LMFDB - Embedded newform 336.7.bh.a.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not 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:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2 x^{7} + 1061 x^{6} + 35442 x^{5} + 1155979 x^{4} + 17325616 x^{3} + 201523590 x^{2} + \cdots + 5192355364 $ x^8 - 2x^7 + 1061x^6 + 35442x^5 + 1155979x^4 + 17325616x^3 + 201523590x^2 + 1200774512*x + 5192355364
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-4.36471 + 7.55990i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.a.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 + 7.79423i) q^{3} +(-167.007 - 96.4218i) q^{5} +(243.806 + 241.263i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 + 7.79423i) q^{3} +(-167.007 - 96.4218i) q^{5} +(243.806 + 241.263i) q^{7} +(121.500 - 210.444i) q^{9} +(-853.820 - 1478.86i) q^{11} +3485.08i q^{13} +3006.13 q^{15} +(-1017.38 + 587.386i) q^{17} +(-5704.28 - 3293.37i) q^{19} +(-5171.83 - 1356.77i) q^{21} +(-1413.35 + 2448.00i) q^{23} +(10781.8 + 18674.7i) q^{25} +3788.00i q^{27} -38077.2 q^{29} +(-7410.22 + 4278.29i) q^{31} +(23053.2 + 13309.7i) q^{33} +(-17454.4 - 63800.9i) q^{35} +(-38962.6 + 67485.2i) q^{37} +(-27163.5 - 47048.5i) q^{39} -8671.70i q^{41} +67638.4 q^{43} +(-40582.8 + 23430.5i) q^{45} +(-65007.2 - 37531.9i) q^{47} +(1233.43 + 117643. i) q^{49} +(9156.44 - 15859.4i) q^{51} +(-52230.5 - 90465.9i) q^{53} +329308. i q^{55} +102677. q^{57} +(109915. - 63459.5i) q^{59} +(-7513.11 - 4337.70i) q^{61} +(80394.8 - 21994.0i) q^{63} +(336037. - 582034. i) q^{65} +(-201844. - 349604. i) q^{67} -44064.0i q^{69} +585872. q^{71} +(380386. - 219616. i) q^{73} +(-291109. - 168072. i) q^{75} +(148628. - 566550. i) q^{77} +(274701. - 475796. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +896743. i q^{83} +226547. q^{85} +(514043. - 296783. i) q^{87} +(-710199. - 410034. i) q^{89} +(-840820. + 849682. i) q^{91} +(66692.0 - 115514. i) q^{93} +(635104. + 1.10003e6i) q^{95} +1.21789e6i q^{97} -414957. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9	$ 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9} - 378 q^{11} + 5292 q^{15} + 852 q^{17} - 3690 q^{19} + 3942 q^{21} - 15600 q^{23} + 3386 q^{25} - 68604 q^{29} - 23028 q^{31} + 10206 q^{33} - 93828 q^{35} + 15914 q^{37} - 25326 q^{39} + 170044 q^{43} - 71442 q^{45} - 102180 q^{47} + 157340 q^{49} - 7668 q^{51} + 196410 q^{53} + 66420 q^{57} + 662550 q^{59} - 23928 q^{61} - 50058 q^{63} + 14892 q^{65} - 774838 q^{67} + 721896 q^{71} - 1219050 q^{73} - 91422 q^{75} + 1584738 q^{77} + 493868 q^{79} - 236196 q^{81} - 1329816 q^{85} + 926154 q^{87} + 604260 q^{89} - 3831690 q^{91} + 207252 q^{93} - 448944 q^{95} - 183708 q^{99}+O(q^{100}) $ 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9 - 378 * q^11 + 5292 * q^15 + 852 * q^17 - 3690 * q^19 + 3942 * q^21 - 15600 * q^23 + 3386 * q^25 - 68604 * q^29 - 23028 * q^31 + 10206 * q^33 - 93828 * q^35 + 15914 * q^37 - 25326 * q^39 + 170044 * q^43 - 71442 * q^45 - 102180 * q^47 + 157340 * q^49 - 7668 * q^51 + 196410 * q^53 + 66420 * q^57 + 662550 * q^59 - 23928 * q^61 - 50058 * q^63 + 14892 * q^65 - 774838 * q^67 + 721896 * q^71 - 1219050 * q^73 - 91422 * q^75 + 1584738 * q^77 + 493868 * q^79 - 236196 * q^81 - 1329816 * q^85 + 926154 * q^87 + 604260 * q^89 - 3831690 * q^91 + 207252 * q^93 - 448944 * q^95 - 183708 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$4$		0			0
$5$	−167.007	−	96.4218i	−1.33606	−	0.771374i	−0.349839	−	0.936810i	$-0.613764\pi$
$5$	−167.007	−	96.4218i	−1.33606	−	0.771374i	−0.986221	+	0.165435i	$0.947097\pi$
$6$		0			0
$7$	243.806	+	241.263i	0.710804	+	0.703390i
$7$	243.806	+	241.263i	0.710804	+	0.703390i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	−853.820	−	1478.86i	−0.641488	−	1.11109i	−0.985101	−	0.171978i	$-0.944984\pi$
$11$	−853.820	−	1478.86i	−0.641488	−	1.11109i	0.343613	−	0.939111i	$-0.388349\pi$
$12$		0			0
$13$			3485.08i			1.58629i	0.609034	+	0.793144i	$0.291557\pi$
$13$			3485.08i			1.58629i	−0.609034	+	0.793144i	$0.708443\pi$
$14$		0			0
$15$	3006.13			0.890706
$16$		0			0
$17$	−1017.38	+	587.386i	−0.207080	+	0.119557i	−0.599953	−	0.800035i	$-0.704814\pi$
$17$	−1017.38	+	587.386i	−0.207080	+	0.119557i	0.392874	+	0.919592i	$0.371481\pi$
$18$		0			0
$19$	−5704.28	−	3293.37i	−0.831648	−	0.480152i	0.0227684	−	0.999741i	$-0.492752\pi$
$19$	−5704.28	−	3293.37i	−0.831648	−	0.480152i	−0.854417	+	0.519588i	$0.826085\pi$
$20$		0			0
$21$	−5171.83	−	1356.77i	−0.558453	−	0.146504i
$22$		0			0
$23$	−1413.35	+	2448.00i	−0.116163	+	0.201200i	−0.918244	−	0.396015i	$-0.870393\pi$
$23$	−1413.35	+	2448.00i	−0.116163	+	0.201200i	0.802081	+	0.597215i	$0.203726\pi$
$24$		0			0
$25$	10781.8	+	18674.7i	0.690037	+	1.19518i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	−38077.2			−1.56125			−0.780623	−	0.625002i	$-0.785098\pi$
$29$	−38077.2			−1.56125			−0.780623	+	0.625002i	$0.785098\pi$
$30$		0			0
$31$	−7410.22	+	4278.29i	−0.248740	+	0.143610i	−0.619187	−	0.785243i	$-0.712538\pi$
$31$	−7410.22	+	4278.29i	−0.248740	+	0.143610i	0.370447	+	0.928854i	$0.379205\pi$
$32$		0			0
$33$	23053.2	+	13309.7i	0.641488	+	0.370363i
$34$		0			0
$35$	−17454.4	−	63800.9i	−0.407099	−	1.48807i
$36$		0			0
$37$	−38962.6	+	67485.2i	−0.769206	+	1.33230i	0.168788	+	0.985652i	$0.446015\pi$
$37$	−38962.6	+	67485.2i	−0.769206	+	1.33230i	−0.937994	+	0.346652i	$0.887319\pi$
$38$		0			0
$39$	−27163.5	−	47048.5i	−0.457922	−	0.793144i
$40$		0			0
$41$		−	8671.70i		−	0.125821i	−0.998019	−	0.0629104i	$-0.979962\pi$
$41$		−	8671.70i		−	0.125821i	0.998019	−	0.0629104i	$-0.0200383\pi$
$42$		0			0
$43$	67638.4			0.850723			0.425362	−	0.905024i	$-0.360147\pi$
$43$	67638.4			0.850723			0.425362	+	0.905024i	$0.360147\pi$
$44$		0			0
$45$	−40582.8	+	23430.5i	−0.445353	+	0.257125i
$46$		0			0
$47$	−65007.2	−	37531.9i	−0.626135	−	0.361499i	0.153119	−	0.988208i	$-0.451068\pi$
$47$	−65007.2	−	37531.9i	−0.626135	−	0.361499i	−0.779254	+	0.626709i	$0.784402\pi$
$48$		0			0
$49$	1233.43	+	117643.i	0.0104840	+	0.999945i
$50$		0			0
$51$	9156.44	−	15859.4i	0.0690265	−	0.119557i
$52$		0			0
$53$	−52230.5	−	90465.9i	−0.350830	−	0.607655i	0.635565	−	0.772047i	$-0.280767\pi$
$53$	−52230.5	−	90465.9i	−0.350830	−	0.607655i	−0.986395	+	0.164392i	$0.947434\pi$
$54$		0			0
$55$			329308.i			1.97931i
$56$		0			0
$57$	102677.			0.554432
$58$		0			0
$59$	109915.	−	63459.5i	0.535181	−	0.308987i	−0.207942	−	0.978141i	$-0.566677\pi$
$59$	109915.	−	63459.5i	0.535181	−	0.308987i	0.743124	+	0.669154i	$0.233343\pi$
$60$		0			0
$61$	−7513.11	−	4337.70i	−0.0331002	−	0.0191104i	0.483359	−	0.875422i	$-0.339417\pi$
$61$	−7513.11	−	4337.70i	−0.0331002	−	0.0191104i	−0.516459	+	0.856312i	$0.672750\pi$
$62$		0			0
$63$	80394.8	−	21994.0i	0.321519	−	0.0879596i
$64$		0			0
$65$	336037.	−	582034.i	1.22362	−	2.11938i
$66$		0			0
$67$	−201844.	−	349604.i	−0.671105	−	1.16239i	−0.977591	−	0.210513i	$-0.932486\pi$
