LMFDB - Embedded newform 76.7.j.a.21.10

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			21.10
Character	$\chi$	$=$	76.21
Dual form			76.7.j.a.29.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(31.0369 - 36.9883i) q^{3} +(186.326 - 67.8172i) q^{5} +(-265.452 - 459.776i) q^{7} +(-278.258 - 1578.08i) q^{9} +O(q^{10})$	\(q+(31.0369 - 36.9883i) q^{3} +(186.326 - 67.8172i) q^{5} +(-265.452 - 459.776i) q^{7} +(-278.258 - 1578.08i) q^{9} +(-237.096 + 410.663i) q^{11} +(2245.11 + 2675.62i) q^{13} +(3274.54 - 8996.73i) q^{15} +(-739.194 + 4192.18i) q^{17} +(-3811.41 + 5702.55i) q^{19} +(-25245.1 - 4451.40i) q^{21} +(2107.51 + 767.071i) q^{23} +(18148.9 - 15228.7i) q^{25} +(-36522.9 - 21086.5i) q^{27} +(39685.9 - 6997.70i) q^{29} +(-31084.1 + 17946.4i) q^{31} +(7830.99 + 21515.5i) q^{33} +(-80641.4 - 67666.2i) q^{35} -23866.1i q^{37} +168648. q^{39} +(75867.2 - 90415.1i) q^{41} +(-94923.9 + 34549.5i) q^{43} +(-158868. - 275167. i) q^{45} +(-3404.64 - 19308.7i) q^{47} +(-82105.0 + 142210. i) q^{49} +(132119. + 157454. i) q^{51} +(22603.7 - 62103.3i) q^{53} +(-16327.3 + 92596.5i) q^{55} +(92633.5 + 317967. i) q^{57} +(40475.3 + 7136.89i) q^{59} +(29450.2 + 10719.0i) q^{61} +(-651699. + 546840. i) q^{63} +(599776. + 346281. i) q^{65} +(97615.5 - 17212.3i) q^{67} +(93783.2 - 54145.8i) q^{69} +(36325.4 + 99803.3i) q^{71} +(41222.1 + 34589.5i) q^{73} -1.14395e6i q^{75} +251751. q^{77} +(140910. - 167930. i) q^{79} +(-815794. + 296925. i) q^{81} +(291613. + 505088. i) q^{83} +(146571. + 831243. i) q^{85} +(972894. - 1.68510e6i) q^{87} +(-188347. - 224464. i) q^{89} +(634217. - 1.74250e6i) q^{91} +(-300946. + 1.70675e6i) q^{93} +(-323434. + 1.32101e6i) q^{95} +(813524. + 143446. i) q^{97} +(714032. + 259886. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

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

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
$3$	31.0369	−	36.9883i	1.14951	−	1.36994i	0.231767	−	0.972771i	$-0.425549\pi$
$3$	31.0369	−	36.9883i	1.14951	−	1.36994i	0.917747	−	0.397166i	$-0.130006\pi$
$4$		0			0
$5$	186.326	−	67.8172i	1.49061	−	0.542538i	0.537000	−	0.843582i	$-0.319557\pi$
$5$	186.326	−	67.8172i	1.49061	−	0.542538i	0.953610	+	0.301044i	$0.0973352\pi$
$6$		0			0
$7$	−265.452	−	459.776i	−0.773913	−	1.34046i	−0.935404	−	0.353582i	$-0.884964\pi$
$7$	−265.452	−	459.776i	−0.773913	−	1.34046i	0.161491	−	0.986874i	$-0.448370\pi$
$8$		0			0
$9$	−278.258	−	1578.08i	−0.381698	−	2.16472i
$10$		0			0
$11$	−237.096	+	410.663i	−0.178134	+	0.308537i	−0.941241	−	0.337735i	$-0.890339\pi$
$11$	−237.096	+	410.663i	−0.178134	+	0.308537i	0.763107	+	0.646272i	$0.223673\pi$
$12$		0			0
$13$	2245.11	+	2675.62i	1.02190	+	1.21785i	0.975744	+	0.218916i	$0.0702519\pi$
$13$	2245.11	+	2675.62i	1.02190	+	1.21785i	0.0461536	+	0.998934i	$0.485304\pi$
$14$		0			0
$15$	3274.54	−	8996.73i	0.970234	−	2.66570i
$16$		0			0
$17$	−739.194	+	4192.18i	−0.150457	+	0.853283i	0.812366	+	0.583148i	$0.198179\pi$
$17$	−739.194	+	4192.18i	−0.150457	+	0.853283i	−0.962823	+	0.270135i	$0.912932\pi$
$18$		0			0
$19$	−3811.41	+	5702.55i	−0.555679	+	0.831397i
$19$	−3811.41	+	5702.55i	−0.555679	+	0.831397i
$20$		0			0
$21$	−25245.1	−	4451.40i	−2.72596	−	0.480661i
$22$		0			0
$23$	2107.51	+	767.071i	0.173215	+	0.0630452i	0.427172	−	0.904170i	$-0.359510\pi$
$23$	2107.51	+	767.071i	0.173215	+	0.0630452i	−0.253957	+	0.967216i	$0.581732\pi$
$24$		0			0
$25$	18148.9	−	15228.7i	1.16153	−	0.974637i
$26$		0			0
$27$	−36522.9	−	21086.5i	−1.85556	−	1.07131i
$28$		0			0
$29$	39685.9	−	6997.70i	1.62721	−	0.286920i	0.715761	−	0.698345i	$-0.246080\pi$
$29$	39685.9	−	6997.70i	1.62721	−	0.286920i	0.911444	+	0.411425i	$0.134969\pi$
$30$		0			0
$31$	−31084.1	+	17946.4i	−1.04341	+	0.602411i	−0.920796	−	0.390044i	$-0.872460\pi$
$31$	−31084.1	+	17946.4i	−1.04341	+	0.602411i	−0.122610	+	0.992455i	$0.539126\pi$
$32$		0			0
$33$	7830.99	+	21515.5i	0.217909	+	0.598700i
$34$		0			0
$35$	−80641.4	−	67666.2i	−1.88085	−	1.57822i
$36$		0			0
$37$		−	23866.1i		−	0.471169i	−0.971854	−	0.235584i	$-0.924300\pi$
$37$		−	23866.1i		−	0.471169i	0.971854	−	0.235584i	$-0.0757004\pi$
$38$		0			0
$39$	168648.			2.84306
$40$		0			0
$41$	75867.2	−	90415.1i	1.10079	−	1.31187i	0.154695	−	0.987962i	$-0.450560\pi$
$41$	75867.2	−	90415.1i	1.10079	−	1.31187i	0.946090	−	0.323903i	$-0.104995\pi$
$42$		0			0
$43$	−94923.9	+	34549.5i	−1.19391	+	0.434546i	−0.861094	−	0.508447i	$-0.830220\pi$
$43$	−94923.9	+	34549.5i	−1.19391	+	0.434546i	−0.332813	+	0.942993i	$0.607998\pi$
$44$		0			0
$45$	−158868.	−	275167.i	−1.74340	−	3.01966i
$46$		0			0
$47$	−3404.64	−	19308.7i	−0.0327927	−	0.185977i	0.964011	−	0.265861i	$-0.0856561\pi$
$47$	−3404.64	−	19308.7i	−0.0327927	−	0.185977i	−0.996804	+	0.0798840i	$0.974545\pi$
$48$		0			0
$49$	−82105.0	+	142210.i	−0.697881	+	1.20877i
$50$		0			0
$51$	132119.	+	157454.i	0.995992	+	1.18698i
$52$		0			0
$53$	22603.7	−	62103.3i	0.151828	−	0.417145i	−0.840339	−	0.542061i	$-0.817644\pi$
$53$	22603.7	−	62103.3i	0.151828	−	0.417145i	0.992167	+	0.124916i	$0.0398663\pi$
$54$		0			0
$55$	−16327.3	+	92596.5i	−0.0981353	+	0.556553i
$56$		0			0
$57$	92633.5	+	317967.i	0.500200	+	1.71695i
$58$		0			0
$59$	40475.3	+	7136.89i	0.197076	+	0.0347499i	0.271315	−	0.962491i	$-0.412542\pi$
$59$	40475.3	+	7136.89i	0.197076	+	0.0347499i	−0.0742386	+	0.997241i	$0.523653\pi$
$60$		0			0
$61$	29450.2	+	10719.0i	0.129747	+	0.0472242i	0.406078	−	0.913839i	$-0.366896\pi$
$61$	29450.2	+	10719.0i	0.129747	+	0.0472242i	−0.276330	+	0.961063i	$0.589118\pi$
$62$		0			0
$63$	−651699.	+	546840.i	−2.60631	+	2.18695i
$64$		0			0
$65$	599776.	+	346281.i	2.18398	+	1.26092i
$66$		0			0
$67$	97615.5	−	17212.3i	0.324560	−	0.0572286i	−0.00899454	−	0.999960i	$-0.502863\pi$
$67$	97615.5	−	17212.3i	0.324560	−	0.0572286i	0.333554	+	0.942731i	$0.391752\pi$
$68$		0			0
$69$	93783.2	−	54145.8i	0.285481	−	0.164823i
$70$		0			0
$71$	36325.4	+	99803.3i	0.101493	+	0.278849i	0.980038	−	0.198810i	$-0.0637076\pi$
$71$	36325.4	+	99803.3i	0.101493	+	0.278849i	−0.878545	+	0.477659i	$0.841485\pi$
$72$		0			0
$73$	41222.1	+	34589.5i	0.105965	+	0.0889151i	0.694231	−	0.719752i	$-0.255745\pi$
$73$	41222.1	+	34589.5i	0.105965	+	0.0889151i	−0.588266	+	0.808668i	$0.700189\pi$
$74$		0			0
$75$		−	1.14395e6i		−	2.71158i
$76$		0			0
$77$	251751.			0.551440
$78$		0			0
$79$	140910.	−	167930.i	0.285799	−	0.340602i	−0.603975	−	0.797003i	$-0.706417\pi$
$79$	140910.	−	167930.i	0.285799	−	0.340602i	0.889774	+	0.456401i	$0.150862\pi$
$80$		0			0
$81$	−815794.	+	296925.i	−1.53506	+	0.558716i
$82$		0			0
$83$	291613.	+	505088.i	0.510002	+	0.883350i	0.999933	+	0.0115882i	$0.00368871\pi$
$83$	291613.	+	505088.i	0.510002	+	0.883350i	−0.489931	+	0.871761i	$0.662978\pi$
$84$		0			0
$85$	146571.	+	831243.i	0.238666	+	1.35354i
$86$		0			0
$87$	972894.	−	1.68510e6i	1.47743	−	2.55899i
