LMFDB - Embedded newform 76.7.h.a.65.4

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			65.4
Root			$-21.8702i$ of defining polynomial
Character	$\chi$	$=$	76.65
Dual form			76.7.h.a.69.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.4402 - 11.8011i) q^{3} +(15.3686 - 26.6192i) q^{5} -77.2273 q^{7} +(-85.9659 - 148.897i) q^{9} +O(q^{10})$	\(q+(-20.4402 - 11.8011i) q^{3} +(15.3686 - 26.6192i) q^{5} -77.2273 q^{7} +(-85.9659 - 148.897i) q^{9} -1577.96 q^{11} +(2818.20 - 1627.09i) q^{13} +(-628.274 + 362.734i) q^{15} +(-3364.22 + 5827.00i) q^{17} +(2770.84 + 6274.42i) q^{19} +(1578.54 + 911.371i) q^{21} +(2290.31 + 3966.93i) q^{23} +(7340.11 + 12713.4i) q^{25} +21264.1i q^{27} +(-22625.8 + 13063.0i) q^{29} +25810.7i q^{31} +(32253.9 + 18621.8i) q^{33} +(-1186.87 + 2055.73i) q^{35} -83385.4i q^{37} -76806.0 q^{39} +(81159.3 + 46857.4i) q^{41} +(-57374.3 + 99375.2i) q^{43} -5284.70 q^{45} +(9487.88 + 16433.5i) q^{47} -111685. q^{49} +(137531. - 79403.3i) q^{51} +(59687.5 - 34460.6i) q^{53} +(-24251.1 + 42004.1i) q^{55} +(17408.9 - 160949. i) q^{57} +(17779.2 + 10264.8i) q^{59} +(39431.6 + 68297.5i) q^{61} +(6638.91 + 11498.9i) q^{63} -100024. i q^{65} +(23781.8 - 13730.4i) q^{67} -108113. i q^{69} +(-345348. - 199387. i) q^{71} +(277015. - 479804. i) q^{73} -346487. i q^{75} +121862. q^{77} +(-424193. - 244908. i) q^{79} +(188271. - 326095. i) q^{81} -516880. q^{83} +(103407. + 179106. i) q^{85} +616633. q^{87} +(-710222. + 410047. i) q^{89} +(-217642. + 125656. i) q^{91} +(304595. - 527575. i) q^{93} +(209604. + 22671.6i) q^{95} +(429465. + 247952. i) q^{97} +(135651. + 234955. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−20.4402	−	11.8011i	−0.757044	−	0.437080i	0.0711895	−	0.997463i	$-0.477320\pi$
$3$	−20.4402	−	11.8011i	−0.757044	−	0.437080i	−0.828233	+	0.560383i	$0.810654\pi$
$4$		0			0
$5$	15.3686	−	26.6192i	0.122949	−	0.212953i	−0.797981	−	0.602683i	$-0.794098\pi$
$5$	15.3686	−	26.6192i	0.122949	−	0.212953i	0.920929	+	0.389730i	$0.127432\pi$
$6$		0			0
$7$	−77.2273			−0.225152			−0.112576	−	0.993643i	$-0.535910\pi$
$7$	−77.2273			−0.225152			−0.112576	+	0.993643i	$0.535910\pi$
$8$		0			0
$9$	−85.9659	−	148.897i	−0.117923	−	0.204249i
$10$		0			0
$11$	−1577.96			−1.18555			−0.592774	−	0.805369i	$-0.701967\pi$
$11$	−1577.96			−1.18555			−0.592774	+	0.805369i	$0.701967\pi$
$12$		0			0
$13$	2818.20	−	1627.09i	1.28275	−	0.740596i	0.305399	−	0.952224i	$-0.401210\pi$
$13$	2818.20	−	1627.09i	1.28275	−	0.740596i	0.977350	+	0.211629i	$0.0678768\pi$
$14$		0			0
$15$	−628.274	+	362.734i	−0.186155	+	0.107477i
$16$		0			0
$17$	−3364.22	+	5827.00i	−0.684759	+	1.18604i	0.288754	+	0.957403i	$0.406759\pi$
$17$	−3364.22	+	5827.00i	−0.684759	+	1.18604i	−0.973513	+	0.228634i	$0.926574\pi$
$18$		0			0
$19$	2770.84	+	6274.42i	0.403971	+	0.914772i
$19$	2770.84	+	6274.42i	0.403971	+	0.914772i
$20$		0			0
$21$	1578.54	+	911.371i	0.170450	+	0.0984095i
$22$		0			0
$23$	2290.31	+	3966.93i	0.188239	+	0.326040i	0.944663	−	0.328042i	$-0.106389\pi$
$23$	2290.31	+	3966.93i	0.188239	+	0.326040i	−0.756424	+	0.654082i	$0.773055\pi$
$24$		0			0
$25$	7340.11	+	12713.4i	0.469767	+	0.813661i
$26$		0			0
$27$			21264.1i			1.08033i
$28$		0			0
$29$	−22625.8	+	13063.0i	−0.927703	+	0.535610i	−0.886084	−	0.463524i	$-0.846585\pi$
$29$	−22625.8	+	13063.0i	−0.927703	+	0.535610i	−0.0416188	+	0.999134i	$0.513251\pi$
$30$		0			0
$31$			25810.7i			0.866391i	0.901300	+	0.433196i	$0.142614\pi$
$31$			25810.7i			0.866391i	−0.901300	+	0.433196i	$0.857386\pi$
$32$		0			0
$33$	32253.9	+	18621.8i	0.897512	+	0.518179i
$34$		0			0
$35$	−1186.87	+	2055.73i	−0.0276822	+	0.0479470i
$36$		0			0
$37$		−	83385.4i		−	1.64621i	−0.567890	−	0.823104i	$-0.692240\pi$
$37$		−	83385.4i		−	1.64621i	0.567890	−	0.823104i	$-0.307760\pi$
$38$		0			0
$39$	−76806.0			−1.29480
$40$		0			0
$41$	81159.3	+	46857.4i	1.17757	+	0.679871i	0.955451	−	0.295149i	$-0.0953693\pi$
$41$	81159.3	+	46857.4i	1.17757	+	0.679871i	0.222119	+	0.975020i	$0.428703\pi$
$42$		0			0
$43$	−57374.3	+	99375.2i	−0.721626	+	1.24989i	0.238722	+	0.971088i	$0.423271\pi$
$43$	−57374.3	+	99375.2i	−0.721626	+	1.24989i	−0.960348	+	0.278804i	$0.910062\pi$
$44$		0			0
$45$	−5284.70			−0.0579939
$46$		0			0
$47$	9487.88	+	16433.5i	0.0913852	+	0.158284i	0.908094	−	0.418766i	$-0.137537\pi$
$47$	9487.88	+	16433.5i	0.0913852	+	0.158284i	−0.816709	+	0.577050i	$0.804204\pi$
$48$		0			0
$49$	−111685.			−0.949306
$50$		0			0
$51$	137531.	−	79403.3i	1.03679	−	0.598588i
$52$		0			0
$53$	59687.5	−	34460.6i	0.400919	−	0.231470i	−0.285962	−	0.958241i	$-0.592313\pi$
$53$	59687.5	−	34460.6i	0.400919	−	0.231470i	0.686880	+	0.726771i	$0.258980\pi$
$54$		0			0
$55$	−24251.1	+	42004.1i	−0.145762	+	0.252467i
$56$		0			0
$57$	17408.9	−	160949.i	0.0940044	−	0.869090i
$58$		0			0
$59$	17779.2	+	10264.8i	0.0865678	+	0.0499799i	0.542659	−	0.839953i	$-0.317418\pi$
$59$	17779.2	+	10264.8i	0.0865678	+	0.0499799i	−0.456091	+	0.889933i	$0.650751\pi$
$60$		0			0
$61$	39431.6	+	68297.5i	0.173722	+	0.300895i	0.939718	−	0.341950i	$-0.111087\pi$
$61$	39431.6	+	68297.5i	0.173722	+	0.300895i	−0.765996	+	0.642845i	$0.777754\pi$
$62$		0			0
$63$	6638.91	+	11498.9i	0.0265507	+	0.0459871i
$64$		0			0
$65$		−	100024.i		−	0.364221i
$66$		0			0
$67$	23781.8	−	13730.4i	0.0790716	−	0.0456520i	−0.459943	−	0.887948i	$-0.652130\pi$
$67$	23781.8	−	13730.4i	0.0790716	−	0.0456520i	0.539015	+	0.842296i	$0.318797\pi$
$68$		0			0
$69$		−	108113.i		−	0.329102i
$70$		0			0
$71$	−345348.	−	199387.i	−0.964898	−	0.557084i	−0.0672212	−	0.997738i	$-0.521413\pi$
$71$	−345348.	−	199387.i	−0.964898	−	0.557084i	−0.897677	+	0.440654i	$0.854747\pi$
$72$		0			0
$73$	277015.	−	479804.i	0.712090	−	1.23338i	−0.251981	−	0.967732i	$-0.581082\pi$
$73$	277015.	−	479804.i	0.712090	−	1.23338i	0.964071	−	0.265644i	$-0.0855845\pi$
$74$		0			0
$75$		−	346487.i		−	0.821302i
$76$		0			0
$77$	121862.			0.266929
$78$		0			0
$79$	−424193.	−	244908.i	−0.860365	−	0.496732i	0.00376977	−	0.999993i	$-0.498800\pi$
$79$	−424193.	−	244908.i	−0.860365	−	0.496732i	−0.864134	+	0.503261i	$0.832133\pi$
$80$		0			0
$81$	188271.	−	326095.i	0.354265	−	0.613606i
$82$		0			0
$83$	−516880.			−0.903974			−0.451987	−	0.892025i	$-0.649285\pi$
$83$	−516880.			−0.903974			−0.451987	+	0.892025i	$0.649285\pi$
$84$		0			0
$85$	103407.	+	179106.i	0.168380	+	0.291644i
$86$		0			0
$87$	616633.			0.936416
$88$		0			0
$89$	−710222.	+	410047.i	−1.00745	+	0.581653i	−0.910445	−	0.413631i	$-0.864260\pi$
