LMFDB - Embedded newform 76.7.j.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	76.13
Dual form			76.7.j.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.8876 + 38.1558i) q^{3} +(-5.33633 - 30.2638i) q^{5} +(187.863 - 325.388i) q^{7} +(-704.551 - 591.189i) q^{9} +O(q^{10})$	\(q+(-13.8876 + 38.1558i) q^{3} +(-5.33633 - 30.2638i) q^{5} +(187.863 - 325.388i) q^{7} +(-704.551 - 591.189i) q^{9} +(-809.075 - 1401.36i) q^{11} +(294.503 + 809.141i) q^{13} +(1228.85 + 216.679i) q^{15} +(2924.70 - 2454.12i) q^{17} +(5986.35 - 3348.06i) q^{19} +(9806.47 + 11686.9i) q^{21} +(-2357.90 + 13372.3i) q^{23} +(13795.3 - 5021.07i) q^{25} +(6706.80 - 3872.17i) q^{27} +(7951.27 - 9475.96i) q^{29} +(10883.0 + 6283.28i) q^{31} +(64706.0 - 11409.4i) q^{33} +(-10850.0 - 3949.07i) q^{35} -30942.5i q^{37} -34963.3 q^{39} +(43510.5 - 119544. i) q^{41} +(9169.48 + 52002.7i) q^{43} +(-14131.9 + 24477.2i) q^{45} +(-94977.3 - 79695.4i) q^{47} +(-11760.4 - 20369.6i) q^{49} +(53021.7 + 145676. i) q^{51} +(143538. + 25309.6i) q^{53} +(-38093.0 + 31963.8i) q^{55} +(44612.2 + 274910. i) q^{57} +(-10791.4 - 12860.7i) q^{59} +(4436.96 - 25163.2i) q^{61} +(-324725. + 118190. i) q^{63} +(22916.1 - 13230.6i) q^{65} +(8156.38 - 9720.39i) q^{67} +(-477485. - 275676. i) q^{69} +(32052.4 - 5651.70i) q^{71} +(-425685. - 154937. i) q^{73} +596100. i q^{75} -607980. q^{77} +(328172. - 901645. i) q^{79} +(-61823.1 - 350616. i) q^{81} +(-172680. + 299090. i) q^{83} +(-89878.1 - 75416.7i) q^{85} +(251139. + 434985. i) q^{87} +(-152386. - 418677. i) q^{89} +(318611. + 56179.7i) q^{91} +(-390881. + 327988. i) q^{93} +(-133270. - 163303. i) q^{95} +(149433. + 178088. i) q^{97} +(-258433. + 1.46564e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	−13.8876	+	38.1558i	−0.514354	+	1.41318i	0.362303	+	0.932060i	$0.381991\pi$
$3$	−13.8876	+	38.1558i	−0.514354	+	1.41318i	−0.876657	+	0.481116i	$0.840232\pi$
$4$		0			0
$5$	−5.33633	−	30.2638i	−0.0426906	−	0.242111i	0.955994	−	0.293387i	$-0.0947823\pi$
$5$	−5.33633	−	30.2638i	−0.0426906	−	0.242111i	−0.998685	+	0.0512760i	$0.983671\pi$
$6$		0			0
$7$	187.863	−	325.388i	0.547705	−	0.948653i	−0.450726	−	0.892662i	$-0.648835\pi$
$7$	187.863	−	325.388i	0.547705	−	0.948653i	0.998431	−	0.0559908i	$-0.0178318\pi$
$8$		0			0
$9$	−704.551	−	591.189i	−0.966462	−	0.810958i
$10$		0			0
$11$	−809.075	−	1401.36i	−0.607870	−	1.05286i	−0.991591	−	0.129412i	$-0.958691\pi$
$11$	−809.075	−	1401.36i	−0.607870	−	1.05286i	0.383721	−	0.923449i	$-0.374642\pi$
$12$		0			0
$13$	294.503	+	809.141i	0.134048	+	0.368293i	0.988497	−	0.151242i	$-0.0483273\pi$
$13$	294.503	+	809.141i	0.134048	+	0.368293i	−0.854449	+	0.519535i	$0.826105\pi$
$14$		0			0
$15$	1228.85	+	216.679i	0.364103	+	0.0642012i
$16$		0			0
$17$	2924.70	−	2454.12i	0.595299	−	0.499515i	−0.294632	−	0.955611i	$-0.595197\pi$
$17$	2924.70	−	2454.12i	0.595299	−	0.499515i	0.889931	+	0.456096i	$0.150753\pi$
$18$		0			0
$19$	5986.35	−	3348.06i	0.872773	−	0.488127i
$19$	5986.35	−	3348.06i	0.872773	−	0.488127i
$20$		0			0
$21$	9806.47	+	11686.9i	1.05890	+	1.26195i
$22$		0			0
$23$	−2357.90	+	13372.3i	−0.193795	+	1.09906i	0.720330	+	0.693631i	$0.243990\pi$
$23$	−2357.90	+	13372.3i	−0.193795	+	1.09906i	−0.914125	+	0.405433i	$0.867121\pi$
$24$		0			0
$25$	13795.3	−	5021.07i	0.882898	−	0.321348i
$26$		0			0
$27$	6706.80	−	3872.17i	0.340740	−	0.196727i
$28$		0			0
$29$	7951.27	−	9475.96i	0.326019	−	0.388534i	−0.577993	−	0.816042i	$-0.696164\pi$
$29$	7951.27	−	9475.96i	0.326019	−	0.388534i	0.904012	+	0.427508i	$0.140608\pi$
$30$		0			0
$31$	10883.0	+	6283.28i	0.365310	+	0.210912i	0.671408	−	0.741088i	$-0.265690\pi$
$31$	10883.0	+	6283.28i	0.365310	+	0.210912i	−0.306097	+	0.952000i	$0.599023\pi$
$32$		0			0
$33$	64706.0	−	11409.4i	1.80054	−	0.317484i
$34$		0			0
$35$	−10850.0	−	3949.07i	−0.253061	−	0.0921066i
$36$		0			0
$37$		−	30942.5i		−	0.610871i	−0.952213	−	0.305436i	$-0.901198\pi$
$37$		−	30942.5i		−	0.610871i	0.952213	−	0.305436i	$-0.0988021\pi$
$38$		0			0
$39$	−34963.3			−0.589411
$40$		0			0
$41$	43510.5	−	119544.i	0.631310	−	1.73451i	−0.0461347	−	0.998935i	$-0.514690\pi$
$41$	43510.5	−	119544.i	0.631310	−	1.73451i	0.677444	−	0.735574i	$-0.263087\pi$
$42$		0			0
$43$	9169.48	+	52002.7i	0.115329	+	0.654065i	0.986587	+	0.163238i	$0.0521939\pi$
$43$	9169.48	+	52002.7i	0.115329	+	0.654065i	−0.871257	+	0.490826i	$0.836695\pi$
$44$		0			0
$45$	−14131.9	+	24477.2i	−0.155083	+	0.268611i
$46$		0			0
$47$	−94977.3	−	79695.4i	−0.914800	−	0.767608i	0.0582263	−	0.998303i	$-0.481455\pi$
$47$	−94977.3	−	79695.4i	−0.914800	−	0.767608i	−0.973026	+	0.230695i	$0.925900\pi$
$48$		0			0
$49$	−11760.4	−	20369.6i	−0.0999618	−	0.173139i
$50$		0			0
$51$	53021.7	+	145676.i	0.399708	+	1.09819i
$52$		0			0
$53$	143538.	+	25309.6i	0.964138	+	0.170004i	0.633490	−	0.773751i	$-0.281622\pi$
$53$	143538.	+	25309.6i	0.964138	+	0.170004i	0.330648	+	0.943754i	$0.392733\pi$
$54$		0			0
$55$	−38093.0	+	31963.8i	−0.228958	+	0.192119i
$56$		0			0
$57$	44612.2	+	274910.i	0.240895	+	1.48445i
$58$		0			0
$59$	−10791.4	−	12860.7i	−0.0525438	−	0.0626193i	0.739132	−	0.673560i	$-0.235236\pi$
$59$	−10791.4	−	12860.7i	−0.0525438	−	0.0626193i	−0.791676	+	0.610941i	$0.790791\pi$
$60$		0			0
$61$	4436.96	−	25163.2i	0.0195477	−	0.110861i	−0.973473	−	0.228803i	$-0.926519\pi$
$61$	4436.96	−	25163.2i	0.0195477	−	0.110861i	0.993020	+	0.117943i	$0.0376299\pi$
$62$		0			0
$63$	−324725.	+	118190.i	−1.29865	+	0.472672i
$64$		0			0
$65$	22916.1	−	13230.6i	0.0834451	−	0.0481771i
$66$		0			0
$67$	8156.38	−	9720.39i	0.0271189	−	0.0323191i	−0.752315	−	0.658804i	$-0.771063\pi$
$67$	8156.38	−	9720.39i	0.0271189	−	0.0323191i	0.779433	+	0.626485i	$0.215507\pi$
$68$		0			0
$69$	−477485.	−	275676.i	−1.45349	−	0.839174i
$70$		0			0
$71$	32052.4	−	5651.70i	0.0895540	−	0.0157908i	−0.128692	−	0.991685i	$-0.541078\pi$
$71$	32052.4	−	5651.70i	0.0895540	−	0.0157908i	0.218246	+	0.975894i	$0.429967\pi$
$72$		0			0
$73$	−425685.	−	154937.i	−1.09426	−	0.398277i	−0.269061	−	0.963123i	$-0.586713\pi$
$73$	−425685.	−	154937.i	−1.09426	−	0.398277i	−0.825196	+	0.564846i	$0.808936\pi$
$74$		0			0
$75$			596100.i			1.41298i
$76$		0			0
$77$	−607980.			−1.33173
$78$		0			0
$79$	328172.	−	901645.i	0.665611	−	1.82875i	0.116149	−	0.993232i	$-0.462945\pi$
$79$	328172.	−	901645.i	0.665611	−	1.82875i	0.549462	−	0.835519i	$-0.314833\pi$
$80$		0			0
$81$	−61823.1	−	350616.i	−0.116331	−	0.659747i
$82$		0			0
$83$	−172680.	+	299090.i	−0.302000	+	0.523080i	−0.976589	−	0.215114i	$-0.930988\pi$
$83$	−172680.	+	299090.i	−0.302000	+	0.523080i	0.674589	+	0.738194i	$0.264321\pi$
$84$		0			0
$85$	−89878.1	−	75416.7i	−0.146352	−	0.122804i
$86$		0			0
$87$	251139.	+	434985.i	0.381378	+	0.660566i
$88$		0			0
$89$	−152386.	−	418677.i	−0.216160	−	0.593894i	0.783461	−	0.621441i	$-0.213453\pi$
