LMFDB - Embedded newform 546.8.c.a.337.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,8,Mod(337,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("546.337");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.c (of order $2$, degree $1$, 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:	$170.562223914$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.11
Character	$\chi$	$=$	546.337
Dual form			546.8.c.a.337.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000i q^{2} -27.0000 q^{3} -64.0000 q^{4} +407.004i q^{5} +216.000i q^{6} +343.000i q^{7} +512.000i q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000i q^{2} -27.0000 q^{3} -64.0000 q^{4} +407.004i q^{5} +216.000i q^{6} +343.000i q^{7} +512.000i q^{8} +729.000 q^{9} +3256.03 q^{10} -2018.30i q^{11} +1728.00 q^{12} +(-6107.68 + 5044.29i) q^{13} +2744.00 q^{14} -10989.1i q^{15} +4096.00 q^{16} +9533.65 q^{17} -5832.00i q^{18} +13164.3i q^{19} -26048.3i q^{20} -9261.00i q^{21} -16146.4 q^{22} -102319. q^{23} -13824.0i q^{24} -87527.3 q^{25} +(40354.3 + 48861.4i) q^{26} -19683.0 q^{27} -21952.0i q^{28} +10385.6 q^{29} -87912.9 q^{30} +105603. i q^{31} -32768.0i q^{32} +54494.0i q^{33} -76269.2i q^{34} -139602. q^{35} -46656.0 q^{36} +532641. i q^{37} +105314. q^{38} +(164907. - 136196. i) q^{39} -208386. q^{40} +181099. i q^{41} -74088.0 q^{42} -156759. q^{43} +129171. i q^{44} +296706. i q^{45} +818548. i q^{46} +152177. i q^{47} -110592. q^{48} -117649. q^{49} +700218. i q^{50} -257409. q^{51} +(390891. - 322834. i) q^{52} +98908.3 q^{53} +157464. i q^{54} +821455. q^{55} -175616. q^{56} -355436. i q^{57} -83085.2i q^{58} +398279. i q^{59} +703303. i q^{60} -2.41495e6 q^{61} +844824. q^{62} +250047. i q^{63} -262144. q^{64} +(-2.05304e6 - 2.48585e6i) q^{65} +435952. q^{66} +4.62291e6i q^{67} -610154. q^{68} +2.76260e6 q^{69} +1.11682e6i q^{70} +5.18516e6i q^{71} +373248. i q^{72} -1.53705e6i q^{73} +4.26113e6 q^{74} +2.36324e6 q^{75} -842515. i q^{76} +692276. q^{77} +(-1.08957e6 - 1.31926e6i) q^{78} +3.16889e6 q^{79} +1.66709e6i q^{80} +531441. q^{81} +1.44879e6 q^{82} -3.62547e6i q^{83} +592704. i q^{84} +3.88023e6i q^{85} +1.25407e6i q^{86} -280412. q^{87} +1.03337e6 q^{88} -3.48215e6i q^{89} +2.37365e6 q^{90} +(-1.73019e6 - 2.09493e6i) q^{91} +6.54838e6 q^{92} -2.85128e6i q^{93} +1.21741e6 q^{94} -5.35792e6 q^{95} +884736. i q^{96} -8.76693e6i q^{97} +941192. i q^{98} -1.47134e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 648 q^{3} - 1536 q^{4} + 17496 q^{9}+O(q^{10}) $ 24 * q - 648 * q^3 - 1536 * q^4 + 17496 * q^9	$ 24 q - 648 q^{3} - 1536 q^{4} + 17496 q^{9} + 1520 q^{10} + 41472 q^{12} + 13718 q^{13} + 65856 q^{14} + 98304 q^{16} + 13586 q^{17} - 11824 q^{22} + 76574 q^{23} - 357850 q^{25} + 132848 q^{26} - 472392 q^{27} + 85198 q^{29} - 41040 q^{30} - 65170 q^{35} - 1119744 q^{36} + 295696 q^{38} - 370386 q^{39} - 97280 q^{40} - 1778112 q^{42} - 91370 q^{43} - 2654208 q^{48} - 2823576 q^{49} - 366822 q^{51} - 877952 q^{52} - 360000 q^{53} - 2519718 q^{55} - 4214784 q^{56} + 874734 q^{61} + 1984480 q^{62} - 6291456 q^{64} - 12450388 q^{65} + 319248 q^{66} - 869504 q^{68} - 2067498 q^{69} - 1405616 q^{74} + 9661950 q^{75} + 506954 q^{77} - 3586896 q^{78} - 2141176 q^{79} + 12754584 q^{81} + 14087488 q^{82} - 2300346 q^{87} + 756736 q^{88} + 1108080 q^{90} - 5695858 q^{91} - 4900736 q^{92} + 8123808 q^{94} + 19191246 q^{95}+O(q^{100}) $ 24 * q - 648 * q^3 - 1536 * q^4 + 17496 * q^9 + 1520 * q^10 + 41472 * q^12 + 13718 * q^13 + 65856 * q^14 + 98304 * q^16 + 13586 * q^17 - 11824 * q^22 + 76574 * q^23 - 357850 * q^25 + 132848 * q^26 - 472392 * q^27 + 85198 * q^29 - 41040 * q^30 - 65170 * q^35 - 1119744 * q^36 + 295696 * q^38 - 370386 * q^39 - 97280 * q^40 - 1778112 * q^42 - 91370 * q^43 - 2654208 * q^48 - 2823576 * q^49 - 366822 * q^51 - 877952 * q^52 - 360000 * q^53 - 2519718 * q^55 - 4214784 * q^56 + 874734 * q^61 + 1984480 * q^62 - 6291456 * q^64 - 12450388 * q^65 + 319248 * q^66 - 869504 * q^68 - 2067498 * q^69 - 1405616 * q^74 + 9661950 * q^75 + 506954 * q^77 - 3586896 * q^78 - 2141176 * q^79 + 12754584 * q^81 + 14087488 * q^82 - 2300346 * q^87 + 756736 * q^88 + 1108080 * q^90 - 5695858 * q^91 - 4900736 * q^92 + 8123808 * q^94 + 19191246 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	8.00000i		−	0.707107i
$2$		−	8.00000i		−	0.707107i
$3$	−27.0000			−0.577350
$3$	−27.0000			−0.577350
$4$	−64.0000			−0.500000
$5$			407.004i			1.45614i	0.685502	+	0.728071i	$0.259583\pi$
$5$			407.004i			1.45614i	−0.685502	+	0.728071i	$0.740417\pi$
$6$			216.000i			0.408248i
$7$			343.000i			0.377964i
$7$			343.000i			0.377964i
$8$			512.000i			0.353553i
$9$	729.000			0.333333
$10$	3256.03			1.02965
$11$		−	2018.30i		−	0.457205i	−0.973520	−	0.228602i	$-0.926584\pi$
$11$		−	2018.30i		−	0.457205i	0.973520	−	0.228602i	$-0.0734156\pi$
$12$	1728.00			0.288675
$13$	−6107.68	+	5044.29i	−0.771035	+	0.636792i
$13$	−6107.68	+	5044.29i	−0.771035	+	0.636792i
$14$	2744.00			0.267261
$15$		−	10989.1i		−	0.840704i
$16$	4096.00			0.250000
$17$	9533.65			0.470639			0.235320	−	0.971918i	$-0.424386\pi$
$17$	9533.65			0.470639			0.235320	+	0.971918i	$0.424386\pi$
$18$		−	5832.00i		−	0.235702i
$19$			13164.3i			0.440312i	0.975465	+	0.220156i	$0.0706566\pi$
$19$			13164.3i			0.440312i	−0.975465	+	0.220156i	$0.929343\pi$
$20$		−	26048.3i		−	0.728071i
$21$		−	9261.00i		−	0.218218i
$22$	−16146.4			−0.323293
$23$	−102319.			−1.75350			−0.876752	−	0.480943i	$-0.840294\pi$
$23$	−102319.			−1.75350			−0.876752	+	0.480943i	$0.840294\pi$
$24$		−	13824.0i		−	0.204124i
$25$	−87527.3			−1.12035
$26$	40354.3	+	48861.4i	0.450280	+	0.545204i
$27$	−19683.0			−0.192450
$28$		−	21952.0i		−	0.188982i
$29$	10385.6			0.0790752			0.0395376	−	0.999218i	$-0.487412\pi$
$29$	10385.6			0.0790752			0.0395376	+	0.999218i	$0.487412\pi$
$30$	−87912.9			−0.594467
$31$			105603.i			0.636664i	0.947979	+	0.318332i	$0.103123\pi$
$31$			105603.i			0.636664i	−0.947979	+	0.318332i	$0.896877\pi$
$32$		−	32768.0i		−	0.176777i
$33$			54494.0i			0.263967i
$34$		−	76269.2i		−	0.332792i
$35$	−139602.			−0.550370
$36$	−46656.0			−0.166667
$37$			532641.i			1.72874i	0.502859	+	0.864368i	$0.332281\pi$
$37$			532641.i			1.72874i	−0.502859	+	0.864368i	$0.667719\pi$
$38$	105314.			0.311347
$39$	164907.	−	136196.i	0.445157	−	0.367652i
$40$	−208386.			−0.514824
$41$			181099.i			0.410366i	0.978724	+	0.205183i	$0.0657790\pi$
$41$			181099.i			0.410366i	−0.978724	+	0.205183i	$0.934221\pi$
$42$	−74088.0			−0.154303
$43$	−156759.			−0.300672			−0.150336	−	0.988635i	$-0.548036\pi$
$43$	−156759.			−0.300672			−0.150336	+	0.988635i	$0.548036\pi$
$44$			129171.i			0.228602i
$45$			296706.i			0.485381i
$46$			818548.i			1.23991i
$47$			152177.i			0.213799i	0.994270	+	0.106900i	$0.0340923\pi$
$47$			152177.i			0.213799i	−0.994270	+	0.106900i	$0.965908\pi$
$48$	−110592.			−0.144338
$49$	−117649.			−0.142857
$50$			700218.i			0.792206i
$51$	−257409.			−0.271724
$52$	390891.	−	322834.i	0.385518	−	0.318396i
$53$	98908.3			0.0912572			0.0456286	−	0.998958i	$-0.485471\pi$
$53$	98908.3			0.0912572			0.0456286	+	0.998958i	$0.485471\pi$
$54$			157464.i			0.136083i
$55$	821455.			0.665755