$88$		0			0
$89$	−188347.	−	224464.i	−0.267171	−	0.318402i	0.615734	−	0.787954i	$-0.288860\pi$
$89$	−188347.	−	224464.i	−0.267171	−	0.318402i	−0.882905	+	0.469552i	$0.844415\pi$
$90$		0			0
$91$	634217.	−	1.74250e6i	0.841615	−	2.31232i
$92$		0			0
$93$	−300946.	+	1.70675e6i	−0.374145	+	2.12188i
$94$		0			0
$95$	−323434.	+	1.32101e6i	−0.377238	+	1.54077i
$96$		0			0
$97$	813524.	+	143446.i	0.891364	+	0.157172i	0.600530	−	0.799602i	$-0.294956\pi$
$97$	813524.	+	143446.i	0.891364	+	0.157172i	0.290834	+	0.956774i	$0.406067\pi$
$98$		0			0
$99$	714032.	+	259886.i	0.735888	+	0.267841i
$100$		0			0
$101$	−905353.	+	759681.i	−0.878726	+	0.737339i	−0.965917	−	0.258853i	$-0.916656\pi$
$101$	−905353.	+	759681.i	−0.878726	+	0.737339i	0.0871905	+	0.996192i	$0.472211\pi$
$102$		0			0
$103$	−444508.	−	256637.i	−0.406788	−	0.234859i	0.282621	−	0.959232i	$-0.408796\pi$
$103$	−444508.	−	256637.i	−0.406788	−	0.234859i	−0.689409	+	0.724373i	$0.742130\pi$
$104$		0			0
$105$	−5.00572e6	+	882643.i	−4.32413	+	0.762460i
$106$		0			0
$107$	−398704.	+	230192.i	−0.325461	+	0.187905i	−0.653824	−	0.756646i	$-0.726836\pi$
$107$	−398704.	+	230192.i	−0.325461	+	0.187905i	0.328363	+	0.944552i	$0.393503\pi$
$108$		0			0
$109$	31614.3	+	86859.5i	0.0244120	+	0.0670715i	0.951300	−	0.308267i	$-0.0997489\pi$
$109$	31614.3	+	86859.5i	0.0244120	+	0.0670715i	−0.926888	+	0.375338i	$0.877527\pi$
$110$		0			0
$111$	−882767.	−	740730.i	−0.645472	−	0.541615i
$112$		0			0
$113$		−	286742.i		−	0.198727i	−0.995051	−	0.0993634i	$-0.968319\pi$
$113$		−	286742.i		−	0.198727i	0.995051	−	0.0993634i	$-0.0316806\pi$
$114$		0			0
$115$	444705.			0.292401
$116$		0			0
$117$	3.59761e6	−	4.28747e6i	2.24624	−	2.67697i
$118$		0			0
$119$	2.12368e6	−	772958.i	1.26023	−	0.458686i
$120$		0			0
$121$	773351.	+	1.33948e6i	0.436537	+	0.756104i
$122$		0			0
$123$	−989618.	−	5.61240e6i	−0.531805	−	3.01601i
$124$		0			0
$125$	799746.	−	1.38520e6i	0.409470	−	0.709223i
$126$		0			0
$127$	−109195.	−	130133.i	−0.0533079	−	0.0635299i	0.738732	−	0.674000i	$-0.235425\pi$
$127$	−109195.	−	130133.i	−0.0533079	−	0.0635299i	−0.792040	+	0.610470i	$0.790981\pi$
$128$		0			0
$129$	−1.66821e6	+	4.58338e6i	−0.777111	+	2.13509i
$130$		0			0
$131$	271293.	−	1.53858e6i	0.120677	−	0.684394i	−0.863105	−	0.505025i	$-0.831483\pi$
$131$	271293.	−	1.53858e6i	0.120677	−	0.684394i	0.983782	−	0.179369i	$-0.0574056\pi$
$132$		0			0
$133$	3.63364e6	+	238641.i	1.54450	+	0.101436i
$134$		0			0
$135$	−8.23521e6	−	1.45209e6i	−3.34713	−	0.590190i
$136$		0			0
$137$	−3.51137e6	−	1.27804e6i	−1.36557	−	0.497028i	−0.447801	−	0.894133i	$-0.647793\pi$
$137$	−3.51137e6	−	1.27804e6i	−1.36557	−	0.497028i	−0.917773	+	0.397105i	$0.870015\pi$
$138$		0			0
$139$	1.29052e6	−	1.08288e6i	0.480531	−	0.403213i	−0.370088	−	0.928997i	$-0.620672\pi$
$139$	1.29052e6	−	1.08288e6i	0.480531	−	0.403213i	0.850618	+	0.525784i	$0.176228\pi$
$140$		0			0
$141$	−819864.	−	473349.i	−0.292472	−	0.168859i
$142$		0			0
$143$	−1.63108e6	+	287604.i	−0.557786	+	0.0983528i
$144$		0			0
$145$	6.91996e6	−	3.99524e6i	2.26986	−	1.31051i
$146$		0			0
$147$	2.71183e6	+	7.45068e6i	0.853709	+	2.34555i
$148$		0			0
$149$	795287.	+	667325.i	0.240417	+	0.201734i	0.755033	−	0.655687i	$-0.227621\pi$
$149$	795287.	+	667325.i	0.240417	+	0.201734i	−0.514616	+	0.857421i	$0.672065\pi$
$150$		0			0
$151$			4.58812e6i			1.33261i	0.745679	+	0.666306i	$0.232125\pi$
$151$			4.58812e6i			1.33261i	−0.745679	+	0.666306i	$0.767875\pi$
$152$		0			0
$153$	6.82127e6			1.90454
$154$		0			0
$155$	−4.57471e6	+	5.45193e6i	−1.22848	+	1.46405i
$156$		0			0
$157$	−3.52737e6	+	1.28386e6i	−0.911490	+	0.331755i	−0.754848	−	0.655900i	$-0.772289\pi$
$157$	−3.52737e6	+	1.28386e6i	−0.911490	+	0.331755i	−0.156642	+	0.987655i	$0.550067\pi$
$158$		0			0
$159$	−1.59555e6	−	2.76357e6i	−0.396934	−	0.687509i
$160$		0			0
$161$	−206762.	−	1.17260e6i	−0.0495442	−	0.280979i
$162$		0			0
$163$	3.19341e6	−	5.53115e6i	0.737381	−	1.27718i	−0.216290	−	0.976329i	$-0.569396\pi$
$163$	3.19341e6	−	5.53115e6i	0.737381	−	1.27718i	0.953671	−	0.300852i	$-0.0972709\pi$
$164$		0			0
$165$	2.91824e6	+	3.47782e6i	0.649635	+	0.774204i
$166$		0			0
$167$	−1.69166e6	+	4.64780e6i	−0.363215	+	0.997926i	0.614670	+	0.788784i	$0.289289\pi$
$167$	−1.69166e6	+	4.64780e6i	−0.363215	+	0.997926i	−0.977885	+	0.209141i	$0.932933\pi$
$168$		0			0
$169$	−1.28024e6	+	7.26062e6i	−0.265236	+	1.50423i
$170$		0			0
$171$	1.00596e7	+	4.42792e6i	2.01184	+	0.885546i
$172$		0			0
$173$	−6.25211e6	−	1.10242e6i	−1.20750	−	0.212915i	−0.466564	−	0.884488i	$-0.654508\pi$
$173$	−6.25211e6	−	1.10242e6i	−1.20750	−	0.212915i	−0.740939	+	0.671572i	$0.765619\pi$
$174$		0			0
$175$	−1.18195e7	−	4.30193e6i	−2.20538	−	0.802692i
$176$		0			0
$177$	1.52021e6	−	1.27561e6i	0.274147	−	0.230037i
$178$		0			0
$179$	6.97755e6	+	4.02849e6i	1.21659	+	0.702397i	0.964187	−	0.265225i	$-0.0854463\pi$
$179$	6.97755e6	+	4.02849e6i	1.21659	+	0.702397i	0.252402	+	0.967623i	$0.418780\pi$
$180$		0			0
$181$	−9.57062e6	+	1.68756e6i	−1.61400	+	0.284592i	−0.906528	−	0.422146i	$-0.861277\pi$
$181$	−9.57062e6	+	1.68756e6i	−1.61400	+	0.284592i	−0.707475	+	0.706738i	$0.750166\pi$
$182$		0			0
$183$	1.31052e6	−	756629.i	0.213841	−	0.123461i
$184$		0			0
$185$	−1.61853e6	−	4.44689e6i	−0.255627	−	0.702329i
$186$		0			0
$187$	−1.54631e6	−	1.29751e6i	−0.236468	−	0.198420i
$188$		0			0
$189$			2.23898e7i			3.31639i
$190$		0			0
$191$	185072.			0.0265607			0.0132804	−	0.999912i	$-0.495773\pi$
$191$	185072.			0.0265607			0.0132804	+	0.999912i	$0.495773\pi$
$192$		0			0
$193$	2.34188e6	−	2.79095e6i	0.325757	−	0.388222i	−0.578165	−	0.815920i	$-0.696231\pi$
$193$	2.34188e6	−	2.79095e6i	0.325757	−	0.388222i	0.903922	+	0.427698i	$0.140675\pi$
$194$		0			0
$195$	3.14235e7	−	1.14372e7i	4.23790	−	1.54247i
$196$		0			0
$197$	4.06557e6	+	7.04177e6i	0.531768	+	0.921049i	0.999312	+	0.0370796i	$0.0118055\pi$
$197$	4.06557e6	+	7.04177e6i	0.531768	+	0.921049i	−0.467544	+	0.883970i	$0.654861\pi$
$198$		0			0
$199$	1.61089e6	+	9.13583e6i	0.204413	+	1.15928i	0.898362	+	0.439257i	$0.144758\pi$
$199$	1.61089e6	+	9.13583e6i	0.204413	+	1.15928i	−0.693949	+	0.720024i	$0.744131\pi$
$200$		0			0
$201$	2.39303e6	−	4.14485e6i	0.294686	−	0.510411i
$202$		0			0
$203$	−1.37521e7	−	1.63891e7i	−1.64392	−	1.95915i
$204$		0			0
$205$	8.00436e6	−	2.19918e7i	0.929106	−	2.55270i
$206$		0			0
$207$	624067.	−	3.53926e6i	0.0703591	−	0.399026i
$208$		0			0
$209$	−1.43815e6	−	2.91726e6i	−0.157531	−	0.319548i
$210$		0			0
$211$	−1.19649e7	−	2.10974e6i	−1.27369	−	0.224586i	−0.504391	−	0.863475i	$-0.668283\pi$
$211$	−1.19649e7	−	2.10974e6i	−1.27369	−	0.224586i	−0.769298	+	0.638890i	$0.779394\pi$
$212$		0			0
$213$	4.81898e6	+	1.75397e6i	0.498674	+	0.181502i
$214$		0			0
$215$	−1.53438e7	+	1.28750e7i	−1.54389	+	1.29548i
$216$		0			0
$217$	1.65027e7	+	9.52783e6i	1.61501	+	0.932427i