$89$	−152386.	−	418677.i	−0.216160	−	0.593894i	−0.999621	+	0.0275470i	$0.991230\pi$
$90$		0			0
$91$	318611.	+	56179.7i	0.422801	+	0.0745513i
$92$		0			0
$93$	−390881.	+	327988.i	−0.485955	+	0.407764i
$94$		0			0
$95$	−133270.	−	163303.i	−0.155440	−	0.190469i
$96$		0			0
$97$	149433.	+	178088.i	0.163732	+	0.195128i	0.841672	−	0.539989i	$-0.181572\pi$
$97$	149433.	+	178088.i	0.163732	+	0.195128i	−0.677940	+	0.735117i	$0.737127\pi$
$98$		0			0
$99$	−258433.	+	1.46564e6i	−0.266343	+	1.51051i
$100$		0			0
$101$	1.38736e6	−	504958.i	1.34656	−	0.490107i	0.434686	−	0.900582i	$-0.356859\pi$
$101$	1.38736e6	−	504958.i	1.34656	−	0.490107i	0.911872	+	0.410475i	$0.134637\pi$
$102$		0			0
$103$	375874.	−	217011.i	0.343978	−	0.198596i	−0.318052	−	0.948073i	$-0.603029\pi$
$103$	375874.	−	217011.i	0.343978	−	0.198596i	0.662030	+	0.749477i	$0.269695\pi$
$104$		0			0
$105$	301359.	−	359146.i	0.260326	−	0.310244i
$106$		0			0
$107$	−29077.6	−	16788.0i	−0.0237360	−	0.0137040i	0.488085	−	0.872796i	$-0.337696\pi$
$107$	−29077.6	−	16788.0i	−0.0237360	−	0.0137040i	−0.511821	+	0.859092i	$0.671029\pi$
$108$		0			0
$109$	1.65046e6	−	291020.i	1.27446	−	0.224721i	0.504832	−	0.863218i	$-0.331554\pi$
$109$	1.65046e6	−	291020.i	1.27446	−	0.224721i	0.769625	+	0.638497i	$0.220443\pi$
$110$		0			0
$111$	1.18063e6	+	429715.i	0.863269	+	0.314204i
$112$		0			0
$113$			967318.i			0.670400i	0.942147	+	0.335200i	$0.108804\pi$
$113$			967318.i			0.670400i	−0.942147	+	0.335200i	$0.891196\pi$
$114$		0			0
$115$	417280.			0.274368
$116$		0			0
$117$	270862.	−	744188.i	0.169118	−	0.464649i
$118$		0			0
$119$	−249097.	−	1.41270e6i	−0.147818	−	0.838319i
$120$		0			0
$121$	−423423.	+	733390.i	−0.239011	+	0.413980i
$122$		0			0
$123$	3.95704e6	+	3.32035e6i	2.12645	+	1.78430i
$124$		0			0
$125$	−465656.	−	806540.i	−0.238416	−	0.412949i
$126$		0			0
$127$	−690115.	−	1.89608e6i	−0.336907	−	0.925645i	−0.986266	−	0.165163i	$-0.947185\pi$
$127$	−690115.	−	1.89608e6i	−0.336907	−	0.925645i	0.649359	−	0.760482i	$-0.275037\pi$
$128$		0			0
$129$	−2.11154e6	−	372322.i	−0.983629	−	0.173440i
$130$		0			0
$131$	−1.07260e6	+	900021.i	−0.477117	+	0.400349i	−0.849383	−	0.527777i	$-0.823026\pi$
$131$	−1.07260e6	+	900021.i	−0.477117	+	0.400349i	0.372265	+	0.928126i	$0.378581\pi$
$132$		0			0
$133$	35192.4	−	2.57686e6i	0.0149587	−	1.09531i
$134$		0			0
$135$	−152976.	−	182310.i	−0.0621760	−	0.0740985i
$136$		0			0
$137$	813149.	−	4.61160e6i	0.316234	−	1.79345i	−0.248982	−	0.968508i	$-0.580096\pi$
$137$	813149.	−	4.61160e6i	0.316234	−	1.79345i	0.565216	−	0.824943i	$-0.308793\pi$
$138$		0			0
$139$	−3.25854e6	+	1.18601e6i	−1.21333	+	0.441616i	−0.867858	−	0.496812i	$-0.834504\pi$
$139$	−3.25854e6	+	1.18601e6i	−1.21333	+	0.441616i	−0.345473	+	0.938429i	$0.612282\pi$
$140$		0			0
$141$	4.35984e6	−	2.51715e6i	1.55530	−	0.897951i
$142$		0			0
$143$	895621.	−	1.06736e6i	0.306278	−	0.365008i
$144$		0			0
$145$	−329209.	−	190069.i	−0.107986	−	0.0623458i
$146$		0			0
$147$	940541.	−	165843.i	0.296091	−	0.0522089i
$148$		0			0
$149$	−3.28004e6	−	1.19384e6i	−0.991564	−	0.360900i	−0.205238	−	0.978712i	$-0.565797\pi$
$149$	−3.28004e6	−	1.19384e6i	−0.991564	−	0.360900i	−0.786326	+	0.617812i	$0.788019\pi$
$150$		0			0
$151$			5.40362e6i			1.56947i	0.619829	+	0.784737i	$0.287202\pi$
$151$			5.40362e6i			1.56947i	−0.619829	+	0.784737i	$0.712798\pi$
$152$		0			0
$153$	−3.51145e6			−0.980420
$154$		0			0
$155$	132081.	−	362889.i	0.0354687	−	0.0974494i
$156$		0			0
$157$	1.04531e6	+	5.92827e6i	0.270114	+	1.53189i	0.754065	+	0.656800i	$0.228090\pi$
$157$	1.04531e6	+	5.92827e6i	0.270114	+	1.53189i	−0.483951	+	0.875095i	$0.660799\pi$
$158$		0			0
$159$	−2.95910e6	+	5.12531e6i	−0.736153	+	1.27506i
$160$		0			0
$161$	3.90823e6	+	3.27939e6i	0.936488	+	0.785807i
$162$		0			0
$163$	3.46373e6	+	5.99935e6i	0.799799	+	1.38529i	0.919747	+	0.392512i	$0.128394\pi$
$163$	3.46373e6	+	5.99935e6i	0.799799	+	1.38529i	−0.119948	+	0.992780i	$0.538273\pi$
$164$		0			0
$165$	−690584.	−	1.89737e6i	−0.153732	−	0.422376i
$166$		0			0
$167$	−7.36891e6	−	1.29934e6i	−1.58217	−	0.278980i	−0.687663	−	0.726030i	$-0.741363\pi$
$167$	−7.36891e6	−	1.29934e6i	−1.58217	−	0.278980i	−0.894509	+	0.447051i	$0.852474\pi$
$168$		0			0
$169$	3.12957e6	−	2.62602e6i	0.648373	−	0.544050i
$170$		0			0
$171$	−6.19702e6	−	1.18018e6i	−1.23935	−	0.236026i
$172$		0			0
$173$	227681.	+	271340.i	0.0439733	+	0.0524054i	0.787583	−	0.616209i	$-0.211332\pi$
$173$	227681.	+	271340.i	0.0439733	+	0.0524054i	−0.743610	+	0.668614i	$0.766888\pi$
$174$		0			0
$175$	957824.	−	5.43209e6i	0.178719	−	1.01357i
$176$		0			0
$177$	640576.	−	233150.i	0.115518	−	0.0420452i
$178$		0			0
$179$	−2.68589e6	+	1.55070e6i	−0.468305	+	0.270376i	−0.715530	−	0.698582i	$-0.753815\pi$
$179$	−2.68589e6	+	1.55070e6i	−0.468305	+	0.270376i	0.247225	+	0.968958i	$0.420481\pi$
$180$		0			0
$181$	−722606.	+	861169.i	−0.121861	+	0.145229i	−0.823526	−	0.567279i	$-0.807996\pi$
$181$	−722606.	+	861169.i	−0.121861	+	0.145229i	0.701664	+	0.712508i	$0.252441\pi$
$182$		0			0
$183$	898504.	+	518751.i	0.146611	+	0.0846459i
$184$		0			0
$185$	−936437.	+	165119.i	−0.147898	+	0.0260785i
$186$		0			0
$187$	−5.80540e6	−	2.11299e6i	−0.887784	−	0.323127i
$188$		0			0
$189$		−	2.90975e6i		−	0.430993i
$190$		0			0
$191$	−1.17032e7			−1.67959			−0.839794	−	0.542905i	$-0.817324\pi$
$191$	−1.17032e7			−1.67959			−0.839794	+	0.542905i	$0.817324\pi$
$192$		0			0
$193$	1.59822e6	−	4.39107e6i	0.222313	−	0.610800i	−0.777524	−	0.628853i	$-0.783525\pi$
$193$	1.59822e6	−	4.39107e6i	0.222313	−	0.610800i	0.999837	+	0.0180535i	$0.00574691\pi$
$194$		0			0
$195$	186576.	+	1.05812e6i	0.0251623	+	0.142703i
$196$		0			0
$197$	−2.38644e6	+	4.13343e6i	−0.312141	+	0.540644i	−0.978826	−	0.204696i	$-0.934380\pi$
$197$	−2.38644e6	+	4.13343e6i	−0.312141	+	0.540644i	0.666685	+	0.745340i	$0.267713\pi$
$198$		0			0
$199$	1.67081e6	+	1.40197e6i	0.212015	+	0.177902i	0.742611	−	0.669723i	$-0.233587\pi$
$199$	1.67081e6	+	1.40197e6i	0.212015	+	0.177902i	−0.530596	+	0.847625i	$0.678032\pi$
$200$		0			0
$201$	257617.	+	446205.i	0.0317238	+	0.0549473i
$202$		0			0
$203$	−1.58961e6	−	4.36743e6i	−0.190022	−	0.522081i
$204$		0			0
$205$	−3.85005e6	−	678867.i	−0.446894	−	0.0787995i
$206$		0			0
$207$	9.56682e6	−	8.02751e6i	1.07859	−	0.905045i
$208$		0			0
$209$	−9.53524e6	−	5.68018e6i	−1.04446	−	0.622191i
$210$		0			0
$211$	1.16886e7	+	1.39300e7i	1.24428	+	1.48287i	0.814746	+	0.579818i	$0.196876\pi$
$211$	1.16886e7	+	1.39300e7i	1.24428	+	1.48287i	0.429530	+	0.903053i	$0.358679\pi$
$212$		0			0
$213$	−229484.	+	1.30147e6i	−0.0237473	+	0.134678i
$214$		0			0
$215$	1.52487e6	−	555007.i	0.153432	−	0.0558448i
$216$		0			0
$217$	4.08901e6	−	2.36079e6i	0.400165	−	0.231035i
$218$		0			0
$219$	1.18234e7	−	1.40906e7i	1.12567	−	1.34152i
$220$		0			0
$221$	2.84706e6	+	1.64375e6i	0.263767	+	0.152286i
$222$		0			0
