LMFDB - Embedded newform 76.7.j.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	76.13
Dual form			76.7.j.a.41.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.6351 - 48.4521i) q^{3} +(11.8840 + 67.3972i) q^{5} +(-186.943 + 323.795i) q^{7} +(-1478.16 - 1240.32i) q^{9} +O(q^{10})$	\(q+(17.6351 - 48.4521i) q^{3} +(11.8840 + 67.3972i) q^{5} +(-186.943 + 323.795i) q^{7} +(-1478.16 - 1240.32i) q^{9} +(-462.506 - 801.084i) q^{11} +(-1082.59 - 2974.39i) q^{13} +(3475.11 + 612.756i) q^{15} +(-6881.88 + 5774.58i) q^{17} +(-6577.56 + 1944.62i) q^{19} +(12391.8 + 14767.9i) q^{21} +(-209.854 + 1190.14i) q^{23} +(10281.5 - 3742.17i) q^{25} +(-53611.3 + 30952.5i) q^{27} +(20758.8 - 24739.4i) q^{29} +(10305.9 + 5950.12i) q^{31} +(-46970.6 + 8282.18i) q^{33} +(-24044.5 - 8751.48i) q^{35} +35746.8i q^{37} -163207. q^{39} +(18775.8 - 51586.2i) q^{41} +(-6291.43 - 35680.4i) q^{43} +(66028.0 - 114364. i) q^{45} +(-105148. - 88229.4i) q^{47} +(-11070.8 - 19175.3i) q^{49} +(158428. + 435277. i) q^{51} +(115562. + 20376.6i) q^{53} +(48494.5 - 40691.7i) q^{55} +(-21775.4 + 352990. i) q^{57} +(-12651.0 - 15076.9i) q^{59} +(37645.8 - 213500. i) q^{61} +(677942. - 246751. i) q^{63} +(187600. - 108311. i) q^{65} +(179950. - 214456. i) q^{67} +(53964.0 + 31156.1i) q^{69} +(-598154. + 105471. i) q^{71} +(-444320. - 161719. i) q^{73} -564156. i q^{75} +345849. q^{77} +(174270. - 478802. i) q^{79} +(310004. + 1.75812e6i) q^{81} +(154246. - 267163. i) q^{83} +(-470975. - 395195. i) q^{85} +(-832590. - 1.44209e6i) q^{87} +(156769. + 430720. i) q^{89} +(1.16547e6 + 205504. i) q^{91} +(470042. - 394412. i) q^{93} +(-209229. - 420200. i) q^{95} +(-242174. - 288612. i) q^{97} +(-309946. + 1.75779e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	17.6351	−	48.4521i	0.653152	−	1.79452i	0.0473893	−	0.998876i	$-0.484910\pi$
$3$	17.6351	−	48.4521i	0.653152	−	1.79452i	0.605763	−	0.795645i	$-0.292868\pi$
$4$		0			0
$5$	11.8840	+	67.3972i	0.0950716	+	0.539178i	0.994725	+	0.102574i	$0.0327078\pi$
$5$	11.8840	+	67.3972i	0.0950716	+	0.539178i	−0.899654	+	0.436604i	$0.856181\pi$
$6$		0			0
$7$	−186.943	+	323.795i	−0.545023	+	0.944008i	0.453582	+	0.891214i	$0.350146\pi$
$7$	−186.943	+	323.795i	−0.545023	+	0.944008i	−0.998605	+	0.0527935i	$0.983188\pi$
$8$		0			0
$9$	−1478.16	−	1240.32i	−2.02765	−	1.70140i
$10$		0			0
$11$	−462.506	−	801.084i	−0.347488	−	0.601867i	0.638315	−	0.769776i	$-0.279632\pi$
$11$	−462.506	−	801.084i	−0.347488	−	0.601867i	−0.985803	+	0.167909i	$0.946299\pi$
$12$		0			0
$13$	−1082.59	−	2974.39i	−0.492757	−	1.35384i	−0.898147	−	0.439695i	$-0.855086\pi$
$13$	−1082.59	−	2974.39i	−0.492757	−	1.35384i	0.405390	−	0.914144i	$-0.367136\pi$
$14$		0			0
$15$	3475.11	+	612.756i	1.02966	+	0.181557i
$16$		0			0
$17$	−6881.88	+	5774.58i	−1.40075	+	1.17537i	−0.439983	+	0.898006i	$0.645015\pi$
$17$	−6881.88	+	5774.58i	−1.40075	+	1.17537i	−0.960766	+	0.277361i	$0.910540\pi$
$18$		0			0
$19$	−6577.56	+	1944.62i	−0.958968	+	0.283513i
$19$	−6577.56	+	1944.62i	−0.958968	+	0.283513i
$20$		0			0
$21$	12391.8	+	14767.9i	1.33806	+	1.59464i
$22$		0			0
$23$	−209.854	+	1190.14i	−0.0172478	+	0.0978171i	−0.992216	−	0.124525i	$-0.960259\pi$
$23$	−209.854	+	1190.14i	−0.0172478	+	0.0978171i	0.974969	+	0.222342i	$0.0713703\pi$
$24$		0			0
$25$	10281.5	−	3742.17i	0.658018	−	0.239499i
$26$		0			0
$27$	−53611.3	+	30952.5i	−2.72373	+	1.57255i
$28$		0			0
$29$	20758.8	−	24739.4i	0.851153	−	1.01437i	−0.148523	−	0.988909i	$-0.547452\pi$
$29$	20758.8	−	24739.4i	0.851153	−	1.01437i	0.999676	−	0.0254561i	$-0.00810381\pi$
$30$		0			0
$31$	10305.9	+	5950.12i	0.345940	+	0.199729i	0.662896	−	0.748712i	$-0.269327\pi$
$31$	10305.9	+	5950.12i	0.345940	+	0.199729i	−0.316955	+	0.948440i	$0.602661\pi$
$32$		0			0
$33$	−46970.6	+	8282.18i	−1.30703	+	0.230464i
$34$		0			0
$35$	−24044.5	−	8751.48i	−0.560804	−	0.204116i
$36$		0			0
$37$			35746.8i			0.705719i	0.935676	+	0.352860i	$0.114791\pi$
$37$			35746.8i			0.705719i	−0.935676	+	0.352860i	$0.885209\pi$
$38$		0			0
$39$	−163207.			−2.75134
$40$		0			0
$41$	18775.8	−	51586.2i	0.272426	−	0.748483i	−0.725742	−	0.687967i	$-0.758503\pi$
$41$	18775.8	−	51586.2i	0.272426	−	0.748483i	0.998167	−	0.0605158i	$-0.0192746\pi$
$42$		0			0
$43$	−6291.43	−	35680.4i	−0.0791305	−	0.448771i	−0.998470	−	0.0553049i	$-0.982387\pi$
$43$	−6291.43	−	35680.4i	−0.0791305	−	0.448771i	0.919339	−	0.393466i	$-0.128724\pi$
$44$		0			0
$45$	66028.0	−	114364.i	0.724587	−	1.25502i
$46$		0			0
$47$	−105148.	−	88229.4i	−1.01276	−	0.849806i	−0.0240587	−	0.999711i	$-0.507659\pi$
$47$	−105148.	−	88229.4i	−1.01276	−	0.849806i	−0.988700	+	0.149905i	$0.952103\pi$
$48$		0			0
$49$	−11070.8	−	19175.3i	−0.0941006	−	0.162987i
$50$		0			0
$51$	158428.	+	435277.i	1.19432	+	3.28137i
$52$		0			0
$53$	115562.	+	20376.6i	0.776222	+	0.136869i	0.547705	−	0.836671i	$-0.315501\pi$
$53$	115562.	+	20376.6i	0.776222	+	0.136869i	0.228516	+	0.973540i	$0.426613\pi$
$54$		0			0
$55$	48494.5	−	40691.7i	0.291477	−	0.244578i
$56$		0			0
$57$	−21775.4	+	352990.i	−0.117582	+	1.90607i
$58$		0			0
$59$	−12651.0	−	15076.9i	−0.0615985	−	0.0734102i	0.734365	−	0.678754i	$-0.237480\pi$
$59$	−12651.0	−	15076.9i	−0.0615985	−	0.0734102i	−0.795964	+	0.605344i	$0.793035\pi$
$60$		0			0
$61$	37645.8	−	213500.i	0.165854	−	0.940607i	−0.782325	−	0.622871i	$-0.785966\pi$
$61$	37645.8	−	213500.i	0.165854	−	0.940607i	0.948179	−	0.317736i	$-0.102923\pi$
$62$		0			0
$63$	677942.	−	246751.i	2.71126	−	0.986817i
$64$		0			0
$65$	187600.	−	108311.i	0.683113	−	0.394396i
$66$		0			0
$67$	179950.	−	214456.i	0.598310	−	0.713039i	−0.378870	−	0.925450i	$-0.623687\pi$
$67$	179950.	−	214456.i	0.598310	−	0.713039i	0.977180	+	0.212411i	$0.0681317\pi$
$68$		0			0
$69$	53964.0	+	31156.1i	0.164270	+	0.0948411i
$70$		0			0
$71$	−598154.	+	105471.i	−1.67124	+	0.294684i	−0.927510	−	0.373799i	$-0.878055\pi$
$71$	−598154.	+	105471.i	−1.67124	+	0.294684i	−0.743727	+	0.668484i	$0.766944\pi$
$72$		0			0
$73$	−444320.	−	161719.i	−1.14216	−	0.415712i	−0.299467	−	0.954107i	$-0.596809\pi$
$73$	−444320.	−	161719.i	−1.14216	−	0.415712i	−0.842693	+	0.538394i	$0.819031\pi$
$74$		0			0
$75$		−	564156.i		−	1.33726i
$76$		0			0
$77$	345849.			0.757556
$78$		0			0
$79$	174270.	−	478802.i	0.353460	−	0.971124i	−0.627789	−	0.778383i	$-0.716040\pi$
$79$	174270.	−	478802.i	0.353460	−	0.971124i	0.981250	−	0.192741i	$-0.0617377\pi$
$80$		0			0
$81$	310004.	+	1.75812e6i	0.583327	+	3.30821i
$82$		0			0
$83$	154246.	−	267163.i	0.269762	−	0.467242i	−0.699038	−	0.715084i	$-0.746388\pi$
$83$	154246.	−	267163.i	0.269762	−	0.467242i	0.968800	+	0.247843i	$0.0797216\pi$
$84$		0			0
$85$	−470975.	−	395195.i	−0.766904	−	0.643509i
$86$		0			0
$87$	−832590.	−	1.44209e6i	−1.26437	−	2.18995i
$88$		0			0
$89$	156769.	+	430720.i	0.222377	+	0.610977i	0.999839	−	0.0179539i	$-0.00571521\pi$
