LMFDB - Embedded newform 546.8.a.p.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,8,Mod(1,546)]

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, 0]))

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

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

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:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 302081x^{4} - 2628147x^{3} + 19116974952x^{2} - 78725393748x - 5138711063280 $ x^6 - x^5 - 302081x^4 - 2628147x^3 + 19116974952x^2 - 78725393748x - 5138711063280
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-315.732$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.732 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.732 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2469.86 q^{10} +4382.78 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +8335.77 q^{15} +4096.00 q^{16} -31724.6 q^{17} -5832.00 q^{18} +1861.12 q^{19} +19758.9 q^{20} +9261.00 q^{21} -35062.2 q^{22} -18277.0 q^{23} -13824.0 q^{24} +17190.6 q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} +136149. q^{29} -66686.2 q^{30} +121778. q^{31} -32768.0 q^{32} +118335. q^{33} +253797. q^{34} +105895. q^{35} +46656.0 q^{36} +34048.2 q^{37} -14889.0 q^{38} -59319.0 q^{39} -158071. q^{40} -93436.0 q^{41} -74088.0 q^{42} -658343. q^{43} +280498. q^{44} +225066. q^{45} +146216. q^{46} +367173. q^{47} +110592. q^{48} +117649. q^{49} -137525. q^{50} -856565. q^{51} -140608. q^{52} +331347. q^{53} -157464. q^{54} +1.35310e6 q^{55} -175616. q^{56} +50250.3 q^{57} -1.08920e6 q^{58} +2.12406e6 q^{59} +533489. q^{60} +2.91611e6 q^{61} -974221. q^{62} +250047. q^{63} +262144. q^{64} -678285. q^{65} -946680. q^{66} +3.68988e6 q^{67} -2.03038e6 q^{68} -493480. q^{69} -847161. q^{70} +3.09723e6 q^{71} -373248. q^{72} -743089. q^{73} -272386. q^{74} +464146. q^{75} +119112. q^{76} +1.50329e6 q^{77} +474552. q^{78} +7.91362e6 q^{79} +1.26457e6 q^{80} +531441. q^{81} +747488. q^{82} -9.45259e6 q^{83} +592704. q^{84} -9.79441e6 q^{85} +5.26674e6 q^{86} +3.67603e6 q^{87} -2.24398e6 q^{88} +1.24663e7 q^{89} -1.80053e6 q^{90} -753571. q^{91} -1.16973e6 q^{92} +3.28799e6 q^{93} -2.93738e6 q^{94} +574588. q^{95} -884736. q^{96} +1.63093e7 q^{97} -941192. q^{98} +3.19504e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) $ 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 344 q^{10} + 7370 q^{11} + 10368 q^{12} - 13182 q^{13} - 16464 q^{14} - 1161 q^{15} + 24576 q^{16} + 7950 q^{17} - 34992 q^{18} - 57145 q^{19} - 2752 q^{20} + 55566 q^{21} - 58960 q^{22} + 31769 q^{23} - 82944 q^{24} + 135721 q^{25} + 105456 q^{26} + 118098 q^{27} + 131712 q^{28} - 36455 q^{29} + 9288 q^{30} + 215069 q^{31} - 196608 q^{32} + 198990 q^{33} - 63600 q^{34} - 14749 q^{35} + 279936 q^{36} + 133074 q^{37} + 457160 q^{38} - 355914 q^{39} + 22016 q^{40} + 516452 q^{41} - 444528 q^{42} - 3085 q^{43} + 471680 q^{44} - 31347 q^{45} - 254152 q^{46} + 1463947 q^{47} + 663552 q^{48} + 705894 q^{49} - 1085768 q^{50} + 214650 q^{51} - 843648 q^{52} - 1344571 q^{53} - 944784 q^{54} - 1568062 q^{55} - 1053696 q^{56} - 1542915 q^{57} + 291640 q^{58} + 1810408 q^{59} - 74304 q^{60} + 4047390 q^{61} - 1720552 q^{62} + 1500282 q^{63} + 1572864 q^{64} + 94471 q^{65} - 1591920 q^{66} + 2393614 q^{67} + 508800 q^{68} + 857763 q^{69} + 117992 q^{70} + 10341084 q^{71} - 2239488 q^{72} + 5180001 q^{73} - 1064592 q^{74} + 3664467 q^{75} - 3657280 q^{76} + 2527910 q^{77} + 2847312 q^{78} + 4624979 q^{79} - 176128 q^{80} + 3188646 q^{81} - 4131616 q^{82} + 11892699 q^{83} + 3556224 q^{84} + 750368 q^{85} + 24680 q^{86} - 984285 q^{87} - 3773440 q^{88} + 9781713 q^{89} + 250776 q^{90} - 4521426 q^{91} + 2033216 q^{92} + 5806863 q^{93} - 11711576 q^{94} + 26244263 q^{95} - 5308416 q^{96} + 5202537 q^{97} - 5647152 q^{98} + 5372730 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 344 * q^10 + 7370 * q^11 + 10368 * q^12 - 13182 * q^13 - 16464 * q^14 - 1161 * q^15 + 24576 * q^16 + 7950 * q^17 - 34992 * q^18 - 57145 * q^19 - 2752 * q^20 + 55566 * q^21 - 58960 * q^22 + 31769 * q^23 - 82944 * q^24 + 135721 * q^25 + 105456 * q^26 + 118098 * q^27 + 131712 * q^28 - 36455 * q^29 + 9288 * q^30 + 215069 * q^31 - 196608 * q^32 + 198990 * q^33 - 63600 * q^34 - 14749 * q^35 + 279936 * q^36 + 133074 * q^37 + 457160 * q^38 - 355914 * q^39 + 22016 * q^40 + 516452 * q^41 - 444528 * q^42 - 3085 * q^43 + 471680 * q^44 - 31347 * q^45 - 254152 * q^46 + 1463947 * q^47 + 663552 * q^48 + 705894 * q^49 - 1085768 * q^50 + 214650 * q^51 - 843648 * q^52 - 1344571 * q^53 - 944784 * q^54 - 1568062 * q^55 - 1053696 * q^56 - 1542915 * q^57 + 291640 * q^58 + 1810408 * q^59 - 74304 * q^60 + 4047390 * q^61 - 1720552 * q^62 + 1500282 * q^63 + 1572864 * q^64 + 94471 * q^65 - 1591920 * q^66 + 2393614 * q^67 + 508800 * q^68 + 857763 * q^69 + 117992 * q^70 + 10341084 * q^71 - 2239488 * q^72 + 5180001 * q^73 - 1064592 * q^74 + 3664467 * q^75 - 3657280 * q^76 + 2527910 * q^77 + 2847312 * q^78 + 4624979 * q^79 - 176128 * q^80 + 3188646 * q^81 - 4131616 * q^82 + 11892699 * q^83 + 3556224 * q^84 + 750368 * q^85 + 24680 * q^86 - 984285 * q^87 - 3773440 * q^88 + 9781713 * q^89 + 250776 * q^90 - 4521426 * q^91 + 2033216 * q^92 + 5806863 * q^93 - 11711576 * q^94 + 26244263 * q^95 - 5308416 * q^96 + 5202537 * q^97 - 5647152 * q^98 + 5372730 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	308.732	1.10455	0.552277	−	0.833661i	$-0.313759\pi$
$5$	308.732	1.10455	0.552277	+	0.833661i	$0.313759\pi$
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−2469.86	−0.781038
$11$	4382.78	0.992830	0.496415	−	0.868085i	$-0.334649\pi$
$11$	4382.78	0.992830	0.496415	+	0.868085i	$0.334649\pi$
$12$	1728.00	0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	8335.77	0.637715
$16$	4096.00	0.250000
$17$	−31724.6	−1.56612	−0.783060	−	0.621946i	$-0.786342\pi$
$17$	−31724.6	−1.56612	−0.783060	+	0.621946i	$0.786342\pi$
$18$	−5832.00	−0.235702
$19$	1861.12	0.0622497	0.0311248	−	0.999516i	$-0.490091\pi$
$19$	1861.12	0.0622497	0.0311248	+	0.999516i	$0.490091\pi$
$20$	19758.9	0.552277
$21$	9261.00	0.218218
$22$	−35062.2	−0.702037
$23$	−18277.0	−0.313226	−0.156613	−	0.987660i	$-0.550058\pi$
$23$	−18277.0	−0.313226	−0.156613	+	0.987660i	$0.550058\pi$
$24$	−13824.0	−0.204124
$25$	17190.6	0.220039
$26$	17576.0	0.196116
$27$	19683.0	0.192450
$28$	21952.0	0.188982
$29$	136149.	1.03663	0.518314	−	0.855191i	$-0.326560\pi$
$29$	136149.	1.03663	0.518314	+	0.855191i	$0.326560\pi$
$30$	−66686.2	−0.450932
$31$	121778.	0.734178	0.367089	−	0.930186i	$-0.380354\pi$