$223$	1.79425e7	−	3.16375e6i	1.61796	−	0.285291i	0.709957	−	0.704245i	$-0.248714\pi$
$223$	1.79425e7	−	3.16375e6i	1.61796	−	0.285291i	0.908007	+	0.418955i	$0.137603\pi$
$224$		0			0
$225$	−1.26879e7	−	4.61801e6i	−1.11389	−	0.405422i
$226$		0			0
$227$			1.89410e7i			1.61930i	0.586916	+	0.809648i	$0.300342\pi$
$227$			1.89410e7i			1.61930i	−0.586916	+	0.809648i	$0.699658\pi$
$228$		0			0
$229$	−2.14046e7			−1.78238			−0.891190	−	0.453631i	$-0.850128\pi$
$229$	−2.14046e7			−1.78238			−0.891190	+	0.453631i	$0.850128\pi$
$230$		0			0
$231$	8.44336e6	−	2.31979e7i	0.684983	−	1.88197i
$232$		0			0
$233$	3.37812e6	+	1.91582e7i	0.267059	+	1.51457i	0.763108	+	0.646271i	$0.223672\pi$
$233$	3.37812e6	+	1.91582e7i	0.267059	+	1.51457i	−0.496049	+	0.868294i	$0.665216\pi$
$234$		0			0
$235$	−1.90506e6	+	3.29965e6i	−0.146793	+	0.254252i
$236$		0			0
$237$	2.98455e7	+	2.50433e7i	2.24199	+	1.88125i
$238$		0			0
$239$	−5.45906e6	−	9.45538e6i	−0.399875	−	0.692604i	0.593835	−	0.804587i	$-0.297613\pi$
$239$	−5.45906e6	−	9.45538e6i	−0.399875	−	0.692604i	−0.993710	+	0.111983i	$0.964280\pi$
$240$		0			0
$241$	8.02224e6	+	2.20409e7i	0.573119	+	1.57463i	0.799548	+	0.600603i	$0.205073\pi$
$241$	8.02224e6	+	2.20409e7i	0.573119	+	1.57463i	−0.226429	+	0.974028i	$0.572705\pi$
$242$		0			0
$243$	1.97965e7	+	3.49065e6i	1.37965	+	0.243269i
$244$		0			0
$245$	−553705.	+	464614.i	−0.0376513	+	0.0315932i
$246$		0			0
$247$	4.47205e6	+	3.85778e6i	0.296767	+	0.256004i
$248$		0			0
$249$	−9.01391e6	−	1.07424e7i	−0.583869	−	0.695828i
$250$		0			0
$251$	1.82302e6	−	1.03389e7i	0.115284	−	0.653810i	−0.871325	−	0.490707i	$-0.836739\pi$
$251$	1.82302e6	−	1.03389e7i	0.115284	−	0.653810i	0.986609	−	0.163103i	$-0.0521504\pi$
$252$		0			0
$253$	2.06471e7	−	7.51494e6i	1.27496	−	0.464049i
$254$		0			0
$255$	4.12577e6	−	2.38201e6i	0.248820	−	0.143656i
$256$		0			0
$257$	5.86682e6	−	6.99181e6i	0.345624	−	0.411898i	−0.565029	−	0.825071i	$-0.691135\pi$
$257$	5.86682e6	−	6.99181e6i	0.345624	−	0.411898i	0.910653	+	0.413173i	$0.135579\pi$
$258$		0			0
$259$	−1.00683e7	−	5.81294e6i	−0.579505	−	0.334577i
$260$		0			0
$261$	−1.12042e7	+	1.97560e6i	−0.630170	+	0.111116i
$262$		0			0
$263$	−8.61887e6	−	3.13701e6i	−0.473787	−	0.172444i	0.0940802	−	0.995565i	$-0.470009\pi$
$263$	−8.61887e6	−	3.13701e6i	−0.473787	−	0.172444i	−0.567867	+	0.823120i	$0.692231\pi$
$264$		0			0
$265$		−	4.47907e6i		−	0.240686i
$266$		0			0
$267$	1.80912e7			0.950460
$268$		0			0
$269$	4.10065e6	−	1.12665e7i	0.210667	−	0.578802i	−0.788685	−	0.614797i	$-0.789238\pi$
$269$	4.10065e6	−	1.12665e7i	0.210667	−	0.578802i	0.999352	+	0.0359950i	$0.0114600\pi$
$270$		0			0
$271$	−1.82788e6	−	1.03664e7i	−0.0918415	−	0.520859i	−0.995670	−	0.0929630i	$-0.970366\pi$
$271$	−1.82788e6	−	1.03664e7i	−0.0918415	−	0.520859i	0.903828	−	0.427896i	$-0.140745\pi$
$272$		0			0
$273$	−6.56831e6	+	1.13766e7i	−0.322824	+	0.559147i
$274$		0			0
$275$	−1.81977e7	−	1.52697e7i	−0.875022	−	0.734231i
$276$		0			0
$277$	1.00530e7	+	1.74124e7i	0.472996	+	0.819253i	0.999522	−	0.0309057i	$-0.00983917\pi$
$277$	1.00530e7	+	1.74124e7i	0.472996	+	0.819253i	−0.526526	+	0.850159i	$0.676506\pi$
$278$		0			0
$279$	−3.95300e6	−	1.08608e7i	−0.182018	−	0.500090i
$280$		0			0
$281$	−2.65348e7	−	4.67880e6i	−1.19591	−	0.210870i	−0.459978	−	0.887931i	$-0.652143\pi$
$281$	−2.65348e7	−	4.67880e6i	−1.19591	−	0.210870i	−0.735928	+	0.677060i	$0.763254\pi$
$282$		0			0
$283$	−1.90317e7	+	1.59695e7i	−0.839690	+	0.704583i	−0.957494	−	0.288454i	$-0.906859\pi$
$283$	−1.90317e7	+	1.59695e7i	−0.839690	+	0.704583i	0.117804	+	0.993037i	$0.462414\pi$
$284$		0			0
$285$	8.08176e6	−	2.81714e6i	0.349117	−	0.121695i
$286$		0			0
$287$	−3.07242e7	−	3.66157e7i	−1.29968	−	1.54889i
$288$		0			0
$289$	−1.66025e6	+	9.41573e6i	−0.0687827	+	0.390086i
$290$		0			0
$291$	−8.87034e6	+	3.22854e6i	−0.359966	+	0.131017i
$292$		0			0
$293$	−3.47302e6	+	2.00515e6i	−0.138072	+	0.0797157i	−0.567445	−	0.823412i	$-0.692068\pi$
$293$	−3.47302e6	+	2.00515e6i	−0.138072	+	0.0797157i	0.429373	+	0.903127i	$0.358735\pi$
$294$		0			0
$295$	−331627.	+	395218.i	−0.0129177	+	0.0153947i
$296$		0			0
$297$	−1.08526e7	−	6.26575e6i	−0.414252	−	0.239168i
$298$		0			0
$299$	−1.15145e7	+	2.03032e6i	−0.430756	+	0.0759539i
$300$		0			0
$301$	1.86437e7	+	6.78574e6i	0.683647	+	0.248827i
$302$		0			0
$303$			5.99484e7i			2.15501i
$304$		0			0
$305$	−785212.			−0.0276750
$306$		0			0
$307$	1.33144e7	−	3.65811e7i	0.460158	−	1.26427i	−0.465208	−	0.885201i	$-0.654021\pi$
$307$	1.33144e7	−	3.65811e7i	0.460158	−	1.26427i	0.925367	−	0.379073i	$-0.123757\pi$
$308$		0			0
$309$	3.06025e6	+	1.73555e7i	0.103724	+	0.588250i
$310$		0			0
$311$	−1.40942e6	+	2.44119e6i	−0.0468554	+	0.0811559i	−0.888502	−	0.458873i	$-0.848253\pi$
$311$	−1.40942e6	+	2.44119e6i	−0.0468554	+	0.0811559i	0.841647	+	0.540029i	$0.181587\pi$
$312$		0			0
$313$	1.83762e7	+	1.54195e7i	0.599271	+	0.502848i	0.891211	−	0.453588i	$-0.149856\pi$
$313$	1.83762e7	+	1.54195e7i	0.599271	+	0.502848i	−0.291940	+	0.956437i	$0.594301\pi$
$314$		0			0
$315$	5.30972e6	+	9.19671e6i	0.169879	+	0.294239i
$316$		0			0
$317$	−4.24531e6	−	1.16639e7i	−0.133270	−	0.366156i	0.855051	−	0.518544i	$-0.173526\pi$
$317$	−4.24531e6	−	1.16639e7i	−0.133270	−	0.366156i	−0.988321	+	0.152388i	$0.951304\pi$
$318$		0			0
$319$	−1.97124e7	−	3.47583e6i	−0.607250	−	0.107074i
$320$		0			0
$321$	1.04438e6	−	876335.i	0.0315749	−	0.0264945i
$322$		0			0
$323$	9.29175e6	−	2.44833e7i	0.275734	−	0.726545i
$324$		0			0
$325$	8.12550e6	+	9.68360e6i	0.236701	+	0.282089i
$326$		0			0
$327$	−1.18167e7	+	6.70160e7i	−0.337951	+	1.91662i
$328$		0			0
$329$	−4.37746e7	+	1.59327e7i	−1.22923	+	0.447405i
$330$		0			0
$331$	−3.24317e7	+	1.87245e7i	−0.894306	+	0.516328i	−0.875349	−	0.483492i	$-0.839368\pi$
$331$	−3.24317e7	+	1.87245e7i	−0.894306	+	0.516328i	−0.0189577	+	0.999820i	$0.506035\pi$
$332$		0			0
$333$	−1.82928e7	+	2.18006e7i	−0.495391	+	0.590384i
$334$		0			0
$335$	−337701.	−	194972.i	−0.00898252	−	0.00518606i
$336$		0			0
$337$	1.26914e6	−	223783.i	0.0331603	−	0.00584706i	−0.157043	−	0.987592i	$-0.550196\pi$
$337$	1.26914e6	−	223783.i	0.0331603	−	0.00584706i	0.190204	+	0.981745i	$0.439085\pi$
$338$		0			0
$339$	−3.69088e7	−	1.34337e7i	−0.947393	−	0.344823i
$340$		0			0
$341$		−	2.03346e7i		−	0.512828i
$342$		0			0
$343$	3.53664e7			0.876412
$344$		0			0
$345$	−5.79500e6	+	1.59216e7i	−0.141122	+	0.387731i
$346$		0			0
$347$	−8.66694e6	−	4.91526e7i	−0.207433	−	1.17641i	−0.893566	−	0.448933i	$-0.851804\pi$
$347$	−8.66694e6	−	4.91526e7i	−0.207433	−	1.17641i	0.686133	−	0.727476i	$-0.259307\pi$
$348$		0			0
$349$	2.37693e7	−	4.11696e7i	0.559165	−	0.968502i	−0.438402	−	0.898779i	$-0.644455\pi$
$349$	2.37693e7	−	4.11696e7i	0.559165	−	0.968502i	0.997566	−	0.0697227i	$-0.0222114\pi$
$350$		0			0
$351$	5.10830e6	+	4.28637e6i	0.118129	+	0.0991217i