$67$	−201844.	−	349604.i	−0.671105	−	1.16239i	0.306486	−	0.951875i	$-0.400847\pi$
$68$		0			0
$69$		−	44064.0i		−	0.134133i
$70$		0			0
$71$	585872.			1.63692			0.818461	−	0.574562i	$-0.194828\pi$
$71$	585872.			1.63692			0.818461	+	0.574562i	$0.194828\pi$
$72$		0			0
$73$	380386.	−	219616.i	0.977814	−	0.564541i	0.0762043	−	0.997092i	$-0.475720\pi$
$73$	380386.	−	219616.i	0.977814	−	0.564541i	0.901609	+	0.432551i	$0.142387\pi$
$74$		0			0
$75$	−291109.	−	168072.i	−0.690037	−	0.398393i
$76$		0			0
$77$	148628.	−	566550.i	0.325558	−	1.24098i
$78$		0			0
$79$	274701.	−	475796.i	0.557159	−	0.965028i	−0.440573	−	0.897717i	$-0.645225\pi$
$79$	274701.	−	475796.i	0.557159	−	0.965028i	0.997732	−	0.0673110i	$-0.0214420\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			896743.i			1.56832i	0.620561	+	0.784158i	$0.286905\pi$
$83$			896743.i			1.56832i	−0.620561	+	0.784158i	$0.713095\pi$
$84$		0			0
$85$	226547.			0.368894
$86$		0			0
$87$	514043.	−	296783.i	0.780623	−	0.450693i
$88$		0			0
$89$	−710199.	−	410034.i	−1.00742	−	0.581634i	−0.0969841	−	0.995286i	$-0.530920\pi$
$89$	−710199.	−	410034.i	−1.00742	−	0.581634i	−0.910435	+	0.413652i	$0.864253\pi$
$90$		0			0
$91$	−840820.	+	849682.i	−1.11578	+	1.12754i
$92$		0			0
$93$	66692.0	−	115514.i	0.0829134	−	0.143610i
$94$		0			0
$95$	635104.	+	1.10003e6i	0.740755	+	1.28302i
$96$		0			0
$97$			1.21789e6i			1.33442i	0.744869	+	0.667211i	$0.232512\pi$
$97$			1.21789e6i			1.33442i	−0.744869	+	0.667211i	$0.767488\pi$
$98$		0			0
$99$	−414957.			−0.427659
$100$		0			0
$101$	−233956.	+	135075.i	−0.227076	+	0.131102i	−0.609222	−	0.793000i	$-0.708518\pi$
$101$	−233956.	+	135075.i	−0.227076	+	0.131102i	0.382147	+	0.924102i	$0.375185\pi$
$102$		0			0
$103$	824434.	+	475987.i	0.754474	+	0.435596i	0.827308	−	0.561748i	$-0.189871\pi$
$103$	824434.	+	475987.i	0.754474	+	0.435596i	−0.0728340	+	0.997344i	$0.523204\pi$
$104$		0			0
$105$	732913.	+	725269.i	0.633118	+	0.626514i
$106$		0			0
$107$	571081.	−	989141.i	0.466172	−	0.807434i	−0.533081	−	0.846064i	$-0.678966\pi$
$107$	571081.	−	989141.i	0.466172	−	0.807434i	0.999254	+	0.0386301i	$0.0122994\pi$
$108$		0			0
$109$	494125.	+	855850.i	0.381555	+	0.660873i	0.991285	−	0.131736i	$-0.0420553\pi$
$109$	494125.	+	855850.i	0.381555	+	0.660873i	−0.609729	+	0.792610i	$0.708722\pi$
$110$		0			0
$111$		−	1.21473e6i		−	0.888203i
$112$		0			0
$113$	2.66635e6			1.84792			0.923958	−	0.382493i	$-0.124934\pi$
$113$	2.66635e6			1.84792			0.923958	+	0.382493i	$0.124934\pi$
$114$		0			0
$115$	472082.	−	272556.i	0.310401	−	0.179210i
$116$		0			0
$117$	733414.	+	423437.i	0.457922	+	0.264381i
$118$		0			0
$119$	−389758.	−	102249.i	−0.231288	−	0.0606759i
$120$		0			0
$121$	−572238.	+	991146.i	−0.323014	+	0.559476i
$122$		0			0
$123$	67589.2	+	117068.i	0.0363214	+	0.0629104i
$124$		0			0
$125$		−	1.14523e6i		−	0.586359i
$126$		0			0
$127$	3.02462e6			1.47659			0.738294	−	0.674479i	$-0.235632\pi$
$127$	3.02462e6			1.47659			0.738294	+	0.674479i	$0.235632\pi$
$128$		0			0
$129$	−913119.	+	527189.i	−0.425362	+	0.245583i
$130$		0			0
$131$	−437621.	−	252661.i	−0.194664	−	0.112389i	0.399500	−	0.916733i	$-0.369184\pi$
$131$	−437621.	−	252661.i	−0.194664	−	0.112389i	−0.594164	+	0.804344i	$0.702517\pi$
$132$		0			0
$133$	−596168.	−	2.17917e6i	−0.253404	−	0.926267i
$134$		0			0
$135$	365245.	−	632623.i	0.148451	−	0.257125i
$136$		0			0
$137$	−1.82864e6	−	3.16729e6i	−0.711158	−	1.23176i	−0.964423	−	0.264365i	$-0.914838\pi$
$137$	−1.82864e6	−	3.16729e6i	−0.711158	−	1.23176i	0.253265	−	0.967397i	$-0.418496\pi$
$138$		0			0
$139$		−	3.58465e6i		−	1.33476i	−0.744719	−	0.667378i	$-0.767417\pi$
$139$		−	3.58465e6i		−	1.33476i	0.744719	−	0.667378i	$-0.232583\pi$
$140$		0			0
$141$	1.17013e6			0.417423
$142$		0			0
$143$	5.15394e6	−	2.97563e6i	1.76251	−	1.01759i
$144$		0			0
$145$	6.35918e6	+	3.67148e6i	2.08592	+	1.20431i
$146$		0			0
$147$	−933584.	−	1.57856e6i	−0.293901	−	0.496946i
$148$		0			0
$149$	−813473.	+	1.40898e6i	−0.245915	+	0.425936i	−0.962388	−	0.271678i	$-0.912422\pi$
$149$	−813473.	+	1.40898e6i	−0.245915	+	0.425936i	0.716474	+	0.697614i	$0.245755\pi$
$150$		0			0
$151$	−2.32898e6	−	4.03392e6i	−0.676450	−	1.17165i	−0.976043	−	0.217578i	$-0.930184\pi$
$151$	−2.32898e6	−	4.03392e6i	−0.676450	−	1.17165i	0.299593	−	0.954067i	$-0.403149\pi$
$152$		0			0
$153$			285469.i			0.0797050i
$154$		0			0
$155$	1.65008e6			0.443109
$156$		0			0
$157$	5.87600e6	−	3.39251e6i	1.51839	−	0.876641i	0.518622	−	0.855004i	$-0.326445\pi$
$157$	5.87600e6	−	3.39251e6i	1.51839	−	0.876641i	0.999766	−	0.0216377i	$-0.00688802\pi$
$158$		0			0
$159$	1.41022e6	+	814193.i	0.350830	+	0.202552i
$160$		0			0
$161$	−935196.	+	255847.i	−0.224091	+	0.0613059i
$162$		0			0
$163$	2.61922e6	−	4.53662e6i	0.604796	−	1.04754i	−0.387287	−	0.921959i	$-0.626588\pi$
$163$	2.61922e6	−	4.53662e6i	0.604796	−	1.04754i	0.992084	−	0.125579i	$-0.0400788\pi$
$164$		0			0
$165$	−2.56670e6	−	4.44565e6i	−0.571377	−	0.989655i
$166$		0			0
$167$			5.79131e6i			1.24345i	0.783236	+	0.621724i	$0.213567\pi$
$167$			5.79131e6i			1.24345i	−0.783236	+	0.621724i	$0.786433\pi$
$168$		0			0
$169$	−7.31895e6			−1.51631
$170$		0			0
$171$	−1.38614e6	+	800288.i	−0.277216	+	0.160051i
$172$		0			0
$173$	8.24140e6	+	4.75817e6i	1.59170	+	0.918971i	0.993015	+	0.117991i	$0.0376453\pi$
$173$	8.24140e6	+	4.75817e6i	1.59170	+	0.918971i	0.598690	+	0.800981i	$0.295688\pi$
$174$		0			0
$175$	−1.87684e6	+	7.15425e6i	−0.350197	+	1.33490i
$176$		0			0
$177$	−989235.	+	1.71341e6i	−0.178394	+	0.308987i
$178$		0			0
$179$	2.55285e6	+	4.42166e6i	0.445108	+	0.770950i	0.998060	−	0.0622636i	$-0.0198320\pi$
$179$	2.55285e6	+	4.42166e6i	0.445108	+	0.770950i	−0.552952	+	0.833213i	$0.686499\pi$
$180$		0			0
$181$		−	8.68278e6i		−	1.46428i	−0.681156	−	0.732138i	$-0.738522\pi$
$181$		−	8.68278e6i		−	1.46428i	0.681156	−	0.732138i	$-0.261478\pi$
$182$		0			0
$183$	135236.			0.0220668
$184$		0			0
$185$	1.30141e7	−	7.51369e6i	2.05541	−	1.18669i
$186$		0			0
$187$	1.73732e6	+	1.00304e6i	0.265678	+	0.153389i
$188$		0			0
$189$	−913903.	+	923535.i	−0.135368	+	0.136794i
$190$		0			0
$191$	960831.	−	1.66421e6i	0.137894	−	0.238840i	−0.788805	−	0.614644i	$-0.789300\pi$
$191$	960831.	−	1.66421e6i	0.137894	−	0.238840i	0.926699	+	0.375803i	$0.122633\pi$
$192$		0			0
$193$	−6.18894e6	−	1.07196e7i	−0.860883	−	1.49109i	−0.871077	−	0.491146i	$-0.836578\pi$
$193$	−6.18894e6	−	1.07196e7i	−0.860883	−	1.49109i	0.0101940	−	0.999948i	$-0.496755\pi$
$194$		0			0
$195$			1.04766e7i			1.41292i
$196$		0			0
$197$	−1.01729e7			−1.33059			−0.665296	−	0.746580i	$-0.731695\pi$
$197$	−1.01729e7			−1.33059			−0.665296	+	0.746580i	$0.731695\pi$
$198$		0			0
$199$	−2.00209e6	+	1.15590e6i	−0.254053	+	0.146677i	−0.621618	−	0.783320i	$-0.713525\pi$
$199$	−2.00209e6	+	1.15590e6i	−0.254053	+	0.146677i	0.367566	+	0.929997i	$0.380191\pi$
$200$		0			0
