LMFDB - Embedded newform 546.8.a.i.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:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 86504x^{3} - 9117228x^{2} + 89606664x + 21810067776 $ x^5 - 2x^4 - 86504x^3 - 9117228x^2 + 89606664x + 21810067776
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 5\cdot 13 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-204.972$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +320.628 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +320.628 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2565.02 q^{10} -1110.99 q^{11} +1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +8656.96 q^{15} +4096.00 q^{16} +3826.09 q^{17} -5832.00 q^{18} -45323.1 q^{19} +20520.2 q^{20} +9261.00 q^{21} +8887.91 q^{22} -5254.10 q^{23} -13824.0 q^{24} +24677.3 q^{25} -17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} +25163.2 q^{29} -69255.7 q^{30} -223416. q^{31} -32768.0 q^{32} -29996.7 q^{33} -30608.7 q^{34} +109975. q^{35} +46656.0 q^{36} +238713. q^{37} +362585. q^{38} +59319.0 q^{39} -164162. q^{40} +42730.0 q^{41} -74088.0 q^{42} -819703. q^{43} -71103.2 q^{44} +233738. q^{45} +42032.8 q^{46} -684959. q^{47} +110592. q^{48} +117649. q^{49} -197419. q^{50} +103304. q^{51} +140608. q^{52} -1.18203e6 q^{53} -157464. q^{54} -356214. q^{55} -175616. q^{56} -1.22372e6 q^{57} -201306. q^{58} -2.74036e6 q^{59} +554045. q^{60} +1.94158e6 q^{61} +1.78733e6 q^{62} +250047. q^{63} +262144. q^{64} +704420. q^{65} +239973. q^{66} -1.62868e6 q^{67} +244870. q^{68} -141861. q^{69} -879803. q^{70} -1.88558e6 q^{71} -373248. q^{72} -5.69023e6 q^{73} -1.90971e6 q^{74} +666288. q^{75} -2.90068e6 q^{76} -381069. q^{77} -474552. q^{78} -4.76272e6 q^{79} +1.31329e6 q^{80} +531441. q^{81} -341840. q^{82} +96910.3 q^{83} +592704. q^{84} +1.22675e6 q^{85} +6.55763e6 q^{86} +679407. q^{87} +568826. q^{88} -485878. q^{89} -1.86990e6 q^{90} +753571. q^{91} -336262. q^{92} -6.03224e6 q^{93} +5.47967e6 q^{94} -1.45319e7 q^{95} -884736. q^{96} +1.65671e7 q^{97} -941192. q^{98} -809910. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} - 340 q^{5} - 1080 q^{6} + 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 - 340 * q^5 - 1080 * q^6 + 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} - 340 q^{5} - 1080 q^{6} + 1715 q^{7} - 2560 q^{8} + 3645 q^{9} + 2720 q^{10} - 1303 q^{11} + 8640 q^{12} + 10985 q^{13} - 13720 q^{14} - 9180 q^{15} + 20480 q^{16} - 4247 q^{17} - 29160 q^{18} - 16984 q^{19} - 21760 q^{20} + 46305 q^{21} + 10424 q^{22} - 78072 q^{23} - 69120 q^{24} - 79555 q^{25} - 87880 q^{26} + 98415 q^{27} + 109760 q^{28} - 213142 q^{29} + 73440 q^{30} - 186027 q^{31} - 163840 q^{32} - 35181 q^{33} + 33976 q^{34} - 116620 q^{35} + 233280 q^{36} + 101025 q^{37} + 135872 q^{38} + 296595 q^{39} + 174080 q^{40} - 23976 q^{41} - 370440 q^{42} - 55528 q^{43} - 83392 q^{44} - 247860 q^{45} + 624576 q^{46} - 985981 q^{47} + 552960 q^{48} + 588245 q^{49} + 636440 q^{50} - 114669 q^{51} + 703040 q^{52} - 1891657 q^{53} - 787320 q^{54} + 1746955 q^{55} - 878080 q^{56} - 458568 q^{57} + 1705136 q^{58} - 2802208 q^{59} - 587520 q^{60} + 1140591 q^{61} + 1488216 q^{62} + 1250235 q^{63} + 1310720 q^{64} - 746980 q^{65} + 281448 q^{66} + 265168 q^{67} - 271808 q^{68} - 2107944 q^{69} + 932960 q^{70} - 4483276 q^{71} - 1866240 q^{72} - 2350578 q^{73} - 808200 q^{74} - 2147985 q^{75} - 1086976 q^{76} - 446929 q^{77} - 2372760 q^{78} - 4079889 q^{79} - 1392640 q^{80} + 2657205 q^{81} + 191808 q^{82} - 8731571 q^{83} + 2963520 q^{84} - 1715895 q^{85} + 444224 q^{86} - 5754834 q^{87} + 667136 q^{88} - 20077879 q^{89} + 1982880 q^{90} + 3767855 q^{91} - 4996608 q^{92} - 5022729 q^{93} + 7887848 q^{94} - 11580740 q^{95} - 4423680 q^{96} + 3780209 q^{97} - 4705960 q^{98} - 949887 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 - 340 * q^5 - 1080 * q^6 + 1715 * q^7 - 2560 * q^8 + 3645 * q^9 + 2720 * q^10 - 1303 * q^11 + 8640 * q^12 + 10985 * q^13 - 13720 * q^14 - 9180 * q^15 + 20480 * q^16 - 4247 * q^17 - 29160 * q^18 - 16984 * q^19 - 21760 * q^20 + 46305 * q^21 + 10424 * q^22 - 78072 * q^23 - 69120 * q^24 - 79555 * q^25 - 87880 * q^26 + 98415 * q^27 + 109760 * q^28 - 213142 * q^29 + 73440 * q^30 - 186027 * q^31 - 163840 * q^32 - 35181 * q^33 + 33976 * q^34 - 116620 * q^35 + 233280 * q^36 + 101025 * q^37 + 135872 * q^38 + 296595 * q^39 + 174080 * q^40 - 23976 * q^41 - 370440 * q^42 - 55528 * q^43 - 83392 * q^44 - 247860 * q^45 + 624576 * q^46 - 985981 * q^47 + 552960 * q^48 + 588245 * q^49 + 636440 * q^50 - 114669 * q^51 + 703040 * q^52 - 1891657 * q^53 - 787320 * q^54 + 1746955 * q^55 - 878080 * q^56 - 458568 * q^57 + 1705136 * q^58 - 2802208 * q^59 - 587520 * q^60 + 1140591 * q^61 + 1488216 * q^62 + 1250235 * q^63 + 1310720 * q^64 - 746980 * q^65 + 281448 * q^66 + 265168 * q^67 - 271808 * q^68 - 2107944 * q^69 + 932960 * q^70 - 4483276 * q^71 - 1866240 * q^72 - 2350578 * q^73 - 808200 * q^74 - 2147985 * q^75 - 1086976 * q^76 - 446929 * q^77 - 2372760 * q^78 - 4079889 * q^79 - 1392640 * q^80 + 2657205 * q^81 + 191808 * q^82 - 8731571 * q^83 + 2963520 * q^84 - 1715895 * q^85 + 444224 * q^86 - 5754834 * q^87 + 667136 * q^88 - 20077879 * q^89 + 1982880 * q^90 + 3767855 * q^91 - 4996608 * q^92 - 5022729 * q^93 + 7887848 * q^94 - 11580740 * q^95 - 4423680 * q^96 + 3780209 * q^97 - 4705960 * q^98 - 949887 * 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
$5$	320.628	1.14711	0.573557	−	0.819166i	$-0.305563\pi$
$5$	320.628	1.14711	0.573557	+	0.819166i	$0.305563\pi$
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−2565.02	−0.811132
$11$	−1110.99	−0.251672	−0.125836	−	0.992051i	$-0.540161\pi$
$11$	−1110.99	−0.251672	−0.125836	+	0.992051i	$0.540161\pi$
$12$	1728.00	0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	8656.96	0.662286
$16$	4096.00	0.250000
$17$	3826.09	0.188879	0.0944396	−	0.995531i	$-0.469894\pi$
$17$	3826.09	0.188879	0.0944396	+	0.995531i	$0.469894\pi$
$18$	−5832.00	−0.235702
$19$	−45323.1	−1.51594	−0.757970	−	0.652289i	$-0.773809\pi$
$19$	−45323.1	−1.51594	−0.757970	+	0.652289i	$0.773809\pi$
$20$	20520.2	0.573557
$21$	9261.00	0.218218
$22$	8887.91	0.177959
$23$	−5254.10	−0.0900432	−0.0450216	−	0.998986i	$-0.514336\pi$
$23$	−5254.10	−0.0900432	−0.0450216	+	0.998986i	$0.514336\pi$
$24$	−13824.0	−0.204124
$25$	24677.3	0.315870
$26$	−17576.0	−0.196116
$27$	19683.0	0.192450
$28$	21952.0	0.188982
$29$	25163.2	0.191590	0.0957951	−	0.995401i	$-0.469461\pi$
$29$	25163.2	0.191590	0.0957951	+	0.995401i	$0.469461\pi$
$30$	−69255.7	−0.468307
$31$	−223416.	−1.34694	−0.673471	−	0.739214i	$-0.735197\pi$
