LMFDB - Embedded newform 336.7.bh.b.241.1

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} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Root			$5.73828 + 9.93899i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.7.bh.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 - 7.79423i) q^{3} +(-175.367 + 101.248i) q^{5} +(-284.280 - 191.921i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 - 7.79423i) q^{3} +(-175.367 + 101.248i) q^{5} +(-284.280 - 191.921i) q^{7} +(121.500 + 210.444i) q^{9} +(437.884 - 758.438i) q^{11} -275.049i q^{13} +3156.61 q^{15} +(-3799.10 - 2193.41i) q^{17} +(11697.8 - 6753.75i) q^{19} +(2341.91 + 4806.68i) q^{21} +(-6367.61 - 11029.0i) q^{23} +(12689.9 - 21979.6i) q^{25} -3788.00i q^{27} +6262.53 q^{29} +(17689.7 + 10213.2i) q^{31} +(-11822.9 + 6825.94i) q^{33} +(69285.1 + 4873.70i) q^{35} +(-7862.08 - 13617.5i) q^{37} +(-2143.79 + 3713.16i) q^{39} -69941.8i q^{41} -113322. q^{43} +(-42614.2 - 24603.3i) q^{45} +(40116.2 - 23161.1i) q^{47} +(43981.8 + 109119. i) q^{49} +(34191.9 + 59222.2i) q^{51} +(-64013.2 + 110874. i) q^{53} +177340. i q^{55} -210561. q^{57} +(-242870. - 140221. i) q^{59} +(84759.3 - 48935.8i) q^{61} +(5848.55 - 83143.6i) q^{63} +(27848.2 + 48234.5i) q^{65} +(87278.8 - 151171. i) q^{67} +198522. i q^{69} -345712. q^{71} +(-104589. - 60384.4i) q^{73} +(-342627. + 197816. i) q^{75} +(-270042. + 131570. i) q^{77} +(381933. + 661527. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -859402. i q^{83} +888317. q^{85} +(-84544.2 - 48811.6i) q^{87} +(-155778. + 89938.3i) q^{89} +(-52787.6 + 78190.9i) q^{91} +(-159207. - 275755. i) q^{93} +(-1.36761e6 + 2.36877e6i) q^{95} +340171. i q^{97} +212812. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9	$ 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99}+O(q^{100}) $ 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9 + 1070 * q^11 + 756 * q^15 + 7212 * q^17 + 24606 * q^19 + 8154 * q^21 + 15224 * q^23 + 22274 * q^25 + 32524 * q^29 - 40200 * q^31 - 28890 * q^33 + 242436 * q^35 - 45670 * q^37 - 93366 * q^39 + 445660 * q^43 - 10206 * q^45 - 82884 * q^47 + 24116 * q^49 - 64908 * q^51 - 13034 * q^53 - 442908 * q^57 - 1810362 * q^59 - 392856 * q^61 - 38394 * q^63 - 389004 * q^65 - 384094 * q^67 - 225688 * q^71 + 903078 * q^73 - 601398 * q^75 - 327674 * q^77 + 559592 * q^79 - 236196 * q^81 + 1953576 * q^85 - 439074 * q^87 - 1770036 * q^89 + 2960718 * q^91 + 361800 * q^93 - 1160112 * q^95 + 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−175.367	+	101.248i	−1.40294	+	0.809986i	−0.994693	−	0.102887i	$-0.967192\pi$
$5$	−175.367	+	101.248i	−1.40294	+	0.809986i	−0.408243	+	0.912873i	$0.633859\pi$
$6$		0			0
$7$	−284.280	−	191.921i	−0.828806	−	0.559536i
$7$	−284.280	−	191.921i	−0.828806	−	0.559536i
$8$		0			0
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$		0			0
$11$	437.884	−	758.438i	0.328989	−	0.569826i	−0.653323	−	0.757080i	$-0.726625\pi$
$11$	437.884	−	758.438i	0.328989	−	0.569826i	0.982312	+	0.187254i	$0.0599588\pi$
$12$		0			0
$13$		−	275.049i		−	0.125193i	−0.998039	−	0.0625964i	$-0.980062\pi$
$13$		−	275.049i		−	0.125193i	0.998039	−	0.0625964i	$-0.0199381\pi$
$14$		0			0
$15$	3156.61			0.935291
$16$		0			0
$17$	−3799.10	−	2193.41i	−0.773276	−	0.446451i	0.0607662	−	0.998152i	$-0.480646\pi$
$17$	−3799.10	−	2193.41i	−0.773276	−	0.446451i	−0.834042	+	0.551701i	$0.813979\pi$
$18$		0			0
$19$	11697.8	−	6753.75i	1.70547	−	0.984655i	0.765482	−	0.643458i	$-0.222501\pi$
$19$	11697.8	−	6753.75i	1.70547	−	0.984655i	0.939992	−	0.341198i	$-0.110833\pi$
$20$		0			0
$21$	2341.91	+	4806.68i	0.252879	+	0.519024i
$22$		0			0
$23$	−6367.61	−	11029.0i	−0.523351	−	0.906470i	−0.999631	−	0.0271766i	$-0.991348\pi$
$23$	−6367.61	−	11029.0i	−0.523351	−	0.906470i	0.476280	−	0.879294i	$-0.341985\pi$
$24$		0			0
$25$	12689.9	−	21979.6i	0.812154	−	1.40669i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	6262.53			0.256777			0.128388	−	0.991724i	$-0.459020\pi$
$29$	6262.53			0.256777			0.128388	+	0.991724i	$0.459020\pi$
$30$		0			0
$31$	17689.7	+	10213.2i	0.593793	+	0.342827i	0.766596	−	0.642130i	$-0.221949\pi$
$31$	17689.7	+	10213.2i	0.593793	+	0.342827i	−0.172803	+	0.984956i	$0.555282\pi$
$32$		0			0
$33$	−11822.9	+	6825.94i	−0.328989	+	0.189942i
$34$		0			0
$35$	69285.1	+	4873.70i	1.61598	+	0.113672i
$36$		0			0
$37$	−7862.08	−	13617.5i	−0.155215	−	0.268840i	0.777923	−	0.628360i	$-0.216274\pi$
$37$	−7862.08	−	13617.5i	−0.155215	−	0.268840i	−0.933137	+	0.359521i	$0.882940\pi$
$38$		0			0
$39$	−2143.79	+	3713.16i	−0.0361400	+	0.0625964i
$40$		0			0
$41$		−	69941.8i		−	1.01481i	−0.861707	−	0.507405i	$-0.830605\pi$
$41$		−	69941.8i		−	1.01481i	0.861707	−	0.507405i	$-0.169395\pi$
$42$		0			0
$43$	−113322.			−1.42530			−0.712652	−	0.701517i	$-0.752506\pi$
$43$	−113322.			−1.42530			−0.712652	+	0.701517i	$0.752506\pi$
$44$		0			0
$45$	−42614.2	−	24603.3i	−0.467645	−	0.269995i
$46$		0			0
$47$	40116.2	−	23161.1i	0.386390	−	0.223083i	−0.294205	−	0.955742i	$-0.595055\pi$
$47$	40116.2	−	23161.1i	0.386390	−	0.223083i	0.680595	+	0.732660i	$0.261721\pi$
$48$		0			0
$49$	43981.8	+	109119.i	0.373839	+	0.927494i
$50$		0			0
$51$	34191.9	+	59222.2i	0.257759	+	0.446451i
$52$		0			0
$53$	−64013.2	+	110874.i	−0.429973	+	0.744736i	−0.996870	−	0.0790529i	$-0.974810\pi$
$53$	−64013.2	+	110874.i	−0.429973	+	0.744736i	0.566897	+	0.823789i	$0.308144\pi$
$54$		0			0
$55$			177340.i			1.06591i
$56$		0			0
$57$	−210561.			−1.13698
$58$		0			0
$59$	−242870.	−	140221.i	−1.18254	−	0.682742i	−0.225942	−	0.974141i	$-0.572546\pi$
$59$	−242870.	−	140221.i	−1.18254	−	0.682742i	−0.956602	+	0.291398i	$0.905879\pi$
$60$		0			0
$61$	84759.3	−	48935.8i	0.373420	−	0.215594i	−0.301531	−	0.953456i	$-0.597498\pi$
$61$	84759.3	−	48935.8i	0.373420	−	0.215594i	0.674952	+	0.737862i	$0.264164\pi$
$62$		0			0
$63$	5848.55	−	83143.6i	0.0233898	−	0.332512i
$64$		0			0
$65$	27848.2	+	48234.5i	0.101404	+	0.175638i
$66$		0			0
$67$	87278.8	−	151171.i	0.290191	−	0.502626i	−0.683663	−	0.729797i	$-0.739614\pi$
$67$	87278.8	−	151171.i	0.290191	−	0.502626i	0.973855	+	0.227171i	$0.0729477\pi$
$68$		0			0
$69$			198522.i			0.604314i
$70$		0			0
$71$	−345712.			−0.965915			−0.482957	−	0.875644i	$-0.660437\pi$
$71$	−345712.			−0.965915			−0.482957	+	0.875644i	$0.660437\pi$
$72$		0			0
$73$	−104589.	−	60384.4i	−0.268854	−	0.155223i	0.359513	−	0.933140i	$-0.382943\pi$
$73$	−104589.	−	60384.4i	−0.268854	−	0.155223i	−0.628367	+	0.777917i	$0.716276\pi$
$74$		0			0
$75$	−342627.	+	197816.i	−0.812154	+	0.468897i
$76$		0			0
$77$	−270042.	+	131570.i	−0.591506	+	0.288194i
$78$		0			0
$79$	381933.	+	661527.i	0.774650	+	1.34173i	0.934991	+	0.354671i	$0.115407\pi$
$79$	381933.	+	661527.i	0.774650	+	1.34173i	−0.160341	+	0.987062i	$0.551259\pi$