$89$	−710222.	+	410047.i	−1.00745	+	0.581653i	−0.0970073	+	0.995284i	$0.530927\pi$
$90$		0			0
$91$	−217642.	+	125656.i	−0.288814	+	0.166747i
$92$		0			0
$93$	304595.	−	527575.i	0.378682	−	0.655896i
$94$		0			0
$95$	209604.	+	22671.6i	0.244472	+	0.0264431i
$96$		0			0
$97$	429465.	+	247952.i	0.470557	+	0.271676i	0.716473	−	0.697615i	$-0.245755\pi$
$97$	429465.	+	247952.i	0.470557	+	0.271676i	−0.245916	+	0.969291i	$0.579089\pi$
$98$		0			0
$99$	135651.	+	234955.i	0.139803	+	0.242147i
$100$		0			0
$101$	127587.	+	220988.i	0.123835	+	0.214489i	0.921277	−	0.388907i	$-0.127147\pi$
$101$	127587.	+	220988.i	0.123835	+	0.214489i	−0.797442	+	0.603396i	$0.793814\pi$
$102$		0			0
$103$			513798.i			0.470198i	0.971971	+	0.235099i	$0.0755415\pi$
$103$			513798.i			0.470198i	−0.971971	+	0.235099i	$0.924459\pi$
$104$		0			0
$105$	48519.9	−	28013.0i	0.0419133	−	0.0241987i
$106$		0			0
$107$			703986.i			0.574663i	0.957831	+	0.287331i	$0.0927681\pi$
$107$			703986.i			0.574663i	−0.957831	+	0.287331i	$0.907232\pi$
$108$		0			0
$109$	870559.	+	502618.i	0.672231	+	0.388113i	0.796922	−	0.604083i	$-0.206460\pi$
$109$	870559.	+	502618.i	0.672231	+	0.388113i	−0.124690	+	0.992196i	$0.539794\pi$
$110$		0			0
$111$	−984044.	+	1.70441e6i	−0.719524	+	1.24625i
$112$		0			0
$113$			2.75055e6i			1.90627i	0.302544	+	0.953135i	$0.402164\pi$
$113$			2.75055e6i			1.90627i	−0.302544	+	0.953135i	$0.597836\pi$
$114$		0			0
$115$	140795.			0.0925751
$116$		0			0
$117$	−484538.	−	279748.i	−0.302531	−	0.174667i
$118$		0			0
$119$	259810.	−	450004.i	0.154175	−	0.267039i
$120$		0			0
$121$	718410.			0.405524
$122$		0			0
$123$	−1.10594e6	−	1.91555e6i	−0.594315	−	1.02938i
$124$		0			0
$125$	931497.			0.476927
$126$		0			0
$127$	−2.71281e6	+	1.56624e6i	−1.32437	+	0.764625i	−0.984422	−	0.175820i	$-0.943742\pi$
$127$	−2.71281e6	+	1.56624e6i	−1.32437	+	0.764625i	−0.339946	+	0.940445i	$0.610409\pi$
$128$		0			0
$129$	2.34548e6	−	1.35416e6i	1.09260	−	0.630816i
$130$		0			0
$131$	−959524.	+	1.66194e6i	−0.426817	+	0.739269i	−0.996588	−	0.0825343i	$-0.973699\pi$
$131$	−959524.	+	1.66194e6i	−0.426817	+	0.739269i	0.569771	+	0.821804i	$0.307032\pi$
$132$		0			0
$133$	−213984.	−	484557.i	−0.0909550	−	0.205963i
$134$		0			0
$135$	566032.	+	326799.i	0.230059	+	0.132825i
$136$		0			0
$137$	−1.47741e6	−	2.55896e6i	−0.574567	−	0.995179i	−0.996089	−	0.0883610i	$-0.971837\pi$
$137$	−1.47741e6	−	2.55896e6i	−0.574567	−	0.995179i	0.421521	−	0.906818i	$-0.361496\pi$
$138$		0			0
$139$	1.71674e6	+	2.97347e6i	0.639233	+	1.10718i	0.985601	+	0.169085i	$0.0540812\pi$
$139$	1.71674e6	+	2.97347e6i	0.639233	+	1.10718i	−0.346369	+	0.938098i	$0.612585\pi$
$140$		0			0
$141$		−	447872.i		−	0.159770i
$142$		0			0
$143$	−4.44702e6	+	2.56749e6i	−1.52076	+	0.878012i
$144$		0			0
$145$			803039.i			0.263410i
$146$		0			0
$147$	2.28286e6	+	1.31801e6i	0.718667	+	0.414922i
$148$		0			0
$149$	3.23720e6	−	5.60700e6i	0.978613	−	1.69501i	0.311157	−	0.950359i	$-0.399284\pi$
$149$	3.23720e6	−	5.60700e6i	0.978613	−	1.69501i	0.667456	−	0.744649i	$-0.267383\pi$
$150$		0			0
$151$		−	5.78816e6i		−	1.68116i	−0.541686	−	0.840581i	$-0.682214\pi$
$151$		−	5.78816e6i		−	1.68116i	0.541686	−	0.840581i	$-0.317786\pi$
$152$		0			0
$153$	1.15683e6			0.322995
$154$		0			0
$155$	687059.	+	396674.i	0.184501	+	0.106522i
$156$		0			0
$157$	−1.04595e6	+	1.81164e6i	−0.270278	+	0.468136i	−0.968933	−	0.247323i	$-0.920449\pi$
$157$	−1.04595e6	+	1.81164e6i	−0.270278	+	0.468136i	0.698655	+	0.715459i	$0.253782\pi$
$158$		0			0
$159$	−1.62670e6			−0.404684
$160$		0			0
$161$	−176874.	−	306355.i	−0.0423825	−	0.0734087i
$162$		0			0
$163$	68232.5			0.0157554			0.00787768	−	0.999969i	$-0.497492\pi$
$163$	68232.5			0.0157554			0.00787768	+	0.999969i	$0.497492\pi$
$164$		0			0
$165$	991393.	−	572381.i	0.220696	−	0.127419i
$166$		0			0
$167$	−5.08247e6	+	2.93437e6i	−1.09125	+	0.630035i	−0.933910	−	0.357508i	$-0.883626\pi$
$167$	−5.08247e6	+	2.93437e6i	−1.09125	+	0.630035i	−0.157344	+	0.987544i	$0.550293\pi$
$168$		0			0
$169$	2.88143e6	−	4.99078e6i	0.596964	−	1.03397i
$170$		0			0
$171$	696047.	−	951956.i	0.139203	−	0.190383i
$172$		0			0
$173$	2.07177e6	+	1.19614e6i	0.400132	+	0.231016i	0.686541	−	0.727091i	$-0.259128\pi$
$173$	2.07177e6	+	1.19614e6i	0.400132	+	0.231016i	−0.286409	+	0.958108i	$0.592462\pi$
$174$		0			0
$175$	−566857.	−	981825.i	−0.105769	−	0.183198i
$176$		0			0
$177$	−242274.	−	419630.i	−0.0436904	−	0.0756740i
$178$		0			0
$179$		−	523538.i		−	0.0912828i	−0.998958	−	0.0456414i	$-0.985467\pi$
$179$		−	523538.i		−	0.0912828i	0.998958	−	0.0456414i	$-0.0145332\pi$
$180$		0			0
$181$	2.77749e6	−	1.60358e6i	0.468399	−	0.270430i	−0.247170	−	0.968972i	$-0.579501\pi$
$181$	2.77749e6	−	1.60358e6i	0.468399	−	0.270430i	0.715569	+	0.698542i	$0.246167\pi$
$182$		0			0
$183$		−	1.86135e6i		−	0.303721i
$184$		0			0
$185$	−2.21965e6	−	1.28152e6i	−0.350566	−	0.202399i
$186$		0			0
$187$	5.30862e6	−	9.19480e6i	0.811814	−	1.40610i
$188$		0			0
$189$		−	1.64217e6i		−	0.243238i
$190$		0			0
$191$	−3.39352e6			−0.487024			−0.243512	−	0.969898i	$-0.578299\pi$
$191$	−3.39352e6			−0.487024			−0.243512	+	0.969898i	$0.578299\pi$
$192$		0			0
$193$	252471.	+	145764.i	0.0351188	+	0.0202759i	0.517457	−	0.855709i	$-0.326879\pi$
$193$	252471.	+	145764.i	0.0351188	+	0.0202759i	−0.482338	+	0.875985i	$0.660212\pi$
$194$		0			0
$195$	−1.18040e6	+	2.04451e6i	−0.159194	+	0.275731i
$196$		0			0
$197$	−9.75772e6			−1.27629			−0.638145	−	0.769916i	$-0.720298\pi$
$197$	−9.75772e6			−1.27629			−0.638145	+	0.769916i	$0.720298\pi$
$198$		0			0
$199$	−3.24761e6	−	5.62502e6i	−0.412101	−	0.713780i	0.583018	−	0.812459i	$-0.301872\pi$
$199$	−3.24761e6	−	5.62502e6i	−0.412101	−	0.713780i	−0.995119	+	0.0986788i	$0.968538\pi$
$200$		0			0
$201$	−648140.			−0.0798142
$202$		0			0
$203$	1.74733e6	−	1.00882e6i	0.208875	−	0.120594i
$204$		0			0
$205$	2.49461e6	−	1.44026e6i	0.289562	−	0.167178i
$206$		0			0
$207$	393776.	−	682041.i	0.0443955	−	0.0768952i
$208$		0			0
$209$	−4.37228e6	−	9.90081e6i	−0.478927	−	1.08451i
$210$		0			0
$211$	1.20320e7	+	6.94670e6i	1.28083	+	0.739488i	0.977000	−	0.213238i	$-0.0684010\pi$
$211$	1.20320e7	+	6.94670e6i	1.28083	+	0.739488i	0.303831	+	0.952726i	$0.401734\pi$
$212$		0			0
$213$	4.70598e6	+	8.15100e6i	0.486980	+	0.843475i
$214$		0			0
$215$	1.76352e6	+	3.05451e6i	0.177446	+	0.307345i
$216$		0			0
$217$		−	1.99329e6i		−	0.195070i
$218$		0			0
$219$	−1.13245e7	+	6.53819e6i	−1.07817	+	0.622480i
$220$		0			0
$221$			2.18955e7i			2.02852i