$31$	−223416.	−1.34694	−0.673471	+	0.739214i	$0.735197\pi$
$32$	−32768.0	−0.176777
$33$	−29996.7	−0.145303
$34$	−30608.7	−0.133558
$35$	109975.	0.433568
$36$	46656.0	0.166667
$37$	238713.	0.774767	0.387383	−	0.921919i	$-0.373379\pi$
$37$	238713.	0.774767	0.387383	+	0.921919i	$0.373379\pi$
$38$	362585.	1.07193
$39$	59319.0	0.160128
$40$	−164162.	−0.405566
$41$	42730.0	0.0968254	0.0484127	−	0.998827i	$-0.484584\pi$
$41$	42730.0	0.0968254	0.0484127	+	0.998827i	$0.484584\pi$
$42$	−74088.0	−0.154303
$43$	−819703.	−1.57223	−0.786117	−	0.618078i	$-0.787912\pi$
$43$	−819703.	−1.57223	−0.786117	+	0.618078i	$0.787912\pi$
$44$	−71103.2	−0.125836
$45$	233738.	0.382371
$46$	42032.8	0.0636702
$47$	−684959.	−0.962325	−0.481163	−	0.876631i	$-0.659785\pi$
$47$	−684959.	−0.962325	−0.481163	+	0.876631i	$0.659785\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	−197419.	−0.223354
$51$	103304.	0.109049
$52$	140608.	0.138675
$53$	−1.18203e6	−1.09059	−0.545295	−	0.838244i	$-0.683583\pi$
$53$	−1.18203e6	−1.09059	−0.545295	+	0.838244i	$0.683583\pi$
$54$	−157464.	−0.136083
$55$	−356214.	−0.288696
$56$	−175616.	−0.133631
$57$	−1.22372e6	−0.875229
$58$	−201306.	−0.135475
$59$	−2.74036e6	−1.73710	−0.868550	−	0.495601i	$-0.834948\pi$
$59$	−2.74036e6	−1.73710	−0.868550	+	0.495601i	$0.834948\pi$
$60$	554045.	0.331143
$61$	1.94158e6	1.09522	0.547608	−	0.836735i	$-0.315539\pi$
$61$	1.94158e6	1.09522	0.547608	+	0.836735i	$0.315539\pi$
$62$	1.78733e6	0.952432
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	704420.	0.318152
$66$	239973.	0.102745
$67$	−1.62868e6	−0.661568	−0.330784	−	0.943706i	$-0.607313\pi$
$67$	−1.62868e6	−0.661568	−0.330784	+	0.943706i	$0.607313\pi$
$68$	244870.	0.0944396
$69$	−141861.	−0.0519865
$70$	−879803.	−0.306579
$71$	−1.88558e6	−0.625231	−0.312615	−	0.949880i	$-0.601205\pi$
$71$	−1.88558e6	−0.625231	−0.312615	+	0.949880i	$0.601205\pi$
$72$	−373248.	−0.117851
$73$	−5.69023e6	−1.71199	−0.855993	−	0.516988i	$-0.827053\pi$
$73$	−5.69023e6	−1.71199	−0.855993	+	0.516988i	$0.827053\pi$
$74$	−1.90971e6	−0.547843
$75$	666288.	0.182367
$76$	−2.90068e6	−0.757970
$77$	−381069.	−0.0951231
$78$	−474552.	−0.113228
$79$	−4.76272e6	−1.08683	−0.543413	−	0.839465i	$-0.682868\pi$
$79$	−4.76272e6	−1.08683	−0.543413	+	0.839465i	$0.682868\pi$
$80$	1.31329e6	0.286778
$81$	531441.	0.111111
$82$	−341840.	−0.0684659
$83$	96910.3	0.0186036	0.00930179	−	0.999957i	$-0.497039\pi$
$83$	96910.3	0.0186036	0.00930179	+	0.999957i	$0.497039\pi$
$84$	592704.	0.109109
$85$	1.22675e6	0.216666
$86$	6.55763e6	1.11174
$87$	679407.	0.110615
$88$	568826.	0.0889795
$89$	−485878.	−0.0730571	−0.0365285	−	0.999333i	$-0.511630\pi$
$89$	−485878.	−0.0730571	−0.0365285	+	0.999333i	$0.511630\pi$
$90$	−1.86990e6	−0.270377
$91$	753571.	0.104828
$92$	−336262.	−0.0450216
$93$	−6.03224e6	−0.777657
$94$	5.47967e6	0.680467
$95$	−1.45319e7	−1.73896
$96$	−884736.	−0.102062
$97$	1.65671e7	1.84309	0.921544	−	0.388274i	$-0.126928\pi$
$97$	1.65671e7	1.84309	0.921544	+	0.388274i	$0.126928\pi$
$98$	−941192.	−0.101015
$99$	−809910.	−0.0838907
$100$	1.57935e6	0.157935
$101$	5.23826e6	0.505897	0.252948	−	0.967480i	$-0.418600\pi$
$101$	5.23826e6	0.505897	0.252948	+	0.967480i	$0.418600\pi$
$102$	−826436.	−0.0771096
$103$	5.76806e6	0.520115	0.260058	−	0.965593i	$-0.416258\pi$
$103$	5.76806e6	0.520115	0.260058	+	0.965593i	$0.416258\pi$
$104$	−1.12486e6	−0.0980581
$105$	2.96934e6	0.250321
$106$	9.45622e6	0.771164
$107$	3.10359e6	0.244918	0.122459	−	0.992474i	$-0.460922\pi$
$107$	3.10359e6	0.244918	0.122459	+	0.992474i	$0.460922\pi$
$108$	1.25971e6	0.0962250
$109$	−7.81668e6	−0.578136	−0.289068	−	0.957309i	$-0.593345\pi$
$109$	−7.81668e6	−0.578136	−0.289068	+	0.957309i	$0.593345\pi$
$110$	2.84971e6	0.204139
$111$	6.44526e6	0.447312
$112$	1.40493e6	0.0944911
$113$	1.46151e7	0.952857	0.476429	−	0.879213i	$-0.341931\pi$
$113$	1.46151e7	0.952857	0.476429	+	0.879213i	$0.341931\pi$
$114$	9.78980e6	0.618880
$115$	−1.68461e6	−0.103290
$116$	1.61045e6	0.0957951
$117$	1.60161e6	0.0924500
$118$	2.19228e7	1.22832
$119$	1.31235e6	0.0713896
$120$	−4.43236e6	−0.234154
$121$	−1.82529e7	−0.936661
$122$	−1.55326e7	−0.774435
$123$	1.15371e6	0.0559022
$124$	−1.42986e7	−0.673471
$125$	−1.71368e7	−0.784775
$126$	−2.00038e6	−0.0890871
$127$	−5.89808e6	−0.255504	−0.127752	−	0.991806i	$-0.540776\pi$
$127$	−5.89808e6	−0.255504	−0.127752	+	0.991806i	$0.540776\pi$
$128$	−2.09715e6	−0.0883883
$129$	−2.21320e7	−0.907730
$130$	−5.63536e6	−0.224967
$131$	−2.33015e6	−0.0905597	−0.0452799	−	0.998974i	$-0.514418\pi$
$131$	−2.33015e6	−0.0905597	−0.0452799	+	0.998974i	$0.514418\pi$
$132$	−1.91979e6	−0.0726515
$133$	−1.55458e7	−0.572972
$134$	1.30295e7	0.467799
$135$	6.31092e6	0.220762
$136$	−1.95896e6	−0.0667789
$137$	2.87952e7	0.956750	0.478375	−	0.878156i	$-0.341226\pi$
$137$	2.87952e7	0.956750	0.478375	+	0.878156i	$0.341226\pi$
$138$	1.13489e6	0.0367600
$139$	−1.11937e7	−0.353527	−0.176764	−	0.984253i	$-0.556563\pi$
$139$	−1.11937e7	−0.353527	−0.176764	+	0.984253i	$0.556563\pi$
$140$	7.03843e6	0.216784
$141$	−1.84939e7	−0.555599
$142$	1.50846e7	0.442105
$143$	−2.44084e6	−0.0698013
$144$	2.98598e6	0.0833333
$145$	8.06804e6	0.219776
$146$	4.55219e7	1.21056
$147$	3.17652e6	0.0824786
$148$	1.52777e7	0.387383
$149$	5.31071e7	1.31523	0.657614	−	0.753355i	$-0.271566\pi$
$149$	5.31071e7	1.31523	0.657614	+	0.753355i	$0.271566\pi$
$150$	−5.33030e6	−0.128953
$151$	5.15820e7	1.21921	0.609605	−	0.792705i	$-0.291328\pi$
$151$	5.15820e7	1.21921	0.609605	+	0.792705i	$0.291328\pi$
$152$	2.32054e7	0.535966
$153$	2.78922e6	0.0629597
$154$	3.04855e6	0.0672622
$155$	−7.16335e7	−1.54510
$156$	3.79642e6	0.0800641
$157$	5.18036e7	1.06834	0.534172	−	0.845376i	$-0.320624\pi$
$157$	5.18036e7	1.06834	0.534172	+	0.845376i	$0.320624\pi$
$158$	3.81017e7	0.768502
$159$	−3.19147e7	−0.629653
$160$	−1.05063e7	−0.202783
$161$	−1.80216e6	−0.0340331
$162$	−4.25153e6	−0.0785674
$163$	−6.58655e7	−1.19125	−0.595623	−	0.803264i	$-0.703095\pi$
$163$	−6.58655e7	−1.19125	−0.595623	+	0.803264i	$0.703095\pi$
$164$	2.73472e6	0.0484127
$165$	−9.61778e6	−0.166679
$166$	−775282.	−0.0131547
$167$	2.02037e6	0.0335678	0.0167839	−	0.999859i	$-0.494657\pi$
$167$	2.02037e6	0.0335678	0.0167839	+	0.999859i	$0.494657\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−9.81402e6	−0.153206
$171$	−3.30406e7	−0.505314
$172$	−5.24610e7	−0.786117
$173$	4.20671e7	0.617705	0.308853	−	0.951110i	$-0.400055\pi$
$173$	4.20671e7	0.617705	0.308853	+	0.951110i	$0.400055\pi$
$174$	−5.43526e6	−0.0782164
$175$	8.46432e6	0.119388
$176$	−4.55061e6	−0.0629180
$177$	−7.39896e7	−1.00292
$178$	3.88702e6	0.0516591