$56$	−175616.			−0.133631
$57$		−	355436.i		−	0.254214i
$58$		−	83085.2i		−	0.0559146i
$59$			398279.i			0.252467i	0.992001	+	0.126234i	$0.0402889\pi$
$59$			398279.i			0.252467i	−0.992001	+	0.126234i	$0.959711\pi$
$60$			703303.i			0.420352i
$61$	−2.41495e6			−1.36224			−0.681120	−	0.732171i	$-0.738507\pi$
$61$	−2.41495e6			−1.36224			−0.681120	+	0.732171i	$0.738507\pi$
$62$	844824.			0.450190
$63$			250047.i			0.125988i
$64$	−262144.			−0.125000
$65$	−2.05304e6	−	2.48585e6i	−0.927260	−	1.12274i
$66$	435952.			0.186653
$67$			4.62291e6i			1.87782i	0.344167	+	0.938909i	$0.388162\pi$
$67$			4.62291e6i			1.87782i	−0.344167	+	0.938909i	$0.611838\pi$
$68$	−610154.			−0.235320
$69$	2.76260e6			1.01239
$70$			1.11682e6i			0.389170i
$71$			5.18516e6i			1.71932i	0.510864	+	0.859662i	$0.329326\pi$
$71$			5.18516e6i			1.71932i	−0.510864	+	0.859662i	$0.670674\pi$
$72$			373248.i			0.117851i
$73$		−	1.53705e6i		−	0.462444i	−0.972901	−	0.231222i	$-0.925728\pi$
$73$		−	1.53705e6i		−	0.462444i	0.972901	−	0.231222i	$-0.0742724\pi$
$74$	4.26113e6			1.22240
$75$	2.36324e6			0.646834
$76$		−	842515.i		−	0.220156i
$77$	692276.			0.172807
$78$	−1.08957e6	−	1.31926e6i	−0.259969	−	0.314774i
$79$	3.16889e6			0.723122			0.361561	−	0.932348i	$-0.382244\pi$
$79$	3.16889e6			0.723122			0.361561	+	0.932348i	$0.382244\pi$
$80$			1.66709e6i			0.364035i
$81$	531441.			0.111111
$82$	1.44879e6			0.290173
$83$		−	3.62547e6i		−	0.695970i	−0.937500	−	0.347985i	$-0.886866\pi$
$83$		−	3.62547e6i		−	0.695970i	0.937500	−	0.347985i	$-0.113134\pi$
$84$			592704.i			0.109109i
$85$			3.88023e6i			0.685317i
$86$			1.25407e6i			0.212607i
$87$	−280412.			−0.0456541
$88$	1.03337e6			0.161646
$89$		−	3.48215e6i		−	0.523580i	−0.965125	−	0.261790i	$-0.915687\pi$
$89$		−	3.48215e6i		−	0.523580i	0.965125	−	0.261790i	$-0.0843127\pi$
$90$	2.37365e6			0.343216
$91$	−1.73019e6	−	2.09493e6i	−0.240685	−	0.291424i
$92$	6.54838e6			0.876752
$93$		−	2.85128e6i		−	0.367578i
$94$	1.21741e6			0.151179
$95$	−5.35792e6			−0.641156
$96$			884736.i			0.102062i
$97$		−	8.76693e6i		−	0.975318i	−0.873034	−	0.487659i	$-0.837851\pi$
$97$		−	8.76693e6i		−	0.975318i	0.873034	−	0.487659i	$-0.162149\pi$
$98$			941192.i			0.101015i
$99$		−	1.47134e6i		−	0.152402i
$100$	5.60175e6			0.560175
$101$	1.07481e7			1.03802			0.519010	−	0.854768i	$-0.326301\pi$
$101$	1.07481e7			1.03802			0.519010	+	0.854768i	$0.326301\pi$
$102$			2.05927e6i			0.192138i
$103$	−2.40277e6			−0.216662			−0.108331	−	0.994115i	$-0.534551\pi$
$103$	−2.40277e6			−0.216662			−0.108331	+	0.994115i	$0.534551\pi$
$104$	−2.58267e6	−	3.12713e6i	−0.225140	−	0.272602i
$105$	3.76926e6			0.317756
$106$		−	791267.i		−	0.0645286i
$107$	−5.57725e6			−0.440126			−0.220063	−	0.975486i	$-0.570626\pi$
$107$	−5.57725e6			−0.440126			−0.220063	+	0.975486i	$0.570626\pi$
$108$	1.25971e6			0.0962250
$109$		−	1.51719e7i		−	1.12214i	−0.827767	−	0.561071i	$-0.810389\pi$
$109$		−	1.51719e7i		−	1.12214i	0.827767	−	0.561071i	$-0.189611\pi$
$110$		−	6.57164e6i		−	0.470760i
$111$		−	1.43813e7i		−	0.998086i
$112$			1.40493e6i			0.0944911i
$113$	−9.85036e6			−0.642211			−0.321105	−	0.947044i	$-0.604054\pi$
$113$	−9.85036e6			−0.642211			−0.321105	+	0.947044i	$0.604054\pi$
$114$	−2.84349e6			−0.179756
$115$		−	4.16440e7i		−	2.55335i
$116$	−664681.			−0.0395376
$117$	−4.45250e6	+	3.67728e6i	−0.257012	+	0.212264i
$118$	3.18623e6			0.178521
$119$			3.27004e6i			0.177885i
$120$	5.62642e6			0.297234
$121$	1.54136e7			0.790964
$122$			1.93196e7i			0.963250i
$123$		−	4.88966e6i		−	0.236925i
$124$		−	6.75860e6i		−	0.318332i
$125$		−	3.82676e6i		−	0.175245i
$126$	2.00038e6			0.0890871
$127$	1.94913e7			0.844359			0.422180	−	0.906512i	$-0.361265\pi$
$127$	1.94913e7			0.844359			0.422180	+	0.906512i	$0.361265\pi$
$128$			2.09715e6i			0.0883883i
$129$	4.23250e6			0.173593
$130$	−1.98868e7	+	1.64244e7i	−0.793895	+	0.655672i
$131$	−1.52787e7			−0.593796			−0.296898	−	0.954909i	$-0.595952\pi$
$131$	−1.52787e7			−0.593796			−0.296898	+	0.954909i	$0.595952\pi$
$132$		−	3.48762e6i		−	0.131984i
$133$	−4.51536e6			−0.166422
$134$	3.69833e7			1.32782
$135$		−	8.01106e6i		−	0.280235i
$136$			4.88123e6i			0.166396i
$137$			1.46968e7i			0.488317i	0.969735	+	0.244158i	$0.0785117\pi$
$137$			1.46968e7i			0.488317i	−0.969735	+	0.244158i	$0.921488\pi$
$138$		−	2.21008e7i		−	0.715865i
$139$	1.63545e7			0.516518			0.258259	−	0.966076i	$-0.416851\pi$
$139$	1.63545e7			0.516518			0.258259	+	0.966076i	$0.416851\pi$
$140$	8.93455e6			0.275185
$141$		−	4.10877e6i		−	0.123437i
$142$	4.14812e7			1.21575
$143$	1.01809e7	+	1.23271e7i	0.291145	+	0.352521i
$144$	2.98598e6			0.0833333
$145$			4.22700e6i			0.115145i
$146$	−1.22964e7			−0.326997
$147$	3.17652e6			0.0824786
$148$		−	3.40890e7i		−	0.864368i
$149$		−	2.18448e7i		−	0.540998i	−0.962720	−	0.270499i	$-0.912811\pi$
$149$		−	2.18448e7i		−	0.540998i	0.962720	−	0.270499i	$-0.0871887\pi$
$150$		−	1.89059e7i		−	0.457381i
$151$			6.40068e7i			1.51289i	0.654059	+	0.756443i	$0.273065\pi$
$151$			6.40068e7i			1.51289i	−0.654059	+	0.756443i	$0.726935\pi$
$152$	−6.74012e6			−0.155674
$153$	6.95003e6			0.156880
$154$		−	5.53821e6i		−	0.122193i
$155$	−4.29809e7			−0.927074
$156$	−1.05541e7	+	8.71653e6i	−0.222579	+	0.183826i
$157$	−6.19865e7			−1.27835			−0.639173	−	0.769063i	$-0.720723\pi$
$157$	−6.19865e7			−1.27835			−0.639173	+	0.769063i	$0.720723\pi$
$158$		−	2.53511e7i		−	0.511325i
$159$	−2.67052e6			−0.0526874
$160$	1.33367e7			0.257412
$161$		−	3.50952e7i		−	0.662762i
$162$		−	4.25153e6i		−	0.0785674i
$163$		−	4.25160e7i		−	0.768947i	−0.923136	−	0.384473i	$-0.874383\pi$
$163$		−	4.25160e7i		−	0.768947i	0.923136	−	0.384473i	$-0.125617\pi$
$164$		−	1.15903e7i		−	0.205183i
$165$	−2.21793e7			−0.384374
$166$	−2.90037e7			−0.492125
$167$			4.71049e7i			0.782634i	0.920256	+	0.391317i	$0.127980\pi$
$167$			4.71049e7i			0.782634i	−0.920256	+	0.391317i	$0.872020\pi$
$168$	4.74163e6			0.0771517
$169$	1.18589e7	−	6.16177e7i	0.188991	−	0.981979i
$170$	3.10419e7			0.484592
$171$			9.59678e6i			0.146771i
$172$	1.00326e7			0.150336
$173$	−4.06833e7			−0.597385			−0.298693	−	0.954349i	$-0.596550\pi$
$173$	−4.06833e7			−0.597385			−0.298693	+	0.954349i	$0.596550\pi$
$174$			2.24330e6i			0.0322823i
$175$		−	3.00219e7i		−	0.423452i
$176$		−	8.26695e6i		−	0.114301i
$177$		−	1.07535e7i		−	0.145762i
$178$	−2.78572e7			−0.370227
$179$	−6.68655e7			−0.871398			−0.435699	−	0.900093i	$-0.643499\pi$
$179$	−6.68655e7			−0.871398			−0.435699	+	0.900093i	$0.643499\pi$
$180$		−	1.89892e7i		−	0.242690i
$181$	−5.25268e7			−0.658425			−0.329212	−	0.944256i	$-0.606783\pi$
$181$	−5.25268e7			−0.658425			−0.329212	+	0.944256i	$0.606783\pi$
$182$	−1.67595e7	+	1.38415e7i	−0.206068	+	0.170190i
$183$	6.52037e7			0.786490
$184$		−	5.23871e7i		−	0.619957i
$185$	−2.16787e8			−2.51729
$186$	−2.28103e7			−0.259917
$187$		−	1.92417e7i		−	0.215178i
$188$		−	9.73931e6i		−	0.106900i
$189$		−	6.75127e6i		−	0.0727393i
$190$			4.28634e7i			0.453366i
$191$	−3.97056e7			−0.412321			−0.206160	−	0.978518i	$-0.566097\pi$
$191$	−3.97056e7			−0.412321			−0.206160	+	0.978518i	$0.566097\pi$
$192$	7.07789e6			0.0721688
$193$			2.49822e7i			0.250138i	0.992148	+	0.125069i	$0.0399152\pi$