$89$	156769.	+	430720.i	0.222377	+	0.610977i	−0.777462	+	0.628931i	$0.783493\pi$
$90$		0			0
$91$	1.16547e6	+	205504.i	1.54660	+	0.272707i
$92$		0			0
$93$	470042.	−	394412.i	0.584370	−	0.490344i
$94$		0			0
$95$	−209229.	−	420200.i	−0.244035	−	0.490100i
$96$		0			0
$97$	−242174.	−	288612.i	−0.265346	−	0.316227i	0.616876	−	0.787060i	$-0.288398\pi$
$97$	−242174.	−	288612.i	−0.265346	−	0.316227i	−0.882222	+	0.470833i	$0.843954\pi$
$98$		0			0
$99$	−309946.	+	1.75779e6i	−0.319433	+	1.81160i
$100$		0			0
$101$	84977.2	−	30929.2i	0.0824780	−	0.0300195i	−0.300452	−	0.953797i	$-0.597137\pi$
$101$	84977.2	−	30929.2i	0.0824780	−	0.0300195i	0.382930	+	0.923778i	$0.374915\pi$
$102$		0			0
$103$	−801514.	+	462754.i	−0.733499	+	0.423486i	−0.819701	−	0.572792i	$-0.805860\pi$
$103$	−801514.	+	462754.i	−0.733499	+	0.423486i	0.0862019	+	0.996278i	$0.472527\pi$
$104$		0			0
$105$	−848055.	+	1.01067e6i	−0.732581	+	0.873057i
$106$		0			0
$107$	991191.	+	572265.i	0.809107	+	0.467138i	0.846646	−	0.532157i	$-0.178618\pi$
$107$	991191.	+	572265.i	0.809107	+	0.467138i	−0.0375385	+	0.999295i	$0.511952\pi$
$108$		0			0
$109$	−1.05836e6	+	186617.i	−0.817245	+	0.144102i	−0.566617	−	0.823981i	$-0.691748\pi$
$109$	−1.05836e6	+	186617.i	−0.817245	+	0.144102i	−0.250628	+	0.968083i	$0.580637\pi$
$110$		0			0
$111$	1.73201e6	+	630399.i	1.26643	+	0.460942i
$112$		0			0
$113$		−	695217.i		−	0.481820i	−0.970547	−	0.240910i	$-0.922554\pi$
$113$		−	695217.i		−	0.481820i	0.970547	−	0.240910i	$-0.0774459\pi$
$114$		0			0
$115$	−82706.1			−0.0543806
$116$		0			0
$117$	−2.08896e6	+	5.73938e6i	−1.30429	+	3.58350i
$118$		0			0
$119$	−583260.	−	3.30783e6i	−0.346116	−	1.96292i
$120$		0			0
$121$	457956.	−	793204.i	0.258504	−	0.447743i
$122$		0			0
$123$	−2.16834e6	−	1.81946e6i	−1.16523	−	0.977747i
$124$		0			0
$125$	909061.	+	1.57454e6i	0.465439	+	0.806164i
$126$		0			0
$127$	−31432.5	−	86360.1i	−0.0153450	−	0.0421601i	0.931784	−	0.363014i	$-0.118252\pi$
$127$	−31432.5	−	86360.1i	−0.0153450	−	0.0421601i	−0.947129	+	0.320854i	$0.896030\pi$
$128$		0			0
$129$	−1.83974e6	−	324396.i	−0.857014	−	0.151115i
$130$		0			0
$131$	1.16831e6	−	980326.i	0.519688	−	0.436070i	−0.344835	−	0.938663i	$-0.612065\pi$
$131$	1.16831e6	−	980326.i	0.519688	−	0.436070i	0.864523	+	0.502593i	$0.167621\pi$
$132$		0			0
$133$	599973.	−	2.49331e6i	0.255021	−	1.05979i
$134$		0			0
$135$	−2.72323e6	−	3.24541e6i	−1.10683	−	1.31907i
$136$		0			0
$137$	548281.	−	3.10946e6i	0.213227	−	1.20927i	−0.670731	−	0.741701i	$-0.734019\pi$
$137$	548281.	−	3.10946e6i	0.213227	−	1.20927i	0.883957	−	0.467567i	$-0.154870\pi$
$138$		0			0
$139$	−4.47990e6	+	1.63055e6i	−1.66811	+	0.607142i	−0.991606	−	0.129299i	$-0.958727\pi$
$139$	−4.47990e6	+	1.63055e6i	−1.66811	+	0.607142i	−0.676502	+	0.736441i	$0.736505\pi$
$140$		0			0
$141$	−6.12919e6	+	3.53869e6i	−2.18648	+	1.26237i
$142$		0			0
$143$	−1.88203e6	+	2.24292e6i	−0.643604	+	0.767017i
$144$		0			0
$145$	1.91406e6	+	1.10508e6i	0.627844	+	0.362486i
$146$		0			0
$147$	−1.12432e6	+	198247.i	−0.353946	+	0.0624102i
$148$		0			0
$149$	3.90020e6	+	1.41956e6i	1.17904	+	0.429135i	0.855862	−	0.517204i	$-0.173027\pi$
$149$	3.90020e6	+	1.41956e6i	1.17904	+	0.429135i	0.323176	+	0.946339i	$0.395249\pi$
$150$		0			0
$151$		−	2.63776e6i		−	0.766133i	−0.923721	−	0.383066i	$-0.874868\pi$
$151$		−	2.63776e6i		−	0.766133i	0.923721	−	0.383066i	$-0.125132\pi$
$152$		0			0
$153$	1.73349e7			4.84001
$154$		0			0
$155$	−278547.	+	765301.i	−0.0748002	+	0.205512i
$156$		0			0
$157$	−82450.1	−	467598.i	−0.0213055	−	0.120830i	0.972300	−	0.233736i	$-0.0750951\pi$
$157$	−82450.1	−	467598.i	−0.0213055	−	0.120830i	−0.993606	+	0.112906i	$0.963984\pi$
$158$		0			0
$159$	3.02523e6	−	5.23985e6i	0.752605	−	1.30355i
$160$		0			0
$161$	−346131.	−	290438.i	−0.0829397	−	0.0695947i
$162$		0			0
$163$	2.38569e6	+	4.13213e6i	0.550872	+	0.954139i	0.998212	+	0.0597748i	$0.0190383\pi$
$163$	2.38569e6	+	4.13213e6i	0.550872	+	0.954139i	−0.447339	+	0.894364i	$0.647628\pi$
$164$		0			0
$165$	−1.11639e6	−	3.06726e6i	−0.248522	−	0.682808i
$166$		0			0
$167$	−507839.	−	89545.8i	−0.109038	−	0.0192263i	0.118863	−	0.992911i	$-0.462075\pi$
$167$	−507839.	−	89545.8i	−0.109038	−	0.0192263i	−0.227901	+	0.973684i	$0.573186\pi$
$168$		0			0
$169$	−3.97742e6	+	3.33745e6i	−0.824027	+	0.691441i
$170$		0			0
$171$	1.21346e7	+	5.28386e6i	2.42683	+	1.05673i
$172$		0			0
$173$	3.82939e6	+	4.56369e6i	0.739590	+	0.881410i	0.996376	−	0.0850589i	$-0.0271078\pi$
$173$	3.82939e6	+	4.56369e6i	0.739590	+	0.881410i	−0.256786	+	0.966468i	$0.582663\pi$
$174$		0			0
$175$	−710365.	+	4.02868e6i	−0.132546	+	0.751707i
$176$		0			0
$177$	−953610.	+	347086.i	−0.171969	+	0.0625917i
$178$		0			0
$179$	−4.16232e6	+	2.40312e6i	−0.725732	+	0.419002i	−0.816859	−	0.576838i	$-0.804287\pi$
$179$	−4.16232e6	+	2.40312e6i	−0.725732	+	0.419002i	0.0911266	+	0.995839i	$0.470953\pi$
$180$		0			0
$181$	4.70797e6	−	5.61074e6i	0.793958	−	0.946202i	−0.205515	−	0.978654i	$-0.565887\pi$
$181$	4.70797e6	−	5.61074e6i	0.793958	−	0.946202i	0.999473	+	0.0324514i	$0.0103314\pi$
$182$		0			0
$183$	−9.68063e6	−	5.58911e6i	−1.57961	−	0.911989i
$184$		0			0
$185$	−2.40923e6	+	424813.i	−0.380508	+	0.0670938i
$186$		0			0
$187$	7.80884e6	+	2.84218e6i	1.19416	+	0.434638i
$188$		0			0
$189$		−	2.31454e7i		−	3.42830i
$190$		0			0
$191$	8.39203e6			1.20439			0.602195	−	0.798349i	$-0.294293\pi$
$191$	8.39203e6			1.20439			0.602195	+	0.798349i	$0.294293\pi$
$192$		0			0
$193$	−4.44669e6	+	1.22172e7i	−0.618537	+	1.69942i	0.0920037	+	0.995759i	$0.470673\pi$
$193$	−4.44669e6	+	1.22172e7i	−0.618537	+	1.69942i	−0.710540	+	0.703657i	$0.751549\pi$
$194$		0			0
$195$	−1.93954e6	−	1.09997e7i	−0.261574	−	1.48346i
$196$		0			0
$197$	3.52150e6	−	6.09942e6i	0.460606	−	0.797793i	−0.538385	−	0.842699i	$-0.680966\pi$
$197$	3.52150e6	−	6.09942e6i	0.460606	−	0.797793i	0.998991	+	0.0449061i	$0.0142989\pi$
$198$		0			0
$199$	−1.12660e7	−	9.45330e6i	−1.42959	−	1.19957i	−0.945956	−	0.324294i	$-0.894873\pi$
$199$	−1.12660e7	−	9.45330e6i	−1.42959	−	1.19957i	−0.483631	−	0.875272i	$-0.660682\pi$
$200$		0			0
$201$	−7.21739e6	−	1.25009e7i	−0.888775	−	1.53940i
$202$		0			0
$203$	4.12976e6	+	1.13464e7i	0.493670	+	1.35635i
$204$		0			0
$205$	3.69990e6	+	652392.i	0.429465	+	0.0757264i
$206$		0			0
$207$	1.78636e6	−	1.49893e6i	0.201399	−	0.168994i
$208$		0			0
$209$	4.59997e6	+	4.36979e6i	0.503867	+	0.478654i
$210$		0			0
$211$	−1.17515e7	−	1.40048e7i	−1.25096	−	1.49084i	−0.802042	−	0.597267i	$-0.796253\pi$
$211$	−1.17515e7	−	1.40048e7i	−1.25096	−	1.49084i	−0.448920	−	0.893572i	$-0.648191\pi$
$212$		0			0
$213$	−5.43824e6	+	3.08418e7i	−0.562755	+	3.19154i
$214$		0			0
$215$	2.33000e6	−	848049.i	0.234444	−	0.0853308i
$216$		0			0
$217$	−3.85324e6	+	2.22467e6i	−0.377091	+	0.217714i
$218$		0			0
$219$	−1.56713e7	+	1.86763e7i	−1.49201	+	1.77811i
