	−	10.0555i	0.388769	−	0.673368i	0.992284	+	0.123984i	$0.0395670\pi$
$224$		0			0
$225$	−1.67692	−	0.357205i	−0.111794	−	0.0238137i
$226$		0			0
$227$	10.3325			0.685790			0.342895	−	0.939374i	$-0.388592\pi$
$227$	10.3325			0.685790			0.342895	+	0.939374i	$0.388592\pi$
$228$		0			0
$229$	−3.72383			−0.246077			−0.123039	−	0.992402i	$-0.539264\pi$
$229$	−3.72383			−0.246077			−0.123039	+	0.992402i	$0.539264\pi$
$230$		0			0
$231$	1.08543	+	1.47178i	0.0714157	+	0.0968363i
$232$		0			0
$233$	13.3649	−	23.1488i	0.875566	−	1.51653i	0.0194083	−	0.999812i	$-0.493822\pi$
$233$	13.3649	−	23.1488i	0.875566	−	1.51653i	0.856158	−	0.516714i	$-0.172845\pi$
$234$		0			0
$235$	12.3499	+	21.3906i	0.805616	+	1.39537i
$236$		0			0
$237$	1.75141	+	3.93604i	0.113766	+	0.255673i
$238$		0			0
$239$	−6.94164	−	12.0233i	−0.449018	−	0.777721i	0.549305	−	0.835622i	$-0.314893\pi$
$239$	−6.94164	−	12.0233i	−0.449018	−	0.777721i	−0.998322	+	0.0579007i	$0.981559\pi$
$240$		0			0
$241$	14.9056			0.960154			0.480077	−	0.877226i	$-0.340609\pi$
$241$	14.9056			0.960154			0.480077	+	0.877226i	$0.340609\pi$
$242$		0			0
$243$	−13.4915	−	7.80897i	−0.865479	−	0.500946i
$244$		0			0
$245$	−1.32439	+	14.6711i	−0.0846120	+	0.937304i
$246$		0			0
$247$	−16.4428			−1.04623
$248$		0			0
$249$	−9.35618	+	12.8718i	−0.592924	+	0.815714i
$250$		0			0
$251$	−22.5515			−1.42344			−0.711720	−	0.702464i	$-0.752083\pi$
$251$	−22.5515			−1.42344			−0.711720	+	0.702464i	$0.752083\pi$
$252$		0			0
$253$	−0.350125			−0.0220122
$254$		0			0
$255$	0.523358	+	1.17617i	0.0327740	+	0.0736548i
$256$		0			0
$257$	11.8953			0.742008			0.371004	−	0.928631i	$-0.379014\pi$
$257$	11.8953			0.742008			0.371004	+	0.928631i	$0.379014\pi$
$258$		0			0
$259$	−17.5470	+	3.86467i	−1.09032	+	0.240139i
$260$		0			0
$261$	3.51463	−	3.89996i	0.217550	−	0.241402i
$262$		0			0
$263$	−24.6059			−1.51727			−0.758633	−	0.651518i	$-0.774132\pi$
$263$	−24.6059			−1.51727			−0.758633	+	0.651518i	$0.774132\pi$
$264$		0			0
$265$	−4.37337	−	7.57490i	−0.268654	−	0.465322i
$266$		0			0
$267$	−14.8553	+	20.4371i	−0.909128	+	1.25073i
$268$		0			0
$269$	6.75722	+	11.7039i	0.411995	+	0.713597i	0.995108	−	0.0987947i	$-0.0314987\pi$
$269$	6.75722	+	11.7039i	0.411995	+	0.713597i	−0.583113	+	0.812391i	$0.698165\pi$
$270$		0			0
$271$	1.34195	−	2.32433i	0.0815177	−	0.141193i	−0.822384	−	0.568932i	$-0.807357\pi$
$271$	1.34195	−	2.32433i	0.0815177	−	0.141193i	0.903902	+	0.427740i	$0.140690\pi$
$272$		0			0
$273$	5.29268	−	12.1193i	0.320328	−	0.733493i
$274$		0			0
$275$	0.228070			0.0137532
$276$		0			0
$277$	19.0524			1.14475			0.572373	−	0.819993i	$-0.306023\pi$
$277$	19.0524			1.14475			0.572373	+	0.819993i	$0.306023\pi$
$278$		0			0
$279$	18.3462	−	20.3577i	1.09836	−	1.21878i
$280$		0			0
$281$	14.2006	−	24.5962i	0.847139	−	1.46729i	−0.0366118	−	0.999330i	$-0.511657\pi$
$281$	14.2006	−	24.5962i	0.847139	−	1.46729i	0.883751	−	0.467958i	$-0.155010\pi$
$282$		0			0
$283$	−7.71105	+	13.3559i	−0.458374	+	0.793928i	−0.998875	−	0.0474156i	$-0.984901\pi$
$283$	−7.71105	+	13.3559i	−0.458374	+	0.793928i	0.540501	+	0.841344i	$0.318235\pi$
$284$		0			0
$285$	12.2107	−	16.7989i	0.723301	−	0.995082i
$286$		0			0
$287$	−1.92381	+	6.07230i	−0.113559	+	0.358436i
$288$		0			0
$289$	8.43763	−	14.6144i	0.496331	−	0.859671i
$290$		0			0
$291$	15.9732	−	21.9751i	0.936364	−	1.28820i
$292$		0			0
$293$	9.02253	+	15.6275i	0.527102	+	0.912967i	0.999501	+	0.0315825i	$0.0100547\pi$
$293$	9.02253	+	15.6275i	0.527102	+	0.912967i	−0.472399	+	0.881385i	$0.656612\pi$
$294$		0			0
$295$	−9.81092	+	16.9930i	−0.571214	+	0.989371i
$296$		0			0
$297$	1.97169	+	0.642070i	0.114409	+	0.0372567i
$298$		0			0
$299$	1.26597	+	2.19272i	0.0732128	+	0.126808i
$300$		0			0
$301$	−1.43012	+	0.314979i	−0.0824308	+	0.0181551i
$302$		0			0
$303$	0.159948	+	0.0168466i	0.00918880	+	0.000967811i
$304$		0			0
$305$	10.5978	+	18.3559i	0.606826	+	1.05105i
$306$		0			0
$307$	7.30860			0.417124			0.208562	−	0.978009i	$-0.433122\pi$
$307$	7.30860			0.417124			0.208562	+	0.978009i	$0.433122\pi$
$308$		0			0
$309$	−34.3047	−	3.61315i	−1.95153	−	0.205545i
$310$		0			0
$311$	−11.8896	+	20.5934i	−0.674197	+	1.16774i	0.302505	+	0.953148i	$0.402177\pi$
$311$	−11.8896	+	20.5934i	−0.674197	+	1.16774i	−0.976703	+	0.214597i	$0.931156\pi$
$312$		0			0
$313$	9.14534	+	15.8402i	0.516925	+	0.895341i	0.999807	+	0.0196551i	$0.00625681\pi$
$313$	9.14534	+	15.8402i	0.516925	+	0.895341i	−0.482882	+	0.875686i	$0.660410\pi$
$314$		0			0
$315$	8.45131	+	14.4073i	0.476177	+	0.811759i
$316$		0			0
$317$	2.34494	+	4.06155i	0.131705	+	0.228120i	0.924334	−	0.381585i	$-0.124622\pi$
$317$	2.34494	+	4.06155i	0.131705	+	0.228120i	−0.792629	+	0.609704i	$0.791288\pi$
$318$		0			0
$319$	−0.349180	+	0.604798i	−0.0195503	+	0.0338622i
$320$		0			0
$321$	−5.89083	+	8.10430i	−0.328794	+	0.452338i
$322$		0			0
$323$	2.01240			0.111973
$324$		0			0
$325$	−0.824648	−	1.42833i	−0.0457432	−	0.0792296i
$326$		0			0
$327$	8.80905	+	19.7971i	0.487142	+	1.09478i
