LMFDB - Embedded newform 76.7.h.a.65.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(65,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("76.65");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9460 x^{18} + 36670708 x^{16} + 75655761912 x^{14} + 90488614064544 x^{12} + \cdots + 10\!\cdots\!00 $ x^20 + 9460x^18 + 36670708x^16 + 75655761912x^14 + 90488614064544x^12 + 64290781142478432x^10 + 26741969359067432592x^8 + 6092313787108272225600x^6 + 632563499034568748983104x^4 + 15152233769669432690883072*x^2 + 103372598905826219735270400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{8}\cdot 19^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.10
Root			$43.6786i$ of defining polynomial
Character	$\chi$	$=$	76.65
Dual form			76.7.h.a.69.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(36.3268 + 20.9733i) q^{3} +(-70.2011 + 121.592i) q^{5} -229.488 q^{7} +(515.258 + 892.453i) q^{9} +O(q^{10})$	\(q+(36.3268 + 20.9733i) q^{3} +(-70.2011 + 121.592i) q^{5} -229.488 q^{7} +(515.258 + 892.453i) q^{9} -2391.15 q^{11} +(-1133.47 + 654.407i) q^{13} +(-5100.36 + 2944.70i) q^{15} +(2798.81 - 4847.68i) q^{17} +(6788.73 - 979.273i) q^{19} +(-8336.55 - 4813.11i) q^{21} +(2551.46 + 4419.26i) q^{23} +(-2043.89 - 3540.12i) q^{25} +12647.6i q^{27} +(-25181.1 + 14538.3i) q^{29} +12804.4i q^{31} +(-86862.8 - 50150.2i) q^{33} +(16110.3 - 27903.8i) q^{35} +74312.0i q^{37} -54900.2 q^{39} +(19205.9 + 11088.5i) q^{41} +(-70087.7 + 121395. i) q^{43} -144687. q^{45} +(54971.9 + 95214.2i) q^{47} -64984.4 q^{49} +(203344. - 117400. i) q^{51} +(176483. - 101893. i) q^{53} +(167861. - 290744. i) q^{55} +(267152. + 106808. i) q^{57} +(-152654. - 88135.0i) q^{59} +(43032.5 + 74534.4i) q^{61} +(-118245. - 204807. i) q^{63} -183760. i q^{65} +(50761.7 - 29307.3i) q^{67} +214050. i q^{69} +(369017. + 213052. i) q^{71} +(-100630. + 174296. i) q^{73} -171469. i q^{75} +548739. q^{77} +(353613. + 204158. i) q^{79} +(110362. - 191153. i) q^{81} -715979. q^{83} +(392959. + 680625. i) q^{85} -1.21967e6 q^{87} +(725566. - 418906. i) q^{89} +(260116. - 150178. i) q^{91} +(-268551. + 465143. i) q^{93} +(-357505. + 894201. i) q^{95} +(1.03140e6 + 595477. i) q^{97} +(-1.23206e6 - 2.13399e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9	$ 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9} - 3644 q^{11} - 7140 q^{13} + 9168 q^{15} + 1132 q^{17} + 2110 q^{19} - 8748 q^{21} + 832 q^{23} - 27698 q^{25} - 10920 q^{29} - 30306 q^{33} + 4172 q^{35} + 81144 q^{39} + 109206 q^{41} + 110740 q^{43} - 785440 q^{45} + 107080 q^{47} + 136092 q^{49} + 199872 q^{51} + 254796 q^{53} + 354840 q^{55} + 212268 q^{57} - 610638 q^{59} + 47864 q^{61} - 254476 q^{63} - 839562 q^{67} + 366660 q^{71} + 854482 q^{73} + 763088 q^{77} + 1718592 q^{79} - 1054142 q^{81} + 439612 q^{83} - 400236 q^{85} - 1604736 q^{87} + 478032 q^{89} + 599856 q^{91} + 829380 q^{93} - 1055660 q^{95} - 191286 q^{97} - 2336728 q^{99}+O(q^{100}) $ 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9 - 3644 * q^11 - 7140 * q^13 + 9168 * q^15 + 1132 * q^17 + 2110 * q^19 - 8748 * q^21 + 832 * q^23 - 27698 * q^25 - 10920 * q^29 - 30306 * q^33 + 4172 * q^35 + 81144 * q^39 + 109206 * q^41 + 110740 * q^43 - 785440 * q^45 + 107080 * q^47 + 136092 * q^49 + 199872 * q^51 + 254796 * q^53 + 354840 * q^55 + 212268 * q^57 - 610638 * q^59 + 47864 * q^61 - 254476 * q^63 - 839562 * q^67 + 366660 * q^71 + 854482 * q^73 + 763088 * q^77 + 1718592 * q^79 - 1054142 * q^81 + 439612 * q^83 - 400236 * q^85 - 1604736 * q^87 + 478032 * q^89 + 599856 * q^91 + 829380 * q^93 - 1055660 * q^95 - 191286 * q^97 - 2336728 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	36.3268	+	20.9733i	1.34544	+	0.776789i	0.987599	−	0.156995i	$-0.0501807\pi$
$3$	36.3268	+	20.9733i	1.34544	+	0.776789i	0.357838	+	0.933784i	$0.383514\pi$
$4$		0			0
$5$	−70.2011	+	121.592i	−0.561609	+	0.972735i	0.435747	+	0.900069i	$0.356484\pi$
$5$	−70.2011	+	121.592i	−0.561609	+	0.972735i	−0.997356	+	0.0726661i	$0.976849\pi$
$6$		0			0
$7$	−229.488			−0.669060			−0.334530	−	0.942385i	$-0.608578\pi$
$7$	−229.488			−0.669060			−0.334530	+	0.942385i	$0.608578\pi$
$8$		0			0
$9$	515.258	+	892.453i	0.706801	+	1.22422i
$10$		0			0
$11$	−2391.15			−1.79650			−0.898252	−	0.439480i	$-0.855163\pi$
$11$	−2391.15			−1.79650			−0.898252	+	0.439480i	$0.855163\pi$
$12$		0			0
$13$	−1133.47	+	654.407i	−0.515915	+	0.297864i	−0.735262	−	0.677783i	$-0.762941\pi$
$13$	−1133.47	+	654.407i	−0.515915	+	0.297864i	0.219347	+	0.975647i	$0.429607\pi$
$14$		0			0
$15$	−5100.36	+	2944.70i	−1.51122	+	0.872503i
$16$		0			0
$17$	2798.81	−	4847.68i	0.569674	−	0.986705i	−0.426924	−	0.904288i	$-0.640403\pi$
$17$	2798.81	−	4847.68i	0.569674	−	0.986705i	0.996598	−	0.0824169i	$-0.0262639\pi$
$18$		0			0
$19$	6788.73	−	979.273i	0.989756	−	0.142772i
$19$	6788.73	−	979.273i	0.989756	−	0.142772i
$20$		0			0
$21$	−8336.55	−	4813.11i	−0.900178	−	0.519718i
$22$		0			0
$23$	2551.46	+	4419.26i	0.209703	+	0.363217i	0.951621	−	0.307274i	$-0.0994168\pi$
$23$	2551.46	+	4419.26i	0.209703	+	0.363217i	−0.741918	+	0.670491i	$0.766083\pi$
$24$		0			0
$25$	−2043.89	−	3540.12i	−0.130809	−	0.226568i
$26$		0			0
$27$			12647.6i			0.642563i
$28$		0			0
$29$	−25181.1	+	14538.3i	−1.03248	+	0.596102i	−0.917694	−	0.397289i	$-0.869951\pi$
$29$	−25181.1	+	14538.3i	−1.03248	+	0.596102i	−0.114785	+	0.993390i	$0.536618\pi$
$30$		0			0
$31$			12804.4i			0.429808i	0.976635	+	0.214904i	$0.0689439\pi$
$31$			12804.4i			0.429808i	−0.976635	+	0.214904i	$0.931056\pi$
$32$		0			0
$33$	−86862.8	−	50150.2i	−2.41708	−	1.39550i
$34$		0			0
$35$	16110.3	−	27903.8i	0.375750	−	0.650818i
$36$		0			0
$37$			74312.0i			1.46708i	0.679646	+	0.733540i	$0.262133\pi$
$37$			74312.0i			1.46708i	−0.679646	+	0.733540i	$0.737867\pi$
$38$		0			0
$39$	−54900.2			−0.925509
$40$		0			0
$41$	19205.9	+	11088.5i	0.278665	+	0.160888i	0.632819	−	0.774300i	$-0.281898\pi$
$41$	19205.9	+	11088.5i	0.278665	+	0.160888i	−0.354154	+	0.935187i	$0.615231\pi$
$42$		0			0
$43$	−70087.7	+	121395.i	−0.881528	+	1.52685i	−0.0318865	+	0.999491i	$0.510152\pi$
$43$	−70087.7	+	121395.i	−0.881528	+	1.52685i	−0.849642	+	0.527360i	$0.823182\pi$
$44$		0			0
$45$	−144687.			−1.58778
$46$		0			0
$47$	54971.9	+	95214.2i	0.529477	+	0.917082i	0.999409	+	0.0343789i	$0.0109453\pi$
$47$	54971.9	+	95214.2i	0.529477	+	0.917082i	−0.469931	+	0.882703i	$0.655721\pi$
$48$		0			0
$49$	−64984.4			−0.552359
$50$		0			0
$51$	203344.	−	117400.i	1.53292	−	0.885033i
$52$		0			0
$53$	176483.	−	101893.i	1.18543	−	0.684408i	0.228165	−	0.973622i	$-0.426727\pi$
$53$	176483.	−	101893.i	1.18543	−	0.684408i	0.957264	+	0.289214i	$0.0933941\pi$
$54$		0			0
$55$	167861.	−	290744.i	1.00893	−	1.74752i
$56$		0			0
$57$	267152.	+	106808.i	1.44256	+	0.576740i
$58$		0			0
$59$	−152654.	−	88135.0i	−0.743281	−	0.429133i	0.0799803	−	0.996796i	$-0.474514\pi$