$80$		0			0
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	859402.i		−	1.50301i	−0.659727	−	0.751505i	$-0.729328\pi$
$83$		−	859402.i		−	1.50301i	0.659727	−	0.751505i	$-0.270672\pi$
$84$		0			0
$85$	888317.			1.44648
$86$		0			0
$87$	−84544.2	−	48811.6i	−0.128388	−	0.0741251i
$88$		0			0
$89$	−155778.	+	89938.3i	−0.220971	+	0.127578i	−0.606400	−	0.795160i	$-0.707387\pi$
$89$	−155778.	+	89938.3i	−0.220971	+	0.127578i	0.385429	+	0.922738i	$0.374054\pi$
$90$		0			0
$91$	−52787.6	+	78190.9i	−0.0700499	+	0.103761i
$92$		0			0
$93$	−159207.	−	275755.i	−0.197931	−	0.342827i
$94$		0			0
$95$	−1.36761e6	+	2.36877e6i	−1.59511	+	2.76282i
$96$		0			0
$97$			340171.i			0.372720i	0.982482	+	0.186360i	$0.0596690\pi$
$97$			340171.i			0.372720i	−0.982482	+	0.186360i	$0.940331\pi$
$98$		0			0
$99$	212812.			0.219326
$100$		0			0
$101$	903587.	+	521686.i	0.877013	+	0.506344i	0.869672	−	0.493630i	$-0.164330\pi$
$101$	903587.	+	521686.i	0.877013	+	0.506344i	0.00734043	+	0.999973i	$0.497663\pi$
$102$		0			0
$103$	675522.	−	390013.i	0.618198	−	0.356917i	−0.157969	−	0.987444i	$-0.550495\pi$
$103$	675522.	−	390013.i	0.618198	−	0.356917i	0.776167	+	0.630527i	$0.217161\pi$
$104$		0			0
$105$	−897362.	−	605819.i	−0.775175	−	0.523329i
$106$		0			0
$107$	−498844.	−	864024.i	−0.407205	−	0.705301i	0.587370	−	0.809319i	$-0.300163\pi$
$107$	−498844.	−	864024.i	−0.407205	−	0.705301i	−0.994575	+	0.104018i	$0.966830\pi$
$108$		0			0
$109$	−727835.	+	1.26065e6i	−0.562023	+	0.973452i	0.435297	+	0.900287i	$0.356643\pi$
$109$	−727835.	+	1.26065e6i	−0.562023	+	0.973452i	−0.997320	+	0.0731648i	$0.976690\pi$
$110$		0			0
$111$			245116.i			0.179226i
$112$		0			0
$113$	177612.			0.123094			0.0615469	−	0.998104i	$-0.480397\pi$
$113$	177612.			0.123094			0.0615469	+	0.998104i	$0.480397\pi$
$114$		0			0
$115$	2.23334e6	+	1.28942e6i	1.46846	+	0.847814i
$116$		0			0
$117$	57882.4	−	33418.4i	0.0361400	−	0.0208655i
$118$		0			0
$119$	659049.	+	1.35267e6i	0.391090	+	0.802697i
$120$		0			0
$121$	502295.	+	870001.i	0.283533	+	0.491093i
$122$		0			0
$123$	−545142.	+	944214.i	−0.292951	+	0.507405i
$124$		0			0
$125$			1.97531e6i			1.01136i
$126$		0			0
$127$	−924373.			−0.451269			−0.225635	−	0.974212i	$-0.572446\pi$
$127$	−924373.			−0.451269			−0.225635	+	0.974212i	$0.572446\pi$
$128$		0			0
$129$	1.52984e6	+	883255.i	0.712652	+	0.411450i
$130$		0			0
$131$	−837624.	+	483602.i	−0.372593	+	0.215117i	−0.674591	−	0.738192i	$-0.735680\pi$
$131$	−837624.	+	483602.i	−0.372593	+	0.215117i	0.301997	+	0.953309i	$0.402347\pi$
$132$		0			0
$133$	−4.62165e6	−	325100.i	−1.96446	−	0.138185i
$134$		0			0
$135$	383528.	+	664290.i	0.155882	+	0.269995i
$136$		0			0
$137$	−2.35006e6	+	4.07043e6i	−0.913940	+	1.58299i	−0.105493	+	0.994420i	$0.533642\pi$
$137$	−2.35006e6	+	4.07043e6i	−0.913940	+	1.58299i	−0.808446	+	0.588570i	$0.799691\pi$
$138$		0			0
$139$		−	1.64306e6i		−	0.611798i	−0.952064	−	0.305899i	$-0.901043\pi$
$139$		−	1.64306e6i		−	0.611798i	0.952064	−	0.305899i	$-0.0989570\pi$
$140$		0			0
$141$	−722092.			−0.257594
$142$		0			0
$143$	−208607.	−	120439.i	−0.0713381	−	0.0411870i
$144$		0			0
$145$	−1.09824e6	+	634070.i	−0.360242	+	0.207986i
$146$		0			0
$147$	256742.	−	1.81591e6i	0.0808249	−	0.571665i
$148$		0			0
$149$	−2.31369e6	−	4.00743e6i	−0.699433	−	1.21145i	−0.968663	−	0.248378i	$-0.920103\pi$
$149$	−2.31369e6	−	4.00743e6i	−0.699433	−	1.21145i	0.269230	−	0.963076i	$-0.413231\pi$
$150$		0			0
$151$	−2.24610e6	+	3.89036e6i	−0.652377	+	1.12995i	0.330168	+	0.943922i	$0.392895\pi$
$151$	−2.24610e6	+	3.89036e6i	−0.652377	+	1.12995i	−0.982545	+	0.186028i	$0.940439\pi$
$152$		0			0
$153$		−	1.06600e6i		−	0.297634i
$154$		0			0
$155$	−4.13625e6			−1.11074
$156$		0			0
$157$	−4.17859e6	−	2.41251e6i	−1.07977	−	0.623405i	−0.148935	−	0.988847i	$-0.547584\pi$
$157$	−4.17859e6	−	2.41251e6i	−1.07977	−	0.623405i	−0.930834	+	0.365442i	$0.880918\pi$
$158$		0			0
$159$	1.72836e6	−	997866.i	0.429973	−	0.248245i
$160$		0			0
$161$	−306513.	+	4.35741e6i	−0.0734464	+	1.04412i
$162$		0			0
$163$	−1.69763e6	−	2.94038e6i	−0.391994	−	0.678954i	0.600718	−	0.799461i	$-0.294881\pi$
$163$	−1.69763e6	−	2.94038e6i	−0.391994	−	0.678954i	−0.992713	+	0.120507i	$0.961548\pi$
$164$		0			0
$165$	1.38223e6	−	2.39409e6i	0.307700	−	0.532953i
$166$		0			0
$167$			2.04579e6i			0.439249i	0.975584	+	0.219625i	$0.0704832\pi$
$167$			2.04579e6i			0.439249i	−0.975584	+	0.219625i	$0.929517\pi$
$168$		0			0
$169$	4.75116e6			0.984327
$170$		0			0
$171$	2.84258e6	+	1.64116e6i	0.568491	+	0.328218i
$172$		0			0
$173$	−272758.	+	157477.i	−0.0526792	+	0.0304144i	−0.526108	−	0.850418i	$-0.676349\pi$
$173$	−272758.	+	157477.i	−0.0526792	+	0.0304144i	0.473429	+	0.880832i	$0.343016\pi$
$174$		0			0
$175$	−7.82583e6	+	3.81290e6i	−1.46021	+	0.711445i
$176$		0			0
$177$	2.18583e6	+	3.78596e6i	0.394181	+	0.682742i
$178$		0			0
$179$	−2.01204e6	+	3.48495e6i	−0.350814	+	0.607627i	−0.986392	−	0.164409i	$-0.947428\pi$
$179$	−2.01204e6	+	3.48495e6i	−0.350814	+	0.607627i	0.635579	+	0.772036i	$0.280762\pi$
$180$		0			0
$181$			1.53820e6i			0.259405i	0.991553	+	0.129703i	$0.0414022\pi$
$181$			1.53820e6i			0.259405i	−0.991553	+	0.129703i	$0.958598\pi$
$182$		0			0
$183$	−1.52567e6			−0.248947
$184$		0			0
$185$	2.75750e6	+	1.59204e6i	0.435512	+	0.251443i
$186$		0			0
$187$	−3.32714e6	+	1.92092e6i	−0.508798	+	0.293755i
$188$		0			0
$189$	−726995.	+	1.07685e6i	−0.107683	+	0.159504i
$190$		0			0
$191$	2.13865e6	+	3.70425e6i	0.306931	+	0.531619i	0.977689	−	0.210056i	$-0.0673647\pi$
$191$	2.13865e6	+	3.70425e6i	0.306931	+	0.531619i	−0.670759	+	0.741676i	$0.734031\pi$
$192$		0			0
$193$	3.22312e6	−	5.58261e6i	0.448337	−	0.776543i	−0.549941	−	0.835204i	$-0.685350\pi$
$193$	3.22312e6	−	5.58261e6i	0.448337	−	0.776543i	0.998278	+	0.0586609i	$0.0186831\pi$
$194$		0			0
$195$		−	868220.i		−	0.117092i
$196$		0			0
$197$	−2.73215e6			−0.357359			−0.178680	−	0.983907i	$-0.557183\pi$
$197$	−2.73215e6			−0.357359			−0.178680	+	0.983907i	$0.557183\pi$
$198$		0			0
$199$	−517231.	−	298623.i	−0.0656334	−	0.0378935i	0.466824	−	0.884350i	$-0.345398\pi$
$199$	−517231.	−	298623.i	−0.0656334	−	0.0378935i	−0.532458	+	0.846457i	$0.678731\pi$
$200$		0			0
$201$	−2.35653e6	+	1.36054e6i	−0.290191	+	0.167542i
$202$		0			0
$203$	−1.78032e6	−	1.20191e6i	−0.212818	−	0.143676i
$204$		0			0
$205$	7.08148e6	+	1.22655e7i	0.821982	+	1.42372i
$206$		0			0
$207$	1.54733e6	−	2.68005e6i	0.174450	−	0.302157i
$208$		0			0
$209$		−	1.18294e7i		−	1.29576i
$210$		0			0
$211$	3.67602e6			0.391319			0.195659	−	0.980672i	$-0.437315\pi$
$211$	3.67602e6			0.391319			0.195659	+	0.980672i	$0.437315\pi$
$212$		0			0
$213$	4.66711e6	+	2.69455e6i	0.482957	+	0.278836i
$214$		0			0