$352$		0			0
$353$	−5.94913e6	−	1.03042e7i	−0.135247	−	0.234255i	0.790445	−	0.612534i	$-0.209850\pi$
$353$	−5.94913e6	−	1.03042e7i	−0.135247	−	0.234255i	−0.925692	+	0.378278i	$0.876516\pi$
$354$		0			0
$355$	−342084.	−	939867.i	−0.00764623	−	0.0210078i
$356$		0			0
$357$	5.73620e7	+	1.01145e7i	1.26072	+	0.222300i
$358$		0			0
$359$	9.39614e6	−	7.88430e6i	0.203079	−	0.170404i	−0.535576	−	0.844487i	$-0.679905\pi$
$359$	9.39614e6	−	7.88430e6i	0.203079	−	0.170404i	0.738656	+	0.674083i	$0.235461\pi$
$360$		0			0
$361$	2.46268e7	−	4.00853e7i	0.523464	−	0.852048i
$362$		0			0
$363$	−2.21028e7	−	2.63410e7i	−0.462090	−	0.550697i
$364$		0			0
$365$	−2.41738e6	+	1.37096e7i	−0.0497126	+	0.281934i
$366$		0			0
$367$	−3.96173e7	+	1.44195e7i	−0.801468	+	0.291711i	−0.710095	−	0.704106i	$-0.751348\pi$
$367$	−3.96173e7	+	1.44195e7i	−0.801468	+	0.291711i	−0.0913736	+	0.995817i	$0.529126\pi$
$368$		0			0
$369$	−1.01328e8	+	5.85020e7i	−2.01675	+	1.16437i
$370$		0			0
$371$	3.52009e7	−	4.19508e7i	0.689338	−	0.821521i
$372$		0			0
$373$	2.58207e7	+	1.49076e7i	0.497555	+	0.287264i	0.727703	−	0.685892i	$-0.240588\pi$
$373$	2.58207e7	+	1.49076e7i	0.497555	+	0.287264i	−0.230148	+	0.973156i	$0.573921\pi$
$374$		0			0
$375$	3.72410e7	−	6.56659e6i	0.706199	−	0.124522i
$376$		0			0
$377$	1.00091e7	+	3.64300e6i	0.186797	+	0.0679884i
$378$		0			0
$379$		−	8.63498e7i		−	1.58615i	−0.609126	−	0.793074i	$-0.708480\pi$
$379$		−	8.63498e7i		−	1.58615i	0.609126	−	0.793074i	$-0.291520\pi$
$380$		0			0
$381$	8.19302e7			1.48139
$382$		0			0
$383$	−1.30633e7	+	3.58912e7i	−0.232518	+	0.638838i	−0.999998	−	0.00223523i	$-0.999289\pi$
$383$	−1.30633e7	+	3.58912e7i	−0.232518	+	0.638838i	0.767479	+	0.641074i	$0.221511\pi$
$384$		0			0
$385$	3.24438e6	+	1.83998e7i	0.0568525	+	0.322427i
$386$		0			0
$387$	2.42830e7	−	4.20595e7i	0.418958	−	0.725656i
$388$		0			0
$389$	−8.94132e6	−	7.50266e6i	−0.151898	−	0.127458i	0.563672	−	0.825999i	$-0.309388\pi$
$389$	−8.94132e6	−	7.50266e6i	−0.151898	−	0.127458i	−0.715570	+	0.698541i	$0.753833\pi$
$390$		0			0
$391$	2.59211e7	+	4.48966e7i	0.433633	+	0.751075i
$392$		0			0
$393$	−1.94451e7	−	5.34251e7i	−0.320356	−	0.880172i
$394$		0			0
$395$	−2.90385e7	−	5.12026e6i	−0.471175	−	0.0830809i
$396$		0			0
$397$	6.14794e7	−	5.15873e7i	0.982558	−	0.824464i	−0.00191563	−	0.999998i	$-0.500610\pi$
$397$	6.14794e7	−	5.15873e7i	0.982558	−	0.824464i	0.984473	+	0.175534i	$0.0561653\pi$
$398$		0			0
$399$	9.78334e7	+	3.71291e7i	1.54017	+	0.584515i
$400$		0			0
$401$	−4.19524e7	−	4.99969e7i	−0.650614	−	0.775372i	0.335393	−	0.942078i	$-0.391131\pi$
$401$	−4.19524e7	−	4.99969e7i	−0.650614	−	0.775372i	−0.986006	+	0.166707i	$0.946687\pi$
$402$		0			0
$403$	−1.87899e6	+	1.06563e7i	−0.0287084	+	0.162814i
$404$		0			0
$405$	−1.02811e7	+	3.74201e6i	−0.154765	+	0.0563300i
$406$		0			0
$407$	−4.33615e7	+	2.50348e7i	−0.643163	+	0.371330i
$408$		0			0
$409$	−6.84354e7	+	8.15582e7i	−1.00026	+	1.19206i	−0.0189075	+	0.999821i	$0.506019\pi$
$409$	−6.84354e7	+	8.15582e7i	−1.00026	+	1.19206i	−0.981348	+	0.192237i	$0.938426\pi$
$410$		0			0
$411$	1.64666e8	+	9.50701e7i	2.37181	+	1.36936i
$412$		0			0
$413$	−6.21202e6	+	1.09535e6i	−0.0881825	+	0.0155490i
$414$		0			0
$415$	9.97309e6	+	3.62991e6i	0.139536	+	0.0507868i
$416$		0			0
$417$		−	1.40803e8i		−	1.94180i
$418$		0			0
$419$	7.45002e7			1.01278			0.506390	−	0.862304i	$-0.330980\pi$
$419$	7.45002e7			1.01278			0.506390	+	0.862304i	$0.330980\pi$
$420$		0			0
$421$	5.41168e6	−	1.48685e7i	0.0725247	−	0.199260i	−0.898134	−	0.439722i	$-0.855077\pi$
$421$	5.41168e6	−	1.48685e7i	0.0725247	−	0.199260i	0.970658	+	0.240462i	$0.0772991\pi$
$422$		0			0
$423$	1.98013e7	+	1.12299e8i	0.261621	+	1.48373i
$424$		0			0
$425$	2.80248e7	−	4.85404e7i	0.365070	−	0.632319i
$426$		0			0
$427$	−7.35427e6	−	6.17097e6i	−0.0944618	−	0.0792629i
$428$		0			0
$429$	2.82879e7	+	4.89961e7i	0.358285	+	0.620569i
$430$		0			0
$431$	4.83471e7	+	1.32833e8i	0.603863	+	1.65910i	0.743371	+	0.668879i	$0.233226\pi$
$431$	4.83471e7	+	1.32833e8i	0.603863	+	1.65910i	−0.139508	+	0.990221i	$0.544552\pi$
$432$		0			0
$433$	6.86052e7	+	1.20970e7i	0.845072	+	0.149009i	0.579389	−	0.815051i	$-0.303291\pi$
$433$	6.86052e7	+	1.20970e7i	0.845072	+	0.149009i	0.265683	+	0.964060i	$0.414403\pi$
$434$		0			0
$435$	1.18241e7	−	9.92163e6i	0.143649	−	0.120536i
$436$		0			0
$437$	3.06562e7	+	8.79457e7i	0.367344	+	1.05383i
$438$		0			0
$439$	−2.66951e7	−	3.18140e7i	−0.315528	−	0.376032i	0.584849	−	0.811142i	$-0.301154\pi$
$439$	−2.66951e7	−	3.18140e7i	−0.315528	−	0.376032i	−0.900377	+	0.435110i	$0.856709\pi$
$440$		0			0
$441$	−3.75648e6	+	2.13040e7i	−0.0437991	+	0.248397i
$442$		0			0
$443$	−1.94651e7	+	7.08471e6i	−0.223895	+	0.0814913i	−0.451532	−	0.892255i	$-0.649122\pi$
$443$	−1.94651e7	+	7.08471e6i	−0.223895	+	0.0814913i	0.227637	+	0.973746i	$0.426900\pi$
$444$		0			0
$445$	−1.18576e7	+	6.84598e6i	−0.134560	+	0.0776883i
$446$		0			0
$447$	9.11036e7	−	1.08573e8i	1.02003	−	1.21562i
$448$		0			0
$449$	−6.17736e7	−	3.56650e7i	−0.682439	−	0.394006i	0.118335	−	0.992974i	$-0.462244\pi$
$449$	−6.17736e7	−	3.56650e7i	−0.682439	−	0.394006i	−0.800773	+	0.598968i	$0.795578\pi$
$450$		0			0
$451$	−2.02727e8	+	3.57463e7i	−2.20995	+	0.389674i
$452$		0			0
$453$	−2.06179e8	−	7.50431e7i	−2.21794	−	0.807265i
$454$		0			0
$455$		−	9.94217e6i		−	0.105547i
$456$		0			0
$457$	−1.05722e7			−0.110769			−0.0553844	−	0.998465i	$-0.517638\pi$
$457$	−1.05722e7			−0.110769			−0.0553844	+	0.998465i	$0.517638\pi$
$458$		0			0
$459$	1.01126e7	−	2.77842e7i	0.104575	−	0.287316i
$460$		0			0
$461$	9.57889e6	+	5.43246e7i	0.0977716	+	0.554490i	0.993863	+	0.110620i	$0.0352837\pi$
$461$	9.57889e6	+	5.43246e7i	0.0977716	+	0.554490i	−0.896091	+	0.443870i	$0.853605\pi$
$462$		0			0
$463$	7.64873e7	−	1.32480e8i	0.770630	−	1.33477i	−0.166588	−	0.986027i	$-0.553275\pi$
$463$	7.64873e7	−	1.32480e8i	0.770630	−	1.33477i	0.937218	−	0.348744i	$-0.113392\pi$
$464$		0			0
$465$	1.20120e7	+	1.00793e7i	0.119470	+	0.100247i
$466$		0			0
$467$	−2.88538e7	−	4.99763e7i	−0.283304	−	0.490697i	0.688893	−	0.724864i	$-0.258097\pi$
$467$	−2.88538e7	−	4.99763e7i	−0.283304	−	0.490697i	−0.972196	+	0.234167i	$0.924764\pi$
$468$		0			0
$469$	−1.63062e6	−	4.48009e6i	−0.0158064	−	0.0434278i
$470$		0			0
$471$	−2.40714e8	−	4.24445e7i	−2.30377	−	0.406217i
$472$		0			0
$473$	6.54556e7	−	5.49238e7i	0.618534	−	0.519012i
$474$		0			0
$475$	6.57724e7	−	7.62453e7i	0.613710	−	0.711430i
$476$		0			0
$477$	−8.61671e7	−	1.02690e8i	−0.793938	−	0.946178i
$478$		0			0
$479$	−2.31280e7	+	1.31165e8i	−0.210441	+	1.19347i	0.678203	+	0.734874i	$0.262759\pi$
$479$	−2.31280e7	+	1.31165e8i	−0.210441	+	1.19347i	−0.888644	+	0.458597i	$0.848352\pi$
$480$		0			0
$481$	2.50368e7	−	9.11265e6i	0.224980	−	0.0818860i
$482$		0			0
$483$	−1.79403e8	+	1.03579e8i	−1.59217	+	0.919240i