$222$		0			0
$223$	−1.01680e6	−	587051.i	−0.0916900	−	0.0529373i	0.453454	−	0.891280i	$-0.350192\pi$
$223$	−1.01680e6	−	587051.i	−0.0916900	−	0.0529373i	−0.545144	+	0.838342i	$0.683525\pi$
$224$		0			0
$225$	1.26200e6	−	2.18585e6i	0.110793	−	0.191899i
$226$		0			0
$227$			983855.i			0.0841112i	0.999115	+	0.0420556i	$0.0133907\pi$
$227$			983855.i			0.0841112i	−0.999115	+	0.0420556i	$0.986609\pi$
$228$		0			0
$229$	3.22566e6			0.268604			0.134302	−	0.990940i	$-0.457121\pi$
$229$	3.22566e6			0.268604			0.134302	+	0.990940i	$0.457121\pi$
$230$		0			0
$231$	−2.49088e6	−	1.43811e6i	−0.202077	−	0.116669i
$232$		0			0
$233$	−8.50061e6	+	1.47235e7i	−0.672020	+	1.16397i	0.305310	+	0.952253i	$0.401240\pi$
$233$	−8.50061e6	+	1.47235e7i	−0.672020	+	1.16397i	−0.977330	+	0.211720i	$0.932093\pi$
$234$		0			0
$235$	583262.			0.0449428
$236$		0			0
$237$	5.78039e6	+	1.00119e7i	0.434223	+	0.752095i
$238$		0			0
$239$	2.18180e7			1.59816			0.799080	−	0.601224i	$-0.205320\pi$
$239$	2.18180e7			1.59816			0.799080	+	0.601224i	$0.205320\pi$
$240$		0			0
$241$	−2.09631e7	+	1.21031e7i	−1.49763	+	0.864657i	−0.999996	−	0.00273047i	$-0.999131\pi$
$241$	−2.09631e7	+	1.21031e7i	−1.49763	+	0.864657i	−0.497633	+	0.867387i	$0.665798\pi$
$242$		0			0
$243$	5.72810e6	−	3.30712e6i	0.399201	−	0.230479i
$244$		0			0
$245$	−1.71644e6	+	2.97296e6i	−0.116716	+	0.202158i
$246$		0			0
$247$	1.80178e7	+	1.31742e7i	1.19567	+	0.874244i
$248$		0			0
$249$	1.05651e7	+	6.09978e6i	0.684348	+	0.395108i
$250$		0			0
$251$	−7.55797e6	−	1.30908e7i	−0.477952	−	0.827837i	0.521729	−	0.853111i	$-0.325287\pi$
$251$	−7.55797e6	−	1.30908e7i	−0.477952	−	0.827837i	−0.999681	+	0.0252745i	$0.991954\pi$
$252$		0			0
$253$	−3.61402e6	−	6.25967e6i	−0.223167	−	0.386536i
$254$		0			0
$255$		−	4.88127e6i		−	0.294383i
$256$		0			0
$257$	−1.48276e7	+	8.56071e6i	−0.873517	+	0.504325i	−0.868515	−	0.495662i	$-0.834925\pi$
$257$	−1.48276e7	+	8.56071e6i	−0.873517	+	0.504325i	−0.00500133	+	0.999987i	$0.501592\pi$
$258$		0			0
$259$			6.43963e6i			0.370648i
$260$		0			0
$261$	3.89009e6	+	2.24594e6i	0.218795	+	0.126321i
$262$		0			0
$263$	−1.35640e7	+	2.34935e7i	−0.745623	+	1.29146i	0.204280	+	0.978913i	$0.434515\pi$
$263$	−1.35640e7	+	2.34935e7i	−0.745623	+	1.29146i	−0.949903	+	0.312545i	$0.898819\pi$
$264$		0			0
$265$		−	2.11845e6i		−	0.113836i
$266$		0			0
$267$	1.93561e7			1.01691
$268$		0			0
$269$	−1.97547e7	−	1.14054e7i	−1.01488	−	0.585939i	−0.102260	−	0.994758i	$-0.532608\pi$
$269$	−1.97547e7	−	1.14054e7i	−1.01488	−	0.585939i	−0.912616	+	0.408819i	$0.865941\pi$
$270$		0			0
$271$	1.14900e7	−	1.99012e7i	0.577313	−	0.999936i	−0.418473	−	0.908229i	$-0.637434\pi$
$271$	1.14900e7	−	1.99012e7i	0.577313	−	0.999936i	0.995786	−	0.0917066i	$-0.0292322\pi$
$272$		0			0
$273$	5.93152e6			0.291527
$274$		0			0
$275$	−1.15824e7	−	2.00614e7i	−0.556931	−	0.964634i
$276$		0			0
$277$	3.56394e6			0.167684			0.0838420	−	0.996479i	$-0.473281\pi$
$277$	3.56394e6			0.167684			0.0838420	+	0.996479i	$0.473281\pi$
$278$		0			0
$279$	3.84314e6	−	2.21884e6i	0.176959	−	0.102167i
$280$		0			0
$281$	−1.75797e7	+	1.01496e7i	−0.792303	+	0.457436i	−0.840773	−	0.541388i	$-0.817899\pi$
$281$	−1.75797e7	+	1.01496e7i	−0.792303	+	0.457436i	0.0484697	+	0.998825i	$0.484566\pi$
$282$		0			0
$283$	7.87521e6	−	1.36403e7i	0.347458	−	0.601816i	−0.638339	−	0.769755i	$-0.720378\pi$
$283$	7.87521e6	−	1.36403e7i	0.347458	−	0.601816i	0.985797	+	0.167940i	$0.0537115\pi$
$284$		0			0
$285$	−4.01679e6	−	2.93698e6i	−0.173518	−	0.126872i
$286$		0			0
$287$	−6.26772e6	−	3.61867e6i	−0.265133	−	0.153075i
$288$		0			0
$289$	−1.05672e7	−	1.83029e7i	−0.437789	−	0.758273i
$290$		0			0
$291$	−5.85223e6	−	1.01364e7i	−0.237488	−	0.411342i
$292$		0			0
$293$			2.45322e7i			0.975288i	0.873042	+	0.487644i	$0.162144\pi$
$293$			2.45322e7i			0.975288i	−0.873042	+	0.487644i	$0.837856\pi$
$294$		0			0
$295$	546483.	−	315512.i	0.0212868	−	0.0122899i
$296$		0			0
$297$		−	3.35539e7i		−	1.28078i
$298$		0			0
$299$	1.29091e7	+	7.45306e6i	0.482927	+	0.278818i
$300$		0			0
$301$	4.43086e6	−	7.67448e6i	0.162476	−	0.281416i
$302$		0			0
$303$		−	6.02272e6i		−	0.216503i
$304$		0			0
$305$	2.42403e6			0.0854356
$306$		0			0
$307$	1.39339e7	+	8.04477e6i	0.481569	+	0.278034i	0.721070	−	0.692862i	$-0.243650\pi$
$307$	1.39339e7	+	8.04477e6i	0.481569	+	0.278034i	−0.239501	+	0.970896i	$0.576984\pi$
$308$		0			0
$309$	6.06341e6	−	1.05021e7i	0.205514	−	0.355961i
$310$		0			0
$311$	−5.71175e6			−0.189884			−0.0949420	−	0.995483i	$-0.530267\pi$
$311$	−5.71175e6			−0.189884			−0.0949420	+	0.995483i	$0.530267\pi$
$312$		0			0
$313$	−4.49327e6	−	7.78256e6i	−0.146531	−	0.253799i	0.783412	−	0.621502i	$-0.213477\pi$
$313$	−4.49327e6	−	7.78256e6i	−0.146531	−	0.253799i	−0.929943	+	0.367704i	$0.880144\pi$
$314$		0			0
$315$	408123.			0.0130575
$316$		0			0
$317$	−1.80051e6	+	1.03952e6i	−0.0565219	+	0.0326329i	−0.527995	−	0.849248i	$-0.677056\pi$
$317$	−1.80051e6	+	1.03952e6i	−0.0565219	+	0.0326329i	0.471473	+	0.881881i	$0.343723\pi$
$318$		0			0
$319$	3.57026e7	−	2.06129e7i	1.09984	−	0.634991i
$320$		0			0
$321$	8.30785e6	−	1.43896e7i	0.251173	−	0.435045i
$322$		0			0
$323$	−4.58828e7	−	4.96287e6i	−1.36158	−	0.147274i
$324$		0			0
$325$	4.13718e7	+	2.38860e7i	1.20519	+	0.695815i
$326$		0			0
$327$	−1.18629e7	−	2.05472e7i	−0.339272	−	0.587637i
$328$		0			0
$329$	−732724.	−	1.26911e6i	−0.0205756	−	0.0356380i
$330$		0			0
$331$			2.97731e7i			0.820994i	0.911862	+	0.410497i	$0.134645\pi$
$331$			2.97731e7i			0.820994i	−0.911862	+	0.410497i	$0.865355\pi$
$332$		0			0
$333$	−1.24159e7	+	7.16830e6i	−0.336236	+	0.194126i
$334$		0			0
$335$		−	844070.i		−	0.0224514i
$336$		0			0
$337$	−3.68887e7	−	2.12977e7i	−0.963837	−	0.556471i	−0.0664850	−	0.997787i	$-0.521178\pi$
$337$	−3.68887e7	−	2.12977e7i	−0.963837	−	0.556471i	−0.897352	+	0.441316i	$0.854512\pi$
$338$		0			0
$339$	3.24597e7	−	5.62218e7i	0.833192	−	1.44313i
$340$		0			0
$341$		−	4.07283e7i		−	1.02715i
$342$		0			0
$343$	1.77108e7			0.438891
$344$		0			0
$345$	−2.87788e6	−	1.66154e6i	−0.0700834	−	0.0404627i
$346$		0			0
$347$	−3.87140e7	+	6.70546e7i	−0.926572	+	1.60487i	−0.137560	+	0.990493i	$0.543926\pi$
$347$	−3.87140e7	+	6.70546e7i	−0.926572	+	1.60487i	−0.789013	+	0.614377i	$0.789407\pi$
$348$		0			0
$349$	3.13837e7			0.738291			0.369145	−	0.929372i	$-0.379650\pi$
$349$	3.13837e7			0.738291			0.369145	+	0.929372i	$0.379650\pi$
$350$		0			0
$351$	3.45985e7	+	5.99264e7i	0.800085	+	1.38579i
$352$		0			0