$215$	1.98729e7	−	1.14736e7i	1.99961	−	1.15448i
$216$		0			0
$217$	−3.06872e6	−	6.29842e6i	−0.300316	−	0.616386i
$218$		0			0
$219$	941299.	+	1.63038e6i	0.0896180	+	0.155223i
$220$		0			0
$221$	−603295.	+	1.04494e6i	−0.0558924	+	0.0968086i
$222$		0			0
$223$		−	1.43225e7i		−	1.29153i	−0.763535	−	0.645766i	$-0.776538\pi$
$223$		−	1.43225e7i		−	1.29153i	0.763535	−	0.645766i	$-0.223462\pi$
$224$		0			0
$225$	6.16729e6			0.541436
$226$		0			0
$227$	2.62502e6	+	1.51555e6i	0.224416	+	0.129567i	0.607994	−	0.793942i	$-0.291975\pi$
$227$	2.62502e6	+	1.51555e6i	0.224416	+	0.129567i	−0.383577	+	0.923509i	$0.625308\pi$
$228$		0			0
$229$	−5.42194e6	+	3.13036e6i	−0.451490	+	0.260668i	−0.708459	−	0.705752i	$-0.750609\pi$
$229$	−5.42194e6	+	3.13036e6i	−0.451490	+	0.260668i	0.256969	+	0.966420i	$0.417276\pi$
$230$		0			0
$231$	4.67105e6	+	328575.i	0.378947	+	0.0266562i
$232$		0			0
$233$	5.92360e6	+	1.02600e7i	0.468293	+	0.811107i	0.999343	−	0.0362330i	$-0.0115359\pi$
$233$	5.92360e6	+	1.02600e7i	0.468293	+	0.811107i	−0.531050	+	0.847340i	$0.678203\pi$
$234$		0			0
$235$	−4.69004e6	+	8.12339e6i	−0.361387	+	0.625941i
$236$		0			0
$237$		−	1.19075e7i		−	0.894489i
$238$		0			0
$239$	−4.29229e6			−0.314410			−0.157205	−	0.987566i	$-0.550248\pi$
$239$	−4.29229e6			−0.314410			−0.157205	+	0.987566i	$0.550248\pi$
$240$		0			0
$241$	1.37366e7	+	7.93085e6i	0.981362	+	0.566589i	0.902681	−	0.430310i	$-0.141596\pi$
$241$	1.37366e7	+	7.93085e6i	0.981362	+	0.566589i	0.0786807	+	0.996900i	$0.474929\pi$
$242$		0			0
$243$	797162.	−	460241.i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−1.87610e7	−	1.46827e7i	−1.27573	−	0.998410i
$246$		0			0
$247$	−1.85761e6	−	3.21747e6i	−0.123272	−	0.213513i
$248$		0			0
$249$	−6.69838e6	+	1.16019e7i	−0.433882	+	0.751505i
$250$		0			0
$251$			7.11752e6i			0.450099i	0.974347	+	0.225049i	$0.0722543\pi$
$251$			7.11752e6i			0.450099i	−0.974347	+	0.225049i	$0.927746\pi$
$252$		0			0
$253$	−1.11531e7			−0.688707
$254$		0			0
$255$	−1.19923e7	−	6.92374e6i	−0.723238	−	0.417562i
$256$		0			0
$257$	−6.24715e6	+	3.60680e6i	−0.368030	+	0.212482i	−0.672597	−	0.740009i	$-0.734821\pi$
$257$	−6.24715e6	+	3.60680e6i	−0.368030	+	0.212482i	0.304568	+	0.952491i	$0.401488\pi$
$258$		0			0
$259$	−378451.	+	5.38010e6i	−0.0217826	+	0.309664i
$260$		0			0
$261$	760898.	+	1.31791e6i	0.0427962	+	0.0741251i
$262$		0			0
$263$	−8.28046e6	+	1.43422e7i	−0.455184	+	0.788402i	−0.998699	−	0.0509974i	$-0.983760\pi$
$263$	−8.28046e6	+	1.43422e7i	−0.455184	+	0.788402i	0.543514	+	0.839400i	$0.317093\pi$
$264$		0			0
$265$		−	2.59249e7i		−	1.39309i
$266$		0			0
$267$	2.80400e6			0.147314
$268$		0			0
$269$	4.73497e6	+	2.73374e6i	0.243254	+	0.140443i	0.616671	−	0.787221i	$-0.288481\pi$
$269$	4.73497e6	+	2.73374e6i	0.243254	+	0.140443i	−0.373417	+	0.927663i	$0.621814\pi$
$270$		0			0
$271$	1.61594e7	−	9.32961e6i	0.811925	−	0.468765i	−0.0356988	−	0.999363i	$-0.511366\pi$
$271$	1.61594e7	−	9.32961e6i	0.811925	−	0.468765i	0.847624	+	0.530597i	$0.178032\pi$
$272$		0			0
$273$	1.32207e6	−	644139.i	0.0649780	−	0.0316586i
$274$		0			0
$275$	−1.11134e7	−	1.92490e7i	−0.534379	−	0.925572i
$276$		0			0
$277$	3.81751e6	−	6.61212e6i	0.179614	−	0.311101i	−0.762134	−	0.647419i	$-0.775848\pi$
$277$	3.81751e6	−	6.61212e6i	0.179614	−	0.311101i	0.941748	+	0.336318i	$0.109182\pi$
$278$		0			0
$279$			4.96359e6i			0.228551i
$280$		0			0
$281$	−2.86272e7			−1.29021			−0.645103	−	0.764095i	$-0.723186\pi$
$281$	−2.86272e7			−1.29021			−0.645103	+	0.764095i	$0.723186\pi$
$282$		0			0
$283$	1.84385e7	+	1.06455e7i	0.813518	+	0.469685i	0.848176	−	0.529714i	$-0.177701\pi$
$283$	1.84385e7	+	1.06455e7i	0.813518	+	0.469685i	−0.0346580	+	0.999399i	$0.511034\pi$
$284$		0			0
$285$	3.69255e7	−	2.13189e7i	1.59511	−	0.920939i
$286$		0			0
$287$	−1.34233e7	+	1.98831e7i	−0.567823	+	0.841081i
$288$		0			0
$289$	−2.44666e6	−	4.23774e6i	−0.101363	−	0.175566i
$290$		0			0
$291$	2.65137e6	−	4.59231e6i	0.107595	−	0.186360i
$292$		0			0
$293$		−	1.72102e7i		−	0.684199i	−0.939664	−	0.342100i	$-0.888862\pi$
$293$		−	1.72102e7i		−	0.684199i	0.939664	−	0.342100i	$-0.111138\pi$
$294$		0			0
$295$	5.67885e7			2.21205
$296$		0			0
$297$	−2.87296e6	−	1.65870e6i	−0.109663	−	0.0633139i
$298$		0			0
$299$	−3.03352e6	+	1.75140e6i	−0.113484	+	0.0655198i
$300$		0			0
$301$	3.22151e7	+	2.17488e7i	1.18130	+	0.797509i
$302$		0			0
$303$	−8.13228e6	−	1.40855e7i	−0.292338	−	0.506344i
$304$		0			0
$305$	−9.90933e6	+	1.71635e7i	−0.349257	+	0.604930i
$306$		0			0
$307$		−	4.11253e7i		−	1.42133i	−0.703533	−	0.710663i	$-0.748395\pi$
$307$		−	4.11253e7i		−	1.42133i	0.703533	−	0.710663i	$-0.251605\pi$
$308$		0			0
$309$	−1.21594e7			−0.412132
$310$		0			0
$311$	−9.88085e6	−	5.70471e6i	−0.328483	−	0.189650i	0.326684	−	0.945133i	$-0.394069\pi$
$311$	−9.88085e6	−	5.70471e6i	−0.328483	−	0.189650i	−0.655167	+	0.755484i	$0.727402\pi$
$312$		0			0
$313$	−930200.	+	537051.i	−0.0303350	+	0.0175139i	−0.515091	−	0.857136i	$-0.672242\pi$
$313$	−930200.	+	537051.i	−0.0303350	+	0.0175139i	0.484756	+	0.874650i	$0.338908\pi$
$314$		0			0
$315$	7.39249e6	+	1.51728e7i	0.236515	+	0.485438i
$316$		0			0
$317$	9.89978e6	+	1.71469e7i	0.310776	+	0.538280i	0.978531	−	0.206101i	$-0.0660777\pi$
$317$	9.89978e6	+	1.71469e7i	0.310776	+	0.538280i	−0.667754	+	0.744382i	$0.732744\pi$
$318$		0			0
$319$	2.74226e6	−	4.74974e6i	0.0844768	−	0.146318i
$320$		0			0
$321$			1.55524e7i			0.470200i
$322$		0			0
$323$	−5.92551e7			−1.75840
$324$		0			0
$325$	−6.04545e6	−	3.49034e6i	−0.176108	−	0.101676i
$326$		0			0
$327$	1.96516e7	−	1.13458e7i	0.562023	−	0.324484i
$328$		0			0
$329$	−1.58494e7	−	1.11489e6i	−0.445065	−	0.0313071i
$330$		0			0
$331$	−9.56610e6	−	1.65690e7i	−0.263785	−	0.456890i	0.703459	−	0.710736i	$-0.251638\pi$
$331$	−9.56610e6	−	1.65690e7i	−0.263785	−	0.456890i	−0.967245	+	0.253846i	$0.918304\pi$
$332$		0			0
$333$	1.91049e6	−	3.30906e6i	0.0517382	−	0.0896132i
$334$		0			0
$335$			3.53473e7i			0.940204i
$336$		0			0
$337$	6.12984e7			1.60162			0.800810	−	0.598919i	$-0.204403\pi$
$337$	6.12984e7			1.60162			0.800810	+	0.598919i	$0.204403\pi$
$338$		0			0
$339$	−2.39776e6	−	1.38435e6i	−0.0615469	−	0.0355341i
$340$		0			0
$341$	1.54921e7	−	8.94435e6i	0.390703	−	0.225572i
$342$		0			0
$343$	8.43899e6	−	3.94613e7i	0.209126	−	0.977889i
$344$		0			0
$345$	−2.01000e7	−	3.48143e7i	−0.489485	−	0.847814i
$346$		0			0
$347$	3.87907e7	−	6.71875e7i	0.928409	−	1.60805i	0.142424	−	0.989806i	$-0.454510\pi$
$347$	3.87907e7	−	6.71875e7i	0.928409	−	1.60805i	0.785985	−	0.618246i	$-0.212156\pi$
$348$		0			0
$349$		−	3.32443e7i		−	0.782061i	−0.920378	−	0.391031i	$-0.872119\pi$
$349$		−	3.32443e7i		−	0.782061i	0.920378	−	0.391031i	$-0.127881\pi$
$350$		0			0
$351$	−1.04188e6			−0.0240934
$352$		0			0