$179$	4.98549e7	0.649713	0.324857	−	0.945763i	$-0.394684\pi$
$179$	4.98549e7	0.649713	0.324857	+	0.945763i	$0.394684\pi$
$180$	1.49592e7	0.191186
$181$	−9.66132e6	−0.121105	−0.0605524	−	0.998165i	$-0.519286\pi$
$181$	−9.66132e6	−0.121105	−0.0605524	+	0.998165i	$0.519286\pi$
$182$	−6.02857e6	−0.0741249
$183$	5.24225e7	0.632323
$184$	2.69010e6	0.0318351
$185$	7.65382e7	0.888745
$186$	4.82579e7	0.549887
$187$	−4.25074e6	−0.0475356
$188$	−4.38374e7	−0.481163
$189$	6.75127e6	0.0727393
$190$	1.16255e8	1.22963
$191$	−1.10454e7	−0.114700	−0.0573501	−	0.998354i	$-0.518265\pi$
$191$	−1.10454e7	−0.114700	−0.0573501	+	0.998354i	$0.518265\pi$
$192$	7.07789e6	0.0721688
$193$	−1.39943e8	−1.40121	−0.700603	−	0.713551i	$-0.747086\pi$
$193$	−1.39943e8	−1.40121	−0.700603	+	0.713551i	$0.747086\pi$
$194$	−1.32537e8	−1.30326
$195$	1.90193e7	0.183685
$196$	7.52954e6	0.0714286
$197$	−1.77512e7	−0.165423	−0.0827117	−	0.996574i	$-0.526358\pi$
$197$	−1.77512e7	−0.165423	−0.0827117	+	0.996574i	$0.526358\pi$
$198$	6.47928e6	0.0593197
$199$	1.70775e8	1.53617	0.768083	−	0.640351i	$-0.221211\pi$
$199$	1.70775e8	1.53617	0.768083	+	0.640351i	$0.221211\pi$
$200$	−1.26348e7	−0.111677
$201$	−4.39744e7	−0.381957
$202$	−4.19060e7	−0.357723
$203$	8.63099e6	0.0724143
$204$	6.61149e6	0.0545247
$205$	1.37004e7	0.111070
$206$	−4.61445e7	−0.367777
$207$	−3.83024e6	−0.0300144
$208$	8.99891e6	0.0693375
$209$	5.03535e7	0.381520
$210$	−2.37547e7	−0.177003
$211$	7.64383e7	0.560173	0.280086	−	0.959975i	$-0.409637\pi$
$211$	7.64383e7	0.560173	0.280086	+	0.959975i	$0.409637\pi$
$212$	−7.56497e7	−0.545295
$213$	−5.09106e7	−0.360977
$214$	−2.48287e7	−0.173183
$215$	−2.62820e8	−1.80353
$216$	−1.00777e7	−0.0680414
$217$	−7.66318e7	−0.509096
$218$	6.25335e7	0.408804
$219$	−1.53636e8	−0.988415
$220$	−2.27977e7	−0.144348
$221$	8.40592e6	0.0523857
$222$	−5.15621e7	−0.316297
$223$	−4.83280e7	−0.291831	−0.145916	−	0.989297i	$-0.546613\pi$
$223$	−4.83280e7	−0.291831	−0.145916	+	0.989297i	$0.546613\pi$
$224$	−1.12394e7	−0.0668153
$225$	1.79898e7	0.105290
$226$	−1.16921e8	−0.673772
$227$	−2.37950e7	−0.135019	−0.0675094	−	0.997719i	$-0.521505\pi$
$227$	−2.37950e7	−0.135019	−0.0675094	+	0.997719i	$0.521505\pi$
$228$	−7.83184e7	−0.437614
$229$	−3.44969e7	−0.189826	−0.0949132	−	0.995486i	$-0.530257\pi$
$229$	−3.44969e7	−0.189826	−0.0949132	+	0.995486i	$0.530257\pi$
$230$	1.34769e7	0.0730369
$231$	−1.02889e7	−0.0549193
$232$	−1.28836e7	−0.0677374
$233$	−1.55458e8	−0.805130	−0.402565	−	0.915391i	$-0.631881\pi$
$233$	−1.55458e8	−0.805130	−0.402565	+	0.915391i	$0.631881\pi$
$234$	−1.28129e7	−0.0653720
$235$	−2.19617e8	−1.10390
$236$	−1.75383e8	−0.868550
$237$	−1.28593e8	−0.627479
$238$	−1.04988e7	−0.0504801
$239$	1.34685e8	0.638158	0.319079	−	0.947728i	$-0.396626\pi$
$239$	1.34685e8	0.638158	0.319079	+	0.947728i	$0.396626\pi$
$240$	3.54589e7	0.165572
$241$	1.98178e8	0.912004	0.456002	−	0.889979i	$-0.349281\pi$
$241$	1.98178e8	0.912004	0.456002	+	0.889979i	$0.349281\pi$
$242$	1.46023e8	0.662319
$243$	1.43489e7	0.0641500
$244$	1.24261e8	0.547608
$245$	3.77216e7	0.163873
$246$	−9.22968e6	−0.0395288
$247$	−9.95749e7	−0.420446
$248$	1.14389e8	0.476216
$249$	2.61658e6	0.0107408
$250$	1.37095e8	0.554920
$251$	−4.24782e8	−1.69554	−0.847770	−	0.530364i	$-0.822055\pi$
$251$	−4.24782e8	−1.69554	−0.847770	+	0.530364i	$0.822055\pi$
$252$	1.60030e7	0.0629941
$253$	5.83724e6	0.0226614
$254$	4.71846e7	0.180669
$255$	3.31223e7	0.125092
$256$	1.67772e7	0.0625000
$257$	−4.34494e8	−1.59668	−0.798340	−	0.602207i	$-0.794288\pi$
$257$	−4.34494e8	−1.59668	−0.798340	+	0.602207i	$0.794288\pi$
$258$	1.77056e8	0.641862
$259$	8.18787e7	0.292834
$260$	4.50829e7	0.159076
$261$	1.83440e7	0.0638634
$262$	1.86412e7	0.0640354
$263$	−5.57596e8	−1.89006	−0.945028	−	0.326989i	$-0.893966\pi$
$263$	−5.57596e8	−1.89006	−0.945028	+	0.326989i	$0.893966\pi$
$264$	1.53583e7	0.0513723
$265$	−3.78991e8	−1.25103
$266$	1.24367e8	0.405152
$267$	−1.31187e7	−0.0421795
$268$	−1.04236e8	−0.330784
$269$	1.32138e7	0.0413899	0.0206950	−	0.999786i	$-0.493412\pi$
$269$	1.32138e7	0.0413899	0.0206950	+	0.999786i	$0.493412\pi$
$270$	−5.04874e7	−0.156102
$271$	2.73603e8	0.835080	0.417540	−	0.908659i	$-0.362892\pi$
$271$	2.73603e8	0.835080	0.417540	+	0.908659i	$0.362892\pi$
$272$	1.56717e7	0.0472198
$273$	2.03464e7	0.0605228
$274$	−2.30362e8	−0.676525
$275$	−2.74162e7	−0.0794956
$276$	−9.07909e6	−0.0259932
$277$	1.43058e8	0.404420	0.202210	−	0.979342i	$-0.435188\pi$
$277$	1.43058e8	0.404420	0.202210	+	0.979342i	$0.435188\pi$
$278$	8.95498e7	0.249982
$279$	−1.62870e8	−0.448981
$280$	−5.63074e7	−0.153290
$281$	3.10101e8	0.833740	0.416870	−	0.908966i	$-0.363127\pi$
$281$	3.10101e8	0.833740	0.416870	+	0.908966i	$0.363127\pi$
$282$	1.47951e8	0.392868
$283$	1.89157e8	0.496100	0.248050	−	0.968747i	$-0.420210\pi$
$283$	1.89157e8	0.496100	0.248050	+	0.968747i	$0.420210\pi$
$284$	−1.20677e8	−0.312615
$285$	−3.92360e8	−1.00399
$286$	1.95267e7	0.0493570
$287$	1.46564e7	0.0365966
$288$	−2.38879e7	−0.0589256
$289$	−3.95700e8	−0.964325
$290$	−6.45443e7	−0.155405
$291$	4.47312e8	1.06411
$292$	−3.64175e8	−0.855993
$293$	−5.03406e8	−1.16918	−0.584591	−	0.811328i	$-0.698745\pi$
$293$	−5.03406e8	−1.16918	−0.584591	+	0.811328i	$0.698745\pi$
$294$	−2.54122e7	−0.0583212
$295$	−8.78635e8	−1.99265
$296$	−1.22221e8	−0.273921
$297$	−2.18676e7	−0.0484343
$298$	−4.24857e8	−0.930007
$299$	−1.15433e7	−0.0249735
$300$	4.26424e7	0.0911837
$301$	−2.81158e8	−0.594248
$302$	−4.12656e8	−0.862112
$303$	1.41433e8	0.292080
$304$	−1.85644e8	−0.378985
$305$	6.22523e8	1.25634
$306$	−2.23138e7	−0.0445193
$307$	−3.81400e7	−0.0752309	−0.0376155	−	0.999292i	$-0.511976\pi$
$307$	−3.81400e7	−0.0752309	−0.0376155	+	0.999292i	$0.511976\pi$
$308$	−2.43884e7	−0.0475616
$309$	1.55738e8	0.300289
$310$	5.73068e8	1.09255
$311$	−2.60068e8	−0.490259	−0.245129	−	0.969490i	$-0.578830\pi$
$311$	−2.60068e8	−0.490259	−0.245129	+	0.969490i	$0.578830\pi$
$312$	−3.03713e7	−0.0566139
$313$	−8.66820e7	−0.159780	−0.0798902	−	0.996804i	$-0.525457\pi$
$313$	−8.66820e7	−0.159780	−0.0798902	+	0.996804i	$0.525457\pi$
$314$	−4.14429e8	−0.755433
$315$	8.01721e7	0.144523
$316$	−3.04814e8	−0.543413
$317$	−5.94023e8	−1.04736	−0.523680	−	0.851915i	$-0.675441\pi$
$317$	−5.94023e8	−1.04736	−0.523680	+	0.851915i	$0.675441\pi$
$318$	2.55318e8	0.445232
$319$	−2.79560e7	−0.0482179
$320$	8.40507e7	0.143389
$321$	8.37968e7	0.141403
$322$	1.44173e7	0.0240651
$323$	−1.73410e8	−0.286330
$324$	3.40122e7	0.0555556
$325$	5.42161e7	0.0876065
$326$	5.26924e8	0.842339
$327$	−2.11050e8	−0.333787
$328$	−2.18777e7	−0.0342329
$329$	−2.34941e8	−0.363725
$330$	7.69422e7	0.117860