$31$	121778.	0.734178	0.367089	+	0.930186i	$0.380354\pi$
$32$	−32768.0	−0.176777
$33$	118335.	0.573211
$34$	253797.	1.10741
$35$	105895.	0.417482
$36$	46656.0	0.166667
$37$	34048.2	0.110507	0.0552533	−	0.998472i	$-0.482403\pi$
$37$	34048.2	0.110507	0.0552533	+	0.998472i	$0.482403\pi$
$38$	−14889.0	−0.0440172
$39$	−59319.0	−0.160128
$40$	−158071.	−0.390519
$41$	−93436.0	−0.211724	−0.105862	−	0.994381i	$-0.533760\pi$
$41$	−93436.0	−0.211724	−0.105862	+	0.994381i	$0.533760\pi$
$42$	−74088.0	−0.154303
$43$	−658343.	−1.26274	−0.631368	−	0.775484i	$-0.717506\pi$
$43$	−658343.	−1.26274	−0.631368	+	0.775484i	$0.717506\pi$
$44$	280498.	0.496415
$45$	225066.	0.368185
$46$	146216.	0.221485
$47$	367173.	0.515855	0.257928	−	0.966164i	$-0.416960\pi$
$47$	367173.	0.515855	0.257928	+	0.966164i	$0.416960\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	−137525.	−0.155591
$51$	−856565.	−0.904200
$52$	−140608.	−0.138675
$53$	331347.	0.305715	0.152858	−	0.988248i	$-0.451152\pi$
$53$	331347.	0.305715	0.152858	+	0.988248i	$0.451152\pi$
$54$	−157464.	−0.136083
$55$	1.35310e6	1.09663
$56$	−175616.	−0.133631
$57$	50250.3	0.0359399
$58$	−1.08920e6	−0.733006
$59$	2.12406e6	1.34643	0.673217	−	0.739445i	$-0.264912\pi$
$59$	2.12406e6	1.34643	0.673217	+	0.739445i	$0.264912\pi$
$60$	533489.	0.318857
$61$	2.91611e6	1.64494	0.822468	−	0.568812i	$-0.192597\pi$
$61$	2.91611e6	1.64494	0.822468	+	0.568812i	$0.192597\pi$
$62$	−974221.	−0.519142
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−678285.	−0.306348
$66$	−946680.	−0.405321
$67$	3.68988e6	1.49882	0.749411	−	0.662105i	$-0.230337\pi$
$67$	3.68988e6	1.49882	0.749411	+	0.662105i	$0.230337\pi$
$68$	−2.03038e6	−0.783060
$69$	−493480.	−0.180841
$70$	−847161.	−0.295204
$71$	3.09723e6	1.02700	0.513498	−	0.858091i	$-0.328349\pi$
$71$	3.09723e6	1.02700	0.513498	+	0.858091i	$0.328349\pi$
$72$	−373248.	−0.117851
$73$	−743089.	−0.223569	−0.111784	−	0.993732i	$-0.535657\pi$
$73$	−743089.	−0.223569	−0.111784	+	0.993732i	$0.535657\pi$
$74$	−272386.	−0.0781400
$75$	464146.	0.127040
$76$	119112.	0.0311248
$77$	1.50329e6	0.375254
$78$	474552.	0.113228
$79$	7.91362e6	1.80585	0.902923	−	0.429803i	$-0.141417\pi$
$79$	7.91362e6	1.80585	0.902923	+	0.429803i	$0.141417\pi$
$80$	1.26457e6	0.276138
$81$	531441.	0.111111
$82$	747488.	0.149712
$83$	−9.45259e6	−1.81459	−0.907293	−	0.420499i	$-0.861855\pi$
$83$	−9.45259e6	−1.81459	−0.907293	+	0.420499i	$0.861855\pi$
$84$	592704.	0.109109
$85$	−9.79441e6	−1.72986
$86$	5.26674e6	0.892889
$87$	3.67603e6	0.598497
$88$	−2.24398e6	−0.351018
$89$	1.24663e7	1.87445	0.937224	−	0.348727i	$-0.113386\pi$
$89$	1.24663e7	1.87445	0.937224	+	0.348727i	$0.113386\pi$
$90$	−1.80053e6	−0.260346
$91$	−753571.	−0.104828
$92$	−1.16973e6	−0.156613
$93$	3.28799e6	0.423878
$94$	−2.93738e6	−0.364765
$95$	574588.	0.0687581
$96$	−884736.	−0.102062
$97$	1.63093e7	1.81440	0.907202	−	0.420694i	$-0.138214\pi$
$97$	1.63093e7	1.81440	0.907202	+	0.420694i	$0.138214\pi$
$98$	−941192.	−0.101015
$99$	3.19504e6	0.330943
$100$	1.10020e6	0.110020
$101$	−1.50179e7	−1.45039	−0.725196	−	0.688543i	$-0.758251\pi$
$101$	−1.50179e7	−1.45039	−0.725196	+	0.688543i	$0.758251\pi$
$102$	6.85252e6	0.639366
$103$	−1.47917e7	−1.33379	−0.666895	−	0.745151i	$-0.732377\pi$
$103$	−1.47917e7	−1.33379	−0.666895	+	0.745151i	$0.732377\pi$
$104$	1.12486e6	0.0980581
$105$	2.85917e6	0.241033
$106$	−2.65077e6	−0.216173
$107$	−1.86861e7	−1.47460	−0.737302	−	0.675564i	$-0.763900\pi$
$107$	−1.86861e7	−1.47460	−0.737302	+	0.675564i	$0.763900\pi$
$108$	1.25971e6	0.0962250
$109$	2.13493e7	1.57903	0.789514	−	0.613732i	$-0.210332\pi$
$109$	2.13493e7	1.57903	0.789514	+	0.613732i	$0.210332\pi$
$110$	−1.08248e7	−0.775437
$111$	919302.	0.0638011
$112$	1.40493e6	0.0944911
$113$	9.34352e6	0.609167	0.304583	−	0.952486i	$-0.401483\pi$
$113$	9.34352e6	0.609167	0.304583	+	0.952486i	$0.401483\pi$
$114$	−402002.	−0.0254133
$115$	−5.64271e6	−0.345975
$116$	8.71356e6	0.518314
$117$	−1.60161e6	−0.0924500
$118$	−1.69925e7	−0.952073
$119$	−1.08815e7	−0.591938
$120$	−4.26791e6	−0.225466
$121$	−278449.	−0.0142888
$122$	−2.33288e7	−1.16315
$123$	−2.52277e6	−0.122239
$124$	7.79377e6	0.367089
$125$	−1.88124e7	−0.861508
$126$	−2.00038e6	−0.0890871
$127$	−1.72944e7	−0.749191	−0.374595	−	0.927188i	$-0.622218\pi$
$127$	−1.72944e7	−0.749191	−0.374595	+	0.927188i	$0.622218\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.77752e7	−0.729041
$130$	5.42628e6	0.216621
$131$	5.95674e6	0.231504	0.115752	−	0.993278i	$-0.463072\pi$
$131$	5.95674e6	0.231504	0.115752	+	0.993278i	$0.463072\pi$
$132$	7.57344e6	0.286605
$133$	638364.	0.0235282
$134$	−2.95190e7	−1.05983
$135$	6.07678e6	0.212572
$136$	1.62430e7	0.553707
$137$	4.17956e7	1.38870	0.694350	−	0.719638i	$-0.255692\pi$
$137$	4.17956e7	1.38870	0.694350	+	0.719638i	$0.255692\pi$
$138$	3.94784e6	0.127874
$139$	2.87624e6	0.0908392	0.0454196	−	0.998968i	$-0.485538\pi$
$139$	2.87624e6	0.0908392	0.0454196	+	0.998968i	$0.485538\pi$
$140$	6.77729e6	0.208741
$141$	9.91366e6	0.297829
$142$	−2.47778e7	−0.726196
$143$	−9.62896e6	−0.275361
$144$	2.98598e6	0.0833333
$145$	4.20337e7	1.14501
$146$	5.94471e6	0.158087
$147$	3.17652e6	0.0824786
$148$	2.17909e6	0.0552533
$149$	1.92599e7	0.476983	0.238491	−	0.971145i	$-0.423347\pi$
$149$	1.92599e7	0.476983	0.238491	+	0.971145i	$0.423347\pi$
$150$	−3.71317e6	−0.0898307
$151$	−6.85628e7	−1.62058	−0.810288	−	0.586032i	$-0.800689\pi$
$151$	−6.85628e7	−1.62058	−0.810288	+	0.586032i	$0.800689\pi$
$152$	−952894.	−0.0220086
$153$	−2.31272e7	−0.522040
$154$	−1.20263e7	−0.265345
$155$	3.75967e7	0.810939
$156$	−3.79642e6	−0.0800641
$157$	−7.33585e7	−1.51287	−0.756435	−	0.654069i	$-0.773061\pi$
$157$	−7.33585e7	−1.51287	−0.756435	+	0.654069i	$0.773061\pi$
$158$	−6.33090e7	−1.27693
$159$	8.94636e6	0.176505
$160$	−1.01165e7	−0.195259
$161$	−6.26902e6	−0.118388
$162$	−4.25153e6	−0.0785674
$163$	2.47131e7	0.446963	0.223481	−	0.974708i	$-0.428258\pi$
$163$	2.47131e7	0.446963	0.223481	+	0.974708i	$0.428258\pi$
$164$	−5.97990e6	−0.105862
$165$	3.65338e7	0.633142
$166$	7.56207e7	1.28311
$167$	−3.53898e7	−0.587992	−0.293996	−	0.955807i	$-0.594985\pi$
$167$	−3.53898e7	−0.587992	−0.293996	+	0.955807i	$0.594985\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	7.83553e7	1.22320
$171$	1.35676e6	0.0207499
$172$	−4.21339e7	−0.631368
$173$	1.47402e7	0.216442	0.108221	−	0.994127i	$-0.465485\pi$
$173$	1.47402e7	0.216442	0.108221	+	0.994127i	$0.465485\pi$
$174$	−2.94083e7	−0.423201
$175$	5.89637e6	0.0831671
$176$	1.79518e7	0.248207
$177$	5.73497e7	0.777364
$178$	−9.97306e7	−1.32544
$179$	1.13009e8	1.47274	0.736369	−	0.676580i	$-0.236539\pi$