$484$		0			0
$485$	4.59219e6	−	5.47276e6i	0.0402527	−	0.0479713i
$486$		0			0
$487$	9.47994e7	+	5.47325e7i	0.820765	+	0.473869i	0.850680	−	0.525683i	$-0.176190\pi$
$487$	9.47994e7	+	5.47325e7i	0.820765	+	0.473869i	−0.0299151	+	0.999552i	$0.509524\pi$
$488$		0			0
$489$	−2.77012e8	+	4.88448e7i	−2.36904	+	0.417726i
$490$		0			0
$491$	−4.38549e7	−	1.59619e7i	−0.370488	−	0.134846i	0.150065	−	0.988676i	$-0.452052\pi$
$491$	−4.38549e7	−	1.59619e7i	−0.370488	−	0.134846i	−0.520552	+	0.853830i	$0.674274\pi$
$492$		0			0
$493$		−	4.72277e7i		−	0.394145i
$494$		0			0
$495$	4.57351e7			0.377080
$496$		0			0
$497$	4.18245e6	−	1.14912e7i	0.0340692	−	0.0936044i
$498$		0			0
$499$	2.73007e7	+	1.54830e8i	0.219722	+	1.24610i	0.872523	+	0.488574i	$0.162483\pi$
$499$	2.73007e7	+	1.54830e8i	0.219722	+	1.24610i	−0.652801	+	0.757530i	$0.726406\pi$
$500$		0			0
$501$	1.51913e8	−	2.63122e8i	1.20804	−	2.09239i
$502$		0			0
$503$	−1.11704e8	−	9.37310e7i	−0.877740	−	0.736511i	0.0879733	−	0.996123i	$-0.471961\pi$
$503$	−1.11704e8	−	9.37310e7i	−0.877740	−	0.736511i	−0.965713	+	0.259612i	$0.916405\pi$
$504$		0			0
$505$	−2.26854e7	−	3.92922e7i	−0.176145	−	0.305093i
$506$		0			0
$507$	5.67358e7	+	1.55880e8i	0.435345	+	1.19610i
$508$		0			0
$509$	2.35438e8	+	4.15140e7i	1.78535	+	0.314805i	0.966010	−	0.258506i	$-0.0832301\pi$
$509$	2.35438e8	+	4.15140e7i	1.78535	+	0.314805i	0.819338	+	0.573311i	$0.194341\pi$
$510$		0			0
$511$	−1.30385e8	+	1.09406e8i	−0.977157	+	0.819932i
$512$		0			0
$513$	2.71849e7	−	4.56349e7i	0.201361	−	0.338022i
$514$		0			0
$515$	−8.57337e6	−	1.02173e7i	−0.0627668	−	0.0748026i
$516$		0			0
$517$	−3.48381e7	+	1.97577e8i	−0.252106	+	1.42976i
$518$		0			0
$519$	−1.35151e7	+	4.91911e6i	−0.0966759	+	0.0351872i
$520$		0			0
$521$	−2.39175e8	+	1.38088e8i	−1.69123	+	0.976433i	−0.737705	+	0.675124i	$0.764090\pi$
$521$	−2.39175e8	+	1.38088e8i	−1.69123	+	0.976433i	−0.953527	+	0.301309i	$0.902576\pi$
$522$		0			0
$523$	−1.51106e8	+	1.80081e8i	−1.05627	+	1.25882i	−0.0914783	+	0.995807i	$0.529159\pi$
$523$	−1.51106e8	+	1.80081e8i	−1.05627	+	1.25882i	−0.964793	+	0.263009i	$0.915285\pi$
$524$		0			0
$525$	1.93964e8	+	1.11985e8i	1.34042	+	0.773895i
$526$		0			0
$527$	4.72493e7	−	8.33133e6i	0.322822	−	0.0569223i
$528$		0			0
$529$	−3.41509e7	−	1.24299e7i	−0.230693	−	0.0839654i
$530$		0			0
$531$			1.54408e7i			0.103130i
$532$		0			0
$533$	1.09542e8			0.723434
$534$		0			0
$535$	−352901.	+	969586.i	−0.00230458	+	0.00633177i
$536$		0			0
$537$	−2.18676e7	−	1.24018e8i	−0.141214	−	0.800867i
$538$		0			0
$539$	−1.90301e7	+	3.29611e7i	−0.121527	+	0.210492i
$540$		0			0
$541$	1.43023e8	+	1.20010e8i	0.903261	+	0.757926i	0.970825	−	0.239789i	$-0.0770781\pi$
$541$	1.43023e8	+	1.20010e8i	0.903261	+	0.757926i	−0.0675637	+	0.997715i	$0.521523\pi$
$542$		0			0
$543$	−2.28233e7	−	3.95311e7i	−0.142554	−	0.246911i
$544$		0			0
$545$	−1.76148e7	−	4.83962e7i	−0.108815	−	0.298966i
$546$		0			0
$547$	1.09124e8	+	1.92415e7i	0.666744	+	0.117565i	0.496768	−	0.867883i	$-0.334520\pi$
$547$	1.09124e8	+	1.92415e7i	0.666744	+	0.117565i	0.169976	+	0.985448i	$0.445631\pi$
$548$		0			0
$549$	−1.80023e7	+	1.51057e7i	−0.108795	+	0.0912902i
$550$		0			0
$551$	1.58730e7	−	8.33478e7i	0.0948863	−	0.498241i
$552$		0			0
$553$	−2.31733e8	−	2.76169e8i	−1.37029	−	1.63305i
$554$		0			0
$555$	6.70458e6	−	3.80236e7i	0.0392187	−	0.222420i
$556$		0			0
$557$	1.73488e8	−	6.31443e7i	1.00393	−	0.365400i	0.212830	−	0.977089i	$-0.431732\pi$
$557$	1.73488e8	−	6.31443e7i	1.00393	−	0.365400i	0.791098	+	0.611689i	$0.209510\pi$
$558$		0			0
$559$	−3.93771e7	+	2.27344e7i	−0.225428	+	0.130151i
$560$		0			0
$561$	1.61246e8	−	1.92165e8i	0.913271	−	1.08839i
$562$		0			0
$563$	1.96653e8	+	1.13538e8i	1.10198	+	0.636230i	0.936741	−	0.350023i	$-0.113826\pi$
$563$	1.96653e8	+	1.13538e8i	1.10198	+	0.636230i	0.165242	+	0.986253i	$0.447159\pi$
$564$		0			0
$565$	2.92747e7	−	5.16193e6i	0.162311	−	0.0286198i
$566$		0			0
$567$	−1.25701e8	−	4.57513e7i	−0.689586	−	0.250989i
$568$		0			0
$569$			2.14825e8i			1.16613i	0.812425	+	0.583065i	$0.198147\pi$
$569$			2.14825e8i			1.16613i	−0.812425	+	0.583065i	$0.801853\pi$
$570$		0			0
$571$	−1.47833e8			−0.794076			−0.397038	−	0.917802i	$-0.629962\pi$
$571$	−1.47833e8			−0.794076			−0.397038	+	0.917802i	$0.629962\pi$
$572$		0			0
$573$	1.62528e8	−	4.46543e8i	0.863903	−	2.37355i
$574$		0			0
$575$	3.46154e7	+	1.96314e8i	0.182082	+	1.03264i
$576$		0			0
$577$	−2.52899e7	+	4.38033e7i	−0.131649	+	0.228024i	−0.924313	−	0.381636i	$-0.875361\pi$
$577$	−2.52899e7	+	4.38033e7i	−0.131649	+	0.228024i	0.792663	+	0.609660i	$0.208694\pi$
$578$		0			0
$579$	1.45349e8	+	1.21963e8i	0.748820	+	0.628335i
$580$		0			0
$581$	6.48802e7	+	1.12376e8i	0.330814	+	0.572987i
$582$		0			0
$583$	−8.06651e7	−	2.21626e8i	−0.407080	−	1.11844i
$584$		0			0
$585$	−2.39674e7	−	4.22609e6i	−0.119716	−	0.0211092i
$586$		0			0
$587$	2.02523e8	−	1.69937e8i	1.00129	−	0.840183i	0.0141283	−	0.999900i	$-0.495503\pi$
$587$	2.02523e8	−	1.69937e8i	1.00129	−	0.840183i	0.987163	+	0.159717i	$0.0510582\pi$
$588$		0			0
$589$	8.61860e7	+	1.17705e6i	0.421785	+	0.00576034i
$590$		0			0
$591$	−1.24572e8	−	1.48459e8i	−0.603475	−	0.719193i
$592$		0			0
$593$	−5.26955e7	+	2.98851e8i	−0.252702	+	1.43315i	0.549200	+	0.835691i	$0.314933\pi$
$593$	−5.26955e7	+	2.98851e8i	−0.252702	+	1.43315i	−0.801902	+	0.597455i	$0.796179\pi$
$594$		0			0
$595$	−4.14245e7	+	1.50773e7i	−0.196655	+	0.0715767i
$596$		0			0
$597$	−7.66967e7	+	4.42809e7i	−0.360457	+	0.208110i
$598$		0			0
$599$	1.61745e8	−	1.92760e8i	0.752576	−	0.896885i	−0.244778	−	0.969579i	$-0.578715\pi$
$599$	1.61745e8	−	1.92760e8i	0.752576	−	0.896885i	0.997354	+	0.0726941i	$0.0231597\pi$
$600$		0			0
$601$	−2.40315e8	−	1.38746e8i	−1.10703	−	0.639142i	−0.168969	−	0.985621i	$-0.554044\pi$
$601$	−2.40315e8	−	1.38746e8i	−1.10703	−	0.639142i	−0.938058	+	0.346479i	$0.887377\pi$
$602$		0			0
$603$	−1.14932e7	+	2.02656e6i	−0.0524189	+	0.00924286i
$604$		0			0
$605$	2.44547e7	+	8.90079e6i	0.110432	+	0.0401941i
$606$		0			0
$607$			2.38403e7i			0.106597i	0.998579	+	0.0532986i	$0.0169735\pi$
$607$			2.38403e7i			0.106597i	−0.998579	+	0.0532986i	$0.983026\pi$
$608$		0			0
$609$	1.88718e8			0.835531
$610$		0			0
$611$	3.65137e7	−	1.00320e8i	0.160078	−	0.439811i
$612$		0			0
$613$	2.30898e6	+	1.30949e7i	0.0100240	+	0.0568487i	0.989409	−	0.145151i	$-0.0463669\pi$
$613$	2.30898e6	+	1.30949e7i	0.0100240	+	0.0568487i	−0.979385	+	0.202000i	$0.935256\pi$
$614$		0			0
$615$	7.93705e7	−	1.37474e8i	0.341219	−	0.591009i
$616$		0			0
$617$	2.79641e8	+	2.34647e8i	1.19054	+	0.998986i	0.999850	+	0.0173363i	$0.00551858\pi$
$617$	2.79641e8	+	2.34647e8i	1.19054	+	0.998986i	0.190695	+	0.981649i	$0.438926\pi$
$618$		0			0
$619$	1.24704e8	+	2.15994e8i	0.525785	+	0.910686i	0.999549	+	0.0300344i	$0.00956168\pi$