$331$	2.52756e8	0.383092	0.191546	−	0.981484i	$-0.438650\pi$
$331$	2.52756e8	0.383092	0.191546	+	0.981484i	$0.438650\pi$
$332$	6.20226e6	0.00930179
$333$	1.74022e8	0.258256
$334$	−1.61630e7	−0.0237360
$335$	−5.22201e8	−0.758894
$336$	3.79331e7	0.0545545
$337$	6.26185e8	0.891246	0.445623	−	0.895221i	$-0.352982\pi$
$337$	6.26185e8	0.891246	0.445623	+	0.895221i	$0.352982\pi$
$338$	−3.86145e7	−0.0543928
$339$	3.94608e8	0.550132
$340$	7.85121e7	0.108333
$341$	2.48213e8	0.338988
$342$	2.64324e8	0.357311
$343$	4.03536e7	0.0539949
$344$	4.19688e8	0.555869
$345$	−4.54845e7	−0.0596344
$346$	−3.36537e8	−0.436783
$347$	−1.39552e9	−1.79301	−0.896504	−	0.443036i	$-0.853901\pi$
$347$	−1.39552e9	−1.79301	−0.896504	+	0.443036i	$0.853901\pi$
$348$	4.34821e7	0.0553073
$349$	−4.92681e8	−0.620407	−0.310204	−	0.950670i	$-0.600397\pi$
$349$	−4.92681e8	−0.620407	−0.310204	+	0.950670i	$0.600397\pi$
$350$	−6.77146e7	−0.0844197
$351$	4.32436e7	0.0533761
$352$	3.64049e7	0.0444898
$353$	−1.01808e9	−1.23189	−0.615945	−	0.787789i	$-0.711226\pi$
$353$	−1.01808e9	−1.23189	−0.615945	+	0.787789i	$0.711226\pi$
$354$	5.91917e8	0.709168
$355$	−6.04569e8	−0.717211
$356$	−3.10962e7	−0.0365285
$357$	3.54334e7	0.0412168
$358$	−3.98839e8	−0.459417
$359$	3.21767e8	0.367038	0.183519	−	0.983016i	$-0.441251\pi$
$359$	3.21767e8	0.367038	0.183519	+	0.983016i	$0.441251\pi$
$360$	−1.19674e8	−0.135189
$361$	1.16031e9	1.29808
$362$	7.72906e7	0.0856341
$363$	−4.92828e8	−0.540782
$364$	4.82285e7	0.0524142
$365$	−1.82445e9	−1.96384
$366$	−4.19380e8	−0.447120
$367$	7.56662e8	0.799044	0.399522	−	0.916724i	$-0.369176\pi$
$367$	7.56662e8	0.799044	0.399522	+	0.916724i	$0.369176\pi$
$368$	−2.15208e7	−0.0225108
$369$	3.11502e7	0.0322751
$370$	−6.12306e8	−0.628438
$371$	−4.05435e8	−0.412205
$372$	−3.86063e8	−0.388829
$373$	5.74749e8	0.573452	0.286726	−	0.958013i	$-0.407433\pi$
$373$	5.74749e8	0.573452	0.286726	+	0.958013i	$0.407433\pi$
$374$	3.40059e7	0.0336128
$375$	−4.62694e8	−0.453090
$376$	3.50699e8	0.340233
$377$	5.52836e7	0.0531376
$378$	−5.40102e7	−0.0514344
$379$	−7.64701e8	−0.721530	−0.360765	−	0.932657i	$-0.617484\pi$
$379$	−7.64701e8	−0.721530	−0.360765	+	0.932657i	$0.617484\pi$
$380$	−9.30039e8	−0.869478
$381$	−1.59248e8	−0.147515
$382$	8.83631e7	0.0811053
$383$	−1.58252e9	−1.43931	−0.719654	−	0.694333i	$-0.755699\pi$
$383$	−1.58252e9	−1.43931	−0.719654	+	0.694333i	$0.755699\pi$
$384$	−5.66231e7	−0.0510310
$385$	−1.22181e8	−0.109117
$386$	1.11955e9	0.990802
$387$	−5.97564e8	−0.524078
$388$	1.06030e9	0.921544
$389$	−2.49156e8	−0.214608	−0.107304	−	0.994226i	$-0.534222\pi$
$389$	−2.49156e8	−0.214608	−0.107304	+	0.994226i	$0.534222\pi$
$390$	−1.52155e8	−0.129885
$391$	−2.01027e7	−0.0170073
$392$	−6.02363e7	−0.0505076
$393$	−6.29142e7	−0.0522847
$394$	1.42010e8	0.116972
$395$	−1.52706e9	−1.24671
$396$	−5.18343e7	−0.0419453
$397$	2.05599e9	1.64913	0.824564	−	0.565768i	$-0.191420\pi$
$397$	2.05599e9	1.64913	0.824564	+	0.565768i	$0.191420\pi$
$398$	−1.36620e9	−1.08623
$399$	−4.19737e8	−0.330805
$400$	1.01078e8	0.0789674
$401$	−1.69943e9	−1.31613	−0.658063	−	0.752963i	$-0.728624\pi$
$401$	−1.69943e9	−1.31613	−0.658063	+	0.752963i	$0.728624\pi$
$402$	3.51795e8	0.270084
$403$	−4.90845e8	−0.373574
$404$	3.35248e8	0.252948
$405$	1.70395e8	0.127457
$406$	−6.90479e7	−0.0512046
$407$	−2.65208e8	−0.194987
$408$	−5.28919e7	−0.0385548
$409$	−3.61692e8	−0.261401	−0.130701	−	0.991422i	$-0.541723\pi$
$409$	−3.61692e8	−0.261401	−0.130701	+	0.991422i	$0.541723\pi$
$410$	−1.09603e8	−0.0785381
$411$	7.77471e8	0.552380
$412$	3.69156e8	0.260058
$413$	−9.39942e8	−0.656562
$414$	3.06419e7	0.0212234
$415$	3.10721e7	0.0213404
$416$	−7.19913e7	−0.0490290
$417$	−3.02231e8	−0.204109
$418$	−4.02828e8	−0.269775
$419$	−9.48233e8	−0.629747	−0.314874	−	0.949134i	$-0.601962\pi$
$419$	−9.48233e8	−0.629747	−0.314874	+	0.949134i	$0.601962\pi$
$420$	1.90038e8	0.125160
$421$	2.30131e9	1.50310	0.751550	−	0.659676i	$-0.229307\pi$
$421$	2.30131e9	1.50310	0.751550	+	0.659676i	$0.229307\pi$
$422$	−6.11506e8	−0.396102
$423$	−4.99335e8	−0.320775
$424$	6.05198e8	0.385582
$425$	9.44177e7	0.0596612
$426$	4.07285e8	0.255249
$427$	6.65960e8	0.413953
$428$	1.98630e8	0.122459
$429$	−6.59027e7	−0.0402998
$430$	2.10256e9	1.27529
$431$	−1.26527e9	−0.761223	−0.380611	−	0.924735i	$-0.624286\pi$
$431$	−1.26527e9	−0.761223	−0.380611	+	0.924735i	$0.624286\pi$
$432$	8.06216e7	0.0481125
$433$	−2.32918e9	−1.37878	−0.689390	−	0.724390i	$-0.742121\pi$
$433$	−2.32918e9	−1.37878	−0.689390	+	0.724390i	$0.742121\pi$
$434$	6.13054e8	0.359985
$435$	2.17837e8	0.126888
$436$	−5.00268e8	−0.289068
$437$	2.38132e8	0.136500
$438$	1.22909e9	0.698915
$439$	2.40266e8	0.135539	0.0677697	−	0.997701i	$-0.478412\pi$
$439$	2.40266e8	0.135539	0.0677697	+	0.997701i	$0.478412\pi$
$440$	1.82382e8	0.102070
$441$	8.57661e7	0.0476190
$442$	−6.72474e7	−0.0370423
$443$	9.37083e8	0.512112	0.256056	−	0.966662i	$-0.417577\pi$
$443$	9.37083e8	0.512112	0.256056	+	0.966662i	$0.417577\pi$
$444$	4.12497e8	0.223656
$445$	−1.55786e8	−0.0838047
$446$	3.86624e8	0.206356
$447$	1.43389e9	0.759347
$448$	8.99154e7	0.0472456
$449$	1.14102e9	0.594884	0.297442	−	0.954740i	$-0.403867\pi$
$449$	1.14102e9	0.594884	0.297442	+	0.954740i	$0.403867\pi$
$450$	−1.43918e8	−0.0744512
$451$	−4.74725e7	−0.0243682
$452$	9.35368e8	0.476429
$453$	1.39271e9	0.703911
$454$	1.90360e8	0.0954728
$455$	2.41616e8	0.120250
$456$	6.26547e8	0.309440
$457$	9.47498e8	0.464378	0.232189	−	0.972671i	$-0.425411\pi$
$457$	9.47498e8	0.464378	0.232189	+	0.972671i	$0.425411\pi$
$458$	2.75976e8	0.134227
$459$	7.53090e7	0.0363498
$460$	−1.07815e8	−0.0516449
$461$	−6.50894e8	−0.309426	−0.154713	−	0.987959i	$-0.549445\pi$
$461$	−6.50894e8	−0.309426	−0.154713	+	0.987959i	$0.549445\pi$
$462$	8.23109e7	0.0388338
$463$	2.35034e9	1.10052	0.550258	−	0.834994i	$-0.314529\pi$
$463$	2.35034e9	1.10052	0.550258	+	0.834994i	$0.314529\pi$
$464$	1.03069e8	0.0478976
$465$	−1.93410e9	−0.892061
$466$	1.24366e9	0.569313
$467$	1.45048e9	0.659028	0.329514	−	0.944151i	$-0.393115\pi$
$467$	1.45048e9	0.659028	0.329514	+	0.944151i	$0.393115\pi$
$468$	1.02503e8	0.0462250
$469$	−5.58638e8	−0.250049
$470$	1.75694e9	0.780573
$471$	1.39870e9	0.616808
$472$	1.40306e9	0.614158
$473$	9.10681e8	0.395687
$474$	1.02875e9	0.443695
$475$	−1.11845e9	−0.478840
$476$	8.39904e7	0.0356948
$477$	−8.61698e8	−0.363530
$478$	−1.07748e9	−0.451246
$479$	4.18056e8	0.173804	0.0869022	−	0.996217i	$-0.472303\pi$
$479$	4.18056e8	0.173804	0.0869022	+	0.996217i	$0.472303\pi$
$480$	−2.83671e8	−0.117077
$481$	5.24454e8	0.214882
$482$	−1.58543e9	−0.644884
$483$	−4.86582e7	−0.0196490
$484$	−1.16818e9	−0.468331