$193$			2.49822e7i			0.250138i	−0.992148	+	0.125069i	$0.960085\pi$
$194$	−7.01354e7			−0.689654
$195$	5.54322e7	+	6.71179e7i	0.535354	+	0.648212i
$196$	7.52954e6			0.0714286
$197$		−	1.11082e8i		−	1.03517i	−0.855631	−	0.517586i	$-0.826831\pi$
$197$		−	1.11082e8i		−	1.03517i	0.855631	−	0.517586i	$-0.173169\pi$
$198$	−1.17707e7			−0.107764
$199$	1.21421e8			1.09221			0.546107	−	0.837715i	$-0.316109\pi$
$199$	1.21421e8			1.09221			0.546107	+	0.837715i	$0.316109\pi$
$200$		−	4.48140e7i		−	0.396103i
$201$		−	1.24818e8i		−	1.08416i
$202$		−	8.59846e7i		−	0.733991i
$203$			3.56228e6i			0.0298876i
$204$	1.64741e7			0.135862
$205$	−7.37079e7			−0.597552
$206$			1.92222e7i			0.153203i
$207$	−7.45902e7			−0.584501
$208$	−2.50170e7	+	2.06614e7i	−0.192759	+	0.159198i
$209$	2.65695e7			0.201313
$210$		−	3.01541e7i		−	0.224688i
$211$	1.50053e8			1.09966			0.549828	−	0.835278i	$-0.314693\pi$
$211$	1.50053e8			1.09966			0.549828	+	0.835278i	$0.314693\pi$
$212$	−6.33013e6			−0.0456286
$213$		−	1.39999e8i		−	0.992652i
$214$			4.46180e7i			0.311216i
$215$		−	6.38016e7i		−	0.437821i
$216$		−	1.00777e7i		−	0.0680414i
$217$	−3.62218e7			−0.240637
$218$	−1.21375e8			−0.793475
$219$			4.15005e7i			0.266992i
$220$	−5.25731e7			−0.332878
$221$	−5.82284e7	+	4.80904e7i	−0.362879	+	0.299699i
$222$	−1.15051e8			−0.705754
$223$		−	8.60645e7i		−	0.519705i	−0.965648	−	0.259852i	$-0.916326\pi$
$223$		−	8.60645e7i		−	0.519705i	0.965648	−	0.259852i	$-0.0836739\pi$
$224$	1.12394e7			0.0668153
$225$	−6.38074e7			−0.373450
$226$			7.88029e7i			0.454111i
$227$		−	1.13924e8i		−	0.646437i	−0.946324	−	0.323218i	$-0.895235\pi$
$227$		−	1.13924e8i		−	0.646437i	0.946324	−	0.323218i	$-0.104765\pi$
$228$			2.27479e7i			0.127107i
$229$			2.64409e8i			1.45497i	0.686126	+	0.727483i	$0.259310\pi$
$229$			2.64409e8i			1.45497i	−0.686126	+	0.727483i	$0.740690\pi$
$230$	−3.33152e8			−1.80549
$231$	−1.86915e7			−0.0997703
$232$			5.31745e6i			0.0279573i
$233$	1.59145e8			0.824229			0.412115	−	0.911132i	$-0.364790\pi$
$233$	1.59145e8			0.824229			0.412115	+	0.911132i	$0.364790\pi$
$234$	2.94183e7	+	3.56200e7i	0.150093	+	0.181735i
$235$	−6.19365e7			−0.311322
$236$		−	2.54898e7i		−	0.126234i
$237$	−8.55599e7			−0.417495
$238$	2.61603e7			0.125784
$239$			2.45781e8i			1.16454i	0.812995	+	0.582271i	$0.197836\pi$
$239$			2.45781e8i			1.16454i	−0.812995	+	0.582271i	$0.802164\pi$
$240$		−	4.50114e7i		−	0.210176i
$241$		−	2.16147e8i		−	0.994696i	−0.867551	−	0.497348i	$-0.834307\pi$
$241$		−	2.16147e8i		−	0.994696i	0.867551	−	0.497348i	$-0.165693\pi$
$242$		−	1.23309e8i		−	0.559296i
$243$	−1.43489e7			−0.0641500
$244$	1.54557e8			0.681120
$245$		−	4.78836e7i		−	0.208020i
$246$	−3.91173e7			−0.167531
$247$	−6.64045e7	−	8.04033e7i	−0.280387	−	0.339496i
$248$	−5.40688e7			−0.225095
$249$			9.78876e7i			0.401818i
$250$	−3.06141e7			−0.123917
$251$	−1.22443e8			−0.488737			−0.244368	−	0.969682i	$-0.578581\pi$
$251$	−1.22443e8			−0.488737			−0.244368	+	0.969682i	$0.578581\pi$
$252$		−	1.60030e7i		−	0.0629941i
$253$			2.06509e8i			0.801710i
$254$		−	1.55930e8i		−	0.597052i
$255$		−	1.04766e8i		−	0.395668i
$256$	1.67772e7			0.0625000
$257$	4.54376e7			0.166974			0.0834872	−	0.996509i	$-0.473394\pi$
$257$	4.54376e7			0.166974			0.0834872	+	0.996509i	$0.473394\pi$
$258$		−	3.38600e7i		−	0.122749i
$259$	−1.82696e8			−0.653401
$260$	1.31395e8	+	1.59094e8i	0.463630	+	0.561368i
$261$	7.57114e6			0.0263584
$262$			1.22230e8i			0.419877i
$263$	2.57749e8			0.873678			0.436839	−	0.899540i	$-0.356098\pi$
$263$	2.57749e8			0.873678			0.436839	+	0.899540i	$0.356098\pi$
$264$	−2.79009e7			−0.0933265
$265$			4.02561e7i			0.132883i
$266$			3.61228e7i			0.117678i
$267$			9.40181e7i			0.302289i
$268$		−	2.95866e8i		−	0.938909i
$269$	2.94842e8			0.923541			0.461770	−	0.887000i	$-0.347214\pi$
$269$	2.94842e8			0.923541			0.461770	+	0.887000i	$0.347214\pi$
$270$	−6.40885e7			−0.198156
$271$		−	2.16409e8i		−	0.660515i	−0.943891	−	0.330257i	$-0.892864\pi$
$271$		−	2.16409e8i		−	0.660515i	0.943891	−	0.330257i	$-0.107136\pi$
$272$	3.90498e7			0.117660
$273$	4.67151e7	+	5.65632e7i	0.138960	+	0.168254i
$274$	1.17575e8			0.345292
$275$			1.76656e8i			0.512229i
$276$	−1.76806e8			−0.506193
$277$	−6.28566e8			−1.77694			−0.888468	−	0.458939i	$-0.848230\pi$
$277$	−6.28566e8			−1.77694			−0.888468	+	0.458939i	$0.848230\pi$
$278$		−	1.30836e8i		−	0.365233i
$279$			7.69846e7i			0.212221i
$280$		−	7.14764e7i		−	0.194585i
$281$			3.94389e8i			1.06036i	0.847886	+	0.530179i	$0.177875\pi$
$281$			3.94389e8i			1.06036i	−0.847886	+	0.530179i	$0.822125\pi$
$282$	−3.28702e7			−0.0872831
$283$	−1.17094e8			−0.307102			−0.153551	−	0.988141i	$-0.549071\pi$
$283$	−1.17094e8			−0.307102			−0.153551	+	0.988141i	$0.549071\pi$
$284$		−	3.31850e8i		−	0.859662i
$285$	1.44664e8			0.370172
$286$	9.86168e7	−	8.14470e7i	0.249270	−	0.205870i
$287$	−6.21169e7			−0.155104
$288$		−	2.38879e7i		−	0.0589256i
$289$	−3.19448e8			−0.778499
$290$	3.38160e7			0.0814196
$291$			2.36707e8i			0.563100i
$292$			9.83715e7i			0.231222i
$293$		−	7.61283e8i		−	1.76811i	−0.467382	−	0.884056i	$-0.654803\pi$
$293$		−	7.61283e8i		−	1.76811i	0.467382	−	0.884056i	$-0.345197\pi$
$294$		−	2.54122e7i		−	0.0583212i
$295$	−1.62101e8			−0.367628
$296$	−2.72712e8			−0.611201
$297$			3.97261e7i			0.0879891i
$298$	−1.74758e8			−0.382543
$299$	6.24928e8	−	5.16124e8i	1.35201	−	1.11662i
$300$	−1.51247e8			−0.323417
$301$		−	5.37684e7i		−	0.113643i
$302$	5.12054e8			1.06977
$303$	−2.90198e8			−0.599301
$304$			5.39210e7i			0.110078i
$305$		−	9.82895e8i		−	1.98362i
$306$		−	5.56002e7i		−	0.110931i
$307$		−	5.21758e8i		−	1.02916i	−0.857441	−	0.514582i	$-0.827947\pi$
$307$		−	5.21758e8i		−	1.02916i	0.857441	−	0.514582i	$-0.172053\pi$
$308$	−4.43057e7			−0.0864036
$309$	6.48749e7			0.125090
$310$			3.43847e8i			0.655540i
$311$	1.93183e8			0.364173			0.182086	−	0.983283i	$-0.441715\pi$
$311$	1.93183e8			0.364173			0.182086	+	0.983283i	$0.441715\pi$
$312$	6.97322e7	+	8.44325e7i	0.129985	+	0.157387i
$313$	−8.95351e8			−1.65040			−0.825198	−	0.564843i	$-0.808937\pi$
$313$	−8.95351e8			−1.65040			−0.825198	+	0.564843i	$0.808937\pi$
$314$			4.95892e8i			0.903927i
$315$	−1.01770e8			−0.183457
$316$	−2.02809e8			−0.361561
$317$		−	6.07343e8i		−	1.07085i	−0.844584	−	0.535423i	$-0.820152\pi$
$317$		−	6.07343e8i		−	1.07085i	0.844584	−	0.535423i	$-0.179848\pi$
$318$			2.13642e7i			0.0372556i
$319$		−	2.09613e7i		−	0.0361536i
$320$		−	1.06694e8i		−	0.182018i
$321$	1.50586e8			0.254107
$322$	−2.80762e8			−0.468644
$323$			1.25504e8i			0.207228i
$324$	−3.40122e7			−0.0555556
$325$	5.34588e8	−	4.41513e8i	0.863829	−	0.713430i
$326$	−3.40128e8			−0.543727
$327$			4.09642e8i			0.647869i
$328$	−9.27225e7			−0.145086
$329$	−5.21966e7			−0.0808084
$330$			1.77434e8i			0.271793i
$331$		−	5.82829e8i		−	0.883370i	−0.897170	−	0.441685i	$-0.854381\pi$
$331$		−	5.82829e8i		−	0.883370i	0.897170	−	0.441685i	$-0.145619\pi$
$332$			2.32030e8i			0.347985i
$333$			3.88295e8i			0.576245i
$334$	3.76839e8			0.553406
$335$	−1.88154e9			−2.73437
$336$		−	3.79331e7i		−	0.0545545i
$337$	−2.93112e8			−0.417186			−0.208593	−	0.978003i	$-0.566888\pi$
$337$	−2.93112e8			−0.417186			−0.208593	+	0.978003i	$0.566888\pi$