$218$		0			0
$219$	2.55881e6	−	451188.i	0.243616	−	0.0429561i
$220$		0			0
$221$	−1.28762e7	+	7.43410e6i	−1.19292	+	0.688734i
$222$		0			0
$223$	−2.70768e6	−	7.43928e6i	−0.244164	−	0.670836i	−0.999873	−	0.0159280i	$-0.994930\pi$
$223$	−2.70768e6	−	7.43928e6i	−0.244164	−	0.670836i	0.755709	−	0.654908i	$-0.227292\pi$
$224$		0			0
$225$	−2.90821e7	−	2.44028e7i	−2.55317	−	2.14236i
$226$		0			0
$227$			9.31158e6i			0.796060i	0.917372	+	0.398030i	$0.130306\pi$
$227$			9.31158e6i			0.796060i	−0.917372	+	0.398030i	$0.869694\pi$
$228$		0			0
$229$	−1.75800e7			−1.46390			−0.731952	−	0.681356i	$-0.761391\pi$
$229$	−1.75800e7			−1.46390			−0.731952	+	0.681356i	$0.761391\pi$
$230$		0			0
$231$	7.81355e6	−	9.31183e6i	0.633888	−	0.755439i
$232$		0			0
$233$	7.84756e6	−	2.85628e6i	0.620393	−	0.225805i	−0.0126515	−	0.999920i	$-0.504027\pi$
$233$	7.84756e6	−	2.85628e6i	0.620393	−	0.225805i	0.633045	+	0.774115i	$0.281805\pi$
$234$		0			0
$235$	−1.94383e6	−	3.36682e6i	−0.149781	−	0.259428i
$236$		0			0
$237$	−1.83804e6	−	1.04240e7i	−0.138073	−	0.783053i
$238$		0			0
$239$	8.80782e6	−	1.52556e7i	0.645171	−	1.11747i	−0.339091	−	0.940754i	$-0.610119\pi$
$239$	8.80782e6	−	1.52556e7i	0.645171	−	1.11747i	0.984262	−	0.176715i	$-0.0565472\pi$
$240$		0			0
$241$	1.07803e7	+	1.28475e7i	0.770159	+	0.917839i	0.998444	−	0.0557549i	$-0.0177566\pi$
$241$	1.07803e7	+	1.28475e7i	0.770159	+	0.917839i	−0.228286	+	0.973594i	$0.573312\pi$
$242$		0			0
$243$	−3.82185e6	+	1.05004e7i	−0.266351	+	0.731793i
$244$		0			0
$245$	−5.65403e6	+	3.20656e7i	−0.384468	+	2.18043i
$246$		0			0
$247$	−2.38149e7	+	2.60498e6i	−1.58036	+	0.172868i
$248$		0			0
$249$	2.77331e7	+	4.89009e6i	1.79639	+	0.316752i
$250$		0			0
$251$	−4.34444e6	−	1.58125e6i	−0.274734	−	0.0999950i	0.200979	−	0.979596i	$-0.435588\pi$
$251$	−4.34444e6	−	1.58125e6i	−0.274734	−	0.0999950i	−0.475713	+	0.879601i	$0.657810\pi$
$252$		0			0
$253$	−814691.	+	683607.i	−0.0503073	+	0.0422128i
$254$		0			0
$255$	3.52954e7	+	2.03778e7i	2.12862	+	1.22896i
$256$		0			0
$257$	−6.66650e6	+	1.17548e6i	−0.392734	+	0.0692496i	−0.366528	−	0.930407i	$-0.619454\pi$
$257$	−6.66650e6	+	1.17548e6i	−0.392734	+	0.0692496i	−0.0262059	+	0.999657i	$0.508343\pi$
$258$		0			0
$259$	−1.09731e7	+	6.33531e6i	−0.631581	+	0.364644i
$260$		0			0
$261$	−2.20858e7	−	6.06803e7i	−1.24220	−	3.41292i
$262$		0			0
$263$	9.03771e6	+	7.58354e6i	0.496811	+	0.416874i	0.856460	−	0.516214i	$-0.172659\pi$
$263$	9.03771e6	+	7.58354e6i	0.496811	+	0.416874i	−0.359649	+	0.933088i	$0.617103\pi$
$264$		0			0
$265$		−	1.31044e7i		−	0.704173i
$266$		0			0
$267$	−1.41482e7			−0.743308
$268$		0			0
$269$	−2.17638e7	+	2.59370e7i	−1.11809	+	1.33249i	−0.180969	+	0.983489i	$0.557923\pi$
$269$	−2.17638e7	+	2.59370e7i	−1.11809	+	1.33249i	−0.937123	+	0.349000i	$0.886521\pi$
$270$		0			0
$271$	2.94773e7	−	1.07289e7i	1.48108	−	0.539070i	0.529998	−	0.847999i	$-0.322193\pi$
$271$	2.94773e7	−	1.07289e7i	1.48108	−	0.539070i	0.951085	+	0.308929i	$0.0999704\pi$
$272$		0			0
$273$	−4.47679e7	−	7.75402e7i	−2.20028	−	3.81100i
$274$		0			0
$275$	1.95083e6	+	1.10637e7i	0.0938042	+	0.531990i
$276$		0			0
$277$	1.87706e7	−	3.25117e7i	0.883160	−	1.52968i	0.0353525	−	0.999375i	$-0.488745\pi$
$277$	1.87706e7	−	3.25117e7i	0.883160	−	1.52968i	0.847808	−	0.530304i	$-0.177922\pi$
$278$		0			0
$279$	3.69702e7	+	4.40594e7i	1.70231	+	2.02874i
$280$		0			0
$281$	4.85818e6	−	1.33477e7i	0.218955	−	0.601573i	−0.780775	−	0.624812i	$-0.785176\pi$
$281$	4.85818e6	−	1.33477e7i	0.218955	−	0.601573i	0.999730	+	0.0232389i	$0.00739784\pi$
$282$		0			0
$283$	4.74125e6	−	2.68890e7i	0.209187	−	1.18636i	−0.681528	−	0.731792i	$-0.738684\pi$
$283$	4.74125e6	−	2.68890e7i	0.209187	−	1.18636i	0.890714	−	0.454564i	$-0.150205\pi$
$284$		0			0
$285$	3.88237e7	+	5.29634e7i	1.67711	+	2.28792i
$286$		0			0
$287$	−6.17098e7	−	1.08811e7i	−2.61041	−	0.460286i
$288$		0			0
$289$	5.65395e6	+	2.05787e6i	0.234239	+	0.0852559i
$290$		0			0
$291$	3.05551e7	−	2.56387e7i	1.23995	−	1.04044i
$292$		0			0
$293$	−2.30668e7	−	1.33176e7i	−0.917031	−	0.529448i	−0.0343446	−	0.999410i	$-0.510934\pi$
$293$	−2.30668e7	−	1.33176e7i	−0.917031	−	0.529448i	−0.882687	+	0.469962i	$0.844268\pi$
$294$		0			0
$295$	8.02562e6	−	1.41513e6i	0.312617	−	0.0551228i
$296$		0			0
$297$	1.73189e7	−	9.99906e6i	0.661075	−	0.381672i
$298$		0			0
$299$	2.67920e6	+	7.36105e6i	0.100229	+	0.275376i
$300$		0			0
$301$	4.10828e7	+	3.44725e7i	1.50647	+	1.26408i
$302$		0			0
$303$			5.70656e7i			2.05138i
$304$		0			0
$305$	6.21428e6			0.219024
$306$		0			0
$307$	9.93668e6	−	1.18421e7i	0.343420	−	0.409273i	−0.566496	−	0.824065i	$-0.691701\pi$
$307$	9.93668e6	−	1.18421e7i	0.343420	−	0.409273i	0.909916	+	0.414792i	$0.136146\pi$
$308$		0			0
$309$	−2.32887e7	+	8.47640e6i	−0.789351	+	0.287300i
$310$		0			0
$311$	2.00478e6	+	3.47238e6i	0.0666478	+	0.115437i	0.897424	−	0.441170i	$-0.145436\pi$
$311$	2.00478e6	+	3.47238e6i	0.0666478	+	0.115437i	−0.830776	+	0.556607i	$0.812103\pi$
$312$		0			0
$313$	715482.	+	4.05770e6i	0.0233327	+	0.132326i	0.994249	−	0.107093i	$-0.0341541\pi$
$313$	715482.	+	4.05770e6i	0.0233327	+	0.132326i	−0.970916	+	0.239419i	$0.923043\pi$
$314$		0			0
$315$	−8.43434e7	+	1.46087e8i	−2.69848	+	4.67391i
$316$		0			0
$317$	1.05309e7	+	1.25502e7i	0.330587	+	0.393978i	0.905577	−	0.424182i	$-0.139438\pi$
$317$	1.05309e7	+	1.25502e7i	0.330587	+	0.393978i	−0.574990	+	0.818161i	$0.694994\pi$
$318$		0			0
$319$	−6.53569e6	+	1.79566e7i	−0.201335	+	0.553163i
$320$		0			0
$321$	−3.86012e6	+	2.18918e7i	−0.116704	+	0.661861i
$322$		0			0
$323$	−2.10887e7	−	2.01934e7i	−0.625811	−	0.599241i
$324$		0			0
$325$	8.14924e7	+	1.43693e7i	2.37392	+	0.418587i
$326$		0			0
$327$	4.19400e6	+	1.52649e6i	0.119946	+	0.0436567i
$328$		0			0
$329$	−7.97390e6	+	6.69089e6i	−0.223915	+	0.187887i
$330$		0			0
$331$	−6.80992e6	−	3.93171e6i	−0.187784	−	0.108417i	0.403161	−	0.915129i	$-0.367912\pi$
$331$	−6.80992e6	−	3.93171e6i	−0.187784	−	0.108417i	−0.590945	+	0.806712i	$0.701245\pi$
$332$		0			0
$333$	−3.76626e7	+	6.64093e6i	−1.01995	+	0.179844i
$334$		0			0
$335$	1.70211e7	−	9.82711e6i	0.452743	−	0.261391i
$336$		0			0
$337$	1.81339e7	+	4.98224e7i	0.473806	+	1.30177i	0.914671	+	0.404199i	$0.132450\pi$
$337$	1.81339e7	+	4.98224e7i	0.473806	+	1.30177i	−0.440865	+	0.897574i	$0.645328\pi$
$338$		0			0
$339$	−1.06061e7	−	8.89959e6i	−0.272243	−	0.228439i
$340$		0			0
$341$		−	1.70201e7i		−	0.429239i
$342$		0			0
$343$	2.47195e7			0.612571
$344$		0			0
$345$	1.38023e7	−	1.64489e7i	0.336119	−	0.400571i
$346$		0			0
$347$	−2.42359e7	+	8.82116e6i	−0.580058	+	0.211124i	−0.615351	−	0.788253i	$-0.710986\pi$
$347$	−2.42359e7	+	8.82116e6i	−0.580058	+	0.211124i	0.0352932	+	0.999377i	$0.488763\pi$
$348$		0			0
$349$	6.64572e6	+	1.15107e7i	0.156338	+	0.270786i	0.933546	−	0.358459i	$-0.116698\pi$