$201$	5.44978e6	+	3.14643e6i	0.671105	+	0.387463i
$202$		0			0
$203$	−9.28344e6	−	9.18662e6i	−1.10974	−	1.09817i
$204$		0			0
$205$	−836141.	+	1.44824e6i	−0.0970550	+	0.168104i
$206$		0			0
$207$	343445.	+	594864.i	0.0387210	+	0.0670667i
$208$		0			0
$209$			1.12478e7i			1.23205i
$210$		0			0
$211$	−410945.			−0.0437458			−0.0218729	−	0.999761i	$-0.506963\pi$
$211$	−410945.			−0.0437458			−0.0218729	+	0.999761i	$0.506963\pi$
$212$		0			0
$213$	−7.90928e6	+	4.56642e6i	−0.818461	+	0.472539i
$214$		0			0
$215$	−1.12961e7	−	6.52182e6i	−1.13662	−	0.656226i
$216$		0			0
$217$	−2.83885e6	−	744739.i	−0.277820	−	0.0728828i
$218$		0			0
$219$	−3.42348e6	+	5.92963e6i	−0.325938	+	0.564541i
$220$		0			0
$221$	−2.04708e6	−	3.54565e6i	−0.189653	−	0.328488i
$222$		0			0
$223$			1.06568e7i			0.960979i	0.877001	+	0.480489i	$0.159541\pi$
$223$			1.06568e7i			0.960979i	−0.877001	+	0.480489i	$0.840459\pi$
$224$		0			0
$225$	5.23997e6			0.460025
$226$		0			0
$227$	1.41111e7	−	8.14705e6i	1.20638	−	0.696503i	0.244412	−	0.969672i	$-0.421405\pi$
$227$	1.41111e7	−	8.14705e6i	1.20638	−	0.696503i	0.961966	+	0.273169i	$0.0880718\pi$
$228$		0			0
$229$	7.57526e6	+	4.37358e6i	0.630799	+	0.364192i	0.781061	−	0.624454i	$-0.214679\pi$
$229$	7.57526e6	+	4.37358e6i	0.630799	+	0.364192i	−0.150262	+	0.988646i	$0.548012\pi$
$230$		0			0
$231$	2.40934e6	+	8.80686e6i	0.195462	+	0.714472i
$232$		0			0
$233$	−6.80919e6	+	1.17939e7i	−0.538304	+	0.932369i	0.460692	+	0.887560i	$0.347601\pi$
$233$	−6.80919e6	+	1.17939e7i	−0.538304	+	0.932369i	−0.998996	+	0.0448093i	$0.985732\pi$
$234$		0			0
$235$	7.23779e6	+	1.25362e7i	0.557702	+	0.965969i
$236$		0			0
$237$			8.56433e6i			0.643352i
$238$		0			0
$239$	−699203.			−0.0512165			−0.0256082	−	0.999672i	$-0.508152\pi$
$239$	−699203.			−0.0512165			−0.0256082	+	0.999672i	$0.508152\pi$
$240$		0			0
$241$	−9.35660e6	+	5.40204e6i	−0.668447	+	0.385928i	−0.795488	−	0.605969i	$-0.792785\pi$
$241$	−9.35660e6	+	5.40204e6i	−0.668447	+	0.385928i	0.127041	+	0.991897i	$0.459452\pi$
$242$		0			0
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$		0			0
$245$	1.11373e7	−	1.97661e7i	0.757325	−	1.34407i
$246$		0			0
$247$	1.14776e7	−	1.98798e7i	0.761660	−	1.31923i
$248$		0			0
$249$	−6.98942e6	−	1.21060e7i	−0.452734	−	0.784158i
$250$		0			0
$251$		−	1.06094e7i		−	0.670915i	−0.942055	−	0.335458i	$-0.891109\pi$
$251$		−	1.06094e7i		−	0.670915i	0.942055	−	0.335458i	$-0.108891\pi$
$252$		0			0
$253$	4.82700e6			0.298069
$254$		0			0
$255$	−3.05839e6	+	1.76576e6i	−0.184447	+	0.106491i
$256$		0			0
$257$	1.98098e7	+	1.14372e7i	1.16703	+	0.673784i	0.952978	−	0.303038i	$-0.0980009\pi$
$257$	1.98098e7	+	1.14372e7i	1.16703	+	0.673784i	0.214051	+	0.976823i	$0.431334\pi$
$258$		0			0
$259$	−2.57810e7	+	7.05305e6i	−1.48388	+	0.405955i
$260$		0			0
$261$	−4.62638e6	+	8.01313e6i	−0.260208	+	0.450693i
$262$		0			0
$263$	−1.05181e7	−	1.82179e7i	−0.578188	−	1.00145i	−0.995687	−	0.0927742i	$-0.970427\pi$
$263$	−1.05181e7	−	1.82179e7i	−0.578188	−	1.00145i	0.417499	−	0.908677i	$-0.362907\pi$
$264$		0			0
$265$			2.01446e7i			1.08248i
$266$		0			0
$267$	1.27836e7			0.671613
$268$		0			0
$269$	−1.12974e7	+	6.52254e6i	−0.580391	+	0.335089i	−0.761289	−	0.648413i	$-0.775433\pi$
$269$	−1.12974e7	+	6.52254e6i	−0.580391	+	0.335089i	0.180898	+	0.983502i	$0.442100\pi$
$270$		0			0
$271$	−1.52485e6	−	880370.i	−0.0766157	−	0.0442341i	0.461203	−	0.887295i	$-0.347418\pi$
$271$	−1.52485e6	−	880370.i	−0.0766157	−	0.0442341i	−0.537818	+	0.843061i	$0.680751\pi$
$272$		0			0
$273$	4.72845e6	−	1.80242e7i	0.232397	−	0.885868i
$274$		0			0
$275$	1.84115e7	−	3.18896e7i	0.885301	−	1.53339i
$276$		0			0
$277$	−1.83722e6	−	3.18216e6i	−0.0864415	−	0.149721i	0.819563	−	0.572989i	$-0.194216\pi$
$277$	−1.83722e6	−	3.18216e6i	−0.0864415	−	0.149721i	−0.906005	+	0.423268i	$0.860883\pi$
$278$		0			0
$279$			2.07925e6i			0.0957402i
$280$		0			0
$281$	−3.50285e6			−0.157871			−0.0789356	−	0.996880i	$-0.525152\pi$
$281$	−3.50285e6			−0.157871			−0.0789356	+	0.996880i	$0.525152\pi$
$282$		0			0
$283$	3.95619e6	−	2.28411e6i	0.174549	−	0.100776i	−0.410180	−	0.912005i	$-0.634534\pi$
$283$	3.95619e6	−	2.28411e6i	0.174549	−	0.100776i	0.584729	+	0.811229i	$0.301201\pi$
$284$		0			0
$285$	−1.71478e7	−	9.90030e6i	−0.740755	−	0.427675i
$286$		0			0
$287$	2.09216e6	−	2.11421e6i	0.0885012	−	0.0894340i
$288$		0			0
$289$	−1.13787e7	+	1.97086e7i	−0.471412	+	0.816510i
$290$		0			0
$291$	−9.49252e6	−	1.64415e7i	−0.385215	−	0.667211i
$292$		0			0
$293$		−	1.09224e7i		−	0.434224i	−0.976147	−	0.217112i	$-0.930336\pi$
$293$		−	1.09224e7i		−	0.434224i	0.976147	−	0.217112i	$-0.0696636\pi$
$294$		0			0
$295$	−2.44755e7			−0.953379
$296$		0			0
$297$	5.60192e6	−	3.23427e6i	0.213829	−	0.123454i
$298$		0			0
$299$	−8.53147e6	−	4.92565e6i	−0.319162	−	0.184268i
$300$		0			0
$301$	1.64906e7	+	1.63186e7i	0.604697	+	0.598390i
$302$		0			0
$303$	2.10561e6	−	3.64702e6i	0.0756918	−	0.131102i
$304$		0			0
$305$	836497.	+	1.44885e6i	0.0294825	+	0.0510652i
$306$		0			0
$307$			2.44425e7i			0.844754i	0.906420	+	0.422377i	$0.138804\pi$
$307$			2.44425e7i			0.844754i	−0.906420	+	0.422377i	$0.861196\pi$
$308$		0			0
$309$	−1.48398e7			−0.502983
$310$		0			0
$311$	−1.20648e7	+	6.96560e6i	−0.401086	+	0.231567i	−0.686953	−	0.726702i	$-0.741052\pi$
$311$	−1.20648e7	+	6.96560e6i	−0.401086	+	0.231567i	0.285866	+	0.958270i	$0.407719\pi$
$312$		0			0
$313$	−2.17154e7	−	1.25374e7i	−0.708167	−	0.408860i	0.102215	−	0.994762i	$-0.467407\pi$
$313$	−2.17154e7	−	1.25374e7i	−0.708167	−	0.408860i	−0.810382	+	0.585902i	$0.800740\pi$
$314$		0			0
$315$	−1.55472e7	−	4.07864e6i	−0.497418	−	0.130492i
$316$		0			0
$317$	6.12809e6	−	1.06142e7i	0.192375	−	0.333203i	−0.753662	−	0.657262i	$-0.771714\pi$
$317$	6.12809e6	−	1.06142e7i	0.192375	−	0.333203i	0.946037	+	0.324060i	$0.105048\pi$
$318$		0			0
$319$	3.25111e7	+	5.63109e7i	1.00152	+	1.73468i
$320$		0			0
$321$			1.78045e7i			0.538289i
$322$		0			0
$323$	7.73790e6			0.229623
$324$		0			0
$325$	−6.50827e7	+	3.75755e7i	−1.89590	+	1.09460i
$326$		0			0
$327$	−1.33414e7	−	7.70265e6i	−0.381555	−	0.220291i
$328$		0			0
$329$	−6.79406e6	−	2.48343e7i	−0.190784	−	0.697372i
$330$		0			0
$331$	−2.36337e7	+	4.09348e7i	−0.651701	+	1.12878i	0.331009	+	0.943628i	$0.392611\pi$
$331$	−2.36337e7	+	4.09348e7i	−0.651701	+	1.12878i	−0.982710	+	0.185152i	$0.940722\pi$
$332$		0			0
$333$	9.46791e6	+	1.63989e7i	0.256402	+	0.444101i
$334$		0			0
$335$			7.78485e7i			2.07069i
$336$		0			0
$337$	−2.40547e7			−0.628508			−0.314254	−	0.949339i	$-0.601754\pi$
$337$	−2.40547e7			−0.628508			−0.314254	+	0.949339i	$0.601754\pi$
$338$		0			0
$339$	−3.59958e7	+	2.07822e7i	−0.923958	+	0.533448i
$340$		0			0
$341$	1.26540e7	+	7.30579e6i	0.319128	+	0.184249i
$342$		0			0
$343$	−2.80821e7	+	2.89795e7i	−0.695900	+	0.718139i
$344$		0			0
$345$	−4.24873e6	+	7.35902e6i	−0.103467	+	0.179210i
$346$		0			0