$220$		0			0
$221$	2.46261e7	+	1.42179e7i	2.28149	+	1.31722i
$222$		0			0
$223$	5.92753e6	−	1.04518e6i	0.534514	−	0.0942492i	0.100125	−	0.994975i	$-0.468076\pi$
$223$	5.92753e6	−	1.04518e6i	0.534514	−	0.0942492i	0.434388	+	0.900726i	$0.356965\pi$
$224$		0			0
$225$	−1.98393e7	−	7.22090e6i	−1.74172	−	0.633934i
$226$		0			0
$227$			3.74521e6i			0.320184i	0.987102	+	0.160092i	$0.0511790\pi$
$227$			3.74521e6i			0.320184i	−0.987102	+	0.160092i	$0.948821\pi$
$228$		0			0
$229$	−1.94412e7			−1.61888			−0.809442	−	0.587200i	$-0.800230\pi$
$229$	−1.94412e7			−1.61888			−0.809442	+	0.587200i	$0.800230\pi$
$230$		0			0
$231$	6.09909e6	−	1.67571e7i	0.494799	−	1.35945i
$232$		0			0
$233$	2.20270e6	+	1.24921e7i	0.174136	+	0.987572i	0.939137	+	0.343543i	$0.111627\pi$
$233$	2.20270e6	+	1.24921e7i	0.174136	+	0.987572i	−0.765001	+	0.644029i	$0.777262\pi$
$234$		0			0
$235$	4.69685e6	−	8.13518e6i	0.361912	−	0.626850i
$236$		0			0
$237$	−2.01257e7	−	1.68875e7i	−1.51184	−	1.26858i
$238$		0			0
$239$	1.77010e6	+	3.06589e6i	0.129659	+	0.224576i	0.923545	−	0.383491i	$-0.125278\pi$
$239$	1.77010e6	+	3.06589e6i	0.129659	+	0.224576i	−0.793885	+	0.608067i	$0.791945\pi$
$240$		0			0
$241$	4.43684e6	+	1.21901e7i	0.316973	+	0.870877i	0.991202	+	0.132355i	$0.0422539\pi$
$241$	4.43684e6	+	1.21901e7i	0.316973	+	0.870877i	−0.674229	+	0.738522i	$0.735524\pi$
$242$		0			0
$243$	4.62084e7	+	8.14779e6i	3.22034	+	0.567833i
$244$		0			0
$245$	1.16079e6	−	974022.i	0.0789327	−	0.0662324i
$246$		0			0
$247$	1.29048e7	+	1.74590e7i	0.856370	+	1.15859i
$248$		0			0
$249$	−1.02244e7	−	1.21850e7i	−0.662279	−	0.789274i
$250$		0			0
$251$	−2.94585e6	+	1.67068e7i	−0.186290	+	1.05650i	0.737996	+	0.674805i	$0.235772\pi$
$251$	−2.94585e6	+	1.67068e7i	−0.186290	+	1.05650i	−0.924286	+	0.381700i	$0.875339\pi$
$252$		0			0
$253$	1.05046e6	−	382337.i	0.0648663	−	0.0236094i
$254$		0			0
$255$	−2.74537e7	+	1.58504e7i	−1.65569	+	0.955916i
$256$		0			0
$257$	915461.	−	1.09100e6i	0.0539312	−	0.0642727i	−0.738404	−	0.674358i	$-0.764420\pi$
$257$	915461.	−	1.09100e6i	0.0539312	−	0.0642727i	0.792336	+	0.610085i	$0.208865\pi$
$258$		0			0
$259$	−1.15746e7	−	6.68261e6i	−0.666204	−	0.384633i
$260$		0			0
$261$	−6.13696e7	+	1.08211e7i	−3.45169	+	0.608626i
$262$		0			0
$263$	−3.09611e6	−	1.12689e6i	−0.170196	−	0.0619463i	0.255517	−	0.966805i	$-0.417754\pi$
$263$	−3.09611e6	−	1.12689e6i	−0.170196	−	0.0619463i	−0.425713	+	0.904858i	$0.639977\pi$
$264$		0			0
$265$			8.03068e6i			0.431534i
$266$		0			0
$267$	2.36339e7			1.24166
$268$		0			0
$269$	5.00178e6	−	1.37423e7i	0.256961	−	0.705995i	−0.742390	−	0.669968i	$-0.766308\pi$
$269$	5.00178e6	−	1.37423e7i	0.256961	−	0.705995i	0.999351	−	0.0360265i	$-0.0114701\pi$
$270$		0			0
$271$	2.05273e6	+	1.16416e7i	0.103139	+	0.584931i	0.991947	+	0.126652i	$0.0404230\pi$
$271$	2.05273e6	+	1.16416e7i	0.103139	+	0.584931i	−0.888808	+	0.458279i	$0.848466\pi$
$272$		0			0
$273$	3.05103e7	−	5.28455e7i	1.49954	−	2.59729i
$274$		0			0
$275$	−7.75307e6	−	6.50560e6i	−0.372800	−	0.312816i
$276$		0			0
$277$	−1.02602e7	−	1.77712e7i	−0.482744	−	0.836137i	0.517060	−	0.855949i	$-0.327026\pi$
$277$	−1.02602e7	−	1.77712e7i	−0.482744	−	0.836137i	−0.999804	+	0.0198123i	$0.993693\pi$
$278$		0			0
$279$	−7.85371e6	−	2.15779e7i	−0.361628	−	0.993566i
$280$		0			0
$281$	−5.84040e6	−	1.02982e6i	−0.263223	−	0.0464133i	0.0404791	−	0.999180i	$-0.487112\pi$
$281$	−5.84040e6	−	1.02982e6i	−0.263223	−	0.0464133i	−0.303702	+	0.952767i	$0.598223\pi$
$282$		0			0
$283$	−2.31441e7	+	1.94202e7i	−1.02113	+	0.856830i	−0.989769	−	0.142678i	$-0.954429\pi$
$283$	−2.31441e7	+	1.94202e7i	−1.02113	+	0.856830i	−0.0313613	+	0.999508i	$0.509984\pi$
$284$		0			0
$285$	−2.40493e7	+	2.72732e6i	−1.03889	+	0.117815i
$286$		0			0
$287$	1.31933e7	+	1.57232e7i	0.558096	+	0.665113i
$288$		0			0
$289$	9.82301e6	−	5.57091e7i	0.406959	−	2.30798i
$290$		0			0
$291$	−1.82546e7	+	6.64415e6i	−0.740789	+	0.269625i
$292$		0			0
$293$	3.62506e7	−	2.09293e7i	1.44116	−	0.832054i	0.443233	−	0.896406i	$-0.353831\pi$
$293$	3.62506e7	−	2.09293e7i	1.44116	−	0.832054i	0.997927	+	0.0643522i	$0.0204981\pi$
$294$		0			0
$295$	865798.	−	1.03182e6i	0.0337249	−	0.0401918i
$296$		0			0
$297$	4.95911e7	+	2.86314e7i	1.89293	+	1.09288i
$298$		0			0
$299$	3.76712e6	−	664246.i	0.140928	−	0.0248494i
$300$		0			0
$301$	1.27293e7	+	4.63308e6i	0.466771	+	0.169891i
$302$		0			0
$303$		−	4.66276e6i		−	0.167616i
$304$		0			0
$305$	1.48367e7			0.522923
$306$		0			0
$307$	−3.57275e6	+	9.81606e6i	−0.123478	+	0.339252i	−0.985995	−	0.166776i	$-0.946664\pi$
$307$	−3.57275e6	+	9.81606e6i	−0.123478	+	0.339252i	0.862517	+	0.506028i	$0.168887\pi$
$308$		0			0
$309$	8.28662e6	+	4.69958e7i	0.280868	+	1.59288i
$310$		0			0
$311$	2.12886e6	−	3.68729e6i	0.0707726	−	0.122582i	−0.828467	−	0.560037i	$-0.810787\pi$
$311$	2.12886e6	−	3.68729e6i	0.0707726	−	0.122582i	0.899240	+	0.437455i	$0.144120\pi$
$312$		0			0
$313$	1.28451e7	+	1.07784e7i	0.418896	+	0.351495i	0.827743	−	0.561108i	$-0.189625\pi$
$313$	1.28451e7	+	1.07784e7i	0.418896	+	0.351495i	−0.408847	+	0.912603i	$0.634069\pi$
$314$		0			0
$315$	2.46869e7	+	4.27590e7i	0.789834	+	1.36803i
$316$		0			0
$317$	1.08084e7	+	2.96959e7i	0.339301	+	0.932222i	0.985593	+	0.169132i	$0.0540964\pi$
$317$	1.08084e7	+	2.96959e7i	0.339301	+	0.932222i	−0.646293	+	0.763090i	$0.723681\pi$
$318$		0			0
$319$	−2.94194e7	−	5.18743e6i	−0.906278	−	0.159801i
$320$		0			0
$321$	4.52072e7	−	3.79333e7i	1.36676	−	1.14685i
$322$		0			0
$323$	3.40366e7	−	5.13653e7i	1.01004	−	1.52427i
$324$		0			0
$325$	−2.22613e7	−	2.65300e7i	−0.648487	−	0.772836i
$326$		0			0
$327$	−9.62226e6	+	5.45706e7i	−0.275191	+	1.56068i
$328$		0			0
$329$	4.82248e7	−	1.75524e7i	1.35420	−	0.492889i
$330$		0			0
$331$	−1.98972e7	+	1.14876e7i	−0.548665	+	0.316772i	−0.748583	−	0.663041i	$-0.769266\pi$
$331$	−1.98972e7	+	1.14876e7i	−0.548665	+	0.316772i	0.199919	+	0.979813i	$0.435932\pi$
$332$		0			0
$333$	4.43376e7	−	5.28395e7i	1.20071	−	1.43095i
$334$		0			0
$335$	1.65922e7	+	9.57953e6i	0.441337	+	0.254806i
$336$		0			0
$337$	1.17348e7	−	2.06916e6i	0.306609	−	0.0540635i	−0.0182267	−	0.999834i	$-0.505802\pi$
$337$	1.17348e7	−	2.06916e6i	0.306609	−	0.0540635i	0.324836	+	0.945770i	$0.394691\pi$
$338$		0			0
$339$	−3.36847e7	−	1.22602e7i	−0.864636	−	0.314702i
$340$		0			0
$341$		−	1.10079e7i		−	0.277613i
$342$		0			0
$343$	−3.57088e7			−0.884898
$344$		0			0
$345$	−1.45853e6	+	4.00728e6i	−0.0355188	+	0.0975872i
$346$		0			0
$347$	−1.38023e7	−	7.82766e7i	−0.330341	−	1.87346i	−0.469122	−	0.883133i	$-0.655430\pi$
$347$	−1.38023e7	−	7.82766e7i	−0.330341	−	1.87346i	0.138782	−	0.990323i	$-0.455681\pi$
$348$		0			0
$349$	−2.97314e7	+	5.14963e7i	−0.699422	+	1.21143i	0.269246	+	0.963072i	$0.413226\pi$
$349$	−2.97314e7	+	5.14963e7i	−0.699422	+	1.21143i	−0.968667	+	0.248362i	$0.920108\pi$
$350$		0			0