$349$	6.64572e6	+	1.15107e7i	0.156338	+	0.270786i	−0.777207	+	0.629245i	$0.783364\pi$
$350$		0			0
$351$	−2.55785e7	−	1.45063e8i	−0.591498	−	3.35455i
$352$		0			0
$353$	6.90406e6	−	1.19582e7i	0.156957	−	0.271857i	−0.776813	−	0.629731i	$-0.783165\pi$
$353$	6.90406e6	−	1.19582e7i	0.156957	−	0.271857i	0.933770	+	0.357874i	$0.116498\pi$
$354$		0			0
$355$	1.35368e7	+	1.61325e7i	0.302573	+	0.360592i
$356$		0			0
$357$	3.73221e7	−	1.02542e8i	0.820279	−	2.25370i
$358$		0			0
$359$	−1.12154e7	+	6.36057e7i	−0.242399	+	1.37472i	0.584056	+	0.811713i	$0.301465\pi$
$359$	−1.12154e7	+	6.36057e7i	−0.242399	+	1.37472i	−0.826455	+	0.563002i	$0.809646\pi$
$360$		0			0
$361$	−1.79923e7	−	4.34695e7i	−0.382441	−	0.923980i
$362$		0			0
$363$	7.35476e7	+	1.29684e7i	1.53762	+	0.271124i
$364$		0			0
$365$	1.00265e7	+	3.64936e6i	0.206192	+	0.0750478i
$366$		0			0
$367$	2.62201e7	−	2.20012e7i	0.530439	−	0.445091i	−0.337814	−	0.941213i	$-0.609687\pi$
$367$	2.62201e7	−	2.20012e7i	0.530439	−	0.445091i	0.868253	+	0.496122i	$0.165243\pi$
$368$		0			0
$369$	−1.63793e8	−	9.45657e7i	−3.25998	−	1.88215i
$370$		0			0
$371$	−3.45538e7	+	6.09277e6i	−0.676666	+	0.119315i
$372$		0			0
$373$	−1.46338e7	+	8.44885e6i	−0.281989	+	0.162806i	−0.634323	−	0.773068i	$-0.718721\pi$
$373$	−1.46338e7	+	8.44885e6i	−0.281989	+	0.162806i	0.352335	+	0.935874i	$0.385388\pi$
$374$		0			0
$375$	−2.64146e7	−	7.25736e7i	−0.500900	−	1.37621i
$376$		0			0
$377$	1.07822e8	+	9.04737e7i	2.01226	+	1.68849i
$378$		0			0
$379$		−	4.24859e7i		−	0.780419i	−0.920726	−	0.390209i	$-0.872403\pi$
$379$		−	4.24859e7i		−	0.780419i	0.920726	−	0.390209i	$-0.127597\pi$
$380$		0			0
$381$	−8.20249e6			−0.148310
$382$		0			0
$383$	2.77243e6	−	3.30406e6i	0.0493474	−	0.0588100i	−0.740806	−	0.671719i	$-0.765556\pi$
$383$	2.77243e6	−	3.30406e6i	0.0493474	−	0.0588100i	0.790154	+	0.612909i	$0.210001\pi$
$384$		0			0
$385$	4.69078e7	−	1.70730e7i	0.821983	−	0.299177i
$386$		0			0
$387$	8.09351e7	+	1.40184e8i	1.39638	+	2.41860i
$388$		0			0
$389$	1.24906e7	+	7.08376e7i	0.212194	+	1.20341i	0.885709	+	0.464240i	$0.153672\pi$
$389$	1.24906e7	+	7.08376e7i	0.212194	+	1.20341i	−0.673515	+	0.739173i	$0.735216\pi$
$390$		0			0
$391$	−4.77356e6	+	8.26805e6i	−0.0798568	+	0.138316i
$392$		0			0
$393$	−4.84894e7	−	5.77874e7i	−0.798857	−	0.952041i
$394$		0			0
$395$	1.48667e7	−	4.08459e7i	0.241225	−	0.662761i
$396$		0			0
$397$	2.03534e7	−	1.15430e8i	0.325286	−	1.84479i	−0.182374	−	0.983229i	$-0.558378\pi$
$397$	2.03534e7	−	1.15430e8i	0.325286	−	1.84479i	0.507660	−	0.861558i	$-0.330511\pi$
$398$		0			0
$399$	1.21604e8	−	1.26996e8i	1.91438	−	1.99926i
$400$		0			0
$401$	−7.42650e7	−	1.30949e7i	−1.15173	−	0.203081i	−0.435000	−	0.900431i	$-0.643252\pi$
$401$	−7.42650e7	−	1.30949e7i	−1.15173	−	0.203081i	−0.716731	+	0.697349i	$0.754363\pi$
$402$		0			0
$403$	−1.17805e8	−	4.28775e7i	−1.79990	−	0.655110i
$404$		0			0
$405$	−1.31867e8	+	1.10650e8i	−1.98505	+	1.66566i
$406$		0			0
$407$	9.80093e6	+	5.65857e6i	0.145373	+	0.0839312i
$408$		0			0
$409$	−6.53898e7	+	1.15300e7i	−0.955741	+	0.168523i	−0.629705	−	0.776834i	$-0.716824\pi$
$409$	−6.53898e7	+	1.15300e7i	−0.955741	+	0.168523i	−0.326036	+	0.945357i	$0.605713\pi$
$410$		0			0
$411$	−1.56254e8	+	9.02135e7i	−2.25064	+	1.29941i
$412$		0			0
$413$	−7.46289e6	−	2.05041e7i	−0.105939	−	0.291066i
$414$		0			0
$415$	8.85887e7	+	7.43348e7i	1.23946	+	1.04003i
$416$		0			0
$417$		−	8.13433e7i		−	1.12180i
$418$		0			0
$419$	1.69411e7			0.230303			0.115151	−	0.993348i	$-0.463265\pi$
$419$	1.69411e7			0.230303			0.115151	+	0.993348i	$0.463265\pi$
$420$		0			0
$421$	−7.75651e7	+	9.24385e7i	−1.03949	+	1.23882i	−0.0690144	+	0.997616i	$0.521985\pi$
$421$	−7.75651e7	+	9.24385e7i	−1.03949	+	1.23882i	−0.970475	+	0.241200i	$0.922459\pi$
$422$		0			0
$423$	−2.95232e7	+	1.07456e7i	−0.390070	+	0.141974i
$424$		0			0
$425$	5.04259e7	+	8.73402e7i	0.656881	+	1.13775i
$426$		0			0
$427$	−2.88927e6	−	1.63859e7i	−0.0371112	−	0.210468i
$428$		0			0
$429$	−3.99857e7	+	6.92573e7i	−0.506446	+	0.877190i
$430$		0			0
$431$	3.36418e7	+	4.00927e7i	0.420191	+	0.500764i	0.934066	−	0.357101i	$-0.116235\pi$
$431$	3.36418e7	+	4.00927e7i	0.420191	+	0.500764i	−0.513875	+	0.857865i	$0.671790\pi$
$432$		0			0
$433$	1.27637e7	−	3.50679e7i	0.157222	−	0.431963i	−0.835924	−	0.548845i	$-0.815068\pi$
$433$	1.27637e7	−	3.50679e7i	0.157222	−	0.431963i	0.993146	+	0.116882i	$0.0372900\pi$
$434$		0			0
$435$	6.69968e7	−	3.79958e8i	0.813928	−	4.61602i
$436$		0			0
$437$	−1.24068e7	+	9.09457e6i	−0.148668	+	0.108978i
$438$		0			0
$439$	−8.24368e7	−	1.45358e7i	−0.974378	−	0.171809i	−0.336278	−	0.941763i	$-0.609168\pi$
$439$	−8.24368e7	−	1.45358e7i	−0.974378	−	0.171809i	−0.638100	+	0.769953i	$0.720279\pi$
$440$		0			0
$441$	2.47265e8	+	8.99971e7i	2.88301	+	1.04933i
$442$		0			0
$443$	−8.64355e7	+	7.25280e7i	−0.994216	+	0.834246i	−0.986173	−	0.165721i	$-0.947005\pi$
$443$	−8.64355e7	+	7.25280e7i	−0.994216	+	0.834246i	−0.00804348	+	0.999968i	$0.502560\pi$
$444$		0			0
$445$	−5.03166e7	−	2.90503e7i	−0.570993	−	0.329663i
$446$		0			0
$447$	4.93664e7	−	8.70463e6i	0.552725	−	0.0974603i
$448$		0			0
$449$	6.61048e7	−	3.81656e7i	0.730287	−	0.421632i	−0.0882400	−	0.996099i	$-0.528124\pi$
$449$	6.61048e7	−	3.81656e7i	0.730287	−	0.421632i	0.818527	+	0.574468i	$0.194791\pi$
$450$		0			0
$451$	1.91423e7	+	5.25929e7i	0.208672	+	0.573321i
$452$		0			0
$453$	1.69707e8	+	1.42401e8i	1.82559	+	1.53186i
$454$		0			0
$455$		−	3.67684e8i		−	3.90337i
$456$		0			0
$457$	−8.06979e7			−0.845500			−0.422750	−	0.906246i	$-0.638935\pi$
$457$	−8.06979e7			−0.845500			−0.422750	+	0.906246i	$0.638935\pi$
$458$		0			0
$459$	1.15396e8	−	1.37523e8i	1.19331	−	1.42213i
$460$		0			0
$461$	−1.27286e8	+	4.63284e7i	−1.29921	+	0.472873i	−0.896738	−	0.442561i	$-0.854070\pi$
$461$	−1.27286e8	+	4.63284e7i	−1.29921	+	0.472873i	−0.402469	+	0.915434i	$0.631848\pi$
$462$		0			0
$463$	−3.71072e7	−	6.42715e7i	−0.373865	−	0.647554i	0.616291	−	0.787518i	$-0.288634\pi$
$463$	−3.71072e7	−	6.42715e7i	−0.373865	−	0.647554i	−0.990156	+	0.139965i	$0.955301\pi$
$464$		0			0
$465$	5.96729e7	+	3.38422e8i	0.593496	+	3.36589i
$466$		0			0
$467$	−8.36960e7	+	1.44966e8i	−0.821777	+	1.42336i	0.0825802	+	0.996584i	$0.473684\pi$
$467$	−8.36960e7	+	1.44966e8i	−0.821777	+	1.42336i	−0.904358	+	0.426776i	$0.859649\pi$
$468$		0			0
$469$	−3.38260e7	−	4.03123e7i	−0.327893	−	0.390768i
$470$		0			0
$471$	−6.19908e7	+	1.70318e8i	−0.593286	+	1.63004i
$472$		0			0
$473$	8.31792e6	−	4.71733e7i	0.0786016	−	0.445772i
$474$		0			0
$475$	1.76698e7	+	1.61538e8i	0.164873	+	1.50728i
$476$		0			0
$477$	−1.04293e8	−	1.83898e7i	−0.960953	−	0.169442i
$478$		0			0
$479$	1.90223e8	+	6.92354e7i	1.73084	+	0.629973i	0.998690	−	0.0511753i	$-0.0162967\pi$
$479$	1.90223e8	+	6.92354e7i	1.73084	+	0.629973i	0.732146	+	0.681148i	$0.238519\pi$
$480$		0			0
$481$	6.38566e7	−	5.35820e7i	0.573813	−	0.481486i