$59$	−152654.	−	88135.0i	−0.743281	−	0.429133i	−0.823261	+	0.567663i	$0.807848\pi$
$60$		0			0
$61$	43032.5	+	74534.4i	0.189586	+	0.328373i	0.945112	−	0.326746i	$-0.105952\pi$
$61$	43032.5	+	74534.4i	0.189586	+	0.328373i	−0.755526	+	0.655119i	$0.772619\pi$
$62$		0			0
$63$	−118245.	−	204807.i	−0.472892	−	0.819074i
$64$		0			0
$65$		−	183760.i		−	0.669132i
$66$		0			0
$67$	50761.7	−	29307.3i	0.168776	−	0.0974430i	−0.413232	−	0.910626i	$-0.635600\pi$
$67$	50761.7	−	29307.3i	0.168776	−	0.0974430i	0.582009	+	0.813183i	$0.302267\pi$
$68$		0			0
$69$			214050.i			0.651581i
$70$		0			0
$71$	369017.	+	213052.i	1.03103	+	0.595266i	0.917280	−	0.398243i	$-0.130380\pi$
$71$	369017.	+	213052.i	1.03103	+	0.595266i	0.113751	+	0.993509i	$0.463713\pi$
$72$		0			0
$73$	−100630.	+	174296.i	−0.258677	+	0.448042i	−0.965888	−	0.258961i	$-0.916620\pi$
$73$	−100630.	+	174296.i	−0.258677	+	0.448042i	0.707210	+	0.707003i	$0.249953\pi$
$74$		0			0
$75$		−	171469.i		−	0.406444i
$76$		0			0
$77$	548739.			1.20197
$78$		0			0
$79$	353613.	+	204158.i	0.717210	+	0.414081i	0.813725	−	0.581250i	$-0.197436\pi$
$79$	353613.	+	204158.i	0.717210	+	0.414081i	−0.0965149	+	0.995332i	$0.530770\pi$
$80$		0			0
$81$	110362.	−	191153.i	0.207666	−	0.359687i
$82$		0			0
$83$	−715979.			−1.25218			−0.626088	−	0.779752i	$-0.715345\pi$
$83$	−715979.			−1.25218			−0.626088	+	0.779752i	$0.715345\pi$
$84$		0			0
$85$	392959.	+	680625.i	0.639868	+	1.10828i
$86$		0			0
$87$	−1.21967e6			−1.85218
$88$		0			0
$89$	725566.	−	418906.i	1.02922	−	0.594218i	0.112456	−	0.993657i	$-0.464128\pi$
$89$	725566.	−	418906.i	1.02922	−	0.594218i	0.916760	+	0.399438i	$0.130795\pi$
$90$		0			0
$91$	260116.	−	150178.i	0.345178	−	0.199289i
$92$		0			0
$93$	−268551.	+	465143.i	−0.333870	+	0.578280i
$94$		0			0
$95$	−357505.	+	894201.i	−0.416976	+	1.04295i
$96$		0			0
$97$	1.03140e6	+	595477.i	1.13008	+	0.652454i	0.943956	−	0.330072i	$-0.107073\pi$
$97$	1.03140e6	+	595477.i	1.13008	+	0.652454i	0.186127	+	0.982526i	$0.440406\pi$
$98$		0			0
$99$	−1.23206e6	−	2.13399e6i	−1.26977	−	2.19931i
$100$		0			0
$101$	−393334.	−	681274.i	−0.381766	−	0.661238i	0.609549	−	0.792748i	$-0.291351\pi$
$101$	−393334.	−	681274.i	−0.381766	−	0.661238i	−0.991315	+	0.131511i	$0.958017\pi$
$102$		0			0
$103$		−	405307.i		−	0.370913i	−0.982652	−	0.185457i	$-0.940624\pi$
$103$		−	405307.i		−	0.370913i	0.982652	−	0.185457i	$-0.0593765\pi$
$104$		0			0
$105$	1.17047e6	−	675771.i	1.01110	−	0.583757i
$106$		0			0
$107$		−	2.19074e6i		−	1.78829i	−0.447774	−	0.894147i	$-0.647783\pi$
$107$		−	2.19074e6i		−	1.78829i	0.447774	−	0.894147i	$-0.352217\pi$
$108$		0			0
$109$	−202372.	−	116840.i	−0.156269	−	0.0902217i	0.419827	−	0.907604i	$-0.362091\pi$
$109$	−202372.	−	116840.i	−0.156269	−	0.0902217i	−0.576095	+	0.817383i	$0.695424\pi$
$110$		0			0
$111$	−1.55857e6	+	2.69952e6i	−1.13961	+	1.97386i
$112$		0			0
$113$			1.81147e6i			1.25544i	0.778439	+	0.627721i	$0.216012\pi$
$113$			1.81147e6i			1.25544i	−0.778439	+	0.627721i	$0.783988\pi$
$114$		0			0
$115$	−716462.			−0.471085
$116$		0			0
$117$	−1.16805e6	−	674376.i	−0.729299	−	0.421061i
$118$		0			0
$119$	−642292.	+	1.11248e6i	−0.381146	+	0.660165i
$120$		0			0
$121$	3.94603e6			2.22743
$122$		0			0
$123$	465126.	+	805622.i	0.249951	+	0.432928i
$124$		0			0
$125$	−1.61985e6			−0.829364
$126$		0			0
$127$	−812834.	+	469290.i	−0.396817	+	0.229103i	−0.685110	−	0.728440i	$-0.740246\pi$
$127$	−812834.	+	469290.i	−0.396817	+	0.229103i	0.288292	+	0.957542i	$0.406912\pi$
$128$		0			0
$129$	−5.09212e6	+	2.93994e6i	−2.37208	+	1.36952i
$130$		0			0
$131$	523067.	−	905978.i	0.232672	−	0.402999i	−0.725922	−	0.687777i	$-0.758587\pi$
$131$	523067.	−	905978.i	0.232672	−	0.402999i	0.958593	+	0.284778i	$0.0919199\pi$
$132$		0			0
$133$	−1.55793e6	+	224731.i	−0.662206	+	0.0955230i
$134$		0			0
$135$	−1.53784e6	−	887873.i	−0.625043	−	0.360869i
$136$		0			0
$137$	1.15410e6	+	1.99896e6i	0.448830	+	0.777396i	0.998310	−	0.0581105i	$-0.0185076\pi$
$137$	1.15410e6	+	1.99896e6i	0.448830	+	0.777396i	−0.549480	+	0.835507i	$0.685174\pi$
$138$		0			0
$139$	−2.10200e6	−	3.64077e6i	−0.782688	−	1.35565i	−0.930371	−	0.366620i	$-0.880515\pi$
$139$	−2.10200e6	−	3.64077e6i	−0.782688	−	1.35565i	0.147683	−	0.989035i	$-0.452818\pi$
$140$		0			0
$141$			4.61177e6i			1.64517i
$142$		0			0
$143$	2.71028e6	−	1.56478e6i	0.926844	−	0.535114i
$144$		0			0
$145$		−	4.08243e6i		−	1.33910i
$146$		0			0
$147$	−2.36068e6	−	1.36294e6i	−0.743164	−	0.429066i
$148$		0			0
$149$	−1.88985e6	+	3.27332e6i	−0.571306	+	0.989530i	0.425127	+	0.905134i	$0.360230\pi$
$149$	−1.88985e6	+	3.27332e6i	−0.571306	+	0.989530i	−0.996432	+	0.0843965i	$0.973104\pi$
$150$		0			0
$151$		−	1.78226e6i		−	0.517655i	−0.965924	−	0.258828i	$-0.916664\pi$
$151$		−	1.78226e6i		−	0.517655i	0.965924	−	0.258828i	$-0.0833361\pi$
$152$		0			0
$153$	5.76843e6			1.61059
$154$		0			0
$155$	−1.55691e6	−	898884.i	−0.418089	−	0.241384i
$156$		0			0
$157$	−1.18731e6	+	2.05647e6i	−0.306806	+	0.531403i	−0.977662	−	0.210184i	$-0.932594\pi$
$157$	−1.18731e6	+	2.05647e6i	−0.306806	+	0.531403i	0.670856	+	0.741588i	$0.265927\pi$
$158$		0			0
$159$	8.54809e6			2.12656
$160$		0			0
$161$	−585529.	−	1.01417e6i	−0.140304	−	0.243014i
$162$		0			0
$163$	2.88835e6			0.666941			0.333470	−	0.942761i	$-0.391780\pi$
$163$	2.88835e6			0.666941			0.333470	+	0.942761i	$0.391780\pi$
$164$		0			0
$165$	1.21957e7	−	7.04121e6i	2.71491	−	1.56746i
$166$		0			0
$167$	4.76043e6	−	2.74844e6i	1.02211	−	0.590115i	0.107395	−	0.994216i	$-0.465749\pi$
$167$	4.76043e6	−	2.74844e6i	1.02211	−	0.590115i	0.914714	+	0.404102i	$0.132416\pi$
$168$		0			0
$169$	−1.55691e6	+	2.69664e6i	−0.322554	+	0.558681i
$170$		0			0
$171$	4.37190e6	+	5.55405e6i	0.874344	+	1.11076i
$172$		0			0
$173$	−1.73922e6	−	1.00414e6i	−0.335905	−	0.193935i	0.322555	−	0.946551i	$-0.395458\pi$
$173$	−1.73922e6	−	1.00414e6i	−0.335905	−	0.193935i	−0.658460	+	0.752616i	$0.728792\pi$
$174$		0			0
$175$	469048.	+	812415.i	0.0875191	+	0.151588i
$176$		0			0
$177$	−3.69696e6	−	6.40332e6i	−0.666692	−	1.15474i
$178$		0			0
$179$		−	4.65224e6i		−	0.811153i	−0.914061	−	0.405577i	$-0.867071\pi$
$179$		−	4.65224e6i		−	0.811153i	0.914061	−	0.405577i	$-0.132929\pi$
$180$		0			0
$181$	4.74712e6	−	2.74075e6i	0.800562	−	0.462205i	−0.0431058	−	0.999071i	$-0.513725\pi$
$181$	4.74712e6	−	2.74075e6i	0.800562	−	0.462205i	0.843668	+	0.536866i	$0.180392\pi$
$182$		0			0
$183$			3.61013e6i			0.589074i
$184$		0			0
$185$	−9.03574e6	−	5.21678e6i	−1.42708	−	0.823925i
$186$		0			0
$187$	−6.69237e6	+	1.15915e7i	−1.02342	+	1.77262i
$188$		0			0
$189$		−	2.90246e6i		−	0.429913i
$190$		0			0
$191$	−9.67348e6			−1.38830			−0.694149	−	0.719831i	$-0.744219\pi$
$191$	−9.67348e6			−1.38830			−0.694149	+	0.719831i	$0.744219\pi$
$192$		0			0
$193$	1.06402e7	+	6.14312e6i	1.48005	+	0.854510i	0.999745	−	0.0225887i	$-0.00719083\pi$