$353$	−9.82054e6			−0.223260			−0.111630	−	0.993750i	$-0.535607\pi$
$353$	−9.82054e6			−0.223260			−0.111630	+	0.993750i	$0.535607\pi$
$354$		0			0
$355$	−1.06150e7	+	6.12858e6i	−0.237266	+	0.136986i
$356$		0			0
$357$	−1.06211e7	+	6.13210e6i	−0.233435	+	0.134774i
$358$		0			0
$359$	1.95871e7	−	3.39259e7i	0.423338	−	0.733242i	−0.572926	−	0.819607i	$-0.694192\pi$
$359$	1.95871e7	−	3.39259e7i	0.423338	−	0.733242i	0.996264	+	0.0863647i	$0.0275250\pi$
$360$		0			0
$361$	−3.16908e7	+	3.47708e7i	−0.673615	+	0.739082i
$362$		0			0
$363$	−1.46844e7	−	8.47806e6i	−0.306999	−	0.177246i
$364$		0			0
$365$	−8.51466e6	−	1.47478e7i	−0.175101	−	0.303284i
$366$		0			0
$367$	−3.82447e7	−	6.62418e7i	−0.773701	−	1.34009i	−0.935522	−	0.353269i	$-0.885070\pi$
$367$	−3.82447e7	−	6.62418e7i	−0.773701	−	1.34009i	0.161821	−	0.986820i	$-0.448263\pi$
$368$		0			0
$369$		−	1.61125e7i		−	0.320690i
$370$		0			0
$371$	−4.60951e6	+	2.66130e6i	−0.0902678	+	0.0521161i
$372$		0			0
$373$			1.59065e6i			0.0306512i	0.999883	+	0.0153256i	$0.00487847\pi$
$373$			1.59065e6i			0.0306512i	−0.999883	+	0.0153256i	$0.995122\pi$
$374$		0			0
$375$	−1.90400e7	−	1.09927e7i	−0.361054	−	0.208455i
$376$		0			0
$377$	−4.25093e7	+	7.36282e7i	−0.793340	+	1.37411i
$378$		0			0
$379$		−	2.73606e7i		−	0.502583i	−0.967911	−	0.251292i	$-0.919145\pi$
$379$		−	2.73606e7i		−	0.502583i	0.967911	−	0.251292i	$-0.0808553\pi$
$380$		0			0
$381$	7.39339e7			1.33681
$382$		0			0
$383$	3.58785e7	+	2.07144e7i	0.638613	+	0.368703i	0.784080	−	0.620660i	$-0.213135\pi$
$383$	3.58785e7	+	2.07144e7i	0.638613	+	0.368703i	−0.145467	+	0.989363i	$0.546469\pi$
$384$		0			0
$385$	1.87285e6	−	3.24386e6i	0.0328186	−	0.0568435i
$386$		0			0
$387$	1.97289e7			0.340385
$388$		0			0
$389$	4.53609e7	+	7.85673e7i	0.770606	+	1.33473i	0.937231	+	0.348709i	$0.113380\pi$
$389$	4.53609e7	+	7.85673e7i	0.770606	+	1.33473i	−0.166625	+	0.986020i	$0.553287\pi$
$390$		0			0
$391$	−3.08204e7			−0.515594
$392$		0			0
$393$	3.92257e7	−	2.26470e7i	0.646239	−	0.373106i
$394$		0			0
$395$	−1.30385e7	+	7.52779e6i	−0.211561	+	0.122145i
$396$		0			0
$397$	−3.15730e7	+	5.46860e7i	−0.504596	+	0.873986i	0.495390	+	0.868671i	$0.335025\pi$
$397$	−3.15730e7	+	5.46860e7i	−0.504596	+	0.873986i	−0.999986	+	0.00531545i	$0.998308\pi$
$398$		0			0
$399$	−1.34445e6	+	1.24297e7i	−0.0211653	+	0.195678i
$400$		0			0
$401$	−4.51360e7	−	2.60593e7i	−0.699986	−	0.404137i	0.107356	−	0.994221i	$-0.465762\pi$
$401$	−4.51360e7	−	2.60593e7i	−0.699986	−	0.404137i	−0.807342	+	0.590083i	$0.799095\pi$
$402$		0			0
$403$	4.19962e7	+	7.27396e7i	0.641646	+	1.11136i
$404$		0			0
$405$	−5.78692e6	−	1.00232e7i	−0.0871129	−	0.150884i
$406$		0			0
$407$			1.31579e8i			1.95166i
$408$		0			0
$409$	−5.51917e7	+	3.18650e7i	−0.806685	+	0.465740i	−0.845803	−	0.533495i	$-0.820878\pi$
$409$	−5.51917e7	+	3.18650e7i	−0.806685	+	0.465740i	0.0391182	+	0.999235i	$0.487545\pi$
$410$		0			0
$411$			6.97408e7i			1.00453i
$412$		0			0
$413$	−1.37304e6	−	792725.i	−0.0194910	−	0.0112531i
$414$		0			0
$415$	−7.94372e6	+	1.37589e7i	−0.111142	+	0.192504i
$416$		0			0
$417$		−	8.10378e7i		−	1.11758i
$418$		0			0
$419$	−8.50633e6			−0.115638			−0.0578189	−	0.998327i	$-0.518415\pi$
$419$	−8.50633e6			−0.115638			−0.0578189	+	0.998327i	$0.518415\pi$
$420$		0			0
$421$	9.03004e7	+	5.21350e7i	1.21016	+	0.698687i	0.962795	−	0.270235i	$-0.0871012\pi$
$421$	9.03004e7	+	5.21350e7i	1.21016	+	0.698687i	0.247367	+	0.968922i	$0.420435\pi$
$422$		0			0
$423$	1.63127e6	−	2.82544e6i	0.0215528	−	0.0373306i
$424$		0			0
$425$	−9.87750e7			−1.28671
$426$		0			0
$427$	−3.04519e6	−	5.27443e6i	−0.0391139	−	0.0677473i
$428$		0			0
$429$	1.21197e8			1.53504
$430$		0			0
$431$	5.21174e7	−	3.00900e7i	0.650955	−	0.375829i	−0.137867	−	0.990451i	$-0.544025\pi$
$431$	5.21174e7	−	3.00900e7i	0.650955	−	0.375829i	0.788822	+	0.614622i	$0.210691\pi$
$432$		0			0
$433$	8.43557e7	−	4.87028e7i	1.03908	−	0.599915i	0.119510	−	0.992833i	$-0.461868\pi$
$433$	8.43557e7	−	4.87028e7i	1.03908	−	0.599915i	0.919574	+	0.392918i	$0.128534\pi$
$434$		0			0
$435$	9.47678e6	−	1.64143e7i	0.115131	−	0.199413i
$436$		0			0
$437$	−1.85441e7	+	2.53621e7i	−0.222209	+	0.303907i
$438$		0			0
$439$	4.39265e7	+	2.53610e7i	0.519199	+	0.299759i	0.736607	−	0.676321i	$-0.236427\pi$
$439$	4.39265e7	+	2.53610e7i	0.519199	+	0.299759i	−0.217408	+	0.976081i	$0.569760\pi$
$440$		0			0
$441$	9.60109e6	+	1.66296e7i	0.111945	+	0.193895i
$442$		0			0
$443$	−8.16568e7	−	1.41434e8i	−0.939250	−	1.62683i	−0.766874	−	0.641798i	$-0.778189\pi$
$443$	−8.16568e7	−	1.41434e8i	−0.939250	−	1.62683i	−0.172376	−	0.985031i	$-0.555144\pi$
$444$		0			0
$445$			2.52074e7i			0.286054i
$446$		0			0
$447$	−1.32338e8	+	7.64054e7i	−1.48171	+	0.855463i
$448$		0			0
$449$			6.29869e7i			0.695843i	0.937524	+	0.347922i	$0.113113\pi$
$449$			6.29869e7i			0.695843i	−0.937524	+	0.347922i	$0.886887\pi$
$450$		0			0
$451$	−1.28067e8	−	7.39392e7i	−1.39607	−	0.806019i
$452$		0			0
$453$	−6.83069e7	+	1.18311e8i	−0.734801	+	1.27271i
$454$		0			0
$455$			7.72460e6i			0.0820053i
$456$		0			0
$457$	4.94545e7			0.518152			0.259076	−	0.965857i	$-0.416582\pi$
$457$	4.94545e7			0.518152			0.259076	+	0.965857i	$0.416582\pi$
$458$		0			0
$459$	−1.23906e8	−	7.15370e7i	−1.28131	−	0.739763i
$460$		0			0
$461$	7.18694e7	−	1.24481e8i	0.733570	−	1.27058i	−0.221778	−	0.975097i	$-0.571186\pi$
$461$	7.18694e7	−	1.24481e8i	0.733570	−	1.27058i	0.955348	−	0.295483i	$-0.0954805\pi$
$462$		0			0
$463$	1.03473e8			1.04252			0.521262	−	0.853397i	$-0.325462\pi$
$463$	1.03473e8			1.04252			0.521262	+	0.853397i	$0.325462\pi$
$464$		0			0
$465$	−9.36240e6	−	1.62162e7i	−0.0931169	−	0.161283i
$466$		0			0
$467$	1.54867e8			1.52058			0.760290	−	0.649584i	$-0.225057\pi$
$467$	1.54867e8			1.52058			0.760290	+	0.649584i	$0.225057\pi$
$468$		0			0
$469$	−1.83661e6	+	1.06036e6i	−0.0178032	+	0.0102787i
$470$		0			0
$471$	4.27587e7	−	2.46868e7i	0.409225	−	0.236266i
$472$		0			0
$473$	9.05346e7	−	1.56810e8i	0.855522	−	1.48181i
$474$		0			0
$475$	−5.94313e7	+	8.12818e7i	−0.554542	+	0.758425i
$476$		0			0
$477$	−1.02622e7	−	5.92488e6i	−0.0945550	−	0.0545914i
$478$		0			0
$479$	−8.38055e7	−	1.45155e8i	−0.762546	−	1.32077i	−0.941534	−	0.336917i	$-0.890616\pi$
$479$	−8.38055e7	−	1.45155e8i	−0.762546	−	1.32077i	0.178988	−	0.983851i	$-0.442718\pi$
$480$		0			0
$481$	−1.35675e8	−	2.34997e8i	−1.21918	−	2.11167i
$482$		0			0
$483$			8.34927e6i			0.0740981i
$484$		0			0
$485$	1.32005e7	−	7.62134e6i	0.115709	−	0.0668045i
$486$		0			0