$353$	−1.68383e7	−	9.72160e6i	−0.382802	−	0.221011i	0.296235	−	0.955115i	$-0.404269\pi$
$353$	−1.68383e7	−	9.72160e6i	−0.382802	−	0.221011i	−0.679037	+	0.734104i	$0.737602\pi$
$354$		0			0
$355$	6.06264e7	−	3.50027e7i	1.35512	−	0.782377i
$356$		0			0
$357$	1.64587e6	−	2.33979e7i	0.0361735	−	0.514246i
$358$		0			0
$359$	1.27237e7	+	2.20381e7i	0.274999	+	0.476311i	0.970135	−	0.242567i	$-0.0779893\pi$
$359$	1.27237e7	+	2.20381e7i	0.274999	+	0.476311i	−0.695136	+	0.718878i	$0.744656\pi$
$360$		0			0
$361$	6.77034e7	−	1.17266e8i	1.43909	−	2.49258i
$362$		0			0
$363$		−	1.56600e7i		−	0.327395i
$364$		0			0
$365$	2.44552e7			0.502914
$366$		0			0
$367$	7.02719e6	+	4.05715e6i	0.142162	+	0.0820773i	0.569394	−	0.822065i	$-0.307178\pi$
$367$	7.02719e6	+	4.05715e6i	0.142162	+	0.0820773i	−0.427232	+	0.904142i	$0.640511\pi$
$368$		0			0
$369$	1.47188e7	−	8.49793e6i	0.292951	−	0.169135i
$370$		0			0
$371$	3.94767e7	−	1.92339e7i	0.773071	−	0.376656i
$372$		0			0
$373$	3.60324e7	+	6.24099e7i	0.694330	+	1.20262i	0.970406	+	0.241480i	$0.0776327\pi$
$373$	3.60324e7	+	6.24099e7i	0.694330	+	1.20262i	−0.276076	+	0.961136i	$0.589034\pi$
$374$		0			0
$375$	1.53960e7	−	2.66667e7i	0.291955	−	0.505680i
$376$		0			0
$377$		−	1.72250e6i		−	0.0321466i
$378$		0			0
$379$	−4.53715e7			−0.833423			−0.416711	−	0.909039i	$-0.636817\pi$
$379$	−4.53715e7			−0.833423			−0.416711	+	0.909039i	$0.636817\pi$
$380$		0			0
$381$	1.24790e7	+	7.20477e6i	0.225635	+	0.130270i
$382$		0			0
$383$	−6.55862e7	+	3.78662e7i	−1.16739	+	0.673994i	−0.953064	−	0.302768i	$-0.902089\pi$
$383$	−6.55862e7	+	3.78662e7i	−1.16739	+	0.673994i	−0.214327	+	0.976762i	$0.568756\pi$
$384$		0			0
$385$	3.40352e7	−	5.04143e7i	0.596412	−	0.883429i
$386$		0			0
$387$	−1.37686e7	−	2.38479e7i	−0.237551	−	0.411450i
$388$		0			0
$389$	−4.41471e6	+	7.64649e6i	−0.0749986	+	0.129901i	−0.901086	−	0.433641i	$-0.857229\pi$
$389$	−4.41471e6	+	7.64649e6i	−0.0749986	+	0.129901i	0.826087	+	0.563542i	$0.190562\pi$
$390$		0			0
$391$			5.58672e7i			0.934602i
$392$		0			0
$393$	1.50772e7			0.248396
$394$		0			0
$395$	−1.33957e8	−	7.73400e7i	−2.17357	−	1.25491i
$396$		0			0
$397$	−3.45140e7	+	1.99267e7i	−0.551599	+	0.318466i	−0.749767	−	0.661702i	$-0.769834\pi$
$397$	−3.45140e7	+	1.99267e7i	−0.551599	+	0.318466i	0.198167	+	0.980168i	$0.436501\pi$
$398$		0			0
$399$	5.98584e7	+	4.04111e7i	0.942338	+	0.636182i
$400$		0			0
$401$	1.65566e6	+	2.86769e6i	0.0256767	+	0.0444733i	0.878578	−	0.477599i	$-0.158493\pi$
$401$	1.65566e6	+	2.86769e6i	0.0256767	+	0.0444733i	−0.852902	+	0.522072i	$0.825159\pi$
$402$		0			0
$403$	2.80911e6	−	4.86553e6i	0.0429194	−	0.0743386i
$404$		0			0
$405$		−	1.19572e7i		−	0.179997i
$406$		0			0
$407$	−1.37707e7			−0.204255
$408$		0			0
$409$	−8.98031e7	−	5.18478e7i	−1.31257	−	0.757811i	−0.330046	−	0.943965i	$-0.607064\pi$
$409$	−8.98031e7	−	5.18478e7i	−1.31257	−	0.757811i	−0.982521	+	0.186154i	$0.940398\pi$
$410$		0			0
$411$	6.34517e7	−	3.66338e7i	0.913940	−	0.527663i
$412$		0			0
$413$	4.21318e7	+	8.64738e7i	0.598081	+	1.22754i
$414$		0			0
$415$	8.70129e7	+	1.50711e8i	1.21742	+	2.10863i
$416$		0			0
$417$	−1.28064e7	+	2.21813e7i	−0.176611	+	0.305899i
$418$		0			0
$419$		−	2.42723e7i		−	0.329965i	−0.986296	−	0.164983i	$-0.947243\pi$
$419$		−	2.42723e7i		−	0.329965i	0.986296	−	0.164983i	$-0.0527568\pi$
$420$		0			0
$421$	−8.03195e7			−1.07640			−0.538201	−	0.842816i	$-0.680896\pi$
$421$	−8.03195e7			−1.07640			−0.538201	+	0.842816i	$0.680896\pi$
$422$		0			0
$423$	9.74824e6	+	5.62815e6i	0.128797	+	0.0743609i
$424$		0			0
$425$	−9.64205e7	+	5.56684e7i	−1.25604	+	0.725174i
$426$		0			0
$427$	−3.34872e7	−	2.35558e6i	−0.430126	−	0.0302562i
$428$		0			0
$429$	1.87747e6	+	3.25186e6i	0.0237794	+	0.0411870i
$430$		0			0
$431$	−2.93452e7	+	5.08273e7i	−0.366526	+	0.634841i	−0.989020	−	0.147783i	$-0.952786\pi$
$431$	−2.93452e7	+	5.08273e7i	−0.366526	+	0.634841i	0.622494	+	0.782625i	$0.286120\pi$
$432$		0			0
$433$			1.51707e8i			1.86871i	0.356344	+	0.934355i	$0.384023\pi$
$433$			1.51707e8i			1.86871i	−0.356344	+	0.934355i	$0.615977\pi$
$434$		0			0
$435$	1.97684e7			0.240161
$436$		0			0
$437$	−1.48975e8	−	8.60105e7i	−1.78512	−	1.03064i
$438$		0			0
$439$	−1.05336e8	+	6.08155e7i	−1.24504	+	0.718821i	−0.970115	−	0.242646i	$-0.921985\pi$
$439$	−1.05336e8	+	6.08155e7i	−1.24504	+	0.718821i	−0.274920	+	0.961467i	$0.588651\pi$
$440$		0			0
$441$	−1.76196e7	+	2.25136e7i	−0.205438	+	0.262500i
$442$		0			0
$443$	4.63310e7	+	8.02476e7i	0.532918	+	0.923041i	0.999261	+	0.0384371i	$0.0122379\pi$
$443$	4.63310e7	+	8.02476e7i	0.532918	+	0.923041i	−0.466343	+	0.884604i	$0.654429\pi$
$444$		0			0
$445$	1.82122e7	−	3.15444e7i	0.206672	−	0.357967i
$446$		0			0
$447$			7.21337e7i			0.807636i
$448$		0			0
$449$	−2.40772e7			−0.265991			−0.132996	−	0.991117i	$-0.542460\pi$
$449$	−2.40772e7			−0.265991			−0.132996	+	0.991117i	$0.542460\pi$
$450$		0			0
$451$	−5.30465e7	−	3.06264e7i	−0.578265	−	0.333862i
$452$		0			0
$453$	6.06447e7	−	3.50133e7i	0.652377	−	0.376650i
$454$		0			0
$455$	1.34051e6	−	1.90568e7i	0.0142310	−	0.202309i
$456$		0			0
$457$	3.25397e7	+	5.63605e7i	0.340930	+	0.590509i	0.984606	−	0.174790i	$-0.0559247\pi$
$457$	3.25397e7	+	5.63605e7i	0.340930	+	0.590509i	−0.643675	+	0.765299i	$0.722591\pi$
$458$		0			0
$459$	−8.30864e6	+	1.43910e7i	−0.0859195	+	0.148817i
$460$		0			0
$461$			1.22022e8i			1.24548i	0.782429	+	0.622740i	$0.213980\pi$
$461$			1.22022e8i			1.24548i	−0.782429	+	0.622740i	$0.786020\pi$
$462$		0			0
$463$	−2.62985e7			−0.264965			−0.132482	−	0.991185i	$-0.542295\pi$
$463$	−2.62985e7			−0.264965			−0.132482	+	0.991185i	$0.542295\pi$
$464$		0			0
$465$	5.58394e7	+	3.22389e7i	0.555369	+	0.320643i
$466$		0			0
$467$	−5.31512e7	+	3.06869e7i	−0.521870	+	0.301302i	−0.737699	−	0.675129i	$-0.764088\pi$
$467$	−5.31512e7	+	3.06869e7i	−0.521870	+	0.301302i	0.215829	+	0.976431i	$0.430755\pi$
$468$		0			0
$469$	−5.38246e7	+	2.62244e7i	−0.521750	+	0.254207i
$470$		0			0
$471$	3.76073e7	+	6.51378e7i	0.359923	+	0.623405i
$472$		0			0
$473$	−4.96218e7	+	8.59475e7i	−0.468909	+	0.812175i
$474$		0			0
$475$		−	3.42818e8i		−	3.19877i
$476$		0			0
$477$	−3.11104e7			−0.286649
$478$		0			0
$479$	1.67375e8	+	9.66342e7i	1.52295	+	0.879274i	0.999632	+	0.0271349i	$0.00863836\pi$
$479$	1.67375e8	+	9.66342e7i	1.52295	+	0.879274i	0.523315	+	0.852139i	$0.324695\pi$
$480$		0			0
$481$	−3.74548e6	+	2.16246e6i	−0.0336568	+	0.0194317i
$482$		0			0
$483$	3.81006e7	−	5.64361e7i	0.338135	−	0.500859i
$484$		0			0
$485$	−3.44417e7	−	5.96548e7i	−0.301898	−	0.522902i
$486$		0			0
$487$	741867.	−	1.28495e6i	0.00642302	−	0.0111250i	−0.862796	−	0.505552i	$-0.831289\pi$
$487$	741867.	−	1.28495e6i	0.00642302	−	0.0111250i	0.869219	+	0.494427i	$0.164622\pi$
$488$		0			0