$193$	1.06402e7	+	6.14312e6i	1.48005	+	0.854510i	0.480310	+	0.877099i	$0.340524\pi$
$194$		0			0
$195$	3.85406e6	−	6.67542e6i	0.519774	−	0.900275i
$196$		0			0
$197$	−104315.			−0.0136443			−0.00682213	−	0.999977i	$-0.502172\pi$
$197$	−104315.			−0.0136443			−0.00682213	+	0.999977i	$0.502172\pi$
$198$		0			0
$199$	7.28502e6	+	1.26180e7i	0.924425	+	1.60115i	0.792484	+	0.609893i	$0.208788\pi$
$199$	7.28502e6	+	1.26180e7i	0.924425	+	1.60115i	0.131941	+	0.991258i	$0.457879\pi$
$200$		0			0
$201$	2.45868e6			0.302771
$202$		0			0
$203$	5.77875e6	−	3.33636e6i	0.690790	−	0.398828i
$204$		0			0
$205$	−2.69655e6	+	1.55685e6i	−0.313002	+	0.180712i
$206$		0			0
$207$	−2.62932e6	+	4.55412e6i	−0.296437	+	0.513444i
$208$		0			0
$209$	−1.62329e7	+	2.34159e6i	−1.77810	+	0.256491i
$210$		0			0
$211$	−1.42186e7	−	8.20910e6i	−1.51359	−	0.873872i	−0.999873	−	0.0159133i	$-0.994934\pi$
$211$	−1.42186e7	−	8.20910e6i	−1.51359	−	0.873872i	−0.513718	−	0.857959i	$-0.671732\pi$
$212$		0			0
$213$	8.93681e6	+	1.54790e7i	0.924792	+	1.60179i
$214$		0			0
$215$	−9.84046e6	−	1.70442e7i	−0.990148	−	1.71499i
$216$		0			0
$217$		−	2.93845e6i		−	0.287567i
$218$		0			0
$219$	−7.31113e6	+	4.22108e6i	−0.696068	+	0.401875i
$220$		0			0
$221$			7.32624e6i			0.678741i
$222$		0			0
$223$	8.83756e6	+	5.10237e6i	0.796926	+	0.460105i	0.842395	−	0.538860i	$-0.181145\pi$
$223$	8.83756e6	+	5.10237e6i	0.796926	+	0.460105i	−0.0454692	+	0.998966i	$0.514478\pi$
$224$		0			0
$225$	2.10626e6	−	3.64816e6i	0.184912	−	0.320277i
$226$		0			0
$227$		−	1.26209e7i		−	1.07898i	−0.841993	−	0.539488i	$-0.818618\pi$
$227$		−	1.26209e7i		−	1.07898i	0.841993	−	0.539488i	$-0.181382\pi$
$228$		0			0
$229$	1.10722e6			0.0921992			0.0460996	−	0.998937i	$-0.485321\pi$
$229$	1.10722e6			0.0921992			0.0460996	+	0.998937i	$0.485321\pi$
$230$		0			0
$231$	1.99339e7	+	1.15089e7i	1.61717	+	0.933676i
$232$		0			0
$233$	6.59278e6	−	1.14190e7i	0.521196	−	0.902737i	−0.478500	−	0.878087i	$-0.658820\pi$
$233$	6.59278e6	−	1.14190e7i	0.521196	−	0.902737i	0.999696	−	0.0246501i	$-0.00784716\pi$
$234$		0			0
$235$	−1.54364e7			−1.18944
$236$		0			0
$237$	8.56374e6	+	1.48328e7i	0.643307	+	1.11424i
$238$		0			0
$239$	−2.72081e7			−1.99299			−0.996494	−	0.0836660i	$-0.973337\pi$
$239$	−2.72081e7			−1.99299			−0.996494	+	0.0836660i	$0.973337\pi$
$240$		0			0
$241$	−1.04936e6	+	605849.i	−0.0749677	+	0.0432826i	−0.537015	−	0.843573i	$-0.680448\pi$
$241$	−1.04936e6	+	605849.i	−0.0749677	+	0.0432826i	0.462048	+	0.886855i	$0.347115\pi$
$242$		0			0
$243$	1.60030e7	−	9.23935e6i	1.11528	−	0.643906i
$244$		0			0
$245$	4.56198e6	−	7.90158e6i	0.310210	−	0.537299i
$246$		0			0
$247$	−7.05395e6	+	5.55256e6i	−0.468103	+	0.368471i
$248$		0			0
$249$	−2.60092e7	−	1.50164e7i	−1.68473	−	0.972677i
$250$		0			0
$251$	−5.39718e6	−	9.34820e6i	−0.341308	−	0.591162i	0.643368	−	0.765557i	$-0.277536\pi$
$251$	−5.39718e6	−	9.34820e6i	−0.341308	−	0.591162i	−0.984676	+	0.174395i	$0.944203\pi$
$252$		0			0
$253$	−6.10092e6	−	1.05671e7i	−0.376733	−	0.652521i
$254$		0			0
$255$			3.29666e7i			1.98817i
$256$		0			0
$257$	−5.22232e6	+	3.01511e6i	−0.307655	+	0.177625i	−0.645877	−	0.763442i	$-0.723508\pi$
$257$	−5.22232e6	+	3.01511e6i	−0.307655	+	0.177625i	0.338222	+	0.941067i	$0.390175\pi$
$258$		0			0
$259$		−	1.70537e7i		−	0.981564i
$260$		0			0
$261$	−2.59495e7	−	1.49820e7i	−1.45951	−	0.842650i
$262$		0			0
$263$	−3.90962e6	+	6.77167e6i	−0.214915	+	0.372244i	−0.953246	−	0.302194i	$-0.902281\pi$
$263$	−3.90962e6	+	6.77167e6i	−0.214915	+	0.372244i	0.738331	+	0.674439i	$0.235614\pi$
$264$		0			0
$265$			2.86119e7i			1.53748i
$266$		0			0
$267$	3.51433e7			1.84633
$268$		0			0
$269$	−1.77556e7	−	1.02512e7i	−0.912174	−	0.526644i	−0.0310441	−	0.999518i	$-0.509883\pi$
$269$	−1.77556e7	−	1.02512e7i	−0.912174	−	0.526644i	−0.881130	+	0.472874i	$0.843217\pi$
$270$		0			0
$271$	−4.18025e6	+	7.24041e6i	−0.210036	+	0.363794i	−0.951726	−	0.306950i	$-0.900692\pi$
$271$	−4.18025e6	+	7.24041e6i	−0.210036	+	0.363794i	0.741689	+	0.670744i	$0.234025\pi$
$272$		0			0
$273$	1.25989e7			0.619221
$274$		0			0
$275$	4.88725e6	+	8.46496e6i	0.234999	+	0.407030i
$276$		0			0
$277$	2.98444e7			1.40418			0.702090	−	0.712088i	$-0.252250\pi$
$277$	2.98444e7			1.40418			0.702090	+	0.712088i	$0.252250\pi$
$278$		0			0
$279$	−1.14273e7	+	6.59758e6i	−0.526178	+	0.303789i
$280$		0			0
$281$	1.63691e6	−	945070.i	0.0737744	−	0.0425937i	−0.462659	−	0.886536i	$-0.653105\pi$
$281$	1.63691e6	−	945070.i	0.0737744	−	0.0425937i	0.536433	+	0.843943i	$0.319771\pi$
$282$		0			0
$283$	−1.04944e7	+	1.81768e7i	−0.463018	+	0.801971i	−0.999110	−	0.0421888i	$-0.986567\pi$
$283$	−1.04944e7	+	1.81768e7i	−0.463018	+	0.801971i	0.536091	+	0.844160i	$0.319900\pi$
$284$		0			0
$285$	−3.17414e7	+	2.49854e7i	−1.37117	+	1.07932i
$286$		0			0
$287$	−4.40752e6	−	2.54468e6i	−0.186444	−	0.107643i
$288$		0			0
$289$	−3.59788e6	−	6.23171e6i	−0.149057	−	0.258175i
$290$		0			0
$291$	2.49782e7	+	4.32635e7i	1.01364	+	1.75567i
$292$		0			0
$293$			1.65979e7i			0.659858i	0.944006	+	0.329929i	$0.107025\pi$
$293$			1.65979e7i			0.659858i	−0.944006	+	0.329929i	$0.892975\pi$
$294$		0			0
$295$	2.14330e7	−	1.23743e7i	0.834866	−	0.482010i
$296$		0			0
$297$		−	3.02422e7i		−	1.15437i
$298$		0			0
$299$	−5.78399e6	−	3.33939e6i	−0.216378	−	0.124926i
$300$		0			0
$301$	1.60842e7	−	2.78587e7i	0.589795	−	1.02156i
$302$		0			0
$303$		−	3.29980e7i		−	1.18621i
$304$		0			0
$305$	−1.20837e7			−0.425893
$306$		0			0
$307$	1.27688e7	+	7.37209e6i	0.441302	+	0.254786i	0.704150	−	0.710051i	$-0.251328\pi$
$307$	1.27688e7	+	7.37209e6i	0.441302	+	0.254786i	−0.262848	+	0.964837i	$0.584662\pi$
$308$		0			0
$309$	8.50063e6	−	1.47235e7i	0.288121	−	0.499041i
$310$		0			0
$311$	5.07279e7			1.68642			0.843211	−	0.537583i	$-0.180663\pi$
$311$	5.07279e7			1.68642			0.843211	+	0.537583i	$0.180663\pi$
$312$		0			0
$313$	−7.35009e6	−	1.27307e7i	−0.239695	−	0.415164i	0.720932	−	0.693006i	$-0.243714\pi$
$313$	−7.35009e6	−	1.27307e7i	−0.239695	−	0.415164i	−0.960627	+	0.277842i	$0.910381\pi$
$314$		0			0
$315$	3.32038e7			1.06232
$316$		0			0
$317$	−2.02172e7	+	1.16724e7i	−0.634664	+	0.366424i	−0.782556	−	0.622580i	$-0.786085\pi$
$317$	−2.02172e7	+	1.16724e7i	−0.634664	+	0.366424i	0.147892	+	0.989004i	$0.452751\pi$
$318$		0			0
$319$	6.02118e7	−	3.47633e7i	1.85485	−	1.07090i
$320$		0			0
$321$	4.59470e7	−	7.95825e7i	1.38913	−	2.40604i
$322$		0			0
$323$	1.42532e7	−	3.56504e7i	0.422964	−	1.05793i
$324$		0			0
$325$	4.63336e6	+	2.67507e6i	0.134973	+	0.0779266i
$326$		0			0
$327$	−4.90103e6	−	8.48883e6i	−0.140166	−	0.242775i
$328$		0			0
$329$	−1.26154e7	−	2.18505e7i	−0.354252	−	0.613583i
$330$		0			0
$331$			5.39389e7i			1.48737i	0.668532	+	0.743684i	$0.266923\pi$
$331$			5.39389e7i			1.48737i	−0.668532	+	0.743684i	$0.733077\pi$
$332$		0			0
$333$	−6.63200e7	+	3.82898e7i	−1.79602	+	1.03693i
$334$		0			0