$482$		0			0
$483$	−4.97899e7	−	2.87462e7i	−0.441875	−	0.255117i
$484$		0			0
$485$	1.61309e8	−	2.84431e7i	1.41395	−	0.249317i
$486$		0			0
$487$	−3.92787e7	+	2.26776e7i	−0.340072	+	0.196341i	−0.660304	−	0.750999i	$-0.729572\pi$
$487$	−3.92787e7	+	2.26776e7i	−0.340072	+	0.196341i	0.320232	+	0.947339i	$0.396239\pi$
$488$		0			0
$489$	−1.05474e8	−	2.89788e8i	−0.902028	−	2.47830i
$490$		0			0
$491$	−1.49438e8	−	1.25393e8i	−1.26246	−	1.05933i	−0.995416	−	0.0956425i	$-0.969509\pi$
$491$	−1.49438e8	−	1.25393e8i	−1.26246	−	1.05933i	−0.267042	−	0.963685i	$-0.586046\pi$
$492$		0			0
$493$			1.71543e8i			1.43164i
$494$		0			0
$495$	1.50668e8			1.24224
$496$		0			0
$497$	3.62445e7	−	4.31946e7i	0.295239	−	0.351852i
$498$		0			0
$499$	1.25262e8	−	4.55915e7i	1.00813	−	0.366929i	0.215415	−	0.976523i	$-0.430890\pi$
$499$	1.25262e8	−	4.55915e7i	1.00813	−	0.366929i	0.792714	+	0.609594i	$0.208667\pi$
$500$		0			0
$501$	1.19410e8	+	2.06825e8i	0.949575	+	1.64471i
$502$		0			0
$503$	−2.81637e7	−	1.59724e8i	−0.221302	−	1.25507i	−0.869630	−	0.493704i	$-0.835642\pi$
$503$	−2.81637e7	−	1.59724e8i	−0.221302	−	1.25507i	0.648328	−	0.761361i	$-0.275469\pi$
$504$		0			0
$505$	−1.17172e8	+	2.02947e8i	−0.909804	+	1.57583i
$506$		0			0
$507$	2.28823e8	+	2.72701e8i	1.75581	+	2.09249i
$508$		0			0
$509$	−1.29984e7	+	3.57127e7i	−0.0985679	+	0.270813i	−0.979170	−	0.203044i	$-0.934917\pi$
$509$	−1.29984e7	+	3.57127e7i	−0.0985679	+	0.270813i	0.880602	+	0.473857i	$0.157139\pi$
$510$		0			0
$511$	4.96093e6	−	2.81348e7i	0.0371792	−	0.210854i
$512$		0			0
$513$	2.59450e8	−	1.27904e8i	1.92177	−	0.947400i
$514$		0			0
$515$	−1.00228e8	−	1.76729e7i	−0.733783	−	0.129386i
$516$		0			0
$517$	8.73657e6	+	3.17985e6i	0.0632222	+	0.0230110i
$518$		0			0
$519$	−2.34822e8	+	1.97039e8i	−1.67972	+	1.40945i
$520$		0			0
$521$	−1.09216e8	−	6.30558e7i	−0.772276	−	0.445873i	0.0614102	−	0.998113i	$-0.480440\pi$
$521$	−1.09216e8	−	6.30558e7i	−0.772276	−	0.445873i	−0.833686	+	0.552239i	$0.813774\pi$
$522$		0			0
$523$	2.10975e8	−	3.72006e7i	1.47478	−	0.260043i	0.622287	−	0.782789i	$-0.286204\pi$
$523$	2.10975e8	−	3.72006e7i	1.47478	−	0.260043i	0.852488	+	0.522746i	$0.175092\pi$
$524$		0			0
$525$	−5.25960e8	+	3.03663e8i	−3.63475	+	2.09852i
$526$		0			0
$527$	−5.22574e7	−	1.43576e8i	−0.357039	−	0.980957i
$528$		0			0
$529$	−1.09549e8	−	9.19224e7i	−0.740016	−	0.620947i
$530$		0			0
$531$		−	6.58591e7i		−	0.439878i
$532$		0			0
$533$	4.12246e8			2.72254
$534$		0			0
$535$	−5.86781e7	+	6.99298e7i	−0.383190	+	0.456668i
$536$		0			0
$537$	3.65568e8	−	1.33056e8i	2.36073	−	0.859234i
$538$		0			0
$539$	−3.89336e7	−	6.74349e7i	−0.248633	−	0.430644i
$540$		0			0
$541$	9.60368e6	+	5.44652e7i	0.0606521	+	0.343975i	0.999999	+	0.00100799i	$0.000320854\pi$
$541$	9.60368e6	+	5.44652e7i	0.0606521	+	0.343975i	−0.939347	+	0.342967i	$0.888568\pi$
$542$		0			0
$543$	−2.34622e8	+	4.06377e8i	−1.46544	+	2.53823i
$544$		0			0
$545$	1.17811e7	+	1.40402e7i	0.0727777	+	0.0867330i
$546$		0			0
$547$	3.37997e7	−	9.28640e7i	0.206515	−	0.567395i	−0.792587	−	0.609758i	$-0.791266\pi$
$547$	3.37997e7	−	9.28640e7i	0.206515	−	0.567395i	0.999102	+	0.0423633i	$0.0134887\pi$
$548$		0			0
$549$	8.72066e6	−	4.94573e7i	0.0527026	−	0.298892i
$550$		0			0
$551$	−1.11354e8	+	2.52982e8i	−0.665660	+	1.51229i
$552$		0			0
$553$	−1.14615e8	−	2.02097e7i	−0.677745	−	0.119505i
$554$		0			0
$555$	−2.14717e8	−	7.81506e7i	−1.25599	−	0.457144i
$556$		0			0
$557$	−8.97858e7	+	7.53392e7i	−0.519568	+	0.435969i	−0.864481	−	0.502666i	$-0.832353\pi$
$557$	−8.97858e7	+	7.53392e7i	−0.519568	+	0.435969i	0.344913	+	0.938635i	$0.387908\pi$
$558$		0			0
$559$	−3.05556e8	−	1.76413e8i	−1.74926	−	1.00994i
$560$		0			0
$561$	−9.59853e7	+	1.69248e7i	−0.543646	+	0.0958595i
$562$		0			0
$563$	−3.93168e7	+	2.26996e7i	−0.220319	+	0.127201i	−0.606098	−	0.795390i	$-0.707266\pi$
$563$	−3.93168e7	+	2.26996e7i	−0.220319	+	0.127201i	0.385779	+	0.922591i	$0.373933\pi$
$564$		0			0
$565$	−1.94461e7	−	5.34276e7i	−0.107817	−	0.296224i
$566$		0			0
$567$	3.53073e8	+	2.96264e8i	1.93694	+	1.62528i
$568$		0			0
$569$		−	2.02040e8i		−	1.09673i	−0.836239	−	0.548365i	$-0.815250\pi$
$569$		−	2.02040e8i		−	1.09673i	0.836239	−	0.548365i	$-0.184750\pi$
$570$		0			0
$571$	−7.22753e7			−0.388223			−0.194112	−	0.980979i	$-0.562182\pi$
$571$	−7.22753e7			−0.388223			−0.194112	+	0.980979i	$0.562182\pi$
$572$		0			0
$573$	5.74404e6	−	6.84548e6i	0.0305319	−	0.0363865i
$574$		0			0
$575$	4.99304e7	−	1.81732e7i	0.262641	−	0.0955934i
$576$		0			0
$577$	9.25365e7	+	1.60278e8i	0.481710	+	0.834346i	0.999780	−	0.0209925i	$-0.00668261\pi$
$577$	9.25365e7	+	1.60278e8i	0.481710	+	0.834346i	−0.518070	+	0.855338i	$0.673349\pi$
$578$		0			0
$579$	−3.05477e7	−	1.73245e8i	−0.157378	−	0.892532i
$580$		0			0
$581$	1.54818e8	−	2.68153e8i	0.789394	−	1.36727i
$582$		0			0
$583$	2.01442e7	+	2.40070e7i	0.101659	+	0.121152i
$584$		0			0
$585$	3.79566e8	−	1.04285e9i	1.89592	−	5.20899i
$586$		0			0
$587$	−1.42594e7	+	8.08688e7i	−0.0704994	+	0.399822i	0.929054	+	0.369944i	$0.120623\pi$
$587$	−1.42594e7	+	8.08688e7i	−0.0704994	+	0.399822i	−0.999554	+	0.0298783i	$0.990488\pi$
$588$		0			0
$589$	1.61338e7	−	2.45660e8i	0.0789571	−	1.20223i
$590$		0			0
$591$	3.86645e8	+	6.81760e7i	1.87305	+	0.330270i
$592$		0			0
$593$	−2.48939e8	−	9.06064e7i	−1.19379	−	0.434505i	−0.332739	−	0.943019i	$-0.607973\pi$
$593$	−2.48939e8	−	9.06064e7i	−1.19379	−	0.434505i	−0.861054	+	0.508514i	$0.830195\pi$
$594$		0			0
$595$	3.43278e8	−	2.88045e8i	1.62965	−	1.36744i
$596$		0			0
$597$	3.87916e8	+	2.23963e8i	1.82312	+	1.05258i
$598$		0			0
$599$	−2.36439e8	+	4.16906e7i	−1.10012	+	0.193980i	−0.694096	−	0.719883i	$-0.744195\pi$
$599$	−2.36439e8	+	4.16906e7i	−1.10012	+	0.193980i	−0.406022	+	0.913863i	$0.633084\pi$
$600$		0			0
$601$	3.49286e8	−	2.01660e8i	1.60901	−	0.928961i	0.619415	−	0.785064i	$-0.287370\pi$
$601$	3.49286e8	−	2.01660e8i	1.60901	−	0.928961i	0.989593	−	0.143897i	$-0.0459633\pi$
$602$		0			0
$603$	−5.43246e7	−	1.49255e8i	−0.247767	−	0.680735i
$604$		0			0
$605$	2.34936e8	+	1.97134e8i	1.06092	+	0.890218i
$606$		0			0
$607$			2.00818e8i			0.897916i	0.893553	+	0.448958i	$0.148205\pi$
$607$			2.00818e8i			0.897916i	−0.893553	+	0.448958i	$0.851795\pi$
$608$		0			0
$609$	−1.03303e9			−4.57361
$610$		0			0
$611$	4.40188e7	−	5.24595e7i	0.192981	−	0.229986i
$612$		0			0
$613$	−3.78241e8	+	1.37668e8i	−1.64205	+	0.597658i	−0.987396	−	0.158270i	$-0.949408\pi$
$613$	−3.78241e8	+	1.37668e8i	−1.64205	+	0.597658i	−0.654655	+	0.755927i	$0.727186\pi$
$614$		0			0
$615$	−5.65009e8	−	9.78625e8i	−2.42902	−	4.20718i
$616$		0			0
$617$	−1.39230e7	−	7.89612e7i	−0.0592757	−	0.336169i	0.940720	−	0.339185i	$-0.110151\pi$
$617$	−1.39230e7	−	7.89612e7i	−0.0592757	−	0.336169i	−0.999995	+	0.00301549i	$0.999040\pi$
$618$		0			0
