LMFDB - Embedded newform 76.7.j.a.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.1
Character	$\chi$	$=$	76.53
Dual form			76.7.j.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-49.6429 + 8.75338i) q^{3} +(-5.51888 + 4.63089i) q^{5} +(269.359 - 466.544i) q^{7} +(1702.76 - 619.753i) q^{9} +O(q^{10})$	\(q+(-49.6429 + 8.75338i) q^{3} +(-5.51888 + 4.63089i) q^{5} +(269.359 - 466.544i) q^{7} +(1702.76 - 619.753i) q^{9} +(767.080 + 1328.62i) q^{11} +(-2559.79 - 451.360i) q^{13} +(233.437 - 278.200i) q^{15} +(-6663.83 - 2425.43i) q^{17} +(6858.04 - 114.728i) q^{19} +(-9287.94 + 25518.4i) q^{21} +(-9977.35 - 8371.99i) q^{23} +(-2704.24 + 15336.5i) q^{25} +(-47280.2 + 27297.2i) q^{27} +(1041.66 + 2861.95i) q^{29} +(35335.6 + 20401.0i) q^{31} +(-49709.9 - 59242.0i) q^{33} +(673.953 + 3822.18i) q^{35} +33512.8i q^{37} +131026. q^{39} +(-71411.8 + 12591.8i) q^{41} +(8906.23 - 7473.22i) q^{43} +(-6527.31 + 11305.6i) q^{45} +(-82699.9 + 30100.3i) q^{47} +(-86284.5 - 149449. i) q^{49} +(352042. + 62074.6i) q^{51} +(-59627.8 + 71061.6i) q^{53} +(-10386.1 - 3780.24i) q^{55} +(-339449. + 65726.5i) q^{57} +(-134795. + 370345. i) q^{59} +(-112828. - 94674.0i) q^{61} +(169512. - 961348. i) q^{63} +(16217.4 - 9363.12i) q^{65} +(132735. + 364686. i) q^{67} +(568587. + 328274. i) q^{69} +(-65421.4 - 77966.2i) q^{71} +(4642.59 + 26329.4i) q^{73} -785019. i q^{75} +826480. q^{77} +(-62138.9 + 10956.8i) q^{79} +(1.09626e6 - 919867. i) q^{81} +(221519. - 383682. i) q^{83} +(48008.8 - 17473.8i) q^{85} +(-76762.8 - 132957. i) q^{87} +(-403805. - 71201.8i) q^{89} +(-900084. + 1.07268e6i) q^{91} +(-1.93274e6 - 703459. i) q^{93} +(-37317.4 + 32392.0i) q^{95} +(-265052. + 728224. i) q^{97} +(2.12957e6 + 1.78692e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−49.6429	+	8.75338i	−1.83862	+	0.324199i	−0.981581	−	0.191045i	$-0.938812\pi$
$3$	−49.6429	+	8.75338i	−1.83862	+	0.324199i	−0.857043	+	0.515244i	$0.827701\pi$
$4$		0			0
$5$	−5.51888	+	4.63089i	−0.0441511	+	0.0370471i	−0.664596	−	0.747203i	$-0.731396\pi$
$5$	−5.51888	+	4.63089i	−0.0441511	+	0.0370471i	0.620445	+	0.784250i	$0.286952\pi$
$6$		0			0
$7$	269.359	−	466.544i	0.785305	−	1.36019i	−0.143512	−	0.989649i	$-0.545840\pi$
$7$	269.359	−	466.544i	0.785305	−	1.36019i	0.928817	−	0.370539i	$-0.120827\pi$
$8$		0			0
$9$	1702.76	−	619.753i	2.33574	−	0.850141i
$10$		0			0
$11$	767.080	+	1328.62i	0.576318	+	0.998212i	0.995897	+	0.0904935i	$0.0288444\pi$
$11$	767.080	+	1328.62i	0.576318	+	0.998212i	−0.419579	+	0.907719i	$0.637822\pi$
$12$		0			0
$13$	−2559.79	−	451.360i	−1.16513	−	0.205444i	−0.442559	−	0.896740i	$-0.645929\pi$
$13$	−2559.79	−	451.360i	−1.16513	−	0.205444i	−0.722572	+	0.691296i	$0.757040\pi$
$14$		0			0
$15$	233.437	−	278.200i	0.0691666	−	0.0824295i
$16$		0			0
$17$	−6663.83	−	2425.43i	−1.35637	−	0.493677i	−0.441437	−	0.897292i	$-0.645531\pi$
$17$	−6663.83	−	2425.43i	−1.35637	−	0.493677i	−0.914929	+	0.403615i	$0.867754\pi$
$18$		0			0
$19$	6858.04	−	114.728i	0.999860	−	0.0167267i
$19$	6858.04	−	114.728i	0.999860	−	0.0167267i
$20$		0			0
$21$	−9287.94	+	25518.4i	−1.00291	+	2.75547i
$22$		0			0
$23$	−9977.35	−	8371.99i	−0.820033	−	0.688090i	0.132947	−	0.991123i	$-0.457556\pi$
$23$	−9977.35	−	8371.99i	−0.820033	−	0.688090i	−0.952980	+	0.303034i	$0.902001\pi$
$24$		0			0
$25$	−2704.24	+	15336.5i	−0.173071	+	0.981536i
$26$		0			0
$27$	−47280.2	+	27297.2i	−2.40208	+	1.38684i
$28$		0			0
$29$	1041.66	+	2861.95i	0.0427104	+	0.117346i	0.959214	−	0.282680i	$-0.0912234\pi$
$29$	1041.66	+	2861.95i	0.0427104	+	0.117346i	−0.916504	+	0.400026i	$0.869001\pi$
$30$		0			0
$31$	35335.6	+	20401.0i	1.18612	+	0.684804i	0.957421	−	0.288694i	$-0.0932209\pi$
$31$	35335.6	+	20401.0i	1.18612	+	0.684804i	0.228695	+	0.973498i	$0.426554\pi$
$32$		0			0
$33$	−49709.9	−	59242.0i	−1.38325	−	1.64850i
$34$		0			0
$35$	673.953	+	3822.18i	0.0157190	+	0.0891470i
$36$		0			0
$37$			33512.8i			0.661616i	0.943698	+	0.330808i	$0.107321\pi$
$37$			33512.8i			0.661616i	−0.943698	+	0.330808i	$0.892679\pi$
$38$		0			0
$39$	131026.			2.20884
$40$		0			0
$41$	−71411.8	+	12591.8i	−1.03614	+	0.182699i	−0.665749	−	0.746176i	$-0.731888\pi$
$41$	−71411.8	+	12591.8i	−1.03614	+	0.182699i	−0.370392	+	0.928876i	$0.620777\pi$
$42$		0			0
$43$	8906.23	−	7473.22i	0.112018	−	0.0939945i	−0.585058	−	0.810991i	$-0.698928\pi$
$43$	8906.23	−	7473.22i	0.112018	−	0.0939945i	0.697076	+	0.716997i	$0.254484\pi$
$44$		0			0
$45$	−6527.31	+	11305.6i	−0.0716303	+	0.124067i
$46$		0			0
$47$	−82699.9	+	30100.3i	−0.796547	+	0.289919i	−0.708055	−	0.706158i	$-0.750427\pi$
$47$	−82699.9	+	30100.3i	−0.796547	+	0.289919i	−0.0884919	+	0.996077i	$0.528205\pi$
$48$		0			0
$49$	−86284.5	−	149449.i	−0.733406	−	1.27030i
$50$		0			0
$51$	352042.	+	62074.6i	2.65390	+	0.467954i
$52$		0			0
$53$	−59627.8	+	71061.6i	−0.400517	+	0.477318i	−0.928178	−	0.372138i	$-0.878625\pi$
$53$	−59627.8	+	71061.6i	−0.400517	+	0.477318i	0.527660	+	0.849455i	$0.323069\pi$
$54$		0			0
$55$	−10386.1	−	3780.24i	−0.0624260	−	0.0227212i
$56$		0			0
$57$	−339449.	+	65726.5i	−1.83294	+	0.354908i
$58$		0			0
$59$	−134795.	+	370345.i	−0.656322	+	1.80323i	−0.0633711	+	0.997990i	$0.520185\pi$
$59$	−134795.	+	370345.i	−0.656322	+	1.80323i	−0.592951	+	0.805239i	$0.702037\pi$
$60$		0			0
$61$	−112828.	−	94674.0i	−0.497082	−	0.417101i	0.359474	−	0.933155i	$-0.382956\pi$
$61$	−112828.	−	94674.0i	−0.497082	−	0.417101i	−0.856556	+	0.516054i	$0.827400\pi$
$62$		0			0
$63$	169512.	−	961348.i	0.677919	−	3.84467i
$64$		0			0
$65$	16217.4	−	9363.12i	0.0590529	−	0.0340942i
$66$		0			0
$67$	132735.	+	364686.i	0.441327	+	1.21254i	0.938620	+	0.344954i	$0.112105\pi$
$67$	132735.	+	364686.i	0.441327	+	1.21254i	−0.497292	+	0.867583i	$0.665672\pi$
$68$		0			0
$69$	568587.	+	328274.i	1.73081	+	0.999285i
$70$		0			0
$71$	−65421.4	−	77966.2i	−0.182787	−	0.217837i	0.666868	−	0.745176i	$-0.267634\pi$
$71$	−65421.4	−	77966.2i	−0.182787	−	0.217837i	−0.849655	+	0.527339i	$0.823190\pi$
$72$		0			0
$73$	4642.59	+	26329.4i	0.0119342	+	0.0676820i	0.990193	−	0.139705i	$-0.0446153\pi$
$73$	4642.59	+	26329.4i	0.0119342	+	0.0676820i	−0.978259	+	0.207387i	$0.933504\pi$
$74$		0			0
$75$		−	785019.i		−	1.86079i
$76$		0			0
$77$	826480.			1.81034
$78$		0			0
$79$	−62138.9	+	10956.8i	−0.126032	+	0.0222229i	−0.236308	−	0.971678i	$-0.575938\pi$
$79$	−62138.9	+	10956.8i	−0.126032	+	0.0222229i	0.110276	+	0.993901i	$0.464826\pi$
$80$		0			0
$81$	1.09626e6	−	919867.i	2.06280	−	1.73089i
$82$		0			0
$83$	221519.	−	383682.i	0.387415	−	0.671022i	−0.604686	−	0.796464i	$-0.706702\pi$
$83$	221519.	−	383682.i	0.387415	−	0.671022i	0.992101	+	0.125442i	$0.0400348\pi$
$84$		0			0
$85$	48008.8	−	17473.8i	0.0781744	−	0.0284531i
$86$		0			0
$87$	−76762.8	−	132957.i	−0.116572	−	0.201908i
$88$		0			0
$89$	−403805.	−	71201.8i	−0.572799	−	0.101000i	−0.120256	−	0.992743i	$-0.538372\pi$