$335$			8.22961e6i			0.218899i
$336$		0			0
$337$	4.00997e7	+	2.31516e7i	1.04773	+	0.604910i	0.922014	−	0.387156i	$-0.126543\pi$
$337$	4.00997e7	+	2.31516e7i	1.04773	+	0.604910i	0.125720	+	0.992066i	$0.459876\pi$
$338$		0			0
$339$	−3.79925e7	+	6.58050e7i	−0.975212	+	1.68912i
$340$		0			0
$341$		−	3.06172e7i		−	0.772152i
$342$		0			0
$343$	4.19121e7			1.03862
$344$		0			0
$345$	−2.60268e7	−	1.50266e7i	−0.633816	−	0.365934i
$346$		0			0
$347$	1.11637e7	−	1.93361e7i	0.267190	−	0.462787i	−0.700945	−	0.713216i	$-0.747238\pi$
$347$	1.11637e7	−	1.93361e7i	0.267190	−	0.462787i	0.968135	+	0.250428i	$0.0805714\pi$
$348$		0			0
$349$	1.27598e7			0.300171			0.150085	−	0.988673i	$-0.452045\pi$
$349$	1.27598e7			0.300171			0.150085	+	0.988673i	$0.452045\pi$
$350$		0			0
$351$	−8.27665e6	−	1.43356e7i	−0.191396	−	0.331508i
$352$		0			0
$353$	3.26929e6			0.0743241			0.0371620	−	0.999309i	$-0.488168\pi$
$353$	3.26929e6			0.0743241			0.0371620	+	0.999309i	$0.488168\pi$
$354$		0			0
$355$	−5.18108e7	+	2.99130e7i	−1.15807	+	0.668613i
$356$		0			0
$357$	−4.66648e7	+	2.69420e7i	−1.02562	+	0.592140i
$358$		0			0
$359$	−2.30495e7	+	3.99229e7i	−0.498171	+	0.862857i	−0.999998	−	0.00211093i	$-0.999328\pi$
$359$	−2.30495e7	+	3.99229e7i	−0.498171	+	0.862857i	0.501827	+	0.864968i	$0.332661\pi$
$360$		0			0
$361$	4.51279e7	−	1.32960e7i	0.959232	−	0.282619i
$362$		0			0
$363$	1.43347e8	+	8.27612e7i	2.99687	+	1.73024i
$364$		0			0
$365$	−1.41287e7	−	2.44716e7i	−0.290551	−	0.503249i
$366$		0			0
$367$	−4.41857e7	−	7.65318e7i	−0.893888	−	1.54826i	−0.835175	−	0.549984i	$-0.814634\pi$
$367$	−4.41857e7	−	7.65318e7i	−0.893888	−	1.54826i	−0.0587130	−	0.998275i	$-0.518700\pi$
$368$		0			0
$369$			2.28538e7i			0.454862i
$370$		0			0
$371$	−4.05007e7	+	2.33831e7i	−0.793123	+	0.457910i
$372$		0			0
$373$			7.10440e7i			1.36899i	0.729017	+	0.684496i	$0.239978\pi$
$373$			7.10440e7i			1.36899i	−0.729017	+	0.684496i	$0.760022\pi$
$374$		0			0
$375$	−5.88440e7	−	3.39736e7i	−1.11586	−	0.644240i
$376$		0			0
$377$	1.90279e7	−	3.29574e7i	0.355114	−	0.615076i
$378$		0			0
$379$		−	4.71949e7i		−	0.866917i	−0.901174	−	0.433458i	$-0.857293\pi$
$379$		−	4.71949e7i		−	0.866917i	0.901174	−	0.433458i	$-0.142707\pi$
$380$		0			0
$381$	−3.93702e7			−0.711857
$382$		0			0
$383$	−6.16450e7	−	3.55908e7i	−1.09724	−	0.633492i	−0.161745	−	0.986833i	$-0.551712\pi$
$383$	−6.16450e7	−	3.55908e7i	−1.09724	−	0.633492i	−0.935495	+	0.353341i	$0.885046\pi$
$384$		0			0
$385$	−3.85221e7	+	6.67222e7i	−0.675037	+	1.16920i
$386$		0			0
$387$	−1.44453e8			−2.49226
$388$		0			0
$389$	1.76555e7	+	3.05803e7i	0.299938	+	0.519508i	0.976122	−	0.217225i	$-0.0697006\pi$
$389$	1.76555e7	+	3.05803e7i	0.299938	+	0.519508i	−0.676183	+	0.736733i	$0.736367\pi$
$390$		0			0
$391$	2.85642e7			0.477850
$392$		0			0
$393$	3.80027e7	−	2.19409e7i	0.626090	−	0.361473i
$394$		0			0
$395$	−4.96480e7	+	2.86643e7i	−0.805583	+	0.465104i
$396$		0			0
$397$	−5.27719e7	+	9.14036e7i	−0.843396	+	1.46080i	0.0436116	+	0.999049i	$0.486114\pi$
$397$	−5.27719e7	+	9.14036e7i	−0.843396	+	1.46080i	−0.887007	+	0.461756i	$0.847220\pi$
$398$		0			0
$399$	−6.13080e7	−	2.45112e7i	−0.965158	−	0.385874i
$400$		0			0
$401$	6.47348e7	+	3.73746e7i	1.00393	+	0.579621i	0.909409	−	0.415902i	$-0.136534\pi$
$401$	6.47348e7	+	3.73746e7i	1.00393	+	0.579621i	0.0945230	+	0.995523i	$0.469867\pi$
$402$		0			0
$403$	−8.37929e6	−	1.45134e7i	−0.128024	−	0.221744i
$404$		0			0
$405$	1.54951e7	+	2.68383e7i	0.233254	+	0.404007i
$406$		0			0
$407$		−	1.77691e8i		−	2.63562i
$408$		0			0
$409$	−3.50076e7	+	2.02117e7i	−0.511673	+	0.295415i	−0.733521	−	0.679667i	$-0.762124\pi$
$409$	−3.50076e7	+	2.02117e7i	−0.511673	+	0.295415i	0.221848	+	0.975081i	$0.428791\pi$
$410$		0			0
$411$			9.68211e7i			1.39458i
$412$		0			0
$413$	3.50323e7	+	2.02259e7i	0.497299	+	0.287116i
$414$		0			0
$415$	5.02625e7	−	8.70572e7i	0.703234	−	1.21804i
$416$		0			0
$417$		−	1.76344e8i		−	2.43193i
$418$		0			0
$419$	6.95684e7			0.945736			0.472868	−	0.881133i	$-0.343219\pi$
$419$	6.95684e7			0.945736			0.472868	+	0.881133i	$0.343219\pi$
$420$		0			0
$421$	−1.30635e6	−	754221.i	−0.0175070	−	0.0101077i	0.491221	−	0.871035i	$-0.336551\pi$
$421$	−1.30635e6	−	754221.i	−0.0175070	−	0.0101077i	−0.508728	+	0.860927i	$0.669884\pi$
$422$		0			0
$423$	−5.66495e7	+	9.81197e7i	−0.748470	+	1.29639i
$424$		0			0
$425$	−2.28819e7			−0.298074
$426$		0			0
$427$	−9.87542e6	−	1.71047e7i	−0.126845	−	0.219701i
$428$		0			0
$429$	1.31275e8			1.66268
$430$		0			0
$431$	−3.17557e7	+	1.83342e7i	−0.396634	+	0.228997i	−0.685030	−	0.728514i	$-0.740211\pi$
$431$	−3.17557e7	+	1.83342e7i	−0.396634	+	0.228997i	0.288397	+	0.957511i	$0.406878\pi$
$432$		0			0
$433$	2.30591e7	−	1.33132e7i	0.284040	−	0.163991i	−0.351211	−	0.936296i	$-0.614230\pi$
$433$	2.30591e7	−	1.33132e7i	0.284040	−	0.163991i	0.635251	+	0.772306i	$0.280897\pi$
$434$		0			0
$435$	8.56219e7	−	1.48301e8i	1.04020	−	1.80168i
$436$		0			0
$437$	2.16489e7	+	2.75026e7i	0.259412	+	0.329556i
$438$		0			0
$439$	1.05585e8	+	6.09595e7i	1.24798	+	0.720524i	0.970707	−	0.240267i	$-0.0772349\pi$
$439$	1.05585e8	+	6.09595e7i	1.24798	+	0.720524i	0.277276	+	0.960790i	$0.410568\pi$
$440$		0			0
$441$	−3.34838e7	−	5.79956e7i	−0.390408	−	0.676206i
$442$		0			0
$443$	−1.36060e7	−	2.35663e7i	−0.156502	−	0.271069i	0.777103	−	0.629373i	$-0.216688\pi$
$443$	−1.36060e7	−	2.35663e7i	−0.156502	−	0.271069i	−0.933605	+	0.358304i	$0.883355\pi$
$444$		0			0
$445$			1.17631e8i			1.33487i
$446$		0			0
$447$	−1.37304e8	+	7.92727e7i	−1.53731	+	0.887567i
$448$		0			0
$449$			1.18295e8i			1.30686i	0.756989	+	0.653428i	$0.226670\pi$
$449$			1.18295e8i			1.30686i	−0.756989	+	0.653428i	$0.773330\pi$
$450$		0			0
$451$	−4.59242e7	−	2.65143e7i	−0.500624	−	0.289035i
$452$		0			0
$453$	3.73799e7	−	6.47439e7i	0.402109	−	0.696473i
$454$		0			0
$455$			4.21707e7i			0.447689i
$456$		0			0
$457$	4.01734e7			0.420910			0.210455	−	0.977604i	$-0.432505\pi$
$457$	4.01734e7			0.420910			0.210455	+	0.977604i	$0.432505\pi$
$458$		0			0
$459$	6.13113e7	+	3.53981e7i	0.634020	+	0.366051i
$460$		0			0
$461$	−8.25825e7	+	1.43037e8i	−0.842918	+	1.45998i	0.0444989	+	0.999009i	$0.485831\pi$
$461$	−8.25825e7	+	1.43037e8i	−0.842918	+	1.45998i	−0.887417	+	0.460968i	$0.847502\pi$
$462$		0			0
$463$	−1.54098e8			−1.55258			−0.776291	−	0.630375i	$-0.782901\pi$
$463$	−1.54098e8			−1.55258			−0.776291	+	0.630375i	$0.782901\pi$
$464$		0			0
$465$	−3.77051e7	−	6.53072e7i	−0.375009	−	0.649534i
$466$		0			0
$467$	−6.14195e7			−0.603054			−0.301527	−	0.953458i	$-0.597496\pi$
$467$	−6.14195e7			−0.603054			−0.301527	+	0.953458i	$0.597496\pi$
$468$		0			0
$469$	−1.16492e7	+	6.72565e6i	−0.112921	+	0.0651952i
$470$		0			0
$471$	−8.62621e7	+	4.98034e7i	−0.825576	+	0.476647i
$472$		0			0
$473$	1.67590e8	−	2.90274e8i	1.58367	−	2.74300i
$474$		0			0
$475$	−1.73422e7	−	2.20314e7i	−0.161817	−	0.205571i