$619$	−8.92193e7	+	1.54532e8i	−0.376173	+	0.651550i	−0.990502	−	0.137500i	$-0.956093\pi$
$619$	−8.92193e7	+	1.54532e8i	−0.376173	+	0.651550i	0.614329	+	0.789050i	$0.289427\pi$
$620$		0			0
$621$	−6.07976e7	−	7.24557e7i	−0.253870	−	0.302551i
$622$		0			0
$623$	−5.32059e7	+	1.46182e8i	−0.220037	+	0.604546i
$624$		0			0
$625$	−9.20821e6	+	5.22223e7i	−0.0377168	+	0.213903i
$626$		0			0
$627$	−1.52540e8	−	3.73476e7i	−0.618844	−	0.151516i
$628$		0			0
$629$	1.00051e8	+	1.76417e7i	0.402040	+	0.0708905i
$630$		0			0
$631$	1.48123e8	+	5.39124e7i	0.589569	+	0.214586i	0.619540	−	0.784965i	$-0.287319\pi$
$631$	1.48123e8	+	5.39124e7i	0.589569	+	0.214586i	−0.0299707	+	0.999551i	$0.509541\pi$
$632$		0			0
$633$	−4.49390e8	+	3.77083e8i	−1.77179	+	1.48671i
$634$		0			0
$635$	−2.91712e7	−	1.68420e7i	−0.113929	−	0.0657767i
$636$		0			0
$637$	−5.64834e8	+	9.95955e7i	−2.18526	+	0.385320i
$638$		0			0
$639$	1.47390e8	−	8.50954e7i	0.564890	−	0.326139i
$640$		0			0
$641$	−5.93595e7	−	1.63089e8i	−0.225380	−	0.619228i	0.774531	−	0.632536i	$-0.217986\pi$
$641$	−5.93595e7	−	1.63089e8i	−0.225380	−	0.619228i	−0.999911	+	0.0133082i	$0.995764\pi$
$642$		0			0
$643$	2.74885e8	+	2.30656e8i	1.03400	+	0.867625i	0.991321	−	0.131464i	$-0.0419677\pi$
$643$	2.74885e8	+	2.30656e8i	1.03400	+	0.867625i	0.0426745	+	0.999089i	$0.486412\pi$
$644$		0			0
$645$			9.67138e8i			3.60420i
$646$		0			0
$647$	4.93325e8			1.82146			0.910730	−	0.413001i	$-0.135519\pi$
$647$	4.93325e8			1.82146			0.910730	+	0.413001i	$0.135519\pi$
$648$		0			0
$649$	−1.25274e7	+	1.49296e7i	−0.0458276	+	0.0546152i
$650$		0			0
$651$	8.64610e8	−	3.14692e8i	3.13384	−	1.14063i
$652$		0			0
$653$	1.17120e8	+	2.02857e8i	0.420620	+	0.728536i	0.996000	−	0.0893506i	$-0.0284791\pi$
$653$	1.17120e8	+	2.02857e8i	0.420620	+	0.728536i	−0.575380	+	0.817886i	$0.695146\pi$
$654$		0			0
$655$	−5.37932e7	−	3.05076e8i	−0.191427	−	1.08564i
$656$		0			0
$657$	4.31145e7	−	7.46765e7i	0.152029	−	0.263323i
$658$		0			0
$659$	2.45135e8	+	2.92141e8i	0.856543	+	1.02079i	0.999517	+	0.0310623i	$0.00988902\pi$
$659$	2.45135e8	+	2.92141e8i	0.856543	+	1.02079i	−0.142974	+	0.989726i	$0.545667\pi$
$660$		0			0
$661$	−9.97134e7	+	2.73960e8i	−0.345262	+	0.948601i	0.638579	+	0.769557i	$0.279523\pi$
$661$	−9.97134e7	+	2.73960e8i	−0.345262	+	0.948601i	−0.983841	+	0.179044i	$0.942699\pi$
$662$		0			0
$663$	−1.24663e8	+	7.07001e8i	−0.427758	+	2.42594i
$664$		0			0
$665$	6.93227e8	−	2.01958e8i	2.35728	−	0.686748i
$666$		0			0
$667$	8.90062e7	+	1.56942e7i	0.299946	+	0.0528886i
$668$		0			0
$669$	−3.59204e8	−	1.30740e8i	−1.19967	−	0.436645i
$670$		0			0
$671$	−1.13844e7	+	9.55266e6i	−0.0376828	+	0.0316196i
$672$		0			0
$673$	3.84804e8	+	2.22167e8i	1.26239	+	0.728844i	0.973537	−	0.228529i	$-0.0733915\pi$
$673$	3.84804e8	+	2.22167e8i	1.26239	+	0.728844i	0.288857	+	0.957372i	$0.406725\pi$
$674$		0			0
$675$	−9.83970e8	+	1.73500e8i	−3.19941	+	0.564143i
$676$		0			0
$677$	1.15833e8	−	6.68760e7i	0.373306	−	0.215528i	−0.301596	−	0.953436i	$-0.597519\pi$
$677$	1.15833e8	−	6.68760e7i	0.373306	−	0.215528i	0.674902	+	0.737908i	$0.264186\pi$
$678$		0			0
$679$	−1.49998e8	−	4.12117e8i	−0.479156	−	1.31647i
$680$		0			0
$681$	3.44419e8	+	2.89002e8i	1.09055	+	0.915082i
$682$		0			0
$683$			3.92879e8i			1.23310i	0.787317	+	0.616548i	$0.211469\pi$
$683$			3.92879e8i			1.23310i	−0.787317	+	0.616548i	$0.788531\pi$
$684$		0			0
$685$	−7.40934e8			−2.30520
$686$		0			0
$687$	−5.45629e8	+	6.50255e8i	−1.68278	+	2.00546i
$688$		0			0
$689$	2.16912e8	−	7.89497e7i	0.663173	−	0.241375i
$690$		0			0
$691$	−2.23489e7	−	3.87094e7i	−0.0677363	−	0.117323i	0.830168	−	0.557513i	$-0.188244\pi$
$691$	−2.23489e7	−	3.87094e7i	−0.0677363	−	0.117323i	−0.897905	+	0.440190i	$0.854911\pi$
$692$		0			0
$693$	−7.00516e7	−	3.97282e8i	−0.210484	−	1.19371i
$694$		0			0
$695$	1.67021e8	−	2.89288e8i	0.497526	−	0.861740i
$696$		0			0
$697$	3.22955e8	+	3.84883e8i	0.953771	+	1.13666i
$698$		0			0
$699$	1.37915e8	−	3.78918e8i	0.403812	−	1.10946i
$700$		0			0
$701$	9.04201e7	−	5.12798e8i	0.262489	−	1.48865i	−0.513602	−	0.858028i	$-0.671689\pi$
$701$	9.04201e7	−	5.12798e8i	0.262489	−	1.48865i	0.776091	−	0.630621i	$-0.217200\pi$
$702$		0			0
$703$	1.36098e8	+	9.09635e7i	0.391728	+	0.261819i
$704$		0			0
$705$	−1.84863e8	−	3.25964e7i	−0.527574	−	0.0930256i
$706$		0			0
$707$	5.89611e8	+	2.14601e8i	1.66843	+	0.607258i
$708$		0			0
$709$	3.21461e8	−	2.69738e8i	0.901966	−	0.756839i	−0.0686079	−	0.997644i	$-0.521856\pi$
$709$	3.21461e8	−	2.69738e8i	0.901966	−	0.756839i	0.970574	+	0.240805i	$0.0774113\pi$
$710$		0			0
$711$	−3.04216e8	−	1.75639e8i	−0.846395	−	0.488666i
$712$		0			0
$713$	−7.92763e7	+	1.39786e7i	−0.218713	+	0.0385650i
$714$		0			0
$715$	−2.84409e8	+	1.64204e8i	−0.778082	+	0.449226i
$716$		0			0
$717$	−2.90911e8	−	7.99272e8i	−0.789229	−	2.16839i
$718$		0			0
$719$	−3.84120e8	−	3.22315e8i	−1.03343	−	0.867148i	−0.0421725	−	0.999110i	$-0.513428\pi$
$719$	−3.84120e8	−	3.22315e8i	−1.03343	−	0.867148i	−0.991255	+	0.131962i	$0.957872\pi$
$720$		0			0
$721$			2.72499e8i			0.727042i
$722$		0			0
$723$	8.09793e8			2.14269
$724$		0			0
$725$	6.13688e8	−	7.31365e8i	1.61040	−	1.91920i
$726$		0			0
$727$	2.14495e8	−	7.80699e7i	0.558232	−	0.203180i	−0.0474683	−	0.998873i	$-0.515115\pi$
$727$	2.14495e8	−	7.80699e7i	0.558232	−	0.203180i	0.605700	+	0.795693i	$0.292893\pi$
$728$		0			0
$729$	−4.66656e7	−	8.08272e7i	−0.120452	−	0.208629i
$730$		0			0
$731$	−7.46704e7	−	4.23477e8i	−0.191160	−	1.08412i
$732$		0			0
$733$	−9.11873e7	+	1.57941e8i	−0.231538	+	0.401036i	−0.958261	−	0.285895i	$-0.907709\pi$
$733$	−9.11873e7	+	1.57941e8i	−0.231538	+	0.401036i	0.726723	+	0.686931i	$0.241042\pi$
$734$		0			0
$735$	1.01057e9	+	1.20435e9i	2.54510	+	3.03313i
$736$		0			0
$737$	−1.60758e7	+	4.41680e7i	−0.0401579	+	0.110333i
$738$		0			0
$739$	−9.15163e7	+	5.19015e8i	−0.226759	+	1.28602i	0.632534	+	0.774533i	$0.282015\pi$
$739$	−9.15163e7	+	5.19015e8i	−0.226759	+	1.28602i	−0.859293	+	0.511483i	$0.829096\pi$
$740$		0			0
$741$	−6.42785e8	+	9.61722e8i	−1.57983	+	2.36371i
$742$		0			0
$743$	−3.86962e8	−	6.82319e7i	−0.943414	−	0.166349i	−0.319275	−	0.947662i	$-0.603439\pi$
$743$	−3.86962e8	−	6.82319e7i	−0.943414	−	0.166349i	−0.624140	+	0.781313i	$0.714550\pi$
$744$		0			0
$745$	1.93439e8	+	7.04060e7i	0.467816	+	0.170271i
$746$		0			0
$747$	7.15924e8	−	6.00732e8i	1.71753	−	1.44118i
$748$		0			0
$749$	2.11674e8	+	1.22210e8i	0.503757	+	0.290844i
$750$		0			0
$751$	−5.60378e8	+	9.88098e7i	−1.32301	+	0.233281i	−0.790144	−	0.612921i	$-0.789994\pi$
$751$	−5.60378e8	+	9.88098e7i	−1.32301	+	0.233281i	−0.532861	+	0.846203i	$0.678883\pi$
$752$		0			0
$753$	−1.93325e8	+	1.11616e8i	−0.452797	+	0.261423i
$754$		0			0
$755$	3.11153e8	+	8.54887e8i	0.722992	+	1.98640i
$756$		0			0
$757$	−2.96782e8	−	2.49029e8i	−0.684147	−	0.574068i	0.233068	−	0.972461i	$-0.425124\pi$