$351$	1.50104e8	+	1.25952e8i	3.47112	+	2.91261i
$352$		0			0
$353$	1.00325e7	+	1.73768e7i	0.228079	+	0.395044i	0.957239	−	0.289299i	$-0.0934223\pi$
$353$	1.00325e7	+	1.73768e7i	0.228079	+	0.395044i	−0.729160	+	0.684343i	$0.760089\pi$
$354$		0			0
$355$	−1.42169e7	−	3.90605e7i	−0.317774	−	0.873078i
$356$		0			0
$357$	−1.70557e8	−	3.00738e7i	−3.74857	−	0.660974i
$358$		0			0
$359$	−7.40990e6	+	6.21765e6i	−0.160151	+	0.134382i	−0.719342	−	0.694657i	$-0.755556\pi$
$359$	−7.40990e6	+	6.21765e6i	−0.160151	+	0.134382i	0.559191	+	0.829039i	$0.311112\pi$
$360$		0			0
$361$	3.94828e7	−	2.55817e7i	0.839241	−	0.543760i
$362$		0			0
$363$	−3.03563e7	−	3.61772e7i	−0.634641	−	0.756336i
$364$		0			0
$365$	5.61915e6	−	3.18678e7i	0.115556	−	0.655350i
$366$		0			0
$367$	−2.83850e7	+	1.03313e7i	−0.574237	+	0.209005i	−0.612782	−	0.790252i	$-0.709950\pi$
$367$	−2.83850e7	+	1.03313e7i	−0.574237	+	0.209005i	0.0385456	+	0.999257i	$0.487728\pi$
$368$		0			0
$369$	−9.17373e7	+	5.29646e7i	−1.82586	+	1.05416i
$370$		0			0
$371$	−2.82013e7	+	3.36090e7i	−0.552264	+	0.658163i
$372$		0			0
$373$	2.78611e6	+	1.60856e6i	0.0536873	+	0.0309964i	0.526603	−	0.850111i	$-0.323465\pi$
$373$	2.78611e6	+	1.60856e6i	0.0536873	+	0.0309964i	−0.472916	+	0.881107i	$0.656799\pi$
$374$		0			0
$375$	9.23211e7	−	1.62787e7i	1.75068	−	0.308693i
$376$		0			0
$377$	−9.60576e7	−	3.49621e7i	−1.79270	−	0.652489i
$378$		0			0
$379$		−	7.47670e7i		−	1.37338i	−0.726948	−	0.686692i	$-0.759062\pi$
$379$		−	7.47670e7i		−	1.37338i	0.726948	−	0.686692i	$-0.240938\pi$
$380$		0			0
$381$	−4.73864e6			−0.0856799
$382$		0			0
$383$	−1.01017e7	+	2.77542e7i	−0.179803	+	0.494006i	−0.996550	−	0.0829903i	$-0.973553\pi$
$383$	−1.01017e7	+	2.77542e7i	−0.179803	+	0.494006i	0.816747	+	0.576996i	$0.195775\pi$
$384$		0			0
$385$	4.11005e6	+	2.33093e7i	0.0720220	+	0.408457i
$386$		0			0
$387$	−3.49556e7	+	6.05448e7i	−0.603092	+	1.04459i
$388$		0			0
$389$	4.07001e7	+	3.41515e7i	0.691428	+	0.580177i	0.919321	−	0.393509i	$-0.128739\pi$
$389$	4.07001e7	+	3.41515e7i	0.691428	+	0.580177i	−0.227893	+	0.973686i	$0.573183\pi$
$390$		0			0
$391$	−5.42838e6	−	9.40222e6i	−0.0908113	−	0.157290i
$392$		0			0
$393$	−2.68956e7	−	7.38951e7i	−0.443102	−	1.21741i
$394$		0			0
$395$	3.43410e7	+	6.05524e6i	0.557213	+	0.0982516i
$396$		0			0
$397$	2.92475e7	−	2.45415e7i	0.467430	−	0.392220i	−0.378426	−	0.925631i	$-0.623535\pi$
$397$	2.92475e7	−	2.45415e7i	0.467430	−	0.392220i	0.845856	+	0.533411i	$0.179090\pi$
$398$		0			0
$399$	−1.10226e8	−	7.30398e7i	−1.73526	−	1.14985i
$400$		0			0
$401$	7.58690e7	+	9.04171e7i	1.17661	+	1.40222i	0.896955	+	0.442122i	$0.145774\pi$
$401$	7.58690e7	+	9.04171e7i	1.17661	+	1.40222i	0.279651	+	0.960102i	$0.409781\pi$
$402$		0			0
$403$	6.54090e6	−	3.70953e7i	0.0999361	−	0.566766i
$404$		0			0
$405$	−1.14808e8	+	4.17868e7i	−1.72826	+	0.629034i
$406$		0			0
$407$	2.86362e7	−	1.65331e7i	0.424749	−	0.245229i
$408$		0			0
$409$	1.82835e7	−	2.17894e7i	0.267232	−	0.318475i	−0.615695	−	0.787984i	$-0.711125\pi$
$409$	1.82835e7	−	2.17894e7i	0.267232	−	0.318475i	0.882928	+	0.469509i	$0.155569\pi$
$410$		0			0
$411$	−1.40991e8	−	8.14010e7i	−2.03079	−	1.17248i
$412$		0			0
$413$	7.24685e6	−	1.27781e6i	0.102872	−	0.0181392i
$414$		0			0
$415$	1.98391e7	+	7.22083e6i	0.277573	+	0.101028i
$416$		0			0
$417$			2.45816e8i			3.39001i
$418$		0			0
$419$	4.25519e7			0.578465			0.289232	−	0.957259i	$-0.406600\pi$
$419$	4.25519e7			0.578465			0.289232	+	0.957259i	$0.406600\pi$
$420$		0			0
$421$	3.38147e7	−	9.29052e7i	0.453168	−	1.24507i	−0.477314	−	0.878733i	$-0.658390\pi$
$421$	3.38147e7	−	9.29052e7i	0.453168	−	1.24507i	0.930482	−	0.366337i	$-0.119388\pi$
$422$		0			0
$423$	4.59921e7	+	2.60834e8i	0.607663	+	3.44623i
$424$		0			0
$425$	−4.91468e7	+	8.51248e7i	−0.640219	+	1.10889i
$426$		0			0
$427$	6.20925e7	+	5.21018e7i	0.797546	+	0.669221i
$428$		0			0
$429$	7.54841e7	+	1.30742e8i	0.956057	+	1.65594i
$430$		0			0
$431$	−1.11223e7	−	3.05582e7i	−0.138919	−	0.381677i	0.850651	−	0.525731i	$-0.176208\pi$
$431$	−1.11223e7	−	3.05582e7i	−0.138919	−	0.381677i	−0.989570	+	0.144054i	$0.953986\pi$
$432$		0			0
$433$	6.07697e7	+	1.07153e7i	0.748554	+	0.131990i	0.534896	−	0.844918i	$-0.320351\pi$
$433$	6.07697e7	+	1.07153e7i	0.748554	+	0.131990i	0.213659	+	0.976908i	$0.431462\pi$
$434$		0			0
$435$	8.72982e7	−	7.32519e7i	1.06057	−	0.889921i
$436$		0			0
$437$	−934039.	−	8.23632e6i	−0.0111923	−	0.0986935i
$438$		0			0
$439$	−7.90147e7	−	9.41660e7i	−0.933930	−	1.11301i	−0.993391	−	0.114783i	$-0.963383\pi$
$439$	−7.90147e7	−	9.41660e7i	−0.933930	−	1.11301i	0.0594610	−	0.998231i	$-0.481062\pi$
$440$		0			0
$441$	−7.41905e6	+	4.20755e7i	−0.0865033	+	0.490585i
$442$		0			0
$443$	−9.83024e7	+	3.57791e7i	−1.13071	+	0.411546i	−0.838552	−	0.544822i	$-0.816597\pi$
$443$	−9.83024e7	+	3.57791e7i	−1.13071	+	0.411546i	−0.292163	+	0.956369i	$0.594375\pi$
$444$		0			0
$445$	−2.71663e7	+	1.56845e7i	−0.308283	+	0.177987i
$446$		0			0
$447$	1.37561e8	−	1.63939e8i	1.54018	−	1.83552i
$448$		0			0
$449$	4.38886e7	+	2.53391e7i	0.484856	+	0.279932i	0.722438	−	0.691436i	$-0.243021\pi$
$449$	4.38886e7	+	2.53391e7i	0.484856	+	0.279932i	−0.237582	+	0.971368i	$0.576355\pi$
$450$		0			0
$451$	−5.00089e7	+	8.81791e6i	−0.545152	+	0.0961249i
$452$		0			0
$453$	−1.27805e8	−	4.65172e7i	−1.37484	−	0.500401i
$454$		0			0
$455$			8.09918e7i			0.859819i
$456$		0			0
$457$	−1.35007e8			−1.41452			−0.707260	−	0.706954i	$-0.750069\pi$
$457$	−1.35007e8			−1.41452			−0.707260	+	0.706954i	$0.750069\pi$
$458$		0			0
$459$	1.90209e8	−	5.22594e8i	1.96694	−	5.40414i
$460$		0			0
$461$	−2.52231e7	−	1.43047e8i	−0.257451	−	1.46008i	−0.789702	−	0.613491i	$-0.789765\pi$
$461$	−2.52231e7	−	1.43047e8i	−0.257451	−	1.46008i	0.532250	−	0.846587i	$-0.321347\pi$
$462$		0			0
$463$	8.56343e6	−	1.48323e7i	0.0862790	−	0.149440i	−0.819657	−	0.572855i	$-0.805836\pi$
$463$	8.56343e6	−	1.48323e7i	0.0862790	−	0.149440i	0.905935	+	0.423416i	$0.139169\pi$
$464$		0			0
$465$	3.21682e7	+	2.69923e7i	0.319940	+	0.268461i
$466$		0			0
$467$	4.16672e7	+	7.21697e7i	0.409113	+	0.708605i	0.994791	−	0.101939i	$-0.0325047\pi$
$467$	4.16672e7	+	7.21697e7i	0.409113	+	0.708605i	−0.585677	+	0.810544i	$0.699171\pi$
$468$		0			0
$469$	3.57993e7	+	9.83577e7i	0.347021	+	0.953432i
$470$		0			0
$471$	−2.41101e7	−	4.25126e6i	−0.230747	−	0.0406869i
$472$		0			0
$473$	−2.56732e7	+	2.15424e7i	−0.242603	+	0.203569i
$474$		0			0
$475$	−6.03504e7	+	4.46080e7i	−0.563118	+	0.416229i
$476$		0			0
$477$	−1.45545e8	−	1.73454e8i	−1.34104	−	1.59819i
$478$		0			0
$479$	−4.50462e6	+	2.55469e7i	−0.0409875	+	0.232452i	−0.998419	−	0.0562089i	$-0.982099\pi$
$479$	−4.50462e6	+	2.55469e7i	−0.0409875	+	0.232452i	0.957432	+	0.288660i	$0.0932098\pi$
$480$		0			0
$481$	1.06325e8	−	3.86990e7i	0.955430	−	0.347748i
$482$		0			0
$483$	−2.01764e7	+	1.16488e7i	−0.179061	+	0.103381i