$338$	−4.92942e8	−	9.48711e7i	−0.694364	−	0.133637i
$339$	2.65960e8			0.370780
$340$		−	2.48335e8i		−	0.342659i
$341$	2.13138e8			0.291086
$342$	7.67742e7			0.103782
$343$		−	4.03536e7i		−	0.0539949i
$344$		−	8.02607e7i		−	0.106304i
$345$			1.12439e9i			1.47418i
$346$			3.25466e8i			0.422415i
$347$	3.71963e8			0.477910			0.238955	−	0.971031i	$-0.423195\pi$
$347$	3.71963e8			0.477910			0.238955	+	0.971031i	$0.423195\pi$
$348$	1.79464e7			0.0228271
$349$		−	1.15476e8i		−	0.145413i	−0.997353	−	0.0727066i	$-0.976836\pi$
$349$		−	1.15476e8i		−	0.145413i	0.997353	−	0.0727066i	$-0.0231637\pi$
$350$	−2.40175e8			−0.299426
$351$	1.20217e8	−	9.92867e7i	0.148386	−	0.122551i
$352$	−6.61356e7			−0.0808232
$353$		−	5.62931e8i		−	0.681152i	−0.940217	−	0.340576i	$-0.889378\pi$
$353$		−	5.62931e8i		−	0.681152i	0.940217	−	0.340576i	$-0.110622\pi$
$354$	−8.60282e7			−0.103069
$355$	−2.11038e9			−2.50358
$356$			2.22858e8i			0.261790i
$357$		−	8.82911e7i		−	0.102702i
$358$			5.34924e8i			0.616171i
$359$			1.10373e9i			1.25902i	0.776994	+	0.629508i	$0.216743\pi$
$359$			1.10373e9i			1.25902i	−0.776994	+	0.629508i	$0.783257\pi$
$360$	−1.51913e8			−0.171608
$361$	7.20573e8			0.806126
$362$			4.20215e8i			0.465577i
$363$	−4.16168e8			−0.456663
$364$	1.10732e8	+	1.34076e8i	0.120342	+	0.145712i
$365$	6.25587e8			0.673384
$366$		−	5.21629e8i		−	0.556132i
$367$	7.74253e8			0.817621			0.408810	−	0.912619i	$-0.365944\pi$
$367$	7.74253e8			0.817621			0.408810	+	0.912619i	$0.365944\pi$
$368$	−4.19097e8			−0.438376
$369$			1.32021e8i			0.136789i
$370$			1.73430e9i			1.77999i
$371$			3.39256e7i			0.0344920i
$372$			1.82482e8i			0.183789i
$373$	−1.69569e9			−1.69187			−0.845933	−	0.533290i	$-0.820956\pi$
$373$	−1.69569e9			−1.69187			−0.845933	+	0.533290i	$0.820956\pi$
$374$	−1.53934e8			−0.152154
$375$			1.03323e8i			0.101178i
$376$	−7.79145e7			−0.0755894
$377$	−6.34322e7	+	5.23882e7i	−0.0609698	+	0.0503545i
$378$	−5.40102e7			−0.0514344
$379$			2.90788e8i			0.274372i	0.990545	+	0.137186i	$0.0438058\pi$
$379$			2.90788e8i			0.274372i	−0.990545	+	0.137186i	$0.956194\pi$
$380$	3.42907e8			0.320578
$381$	−5.26265e8			−0.487491
$382$			3.17645e8i			0.291555i
$383$		−	1.24667e9i		−	1.13385i	−0.823770	−	0.566924i	$-0.808133\pi$
$383$		−	1.24667e9i		−	1.13385i	0.823770	−	0.566924i	$-0.191867\pi$
$384$		−	5.66231e7i		−	0.0510310i
$385$			2.81759e8i			0.251632i
$386$	1.99857e8			0.176874
$387$	−1.14277e8			−0.100224
$388$			5.61083e8i			0.487659i
$389$	1.99977e9			1.72249			0.861245	−	0.508191i	$-0.169685\pi$
$389$	1.99977e9			1.72249			0.861245	+	0.508191i	$0.169685\pi$
$390$	5.36943e8	−	4.43458e8i	0.458355	−	0.378552i
$391$	−9.75469e8			−0.825267
$392$		−	6.02363e7i		−	0.0505076i
$393$	4.12525e8			0.342828
$394$	−8.88657e8			−0.731977
$395$			1.28975e9i			1.05297i
$396$			9.41657e7i			0.0762008i
$397$		−	1.66409e9i		−	1.33478i	−0.744707	−	0.667391i	$-0.767411\pi$
$397$		−	1.66409e9i		−	1.33478i	0.744707	−	0.667391i	$-0.232589\pi$
$398$		−	9.71367e8i		−	0.772312i
$399$	1.21915e8			0.0960839
$400$	−3.58512e8			−0.280087
$401$		−	2.18277e9i		−	1.69045i	−0.534408	−	0.845227i	$-0.679465\pi$
$401$		−	2.18277e9i		−	1.69045i	0.534408	−	0.845227i	$-0.320535\pi$
$402$	−9.98548e8			−0.766616
$403$	−5.32692e8	−	6.44989e8i	−0.405423	−	0.490891i
$404$	−6.87876e8			−0.519010
$405$			2.16299e8i			0.161794i
$406$	2.84982e7			0.0211337
$407$	1.07503e9			0.790387
$408$		−	1.31793e8i		−	0.0960688i
$409$			1.33283e8i			0.0963258i	0.998839	+	0.0481629i	$0.0153367\pi$
$409$			1.33283e8i			0.0963258i	−0.998839	+	0.0481629i	$0.984663\pi$
$410$			5.89663e8i			0.422533i
$411$		−	3.96814e8i		−	0.281930i
$412$	1.53778e8			0.108331
$413$	−1.36610e8			−0.0954236
$414$			5.96722e8i			0.413305i
$415$	1.47558e9			1.01343
$416$	1.65291e8	+	2.00136e8i	0.112570	+	0.136301i
$417$	−4.41571e8			−0.298212
$418$		−	2.12556e8i		−	0.142350i
$419$	−3.06674e8			−0.203670			−0.101835	−	0.994801i	$-0.532471\pi$
$419$	−3.06674e8			−0.203670			−0.101835	+	0.994801i	$0.532471\pi$
$420$	−2.41233e8			−0.158878
$421$		−	1.55295e8i		−	0.101431i	−0.998713	−	0.0507153i	$-0.983850\pi$
$421$		−	1.55295e8i		−	0.101431i	0.998713	−	0.0507153i	$-0.0161501\pi$
$422$		−	1.20043e9i		−	0.777575i
$423$			1.10937e8i			0.0712663i
$424$			5.06411e7i			0.0322643i
$425$	−8.34454e8			−0.527280
$426$	−1.11999e9			−0.701911
$427$		−	8.28328e8i		−	0.514879i
$428$	3.56944e8			0.220063
$429$	−2.74883e8	−	3.32832e8i	−0.168092	−	0.203528i
$430$	−5.10413e8			−0.309586
$431$		−	4.85256e8i		−	0.291945i	−0.989289	−	0.145972i	$-0.953369\pi$
$431$		−	4.85256e8i		−	0.291945i	0.989289	−	0.145972i	$-0.0466311\pi$
$432$	−8.06216e7			−0.0481125
$433$	−1.28137e9			−0.758520			−0.379260	−	0.925290i	$-0.623821\pi$
$433$	−1.28137e9			−0.758520			−0.379260	+	0.925290i	$0.623821\pi$
$434$			2.89775e8i			0.170156i
$435$		−	1.14129e8i		−	0.0664789i
$436$			9.71003e8i			0.561071i
$437$		−	1.34695e9i		−	0.772088i
$438$	3.32004e8			0.188792
$439$	1.23266e8			0.0695373			0.0347687	−	0.999395i	$-0.488931\pi$
$439$	1.23266e8			0.0695373			0.0347687	+	0.999395i	$0.488931\pi$
$440$			4.20585e8i			0.235380i
$441$	−8.57661e7			−0.0476190
$442$	3.84724e8	+	4.65827e8i	0.211919	+	0.256594i
$443$	2.14521e9			1.17235			0.586174	−	0.810185i	$-0.300634\pi$
$443$	2.14521e9			1.17235			0.586174	+	0.810185i	$0.300634\pi$
$444$			9.20404e8i			0.499043i
$445$	1.41725e9			0.762406
$446$	−6.88516e8			−0.367487
$447$			5.89809e8i			0.312345i
$448$		−	8.99154e7i		−	0.0472456i
$449$			1.00373e9i			0.523306i	0.965162	+	0.261653i	$0.0842675\pi$
$449$			1.00373e9i			0.523306i	−0.965162	+	0.261653i	$0.915732\pi$
$450$			5.10459e8i			0.264069i
$451$	3.65511e8			0.187622
$452$	6.30423e8			0.321105
$453$		−	1.72818e9i		−	0.873466i
$454$	−9.11395e8			−0.457100
$455$	8.52646e8	−	7.04194e8i	0.424355	−	0.350471i
$456$	1.81983e8			0.0898782
$457$		−	1.06094e9i		−	0.519979i	−0.965611	−	0.259990i	$-0.916281\pi$
$457$		−	1.06094e9i		−	0.519979i	0.965611	−	0.259990i	$-0.0837192\pi$
$458$	2.11528e9			1.02882
$459$	−1.87651e8			−0.0905745
$460$			2.66522e9i			1.27668i
$461$		−	3.76344e9i		−	1.78909i	−0.446982	−	0.894543i	$-0.647501\pi$
$461$		−	3.76344e9i		−	1.78909i	0.446982	−	0.894543i	$-0.352499\pi$
$462$			1.49532e8i			0.0705482i
$463$			2.08330e9i			0.975478i	0.872989	+	0.487739i	$0.162178\pi$
$463$			2.08330e9i			0.975478i	−0.872989	+	0.487739i	$0.837822\pi$
$464$	4.25396e7			0.0197688
$465$	1.16048e9			0.535246
$466$		−	1.27316e9i		−	0.582818i
$467$	3.51343e9			1.59633			0.798164	−	0.602441i	$-0.205805\pi$
$467$	3.51343e9			1.59633			0.798164	+	0.602441i	$0.205805\pi$
$468$	2.84960e8	−	2.35346e8i	0.128506	−	0.106132i
$469$	−1.58566e9			−0.709748
$470$			4.95492e8i			0.220138i
$471$	1.67364e9			0.738053
$472$	−2.03919e8			−0.0892606
$473$			3.16387e8i			0.137469i
$474$			6.84479e8i			0.295214i
$475$		−	1.15224e9i		−	0.493303i
$476$		−	2.09283e8i		−	0.0889424i
$477$	7.21042e7			0.0304191
$478$	1.96625e9			0.823456
$479$		−	8.10161e8i		−	0.336819i	−0.985717	−	0.168410i	$-0.946137\pi$
$479$		−	8.10161e8i		−	0.336819i	0.985717	−	0.168410i	$-0.0538631\pi$
$480$	−3.60091e8			−0.148617
$481$	−2.68679e9	−	3.25320e9i	−1.10085	−	1.33292i
$482$	−1.72918e9			−0.703356