$757$	−2.96782e8	−	2.49029e8i	−0.684147	−	0.574068i	−0.917215	+	0.398393i	$0.869568\pi$
$758$		0			0
$759$			5.13510e7i			0.117442i
$760$		0			0
$761$	−1.85846e8			−0.421695			−0.210848	−	0.977519i	$-0.567622\pi$
$761$	−1.85846e8			−0.421695			−0.210848	+	0.977519i	$0.567622\pi$
$762$		0			0
$763$	3.15439e7	−	3.75925e7i	0.0710136	−	0.0846307i
$764$		0			0
$765$	1.27098e9	−	4.62600e8i	2.83893	−	1.03329i
$766$		0			0
$767$	7.17760e7	+	1.24320e8i	0.159072	+	0.275520i
$768$		0			0
$769$	−1.21843e8	−	6.91006e8i	−0.267930	−	1.51951i	−0.760560	−	0.649268i	$-0.775075\pi$
$769$	−1.21843e8	−	6.91006e8i	−0.267930	−	1.51951i	0.492630	−	0.870239i	$-0.336036\pi$
$770$		0			0
$771$	−1.63428e8	+	2.83066e8i	−0.356586	+	0.617625i
$772$		0			0
$773$	−5.62078e8	−	6.69859e8i	−1.21691	−	1.45026i	−0.855463	−	0.517863i	$-0.826728\pi$
$773$	−5.62078e8	−	6.69859e8i	−1.21691	−	1.45026i	−0.361446	−	0.932393i	$-0.617717\pi$
$774$		0			0
$775$	−2.90841e8	+	7.99078e8i	−0.624813	+	1.71666i
$776$		0			0
$777$	−1.06238e8	+	6.02504e8i	−0.226472	+	1.28439i
$778$		0			0
$779$	2.26435e8	+	7.77245e8i	0.478996	+	1.64417i
$780$		0			0
$781$	−4.95981e7	−	8.74548e6i	−0.104115	−	0.0183582i
$782$		0			0
$783$	−1.59700e9	−	5.81261e8i	−3.32675	−	1.21084i
$784$		0			0
$785$	−5.70174e8	+	4.78433e8i	−1.17869	+	0.989035i
$786$		0			0
$787$	3.18669e8	+	1.83984e8i	0.653757	+	0.377447i	0.789894	−	0.613243i	$-0.210136\pi$
$787$	3.18669e8	+	1.83984e8i	0.653757	+	0.377447i	−0.136137	+	0.990690i	$0.543469\pi$
$788$		0			0
$789$	5.61004e8	−	9.89202e7i	1.14218	−	0.201398i
$790$		0			0
$791$	−1.31837e8	+	7.61163e7i	−0.266385	+	0.153797i
$792$		0			0
$793$	3.74390e7	+	1.02863e8i	0.0750765	+	0.206271i
$794$		0			0
$795$	−4.84709e8	−	4.06720e8i	−0.964673	−	0.809457i
$796$		0			0
$797$		−	1.73636e8i		−	0.342978i	−0.985186	−	0.171489i	$-0.945142\pi$
$797$		−	1.73636e8i		−	0.342978i	0.985186	−	0.171489i	$-0.0548578\pi$
$798$		0			0
$799$	8.34620e7			0.163625
$800$		0			0
$801$	−3.01812e8	+	3.59685e8i	−0.587271	+	0.699883i
$802$		0			0
$803$	−2.39782e7	+	8.72736e6i	−0.0463095	+	0.0168553i
$804$		0			0
$805$	−1.18048e8	−	2.04465e8i	−0.226293	−	0.391951i
$806$		0			0
$807$	2.83888e8	+	1.61001e9i	0.540165	+	3.06343i
$808$		0			0
$809$	1.34109e8	−	2.32284e8i	0.253287	−	0.438706i	−0.711142	−	0.703048i	$-0.751822\pi$
$809$	1.34109e8	−	2.32284e8i	0.253287	−	0.438706i	0.964429	+	0.264343i	$0.0851550\pi$
$810$		0			0
$811$	−8.79534e7	−	1.04819e8i	−0.164888	−	0.196506i	0.677273	−	0.735732i	$-0.263162\pi$
$811$	−8.79534e7	−	1.04819e8i	−0.164888	−	0.196506i	−0.842162	+	0.539225i	$0.818717\pi$
$812$		0			0
$813$	5.18041e8	−	1.42330e9i	0.964033	−	2.64866i
$814$		0			0
$815$	2.19909e8	−	1.24717e9i	0.406228	−	2.30384i
$816$		0			0
$817$	1.64773e8	−	6.72990e8i	0.302149	−	1.23408i
$818$		0			0
$819$	−2.92627e9	−	5.15980e8i	−5.32675	−	0.939250i
$820$		0			0
$821$	2.31094e8	+	8.41112e7i	0.417598	+	0.151993i	0.542269	−	0.840205i	$-0.317565\pi$
$821$	2.31094e8	+	8.41112e7i	0.417598	+	0.151993i	−0.124671	+	0.992198i	$0.539788\pi$
$822$		0			0
$823$	−3.47199e6	+	2.91335e6i	−0.00622844	+	0.00522628i	−0.645897	−	0.763425i	$-0.723516\pi$
$823$	−3.47199e6	+	2.91335e6i	−0.00622844	+	0.00522628i	0.639668	+	0.768651i	$0.279072\pi$
$824$		0			0
$825$	4.69776e8	+	2.71226e8i	0.836622	+	0.483024i
$826$		0			0
$827$	4.92063e8	−	8.67640e7i	0.869970	−	0.153399i	0.279194	−	0.960235i	$-0.409933\pi$
$827$	4.92063e8	−	8.67640e7i	0.869970	−	0.153399i	0.590776	+	0.806836i	$0.298822\pi$
$828$		0			0
$829$	3.66960e8	−	2.11865e8i	0.644103	−	0.371873i	−0.142090	−	0.989854i	$-0.545382\pi$
$829$	3.66960e8	−	2.11865e8i	0.644103	−	0.371873i	0.786193	+	0.617981i	$0.212049\pi$
$830$		0			0
$831$	−6.19970e8	−	1.70335e9i	−1.08036	−	2.96826i
$832$		0			0
$833$	−5.35478e8	−	4.49320e8i	−0.926418	−	0.777357i
$834$		0			0
$835$			9.80732e8i			1.68458i
$836$		0			0
$837$	1.51371e9			2.58147
$838$		0			0
$839$	6.64336e8	−	7.91725e8i	1.12487	−	1.34057i	0.191565	−	0.981480i	$-0.438644\pi$
$839$	6.64336e8	−	7.91725e8i	1.12487	−	1.34057i	0.933304	−	0.359087i	$-0.116912\pi$
$840$		0			0
$841$	9.67052e8	−	3.51978e8i	1.62578	−	0.591736i
$842$		0			0
$843$	−3.42927e8	−	5.93967e8i	−0.572426	−	0.991471i
$844$		0			0
$845$	2.53852e8	+	1.43967e9i	0.420737	+	2.38612i
$846$		0			0
$847$	4.10575e8	−	7.11137e8i	0.675682	−	1.17032i
$848$		0			0
$849$	−8.47424e8	−	1.00992e9i	−1.38477	−	1.65030i
$850$		0			0
$851$	1.83070e7	−	5.02981e7i	0.0297050	−	0.0816137i
$852$		0			0
$853$	−2.77528e7	+	1.57394e8i	−0.0447157	+	0.253595i	−0.998969	−	0.0454052i	$-0.985542\pi$
$853$	−2.77528e7	+	1.57394e8i	−0.0447157	+	0.253595i	0.954253	+	0.299000i	$0.0966532\pi$
$854$		0			0
$855$	2.17466e9	+	1.42822e8i	3.47931	+	0.228505i
$856$		0			0
$857$	3.10258e8	+	5.47068e7i	0.492924	+	0.0869158i	0.414584	−	0.910011i	$-0.363927\pi$
$857$	3.10258e8	+	5.47068e7i	0.492924	+	0.0869158i	0.0783397	+	0.996927i	$0.475038\pi$
$858$		0			0
$859$	1.36644e8	+	4.97344e7i	0.215581	+	0.0784652i	0.447553	−	0.894257i	$-0.352295\pi$
$859$	1.36644e8	+	4.97344e7i	0.215581	+	0.0784652i	−0.231972	+	0.972723i	$0.574518\pi$
$860$		0			0
$861$	−2.31775e9	+	1.94483e9i	−3.63126	+	3.04699i
$862$		0			0
$863$	−1.03667e8	−	5.98522e7i	−0.161290	−	0.0931210i	0.417182	−	0.908823i	$-0.363018\pi$
$863$	−1.03667e8	−	5.98522e7i	−0.161290	−	0.0931210i	−0.578473	+	0.815702i	$0.696351\pi$
$864$		0			0
$865$	−1.23970e9	+	2.18592e8i	−1.91543	+	0.337742i
$866$		0			0
$867$	2.51598e8	−	1.45260e8i	0.386056	−	0.222889i
$868$		0			0
$869$	3.55534e7	+	9.76820e7i	0.0541778	+	0.148852i
$870$		0			0
$871$	2.65211e8	+	2.22538e8i	0.401363	+	0.336783i
$872$		0			0
$873$		−	1.32372e9i		−	1.98954i
$874$		0			0
$875$	−8.49177e8			−1.26758
$876$		0			0
$877$	1.14403e8	−	1.36341e8i	0.169605	−	0.202128i	−0.674546	−	0.738233i	$-0.735660\pi$
$877$	1.14403e8	−	1.36341e8i	0.169605	−	0.202128i	0.844151	+	0.536105i	$0.180105\pi$
$878$		0			0
$879$	−1.20852e9	+	4.39864e8i	−1.77945	+	0.647667i
$880$		0			0
$881$	2.89596e8	+	5.01596e8i	0.423512	+	0.733544i	0.996280	−	0.0861733i	$-0.0274639\pi$
$881$	2.89596e8	+	5.01596e8i	0.423512	+	0.733544i	−0.572768	+	0.819717i	$0.694131\pi$
$882$		0			0
$883$	−2.29199e8	−	1.29985e9i	−0.332913	−	1.88804i	−0.446939	−	0.894564i	$-0.647486\pi$
$883$	−2.29199e8	−	1.29985e9i	−0.332913	−	1.88804i	0.114026	−	0.993478i	$-0.463625\pi$
$884$		0			0
$885$	1.96747e8	−	3.40776e8i	0.283843	−	0.491630i
$886$		0			0
$887$	−2.04092e8	−	2.43227e8i	−0.292452	−	0.348531i	0.599733	−	0.800200i	$-0.295273\pi$
$887$	−2.04092e8	−	2.43227e8i	−0.292452	−	0.348531i	−0.892186	+	0.451669i	$0.850829\pi$
$888$		0			0
$889$	−3.08463e7	+	8.47495e7i	−0.0439033	+	0.120623i
$890$		0			0
$891$	7.14858e7	−	4.05416e8i	0.101062	−	0.573149i
$892$		0			0
$893$	1.23085e8	+	5.41780e7i	0.172843	+	0.0760797i
$894$		0			0
$895$	1.57330e9	+	2.77415e8i	2.19454	+	0.386956i
$896$		0			0
$897$	3.55427e8	+	1.29365e8i	0.492462	+	0.179242i