$476$		0			0
$477$	1.81869e8	+	1.05002e8i	1.67573	+	0.967481i
$478$		0			0
$479$	−2.06635e7	−	3.57903e7i	−0.188017	−	0.325655i	0.756572	−	0.653911i	$-0.226873\pi$
$479$	−2.06635e7	−	3.57903e7i	−0.188017	−	0.325655i	−0.944589	+	0.328255i	$0.893539\pi$
$480$		0			0
$481$	−4.86303e7	−	8.42301e7i	−0.436990	−	0.756889i
$482$		0			0
$483$		−	4.91219e7i		−	0.435947i
$484$		0			0
$485$	−1.44810e8	+	8.36063e7i	−1.26933	+	0.732848i
$486$		0			0
$487$		−	3.96183e7i		−	0.343012i	−0.985183	−	0.171506i	$-0.945137\pi$
$487$		−	3.96183e7i		−	0.343012i	0.985183	−	0.171506i	$-0.0548633\pi$
$488$		0			0
$489$	1.04925e8	+	6.05783e7i	0.897327	+	0.518072i
$490$		0			0
$491$	8.04409e7	−	1.39328e8i	0.679568	−	1.17705i	−0.295544	−	0.955329i	$-0.595501\pi$
$491$	8.04409e7	−	1.39328e8i	0.679568	−	1.17705i	0.975111	−	0.221716i	$-0.0711659\pi$
$492$		0			0
$493$			1.62760e8i			1.35833i
$494$		0			0
$495$	3.45967e8			2.85246
$496$		0			0
$497$	−8.46849e7	−	4.88928e7i	−0.689821	−	0.398269i
$498$		0			0
$499$	−4.58279e7	+	7.93762e7i	−0.368832	+	0.638835i	−0.989383	−	0.145330i	$-0.953575\pi$
$499$	−4.58279e7	+	7.93762e7i	−0.368832	+	0.638835i	0.620551	+	0.784166i	$0.286909\pi$
$500$		0			0
$501$	2.30575e8			1.83358
$502$		0			0
$503$	−2.91135e7	−	5.04260e7i	−0.228765	−	0.396233i	0.728677	−	0.684857i	$-0.240135\pi$
$503$	−2.91135e7	−	5.04260e7i	−0.228765	−	0.396233i	−0.957442	+	0.288624i	$0.906802\pi$
$504$		0			0
$505$	1.10450e8			0.857612
$506$		0			0
$507$	−1.13115e8	+	6.53070e7i	−0.867953	+	0.501113i
$508$		0			0
$509$	1.04940e8	−	6.05869e7i	0.795767	−	0.459436i	−0.0462221	−	0.998931i	$-0.514718\pi$
$509$	1.04940e8	−	6.05869e7i	0.795767	−	0.459436i	0.841989	+	0.539495i	$0.181385\pi$
$510$		0			0
$511$	2.30933e7	−	3.99988e7i	0.173071	−	0.299767i
$512$		0			0
$513$	1.23854e7	+	8.58609e7i	0.0917400	+	0.635980i
$514$		0			0
$515$	4.92821e7	+	2.84530e7i	0.360801	+	0.208308i
$516$		0			0
$517$	−1.31446e8	−	2.27671e8i	−0.951209	−	1.64754i
$518$		0			0
$519$	−4.21202e7	−	7.29543e7i	−0.301292	−	0.521854i
$520$		0			0
$521$			2.64963e8i			1.87358i	0.349891	+	0.936790i	$0.386219\pi$
$521$			2.64963e8i			1.87358i	−0.349891	+	0.936790i	$0.613781\pi$
$522$		0			0
$523$	−3.17106e7	+	1.83081e7i	−0.221666	+	0.127979i	−0.606722	−	0.794914i	$-0.707516\pi$
$523$	−3.17106e7	+	1.83081e7i	−0.221666	+	0.127979i	0.385055	+	0.922894i	$0.374182\pi$
$524$		0			0
$525$			3.93499e7i			0.271935i
$526$		0			0
$527$	6.20717e7	+	3.58371e7i	0.424094	+	0.244851i
$528$		0			0
$529$	6.09980e7	−	1.05652e8i	0.412049	−	0.713690i
$530$		0			0
$531$		−	1.81649e8i		−	1.21325i
$532$		0			0
$533$	−2.90256e7			−0.191690
$534$		0			0
$535$	2.66376e8	+	1.53792e8i	1.73954	+	1.00432i
$536$		0			0
$537$	9.75727e7	−	1.69001e8i	0.630094	−	1.09136i
$538$		0			0
$539$	1.55387e8			0.992315
$540$		0			0
$541$	−1.09170e8	−	1.89088e8i	−0.689463	−	1.19418i	−0.972012	−	0.234932i	$-0.924513\pi$
$541$	−1.09170e8	−	1.89088e8i	−0.689463	−	1.19418i	0.282549	−	0.959253i	$-0.408820\pi$
$542$		0			0
$543$	2.29930e8			1.43614
$544$		0			0
$545$	2.84135e7	−	1.64046e7i	0.175524	−	0.101339i
$546$		0			0
$547$	5.62038e7	−	3.24493e7i	0.343403	−	0.198264i	−0.318373	−	0.947966i	$-0.603136\pi$
$547$	5.62038e7	−	3.24493e7i	0.343403	−	0.198264i	0.661776	+	0.749702i	$0.269803\pi$
$548$		0			0
$549$	−4.43456e7	+	7.68089e7i	−0.267999	+	0.464189i
$550$		0			0
$551$	−1.56711e8	+	1.23356e8i	−0.936794	+	0.737404i
$552$		0			0
$553$	−8.11497e7	−	4.68518e7i	−0.479857	−	0.277045i
$554$		0			0
$555$	−2.18826e8	−	3.79018e8i	−1.28003	−	2.21708i
$556$		0			0
$557$	6.42428e7	+	1.11272e8i	0.371757	+	0.643902i	0.989836	−	0.142214i	$-0.0454221\pi$
$557$	6.42428e7	+	1.11272e8i	0.371757	+	0.643902i	−0.618079	+	0.786116i	$0.712089\pi$
$558$		0			0
$559$		−	1.83463e8i		−	1.05030i
$560$		0			0
$561$	−4.86225e8	+	2.80722e8i	−2.75390	+	1.58997i
$562$		0			0
$563$			1.65443e8i			0.927094i	0.886072	+	0.463547i	$0.153424\pi$
$563$			1.65443e8i			0.927094i	−0.886072	+	0.463547i	$0.846576\pi$
$564$		0			0
$565$	−2.20260e8	−	1.27167e8i	−1.22121	−	0.705067i
$566$		0			0
$567$	−2.53267e7	+	4.38672e7i	−0.138941	+	0.240652i
$568$		0			0
$569$			9.56660e7i			0.519303i	0.965702	+	0.259652i	$0.0836077\pi$
$569$			9.56660e7i			0.519303i	−0.965702	+	0.259652i	$0.916392\pi$
$570$		0			0
$571$	9.14624e6			0.0491286			0.0245643	−	0.999698i	$-0.492180\pi$
$571$	9.14624e6			0.0491286			0.0245643	+	0.999698i	$0.492180\pi$
$572$		0			0
$573$	−3.51407e8	−	2.02885e8i	−1.86787	−	1.07841i
$574$		0			0
$575$	1.04298e7	−	1.80650e7i	0.0548622	−	0.0950242i
$576$		0			0
$577$	−3.04795e8			−1.58664			−0.793322	−	0.608802i	$-0.791650\pi$
$577$	−3.04795e8			−1.58664			−0.793322	+	0.608802i	$0.791650\pi$
$578$		0			0
$579$	2.57683e8	+	4.46320e8i	1.32755	+	2.29938i
$580$		0			0
$581$	1.64308e8			0.837782
$582$		0			0
$583$	−4.21997e8	+	2.43640e8i	−2.12963	+	1.22954i
$584$		0			0
$585$	1.63997e8	−	9.46840e7i	0.819161	−	0.472943i
$586$		0			0
$587$	−2.78667e7	+	4.82665e7i	−0.137775	+	0.238634i	−0.926654	−	0.375915i	$-0.877328\pi$
$587$	−2.78667e7	+	4.82665e7i	−0.137775	+	0.238634i	0.788879	+	0.614549i	$0.210662\pi$
$588$		0			0
$589$	1.25390e7	+	8.69257e7i	0.0613646	+	0.425405i
$590$		0			0
$591$	−3.78945e6	−	2.18784e6i	−0.0183575	−	0.0105987i
$592$		0			0
$593$	8.28328e7	+	1.43471e8i	0.397227	+	0.688017i	0.993383	−	0.114852i	$-0.0366394\pi$
$593$	8.28328e7	+	1.43471e8i	0.397227	+	0.688017i	−0.596156	+	0.802869i	$0.703306\pi$
$594$		0			0
$595$	−9.01792e7	−	1.56195e8i	−0.428110	−	0.741509i
$596$		0			0
$597$			6.11163e8i			2.87233i
$598$		0			0
$599$	7.86342e7	−	4.53995e7i	0.365874	−	0.211237i	−0.305781	−	0.952102i	$-0.598917\pi$
$599$	7.86342e7	−	4.53995e7i	0.365874	−	0.211237i	0.671654	+	0.740865i	$0.265584\pi$
$600$		0			0
$601$		−	3.23302e8i		−	1.48931i	−0.667450	−	0.744655i	$-0.732614\pi$
$601$		−	3.23302e8i		−	1.48931i	0.667450	−	0.744655i	$-0.267386\pi$
$602$		0			0
$603$	5.23107e7	+	3.02016e7i	0.238582	+	0.137746i
$604$		0			0
$605$	−2.77015e8	+	4.79805e8i	−1.25094	+	2.16670i
$606$		0			0
$607$		−	3.15351e8i		−	1.41003i	−0.709194	−	0.705014i	$-0.750941\pi$
$607$		−	3.15351e8i		−	1.41003i	0.709194	−	0.705014i	$-0.249059\pi$
$608$		0			0
$609$	2.79898e8			1.23922
$610$		0			0
$611$	−1.24618e8	−	7.19480e7i	−0.546331	−	0.315424i
$612$		0			0
$613$	1.57153e7	−	2.72198e7i	0.0682248	−	0.118169i	−0.829895	−	0.557919i	$-0.811600\pi$
$613$	1.57153e7	−	2.72198e7i	0.0682248	−	0.118169i	0.898120	+	0.439751i	$0.144933\pi$
$614$		0			0
$615$	−1.30609e8			−0.561499
$616$		0			0
$617$	2.53739e7	+	4.39490e7i	0.108027	+	0.187108i	0.914971	−	0.403520i	$-0.132213\pi$
$617$	2.53739e7	+	4.39490e7i	0.108027	+	0.187108i	−0.806944	+	0.590628i	$0.798880\pi$
$618$		0			0
$619$	−3.73627e7			−0.157531			−0.0787656	−	0.996893i	$-0.525098\pi$
$619$	−3.73627e7			−0.157531			−0.0787656	+	0.996893i	$0.525098\pi$
$620$		0			0
$621$	−5.58929e7	+	3.22698e7i	−0.233390	+	0.134748i