$483$			9.47572e8i			0.382646i
$484$	−9.86473e8			−0.395482
$485$	3.56817e9			1.42020
$486$			1.14791e8i			0.0453609i
$487$		−	3.61323e9i		−	1.41757i	−0.705426	−	0.708784i	$-0.749244\pi$
$487$		−	3.61323e9i		−	1.41757i	0.705426	−	0.708784i	$-0.250756\pi$
$488$		−	1.23645e9i		−	0.481625i
$489$			1.14793e9i			0.443952i
$490$	−3.83069e8			−0.147093
$491$	1.05056e9			0.400531			0.200265	−	0.979742i	$-0.435820\pi$
$491$	1.05056e9			0.400531			0.200265	+	0.979742i	$0.435820\pi$
$492$			3.12939e8i			0.118463i
$493$	9.90131e7			0.0372159
$494$	−6.43226e8	+	5.31236e8i	−0.240060	+	0.198264i
$495$	5.98841e8			0.221918
$496$			4.32550e8i			0.159166i
$497$	−1.77851e9			−0.649843
$498$	7.83101e8			0.284129
$499$			1.58084e9i			0.569555i	0.958594	+	0.284778i	$0.0919198\pi$
$499$			1.58084e9i			0.569555i	−0.958594	+	0.284778i	$0.908080\pi$
$500$			2.44913e8i			0.0876227i
$501$		−	1.27183e9i		−	0.451854i
$502$			9.79542e8i			0.345589i
$503$	−3.13221e9			−1.09739			−0.548697	−	0.836022i	$-0.684876\pi$
$503$	−3.13221e9			−1.09739			−0.548697	+	0.836022i	$0.684876\pi$
$504$	−1.28024e8			−0.0445435
$505$			4.37451e9i			1.51150i
$506$	1.65207e9			0.566895
$507$	−3.20190e8	+	1.66368e9i	−0.109114	+	0.566946i
$508$	−1.24744e9			−0.422180
$509$		−	3.33653e9i		−	1.12146i	−0.827999	−	0.560729i	$-0.810521\pi$
$509$		−	3.33653e9i		−	1.12146i	0.827999	−	0.560729i	$-0.189479\pi$
$510$	−8.38130e8			−0.279780
$511$	5.27210e8			0.174787
$512$		−	1.34218e8i		−	0.0441942i
$513$		−	2.59113e8i		−	0.0847380i
$514$		−	3.63501e8i		−	0.118069i
$515$		−	9.77939e8i		−	0.315491i
$516$	−2.70880e8			−0.0867966
$517$	3.07138e8			0.0977499
$518$			1.46157e9i			0.462024i
$519$	1.09845e9			0.344900
$520$	1.27275e9	−	1.05116e9i	0.396947	−	0.327836i
$521$	4.20785e9			1.30355			0.651776	−	0.758412i	$-0.274024\pi$
$521$	4.20785e9			1.30355			0.651776	+	0.758412i	$0.274024\pi$
$522$		−	6.05691e7i		−	0.0186382i
$523$	−3.47380e9			−1.06182			−0.530908	−	0.847429i	$-0.678149\pi$
$523$	−3.47380e9			−1.06182			−0.530908	+	0.847429i	$0.678149\pi$
$524$	9.77838e8			0.296898
$525$			8.10590e8i			0.244480i
$526$		−	2.06199e9i		−	0.617784i
$527$			1.00678e9i			0.299639i
$528$			2.23208e8i			0.0659918i
$529$	7.06425e9			2.07478
$530$	3.22049e8			0.0939628
$531$			2.90345e8i			0.0841557i
$532$	2.88983e8			0.0832111
$533$	−9.13514e8	−	1.10609e9i	−0.261318	−	0.316407i
$534$	7.52145e8			0.213750
$535$		−	2.26996e9i		−	0.640885i
$536$	−2.36693e9			−0.663909
$537$	1.80537e9			0.503102
$538$		−	2.35873e9i		−	0.653042i
$539$			2.37451e8i			0.0653150i
$540$			5.12708e8i			0.140117i
$541$		−	1.76177e8i		−	0.0478364i	−0.999714	−	0.0239182i	$-0.992386\pi$
$541$		−	1.76177e8i		−	0.0478364i	0.999714	−	0.0239182i	$-0.00761413\pi$
$542$	−1.73127e9			−0.467054
$543$	1.41822e9			0.380142
$544$		−	3.12399e8i		−	0.0831980i
$545$	6.17504e9			1.63400
$546$	4.52505e8	−	3.73721e8i	0.118973	−	0.0982592i
$547$	1.46571e8			0.0382907			0.0191453	−	0.999817i	$-0.493905\pi$
$547$	1.46571e8			0.0382907			0.0191453	+	0.999817i	$0.493905\pi$
$548$		−	9.40597e8i		−	0.244158i
$549$	−1.76050e9			−0.454080
$550$	1.41325e9			0.362201
$551$			1.36720e8i			0.0348178i
$552$			1.41445e9i			0.357933i
$553$			1.08693e9i			0.273315i
$554$			5.02853e9i			1.25648i
$555$	5.85325e9			1.45336
$556$	−1.04669e9			−0.258259
$557$			4.38596e9i			1.07540i	0.843135	+	0.537701i	$0.180707\pi$
$557$			4.38596e9i			1.07540i	−0.843135	+	0.537701i	$0.819293\pi$
$558$	6.15877e8			0.150063
$559$	9.57434e8	−	7.90738e8i	0.231829	−	0.191466i
$560$	−5.71811e8			−0.137592
$561$			5.19527e8i			0.124233i
$562$	3.15511e9			0.749786
$563$	5.11438e9			1.20785			0.603926	−	0.797040i	$-0.293602\pi$
$563$	5.11438e9			1.20785			0.603926	+	0.797040i	$0.293602\pi$
$564$			2.62961e8i			0.0617185i
$565$		−	4.00913e9i		−	0.935150i
$566$			9.36754e8i			0.217154i
$567$			1.82284e8i			0.0419961i
$568$	−2.65480e9			−0.607873
$569$	−4.55124e9			−1.03571			−0.517854	−	0.855469i	$-0.673269\pi$
$569$	−4.55124e9			−1.03571			−0.517854	+	0.855469i	$0.673269\pi$
$570$		−	1.15731e9i		−	0.261751i
$571$	2.52524e9			0.567643			0.283822	−	0.958877i	$-0.408398\pi$
$571$	2.52524e9			0.567643			0.283822	+	0.958877i	$0.408398\pi$
$572$	−6.51576e8	−	7.88935e8i	−0.145572	−	0.176261i
$573$	1.07205e9			0.238054
$574$			4.96935e8i			0.109675i
$575$	8.95566e9			1.96454
$576$	−1.91103e8			−0.0416667
$577$		−	4.22939e9i		−	0.916564i	−0.888807	−	0.458282i	$-0.848465\pi$
$577$		−	4.22939e9i		−	0.916564i	0.888807	−	0.458282i	$-0.151535\pi$
$578$			2.55559e9i			0.550482i
$579$		−	6.74519e8i		−	0.144417i
$580$		−	2.70528e8i		−	0.0575724i
$581$	1.24353e9			0.263052
$582$	1.89366e9			0.398172
$583$		−	1.99626e8i		−	0.0417232i
$584$	7.86972e8			0.163499
$585$	−1.49667e9	−	1.81218e9i	−0.309087	−	0.374246i
$586$	−6.09027e9			−1.25024
$587$			4.12125e9i			0.841000i	0.907293	+	0.420500i	$0.138145\pi$
$587$			4.12125e9i			0.841000i	−0.907293	+	0.420500i	$0.861855\pi$
$588$	−2.03297e8			−0.0412393
$589$	−1.39019e9			−0.280331
$590$			1.29681e9i			0.259952i
$591$			2.99922e9i			0.597657i
$592$			2.18170e9i			0.432184i
$593$			4.92877e9i			0.970616i	0.874343	+	0.485308i	$0.161293\pi$
$593$			4.92877e9i			0.970616i	−0.874343	+	0.485308i	$0.838707\pi$
$594$	3.17809e8			0.0622177
$595$	−1.33092e9			−0.259026
$596$			1.39807e9i			0.270499i
$597$	−3.27836e9			−0.630590
$598$	−4.12899e9	−	4.99943e9i	−0.789568	−	0.956018i
$599$	3.57249e9			0.679169			0.339584	−	0.940576i	$-0.389714\pi$
$599$	3.57249e9			0.679169			0.339584	+	0.940576i	$0.389714\pi$
$600$			1.20998e9i			0.228690i
$601$	−1.57453e8			−0.0295862			−0.0147931	−	0.999891i	$-0.504709\pi$
$601$	−1.57453e8			−0.0295862			−0.0147931	+	0.999891i	$0.504709\pi$
$602$	−4.30147e8			−0.0803580
$603$			3.37010e9i			0.625939i
$604$		−	4.09643e9i		−	0.756443i
$605$			6.27342e9i			1.15176i
$606$			2.32158e9i			0.423770i
$607$	1.00076e10			1.81623			0.908113	−	0.418726i	$-0.137523\pi$
$607$	1.00076e10			1.81623			0.908113	+	0.418726i	$0.137523\pi$
$608$	4.31368e8			0.0778368
$609$		−	9.61815e7i		−	0.0172556i
$610$	−7.86316e9			−1.40263
$611$	−7.67623e8	−	9.29446e8i	−0.136146	−	0.164847i
$612$	−4.44802e8			−0.0784398
$613$		−	4.98208e9i		−	0.873572i	−0.899565	−	0.436786i	$-0.856117\pi$
$613$		−	4.98208e9i		−	0.873572i	0.899565	−	0.436786i	$-0.143883\pi$
$614$	−4.17406e9			−0.727729
$615$	1.99011e9			0.344997
$616$			3.54445e8i			0.0610966i
$617$			2.08850e9i			0.357961i	0.983853	+	0.178981i	$0.0572799\pi$
$617$			2.08850e9i			0.357961i	−0.983853	+	0.178981i	$0.942720\pi$
$618$		−	5.18999e8i		−	0.0884519i
$619$			5.29605e9i			0.897500i	0.893657	+	0.448750i	$0.148131\pi$
$619$			5.29605e9i			0.897500i	−0.893657	+	0.448750i	$0.851869\pi$
$620$	2.75078e9			0.463537
$621$	2.01394e9			0.337462
$622$		−	1.54546e9i		−	0.257509i
$623$	1.19438e9			0.197894
$624$	6.75460e8	−	5.57858e8i	0.111289	−	0.0919131i
$625$	−5.28056e9			−0.865167
$626$			7.16281e9i			1.16701i
$627$	−7.17376e8			−0.116228
$628$	3.96714e9			0.639173
$629$			5.07801e9i			0.813611i
$630$			8.14161e8i			0.129723i
$631$			9.88962e9i			1.56703i	0.621374	+	0.783514i	$0.286575\pi$
$631$			9.88962e9i			1.56703i	−0.621374	+	0.783514i	$0.713425\pi$
$632$			1.62247e9i			0.255662i
$633$	−4.05144e9			−0.634887