$619$	1.24704e8	+	2.15994e8i	0.525785	+	0.910686i	−0.473764	+	0.880652i	$0.657105\pi$
$620$		0			0
$621$	3.59659e7	+	9.88156e7i	0.150181	+	0.412620i
$622$		0			0
$623$	−1.64860e8	−	2.90693e7i	−0.681792	−	0.120218i
$624$		0			0
$625$	1.53795e8	−	1.29049e8i	0.629944	−	0.528585i
$626$		0			0
$627$	3.49153e8	−	2.84940e8i	1.41649	−	1.15598i
$628$		0			0
$629$	−7.59365e7	−	9.04976e7i	−0.305139	−	0.363651i
$630$		0			0
$631$	6.78258e7	−	3.84660e8i	0.269965	−	1.53105i	−0.484550	−	0.874764i	$-0.661017\pi$
$631$	6.78258e7	−	3.84660e8i	0.269965	−	1.53105i	0.754515	−	0.656283i	$-0.227872\pi$
$632$		0			0
$633$	−6.93836e8	+	2.52536e8i	−2.73556	+	0.995661i
$634$		0			0
$635$	−5.36998e7	+	3.10036e7i	−0.209726	+	0.121085i
$636$		0			0
$637$	1.30184e7	−	1.55147e7i	0.0503662	−	0.0600241i
$638$		0			0
$639$	−2.59237e7	−	1.49671e7i	−0.0993562	−	0.0573633i
$640$		0			0
$641$	3.11309e8	−	5.48922e7i	1.18200	−	0.208419i	0.452097	−	0.891969i	$-0.350676\pi$
$641$	3.11309e8	−	5.48922e7i	1.18200	−	0.208419i	0.729904	+	0.683550i	$0.239565\pi$
$642$		0			0
$643$	−6.69584e7	−	2.43709e7i	−0.251868	−	0.0916723i	0.213001	−	0.977052i	$-0.431676\pi$
$643$	−6.69584e7	−	2.43709e7i	−0.251868	−	0.0916723i	−0.464869	+	0.885380i	$0.653898\pi$
$644$		0			0
$645$			6.58902e7i			0.245551i
$646$		0			0
$647$	4.72897e8			1.74604			0.873019	−	0.487686i	$-0.162159\pi$
$647$	4.72897e8			1.74604			0.873019	+	0.487686i	$0.162159\pi$
$648$		0			0
$649$	−9.29139e6	+	2.55279e7i	−0.0339896	+	0.0933858i
$650$		0			0
$651$	3.32914e7	+	1.88805e8i	0.120667	+	0.684337i
$652$		0			0
$653$	−2.39780e8	+	4.15312e8i	−0.861140	+	1.49154i	0.00968924	+	0.999953i	$0.496916\pi$
$653$	−2.39780e8	+	4.15312e8i	−0.861140	+	1.49154i	−0.870829	+	0.491585i	$0.836418\pi$
$654$		0			0
$655$	3.29618e7	+	2.76583e7i	0.117297	+	0.0984240i
$656$		0			0
$657$	2.08320e8	+	3.60821e8i	0.734572	+	1.27232i
$658$		0			0
$659$	6.32294e7	+	1.73721e8i	0.220934	+	0.607011i	0.999796	−	0.0201836i	$-0.00642508\pi$
$659$	6.32294e7	+	1.73721e8i	0.220934	+	0.607011i	−0.778862	+	0.627195i	$0.784203\pi$
$660$		0			0
$661$	−1.30414e8	−	2.29955e7i	−0.451564	−	0.0796230i	−0.0567593	−	0.998388i	$-0.518077\pi$
$661$	−1.30414e8	−	2.29955e7i	−0.451564	−	0.0796230i	−0.394805	+	0.918765i	$0.629188\pi$
$662$		0			0
$663$	−1.02257e8	+	8.58041e7i	−0.350876	+	0.294420i
$664$		0			0
$665$	−7.81735e7	+	1.26859e7i	−0.265824	+	0.0431377i
$666$		0			0
$667$	1.07967e8	+	1.28670e8i	0.363843	+	0.433612i
$668$		0			0
$669$	−1.28463e8	+	7.28547e8i	−0.429040	+	2.43321i
$670$		0			0
$671$	−3.88525e7	+	1.41412e7i	−0.128603	+	0.0468077i
$672$		0			0
$673$	9.74086e7	−	5.62389e7i	0.319560	−	0.184498i	−0.331637	−	0.943407i	$-0.607601\pi$
$673$	9.74086e7	−	5.62389e7i	0.319560	−	0.184498i	0.651196	+	0.758909i	$0.274267\pi$
$674$		0			0
$675$	7.30797e7	−	8.70929e7i	0.237621	−	0.283186i
$676$		0			0
$677$	−3.57325e8	−	2.06302e8i	−1.15159	−	0.664871i	−0.202316	−	0.979320i	$-0.564847\pi$
$677$	−3.57325e8	−	2.06302e8i	−1.15159	−	0.664871i	−0.949274	+	0.314450i	$0.898180\pi$
$678$		0			0
$679$	8.60207e7	−	1.51678e7i	0.274785	−	0.0484521i
$680$		0			0
$681$	−7.22710e8	−	2.63045e8i	−2.28835	−	0.832891i
$682$		0			0
$683$			9.62307e7i			0.302031i	0.988531	+	0.151016i	$0.0482543\pi$
$683$			9.62307e7i			0.302031i	−0.988531	+	0.151016i	$0.951746\pi$
$684$		0			0
$685$	−1.43904e8			−0.447714
$686$		0			0
$687$	2.97257e8	−	8.16708e8i	0.916774	−	2.51882i
$688$		0			0
$689$	2.17933e7	+	1.23596e8i	0.0666294	+	0.377874i
$690$		0			0
$691$	−3.51487e7	+	6.08794e7i	−0.106531	+	0.184517i	−0.914363	−	0.404896i	$-0.867308\pi$
$691$	−3.51487e7	+	6.08794e7i	−0.106531	+	0.184517i	0.807832	+	0.589413i	$0.200641\pi$
$692$		0			0
$693$	4.28353e8	+	3.59431e8i	1.28707	+	1.07998i
$694$		0			0
$695$	5.32820e7	+	9.22870e7i	0.158718	+	0.274907i
$696$		0			0
$697$	−1.66120e8	−	4.56411e8i	−0.490596	−	1.34790i
$698$		0			0
$699$	−7.77911e8	−	1.37167e8i	−2.27771	−	0.401622i
$700$		0			0
$701$	3.42178e8	−	2.87122e8i	0.993341	−	0.833512i	0.00729343	−	0.999973i	$-0.497678\pi$
$701$	3.42178e8	−	2.87122e8i	0.993341	−	0.833512i	0.986048	+	0.166461i	$0.0532340\pi$
$702$		0			0
$703$	−1.03597e8	−	1.85232e8i	−0.298183	−	0.533152i
$704$		0			0
$705$	−9.94442e7	−	1.18513e8i	−0.283800	−	0.338220i
$706$		0			0
$707$	9.63262e7	−	5.46293e8i	0.272575	−	1.54585i
$708$		0			0
$709$	−1.51259e8	+	5.50539e7i	−0.424408	+	0.154472i	−0.545389	−	0.838183i	$-0.683618\pi$
$709$	−1.51259e8	+	5.50539e7i	−0.424408	+	0.154472i	0.120981	+	0.992655i	$0.461396\pi$
$710$		0			0
$711$	−7.64256e8	+	4.41244e8i	−2.12633	+	1.22764i
$712$		0			0
$713$	−1.09683e8	+	1.30715e8i	−0.302601	+	0.360626i
$714$		0			0
$715$	−3.70817e7	−	2.14091e7i	−0.101448	−	0.0585708i
$716$		0			0
$717$	4.36590e8	−	7.69826e7i	1.18445	−	0.208850i
$718$		0			0
$719$	−6.85650e7	−	2.49556e7i	−0.184466	−	0.0671400i	0.248136	−	0.968725i	$-0.420182\pi$
$719$	−6.85650e7	−	2.49556e7i	−0.184466	−	0.0671400i	−0.432602	+	0.901585i	$0.642404\pi$
$720$		0			0
$721$		−	1.63073e8i		−	0.435088i
$722$		0			0
$723$	−9.52397e8			−2.52002
$724$		0			0
$725$	6.21106e7	−	1.70647e8i	0.162986	−	0.447802i
$726$		0			0
$727$	−1.44327e7	−	8.18522e7i	−0.0375617	−	0.213023i	0.960250	−	0.279141i	$-0.0900497\pi$
$727$	−1.44327e7	−	8.18522e7i	−0.0375617	−	0.213023i	−0.997812	+	0.0661180i	$0.978939\pi$
$728$		0			0
$729$	−2.78342e8	+	4.82102e8i	−0.718449	+	1.24439i
$730$		0			0
$731$	1.54439e8	+	1.29590e8i	0.395370	+	0.331755i
$732$		0			0
$733$	−4.39893e7	−	7.61917e7i	−0.111695	−	0.193462i	0.804759	−	0.593602i	$-0.202295\pi$
$733$	−4.39893e7	−	7.61917e7i	−0.111695	−	0.193462i	−0.916454	+	0.400140i	$0.868961\pi$
$734$		0			0
$735$	−1.00381e7	−	2.75794e7i	−0.0252807	−	0.0694580i
$736$		0			0
$737$	−2.02209e7	−	3.56548e6i	−0.0505123	−	0.00890668i
$738$		0			0
$739$	−4.23768e8	+	3.55583e8i	−1.05001	+	0.881065i	−0.993095	−	0.117314i	$-0.962572\pi$
$739$	−4.23768e8	+	3.55583e8i	−1.05001	+	0.881065i	−0.0569178	+	0.998379i	$0.518127\pi$
$740$		0			0
$741$	−2.09302e8	+	1.17059e8i	−0.514422	+	0.287708i
$742$		0			0
$743$	−1.10592e7	−	1.31798e7i	−0.0269622	−	0.0321323i	0.752395	−	0.658712i	$-0.228899\pi$
$743$	−1.10592e7	−	1.31798e7i	−0.0269622	−	0.0321323i	−0.779357	+	0.626580i	$0.784454\pi$
$744$		0			0
$745$	−1.86267e7	+	1.05637e8i	−0.0450471	+	0.255475i
$746$		0			0
$747$	2.98480e8	−	1.08638e8i	0.716068	−	0.260627i
$748$		0			0
$749$	−1.09252e7	+	6.30768e6i	−0.0260007	+	0.0150115i
$750$		0			0
$751$	4.09765e8	−	4.88339e8i	0.967421	−	1.15293i	−0.0207830	−	0.999784i	$-0.506616\pi$
$751$	4.09765e8	−	4.88339e8i	0.967421	−	1.15293i	0.988204	−	0.153143i	$-0.0489396\pi$
$752$		0			0
$753$	3.69170e8	+	2.13140e8i	0.864652	+	0.499207i
$754$		0			0
$755$	1.63534e8	−	2.88355e7i	0.379986	−	0.0670018i
$756$		0			0
$757$	−5.52279e8	−	2.01013e8i	−1.27312	−	0.463380i	−0.384972	−	0.922928i	$-0.625789\pi$
$757$	−5.52279e8	−	2.01013e8i	−1.27312	−	0.463380i	−0.888153	+	0.459549i	$0.848011\pi$