$89$	−403805.	−	71201.8i	−0.572799	−	0.101000i	−0.452542	+	0.891743i	$0.649483\pi$
$90$		0			0
$91$	−900084.	+	1.07268e6i	−1.19442	+	1.42346i
$92$		0			0
$93$	−1.93274e6	−	703459.i	−2.40284	−	0.874561i
$94$		0			0
$95$	−37317.4	+	32392.0i	−0.0435252	+	0.0377805i
$96$		0			0
$97$	−265052.	+	728224.i	−0.290413	+	0.797903i	0.705593	+	0.708617i	$0.250681\pi$
$97$	−265052.	+	728224.i	−0.290413	+	0.797903i	−0.996006	+	0.0892858i	$0.971542\pi$
$98$		0			0
$99$	2.12957e6	+	1.78692e6i	2.19475	+	1.84162i
$100$		0			0
$101$	−178953.	+	1.01489e6i	−0.173690	+	0.985045i	0.765955	+	0.642894i	$0.222267\pi$
$101$	−178953.	+	1.01489e6i	−0.173690	+	0.985045i	−0.939645	+	0.342151i	$0.888845\pi$
$102$		0			0
$103$	−358351.	+	206894.i	−0.327942	+	0.189337i	−0.654927	−	0.755692i	$-0.727301\pi$
$103$	−358351.	+	206894.i	−0.327942	+	0.189337i	0.326985	+	0.945029i	$0.393967\pi$
$104$		0			0
$105$	−66913.9	−	183845.i	−0.0578028	−	0.158812i
$106$		0			0
$107$	−498874.	−	288025.i	−0.407230	−	0.235114i	0.282369	−	0.959306i	$-0.408880\pi$
$107$	−498874.	−	288025.i	−0.407230	−	0.235114i	−0.689599	+	0.724192i	$0.742213\pi$
$108$		0			0
$109$	−393884.	−	469412.i	−0.304150	−	0.362472i	0.592222	−	0.805775i	$-0.298251\pi$
$109$	−393884.	−	469412.i	−0.304150	−	0.362472i	−0.896372	+	0.443303i	$0.853807\pi$
$110$		0			0
$111$	−293350.	−	1.66367e6i	−0.214495	−	1.21646i
$112$		0			0
$113$			2.11327e6i			1.46460i	0.680981	+	0.732301i	$0.261554\pi$
$113$			2.11327e6i			1.46460i	−0.680981	+	0.732301i	$0.738446\pi$
$114$		0			0
$115$	93833.6			0.0616971
$116$		0			0
$117$	−4.63844e6	+	817881.i	−2.89610	+	0.510661i
$118$		0			0
$119$	−2.92654e6	+	2.45566e6i	−1.73665	+	1.45723i
$120$		0			0
$121$	−291041.	+	504099.i	−0.164285	+	0.284551i
$122$		0			0
$123$	3.43487e6	−	1.25019e6i	1.84584	−	0.671832i
$124$		0			0
$125$	−112382.	−	194651.i	−0.0575394	−	0.0996612i
$126$		0			0
$127$	1.10953e6	+	195641.i	0.541663	+	0.0955099i	0.437784	−	0.899080i	$-0.355763\pi$
$127$	1.10953e6	+	195641.i	0.541663	+	0.0955099i	0.103879	+	0.994590i	$0.466875\pi$
$128$		0			0
$129$	−376715.	+	448952.i	−0.175487	+	0.209137i
$130$		0			0
$131$	276034.	+	100468.i	0.122786	+	0.0446904i	0.402682	−	0.915340i	$-0.368078\pi$
$131$	276034.	+	100468.i	0.122786	+	0.0446904i	−0.279896	+	0.960030i	$0.590300\pi$
$132$		0			0
$133$	1.79375e6	−	3.23048e6i	0.762443	−	1.37313i
$134$		0			0
$135$	134523.	−	369600.i	0.0546759	−	0.150221i
$136$		0			0
$137$	3.34579e6	+	2.80745e6i	1.30118	+	1.09182i	0.989940	+	0.141485i	$0.0451877\pi$
$137$	3.34579e6	+	2.80745e6i	1.30118	+	1.09182i	0.311237	+	0.950332i	$0.399257\pi$
$138$		0			0
$139$	178315.	−	1.01127e6i	0.0663961	−	0.376551i	−0.933445	−	0.358721i	$-0.883213\pi$
$139$	178315.	−	1.01127e6i	0.0663961	−	0.376551i	0.999841	−	0.0178302i	$-0.00567584\pi$
$140$		0			0
$141$	3.84198e6	−	2.21817e6i	1.37056	−	0.791292i
$142$		0			0
$143$	−1.36388e6	−	3.74722e6i	−0.466409	−	1.28145i
$144$		0			0
$145$	−19002.2	−	10970.9i	−0.00623304	−	0.00359864i
$146$		0			0
$147$	5.59160e6	+	6.66380e6i	1.76029	+	2.09783i
$148$		0			0
$149$	−100685.	−	571011.i	−0.0304372	−	0.172618i	0.965800	−	0.259289i	$-0.0834882\pi$
$149$	−100685.	−	571011.i	−0.0304372	−	0.172618i	−0.996237	+	0.0866712i	$0.972377\pi$
$150$		0			0
$151$		−	4.45821e6i		−	1.29488i	−0.762117	−	0.647440i	$-0.775840\pi$
$151$		−	4.45821e6i		−	1.29488i	0.762117	−	0.647440i	$-0.224160\pi$
$152$		0			0
$153$	−1.28500e7			−3.58782
$154$		0			0
$155$	−289488.	+	51044.5i	−0.0777383	+	0.0137074i
$156$		0			0
$157$	−4.85229e6	+	4.07156e6i	−1.25386	+	1.05211i	−0.257549	+	0.966265i	$0.582915\pi$
$157$	−4.85229e6	+	4.07156e6i	−1.25386	+	1.05211i	−0.996308	+	0.0858461i	$0.972641\pi$
$158$		0			0
$159$	2.33806e6	−	4.04965e6i	0.581655	−	1.00746i
$160$		0			0
$161$	−6.59339e6	+	2.39980e6i	−1.57991	+	0.575039i
$162$		0			0
$163$	2.02381e6	+	3.50534e6i	0.467311	+	0.809407i	0.999303	−	0.0373432i	$-0.0118895\pi$
$163$	2.02381e6	+	3.50534e6i	0.467311	+	0.809407i	−0.531991	+	0.846750i	$0.678556\pi$
$164$		0			0
$165$	548687.	+	96748.3i	0.122144	+	0.0215373i
$166$		0			0
$167$	−2.12655e6	+	2.53433e6i	−0.456590	+	0.544143i	−0.944397	−	0.328809i	$-0.893353\pi$
$167$	−2.12655e6	+	2.53433e6i	−0.456590	+	0.544143i	0.487806	+	0.872952i	$0.337797\pi$
$168$		0			0
$169$	1.81309e6	+	659911.i	0.375629	+	0.136718i
$170$		0			0
$171$	1.16065e7	−	4.44564e6i	2.32120	−	0.889091i
$172$		0			0
$173$	217604.	−	597861.i	0.0420270	−	0.115468i	−0.916904	−	0.399108i	$-0.869320\pi$
$173$	217604.	−	597861.i	0.0420270	−	0.115468i	0.958931	+	0.283640i	$0.0915420\pi$
$174$		0			0
$175$	6.42675e6	+	5.39268e6i	1.19916	+	1.00621i
$176$		0			0
$177$	3.44982e6	−	1.95649e7i	0.622124	−	3.52824i
$178$		0			0
$179$	−1.85204e6	+	1.06928e6i	−0.322918	+	0.186437i	−0.652692	−	0.757623i	$-0.726361\pi$
$179$	−1.85204e6	+	1.06928e6i	−0.322918	+	0.186437i	0.329775	+	0.944060i	$0.393027\pi$
$180$		0			0
$181$	−3.32396e6	−	9.13251e6i	−0.560557	−	1.54012i	−0.818824	−	0.574045i	$-0.805373\pi$
$181$	−3.32396e6	−	9.13251e6i	−0.560557	−	1.54012i	0.258266	−	0.966074i	$-0.416849\pi$
$182$		0			0
$183$	6.42983e6	+	3.71226e6i	1.04917	+	0.605739i
$184$		0			0
$185$	−155194.	−	184953.i	−0.0245110	−	0.0292110i
$186$		0			0
$187$	−1.88920e6	−	1.07142e7i	−0.288904	−	1.63846i
$188$		0			0
$189$			2.94111e7i			4.35637i
$190$		0			0
$191$	−145774.			−0.0209208			−0.0104604	−	0.999945i	$-0.503330\pi$
$191$	−145774.			−0.0209208			−0.0104604	+	0.999945i	$0.503330\pi$
$192$		0			0
$193$	6.36645e6	−	1.12258e6i	0.885575	−	0.156151i	0.287681	−	0.957726i	$-0.407116\pi$
$193$	6.36645e6	−	1.12258e6i	0.885575	−	0.156151i	0.597894	+	0.801575i	$0.296004\pi$
$194$		0			0
$195$	−723119.	+	606769.i	−0.0975228	+	0.0818313i
$196$		0			0
$197$	6.13807e6	−	1.06314e7i	0.802848	−	1.39057i	−0.114887	−	0.993379i	$-0.536651\pi$
$197$	6.13807e6	−	1.06314e7i	0.802848	−	1.39057i	0.917735	−	0.397194i	$-0.130016\pi$
$198$		0			0
$199$	8.20338e6	−	2.98578e6i	1.04096	−	0.378878i	0.235715	−	0.971822i	$-0.424257\pi$
$199$	8.20338e6	−	2.98578e6i	1.04096	−	0.378878i	0.805243	+	0.592944i	$0.202035\pi$
$200$		0			0
$201$	−9.78158e6	−	1.69422e7i	−1.20454	−	2.08632i
$202$		0			0
$203$	1.61581e6	+	284910.i	0.193153	+	0.0340581i
$204$		0			0
$205$	335802.	−	400193.i	0.0389782	−	0.0464524i
$206$		0			0
$207$	−2.21776e7	−	8.07197e6i	−2.50036	−	0.910057i
$208$		0			0
$209$	5.41309e6	+	9.02373e6i	0.592934	+	0.988433i
$210$		0			0
$211$	−4.15672e6	+	1.14205e7i	−0.442490	+	1.21573i	0.495359	+	0.868688i	$0.335036\pi$
$211$	−4.15672e6	+	1.14205e7i	−0.442490	+	1.21573i	−0.937849	+	0.347043i	$0.887186\pi$
$212$		0			0
$213$	3.93018e6	+	3.29781e6i	0.406699	+	0.341261i
$214$		0			0
$215$	−14544.8	+	82487.6i	−0.00146350	+	0.00829991i
$216$		0			0
$217$	1.90359e7	−	1.09904e7i	1.86292	−	1.07556i
$218$		0			0
$219$	−460943.	−	1.26643e6i	−0.0438849	−	0.120573i
$220$		0			0