$487$		−	1.20779e8i		−	1.04570i	−0.852425	−	0.522849i	$-0.824869\pi$
$487$		−	1.20779e8i		−	1.04570i	0.852425	−	0.522849i	$-0.175131\pi$
$488$		0			0
$489$	−1.39469e6	−	805222.i	−0.0119275	−	0.00688635i
$490$		0			0
$491$	−2.42386e7	+	4.19824e7i	−0.204768	+	0.354669i	−0.950059	−	0.312071i	$-0.898977\pi$
$491$	−2.42386e7	+	4.19824e7i	−0.204768	+	0.354669i	0.745291	+	0.666740i	$0.232311\pi$
$492$		0			0
$493$		−	1.75787e8i		−	1.46705i
$494$		0			0
$495$	8.33906e6			0.0687546
$496$		0			0
$497$	2.66703e7	+	1.53981e7i	0.217249	+	0.125429i
$498$		0			0
$499$	−5.53120e7	+	9.58031e7i	−0.445161	+	0.771042i	−0.998063	−	0.0622042i	$-0.980187\pi$
$499$	−5.53120e7	+	9.58031e7i	−0.445161	+	0.771042i	0.552902	+	0.833246i	$0.313520\pi$
$500$		0			0
$501$	1.38516e8			1.10150
$502$		0			0
$503$	7.61532e7	+	1.31901e8i	0.598390	+	1.03644i	0.993059	+	0.117619i	$0.0375261\pi$
$503$	7.61532e7	+	1.31901e8i	0.598390	+	1.03644i	−0.394669	+	0.918824i	$0.629141\pi$
$504$		0			0
$505$	7.84336e6			0.0609015
$506$		0			0
$507$	−1.17794e8	+	6.80084e7i	−0.903856	+	0.521841i
$508$		0			0
$509$	7.54976e7	−	4.35886e7i	0.572506	−	0.330536i	−0.185644	−	0.982617i	$-0.559437\pi$
$509$	7.54976e7	−	4.35886e7i	0.572506	−	0.330536i	0.758150	+	0.652081i	$0.226104\pi$
$510$		0			0
$511$	−2.13931e7	+	3.70540e7i	−0.160329	+	0.277698i
$512$		0			0
$513$	−1.33420e8	+	5.89192e7i	−0.988252	+	0.436420i
$514$		0			0
$515$	1.36769e7	+	7.89636e6i	0.100130	+	0.0578103i
$516$		0			0
$517$	−1.49715e7	−	2.59315e7i	−0.108342	−	0.187653i
$518$		0			0
$519$	−2.82316e7	−	4.88986e7i	−0.201945	−	0.349779i
$520$		0			0
$521$			4.64184e7i			0.328229i	0.986441	+	0.164115i	$0.0524767\pi$
$521$			4.64184e7i			0.328229i	−0.986441	+	0.164115i	$0.947523\pi$
$522$		0			0
$523$	4.36597e7	−	2.52070e7i	0.305194	−	0.176204i	−0.339580	−	0.940577i	$-0.610285\pi$
$523$	4.36597e7	−	2.52070e7i	0.305194	−	0.176204i	0.644774	+	0.764373i	$0.276952\pi$
$524$		0			0
$525$			2.67583e7i			0.184918i
$526$		0			0
$527$	−1.50399e8	−	8.68327e7i	−1.02757	−	0.593269i
$528$		0			0
$529$	6.35269e7	−	1.10032e8i	0.429132	−	0.743278i
$530$		0			0
$531$		−	3.52970e6i		−	0.0235751i
$532$		0			0
$533$	3.04964e8			2.01404
$534$		0			0
$535$	1.87395e7	+	1.08193e7i	0.122376	+	0.0706540i
$536$		0			0
$537$	−6.17835e6	+	1.07012e7i	−0.0398979	+	0.0691051i
$538$		0			0
$539$	1.76235e8			1.12545
$540$		0			0
$541$	1.83173e7	+	3.17265e7i	0.115683	+	0.200369i	0.918053	−	0.396459i	$-0.129761\pi$
$541$	1.83173e7	+	3.17265e7i	0.115683	+	0.200369i	−0.802370	+	0.596827i	$0.796428\pi$
$542$		0			0
$543$	−7.56965e7			−0.472798
$544$		0			0
$545$	2.67585e7	−	1.54490e7i	0.165300	−	0.0954360i
$546$		0			0
$547$	−1.52395e8	+	8.79852e7i	−0.931126	+	0.537586i	−0.887168	−	0.461447i	$-0.847330\pi$
$547$	−1.52395e8	+	8.79852e7i	−0.931126	+	0.537586i	−0.0439585	+	0.999033i	$0.513997\pi$
$548$		0			0
$549$	6.77954e6	−	1.17425e7i	0.0409716	−	0.0709650i
$550$		0			0
$551$	−1.44655e8	−	1.05768e8i	−0.864726	−	0.632266i
$552$		0			0
$553$	3.27593e7	+	1.89136e7i	0.193713	+	0.111840i
$554$		0			0
$555$	3.02467e7	+	5.23889e7i	0.176929	+	0.306450i
$556$		0			0
$557$	2.38942e7	+	4.13859e7i	0.138269	+	0.239490i	0.926842	−	0.375452i	$-0.122513\pi$
$557$	2.38942e7	+	4.13859e7i	0.138269	+	0.239490i	−0.788572	+	0.614942i	$0.789179\pi$
$558$		0			0
$559$			3.73412e8i			2.13773i
$560$		0			0
$561$	−2.17018e8	+	1.25296e8i	−1.22916	+	0.709655i
$562$		0			0
$563$		−	4.75359e7i		−	0.266377i	−0.991091	−	0.133188i	$-0.957478\pi$
$563$		−	4.75359e7i		−	0.266377i	0.991091	−	0.133188i	$-0.0425215\pi$
$564$		0			0
$565$	7.32175e7	+	4.22721e7i	0.405947	+	0.234374i
$566$		0			0
$567$	−1.45397e7	+	2.51834e7i	−0.0797637	+	0.138155i
$568$		0			0
$569$		−	1.14456e8i		−	0.621300i	−0.950524	−	0.310650i	$-0.899453\pi$
$569$		−	1.14456e8i		−	0.621300i	0.950524	−	0.310650i	$-0.100547\pi$
$570$		0			0
$571$	3.08831e8			1.65887			0.829436	−	0.558601i	$-0.188662\pi$
$571$	3.08831e8			1.65887			0.829436	+	0.558601i	$0.188662\pi$
$572$		0			0
$573$	6.93641e7	+	4.00474e7i	0.368698	+	0.212868i
$574$		0			0
$575$	−3.36222e7	+	5.82354e7i	−0.176857	+	0.306326i
$576$		0			0
$577$	−2.35527e8			−1.22607			−0.613033	−	0.790057i	$-0.710051\pi$
$577$	−2.35527e8			−1.22607			−0.613033	+	0.790057i	$0.710051\pi$
$578$		0			0
$579$	−3.44037e6	−	5.95890e6i	−0.0177243	−	0.0306994i
$580$		0			0
$581$	3.99173e7			0.203532
$582$		0			0
$583$	−9.41848e7	+	5.43776e7i	−0.475308	+	0.274419i
$584$		0			0
$585$	−1.48933e7	+	8.59867e6i	−0.0743917	+	0.0429501i
$586$		0			0
$587$	1.18154e8	−	2.04648e8i	0.584162	−	1.01180i	−0.410817	−	0.911718i	$-0.634756\pi$
$587$	1.18154e8	−	2.04648e8i	0.584162	−	1.01180i	0.994979	−	0.100081i	$-0.0319102\pi$
$588$		0			0
$589$	−1.61947e8	+	7.15171e7i	−0.792550	+	0.349997i
$590$		0			0
$591$	1.99450e8	+	1.15152e8i	0.966208	+	0.557840i
$592$		0			0
$593$	−1.64404e8	−	2.84756e8i	−0.788404	−	1.36556i	−0.926944	−	0.375199i	$-0.877574\pi$
$593$	−1.64404e8	−	2.84756e8i	−0.788404	−	1.36556i	0.138540	−	0.990357i	$-0.455759\pi$
$594$		0			0
$595$	−7.98582e6	−	1.38318e7i	−0.0379113	−	0.0656643i
$596$		0			0
$597$			1.53302e8i			0.720484i
$598$		0			0
$599$	−1.73934e8	+	1.00421e8i	−0.809289	+	0.467243i	−0.846709	−	0.532057i	$-0.821419\pi$
$599$	−1.73934e8	+	1.00421e8i	−0.809289	+	0.467243i	0.0374200	+	0.999300i	$0.488086\pi$
$600$		0			0
$601$			6.71399e7i			0.309284i	0.987971	+	0.154642i	$0.0494224\pi$
$601$			6.71399e7i			0.309284i	−0.987971	+	0.154642i	$0.950578\pi$
$602$		0			0
$603$	−4.08885e6	−	2.36070e6i	−0.0186487	−	0.0107668i
$604$		0			0
$605$	1.10409e7	−	1.91235e7i	0.0498586	−	0.0863577i
$606$		0			0
$607$		−	2.51159e8i		−	1.12301i	−0.827473	−	0.561505i	$-0.810223\pi$
$607$		−	2.51159e8i		−	1.12301i	0.827473	−	0.561505i	$-0.189777\pi$
$608$		0			0
$609$	−4.76209e7			−0.210836
$610$		0			0
$611$	5.34775e7	+	3.08753e7i	0.234449	+	0.135359i
$612$		0			0
$613$	−1.71977e8	+	2.97872e8i	−0.746600	+	1.29315i	0.202843	+	0.979211i	$0.434982\pi$
$613$	−1.71977e8	+	2.97872e8i	−0.746600	+	1.29315i	−0.949443	+	0.313938i	$0.898351\pi$
$614$		0			0
$615$	−6.79870e7			−0.292281
$616$		0			0
$617$	1.18205e8	+	2.04738e8i	0.503248	+	0.871651i	0.999993	+	0.00375422i	$0.00119501\pi$
$617$	1.18205e8	+	2.04738e8i	0.503248	+	0.871651i	−0.496745	+	0.867896i	$0.665472\pi$
$618$		0			0
$619$	3.71139e8			1.56482			0.782411	−	0.622762i	$-0.213990\pi$
$619$	3.71139e8			1.56482			0.782411	+	0.622762i	$0.213990\pi$
$620$		0			0
$621$	−8.43530e7	+	4.87012e7i	−0.352229	+	0.203360i
$622$		0			0