$328$		0			0
$329$	−9.37890	+	29.6035i	−0.517076	+	1.63209i
$330$		0			0
$331$	−5.71433	−	9.89751i	−0.314088	−	0.544016i	0.665155	−	0.746705i	$-0.268365\pi$
$331$	−5.71433	−	9.89751i	−0.314088	−	0.544016i	−0.979243	+	0.202689i	$0.935032\pi$
$332$		0			0
$333$	−13.6390	+	15.1344i	−0.747413	+	0.829357i
$334$		0			0
$335$	1.26517	−	2.19134i	0.0691238	−	0.119726i
$336$		0			0
$337$	8.74160	+	15.1409i	0.476185	+	0.824777i	0.999628	−	0.0272840i	$-0.00868584\pi$
$337$	8.74160	+	15.1409i	0.476185	+	0.824777i	−0.523442	+	0.852061i	$0.675353\pi$
$338$		0			0
$339$	−2.38579	−	5.36172i	−0.129578	−	0.291209i
$340$		0			0
$341$	−1.82271	+	3.15702i	−0.0987051	+	0.170962i
$342$		0			0
$343$	−14.7397	+	11.2135i	−0.795868	+	0.605470i
$344$		0			0
$345$	−3.18033	−	0.334969i	−0.171223	−	0.0180341i
$346$		0			0
$347$	7.05929	−	12.2270i	0.378962	−	0.656382i	−0.611949	−	0.790897i	$-0.709614\pi$
$347$	7.05929	−	12.2270i	0.378962	−	0.656382i	0.990912	+	0.134515i	$0.0429476\pi$
$348$		0			0
$349$	10.7216	−	18.5704i	0.573916	−	0.994052i	−0.422242	−	0.906483i	$-0.638757\pi$
$349$	10.7216	−	18.5704i	0.573916	−	0.994052i	0.996158	−	0.0875692i	$-0.0279099\pi$
$350$		0			0
$351$	−3.10808	−	14.6696i	−0.165897	−	0.783007i
$352$		0			0
$353$	−31.3760			−1.66997			−0.834987	−	0.550269i	$-0.814525\pi$
$353$	−31.3760			−1.66997			−0.834987	+	0.550269i	$0.814525\pi$
$354$		0			0
$355$	30.8979			1.63989
$356$		0			0
$357$	−0.647759	+	1.48325i	−0.0342831	+	0.0785021i
$358$		0			0
$359$	−0.313156	+	0.542402i	−0.0165277	+	0.0286269i	−0.874171	−	0.485618i	$-0.838595\pi$
$359$	−0.313156	+	0.542402i	−0.0165277	+	0.0286269i	0.857643	+	0.514245i	$0.171928\pi$
$360$		0			0
$361$	−6.73223	−	11.6606i	−0.354328	−	0.613714i
$362$		0			0
$363$	18.6734	+	1.96678i	0.980101	+	0.103229i
$364$		0			0
$365$	0.664223	+	1.15047i	0.0347670	+	0.0602182i
$366$		0			0
$367$	3.24397			0.169334			0.0846670	−	0.996409i	$-0.473017\pi$
$367$	3.24397			0.169334			0.0846670	+	0.996409i	$0.473017\pi$
$368$		0			0
$369$	2.22891	+	6.87010i	0.116033	+	0.357643i
$370$		0			0
$371$	3.32129	−	10.4833i	0.172433	−	0.544265i
$372$		0			0
$373$	−27.6027			−1.42921			−0.714606	−	0.699527i	$-0.753394\pi$
$373$	−27.6027			−1.42921			−0.714606	+	0.699527i	$0.753394\pi$
$374$		0			0
$375$	20.1960	+	2.12715i	1.04292	+	0.109846i
$376$		0			0
$377$	5.05021			0.260099
$378$		0			0
$379$	12.7800			0.656463			0.328231	−	0.944597i	$-0.393547\pi$
$379$	12.7800			0.656463			0.328231	+	0.944597i	$0.393547\pi$
$380$		0			0
$381$	25.3811	+	2.67326i	1.30031	+	0.136956i
$382$		0			0
$383$	5.16557			0.263948			0.131974	−	0.991253i	$-0.457868\pi$
$383$	5.16557			0.263948			0.131974	+	0.991253i	$0.457868\pi$
$384$		0			0
$385$	−1.49881	−	1.64021i	−0.0763866	−	0.0835928i
$386$		0			0
$387$	−1.11161	+	1.23348i	−0.0565063	+	0.0627015i
$388$		0			0
$389$	32.9413			1.67019			0.835095	−	0.550105i	$-0.185412\pi$
$389$	32.9413			1.67019			0.835095	+	0.550105i	$0.185412\pi$
$390$		0			0
$391$	−0.154939	−	0.268362i	−0.00783560	−	0.0135717i
$392$		0			0
$393$	−23.9566	−	2.52323i	−1.20845	−	0.127280i
$394$		0			0
$395$	−2.61712	−	4.53299i	−0.131682	−	0.228079i
$396$		0			0
$397$	−0.411705	+	0.713095i	−0.0206629	+	0.0357892i	−0.876172	−	0.481999i	$-0.839911\pi$
$397$	−0.411705	+	0.713095i	−0.0206629	+	0.0357892i	0.855509	+	0.517788i	$0.173244\pi$
$398$		0			0
$399$	25.9473	−	2.91429i	1.29899	−	0.145897i
$400$		0			0
$401$	−19.7385			−0.985691			−0.492846	−	0.870117i	$-0.664043\pi$
$401$	−19.7385			−0.985691			−0.492846	+	0.870117i	$0.664043\pi$
$402$		0			0
$403$	26.3619			1.31318
$404$		0			0
$405$	17.2954	+	7.71854i	0.859416	+	0.383537i
$406$		0			0
$407$	1.35504	−	2.34700i	0.0671670	−	0.116337i
$408$		0			0
$409$	12.6276	−	21.8716i	0.624393	−	1.08148i	−0.364265	−	0.931295i	$-0.618680\pi$
$409$	12.6276	−	21.8716i	0.624393	−	1.08148i	0.988658	−	0.150185i	$-0.0479869\pi$
$410$		0			0
$411$	−25.0756	−	2.64109i	−1.23689	−	0.130275i
$412$		0			0
$413$	−24.0921	+	5.30621i	−1.18550	+	0.261101i
$414$		0			0
$415$	9.66688	−	16.7435i	0.474528	−	0.821907i
$416$		0			0
$417$	−5.12610	−	11.5202i	−0.251026	−	0.564146i
$418$		0			0
$419$	−0.406717	−	0.704455i	−0.0198694	−	0.0344149i	0.855920	−	0.517109i	$-0.172992\pi$
$419$	−0.406717	−	0.704455i	−0.0198694	−	0.0344149i	−0.875789	+	0.482694i	$0.839658\pi$
$420$		0			0
$421$	5.12114	−	8.87008i	0.249589	−	0.432301i	−0.713823	−	0.700326i	$-0.753038\pi$
$421$	5.12114	−	8.87008i	0.249589	−	0.432301i	0.963412	+	0.268025i	$0.0863711\pi$
$422$		0			0
$423$	10.8663	+	33.4929i	0.528339	+	1.62848i
$424$		0			0
$425$	0.100927	+	0.174810i	0.00489567	+	0.00847955i
$426$		0			0
$427$	−8.04830	+	25.4036i	−0.389485	+	1.22937i
$428$		0			0
$429$	0.810917	+	1.82242i	0.0391514	+	0.0879873i
$430$		0			0
$431$	−16.3348	−	28.2928i	−0.786822	−	1.36281i	−0.927905	−	0.372817i	$-0.878392\pi$
$431$	−16.3348	−	28.2928i	−0.786822	−	1.36281i	0.141083	−	0.989998i	$-0.454941\pi$
$432$		0			0
$433$	−14.3151			−0.687941			−0.343970	−	0.938980i	$-0.611772\pi$