$221$	1.59633e7	+	9.21640e6i	1.47892	+	0.853855i
$222$		0			0
$223$	−1.39142e7	−	1.65823e7i	−1.25471	−	1.49530i	−0.794213	−	0.607640i	$-0.792116\pi$
$223$	−1.39142e7	−	1.65823e7i	−1.25471	−	1.49530i	−0.460495	−	0.887662i	$-0.652328\pi$
$224$		0			0
$225$	4.90018e6	+	2.77903e7i	0.430194	+	2.43975i
$226$		0			0
$227$			1.16156e7i			0.993033i	0.868027	+	0.496517i	$0.165388\pi$
$227$			1.16156e7i			0.993033i	−0.868027	+	0.496517i	$0.834612\pi$
$228$		0			0
$229$	41161.2			0.00342753			0.00171377	−	0.999999i	$-0.499454\pi$
$229$	41161.2			0.00342753			0.00171377	+	0.999999i	$0.499454\pi$
$230$		0			0
$231$	−4.10289e7	+	7.23450e6i	−3.32854	+	0.586911i
$232$		0			0
$233$	−1.36939e7	+	1.14906e7i	−1.08258	+	0.908394i	−0.996133	−	0.0878622i	$-0.971996\pi$
$233$	−1.36939e7	+	1.14906e7i	−1.08258	+	0.908394i	−0.0864493	+	0.996256i	$0.527552\pi$
$234$		0			0
$235$	317020.	−	549094.i	0.0244277	−	0.0423100i
$236$		0			0
$237$	2.98884e6	−	1.08785e6i	0.224522	−	0.0817192i
$238$		0			0
$239$	1.87259e6	+	3.24343e6i	0.137167	+	0.237580i	0.926423	−	0.376484i	$-0.122867\pi$
$239$	1.87259e6	+	3.24343e6i	0.137167	+	0.237580i	−0.789256	+	0.614064i	$0.789534\pi$
$240$		0			0
$241$	−1.07864e7	−	1.90193e6i	−0.770591	−	0.135876i	−0.225489	−	0.974246i	$-0.572398\pi$
$241$	−1.07864e7	−	1.90193e6i	−0.770591	−	0.135876i	−0.545102	+	0.838370i	$0.683509\pi$
$242$		0			0
$243$	−2.07868e7	+	2.47727e7i	−1.44867	+	1.72645i
$244$		0			0
$245$	1.16828e6	+	425218.i	0.0794416	+	0.0289144i
$246$		0			0
$247$	−1.76069e7	−	2.80177e6i	−1.16840	−	0.185926i
$248$		0			0
$249$	−7.63831e6	+	2.09861e7i	−0.494765	+	1.35936i
$250$		0			0
$251$	−3.69619e6	−	3.10147e6i	−0.233740	−	0.196131i	0.518393	−	0.855142i	$-0.326530\pi$
$251$	−3.69619e6	−	3.10147e6i	−0.233740	−	0.196131i	−0.752133	+	0.659011i	$0.770975\pi$
$252$		0			0
$253$	3.46978e6	−	1.96781e7i	0.214260	−	1.21513i
$254$		0			0
$255$	−2.23034e6	+	1.28769e6i	−0.134509	+	0.0776587i
$256$		0			0
$257$	−2.20550e6	−	6.05955e6i	−0.129929	−	0.356978i	0.857621	−	0.514283i	$-0.171942\pi$
$257$	−2.20550e6	−	6.05955e6i	−0.129929	−	0.356978i	−0.987550	+	0.157305i	$0.949720\pi$
$258$		0			0
$259$	1.56352e7	+	9.02700e6i	0.899921	+	0.519570i
$260$		0			0
$261$	3.54740e6	+	4.22763e6i	0.199521	+	0.237780i
$262$		0			0
$263$	−3.02799e6	−	1.71726e7i	−0.166451	−	0.943992i	−0.947555	−	0.319591i	$-0.896454\pi$
$263$	−3.02799e6	−	1.71726e7i	−0.166451	−	0.943992i	0.781104	−	0.624401i	$-0.214657\pi$
$264$		0			0
$265$		−	668311.i		−	0.0359121i
$266$		0			0
$267$	2.06693e7			1.08591
$268$		0			0
$269$	2.33041e6	−	410914.i	0.119722	−	0.0211103i	−0.113466	−	0.993542i	$-0.536195\pi$
$269$	2.33041e6	−	410914.i	0.119722	−	0.0211103i	0.233188	+	0.972432i	$0.425084\pi$
$270$		0			0
$271$	1.58734e7	−	1.33193e7i	0.797556	−	0.669229i	−0.150047	−	0.988679i	$-0.547942\pi$
$271$	1.58734e7	−	1.33193e7i	0.797556	−	0.669229i	0.947603	+	0.319450i	$0.103498\pi$
$272$		0			0
$273$	3.52932e7	−	6.11296e7i	1.73461	−	3.00444i
$274$		0			0
$275$	−2.24508e7	+	8.17141e6i	−1.07953	+	0.392915i
$276$		0			0
$277$	1.45737e7	+	2.52423e7i	0.685692	+	1.18765i	0.973219	+	0.229881i	$0.0738338\pi$
$277$	1.45737e7	+	2.52423e7i	0.685692	+	1.18765i	−0.287526	+	0.957773i	$0.592833\pi$
$278$		0			0
$279$	7.28115e7	+	1.28386e7i	3.35264	+	0.591161i
$280$		0			0
$281$	−1.17619e7	+	1.40173e7i	−0.530101	+	0.631749i	−0.962938	−	0.269723i	$-0.913068\pi$
$281$	−1.17619e7	+	1.40173e7i	−0.530101	+	0.631749i	0.432838	+	0.901472i	$0.357512\pi$
$282$		0			0
$283$	−4.16050e7	−	1.51430e7i	−1.83563	−	0.668116i	−0.991186	−	0.132480i	$-0.957706\pi$
$283$	−4.16050e7	−	1.51430e7i	−1.83563	−	0.668116i	−0.844449	−	0.535636i	$-0.820072\pi$
$284$		0			0
$285$	1.56900e6	−	1.93469e6i	0.0677782	−	0.0835749i
$286$		0			0
$287$	−1.33608e7	+	3.67085e7i	−0.565180	+	1.55282i
$288$		0			0
$289$	2.00334e7	+	1.68100e7i	0.829968	+	0.696426i
$290$		0			0
$291$	6.78352e6	−	3.84713e7i	0.275281	−	1.56120i
$292$		0			0
$293$	1.51233e7	−	8.73143e6i	0.601234	−	0.347122i	−0.168293	−	0.985737i	$-0.553826\pi$
$293$	1.51233e7	−	8.73143e6i	0.601234	−	0.347122i	0.769527	+	0.638615i	$0.220492\pi$
$294$		0			0
$295$	−971114.	−	2.66811e6i	−0.0378272	−	0.103929i
$296$		0			0
$297$	−7.25353e7	−	4.18783e7i	−2.76873	−	1.59852i
$298$		0			0
$299$	2.17611e7	+	2.59339e7i	0.814082	+	0.970185i
$300$		0			0
$301$	−1.08761e6	−	6.16813e6i	−0.0398816	−	0.226180i
$302$		0			0
$303$		−	5.19486e7i		−	1.86744i
$304$		0			0
$305$	1.06111e6			0.0373991
$306$		0			0
$307$	2.66021e7	−	4.69067e6i	0.919393	−	0.162114i	0.306127	−	0.951991i	$-0.400967\pi$
$307$	2.66021e7	−	4.69067e6i	0.919393	−	0.162114i	0.613266	+	0.789877i	$0.289856\pi$
$308$		0			0
$309$	1.59785e7	−	1.34076e7i	0.541578	−	0.454438i
$310$		0			0
$311$	−2.59165e7	+	4.48888e7i	−0.861580	+	1.49230i	0.00882295	+	0.999961i	$0.497192\pi$
$311$	−2.59165e7	+	4.48888e7i	−0.861580	+	1.49230i	−0.870403	+	0.492340i	$0.836142\pi$
$312$		0			0
$313$	3.99736e7	−	1.45492e7i	1.30359	−	0.474467i	0.405424	−	0.914129i	$-0.367124\pi$
$313$	3.99736e7	−	1.45492e7i	1.30359	−	0.474467i	0.898163	+	0.439662i	$0.144902\pi$
$314$		0			0
$315$	3.51638e6	+	6.09056e6i	0.112503	+	0.194861i
$316$		0			0
$317$	−3.52390e7	−	6.21359e6i	−1.10623	−	0.195058i	−0.409443	−	0.912336i	$-0.634277\pi$
$317$	−3.52390e7	−	6.21359e6i	−1.10623	−	0.195058i	−0.696788	+	0.717277i	$0.745388\pi$
$318$		0			0
$319$	−3.00340e6	+	3.57932e6i	−0.0925212	+	0.110263i
$320$		0			0
$321$	2.72867e7	+	9.93156e6i	0.824967	+	0.300264i
$322$		0			0
$323$	−4.59791e7	−	1.58692e7i	−1.36443	−	0.470920i
$324$		0			0
$325$	1.38446e7	−	3.80377e7i	0.403301	−	1.10806i
$326$		0			0
$327$	2.36624e7	+	1.98552e7i	0.676732	+	0.567845i
$328$		0			0
$329$	−8.23287e6	+	4.66909e7i	−0.231187	+	1.31113i
$330$		0			0
$331$	−2.36064e7	+	1.36291e7i	−0.650946	+	0.375824i	−0.788819	−	0.614626i	$-0.789307\pi$
$331$	−2.36064e7	+	1.36291e7i	−0.650946	+	0.375824i	0.137872	+	0.990450i	$0.455974\pi$
$332$		0			0
$333$	2.07697e7	+	5.70642e7i	0.562467	+	1.54536i
$334$		0			0
$335$	−2.42137e6	−	1.39798e6i	−0.0644061	−	0.0371849i
$336$		0			0
$337$	−7.40205e6	−	8.82142e6i	−0.193403	−	0.230488i	0.660625	−	0.750716i	$-0.270291\pi$
$337$	−7.40205e6	−	8.82142e6i	−0.193403	−	0.230488i	−0.854027	+	0.520228i	$0.825847\pi$
$338$		0			0
$339$	−1.84982e7	−	1.04909e8i	−0.474823	−	2.69285i
$340$		0			0
$341$			6.25968e7i			1.57866i
$342$		0			0
$343$	−2.95865e7			−0.733180
$344$		0			0
$345$	−4.65817e6	+	821361.i	−0.113438	+	0.0200022i
$346$		0			0
$347$	−2.96573e7	+	2.48854e7i	−0.709811	+	0.595602i	−0.924546	−	0.381070i	$-0.875556\pi$
$347$	−2.96573e7	+	2.48854e7i	−0.709811	+	0.595602i	0.214735	+	0.976672i	$0.431111\pi$
$348$		0			0
$349$	−3.51885e7	+	6.09483e7i	−0.827798	+	1.43379i	0.0719635	+	0.997407i	$0.477073\pi$
$349$	−3.51885e7	+	6.09483e7i	−0.827798	+	1.43379i	−0.899762	+	0.436381i	$0.856260\pi$
$350$		0			0