$622$		0			0
$623$	−1.66508e8	+	9.61336e7i	−0.688608	+	0.397568i
$624$		0			0
$625$	1.45651e8	−	2.52275e8i	0.596587	−	1.03332i
$626$		0			0
$627$	−6.38799e8	−	2.55394e8i	−2.59156	−	1.03612i
$628$		0			0
$629$	3.60241e8	+	2.07985e8i	1.44757	+	0.835757i
$630$		0			0
$631$	2.25428e8	+	3.90452e8i	0.897262	+	1.55410i	0.830979	+	0.556303i	$0.187781\pi$
$631$	2.25428e8	+	3.90452e8i	0.897262	+	1.55410i	0.0662831	+	0.997801i	$0.478886\pi$
$632$		0			0
$633$	−3.44344e8	−	5.96421e8i	−1.35763	−	2.35148i
$634$		0			0
$635$		−	1.31779e8i		−	0.514664i
$636$		0			0
$637$	7.36576e7	−	4.25263e7i	0.284970	−	0.164528i
$638$		0			0
$639$			4.39107e8i			1.68294i
$640$		0			0
$641$	−1.75198e8	−	1.01151e8i	−0.665206	−	0.384057i	0.129052	−	0.991638i	$-0.458807\pi$
$641$	−1.75198e8	−	1.01151e8i	−0.665206	−	0.384057i	−0.794258	+	0.607581i	$0.792140\pi$
$642$		0			0
$643$	−1.12127e8	+	1.94209e8i	−0.421770	+	0.730527i	−0.996113	−	0.0880877i	$-0.971924\pi$
$643$	−1.12127e8	+	1.94209e8i	−0.421770	+	0.730527i	0.574343	+	0.818615i	$0.305258\pi$
$644$		0			0
$645$		−	8.25548e8i		−	3.07654i
$646$		0			0
$647$	2.54305e8			0.938947			0.469474	−	0.882946i	$-0.344444\pi$
$647$	2.54305e8			0.938947			0.469474	+	0.882946i	$0.344444\pi$
$648$		0			0
$649$	3.65019e8	+	2.10744e8i	1.33531	+	0.770940i
$650$		0			0
$651$	6.16290e7	−	1.06745e8i	0.223379	−	0.386904i
$652$		0			0
$653$	2.32989e8			0.836749			0.418375	−	0.908275i	$-0.362600\pi$
$653$	2.32989e8			0.836749			0.418375	+	0.908275i	$0.362600\pi$
$654$		0			0
$655$	7.34398e7	+	1.27201e8i	0.261341	+	0.452656i
$656$		0			0
$657$	−2.07401e8			−0.731334
$658$		0			0
$659$	3.85410e8	−	2.22516e8i	1.34669	−	0.777510i	0.358908	−	0.933373i	$-0.383149\pi$
$659$	3.85410e8	−	2.22516e8i	1.34669	−	0.777510i	0.987779	+	0.155863i	$0.0498160\pi$
$660$		0			0
$661$	3.45375e8	−	1.99402e8i	1.19588	−	0.690439i	0.236242	−	0.971694i	$-0.424084\pi$
$661$	3.45375e8	−	1.99402e8i	1.19588	−	0.690439i	0.959633	+	0.281255i	$0.0907507\pi$
$662$		0			0
$663$	−1.53655e8	+	2.66139e8i	−0.527238	+	0.913204i
$664$		0			0
$665$	8.20430e7	−	2.05208e8i	0.278982	−	0.697798i
$666$		0			0
$667$	−1.28497e8	−	7.41879e7i	−0.433028	−	0.250009i
$668$		0			0
$669$	2.14027e8	+	3.70706e8i	0.714809	+	1.23809i
$670$		0			0
$671$	−1.02897e8	−	1.78223e8i	−0.340593	−	0.589924i
$672$		0			0
$673$			4.97946e8i			1.63357i	0.576944	+	0.816784i	$0.304245\pi$
$673$			4.97946e8i			1.63357i	−0.576944	+	0.816784i	$0.695755\pi$
$674$		0			0
$675$	4.47740e7	−	2.58503e7i	0.145584	−	0.0840531i
$676$		0			0
$677$		−	4.71221e8i		−	1.51865i	−0.650710	−	0.759326i	$-0.725529\pi$
$677$		−	4.71221e8i		−	1.51865i	0.650710	−	0.759326i	$-0.274471\pi$
$678$		0			0
$679$	−2.36693e8	−	1.36655e8i	−0.756093	−	0.436531i
$680$		0			0
$681$	2.64701e8	−	4.58476e8i	0.838136	−	1.45169i
$682$		0			0
$683$		−	3.99183e8i		−	1.25288i	−0.779469	−	0.626441i	$-0.784511\pi$
$683$		−	3.99183e8i		−	1.25288i	0.779469	−	0.626441i	$-0.215489\pi$
$684$		0			0
$685$	−3.24076e8			−1.00827
$686$		0			0
$687$	4.02217e7	+	2.32220e7i	0.124048	+	0.0716193i
$688$		0			0
$689$	−1.33358e8	+	2.30984e8i	−0.407721	+	0.706193i
$690$		0			0
$691$	1.50631e8			0.456543			0.228271	−	0.973598i	$-0.426693\pi$
$691$	1.50631e8			0.456543			0.228271	+	0.973598i	$0.426693\pi$
$692$		0			0
$693$	2.82742e8	+	4.89724e8i	0.849553	+	1.47147i
$694$		0			0
$695$	5.90251e8			1.75826
$696$		0			0
$697$	1.07507e8	−	6.20694e7i	0.317497	−	0.183307i
$698$		0			0
$699$	4.78989e8	−	2.76545e8i	1.40247	−	0.809718i
$700$		0			0
$701$	−8.65506e7	+	1.49910e8i	−0.251256	+	0.435188i	−0.963872	−	0.266366i	$-0.914177\pi$
$701$	−8.65506e7	+	1.49910e8i	−0.251256	+	0.435188i	0.712616	+	0.701554i	$0.247510\pi$
$702$		0			0
$703$	7.27717e7	+	5.04484e8i	0.209458	+	1.45205i
$704$		0			0
$705$	−5.60754e8	−	3.23751e8i	−1.60031	−	0.923941i
$706$		0			0
$707$	9.02652e7	+	1.56344e8i	0.255424	+	0.442408i
$708$		0			0
$709$	1.02388e8	+	1.77340e8i	0.287282	+	0.497587i	0.973160	−	0.230129i	$-0.0739150\pi$
$709$	1.02388e8	+	1.77340e8i	0.287282	+	0.497587i	−0.685878	+	0.727717i	$0.740582\pi$
$710$		0			0
$711$			4.20777e8i			1.17069i
$712$		0			0
$713$	−5.65860e7	+	3.26700e7i	−0.156114	+	0.0901322i
$714$		0			0
$715$			4.39398e8i			1.20210i
$716$		0			0
$717$	−9.88384e8	−	5.70644e8i	−2.68144	−	1.54813i
$718$		0			0
$719$	−2.50978e8	+	4.34707e8i	−0.675226	+	1.16953i	0.301177	+	0.953568i	$0.402620\pi$
$719$	−2.50978e8	+	4.34707e8i	−0.675226	+	1.16953i	−0.976403	+	0.215957i	$0.930713\pi$
$720$		0			0
$721$			9.30130e7i			0.248163i
$722$		0			0
$723$	−5.08266e7			−0.134486
$724$		0			0
$725$	1.02935e8	+	5.94295e7i	0.270115	+	0.155951i
$726$		0			0
$727$	2.91970e8	−	5.05707e8i	0.759862	−	1.31612i	−0.183058	−	0.983102i	$-0.558600\pi$
$727$	2.91970e8	−	5.05707e8i	0.759862	−	1.31612i	0.942920	−	0.333018i	$-0.108067\pi$
$728$		0			0
$729$	6.14210e8			1.58538
$730$		0			0
$731$	3.92324e8	+	6.79525e8i	1.00437	+	1.73962i
$732$		0			0
$733$	1.45519e8			0.369493			0.184747	−	0.982786i	$-0.440854\pi$
$733$	1.45519e8			0.369493			0.184747	+	0.982786i	$0.440854\pi$
$734$		0			0
$735$	3.31444e8	−	1.91360e8i	0.834735	−	0.481934i
$736$		0			0
$737$	−1.21379e8	+	7.00780e7i	−0.303207	+	0.175057i
$738$		0			0
$739$	9.05558e7	−	1.56847e8i	0.224379	−	0.388636i	−0.731754	−	0.681569i	$-0.761298\pi$
$739$	9.05558e7	−	1.56847e8i	0.224379	−	0.388636i	0.956133	+	0.292933i	$0.0946312\pi$
$740$		0			0
$741$	−3.72703e8	+	5.37623e7i	−0.916027	+	0.132137i
$742$		0			0
$743$	3.76885e8	+	2.17595e8i	0.918846	+	0.530496i	0.883267	−	0.468871i	$-0.155339\pi$
$743$	3.76885e8	+	2.17595e8i	0.918846	+	0.530496i	0.0355794	+	0.999367i	$0.488672\pi$
$744$		0			0
$745$	−2.65339e8	−	4.59581e8i	−0.641701	−	1.11146i
$746$		0			0
$747$	−3.68914e8	−	6.38977e8i	−0.885040	−	1.53293i
$748$		0			0
$749$			5.02747e8i			1.19648i
$750$		0			0
$751$	−2.51454e8	+	1.45177e8i	−0.593660	+	0.342750i	−0.766544	−	0.642192i	$-0.778025\pi$
$751$	−2.51454e8	+	1.45177e8i	−0.593660	+	0.342750i	0.172883	+	0.984942i	$0.444692\pi$
$752$		0			0
$753$		−	4.52787e8i		−	1.06050i
$754$		0			0
$755$	2.16709e8	+	1.25117e8i	0.503541	+	0.290720i
$756$		0			0
$757$	1.12548e8	−	1.94940e8i	0.259449	−	0.449379i	−0.706645	−	0.707568i	$-0.749792\pi$
$757$	1.12548e8	−	1.94940e8i	0.259449	−	0.449379i	0.966094	+	0.258189i	$0.0831257\pi$
$758$		0			0
$759$		−	5.11826e8i		−	1.17057i
$760$		0			0
$761$	3.68003e8			0.835020			0.417510	−	0.908672i	$-0.362903\pi$
$761$	3.68003e8			0.835020			0.417510	+	0.908672i	$0.362903\pi$
$762$		0			0
$763$	4.64419e7	+	2.68133e7i	0.104553	+	0.0603637i
$764$		0			0
$765$	−4.04951e8	+	7.01395e8i	−0.904519	+	1.56667i
$766$		0			0
$767$	2.30704e8			0.511293
$768$		0			0
$769$	1.19879e7	+	2.07636e7i	0.0263610	+	0.0456587i	0.878905	−	0.476997i	$-0.158275\pi$
$769$	1.19879e7	+	2.07636e7i	0.0263610	+	0.0456587i	−0.852544	+	0.522656i	$0.824941\pi$
$770$		0			0