$485$	5.31189e9	2.11423
$486$	−1.14791e8	−0.0453609
$487$	8.19072e8	0.321345	0.160672	−	0.987008i	$-0.448634\pi$
$487$	8.19072e8	0.321345	0.160672	+	0.987008i	$0.448634\pi$
$488$	−9.94087e8	−0.387217
$489$	−1.77837e9	−0.687767
$490$	−3.01773e8	−0.115876
$491$	−7.02054e7	−0.0267661	−0.0133831	−	0.999910i	$-0.504260\pi$
$491$	−7.02054e7	−0.0267661	−0.0133831	+	0.999910i	$0.504260\pi$
$492$	7.38374e7	0.0279511
$493$	9.62768e7	0.0361874
$494$	7.96599e8	0.297300
$495$	−2.59680e8	−0.0962322
$496$	−9.15113e8	−0.336735
$497$	−6.46753e8	−0.236315
$498$	−2.09326e7	−0.00759488
$499$	2.19043e8	0.0789184	0.0394592	−	0.999221i	$-0.487436\pi$
$499$	2.19043e8	0.0789184	0.0394592	+	0.999221i	$0.487436\pi$
$500$	−1.09676e9	−0.392388
$501$	5.45500e7	0.0193804
$502$	3.39826e9	1.19893
$503$	1.81072e9	0.634400	0.317200	−	0.948359i	$-0.397257\pi$
$503$	1.81072e9	0.634400	0.317200	+	0.948359i	$0.397257\pi$
$504$	−1.28024e8	−0.0445435
$505$	1.67953e9	0.580321
$506$	−4.66980e7	−0.0160240
$507$	1.30324e8	0.0444116
$508$	−3.77477e8	−0.127752
$509$	−5.30736e9	−1.78388	−0.891941	−	0.452153i	$-0.850656\pi$
$509$	−5.30736e9	−1.78388	−0.891941	+	0.452153i	$0.850656\pi$
$510$	−2.64978e8	−0.0884535
$511$	−1.95175e9	−0.647070
$512$	−1.34218e8	−0.0441942
$513$	−8.92095e8	−0.291743
$514$	3.47595e9	1.12902
$515$	1.84940e9	0.596632
$516$	−1.41645e9	−0.453865
$517$	7.60981e8	0.242190
$518$	−6.55030e8	−0.207065
$519$	1.13581e9	0.356632
$520$	−3.60663e8	−0.112484
$521$	6.31200e9	1.95540	0.977699	−	0.210012i	$-0.0673504\pi$
$521$	6.31200e9	1.95540	0.977699	+	0.210012i	$0.0673504\pi$
$522$	−1.46752e8	−0.0451583
$523$	1.84810e9	0.564896	0.282448	−	0.959283i	$-0.408853\pi$
$523$	1.84810e9	0.564896	0.282448	+	0.959283i	$0.408853\pi$
$524$	−1.49130e8	−0.0452799
$525$	2.28537e8	0.0689284
$526$	4.46077e9	1.33647
$527$	−8.54811e8	−0.254409
$528$	−1.22866e8	−0.0363257
$529$	−3.37722e9	−0.991892
$530$	3.03193e9	0.884613
$531$	−1.99772e9	−0.579033
$532$	−9.94933e8	−0.286486
$533$	9.38778e7	0.0268545
$534$	1.04950e8	0.0298254
$535$	9.95097e8	0.280949
$536$	8.33885e8	0.233900
$537$	1.34608e9	0.375112
$538$	−1.05710e8	−0.0292671
$539$	−1.30707e8	−0.0359532
$540$	4.03899e8	0.110381
$541$	6.08437e9	1.65206	0.826029	−	0.563628i	$-0.190595\pi$
$541$	6.08437e9	1.65206	0.826029	+	0.563628i	$0.190595\pi$
$542$	−2.18882e9	−0.590491
$543$	−2.60856e8	−0.0699199
$544$	−1.25373e8	−0.0333894
$545$	−2.50625e9	−0.663187
$546$	−1.62771e8	−0.0427960
$547$	2.54355e9	0.664483	0.332242	−	0.943194i	$-0.392195\pi$
$547$	2.54355e9	0.664483	0.332242	+	0.943194i	$0.392195\pi$
$548$	1.84290e9	0.478375
$549$	1.41541e9	0.365072
$550$	2.19330e8	0.0562119
$551$	−1.14048e9	−0.290439
$552$	7.26327e7	0.0183800
$553$	−1.63361e9	−0.410782
$554$	−1.14446e9	−0.285968
$555$	2.06653e9	0.513117
$556$	−7.16399e8	−0.176764
$557$	7.37210e9	1.80758	0.903791	−	0.427974i	$-0.140773\pi$
$557$	7.37210e9	1.80758	0.903791	+	0.427974i	$0.140773\pi$
$558$	1.30296e9	0.317477
$559$	−1.80089e9	−0.436059
$560$	4.50459e8	0.108392
$561$	−1.14770e8	−0.0274447
$562$	−2.48081e9	−0.589544
$563$	4.40072e9	1.03931	0.519654	−	0.854377i	$-0.326061\pi$
$563$	4.40072e9	1.03931	0.519654	+	0.854377i	$0.326061\pi$
$564$	−1.18361e9	−0.277799
$565$	4.68602e9	1.09304
$566$	−1.51325e9	−0.350796
$567$	1.82284e8	0.0419961
$568$	9.65416e8	0.221052
$569$	−8.50460e9	−1.93536	−0.967678	−	0.252189i	$-0.918849\pi$
$569$	−8.50460e9	−1.93536	−0.967678	+	0.252189i	$0.918849\pi$
$570$	3.13888e9	0.709926
$571$	−1.25169e9	−0.281365	−0.140683	−	0.990055i	$-0.544930\pi$
$571$	−1.25169e9	−0.281365	−0.140683	+	0.990055i	$0.544930\pi$
$572$	−1.56214e8	−0.0349006
$573$	−2.98226e8	−0.0662222
$574$	−1.17251e8	−0.0258777
$575$	−1.29657e8	−0.0284419
$576$	1.91103e8	0.0416667
$577$	−3.77454e9	−0.817991	−0.408996	−	0.912536i	$-0.634121\pi$
$577$	−3.77454e9	−0.817991	−0.408996	+	0.912536i	$0.634121\pi$
$578$	3.16560e9	0.681881
$579$	−3.77847e9	−0.808987
$580$	5.16354e8	0.109888
$581$	3.32402e7	0.00703149
$582$	−3.57850e9	−0.752438
$583$	1.31322e9	0.274471
$584$	2.91340e9	0.605278
$585$	5.13522e8	0.106051
$586$	4.02725e9	0.826736
$587$	−2.36405e9	−0.482419	−0.241209	−	0.970473i	$-0.577544\pi$
$587$	−2.36405e9	−0.482419	−0.241209	+	0.970473i	$0.577544\pi$
$588$	2.03297e8	0.0412393
$589$	1.01259e10	2.04188
$590$	7.02908e9	1.40902
$591$	−4.79283e8	−0.0955072
$592$	9.77770e8	0.193692
$593$	1.33822e9	0.263533	0.131767	−	0.991281i	$-0.457935\pi$
$593$	1.33822e9	0.263533	0.131767	+	0.991281i	$0.457935\pi$
$594$	1.74941e8	0.0342482
$595$	4.20776e8	0.0818920
$596$	3.39886e9	0.657614
$597$	4.61092e9	0.886906
$598$	9.23461e7	0.0176589
$599$	3.05277e9	0.580364	0.290182	−	0.956971i	$-0.406284\pi$
$599$	3.05277e9	0.580364	0.290182	+	0.956971i	$0.406284\pi$
$600$	−3.41139e8	−0.0644766
$601$	−1.83491e9	−0.344789	−0.172394	−	0.985028i	$-0.555150\pi$
$601$	−1.83491e9	−0.344789	−0.172394	+	0.985028i	$0.555150\pi$
$602$	2.24927e9	0.420197
$603$	−1.18731e9	−0.220523
$604$	3.30125e9	0.609605
$605$	−5.85238e9	−1.07446
$606$	−1.13146e9	−0.206531
$607$	−1.77447e9	−0.322039	−0.161019	−	0.986951i	$-0.551478\pi$
$607$	−1.77447e9	−0.322039	−0.161019	+	0.986951i	$0.551478\pi$
$608$	1.48515e9	0.267983
$609$	2.33037e8	0.0418084
$610$	−4.98019e9	−0.888365
$611$	−1.50485e9	−0.266901
$612$	1.78510e8	0.0314799
$613$	−3.51920e9	−0.617066	−0.308533	−	0.951214i	$-0.599838\pi$
$613$	−3.51920e9	−0.617066	−0.308533	+	0.951214i	$0.599838\pi$
$614$	3.05120e8	0.0531963
$615$	3.69912e8	0.0641261
$616$	1.95107e8	0.0336311
$617$	1.64076e9	0.281220	0.140610	−	0.990065i	$-0.455094\pi$
$617$	1.64076e9	0.281220	0.140610	+	0.990065i	$0.455094\pi$
$618$	−1.24590e9	−0.212336
$619$	−1.78142e9	−0.301890	−0.150945	−	0.988542i	$-0.548232\pi$
$619$	−1.78142e9	−0.301890	−0.150945	+	0.988542i	$0.548232\pi$
$620$	−4.58454e9	−0.772548
$621$	−1.03416e8	−0.0173288
$622$	2.08054e9	0.346665
$623$	−1.66656e8	−0.0276130
$624$	2.42971e8	0.0400320
$625$	−7.42246e9	−1.21610
$626$	6.93456e8	0.112982
$627$	1.35954e9	0.220271
$628$	3.31543e9	0.534172
$629$	9.13340e8	0.146337
$630$	−6.41377e8	−0.102193
$631$	1.15408e8	0.0182867	0.00914334	−	0.999958i	$-0.497090\pi$
$631$	1.15408e8	0.0182867	0.00914334	+	0.999958i	$0.497090\pi$
$632$	2.43851e9	0.384251
$633$	2.06383e9	0.323416
$634$	4.75218e9	0.740595
$635$	−1.89109e9	−0.293092
$636$	−2.04254e9	−0.314826
$637$	2.58475e8	0.0396214
$638$	2.23648e8	0.0340952
$639$	−1.37459e9	−0.208410
$640$	−6.72406e8	−0.101391
$641$	−4.00292e9	−0.600308	−0.300154	−	0.953891i	$-0.597038\pi$
$641$	−4.00292e9	−0.600308	−0.300154	+	0.953891i	$0.597038\pi$
$642$	−6.70375e8	−0.0999874
$643$	7.66717e9	1.13736	0.568679	−	0.822560i	$-0.307455\pi$