$484$		0			0
$485$	1.65737e7	−	1.97517e7i	0.145276	−	0.173133i
$486$		0			0
$487$	−2.53672e7	−	1.46457e7i	−0.219627	−	0.126802i	0.386151	−	0.922436i	$-0.373804\pi$
$487$	−2.53672e7	−	1.46457e7i	−0.219627	−	0.126802i	−0.605777	+	0.795634i	$0.707138\pi$
$488$		0			0
$489$	2.42282e8	−	4.27209e7i	2.07203	−	0.365354i
$490$		0			0
$491$	−1.73330e8	−	6.30869e7i	−1.46430	−	0.532960i	−0.517751	−	0.855531i	$-0.673231\pi$
$491$	−1.73330e8	−	6.30869e7i	−1.46430	−	0.532960i	−0.946545	+	0.322571i	$0.895453\pi$
$492$		0			0
$493$			2.90126e8i			2.42129i
$494$		0			0
$495$	−1.22153e8			−1.00714
$496$		0			0
$497$	7.76698e7	−	2.13396e8i	0.632679	−	1.73827i
$498$		0			0
$499$	1.95251e7	+	1.10733e8i	0.157142	+	0.891197i	0.956801	+	0.290743i	$0.0939024\pi$
$499$	1.95251e7	+	1.10733e8i	0.157142	+	0.891197i	−0.799659	+	0.600454i	$0.794986\pi$
$500$		0			0
$501$	−1.32945e7	+	2.30267e7i	−0.105720	+	0.183113i
$502$		0			0
$503$	5.85948e7	+	4.91669e7i	0.460421	+	0.386339i	0.843286	−	0.537465i	$-0.180618\pi$
$503$	5.85948e7	+	4.91669e7i	0.460421	+	0.386339i	−0.382865	+	0.923804i	$0.625062\pi$
$504$		0			0
$505$	3.09440e6	+	5.35966e6i	0.0240272	+	0.0416163i
$506$		0			0
$507$	9.15643e7	+	2.51571e8i	0.702590	+	1.93035i
$508$		0			0
$509$	6.15054e7	+	1.08451e7i	0.466402	+	0.0822392i	0.401910	−	0.915679i	$-0.368346\pi$
$509$	6.15054e7	+	1.08451e7i	0.466402	+	0.0822392i	0.0644914	+	0.997918i	$0.479458\pi$
$510$		0			0
$511$	1.35426e8	−	1.13636e8i	1.01494	−	0.851635i
$512$		0			0
$513$	2.92441e8	−	3.07845e8i	2.16614	−	2.28024i
$514$		0			0
$515$	−4.07135e7	−	4.85205e7i	−0.298069	−	0.355225i
$516$		0			0
$517$	−2.20477e7	+	1.25039e8i	−0.159548	+	0.904843i
$518$		0			0
$519$	2.88652e8	−	1.05061e8i	2.06477	−	0.751516i
$520$		0			0
$521$	5.47933e7	−	3.16349e7i	0.387449	−	0.223694i	−0.293605	−	0.955927i	$-0.594855\pi$
$521$	5.47933e7	−	3.16349e7i	0.387449	−	0.223694i	0.681054	+	0.732233i	$0.261522\pi$
$522$		0			0
$523$	−4.93338e7	+	5.87937e7i	−0.344857	+	0.410985i	−0.910397	−	0.413736i	$-0.864224\pi$
$523$	−4.93338e7	+	5.87937e7i	−0.344857	+	0.410985i	0.565540	+	0.824721i	$0.308668\pi$
$524$		0			0
$525$	1.82671e8	+	1.05465e8i	1.26238	+	0.728836i
$526$		0			0
$527$	−1.05283e8	+	1.85643e7i	−0.719330	+	0.126837i
$528$		0			0
$529$	1.37736e8	+	5.01317e7i	0.930422	+	0.338646i
$530$		0			0
$531$			3.79775e7i			0.253655i
$532$		0			0
$533$	−1.73764e8			−1.14757
$534$		0			0
$535$	−2.67898e7	+	7.36043e7i	−0.174948	+	0.480664i
$536$		0			0
$537$	4.30330e7	+	2.44052e8i	0.277894	+	1.57601i
$538$		0			0
$539$	−1.02407e7	+	1.77374e7i	−0.0653976	+	0.113272i
$540$		0			0
$541$	−4.64458e6	−	3.89726e6i	−0.0293329	−	0.0246132i	0.628003	−	0.778211i	$-0.283872\pi$
$541$	−4.64458e6	−	3.89726e6i	−0.0293329	−	0.0246132i	−0.657336	+	0.753597i	$0.728317\pi$
$542$		0			0
$543$	−1.88826e8	−	3.27057e8i	−1.17941	−	2.04279i
$544$		0			0
$545$	−2.51549e7	−	6.91125e7i	−0.155394	−	0.426940i
$546$		0			0
$547$	9.47598e7	+	1.67087e7i	0.578978	+	0.102089i	0.455465	−	0.890253i	$-0.349473\pi$
$547$	9.47598e7	+	1.67087e7i	0.578978	+	0.102089i	0.123513	+	0.992343i	$0.460584\pi$
$548$		0			0
$549$	−3.20456e8	+	2.68894e8i	−1.93665	+	1.62504i
$550$		0			0
$551$	−8.84337e7	+	2.03093e8i	−0.528643	+	1.21406i
$552$		0			0
$553$	1.22455e8	+	1.45936e8i	0.724105	+	0.862955i
$554$		0			0
$555$	−2.19041e7	+	1.24224e8i	−0.128128	+	0.726652i
$556$		0			0
$557$	−1.45478e8	+	5.29497e7i	−0.841845	+	0.306407i	−0.726711	−	0.686943i	$-0.758952\pi$
$557$	−1.45478e8	+	5.29497e7i	−0.841845	+	0.306407i	−0.115134	+	0.993350i	$0.536730\pi$
$558$		0			0
$559$	−9.93164e7	+	5.73403e7i	−0.568572	+	0.328265i
$560$		0			0
$561$	2.75420e8	−	3.28232e8i	1.55993	−	1.85906i
$562$		0			0
$563$	−8.39192e7	−	4.84508e7i	−0.470258	−	0.271504i	0.246090	−	0.969247i	$-0.420854\pi$
$563$	−8.39192e7	−	4.84508e7i	−0.470258	−	0.271504i	−0.716348	+	0.697743i	$0.754188\pi$
$564$		0			0
$565$	4.68557e7	−	8.26192e6i	0.259787	−	0.0458074i
$566$		0			0
$567$	−6.27223e8	−	2.28290e8i	−3.44090	−	1.25239i
$568$		0			0
$569$		−	1.03600e8i		−	0.562371i	−0.959653	−	0.281186i	$-0.909272\pi$
$569$		−	1.03600e8i		−	0.562371i	0.959653	−	0.281186i	$-0.0907276\pi$
$570$		0			0
$571$	2.80698e7			0.150776			0.0753879	−	0.997154i	$-0.475980\pi$
$571$	2.80698e7			0.150776			0.0753879	+	0.997154i	$0.475980\pi$
$572$		0			0
$573$	1.47994e8	−	4.06612e8i	0.786650	−	2.16130i
$574$		0			0
$575$	2.29609e6	+	1.30218e7i	0.0120777	+	0.0684963i
$576$		0			0
$577$	6.88306e7	−	1.19218e8i	0.358306	−	0.620604i	−0.629372	−	0.777104i	$-0.716688\pi$
$577$	6.88306e7	−	1.19218e8i	0.358306	−	0.620604i	0.987678	+	0.156500i	$0.0500211\pi$
$578$		0			0
$579$	5.13530e8	+	4.30903e8i	2.64564	+	2.21995i
$580$		0			0
$581$	5.76706e7	+	9.98883e7i	0.294053	+	0.509315i
$582$		0			0
$583$	−3.71246e7	−	1.01999e8i	−0.187351	−	0.514742i
$584$		0			0
$585$	−4.11643e8	−	7.25838e7i	−2.05614	−	0.362554i
$586$		0			0
$587$	−2.59612e6	+	2.17841e6i	−0.0128354	+	0.0107702i	−0.649183	−	0.760632i	$-0.724889\pi$
$587$	−2.59612e6	+	2.17841e6i	−0.0128354	+	0.0107702i	0.636347	+	0.771403i	$0.280445\pi$
$588$		0			0
$589$	−7.93585e7	−	1.90963e7i	−0.388372	−	0.0934550i
$590$		0			0
$591$	−2.33428e8	−	2.78188e8i	−1.13081	−	1.34765i
$592$		0			0
$593$	−1.86783e7	+	1.05930e8i	−0.0895721	+	0.507989i	0.906704	+	0.421768i	$0.138590\pi$
$593$	−1.86783e7	+	1.05930e8i	−0.0895721	+	0.507989i	−0.996276	+	0.0862210i	$0.972521\pi$
$594$		0			0
$595$	2.16007e8	−	7.86202e7i	1.02546	−	0.373236i
$596$		0			0
$597$	−6.56709e8	+	3.79151e8i	−3.08639	+	1.78193i
$598$		0			0
$599$	−2.49660e7	+	2.97533e7i	−0.116163	+	0.138438i	−0.820992	−	0.570939i	$-0.806579\pi$
$599$	−2.49660e7	+	2.97533e7i	−0.116163	+	0.138438i	0.704829	+	0.709377i	$0.251024\pi$
$600$		0			0
$601$	−3.13553e8	−	1.81030e8i	−1.44440	−	0.833924i	−0.446260	−	0.894903i	$-0.647244\pi$
$601$	−3.13553e8	−	1.81030e8i	−1.44440	−	0.833924i	−0.998139	+	0.0609791i	$0.980578\pi$
$602$		0			0
$603$	−5.31989e8	+	9.38040e7i	−2.42633	+	0.427828i
$604$		0			0
$605$	5.89021e7	+	2.14386e7i	0.265989	+	0.0968122i
$606$		0			0
$607$		−	3.23222e8i		−	1.44522i	−0.691253	−	0.722612i	$-0.742941\pi$
$607$		−	3.23222e8i		−	1.44522i	0.691253	−	0.722612i	$-0.257059\pi$
$608$		0			0
$609$	6.22587e8			2.75644
$610$		0			0
$611$	−1.48597e8	+	4.08266e8i	−0.651456	+	1.78986i
$612$		0			0
$613$	6.08979e6	+	3.45369e7i	0.0264375	+	0.149935i	0.995169	−	0.0981770i	$-0.0313011\pi$
$613$	6.08979e6	+	3.45369e7i	0.0264375	+	0.149935i	−0.968731	+	0.248112i	$0.920190\pi$
$614$		0			0
$615$	9.68579e7	−	1.67763e8i	0.416399	−	0.721224i
$616$		0			0
$617$	2.80289e7	+	2.35190e7i	0.119330	+	0.100130i	0.700500	−	0.713652i	$-0.252960\pi$
$617$	2.80289e7	+	2.35190e7i	0.119330	+	0.100130i	−0.581170	+	0.813782i	$0.697405\pi$
$618$		0			0
$619$	2.00007e8	+	3.46422e8i	0.843281	+	1.46061i	0.887106	+	0.461567i	$0.152712\pi$