$351$	1.33348e8	−	4.85348e7i	3.08366	−	1.12236i
$352$		0			0
$353$	−2.84557e7	−	4.92866e7i	−0.646911	−	1.12048i	−0.983857	−	0.178959i	$-0.942727\pi$
$353$	−2.84557e7	−	4.92866e7i	−0.646911	−	1.12048i	0.336946	−	0.941524i	$-0.390606\pi$
$354$		0			0
$355$	722107.	+	127327.i	0.0161405	+	0.00284600i
$356$		0			0
$357$	1.23786e8	−	1.47523e8i	2.72062	−	3.24231i
$358$		0			0
$359$	1.25198e7	+	4.55682e6i	0.270591	+	0.0984870i	0.473752	−	0.880658i	$-0.342899\pi$
$359$	1.25198e7	+	4.55682e6i	0.270591	+	0.0984870i	−0.203161	+	0.979145i	$0.565122\pi$
$360$		0			0
$361$	4.70196e7	−	1.57362e6i	0.999440	−	0.0334487i
$362$		0			0
$363$	1.00356e7	−	2.75725e7i	0.209808	−	0.576443i
$364$		0			0
$365$	−147551.	−	123810.i	−0.00303433	−	0.00254610i
$366$		0			0
$367$	−6.80531e6	+	3.85949e7i	−0.137673	+	0.780785i	0.835287	+	0.549814i	$0.185301\pi$
$367$	−6.80531e6	+	3.85949e7i	−0.137673	+	0.780785i	−0.972961	+	0.230971i	$0.925810\pi$
$368$		0			0
$369$	−1.13793e8	+	6.56985e7i	−2.26484	+	1.30760i
$370$		0			0
$371$	1.70921e7	+	4.69601e7i	0.334714	+	0.919618i
$372$		0			0
$373$	−3.66679e7	−	2.11702e7i	−0.706576	−	0.407942i	0.103216	−	0.994659i	$-0.467087\pi$
$373$	−3.66679e7	−	2.11702e7i	−0.706576	−	0.407942i	−0.809792	+	0.586717i	$0.800420\pi$
$374$		0			0
$375$	7.28280e6	+	8.67930e6i	0.138103	+	0.164585i
$376$		0			0
$377$	−1.37467e6	−	7.79615e6i	−0.0256552	−	0.145498i
$378$		0			0
$379$		−	9.86080e6i		−	0.181132i	−0.995890	−	0.0905659i	$-0.971132\pi$
$379$		−	9.86080e6i		−	0.181132i	0.995890	−	0.0905659i	$-0.0288676\pi$
$380$		0			0
$381$	−5.67930e7			−1.02688
$382$		0			0
$383$	5.78700e7	−	1.02040e7i	1.03005	−	0.181625i	0.367014	−	0.930215i	$-0.380380\pi$
$383$	5.78700e7	−	1.02040e7i	1.03005	−	0.181625i	0.663033	+	0.748590i	$0.269269\pi$
$384$		0			0
$385$	−4.56125e6	+	3.82734e6i	−0.0799285	+	0.0670680i
$386$		0			0
$387$	1.05336e7	−	1.82447e7i	0.181737	−	0.314778i
$388$		0			0
$389$	−3.95303e7	+	1.43878e7i	−0.671554	+	0.244426i	−0.655217	−	0.755441i	$-0.727423\pi$
$389$	−3.95303e7	+	1.43878e7i	−0.671554	+	0.244426i	−0.0163373	+	0.999867i	$0.505201\pi$
$390$		0			0
$391$	4.61816e7	+	7.99889e7i	0.772572	+	1.33813i
$392$		0			0
$393$	−1.45825e7	−	2.57130e6i	−0.240246	−	0.0423618i
$394$		0			0
$395$	292198.	−	348228.i	0.00474117	−	0.00565030i
$396$		0			0
$397$	−2.54354e7	−	9.25774e6i	−0.406507	−	0.147956i	0.130670	−	0.991426i	$-0.458287\pi$
$397$	−2.54354e7	−	9.25774e6i	−0.406507	−	0.147956i	−0.537177	+	0.843470i	$0.680509\pi$
$398$		0			0
$399$	−6.07694e7	+	1.76072e8i	−0.956679	+	2.77186i
$400$		0			0
$401$	2.77966e6	−	7.63705e6i	0.0431081	−	0.118438i	−0.916271	−	0.400560i	$-0.868816\pi$
$401$	2.77966e6	−	7.63705e6i	0.0431081	−	0.118438i	0.959379	+	0.282121i	$0.0910380\pi$
$402$		0			0
$403$	−8.12435e7	−	6.81714e7i	−1.24129	−	1.04157i
$404$		0			0
$405$	−1.79030e6	+	1.01533e7i	−0.0269501	+	0.152842i
$406$		0			0
$407$	−4.45258e7	+	2.57070e7i	−0.660433	+	0.381301i
$408$		0			0
$409$	−9.79616e6	−	2.69147e7i	−0.143181	−	0.393387i	0.847286	−	0.531137i	$-0.178235\pi$
$409$	−9.79616e6	−	2.69147e7i	−0.143181	−	0.393387i	−0.990467	+	0.137750i	$0.956013\pi$
$410$		0			0
$411$	−1.90669e8	−	1.10083e8i	−2.74634	−	1.58560i
$412$		0			0
$413$	1.36474e8	+	1.62644e8i	1.93732	+	2.30880i
$414$		0			0
$415$	554253.	+	3.14332e6i	0.00775467	+	0.0439789i
$416$		0			0
$417$			5.17633e7i			0.713861i
$418$		0			0
$419$	6.68449e7			0.908712			0.454356	−	0.890820i	$-0.349869\pi$
$419$	6.68449e7			0.908712			0.454356	+	0.890820i	$0.349869\pi$
$420$		0			0
$421$	3.99634e7	−	7.04662e6i	0.535570	−	0.0944354i	0.100679	−	0.994919i	$-0.467898\pi$
$421$	3.99634e7	−	7.04662e6i	0.535570	−	0.0944354i	0.434890	+	0.900484i	$0.356787\pi$
$422$		0			0
$423$	−1.22163e8	+	1.02507e8i	−1.61406	+	1.35435i
$424$		0			0
$425$	5.52183e7	−	9.56409e7i	0.719310	−	1.24588i
$426$		0			0
$427$	−7.45609e7	+	2.71380e7i	−0.957696	+	0.348573i
$428$		0			0
$429$	1.00508e8	+	1.74084e8i	1.27300	+	2.20489i
$430$		0			0
$431$	1.78553e7	+	3.14837e6i	0.223016	+	0.0393237i	0.284039	−	0.958813i	$-0.408325\pi$
$431$	1.78553e7	+	3.14837e6i	0.223016	+	0.0393237i	−0.0610236	+	0.998136i	$0.519437\pi$
$432$		0			0
$433$	−9.70660e6	+	1.15679e7i	−0.119565	+	0.142492i	−0.822507	−	0.568756i	$-0.807425\pi$
$433$	−9.70660e6	+	1.15679e7i	−0.119565	+	0.142492i	0.702942	+	0.711247i	$0.251869\pi$
$434$		0			0
$435$	1.03936e6	+	378295.i	0.0126269	+	0.00459581i
$436$		0			0
$437$	−6.93855e7	−	5.62707e7i	−0.831428	−	0.674277i
$438$		0			0
$439$	3.07096e7	−	8.43740e7i	0.362978	−	0.997275i	−0.614992	−	0.788533i	$-0.710841\pi$
$439$	3.07096e7	−	8.43740e7i	0.362978	−	0.997275i	0.977971	−	0.208742i	$-0.0669368\pi$
$440$		0			0
$441$	−2.39543e8	−	2.01001e8i	−2.79298	−	2.34359i
$442$		0			0
$443$	−1.49620e7	+	8.48536e7i	−0.172099	+	0.976020i	0.769341	+	0.638839i	$0.220585\pi$
$443$	−1.49620e7	+	8.48536e7i	−0.172099	+	0.976020i	−0.941440	+	0.337182i	$0.890526\pi$
$444$		0			0
$445$	2.55828e6	−	1.47703e6i	0.0290314	−	0.0167613i
$446$		0			0
$447$	9.99654e6	+	2.74653e7i	0.111925	+	0.307511i
$448$		0			0
$449$	−1.29236e8	−	7.46146e7i	−1.42773	−	0.824299i	−0.430787	−	0.902454i	$-0.641764\pi$
$449$	−1.29236e8	−	7.46146e7i	−1.42773	−	0.824299i	−0.996941	+	0.0781545i	$0.975097\pi$
$450$		0			0
$451$	−7.15083e7	−	8.52203e7i	−0.779519	−	0.928995i
$452$		0			0
$453$	3.90244e7	+	2.21318e8i	0.419799	+	2.38080i
$454$		0			0
$455$		−	1.00882e7i		−	0.107097i
$456$		0			0
$457$	4.57887e7			0.479744			0.239872	−	0.970805i	$-0.422895\pi$
$457$	4.57887e7			0.479744			0.239872	+	0.970805i	$0.422895\pi$
$458$		0			0
$459$	3.81274e8	−	6.72290e7i	3.94275	−	0.695214i
$460$		0			0
$461$	1.15235e8	−	9.66933e7i	1.17620	−	0.986946i	0.176200	−	0.984354i	$-0.443620\pi$
$461$	1.15235e8	−	9.66933e7i	1.17620	−	0.986946i	0.999997	−	0.00259156i	$-0.000824919\pi$
$462$		0			0
$463$	−2.24185e7	+	3.88299e7i	−0.225872	+	0.391222i	−0.956581	−	0.291467i	$-0.905857\pi$
$463$	−2.24185e7	+	3.88299e7i	−0.225872	+	0.391222i	0.730709	+	0.682690i	$0.239190\pi$
$464$		0			0
$465$	1.39242e7	−	5.06799e6i	0.138488	−	0.0504054i
$466$		0			0
$467$	−4.89770e7	−	8.48306e7i	−0.480885	−	0.832917i	0.518874	−	0.854850i	$-0.326351\pi$
$467$	−4.89770e7	−	8.48306e7i	−0.480885	−	0.832917i	−0.999759	+	0.0219332i	$0.993018\pi$
$468$		0			0
$469$	2.05896e8	+	3.63050e7i	1.99585	+	0.351923i
$470$		0			0
$471$	2.05242e8	−	2.44598e8i	1.96428	−	2.34094i
$472$		0			0
$473$	1.67609e7	+	6.10045e6i	0.158385	+	0.0576473i
$474$		0			0
$475$	−1.67863e7	+	1.05489e8i	−0.156629	+	0.984294i
$476$		0			0
$477$	−5.74910e7	+	1.57955e8i	−0.529718	+	1.45539i
$478$		0			0
$479$	−1.01238e8	−	8.49490e7i	−0.921167	−	0.772951i	0.0530436	−	0.998592i	$-0.483108\pi$
$479$	−1.01238e8	−	8.49490e7i	−0.921167	−	0.772951i	−0.974210	+	0.225641i	$0.927552\pi$
$480$		0			0
$481$	1.51264e7	−	8.57859e7i	0.135925	−	0.770869i
$482$		0			0