$623$	5.48486e7	−	3.16668e7i	0.226830	−	0.130961i
$624$		0			0
$625$	−1.00373e8	+	1.73852e8i	−0.411130	+	0.712098i
$626$		0			0
$627$	−2.74707e7	+	2.53972e8i	−0.111447	+	1.03035i
$628$		0			0
$629$	4.85887e8	+	2.80527e8i	1.95246	+	1.12726i
$630$		0			0
$631$	−8.09392e7	−	1.40191e8i	−0.322159	−	0.557996i	0.658774	−	0.752341i	$-0.271075\pi$
$631$	−8.09392e7	−	1.40191e8i	−0.322159	−	0.557996i	−0.980933	+	0.194344i	$0.937742\pi$
$632$		0			0
$633$	−1.63958e8	−	2.83984e8i	−0.646430	−	1.11965i
$634$		0			0
$635$			9.62839e7i			0.376039i
$636$		0			0
$637$	−3.14751e8	+	1.81721e8i	−1.21772	+	0.703052i
$638$		0			0
$639$			6.85618e7i			0.262772i
$640$		0			0
$641$	9.49604e7	+	5.48254e7i	0.360553	+	0.208165i	0.669323	−	0.742971i	$-0.266584\pi$
$641$	9.49604e7	+	5.48254e7i	0.360553	+	0.208165i	−0.308771	+	0.951137i	$0.599918\pi$
$642$		0			0
$643$	−1.25704e7	+	2.17725e7i	−0.0472840	+	0.0818984i	−0.888699	−	0.458492i	$-0.848390\pi$
$643$	−1.25704e7	+	2.17725e7i	−0.0472840	+	0.0818984i	0.841415	+	0.540390i	$0.181723\pi$
$644$		0			0
$645$		−	8.32464e7i		−	0.310232i
$646$		0			0
$647$	−7.97665e7			−0.294515			−0.147258	−	0.989098i	$-0.547045\pi$
$647$	−7.97665e7			−0.294515			−0.147258	+	0.989098i	$0.547045\pi$
$648$		0			0
$649$	−2.80549e7	−	1.61975e7i	−0.102630	−	0.0592536i
$650$		0			0
$651$	−2.35231e7	+	4.07432e7i	−0.0852612	+	0.147677i
$652$		0			0
$653$	1.37333e8			0.493215			0.246607	−	0.969115i	$-0.420684\pi$
$653$	1.37333e8			0.493215			0.246607	+	0.969115i	$0.420684\pi$
$654$		0			0
$655$	2.94931e7	+	5.10835e7i	0.104953	+	0.181784i
$656$		0			0
$657$	−9.52554e7			−0.335887
$658$		0			0
$659$	3.48871e8	−	2.01421e8i	1.21901	−	0.703798i	0.254308	−	0.967123i	$-0.418152\pi$
$659$	3.48871e8	−	2.01421e8i	1.21901	−	0.703798i	0.964707	+	0.263325i	$0.0848191\pi$
$660$		0			0
$661$	2.46746e8	−	1.42459e8i	0.854369	−	0.493270i	−0.00775379	−	0.999970i	$-0.502468\pi$
$661$	2.46746e8	−	1.42459e8i	0.854369	−	0.493270i	0.862122	+	0.506700i	$0.169135\pi$
$662$		0			0
$663$	2.58392e8	−	4.47549e8i	0.886623	−	1.53568i
$664$		0			0
$665$	−1.61871e7	−	1.75087e6i	−0.0550434	−	0.00595372i
$666$		0			0
$667$	−1.03640e8	−	5.98365e7i	−0.349260	−	0.201645i
$668$		0			0
$669$	1.38558e7	+	2.39989e7i	0.0462756	+	0.0801517i
$670$		0			0
$671$	−6.22216e7	−	1.07771e8i	−0.205956	−	0.356726i
$672$		0			0
$673$		−	2.25275e8i		−	0.739038i	−0.929223	−	0.369519i	$-0.879522\pi$
$673$		−	2.25275e8i		−	0.739038i	0.929223	−	0.369519i	$-0.120478\pi$
$674$		0			0
$675$	−2.70339e8	+	1.56081e8i	−0.879019	+	0.507502i
$676$		0			0
$677$			4.96421e8i			1.59987i	0.600089	+	0.799934i	$0.295132\pi$
$677$			4.96421e8i			1.59987i	−0.600089	+	0.799934i	$0.704868\pi$
$678$		0			0
$679$	−3.31664e7	−	1.91486e7i	−0.105947	−	0.0611686i
$680$		0			0
$681$	1.16106e7	−	2.01102e7i	0.0367633	−	0.0636758i
$682$		0			0
$683$		−	4.77653e8i		−	1.49917i	−0.661909	−	0.749584i	$-0.730253\pi$
$683$		−	4.77653e8i		−	1.49917i	0.661909	−	0.749584i	$-0.269747\pi$
$684$		0			0
$685$	−9.08232e7			−0.282569
$686$		0			0
$687$	−6.59332e7	−	3.80665e7i	−0.203345	−	0.117401i
$688$		0			0
$689$	1.12141e8	−	1.94234e8i	0.342852	−	0.593837i
$690$		0			0
$691$	−2.70566e8			−0.820047			−0.410024	−	0.912075i	$-0.634480\pi$
$691$	−2.70566e8			−0.820047			−0.410024	+	0.912075i	$0.634480\pi$
$692$		0			0
$693$	−1.04760e7	−	1.81449e7i	−0.0314771	−	0.0545199i
$694$		0			0
$695$	1.05535e8			0.314371
$696$		0			0
$697$	−5.46076e8	+	3.15277e8i	−1.61270	+	0.931095i
$698$		0			0
$699$	3.47508e8	−	2.00634e8i	1.01750	−	0.587453i
$700$		0			0
$701$	−1.86703e6	+	3.23379e6i	−0.00541997	+	0.00938767i	−0.868723	−	0.495299i	$-0.835059\pi$
$701$	−1.86703e6	+	3.23379e6i	−0.00541997	+	0.00938767i	0.863303	+	0.504686i	$0.168392\pi$
$702$		0			0
$703$	5.23195e8	−	2.31047e8i	1.50591	−	0.665020i
$704$		0			0
$705$	−1.19220e7	−	6.88316e6i	−0.0340237	−	0.0196436i
$706$		0			0
$707$	−9.85324e6	−	1.70663e7i	−0.0278818	−	0.0482927i
$708$		0			0
$709$	−2.65430e8	−	4.59738e8i	−0.744751	−	1.28995i	−0.950311	−	0.311302i	$-0.899235\pi$
$709$	−2.65430e8	−	4.59738e8i	−0.744751	−	1.28995i	0.205560	−	0.978644i	$-0.434098\pi$
$710$		0			0
$711$			8.42150e7i			0.234304i
$712$		0			0
$713$	−1.02389e8	+	5.91143e7i	−0.282478	+	0.163089i
$714$		0			0
$715$			1.57835e8i			0.431802i
$716$		0			0
$717$	−4.45963e8	−	2.57477e8i	−1.20988	−	0.698523i
$718$		0			0
$719$	2.41180e8	−	4.17736e8i	0.648865	−	1.12387i	−0.334529	−	0.942385i	$-0.608577\pi$
$719$	2.41180e8	−	4.17736e8i	0.648865	−	1.12387i	0.983394	−	0.181482i	$-0.0580893\pi$
$720$		0			0
$721$		−	3.96793e7i		−	0.105866i
$722$		0			0
$723$	5.71320e8			1.51170
$724$		0			0
$725$	−3.32151e8	−	1.91768e8i	−0.871609	−	0.503224i
$726$		0			0
$727$	−6.54785e7	+	1.13412e8i	−0.170410	+	0.295159i	−0.938563	−	0.345107i	$-0.887843\pi$
$727$	−6.54785e7	+	1.13412e8i	−0.170410	+	0.295159i	0.768153	+	0.640266i	$0.221176\pi$
$728$		0			0
$729$	−4.30610e8			−1.11148
$730$		0			0
$731$	−3.86040e8	−	6.68640e8i	−0.988279	−	1.71175i
$732$		0			0
$733$	5.41677e8			1.37540			0.687699	−	0.725996i	$-0.258621\pi$
$733$	5.41677e8			1.37540			0.687699	+	0.725996i	$0.258621\pi$
$734$		0			0
$735$	7.01687e7	−	4.05119e7i	0.176718	−	0.102028i
$736$		0			0
$737$	−3.75269e7	+	2.16661e7i	−0.0937432	+	0.0541226i
$738$		0			0
$739$	2.36489e8	−	4.09611e8i	0.585973	−	1.01493i	−0.408781	−	0.912633i	$-0.634046\pi$
$739$	2.36489e8	−	4.09611e8i	0.585973	−	1.01493i	0.994753	−	0.102302i	$-0.0326208\pi$
$740$		0			0
$741$	−2.12817e8	−	4.81913e8i	−0.523060	−	1.18444i
$742$		0			0
$743$	4.54508e8	+	2.62410e8i	1.10809	+	0.639757i	0.938334	−	0.345729i	$-0.112368\pi$
$743$	4.54508e8	+	2.62410e8i	1.10809	+	0.639757i	0.169757	+	0.985486i	$0.445702\pi$
$744$		0			0
$745$	−9.95025e7	−	1.72343e8i	−0.240638	−	0.416798i
$746$		0			0
$747$	4.44341e7	+	7.69621e7i	0.106599	+	0.184635i
$748$		0			0
$749$		−	5.43670e7i		−	0.129387i
$750$		0			0
$751$	−7.13094e8	+	4.11705e8i	−1.68355	+	0.972000i	−0.724286	+	0.689499i	$0.757831\pi$
$751$	−7.13094e8	+	4.11705e8i	−1.68355	+	0.972000i	−0.959267	+	0.282501i	$0.908836\pi$
$752$		0			0
$753$			3.56771e8i			0.835612i
$754$		0			0
$755$	−1.54076e8	−	8.89558e7i	−0.358009	−	0.206697i
$756$		0			0
$757$	−8.72006e7	+	1.51036e8i	−0.201017	+	0.348171i	−0.948856	−	0.315708i	$-0.897758\pi$
$757$	−8.72006e7	+	1.51036e8i	−0.201017	+	0.348171i	0.747840	+	0.663879i	$0.231091\pi$
$758$		0			0
$759$			1.70598e8i			0.390166i
$760$		0			0
$761$	7.25630e8			1.64650			0.823249	−	0.567680i	$-0.192159\pi$