$347$	1.02195e7	+	1.77006e7i	0.244591	+	0.423643i	0.962016	−	0.272992i	$-0.0880131\pi$
$347$	1.02195e7	+	1.77006e7i	0.244591	+	0.423643i	−0.717426	+	0.696635i	$0.754680\pi$
$348$		0			0
$349$			7.35149e6i			0.172941i	0.996254	+	0.0864707i	$0.0275589\pi$
$349$			7.35149e6i			0.172941i	−0.996254	+	0.0864707i	$0.972441\pi$
$350$		0			0
$351$	−1.32015e7			−0.305281
$352$		0			0
$353$	2.95693e7	−	1.70718e7i	0.672228	−	0.388111i	−0.124692	−	0.992195i	$-0.539794\pi$
$353$	2.95693e7	−	1.70718e7i	0.672228	−	0.388111i	0.796920	+	0.604084i	$0.206461\pi$
$354$		0			0
$355$	−9.78451e7	−	5.64909e7i	−2.18703	−	1.26268i
$356$		0			0
$357$	6.05868e6	−	1.65751e6i	0.133160	−	0.0364293i
$358$		0			0
$359$	779253.	−	1.34971e6i	0.0168421	−	0.0291713i	−0.857482	−	0.514515i	$-0.827972\pi$
$359$	779253.	−	1.34971e6i	0.0168421	−	0.0291713i	0.874324	+	0.485343i	$0.161305\pi$
$360$		0			0
$361$	−1.83043e6	−	3.17041e6i	−0.0389074	−	0.0673896i
$362$		0			0
$363$		−	1.78406e7i		−	0.372984i
$364$		0			0
$365$	−8.47031e7			−1.74189
$366$		0			0
$367$	1.63480e7	−	9.43852e6i	0.330724	−	0.190944i	−0.325438	−	0.945563i	$-0.605512\pi$
$367$	1.63480e7	−	9.43852e6i	0.330724	−	0.190944i	0.656163	+	0.754619i	$0.272178\pi$
$368$		0			0
$369$	−1.82491e6	−	1.05361e6i	−0.0363214	−	0.0209701i
$370$		0			0
$371$	9.09197e6	−	3.46574e7i	0.178048	−	0.678694i
$372$		0			0
$373$	4.54135e7	−	7.86585e7i	0.875102	−	1.51572i	0.0184477	−	0.999830i	$-0.494128\pi$
$373$	4.54135e7	−	7.86585e7i	0.875102	−	1.51572i	0.856654	−	0.515891i	$-0.172539\pi$
$374$		0			0
$375$	8.92620e6	+	1.54606e7i	0.169267	+	0.293179i
$376$		0			0
$377$		−	1.32702e8i		−	2.47659i
$378$		0			0
$379$	−4.69734e7			−0.862849			−0.431425	−	0.902149i	$-0.641989\pi$
$379$	−4.69734e7			−0.862849			−0.431425	+	0.902149i	$0.641989\pi$
$380$		0			0
$381$	−4.08324e7	+	2.35746e7i	−0.738294	+	0.426254i
$382$		0			0
$383$	4.08312e7	+	2.35739e7i	0.726767	+	0.419599i	0.817238	−	0.576300i	$-0.195504\pi$
$383$	4.08312e7	+	2.35739e7i	0.726767	+	0.419599i	−0.0904710	+	0.995899i	$0.528837\pi$
$384$		0			0
$385$	−7.94497e7	+	8.02871e7i	−1.39223	+	1.40690i
$386$		0			0
$387$	8.21807e6	−	1.42341e7i	0.141787	−	0.245583i
$388$		0			0
$389$	−5.72685e6	−	9.91920e6i	−0.0972898	−	0.168511i	0.813272	−	0.581883i	$-0.197684\pi$
$389$	−5.72685e6	−	9.91920e6i	−0.0972898	−	0.168511i	−0.910562	+	0.413373i	$0.864351\pi$
$390$		0			0
$391$		−	3.32074e6i		−	0.0555526i
$392$		0			0
$393$	7.87719e6			0.129776
$394$		0			0
$395$	−9.17543e7	+	5.29744e7i	−1.48880	+	0.859557i
$396$		0			0
$397$	5.31670e7	+	3.06960e7i	0.849710	+	0.490580i	0.860553	−	0.509361i	$-0.170118\pi$
$397$	5.31670e7	+	3.06960e7i	0.849710	+	0.490580i	−0.0108429	+	0.999941i	$0.503451\pi$
$398$		0			0
$399$	2.50332e7	+	2.47721e7i	0.394092	+	0.389982i
$400$		0			0
$401$	1.99922e7	−	3.46275e7i	0.310047	−	0.537018i	−0.668325	−	0.743869i	$-0.732988\pi$
$401$	1.99922e7	−	3.46275e7i	0.310047	−	0.537018i	0.978372	+	0.206852i	$0.0663218\pi$
$402$		0			0
$403$	−1.49102e7	−	2.58252e7i	−0.227807	−	0.394574i
$404$		0			0
$405$			1.13872e7i			0.171417i
$406$		0			0
$407$	1.33068e8			1.97375
$408$		0			0
$409$	2.08460e7	−	1.20355e7i	0.304686	−	0.175911i	−0.339860	−	0.940476i	$-0.610380\pi$
$409$	2.08460e7	−	1.20355e7i	0.304686	−	0.175911i	0.644546	+	0.764565i	$0.277046\pi$
$410$		0			0
$411$	4.93732e7	+	2.85057e7i	0.711158	+	0.410587i
$412$		0			0
$413$	4.21083e7	+	1.10466e7i	0.597747	+	0.156812i
$414$		0			0
$415$	8.64656e7	−	1.49763e8i	1.20976	−	2.09536i
$416$		0			0
$417$	2.79395e7	+	4.83927e7i	0.385311	+	0.667378i
$418$		0			0
$419$		−	1.27232e8i		−	1.72963i	−0.502088	−	0.864817i	$-0.667435\pi$
$419$		−	1.27232e8i		−	1.72963i	0.502088	−	0.864817i	$-0.332565\pi$
$420$		0			0
$421$	2.39926e7			0.321537			0.160769	−	0.986992i	$-0.448603\pi$
$421$	2.39926e7			0.321537			0.160769	+	0.986992i	$0.448603\pi$
$422$		0			0
$423$	−1.57967e7	+	9.12026e6i	−0.208712	+	0.120500i
$424$		0			0
$425$	−2.19385e7	−	1.26662e7i	−0.285785	−	0.164998i
$426$		0			0
$427$	−785214.	−	2.87019e6i	−0.0100857	−	0.0368661i
$428$		0			0
$429$	−4.63855e7	+	8.03420e7i	−0.587503	+	1.01759i
$430$		0			0
$431$	−2.23040e7	−	3.86317e7i	−0.278581	−	0.482516i	0.692451	−	0.721465i	$-0.256531\pi$
$431$	−2.23040e7	−	3.86317e7i	−0.278581	−	0.482516i	−0.971032	+	0.238948i	$0.923197\pi$
$432$		0			0
$433$			7.71008e7i			0.949719i	0.880062	+	0.474860i	$0.157501\pi$
$433$			7.71008e7i			0.949719i	−0.880062	+	0.474860i	$0.842499\pi$
$434$		0			0
$435$	−1.14465e8			−1.39061
$436$		0			0
$437$	1.61243e7	−	9.30938e6i	0.193213	−	0.111552i
$438$		0			0
$439$	1.43210e8	+	8.26821e7i	1.69269	+	0.977278i	0.952329	+	0.305073i	$0.0986810\pi$
$439$	1.43210e8	+	8.26821e7i	1.69269	+	0.977278i	0.740366	+	0.672204i	$0.234652\pi$
$440$		0			0
$441$	2.49070e7	+	1.40340e7i	0.290407	+	0.163631i
$442$		0			0
$443$	−1.17857e7	+	2.04134e7i	−0.135564	+	0.234804i	−0.925813	−	0.377983i	$-0.876618\pi$
$443$	−1.17857e7	+	2.04134e7i	−0.135564	+	0.234804i	0.790249	+	0.612786i	$0.209951\pi$
$444$		0			0
$445$	7.90724e7	+	1.36957e8i	0.897315	+	1.55419i
$446$		0			0
$447$		−	2.53616e7i		−	0.283958i
$448$		0			0
$449$	6.19349e7			0.684221			0.342110	−	0.939660i	$-0.388858\pi$
$449$	6.19349e7			0.684221			0.342110	+	0.939660i	$0.388858\pi$
$450$		0			0
$451$	−1.28242e7	+	7.40408e6i	−0.139798	+	0.0807126i
$452$		0			0
$453$	6.28825e7	+	3.63053e7i	0.676450	+	0.390548i
$454$		0			0
$455$	2.22351e8	−	6.08298e7i	2.36050	−	0.645776i
$456$		0			0
$457$	2.44138e7	−	4.22860e7i	0.255792	−	0.443045i	−0.709318	−	0.704888i	$-0.750997\pi$
$457$	2.44138e7	−	4.22860e7i	0.255792	−	0.443045i	0.965110	+	0.261843i	$0.0843304\pi$
$458$		0			0
$459$	−2.22501e6	−	3.85384e6i	−0.0230088	−	0.0398525i
$460$		0			0
$461$			3.55794e7i			0.363158i	0.983376	+	0.181579i	$0.0581208\pi$
$461$			3.55794e7i			0.363158i	−0.983376	+	0.181579i	$0.941879\pi$
$462$		0			0
$463$	−1.28691e8			−1.29660			−0.648300	−	0.761385i	$-0.724520\pi$
$463$	−1.28691e8			−1.29660			−0.648300	+	0.761385i	$0.724520\pi$
$464$		0			0
$465$	−2.22761e7	+	1.28611e7i	−0.221555	+	0.127915i
$466$		0			0
$467$	−4.65261e7	−	2.68618e7i	−0.456821	−	0.263746i	0.253886	−	0.967234i	$-0.418291\pi$
$467$	−4.65261e7	−	2.68618e7i	−0.456821	−	0.263746i	−0.710707	+	0.703489i	$0.751625\pi$
$468$		0			0
$469$	3.51357e7	−	1.33933e8i	0.340589	−	1.29828i
$470$		0			0
$471$	−5.28840e7	+	9.15977e7i	−0.506129	+	0.876641i
$472$		0			0
$473$	−5.77511e7	−	1.00028e8i	−0.545729	−	0.945230i
$474$		0			0
$475$		−	1.42034e8i		−	1.32529i
$476$		0			0
$477$	−2.53840e7			−0.233887
$478$		0			0
$479$	1.15977e8	−	6.69595e7i	1.05528	−	0.609264i	0.131154	−	0.991362i	$-0.458132\pi$
$479$	1.15977e8	−	6.69595e7i	1.05528	−	0.609264i	0.924122	+	0.382098i	$0.124798\pi$
$480$		0			0
$481$	−2.35191e8	−	1.35788e8i	−2.11342	−	1.22018i
$482$		0			0
$483$	1.06310e7	−	1.07431e7i	0.0943482	−	0.0953425i
$484$		0			0
$485$	1.17431e8	−	2.03397e8i	1.02934	−	1.78287i
$486$		0			0