$483$	3.06309e8	−	1.76847e8i	2.71843	−	1.56949i
$484$		0			0
$485$	−1.90954e6	−	5.24641e6i	−0.0167380	−	0.0459872i
$486$		0			0
$487$	1.11387e8	+	6.43094e7i	0.964380	+	0.556785i	0.897518	−	0.440977i	$-0.145368\pi$
$487$	1.11387e8	+	6.43094e7i	0.964380	+	0.556785i	0.0668617	+	0.997762i	$0.478701\pi$
$488$		0			0
$489$	−1.31151e8	−	1.56300e8i	−1.12162	−	1.33669i
$490$		0			0
$491$	1.22354e7	+	6.93902e7i	0.103365	+	0.586210i	0.991861	+	0.127326i	$0.0406396\pi$
$491$	1.22354e7	+	6.93902e7i	0.103365	+	0.586210i	−0.888496	+	0.458884i	$0.848249\pi$
$492$		0			0
$493$		−	2.15980e7i		−	0.180249i
$494$		0			0
$495$	−2.00279e7			−0.165127
$496$		0			0
$497$	−5.39966e7	+	9.52105e6i	−0.439842	+	0.0775561i
$498$		0			0
$499$	4.62189e6	−	3.87822e6i	0.0371978	−	0.0312127i	−0.623999	−	0.781425i	$-0.714493\pi$
$499$	4.62189e6	−	3.87822e6i	0.0371978	−	0.0312127i	0.661197	+	0.750212i	$0.270049\pi$
$500$		0			0
$501$	8.33843e7	−	1.44426e8i	0.663088	−	1.14850i
$502$		0			0
$503$	2.15116e8	−	7.82960e7i	1.69032	−	0.615227i	0.695657	−	0.718374i	$-0.255113\pi$
$503$	2.15116e8	−	7.82960e7i	1.69032	−	0.615227i	0.994666	+	0.103147i	$0.0328912\pi$
$504$		0			0
$505$	−3.71224e6	−	6.42979e6i	−0.0288245	−	0.0499255i
$506$		0			0
$507$	−9.57835e7	−	1.68892e7i	−0.734966	−	0.129594i
$508$		0			0
$509$	−6.20735e7	+	7.39763e7i	−0.470710	+	0.560970i	−0.948203	−	0.317666i	$-0.897101\pi$
$509$	−6.20735e7	+	7.39763e7i	−0.470710	+	0.560970i	0.477493	+	0.878635i	$0.341545\pi$
$510$		0			0
$511$	1.35344e7	+	4.92611e6i	0.101432	+	0.0369183i
$512$		0			0
$513$	−3.21118e8	+	1.92630e8i	−2.37855	+	1.42683i
$514$		0			0
$515$	1.01959e6	−	2.80131e6i	0.00746457	−	0.0205087i
$516$		0			0
$517$	−1.03429e8	−	8.67874e7i	−0.748465	−	0.628037i
$518$		0			0
$519$	−5.56917e6	+	3.15843e7i	−0.0398372	+	0.225928i
$520$		0			0
$521$	−8.33450e7	+	4.81193e7i	−0.589341	+	0.340256i	−0.764837	−	0.644224i	$-0.777180\pi$
$521$	−8.33450e7	+	4.81193e7i	−0.589341	+	0.340256i	0.175496	+	0.984480i	$0.443847\pi$
$522$		0			0
$523$	3.09699e7	+	8.50890e7i	0.216488	+	0.594796i	0.999634	−	0.0270413i	$-0.00860857\pi$
$523$	3.09699e7	+	8.50890e7i	0.216488	+	0.594796i	−0.783146	+	0.621838i	$0.786386\pi$
$524$		0			0
$525$	−3.66246e8	−	2.11452e8i	−2.53102	−	1.46128i
$526$		0			0
$527$	−1.85989e8	−	2.21653e8i	−1.27074	−	1.51440i
$528$		0			0
$529$	3.75110e6	+	2.12735e7i	0.0253391	+	0.143705i
$530$		0			0
$531$			7.14147e8i			4.76985i
$532$		0			0
$533$	1.88483e8			1.24477
$534$		0			0
$535$	4.08704e6	−	720656.i	0.0266900	−	0.00470616i
$536$		0			0
$537$	8.25809e7	−	6.92936e7i	0.533282	−	0.447477i
$538$		0			0
$539$	1.32374e8	−	2.29279e8i	0.845351	−	1.46419i
$540$		0			0
$541$	1.94490e8	−	7.07886e7i	1.22830	−	0.447066i	0.355287	−	0.934757i	$-0.384383\pi$
$541$	1.94490e8	−	7.07886e7i	1.22830	−	0.447066i	0.873016	+	0.487691i	$0.162161\pi$
$542$		0			0
$543$	2.44951e8	+	4.24268e8i	1.52996	+	2.64997i
$544$		0			0
$545$	4.34760e6	+	766598.i	0.0268571	+	0.00473564i
$546$		0			0
$547$	7.60485e7	−	9.06311e7i	0.464653	−	0.553752i	−0.481931	−	0.876209i	$-0.660064\pi$
$547$	7.60485e7	−	9.06311e7i	0.464653	−	0.553752i	0.946584	+	0.322457i	$0.104509\pi$
$548$		0			0
$549$	−2.50793e8	−	9.12813e7i	−1.51565	−	0.551652i
$550$		0			0
$551$	7.47211e6	+	1.95078e7i	0.0446672	+	0.116615i
$552$		0			0
$553$	−1.16259e7	+	3.19418e7i	−0.0687465	+	0.188879i
$554$		0			0
$555$	9.32326e6	+	7.82314e6i	0.0545367	+	0.0457617i
$556$		0			0
$557$	−6.84771e6	+	3.88353e7i	−0.0396260	+	0.224730i	−0.998189	−	0.0601491i	$-0.980842\pi$
$557$	−6.84771e6	+	3.88353e7i	−0.0396260	+	0.224730i	0.958563	+	0.284879i	$0.0919535\pi$
$558$		0			0
$559$	−2.61712e7	+	1.51100e7i	−0.149826	+	0.0865024i
$560$		0			0
$561$	1.87571e8	+	5.15347e8i	1.06237	+	2.91884i
$562$		0			0
$563$	−1.64066e7	−	9.47234e6i	−0.0919375	−	0.0530801i	0.453326	−	0.891345i	$-0.350237\pi$
$563$	−1.64066e7	−	9.47234e6i	−0.0919375	−	0.0530801i	−0.545264	+	0.838264i	$0.683571\pi$
$564$		0			0
$565$	−9.78633e6	−	1.16629e7i	−0.0542593	−	0.0646638i
$566$		0			0
$567$	−1.33872e8	−	7.59226e8i	−0.734414	−	4.16507i
$568$		0			0
$569$		−	8.32417e7i		−	0.451860i	−0.974144	−	0.225930i	$-0.927458\pi$
$569$		−	8.32417e7i		−	0.451860i	0.974144	−	0.225930i	$-0.0725421\pi$
$570$		0			0
$571$	−2.14036e8			−1.14969			−0.574843	−	0.818264i	$-0.694937\pi$
$571$	−2.14036e8			−1.14969			−0.574843	+	0.818264i	$0.694937\pi$
$572$		0			0
$573$	7.23662e6	−	1.27601e6i	0.0384655	−	0.00678251i
$574$		0			0
$575$	1.55378e8	−	1.30378e8i	0.817309	−	0.685804i
$576$		0			0
$577$	−9.50985e6	+	1.64715e7i	−0.0495047	+	0.0857446i	−0.889716	−	0.456515i	$-0.849098\pi$
$577$	−9.50985e6	+	1.64715e7i	−0.0495047	+	0.0857446i	0.840211	+	0.542259i	$0.182431\pi$
$578$		0			0
$579$	−3.06223e8	+	1.11456e8i	−1.57762	+	0.574205i
$580$		0			0
$581$	−1.19336e8	−	2.06697e8i	−0.608477	−	1.05391i
$582$		0			0
$583$	−1.40153e8	−	2.47128e7i	−0.707290	−	0.124714i
$584$		0			0
$585$	2.18115e7	−	2.59939e7i	0.108947	−	0.129839i
$586$		0			0
$587$	2.28088e8	+	8.30171e7i	1.12768	+	0.410444i	0.837451	−	0.546512i	$-0.184045\pi$
$587$	2.28088e8	+	8.30171e7i	1.12768	+	0.410444i	0.290233	+	0.956956i	$0.406267\pi$
$588$		0			0
$589$	2.44673e8	+	1.35857e8i	1.19740	+	0.664869i
$590$		0			0
$591$	−2.11650e8	+	5.81504e8i	−1.02531	+	2.81702i
$592$		0			0
$593$	8.12629e7	+	6.81877e7i	0.389698	+	0.326996i	0.816496	−	0.577352i	$-0.195914\pi$
$593$	8.12629e7	+	6.81877e7i	0.389698	+	0.326996i	−0.426797	+	0.904347i	$0.640358\pi$
$594$		0			0
$595$	4.77934e6	−	2.71050e7i	0.0226891	−	0.128676i
$596$		0			0
$597$	−3.81103e8	+	2.20030e8i	−1.79110	+	1.03409i
$598$		0			0
$599$	−1.40446e8	−	3.85873e8i	−0.653477	−	1.79541i	−0.604490	−	0.796613i	$-0.706623\pi$
$599$	−1.40446e8	−	3.85873e8i	−0.653477	−	1.79541i	−0.0489865	−	0.998799i	$-0.515599\pi$
$600$		0			0
$601$	−2.23617e8	−	1.29105e8i	−1.03011	−	0.594732i	−0.113090	−	0.993585i	$-0.536075\pi$
$601$	−2.23617e8	−	1.29105e8i	−1.03011	−	0.594732i	−0.917015	+	0.398853i	$0.869408\pi$
$602$		0			0
$603$	4.52031e8	+	5.38709e8i	2.06166	+	2.45698i
$604$		0			0
$605$	−728203.	−	4.12984e6i	−0.00328841	−	0.0186495i
$606$		0			0
$607$		−	2.38329e8i		−	1.06564i	−0.846229	−	0.532820i	$-0.821132\pi$
$607$		−	2.38329e8i		−	1.06564i	0.846229	−	0.532820i	$-0.178868\pi$
$608$		0			0
$609$	−8.27072e7			−0.366177
$610$		0			0
$611$	2.25281e8	−	3.97230e7i	0.987643	−	0.174148i
$612$		0			0
$613$	−2.33977e8	+	1.96330e8i	−1.01576	+	0.852324i	−0.989089	−	0.147320i	$-0.952935\pi$
$613$	−2.33977e8	+	1.96330e8i	−1.01576	+	0.852324i	−0.0266714	+	0.999644i	$0.508491\pi$
$614$		0			0
$615$	−1.31671e7	+	2.28062e7i	−0.0566065	+	0.0980453i
$616$		0			0
$617$	4.19849e8	−	1.52812e8i	1.78746	−	0.650584i	0.788077	−	0.615576i	$-0.211077\pi$
$617$	4.19849e8	−	1.52812e8i	1.78746	−	0.650584i	0.999387	−	0.0350075i	$-0.0111455\pi$
$618$		0			0
$619$	4.01031e7	+	6.94606e7i	0.169085	+	0.292864i	0.938099	−	0.346369i	$-0.112585\pi$