$771$	−2.52947e8			−0.551908
$772$		0			0
$773$	4.57142e8	−	2.63931e8i	0.989721	−	0.571416i	0.0845302	−	0.996421i	$-0.473061\pi$
$773$	4.57142e8	−	2.63931e8i	0.989721	−	0.571416i	0.905191	+	0.425005i	$0.139728\pi$
$774$		0			0
$775$	4.53292e7	−	2.61708e7i	0.0973808	−	0.0562228i
$776$		0			0
$777$	3.57672e8	−	6.19506e8i	0.762468	−	1.32063i
$778$		0			0
$779$	1.41242e8	+	5.64693e7i	0.298781	+	0.119454i
$780$		0			0
$781$	−8.82375e8	−	5.09439e8i	−1.85225	−	1.06940i
$782$		0			0
$783$	−1.83874e8	−	3.18480e8i	−0.383033	−	0.663432i
$784$		0			0
$785$	−1.66700e8	−	2.88734e8i	−0.344610	−	0.596882i
$786$		0			0
$787$		−	1.42717e8i		−	0.292787i	−0.989226	−	0.146393i	$-0.953233\pi$
$787$		−	1.42717e8i		−	0.292787i	0.989226	−	0.146393i	$-0.0467665\pi$
$788$		0			0
$789$	−2.84048e8	+	1.63995e8i	−0.578311	+	0.333888i
$790$		0			0
$791$		−	4.15710e8i		−	0.839966i
$792$		0			0
$793$	−9.75516e7	−	5.63215e7i	−0.195621	−	0.112942i
$794$		0			0
$795$	−6.00086e8	+	1.03938e9i	−1.19430	+	2.06858i
$796$		0			0
$797$			4.07190e8i			0.804308i	0.915572	+	0.402154i	$0.131738\pi$
$797$			4.07190e8i			0.804308i	−0.915572	+	0.402154i	$0.868262\pi$
$798$		0			0
$799$	6.15424e8			1.20652
$800$		0			0
$801$	7.47707e8	+	4.31689e8i	1.45490	+	0.839988i
$802$		0			0
$803$	2.40621e8	−	4.16768e8i	0.464715	−	0.804910i
$804$		0			0
$805$	1.64419e8			0.315184
$806$		0			0
$807$	−4.30002e8	−	7.44785e8i	−0.818182	−	1.41713i
$808$		0			0
$809$	−4.87624e7			−0.0920958			−0.0460479	−	0.998939i	$-0.514663\pi$
$809$	−4.87624e7			−0.0920958			−0.0460479	+	0.998939i	$0.514663\pi$
$810$		0			0
$811$	8.71113e7	−	5.02938e7i	0.163310	−	0.0942869i	−0.416118	−	0.909311i	$-0.636610\pi$
$811$	8.71113e7	−	5.02938e7i	0.163310	−	0.0942869i	0.579427	+	0.815024i	$0.303276\pi$
$812$		0			0
$813$	−3.03710e8	+	1.75347e8i	−0.565181	+	0.326308i
$814$		0			0
$815$	−2.02766e8	+	3.51200e8i	−0.374560	+	0.648757i
$816$		0			0
$817$	−3.56927e8	+	8.92756e8i	−0.654506	+	1.63707i
$818$		0			0
$819$	2.68054e8	+	1.54761e8i	0.487945	+	0.281715i
$820$		0			0
$821$	−7.09385e7	−	1.22869e8i	−0.128189	−	0.222031i	0.794786	−	0.606890i	$-0.207583\pi$
$821$	−7.09385e7	−	1.22869e8i	−0.128189	−	0.222031i	−0.922975	+	0.384860i	$0.874250\pi$
$822$		0			0
$823$	−4.33452e8	−	7.50760e8i	−0.777573	−	1.34680i	−0.933337	−	0.359001i	$-0.883117\pi$
$823$	−4.33452e8	−	7.50760e8i	−0.777573	−	1.34680i	0.155764	−	0.987794i	$-0.450216\pi$
$824$		0			0
$825$			4.10007e8i			0.730179i
$826$		0			0
$827$	−4.64027e8	+	2.67906e8i	−0.820403	+	0.473660i	−0.850555	−	0.525886i	$-0.823734\pi$
$827$	−4.64027e8	+	2.67906e8i	−0.820403	+	0.473660i	0.0301526	+	0.999545i	$0.490401\pi$
$828$		0			0
$829$			3.33270e8i			0.584969i	0.956270	+	0.292484i	$0.0944819\pi$
$829$			3.33270e8i			0.584969i	−0.956270	+	0.292484i	$0.905518\pi$
$830$		0			0
$831$	1.08415e9	+	6.25935e8i	1.88924	+	1.09075i
$832$		0			0
$833$	−1.81879e8	+	3.15024e8i	−0.314664	+	0.545015i
$834$		0			0
$835$			7.71773e8i			1.32565i
$836$		0			0
$837$	−1.61945e8			−0.276179
$838$		0			0
$839$	9.73553e7	+	5.62081e7i	0.164844	+	0.0951729i	0.580153	−	0.814508i	$-0.302993\pi$
$839$	9.73553e7	+	5.62081e7i	0.164844	+	0.0951729i	−0.415308	+	0.909681i	$0.636326\pi$
$840$		0			0
$841$	1.25314e8	−	2.17050e8i	0.210674	−	0.364898i
$842$		0			0
$843$	7.92849e7			0.132345
$844$		0			0
$845$	−2.18593e8	−	3.78615e8i	−0.362299	−	0.627520i
$846$		0			0
$847$	−9.05564e8			−1.49028
$848$		0			0
$849$	−7.62456e8	+	4.40204e8i	−1.24592	+	0.719335i
$850$		0			0
$851$	−3.28404e8	+	1.89604e8i	−0.532868	+	0.307652i
$852$		0			0
$853$	3.35920e8	−	5.81831e8i	0.541239	−	0.937454i	−0.457594	−	0.889161i	$-0.651289\pi$
$853$	3.35920e8	−	5.81831e8i	0.541239	−	0.937454i	0.998833	−	0.0482924i	$-0.0153779\pi$
$854$		0			0
$855$	−9.82240e8	+	1.41688e8i	−1.57152	+	0.226691i
$856$		0			0
$857$	−8.80294e8	−	5.08238e8i	−1.39857	−	0.807467i	−0.404330	−	0.914613i	$-0.632495\pi$
$857$	−8.80294e8	−	5.08238e8i	−1.39857	−	0.807467i	−0.994243	+	0.107147i	$0.965829\pi$
$858$		0			0
$859$	−5.37147e7	−	9.30366e7i	−0.0847449	−	0.146782i	0.820538	−	0.571593i	$-0.193674\pi$
$859$	−5.37147e7	−	9.30366e7i	−0.0847449	−	0.146782i	−0.905282	+	0.424810i	$0.860341\pi$
$860$		0			0
$861$	−1.06741e8	−	1.84880e8i	−0.167232	−	0.289655i
$862$		0			0
$863$		−	6.87740e8i		−	1.07002i	−0.844846	−	0.535010i	$-0.820308\pi$
$863$		−	6.87740e8i		−	1.07002i	0.844846	−	0.535010i	$-0.179692\pi$
$864$		0			0
$865$	2.44190e8	−	1.40983e8i	0.377294	−	0.217831i
$866$		0			0
$867$		−	3.01838e8i		−	0.463144i
$868$		0			0
$869$	−8.45540e8	−	4.88173e8i	−1.28847	−	0.743899i
$870$		0			0
$871$	−3.83577e7	+	6.64375e7i	−0.0580495	+	0.100545i
$872$		0			0
$873$			1.22730e9i			1.84462i
$874$		0			0
$875$	3.71736e8			0.554894
$876$		0			0
$877$	−7.61892e8	−	4.39879e8i	−1.12952	−	0.652130i	−0.185707	−	0.982605i	$-0.559458\pi$
$877$	−7.61892e8	−	4.39879e8i	−1.12952	−	0.652130i	−0.943815	+	0.330475i	$0.892791\pi$
$878$		0			0
$879$	−3.48113e8	+	6.02949e8i	−0.512570	+	0.887798i
$880$		0			0
$881$	−5.10791e8			−0.746991			−0.373496	−	0.927632i	$-0.621841\pi$
$881$	−5.10791e8			−0.746991			−0.373496	+	0.927632i	$0.621841\pi$
$882$		0			0
$883$	5.27159e8	+	9.13066e8i	0.765702	+	1.32623i	0.939875	+	0.341519i	$0.110941\pi$
$883$	5.27159e8	+	9.13066e8i	0.765702	+	1.32623i	−0.174173	+	0.984715i	$0.555725\pi$
$884$		0			0
$885$	1.03812e9			1.49768
$886$		0			0
$887$	−4.85026e8	+	2.80030e8i	−0.695015	+	0.401267i	−0.805488	−	0.592612i	$-0.798097\pi$
$887$	−4.85026e8	+	2.80030e8i	−0.695015	+	0.401267i	0.110473	+	0.993879i	$0.464763\pi$
$888$		0			0
$889$	1.86535e8	−	1.07696e8i	0.265495	−	0.153283i
$890$		0			0
$891$	−2.63892e8	+	4.57074e8i	−0.373072	+	0.646180i
$892$		0			0
$893$	4.66431e8	+	5.92551e8i	0.654987	+	0.832092i
$894$		0			0
$895$	5.65674e8	+	3.26592e8i	0.789037	+	0.455551i
$896$		0			0
$897$	−1.40076e8	−	2.42619e8i	−0.194082	−	0.336160i
$898$		0			0
$899$	−1.86155e8	−	3.22429e8i	−0.256209	−	0.443767i
$900$		0			0
$901$		−	1.14071e9i		−	1.55956i
$902$		0			0
$903$	1.16858e9	−	6.74679e8i	1.58707	−	0.916293i
$904$		0			0
$905$			7.69616e8i			1.03831i
$906$		0			0
$907$	4.49999e8	+	2.59807e8i	0.603101	+	0.348201i	0.770261	−	0.637729i	$-0.220126\pi$
$907$	4.49999e8	+	2.59807e8i	0.603101	+	0.348201i	−0.167159	+	0.985930i	$0.553459\pi$
$908$		0			0
$909$	4.05337e8	−	7.02064e8i	0.539665	−	0.934727i
$910$		0			0
$911$		−	5.61058e8i		−	0.742083i	−0.928616	−	0.371041i	$-0.879001\pi$
$911$		−	5.61058e8i		−	0.742083i	0.928616	−	0.371041i	$-0.120999\pi$
$912$		0			0
$913$	1.71201e9			2.24954
$914$		0			0
$915$	−4.38963e8	−	2.53435e8i	−0.573013	−	0.330829i
$916$		0			0
$917$	−1.20037e8	+	2.07911e8i	−0.155671	+	0.269631i
$918$		0			0
$919$	−1.49412e9			−1.92504			−0.962519	−	0.271214i	$-0.912575\pi$
$919$	−1.49412e9			−1.92504			−0.962519	+	0.271214i	$0.912575\pi$
$920$		0			0
$921$	3.09234e8	+	5.35609e8i	0.395830	+	0.685597i
$922$		0			0