$179$	1.13009e8	1.47274	0.736369	+	0.676580i	$0.236539\pi$
$180$	1.44042e7	0.184092
$181$	−8.97042e6	−0.112444	−0.0562222	−	0.998418i	$-0.517906\pi$
$181$	−8.97042e6	−0.112444	−0.0562222	+	0.998418i	$0.517906\pi$
$182$	6.02857e6	0.0741249
$183$	7.87349e7	0.949704
$184$	9.35784e6	0.110742
$185$	1.05118e7	0.122061
$186$	−2.63040e7	−0.299727
$187$	−1.39042e8	−1.55489
$188$	2.34990e7	0.257928
$189$	6.75127e6	0.0727393
$190$	−4.59670e6	−0.0486193
$191$	3.69598e7	0.383807	0.191904	−	0.981414i	$-0.438534\pi$
$191$	3.69598e7	0.383807	0.191904	+	0.981414i	$0.438534\pi$
$192$	7.07789e6	0.0721688
$193$	7.89979e7	0.790979	0.395489	−	0.918471i	$-0.370575\pi$
$193$	7.89979e7	0.790979	0.395489	+	0.918471i	$0.370575\pi$
$194$	−1.30474e8	−1.28298
$195$	−1.83137e7	−0.176870
$196$	7.52954e6	0.0714286
$197$	1.02705e6	0.00957104	0.00478552	−	0.999989i	$-0.498477\pi$
$197$	1.02705e6	0.00957104	0.00478552	+	0.999989i	$0.498477\pi$
$198$	−2.55603e7	−0.234012
$199$	−2.05604e8	−1.84947	−0.924733	−	0.380617i	$-0.875712\pi$
$199$	−2.05604e8	−1.84947	−0.924733	+	0.380617i	$0.875712\pi$
$200$	−8.80158e6	−0.0777957
$201$	9.96266e7	0.865345
$202$	1.20143e8	1.02558
$203$	4.66992e7	0.391808
$204$	−5.48201e7	−0.452100
$205$	−2.88467e7	−0.233861
$206$	1.18334e8	0.943133
$207$	−1.33240e7	−0.104409
$208$	−8.99891e6	−0.0693375
$209$	8.15688e6	0.0618033
$210$	−2.28734e7	−0.170436
$211$	5.85059e7	0.428757	0.214379	−	0.976751i	$-0.431227\pi$
$211$	5.85059e7	0.428757	0.214379	+	0.976751i	$0.431227\pi$
$212$	2.12062e7	0.152858
$213$	8.36251e7	0.592936
$214$	1.49489e8	1.04270
$215$	−2.03252e8	−1.39476
$216$	−1.00777e7	−0.0680414
$217$	4.17697e7	0.277493
$218$	−1.70794e8	−1.11654
$219$	−2.00634e7	−0.129077
$220$	8.65987e7	0.548317
$221$	6.96990e7	0.434364
$222$	−7.35442e6	−0.0451142
$223$	1.28888e8	0.778299	0.389150	−	0.921175i	$-0.372769\pi$
$223$	1.28888e8	0.778299	0.389150	+	0.921175i	$0.372769\pi$
$224$	−1.12394e7	−0.0668153
$225$	1.25319e7	0.0733465
$226$	−7.47482e7	−0.430746
$227$	1.55815e8	0.884136	0.442068	−	0.896982i	$-0.354245\pi$
$227$	1.55815e8	0.884136	0.442068	+	0.896982i	$0.354245\pi$
$228$	3.21602e6	0.0179699
$229$	2.61867e8	1.44098	0.720489	−	0.693467i	$-0.243918\pi$
$229$	2.61867e8	1.44098	0.720489	+	0.693467i	$0.243918\pi$
$230$	4.51417e7	0.244642
$231$	4.05889e7	0.216653
$232$	−6.97085e7	−0.366503
$233$	−3.66961e7	−0.190053	−0.0950264	−	0.995475i	$-0.530294\pi$
$233$	−3.66961e7	−0.190053	−0.0950264	+	0.995475i	$0.530294\pi$
$234$	1.28129e7	0.0653720
$235$	1.13358e8	0.569790
$236$	1.35940e8	0.673217
$237$	2.13668e8	1.04261
$238$	8.70523e7	0.418563
$239$	1.99862e8	0.946975	0.473487	−	0.880801i	$-0.342995\pi$
$239$	1.99862e8	0.946975	0.473487	+	0.880801i	$0.342995\pi$
$240$	3.41433e7	0.159429
$241$	−1.35683e8	−0.624405	−0.312202	−	0.950016i	$-0.601067\pi$
$241$	−1.35683e8	−0.624405	−0.312202	+	0.950016i	$0.601067\pi$
$242$	2.22759e6	0.0101037
$243$	1.43489e7	0.0641500
$244$	1.86631e8	0.822468
$245$	3.63220e7	0.157793
$246$	2.01822e7	0.0864361
$247$	−4.08888e6	−0.0172649
$248$	−6.23501e7	−0.259571
$249$	−2.55220e8	−1.04765
$250$	1.50499e8	0.609178
$251$	1.88164e8	0.751066	0.375533	−	0.926809i	$-0.377460\pi$
$251$	1.88164e8	0.751066	0.375533	+	0.926809i	$0.377460\pi$
$252$	1.60030e7	0.0629941
$253$	−8.01041e7	−0.310981
$254$	1.38355e8	0.529758
$255$	−2.64449e8	−0.998738
$256$	1.67772e7	0.0625000
$257$	−5.60956e7	−0.206140	−0.103070	−	0.994674i	$-0.532867\pi$
$257$	−5.60956e7	−0.206140	−0.103070	+	0.994674i	$0.532867\pi$
$258$	1.42202e8	0.515510
$259$	1.16785e7	0.0417676
$260$	−4.34102e7	−0.153174
$261$	9.92529e7	0.345543
$262$	−4.76539e7	−0.163698
$263$	−3.92958e8	−1.33199	−0.665996	−	0.745956i	$-0.731993\pi$
$263$	−3.92958e8	−1.33199	−0.665996	+	0.745956i	$0.731993\pi$
$264$	−6.05875e7	−0.202661
$265$	1.02297e8	0.337679
$266$	−5.10692e6	−0.0166369
$267$	3.36591e8	1.08221
$268$	2.36152e8	0.749411
$269$	4.65240e7	0.145728	0.0728641	−	0.997342i	$-0.476786\pi$
$269$	4.65240e7	0.145728	0.0728641	+	0.997342i	$0.476786\pi$
$270$	−4.86142e7	−0.150311
$271$	5.49984e8	1.67864	0.839319	−	0.543639i	$-0.182954\pi$
$271$	5.49984e8	1.67864	0.839319	+	0.543639i	$0.182954\pi$
$272$	−1.29944e8	−0.391530
$273$	−2.03464e7	−0.0605228
$274$	−3.34365e8	−0.981959
$275$	7.53425e7	0.218462
$276$	−3.15827e7	−0.0904207
$277$	−5.41628e8	−1.53117	−0.765583	−	0.643338i	$-0.777549\pi$
$277$	−5.41628e8	−1.53117	−0.765583	+	0.643338i	$0.777549\pi$
$278$	−2.30099e7	−0.0642330
$279$	8.87759e7	0.244726
$280$	−5.42183e7	−0.147602
$281$	1.43709e8	0.386378	0.193189	−	0.981162i	$-0.438117\pi$
$281$	1.43709e8	0.386378	0.193189	+	0.981162i	$0.438117\pi$
$282$	−7.93093e7	−0.210597
$283$	3.09717e8	0.812292	0.406146	−	0.913808i	$-0.366873\pi$
$283$	3.09717e8	0.812292	0.406146	+	0.913808i	$0.366873\pi$
$284$	1.98222e8	0.513498
$285$	1.55139e7	0.0396975
$286$	7.70317e7	0.194710
$287$	−3.20485e7	−0.0800243
$288$	−2.38879e7	−0.0589256
$289$	5.96113e8	1.45273
$290$	−3.36270e8	−0.809645
$291$	4.40351e8	1.04755
$292$	−4.75577e7	−0.111784
$293$	4.83600e8	1.12318	0.561591	−	0.827415i	$-0.310190\pi$
$293$	4.83600e8	1.12318	0.561591	+	0.827415i	$0.310190\pi$
$294$	−2.54122e7	−0.0583212
$295$	6.55767e8	1.48721
$296$	−1.74327e7	−0.0390700
$297$	8.62662e7	0.191070
$298$	−1.54079e8	−0.337278
$299$	4.01546e7	0.0868734
$300$	2.97053e7	0.0635199
$301$	−2.25812e8	−0.477269
$302$	5.48503e8	1.14592
$303$	−4.05484e8	−0.837384
$304$	7.62315e6	0.0155624
$305$	9.00296e8	1.81692
$306$	1.85018e8	0.369138
$307$	−4.77167e8	−0.941208	−0.470604	−	0.882344i	$-0.655964\pi$
$307$	−4.77167e8	−0.941208	−0.470604	+	0.882344i	$0.655964\pi$
$308$	9.62107e7	0.187627
$309$	−3.99376e8	−0.770065
$310$	−3.00773e8	−0.573421
$311$	4.57713e8	0.862844	0.431422	−	0.902150i	$-0.358012\pi$
$311$	4.57713e8	0.862844	0.431422	+	0.902150i	$0.358012\pi$
$312$	3.03713e7	0.0566139
$313$	−1.40141e8	−0.258320	−0.129160	−	0.991624i	$-0.541228\pi$
$313$	−1.40141e8	−0.258320	−0.129160	+	0.991624i	$0.541228\pi$
$314$	5.86868e8	1.06976
$315$	7.71976e7	0.139161
$316$	5.06472e8	0.902923
$317$	−5.30164e7	−0.0934766	−0.0467383	−	0.998907i	$-0.514883\pi$
$317$	−5.30164e7	−0.0934766	−0.0467383	+	0.998907i	$0.514883\pi$
$318$	−7.15709e7	−0.124808
$319$	5.96712e8	1.02919
$320$	8.09323e7	0.138069
$321$	−5.04524e8	−0.851363
$322$	5.01522e7	0.0837133
$323$	−5.90433e7	−0.0974905
$324$	3.40122e7	0.0555556
$325$	−3.77677e7	−0.0610280
$326$	−1.97705e8	−0.316050
$327$	5.76430e8	0.911653
$328$	4.78392e7	0.0748558
$329$	1.25940e8	0.194975
$330$	−2.92270e8	−0.447699
$331$	9.84156e7	0.149165	0.0745824	−	0.997215i	$-0.476238\pi$