$489$			5.29268e7i			0.452636i
$490$		0			0
$491$	−1.33332e8			−1.12639			−0.563195	−	0.826324i	$-0.690428\pi$
$491$	−1.33332e8			−1.12639			−0.563195	+	0.826324i	$0.690428\pi$
$492$		0			0
$493$	−2.37920e7	−	1.37363e7i	−0.198559	−	0.114638i
$494$		0			0
$495$	−3.73202e7	+	2.15468e7i	−0.307700	+	0.177651i
$496$		0			0
$497$	9.82790e7	+	6.63493e7i	0.800556	+	0.540464i
$498$		0			0
$499$	7.54918e7	+	1.30756e8i	0.607573	+	1.05235i	0.991639	+	0.129042i	$0.0411901\pi$
$499$	7.54918e7	+	1.30756e8i	0.607573	+	1.05235i	−0.384066	+	0.923306i	$0.625477\pi$
$500$		0			0
$501$	1.59453e7	−	2.76181e7i	0.126800	−	0.219625i
$502$		0			0
$503$			9.92575e7i			0.779937i	0.920828	+	0.389968i	$0.127514\pi$
$503$			9.92575e7i			0.779937i	−0.920828	+	0.389968i	$0.872486\pi$
$504$		0			0
$505$	−2.11279e8			−1.64052
$506$		0			0
$507$	−6.41406e7	−	3.70316e7i	−0.492163	−	0.284151i
$508$		0			0
$509$	1.07059e8	−	6.18103e7i	0.811835	−	0.468713i	−0.0357576	−	0.999360i	$-0.511384\pi$
$509$	1.07059e8	−	6.18103e7i	0.811835	−	0.468713i	0.847593	+	0.530647i	$0.178051\pi$
$510$		0			0
$511$	1.81435e7	+	3.72389e7i	0.135975	+	0.279083i
$512$		0			0
$513$	−2.55832e7	−	4.43114e7i	−0.189497	−	0.328218i
$514$		0			0
$515$	−7.89762e7	+	1.36791e8i	−0.578195	+	1.00146i
$516$		0			0
$517$		−	4.05675e7i		−	0.293567i
$518$		0			0
$519$	4.90965e6			0.0351195
$520$		0			0
$521$	1.41733e8	+	8.18296e7i	1.00221	+	0.578625i	0.908901	−	0.417012i	$-0.136923\pi$
$521$	1.41733e8	+	8.18296e7i	1.00221	+	0.578625i	0.0933071	+	0.995637i	$0.470256\pi$
$522$		0			0
$523$	−2.21384e8	+	1.27816e8i	−1.54754	+	0.893471i	−0.549208	+	0.835686i	$0.685070\pi$
$523$	−2.21384e8	+	1.27816e8i	−1.54754	+	0.893471i	−0.998329	+	0.0577847i	$0.981596\pi$
$524$		0			0
$525$	1.35367e8	+	9.52211e6i	0.935483	+	0.0658044i
$526$		0			0
$527$	−4.48033e7	−	7.76016e7i	−0.306111	−	0.530199i
$528$		0			0
$529$	−7.07498e6	+	1.22542e7i	−0.0477924	+	0.0827788i
$530$		0			0
$531$		−	6.81474e7i		−	0.455161i
$532$		0			0
$533$	−1.92374e7			−0.127047
$534$		0			0
$535$	1.74962e8	+	1.01014e8i	1.14257	+	0.659661i
$536$		0			0
$537$	5.43250e7	−	3.13645e7i	0.350814	−	0.202542i
$538$		0			0
$539$	1.02019e8	+	1.44239e7i	0.651498	+	0.0921122i
$540$		0			0
$541$	1.21035e8	+	2.09639e8i	0.764398	+	1.32398i	0.940564	+	0.339616i	$0.110297\pi$
$541$	1.21035e8	+	2.09639e8i	0.764398	+	1.32398i	−0.176166	+	0.984361i	$0.556369\pi$
$542$		0			0
$543$	1.19891e7	−	2.07658e7i	0.0748838	−	0.129703i
$544$		0			0
$545$		−	2.94768e8i		−	1.82092i
$546$		0			0
$547$	3.05715e7			0.186790			0.0933952	−	0.995629i	$-0.470228\pi$
$547$	3.05715e7			0.186790			0.0933952	+	0.995629i	$0.470228\pi$
$548$		0			0
$549$	2.05965e7	+	1.18914e7i	0.124473	+	0.0718648i
$550$		0			0
$551$	7.32581e7	−	4.22956e7i	0.437926	−	0.252837i
$552$		0			0
$553$	1.83848e7	−	2.61360e8i	0.108713	−	1.54548i
$554$		0			0
$555$	−2.48175e7	−	4.29852e7i	−0.145171	−	0.251443i
$556$		0			0
$557$	−1.16542e8	+	2.01856e8i	−0.674396	+	1.16809i	0.302249	+	0.953229i	$0.402263\pi$
$557$	−1.16542e8	+	2.01856e8i	−0.674396	+	1.16809i	−0.976645	+	0.214860i	$0.931071\pi$
$558$		0			0
$559$			3.11690e7i			0.178438i
$560$		0			0
$561$	5.98884e7			0.339199
$562$		0			0
$563$	−1.95271e8	−	1.12740e8i	−1.09424	−	0.631758i	−0.159536	−	0.987192i	$-0.551000\pi$
$563$	−1.95271e8	−	1.12740e8i	−1.09424	−	0.631758i	−0.934702	+	0.355434i	$0.884333\pi$
$564$		0			0
$565$	−3.11472e7	+	1.79829e7i	−0.172693	+	0.0997042i
$566$		0			0
$567$	1.82077e7	−	8.87115e6i	0.0998862	−	0.0486666i
$568$		0			0
$569$	−1.07390e8	−	1.86004e8i	−0.582943	−	1.00969i	−0.995128	−	0.0985864i	$-0.968568\pi$
$569$	−1.07390e8	−	1.86004e8i	−0.582943	−	1.00969i	0.412186	−	0.911100i	$-0.364765\pi$
$570$		0			0
$571$	1.71362e8	−	2.96807e8i	0.920460	−	1.59428i	0.121757	−	0.992560i	$-0.461147\pi$
$571$	1.71362e8	−	2.96807e8i	0.920460	−	1.59428i	0.798704	−	0.601724i	$-0.205519\pi$
$572$		0			0
$573$		−	6.66766e7i		−	0.354413i
$574$		0			0
$575$	−3.23217e8			−1.70017
$576$		0			0
$577$	2.42646e8	+	1.40092e8i	1.26312	+	0.729263i	0.973677	−	0.227931i	$-0.0731962\pi$
$577$	2.42646e8	+	1.40092e8i	1.26312	+	0.729263i	0.289444	+	0.957195i	$0.406530\pi$
$578$		0			0
$579$	−8.70243e7	+	5.02435e7i	−0.448337	+	0.258848i
$580$		0			0
$581$	−1.64937e8	+	2.44311e8i	−0.840989	+	1.24570i
$582$		0			0
$583$	5.60607e7	+	9.71000e7i	0.282913	+	0.490020i
$584$		0			0
$585$	−6.76711e6	+	1.17210e7i	−0.0338015	+	0.0585458i
$586$		0			0
$587$			2.73172e8i			1.35059i	0.737549	+	0.675293i	$0.235983\pi$
$587$			2.73172e8i			1.35059i	−0.737549	+	0.675293i	$0.764017\pi$
$588$		0			0
$589$	2.75908e8			1.35026
$590$		0			0
$591$	3.68840e7	+	2.12950e7i	0.178680	+	0.103161i
$592$		0			0
$593$	−3.17713e8	+	1.83432e8i	−1.52360	+	0.879651i	−0.523991	+	0.851724i	$0.675557\pi$
$593$	−3.17713e8	+	1.83432e8i	−1.52360	+	0.879651i	−0.999610	+	0.0279272i	$0.991109\pi$
$594$		0			0
$595$	−2.52531e8	−	1.70487e8i	−1.19885	−	0.809355i
$596$		0			0
$597$	4.65507e6	+	8.06283e6i	0.0218778	+	0.0378935i
$598$		0			0
$599$	−8.45253e7	+	1.46402e8i	−0.393284	+	0.681188i	−0.992881	−	0.119114i	$-0.961994\pi$
$599$	−8.45253e7	+	1.46402e8i	−0.393284	+	0.681188i	0.599596	+	0.800303i	$0.295328\pi$
$600$		0			0
$601$			1.61411e8i			0.743551i	0.928323	+	0.371775i	$0.121251\pi$
$601$			1.61411e8i			0.743551i	−0.928323	+	0.371775i	$0.878749\pi$
$602$		0			0
$603$	4.24175e7			0.193461
$604$		0			0
$605$	−1.76172e8	−	1.01713e8i	−0.795556	−	0.459315i
$606$		0			0
$607$	−1.67933e8	+	9.69564e7i	−0.750881	+	0.433521i	−0.826012	−	0.563652i	$-0.809396\pi$
$607$	−1.67933e8	+	9.69564e7i	−0.750881	+	0.433521i	0.0751313	+	0.997174i	$0.476062\pi$
$608$		0			0
$609$	1.46663e7	+	3.01020e7i	0.0649335	+	0.133273i
$610$		0			0
$611$	−6.37043e6	−	1.10339e7i	−0.0279283	−	0.0483733i
$612$		0			0
$613$	5.21774e7	−	9.03739e7i	0.226517	−	0.392339i	−0.730256	−	0.683173i	$-0.760599\pi$
$613$	5.21774e7	−	9.03739e7i	0.226517	−	0.392339i	0.956773	+	0.290834i	$0.0939328\pi$
$614$		0			0
$615$		−	2.20779e8i		−	0.949143i
$616$		0			0
$617$	−3.99769e8			−1.70198			−0.850989	−	0.525183i	$-0.823997\pi$
$617$	−3.99769e8			−1.70198			−0.850989	+	0.525183i	$0.823997\pi$
$618$		0			0
$619$	2.11757e8	+	1.22258e8i	0.892822	+	0.515471i	0.874865	−	0.484368i	$-0.160950\pi$
$619$	2.11757e8	+	1.22258e8i	0.892822	+	0.515471i	0.0179577	+	0.999839i	$0.494284\pi$
$620$		0			0
$621$	−4.17779e7	+	2.41205e7i	−0.174450	+	0.100719i
$622$		0			0
$623$	6.15456e7	+	4.32929e6i	0.254526	+	0.0179041i
$624$		0			0
$625$	−1.71720e6	−	2.97427e6i	−0.00703363	−	0.0121826i
$626$		0			0
$627$	−9.22014e7	+	1.59698e8i	−0.374055	+	0.647881i
$628$		0			0
$629$			6.89792e7i			0.277183i
$630$		0			0
$631$	2.46592e8			0.981500			0.490750	−	0.871301i	$-0.336723\pi$
$631$	2.46592e8			0.981500			0.490750	+	0.871301i	$0.336723\pi$