$923$	−5.57691e8			−0.709233
$924$		0			0
$925$	2.63074e8	−	1.51886e8i	0.332393	−	0.191907i
$926$		0			0
$927$	3.61718e8	−	2.08838e8i	0.454078	−	0.262162i
$928$		0			0
$929$	7.99812e7	−	1.38531e8i	0.0997563	−	0.172783i	−0.811827	−	0.583897i	$-0.801527\pi$
$929$	7.99812e7	−	1.38531e8i	0.0997563	−	0.172783i	0.911584	+	0.411114i	$0.134860\pi$
$930$		0			0
$931$	−4.41162e8	+	6.36375e7i	−0.546700	+	0.0788614i
$932$		0			0
$933$	1.84278e9	+	1.06393e9i	2.26897	+	1.30999i
$934$		0			0
$935$	−9.39623e8	−	1.62747e9i	−1.14953	−	1.99104i
$936$		0			0
$937$	4.42947e8	+	7.67206e8i	0.538434	+	0.932595i	0.998989	+	0.0449639i	$0.0143173\pi$
$937$	4.42947e8	+	7.67206e8i	0.538434	+	0.932595i	−0.460554	+	0.887631i	$0.652349\pi$
$938$		0			0
$939$		−	6.16622e8i		−	0.744770i
$940$		0			0
$941$	1.22133e9	−	7.05136e8i	1.46577	−	0.846260i	0.466498	−	0.884522i	$-0.345515\pi$
$941$	1.22133e9	−	7.05136e8i	1.46577	−	0.846260i	0.999268	+	0.0382620i	$0.0121821\pi$
$942$		0			0
$943$			1.13168e8i			0.134955i
$944$		0			0
$945$	3.52915e8	+	2.03756e8i	0.418192	+	0.241443i
$946$		0			0
$947$	1.60795e8	−	2.78506e8i	0.189332	−	0.327933i	−0.755696	−	0.654923i	$-0.772701\pi$
$947$	1.60795e8	−	2.78506e8i	0.189332	−	0.327933i	0.945028	+	0.326990i	$0.106034\pi$
$948$		0			0
$949$		−	2.63412e8i		−	0.308202i
$950$		0			0
$951$	−9.79237e8			−1.13853
$952$		0			0
$953$	1.17909e8	+	6.80750e7i	0.136229	+	0.0786519i	0.566566	−	0.824017i	$-0.308272\pi$
$953$	1.17909e8	+	6.80750e7i	0.136229	+	0.0786519i	−0.430337	+	0.902669i	$0.641605\pi$
$954$		0			0
$955$	6.79089e8	−	1.17622e9i	0.779681	−	1.35045i
$956$		0			0
$957$	2.91640e9			3.32745
$958$		0			0
$959$	−2.64852e8	−	4.58737e8i	−0.300294	−	0.520125i
$960$		0			0
$961$	7.23551e8			0.815265
$962$		0			0
$963$	1.95513e9	−	1.12879e9i	2.18926	−	1.26397i
$964$		0			0
$965$	−1.49391e9	+	8.62508e8i	−1.66242	+	0.959801i
$966$		0			0
$967$	2.00743e8	−	3.47698e8i	0.222005	−	0.384523i	−0.733412	−	0.679784i	$-0.762073\pi$
$967$	2.00743e8	−	3.47698e8i	0.222005	−	0.384523i	0.955417	+	0.295261i	$0.0954067\pi$
$968$		0			0
$969$	1.26548e9	−	9.96130e8i	1.39086	−	1.09482i
$970$		0			0
$971$	1.13136e9	+	6.53189e8i	1.23578	+	0.713479i	0.968229	−	0.250064i	$-0.0804515\pi$
$971$	1.13136e9	+	6.53189e8i	1.23578	+	0.713479i	0.267553	+	0.963543i	$0.413785\pi$
$972$		0			0
$973$	4.82383e8	+	8.35512e8i	0.523665	+	0.907014i
$974$		0			0
$975$	1.12210e8	+	1.94354e8i	0.121065	+	0.209691i
$976$		0			0
$977$			1.73565e8i			0.186114i	0.995661	+	0.0930571i	$0.0296639\pi$
$977$			1.73565e8i			0.186114i	−0.995661	+	0.0930571i	$0.970336\pi$
$978$		0			0
$979$	−1.73494e9	+	1.00167e9i	−1.84899	+	1.06752i
$980$		0			0
$981$		−	2.40810e8i		−	0.255075i
$982$		0			0
$983$	−1.88296e8	−	1.08713e8i	−0.198235	−	0.114451i	0.397597	−	0.917560i	$-0.369844\pi$
$983$	−1.88296e8	−	1.08713e8i	−0.198235	−	0.114451i	−0.595832	+	0.803109i	$0.703178\pi$
$984$		0			0
$985$	7.32306e6	−	1.26839e7i	0.00766274	−	0.0132722i
$986$		0			0
$987$		−	1.05834e9i		−	1.10072i
$988$		0			0
$989$	−7.15304e8			−0.739438
$990$		0			0
$991$	−1.43410e7	−	8.27979e6i	−0.0147353	−	0.00850743i	0.492614	−	0.870248i	$-0.336041\pi$
$991$	−1.43410e7	−	8.27979e6i	−0.0147353	−	0.00850743i	−0.507350	+	0.861740i	$0.669375\pi$
$992$		0			0
$993$	−1.13128e9	+	1.95943e9i	−1.15537	+	2.00116i
$994$		0			0
$995$	−2.04567e9			−2.07666
$996$		0			0
$997$	−4.56396e8	−	7.90500e8i	−0.460528	−	0.797658i	0.538459	−	0.842651i	$-0.319007\pi$
$997$	−4.56396e8	−	7.90500e8i	−0.460528	−	0.797658i	−0.998987	+	0.0449937i	$0.985673\pi$
$998$		0			0
$999$	−9.39866e8			−0.942691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.h.a.65.10	✓	20
3.2	odd	2		684.7.y.c.217.8		20
19.12	odd	6	inner	76.7.h.a.69.10	yes	20
57.50	even	6		684.7.y.c.145.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.h.a.65.10	✓	20	1.1	even	1	trivial
76.7.h.a.69.10	yes	20	19.12	odd	6	inner
684.7.y.c.145.8		20	57.50	even	6
684.7.y.c.217.8		20	3.2	odd	2

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.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(36.3268 + 20.9733i) q^{3} +(-70.2011 + 121.592i) q^{5} -229.488 q^{7} +(515.258 + 892.453i) q^{9} +O(q^{10})\)	\(q+(36.3268 + 20.9733i) q^{3} +(-70.2011 + 121.592i) q^{5} -229.488 q^{7} +(515.258 + 892.453i) q^{9} -2391.15 q^{11} +(-1133.47 + 654.407i) q^{13} +(-5100.36 + 2944.70i) q^{15} +(2798.81 - 4847.68i) q^{17} +(6788.73 - 979.273i) q^{19} +(-8336.55 - 4813.11i) q^{21} +(2551.46 + 4419.26i) q^{23} +(-2043.89 - 3540.12i) q^{25} +12647.6i q^{27} +(-25181.1 + 14538.3i) q^{29} +12804.4i q^{31} +(-86862.8 - 50150.2i) q^{33} +(16110.3 - 27903.8i) q^{35} +74312.0i q^{37} -54900.2 q^{39} +(19205.9 + 11088.5i) q^{41} +(-70087.7 + 121395. i) q^{43} -144687. q^{45} +(54971.9 + 95214.2i) q^{47} -64984.4 q^{49} +(203344. - 117400. i) q^{51} +(176483. - 101893. i) q^{53} +(167861. - 290744. i) q^{55} +(267152. + 106808. i) q^{57} +(-152654. - 88135.0i) q^{59} +(43032.5 + 74534.4i) q^{61} +(-118245. - 204807. i) q^{63} -183760. i q^{65} +(50761.7 - 29307.3i) q^{67} +214050. i q^{69} +(369017. + 213052. i) q^{71} +(-100630. + 174296. i) q^{73} -171469. i q^{75} +548739. q^{77} +(353613. + 204158. i) q^{79} +(110362. - 191153. i) q^{81} -715979. q^{83} +(392959. + 680625. i) q^{85} -1.21967e6 q^{87} +(725566. - 418906. i) q^{89} +(260116. - 150178. i) q^{91} +(-268551. + 465143. i) q^{93} +(-357505. + 894201. i) q^{95} +(1.03140e6 + 595477. i) q^{97} +(-1.23206e6 - 2.13399e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9} - 3644 q^{11} - 7140 q^{13} + 9168 q^{15} + 1132 q^{17} + 2110 q^{19} - 8748 q^{21} + 832 q^{23} - 27698 q^{25} - 10920 q^{29} - 30306 q^{33} + 4172 q^{35} + 81144 q^{39} + 109206 q^{41} + 110740 q^{43} - 785440 q^{45} + 107080 q^{47} + 136092 q^{49} + 199872 q^{51} + 254796 q^{53} + 354840 q^{55} + 212268 q^{57} - 610638 q^{59} + 47864 q^{61} - 254476 q^{63} - 839562 q^{67} + 366660 q^{71} + 854482 q^{73} + 763088 q^{77} + 1718592 q^{79} - 1054142 q^{81} + 439612 q^{83} - 400236 q^{85} - 1604736 q^{87} + 478032 q^{89} + 599856 q^{91} + 829380 q^{93} - 1055660 q^{95} - 191286 q^{97} - 2336728 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9 - 3644 * q^11 - 7140 * q^13 + 9168 * q^15 + 1132 * q^17 + 2110 * q^19 - 8748 * q^21 + 832 * q^23 - 27698 * q^25 - 10920 * q^29 - 30306 * q^33 + 4172 * q^35 + 81144 * q^39 + 109206 * q^41 + 110740 * q^43 - 785440 * q^45 + 107080 * q^47 + 136092 * q^49 + 199872 * q^51 + 254796 * q^53 + 354840 * q^55 + 212268 * q^57 - 610638 * q^59 + 47864 * q^61 - 254476 * q^63 - 839562 * q^67 + 366660 * q^71 + 854482 * q^73 + 763088 * q^77 + 1718592 * q^79 - 1054142 * q^81 + 439612 * q^83 - 400236 * q^85 - 1604736 * q^87 + 478032 * q^89 + 599856 * q^91 + 829380 * q^93 - 1055660 * q^95 - 191286 * q^97 - 2336728 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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