$619$	4.01031e7	+	6.94606e7i	0.169085	+	0.292864i	−0.769013	+	0.639233i	$0.779252\pi$
$620$		0			0
$621$	7.00262e8	+	1.23475e8i	2.92406	+	0.515590i
$622$		0			0
$623$	−1.41988e8	+	1.69214e8i	−0.587200	+	0.699798i
$624$		0			0
$625$	−2.27133e8	−	8.26698e7i	−0.930339	−	0.338616i
$626$		0			0
$627$	−3.47710e8	−	4.00581e8i	−1.41063	−	1.62513i
$628$		0			0
$629$	8.12832e7	−	2.23324e8i	0.326625	−	0.897393i
$630$		0			0
$631$	3.70354e7	+	3.10764e7i	0.147411	+	0.123692i	0.713511	−	0.700644i	$-0.247104\pi$
$631$	3.70354e7	+	3.10764e7i	0.147411	+	0.123692i	−0.566100	+	0.824336i	$0.691548\pi$
$632$		0			0
$633$	1.06384e8	−	6.03331e8i	0.419434	−	2.37873i
$634$		0			0
$635$	−7.02938e6	+	4.05841e6i	−0.0274534	+	0.0158502i
$636$		0			0
$637$	1.53415e8	+	4.21504e8i	0.593539	+	1.63074i
$638$		0			0
$639$	−1.59717e8	−	9.22124e7i	−0.612135	−	0.353417i
$640$		0			0
$641$	2.51496e8	+	2.99721e8i	0.954898	+	1.13800i	0.990344	+	0.138631i	$0.0442703\pi$
$641$	2.51496e8	+	2.99721e8i	0.954898	+	1.13800i	−0.0354463	+	0.999372i	$0.511285\pi$
$642$		0			0
$643$	5.80487e7	+	3.29210e8i	0.218353	+	1.23834i	0.874992	+	0.484137i	$0.160866\pi$
$643$	5.80487e7	+	3.29210e8i	0.218353	+	1.23834i	−0.656639	+	0.754205i	$0.728022\pi$
$644$		0			0
$645$		−	4.22224e6i		−	0.0157349i
$646$		0			0
$647$	−3.90056e8			−1.44017			−0.720086	−	0.693885i	$-0.755898\pi$
$647$	−3.90056e8			−1.44017			−0.720086	+	0.693885i	$0.755898\pi$
$648$		0			0
$649$	−5.95447e8	+	1.04993e8i	−2.17826	+	0.384085i
$650$		0			0
$651$	−8.48796e8	+	7.12224e8i	−3.07652	+	2.58151i
$652$		0			0
$653$	−4.59466e7	+	7.95818e7i	−0.165011	+	0.285808i	−0.936659	−	0.350242i	$-0.886099\pi$
$653$	−4.59466e7	+	7.95818e7i	−0.165011	+	0.285808i	0.771648	+	0.636050i	$0.219433\pi$
$654$		0			0
$655$	−1.98866e6	+	723812.i	−0.00707678	+	0.00257574i
$656$		0			0
$657$	2.42229e7	+	4.19554e7i	0.0854143	+	0.147942i
$658$		0			0
$659$	1.31868e8	+	2.32520e7i	0.460770	+	0.0812462i	0.399215	−	0.916857i	$-0.369283\pi$
$659$	1.31868e8	+	2.32520e7i	0.460770	+	0.0812462i	0.0615555	+	0.998104i	$0.480394\pi$
$660$		0			0
$661$	−7.68085e7	+	9.15368e7i	−0.265953	+	0.316950i	−0.882449	−	0.470407i	$-0.844107\pi$
$661$	−7.68085e7	+	9.15368e7i	−0.265953	+	0.316950i	0.616497	+	0.787358i	$0.288551\pi$
$662$		0			0
$663$	−8.73137e8	−	3.17796e8i	−2.99600	−	1.09045i
$664$		0			0
$665$	5.06051e6	+	2.61353e7i	0.0172080	+	0.0888716i
$666$		0			0
$667$	1.35671e7	−	3.72754e7i	0.0457205	−	0.125616i
$668$		0			0
$669$	8.35890e8	+	7.01395e8i	2.79171	+	2.34252i
$670$		0			0
$671$	3.92377e7	−	2.22528e8i	0.129878	−	0.736576i
$672$		0			0
$673$	9.35429e7	−	5.40070e7i	0.306878	−	0.177176i	−0.338651	−	0.940912i	$-0.609970\pi$
$673$	9.35429e7	−	5.40070e7i	0.306878	−	0.177176i	0.645528	+	0.763736i	$0.276637\pi$
$674$		0			0
$675$	−2.90787e8	−	7.98931e8i	−0.945505	−	2.59775i
$676$		0			0
$677$	−2.87670e8	−	1.66086e8i	−0.927104	−	0.535264i	−0.0412097	−	0.999151i	$-0.513121\pi$
$677$	−2.87670e8	−	1.66086e8i	−0.927104	−	0.535264i	−0.885895	+	0.463887i	$0.846455\pi$
$678$		0			0
$679$	2.68355e8	+	3.19813e8i	0.857235	+	1.02161i
$680$		0			0
$681$	−1.01676e8	−	5.76631e8i	−0.321941	−	1.82582i
$682$		0			0
$683$			1.51210e8i			0.474590i	0.971438	+	0.237295i	$0.0762608\pi$
$683$			1.51210e8i			0.474590i	−0.971438	+	0.237295i	$0.923739\pi$
$684$		0			0
$685$	−3.14660e7			−0.0978971
$686$		0			0
$687$	−2.04336e6	+	360299.i	−0.00630194	+	0.00111120i
$688$		0			0
$689$	1.84709e8	−	1.54989e8i	0.564717	−	0.473854i
$690$		0			0
$691$	1.16141e8	−	2.01162e8i	0.352006	−	0.609693i	−0.634594	−	0.772845i	$-0.718833\pi$
$691$	1.16141e8	−	2.01162e8i	0.352006	−	0.609693i	0.986601	+	0.163152i	$0.0521662\pi$
$692$		0			0
$693$	1.40730e9	−	5.12214e8i	4.22849	−	1.53905i
$694$		0			0
$695$	3.69900e6	+	6.40685e6i	0.0110187	+	0.0190849i
$696$		0			0
$697$	5.06417e8	+	8.92949e7i	1.49558	+	0.263711i
$698$		0			0
$699$	5.79225e8	−	6.90294e8i	1.69596	−	2.02117i
$700$		0			0
$701$	1.07639e8	+	3.91773e7i	0.312474	+	0.113731i	0.493497	−	0.869748i	$-0.335718\pi$
$701$	1.07639e8	+	3.91773e7i	0.312474	+	0.113731i	−0.181023	+	0.983479i	$0.557941\pi$
$702$		0			0
$703$	3.84487e6	+	2.29832e8i	0.0110666	+	0.661523i
$704$		0			0
$705$	−1.09313e7	+	3.00336e7i	−0.0311965	+	0.0857117i
$706$		0			0
$707$	4.25290e8	+	3.56860e8i	1.20345	+	1.00981i
$708$		0			0
$709$	1.22592e7	−	6.95253e7i	0.0343972	−	0.195076i	−0.962767	−	0.270332i	$-0.912866\pi$
$709$	1.22592e7	−	6.95253e7i	0.0343972	−	0.195076i	0.997164	+	0.0752563i	$0.0239775\pi$
$710$		0			0
$711$	−9.90169e7	+	5.71674e7i	−0.275487	+	0.159052i
$712$		0			0
$713$	−1.81758e8	−	4.99377e8i	−0.501448	−	1.37772i
$714$		0			0
$715$	2.48801e7	+	1.43645e7i	0.0680665	+	0.0392982i
$716$		0			0
$717$	−1.21352e8	−	1.44622e8i	−0.329222	−	0.392352i
$718$		0			0
$719$	−6.11135e7	−	3.46592e8i	−0.164418	−	0.932463i	−0.949662	−	0.313276i	$-0.898574\pi$
$719$	−6.11135e7	−	3.46592e8i	−0.164418	−	0.932463i	0.785244	−	0.619187i	$-0.212538\pi$
$720$		0			0
$721$			2.22915e8i			0.594749i
$722$		0			0
$723$	5.52114e8			1.46088
$724$		0			0
$725$	−4.67092e7	+	8.23609e6i	−0.122571	+	0.0216126i
$726$		0			0
$727$	−2.42783e8	+	2.03719e8i	−0.631852	+	0.530187i	−0.901504	−	0.432771i	$-0.857536\pi$
$727$	−2.42783e8	+	2.03719e8i	−0.631852	+	0.530187i	0.269652	+	0.962958i	$0.413091\pi$
$728$		0			0
$729$	2.93449e8	−	5.08269e8i	0.757444	−	1.31193i
$730$		0			0
$731$	−7.74754e7	+	2.81987e7i	−0.198341	+	0.0721901i
$732$		0			0
$733$	−1.02526e8	−	1.77580e8i	−0.260329	−	0.450903i	0.706000	−	0.708211i	$-0.250498\pi$
$733$	−1.02526e8	−	1.77580e8i	−0.260329	−	0.450903i	−0.966329	+	0.257309i	$0.917164\pi$
$734$		0			0
$735$	−6.17187e7	−	1.08827e7i	−0.155437	−	0.0274078i
$736$		0			0
$737$	−3.82711e8	+	4.56098e8i	−0.956025	+	1.13935i
$738$		0			0
$739$	−4.17485e8	−	1.51952e8i	−1.03445	−	0.376507i	−0.231674	−	0.972794i	$-0.574420\pi$
$739$	−4.17485e8	−	1.51952e8i	−1.03445	−	0.376507i	−0.802772	+	0.596286i	$0.796642\pi$
$740$		0			0
$741$	8.98584e8	−	1.50324e7i	2.20853	−	0.0369466i
$742$		0			0
$743$	−1.97258e7	+	5.41963e7i	−0.0480916	+	0.132130i	−0.961413	−	0.275109i	$-0.911286\pi$
$743$	−1.97258e7	+	5.41963e7i	−0.0480916	+	0.132130i	0.913322	+	0.407239i	$0.133508\pi$
$744$		0			0
$745$	3.19996e6	+	2.68508e6i	0.00773883	+	0.00649365i
$746$		0			0
$747$	1.39405e8	−	7.90603e8i	0.334438	−	1.89669i
$748$		0			0
$749$	−2.68753e8	+	1.55165e8i	−0.639599	+	0.369273i
$750$		0			0
$751$	9.57311e7	+	2.63019e8i	0.226013	+	0.620966i	0.999924	−	0.0123288i	$-0.00392446\pi$
$751$	9.57311e7	+	2.63019e8i	0.226013	+	0.620966i	−0.773911	+	0.633294i	$0.781702\pi$
$752$		0			0
$753$	2.10638e8	+	1.21612e8i	0.493345	+	0.284833i
$754$		0			0
$755$	2.06455e7	+	2.46043e7i	0.0479716	+	0.0571703i
$756$		0			0
$757$	−6.41951e7	−	3.64069e8i	−0.147984	−	0.839258i	−0.964923	−	0.262534i	$-0.915442\pi$