$643$	7.66717e9	1.13736	0.568679	+	0.822560i	$0.307455\pi$
$644$	−1.15338e8	−0.0170166
$645$	−7.09614e9	−1.04127
$646$	1.38728e9	0.202466
$647$	−1.11982e10	−1.62548	−0.812741	−	0.582624i	$-0.802026\pi$
$647$	−1.11982e10	−1.62548	−0.812741	+	0.582624i	$0.802026\pi$
$648$	−2.72098e8	−0.0392837
$649$	3.04450e9	0.437180
$650$	−4.33729e8	−0.0619471
$651$	−2.06906e9	−0.293927
$652$	−4.21540e9	−0.595623
$653$	1.05903e10	1.48837	0.744185	−	0.667973i	$-0.232838\pi$
$653$	1.05903e10	1.48837	0.744185	+	0.667973i	$0.232838\pi$
$654$	1.68840e9	0.236023
$655$	−7.47113e8	−0.103882
$656$	1.75022e8	0.0242063
$657$	−4.14818e9	−0.570662
$658$	1.87953e9	0.257192
$659$	1.06277e10	1.44658	0.723288	−	0.690547i	$-0.242630\pi$
$659$	1.06277e10	1.44658	0.723288	+	0.690547i	$0.242630\pi$
$660$	−6.15538e8	−0.0833395
$661$	−6.29528e9	−0.847832	−0.423916	−	0.905702i	$-0.639345\pi$
$661$	−6.29528e9	−0.847832	−0.423916	+	0.905702i	$0.639345\pi$
$662$	−2.02205e9	−0.270887
$663$	2.26960e8	0.0302449
$664$	−4.96181e7	−0.00657736
$665$	−4.98443e9	−0.657264
$666$	−1.39218e9	−0.182614
$667$	−1.32210e8	−0.0172514
$668$	1.29304e8	0.0167839
$669$	−1.30486e9	−0.168489
$670$	4.17761e9	0.536619
$671$	−2.15707e9	−0.275635
$672$	−3.03464e8	−0.0385758
$673$	−5.77604e9	−0.730428	−0.365214	−	0.930924i	$-0.619004\pi$
$673$	−5.77604e9	−0.730428	−0.365214	+	0.930924i	$0.619004\pi$
$674$	−5.00948e9	−0.630206
$675$	4.85724e8	0.0607892
$676$	3.08916e8	0.0384615
$677$	−9.02566e9	−1.11794	−0.558970	−	0.829188i	$-0.688803\pi$
$677$	−9.02566e9	−1.11794	−0.558970	+	0.829188i	$0.688803\pi$
$678$	−3.15687e9	−0.389002
$679$	5.68252e9	0.696622
$680$	−6.28097e8	−0.0766030
$681$	−6.42464e8	−0.0779532
$682$	−1.98570e9	−0.239700
$683$	−7.49694e9	−0.900351	−0.450175	−	0.892940i	$-0.648639\pi$
$683$	−7.49694e9	−0.900351	−0.450175	+	0.892940i	$0.648639\pi$
$684$	−2.11460e9	−0.252657
$685$	9.23256e9	1.09750
$686$	−3.22829e8	−0.0381802
$687$	−9.31418e8	−0.109596
$688$	−3.35750e9	−0.393058
$689$	−2.59691e9	−0.302475
$690$	3.63876e8	0.0421679
$691$	7.10232e9	0.818893	0.409446	−	0.912334i	$-0.365722\pi$
$691$	7.10232e9	0.818893	0.409446	+	0.912334i	$0.365722\pi$
$692$	2.69229e9	0.308853
$693$	−2.77799e8	−0.0317077
$694$	1.11641e10	1.26785
$695$	−3.58902e9	−0.405536
$696$	−3.47856e8	−0.0391082
$697$	1.63489e8	0.0182883
$698$	3.94145e9	0.438694
$699$	−4.19735e9	−0.464842
$700$	5.41717e8	0.0596938
$701$	−1.51925e10	−1.66577	−0.832886	−	0.553445i	$-0.813313\pi$
$701$	−1.51925e10	−1.66577	−0.832886	+	0.553445i	$0.813313\pi$
$702$	−3.45948e8	−0.0377426
$703$	−1.08192e10	−1.17450
$704$	−2.91239e8	−0.0314590
$705$	−5.92966e9	−0.637335
$706$	8.14467e9	0.871078
$707$	1.79672e9	0.191211
$708$	−4.73533e9	−0.501458
$709$	1.65464e9	0.174358	0.0871790	−	0.996193i	$-0.472215\pi$
$709$	1.65464e9	0.174358	0.0871790	+	0.996193i	$0.472215\pi$
$710$	4.83655e9	0.507144
$711$	−3.47202e9	−0.362275
$712$	2.48770e8	0.0258296
$713$	1.17385e9	0.121283
$714$	−2.83467e8	−0.0291447
$715$	−7.82602e8	−0.0800700
$716$	3.19071e9	0.324857
$717$	3.63651e9	0.368441
$718$	−2.57414e9	−0.259535
$719$	1.32039e10	1.32480	0.662399	−	0.749151i	$-0.269538\pi$
$719$	1.32039e10	1.32480	0.662399	+	0.749151i	$0.269538\pi$
$720$	9.57390e8	0.0955928
$721$	1.97845e9	0.196585
$722$	−9.28251e9	−0.917879
$723$	5.35082e9	0.526546
$724$	−6.18325e8	−0.0605524
$725$	6.20961e8	0.0605176
$726$	3.94262e9	0.382390
$727$	−1.52218e10	−1.46925	−0.734626	−	0.678473i	$-0.762642\pi$
$727$	−1.52218e10	−1.46925	−0.734626	+	0.678473i	$0.762642\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	1.45956e10	1.38865
$731$	−3.13626e9	−0.296962
$732$	3.35504e9	0.316162
$733$	3.32757e9	0.312078	0.156039	−	0.987751i	$-0.450127\pi$
$733$	3.32757e9	0.312078	0.156039	+	0.987751i	$0.450127\pi$
$734$	−6.05330e9	−0.565009
$735$	1.01848e9	0.0946123
$736$	1.72166e8	0.0159175
$737$	1.80945e9	0.166498
$738$	−2.49201e8	−0.0228220
$739$	−8.46389e9	−0.771462	−0.385731	−	0.922611i	$-0.626051\pi$
$739$	−8.46389e9	−0.771462	−0.385731	+	0.922611i	$0.626051\pi$
$740$	4.89845e9	0.444373
$741$	−2.68852e9	−0.242745
$742$	3.24348e9	0.291473
$743$	5.37695e9	0.480922	0.240461	−	0.970659i	$-0.422701\pi$
$743$	5.37695e9	0.480922	0.240461	+	0.970659i	$0.422701\pi$
$744$	3.08851e9	0.274943
$745$	1.70276e10	1.50872
$746$	−4.59799e9	−0.405492
$747$	7.06476e7	0.00620119
$748$	−2.72047e8	−0.0237678
$749$	1.06453e9	0.0925703
$750$	3.70155e9	0.320383
$751$	2.09510e10	1.80495	0.902473	−	0.430747i	$-0.141750\pi$
$751$	2.09510e10	1.80495	0.902473	+	0.430747i	$0.141750\pi$
$752$	−2.80559e9	−0.240581
$753$	−1.14691e10	−0.978921
$754$	−4.42269e8	−0.0375739
$755$	1.65386e10	1.39857
$756$	4.32081e8	0.0363696
$757$	−1.41362e9	−0.118439	−0.0592197	−	0.998245i	$-0.518861\pi$
$757$	−1.41362e9	−0.118439	−0.0592197	+	0.998245i	$0.518861\pi$
$758$	6.11760e9	0.510199
$759$	1.57606e8	0.0130835
$760$	7.44031e9	0.614814
$761$	−2.03319e10	−1.67237	−0.836184	−	0.548449i	$-0.815219\pi$
$761$	−2.03319e10	−1.67237	−0.836184	+	0.548449i	$0.815219\pi$
$762$	1.27399e9	0.104309
$763$	−2.68112e9	−0.218515
$764$	−7.06905e8	−0.0573501
$765$	8.94302e8	0.0722220
$766$	1.26602e10	1.01774
$767$	−6.02056e9	−0.481785
$768$	4.52985e8	0.0360844
$769$	−5.34010e9	−0.423455	−0.211728	−	0.977329i	$-0.567909\pi$
$769$	−5.34010e9	−0.423455	−0.211728	+	0.977329i	$0.567909\pi$
$770$	9.77451e8	0.0771574
$771$	−1.17313e10	−0.921844
$772$	−8.95638e9	−0.700603
$773$	3.06137e7	0.00238389	0.00119195	−	0.999999i	$-0.499621\pi$
$773$	3.06137e7	0.00238389	0.00119195	+	0.999999i	$0.499621\pi$
$774$	4.78051e9	0.370579
$775$	−5.51331e9	−0.425458
$776$	−8.48237e9	−0.651630
$777$	2.21073e9	0.169068
$778$	1.99324e9	0.151751
$779$	−1.93666e9	−0.146782
$780$	1.21724e9	0.0918426
$781$	2.09485e9	0.157353
$782$	1.60821e8	0.0120260
$783$	4.95288e8	0.0368716
$784$	4.81890e8	0.0357143
$785$	1.66097e10	1.22551
$786$	5.03313e8	0.0369709
$787$	−2.31371e10	−1.69199	−0.845993	−	0.533194i	$-0.820992\pi$
$787$	−2.31371e10	−1.69199	−0.845993	+	0.533194i	$0.820992\pi$
$788$	−1.13608e9	−0.0827117
$789$	−1.50551e10	−1.09122
$790$	1.22165e10	0.881559
$791$	5.01299e9	0.360146
$792$	4.14674e8	0.0296598
$793$	4.26564e9	0.303758
$794$	−1.64479e10	−1.16611
$795$	−1.02328e10	−0.722283
$796$	1.09296e10	0.768083
$797$	1.30643e9	0.0914075	0.0457037	−	0.998955i	$-0.485447\pi$
$797$	1.30643e9	0.0914075	0.0457037	+	0.998955i	$0.485447\pi$
$798$	3.35790e9	0.233915
$799$	−2.62071e9	−0.181763
$800$	−8.08626e8	−0.0558384
$801$	−3.54205e8	−0.0243524
$802$	1.35954e10	0.930642
$803$	6.32178e9	0.430859
$804$	−2.81436e9	−0.190978
$805$	−5.77822e8	−0.0390399
$806$	3.92676e9	0.264157
$807$	3.56772e8	0.0238965
$808$	−2.68199e9	−0.178862