$331$	9.84156e7	0.149165	0.0745824	+	0.997215i	$0.476238\pi$
$332$	−6.04966e8	−0.907293
$333$	2.48212e7	0.0368356
$334$	2.83119e8	0.415773
$335$	1.13918e9	1.65553
$336$	3.79331e7	0.0545545
$337$	2.22568e8	0.316780	0.158390	−	0.987377i	$-0.449370\pi$
$337$	2.22568e8	0.316780	0.158390	+	0.987377i	$0.449370\pi$
$338$	−3.86145e7	−0.0543928
$339$	2.52275e8	0.351702
$340$	−6.26842e8	−0.864932
$341$	5.33724e8	0.728914
$342$	−1.08541e7	−0.0146724
$343$	4.03536e7	0.0539949
$344$	3.37071e8	0.446444
$345$	−1.52353e8	−0.199749
$346$	−1.17921e8	−0.153048
$347$	−2.76199e8	−0.354870	−0.177435	−	0.984133i	$-0.556780\pi$
$347$	−2.76199e8	−0.354870	−0.177435	+	0.984133i	$0.556780\pi$
$348$	2.35266e8	0.299249
$349$	−4.11034e8	−0.517594	−0.258797	−	0.965932i	$-0.583326\pi$
$349$	−4.11034e8	−0.517594	−0.258797	+	0.965932i	$0.583326\pi$
$350$	−4.71710e7	−0.0588080
$351$	−4.32436e7	−0.0533761
$352$	−1.43615e8	−0.175509
$353$	−2.70714e8	−0.327567	−0.163783	−	0.986496i	$-0.552370\pi$
$353$	−2.70714e8	−0.327567	−0.163783	+	0.986496i	$0.552370\pi$
$354$	−4.58798e8	−0.549680
$355$	9.56213e8	1.13437
$356$	7.97845e8	0.937224
$357$	−2.93802e8	−0.341755
$358$	−9.04068e8	−1.04138
$359$	1.33207e9	1.51949	0.759743	−	0.650223i	$-0.225325\pi$
$359$	1.33207e9	1.51949	0.759743	+	0.650223i	$0.225325\pi$
$360$	−1.15234e8	−0.130173
$361$	−8.90408e8	−0.996125
$362$	7.17634e7	0.0795102
$363$	−7.51811e6	−0.00824965
$364$	−4.82285e7	−0.0524142
$365$	−2.29415e8	−0.246944
$366$	−6.29879e8	−0.671542
$367$	−7.51897e8	−0.794012	−0.397006	−	0.917816i	$-0.629951\pi$
$367$	−7.51897e8	−0.794012	−0.397006	+	0.917816i	$0.629951\pi$
$368$	−7.48627e7	−0.0783066
$369$	−6.81148e7	−0.0705748
$370$	−8.40943e7	−0.0863099
$371$	1.13652e8	0.115550
$372$	2.10432e8	0.211939
$373$	1.50437e9	1.50098	0.750488	−	0.660884i	$-0.229818\pi$
$373$	1.50437e9	1.50098	0.750488	+	0.660884i	$0.229818\pi$
$374$	1.11234e9	1.09947
$375$	−5.07935e8	−0.497392
$376$	−1.87992e8	−0.182382
$377$	−2.99120e8	−0.287509
$378$	−5.40102e7	−0.0514344
$379$	−1.86276e9	−1.75760	−0.878798	−	0.477194i	$-0.841654\pi$
$379$	−1.86276e9	−1.75760	−0.878798	+	0.477194i	$0.841654\pi$
$380$	3.67736e7	0.0343791
$381$	−4.66949e8	−0.432545
$382$	−2.95679e8	−0.271393
$383$	1.73834e9	1.58103	0.790514	−	0.612444i	$-0.209813\pi$
$383$	1.73834e9	1.58103	0.790514	+	0.612444i	$0.209813\pi$
$384$	−5.66231e7	−0.0510310
$385$	4.64115e8	0.414489
$386$	−6.31983e8	−0.559306
$387$	−4.79932e8	−0.420912
$388$	1.04380e9	0.907202
$389$	1.36782e9	1.17816	0.589082	−	0.808074i	$-0.299490\pi$
$389$	1.36782e9	1.17816	0.589082	+	0.808074i	$0.299490\pi$
$390$	1.46509e8	0.125066
$391$	5.79832e8	0.490550
$392$	−6.02363e7	−0.0505076
$393$	1.60832e8	0.133659
$394$	−8.21639e6	−0.00676775
$395$	2.44319e9	1.99465
$396$	2.04483e8	0.165472
$397$	−2.06928e9	−1.65978	−0.829892	−	0.557924i	$-0.811598\pi$
$397$	−2.06928e9	−1.65978	−0.829892	+	0.557924i	$0.811598\pi$
$398$	1.64483e9	1.30777
$399$	1.72358e7	0.0135840
$400$	7.04126e7	0.0550099
$401$	2.56870e9	1.98933	0.994667	−	0.103143i	$-0.0328898\pi$
$401$	2.56870e9	1.98933	0.994667	+	0.103143i	$0.0328898\pi$
$402$	−7.97013e8	−0.611891
$403$	−2.67545e8	−0.203624
$404$	−9.61147e8	−0.725196
$405$	1.64073e8	0.122728
$406$	−3.73594e8	−0.277050
$407$	1.49226e8	0.109714
$408$	4.38561e8	0.319683
$409$	−1.31661e8	−0.0951537	−0.0475769	−	0.998868i	$-0.515150\pi$
$409$	−1.31661e8	−0.0951537	−0.0475769	+	0.998868i	$0.515150\pi$
$410$	2.30774e8	0.165365
$411$	1.12848e9	0.801766
$412$	−9.46669e8	−0.666895
$413$	7.28554e8	0.508904
$414$	1.06592e8	0.0738282
$415$	−2.91832e9	−2.00431
$416$	7.19913e7	0.0490290
$417$	7.76585e7	0.0524461
$418$	−6.52550e7	−0.0437015
$419$	2.13160e9	1.41565	0.707826	−	0.706387i	$-0.249676\pi$
$419$	2.13160e9	1.41565	0.707826	+	0.706387i	$0.249676\pi$
$420$	1.82987e8	0.120517
$421$	1.75380e9	1.14550	0.572748	−	0.819731i	$-0.305877\pi$
$421$	1.75380e9	1.14550	0.572748	+	0.819731i	$0.305877\pi$
$422$	−4.68048e8	−0.303177
$423$	2.67669e8	0.171952
$424$	−1.69650e8	−0.108087
$425$	−5.45365e8	−0.344608
$426$	−6.69001e8	−0.419269
$427$	1.00022e9	0.621727
$428$	−1.19591e9	−0.737302
$429$	−2.59982e8	−0.158980
$430$	1.62601e9	0.986244
$431$	2.12388e8	0.127779	0.0638895	−	0.997957i	$-0.479649\pi$
$431$	2.12388e8	0.127779	0.0638895	+	0.997957i	$0.479649\pi$
$432$	8.06216e7	0.0481125
$433$	1.44388e9	0.854718	0.427359	−	0.904082i	$-0.359444\pi$
$433$	1.44388e9	0.854718	0.427359	+	0.904082i	$0.359444\pi$
$434$	−3.34158e8	−0.196217
$435$	1.13491e9	0.661072
$436$	1.36635e9	0.789514
$437$	−3.40158e7	−0.0194982
$438$	1.60507e8	0.0912715
$439$	−8.25411e8	−0.465634	−0.232817	−	0.972521i	$-0.574794\pi$
$439$	−8.25411e8	−0.465634	−0.232817	+	0.972521i	$0.574794\pi$
$440$	−6.92789e8	−0.387719
$441$	8.57661e7	0.0476190
$442$	−5.57592e8	−0.307141
$443$	1.13603e9	0.620837	0.310419	−	0.950600i	$-0.399531\pi$
$443$	1.13603e9	0.620837	0.310419	+	0.950600i	$0.399531\pi$
$444$	5.88354e7	0.0319005
$445$	3.84876e9	2.07043
$446$	−1.03111e9	−0.550341
$447$	5.20018e8	0.275386
$448$	8.99154e7	0.0472456
$449$	−2.74704e9	−1.43220	−0.716099	−	0.697999i	$-0.754074\pi$
$449$	−2.74704e9	−1.43220	−0.716099	+	0.697999i	$0.754074\pi$
$450$	−1.00255e8	−0.0518638
$451$	−4.09509e8	−0.210206
$452$	5.97985e8	0.304583
$453$	−1.85120e9	−0.935640
$454$	−1.24652e9	−0.625178
$455$	−2.32652e8	−0.115789
$456$	−2.57281e7	−0.0127067
$457$	−2.44131e9	−1.19651	−0.598254	−	0.801306i	$-0.704139\pi$
$457$	−2.44131e9	−1.19651	−0.598254	+	0.801306i	$0.704139\pi$
$458$	−2.09494e9	−1.01892
$459$	−6.24436e8	−0.301400
$460$	−3.61133e8	−0.172988
$461$	−2.81849e9	−1.33987	−0.669936	−	0.742418i	$-0.733679\pi$
$461$	−2.81849e9	−1.33987	−0.669936	+	0.742418i	$0.733679\pi$
$462$	−3.24711e8	−0.153197
$463$	−4.04897e9	−1.89588	−0.947941	−	0.318446i	$-0.896839\pi$
$463$	−4.04897e9	−1.89588	−0.947941	+	0.318446i	$0.896839\pi$
$464$	5.57668e8	0.259157
$465$	1.01511e9	0.468196
$466$	2.93569e8	0.134388
$467$	7.17569e8	0.326028	0.163014	−	0.986624i	$-0.447878\pi$
$467$	7.17569e8	0.326028	0.163014	+	0.986624i	$0.447878\pi$
$468$	−1.02503e8	−0.0462250
$469$	1.26563e9	0.566501
$470$	−9.06864e8	−0.402902
$471$	−1.98068e9	−0.873456
$472$	−1.08752e9	−0.476037
$473$	−2.88537e9	−1.25368
$474$	−1.70934e9	−0.737233
$475$	3.19938e7	0.0136974
$476$	−6.96419e8	−0.295969
$477$	2.41552e8	0.101905
$478$	−1.59890e9	−0.669612
$479$	−3.51916e8	−0.146307	−0.0731535	−	0.997321i	$-0.523306\pi$
$479$	−3.51916e8	−0.146307	−0.0731535	+	0.997321i	$0.523306\pi$
$480$	−2.73147e8	−0.112733
$481$	−7.48040e7	−0.0306490
$482$	1.08547e9	0.441521
$483$	−1.69264e8	−0.0683516
$484$	−1.78207e7	−0.00714441
$485$	5.03521e9	2.00411