$487$	8.24788e7	+	1.42858e8i	0.714094	+	1.23685i	0.963308	+	0.268399i	$0.0864946\pi$
$487$	8.24788e7	+	1.42858e8i	0.714094	+	1.23685i	−0.249214	+	0.968449i	$0.580172\pi$
$488$		0			0
$489$			8.16592e7i			0.698359i
$490$		0			0
$491$	−4.96496e7			−0.419441			−0.209721	−	0.977761i	$-0.567255\pi$
$491$	−4.96496e7			−0.419441			−0.209721	+	0.977761i	$0.567255\pi$
$492$		0			0
$493$	3.87391e7	−	2.23660e7i	0.323302	−	0.186659i
$494$		0			0
$495$	6.93009e7	+	4.00109e7i	0.571377	+	0.329885i
$496$		0			0
$497$	1.42839e8	+	1.41349e8i	1.16353	+	1.15140i
$498$		0			0
$499$	1.63842e7	−	2.83782e7i	0.131863	−	0.228393i	−0.792532	−	0.609831i	$-0.791237\pi$
$499$	1.63842e7	−	2.83782e7i	0.131863	−	0.228393i	0.924395	+	0.381437i	$0.124571\pi$
$500$		0			0
$501$	−4.51388e7	−	7.81827e7i	−0.358953	−	0.621724i
$502$		0			0
$503$			4.65312e7i			0.365629i	0.983147	+	0.182814i	$0.0585207\pi$
$503$			4.65312e7i			0.365629i	−0.983147	+	0.182814i	$0.941479\pi$
$504$		0			0
$505$	5.20966e7			0.404515
$506$		0			0
$507$	9.88058e7	−	5.70456e7i	0.758156	−	0.437722i
$508$		0			0
$509$	1.74298e8	+	1.00631e8i	1.32172	+	0.763093i	0.984002	−	0.178157i	$-0.0570134\pi$
$509$	1.74298e8	+	1.00631e8i	1.32172	+	0.763093i	0.337713	+	0.941249i	$0.390347\pi$
$510$		0			0
$511$	1.45725e8	+	3.82294e7i	1.09213	+	0.286507i
$512$		0			0
$513$	1.24753e7	−	2.16078e7i	0.0924054	−	0.160051i
$514$		0			0
$515$	−9.17911e7	−	1.58987e8i	−0.672015	−	1.16396i
$516$		0			0
$517$			1.28182e8i			0.927589i
$518$		0			0
$519$	−1.48345e8			−1.06114
$520$		0			0
$521$	−4.59588e7	+	2.65343e7i	−0.324979	+	0.187627i	−0.653610	−	0.756832i	$-0.726746\pi$
$521$	−4.59588e7	+	2.65343e7i	−0.324979	+	0.187627i	0.328631	+	0.944459i	$0.393413\pi$
$522$		0			0
$523$	5.00830e6	+	2.89155e6i	0.0350095	+	0.0202127i	0.517403	−	0.855742i	$-0.326899\pi$
$523$	5.00830e6	+	2.89155e6i	0.0350095	+	0.0202127i	−0.482393	+	0.875955i	$0.660232\pi$
$524$		0			0
$525$	−3.04246e7	−	1.11211e8i	−0.210255	−	0.768545i
$526$		0			0
$527$	5.02602e6	−	8.70532e6i	0.0343394	−	0.0594775i
$528$		0			0
$529$	7.00228e7	+	1.21283e8i	0.473012	+	0.819281i
$530$		0			0
$531$		−	3.08413e7i		−	0.205991i
$532$		0			0
$533$	3.02215e7			0.199588
$534$		0			0
$535$	−1.90750e8	+	1.10129e8i	−1.24567	+	0.719187i
$536$		0			0
$537$	−6.89268e7	−	3.97949e7i	−0.445108	−	0.256983i
$538$		0			0
$539$	1.72924e8	−	1.02270e8i	1.10430	−	0.653101i
$540$		0			0
$541$	7.12304e7	−	1.23375e8i	0.449856	−	0.779174i	−0.548520	−	0.836137i	$-0.684809\pi$
$541$	7.12304e7	−	1.23375e8i	0.449856	−	0.779174i	0.998376	+	0.0569637i	$0.0181419\pi$
$542$		0			0
$543$	6.76756e7	+	1.17218e8i	0.422700	+	0.732138i
$544$		0			0
$545$		−	1.90578e8i		−	1.17729i
$546$		0			0
$547$	1.32718e8			0.810899			0.405449	−	0.914118i	$-0.367115\pi$
$547$	1.32718e8			0.810899			0.405449	+	0.914118i	$0.367115\pi$
$548$		0			0
$549$	−1.82569e6	+	1.05406e6i	−0.0110334	+	0.00637013i
$550$		0			0
$551$	2.17203e8	+	1.25402e8i	1.29841	+	0.749636i
$552$		0			0
$553$	1.81766e8	−	4.97267e7i	1.07482	−	0.294045i
$554$		0			0
$555$	−1.17127e8	+	2.02870e8i	−0.685137	+	1.18669i
$556$		0			0
$557$	7.91549e7	+	1.37100e8i	0.458049	+	0.793364i	0.998858	−	0.0477813i	$-0.0152151\pi$
$557$	7.91549e7	+	1.37100e8i	0.458049	+	0.793364i	−0.540809	+	0.841146i	$0.681882\pi$
$558$		0			0
$559$			2.35725e8i			1.34949i
$560$		0			0
$561$	−3.12718e7			−0.177119
$562$		0			0
$563$	−1.59660e8	+	9.21799e7i	−0.894688	+	0.516548i	−0.875473	−	0.483267i	$-0.839450\pi$
$563$	−1.59660e8	+	9.21799e7i	−0.894688	+	0.516548i	−0.0192150	+	0.999815i	$0.506117\pi$
$564$		0			0
$565$	−4.45301e8	−	2.57095e8i	−2.46893	−	1.42544i
$566$		0			0
$567$	5.13945e6	−	1.95909e7i	0.0281947	−	0.107474i
$568$		0			0
$569$	5.13849e7	−	8.90013e7i	0.278932	−	0.483125i	−0.692187	−	0.721718i	$-0.743353\pi$
$569$	5.13849e7	−	8.90013e7i	0.278932	−	0.483125i	0.971120	+	0.238593i	$0.0766861\pi$
$570$		0			0
$571$	−1.29861e8	−	2.24926e8i	−0.697543	−	1.20818i	−0.969316	−	0.245819i	$-0.920943\pi$
$571$	−1.29861e8	−	2.24926e8i	−0.697543	−	1.20818i	0.271773	−	0.962361i	$-0.412390\pi$
$572$		0			0
$573$			2.99557e7i			0.159227i
$574$		0			0
$575$	−6.09542e7			−0.320627
$576$		0			0
$577$	2.21124e8	−	1.27666e8i	1.15109	−	0.664582i	0.201938	−	0.979398i	$-0.435276\pi$
$577$	2.21124e8	−	1.27666e8i	1.15109	−	0.664582i	0.949153	+	0.314816i	$0.101943\pi$
$578$		0			0
$579$	1.67101e8	+	9.64760e7i	0.860883	+	0.497031i
$580$		0			0
$581$	−2.16351e8	+	2.18631e8i	−1.10314	+	1.11477i
$582$		0			0
$583$	−8.91909e7	+	1.54483e8i	−0.450106	+	0.779607i
$584$		0			0
$585$	−8.16571e7	−	1.41434e8i	−0.407874	−	0.706459i
$586$		0			0
$587$			2.41324e8i			1.19313i	0.802566	+	0.596563i	$0.203467\pi$
$587$			2.41324e8i			1.19313i	−0.802566	+	0.596563i	$0.796533\pi$
$588$		0			0
$589$	5.63599e7			0.275819
$590$		0			0
$591$	1.37334e8	−	7.92897e7i	0.665296	−	0.384109i
$592$		0			0
$593$	6.91547e7	+	3.99265e7i	0.331633	+	0.191468i	0.656566	−	0.754269i	$-0.272008\pi$
$593$	6.91547e7	+	3.99265e7i	0.331633	+	0.191468i	−0.324933	+	0.945737i	$0.605342\pi$
$594$		0			0
$595$	5.52335e7	+	5.46574e7i	0.262211	+	0.259477i
$596$		0			0
$597$	1.80188e7	−	3.12094e7i	0.0846842	−	0.146677i
$598$		0			0
$599$	−1.69307e8	−	2.93248e8i	−0.787761	−	1.36444i	−0.927336	−	0.374230i	$-0.877907\pi$
$599$	−1.69307e8	−	2.93248e8i	−0.787761	−	1.36444i	0.139575	−	0.990211i	$-0.455426\pi$
$600$		0			0
$601$			2.17641e8i			1.00258i	0.865280	+	0.501289i	$0.167141\pi$
$601$			2.17641e8i			1.00258i	−0.865280	+	0.501289i	$0.832859\pi$
$602$		0			0
$603$	−9.80960e7			−0.447404
$604$		0			0
$605$	1.91136e8	−	1.10353e8i	0.863131	−	0.498329i
$606$		0			0
$607$	−2.34560e8	−	1.35424e8i	−1.04879	−	0.605519i	−0.126480	−	0.991969i	$-0.540368\pi$
$607$	−2.34560e8	−	1.35424e8i	−1.04879	−	0.605519i	−0.922310	+	0.386450i	$0.873701\pi$
$608$		0			0
$609$	1.96929e8	+	5.16621e7i	0.871883	+	0.228728i
$610$		0			0
$611$	1.30802e8	−	2.26555e8i	0.573442	−	0.993231i
$612$		0			0
$613$	5.68826e7	+	9.85236e7i	0.246944	+	0.427719i	0.962676	−	0.270655i	$-0.0872403\pi$
$613$	5.68826e7	+	9.85236e7i	0.246944	+	0.427719i	−0.715732	+	0.698375i	$0.753907\pi$
$614$		0			0
$615$		−	2.60683e7i		−	0.112069i
$616$		0			0
$617$	−2.54469e8			−1.08338			−0.541688	−	0.840580i	$-0.682215\pi$
$617$	−2.54469e8			−1.08338			−0.541688	+	0.840580i	$0.682215\pi$
$618$		0			0
$619$	2.21047e8	−	1.27621e8i	0.931992	−	0.538086i	0.0445511	−	0.999007i	$-0.485814\pi$
$619$	2.21047e8	−	1.27621e8i	0.931992	−	0.538086i	0.887441	+	0.460921i	$0.152481\pi$
$620$		0			0
$621$	−9.27302e6	−	5.35378e6i	−0.0387210	−	0.0223556i
$622$		0			0
$623$	−7.42247e7	−	2.71313e8i	−0.306962	−	1.12204i
$624$		0			0
$625$	5.80407e7	−	1.00529e8i	0.237735	−	0.411769i
$626$		0			0
$627$	−8.76677e7	−	1.51845e8i	−0.355662	−	0.616024i
$628$		0			0
$629$		−	9.15443e7i		−	0.367857i
$630$		0			0
$631$	3.75463e8			1.49444			0.747222	−	0.664575i	$-0.231387\pi$