$619$	2.00007e8	+	3.46422e8i	0.843281	+	1.46061i	−0.0438243	+	0.999039i	$0.513954\pi$
$620$		0			0
$621$	−2.55873e7	−	7.03005e7i	−0.106844	−	0.293551i
$622$		0			0
$623$	−1.68772e8	−	2.97590e7i	−0.697968	−	0.123071i
$624$		0			0
$625$	3.56459e7	−	2.99105e7i	0.146006	−	0.122513i
$626$		0			0
$627$	2.92846e8	−	1.45816e8i	1.18806	−	0.591566i
$628$		0			0
$629$	−2.06423e8	−	2.46005e8i	−0.829479	−	0.988535i
$630$		0			0
$631$	−3.07315e7	+	1.74287e8i	−0.122320	+	0.693709i	0.860544	+	0.509376i	$0.170124\pi$
$631$	−3.07315e7	+	1.74287e8i	−0.122320	+	0.693709i	−0.982864	+	0.184333i	$0.940987\pi$
$632$		0			0
$633$	−8.85802e8	+	3.22406e8i	−3.49241	+	1.27113i
$634$		0			0
$635$	5.44689e6	−	3.14476e6i	0.0212729	−	0.0122819i
$636$		0			0
$637$	−4.50494e7	+	5.36878e7i	−0.174289	+	0.207710i
$638$		0			0
$639$	1.01499e9	+	5.86002e8i	3.89007	+	2.24593i
$640$		0			0
$641$	−2.94355e8	+	5.19027e7i	−1.11763	+	0.197068i	−0.701799	−	0.712375i	$-0.747620\pi$
$641$	−2.94355e8	+	5.19027e7i	−1.11763	+	0.197068i	−0.415829	+	0.909443i	$0.636509\pi$
$642$		0			0
$643$	−1.69490e7	−	6.16895e6i	−0.0637547	−	0.0232048i	0.309946	−	0.950754i	$-0.399689\pi$
$643$	−1.69490e7	−	6.16895e6i	−0.0637547	−	0.0232048i	−0.373701	+	0.927549i	$0.621911\pi$
$644$		0			0
$645$		−	1.27849e8i		−	0.476450i
$646$		0			0
$647$	5.46840e6			0.0201905			0.0100953	−	0.999949i	$-0.496787\pi$
$647$	5.46840e6			0.0201905			0.0100953	+	0.999949i	$0.496787\pi$
$648$		0			0
$649$	−6.22670e6	+	1.71077e7i	−0.0227784	+	0.0625832i
$650$		0			0
$651$	3.98375e7	+	2.25930e8i	0.144394	+	0.818898i
$652$		0			0
$653$	1.76619e8	−	3.05914e8i	0.634306	−	1.09865i	−0.352355	−	0.935866i	$-0.614619\pi$
$653$	1.76619e8	−	3.05914e8i	0.634306	−	1.09865i	0.986662	−	0.162785i	$-0.0520476\pi$
$654$		0			0
$655$	7.99554e7	+	6.70905e7i	0.284527	+	0.238747i
$656$		0			0
$657$	4.56192e8	+	7.90147e8i	1.60861	+	2.78620i
$658$		0			0
$659$	−1.90229e8	−	5.22651e8i	−0.664694	−	1.82623i	−0.554253	−	0.832348i	$-0.686996\pi$
$659$	−1.90229e8	−	5.22651e8i	−0.664694	−	1.82623i	−0.110440	−	0.993883i	$-0.535226\pi$
$660$		0			0
$661$	−1.69015e8	−	2.98018e7i	−0.585221	−	0.103190i	−0.126804	−	0.991928i	$-0.540472\pi$
$661$	−1.69015e8	−	2.98018e7i	−0.585221	−	0.103190i	−0.458416	+	0.888737i	$0.651583\pi$
$662$		0			0
$663$	1.12317e9	−	9.42450e8i	3.85393	−	3.23384i
$664$		0			0
$665$	1.75172e8	+	1.08061e7i	0.595663	+	0.0367455i
$666$		0			0
$667$	2.50870e7	+	2.98975e7i	0.0845418	+	0.100753i
$668$		0			0
$669$	5.38913e7	−	3.05633e8i	0.179987	−	1.02076i
$670$		0			0
$671$	−1.88443e8	+	6.85876e7i	−0.623753	+	0.227027i
$672$		0			0
$673$	1.90333e8	−	1.09889e8i	0.624409	−	0.360503i	−0.154175	−	0.988044i	$-0.549272\pi$
$673$	1.90333e8	−	1.09889e8i	0.624409	−	0.360503i	0.778584	+	0.627541i	$0.215938\pi$
$674$		0			0
$675$	−4.35377e8	+	5.18862e8i	−1.41564	+	1.68710i
$676$		0			0
$677$	2.78519e8	+	1.60803e8i	0.897613	+	0.518237i	0.876425	−	0.481538i	$-0.159922\pi$
$677$	2.78519e8	+	1.60803e8i	0.897613	+	0.518237i	0.0211880	+	0.999776i	$0.493255\pi$
$678$		0			0
$679$	1.38724e8	−	2.44608e7i	0.443141	−	0.0781377i
$680$		0			0
$681$	1.81463e8	+	6.60473e7i	0.574576	+	0.209129i
$682$		0			0
$683$		−	4.05444e8i		−	1.27253i	−0.771470	−	0.636266i	$-0.780478\pi$
$683$		−	4.05444e8i		−	1.27253i	0.771470	−	0.636266i	$-0.219522\pi$
$684$		0			0
$685$	2.16084e8			0.672283
$686$		0			0
$687$	−3.42847e8	+	9.41964e8i	−1.05738	+	2.90512i
$688$		0			0
$689$	−6.44976e7	−	3.65784e8i	−0.197190	−	1.11832i
$690$		0			0
$691$	1.13606e8	−	1.96772e8i	0.344325	−	0.596389i	−0.640906	−	0.767620i	$-0.721441\pi$
$691$	1.13606e8	−	1.96772e8i	0.344325	−	0.596389i	0.985231	+	0.171231i	$0.0547744\pi$
$692$		0			0
$693$	−5.11221e8	−	4.28965e8i	−1.53606	−	1.28891i
$694$		0			0
$695$	−1.63134e8	−	2.82556e8i	−0.485947	−	0.841685i
$696$		0			0
$697$	1.68676e8	+	4.63433e8i	0.498143	+	1.36864i
$698$		0			0
$699$	6.44115e8	+	1.13575e8i	1.88596	+	0.332545i
$700$		0			0
$701$	−3.53751e8	+	2.96832e8i	−1.02694	+	0.861702i	−0.990483	−	0.137634i	$-0.956050\pi$
$701$	−3.53751e8	+	2.96832e8i	−1.02694	+	0.861702i	−0.0364528	+	0.999335i	$0.511606\pi$
$702$		0			0
$703$	−6.95138e7	−	2.35127e8i	−0.200081	−	0.676762i
$704$		0			0
$705$	−3.11337e8	−	3.71037e8i	−0.888512	−	1.05889i
$706$		0			0
$707$	−5.87118e6	+	3.32971e7i	−0.0166137	+	0.0942212i
$708$		0			0
$709$	2.64727e8	−	9.63528e7i	0.742780	−	0.270350i	0.0572154	−	0.998362i	$-0.481778\pi$
$709$	2.64727e8	−	9.63528e7i	0.742780	−	0.270350i	0.685564	+	0.728012i	$0.259556\pi$
$710$		0			0
$711$	−8.51468e8	+	4.91595e8i	−2.36897	+	1.36773i
$712$		0			0
$713$	−9.24422e6	+	1.10168e7i	−0.0255036	+	0.0303940i
$714$		0			0
$715$	−1.73532e8	−	1.00189e8i	−0.474747	−	0.274095i
$716$		0			0
$717$	1.79765e8	−	3.16974e7i	0.487694	−	0.0859936i
$718$		0			0
$719$	−3.28341e8	−	1.19506e8i	−0.883362	−	0.321518i	−0.139796	−	0.990180i	$-0.544645\pi$
$719$	−3.28341e8	−	1.19506e8i	−0.883362	−	0.321518i	−0.743566	+	0.668663i	$0.766867\pi$
$720$		0			0
$721$		−	3.46035e8i		−	0.923238i
$722$		0			0
$723$	6.68881e8			1.76984
$724$		0			0
$725$	1.20853e8	−	3.32042e8i	0.317135	−	0.871321i
$726$		0			0
$727$	−2.28109e7	−	1.29367e8i	−0.0593661	−	0.336682i	0.940630	−	0.339433i	$-0.110235\pi$
$727$	−2.28109e7	−	1.29367e8i	−0.0593661	−	0.336682i	−0.999996	+	0.00275141i	$0.999124\pi$
$728$		0			0
$729$	5.58947e8	−	9.68125e8i	1.44274	−	2.49890i
$730$		0			0
$731$	2.49336e8	+	2.09218e8i	0.638313	+	0.535608i
$732$		0			0
$733$	−2.87149e8	−	4.97357e8i	−0.729114	−	1.26286i	−0.957258	−	0.289236i	$-0.906599\pi$
$733$	−2.87149e8	−	4.97357e8i	−0.729114	−	1.26286i	0.228144	−	0.973628i	$-0.426734\pi$
$734$		0			0
$735$	−2.67226e7	−	7.34199e7i	−0.0673004	−	0.184906i
$736$		0			0
$737$	−2.55025e8	−	4.49678e7i	−0.637060	−	0.112331i
$738$		0			0
$739$	−7.65457e7	+	6.42295e7i	−0.189665	+	0.159148i	−0.732676	−	0.680578i	$-0.761729\pi$
$739$	−7.65457e7	+	6.42295e7i	−0.189665	+	0.159148i	0.543011	+	0.839726i	$0.317284\pi$
$740$		0			0
$741$	1.07350e9	−	3.17374e8i	2.63845	−	0.780041i
$742$		0			0
$743$	4.78895e6	+	5.70725e6i	0.0116755	+	0.0139143i	0.771851	−	0.635804i	$-0.219331\pi$
$743$	4.78895e6	+	5.70725e6i	0.0116755	+	0.0139143i	−0.760175	+	0.649718i	$0.774887\pi$
$744$		0			0
$745$	−4.93244e7	+	2.79732e8i	−0.119287	+	0.676510i
$746$		0			0
$747$	−5.59369e8	+	2.03594e8i	−1.34195	+	0.488430i
$748$		0			0
$749$	−3.70592e8	+	2.13962e8i	−0.881965	+	0.509202i
$750$		0			0
$751$	3.46321e8	−	4.12729e8i	0.817634	−	0.974418i	−0.182327	−	0.983238i	$-0.558363\pi$
$751$	3.46321e8	−	4.12729e8i	0.817634	−	0.974418i	0.999961	+	0.00881953i	$0.00280738\pi$
$752$		0			0
$753$	7.57527e8	+	4.37359e8i	1.77424	+	1.02436i
$754$		0			0
$755$	1.77778e8	−	3.13470e7i	0.413082	−	0.0728375i
$756$		0			0
$757$	−2.33118e8	−	8.48479e7i	−0.537387	−	0.195593i	0.0590466	−	0.998255i	$-0.481194\pi$