$761$	7.25630e8			1.64650			0.823249	+	0.567680i	$0.192159\pi$
$762$		0			0
$763$	−6.72309e7	−	3.88158e7i	−0.151355	−	0.0873846i
$764$		0			0
$765$	1.77789e7	−	3.07939e7i	0.0397119	−	0.0687830i
$766$		0			0
$767$	6.68071e7			0.148060
$768$		0			0
$769$	2.42126e8	+	4.19375e8i	0.532431	+	0.922197i	0.999283	+	0.0378619i	$0.0120547\pi$
$769$	2.42126e8	+	4.19375e8i	0.532431	+	0.922197i	−0.466852	+	0.884335i	$0.654612\pi$
$770$		0			0
$771$	4.04105e8			0.881721
$772$		0			0
$773$	−4.22187e8	+	2.43750e8i	−0.914043	+	0.527723i	−0.881730	−	0.471755i	$-0.843621\pi$
$773$	−4.22187e8	+	2.43750e8i	−0.914043	+	0.527723i	−0.0323133	+	0.999478i	$0.510287\pi$
$774$		0			0
$775$	−3.28142e8	+	1.89453e8i	−0.704948	+	0.407002i
$776$		0			0
$777$	7.59950e7	−	1.31627e8i	0.162003	−	0.280597i
$778$		0			0
$779$	−6.91236e7	+	6.39062e8i	−0.146222	+	1.35186i
$780$		0			0
$781$	5.44946e8	+	3.14625e8i	1.14393	+	0.660450i
$782$		0			0
$783$	−2.77772e8	−	4.81115e8i	−0.578633	−	1.00222i
$784$		0			0
$785$	3.21495e7	+	5.56846e7i	0.0664608	+	0.115113i
$786$		0			0
$787$			3.14248e8i			0.644686i	0.946623	+	0.322343i	$0.104471\pi$
$787$			3.14248e8i			0.644686i	−0.946623	+	0.322343i	$0.895529\pi$
$788$		0			0
$789$	5.54500e8	−	3.20141e8i	1.12894	−	0.651793i
$790$		0			0
$791$		−	2.12418e8i		−	0.429202i
$792$		0			0
$793$	2.22252e8	+	1.28317e8i	0.445683	+	0.257315i
$794$		0			0
$795$	−2.50001e7	+	4.33014e7i	−0.0497554	+	0.0861788i
$796$		0			0
$797$		−	3.43566e8i		−	0.678633i	−0.940672	−	0.339317i	$-0.889804\pi$
$797$		−	3.43566e8i		−	0.678633i	0.940672	−	0.339317i	$-0.110196\pi$
$798$		0			0
$799$	−1.27677e8			−0.250307
$800$		0			0
$801$	1.22110e8	+	7.05001e7i	0.237604	+	0.137180i
$802$		0			0
$803$	−4.37120e8	+	7.57114e8i	−0.844217	+	1.46223i
$804$		0			0
$805$	−1.08732e7			−0.0208435
$806$		0			0
$807$	2.69193e8	+	4.66256e8i	0.512204	+	0.887163i
$808$		0			0
$809$	1.39743e8			0.263926			0.131963	−	0.991255i	$-0.457872\pi$
$809$	1.39743e8			0.263926			0.131963	+	0.991255i	$0.457872\pi$
$810$		0			0
$811$	3.05685e7	−	1.76487e7i	0.0573075	−	0.0330865i	−0.471072	−	0.882095i	$-0.656133\pi$
$811$	3.05685e7	−	1.76487e7i	0.0573075	−	0.0330865i	0.528380	+	0.849008i	$0.322800\pi$
$812$		0			0
$813$	−4.69715e8	+	2.71190e8i	−0.874103	+	0.504664i
$814$		0			0
$815$	1.04864e6	−	1.81629e6i	0.00193710	−	0.00335516i
$816$		0			0
$817$	−7.82496e8	−	8.46381e7i	−1.43488	−	0.155203i
$818$		0			0
$819$	3.74196e7	+	2.16042e7i	0.0681157	+	0.0393266i
$820$		0			0
$821$	4.09482e8	+	7.09244e8i	0.739955	+	1.28164i	0.952515	+	0.304492i	$0.0984868\pi$
$821$	4.09482e8	+	7.09244e8i	0.739955	+	1.28164i	−0.212559	+	0.977148i	$0.568180\pi$
$822$		0			0
$823$	3.00075e8	+	5.19745e8i	0.538307	+	0.932375i	0.998995	+	0.0448133i	$0.0142693\pi$
$823$	3.00075e8	+	5.19745e8i	0.538307	+	0.932375i	−0.460688	+	0.887562i	$0.652397\pi$
$824$		0			0
$825$			5.46744e8i			0.973693i
$826$		0			0
$827$	−6.19418e8	+	3.57621e8i	−1.09513	+	0.632276i	−0.934939	−	0.354809i	$-0.884546\pi$
$827$	−6.19418e8	+	3.57621e8i	−1.09513	+	0.632276i	−0.160195	+	0.987085i	$0.551212\pi$
$828$		0			0
$829$		−	6.10758e8i		−	1.07203i	−0.844209	−	0.536014i	$-0.819930\pi$
$829$		−	6.10758e8i		−	1.07203i	0.844209	−	0.536014i	$-0.180070\pi$
$830$		0			0
$831$	−7.28477e7	−	4.20586e7i	−0.126944	−	0.0732912i
$832$		0			0
$833$	3.75733e8	−	6.50788e8i	0.650046	−	1.12591i
$834$		0			0
$835$			1.80388e8i			0.309848i
$836$		0			0
$837$	−5.48839e8			−0.935985
$838$		0			0
$839$	1.95923e8	+	1.13116e8i	0.331741	+	0.191531i	0.656614	−	0.754227i	$-0.271988\pi$
$839$	1.95923e8	+	1.13116e8i	0.331741	+	0.191531i	−0.324873	+	0.945758i	$0.605321\pi$
$840$		0			0
$841$	4.38715e7	−	7.59877e7i	0.0737555	−	0.127748i
$842$		0			0
$843$	4.79108e8			0.799744
$844$		0			0
$845$	−8.85671e7	−	1.53403e8i	−0.146792	−	0.254251i
$846$		0			0
$847$	−5.54809e7			−0.0913047
$848$		0			0
$849$	−3.21941e8	+	1.85873e8i	−0.526083	+	0.303734i
$850$		0			0
$851$	3.30784e8	−	1.90978e8i	0.536730	−	0.309881i
$852$		0			0
$853$	−1.88893e8	+	3.27172e8i	−0.304346	+	0.527143i	−0.977116	−	0.212709i	$-0.931771\pi$
$853$	−1.88893e8	+	3.27172e8i	−0.304346	+	0.527143i	0.672769	+	0.739852i	$0.265105\pi$
$854$		0			0
$855$	−1.46430e7	−	3.31584e7i	−0.0234279	−	0.0530512i
$856$		0			0
$857$	2.10139e7	+	1.21324e7i	0.0333859	+	0.0192754i	0.516600	−	0.856227i	$-0.327197\pi$
$857$	2.10139e7	+	1.21324e7i	0.0333859	+	0.0192754i	−0.483214	+	0.875502i	$0.660531\pi$
$858$		0			0
$859$	−2.38152e8	−	4.12492e8i	−0.375730	−	0.650783i	0.614706	−	0.788756i	$-0.289275\pi$
$859$	−2.38152e8	−	4.12492e8i	−0.375730	−	0.650783i	−0.990436	+	0.137973i	$0.955941\pi$
$860$		0			0
$861$	8.54089e7	+	1.47932e8i	0.133812	+	0.231768i
$862$		0			0
$863$		−	2.19370e8i		−	0.341307i	−0.985331	−	0.170653i	$-0.945412\pi$
$863$		−	2.19370e8i		−	0.341307i	0.985331	−	0.170653i	$-0.0545878\pi$
$864$		0			0
$865$	6.36804e7	−	3.67659e7i	0.0983915	−	0.0568064i
$866$		0			0
$867$			4.98819e8i			0.765395i
$868$		0			0
$869$	6.69362e8	+	3.86456e8i	1.02000	+	0.588899i
$870$		0			0
$871$	4.46813e7	−	7.73902e7i	0.0676194	−	0.117120i
$872$		0			0
$873$		−	8.52615e7i		−	0.128148i
$874$		0			0
$875$	−7.19370e7			−0.107381
$876$		0			0
$877$	−1.45206e8	−	8.38347e7i	−0.215271	−	0.124287i	0.388488	−	0.921454i	$-0.372998\pi$
$877$	−1.45206e8	−	8.38347e7i	−0.215271	−	0.124287i	−0.603759	+	0.797167i	$0.706331\pi$
$878$		0			0
$879$	2.89508e8	−	5.01442e8i	0.426279	−	0.738336i
$880$		0			0
$881$	−1.61942e7			−0.0236827			−0.0118413	−	0.999930i	$-0.503769\pi$
$881$	−1.61942e7			−0.0236827			−0.0118413	+	0.999930i	$0.503769\pi$
$882$		0			0
$883$	−3.62142e8	−	6.27248e8i	−0.526013	−	0.911082i	−0.999541	−	0.0303026i	$-0.990353\pi$
$883$	−3.62142e8	−	6.27248e8i	−0.526013	−	0.911082i	0.473528	−	0.880779i	$-0.342980\pi$
$884$		0			0
$885$	−1.48936e7			−0.0214867
$886$		0			0
$887$	−7.22803e8	+	4.17311e8i	−1.03574	+	0.597983i	−0.918623	−	0.395136i	$-0.870698\pi$
$887$	−7.22803e8	+	4.17311e8i	−1.03574	+	0.597983i	−0.117114	+	0.993118i	$0.537364\pi$
$888$		0			0
$889$	2.09503e8	−	1.20957e8i	0.298185	−	0.172157i
$890$		0			0
$891$	−2.97085e8	+	5.14566e8i	−0.419998	+	0.727459i
$892$		0			0
$893$	−7.68213e7	+	1.05065e8i	−0.107877	+	0.147539i
$894$		0			0
$895$	−1.39362e7	−	8.04604e6i	−0.0194390	−	0.0112231i
$896$		0			0
$897$	−1.75909e8	−	3.04684e8i	−0.243732	−	0.422155i
$898$		0			0
$899$	−3.37164e8	−	5.83986e8i	−0.464048	−	0.803754i
$900$		0			0
$901$			4.63732e8i			0.634006i
$902$		0			0
$903$	−1.81135e8	+	1.04578e8i	−0.246003	+	0.142030i
$904$		0			0