$631$	3.75463e8			1.49444			0.747222	+	0.664575i	$0.231387\pi$
$632$		0			0
$633$	5.54776e6	−	3.20300e6i	0.0218729	−	0.0126283i
$634$		0			0
$635$	−5.05134e8	−	2.91639e8i	−1.97281	−	1.13900i
$636$		0			0
$637$	−4.09993e8	+	4.29859e6i	−1.58620	+	0.0166306i
$638$		0			0
$639$	7.11835e7	−	1.23293e8i	0.272820	−	0.472539i
$640$		0			0
$641$	1.72639e8	+	2.99019e8i	0.655488	+	1.13534i	0.981771	+	0.190066i	$0.0608703\pi$
$641$	1.72639e8	+	2.99019e8i	0.655488	+	1.13534i	−0.326283	+	0.945272i	$0.605796\pi$
$642$		0			0
$643$			2.39334e8i			0.900267i	0.892961	+	0.450134i	$0.148624\pi$
$643$			2.39334e8i			0.900267i	−0.892961	+	0.450134i	$0.851376\pi$
$644$		0			0
$645$	2.03330e8			0.757745
$646$		0			0
$647$	3.33565e8	−	1.92584e8i	1.23160	−	0.711062i	0.264234	−	0.964459i	$-0.414881\pi$
$647$	3.33565e8	−	1.92584e8i	1.23160	−	0.711062i	0.967363	+	0.253396i	$0.0815477\pi$
$648$		0			0
$649$	−1.87695e8	−	1.08366e8i	−0.686625	−	0.396423i
$650$		0			0
$651$	4.41291e7	−	1.20726e7i	0.159949	−	0.0437582i
$652$		0			0
$653$	1.26341e8	−	2.18829e8i	0.453738	−	0.785897i	−0.544877	−	0.838516i	$-0.683424\pi$
$653$	1.26341e8	−	2.18829e8i	0.453738	−	0.785897i	0.998615	+	0.0526192i	$0.0167569\pi$
$654$		0			0
$655$	4.87240e7	+	8.43925e7i	0.173388	+	0.300317i
$656$		0			0
$657$		−	1.06733e8i		−	0.376361i
$658$		0			0
$659$	4.27761e8			1.49467			0.747334	−	0.664449i	$-0.231334\pi$
$659$	4.27761e8			1.49467			0.747334	+	0.664449i	$0.231334\pi$
$660$		0			0
$661$	−2.74282e8	+	1.58357e8i	−0.949716	+	0.548319i	−0.892993	−	0.450071i	$-0.851399\pi$
$661$	−2.74282e8	+	1.58357e8i	−0.949716	+	0.548319i	−0.0567232	+	0.998390i	$0.518065\pi$
$662$		0			0
$663$	5.52713e7	+	3.19109e7i	0.189653	+	0.109496i
$664$		0			0
$665$	−1.10555e8	+	4.21421e8i	−0.375936	+	1.43302i
$666$		0			0
$667$	5.38166e7	−	9.32131e7i	0.181359	−	0.314123i
$668$		0			0
$669$	−8.30618e7	−	1.43867e8i	−0.277411	−	0.480489i
$670$		0			0
$671$			1.48145e7i			0.0490363i
$672$		0			0
$673$	3.23240e8			1.06043			0.530213	−	0.847865i	$-0.322112\pi$
$673$	3.23240e8			1.06043			0.530213	+	0.847865i	$0.322112\pi$
$674$		0			0
$675$	−7.07396e7	+	4.08415e7i	−0.230012	+	0.132798i
$676$		0			0
$677$	2.77370e8	+	1.60140e8i	0.893910	+	0.516099i	0.875219	−	0.483726i	$-0.160717\pi$
$677$	2.77370e8	+	1.60140e8i	0.893910	+	0.516099i	0.0186906	+	0.999825i	$0.494050\pi$
$678$		0			0
$679$	−2.93832e8	+	2.96929e8i	−0.938620	+	0.948512i
$680$		0			0
$681$	−1.27000e8	+	2.19970e8i	−0.402126	+	0.696503i
$682$		0			0
$683$	−9.81458e7	−	1.69994e8i	−0.308042	−	0.533544i	0.669892	−	0.742458i	$-0.266340\pi$
$683$	−9.81458e7	−	1.69994e8i	−0.308042	−	0.533544i	−0.977934	+	0.208914i	$0.933007\pi$
$684$		0			0
$685$			7.05282e8i			2.19428i
$686$		0			0
$687$	−1.36355e8			−0.420533
$688$		0			0
$689$	3.15281e8	−	1.82027e8i	0.963917	−	0.556518i
$690$		0			0
$691$	8.11495e7	+	4.68517e7i	0.245953	+	0.142001i	0.617910	−	0.786249i	$-0.287980\pi$
$691$	8.11495e7	+	4.68517e7i	0.245953	+	0.142001i	−0.371957	+	0.928250i	$0.621313\pi$
$692$		0			0
$693$	−1.01169e8	−	1.00114e8i	−0.303981	−	0.300811i
$694$		0			0
$695$	−3.45638e8	+	5.98663e8i	−1.02960	+	1.78331i
$696$		0			0
$697$	5.09363e6	+	8.82243e6i	0.0150428	+	0.0260549i
$698$		0			0
$699$		−	2.12289e8i		−	0.621580i
$700$		0			0
$701$	−6.60582e8			−1.91767			−0.958833	−	0.283972i	$-0.908348\pi$
$701$	−6.60582e8			−1.91767			−0.958833	+	0.283972i	$0.908348\pi$
$702$		0			0
$703$	4.44507e8	−	2.56636e8i	1.27942	−	0.738672i
$704$		0			0
$705$	−1.95420e8	−	1.12826e8i	−0.557702	−	0.321990i
$706$		0			0
$707$	−8.96283e7	−	2.35130e7i	−0.253622	−	0.0665349i
$708$		0			0
$709$	5.67777e7	−	9.83418e7i	0.159309	−	0.275930i	−0.775311	−	0.631580i	$-0.782407\pi$
$709$	5.67777e7	−	9.83418e7i	0.159309	−	0.275930i	0.934620	+	0.355649i	$0.115740\pi$
$710$		0			0
$711$	−6.67524e7	−	1.15619e8i	−0.185720	−	0.321676i
$712$		0			0
$713$		−	2.41870e7i		−	0.0667288i
$714$		0			0
$715$	−1.14766e9			−3.13976
$716$		0			0
$717$	9.43924e6	−	5.44975e6i	0.0256082	−	0.0147849i
$718$		0			0
$719$	4.14745e8	+	2.39453e8i	1.11582	+	0.644219i	0.940330	−	0.340263i	$-0.110516\pi$
$719$	4.14745e8	+	2.39453e8i	1.11582	+	0.644219i	0.175489	+	0.984481i	$0.443849\pi$
$720$		0			0
$721$	8.61637e7	+	3.14954e8i	0.229889	+	0.840313i
$722$		0			0
$723$	8.42094e7	−	1.45855e8i	0.222816	−	0.385928i
$724$		0			0
$725$	−4.10542e8	−	7.11080e8i	−1.07732	−	1.86597i
$726$		0			0
$727$			4.88124e6i			0.0127036i	0.999980	+	0.00635180i	$0.00202186\pi$
$727$			4.88124e6i			0.0127036i	−0.999980	+	0.00635180i	$0.997978\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	−6.88141e7	+	3.97299e7i	−0.176167	+	0.101710i
$732$		0			0
$733$	2.13462e8	+	1.23243e8i	0.542013	+	0.312931i	0.745894	−	0.666064i	$-0.232022\pi$
$733$	2.13462e8	+	1.23243e8i	0.542013	+	0.312931i	−0.203882	+	0.978996i	$0.565356\pi$
$734$		0			0
$735$	3.70785e6	+	3.53649e8i	0.00933814	+	0.890658i
$736$		0			0
$737$	−3.44677e8	+	5.96997e8i	−0.861012	+	1.49132i
$738$		0			0
$739$	−4.37101e7	−	7.57081e7i	−0.108305	−	0.187590i	0.806779	−	0.590854i	$-0.201209\pi$
$739$	−4.37101e7	−	7.57081e7i	−0.108305	−	0.187590i	−0.915084	+	0.403264i	$0.867876\pi$
$740$		0			0
$741$			3.57837e8i			0.879490i
$742$		0			0
$743$	−5.61828e8			−1.36974			−0.684868	−	0.728667i	$-0.740140\pi$
$743$	−5.61828e8			−1.36974			−0.684868	+	0.728667i	$0.740140\pi$
$744$		0			0
$745$	2.71712e8	−	1.56873e8i	0.657113	−	0.379384i
$746$		0			0
$747$	1.88714e8	+	1.08954e8i	0.452734	+	0.261386i
$748$		0			0
$749$	3.77876e8	−	1.03378e8i	0.899298	−	0.246026i
$750$		0			0
$751$	1.32736e8	−	2.29906e8i	0.313378	−	0.542787i	−0.665713	−	0.746208i	$-0.731873\pi$
$751$	1.32736e8	−	2.29906e8i	0.313378	−	0.542787i	0.979091	+	0.203420i	$0.0652058\pi$
$752$		0			0
$753$	8.26917e7	+	1.43226e8i	0.193677	+	0.335458i
$754$		0			0
$755$			8.98259e8i			2.08718i
$756$		0			0
$757$	−9.32094e7			−0.214868			−0.107434	−	0.994212i	$-0.534263\pi$
$757$	−9.32094e7			−0.214868			−0.107434	+	0.994212i	$0.534263\pi$
$758$		0			0
$759$	−6.51646e7	+	3.76228e7i	−0.149034	+	0.0860450i
$760$		0			0
$761$	−6.08204e8	−	3.51147e8i	−1.38005	−	0.796773i	−0.387886	−	0.921707i	$-0.626795\pi$
$761$	−6.08204e8	−	3.51147e8i	−1.38005	−	0.796773i	−0.992165	+	0.124935i	$0.960128\pi$
$762$		0			0
$763$	−8.60143e7	+	3.27875e8i	−0.193641	+	0.738133i
$764$		0			0
$765$	2.75255e7	−	4.76755e7i	0.0614824	−	0.106491i
$766$		0			0
$767$	2.21161e8	+	3.83062e8i	0.490143	+	0.848952i
$768$		0			0
$769$			2.56752e8i			0.564592i	0.959327	+	0.282296i	$0.0910960\pi$
$769$			2.56752e8i			0.564592i	−0.959327	+	0.282296i	$0.908904\pi$
$770$		0			0
$771$	−3.56577e8			−0.778019
$772$		0			0
$773$	4.75686e8	−	2.74637e8i	1.02987	−	0.594594i	0.112921	−	0.993604i	$-0.463979\pi$
$773$	4.75686e8	−	2.74637e8i	1.02987	−	0.594594i	0.916947	+	0.399010i	$0.130646\pi$
$774$		0			0
$775$	−1.59792e8	−	9.22557e7i	−0.343280	−	0.198193i
$776$		0			0
$777$	2.93070e8	−	2.96159e8i	0.624753	−	0.631338i