$632$		0			0
$633$	−4.96263e7	−	2.86517e7i	−0.195659	−	0.112964i
$634$		0			0
$635$	1.62105e8	−	9.35911e7i	0.633102	−	0.365522i
$636$		0			0
$637$	3.00129e7	−	1.20971e7i	0.116116	−	0.0468019i
$638$		0			0
$639$	−4.20040e7	−	7.27530e7i	−0.160986	−	0.278836i
$640$		0			0
$641$	−1.80422e8	+	3.12501e8i	−0.685040	+	1.18652i	0.288384	+	0.957515i	$0.406882\pi$
$641$	−1.80422e8	+	3.12501e8i	−0.685040	+	1.18652i	−0.973424	+	0.229010i	$0.926451\pi$
$642$		0			0
$643$			9.49305e7i			0.357086i	0.983932	+	0.178543i	$0.0571384\pi$
$643$			9.49305e7i			0.357086i	−0.983932	+	0.178543i	$0.942862\pi$
$644$		0			0
$645$	−3.57712e8			−1.33307
$646$		0			0
$647$	1.29149e8	+	7.45642e7i	0.476846	+	0.275307i	0.719101	−	0.694905i	$-0.244554\pi$
$647$	1.29149e8	+	7.45642e7i	0.476846	+	0.275307i	−0.242255	+	0.970213i	$0.577887\pi$
$648$		0			0
$649$	−2.12698e8	+	1.22801e8i	−0.778088	+	0.449229i
$650$		0			0
$651$	−7.66363e6	+	1.08947e8i	−0.0277774	+	0.394886i
$652$		0			0
$653$	2.54667e6	+	4.41096e6i	0.00914604	+	0.0158414i	0.870562	−	0.492058i	$-0.163755\pi$
$653$	2.54667e6	+	4.41096e6i	0.00914604	+	0.0158414i	−0.861416	+	0.507900i	$0.830422\pi$
$654$		0			0
$655$	9.79278e7	−	1.69616e8i	0.348483	−	0.603591i
$656$		0			0
$657$		−	2.93468e7i		−	0.103482i
$658$		0			0
$659$	−5.76822e6			−0.0201551			−0.0100776	−	0.999949i	$-0.503208\pi$
$659$	−5.76822e6			−0.0201551			−0.0100776	+	0.999949i	$0.503208\pi$
$660$		0			0
$661$	1.29229e7	+	7.46102e6i	0.0447460	+	0.0258341i	0.522206	−	0.852819i	$-0.325109\pi$
$661$	1.29229e7	+	7.46102e6i	0.0447460	+	0.0258341i	−0.477460	+	0.878653i	$0.658442\pi$
$662$		0			0
$663$	1.62890e7	−	9.40444e6i	0.0558924	−	0.0322695i
$664$		0			0
$665$	8.43402e8	−	4.10922e8i	2.86794	−	1.39732i
$666$		0			0
$667$	−3.98774e7	−	6.90696e7i	−0.134384	−	0.232761i
$668$		0			0
$669$	−1.11633e8	+	1.93354e8i	−0.372833	+	0.645766i
$670$		0			0
$671$		−	8.57129e7i		−	0.283713i
$672$		0			0
$673$	2.64968e8			0.869257			0.434629	−	0.900610i	$-0.356880\pi$
$673$	2.64968e8			0.869257			0.434629	+	0.900610i	$0.356880\pi$
$674$		0			0
$675$	−8.32584e7	−	4.80693e7i	−0.270718	−	0.156299i
$676$		0			0
$677$	2.64867e8	−	1.52921e8i	0.853615	−	0.492835i	−0.00825369	−	0.999966i	$-0.502627\pi$
$677$	2.64867e8	−	1.52921e8i	0.853615	−	0.492835i	0.861869	+	0.507131i	$0.169294\pi$
$678$		0			0
$679$	6.52860e7	−	9.67041e7i	0.208550	−	0.308912i
$680$		0			0
$681$	−2.36252e7	−	4.09200e7i	−0.0748055	−	0.129567i
$682$		0			0
$683$	7.48455e7	−	1.29636e8i	0.234911	−	0.406878i	−0.724336	−	0.689447i	$-0.757853\pi$
$683$	7.48455e7	−	1.29636e8i	0.234911	−	0.406878i	0.959247	+	0.282570i	$0.0911868\pi$
$684$		0			0
$685$		−	9.51758e8i		−	2.96111i
$686$		0			0
$687$	9.75949e7			0.300993
$688$		0			0
$689$	3.04957e7	+	1.76067e7i	0.0932356	+	0.0538296i
$690$		0			0
$691$	−2.20972e8	+	1.27578e8i	−0.669736	+	0.386672i	−0.795977	−	0.605327i	$-0.793042\pi$
$691$	−2.20972e8	+	1.27578e8i	−0.669736	+	0.386672i	0.126241	+	0.992000i	$0.459709\pi$
$692$		0			0
$693$	−6.04982e7	−	4.08430e7i	−0.181779	−	0.122721i
$694$		0			0
$695$	1.66356e8	+	2.88138e8i	0.495548	+	0.858313i
$696$		0			0
$697$	−1.53411e8	+	2.65716e8i	−0.453063	+	0.784729i
$698$		0			0
$699$		−	1.84679e8i		−	0.540738i
$700$		0			0
$701$	−2.47105e8			−0.717343			−0.358672	−	0.933464i	$-0.616770\pi$
$701$	−2.47105e8			−0.717343			−0.358672	+	0.933464i	$0.616770\pi$
$702$		0			0
$703$	−1.83939e8	−	1.06197e8i	−0.529429	−	0.305666i
$704$		0			0
$705$	1.26631e8	−	7.31105e7i	0.361387	−	0.208647i
$706$		0			0
$707$	−1.56750e8	−	3.21722e8i	−0.443556	−	0.910381i
$708$		0			0
$709$	5.21037e7	+	9.02462e7i	0.146194	+	0.253215i	0.929818	−	0.368020i	$-0.119964\pi$
$709$	5.21037e7	+	9.02462e7i	0.146194	+	0.253215i	−0.783624	+	0.621236i	$0.786631\pi$
$710$		0			0
$711$	−9.28096e7	+	1.60751e8i	−0.258217	+	0.447244i
$712$		0			0
$713$		−	2.60133e8i		−	0.717675i
$714$		0			0
$715$	4.87771e7			0.133444
$716$		0			0
$717$	5.79460e7	+	3.34551e7i	0.157205	+	0.0907622i
$718$		0			0
$719$	4.11126e8	−	2.37363e8i	1.10608	−	0.638598i	0.168271	−	0.985741i	$-0.446182\pi$
$719$	4.11126e8	−	2.37363e8i	1.10608	−	0.638598i	0.937812	+	0.347143i	$0.112848\pi$
$720$		0			0
$721$	−2.66889e8	−	1.87737e7i	−0.712074	−	0.0500893i
$722$		0			0
$723$	−1.23630e8	−	2.14133e8i	−0.327121	−	0.566589i
$724$		0			0
$725$	7.94709e7	−	1.37648e8i	0.208542	−	0.361206i
$726$		0			0
$727$			1.04048e8i			0.270790i	0.990792	+	0.135395i	$0.0432303\pi$
$727$			1.04048e8i			0.270790i	−0.990792	+	0.135395i	$0.956770\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	4.30521e8	+	2.48561e8i	1.10215	+	0.636329i
$732$		0			0
$733$	5.79355e8	−	3.34491e8i	1.47107	−	0.849322i	0.471597	−	0.881814i	$-0.343678\pi$
$733$	5.79355e8	−	3.34491e8i	1.47107	−	0.849322i	0.999472	+	0.0324917i	$0.0103443\pi$
$734$		0			0
$735$	1.38833e8	+	3.44445e8i	0.349648	+	0.867476i
$736$		0			0
$737$	−7.64361e7	−	1.32391e8i	−0.190940	−	0.330717i
$738$		0			0
$739$	−1.54148e8	+	2.66992e8i	−0.381948	+	0.661554i	−0.991341	−	0.131315i	$-0.958080\pi$
$739$	−1.54148e8	+	2.66992e8i	−0.381948	+	0.661554i	0.609393	+	0.792869i	$0.291413\pi$
$740$		0			0
$741$			5.79145e7i			0.142342i
$742$		0			0
$743$	−1.83763e8			−0.448014			−0.224007	−	0.974588i	$-0.571914\pi$
$743$	−1.83763e8			−0.448014			−0.224007	+	0.974588i	$0.571914\pi$
$744$		0			0
$745$	8.11490e8	+	4.68514e8i	1.96252	+	1.13306i
$746$		0			0
$747$	1.80856e8	−	1.04417e8i	0.433882	−	0.250502i
$748$		0			0
$749$	−2.40125e7	+	3.41364e8i	−0.0571467	+	0.812404i
$750$		0			0
$751$	1.22666e8	+	2.12463e8i	0.289603	+	0.501608i	0.973715	−	0.227770i	$-0.0731433\pi$
$751$	1.22666e8	+	2.12463e8i	0.289603	+	0.501608i	−0.684112	+	0.729377i	$0.739810\pi$
$752$		0			0
$753$	5.54756e7	−	9.60865e7i	0.129932	−	0.225049i
$754$		0			0
$755$		−	9.09655e8i		−	2.11366i
$756$		0			0
$757$	−8.44770e8			−1.94738			−0.973690	−	0.227876i	$-0.926822\pi$
$757$	−8.44770e8			−1.94738			−0.973690	+	0.227876i	$0.926822\pi$
$758$		0			0
$759$	1.50567e8	+	8.69299e7i	0.344353	+	0.198812i
$760$		0			0
$761$	4.91638e8	−	2.83847e8i	1.11556	−	0.644066i	0.175293	−	0.984516i	$-0.443913\pi$
$761$	4.91638e8	−	2.83847e8i	1.11556	−	0.644066i	0.940263	+	0.340450i	$0.110579\pi$
$762$		0			0
$763$	4.48854e8	−	2.18691e8i	1.01049	−	0.492331i
$764$		0			0
$765$	1.07930e8	+	1.86941e8i	0.241079	+	0.417562i
$766$		0			0
$767$	−3.85676e7	+	6.68010e7i	−0.0854744	+	0.148046i
$768$		0			0
$769$			2.83103e6i			0.00622536i	0.999995	+	0.00311268i	$0.000990799\pi$
$769$			2.83103e6i			0.00622536i	−0.999995	+	0.00311268i	$0.999009\pi$
$770$		0			0
$771$	1.12449e8			0.245353
$772$		0			0
$773$	3.83914e8	+	2.21653e8i	0.831181	+	0.479883i	0.854257	−	0.519851i	$-0.174013\pi$
$773$	3.83914e8	+	2.21653e8i	0.831181	+	0.479883i	−0.0230756	+	0.999734i	$0.507346\pi$