$433$	−14.3151			−0.687941			−0.343970	+	0.938980i	$0.611772\pi$
$434$		0			0
$435$	−3.75037	+	5.15957i	−0.179817	+	0.247382i
$436$		0			0
$437$	−2.49951	+	4.32927i	−0.119568	+	0.207097i
$438$		0			0
$439$	−4.93330	−	8.54472i	−0.235453	−	0.407817i	0.723951	−	0.689852i	$-0.242324\pi$
$439$	−4.93330	−	8.54472i	−0.235453	−	0.407817i	−0.959404	+	0.282034i	$0.908991\pi$
$440$		0			0
$441$	−6.20400	+	20.0627i	−0.295429	+	0.955365i
$442$		0			0
$443$	18.6400	+	32.2855i	0.885615	+	1.53393i	0.845007	+	0.534756i	$0.179596\pi$
$443$	18.6400	+	32.2855i	0.885615	+	1.53393i	0.0406086	+	0.999175i	$0.487070\pi$
$444$		0			0
$445$	15.3486	−	26.5845i	0.727593	−	1.26023i
$446$		0			0
$447$	1.24308	+	0.130928i	0.0587958	+	0.00619267i
$448$		0			0
$449$	−36.2926			−1.71276			−0.856378	−	0.516350i	$-0.827290\pi$
$449$	−36.2926			−1.71276			−0.856378	+	0.516350i	$0.827290\pi$
$450$		0			0
$451$	−0.480382	−	0.832046i	−0.0226203	−	0.0391795i
$452$		0			0
$453$	37.5585	+	3.95585i	1.76465	+	0.185862i
$454$		0			0
$455$	−4.85275	+	15.3172i	−0.227501	+	0.718081i
$456$		0			0
$457$	6.59716	+	11.4266i	0.308602	+	0.534515i	0.978057	−	0.208338i	$-0.0668054\pi$
$457$	6.59716	+	11.4266i	0.308602	+	0.534515i	−0.669455	+	0.742853i	$0.733472\pi$
$458$		0			0
$459$	0.380391	+	1.79538i	0.0177551	+	0.0838013i
$460$		0			0
$461$	10.1326	−	17.5502i	0.471924	−	0.817396i	−0.527560	−	0.849518i	$-0.676893\pi$
$461$	10.1326	−	17.5502i	0.471924	−	0.817396i	0.999484	+	0.0321215i	$0.0102263\pi$
$462$		0			0
$463$	−12.7106	−	22.0154i	−0.590712	−	1.02314i	−0.994137	−	0.108131i	$-0.965513\pi$
$463$	−12.7106	−	22.0154i	−0.590712	−	1.02314i	0.403424	−	0.915013i	$-0.367820\pi$
$464$		0			0
$465$	−19.5768	+	26.9328i	−0.907852	+	1.24898i
$466$		0			0
$467$	4.40661	−	7.63248i	0.203914	−	0.353189i	−0.745872	−	0.666089i	$-0.767967\pi$
$467$	4.40661	−	7.63248i	0.203914	−	0.353189i	0.949786	+	0.312900i	$0.101300\pi$
$468$		0			0
$469$	3.10681	−	0.684265i	0.143459	−	0.0315964i
$470$		0			0
$471$	5.27493	−	7.25698i	0.243056	−	0.334384i
$472$		0			0
$473$	0.110439	−	0.191286i	0.00507799	−	0.00879534i
$474$		0			0
$475$	1.62817	−	2.82008i	0.0747056	−	0.129394i
$476$		0			0
$477$	−3.84802	−	11.8606i	−0.176189	−	0.543061i
$478$		0			0
$479$	−24.2687			−1.10887			−0.554433	−	0.832229i	$-0.687065\pi$
$479$	−24.2687			−1.10887			−0.554433	+	0.832229i	$0.687065\pi$
$480$		0			0
$481$	−19.5980			−0.893594
$482$		0			0
$483$	−2.38637	−	3.23580i	−0.108583	−	0.147234i
$484$		0			0
$485$	−16.5036	+	28.5851i	−0.749391	+	1.29798i
$486$		0			0
$487$	5.37220	+	9.30492i	0.243438	+	0.421646i	0.961691	−	0.274135i	$-0.0883916\pi$
$487$	5.37220	+	9.30492i	0.243438	+	0.421646i	−0.718254	+	0.695781i	$0.755058\pi$
$488$		0			0
$489$	5.37513	−	7.39483i	0.243072	−	0.334406i
$490$		0			0
$491$	−11.3934	−	19.7340i	−0.514179	−	0.890584i	−0.999865	−	0.0164507i	$-0.994763\pi$
$491$	−11.3934	−	19.7340i	−0.514179	−	0.890584i	0.485686	−	0.874134i	$-0.338570\pi$
$492$		0			0
$493$	−0.618084			−0.0278371
$494$		0			0
$495$	−2.46409	−	0.524883i	−0.110752	−	0.0235917i
$496$		0			0
$497$	26.2047	+	28.6768i	1.17544	+	1.28633i
$498$		0			0
$499$	−23.1509			−1.03638			−0.518189	−	0.855266i	$-0.673394\pi$
$499$	−23.1509			−1.03638			−0.518189	+	0.855266i	$0.673394\pi$
$500$		0			0
$501$	−9.62859	−	21.6389i	−0.430174	−	0.966755i
$502$		0			0
$503$	−9.43360			−0.420623			−0.210312	−	0.977634i	$-0.567448\pi$
$503$	−9.43360			−0.420623			−0.210312	+	0.977634i	$0.567448\pi$
$504$		0			0
$505$	−0.195408			−0.00869555
$506$		0			0
$507$	−4.75778	+	6.54552i	−0.211301	+	0.290697i
$508$		0			0
$509$	−9.45963			−0.419291			−0.209645	−	0.977777i	$-0.567231\pi$
$509$	−9.45963			−0.419291			−0.209645	+	0.977777i	$0.567231\pi$
$510$		0			0
$511$	−0.504433	+	1.59219i	−0.0223148	+	0.0704343i
$512$		0			0
$513$	22.0148	−	19.7961i	0.971979	−	0.874021i
$514$		0			0
$515$	41.9099			1.84677
$516$		0			0
$517$	−2.34195	−	4.05637i	−0.102999	−	0.178399i
$518$		0			0
$519$	14.2113	+	31.9378i	0.623805	+	1.40191i
$520$		0			0
$521$	−14.3368	−	24.8320i	−0.628105	−	1.08791i	−0.987932	−	0.154891i	$-0.950497\pi$
$521$	−14.3368	−	24.8320i	−0.628105	−	1.08791i	0.359826	−	0.933019i	$-0.382836\pi$
$522$		0			0
$523$	13.5104	−	23.4006i	0.590767	−	1.02324i	−0.403362	−	0.915040i	$-0.632159\pi$
$523$	13.5104	−	23.4006i	0.590767	−	1.02324i	0.994129	−	0.108198i	$-0.0345081\pi$
$524$		0			0
$525$	1.55447	+	2.10779i	0.0678427	+	0.0919915i
$526$		0			0
$527$	−3.22637			−0.140543
$528$		0			0
$529$	−22.2302			−0.966532
$530$		0			0
$531$	−18.7264	+	20.7795i	−0.812658	+	0.901755i
$532$		0			0
$533$	−3.47389	+	6.01696i	−0.150471	+	0.260624i
$534$		0			0
$535$	6.08645	−	10.5420i	0.263140	−	0.455772i
$536$		0			0
$537$	17.7399	+	39.8679i	0.765532	+	1.72043i
$538$		0			0
$539$	0.251148	−	2.78214i	0.0108177	−	0.119835i
$540$		0			0
$541$	−1.52907	+	2.64842i	−0.0657397	+	0.113864i	−0.897022	−	0.441986i	$-0.854274\pi$
$541$	−1.52907	+	2.64842i	−0.0657397	+	0.113864i	0.831282	+	0.555851i	$0.187607\pi$