$486$	−1.14791e8	−0.0453609
$487$	−1.99851e9	−0.784071	−0.392036	−	0.919950i	$-0.628229\pi$
$487$	−1.99851e9	−0.784071	−0.392036	+	0.919950i	$0.628229\pi$
$488$	−1.49305e9	−0.581573
$489$	6.67255e8	0.258054
$490$	−2.90576e8	−0.111577
$491$	−2.73329e9	−1.04208	−0.521040	−	0.853532i	$-0.674456\pi$
$491$	−2.73329e9	−1.04208	−0.521040	+	0.853532i	$0.674456\pi$
$492$	−1.61457e8	−0.0611195
$493$	−4.31929e9	−1.62348
$494$	3.27111e7	0.0122082
$495$	9.86413e8	0.365545
$496$	4.98801e8	0.183545
$497$	1.06235e9	0.388168
$498$	2.04176e9	0.740802
$499$	1.60818e9	0.579405	0.289702	−	0.957117i	$-0.406444\pi$
$499$	1.60818e9	0.579405	0.289702	+	0.957117i	$0.406444\pi$
$500$	−1.20399e9	−0.430754
$501$	−9.55526e8	−0.339477
$502$	−1.50531e9	−0.531084
$503$	1.42483e9	0.499200	0.249600	−	0.968349i	$-0.419701\pi$
$503$	1.42483e9	0.499200	0.249600	+	0.968349i	$0.419701\pi$
$504$	−1.28024e8	−0.0445435
$505$	−4.63652e9	−1.60204
$506$	6.40833e8	0.219896
$507$	1.30324e8	0.0444116
$508$	−1.10684e9	−0.374595
$509$	−4.33070e9	−1.45561	−0.727806	−	0.685783i	$-0.759460\pi$
$509$	−4.33070e9	−1.45561	−0.727806	+	0.685783i	$0.759460\pi$
$510$	2.11559e9	0.706214
$511$	−2.54879e8	−0.0845010
$512$	−1.34218e8	−0.0441942
$513$	3.66324e7	0.0119800
$514$	4.48765e8	0.145763
$515$	−4.56667e9	−1.47324
$516$	−1.13762e9	−0.364520
$517$	1.60923e9	0.512156
$518$	−9.34284e7	−0.0295342
$519$	3.97985e8	0.124963
$520$	3.47282e8	0.108310
$521$	−2.39067e9	−0.740608	−0.370304	−	0.928911i	$-0.620747\pi$
$521$	−2.39067e9	−0.740608	−0.370304	+	0.928911i	$0.620747\pi$
$522$	−7.94023e8	−0.244335
$523$	−4.79211e9	−1.46478	−0.732388	−	0.680888i	$-0.761594\pi$
$523$	−4.79211e9	−1.46478	−0.732388	+	0.680888i	$0.761594\pi$
$524$	3.81232e8	0.115752
$525$	1.59202e8	0.0480165
$526$	3.14367e9	0.941860
$527$	−3.86335e9	−1.14981
$528$	4.84700e8	0.143303
$529$	−3.07078e9	−0.901889
$530$	−8.18379e8	−0.238775
$531$	1.54844e9	0.448812
$532$	4.08553e7	0.0117641
$533$	2.05279e8	0.0587218
$534$	−2.69273e9	−0.765240
$535$	−5.76900e9	−1.62878
$536$	−1.88922e9	−0.529913
$537$	3.05123e9	0.850286
$538$	−3.72192e8	−0.103045
$539$	5.15629e8	0.141833
$540$	3.88914e8	0.106286
$541$	−1.59880e8	−0.0434115	−0.0217058	−	0.999764i	$-0.506910\pi$
$541$	−1.59880e8	−0.0434115	−0.0217058	+	0.999764i	$0.506910\pi$
$542$	−4.39987e9	−1.18698
$543$	−2.42201e8	−0.0649198
$544$	1.03955e9	0.276854
$545$	6.59120e9	1.74412
$546$	1.62771e8	0.0427960
$547$	5.61782e9	1.46761	0.733807	−	0.679358i	$-0.237742\pi$
$547$	5.61782e9	1.46761	0.733807	+	0.679358i	$0.237742\pi$
$548$	2.67492e9	0.694350
$549$	2.12584e9	0.548312
$550$	−6.02740e8	−0.154476
$551$	2.53391e8	0.0645297
$552$	2.52662e8	0.0639371
$553$	2.71437e9	0.682545
$554$	4.33302e9	1.08270
$555$	2.83818e8	0.0704717
$556$	1.84079e8	0.0454196
$557$	3.10342e9	0.760934	0.380467	−	0.924795i	$-0.375763\pi$
$557$	3.10342e9	0.760934	0.380467	+	0.924795i	$0.375763\pi$
$558$	−7.10207e8	−0.173047
$559$	1.44638e9	0.350220
$560$	4.33747e8	0.104371
$561$	−3.75413e9	−0.897717
$562$	−1.14967e9	−0.273211
$563$	3.64245e9	0.860228	0.430114	−	0.902775i	$-0.358473\pi$
$563$	3.64245e9	0.860228	0.430114	+	0.902775i	$0.358473\pi$
$564$	6.34474e8	0.148915
$565$	2.88465e9	0.672857
$566$	−2.47773e9	−0.574377
$567$	1.82284e8	0.0419961
$568$	−1.58578e9	−0.363098
$569$	−4.23764e9	−0.964342	−0.482171	−	0.876077i	$-0.660152\pi$
$569$	−4.23764e9	−0.964342	−0.482171	+	0.876077i	$0.660152\pi$
$570$	−1.24111e8	−0.0280704
$571$	2.48978e9	0.559674	0.279837	−	0.960048i	$-0.409720\pi$
$571$	2.48978e9	0.559674	0.279837	+	0.960048i	$0.409720\pi$
$572$	−6.16253e8	−0.137681
$573$	9.97915e8	0.221591
$574$	2.56388e8	0.0565857
$575$	−3.14193e8	−0.0689222
$576$	1.91103e8	0.0416667
$577$	2.57246e8	0.0557486	0.0278743	−	0.999611i	$-0.491126\pi$
$577$	2.57246e8	0.0557486	0.0278743	+	0.999611i	$0.491126\pi$
$578$	−4.76890e9	−1.02724
$579$	2.13294e9	0.456672
$580$	2.69016e9	0.572506
$581$	−3.24224e9	−0.685849
$582$	−3.52281e9	−0.740728
$583$	1.45222e9	0.303523
$584$	3.80462e8	0.0790434
$585$	−4.94470e8	−0.102116
$586$	−3.86880e9	−0.794209
$587$	2.47247e9	0.504542	0.252271	−	0.967657i	$-0.418823\pi$
$587$	2.47247e9	0.504542	0.252271	+	0.967657i	$0.418823\pi$
$588$	2.03297e8	0.0412393
$589$	2.26643e8	0.0457023
$590$	−5.24613e9	−1.05162
$591$	2.77303e7	0.00552584
$592$	1.39462e8	0.0276267
$593$	2.85607e8	0.0562442	0.0281221	−	0.999604i	$-0.491047\pi$
$593$	2.85607e8	0.0562442	0.0281221	+	0.999604i	$0.491047\pi$
$594$	−6.90129e8	−0.135107
$595$	−3.35948e9	−0.653827
$596$	1.23264e9	0.238491
$597$	−5.55131e9	−1.06779
$598$	−3.21237e8	−0.0614287
$599$	1.69378e9	0.322006	0.161003	−	0.986954i	$-0.448527\pi$
$599$	1.69378e9	0.322006	0.161003	+	0.986954i	$0.448527\pi$
$600$	−2.37643e8	−0.0449154
$601$	−1.02478e10	−1.92561	−0.962805	−	0.270197i	$-0.912911\pi$
$601$	−1.02478e10	−1.92561	−0.962805	+	0.270197i	$0.912911\pi$
$602$	1.80649e9	0.337480
$603$	2.68992e9	0.499607
$604$	−4.38802e9	−0.810288
$605$	−8.59661e7	−0.0157828
$606$	3.24387e9	0.592120
$607$	−8.48648e9	−1.54016	−0.770082	−	0.637945i	$-0.779785\pi$
$607$	−8.48648e9	−1.54016	−0.770082	+	0.637945i	$0.779785\pi$
$608$	−6.09852e7	−0.0110043
$609$	1.26088e9	0.226211
$610$	−7.20237e9	−1.28476
$611$	−8.06678e8	−0.143072
$612$	−1.48014e9	−0.261020
$613$	1.81539e9	0.318315	0.159158	−	0.987253i	$-0.449122\pi$
$613$	1.81539e9	0.318315	0.159158	+	0.987253i	$0.449122\pi$
$614$	3.81733e9	0.665535
$615$	−7.78861e8	−0.135020
$616$	−7.69686e8	−0.132672
$617$	5.76271e9	0.987709	0.493854	−	0.869545i	$-0.335588\pi$
$617$	5.76271e9	0.987709	0.493854	+	0.869545i	$0.335588\pi$
$618$	3.19501e9	0.544518
$619$	7.08621e9	1.20087	0.600436	−	0.799673i	$-0.294994\pi$
$619$	7.08621e9	1.20087	0.600436	+	0.799673i	$0.294994\pi$
$620$	2.40619e9	0.405470
$621$	−3.59747e8	−0.0602804
$622$	−3.66171e9	−0.610123
$623$	4.27595e9	0.708475
$624$	−2.42971e8	−0.0400320
$625$	−7.15101e9	−1.17162
$626$	1.12112e9	0.182660
$627$	2.20236e8	0.0356822
$628$	−4.69494e9	−0.756435
$629$	−1.08017e9	−0.173067
$630$	−6.17581e8	−0.0984015
$631$	−1.28125e9	−0.203016	−0.101508	−	0.994835i	$-0.532367\pi$
$631$	−1.28125e9	−0.203016	−0.101508	+	0.994835i	$0.532367\pi$
$632$	−4.05177e9	−0.638463
$633$	1.57966e9	0.247543
$634$	4.24131e8	0.0660979
$635$	−5.33934e9	−0.827521
$636$	5.72567e8	0.0882524
$637$	−2.58475e8	−0.0396214
$638$	−4.77370e9	−0.727751
$639$	2.25788e9	0.342332
$640$	−6.47458e8	−0.0976297
$641$	3.46840e9	0.520147	0.260073	−	0.965589i	$-0.416253\pi$
$641$	3.46840e9	0.520147	0.260073	+	0.965589i	$0.416253\pi$
$642$	4.03620e9	0.602004
$643$	7.93088e9	1.17648	0.588238	−	0.808688i	$-0.299822\pi$