$757$	−2.33118e8	−	8.48479e7i	−0.537387	−	0.195593i	−0.596434	+	0.802662i	$0.703416\pi$
$758$		0			0
$759$		−	5.76396e7i		−	0.131824i
$760$		0			0
$761$	−6.92686e7			−0.157175			−0.0785873	−	0.996907i	$-0.525041\pi$
$761$	−6.92686e7			−0.157175			−0.0785873	+	0.996907i	$0.525041\pi$
$762$		0			0
$763$	1.37427e8	−	3.77577e8i	0.309384	−	0.850025i
$764$		0			0
$765$	2.06007e8	+	1.16832e9i	0.460148	+	2.60963i
$766$		0			0
$767$	−3.11487e7	+	5.39511e7i	−0.0690325	+	0.119568i
$768$		0			0
$769$	−4.30828e8	−	3.61508e8i	−0.947382	−	0.794948i	0.0314728	−	0.999505i	$-0.489980\pi$
$769$	−4.30828e8	−	3.61508e8i	−0.947382	−	0.794948i	−0.978855	+	0.204557i	$0.934425\pi$
$770$		0			0
$771$	−3.67171e7	−	6.35960e7i	−0.0801135	−	0.138761i
$772$		0			0
$773$	−1.09093e8	−	2.99729e8i	−0.236187	−	0.648920i	−0.999994	−	0.00347431i	$-0.998894\pi$
$773$	−1.09093e8	−	2.99729e8i	−0.236187	−	0.648920i	0.763807	−	0.645445i	$-0.223328\pi$
$774$		0			0
$775$	1.28227e8	+	2.26099e7i	0.275470	+	0.0485728i
$776$		0			0
$777$	−5.27906e8	+	4.42966e8i	−1.12537	+	0.944294i
$778$		0			0
$779$	−2.31840e7	+	3.75823e8i	−0.0490428	+	0.795008i
$780$		0			0
$781$	3.61141e8	+	4.30391e8i	0.758095	+	0.903462i
$782$		0			0
$783$	−3.47160e8	+	1.96884e9i	−0.723177	+	4.10134i
$784$		0			0
$785$	3.05350e7	−	1.11138e7i	0.0631231	−	0.0229749i
$786$		0			0
$787$	−2.71646e8	+	1.56835e8i	−0.557287	+	0.321750i	−0.752056	−	0.659099i	$-0.770938\pi$
$787$	−2.71646e8	+	1.56835e8i	−0.557287	+	0.321750i	0.194769	+	0.980849i	$0.437604\pi$
$788$		0			0
$789$	−1.09201e8	+	1.30140e8i	−0.222328	+	0.264960i
$790$		0			0
$791$	2.25107e8	+	1.29966e8i	0.454842	+	0.262603i
$792$		0			0
$793$	−6.75786e8	+	1.19159e8i	−1.35516	+	0.238951i
$794$		0			0
$795$	3.89103e8	+	1.41622e8i	0.774397	+	0.281857i
$796$		0			0
$797$		−	5.50596e8i		−	1.08757i	−0.839224	−	0.543786i	$-0.816990\pi$
$797$		−	5.50596e8i		−	1.08757i	0.839224	−	0.543786i	$-0.183010\pi$
$798$		0			0
$799$	1.23310e9			2.41746
$800$		0			0
$801$	3.02502e8	−	8.31117e8i	0.588614	−	1.61720i
$802$		0			0
$803$	7.59500e7	+	4.30734e8i	0.146683	+	0.831883i
$804$		0			0
$805$	1.54613e7	−	2.67798e7i	0.0296387	−	0.0513357i
$806$		0			0
$807$	−5.77634e8	−	4.84693e8i	−1.09909	−	0.922244i
$808$		0			0
$809$	−3.72042e8	−	6.44395e8i	−0.702662	−	1.21705i	−0.967529	−	0.252761i	$-0.918661\pi$
$809$	−3.72042e8	−	6.44395e8i	−0.702662	−	1.21705i	0.264867	−	0.964285i	$-0.414672\pi$
$810$		0			0
$811$	3.07944e8	+	8.46069e8i	0.577310	+	1.58615i	0.792695	+	0.609618i	$0.208677\pi$
$811$	3.07944e8	+	8.46069e8i	0.577310	+	1.58615i	−0.215385	+	0.976529i	$0.569101\pi$
$812$		0			0
$813$	6.00260e8	+	1.05842e8i	1.11704	+	0.196964i
$814$		0			0
$815$	−2.50143e8	+	2.09895e8i	−0.462078	+	0.387730i
$816$		0			0
$817$	1.10767e8	+	2.22456e8i	0.203116	+	0.407923i
$818$		0			0
$819$	−1.46786e9	−	1.74933e9i	−2.67198	−	3.18435i
$820$		0			0
$821$	6.72755e7	−	3.81538e8i	0.121570	−	0.689459i	−0.861716	−	0.507391i	$-0.830610\pi$
$821$	6.72755e7	−	3.81538e8i	0.121570	−	0.689459i	0.983286	−	0.182068i	$-0.0582790\pi$
$822$		0			0
$823$	4.49712e8	−	1.63682e8i	0.806743	−	0.293630i	0.0944652	−	0.995528i	$-0.469886\pi$
$823$	4.49712e8	−	1.63682e8i	0.806743	−	0.293630i	0.712278	+	0.701898i	$0.247664\pi$
$824$		0			0
$825$	−4.51936e8	+	2.60926e8i	−0.804851	+	0.464681i
$826$		0			0
$827$	1.27485e7	−	1.51930e7i	0.0225393	−	0.0268613i	−0.754657	−	0.656119i	$-0.772197\pi$
$827$	1.27485e7	−	1.51930e7i	0.0225393	−	0.0268613i	0.777196	+	0.629258i	$0.216641\pi$
$828$		0			0
$829$	−5.78222e7	−	3.33837e7i	−0.101492	−	0.0585963i	0.448395	−	0.893836i	$-0.351996\pi$
$829$	−5.78222e7	−	3.33837e7i	−0.101492	−	0.0585963i	−0.549887	+	0.835239i	$0.685329\pi$
$830$		0			0
$831$	−1.04199e9	+	1.83731e8i	−1.81577	+	0.320169i
$832$		0			0
$833$	1.86917e8	+	6.80323e7i	0.323381	+	0.117701i
$834$		0			0
$835$		−	3.52911e7i		−	0.0606186i
$836$		0			0
$837$	−7.36684e8			−1.25633
$838$		0			0
$839$	−1.02866e8	+	2.82622e8i	−0.174175	+	0.478543i	−0.995807	−	0.0914756i	$-0.970842\pi$
$839$	−1.02866e8	+	2.82622e8i	−0.174175	+	0.478543i	0.821632	+	0.570018i	$0.193064\pi$
$840$		0			0
$841$	−7.78185e7	−	4.41331e8i	−0.130826	−	0.741953i
$842$		0			0
$843$	−1.52893e8	+	2.64818e8i	−0.255214	+	0.442044i
$844$		0			0
$845$	−2.72203e8	−	2.28405e8i	−0.451151	−	0.378561i
$846$		0			0
$847$	1.71223e8	+	2.96568e8i	0.281782	+	0.488060i
$848$		0			0
$849$	5.32801e8	+	1.46386e9i	0.870646	+	2.39208i
$850$		0			0
$851$	−4.25437e7	−	7.50161e6i	−0.0690314	−	0.0121721i
$852$		0			0
$853$	−6.24011e8	+	5.23608e8i	−1.00542	+	0.843643i	−0.987725	−	0.156200i	$-0.950076\pi$
$853$	−6.24011e8	+	5.23608e8i	−1.00542	+	0.843643i	−0.0176896	+	0.999844i	$0.505631\pi$
$854$		0			0
$855$	−2.11910e8	+	8.80635e8i	−0.339041	+	1.40896i
$856$		0			0
$857$	3.23699e8	+	3.85770e8i	0.514280	+	0.612895i	0.959218	−	0.282666i	$-0.0912189\pi$
$857$	3.23699e8	+	3.85770e8i	0.514280	+	0.612895i	−0.444938	+	0.895561i	$0.646774\pi$
$858$		0			0
$859$	−4.02285e7	+	2.28147e8i	−0.0634680	+	0.359945i	0.936489	+	0.350696i	$0.114055\pi$
$859$	−4.02285e7	+	2.28147e8i	−0.0634680	+	0.359945i	−0.999957	+	0.00924849i	$0.997056\pi$
$860$		0			0
$861$	9.94487e8	−	3.61964e8i	1.55808	−	0.567095i
$862$		0			0
$863$	7.47697e8	−	4.31683e8i	1.16330	−	0.671634i	0.211210	−	0.977441i	$-0.432260\pi$
$863$	7.47697e8	−	4.31683e8i	1.16330	−	0.671634i	0.952094	+	0.305807i	$0.0989262\pi$
$864$		0			0
$865$	−2.62072e8	+	3.12325e8i	−0.404922	+	0.482568i
$866$		0			0
$867$	−2.52599e9	−	1.45838e9i	−3.87592	−	2.23776i
$868$		0			0
$869$	−4.64162e8	+	8.18443e7i	−0.707310	+	0.124718i
$870$		0			0
$871$	−8.32685e8	−	3.03073e8i	−1.26016	−	0.458661i
$872$		0			0
$873$			7.26990e8i			1.09266i
$874$		0			0
$875$	−6.79770e8			−1.01470
$876$		0			0
$877$	7.94370e7	−	2.18251e8i	0.117767	−	0.323562i	−0.866778	−	0.498694i	$-0.833813\pi$
$877$	7.94370e7	−	2.18251e8i	0.117767	−	0.323562i	0.984545	+	0.175132i	$0.0560352\pi$
$878$		0			0
$879$	−3.74784e8	−	2.12551e9i	−0.551842	−	3.12965i
$880$		0			0
$881$	5.20919e8	−	9.02258e8i	0.761802	−	1.31948i	−0.180119	−	0.983645i	$-0.557648\pi$
$881$	5.20919e8	−	9.02258e8i	0.761802	−	1.31948i	0.941921	−	0.335835i	$-0.109018\pi$
$882$		0			0
$883$	4.34122e6	+	3.64272e6i	0.00630565	+	0.00529107i	0.645935	−	0.763392i	$-0.276468\pi$
$883$	4.34122e6	+	3.64272e6i	0.00630565	+	0.00529107i	−0.639629	+	0.768683i	$0.720912\pi$
$884$		0			0
$885$	−3.47253e7	−	6.01460e7i	−0.0500975	−	0.0867714i
$886$		0			0
$887$	−2.16930e7	−	5.96010e7i	−0.0310848	−	0.0854049i	0.923179	−	0.384369i	$-0.125581\pi$
$887$	−2.16930e7	−	5.96010e7i	−0.0310848	−	0.0854049i	−0.954264	+	0.298964i	$0.903359\pi$
$888$		0			0
$889$	3.38390e7	+	5.96673e6i	0.0481629	+	0.00849241i
$890$		0			0
$891$	1.26502e9	−	1.06148e9i	1.78840	−	1.50065i
$892$		0			0
$893$	8.63188e8	+	3.75863e8i	1.21214	+	0.527806i
$894$		0			0
$895$	−2.11428e8	−	2.51970e8i	−0.294913	−	0.351464i
$896$		0			0