$542$		0			0
$543$	29.7678	+	3.13530i	1.27746	+	0.134549i
$544$		0			0
$545$	−13.1633	−	22.7996i	−0.563856	−	0.976627i
$546$		0			0
$547$	−3.58144	+	6.20323i	−0.153131	+	0.265231i	−0.932377	−	0.361487i	$-0.882269\pi$
$547$	−3.58144	+	6.20323i	−0.153131	+	0.265231i	0.779246	+	0.626719i	$0.215602\pi$
$548$		0			0
$549$	9.32471	+	28.7412i	0.397969	+	1.22665i
$550$		0			0
$551$	4.98552	+	8.63518i	0.212390	+	0.367871i
$552$		0			0
$553$	1.98753	−	6.27343i	0.0845185	−	0.266774i
$554$		0			0
$555$	14.5538	−	20.0224i	0.617776	−	0.849906i
$556$		0			0
$557$	−14.3518	−	24.8580i	−0.608104	−	1.05327i	−0.991553	−	0.129704i	$-0.958597\pi$
$557$	−14.3518	−	24.8580i	−0.608104	−	1.05327i	0.383449	−	0.923562i	$-0.374736\pi$
$558$		0			0
$559$	−1.59729			−0.0675580
$560$		0			0
$561$	−0.0992463	−	0.223042i	−0.00419018	−	0.00941684i
$562$		0			0
$563$	17.8859	−	30.9794i	0.753803	−	1.30562i	−0.192165	−	0.981363i	$-0.561551\pi$
$563$	17.8859	−	30.9794i	0.753803	−	1.30562i	0.945967	−	0.324262i	$-0.105116\pi$
$564$		0			0
$565$	3.56508	+	6.17490i	0.149984	+	0.259780i
$566$		0			0
$567$	7.50465	+	22.5982i	0.315166	+	0.949037i
$568$		0			0
$569$	12.6001	+	21.8240i	0.528223	+	0.914909i	0.999459	+	0.0329018i	$0.0104749\pi$
$569$	12.6001	+	21.8240i	0.528223	+	0.914909i	−0.471235	+	0.882007i	$0.656192\pi$
$570$		0			0
$571$	−3.02469	+	5.23891i	−0.126579	+	0.219242i	−0.922349	−	0.386357i	$-0.873733\pi$
$571$	−3.02469	+	5.23891i	−0.126579	+	0.219242i	0.795770	+	0.605599i	$0.207066\pi$
$572$		0			0
$573$	3.53408	+	7.94234i	0.147638	+	0.331796i
$574$		0			0
$575$	−0.501425			−0.0209109
$576$		0			0
$577$	9.57977	+	16.5926i	0.398811	+	0.690761i	0.993580	−	0.113136i	$-0.0360896\pi$
$577$	9.57977	+	16.5926i	0.398811	+	0.690761i	−0.594768	+	0.803897i	$0.702756\pi$
$578$		0			0
$579$	−5.53759	+	7.61834i	−0.230135	+	0.316608i
$580$		0			0
$581$	23.7384	−	5.22830i	0.984835	−	0.216907i
$582$		0			0
$583$	0.829338	+	1.43645i	0.0343477	+	0.0594919i
$584$		0			0
$585$	5.62237	+	17.3296i	0.232456	+	0.716492i
$586$		0			0
$587$	−18.4147	+	31.8953i	−0.760058	+	1.31646i	0.182763	+	0.983157i	$0.441496\pi$
$587$	−18.4147	+	31.8953i	−0.760058	+	1.31646i	−0.942820	+	0.333301i	$0.891837\pi$
$588$		0			0
$589$	26.0242	+	45.0753i	1.07231	+	1.85730i
$590$		0			0
$591$	−10.2635	−	1.08100i	−0.422182	−	0.0444664i
$592$		0			0
$593$	8.97285	−	15.5414i	0.368471	−	0.638210i	−0.620856	−	0.783925i	$-0.713215\pi$
$593$	8.97285	−	15.5414i	0.368471	−	0.638210i	0.989327	+	0.145715i	$0.0465481\pi$
$594$		0			0
$595$	0.593918	−	1.87464i	0.0243482	−	0.0768526i
$596$		0			0
$597$	7.91544	+	17.7888i	0.323957	+	0.728048i
$598$		0			0
$599$	−20.2457	+	35.0665i	−0.827215	+	1.43278i	0.0729993	+	0.997332i	$0.476743\pi$
$599$	−20.2457	+	35.0665i	−0.827215	+	1.43278i	−0.900214	+	0.435447i	$0.856590\pi$
$600$		0			0
$601$	13.2589	−	22.9651i	0.540841	−	0.936765i	−0.458015	−	0.888945i	$-0.651439\pi$
$601$	13.2589	−	22.9651i	0.540841	−	0.936765i	0.998856	−	0.0478200i	$-0.0152274\pi$
$602$		0			0
$603$	2.41488	−	2.67964i	0.0983414	−	0.109123i
$604$		0			0
$605$	−22.8132			−0.927490
$606$		0			0
$607$	42.1696			1.71161			0.855806	−	0.517297i	$-0.173062\pi$
$607$	42.1696			1.71161			0.855806	+	0.517297i	$0.173062\pi$
$608$		0			0
$609$	−7.96937	+	0.895088i	−0.322935	+	0.0362708i
$610$		0			0
$611$	−16.9358	+	29.3337i	−0.685151	+	1.18672i
$612$		0			0
$613$	−0.700827	−	1.21387i	−0.0283061	−	0.0490277i	0.851525	−	0.524313i	$-0.175678\pi$
$613$	−0.700827	−	1.21387i	−0.0283061	−	0.0490277i	−0.879831	+	0.475286i	$0.842345\pi$
$614$		0			0
$615$	−3.56749	−	8.01742i	−0.143855	−	0.323294i
$616$		0			0
$617$	−6.76787	−	11.7223i	−0.272464	−	0.471922i	0.697028	−	0.717044i	$-0.254505\pi$
$617$	−6.76787	−	11.7223i	−0.272464	−	0.471922i	−0.969492	+	0.245122i	$0.921172\pi$
$618$		0			0
$619$	29.8245			1.19875			0.599374	−	0.800469i	$-0.295416\pi$
$619$	29.8245			1.19875			0.599374	+	0.800469i	$0.295416\pi$
$620$		0			0
$621$	−4.33487	−	1.41163i	−0.173952	−	0.0566466i
$622$		0			0
$623$	37.6907	−	8.30124i	1.51004	−	0.332582i
$624$		0			0
$625$	−21.8158			−0.872632
$626$		0			0
$627$	−2.31556	+	3.18564i	−0.0924747	+	0.127222i
$628$		0			0
$629$	2.39856			0.0956369
$630$		0			0
$631$	−6.84708			−0.272578			−0.136289	−	0.990669i	$-0.543518\pi$
$631$	−6.84708			−0.272578			−0.136289	+	0.990669i	$0.543518\pi$
$632$		0			0
$633$	0.536675	+	1.20610i	0.0213309	+	0.0479382i
$634$		0			0
$635$	−31.0079			−1.23051
$636$		0			0
$637$	−18.3317	+	8.48668i	−0.726330	+	0.336255i
$638$		0			0
$639$	43.0811	+	9.17686i	1.70426	+	0.363031i
$640$		0			0
$641$	32.2417			1.27347			0.636735	−	0.771082i	$-0.280284\pi$
$641$	32.2417			1.27347			0.636735	+	0.771082i	$0.280284\pi$
$642$		0			0
$643$	−1.16002	−	2.00921i	−0.0457465	−	0.0792353i	0.842245	−	0.539094i	$-0.181233\pi$
$643$	−1.16002	−	2.00921i	−0.0457465	−	0.0792353i	−0.887992	+	0.459859i	$0.847900\pi$
$644$		0			0
$645$	1.18617	−	1.63187i	0.0467055	−	0.0642550i
$646$		0			0