$643$	7.93088e9	1.17648	0.588238	+	0.808688i	$0.299822\pi$
$644$	−4.01217e8	−0.0591942
$645$	−5.48779e9	−0.805265
$646$	4.72347e8	0.0689362
$647$	−6.31448e9	−0.916585	−0.458292	−	0.888801i	$-0.651539\pi$
$647$	−6.31448e9	−0.916585	−0.458292	+	0.888801i	$0.651539\pi$
$648$	−2.72098e8	−0.0392837
$649$	9.30929e9	1.33678
$650$	3.02142e8	0.0431533
$651$	1.12778e9	0.160211
$652$	1.58164e9	0.223481
$653$	−7.67644e9	−1.07886	−0.539428	−	0.842032i	$-0.681360\pi$
$653$	−7.67644e9	−1.07886	−0.539428	+	0.842032i	$0.681360\pi$
$654$	−4.61144e9	−0.644636
$655$	1.83904e9	0.255709
$656$	−3.82714e8	−0.0529311
$657$	−5.41712e8	−0.0745229
$658$	−1.00752e9	−0.137868
$659$	−2.64433e9	−0.359929	−0.179965	−	0.983673i	$-0.557598\pi$
$659$	−2.64433e9	−0.359929	−0.179965	+	0.983673i	$0.557598\pi$
$660$	2.33816e9	0.316571
$661$	7.25813e9	0.977507	0.488753	−	0.872422i	$-0.337452\pi$
$661$	7.25813e9	0.977507	0.488753	+	0.872422i	$0.337452\pi$
$662$	−7.87325e8	−0.105475
$663$	1.88187e9	0.250780
$664$	4.83973e9	0.641553
$665$	1.97084e8	0.0259881
$666$	−1.98569e8	−0.0260467
$667$	−2.48841e9	−0.324699
$668$	−2.26495e9	−0.293996
$669$	3.47999e9	0.449351
$670$	−9.11347e9	−1.17064
$671$	1.27806e10	1.63314
$672$	−3.03464e8	−0.0385758
$673$	7.91518e9	1.00094	0.500470	−	0.865754i	$-0.333160\pi$
$673$	7.91518e9	1.00094	0.500470	+	0.865754i	$0.333160\pi$
$674$	−1.78054e9	−0.223997
$675$	3.38362e8	0.0423466
$676$	3.08916e8	0.0384615
$677$	1.23822e10	1.53369	0.766845	−	0.641833i	$-0.221826\pi$
$677$	1.23822e10	1.53369	0.766845	+	0.641833i	$0.221826\pi$
$678$	−2.01820e9	−0.248691
$679$	5.59409e9	0.685781
$680$	5.01474e9	0.611599
$681$	4.20701e9	0.510456
$682$	−4.26979e9	−0.515420
$683$	−1.18010e10	−1.41725	−0.708626	−	0.705584i	$-0.750685\pi$
$683$	−1.18010e10	−1.41725	−0.708626	+	0.705584i	$0.750685\pi$
$684$	8.68325e7	0.0103749
$685$	1.29036e10	1.53389
$686$	−3.22829e8	−0.0381802
$687$	7.07042e9	0.831948
$688$	−2.69657e9	−0.315684
$689$	−7.27969e8	−0.0847902
$690$	1.21883e9	0.141244
$691$	−9.81382e9	−1.13153	−0.565763	−	0.824568i	$-0.691418\pi$
$691$	−9.81382e9	−1.13153	−0.565763	+	0.824568i	$0.691418\pi$
$692$	9.43372e8	0.108221
$693$	1.09590e9	0.125085
$694$	2.20959e9	0.250931
$695$	8.87988e8	0.100337
$696$	−1.88213e9	−0.211601
$697$	2.96422e9	0.331586
$698$	3.28827e9	0.365994
$699$	−9.90795e8	−0.109727
$700$	3.77368e8	0.0415836
$701$	−6.35597e9	−0.696897	−0.348449	−	0.937328i	$-0.613291\pi$
$701$	−6.35597e9	−0.696897	−0.348449	+	0.937328i	$0.613291\pi$
$702$	3.45948e8	0.0377426
$703$	6.33679e7	0.00687900
$704$	1.14892e9	0.124104
$705$	3.06067e9	0.328968
$706$	2.16572e9	0.231625
$707$	−5.15115e9	−0.548196
$708$	3.67038e9	0.388682
$709$	−1.71404e10	−1.80617	−0.903084	−	0.429464i	$-0.858703\pi$
$709$	−1.71404e10	−1.80617	−0.903084	+	0.429464i	$0.858703\pi$
$710$	−7.64971e9	−0.802122
$711$	5.76903e9	0.601948
$712$	−6.38276e9	−0.662718
$713$	−2.22573e9	−0.229964
$714$	2.35041e9	0.241658
$715$	−2.97277e9	−0.304152
$716$	7.23255e9	0.736369
$717$	5.39628e9	0.546736
$718$	−1.06566e10	−1.07444
$719$	1.12801e10	1.13178	0.565892	−	0.824479i	$-0.308532\pi$
$719$	1.12801e10	1.13178	0.565892	+	0.824479i	$0.308532\pi$
$720$	9.21869e8	0.0920462
$721$	−5.07355e9	−0.504126
$722$	7.12326e9	0.704367
$723$	−3.66345e9	−0.360500
$724$	−5.74107e8	−0.0562222
$725$	2.34049e9	0.228099
$726$	6.01449e7	0.00583339
$727$	−7.72115e9	−0.745266	−0.372633	−	0.927979i	$-0.621545\pi$
$727$	−7.72115e9	−0.745266	−0.372633	+	0.927979i	$0.621545\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	1.83532e9	0.174615
$731$	2.08857e10	1.97760
$732$	5.03903e9	0.474852
$733$	−9.79386e9	−0.918523	−0.459261	−	0.888301i	$-0.651886\pi$
$733$	−9.79386e9	−0.918523	−0.459261	+	0.888301i	$0.651886\pi$
$734$	6.01517e9	0.561451
$735$	9.80695e8	0.0911021
$736$	5.98902e8	0.0553711
$737$	1.61719e10	1.48807
$738$	5.44919e8	0.0499039
$739$	4.91245e9	0.447757	0.223879	−	0.974617i	$-0.428128\pi$
$739$	4.91245e9	0.447757	0.223879	+	0.974617i	$0.428128\pi$
$740$	6.72754e8	0.0610303
$741$	−1.10400e8	−0.00996792
$742$	−9.09216e8	−0.0817059
$743$	1.01342e10	0.906421	0.453210	−	0.891404i	$-0.350279\pi$
$743$	1.01342e10	0.906421	0.453210	+	0.891404i	$0.350279\pi$
$744$	−1.68345e9	−0.149863
$745$	5.94616e9	0.526853
$746$	−1.20350e10	−1.06135
$747$	−6.89094e9	−0.604862
$748$	−8.89868e9	−0.777446
$749$	−6.40933e9	−0.557348
$750$	4.06348e9	0.351709
$751$	−1.31146e10	−1.12983	−0.564916	−	0.825149i	$-0.691091\pi$
$751$	−1.31146e10	−1.12983	−0.564916	+	0.825149i	$0.691091\pi$
$752$	1.50394e9	0.128964
$753$	5.08042e9	0.433628
$754$	2.39296e9	0.203299
$755$	−2.11676e10	−1.79001
$756$	4.32081e8	0.0363696
$757$	−8.58663e9	−0.719427	−0.359714	−	0.933063i	$-0.617126\pi$
$757$	−8.58663e9	−0.719427	−0.359714	+	0.933063i	$0.617126\pi$
$758$	1.49021e10	1.24281
$759$	−2.16281e9	−0.179545
$760$	−2.94189e8	−0.0243097
$761$	3.98925e9	0.328130	0.164065	−	0.986450i	$-0.447539\pi$
$761$	3.98925e9	0.328130	0.164065	+	0.986450i	$0.447539\pi$
$762$	3.73559e9	0.305856
$763$	7.32280e9	0.596817
$764$	2.36543e9	0.191904
$765$	−7.14013e9	−0.576622
$766$	−1.39067e10	−1.11796
$767$	−4.66657e9	−0.373434
$768$	4.52985e8	0.0360844
$769$	−2.41781e9	−0.191726	−0.0958628	−	0.995395i	$-0.530561\pi$
$769$	−2.41781e9	−0.191726	−0.0958628	+	0.995395i	$0.530561\pi$
$770$	−3.71292e9	−0.293088
$771$	−1.51458e9	−0.119015
$772$	5.05586e9	0.395489
$773$	−7.32994e8	−0.0570785	−0.0285392	−	0.999593i	$-0.509086\pi$
$773$	−7.32994e8	−0.0570785	−0.0285392	+	0.999593i	$0.509086\pi$
$774$	3.83945e9	0.297630
$775$	2.09343e9	0.161548
$776$	−8.35036e9	−0.641489
$777$	3.15321e8	0.0241145
$778$	−1.09426e10	−0.833087
$779$	−1.73896e8	−0.0131798
$780$	−1.17208e9	−0.0884351
$781$	1.35744e10	1.01963
$782$	−4.63866e9	−0.346871
$783$	2.67983e9	0.199499
$784$	4.81890e8	0.0357143
$785$	−2.26481e10	−1.67105
$786$	−1.28666e9	−0.0945113
$787$	1.17720e10	0.860870	0.430435	−	0.902622i	$-0.358360\pi$
$787$	1.17720e10	0.860870	0.430435	+	0.902622i	$0.358360\pi$
$788$	6.57311e7	0.00478552
$789$	−1.06099e10	−0.769025
$790$	−1.95455e10	−1.41043
$791$	3.20483e9	0.230243
$792$	−1.63586e9	−0.117006
$793$	−6.40668e9	−0.456223
$794$	1.65542e10	1.17364
$795$	2.76203e9	0.194959
$796$	−1.31587e10	−0.924733
$797$	1.55259e10	1.08631	0.543154	−	0.839633i	$-0.317230\pi$
$797$	1.55259e10	1.08631	0.543154	+	0.839633i	$0.317230\pi$
$798$	−1.37887e8	−0.00960533
$799$	−1.16484e10	−0.807891
$800$	−5.63301e8	−0.0388979
$801$	9.08795e9	0.624816
$802$	−2.05496e10	−1.40667
$803$	−3.25679e9	−0.221966
$804$	6.37610e9	0.432672
$805$	−1.93545e9	−0.130766
$806$	2.14036e9	0.143984
$807$	1.25615e9	0.0841362