$634$	−4.85875e9			−0.757202
$635$			7.93303e9i			1.22951i
$636$	1.70914e8			0.0263437
$637$	7.18562e8	−	5.93455e8i	0.110148	−	0.0909704i
$638$	−1.67691e8			−0.0255644
$639$			3.77998e9i			0.573108i
$640$	−8.53549e8			−0.128706
$641$	−6.28298e9			−0.942243			−0.471121	−	0.882068i	$-0.656151\pi$
$641$	−6.28298e9			−0.942243			−0.471121	+	0.882068i	$0.656151\pi$
$642$		−	1.20469e9i		−	0.179681i
$643$			1.01248e9i			0.150192i	0.997176	+	0.0750961i	$0.0239264\pi$
$643$			1.01248e9i			0.150192i	−0.997176	+	0.0750961i	$0.976074\pi$
$644$			2.24610e9i			0.331381i
$645$			1.72264e9i			0.252776i
$646$	1.00403e9			0.146532
$647$	7.53763e9			1.09413			0.547066	−	0.837089i	$-0.315745\pi$
$647$	7.53763e9			1.09413			0.547066	+	0.837089i	$0.315745\pi$
$648$			2.72098e8i			0.0392837i
$649$	8.03845e8			0.115429
$650$	−3.53210e9	−	4.27671e9i	−0.504471	−	0.610819i
$651$	9.77990e8			0.138932
$652$			2.72103e9i			0.384473i
$653$	−4.93185e9			−0.693128			−0.346564	−	0.938026i	$-0.612652\pi$
$653$	−4.93185e9			−0.693128			−0.346564	+	0.938026i	$0.612652\pi$
$654$	3.27714e9			0.458113
$655$		−	6.21850e9i		−	0.864651i
$656$			7.41780e8i			0.102592i
$657$		−	1.12051e9i		−	0.154148i
$658$			4.17573e8i			0.0571402i
$659$	−6.28838e9			−0.855933			−0.427966	−	0.903795i	$-0.640770\pi$
$659$	−6.28838e9			−0.855933			−0.427966	+	0.903795i	$0.640770\pi$
$660$	1.41947e9			0.192187
$661$		−	8.80626e9i		−	1.18600i	−0.805201	−	0.593002i	$-0.797943\pi$
$661$		−	8.80626e9i		−	1.18600i	0.805201	−	0.593002i	$-0.202057\pi$
$662$	−4.66263e9			−0.624637
$663$	1.57217e9	−	1.29844e9i	0.209508	−	0.173032i
$664$	1.85624e9			0.246063
$665$		−	1.83777e9i		−	0.242334i
$666$	3.10636e9			0.407467
$667$	−1.06264e9			−0.138659
$668$		−	3.01471e9i		−	0.391317i
$669$			2.32374e9i			0.300052i
$670$			1.50523e10i			1.93349i
$671$			4.87409e9i			0.622823i
$672$	−3.03464e8			−0.0385758
$673$	1.11377e10			1.40846			0.704229	−	0.709973i	$-0.251293\pi$
$673$	1.11377e10			1.40846			0.704229	+	0.709973i	$0.251293\pi$
$674$			2.34490e9i			0.294995i
$675$	1.72280e9			0.215611
$676$	−7.58969e8	+	3.94353e9i	−0.0944953	+	0.490989i
$677$	1.05402e10			1.30554			0.652768	−	0.757558i	$-0.273608\pi$
$677$	1.05402e10			1.30554			0.652768	+	0.757558i	$0.273608\pi$
$678$		−	2.12768e9i		−	0.262181i
$679$	3.00706e9			0.368636
$680$	−1.98668e9			−0.242296
$681$			3.07596e9i			0.373220i
$682$		−	1.70511e9i		−	0.205829i
$683$		−	3.32543e9i		−	0.399370i	−0.979860	−	0.199685i	$-0.936008\pi$
$683$		−	3.32543e9i		−	0.399370i	0.979860	−	0.199685i	$-0.0639918\pi$
$684$		−	6.14194e8i		−	0.0733853i
$685$	−5.98167e9			−0.711059
$686$	−3.22829e8			−0.0381802
$687$		−	7.13905e9i		−	0.840025i
$688$	−6.42085e8			−0.0751680
$689$	−6.04100e8	+	4.98922e8i	−0.0703625	+	0.0581119i
$690$	8.99511e9			1.04240
$691$			9.34344e9i			1.07729i	0.842532	+	0.538646i	$0.181064\pi$
$691$			9.34344e9i			1.07729i	−0.842532	+	0.538646i	$0.818936\pi$
$692$	2.60373e9			0.298693
$693$	5.04669e8			0.0576024
$694$		−	2.97570e9i		−	0.337933i
$695$			6.65634e9i			0.752123i
$696$		−	1.43571e8i		−	0.0161412i
$697$			1.72653e9i			0.193134i
$698$	−9.23810e8			−0.102823
$699$	−4.29692e9			−0.475869
$700$			1.92140e9i			0.211726i
$701$	−4.90202e9			−0.537479			−0.268740	−	0.963213i	$-0.586607\pi$
$701$	−4.90202e9			−0.537479			−0.268740	+	0.963213i	$0.586607\pi$
$702$	−7.94293e8	−	9.61739e8i	−0.0866565	−	0.104925i
$703$	−7.01185e9			−0.761183
$704$			5.29085e8i			0.0571506i
$705$	1.67229e9			0.179742
$706$	−4.50345e9			−0.481647
$707$			3.68659e9i			0.392335i
$708$			6.88226e8i			0.0728810i
$709$		−	5.90156e9i		−	0.621877i	−0.950430	−	0.310939i	$-0.899357\pi$
$709$		−	5.90156e9i		−	0.621877i	0.950430	−	0.310939i	$-0.100643\pi$
$710$			1.68830e10i			1.77030i
$711$	2.31012e9			0.241041
$712$	1.78286e9			0.185113
$713$		−	1.08051e10i		−	1.11639i
$714$	−7.06329e8			−0.0726212
$715$	−5.01718e9	+	4.14365e9i	−0.513321	+	0.423948i
$716$	4.27939e9			0.435699
$717$		−	6.63608e9i		−	0.672349i
$718$	8.82982e9			0.890259
$719$	7.94141e9			0.796795			0.398397	−	0.917213i	$-0.369567\pi$
$719$	7.94141e9			0.796795			0.398397	+	0.917213i	$0.369567\pi$
$720$			1.21531e9i			0.121345i
$721$		−	8.24152e8i		−	0.0818905i
$722$		−	5.76458e9i		−	0.570017i
$723$			5.83598e9i			0.574288i
$724$	3.36172e9			0.329212
$725$	−9.09027e8			−0.0885919
$726$			3.32935e9i			0.322910i
$727$	−1.43223e10			−1.38243			−0.691215	−	0.722649i	$-0.742924\pi$
$727$	−1.43223e10			−1.38243			−0.691215	+	0.722649i	$0.742924\pi$
$728$	1.07261e9	−	8.85857e8i	0.103034	−	0.0850950i
$729$	3.87420e8			0.0370370
$730$		−	5.00470e9i		−	0.476155i
$731$	−1.49449e9			−0.141508
$732$	−4.17303e9			−0.393245
$733$			1.18990e10i			1.11596i	0.829856	+	0.557978i	$0.188423\pi$
$733$			1.18990e10i			1.11596i	−0.829856	+	0.557978i	$0.811577\pi$
$734$		−	6.19403e9i		−	0.578145i
$735$			1.29286e9i			0.120101i
$736$			3.35277e9i			0.309979i
$737$	9.33040e9			0.858547
$738$	1.05617e9			0.0967243
$739$		−	6.69305e9i		−	0.610054i	−0.952344	−	0.305027i	$-0.901334\pi$
$739$		−	6.69305e9i		−	0.610054i	0.952344	−	0.305027i	$-0.0986655\pi$
$740$	1.38744e10			1.25864
$741$	1.79292e9	+	2.17089e9i	0.161882	+	0.196008i
$742$	2.71404e8			0.0243895
$743$		−	2.84752e9i		−	0.254686i	−0.991859	−	0.127343i	$-0.959355\pi$
$743$		−	2.84752e9i		−	0.254686i	0.991859	−	0.127343i	$-0.0406449\pi$
$744$	1.45986e9			0.129959
$745$	8.89091e9			0.787770
$746$			1.35655e10i			1.19633i
$747$		−	2.64296e9i		−	0.231990i
$748$			1.23147e9i			0.107589i
$749$		−	1.91300e9i		−	0.166352i
$750$	8.26581e8			0.0715436
$751$	5.55372e9			0.478459			0.239229	−	0.970963i	$-0.423105\pi$
$751$	5.55372e9			0.478459			0.239229	+	0.970963i	$0.423105\pi$
$752$			6.23316e8i			0.0534498i
$753$	3.30595e9			0.282172
$754$	4.19105e8	+	5.07457e8i	0.0356060	+	0.0431122i
$755$	−2.60510e10			−2.20298
$756$			4.32081e8i			0.0363696i
$757$	9.08545e9			0.761221			0.380610	−	0.924735i	$-0.375714\pi$
$757$	9.08545e9			0.761221			0.380610	+	0.924735i	$0.375714\pi$
$758$	2.32631e9			0.194010
$759$		−	5.57575e9i		−	0.462868i
$760$		−	2.74326e9i		−	0.226683i
$761$		−	6.79313e9i		−	0.558758i	−0.960181	−	0.279379i	$-0.909871\pi$
$761$		−	6.79313e9i		−	0.558758i	0.960181	−	0.279379i	$-0.0901285\pi$
$762$			4.21012e9i			0.344708i
$763$	5.20397e9			0.424130
$764$	2.54116e9			0.206160
$765$			2.82869e9i			0.228439i
$766$	−9.97333e9			−0.801751
$767$	−2.00903e9	−	2.43256e9i	−0.160769	−	0.194661i
$768$	−4.52985e8			−0.0360844
$769$			1.72401e10i			1.36709i	0.729906	+	0.683547i	$0.239564\pi$
$769$			1.72401e10i			1.36709i	−0.729906	+	0.683547i	$0.760436\pi$
$770$	2.25407e9			0.177931
$771$	−1.22682e9			−0.0964027
$772$		−	1.59886e9i		−	0.125069i
$773$		−	9.45521e9i		−	0.736280i	−0.929770	−	0.368140i	$-0.879995\pi$
$773$		−	9.45521e9i		−	0.736280i	0.929770	−	0.368140i	$-0.120005\pi$
$774$			9.14219e8i			0.0708691i
$775$		−	9.24315e9i		−	0.713286i
$776$	4.48867e9			0.344827
$777$	4.93279e9			0.377241
$778$		−	1.59982e10i		−	1.21798i
$779$	−2.38404e9			−0.180689
$780$	−3.54766e9	−	4.29555e9i	−0.267677	−	0.324106i
$781$	1.04652e10			0.786083
$782$			7.80375e9i			0.583552i
$783$	−2.04421e8			−0.0152180
$784$	−4.81890e8			−0.0357143
$785$		−	2.52288e10i		−	1.86145i