$647$	−1.06813	−	1.85005i	−0.0419924	−	0.0727329i	0.844265	−	0.535925i	$-0.180037\pi$
$647$	−1.06813	−	1.85005i	−0.0419924	−	0.0727329i	−0.886258	+	0.463193i	$0.846704\pi$
$648$		0			0
$649$	1.86048	−	3.22244i	0.0730302	−	0.126492i
$650$		0			0
$651$	−41.5998	+	4.67233i	−1.63043	+	0.183123i
$652$		0			0
$653$	3.03865			0.118912			0.0594558	−	0.998231i	$-0.481063\pi$
$653$	3.03865			0.118912			0.0594558	+	0.998231i	$0.481063\pi$
$654$		0			0
$655$	29.2676			1.14358
$656$		0			0
$657$	0.584433	+	1.80138i	0.0228009	+	0.0702785i
$658$		0			0
$659$	19.8000	−	34.2946i	0.771298	−	1.33593i	−0.165554	−	0.986201i	$-0.552941\pi$
$659$	19.8000	−	34.2946i	0.771298	−	1.33593i	0.936852	−	0.349726i	$-0.113725\pi$
$660$		0			0
$661$	−3.06199	+	5.30352i	−0.119098	+	0.206283i	−0.919410	−	0.393300i	$-0.871333\pi$
$661$	−3.06199	+	5.30352i	−0.119098	+	0.206283i	0.800313	+	0.599583i	$0.204667\pi$
$662$		0			0
$663$	−1.03799	+	1.42801i	−0.0403122	+	0.0554595i
$664$		0			0
$665$	−30.9810	+	6.82345i	−1.20139	+	0.264602i
$666$		0			0
$667$	0.767691	−	1.32968i	0.0297251	−	0.0514854i
$668$		0			0
$669$	−11.8245	+	16.2676i	−0.457163	+	0.628942i
$670$		0			0
$671$	−2.00969	−	3.48089i	−0.0775832	−	0.134378i
$672$		0			0
$673$	−4.36248	+	7.55603i	−0.168161	+	0.291264i	−0.937773	−	0.347248i	$-0.887116\pi$
$673$	−4.36248	+	7.55603i	−0.168161	+	0.291264i	0.769612	+	0.638512i	$0.220450\pi$
$674$		0			0
$675$	2.82372	+	0.919529i	0.108685	+	0.0353927i
$676$		0			0
$677$	−7.48007	−	12.9559i	−0.287482	−	0.497934i	0.685726	−	0.727860i	$-0.259485\pi$
$677$	−7.48007	−	12.9559i	−0.287482	−	0.497934i	−0.973208	+	0.229926i	$0.926152\pi$
$678$		0			0
$679$	−40.5270	+	8.92594i	−1.55528	+	0.342546i
$680$		0			0
$681$	−17.7979	−	1.87457i	−0.682018	−	0.0718336i
$682$		0			0
$683$	8.89558	+	15.4076i	0.340380	+	0.589555i	0.984503	−	0.175366i	$-0.0561110\pi$
$683$	8.89558	+	15.4076i	0.340380	+	0.589555i	−0.644123	+	0.764922i	$0.722778\pi$
$684$		0			0
$685$	30.6347			1.17049
$686$		0			0
$687$	6.41437	+	0.675595i	0.244724	+	0.0257756i
$688$		0			0
$689$	5.99738	−	10.3878i	0.228482	−	0.395742i
$690$		0			0
$691$	−14.7694	−	25.5814i	−0.561856	−	0.973164i	−0.997335	−	0.0729644i	$-0.976754\pi$
$691$	−14.7694	−	25.5814i	−0.561856	−	0.973164i	0.435478	−	0.900199i	$-0.356579\pi$
$692$		0			0
$693$	−1.60265	−	2.73211i	−0.0608797	−	0.103784i
$694$		0			0
$695$	7.65992	+	13.2674i	0.290557	+	0.503260i
$696$		0			0
$697$	0.425162	−	0.736402i	0.0161042	−	0.0278932i
$698$		0			0
$699$	−27.2212	+	37.4495i	−1.02960	+	1.41647i
$700$		0			0
$701$	27.7740			1.04901			0.524504	−	0.851408i	$-0.324251\pi$
$701$	27.7740			1.04901			0.524504	+	0.851408i	$0.324251\pi$
$702$		0			0
$703$	−19.3470	−	33.5100i	−0.729687	−	1.26385i
$704$		0			0
$705$	−17.3921	−	39.0863i	−0.655025	−	1.47208i
$706$		0			0
$707$	−0.165727	−	0.181361i	−0.00623279	−	0.00682078i
$708$		0			0
$709$	−23.5492	−	40.7884i	−0.884409	−	1.53184i	−0.846389	−	0.532565i	$-0.821228\pi$
$709$	−23.5492	−	40.7884i	−0.884409	−	1.53184i	−0.0380203	−	0.999277i	$-0.512105\pi$
$710$		0			0
$711$	−2.30274	−	7.09766i	−0.0863596	−	0.266183i
$712$		0			0
$713$	4.00732	−	6.94088i	0.150075	−	0.259938i
$714$		0			0
$715$	−1.21175	−	2.09881i	−0.0453169	−	0.0784912i
$716$		0			0
$717$	9.77582	+	21.9698i	0.365085	+	0.820476i
$718$		0			0
$719$	−1.63394	+	2.83007i	−0.0609357	+	0.105544i	−0.894884	−	0.446299i	$-0.852742\pi$
$719$	−1.63394	+	2.83007i	−0.0609357	+	0.105544i	0.833948	+	0.551843i	$0.186075\pi$
$720$		0			0
$721$	35.5440	+	38.8971i	1.32373	+	1.44860i
$722$		0			0
$723$	−25.6752	−	2.70425i	−0.954872	−	0.100572i
$724$		0			0
$725$	−0.500072	+	0.866150i	−0.0185722	+	0.0321680i
$726$		0			0
$727$	6.37047	−	11.0340i	0.236268	−	0.409228i	−0.723373	−	0.690458i	$-0.757409\pi$
$727$	6.37047	−	11.0340i	0.236268	−	0.409228i	0.959640	+	0.281230i	$0.0907424\pi$
$728$		0			0
$729$	21.8226	+	15.8988i	0.808246	+	0.588845i
$730$		0			0
$731$	0.195488			0.00723039
$732$		0			0
$733$	9.17716			0.338966			0.169483	−	0.985533i	$-0.445790\pi$
$733$	9.17716			0.338966			0.169483	+	0.985533i	$0.445790\pi$
$734$		0			0
$735$	4.94299	−	25.0311i	0.182325	−	0.923285i
$736$		0			0
$737$	−0.239919	+	0.415552i	−0.00883754	+	0.0153071i
$738$		0			0
$739$	23.3467	+	40.4377i	0.858823	+	1.48752i	0.873053	+	0.487626i	$0.162137\pi$
$739$	23.3467	+	40.4377i	0.858823	+	1.48752i	−0.0142303	+	0.999899i	$0.504530\pi$
$740$		0			0
$741$	28.3232	+	2.98314i	1.04048	+	0.109588i
$742$		0			0
$743$	7.62654	+	13.2095i	0.279790	+	0.484611i	0.971333	−	0.237725i	$-0.0764017\pi$
$743$	7.62654	+	13.2095i	0.279790	+	0.484611i	−0.691542	+	0.722336i	$0.743068\pi$
$744$		0			0
$745$	−1.51867			−0.0556396
$746$		0			0
$747$	18.4515	−	20.4744i	0.675104	−	0.749121i
$748$		0			0
$749$	14.9462	−	3.29184i	0.546121	−	0.120281i
$750$		0			0
$751$	−6.34887			−0.231673			−0.115837	−	0.993268i	$-0.536955\pi$
$751$	−6.34887			−0.231673			−0.115837	+	0.993268i	$0.536955\pi$
$752$		0			0
$753$	38.8455	+	4.09141i	1.41561	+	0.149099i
$754$		0			0