$808$	7.68918e9	0.512791
$809$	8.57974e9	0.569711	0.284855	−	0.958571i	$-0.408054\pi$
$809$	8.57974e9	0.569711	0.284855	+	0.958571i	$0.408054\pi$
$810$	−1.31258e9	−0.0867820
$811$	−5.30222e9	−0.349048	−0.174524	−	0.984653i	$-0.555839\pi$
$811$	−5.30222e9	−0.349048	−0.174524	+	0.984653i	$0.555839\pi$
$812$	2.98875e9	0.195904
$813$	1.48496e10	0.969163
$814$	−1.19381e9	−0.0775798
$815$	7.62974e9	0.493694
$816$	−3.50849e9	−0.226050
$817$	−1.22526e9	−0.0786048
$818$	1.05329e9	0.0672839
$819$	−5.49353e8	−0.0349428
$820$	−1.84619e9	−0.116930
$821$	−8.52445e9	−0.537608	−0.268804	−	0.963195i	$-0.586628\pi$
$821$	−8.52445e9	−0.537608	−0.268804	+	0.963195i	$0.586628\pi$
$822$	−9.02784e9	−0.566934
$823$	1.60987e10	1.00668	0.503341	−	0.864088i	$-0.332104\pi$
$823$	1.60987e10	1.00668	0.503341	+	0.864088i	$0.332104\pi$
$824$	7.57335e9	0.471566
$825$	2.03425e9	0.126129
$826$	−5.82843e9	−0.359850
$827$	1.64563e10	1.01172	0.505862	−	0.862614i	$-0.331174\pi$
$827$	1.64563e10	1.01172	0.505862	+	0.862614i	$0.331174\pi$
$828$	−8.52733e8	−0.0522044
$829$	−1.90918e10	−1.16388	−0.581938	−	0.813233i	$-0.697705\pi$
$829$	−1.90918e10	−1.16388	−0.581938	+	0.813233i	$0.697705\pi$
$830$	2.33466e10	1.41726
$831$	−1.46240e10	−0.884019
$832$	−5.75930e8	−0.0346688
$833$	−3.73237e9	−0.223731
$834$	−6.21268e8	−0.0370850
$835$	−1.09260e10	−0.649468
$836$	5.22040e8	0.0309017
$837$	2.39695e9	0.141293
$838$	−1.70528e10	−1.00102
$839$	−1.55215e10	−0.907334	−0.453667	−	0.891171i	$-0.649885\pi$
$839$	−1.55215e10	−0.907334	−0.453667	+	0.891171i	$0.649885\pi$
$840$	−1.46389e9	−0.0852182
$841$	1.28678e9	0.0745967
$842$	−1.40304e10	−0.809988
$843$	3.88015e9	0.223076
$844$	3.74438e9	0.214379
$845$	1.49019e9	0.0849657
$846$	−2.14135e9	−0.121588
$847$	−9.55079e7	−0.00540067
$848$	1.35720e9	0.0764288
$849$	8.36235e9	0.468977
$850$	4.36292e9	0.243675
$851$	−6.22301e8	−0.0346136
$852$	5.35201e9	0.296468
$853$	−2.50536e10	−1.38213	−0.691065	−	0.722792i	$-0.742858\pi$
$853$	−2.50536e10	−1.38213	−0.691065	+	0.722792i	$0.742858\pi$
$854$	−8.00179e9	−0.439628
$855$	4.18875e8	0.0229194
$856$	9.56728e9	0.521351
$857$	2.44961e10	1.32943	0.664713	−	0.747099i	$-0.268554\pi$
$857$	2.44961e10	1.32943	0.664713	+	0.747099i	$0.268554\pi$
$858$	2.07985e9	0.112416
$859$	−3.12665e10	−1.68308	−0.841538	−	0.540198i	$-0.818349\pi$
$859$	−3.12665e10	−1.68308	−0.841538	+	0.540198i	$0.818349\pi$
$860$	−1.30081e10	−0.697380
$861$	−8.65311e8	−0.0462020
$862$	−1.69910e9	−0.0903533
$863$	−2.66767e10	−1.41284	−0.706421	−	0.707791i	$-0.749692\pi$
$863$	−2.66767e10	−1.41284	−0.706421	+	0.707791i	$0.749692\pi$
$864$	−6.44973e8	−0.0340207
$865$	4.55077e9	0.239072
$866$	−1.15510e10	−0.604377
$867$	1.60950e10	0.838736
$868$	2.67326e9	0.138747
$869$	3.46836e10	1.79290
$870$	−9.07928e9	−0.467449
$871$	−8.10666e9	−0.415698
$872$	−1.09308e10	−0.558271
$873$	1.18895e10	0.604802
$874$	2.72126e8	0.0137873
$875$	−6.45266e9	−0.325620
$876$	−1.28406e9	−0.0645387
$877$	2.92563e10	1.46461	0.732304	−	0.680978i	$-0.238445\pi$
$877$	2.92563e10	1.46461	0.732304	+	0.680978i	$0.238445\pi$
$878$	6.60329e9	0.329253
$879$	1.30572e10	0.648469
$880$	5.54231e9	0.274159
$881$	3.29103e10	1.62150	0.810748	−	0.585395i	$-0.199061\pi$
$881$	3.29103e10	1.62150	0.810748	+	0.585395i	$0.199061\pi$
$882$	−6.86129e8	−0.0336718
$883$	2.00316e10	0.979161	0.489580	−	0.871958i	$-0.337150\pi$
$883$	2.00316e10	0.979161	0.489580	+	0.871958i	$0.337150\pi$
$884$	4.46073e9	0.217182
$885$	1.77057e10	0.858641
$886$	−9.08826e9	−0.438998
$887$	−5.94155e9	−0.285869	−0.142934	−	0.989732i	$-0.545654\pi$
$887$	−5.94155e9	−0.285869	−0.142934	+	0.989732i	$0.545654\pi$
$888$	−4.70683e8	−0.0225571
$889$	−5.93198e9	−0.283167
$890$	−3.07901e10	−1.46401
$891$	2.32919e9	0.110314
$892$	8.24886e9	0.389150
$893$	6.83353e8	0.0321118
$894$	−4.16014e9	−0.194727
$895$	3.48894e10	1.62672
$896$	−7.19323e8	−0.0334077
$897$	1.08418e9	0.0501564
$898$	2.19763e10	1.01272
$899$	1.65799e10	0.761069
$900$	8.02044e8	0.0366732
$901$	−1.05118e10	−0.478787
$902$	3.27607e9	0.148638
$903$	−6.09691e9	−0.275551
$904$	−4.78388e9	−0.215373
$905$	−2.76946e9	−0.124201
$906$	1.48096e10	0.661598
$907$	3.93192e10	1.74976	0.874881	−	0.484338i	$-0.160939\pi$
$907$	3.93192e10	1.74976	0.874881	+	0.484338i	$0.160939\pi$
$908$	9.97217e9	0.442068
$909$	−1.09481e10	−0.483464
$910$	1.86121e9	0.0818750
$911$	−1.93623e10	−0.848483	−0.424241	−	0.905549i	$-0.639459\pi$
$911$	−1.93623e10	−0.848483	−0.424241	+	0.905549i	$0.639459\pi$
$912$	2.05825e8	0.00898496
$913$	−4.14286e10	−1.80158
$914$	1.95305e10	0.846059
$915$	2.43080e10	1.04900
$916$	1.67595e10	0.720489
$917$	2.04316e9	0.0875004
$918$	4.99549e9	0.213122
$919$	8.13769e9	0.345857	0.172929	−	0.984934i	$-0.444677\pi$
$919$	8.13769e9	0.345857	0.172929	+	0.984934i	$0.444677\pi$
$920$	2.88907e9	0.122321
$921$	−1.28835e10	−0.543407
$922$	2.25479e10	0.947433
$923$	−6.80461e9	−0.284837
$924$	2.59769e9	0.108327
$925$	5.85309e8	0.0243158
$926$	3.23918e10	1.34059
$927$	−1.07831e10	−0.444597
$928$	−4.46134e9	−0.183252
$929$	−1.42265e10	−0.582161	−0.291080	−	0.956699i	$-0.594015\pi$
$929$	−1.42265e10	−0.582161	−0.291080	+	0.956699i	$0.594015\pi$
$930$	−8.12088e9	−0.331065
$931$	2.18959e8	0.00889281
$932$	−2.34855e9	−0.0950264
$933$	1.23583e10	0.498163
$934$	−5.74055e9	−0.230536
$935$	−4.29267e10	−1.71746
$936$	8.20026e8	0.0326860
$937$	−3.65372e10	−1.45093	−0.725465	−	0.688259i	$-0.758375\pi$
$937$	−3.65372e10	−1.45093	−0.725465	+	0.688259i	$0.758375\pi$
$938$	−1.01250e10	−0.400577
$939$	−3.78379e9	−0.149141
$940$	7.25491e9	0.284895
$941$	4.06222e10	1.58928	0.794638	−	0.607083i	$-0.207661\pi$
$941$	4.06222e10	1.58928	0.794638	+	0.607083i	$0.207661\pi$
$942$	1.58454e10	0.617626
$943$	1.70773e9	0.0663176
$944$	8.70016e9	0.336609
$945$	2.08433e9	0.0803445
$946$	2.30829e10	0.886487
$947$	−4.45964e10	−1.70638	−0.853189	−	0.521603i	$-0.825334\pi$
$947$	−4.45964e10	−1.70638	−0.853189	+	0.521603i	$0.825334\pi$
$948$	1.36747e10	0.521303
$949$	1.63257e9	0.0620068
$950$	−2.55950e8	−0.00968551
$951$	−1.43144e9	−0.0539687
$952$	5.57135e9	0.209282
$953$	4.23573e9	0.158527	0.0792634	−	0.996854i	$-0.474743\pi$
$953$	4.23573e9	0.158527	0.0792634	+	0.996854i	$0.474743\pi$
$954$	−1.93241e9	−0.0720578
$955$	1.14107e10	0.423936
$956$	1.27912e10	0.473487
$957$	1.61112e10	0.594206
$958$	2.81533e9	0.103455
$959$	1.43359e10	0.524879
$960$	2.18517e9	0.0797143
$961$	−1.26828e10	−0.460982
$962$	5.98432e8	0.0216721
$963$	−1.36222e10	−0.491534
$964$	−8.68372e9	−0.312202
$965$	2.43892e10	0.873679
$966$	1.35411e9	0.0483319
$967$	5.29046e9	0.188148	0.0940742	−	0.995565i	$-0.470011\pi$