$778$		0			0
$779$	−2.85591e7	+	4.94658e7i	−0.0604132	+	0.104639i
$780$		0			0
$781$	−5.00230e8	−	8.66424e8i	−1.05007	−	1.81877i
$782$		0			0
$783$		−	1.44236e8i		−	0.300462i
$784$		0			0
$785$	−1.30845e9			−2.70488
$786$		0			0
$787$	−2.02231e7	+	1.16758e7i	−0.0414881	+	0.0239532i	−0.520601	−	0.853800i	$-0.674292\pi$
$787$	−2.02231e7	+	1.16758e7i	−0.0414881	+	0.0239532i	0.479112	+	0.877754i	$0.340959\pi$
$788$		0			0
$789$	2.83988e8	+	1.63961e8i	0.578188	+	0.333817i
$790$		0			0
$791$	6.50072e8	+	6.43292e8i	1.31351	+	1.29981i
$792$		0			0
$793$	1.51172e7	−	2.61838e7i	0.0303146	−	0.0525064i
$794$		0			0
$795$	−1.57012e8	−	2.71953e8i	−0.312486	−	0.541242i
$796$		0			0
$797$			1.70637e8i			0.337052i	0.985697	+	0.168526i	$0.0539008\pi$
$797$			1.70637e8i			0.337052i	−0.985697	+	0.168526i	$0.946099\pi$
$798$		0			0
$799$	8.81828e7			0.172880
$800$		0			0
$801$	−1.72578e8	+	9.96382e7i	−0.335806	+	0.193878i
$802$		0			0
$803$	−6.49563e8	−	3.75025e8i	−1.25451	−	0.724292i
$804$		0			0
$805$	1.80854e8	+	4.74450e7i	0.346689	+	0.0909499i
$806$		0			0
$807$	1.01676e8	−	1.76109e8i	0.193464	−	0.335089i
$808$		0			0
$809$	−5.13103e6	−	8.88720e6i	−0.00969079	−	0.0167849i	0.861139	−	0.508369i	$-0.169751\pi$
$809$	−5.13103e6	−	8.88720e6i	−0.00969079	−	0.0167849i	−0.870830	+	0.491584i	$0.836418\pi$
$810$		0			0
$811$			2.25870e8i			0.423443i	0.977330	+	0.211722i	$0.0679070\pi$
$811$			2.25870e8i			0.423443i	−0.977330	+	0.211722i	$0.932093\pi$
$812$		0			0
$813$	2.74472e7			0.0510772
$814$		0			0
$815$	−8.74858e8	+	5.05100e8i	−1.61609	+	0.933049i
$816$		0			0
$817$	−3.85828e8	−	2.22758e8i	−0.707502	−	0.408477i
$818$		0			0
$819$	7.66509e7	+	2.80182e8i	0.139529	+	0.510021i
$820$		0			0
$821$	9.92145e7	−	1.71845e8i	0.179286	−	0.310532i	−0.762350	−	0.647165i	$-0.775955\pi$
$821$	9.92145e7	−	1.71845e8i	0.179286	−	0.310532i	0.941636	+	0.336632i	$0.109288\pi$
$822$		0			0
$823$	1.41678e8	+	2.45394e8i	0.254158	+	0.440214i	0.964666	−	0.263474i	$-0.0848684\pi$
$823$	1.41678e8	+	2.45394e8i	0.254158	+	0.440214i	−0.710509	+	0.703689i	$0.751535\pi$
$824$		0			0
$825$			5.74014e8i			1.02226i
$826$		0			0
$827$	−1.88816e8			−0.333828			−0.166914	−	0.985971i	$-0.553380\pi$
$827$	−1.88816e8			−0.333828			−0.166914	+	0.985971i	$0.553380\pi$
$828$		0			0
$829$	−4.80502e8	+	2.77418e8i	−0.843397	+	0.486935i	−0.858417	−	0.512952i	$-0.828552\pi$
$829$	−4.80502e8	+	2.77418e8i	−0.843397	+	0.486935i	0.0150205	+	0.999887i	$0.495219\pi$
$830$		0			0
$831$	4.96050e7	+	2.86395e7i	0.0864415	+	0.0499070i
$832$		0			0
$833$	−7.03564e7	−	1.18963e8i	−0.121722	−	0.205815i
$834$		0			0
$835$	5.58409e8	−	9.67192e8i	0.959164	−	1.66132i
$836$		0			0
$837$	−1.62062e7	−	2.80699e7i	−0.0276378	−	0.0478701i
$838$		0			0
$839$			6.98389e8i			1.18253i	0.806478	+	0.591264i	$0.201371\pi$
$839$			6.98389e8i			1.18253i	−0.806478	+	0.591264i	$0.798629\pi$
$840$		0			0
$841$	8.55052e8			1.43749
$842$		0			0
$843$	4.72885e7	−	2.73020e7i	0.0789356	−	0.0455735i
$844$		0			0
$845$	1.22232e9	+	7.05706e8i	2.02588	+	1.16964i
$846$		0			0
$847$	−3.78642e8	+	1.03587e8i	−0.623129	+	0.170473i
$848$		0			0
$849$	−3.56057e7	+	6.16708e7i	−0.0581830	+	0.100776i
$850$		0			0
$851$	−1.10136e8	−	1.90761e8i	−0.178707	−	0.309529i
$852$		0			0
$853$		−	1.18238e8i		−	0.190507i	−0.995453	−	0.0952533i	$-0.969634\pi$
$853$		−	1.18238e8i		−	0.190507i	0.995453	−	0.0952533i	$-0.0303661\pi$
$854$		0			0
$855$	3.08661e8			0.493836
$856$		0			0
$857$	−5.54162e8	+	3.19945e8i	−0.880428	+	0.508315i	−0.870800	−	0.491638i	$-0.836398\pi$
$857$	−5.54162e8	+	3.19945e8i	−0.880428	+	0.508315i	−0.00962859	+	0.999954i	$0.503065\pi$
$858$		0			0
$859$	−6.94847e8	−	4.01170e8i	−1.09625	−	0.632920i	−0.161017	−	0.986952i	$-0.551477\pi$
$859$	−6.94847e8	−	4.01170e8i	−1.09625	−	0.632920i	−0.935234	+	0.354031i	$0.884811\pi$
$860$		0			0
$861$	−1.17655e7	+	4.48486e7i	−0.0184332	+	0.0702651i
$862$		0			0
$863$	−1.34382e8	+	2.32757e8i	−0.209079	+	0.362135i	−0.951425	−	0.307882i	$-0.900380\pi$
$863$	−1.34382e8	+	2.32757e8i	−0.209079	+	0.362135i	0.742346	+	0.670017i	$0.233713\pi$
$864$		0			0
$865$	−9.17583e8	−	1.58930e9i	−1.41774	−	2.45560i
$866$		0			0
$867$		−	3.54754e8i		−	0.544340i
$868$		0			0
$869$	−9.38182e8			−1.42964
$870$		0			0
$871$	1.21840e9	−	7.03441e8i	1.84388	−	1.06457i
$872$		0			0
$873$	2.56298e8	+	1.47974e8i	0.385215	+	0.222404i
$874$		0			0
$875$	2.76302e8	−	2.79214e8i	0.412439	−	0.416786i
$876$		0			0
$877$	2.16753e8	−	3.75427e8i	0.321341	−	0.556579i	−0.659424	−	0.751771i	$-0.729200\pi$
$877$	2.16753e8	−	3.75427e8i	0.321341	−	0.556579i	0.980765	+	0.195192i	$0.0625330\pi$
$878$		0			0
$879$	8.51313e7	+	1.47452e8i	0.125350	+	0.217112i
$880$		0			0
$881$		−	9.63152e8i		−	1.40853i	−0.709935	−	0.704267i	$-0.751276\pi$
$881$		−	9.63152e8i		−	1.40853i	0.709935	−	0.704267i	$-0.248724\pi$
$882$		0			0
$883$	−7.01188e8			−1.01848			−0.509240	−	0.860625i	$-0.670073\pi$
$883$	−7.01188e8			−1.01848			−0.509240	+	0.860625i	$0.670073\pi$
$884$		0			0
$885$	3.30419e8	−	1.90768e8i	0.476689	−	0.275217i
$886$		0			0
$887$	−8.65358e8	−	4.99615e8i	−1.24001	−	0.715920i	−0.270914	−	0.962604i	$-0.587326\pi$
$887$	−8.65358e8	−	4.99615e8i	−1.24001	−	0.715920i	−0.969096	+	0.246684i	$0.920659\pi$
$888$		0			0
$889$	7.37419e8	+	7.29728e8i	1.04956	+	1.03862i
$890$		0			0
$891$	−5.04172e7	+	8.73252e7i	−0.0712764	+	0.123454i
$892$		0			0
$893$	2.47213e8	+	4.28185e8i	0.347149	+	0.601280i
$894$		0			0
$895$		−	9.84600e8i		−	1.37338i
$896$		0			0
$897$	1.53567e8			0.212774
$898$		0			0
$899$	2.82161e8	−	1.62906e8i	0.388345	−	0.224211i
$900$		0			0
$901$	1.06277e8	+	6.13589e7i	0.145299	+	0.0838886i
$902$		0			0
$903$	−3.49815e8	−	9.17699e7i	−0.475089	−	0.124634i
$904$		0			0
$905$	−8.37209e8	+	1.45009e9i	−1.12951	+	1.95636i
$906$		0			0
$907$	−2.23560e7	−	3.87218e7i	−0.0299622	−	0.0518960i	0.850656	−	0.525724i	$-0.176205\pi$
$907$	−2.23560e7	−	3.87218e7i	−0.0299622	−	0.0518960i	−0.880618	+	0.473828i	$0.842872\pi$
$908$		0			0
$909$			6.56463e7i			0.0874014i
$910$		0			0
$911$	1.05630e9			1.39711			0.698556	−	0.715556i	$-0.253826\pi$
$911$	1.05630e9			1.39711			0.698556	+	0.715556i	$0.253826\pi$
$912$		0			0
$913$	1.32616e9	−	7.65658e8i	1.74254	−	1.00606i
$914$		0			0
$915$	−2.25854e7	−	1.30397e7i	−0.0294825	−	0.0170217i
$916$		0			0
$917$	−4.57369e7	−	1.67182e8i	−0.0593142	−	0.216811i
$918$		0			0
$919$	3.53449e8	−	6.12191e8i	0.455386	−	0.788752i	−0.543324	−	0.839523i	$-0.682835\pi$
$919$	3.53449e8	−	6.12191e8i	0.455386	−	0.788752i	0.998710	+	0.0507709i	$0.0161678\pi$
$920$		0			0
$921$	−1.90510e8	−	3.29974e8i	−0.243860	−	0.422377i
$922$		0			0
$923$			2.04181e9i			2.59663i
$924$		0			0
$925$	−1.68035e9			−2.12312
$926$		0			0
$927$	2.00338e8	−	1.15665e8i	0.251491	−	0.145199i
$928$		0			0
$929$	−9.33756e7	−	5.39104e7i	−0.116463	−	0.0672397i	0.440637	−	0.897685i	$-0.354753\pi$
$929$	−9.33756e7	−	5.39104e7i	−0.116463	−	0.0672397i	−0.557100	+	0.830446i	$0.688086\pi$