$897$	3.42496e7	−	1.94239e8i	0.0474546	−	0.269128i
$898$		0			0
$899$	3.61140e8	−	1.31444e8i	0.497046	−	0.180910i
$900$		0			0
$901$	−9.12947e8	+	5.27090e8i	−1.24816	+	0.720627i
$902$		0			0
$903$	4.48965e8	−	5.35055e8i	0.609746	−	0.726667i
$904$		0			0
$905$	4.34097e8	+	2.50626e8i	0.585654	+	0.338128i
$906$		0			0
$907$	−2.22126e8	+	3.91668e7i	−0.297699	+	0.0524924i	−0.320503	−	0.947248i	$-0.603852\pi$
$907$	−2.22126e8	+	3.91668e7i	−0.297699	+	0.0524924i	0.0228036	+	0.999740i	$0.492741\pi$
$908$		0			0
$909$	−1.63972e8	−	5.96809e7i	−0.218312	−	0.0794592i
$910$		0			0
$911$			1.12572e9i			1.48894i	0.667659	+	0.744468i	$0.267297\pi$
$911$			1.12572e9i			1.48894i	−0.667659	+	0.744468i	$0.732703\pi$
$912$		0			0
$913$	−2.85360e8			−0.374956
$914$		0			0
$915$	2.61647e8	−	7.18868e8i	0.341548	−	0.938396i
$916$		0			0
$917$	9.90176e7	+	5.61557e8i	0.128412	+	0.728258i
$918$		0			0
$919$	−1.48089e8	+	2.56497e8i	−0.190799	+	0.330473i	−0.945515	−	0.325578i	$-0.894441\pi$
$919$	−1.48089e8	+	2.56497e8i	−0.190799	+	0.330473i	0.754716	+	0.656051i	$0.227774\pi$
$920$		0			0
$921$	4.12603e8	+	3.46215e8i	0.528145	+	0.443166i
$922$		0			0
$923$	9.61265e8	+	1.66496e9i	1.22247	+	2.11738i
$924$		0			0
$925$	1.33771e8	+	3.67532e8i	0.169019	+	0.464376i
$926$		0			0
$927$	1.75873e9	+	3.10112e8i	2.20780	+	0.389295i
$928$		0			0
$929$	3.65352e6	−	3.06566e6i	0.00455684	−	0.00382364i	−0.640506	−	0.767953i	$-0.721275\pi$
$929$	3.65352e6	−	3.06566e6i	0.00455684	−	0.00382364i	0.645063	+	0.764129i	$0.276831\pi$
$930$		0			0
$931$	1.10108e8	+	1.04598e8i	0.136448	+	0.129621i
$932$		0			0
$933$	−1.41114e8	−	1.68173e8i	−0.173750	−	0.207068i
$934$		0			0
$935$	−9.87555e7	+	5.60071e8i	−0.120817	+	0.685185i
$936$		0			0
$937$	−1.35719e8	+	4.93977e7i	−0.164976	+	0.0600465i	−0.423188	−	0.906042i	$-0.639089\pi$
$937$	−1.35719e8	+	4.93977e7i	−0.164976	+	0.0600465i	0.258212	+	0.966088i	$0.416867\pi$
$938$		0			0
$939$	7.48759e8	−	4.32296e8i	0.904369	−	0.522137i
$940$		0			0
$941$	3.03360e8	−	3.61530e8i	0.364073	−	0.433886i	−0.552647	−	0.833416i	$-0.686382\pi$
$941$	3.03360e8	−	3.61530e8i	0.364073	−	0.433886i	0.916720	+	0.399530i	$0.130827\pi$
$942$		0			0
$943$	5.74547e7	+	3.31715e7i	0.0685157	+	0.0395576i
$944$		0			0
$945$	1.55994e9	−	2.75059e8i	1.84846	−	0.325934i
$946$		0			0
$947$	7.44414e8	+	2.70945e8i	0.876526	+	0.319029i	0.740807	−	0.671718i	$-0.234443\pi$
$947$	7.44414e8	+	2.70945e8i	0.876526	+	0.319029i	0.135719	+	0.990747i	$0.456666\pi$
$948$		0			0
$949$			1.49665e9i			1.75115i
$950$		0			0
$951$	1.62944e9			1.89451
$952$		0			0
$953$	−3.38447e8	+	9.29874e8i	−0.391031	+	1.07435i	0.575500	+	0.817801i	$0.304807\pi$
$953$	−3.38447e8	+	9.29874e8i	−0.391031	+	1.07435i	−0.966532	+	0.256548i	$0.917415\pi$
$954$		0			0
$955$	9.97305e7	+	5.65600e8i	0.114503	+	0.649380i
$956$		0			0
$957$	−7.70156e8	+	1.33395e9i	−0.878704	+	1.52196i
$958$		0			0
$959$	9.04328e8	+	7.58821e8i	1.02535	+	0.860367i
$960$		0			0
$961$	−3.72944e8	−	6.45958e8i	−0.420217	−	0.727837i
$962$		0			0
$963$	−7.55346e8	−	2.07530e9i	−0.845799	−	2.32381i
$964$		0			0
$965$	−8.76249e8	−	1.54506e8i	−0.975092	−	0.171935i
$966$		0			0
$967$	2.73764e8	−	2.29715e8i	0.302759	−	0.254045i	−0.478733	−	0.877961i	$-0.658904\pi$
$967$	2.73764e8	−	2.29715e8i	0.302759	−	0.254045i	0.781491	+	0.623916i	$0.214459\pi$
$968$		0			0
$969$	−1.88851e9	−	2.55498e9i	−2.07563	−	2.80812i
$970$		0			0
$971$	6.98073e8	+	8.31931e8i	0.762506	+	0.908719i	0.998004	−	0.0631555i	$-0.0201164\pi$
$971$	6.98073e8	+	8.31931e8i	0.762506	+	0.908719i	−0.235498	+	0.971875i	$0.575672\pi$
$972$		0			0
$973$	3.09522e8	−	1.75539e9i	0.336011	−	1.90561i
$974$		0			0
$975$	−1.67802e9	+	6.10748e8i	−1.81043	+	0.658943i
$976$		0			0
$977$	−9.99279e8	+	5.76934e8i	−1.07153	+	0.618647i	−0.928598	−	0.371086i	$-0.878985\pi$
$977$	−9.99279e8	+	5.76934e8i	−1.07153	+	0.618647i	−0.142929	+	0.989733i	$0.545652\pi$
$978$		0			0
$979$	2.72536e8	−	3.24796e8i	0.290453	−	0.346148i
$980$		0			0
$981$	1.79589e9	+	1.03685e9i	1.90227	+	1.09827i
$982$		0			0
$983$	1.84567e9	−	3.25441e8i	1.94309	−	0.342619i	0.943140	−	0.332395i	$-0.107857\pi$
$983$	1.84567e9	−	3.25441e8i	1.94309	−	0.342619i	0.999948	−	0.0102233i	$-0.00325424\pi$
$984$		0			0
$985$	4.52934e8	+	1.64854e8i	0.473943	+	0.172501i
$986$		0			0
$987$		−	2.64613e9i		−	2.75207i
$988$		0			0
$989$	4.37850e7			0.0452623
$990$		0			0
$991$	4.93201e8	−	1.35506e9i	0.506760	−	1.39231i	−0.377800	−	0.925887i	$-0.623319\pi$
$991$	4.93201e8	−	1.35506e9i	0.506760	−	1.39231i	0.884560	−	0.466425i	$-0.154458\pi$
$992$		0			0
$993$	2.05711e8	+	1.16664e9i	0.210092	+	1.19149i
$994$		0			0
$995$	5.03242e8	−	8.71640e8i	0.510866	−	0.884846i
$996$		0			0
$997$	2.39912e8	+	2.01310e8i	0.242084	+	0.203133i	0.755755	−	0.654855i	$-0.227270\pi$
$997$	2.39912e8	+	2.01310e8i	0.242084	+	0.203133i	−0.513671	+	0.857987i	$0.671715\pi$
$998$		0			0
$999$	−1.10645e9	−	1.91643e9i	−1.10978	−	1.92219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.13.10	✓	60
19.3	odd	18	inner	76.7.j.a.41.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.13.10	✓	60	1.1	even	1	trivial
76.7.j.a.41.10	yes	60	19.3	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(17.6351 - 48.4521i) q^{3} +(11.8840 + 67.3972i) q^{5} +(-186.943 + 323.795i) q^{7} +(-1478.16 - 1240.32i) q^{9} +O(q^{10})\)	\(q+(17.6351 - 48.4521i) q^{3} +(11.8840 + 67.3972i) q^{5} +(-186.943 + 323.795i) q^{7} +(-1478.16 - 1240.32i) q^{9} +(-462.506 - 801.084i) q^{11} +(-1082.59 - 2974.39i) q^{13} +(3475.11 + 612.756i) q^{15} +(-6881.88 + 5774.58i) q^{17} +(-6577.56 + 1944.62i) q^{19} +(12391.8 + 14767.9i) q^{21} +(-209.854 + 1190.14i) q^{23} +(10281.5 - 3742.17i) q^{25} +(-53611.3 + 30952.5i) q^{27} +(20758.8 - 24739.4i) q^{29} +(10305.9 + 5950.12i) q^{31} +(-46970.6 + 8282.18i) q^{33} +(-24044.5 - 8751.48i) q^{35} +35746.8i q^{37} -163207. q^{39} +(18775.8 - 51586.2i) q^{41} +(-6291.43 - 35680.4i) q^{43} +(66028.0 - 114364. i) q^{45} +(-105148. - 88229.4i) q^{47} +(-11070.8 - 19175.3i) q^{49} +(158428. + 435277. i) q^{51} +(115562. + 20376.6i) q^{53} +(48494.5 - 40691.7i) q^{55} +(-21775.4 + 352990. i) q^{57} +(-12651.0 - 15076.9i) q^{59} +(37645.8 - 213500. i) q^{61} +(677942. - 246751. i) q^{63} +(187600. - 108311. i) q^{65} +(179950. - 214456. i) q^{67} +(53964.0 + 31156.1i) q^{69} +(-598154. + 105471. i) q^{71} +(-444320. - 161719. i) q^{73} -564156. i q^{75} +345849. q^{77} +(174270. - 478802. i) q^{79} +(310004. + 1.75812e6i) q^{81} +(154246. - 267163. i) q^{83} +(-470975. - 395195. i) q^{85} +(-832590. - 1.44209e6i) q^{87} +(156769. + 430720. i) q^{89} +(1.16547e6 + 205504. i) q^{91} +(470042. - 394412. i) q^{93} +(-209229. - 420200. i) q^{95} +(-242174. - 288612. i) q^{97} +(-309946. + 1.75779e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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