$757$	−6.41951e7	−	3.64069e8i	−0.147984	−	0.839258i	0.816939	−	0.576724i	$-0.195669\pi$
$758$		0			0
$759$			1.00725e9i			2.30362i
$760$		0			0
$761$	−3.96802e8			−0.900367			−0.450184	−	0.892936i	$-0.648641\pi$
$761$	−3.96802e8			−0.900367			−0.450184	+	0.892936i	$0.648641\pi$
$762$		0			0
$763$	−3.25098e8	+	5.73235e7i	−0.731881	+	0.129050i
$764$		0			0
$765$	7.09179e7	−	5.95072e7i	0.158406	−	0.132918i
$766$		0			0
$767$	5.12206e8	−	8.87166e8i	1.13516	−	1.96616i
$768$		0			0
$769$	−5.18631e8	+	1.88766e8i	−1.14046	+	0.415093i	−0.842079	−	0.539354i	$-0.818668\pi$
$769$	−5.18631e8	+	1.88766e8i	−1.14046	+	0.415093i	−0.298380	+	0.954447i	$0.596446\pi$
$770$		0			0
$771$	1.62529e8	+	2.81508e8i	0.354623	+	0.614225i
$772$		0			0
$773$	−8.48405e8	−	1.49597e8i	−1.83681	−	0.323879i	−0.855722	−	0.517436i	$-0.826887\pi$
$773$	−8.48405e8	−	1.49597e8i	−1.83681	−	0.323879i	−0.981089	+	0.193557i	$0.937998\pi$
$774$		0			0
$775$	−4.08436e8	+	4.86755e8i	−0.877443	+	1.04570i
$776$		0			0
$777$	−8.55194e8	−	3.11265e8i	−1.82306	−	0.663540i
$778$		0			0
$779$	−4.88301e8	+	9.45482e7i	−1.03294	+	0.200005i
$780$		0			0
$781$	5.34041e7	−	1.46727e8i	0.112104	−	0.308004i
$782$		0			0
$783$	−1.27373e8	−	1.06879e8i	−0.265334	−	0.222642i
$784$		0			0
$785$	7.92430e6	−	4.49409e7i	0.0163814	−	0.0929037i
$786$		0			0
$787$	7.54874e8	−	4.35826e8i	1.54864	−	0.894107i	0.550392	−	0.834906i	$-0.314478\pi$
$787$	7.54874e8	−	4.35826e8i	1.54864	−	0.894107i	0.998246	−	0.0592006i	$-0.0188552\pi$
$788$		0			0
$789$	3.00636e8	+	8.25991e8i	0.612083	+	1.68168i
$790$		0			0
$791$	9.85934e8	+	5.69229e8i	1.99213	+	1.15016i
$792$		0			0
$793$	2.46084e8	+	2.93272e8i	0.493474	+	0.588100i
$794$		0			0
$795$	5.84998e6	+	3.31769e7i	0.0116427	+	0.0660289i
$796$		0			0
$797$			7.33323e8i			1.44851i	0.689534	+	0.724253i	$0.257815\pi$
$797$			7.33323e8i			1.44851i	−0.689534	+	0.724253i	$0.742185\pi$
$798$		0			0
$799$	6.24104e8			1.22354
$800$		0			0
$801$	−7.31710e8	+	1.29020e8i	−1.42377	+	0.251050i
$802$		0			0
$803$	−3.14206e7	+	2.63650e7i	−0.0606831	+	0.0509192i
$804$		0			0
$805$	2.52750e7	−	4.37775e7i	0.0484510	−	0.0839196i
$806$		0			0
$807$	−1.12091e8	+	4.07979e7i	−0.213280	+	0.0776277i
$808$		0			0
$809$	−1.84688e8	−	3.19890e8i	−0.348814	−	0.604164i	0.637225	−	0.770678i	$-0.280082\pi$
$809$	−1.84688e8	−	3.19890e8i	−0.348814	−	0.604164i	−0.986039	+	0.166514i	$0.946749\pi$
$810$		0			0
$811$	−7.89772e8	−	1.39258e8i	−1.48061	−	0.261071i	−0.625785	−	0.779995i	$-0.715221\pi$
$811$	−7.89772e8	−	1.39258e8i	−1.48061	−	0.261071i	−0.854820	+	0.518925i	$0.826333\pi$
$812$		0			0
$813$	−6.71411e8	+	8.00156e8i	−1.24944	+	1.48903i
$814$		0			0
$815$	−2.74020e7	−	9.97351e6i	−0.0506185	−	0.0184236i
$816$		0			0
$817$	6.02219e7	−	5.22734e7i	0.110430	−	0.0958550i
$818$		0			0
$819$	−8.67829e8	+	2.38434e9i	−1.57973	+	4.34027i
$820$		0			0
$821$	−4.79937e8	−	4.02715e8i	−0.867272	−	0.727727i	0.0962501	−	0.995357i	$-0.469315\pi$
$821$	−4.79937e8	−	4.02715e8i	−0.867272	−	0.727727i	−0.963522	+	0.267630i	$0.913760\pi$
$822$		0			0
$823$	−4.54074e7	+	2.57518e8i	−0.0814568	+	0.461965i	0.916608	+	0.399787i	$0.130916\pi$
$823$	−4.54074e7	+	2.57518e8i	−0.0814568	+	0.461965i	−0.998065	+	0.0621780i	$0.980195\pi$
$824$		0			0
$825$	1.04299e9	−	6.02172e8i	1.85746	−	1.07241i
$826$		0			0
$827$	−2.39736e8	−	6.58669e8i	−0.423854	−	1.16453i	−0.949484	−	0.313816i	$-0.898392\pi$
$827$	−2.39736e8	−	6.58669e8i	−0.423854	−	1.16453i	0.525630	−	0.850714i	$-0.323830\pi$
$828$		0			0
$829$	−2.02908e8	−	1.17149e8i	−0.356153	−	0.205625i	0.311239	−	0.950332i	$-0.399256\pi$
$829$	−2.02908e8	−	1.17149e8i	−0.356153	−	0.205625i	−0.667392	+	0.744707i	$0.732589\pi$
$830$		0			0
$831$	−9.44434e8	−	1.12553e9i	−1.64577	−	1.96135i
$832$		0			0
$833$	2.12506e8	+	1.20518e9i	0.367651	+	2.08505i
$834$		0			0
$835$		−	2.38345e7i		−	0.0409399i
$836$		0			0
$837$	−2.22756e9			−3.79886
$838$		0			0
$839$	8.30512e8	−	1.46442e8i	1.40624	−	0.247958i	0.581536	−	0.813520i	$-0.302452\pi$
$839$	8.30512e8	−	1.46442e8i	1.40624	−	0.247958i	0.824706	+	0.565562i	$0.191341\pi$
$840$		0			0
$841$	4.48555e8	−	3.76383e8i	0.754099	−	0.632764i
$842$		0			0
$843$	4.61196e8	−	7.98814e8i	0.769843	−	1.33341i
$844$		0			0
$845$	−1.30622e7	+	4.75426e6i	−0.0216495	+	0.00787976i
$846$		0			0
$847$	1.56790e8	+	2.71567e8i	0.258028	+	0.446918i
$848$		0			0
$849$	2.19794e9	+	3.87557e8i	3.59165	+	0.633304i
$850$		0			0
$851$	2.80569e8	−	3.34369e8i	0.455251	−	0.542547i
$852$		0			0
$853$	−1.10896e8	−	4.03627e7i	−0.178676	−	0.0650329i	0.251133	−	0.967953i	$-0.419197\pi$
$853$	−1.10896e8	−	4.03627e7i	−0.178676	−	0.0650329i	−0.429809	+	0.902920i	$0.641419\pi$
$854$		0			0
$855$	−4.34675e7	+	7.82833e7i	−0.0695450	+	0.125248i
$856$		0			0
$857$	−1.42613e8	+	3.91827e8i	−0.226578	+	0.622517i	−0.999934	−	0.0114539i	$-0.996354\pi$
$857$	−1.42613e8	+	3.91827e8i	−0.226578	+	0.622517i	0.773357	+	0.633971i	$0.218576\pi$
$858$		0			0
$859$	8.29184e8	+	6.95768e8i	1.30819	+	1.09770i	0.988667	+	0.150125i	$0.0479677\pi$
$859$	8.29184e8	+	6.95768e8i	1.30819	+	1.09770i	0.319525	+	0.947578i	$0.396477\pi$
$860$		0			0
$861$	3.41945e8	−	1.93927e9i	0.535731	−	3.03828i
$862$		0			0
$863$	5.00942e8	−	2.89219e8i	0.779390	−	0.449981i	−0.0568241	−	0.998384i	$-0.518097\pi$
$863$	5.00942e8	−	2.89219e8i	0.779390	−	0.449981i	0.836214	+	0.548403i	$0.184764\pi$
$864$		0			0
$865$	1.56770e6	+	4.30723e6i	0.00242223	+	0.00665502i
$866$		0			0
$867$	−1.14166e9	−	6.59138e8i	−1.75178	−	1.01139i
$868$		0			0
$869$	−6.22228e7	−	7.41543e7i	−0.0948179	−	0.113000i
$870$		0			0
$871$	−1.75169e8	−	9.93432e8i	−0.265096	−	1.50343i
$872$		0			0
$873$			1.40426e9i			2.11059i
$874$		0			0
$875$	−1.21084e8			−0.180744
$876$		0			0
$877$	1.69813e8	−	2.99426e7i	0.251751	−	0.0443906i	−0.0463481	−	0.998925i	$-0.514758\pi$
$877$	1.69813e8	−	2.99426e7i	0.251751	−	0.0443906i	0.298100	+	0.954535i	$0.403647\pi$
$878$		0			0
$879$	−6.74334e8	+	5.65833e8i	−0.992906	+	0.833147i
$880$		0			0
$881$	−3.18684e8	+	5.51977e8i	−0.466050	+	0.807223i	−0.999248	−	0.0387677i	$-0.987657\pi$
$881$	−3.18684e8	+	5.51977e8i	−0.466050	+	0.807223i	0.533198	+	0.845991i	$0.320990\pi$
$882$		0			0
$883$	−7.07680e8	+	2.57575e8i	−1.02791	+	0.374129i	−0.800285	−	0.599620i	$-0.795318\pi$
$883$	−7.07680e8	+	2.57575e8i	−1.02791	+	0.374129i	−0.227625	+	0.973749i	$0.573096\pi$
$884$		0			0
$885$	7.15639e7	+	1.23952e8i	0.103244	+	0.178824i
$886$		0			0
$887$	1.09671e9	+	1.93379e8i	1.57152	+	0.277102i	0.890438	−	0.455105i	$-0.150398\pi$
$887$	1.09671e9	+	1.93379e8i	1.57152	+	0.277102i	0.681083	+	0.732206i	$0.261509\pi$
$888$		0			0
$889$	3.90139e8	−	4.64949e8i	0.555282	−	0.661759i
$890$		0			0
$891$	2.06307e9	+	7.50896e8i	2.91663	+	1.06157i
$892$		0			0
$893$	−5.63706e8	+	2.15917e8i	−0.791586	+	0.303202i
$894$		0			0
$895$	5.26950e6	−	1.44778e7i	0.00735022	−	0.0201946i
$896$		0			0