$755$	−45.8850			−1.66993
$756$		0			0
$757$	28.4278			1.03323			0.516614	−	0.856219i	$-0.327192\pi$
$757$	28.4278			1.03323			0.516614	+	0.856219i	$0.327192\pi$
$758$		0			0
$759$	0.603098	+	0.0635214i	0.0218911	+	0.00230568i
$760$		0			0
$761$	−18.0687			−0.654991			−0.327496	−	0.944853i	$-0.606205\pi$
$761$	−18.0687			−0.654991			−0.327496	+	0.944853i	$0.606205\pi$
$762$		0			0
$763$	9.99670	−	31.5535i	0.361905	−	1.14231i
$764$		0			0
$765$	−0.688109	−	2.12094i	−0.0248786	−	0.0766826i
$766$		0			0
$767$	−26.9082			−0.971599
$768$		0			0
$769$	−1.72471	−	2.98728i	−0.0621946	−	0.107724i	0.833252	−	0.552894i	$-0.186477\pi$
$769$	−1.72471	−	2.98728i	−0.0621946	−	0.107724i	−0.895446	+	0.445170i	$0.853143\pi$
$770$		0			0
$771$	−20.4899	−	2.15810i	−0.737926	−	0.0777222i
$772$		0			0
$773$	−20.1837	−	34.9592i	−0.725957	−	1.25740i	−0.958579	−	0.284828i	$-0.908064\pi$
$773$	−20.1837	−	34.9592i	−0.725957	−	1.25740i	0.232621	−	0.972567i	$-0.425270\pi$
$774$		0			0
$775$	−2.61036	+	4.52127i	−0.0937668	+	0.162409i
$776$		0			0
$777$	30.9263	−	3.47352i	1.10947	−	0.124612i
$778$		0			0
$779$	−13.7176			−0.491484
$780$		0			0
$781$	−5.85929			−0.209662
$782$		0			0
$783$	−6.76158	+	6.08013i	−0.241639	+	0.217286i
$784$		0			0
$785$	−5.45010	+	9.43985i	−0.194522	+	0.336923i
$786$		0			0
$787$	9.16031	−	15.8661i	0.326530	−	0.565566i	−0.655291	−	0.755377i	$-0.727454\pi$
$787$	9.16031	−	15.8661i	0.326530	−	0.565566i	0.981821	+	0.189810i	$0.0607873\pi$
$788$		0			0
$789$	42.3843	+	4.46413i	1.50892	+	0.158927i
$790$		0			0
$791$	−2.70744	+	8.54575i	−0.0962656	+	0.303852i
$792$		0			0
$793$	−14.5331	+	25.1721i	−0.516086	+	0.893888i
$794$		0			0
$795$	6.15895	+	13.8414i	0.218436	+	0.490903i
$796$		0			0
$797$	−4.86884	−	8.43307i	−0.172463	−	0.298715i	0.766817	−	0.641865i	$-0.221839\pi$
$797$	−4.86884	−	8.43307i	−0.172463	−	0.298715i	−0.939280	+	0.343151i	$0.888506\pi$
$798$		0			0
$799$	2.07274	−	3.59009i	0.0733283	−	0.127008i
$800$		0			0
$801$	29.2963	−	32.5083i	1.03514	−	1.14862i
$802$		0			0
$803$	−0.125959	−	0.218167i	−0.00444499	−	0.00769895i
$804$		0			0
$805$	3.29522	+	3.60609i	0.116141	+	0.127098i
$806$		0			0
$807$	−9.51610	−	21.3861i	−0.334983	−	0.752826i
$808$		0			0
$809$	−5.98714	−	10.3700i	−0.210497	−	0.364591i	0.741373	−	0.671093i	$-0.234175\pi$
$809$	−5.98714	−	10.3700i	−0.210497	−	0.364591i	−0.951870	+	0.306502i	$0.900841\pi$
$810$		0			0
$811$	−4.05517			−0.142396			−0.0711982	−	0.997462i	$-0.522682\pi$
$811$	−4.05517			−0.142396			−0.0711982	+	0.997462i	$0.522682\pi$
$812$		0			0
$813$	−2.73323	+	3.76024i	−0.0958586	+	0.131877i
$814$		0			0
$815$	−5.55362	+	9.61916i	−0.194535	+	0.336944i
$816$		0			0
$817$	−1.57683	−	2.73114i	−0.0551662	−	0.0955506i
$818$		0			0
$819$	−11.3155	+	19.9155i	−0.395396	+	0.695905i
$820$		0			0
$821$	−3.99256	−	6.91532i	−0.139341	−	0.241346i	0.787906	−	0.615795i	$-0.211165\pi$
$821$	−3.99256	−	6.91532i	−0.139341	−	0.241346i	−0.927248	+	0.374449i	$0.877832\pi$
$822$		0			0
$823$	23.7901	−	41.2056i	0.829270	−	1.43634i	−0.0693409	−	0.997593i	$-0.522090\pi$
$823$	23.7901	−	41.2056i	0.829270	−	1.43634i	0.898611	−	0.438746i	$-0.144577\pi$
$824$		0			0
$825$	−0.392856	−	0.0413776i	−0.0136775	−	0.00144058i
$826$		0			0
$827$	29.2725			1.01790			0.508952	−	0.860795i	$-0.330033\pi$
$827$	29.2725			1.01790			0.508952	+	0.860795i	$0.330033\pi$
$828$		0			0
$829$	3.15249	+	5.46028i	0.109491	+	0.189643i	0.915564	−	0.402172i	$-0.131745\pi$
$829$	3.15249	+	5.46028i	0.109491	+	0.189643i	−0.806073	+	0.591816i	$0.798411\pi$
$830$		0			0
$831$	−32.8181	−	3.45658i	−1.13845	−	0.119907i
$832$		0			0
$833$	2.24358	−	1.03867i	0.0777354	−	0.0359876i
$834$		0			0
$835$	14.3880	+	24.9207i	0.497917	+	0.862417i
$836$		0			0
$837$	−35.2952	+	31.7381i	−1.21998	+	1.09703i
$838$		0			0
$839$	0.501711	−	0.868989i	0.0173210	−	0.0300008i	−0.857235	−	0.514925i	$-0.827820\pi$
$839$	0.501711	−	0.868989i	0.0173210	−	0.0300008i	0.874556	+	0.484925i	$0.161153\pi$
$840$		0			0
$841$	12.9688	+	22.4626i	0.447199	+	0.774571i
$842$		0			0
$843$	−28.9233	+	39.7912i	−0.996171	+	1.37048i
$844$		0			0
$845$	4.91578	−	8.51438i	0.169108	−	0.292904i
$846$		0			0
$847$	−19.3480	−	21.1733i	−0.664806	−	0.727522i
$848$		0			0
$849$	15.7056	−	21.6069i	0.539014	−	0.741548i
$850$		0			0
$851$	−2.97913	+	5.16001i	−0.102123	+	0.176883i
$852$		0			0
$853$	20.0519	−	34.7309i	0.686565	−	1.18916i	−0.286378	−	0.958117i	$-0.592451\pi$
$853$	20.0519	−	34.7309i	0.686565	−	1.18916i	0.972942	−	0.231048i	$-0.0742154\pi$
$854$		0			0
$855$	−24.0810	+	26.7212i	−0.823553	+	0.913845i
$856$		0			0
$857$	−37.4776			−1.28021			−0.640106	−	0.768287i	$-0.721110\pi$
$857$	−37.4776			−1.28021			−0.640106	+	0.768287i	$0.721110\pi$
$858$		0			0
$859$	−24.5032			−0.836039			−0.418019	−	0.908438i	$-0.637276\pi$
$859$	−24.5032			−0.836039			−0.418019	+	0.908438i	$0.637276\pi$
$860$		0			0
$861$	4.41547	−	10.1106i	0.150479	−	0.344570i
$862$		0			0
$863$	−9.79806	+	16.9707i	−0.333530	+	0.577691i	−0.983201	−	0.182524i	$-0.941573\pi$