$809$	−3.52571e9	−0.234114	−0.117057	−	0.993125i	$-0.537346\pi$
$809$	−3.52571e9	−0.234114	−0.117057	+	0.993125i	$0.537346\pi$
$810$	−1.36316e9	−0.0901258
$811$	−9.55800e9	−0.629208	−0.314604	−	0.949223i	$-0.601872\pi$
$811$	−9.55800e9	−0.629208	−0.314604	+	0.949223i	$0.601872\pi$
$812$	5.52383e8	0.0362072
$813$	7.38728e9	0.482134
$814$	2.12166e9	0.137877
$815$	−2.11183e10	−1.36650
$816$	4.23135e8	0.0272624
$817$	3.71515e10	2.38341
$818$	2.89354e9	0.184839
$819$	5.49353e8	0.0349428
$820$	8.76827e8	0.0555349
$821$	1.56683e10	0.988144	0.494072	−	0.869421i	$-0.335508\pi$
$821$	1.56683e10	0.988144	0.494072	+	0.869421i	$0.335508\pi$
$822$	−6.21977e9	−0.390592
$823$	3.18921e10	1.99427	0.997135	−	0.0756368i	$-0.0240990\pi$
$823$	3.18921e10	1.99427	0.997135	+	0.0756368i	$0.0240990\pi$
$824$	−2.95325e9	−0.183889
$825$	−7.40238e8	−0.0458968
$826$	7.51954e9	0.464260
$827$	−2.60377e10	−1.60079	−0.800395	−	0.599473i	$-0.795377\pi$
$827$	−2.60377e10	−1.60079	−0.800395	+	0.599473i	$0.795377\pi$
$828$	−2.45135e8	−0.0150072
$829$	1.92272e10	1.17213	0.586064	−	0.810265i	$-0.300677\pi$
$829$	1.92272e10	1.17213	0.586064	+	0.810265i	$0.300677\pi$
$830$	−2.48577e8	−0.0150900
$831$	3.86256e9	0.233492
$832$	5.75930e8	0.0346688
$833$	4.50136e8	0.0269827
$834$	2.41785e9	0.144327
$835$	6.47787e8	0.0385061
$836$	3.22262e9	0.190760
$837$	−4.39750e9	−0.259219
$838$	7.58587e9	0.445298
$839$	1.73816e10	1.01607	0.508033	−	0.861337i	$-0.330373\pi$
$839$	1.73816e10	1.01607	0.508033	+	0.861337i	$0.330373\pi$
$840$	−1.52030e9	−0.0885017
$841$	−1.66167e10	−0.963293
$842$	−1.84105e10	−1.06285
$843$	8.37272e9	0.481360
$844$	4.89205e9	0.280086
$845$	1.54761e9	0.0882395
$846$	3.99468e9	0.226822
$847$	−6.26074e9	−0.354025
$848$	−4.84158e9	−0.272648
$849$	5.10723e9	0.286424
$850$	−7.55341e8	−0.0421869
$851$	−1.25422e9	−0.0697625
$852$	−3.25828e9	−0.180489
$853$	6.38256e9	0.352106	0.176053	−	0.984381i	$-0.443667\pi$
$853$	6.38256e9	0.352106	0.176053	+	0.984381i	$0.443667\pi$
$854$	−5.32768e9	−0.292709
$855$	−1.05937e10	−0.579652
$856$	−1.58904e9	−0.0865916
$857$	−1.63505e9	−0.0887355	−0.0443678	−	0.999015i	$-0.514127\pi$
$857$	−1.63505e9	−0.0887355	−0.0443678	+	0.999015i	$0.514127\pi$
$858$	5.27222e8	0.0284963
$859$	2.60092e10	1.40008	0.700038	−	0.714106i	$-0.253167\pi$
$859$	2.60092e10	1.40008	0.700038	+	0.714106i	$0.253167\pi$
$860$	−1.68205e10	−0.901765
$861$	3.95722e8	0.0211290
$862$	1.01221e10	0.538266
$863$	−1.30487e10	−0.691084	−0.345542	−	0.938403i	$-0.612305\pi$
$863$	−1.30487e10	−0.691084	−0.345542	+	0.938403i	$0.612305\pi$
$864$	−6.44973e8	−0.0340207
$865$	1.34879e10	0.708578
$866$	1.86334e10	0.974945
$867$	−1.06839e10	−0.556753
$868$	−4.90443e9	−0.254548
$869$	5.29132e9	0.273524
$870$	−1.74270e9	−0.0897231
$871$	−3.57822e9	−0.183486
$872$	4.00214e9	0.204402
$873$	1.20774e10	0.614363
$874$	−1.90506e9	−0.0965202
$875$	−5.87793e9	−0.296617
$876$	−9.83272e9	−0.494208
$877$	−2.14559e10	−1.07411	−0.537055	−	0.843547i	$-0.680463\pi$
$877$	−2.14559e10	−1.07411	−0.537055	+	0.843547i	$0.680463\pi$
$878$	−1.92212e9	−0.0958409
$879$	−1.35920e10	−0.675028
$880$	−1.45905e9	−0.0721741
$881$	−3.01082e10	−1.48344	−0.741720	−	0.670710i	$-0.765989\pi$
$881$	−3.01082e10	−1.48344	−0.741720	+	0.670710i	$0.765989\pi$
$882$	−6.86129e8	−0.0336718
$883$	−1.58149e10	−0.773043	−0.386521	−	0.922280i	$-0.626323\pi$
$883$	−1.58149e10	−0.773043	−0.386521	+	0.922280i	$0.626323\pi$
$884$	5.37979e8	0.0261928
$885$	−2.37231e10	−1.15046
$886$	−7.49667e9	−0.362118
$887$	1.11270e10	0.535361	0.267681	−	0.963508i	$-0.413743\pi$
$887$	1.11270e10	0.535361	0.267681	+	0.963508i	$0.413743\pi$
$888$	−3.29998e9	−0.158149
$889$	−2.02304e9	−0.0965714
$890$	1.24629e9	0.0592589
$891$	−5.90425e8	−0.0279636
$892$	−3.09299e9	−0.145916
$893$	3.10445e10	1.45883
$894$	−1.14711e10	−0.536940
$895$	1.59849e10	0.745295
$896$	−7.19323e8	−0.0334077
$897$	−3.11668e8	−0.0144185
$898$	−9.12818e9	−0.420646
$899$	−5.62187e9	−0.258061
$900$	1.15135e9	0.0526450
$901$	−4.52254e9	−0.205990
$902$	3.79780e8	0.0172309
$903$	−7.59127e9	−0.343090
$904$	−7.48294e9	−0.336886
$905$	−3.09769e9	−0.138921
$906$	−1.11417e10	−0.497740
$907$	−1.75118e10	−0.779303	−0.389652	−	0.920962i	$-0.627405\pi$
$907$	−1.75118e10	−0.779303	−0.389652	+	0.920962i	$0.627405\pi$
$908$	−1.52288e9	−0.0675094
$909$	3.81869e9	0.168632
$910$	−1.93293e9	−0.0850297
$911$	8.91656e9	0.390736	0.195368	−	0.980730i	$-0.437410\pi$
$911$	8.91656e9	0.390736	0.195368	+	0.980730i	$0.437410\pi$
$912$	−5.01238e9	−0.218807
$913$	−1.07666e8	−0.00468200
$914$	−7.57998e9	−0.328365
$915$	1.68081e10	0.725347
$916$	−2.20780e9	−0.0949132
$917$	−7.99243e8	−0.0342284
$918$	−6.02472e8	−0.0257032
$919$	3.42415e10	1.45529	0.727643	−	0.685956i	$-0.240616\pi$
$919$	3.42415e10	1.45529	0.727643	+	0.685956i	$0.240616\pi$
$920$	8.62521e8	0.0365185
$921$	−1.02978e9	−0.0434346
$922$	5.20715e9	0.218797
$923$	−4.14261e9	−0.173408
$924$	−6.58487e8	−0.0274597
$925$	5.89081e9	0.244725
$926$	−1.88027e10	−0.778183
$927$	4.20492e9	0.173372
$928$	−8.24549e8	−0.0338687
$929$	−4.09072e10	−1.67396	−0.836980	−	0.547234i	$-0.815681\pi$
$929$	−4.09072e10	−1.67396	−0.836980	+	0.547234i	$0.815681\pi$
$930$	1.54728e10	0.630782
$931$	−5.33222e9	−0.216563
$932$	−9.94928e9	−0.402565
$933$	−7.02183e9	−0.283051
$934$	−1.16039e10	−0.466003
$935$	−1.36291e9	−0.0545288
$936$	−8.20026e8	−0.0326860
$937$	−3.49842e10	−1.38926	−0.694629	−	0.719368i	$-0.744432\pi$
$937$	−3.49842e10	−1.38926	−0.694629	+	0.719368i	$0.744432\pi$
$938$	4.46910e9	0.176812
$939$	−2.34041e9	−0.0922493
$940$	−1.40555e10	−0.551948
$941$	−4.53033e10	−1.77242	−0.886209	−	0.463286i	$-0.846670\pi$
$941$	−4.53033e10	−1.77242	−0.886209	+	0.463286i	$0.846670\pi$
$942$	−1.11896e10	−0.436149
$943$	−2.24508e8	−0.00871847
$944$	−1.12245e10	−0.434275
$945$	2.16465e9	0.0834402
$946$	−7.28545e9	−0.279793
$947$	1.56611e10	0.599234	0.299617	−	0.954059i	$-0.403141\pi$
$947$	1.56611e10	0.599234	0.299617	+	0.954059i	$0.403141\pi$
$948$	−8.22998e9	−0.313740
$949$	−1.25014e10	−0.474819
$950$	8.94763e9	0.338591
$951$	−1.60386e10	−0.604693
$952$	−6.71923e8	−0.0252400
$953$	8.65764e9	0.324022	0.162011	−	0.986789i	$-0.448202\pi$
$953$	8.65764e9	0.324022	0.162011	+	0.986789i	$0.448202\pi$
$954$	6.89358e9	0.257055
$955$	−3.54146e9	−0.131574
$956$	8.61987e9	0.319079
$957$	−7.54813e8	−0.0278386
$958$	−3.34445e9	−0.122898
$959$	9.87677e9	0.361618
$960$	2.26937e9	0.0827858
$961$	2.24022e10	0.814252
$962$	−4.19563e9	−0.151944
$963$	2.26251e9	0.0816393
$964$	1.26834e10	0.456002
$965$	−4.48698e10	−1.60734
$966$	3.89266e8	0.0138940
$967$	1.98037e10	0.704293	0.352146	−	0.935945i	$-0.385452\pi$