$758$		0			0
$759$			8.92171e8i			2.04043i
$760$		0			0
$761$	−4.81064e7			−0.109156			−0.0545781	−	0.998510i	$-0.517381\pi$
$761$	−4.81064e7			−0.109156			−0.0545781	+	0.998510i	$0.517381\pi$
$762$		0			0
$763$	2.15365e8	−	5.91711e8i	0.484844	−	1.33210i
$764$		0			0
$765$	1.87382e7	+	1.06270e8i	0.0418547	+	0.237370i
$766$		0			0
$767$	7.22801e6	−	1.25193e7i	0.0160189	−	0.0277455i
$768$		0			0
$769$	6.06190e8	+	5.08654e8i	1.33300	+	1.11852i	0.983367	+	0.181631i	$0.0581376\pi$
$769$	6.06190e8	+	5.08654e8i	1.33300	+	1.11852i	0.349631	+	0.936887i	$0.386307\pi$
$770$		0			0
$771$	1.85302e8	+	3.20952e8i	0.404312	+	0.700289i
$772$		0			0
$773$	8.56055e7	+	2.35199e8i	0.185337	+	0.509210i	0.997212	−	0.0746216i	$-0.0237749\pi$
$773$	8.56055e7	+	2.35199e8i	0.185337	+	0.509210i	−0.811875	+	0.583832i	$0.801553\pi$
$774$		0			0
$775$	1.81682e8	+	3.20355e7i	0.390308	+	0.0688218i
$776$		0			0
$777$	3.61621e8	−	3.03436e8i	0.770888	−	0.646851i
$778$		0			0
$779$	−1.39772e8	−	8.61308e8i	−0.295671	−	1.82199i
$780$		0			0
$781$	−3.38528e7	−	4.03442e7i	−0.0710627	−	0.0846892i
$782$		0			0
$783$	1.66350e7	−	9.43420e7i	0.0346528	−	0.196526i
$784$		0			0
$785$	1.73834e8	−	6.32704e7i	0.359357	−	0.130795i
$786$		0			0
$787$	−1.48871e8	+	8.59506e7i	−0.305412	+	0.176329i	−0.644871	−	0.764291i	$-0.723089\pi$
$787$	−1.48871e8	+	8.59506e7i	−0.305412	+	0.176329i	0.339460	+	0.940621i	$0.389756\pi$
$788$		0			0
$789$	2.39390e8	−	2.85294e8i	0.487388	−	0.580847i
$790$		0			0
$791$	3.14754e8	+	1.81723e8i	0.635977	+	0.367181i
$792$		0			0
$793$	2.16673e7	−	3.82053e6i	0.0434495	−	0.00766132i
$794$		0			0
$795$	1.70902e8	+	6.22033e7i	0.340131	+	0.123798i
$796$		0			0
$797$			3.62014e8i			0.715073i	0.933899	+	0.357537i	$0.116383\pi$
$797$			3.62014e8i			0.715073i	−0.933899	+	0.357537i	$0.883617\pi$
$798$		0			0
$799$	−4.73362e8			−0.928011
$800$		0			0
$801$	−1.40153e8	+	3.85068e8i	−0.272713	+	0.749273i
$802$		0			0
$803$	1.27289e8	+	7.21892e8i	0.245835	+	1.39420i
$804$		0			0
$805$	7.83914e7	−	1.35778e8i	0.150273	−	0.260280i
$806$		0			0
$807$	3.72932e8	+	3.12927e8i	0.709592	+	0.595419i
$808$		0			0
$809$	−2.55144e8	−	4.41923e8i	−0.481881	−	0.834643i	0.517902	−	0.855440i	$-0.326713\pi$
$809$	−2.55144e8	−	4.41923e8i	−0.481881	−	0.834643i	−0.999784	+	0.0207967i	$0.993380\pi$
$810$		0			0
$811$	1.34322e8	+	3.69046e8i	0.251816	+	0.691860i	0.999610	+	0.0279284i	$0.00889106\pi$
$811$	1.34322e8	+	3.69046e8i	0.251816	+	0.691860i	−0.747794	+	0.663931i	$0.768887\pi$
$812$		0			0
$813$	4.20922e8	+	7.42200e7i	0.783304	+	0.138118i
$814$		0			0
$815$	1.63080e8	−	1.36840e8i	0.301250	−	0.252779i
$816$		0			0
$817$	2.29000e8	+	2.80606e8i	0.419923	+	0.514554i
$818$		0			0
$819$	−1.91265e8	−	2.27941e8i	−0.348164	−	0.414925i
$820$		0			0
$821$	9.57100e6	−	5.42798e7i	0.0172953	−	0.0980864i	−0.974938	−	0.222476i	$-0.928586\pi$
$821$	9.57100e6	−	5.42798e7i	0.0172953	−	0.0980864i	0.992233	+	0.124390i	$0.0396972\pi$
$822$		0			0
$823$	−6.28851e8	+	2.28883e8i	−1.12810	+	0.410595i	−0.837603	−	0.546280i	$-0.816044\pi$
$823$	−6.28851e8	+	2.28883e8i	−1.12810	+	0.410595i	−0.290499	+	0.956875i	$0.593821\pi$
$824$		0			0
$825$	8.35349e8	−	4.82289e8i	1.48767	−	0.858906i
$826$		0			0
$827$	2.78880e8	−	3.32356e8i	0.493060	−	0.587607i	−0.460933	−	0.887435i	$-0.652485\pi$
$827$	2.78880e8	−	3.32356e8i	0.493060	−	0.587607i	0.953993	+	0.299829i	$0.0969295\pi$
$828$		0			0
$829$	2.79462e8	+	1.61347e8i	0.490523	+	0.283203i	0.724791	−	0.688969i	$-0.241936\pi$
$829$	2.79462e8	+	1.61347e8i	0.490523	+	0.283203i	−0.234269	+	0.972172i	$0.575270\pi$
$830$		0			0
$831$	−8.03993e8	+	1.41766e8i	−1.40104	+	0.247041i
$832$		0			0
$833$	−8.43851e7	−	3.07137e7i	−0.145993	−	0.0531370i
$834$		0			0
$835$			2.29945e8i			0.394970i
$836$		0			0
$837$	9.73197e7			0.165968
$838$		0			0
$839$	2.27326e8	−	6.24572e8i	0.384913	−	1.05754i	−0.584348	−	0.811503i	$-0.698650\pi$
$839$	2.27326e8	−	6.24572e8i	0.384913	−	1.05754i	0.969261	−	0.246036i	$-0.0791282\pi$
$840$		0			0
$841$	7.67189e7	+	4.35095e8i	0.128978	+	0.731469i
$842$		0			0
$843$	5.47027e8	−	9.47478e8i	0.913116	−	1.58156i
$844$		0			0
$845$	−9.61739e7	−	8.06995e7i	−0.159400	−	0.133752i
$846$		0			0
$847$	1.59091e8	+	2.75554e8i	0.261815	+	0.453478i
$848$		0			0
$849$	−3.45025e8	−	9.47947e8i	−0.563803	−	1.54903i
$850$		0			0
$851$	4.13772e8	+	7.29592e7i	0.671387	+	0.118384i
$852$		0			0
$853$	2.06522e8	−	1.73292e8i	0.332750	−	0.279211i	−0.461069	−	0.887364i	$-0.652534\pi$
$853$	2.06522e8	−	1.73292e8i	0.332750	−	0.279211i	0.793819	+	0.608154i	$0.208090\pi$
$854$		0			0
$855$	−2.64733e6	+	1.93843e8i	−0.00423556	+	0.310136i
$856$		0			0
$857$	−1.19616e8	−	1.42553e8i	−0.190041	−	0.226482i	0.662608	−	0.748967i	$-0.269450\pi$
$857$	−1.19616e8	−	1.42553e8i	−0.190041	−	0.226482i	−0.852649	+	0.522485i	$0.825005\pi$
$858$		0			0
$859$	244959.	−	1.38923e6i	0.000386468	−	0.00219177i	−0.984614	−	0.174744i	$-0.944090\pi$
$859$	244959.	−	1.38923e6i	0.000386468	−	0.00219177i	0.985000	+	0.172552i	$0.0552013\pi$
$860$		0			0
$861$	1.82378e9	−	6.63803e8i	2.85735	−	1.03999i
$862$		0			0
$863$	5.09952e8	−	2.94421e8i	0.793408	−	0.458074i	−0.0477530	−	0.998859i	$-0.515206\pi$
$863$	5.09952e8	−	2.94421e8i	0.793408	−	0.458074i	0.841161	+	0.540785i	$0.181873\pi$
$864$		0			0
$865$	6.99681e6	−	8.33847e6i	0.0108106	−	0.0128836i
$866$		0			0
$867$	−3.36208e8	−	1.94110e8i	−0.515882	−	0.297844i
$868$		0			0
$869$	−1.52904e9	+	2.69612e8i	−2.33003	+	0.410846i
$870$		0			0
$871$	1.02672e7	+	3.73697e6i	0.0155381	+	0.00565542i
$872$		0			0
$873$		−	2.13815e8i		−	0.321363i
$874$		0			0
$875$	−3.49918e8			−0.522327
$876$		0			0
$877$	1.99615e8	−	5.48437e8i	0.295933	−	0.813070i	−0.699236	−	0.714891i	$-0.746476\pi$
$877$	1.99615e8	−	5.48437e8i	0.295933	−	0.813070i	0.995169	−	0.0981785i	$-0.0313016\pi$
$878$		0			0
$879$	−2.82762e7	−	1.60362e8i	−0.0416346	−	0.236122i
$880$		0			0
$881$	−2.12591e8	+	3.68218e8i	−0.310897	+	0.538490i	−0.978557	−	0.205977i	$-0.933963\pi$
$881$	−2.12591e8	+	3.68218e8i	−0.310897	+	0.538490i	0.667659	+	0.744467i	$0.267296\pi$
$882$		0			0
$883$	−2.53860e8	−	2.13013e8i	−0.368733	−	0.309403i	0.439527	−	0.898229i	$-0.355146\pi$
$883$	−2.53860e8	−	2.13013e8i	−0.368733	−	0.309403i	−0.808260	+	0.588826i	$0.799590\pi$
$884$		0			0
$885$	−1.04743e7	−	1.81421e7i	−0.0151111	−	0.0261733i
$886$		0			0
$887$	3.99561e8	+	1.09778e9i	0.572548	+	1.57306i	0.800463	+	0.599382i	$0.204587\pi$
$887$	3.99561e8	+	1.09778e9i	0.572548	+	1.57306i	−0.227915	+	0.973681i	$0.573191\pi$
$888$		0			0
$889$	−7.46608e8	−	1.31647e8i	−1.06264	−	0.187372i
$890$		0			0
$891$	−4.41320e8	+	3.70311e8i	−0.623908	+	0.523521i
$892$		0			0
$893$	−8.35392e8	−	1.59094e8i	−1.17310	−	0.223409i
$894$		0			0
$895$	6.12628e7	+	7.30102e7i	0.0854531	+	0.101839i
$896$		0			0
$897$	8.24400e7	−	4.67540e8i	0.114225	−	0.647801i