$863$	−9.79806	+	16.9707i	−0.333530	+	0.577691i	0.649671	+	0.760215i	$0.274906\pi$
$864$		0			0
$865$	−21.2359	−	36.7816i	−0.722041	−	1.25061i
$866$		0			0
$867$	−17.1854	+	23.6428i	−0.583648	+	0.802953i
$868$		0			0
$869$	0.496294	+	0.859607i	0.0168356	+	0.0291602i
$870$		0			0
$871$	3.46996			0.117575
$872$		0			0
$873$	−31.5010	+	34.9547i	−1.06615	+	1.18304i
$874$		0			0
$875$	−20.9256	−	22.8997i	−0.707414	−	0.774150i
$876$		0			0
$877$	34.2269			1.15576			0.577880	−	0.816122i	$-0.303880\pi$
$877$	34.2269			1.15576			0.577880	+	0.816122i	$0.303880\pi$
$878$		0			0
$879$	−12.7063	−	28.5556i	−0.428573	−	0.963157i
$880$		0			0
$881$	−25.2818			−0.851764			−0.425882	−	0.904779i	$-0.640036\pi$
$881$	−25.2818			−0.851764			−0.425882	+	0.904779i	$0.640036\pi$
$882$		0			0
$883$	45.4688			1.53015			0.765073	−	0.643943i	$-0.222703\pi$
$883$	45.4688			1.53015			0.765073	+	0.643943i	$0.222703\pi$
$884$		0			0
$885$	19.9825	−	27.4909i	0.671704	−	0.924097i
$886$		0			0
$887$	−10.8301			−0.363638			−0.181819	−	0.983332i	$-0.558199\pi$
$887$	−10.8301			−0.363638			−0.181819	+	0.983332i	$0.558199\pi$
$888$		0			0
$889$	−26.2980	−	28.7789i	−0.882005	−	0.965212i
$890$		0			0
$891$	−3.27979	−	1.46369i	−0.109877	−	0.0490356i
$892$		0			0
$893$	−66.8757			−2.23791
$894$		0			0
$895$	−26.5087	−	45.9143i	−0.886086	−	1.53475i
$896$		0			0
$897$	−1.78284	−	4.00669i	−0.0595274	−	0.133779i
$898$		0			0
$899$	−7.99301	−	13.8443i	−0.266582	−	0.461733i
$900$		0			0
$901$	−0.734005	+	1.27133i	−0.0244533	+	0.0423543i
$902$		0			0
$903$	2.52056	−	0.283100i	0.0838790	−	0.00942096i
$904$		0			0
$905$	−36.3672			−1.20889
$906$		0			0
$907$	−4.01683			−0.133377			−0.0666883	−	0.997774i	$-0.521243\pi$
$907$	−4.01683			−0.133377			−0.0666883	+	0.997774i	$0.521243\pi$
$908$		0			0
$909$	−0.272458	−	0.0580373i	−0.00903688	−	0.00192498i
$910$		0			0
$911$	8.43681	−	14.6130i	0.279524	−	0.484150i	−0.691743	−	0.722144i	$-0.743157\pi$
$911$	8.43681	−	14.6130i	0.279524	−	0.484150i	0.971266	+	0.237995i	$0.0764901\pi$
$912$		0			0
$913$	−1.83316	+	3.17513i	−0.0606689	+	0.105082i
$914$		0			0
$915$	−14.9247	−	33.5411i	−0.493394	−	1.10883i
$916$		0			0
$917$	24.8220	+	27.1637i	0.819695	+	0.897023i
$918$		0			0
$919$	16.9485	−	29.3557i	0.559081	−	0.968356i	−0.438493	−	0.898735i	$-0.644488\pi$
$919$	16.9485	−	29.3557i	0.559081	−	0.968356i	0.997573	−	0.0696214i	$-0.0221791\pi$
$920$		0			0
$921$	−12.5892	−	1.32596i	−0.414829	−	0.0436920i
$922$		0			0
$923$	21.1858	+	36.6949i	0.697339	+	1.20783i
$924$		0			0
$925$	1.94060	−	3.36122i	0.0638065	−	0.110516i
$926$		0			0
$927$	58.4351	+	12.4475i	1.91926	+	0.408828i
$928$		0			0
$929$	19.3050	+	33.4373i	0.633377	+	1.09704i	0.986857	+	0.161599i	$0.0516650\pi$
$929$	19.3050	+	33.4373i	0.633377	+	1.09704i	−0.353480	+	0.935442i	$0.615002\pi$
$930$		0			0
$931$	−32.6080	−	22.9668i	−1.06868	−	0.752707i
$932$		0			0
$933$	24.2163	−	33.3155i	0.792805	−	1.09070i
$934$		0			0
$935$	0.148303	+	0.256869i	0.00485004	+	0.00840052i
$936$		0			0
$937$	−45.4955			−1.48627			−0.743136	−	0.669140i	$-0.766663\pi$
$937$	−45.4955			−1.48627			−0.743136	+	0.669140i	$0.766663\pi$
$938$		0			0
$939$	−12.8793	−	28.9443i	−0.420298	−	0.944561i
$940$		0			0
$941$	8.99460	−	15.5791i	0.293216	−	0.507864i	−0.681353	−	0.731955i	$-0.738608\pi$
$941$	8.99460	−	15.5791i	0.293216	−	0.507864i	0.974568	+	0.224091i	$0.0719413\pi$
$942$		0			0
$943$	1.05615	+	1.82930i	0.0343928	+	0.0595702i
$944$		0			0
$945$	−11.9437	−	26.3502i	−0.388530	−	0.857171i
$946$		0			0
$947$	8.26121	+	14.3088i	0.268453	+	0.464975i	0.968463	−	0.249159i	$-0.0801542\pi$
$947$	8.26121	+	14.3088i	0.268453	+	0.464975i	−0.700009	+	0.714134i	$0.746821\pi$
$948$		0			0
$949$	−0.910875	+	1.57768i	−0.0295682	+	0.0512137i
$950$		0			0
$951$	−3.30234	−	7.42155i	−0.107086	−	0.240660i
$952$		0			0
$953$	−15.6799			−0.507922			−0.253961	−	0.967214i	$-0.581734\pi$
$953$	−15.6799			−0.507922			−0.253961	+	0.967214i	$0.581734\pi$
$954$		0			0
$955$	−5.28096	−	9.14690i	−0.170888	−	0.295987i
$956$		0			0
$957$	0.711196	−	0.978428i	0.0229897	−	0.0316281i
$958$		0			0
$959$	25.9815	+	28.4325i	0.838985	+	0.918133i
$960$		0			0
$961$	−26.2232	−	45.4200i	−0.845911	−	1.46516i
$962$		0			0
$963$	11.6174	−	12.8911i	0.374366	−	0.415410i
$964$		0			0
$965$	5.72149	−	9.90991i	0.184181	−	0.319011i
$966$		0			0
$967$	25.3908	+	43.9782i	0.816513	+	1.41424i	0.908236	+	0.418458i	$0.137429\pi$
$967$	25.3908	+	43.9782i	0.816513	+	1.41424i	−0.0917230	+	0.995785i	$0.529237\pi$
$968$		0			0
$969$	−3.46641	−	0.365100i	−0.111357	−	0.0117287i
$970$		0			0
$971$	9.23027	−	15.9873i	0.296214	−	0.513057i	−0.679053	−	0.734089i	$-0.737609\pi$
$971$	9.23027	−	15.9873i	0.296214	−	0.513057i	0.975266	+	0.221032i	$0.0709427\pi$
$972$		0			0
$973$	−5.81721	+	18.3614i	−0.186491	+	0.588639i
$974$		0			0
$975$	1.16134	+	2.60995i	0.0371926	+	0.0835852i
$976$		0			0
$977$	−15.8151	+	27.3925i	−0.505970	+	0.876365i	0.494007	+	0.869458i	$0.335532\pi$