$786$		−	3.30020e9i		−	0.242416i
$787$			3.79602e8i			0.0277598i	0.999904	+	0.0138799i	$0.00441826\pi$
$787$			3.79602e8i			0.0277598i	−0.999904	+	0.0138799i	$0.995582\pi$
$788$			7.10925e9i			0.517586i
$789$	−6.95922e9			−0.504418
$790$	1.03180e10			0.744561
$791$		−	3.37867e9i		−	0.242733i
$792$	7.53326e8			0.0538821
$793$	1.47497e10	−	1.21817e10i	1.05034	−	0.867465i
$794$	−1.33127e10			−0.943834
$795$		−	1.08691e9i		−	0.0767203i
$796$	−7.77094e9			−0.546107
$797$	−4.60537e9			−0.322226			−0.161113	−	0.986936i	$-0.551508\pi$
$797$	−4.60537e9			−0.322226			−0.161113	+	0.986936i	$0.551508\pi$
$798$		−	9.75317e8i		−	0.0679416i
$799$			1.45080e9i			0.100622i
$800$			2.86809e9i			0.198052i
$801$		−	2.53849e9i		−	0.174527i
$802$	−1.74622e10			−1.19533
$803$	−3.10223e9			−0.211432
$804$			7.98838e9i			0.542079i
$805$	1.42839e10			0.965076
$806$	−5.15991e9	+	4.26154e9i	−0.347112	+	0.286677i
$807$	−7.96073e9			−0.533207
$808$			5.50301e9i			0.366995i
$809$	3.30820e9			0.219671			0.109835	−	0.993950i	$-0.464968\pi$
$809$	3.30820e9			0.219671			0.109835	+	0.993950i	$0.464968\pi$
$810$	1.73039e9			0.114405
$811$		−	7.49638e9i		−	0.493490i	−0.969080	−	0.246745i	$-0.920639\pi$
$811$		−	7.49638e9i		−	0.493490i	0.969080	−	0.246745i	$-0.0793611\pi$
$812$		−	2.27986e8i		−	0.0149438i
$813$			5.84304e9i			0.381348i
$814$		−	8.60023e9i		−	0.558888i
$815$	1.73042e10			1.11970
$816$	−1.05435e9			−0.0679309
$817$		−	2.06362e9i		−	0.132389i
$818$	1.06626e9			0.0681126
$819$	−1.26131e9	−	1.52721e9i	−0.0802283	−	0.0971413i
$820$	4.71731e9			0.298776
$821$			2.10217e10i			1.32576i	0.748724	+	0.662882i	$0.230667\pi$
$821$			2.10217e10i			1.32576i	−0.748724	+	0.662882i	$0.769333\pi$
$822$	−3.17452e9			−0.199355
$823$	−1.29014e10			−0.806750			−0.403375	−	0.915035i	$-0.632163\pi$
$823$	−1.29014e10			−0.806750			−0.403375	+	0.915035i	$0.632163\pi$
$824$		−	1.23022e9i		−	0.0766016i
$825$		−	4.76971e9i		−	0.295736i
$826$			1.09288e9i			0.0674747i
$827$			2.12055e10i			1.30371i	0.758345	+	0.651853i	$0.226008\pi$
$827$			2.12055e10i			1.30371i	−0.758345	+	0.651853i	$0.773992\pi$
$828$	4.77377e9			0.292251
$829$	−2.62724e10			−1.60162			−0.800808	−	0.598921i	$-0.795596\pi$
$829$	−2.62724e10			−1.60162			−0.800808	+	0.598921i	$0.795596\pi$
$830$		−	1.18046e10i		−	0.716604i
$831$	1.69713e10			1.02591
$832$	1.60109e9	−	1.32233e9i	0.0963794	−	0.0795991i
$833$	−1.12162e9			−0.0672341
$834$			3.53257e9i			0.210867i
$835$	−1.91719e10			−1.13963
$836$	−1.70045e9			−0.100656
$837$		−	2.07858e9i		−	0.122526i
$838$			2.45339e9i			0.144017i
$839$			2.11677e10i			1.23739i	0.785631	+	0.618695i	$0.212339\pi$
$839$			2.11677e10i			1.23739i	−0.785631	+	0.618695i	$0.787661\pi$
$840$			1.92986e9i			0.112344i
$841$	−1.71420e10			−0.993747
$842$	−1.24236e9			−0.0717222
$843$		−	1.06485e10i		−	0.612198i
$844$	−9.60342e9			−0.549828
$845$	2.50787e10	+	4.82661e9i	1.42990	+	0.275197i
$846$	8.87495e8			0.0503929
$847$			5.28688e9i			0.298956i
$848$	4.05129e8			0.0228143
$849$	3.16155e9			0.177306
$850$			6.67563e9i			0.372843i
$851$		−	5.44991e10i		−	3.03135i
$852$			8.95995e9i			0.496326i
$853$			2.16664e10i			1.19527i	0.801770	+	0.597633i	$0.203892\pi$
$853$			2.16664e10i			1.19527i	−0.801770	+	0.597633i	$0.796108\pi$
$854$	−6.62662e9			−0.364074
$855$	−3.90593e9			−0.213719
$856$		−	2.85555e9i		−	0.155608i
$857$	2.57862e10			1.39944			0.699720	−	0.714417i	$-0.253308\pi$
$857$	2.57862e10			1.39944			0.699720	+	0.714417i	$0.253308\pi$
$858$	−2.66265e9	+	2.19907e9i	−0.143916	+	0.118859i
$859$	−3.56641e10			−1.91980			−0.959898	−	0.280351i	$-0.909549\pi$
$859$	−3.56641e10			−1.91980			−0.959898	+	0.280351i	$0.909549\pi$
$860$			4.08330e9i			0.218911i
$861$	1.67716e9			0.0895493
$862$	−3.88205e9			−0.206436
$863$			1.17828e10i			0.624036i	0.950076	+	0.312018i	$0.101005\pi$
$863$			1.17828e10i			0.624036i	−0.950076	+	0.312018i	$0.898995\pi$
$864$			6.44973e8i			0.0340207i
$865$		−	1.65582e10i		−	0.869877i
$866$			1.02510e10i			0.536355i
$867$	8.62510e9			0.449467
$868$	2.31820e9			0.120318
$869$		−	6.39576e9i		−	0.330615i
$870$	−9.13032e8			−0.0470077
$871$	−2.33193e10	−	2.82352e10i	−1.19578	−	1.44786i
$872$	7.76803e9			0.396737
$873$		−	6.39109e9i		−	0.325106i
$874$	−1.07756e10			−0.545949
$875$	1.31258e9			0.0662365
$876$		−	2.65603e9i		−	0.133496i
$877$		−	4.04489e9i		−	0.202492i	−0.994861	−	0.101246i	$-0.967717\pi$
$877$		−	4.04489e9i		−	0.202492i	0.994861	−	0.101246i	$-0.0322829\pi$
$878$		−	9.86129e8i		−	0.0491703i
$879$			2.05546e10i			1.02082i
$880$	3.36468e9			0.166439
$881$	−5.97216e9			−0.294249			−0.147125	−	0.989118i	$-0.547002\pi$
$881$	−5.97216e9			−0.294249			−0.147125	+	0.989118i	$0.547002\pi$
$882$			6.86129e8i			0.0336718i
$883$	−3.08080e10			−1.50592			−0.752958	−	0.658069i	$-0.771374\pi$
$883$	−3.08080e10			−1.50592			−0.752958	+	0.658069i	$0.771374\pi$
$884$	3.72662e9	−	3.07779e9i	0.181440	−	0.149850i
$885$	4.37673e9			0.212250
$886$		−	1.71617e10i		−	0.828975i
$887$	1.72033e10			0.827710			0.413855	−	0.910343i	$-0.364182\pi$
$887$	1.72033e10			0.827710			0.413855	+	0.910343i	$0.364182\pi$
$888$	7.36323e9			0.352877
$889$			6.68551e9i			0.319138i
$890$		−	1.13380e10i		−	0.539102i
$891$		−	1.07261e9i		−	0.0508005i
$892$			5.50813e9i			0.259852i
$893$	−2.00330e9			−0.0941382
$894$	4.71847e9			0.220862
$895$		−	2.72145e10i		−	1.26888i
$896$	−7.19323e8			−0.0334077
$897$	−1.68731e10	+	1.39353e10i	−0.780585	+	0.644680i
$898$	8.02985e9			0.370033
$899$			1.09676e9i			0.0503444i
$900$	4.08367e9			0.186725
$901$	9.42957e8			0.0429492
$902$		−	2.92409e9i		−	0.132668i
$903$			1.45175e9i			0.0656120i
$904$		−	5.04338e9i		−	0.227056i
$905$		−	2.13786e10i		−	0.958760i
$906$	−1.38255e10			−0.617634
$907$	−2.80631e10			−1.24885			−0.624425	−	0.781085i	$-0.714667\pi$
$907$	−2.80631e10			−1.24885			−0.624425	+	0.781085i	$0.714667\pi$
$908$			7.29116e9i			0.323218i
$909$	7.83534e9			0.346007
$910$	−5.63355e9	−	6.82117e9i	−0.247821	−	0.300064i
$911$	−1.63734e10			−0.717506			−0.358753	−	0.933433i	$-0.616798\pi$
$911$	−1.63734e10			−0.717506			−0.358753	+	0.933433i	$0.616798\pi$
$912$		−	1.45587e9i		−	0.0635535i
$913$	−7.31727e9			−0.318201
$914$	−8.48756e9			−0.367681
$915$			2.65382e10i			1.14524i
$916$		−	1.69222e10i		−	0.727483i
$917$		−	5.24060e9i		−	0.224434i
$918$			1.50121e9i			0.0640459i
$919$	2.51376e10			1.06836			0.534182	−	0.845369i	$-0.320620\pi$
$919$	2.51376e10			1.06836			0.534182	+	0.845369i	$0.320620\pi$
$920$	2.13217e10			0.902746
$921$			1.40875e10i			0.594188i
$922$	−3.01075e10			−1.26507
$923$	−2.61554e10	−	3.16693e10i	−1.09485	−	1.32566i
$924$	1.19625e9			0.0498851
$925$		−	4.66206e10i		−	1.93679i
$926$	1.66664e10			0.689767
$927$	−1.75162e9			−0.0722207
$928$		−	3.40317e8i		−	0.0139787i
$929$		−	2.89186e10i		−	1.18337i	−0.806168	−	0.591686i	$-0.798462\pi$
$929$		−	2.89186e10i		−	1.18337i	0.806168	−	0.591686i	$-0.201538\pi$
$930$		−	9.28387e9i		−	0.378476i
$931$		−	1.54877e9i		−	0.0629017i
$932$	−1.01853e10			−0.412115
$933$	−5.21594e9			−0.210255
$934$		−	2.81074e10i		−	1.12877i
$935$	7.83147e9			0.313330
$936$	−1.88277e9	−	2.27968e9i	−0.0750467	−	0.0908674i
$937$	−2.25485e10			−0.895427			−0.447713	−	0.894177i	$-0.647761\pi$