$930$		0			0
$931$	3.80404e8	−	6.75128e8i	0.471407	−	0.836636i
$932$		0			0
$933$	1.08583e8	−	1.88071e8i	0.133695	−	0.231567i
$934$		0			0
$935$	−1.93431e8	−	3.35032e8i	−0.236641	−	0.409875i
$936$		0			0
$937$			2.44646e8i			0.297385i	0.988884	+	0.148692i	$0.0475064\pi$
$937$			2.44646e8i			0.297385i	−0.988884	+	0.148692i	$0.952494\pi$
$938$		0			0
$939$	3.90878e8			0.472111
$940$		0			0
$941$	−3.24143e8	+	1.87144e8i	−0.389016	+	0.224598i	−0.681734	−	0.731600i	$-0.738774\pi$
$941$	−3.24143e8	+	1.87144e8i	−0.389016	+	0.224598i	0.292718	+	0.956199i	$0.405440\pi$
$942$		0			0
$943$	2.12283e7	+	1.22562e7i	0.0253152	+	0.0146157i
$944$		0			0
$945$	2.41677e8	−	6.61171e7i	0.286379	−	0.0783462i
$946$		0			0
$947$	1.23507e8	−	2.13921e8i	0.145426	−	0.251886i	−0.784106	−	0.620628i	$-0.786878\pi$
$947$	1.23507e8	−	2.13921e8i	0.145426	−	0.251886i	0.929532	+	0.368742i	$0.120211\pi$
$948$		0			0
$949$	7.65379e8	+	1.32567e9i	0.895525	+	1.55109i
$950$		0			0
$951$			1.91055e8i			0.222135i
$952$		0			0
$953$	−1.15026e8			−0.132898			−0.0664489	−	0.997790i	$-0.521167\pi$
$953$	−1.15026e8			−0.132898			−0.0664489	+	0.997790i	$0.521167\pi$
$954$		0			0
$955$	−3.20932e8	+	1.85290e8i	−0.368470	+	0.212736i
$956$		0			0
$957$	−8.77800e8	−	5.06798e8i	−1.00152	−	0.578228i
$958$		0			0
$959$	3.18318e8	−	1.21339e9i	0.360916	−	1.37576i
$960$		0			0
$961$	−4.07144e8	+	7.05195e8i	−0.458752	+	0.794582i
$962$		0			0
$963$	−1.38773e8	−	2.40361e8i	−0.155391	−	0.269145i
$964$		0			0
$965$			2.38700e9i			2.65625i
$966$		0			0
$967$	−1.68335e8			−0.186164			−0.0930820	−	0.995658i	$-0.529672\pi$
$967$	−1.68335e8			−0.186164			−0.0930820	+	0.995658i	$0.529672\pi$
$968$		0			0
$969$	−1.04462e8	+	6.03110e7i	−0.114812	+	0.0662865i
$970$		0			0
$971$	−1.21758e9	−	7.02969e8i	−1.32996	−	0.767854i	−0.344669	−	0.938724i	$-0.612009\pi$
$971$	−1.21758e9	−	7.02969e8i	−1.32996	−	0.767854i	−0.985294	+	0.170870i	$0.945342\pi$
$972$		0			0
$973$	8.64842e8	−	8.73957e8i	0.938854	−	0.948749i
$974$		0			0
$975$	5.85744e8	−	1.01454e9i	0.631967	−	1.09460i
$976$		0			0
$977$	−9.00128e7	−	1.55907e8i	−0.0965207	−	0.167179i	0.813722	−	0.581255i	$-0.197438\pi$
$977$	−9.00128e7	−	1.55907e8i	−0.0965207	−	0.167179i	−0.910242	+	0.414076i	$0.864105\pi$
$978$		0			0
$979$			1.40038e9i			1.49244i
$980$		0			0
$981$	2.40145e8			0.254370
$982$		0			0
$983$	−1.06231e9	+	6.13326e8i	−1.11839	+	0.645700i	−0.940988	−	0.338439i	$-0.890101\pi$
$983$	−1.06231e9	+	6.13326e8i	−1.11839	+	0.645700i	−0.177398	+	0.984139i	$0.556768\pi$
$984$		0			0
$985$	1.69895e9	+	9.80887e8i	1.77775	+	1.02638i
$986$		0			0
$987$	2.85284e8	+	2.82309e8i	0.296706	+	0.293611i
$988$		0			0
$989$	−9.55971e7	+	1.65579e8i	−0.0988225	+	0.171166i
$990$		0			0
$991$	−2.62311e8	−	4.54336e8i	−0.269523	−	0.466828i	0.699216	−	0.714911i	$-0.253533\pi$
$991$	−2.62311e8	−	4.54336e8i	−0.269523	−	0.466828i	−0.968739	+	0.248083i	$0.920199\pi$
$992$		0			0
$993$		−	7.36827e8i		−	0.752519i
$994$		0			0
$995$	4.45818e8			0.452572
$996$		0			0
$997$	−1.58844e9	+	9.17084e8i	−1.60282	+	0.925387i	−0.611898	+	0.790937i	$0.709594\pi$
$997$	−1.58844e9	+	9.17084e8i	−1.60282	+	0.925387i	−0.990920	+	0.134450i	$0.957073\pi$
$998$		0			0
$999$	−2.55634e8	−	1.47590e8i	−0.256402	−	0.148034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.a.145.1		8
4.3	odd	2		84.7.m.b.61.1	✓	8
7.3	odd	6	inner	336.7.bh.a.241.1		8
12.11	even	2		252.7.z.e.145.4		8
28.3	even	6		84.7.m.b.73.1	yes	8
28.11	odd	6		588.7.m.b.325.4		8
28.19	even	6		588.7.d.a.97.1		8
28.23	odd	6		588.7.d.a.97.8		8
28.27	even	2		588.7.m.b.313.4		8
84.59	odd	6		252.7.z.e.73.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.7.m.b.61.1	✓	8	4.3	odd	2
84.7.m.b.73.1	yes	8	28.3	even	6
252.7.z.e.73.4		8	84.59	odd	6
252.7.z.e.145.4		8	12.11	even	2
336.7.bh.a.145.1		8	1.1	even	1	trivial
336.7.bh.a.241.1		8	7.3	odd	6	inner
588.7.d.a.97.1		8	28.19	even	6
588.7.d.a.97.8		8	28.23	odd	6
588.7.m.b.313.4		8	28.27	even	2
588.7.m.b.325.4		8	28.11	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-13.5000 + 7.79423i) q^{3} +(-167.007 - 96.4218i) q^{5} +(243.806 + 241.263i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 + 7.79423i) q^{3} +(-167.007 - 96.4218i) q^{5} +(243.806 + 241.263i) q^{7} +(121.500 - 210.444i) q^{9} +(-853.820 - 1478.86i) q^{11} +3485.08i q^{13} +3006.13 q^{15} +(-1017.38 + 587.386i) q^{17} +(-5704.28 - 3293.37i) q^{19} +(-5171.83 - 1356.77i) q^{21} +(-1413.35 + 2448.00i) q^{23} +(10781.8 + 18674.7i) q^{25} +3788.00i q^{27} -38077.2 q^{29} +(-7410.22 + 4278.29i) q^{31} +(23053.2 + 13309.7i) q^{33} +(-17454.4 - 63800.9i) q^{35} +(-38962.6 + 67485.2i) q^{37} +(-27163.5 - 47048.5i) q^{39} -8671.70i q^{41} +67638.4 q^{43} +(-40582.8 + 23430.5i) q^{45} +(-65007.2 - 37531.9i) q^{47} +(1233.43 + 117643. i) q^{49} +(9156.44 - 15859.4i) q^{51} +(-52230.5 - 90465.9i) q^{53} +329308. i q^{55} +102677. q^{57} +(109915. - 63459.5i) q^{59} +(-7513.11 - 4337.70i) q^{61} +(80394.8 - 21994.0i) q^{63} +(336037. - 582034. i) q^{65} +(-201844. - 349604. i) q^{67} -44064.0i q^{69} +585872. q^{71} +(380386. - 219616. i) q^{73} +(-291109. - 168072. i) q^{75} +(148628. - 566550. i) q^{77} +(274701. - 475796. i) q^{79} +(-29524.5 - 51137.9i) q^{81} +896743. i q^{83} +226547. q^{85} +(514043. - 296783. i) q^{87} +(-710199. - 410034. i) q^{89} +(-840820. + 849682. i) q^{91} +(66692.0 - 115514. i) q^{93} +(635104. + 1.10003e6i) q^{95} +1.21789e6i q^{97} -414957. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9	\( 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9} - 378 q^{11} + 5292 q^{15} + 852 q^{17} - 3690 q^{19} + 3942 q^{21} - 15600 q^{23} + 3386 q^{25} - 68604 q^{29} - 23028 q^{31} + 10206 q^{33} - 93828 q^{35} + 15914 q^{37} - 25326 q^{39} + 170044 q^{43} - 71442 q^{45} - 102180 q^{47} + 157340 q^{49} - 7668 q^{51} + 196410 q^{53} + 66420 q^{57} + 662550 q^{59} - 23928 q^{61} - 50058 q^{63} + 14892 q^{65} - 774838 q^{67} + 721896 q^{71} - 1219050 q^{73} - 91422 q^{75} + 1584738 q^{77} + 493868 q^{79} - 236196 q^{81} - 1329816 q^{85} + 926154 q^{87} + 604260 q^{89} - 3831690 q^{91} + 207252 q^{93} - 448944 q^{95} - 183708 q^{99}+O(q^{100}) \) 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9 - 378 * q^11 + 5292 * q^15 + 852 * q^17 - 3690 * q^19 + 3942 * q^21 - 15600 * q^23 + 3386 * q^25 - 68604 * q^29 - 23028 * q^31 + 10206 * q^33 - 93828 * q^35 + 15914 * q^37 - 25326 * q^39 + 170044 * q^43 - 71442 * q^45 - 102180 * q^47 + 157340 * q^49 - 7668 * q^51 + 196410 * q^53 + 66420 * q^57 + 662550 * q^59 - 23928 * q^61 - 50058 * q^63 + 14892 * q^65 - 774838 * q^67 + 721896 * q^71 - 1219050 * q^73 - 91422 * q^75 + 1584738 * q^77 + 493868 * q^79 - 236196 * q^81 - 1329816 * q^85 + 926154 * q^87 + 604260 * q^89 - 3831690 * q^91 + 207252 * q^93 - 448944 * q^95 - 183708 * q^99

Introduction

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