$898$		0			0
$899$	1.46073e8	−	5.31664e7i	0.201045	−	0.0731742i
$900$		0			0
$901$	4.81919e8	−	2.78236e8i	0.658870	−	0.380399i
$902$		0			0
$903$	−5.17830e8	+	6.17126e8i	−0.703273	+	0.838128i
$904$		0			0
$905$	2.99183e7	+	1.72733e7i	0.0403637	+	0.0233040i
$906$		0			0
$907$	1.05790e9	−	1.86536e8i	1.41782	−	0.250000i	0.588376	−	0.808588i	$-0.299768\pi$
$907$	1.05790e9	−	1.86536e8i	1.41782	−	0.250000i	0.829446	+	0.558588i	$0.188657\pi$
$908$		0			0
$909$	−1.27599e9	−	4.64423e8i	−1.69885	−	0.618332i
$910$		0			0
$911$			4.93164e8i			0.652284i	0.945321	+	0.326142i	$0.105749\pi$
$911$			4.93164e8i			0.652284i	−0.945321	+	0.326142i	$0.894251\pi$
$912$		0			0
$913$	5.58843e8			0.734307
$914$		0			0
$915$	1.09047e7	−	2.99604e7i	0.0142347	−	0.0391097i
$916$		0			0
$917$	9.13537e7	+	5.18093e8i	0.118473	+	0.671892i
$918$		0			0
$919$	−3.23005e8	+	5.59461e8i	−0.416163	+	0.720815i	−0.995550	−	0.0942378i	$-0.969959\pi$
$919$	−3.23005e8	+	5.59461e8i	−0.416163	+	0.720815i	0.579387	+	0.815052i	$0.303292\pi$
$920$		0			0
$921$	1.21087e9	+	1.01604e9i	1.54996	+	1.30057i
$922$		0			0
$923$	1.40125e7	+	2.42704e7i	0.0178202	+	0.0308654i
$924$		0			0
$925$	−1.55364e8	−	4.26860e8i	−0.196303	−	0.539337i
$926$		0			0
$927$	−3.93117e8	−	6.93172e7i	−0.493495	−	0.0870165i
$928$		0			0
$929$	−1.00780e8	+	8.45647e7i	−0.125698	+	0.105473i	−0.703470	−	0.710725i	$-0.748367\pi$
$929$	−1.00780e8	+	8.45647e7i	−0.125698	+	0.105473i	0.577772	+	0.816199i	$0.303922\pi$
$930$		0			0
$931$	−1.38601e8	−	8.25650e7i	−0.171758	−	0.102317i
$932$		0			0
$933$	−7.35720e7	−	8.76797e7i	−0.0905874	−	0.107958i
$934$		0			0
$935$	−3.29677e7	+	1.86969e8i	−0.0403324	+	0.228736i
$936$		0			0
$937$	−7.17341e8	+	2.61091e8i	−0.871981	+	0.317375i	−0.738969	−	0.673739i	$-0.764687\pi$
$937$	−7.17341e8	+	2.61091e8i	−0.871981	+	0.317375i	−0.133012	+	0.991114i	$0.542465\pi$
$938$		0			0
$939$	−8.43543e8	+	4.87020e8i	−1.01885	+	0.588234i
$940$		0			0
$941$	−3.93607e8	+	4.69083e8i	−0.472383	+	0.562964i	−0.948646	−	0.316339i	$-0.897546\pi$
$941$	−3.93607e8	+	4.69083e8i	−0.472383	+	0.562964i	0.476263	+	0.879303i	$0.341991\pi$
$942$		0			0
$943$	1.49599e9	+	8.63709e8i	1.78399	+	1.02999i
$944$		0			0
$945$	−8.80601e7	+	1.55274e7i	−0.104348	+	0.0183993i
$946$		0			0
$947$	8.38869e8	+	3.05323e8i	0.987743	+	0.359509i	0.784846	−	0.619691i	$-0.212742\pi$
$947$	8.38869e8	+	3.05323e8i	0.987743	+	0.359509i	0.202897	+	0.979200i	$0.434964\pi$
$948$		0			0
$949$		−	3.90068e8i		−	0.456396i
$950$		0			0
$951$	5.04002e8			0.585991
$952$		0			0
$953$	−3.14727e8	+	8.64706e8i	−0.363627	+	0.999056i	0.614110	+	0.789220i	$0.289515\pi$
$953$	−3.14727e8	+	8.64706e8i	−0.363627	+	0.999056i	−0.977737	+	0.209835i	$0.932707\pi$
$954$		0			0
$955$	6.24518e7	+	3.54182e8i	0.0717026	+	0.406646i
$956$		0			0
$957$	4.06380e8	−	7.03870e8i	0.463656	−	0.803076i
$958$		0			0
$959$	−1.34780e9	−	1.13094e9i	−1.52816	−	1.28228i
$960$		0			0
$961$	−3.64793e8	−	6.31839e8i	−0.411032	−	0.711929i
$962$		0			0
$963$	1.05618e7	+	2.90184e7i	0.0118266	+	0.0324933i
$964$		0			0
$965$	−1.41419e8	−	2.49360e7i	−0.157372	−	0.0277489i
$966$		0			0
$967$	1.31016e8	−	1.09935e8i	0.144892	−	0.121579i	−0.567461	−	0.823400i	$-0.692074\pi$
$967$	1.31016e8	−	1.09935e8i	0.144892	−	0.121579i	0.712353	+	0.701822i	$0.247630\pi$
$968$		0			0
$969$	8.05139e8	+	6.94547e8i	0.884911	+	0.763361i
$970$		0			0
$971$	−6.84586e7	−	8.15858e7i	−0.0747774	−	0.0891162i	0.727359	−	0.686257i	$-0.240748\pi$
$971$	−6.84586e7	−	8.15858e7i	−0.0747774	−	0.0891162i	−0.802136	+	0.597141i	$0.796303\pi$
$972$		0			0
$973$	−2.26245e8	+	1.28310e9i	−0.245607	+	1.39291i
$974$		0			0
$975$	−4.82328e8	+	1.75553e8i	−0.520390	+	0.189406i
$976$		0			0
$977$	−1.19375e9	+	6.89214e8i	−1.28006	+	0.739045i	−0.976860	−	0.213881i	$-0.931389\pi$
$977$	−1.19375e9	+	6.89214e8i	−1.28006	+	0.739045i	−0.303203	+	0.952926i	$0.598056\pi$
$978$		0			0
$979$	−4.63425e8	+	5.52289e8i	−0.493891	+	0.588597i
$980$		0			0
$981$	−1.33488e9	−	7.70693e8i	−1.41395	−	0.816347i
$982$		0			0
$983$	5.11271e8	−	9.01508e7i	0.538258	−	0.0949093i	0.102091	−	0.994775i	$-0.467447\pi$
$983$	5.11271e8	−	9.01508e7i	0.538258	−	0.0949093i	0.436167	+	0.899866i	$0.356336\pi$
$984$		0			0
$985$	1.37828e8	+	5.01653e7i	0.144221	+	0.0524922i
$986$		0			0
$987$		−	1.89152e9i		−	1.96725i
$988$		0			0
$989$	−7.17017e8			−0.741209
$990$		0			0
$991$	−6.30465e8	+	1.73219e9i	−0.647799	+	1.77981i	−0.0220897	+	0.999756i	$0.507032\pi$
$991$	−6.30465e8	+	1.73219e9i	−0.647799	+	1.77981i	−0.625709	+	0.780056i	$0.715190\pi$
$992$		0			0
$993$	−2.64049e8	−	1.49750e9i	−0.269672	−	1.52939i
$994$		0			0
$995$	3.35131e7	−	5.80463e7i	0.0340208	−	0.0589258i
$996$		0			0
$997$	−1.15829e9	−	9.71921e8i	−1.16878	−	0.980721i	−0.168790	−	0.985652i	$-0.553986\pi$
$997$	−1.15829e9	−	9.71921e8i	−1.16878	−	0.980721i	−0.999988	+	0.00493147i	$0.998430\pi$
$998$		0			0
$999$	−1.19815e8	−	2.07525e8i	−0.120175	−	0.208149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.13.2	✓	60
19.3	odd	18	inner	76.7.j.a.41.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.13.2	✓	60	1.1	even	1	trivial
76.7.j.a.41.2	yes	60	19.3	odd	18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.8876 + 38.1558i) q^{3} +(-5.33633 - 30.2638i) q^{5} +(187.863 - 325.388i) q^{7} +(-704.551 - 591.189i) q^{9} +O(q^{10})\)	\(q+(-13.8876 + 38.1558i) q^{3} +(-5.33633 - 30.2638i) q^{5} +(187.863 - 325.388i) q^{7} +(-704.551 - 591.189i) q^{9} +(-809.075 - 1401.36i) q^{11} +(294.503 + 809.141i) q^{13} +(1228.85 + 216.679i) q^{15} +(2924.70 - 2454.12i) q^{17} +(5986.35 - 3348.06i) q^{19} +(9806.47 + 11686.9i) q^{21} +(-2357.90 + 13372.3i) q^{23} +(13795.3 - 5021.07i) q^{25} +(6706.80 - 3872.17i) q^{27} +(7951.27 - 9475.96i) q^{29} +(10883.0 + 6283.28i) q^{31} +(64706.0 - 11409.4i) q^{33} +(-10850.0 - 3949.07i) q^{35} -30942.5i q^{37} -34963.3 q^{39} +(43510.5 - 119544. i) q^{41} +(9169.48 + 52002.7i) q^{43} +(-14131.9 + 24477.2i) q^{45} +(-94977.3 - 79695.4i) q^{47} +(-11760.4 - 20369.6i) q^{49} +(53021.7 + 145676. i) q^{51} +(143538. + 25309.6i) q^{53} +(-38093.0 + 31963.8i) q^{55} +(44612.2 + 274910. i) q^{57} +(-10791.4 - 12860.7i) q^{59} +(4436.96 - 25163.2i) q^{61} +(-324725. + 118190. i) q^{63} +(22916.1 - 13230.6i) q^{65} +(8156.38 - 9720.39i) q^{67} +(-477485. - 275676. i) q^{69} +(32052.4 - 5651.70i) q^{71} +(-425685. - 154937. i) q^{73} +596100. i q^{75} -607980. q^{77} +(328172. - 901645. i) q^{79} +(-61823.1 - 350616. i) q^{81} +(-172680. + 299090. i) q^{83} +(-89878.1 - 75416.7i) q^{85} +(251139. + 434985. i) q^{87} +(-152386. - 418677. i) q^{89} +(318611. + 56179.7i) q^{91} +(-390881. + 327988. i) q^{93} +(-133270. - 163303. i) q^{95} +(149433. + 178088. i) q^{97} +(-258433. + 1.46564e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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