$774$		0			0
$775$	4.48961e8	−	2.59208e8i	0.964503	−	0.556856i
$776$		0			0
$777$	4.70428e7	−	6.96816e7i	0.100284	−	0.148544i
$778$		0			0
$779$	−4.72369e8	−	8.18168e8i	−0.999239	−	1.73073i
$780$		0			0
$781$	−1.51382e8	+	2.62201e8i	−0.317775	+	0.550403i
$782$		0			0
$783$		−	2.37224e7i		−	0.0494168i
$784$		0			0
$785$	9.77049e8			2.01980
$786$		0			0
$787$	−6.26836e7	−	3.61904e7i	−0.128597	−	0.0742454i	0.434322	−	0.900758i	$-0.356988\pi$
$787$	−6.26836e7	−	3.61904e7i	−0.128597	−	0.0742454i	−0.562918	+	0.826512i	$0.690321\pi$
$788$		0			0
$789$	2.23572e8	−	1.29080e8i	0.455184	−	0.262801i
$790$		0			0
$791$	−5.04915e7	−	3.40874e7i	−0.102021	−	0.0688754i
$792$		0			0
$793$	−1.34597e7	−	2.33129e7i	−0.0269909	−	0.0467495i
$794$		0			0
$795$	−2.02064e8	+	3.49986e8i	−0.402150	+	0.696545i
$796$		0			0
$797$		−	8.26919e8i		−	1.63338i	−0.577075	−	0.816691i	$-0.695806\pi$
$797$		−	8.26919e8i		−	1.63338i	0.577075	−	0.816691i	$-0.304194\pi$
$798$		0			0
$799$	−2.03207e8			−0.398382
$800$		0			0
$801$	−3.78540e7	−	2.18550e7i	−0.0736570	−	0.0425259i
$802$		0			0
$803$	−9.15956e7	+	5.28827e7i	−0.176900	+	0.102133i
$804$		0			0
$805$	−3.87428e8	−	7.95181e8i	−0.742683	−	1.52433i
$806$		0			0
$807$	−4.26147e7	−	7.38109e7i	−0.0810847	−	0.140443i
$808$		0			0
$809$	1.39404e8	−	2.41454e8i	0.263287	−	0.456026i	−0.703827	−	0.710372i	$-0.748527\pi$
$809$	1.39404e8	−	2.41454e8i	0.263287	−	0.456026i	0.967113	+	0.254346i	$0.0818602\pi$
$810$		0			0
$811$		−	8.06633e8i		−	1.51222i	−0.654447	−	0.756108i	$-0.727099\pi$
$811$		−	8.06633e8i		−	1.51222i	0.654447	−	0.756108i	$-0.272901\pi$
$812$		0			0
$813$	−2.90868e8			−0.541284
$814$		0			0
$815$	5.95416e8	+	3.43764e8i	1.09989	+	0.635020i
$816$		0			0
$817$	−1.32562e9	+	7.65347e8i	−2.43082	+	1.40343i
$818$		0			0
$819$	−2.28685e7	−	1.60863e6i	−0.0416281	−	0.00292823i
$820$		0			0
$821$	5.29504e8	+	9.17127e8i	0.956840	+	1.65730i	0.730100	+	0.683341i	$0.239474\pi$
$821$	5.29504e8	+	9.17127e8i	0.956840	+	1.65730i	0.226741	+	0.973955i	$0.427193\pi$
$822$		0			0
$823$	−5.41564e8	+	9.38017e8i	−0.971517	+	1.68272i	−0.280538	+	0.959843i	$0.590513\pi$
$823$	−5.41564e8	+	9.38017e8i	−0.971517	+	1.68272i	−0.690979	+	0.722875i	$0.742820\pi$
$824$		0			0
$825$			3.46482e8i			0.617048i
$826$		0			0
$827$	1.33362e8			0.235785			0.117892	−	0.993026i	$-0.462386\pi$
$827$	1.33362e8			0.235785			0.117892	+	0.993026i	$0.462386\pi$
$828$		0			0
$829$	2.16051e8	+	1.24737e8i	0.379221	+	0.218944i	0.677479	−	0.735542i	$-0.263072\pi$
$829$	2.16051e8	+	1.24737e8i	0.379221	+	0.218944i	−0.298258	+	0.954485i	$0.596406\pi$
$830$		0			0
$831$	−1.03073e8	+	5.95090e7i	−0.179614	+	0.103700i
$832$		0			0
$833$	7.22511e7	−	5.11023e8i	0.125000	−	0.884109i
$834$		0			0
$835$	−2.07132e8	−	3.58764e8i	−0.355786	−	0.616239i
$836$		0			0
$837$	3.86874e7	−	6.70085e7i	0.0659770	−	0.114276i
$838$		0			0
$839$		−	4.92485e8i		−	0.833887i	−0.908932	−	0.416943i	$-0.863101\pi$
$839$		−	4.92485e8i		−	0.833887i	0.908932	−	0.416943i	$-0.136899\pi$
$840$		0			0
$841$	−5.55604e8			−0.934066
$842$		0			0
$843$	3.86467e8	+	2.23127e8i	0.645103	+	0.372450i
$844$		0			0
$845$	−8.33196e8	+	4.81046e8i	−1.38095	+	0.797291i
$846$		0			0
$847$	2.41786e7	−	3.43725e8i	0.0397906	−	0.565667i
$848$		0			0
$849$	−1.65947e8	−	2.87428e8i	−0.271173	−	0.469685i
$850$		0			0
$851$	−1.00125e8	+	1.73422e8i	−0.162463	+	0.281395i
$852$		0			0
$853$		−	6.41660e8i		−	1.03385i	−0.856031	−	0.516925i	$-0.827077\pi$
$853$		−	6.41660e8i		−	1.03385i	0.856031	−	0.516925i	$-0.172923\pi$
$854$		0			0
$855$	−6.64659e8			−1.06341
$856$		0			0
$857$	6.22262e8	+	3.59263e8i	0.988623	+	0.570782i	0.904863	−	0.425704i	$-0.139973\pi$
$857$	6.22262e8	+	3.59263e8i	0.988623	+	0.570782i	0.0837609	+	0.996486i	$0.473307\pi$
$858$		0			0
$859$	−6.76979e8	+	3.90854e8i	−1.06806	+	0.616645i	−0.927651	−	0.373449i	$-0.878175\pi$
$859$	−6.76979e8	+	3.90854e8i	−1.06806	+	0.616645i	−0.140409	+	0.990094i	$0.544842\pi$
$860$		0			0
$861$	3.36188e8	−	1.63797e8i	0.526711	−	0.256624i
$862$		0			0
$863$	5.41290e8	+	9.37542e8i	0.842166	+	1.45867i	0.888060	+	0.459729i	$0.152053\pi$
$863$	5.41290e8	+	9.37542e8i	0.842166	+	1.45867i	−0.0458932	+	0.998946i	$0.514613\pi$
$864$		0			0
$865$	3.18885e7	−	5.52325e7i	0.0492704	−	0.0853388i
$866$		0			0
$867$			7.62793e7i			0.117044i
$868$		0			0
$869$	6.68969e8			1.01940
$870$		0			0
$871$	−4.15795e7	−	2.40059e7i	−0.0629252	−	0.0363299i
$872$		0			0
$873$	−7.15871e7	+	4.13308e7i	−0.107595	+	0.0621200i
$874$		0			0
$875$	3.79104e8	−	5.61543e8i	0.565892	−	0.838221i
$876$		0			0
$877$	1.21581e8	+	2.10585e8i	0.180247	+	0.312196i	0.941964	−	0.335713i	$-0.108977\pi$
$877$	1.21581e8	+	2.10585e8i	0.180247	+	0.312196i	−0.761718	+	0.647909i	$0.775644\pi$
$878$		0			0
$879$	−1.34140e8	+	2.32337e8i	−0.197511	+	0.342100i
$880$		0			0
$881$		−	1.21869e9i		−	1.78224i	−0.453767	−	0.891120i	$-0.649920\pi$
$881$		−	1.21869e9i		−	1.78224i	0.453767	−	0.891120i	$-0.350080\pi$
$882$		0			0
$883$	−5.63745e8			−0.818842			−0.409421	−	0.912346i	$-0.634269\pi$
$883$	−5.63745e8			−0.818842			−0.409421	+	0.912346i	$0.634269\pi$
$884$		0			0
$885$	−7.66644e8	−	4.42622e8i	−1.10602	−	0.638563i
$886$		0			0
$887$	2.33059e8	−	1.34557e8i	0.333961	−	0.192812i	−0.323637	−	0.946181i	$-0.604906\pi$
$887$	2.33059e8	−	1.34557e8i	0.333961	−	0.192812i	0.657598	+	0.753369i	$0.271572\pi$
$888$		0			0
$889$	2.62781e8	+	1.77406e8i	0.374015	+	0.252502i
$890$		0			0
$891$	2.58566e7	+	4.47850e7i	0.0365543	+	0.0633139i
$892$		0			0
$893$	3.12849e8	−	5.41870e8i	0.439319	−	0.760923i
$894$		0			0
$895$		−	8.14860e8i		−	1.13662i
$896$		0			0
$897$	5.46033e7			0.0756557
$898$		0			0
$899$	1.10782e8	+	6.39602e7i	0.152472	+	0.0880300i
$900$		0			0
$901$	4.86385e8	−	2.80815e8i	0.664976	−	0.383924i
$902$		0			0
$903$	−2.65389e8	−	5.44701e8i	−0.360429	−	0.739767i
$904$		0			0
$905$	−1.55741e8	−	2.69750e8i	−0.210114	−	0.363929i
$906$		0			0
$907$	3.93227e8	−	6.81089e8i	0.527013	−	0.912814i	−0.472491	−	0.881335i	$-0.656645\pi$
$907$	3.93227e8	−	6.81089e8i	0.527013	−	0.912814i	0.999504	−	0.0314782i	$-0.0100215\pi$
$908$		0			0
$909$			2.53540e8i			0.337562i
$910$		0			0
$911$	−1.05328e9			−1.39312			−0.696559	−	0.717500i	$-0.745287\pi$
$911$	−1.05328e9			−1.39312			−0.696559	+	0.717500i	$0.745287\pi$
$912$		0			0
$913$	−6.51803e8	−	3.76319e8i	−0.856454	−	0.494474i
$914$		0			0
$915$	2.67552e8	−	1.54471e8i	0.349257	−	0.201643i
$916$		0			0
$917$	3.30934e8	+	2.32788e7i	0.429173	+	0.0301892i
$918$		0			0
$919$	5.81563e8	+	1.00730e9i	0.749290	+	1.29781i	0.948163	+	0.317784i	$0.102939\pi$
$919$	5.81563e8	+	1.00730e9i	0.749290	+	1.29781i	−0.198873	+	0.980025i	$0.563728\pi$
$920$		0			0
$921$	−3.20540e8	+	5.55191e8i	−0.410301	+	0.710663i