$967$	1.98037e10	0.704293	0.352146	+	0.935945i	$0.385452\pi$
$968$	9.34547e9	0.331160
$969$	−4.68208e9	−0.165313
$970$	−4.24951e10	−1.49499
$971$	2.81016e10	0.985061	0.492530	−	0.870295i	$-0.336072\pi$
$971$	2.81016e10	0.985061	0.492530	+	0.870295i	$0.336072\pi$
$972$	9.18330e8	0.0320750
$973$	−3.83945e9	−0.133621
$974$	−6.55258e9	−0.227225
$975$	1.46383e9	0.0505796
$976$	7.95269e9	0.273804
$977$	−2.41616e10	−0.828885	−0.414443	−	0.910075i	$-0.636023\pi$
$977$	−2.41616e10	−0.828885	−0.414443	+	0.910075i	$0.636023\pi$
$978$	1.42270e10	0.486324
$979$	5.39805e8	0.0183864
$980$	2.41418e9	0.0819367
$981$	−5.69836e9	−0.192712
$982$	5.61643e8	0.0189265
$983$	−3.43109e9	−0.115211	−0.0576057	−	0.998339i	$-0.518347\pi$
$983$	−3.43109e9	−0.115211	−0.0576057	+	0.998339i	$0.518347\pi$
$984$	−5.90699e8	−0.0197644
$985$	−5.69154e9	−0.189759
$986$	−7.70214e8	−0.0255884
$987$	−6.34340e9	−0.209997
$988$	−6.37279e9	−0.210223
$989$	4.30680e9	0.141569
$990$	2.07744e9	0.0680464
$991$	−2.49715e10	−0.815054	−0.407527	−	0.913193i	$-0.633609\pi$
$991$	−2.49715e10	−0.815054	−0.407527	+	0.913193i	$0.633609\pi$
$992$	7.32090e9	0.238108
$993$	6.82440e9	0.221178
$994$	5.17403e9	0.167100
$995$	5.47552e10	1.76216
$996$	1.67461e8	0.00537039
$997$	1.13671e10	0.363258	0.181629	−	0.983367i	$-0.441863\pi$
$997$	1.13671e10	0.363258	0.181629	+	0.983367i	$0.441863\pi$
$998$	−1.75235e9	−0.0558037
$999$	4.69860e9	0.149104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.i.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.i.1.5	✓	5	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +320.628 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +320.628 q^{5} -216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2565.02 q^{10} -1110.99 q^{11} +1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +8656.96 q^{15} +4096.00 q^{16} +3826.09 q^{17} -5832.00 q^{18} -45323.1 q^{19} +20520.2 q^{20} +9261.00 q^{21} +8887.91 q^{22} -5254.10 q^{23} -13824.0 q^{24} +24677.3 q^{25} -17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} +25163.2 q^{29} -69255.7 q^{30} -223416. q^{31} -32768.0 q^{32} -29996.7 q^{33} -30608.7 q^{34} +109975. q^{35} +46656.0 q^{36} +238713. q^{37} +362585. q^{38} +59319.0 q^{39} -164162. q^{40} +42730.0 q^{41} -74088.0 q^{42} -819703. q^{43} -71103.2 q^{44} +233738. q^{45} +42032.8 q^{46} -684959. q^{47} +110592. q^{48} +117649. q^{49} -197419. q^{50} +103304. q^{51} +140608. q^{52} -1.18203e6 q^{53} -157464. q^{54} -356214. q^{55} -175616. q^{56} -1.22372e6 q^{57} -201306. q^{58} -2.74036e6 q^{59} +554045. q^{60} +1.94158e6 q^{61} +1.78733e6 q^{62} +250047. q^{63} +262144. q^{64} +704420. q^{65} +239973. q^{66} -1.62868e6 q^{67} +244870. q^{68} -141861. q^{69} -879803. q^{70} -1.88558e6 q^{71} -373248. q^{72} -5.69023e6 q^{73} -1.90971e6 q^{74} +666288. q^{75} -2.90068e6 q^{76} -381069. q^{77} -474552. q^{78} -4.76272e6 q^{79} +1.31329e6 q^{80} +531441. q^{81} -341840. q^{82} +96910.3 q^{83} +592704. q^{84} +1.22675e6 q^{85} +6.55763e6 q^{86} +679407. q^{87} +568826. q^{88} -485878. q^{89} -1.86990e6 q^{90} +753571. q^{91} -336262. q^{92} -6.03224e6 q^{93} +5.47967e6 q^{94} -1.45319e7 q^{95} -884736. q^{96} +1.65671e7 q^{97} -941192. q^{98} -809910. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} - 340 q^{5} - 1080 q^{6} + 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 - 340 * q^5 - 1080 * q^6 + 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} - 340 q^{5} - 1080 q^{6} + 1715 q^{7} - 2560 q^{8} + 3645 q^{9} + 2720 q^{10} - 1303 q^{11} + 8640 q^{12} + 10985 q^{13} - 13720 q^{14} - 9180 q^{15} + 20480 q^{16} - 4247 q^{17} - 29160 q^{18} - 16984 q^{19} - 21760 q^{20} + 46305 q^{21} + 10424 q^{22} - 78072 q^{23} - 69120 q^{24} - 79555 q^{25} - 87880 q^{26} + 98415 q^{27} + 109760 q^{28} - 213142 q^{29} + 73440 q^{30} - 186027 q^{31} - 163840 q^{32} - 35181 q^{33} + 33976 q^{34} - 116620 q^{35} + 233280 q^{36} + 101025 q^{37} + 135872 q^{38} + 296595 q^{39} + 174080 q^{40} - 23976 q^{41} - 370440 q^{42} - 55528 q^{43} - 83392 q^{44} - 247860 q^{45} + 624576 q^{46} - 985981 q^{47} + 552960 q^{48} + 588245 q^{49} + 636440 q^{50} - 114669 q^{51} + 703040 q^{52} - 1891657 q^{53} - 787320 q^{54} + 1746955 q^{55} - 878080 q^{56} - 458568 q^{57} + 1705136 q^{58} - 2802208 q^{59} - 587520 q^{60} + 1140591 q^{61} + 1488216 q^{62} + 1250235 q^{63} + 1310720 q^{64} - 746980 q^{65} + 281448 q^{66} + 265168 q^{67} - 271808 q^{68} - 2107944 q^{69} + 932960 q^{70} - 4483276 q^{71} - 1866240 q^{72} - 2350578 q^{73} - 808200 q^{74} - 2147985 q^{75} - 1086976 q^{76} - 446929 q^{77} - 2372760 q^{78} - 4079889 q^{79} - 1392640 q^{80} + 2657205 q^{81} + 191808 q^{82} - 8731571 q^{83} + 2963520 q^{84} - 1715895 q^{85} + 444224 q^{86} - 5754834 q^{87} + 667136 q^{88} - 20077879 q^{89} + 1982880 q^{90} + 3767855 q^{91} - 4996608 q^{92} - 5022729 q^{93} + 7887848 q^{94} - 11580740 q^{95} - 4423680 q^{96} + 3780209 q^{97} - 4705960 q^{98} - 949887 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 - 340 * q^5 - 1080 * q^6 + 1715 * q^7 - 2560 * q^8 + 3645 * q^9 + 2720 * q^10 - 1303 * q^11 + 8640 * q^12 + 10985 * q^13 - 13720 * q^14 - 9180 * q^15 + 20480 * q^16 - 4247 * q^17 - 29160 * q^18 - 16984 * q^19 - 21760 * q^20 + 46305 * q^21 + 10424 * q^22 - 78072 * q^23 - 69120 * q^24 - 79555 * q^25 - 87880 * q^26 + 98415 * q^27 + 109760 * q^28 - 213142 * q^29 + 73440 * q^30 - 186027 * q^31 - 163840 * q^32 - 35181 * q^33 + 33976 * q^34 - 116620 * q^35 + 233280 * q^36 + 101025 * q^37 + 135872 * q^38 + 296595 * q^39 + 174080 * q^40 - 23976 * q^41 - 370440 * q^42 - 55528 * q^43 - 83392 * q^44 - 247860 * q^45 + 624576 * q^46 - 985981 * q^47 + 552960 * q^48 + 588245 * q^49 + 636440 * q^50 - 114669 * q^51 + 703040 * q^52 - 1891657 * q^53 - 787320 * q^54 + 1746955 * q^55 - 878080 * q^56 - 458568 * q^57 + 1705136 * q^58 - 2802208 * q^59 - 587520 * q^60 + 1140591 * q^61 + 1488216 * q^62 + 1250235 * q^63 + 1310720 * q^64 - 746980 * q^65 + 281448 * q^66 + 265168 * q^67 - 271808 * q^68 - 2107944 * q^69 + 932960 * q^70 - 4483276 * q^71 - 1866240 * q^72 - 2350578 * q^73 - 808200 * q^74 - 2147985 * q^75 - 1086976 * q^76 - 446929 * q^77 - 2372760 * q^78 - 4079889 * q^79 - 1392640 * q^80 + 2657205 * q^81 + 191808 * q^82 - 8731571 * q^83 + 2963520 * q^84 - 1715895 * q^85 + 444224 * q^86 - 5754834 * q^87 + 667136 * q^88 - 20077879 * q^89 + 1982880 * q^90 + 3767855 * q^91 - 4996608 * q^92 - 5022729 * q^93 + 7887848 * q^94 - 11580740 * q^95 - 4423680 * q^96 + 3780209 * q^97 - 4705960 * q^98 - 949887 * q^99

Introduction

L-functions

Modular forms

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