$967$	5.29046e9	0.188148	0.0940742	+	0.995565i	$0.470011\pi$
$968$	1.42566e8	0.00505186
$969$	−1.59417e9	−0.0562861
$970$	−4.02816e10	−1.41712
$971$	−2.80447e10	−0.983067	−0.491534	−	0.870859i	$-0.663564\pi$
$971$	−2.80447e10	−0.983067	−0.491534	+	0.870859i	$0.663564\pi$
$972$	9.18330e8	0.0320750
$973$	9.86551e8	0.0343340
$974$	1.59881e10	0.554422
$975$	−1.01973e9	−0.0352345
$976$	1.19444e10	0.411234
$977$	−1.05419e10	−0.361649	−0.180824	−	0.983515i	$-0.557877\pi$
$977$	−1.05419e10	−0.361649	−0.180824	+	0.983515i	$0.557877\pi$
$978$	−5.33804e9	−0.182472
$979$	5.46371e10	1.86101
$980$	2.32461e9	0.0788967
$981$	1.55636e10	0.526343
$982$	2.18664e10	0.736862
$983$	2.43665e10	0.818194	0.409097	−	0.912491i	$-0.365844\pi$
$983$	2.43665e10	0.818194	0.409097	+	0.912491i	$0.365844\pi$
$984$	1.29166e9	0.0432180
$985$	3.17083e8	0.0105717
$986$	3.45543e10	1.14798
$987$	3.40039e9	0.112569
$988$	−2.61688e8	−0.00863247
$989$	1.20326e10	0.395522
$990$	−7.89130e9	−0.258479
$991$	−2.59196e10	−0.846001	−0.423000	−	0.906130i	$-0.639023\pi$
$991$	−2.59196e10	−0.846001	−0.423000	+	0.906130i	$0.639023\pi$
$992$	−3.99041e9	−0.129786
$993$	2.65722e9	0.0861203
$994$	−8.49879e9	−0.274476
$995$	−6.34766e10	−2.04283
$996$	−1.63341e10	−0.523826
$997$	4.81451e10	1.53858	0.769288	−	0.638902i	$-0.220611\pi$
$997$	4.81451e10	1.53858	0.769288	+	0.638902i	$0.220611\pi$
$998$	−1.28654e10	−0.409701
$999$	6.70171e8	0.0212670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.p.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.p.1.5	✓	6	1.1	even	1	trivial

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.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.732 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.732 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2469.86 q^{10} +4382.78 q^{11} +1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +8335.77 q^{15} +4096.00 q^{16} -31724.6 q^{17} -5832.00 q^{18} +1861.12 q^{19} +19758.9 q^{20} +9261.00 q^{21} -35062.2 q^{22} -18277.0 q^{23} -13824.0 q^{24} +17190.6 q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} +136149. q^{29} -66686.2 q^{30} +121778. q^{31} -32768.0 q^{32} +118335. q^{33} +253797. q^{34} +105895. q^{35} +46656.0 q^{36} +34048.2 q^{37} -14889.0 q^{38} -59319.0 q^{39} -158071. q^{40} -93436.0 q^{41} -74088.0 q^{42} -658343. q^{43} +280498. q^{44} +225066. q^{45} +146216. q^{46} +367173. q^{47} +110592. q^{48} +117649. q^{49} -137525. q^{50} -856565. q^{51} -140608. q^{52} +331347. q^{53} -157464. q^{54} +1.35310e6 q^{55} -175616. q^{56} +50250.3 q^{57} -1.08920e6 q^{58} +2.12406e6 q^{59} +533489. q^{60} +2.91611e6 q^{61} -974221. q^{62} +250047. q^{63} +262144. q^{64} -678285. q^{65} -946680. q^{66} +3.68988e6 q^{67} -2.03038e6 q^{68} -493480. q^{69} -847161. q^{70} +3.09723e6 q^{71} -373248. q^{72} -743089. q^{73} -272386. q^{74} +464146. q^{75} +119112. q^{76} +1.50329e6 q^{77} +474552. q^{78} +7.91362e6 q^{79} +1.26457e6 q^{80} +531441. q^{81} +747488. q^{82} -9.45259e6 q^{83} +592704. q^{84} -9.79441e6 q^{85} +5.26674e6 q^{86} +3.67603e6 q^{87} -2.24398e6 q^{88} +1.24663e7 q^{89} -1.80053e6 q^{90} -753571. q^{91} -1.16973e6 q^{92} +3.28799e6 q^{93} -2.93738e6 q^{94} +574588. q^{95} -884736. q^{96} +1.63093e7 q^{97} -941192. q^{98} +3.19504e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} + 162 q^{3} + 384 q^{4} - 43 q^{5} - 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 344 q^{10} + 7370 q^{11} + 10368 q^{12} - 13182 q^{13} - 16464 q^{14} - 1161 q^{15} + 24576 q^{16} + 7950 q^{17} - 34992 q^{18} - 57145 q^{19} - 2752 q^{20} + 55566 q^{21} - 58960 q^{22} + 31769 q^{23} - 82944 q^{24} + 135721 q^{25} + 105456 q^{26} + 118098 q^{27} + 131712 q^{28} - 36455 q^{29} + 9288 q^{30} + 215069 q^{31} - 196608 q^{32} + 198990 q^{33} - 63600 q^{34} - 14749 q^{35} + 279936 q^{36} + 133074 q^{37} + 457160 q^{38} - 355914 q^{39} + 22016 q^{40} + 516452 q^{41} - 444528 q^{42} - 3085 q^{43} + 471680 q^{44} - 31347 q^{45} - 254152 q^{46} + 1463947 q^{47} + 663552 q^{48} + 705894 q^{49} - 1085768 q^{50} + 214650 q^{51} - 843648 q^{52} - 1344571 q^{53} - 944784 q^{54} - 1568062 q^{55} - 1053696 q^{56} - 1542915 q^{57} + 291640 q^{58} + 1810408 q^{59} - 74304 q^{60} + 4047390 q^{61} - 1720552 q^{62} + 1500282 q^{63} + 1572864 q^{64} + 94471 q^{65} - 1591920 q^{66} + 2393614 q^{67} + 508800 q^{68} + 857763 q^{69} + 117992 q^{70} + 10341084 q^{71} - 2239488 q^{72} + 5180001 q^{73} - 1064592 q^{74} + 3664467 q^{75} - 3657280 q^{76} + 2527910 q^{77} + 2847312 q^{78} + 4624979 q^{79} - 176128 q^{80} + 3188646 q^{81} - 4131616 q^{82} + 11892699 q^{83} + 3556224 q^{84} + 750368 q^{85} + 24680 q^{86} - 984285 q^{87} - 3773440 q^{88} + 9781713 q^{89} + 250776 q^{90} - 4521426 q^{91} + 2033216 q^{92} + 5806863 q^{93} - 11711576 q^{94} + 26244263 q^{95} - 5308416 q^{96} + 5202537 q^{97} - 5647152 q^{98} + 5372730 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 162 * q^3 + 384 * q^4 - 43 * q^5 - 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 344 * q^10 + 7370 * q^11 + 10368 * q^12 - 13182 * q^13 - 16464 * q^14 - 1161 * q^15 + 24576 * q^16 + 7950 * q^17 - 34992 * q^18 - 57145 * q^19 - 2752 * q^20 + 55566 * q^21 - 58960 * q^22 + 31769 * q^23 - 82944 * q^24 + 135721 * q^25 + 105456 * q^26 + 118098 * q^27 + 131712 * q^28 - 36455 * q^29 + 9288 * q^30 + 215069 * q^31 - 196608 * q^32 + 198990 * q^33 - 63600 * q^34 - 14749 * q^35 + 279936 * q^36 + 133074 * q^37 + 457160 * q^38 - 355914 * q^39 + 22016 * q^40 + 516452 * q^41 - 444528 * q^42 - 3085 * q^43 + 471680 * q^44 - 31347 * q^45 - 254152 * q^46 + 1463947 * q^47 + 663552 * q^48 + 705894 * q^49 - 1085768 * q^50 + 214650 * q^51 - 843648 * q^52 - 1344571 * q^53 - 944784 * q^54 - 1568062 * q^55 - 1053696 * q^56 - 1542915 * q^57 + 291640 * q^58 + 1810408 * q^59 - 74304 * q^60 + 4047390 * q^61 - 1720552 * q^62 + 1500282 * q^63 + 1572864 * q^64 + 94471 * q^65 - 1591920 * q^66 + 2393614 * q^67 + 508800 * q^68 + 857763 * q^69 + 117992 * q^70 + 10341084 * q^71 - 2239488 * q^72 + 5180001 * q^73 - 1064592 * q^74 + 3664467 * q^75 - 3657280 * q^76 + 2527910 * q^77 + 2847312 * q^78 + 4624979 * q^79 - 176128 * q^80 + 3188646 * q^81 - 4131616 * q^82 + 11892699 * q^83 + 3556224 * q^84 + 750368 * q^85 + 24680 * q^86 - 984285 * q^87 - 3773440 * q^88 + 9781713 * q^89 + 250776 * q^90 - 4521426 * q^91 + 2033216 * q^92 + 5806863 * q^93 - 11711576 * q^94 + 26244263 * q^95 - 5308416 * q^96 + 5202537 * q^97 - 5647152 * q^98 + 5372730 * q^99

Introduction

L-functions

Modular forms

Varieties

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