$937$	−2.25485e10			−0.895427			−0.447713	+	0.894177i	$0.647761\pi$
$938$			1.26853e10i			0.501868i
$939$	2.41745e10			0.952857
$940$	3.96394e9			0.155661
$941$			3.81737e10i			1.49348i	0.665114	+	0.746742i	$0.268383\pi$
$941$			3.81737e10i			1.49348i	−0.665114	+	0.746742i	$0.731617\pi$
$942$		−	1.33891e10i		−	0.521882i
$943$		−	1.85297e10i		−	0.719579i
$944$			1.63135e9i			0.0631168i
$945$	2.74779e9			0.105919
$946$	2.53109e9			0.0972051
$947$			3.21216e10i			1.22906i	0.788895	+	0.614528i	$0.210654\pi$
$947$			3.21216e10i			1.22906i	−0.788895	+	0.614528i	$0.789346\pi$
$948$	5.47584e9			0.208747
$949$	7.75334e9	+	9.38783e9i	0.294481	+	0.356561i
$950$	−9.21788e9			−0.348818
$951$			1.63983e10i			0.618253i
$952$	−1.67426e9			−0.0628918
$953$	−9.56372e9			−0.357933			−0.178967	−	0.983855i	$-0.557275\pi$
$953$	−9.56372e9			−0.357933			−0.178967	+	0.983855i	$0.557275\pi$
$954$		−	5.76833e8i		−	0.0215095i
$955$		−	1.61603e10i		−	0.600398i
$956$		−	1.57300e10i		−	0.582271i
$957$			5.65956e8i			0.0208733i
$958$	−6.48129e9			−0.238167
$959$	−5.04101e9			−0.184566
$960$			2.88073e9i			0.105088i
$961$	1.63606e10			0.594658
$962$	−2.60256e10	+	2.14944e10i	−0.942514	+	0.778416i
$963$	−4.06581e9			−0.146709
$964$			1.38334e10i			0.497348i
$965$	−1.01678e10			−0.364236
$966$	7.58057e9			0.270572
$967$		−	3.18968e10i		−	1.13437i	−0.823590	−	0.567185i	$-0.808032\pi$
$967$		−	3.18968e10i		−	1.13437i	0.823590	−	0.567185i	$-0.191968\pi$
$968$			7.89179e9i			0.279648i
$969$		−	3.38860e9i		−	0.119643i
$970$		−	2.85454e10i		−	1.00423i
$971$	−2.03452e10			−0.713173			−0.356587	−	0.934262i	$-0.616060\pi$
$971$	−2.03452e10			−0.713173			−0.356587	+	0.934262i	$0.616060\pi$
$972$	9.18330e8			0.0320750
$973$			5.60959e9i			0.195225i
$974$	−2.89058e10			−1.00237
$975$	−1.44339e10	+	1.19208e10i	−0.498732	+	0.411899i
$976$	−9.89164e9			−0.340560
$977$		−	4.04303e10i		−	1.38700i	−0.720458	−	0.693499i	$-0.756068\pi$
$977$		−	4.04303e10i		−	1.38700i	0.720458	−	0.693499i	$-0.243932\pi$
$978$	9.18346e9			0.313921
$979$	−7.02802e9			−0.239383
$980$			3.06455e9i			0.104010i
$981$		−	1.10603e10i		−	0.374048i
$982$		−	8.40448e9i		−	0.283218i
$983$			7.25812e9i			0.243717i	0.992547	+	0.121859i	$0.0388855\pi$
$983$			7.25812e9i			0.243717i	−0.992547	+	0.121859i	$0.961115\pi$
$984$	2.50351e9			0.0837657
$985$	4.52109e10			1.50736
$986$		−	7.92105e8i		−	0.0263156i
$987$	1.40931e9			0.0466548
$988$	4.24989e9	+	5.14581e9i	0.140194	+	0.169748i
$989$	1.60394e10			0.527230
$990$		−	4.79073e9i		−	0.156920i
$991$	−1.23978e10			−0.404658			−0.202329	−	0.979318i	$-0.564851\pi$
$991$	−1.23978e10			−0.404658			−0.202329	+	0.979318i	$0.564851\pi$
$992$	3.46040e9			0.112547
$993$			1.57364e10i			0.510014i
$994$			1.42281e10i			0.459509i
$995$			4.94188e10i			1.59042i
$996$		−	6.26481e9i		−	0.200909i
$997$	−2.19937e10			−0.702855			−0.351427	−	0.936215i	$-0.614304\pi$
$997$	−2.19937e10			−0.702855			−0.351427	+	0.936215i	$0.614304\pi$
$998$	1.26467e10			0.402737
$999$		−	1.04840e10i		−	0.332695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.c.a.337.11	✓	24
13.12	even	2	inner	546.8.c.a.337.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.c.a.337.11	✓	24	1.1	even	1	trivial
546.8.c.a.337.14	yes	24	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	546.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.00000i q^{2} -27.0000 q^{3} -64.0000 q^{4} +407.004i q^{5} +216.000i q^{6} +343.000i q^{7} +512.000i q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000i q^{2} -27.0000 q^{3} -64.0000 q^{4} +407.004i q^{5} +216.000i q^{6} +343.000i q^{7} +512.000i q^{8} +729.000 q^{9} +3256.03 q^{10} -2018.30i q^{11} +1728.00 q^{12} +(-6107.68 + 5044.29i) q^{13} +2744.00 q^{14} -10989.1i q^{15} +4096.00 q^{16} +9533.65 q^{17} -5832.00i q^{18} +13164.3i q^{19} -26048.3i q^{20} -9261.00i q^{21} -16146.4 q^{22} -102319. q^{23} -13824.0i q^{24} -87527.3 q^{25} +(40354.3 + 48861.4i) q^{26} -19683.0 q^{27} -21952.0i q^{28} +10385.6 q^{29} -87912.9 q^{30} +105603. i q^{31} -32768.0i q^{32} +54494.0i q^{33} -76269.2i q^{34} -139602. q^{35} -46656.0 q^{36} +532641. i q^{37} +105314. q^{38} +(164907. - 136196. i) q^{39} -208386. q^{40} +181099. i q^{41} -74088.0 q^{42} -156759. q^{43} +129171. i q^{44} +296706. i q^{45} +818548. i q^{46} +152177. i q^{47} -110592. q^{48} -117649. q^{49} +700218. i q^{50} -257409. q^{51} +(390891. - 322834. i) q^{52} +98908.3 q^{53} +157464. i q^{54} +821455. q^{55} -175616. q^{56} -355436. i q^{57} -83085.2i q^{58} +398279. i q^{59} +703303. i q^{60} -2.41495e6 q^{61} +844824. q^{62} +250047. i q^{63} -262144. q^{64} +(-2.05304e6 - 2.48585e6i) q^{65} +435952. q^{66} +4.62291e6i q^{67} -610154. q^{68} +2.76260e6 q^{69} +1.11682e6i q^{70} +5.18516e6i q^{71} +373248. i q^{72} -1.53705e6i q^{73} +4.26113e6 q^{74} +2.36324e6 q^{75} -842515. i q^{76} +692276. q^{77} +(-1.08957e6 - 1.31926e6i) q^{78} +3.16889e6 q^{79} +1.66709e6i q^{80} +531441. q^{81} +1.44879e6 q^{82} -3.62547e6i q^{83} +592704. i q^{84} +3.88023e6i q^{85} +1.25407e6i q^{86} -280412. q^{87} +1.03337e6 q^{88} -3.48215e6i q^{89} +2.37365e6 q^{90} +(-1.73019e6 - 2.09493e6i) q^{91} +6.54838e6 q^{92} -2.85128e6i q^{93} +1.21741e6 q^{94} -5.35792e6 q^{95} +884736. i q^{96} -8.76693e6i q^{97} +941192. i q^{98} -1.47134e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 648 q^{3} - 1536 q^{4} + 17496 q^{9}+O(q^{10}) \) 24 * q - 648 * q^3 - 1536 * q^4 + 17496 * q^9	\( 24 q - 648 q^{3} - 1536 q^{4} + 17496 q^{9} + 1520 q^{10} + 41472 q^{12} + 13718 q^{13} + 65856 q^{14} + 98304 q^{16} + 13586 q^{17} - 11824 q^{22} + 76574 q^{23} - 357850 q^{25} + 132848 q^{26} - 472392 q^{27} + 85198 q^{29} - 41040 q^{30} - 65170 q^{35} - 1119744 q^{36} + 295696 q^{38} - 370386 q^{39} - 97280 q^{40} - 1778112 q^{42} - 91370 q^{43} - 2654208 q^{48} - 2823576 q^{49} - 366822 q^{51} - 877952 q^{52} - 360000 q^{53} - 2519718 q^{55} - 4214784 q^{56} + 874734 q^{61} + 1984480 q^{62} - 6291456 q^{64} - 12450388 q^{65} + 319248 q^{66} - 869504 q^{68} - 2067498 q^{69} - 1405616 q^{74} + 9661950 q^{75} + 506954 q^{77} - 3586896 q^{78} - 2141176 q^{79} + 12754584 q^{81} + 14087488 q^{82} - 2300346 q^{87} + 756736 q^{88} + 1108080 q^{90} - 5695858 q^{91} - 4900736 q^{92} + 8123808 q^{94} + 19191246 q^{95}+O(q^{100}) \) 24 * q - 648 * q^3 - 1536 * q^4 + 17496 * q^9 + 1520 * q^10 + 41472 * q^12 + 13718 * q^13 + 65856 * q^14 + 98304 * q^16 + 13586 * q^17 - 11824 * q^22 + 76574 * q^23 - 357850 * q^25 + 132848 * q^26 - 472392 * q^27 + 85198 * q^29 - 41040 * q^30 - 65170 * q^35 - 1119744 * q^36 + 295696 * q^38 - 370386 * q^39 - 97280 * q^40 - 1778112 * q^42 - 91370 * q^43 - 2654208 * q^48 - 2823576 * q^49 - 366822 * q^51 - 877952 * q^52 - 360000 * q^53 - 2519718 * q^55 - 4214784 * q^56 + 874734 * q^61 + 1984480 * q^62 - 6291456 * q^64 - 12450388 * q^65 + 319248 * q^66 - 869504 * q^68 - 2067498 * q^69 - 1405616 * q^74 + 9661950 * q^75 + 506954 * q^77 - 3586896 * q^78 - 2141176 * q^79 + 12754584 * q^81 + 14087488 * q^82 - 2300346 * q^87 + 756736 * q^88 + 1108080 * q^90 - 5695858 * q^91 - 4900736 * q^92 + 8123808 * q^94 + 19191246 * q^95

Introduction

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