$898$		0			0
$899$	−1.10802e9	+	9.29737e8i	−1.52499	+	1.27962i
$900$		0			0
$901$	2.43639e8	+	1.40665e8i	0.333099	+	0.192315i
$902$		0			0
$903$	2.55016e9	−	4.49662e8i	3.46341	−	0.610693i
$904$		0			0
$905$	−1.66881e9	+	9.63489e8i	−2.25145	+	1.29987i
$906$		0			0
$907$	−1.36056e8	−	3.73810e8i	−0.182346	−	0.500990i	0.814517	−	0.580139i	$-0.197002\pi$
$907$	−1.36056e8	−	3.73810e8i	−0.182346	−	0.500990i	−0.996863	+	0.0791491i	$0.974780\pi$
$908$		0			0
$909$	1.45076e9	+	1.21733e9i	1.93154	+	1.62075i
$910$		0			0
$911$		−	8.77556e8i		−	1.16070i	−0.814367	−	0.580350i	$-0.802916\pi$
$911$		−	8.77556e8i		−	1.16070i	0.814367	−	0.580350i	$-0.197084\pi$
$912$		0			0
$913$	−2.76561e8			−0.363395
$914$		0			0
$915$	1.92872e8	−	2.29856e8i	0.251771	−	0.300049i
$916$		0			0
$917$	−7.79418e8	+	2.83685e8i	−1.01079	+	0.367899i
$918$		0			0
$919$	4.66156e8	+	8.07406e8i	0.600599	+	1.04027i	0.992730	+	0.120359i	$0.0384046\pi$
$919$	4.66156e8	+	8.07406e8i	0.600599	+	1.04027i	−0.392131	+	0.919909i	$0.628262\pi$
$920$		0			0
$921$	−1.29615e8	−	7.35082e8i	−0.165911	−	0.940929i
$922$		0			0
$923$	−1.85481e8	+	3.21262e8i	−0.235881	+	0.408559i
$924$		0			0
$925$	−3.63450e8	−	4.33143e8i	−0.459219	−	0.547276i
$926$		0			0
$927$	−2.81305e8	+	7.72880e8i	−0.353133	+	0.970226i
$928$		0			0
$929$	−1.43095e8	+	8.11534e8i	−0.178475	+	1.01218i	0.755580	+	0.655056i	$0.227355\pi$
$929$	−1.43095e8	+	8.11534e8i	−0.178475	+	1.01218i	−0.934056	+	0.357128i	$0.883756\pi$
$930$		0			0
$931$	−4.98024e8	−	1.01023e9i	−0.617165	−	1.25190i
$932$		0			0
$933$	1.90660e8	+	3.36185e7i	0.234755	+	0.0413936i
$934$		0			0
$935$	−3.76112e8	−	1.36894e8i	−0.460132	−	0.167474i
$936$		0			0
$937$	−3.42082e8	+	2.87041e8i	−0.415826	+	0.348919i	−0.826572	−	0.562830i	$-0.809712\pi$
$937$	−3.42082e8	+	2.87041e8i	−0.415826	+	0.348919i	0.410747	+	0.911749i	$0.365268\pi$
$938$		0			0
$939$	1.72294e8	+	9.94738e7i	0.208100	+	0.120147i
$940$		0			0
$941$	−1.40645e9	+	2.47995e8i	−1.68793	+	0.297628i	−0.933455	−	0.358695i	$-0.883222\pi$
$941$	−1.40645e9	+	2.47995e8i	−1.68793	+	0.297628i	−0.754479	+	0.656324i	$0.772111\pi$
$942$		0			0
$943$	2.29246e8	−	1.32355e8i	0.273380	−	0.157836i
$944$		0			0
$945$	1.51842e9	+	4.17181e9i	1.79927	+	4.94344i
$946$		0			0
$947$	−1.12825e9	−	9.46712e8i	−1.32848	−	1.11473i	−0.984431	−	0.175773i	$-0.943757\pi$
$947$	−1.12825e9	−	9.46712e8i	−1.32848	−	1.11473i	−0.344047	−	0.938952i	$-0.611798\pi$
$948$		0			0
$949$			1.87952e8i			0.219911i
$950$		0			0
$951$	7.91055e8			0.919740
$952$		0			0
$953$	1.03278e8	−	1.23081e8i	0.119324	−	0.142205i	−0.703076	−	0.711115i	$-0.748190\pi$
$953$	1.03278e8	−	1.23081e8i	0.119324	−	0.142205i	0.822399	+	0.568910i	$0.192635\pi$
$954$		0			0
$955$	3.44837e7	−	1.25510e7i	0.0395917	−	0.0144102i
$956$		0			0
$957$	4.61339e8	+	7.99062e8i	0.526362	+	0.911685i
$958$		0			0
$959$	3.44491e8	+	1.95370e9i	0.390590	+	2.21515i
$960$		0			0
$961$	2.00396e8	−	3.47097e8i	0.225798	−	0.391093i
$962$		0			0
$963$	4.74203e8	+	5.65133e8i	0.530989	+	0.632808i
$964$		0			0
$965$	2.47080e8	−	6.78847e8i	0.274951	−	0.755423i
$966$		0			0
$967$	8.55408e7	−	4.85126e8i	0.0946006	−	0.536506i	−0.900268	−	0.435335i	$-0.856630\pi$
$967$	8.55408e7	−	4.85126e8i	0.0946006	−	0.536506i	0.994869	−	0.101171i	$-0.0322590\pi$
$968$		0			0
$969$	−1.40145e9	+	1.53297e8i	−1.54030	+	0.168486i
$970$		0			0
$971$	−1.48314e9	−	2.61518e8i	−1.62004	−	0.285657i	−0.711259	−	0.702930i	$-0.751874\pi$
$971$	−1.48314e9	−	2.61518e8i	−1.62004	−	0.285657i	−0.908781	+	0.417274i	$0.862986\pi$
$972$		0			0
$973$	−8.40453e8	−	3.05900e8i	−0.912378	−	0.332078i
$974$		0			0
$975$	3.06076e9	−	2.56829e9i	3.30230	−	2.77096i
$976$		0			0
$977$	6.64452e8	+	3.83621e8i	0.712491	+	0.411357i	0.811983	−	0.583681i	$-0.198388\pi$
$977$	6.64452e8	+	3.83621e8i	0.712491	+	0.411357i	−0.0994914	+	0.995038i	$0.531722\pi$
$978$		0			0
$979$	1.36835e8	−	2.41277e7i	0.145831	−	0.0257139i
$980$		0			0
$981$	1.28274e8	−	7.40591e7i	0.135873	−	0.0784462i
$982$		0			0
$983$	−1.10268e8	−	3.02958e8i	−0.116088	−	0.318949i	0.868018	−	0.496533i	$-0.165394\pi$
$983$	−1.10268e8	−	3.02958e8i	−0.116088	−	0.318949i	−0.984106	+	0.177584i	$0.943172\pi$
$984$		0			0
$985$	1.23507e9	+	1.03635e9i	1.29236	+	1.08442i
$986$		0			0
$987$			5.02605e8i			0.522728i
$988$		0			0
$989$	−2.26555e8			−0.234199
$990$		0			0
$991$	−7.19841e8	+	8.57874e8i	−0.739632	+	0.881459i	−0.996379	−	0.0850192i	$-0.972905\pi$
$991$	−7.19841e8	+	8.57874e8i	−0.739632	+	0.881459i	0.256747	+	0.966479i	$0.417349\pi$
$992$		0			0
$993$	−3.56786e8	+	1.29859e8i	−0.364385	+	0.132625i
$994$		0			0
$995$	9.19718e8	+	1.59300e9i	0.933653	+	1.61713i
$996$		0			0
$997$	−1.60135e8	−	9.08170e8i	−0.161585	−	0.916393i	−0.952516	−	0.304488i	$-0.901515\pi$
$997$	−1.60135e8	−	9.08170e8i	−0.161585	−	0.916393i	0.790931	−	0.611905i	$-0.209597\pi$
$998$		0			0
$999$	−5.03253e8	+	8.71660e8i	−0.504766	+	0.874280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.21.10	✓	60
19.10	odd	18	inner	76.7.j.a.29.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.10	✓	60	1.1	even	1	trivial
76.7.j.a.29.10	yes	60	19.10	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)

\(f(q)\)	\(=\)	\(q+(31.0369 - 36.9883i) q^{3} +(186.326 - 67.8172i) q^{5} +(-265.452 - 459.776i) q^{7} +(-278.258 - 1578.08i) q^{9} +O(q^{10})\)	\(q+(31.0369 - 36.9883i) q^{3} +(186.326 - 67.8172i) q^{5} +(-265.452 - 459.776i) q^{7} +(-278.258 - 1578.08i) q^{9} +(-237.096 + 410.663i) q^{11} +(2245.11 + 2675.62i) q^{13} +(3274.54 - 8996.73i) q^{15} +(-739.194 + 4192.18i) q^{17} +(-3811.41 + 5702.55i) q^{19} +(-25245.1 - 4451.40i) q^{21} +(2107.51 + 767.071i) q^{23} +(18148.9 - 15228.7i) q^{25} +(-36522.9 - 21086.5i) q^{27} +(39685.9 - 6997.70i) q^{29} +(-31084.1 + 17946.4i) q^{31} +(7830.99 + 21515.5i) q^{33} +(-80641.4 - 67666.2i) q^{35} -23866.1i q^{37} +168648. q^{39} +(75867.2 - 90415.1i) q^{41} +(-94923.9 + 34549.5i) q^{43} +(-158868. - 275167. i) q^{45} +(-3404.64 - 19308.7i) q^{47} +(-82105.0 + 142210. i) q^{49} +(132119. + 157454. i) q^{51} +(22603.7 - 62103.3i) q^{53} +(-16327.3 + 92596.5i) q^{55} +(92633.5 + 317967. i) q^{57} +(40475.3 + 7136.89i) q^{59} +(29450.2 + 10719.0i) q^{61} +(-651699. + 546840. i) q^{63} +(599776. + 346281. i) q^{65} +(97615.5 - 17212.3i) q^{67} +(93783.2 - 54145.8i) q^{69} +(36325.4 + 99803.3i) q^{71} +(41222.1 + 34589.5i) q^{73} -1.14395e6i q^{75} +251751. q^{77} +(140910. - 167930. i) q^{79} +(-815794. + 296925. i) q^{81} +(291613. + 505088. i) q^{83} +(146571. + 831243. i) q^{85} +(972894. - 1.68510e6i) q^{87} +(-188347. - 224464. i) q^{89} +(634217. - 1.74250e6i) q^{91} +(-300946. + 1.70675e6i) q^{93} +(-323434. + 1.32101e6i) q^{95} +(813524. + 143446. i) q^{97} +(714032. + 259886. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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