$905$		−	9.85792e7i		−	0.132996i
$906$		0			0
$907$	5.51139e8	+	3.18200e8i	0.738651	+	0.426460i	0.821579	−	0.570095i	$-0.193094\pi$
$907$	5.51139e8	+	3.18200e8i	0.738651	+	0.426460i	−0.0829278	+	0.996556i	$0.526427\pi$
$908$		0			0
$909$	2.19363e7	−	3.79949e7i	0.0292060	−	0.0505863i
$910$		0			0
$911$			2.53776e8i			0.335656i	0.985816	+	0.167828i	$0.0536754\pi$
$911$			2.53776e8i			0.335656i	−0.985816	+	0.167828i	$0.946325\pi$
$912$		0			0
$913$	8.15619e8			1.07170
$914$		0			0
$915$	−4.95477e7	−	2.86064e7i	−0.0646785	−	0.0373421i
$916$		0			0
$917$	7.41015e7	−	1.28347e8i	0.0960990	−	0.166448i
$918$		0			0
$919$	1.10261e9			1.42061			0.710306	−	0.703893i	$-0.248557\pi$
$919$	1.10261e9			1.42061			0.710306	+	0.703893i	$0.248557\pi$
$920$		0			0
$921$	−1.89875e8	−	3.28873e8i	−0.243046	−	0.420968i
$922$		0			0
$923$	−1.29768e9			−1.65030
$924$		0			0
$925$	1.06012e9	−	6.12058e8i	1.33946	−	0.773335i
$926$		0			0
$927$	7.65032e7	−	4.41691e7i	0.0960374	−	0.0554472i
$928$		0			0
$929$	9.38726e7	−	1.62592e8i	0.117082	−	0.202793i	−0.801528	−	0.597957i	$-0.795979\pi$
$929$	9.38726e7	−	1.62592e8i	0.117082	−	0.202793i	0.918610	+	0.395165i	$0.129312\pi$
$930$		0			0
$931$	−3.09461e8	−	7.00758e8i	−0.383492	−	0.868399i
$932$		0			0
$933$	1.16749e8	+	6.74052e7i	0.143750	+	0.0829944i
$934$		0			0
$935$	−1.63172e8	−	2.82622e8i	−0.199623	−	0.345757i
$936$		0			0
$937$	3.47001e8	+	6.01023e8i	0.421805	+	0.730588i	0.996116	−	0.0880492i	$-0.0280633\pi$
$937$	3.47001e8	+	6.01023e8i	0.421805	+	0.730588i	−0.574311	+	0.818637i	$0.694730\pi$
$938$		0			0
$939$			2.12103e8i			0.256183i
$940$		0			0
$941$	−3.46330e8	+	1.99954e8i	−0.415644	+	0.239972i	−0.693212	−	0.720734i	$-0.743805\pi$
$941$	−3.46330e8	+	1.99954e8i	−0.415644	+	0.239972i	0.277568	+	0.960706i	$0.410472\pi$
$942$		0			0
$943$			4.29271e8i			0.511913i
$944$		0			0
$945$	−4.37131e7	−	2.52378e7i	−0.0517984	−	0.0299058i
$946$		0			0
$947$	−3.24255e8	+	5.61626e8i	−0.381800	+	0.661298i	−0.991320	−	0.131474i	$-0.958029\pi$
$947$	−3.24255e8	+	5.61626e8i	−0.381800	+	0.661298i	0.609519	+	0.792771i	$0.291362\pi$
$948$		0			0
$949$		−	1.80291e9i		−	2.10948i
$950$		0			0
$951$	4.90702e7			0.0570527
$952$		0			0
$953$	7.87604e8	+	4.54723e8i	0.909974	+	0.525374i	0.880423	−	0.474190i	$-0.157259\pi$
$953$	7.87604e8	+	4.54723e8i	0.909974	+	0.525374i	0.0295512	+	0.999563i	$0.490592\pi$
$954$		0			0
$955$	−5.21536e7	+	9.03327e7i	−0.0598789	+	0.103713i
$956$		0			0
$957$	−9.73024e8			−1.11017
$958$		0			0
$959$	1.14097e8	+	1.97621e8i	0.129365	+	0.224067i
$960$		0			0
$961$	2.21313e8			0.249366
$962$		0			0
$963$	1.04822e8	−	6.05188e7i	0.117374	−	0.0677659i
$964$		0			0
$965$	7.76025e6	−	4.48038e6i	0.00863563	−	0.00498578i
$966$		0			0
$967$	2.87861e8	−	4.98590e8i	0.318349	−	0.551397i	−0.661795	−	0.749685i	$-0.730205\pi$
$967$	2.87861e8	−	4.98590e8i	0.318349	−	0.551397i	0.980144	+	0.198288i	$0.0635383\pi$
$968$		0			0
$969$	8.79284e8	+	6.42911e8i	0.966402	+	0.706610i
$970$		0			0
$971$	−1.10914e9	−	6.40364e8i	−1.21152	−	0.699471i	−0.248429	−	0.968650i	$-0.579914\pi$
$971$	−1.10914e9	−	6.40364e8i	−1.21152	−	0.699471i	−0.963090	+	0.269180i	$0.913247\pi$
$972$		0			0
$973$	−1.32579e8	−	2.29633e8i	−0.143925	−	0.249285i
$974$		0			0
$975$	−5.63765e8	−	9.76470e8i	−0.608253	−	1.05353i
$976$		0			0
$977$		−	1.41721e9i		−	1.51968i	−0.650112	−	0.759838i	$-0.725278\pi$
$977$		−	1.41721e9i		−	1.51968i	0.650112	−	0.759838i	$-0.274722\pi$
$978$		0			0
$979$	1.12071e9	−	6.47040e8i	1.19438	−	0.689577i
$980$		0			0
$981$		−	1.72832e8i		−	0.183070i
$982$		0			0
$983$	−1.16009e9	−	6.69779e8i	−1.22133	−	0.705132i	−0.256125	−	0.966644i	$-0.582446\pi$
$983$	−1.16009e9	−	6.69779e8i	−1.22133	−	0.705132i	−0.965200	+	0.261511i	$0.915779\pi$
$984$		0			0
$985$	−1.49962e8	+	2.59742e8i	−0.156918	+	0.271790i
$986$		0			0
$987$			3.45879e7i			0.0359727i
$988$		0			0
$989$	−5.25619e8			−0.543353
$990$		0			0
$991$	−1.26839e8	−	7.32305e7i	−0.130326	−	0.0752439i	0.433419	−	0.901192i	$-0.357307\pi$
$991$	−1.26839e8	−	7.32305e7i	−0.130326	−	0.0752439i	−0.563746	+	0.825948i	$0.690640\pi$
$992$		0			0
$993$	3.51357e8	−	6.08568e8i	0.358840	−	0.621528i
$994$		0			0
$995$	−1.99644e8			−0.202669
$996$		0			0
$997$	3.20649e8	+	5.55380e8i	0.323552	+	0.560409i	0.981218	−	0.192901i	$-0.0617895\pi$
$997$	3.20649e8	+	5.55380e8i	0.323552	+	0.560409i	−0.657666	+	0.753310i	$0.728456\pi$
$998$		0			0
$999$	1.77311e9			1.77844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.h.a.65.4	✓	20
3.2	odd	2		684.7.y.c.217.6		20
19.12	odd	6	inner	76.7.h.a.69.4	yes	20
57.50	even	6		684.7.y.c.145.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.h.a.65.4	✓	20	1.1	even	1	trivial
76.7.h.a.69.4	yes	20	19.12	odd	6	inner
684.7.y.c.145.6		20	57.50	even	6
684.7.y.c.217.6		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)

\(f(q)\)	\(=\)	\(q+(-20.4402 - 11.8011i) q^{3} +(15.3686 - 26.6192i) q^{5} -77.2273 q^{7} +(-85.9659 - 148.897i) q^{9} +O(q^{10})\)	\(q+(-20.4402 - 11.8011i) q^{3} +(15.3686 - 26.6192i) q^{5} -77.2273 q^{7} +(-85.9659 - 148.897i) q^{9} -1577.96 q^{11} +(2818.20 - 1627.09i) q^{13} +(-628.274 + 362.734i) q^{15} +(-3364.22 + 5827.00i) q^{17} +(2770.84 + 6274.42i) q^{19} +(1578.54 + 911.371i) q^{21} +(2290.31 + 3966.93i) q^{23} +(7340.11 + 12713.4i) q^{25} +21264.1i q^{27} +(-22625.8 + 13063.0i) q^{29} +25810.7i q^{31} +(32253.9 + 18621.8i) q^{33} +(-1186.87 + 2055.73i) q^{35} -83385.4i q^{37} -76806.0 q^{39} +(81159.3 + 46857.4i) q^{41} +(-57374.3 + 99375.2i) q^{43} -5284.70 q^{45} +(9487.88 + 16433.5i) q^{47} -111685. q^{49} +(137531. - 79403.3i) q^{51} +(59687.5 - 34460.6i) q^{53} +(-24251.1 + 42004.1i) q^{55} +(17408.9 - 160949. i) q^{57} +(17779.2 + 10264.8i) q^{59} +(39431.6 + 68297.5i) q^{61} +(6638.91 + 11498.9i) q^{63} -100024. i q^{65} +(23781.8 - 13730.4i) q^{67} -108113. i q^{69} +(-345348. - 199387. i) q^{71} +(277015. - 479804. i) q^{73} -346487. i q^{75} +121862. q^{77} +(-424193. - 244908. i) q^{79} +(188271. - 326095. i) q^{81} -516880. q^{83} +(103407. + 179106. i) q^{85} +616633. q^{87} +(-710222. + 410047. i) q^{89} +(-217642. + 125656. i) q^{91} +(304595. - 527575. i) q^{93} +(209604. + 22671.6i) q^{95} +(429465. + 247952. i) q^{97} +(135651. + 234955. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9}+O(q^{10}) \) 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

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Database

Properties

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