$922$		0			0
$923$			9.50875e7i			0.120926i
$924$		0			0
$925$	−3.99076e8			−0.504232
$926$		0			0
$927$	1.64152e8	+	9.47731e7i	0.206066	+	0.118972i
$928$		0			0
$929$	−1.01867e9	+	5.88131e8i	−1.27054	+	0.733545i	−0.975089	−	0.221814i	$-0.928802\pi$
$929$	−1.01867e9	+	5.88131e8i	−1.27054	+	0.733545i	−0.295448	+	0.955359i	$0.595469\pi$
$930$		0			0
$931$	1.25145e9	+	9.79411e8i	1.55083	+	1.21371i
$932$		0			0
$933$	8.89276e7	+	1.54027e8i	0.109494	+	0.189650i
$934$		0			0
$935$	3.88980e8	−	6.73733e8i	0.475874	−	0.824239i
$936$		0			0
$937$			4.63976e8i			0.563997i	0.959415	+	0.281999i	$0.0909974\pi$
$937$			4.63976e8i			0.563997i	−0.959415	+	0.281999i	$0.909003\pi$
$938$		0			0
$939$	1.67436e7			0.0202233
$940$		0			0
$941$	−1.01174e9	−	5.84130e8i	−1.21423	−	0.701036i	−0.250552	−	0.968103i	$-0.580612\pi$
$941$	−1.01174e9	−	5.84130e8i	−1.21423	−	0.701036i	−0.963678	+	0.267067i	$0.913946\pi$
$942$		0			0
$943$	−7.71390e8	+	4.45362e8i	−0.919896	+	0.531102i
$944$		0			0
$945$	1.84616e7	−	2.62452e8i	0.0218763	−	0.310995i
$946$		0			0
$947$	2.84555e8	+	4.92863e8i	0.335055	+	0.580332i	0.983495	−	0.180934i	$-0.0579119\pi$
$947$	2.84555e8	+	4.92863e8i	0.335055	+	0.580332i	−0.648441	+	0.761265i	$0.724579\pi$
$948$		0			0
$949$	−1.66086e7	+	2.87670e7i	−0.0194328	+	0.0336586i
$950$		0			0
$951$		−	3.08645e8i		−	0.358853i
$952$		0			0
$953$	5.61708e8			0.648981			0.324491	−	0.945889i	$-0.394807\pi$
$953$	5.61708e8			0.648981			0.324491	+	0.945889i	$0.394807\pi$
$954$		0			0
$955$	−7.50098e8	−	4.33069e8i	−0.861208	−	0.497219i
$956$		0			0
$957$	−7.40411e7	+	4.27477e7i	−0.0844768	+	0.0487727i
$958$		0			0
$959$	1.44928e9	−	7.06117e8i	1.64322	−	0.800609i
$960$		0			0
$961$	−2.35135e8	−	4.07266e8i	−0.264940	−	0.458889i
$962$		0			0
$963$	1.21219e8	−	2.09958e8i	0.135735	−	0.235100i
$964$		0			0
$965$			1.30534e9i			1.45259i
$966$		0			0
$967$	−6.95843e8			−0.769541			−0.384771	−	0.923012i	$-0.625719\pi$
$967$	−6.95843e8			−0.769541			−0.384771	+	0.923012i	$0.625719\pi$
$968$		0			0
$969$	7.99944e8	+	4.61848e8i	0.879201	+	0.507607i
$970$		0			0
$971$	7.65735e8	−	4.42097e8i	0.836413	−	0.482903i	−0.0196301	−	0.999807i	$-0.506249\pi$
$971$	7.65735e8	−	4.42097e8i	0.836413	−	0.482903i	0.856043	+	0.516904i	$0.172916\pi$
$972$		0			0
$973$	−3.15337e8	+	4.67089e8i	−0.342323	+	0.507062i
$974$		0			0
$975$	5.44090e7	+	9.42392e7i	0.0587026	+	0.101676i
$976$		0			0
$977$	1.79936e8	−	3.11659e8i	0.192946	−	0.334192i	−0.753279	−	0.657701i	$-0.771529\pi$
$977$	1.79936e8	−	3.11659e8i	0.192946	−	0.334192i	0.946225	+	0.323509i	$0.104863\pi$
$978$		0			0
$979$			1.57530e8i			0.167887i
$980$		0			0
$981$	−3.53728e8			−0.374682
$982$		0			0
$983$	4.76200e7	+	2.74934e7i	0.0501336	+	0.0289446i	0.524857	−	0.851190i	$-0.324119\pi$
$983$	4.76200e7	+	2.74934e7i	0.0501336	+	0.0289446i	−0.474724	+	0.880135i	$0.657452\pi$
$984$		0			0
$985$	4.79128e8	−	2.76625e8i	0.501352	−	0.289456i
$986$		0			0
$987$	2.05277e8	+	1.38584e8i	0.213495	+	0.144133i
$988$		0			0
$989$	7.21589e8	+	1.24983e9i	0.745935	+	1.29200i
$990$		0			0
$991$	1.53556e8	−	2.65967e8i	0.157778	−	0.273280i	−0.776289	−	0.630377i	$-0.782900\pi$
$991$	1.53556e8	−	2.65967e8i	0.157778	−	0.273280i	0.934067	+	0.357098i	$0.116234\pi$
$992$		0			0
$993$			2.98241e8i			0.304593i
$994$		0			0
$995$	1.20940e8			0.122773
$996$		0			0
$997$	1.03839e9	+	5.99516e8i	1.04779	+	0.604945i	0.922031	−	0.387116i	$-0.126529\pi$
$997$	1.03839e9	+	5.99516e8i	1.04779	+	0.604945i	0.125764	+	0.992060i	$0.459862\pi$
$998$		0			0
$999$	−5.15831e7	+	2.97815e7i	−0.0517382	+	0.0298711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.b.241.1		8
4.3	odd	2		21.7.f.b.10.1	✓	8
7.5	odd	6	inner	336.7.bh.b.145.1		8
12.11	even	2		63.7.m.c.10.4		8
28.3	even	6		147.7.d.a.97.8		8
28.11	odd	6		147.7.d.a.97.7		8
28.19	even	6		21.7.f.b.19.1	yes	8
28.23	odd	6		147.7.f.a.19.1		8
28.27	even	2		147.7.f.a.31.1		8
84.11	even	6		441.7.d.d.244.2		8
84.47	odd	6		63.7.m.c.19.4		8
84.59	odd	6		441.7.d.d.244.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.1	✓	8	4.3	odd	2
21.7.f.b.19.1	yes	8	28.19	even	6
63.7.m.c.10.4		8	12.11	even	2
63.7.m.c.19.4		8	84.47	odd	6
147.7.d.a.97.7		8	28.11	odd	6
147.7.d.a.97.8		8	28.3	even	6
147.7.f.a.19.1		8	28.23	odd	6
147.7.f.a.31.1		8	28.27	even	2
336.7.bh.b.145.1		8	7.5	odd	6	inner
336.7.bh.b.241.1		8	1.1	even	1	trivial
441.7.d.d.244.1		8	84.59	odd	6
441.7.d.d.244.2		8	84.11	even	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)

\(f(q)\)	\(=\)	\(q+(-13.5000 - 7.79423i) q^{3} +(-175.367 + 101.248i) q^{5} +(-284.280 - 191.921i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 - 7.79423i) q^{3} +(-175.367 + 101.248i) q^{5} +(-284.280 - 191.921i) q^{7} +(121.500 + 210.444i) q^{9} +(437.884 - 758.438i) q^{11} -275.049i q^{13} +3156.61 q^{15} +(-3799.10 - 2193.41i) q^{17} +(11697.8 - 6753.75i) q^{19} +(2341.91 + 4806.68i) q^{21} +(-6367.61 - 11029.0i) q^{23} +(12689.9 - 21979.6i) q^{25} -3788.00i q^{27} +6262.53 q^{29} +(17689.7 + 10213.2i) q^{31} +(-11822.9 + 6825.94i) q^{33} +(69285.1 + 4873.70i) q^{35} +(-7862.08 - 13617.5i) q^{37} +(-2143.79 + 3713.16i) q^{39} -69941.8i q^{41} -113322. q^{43} +(-42614.2 - 24603.3i) q^{45} +(40116.2 - 23161.1i) q^{47} +(43981.8 + 109119. i) q^{49} +(34191.9 + 59222.2i) q^{51} +(-64013.2 + 110874. i) q^{53} +177340. i q^{55} -210561. q^{57} +(-242870. - 140221. i) q^{59} +(84759.3 - 48935.8i) q^{61} +(5848.55 - 83143.6i) q^{63} +(27848.2 + 48234.5i) q^{65} +(87278.8 - 151171. i) q^{67} +198522. i q^{69} -345712. q^{71} +(-104589. - 60384.4i) q^{73} +(-342627. + 197816. i) q^{75} +(-270042. + 131570. i) q^{77} +(381933. + 661527. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -859402. i q^{83} +888317. q^{85} +(-84544.2 - 48811.6i) q^{87} +(-155778. + 89938.3i) q^{89} +(-52787.6 + 78190.9i) q^{91} +(-159207. - 275755. i) q^{93} +(-1.36761e6 + 2.36877e6i) q^{95} +340171. i q^{97} +212812. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9	\( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99}+O(q^{100}) \) 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9 + 1070 * q^11 + 756 * q^15 + 7212 * q^17 + 24606 * q^19 + 8154 * q^21 + 15224 * q^23 + 22274 * q^25 + 32524 * q^29 - 40200 * q^31 - 28890 * q^33 + 242436 * q^35 - 45670 * q^37 - 93366 * q^39 + 445660 * q^43 - 10206 * q^45 - 82884 * q^47 + 24116 * q^49 - 64908 * q^51 - 13034 * q^53 - 442908 * q^57 - 1810362 * q^59 - 392856 * q^61 - 38394 * q^63 - 389004 * q^65 - 384094 * q^67 - 225688 * q^71 + 903078 * q^73 - 601398 * q^75 - 327674 * q^77 + 559592 * q^79 - 236196 * q^81 + 1953576 * q^85 - 439074 * q^87 - 1770036 * q^89 + 2960718 * q^91 + 361800 * q^93 - 1160112 * q^95 + 520020 * q^99

Introduction

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