$977$	−15.8151	+	27.3925i	−0.505970	+	0.876365i	−0.999976	+	0.00690692i	$0.997801\pi$
$978$		0			0
$979$	−2.91061	+	5.04132i	−0.0930234	+	0.161121i
$980$		0			0
$981$	−11.5821	−	35.6991i	−0.369788	−	1.13979i
$982$		0			0
$983$	−40.4132			−1.28898			−0.644490	−	0.764613i	$-0.722930\pi$
$983$	−40.4132			−1.28898			−0.644490	+	0.764613i	$0.722930\pi$
$984$		0			0
$985$	12.5388			0.399520
$986$		0			0
$987$	21.5262	−	49.2911i	0.685186	−	1.56895i
$988$		0			0
$989$	−0.242806	+	0.420553i	−0.00772079	+	0.0133728i
$990$		0			0
$991$	−16.6187	−	28.7845i	−0.527911	−	0.914368i	−0.999471	−	0.0325343i	$-0.989642\pi$
$991$	−16.6187	−	28.7845i	−0.527911	−	0.914368i	0.471560	−	0.881834i	$-0.343691\pi$
$992$		0			0
$993$	8.04741	+	18.0854i	0.255377	+	0.573923i
$994$		0			0
$995$	−11.8280	−	20.4867i	−0.374973	−	0.649473i
$996$		0			0
$997$	−41.1185			−1.30223			−0.651117	−	0.758977i	$-0.725699\pi$
$997$	−41.1185			−1.30223			−0.651117	+	0.758977i	$0.725699\pi$
$998$		0			0
$999$	26.2393	−	23.5948i	0.830174	−	0.746507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.l.961.1		22
3.2	odd	2		3024.2.t.k.289.4		22
4.3	odd	2		504.2.t.c.457.11	yes	22
7.4	even	3		1008.2.q.l.529.7		22
9.4	even	3		1008.2.q.l.625.7		22
9.5	odd	6		3024.2.q.l.2305.8		22
12.11	even	2		1512.2.t.c.289.4		22
21.11	odd	6		3024.2.q.l.2881.8		22
28.11	odd	6		504.2.q.c.25.5	✓	22
36.23	even	6		1512.2.q.d.793.8		22
36.31	odd	6		504.2.q.c.121.5	yes	22
63.4	even	3	inner	1008.2.t.l.193.1		22
63.32	odd	6		3024.2.t.k.1873.4		22
84.11	even	6		1512.2.q.d.1369.8		22
252.67	odd	6		504.2.t.c.193.11	yes	22
252.95	even	6		1512.2.t.c.361.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.5	✓	22	28.11	odd	6
504.2.q.c.121.5	yes	22	36.31	odd	6
504.2.t.c.193.11	yes	22	252.67	odd	6
504.2.t.c.457.11	yes	22	4.3	odd	2
1008.2.q.l.529.7		22	7.4	even	3
1008.2.q.l.625.7		22	9.4	even	3
1008.2.t.l.193.1		22	63.4	even	3	inner
1008.2.t.l.961.1		22	1.1	even	1	trivial
1512.2.q.d.793.8		22	36.23	even	6
1512.2.q.d.1369.8		22	84.11	even	6
1512.2.t.c.289.4		22	12.11	even	2
1512.2.t.c.361.4		22	252.95	even	6
3024.2.q.l.2305.8		22	9.5	odd	6
3024.2.q.l.2881.8		22	21.11	odd	6
3024.2.t.k.289.4		22	3.2	odd	2
3024.2.t.k.1873.4		22	63.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72252 - 0.181425i) q^{3} +2.10440 q^{5} +(1.78475 + 1.95312i) q^{7} +(2.93417 + 0.625017i) q^{9} +O(q^{10})\)	\(q+(-1.72252 - 0.181425i) q^{3} +2.10440 q^{5} +(1.78475 + 1.95312i) q^{7} +(2.93417 + 0.625017i) q^{9} -0.399064 q^{11} +(1.44292 + 2.49921i) q^{13} +(-3.62487 - 0.381790i) q^{15} +(-0.176596 - 0.305873i) q^{17} +(-2.84888 + 4.93440i) q^{19} +(-2.71993 - 3.68809i) q^{21} +0.877364 q^{23} -0.571513 q^{25} +(-4.94078 - 1.60894i) q^{27} +(0.874997 - 1.51554i) q^{29} +(4.56745 - 7.91106i) q^{31} +(0.687397 + 0.0724002i) q^{33} +(3.75582 + 4.11014i) q^{35} +(-3.39555 + 5.88127i) q^{37} +(-2.03205 - 4.56673i) q^{39} +(1.20377 + 2.08499i) q^{41} +(-0.276745 + 0.479336i) q^{43} +(6.17466 + 1.31528i) q^{45} +(5.86859 + 10.1647i) q^{47} +(-0.629343 + 6.97165i) q^{49} +(0.248697 + 0.558912i) q^{51} +(-2.07821 - 3.59956i) q^{53} -0.839790 q^{55} +(5.80248 - 7.98277i) q^{57} +(-4.66210 + 8.07500i) q^{59} +(5.03601 + 8.72262i) q^{61} +(4.01602 + 6.84628i) q^{63} +(3.03648 + 5.25934i) q^{65} +(0.601204 - 1.04132i) q^{67} +(-1.51128 - 0.159176i) q^{69} +14.6826 q^{71} +(0.315636 + 0.546697i) q^{73} +(0.984444 + 0.103687i) q^{75} +(-0.712229 - 0.779420i) q^{77} +(-1.24364 - 2.15406i) q^{79} +(8.21871 + 3.66781i) q^{81} +(4.59366 - 7.95645i) q^{83} +(-0.371628 - 0.643678i) q^{85} +(-1.78216 + 2.45180i) q^{87} +(7.29358 - 12.6328i) q^{89} +(-2.30601 + 7.27866i) q^{91} +(-9.30280 + 12.7983i) q^{93} +(-5.99517 + 10.3839i) q^{95} +(-7.84245 + 13.5835i) q^{97} +(-1.17092 - 0.249422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 2 q^{5} + q^{7}+O(q^{10}) \) 22 * q + 2 * q^3 - 2 * q^5 + q^7	\( 22 q + 2 q^{3} - 2 q^{5} + q^{7} + 6 q^{11} + 7 q^{13} + q^{15} - q^{17} - 13 q^{19} + 33 q^{21} + 44 q^{25} + 2 q^{27} - 7 q^{29} - 6 q^{31} + 9 q^{33} - 2 q^{35} + 6 q^{37} + 4 q^{39} + 4 q^{41} - 2 q^{43} - 17 q^{47} + 29 q^{49} + 25 q^{51} + q^{53} - 2 q^{55} - 21 q^{57} + 21 q^{59} + 31 q^{61} + 7 q^{63} - 3 q^{65} + 26 q^{67} - 40 q^{69} + 32 q^{71} + 17 q^{73} + 16 q^{75} - 4 q^{77} + 16 q^{79} + 36 q^{83} + 28 q^{85} - 7 q^{87} - 2 q^{89} - 15 q^{91} - 56 q^{93} + 24 q^{95} + 19 q^{97} - 24 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 2 * q^5 + q^7 + 6 * q^11 + 7 * q^13 + q^15 - q^17 - 13 * q^19 + 33 * q^21 + 44 * q^25 + 2 * q^27 - 7 * q^29 - 6 * q^31 + 9 * q^33 - 2 * q^35 + 6 * q^37 + 4 * q^39 + 4 * q^41 - 2 * q^43 - 17 * q^47 + 29 * q^49 + 25 * q^51 + q^53 - 2 * q^55 - 21 * q^57 + 21 * q^59 + 31 * q^61 + 7 * q^63 - 3 * q^65 + 26 * q^67 - 40 * q^69 + 32 * q^71 + 17 * q^73 + 16 * q^75 - 4 * q^77 + 16 * q^79 + 36 * q^83 + 28 * q^85 - 7 * q^87 - 2 * q^89 - 15 * q^91 - 56 * q^93 + 24 * q^95 + 19 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more