$897$	−1.30730e9	−	1.09695e9i	−1.81132	−	1.51988i
$898$		0			0
$899$	−2.15788e7	+	1.22380e8i	−0.0296995	+	0.168434i
$900$		0			0
$901$	5.69705e8	−	3.28919e8i	0.778889	−	0.449692i
$902$		0			0
$903$	1.07984e8	+	2.96684e8i	0.146655	+	0.402931i
$904$		0			0
$905$	6.06362e7	+	3.50083e7i	0.0818062	+	0.0472308i
$906$		0			0
$907$	−6.99655e8	−	8.33816e8i	−0.937696	−	1.11750i	−0.992891	−	0.119027i	$-0.962023\pi$
$907$	−6.99655e8	−	8.33816e8i	−0.937696	−	1.11750i	0.0551950	−	0.998476i	$-0.482422\pi$
$908$		0			0
$909$	3.24269e8	+	1.83902e9i	0.431732	+	2.44847i
$910$		0			0
$911$		−	2.88878e8i		−	0.382084i	−0.981582	−	0.191042i	$-0.938813\pi$
$911$		−	2.88878e8i		−	0.382084i	0.981582	−	0.191042i	$-0.0611866\pi$
$912$		0			0
$913$	6.79690e8			0.893096
$914$		0			0
$915$	−5.26766e7	+	9.28830e6i	−0.0687629	+	0.0121248i
$916$		0			0
$917$	1.21225e8	−	1.01720e8i	0.157212	−	0.131916i
$918$		0			0
$919$	−2.20420e8	+	3.81778e8i	−0.283990	+	0.491886i	−0.972364	−	0.233471i	$-0.924992\pi$
$919$	−2.20420e8	+	3.81778e8i	−0.283990	+	0.491886i	0.688373	+	0.725357i	$0.258325\pi$
$920$		0			0
$921$	−1.27955e9	+	4.65717e8i	−1.63786	+	0.596133i
$922$		0			0
$923$	1.32274e8	+	2.29106e8i	0.168217	+	0.291361i
$924$		0			0
$925$	−5.13970e8	−	9.06267e7i	−0.649400	−	0.114507i
$926$		0			0
$927$	−4.81961e8	+	5.74379e8i	−0.605024	+	0.721039i
$928$		0			0
$929$	−1.64728e8	−	5.99563e7i	−0.205457	−	0.0747803i	0.237242	−	0.971451i	$-0.423757\pi$
$929$	−1.64728e8	−	5.99563e7i	−0.205457	−	0.0747803i	−0.442699	+	0.896670i	$0.645979\pi$
$930$		0			0
$931$	−6.08889e8	−	1.01503e9i	−0.754552	−	1.25785i
$932$		0			0
$933$	8.93643e8	−	2.45526e9i	1.10032	−	3.02310i
$934$		0			0
$935$	6.00426e7	+	5.03817e7i	0.0734556	+	0.0616365i
$936$		0			0
$937$	−1.10821e8	+	6.28498e8i	−0.134711	+	0.763985i	0.840349	+	0.542045i	$0.182350\pi$
$937$	−1.10821e8	+	6.28498e8i	−0.134711	+	0.763985i	−0.975060	+	0.221940i	$0.928761\pi$
$938$		0			0
$939$	−1.85705e9	+	1.07217e9i	−2.24299	+	1.29499i
$940$		0			0
$941$	−4.75093e8	−	1.30531e9i	−0.570177	−	1.56655i	−0.804227	−	0.594323i	$-0.797420\pi$
$941$	−4.75093e8	−	1.30531e9i	−0.570177	−	1.56655i	0.234050	−	0.972225i	$-0.424802\pi$
$942$		0			0
$943$	8.17919e8	+	4.72226e8i	0.975383	+	0.563138i
$944$		0			0
$945$	−1.36199e8	−	1.62316e8i	−0.161391	−	0.192339i
$946$		0			0
$947$	−9.19613e7	−	5.21538e8i	−0.108282	−	0.614096i	−0.989859	−	0.142056i	$-0.954629\pi$
$947$	−9.19613e7	−	5.21538e8i	−0.108282	−	0.614096i	0.881577	−	0.472040i	$-0.156482\pi$
$948$		0			0
$949$		−	6.94933e7i		−	0.0813101i
$950$		0			0
$951$	1.80375e9			2.09718
$952$		0			0
$953$	−3.95037e8	+	6.96557e7i	−0.456414	+	0.0804781i	−0.397129	−	0.917763i	$-0.629993\pi$
$953$	−3.95037e8	+	6.96557e7i	−0.456414	+	0.0804781i	−0.0592855	+	0.998241i	$0.518882\pi$
$954$		0			0
$955$	804507.	−	675062.i	0.000923677	−	0.000775057i
$956$		0			0
$957$	1.17766e8	−	2.03977e8i	0.134365	−	0.232727i
$958$		0			0
$959$	2.21102e9	−	8.04745e8i	2.50690	−	0.912436i
$960$		0			0
$961$	3.88651e8	+	6.73162e8i	0.437914	+	0.758490i
$962$		0			0
$963$	−1.02797e9	−	1.81258e8i	−1.15107	−	0.202964i
$964$		0			0
$965$	−2.99372e7	+	3.56777e7i	−0.0333142	+	0.0397023i
$966$		0			0
$967$	−8.61137e8	−	3.13428e8i	−0.952342	−	0.346624i	−0.181314	−	0.983425i	$-0.558035\pi$
$967$	−8.61137e8	−	3.13428e8i	−0.952342	−	0.346624i	−0.771028	+	0.636801i	$0.780257\pi$
$968$		0			0
$969$	2.42144e9	+	3.85321e8i	2.66135	+	0.423498i
$970$		0			0
$971$	−1.56569e8	+	4.30169e8i	−0.171020	+	0.469874i	−0.995360	−	0.0962212i	$-0.969324\pi$
$971$	−1.56569e8	+	4.30169e8i	−0.171020	+	0.469874i	0.824340	+	0.566095i	$0.191547\pi$
$972$		0			0
$973$	−4.23773e8	−	3.55587e8i	−0.460039	−	0.386018i
$974$		0			0
$975$	−3.54327e8	+	2.00949e9i	−0.382287	+	2.16806i
$976$		0			0
$977$	4.37410e7	−	2.52539e7i	0.0469034	−	0.0270797i	−0.476365	−	0.879248i	$-0.658046\pi$
$977$	4.37410e7	−	2.52539e7i	0.0469034	−	0.0270797i	0.523268	+	0.852168i	$0.324713\pi$
$978$		0			0
$979$	−2.15151e8	−	5.91122e8i	−0.229295	−	0.629983i
$980$		0			0
$981$	−9.61607e8	−	5.55184e8i	−1.01857	−	0.588072i
$982$		0			0
$983$	1.17938e9	+	1.40553e9i	1.24164	+	1.47972i	0.819384	+	0.573246i	$0.194316\pi$
$983$	1.17938e9	+	1.40553e9i	1.24164	+	1.47972i	0.422252	+	0.906478i	$0.361240\pi$
$984$		0			0
$985$	1.53578e7	+	8.70985e7i	0.0160702	+	0.0911385i
$986$		0			0
$987$		−	2.38994e9i		−	2.48562i
$988$		0			0
$989$	−1.51426e8			−0.156535
$990$		0			0
$991$	1.03602e9	−	1.82677e8i	1.06450	−	0.187700i	0.386147	−	0.922437i	$-0.373806\pi$
$991$	1.03602e9	−	1.82677e8i	1.06450	−	0.187700i	0.678352	+	0.734737i	$0.262695\pi$
$992$		0			0
$993$	1.05259e9	−	8.83225e8i	1.07500	−	0.902036i
$994$		0			0
$995$	−3.14466e7	+	5.44672e7i	−0.0319231	+	0.0552924i
$996$		0			0
$997$	6.61709e8	−	2.40842e8i	0.667700	−	0.243023i	0.0141429	−	0.999900i	$-0.495498\pi$
$997$	6.61709e8	−	2.40842e8i	0.667700	−	0.243023i	0.653557	+	0.756877i	$0.273276\pi$
$998$		0			0
$999$	−9.14807e8	−	1.58449e9i	−0.917557	−	1.58925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.53.1	yes	60
19.14	odd	18	inner	76.7.j.a.33.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.33.1	✓	60	19.14	odd	18	inner
76.7.j.a.53.1	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-49.6429 + 8.75338i) q^{3} +(-5.51888 + 4.63089i) q^{5} +(269.359 - 466.544i) q^{7} +(1702.76 - 619.753i) q^{9} +O(q^{10})\)	\(q+(-49.6429 + 8.75338i) q^{3} +(-5.51888 + 4.63089i) q^{5} +(269.359 - 466.544i) q^{7} +(1702.76 - 619.753i) q^{9} +(767.080 + 1328.62i) q^{11} +(-2559.79 - 451.360i) q^{13} +(233.437 - 278.200i) q^{15} +(-6663.83 - 2425.43i) q^{17} +(6858.04 - 114.728i) q^{19} +(-9287.94 + 25518.4i) q^{21} +(-9977.35 - 8371.99i) q^{23} +(-2704.24 + 15336.5i) q^{25} +(-47280.2 + 27297.2i) q^{27} +(1041.66 + 2861.95i) q^{29} +(35335.6 + 20401.0i) q^{31} +(-49709.9 - 59242.0i) q^{33} +(673.953 + 3822.18i) q^{35} +33512.8i q^{37} +131026. q^{39} +(-71411.8 + 12591.8i) q^{41} +(8906.23 - 7473.22i) q^{43} +(-6527.31 + 11305.6i) q^{45} +(-82699.9 + 30100.3i) q^{47} +(-86284.5 - 149449. i) q^{49} +(352042. + 62074.6i) q^{51} +(-59627.8 + 71061.6i) q^{53} +(-10386.1 - 3780.24i) q^{55} +(-339449. + 65726.5i) q^{57} +(-134795. + 370345. i) q^{59} +(-112828. - 94674.0i) q^{61} +(169512. - 961348. i) q^{63} +(16217.4 - 9363.12i) q^{65} +(132735. + 364686. i) q^{67} +(568587. + 328274. i) q^{69} +(-65421.4 - 77966.2i) q^{71} +(4642.59 + 26329.4i) q^{73} -785019. i q^{75} +826480. q^{77} +(-62138.9 + 10956.8i) q^{79} +(1.09626e6 - 919867. i) q^{81} +(221519. - 383682. i) q^{83} +(48008.8 - 17473.8i) q^{85} +(-76762.8 - 132957. i) q^{87} +(-403805. - 71201.8i) q^{89} +(-900084. + 1.07268e6i) q^{91} +(-1.93274e6 - 703459. i) q^{93} +(-37317.4 + 32392.0i) q^{95} +(-265052. + 728224. i) q^{97} +(2.12957e6 + 1.78692e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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