LMFDB - Embedded newform 15.8.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,8,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("15.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	15.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:	$4.68577538226$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{601}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 150 $ x^2 - x - 150
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$12.7577$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.75765 q^{2} +27.0000 q^{3} -51.3036 q^{4} +125.000 q^{5} -236.457 q^{6} +1338.43 q^{7} +1570.28 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.75765 q^{2} +27.0000 q^{3} -51.3036 q^{4} +125.000 q^{5} -236.457 q^{6} +1338.43 q^{7} +1570.28 q^{8} +729.000 q^{9} -1094.71 q^{10} +7411.55 q^{11} -1385.20 q^{12} -14594.3 q^{13} -11721.5 q^{14} +3375.00 q^{15} -7185.09 q^{16} +14414.7 q^{17} -6384.33 q^{18} +409.730 q^{19} -6412.94 q^{20} +36137.6 q^{21} -64907.8 q^{22} -17913.8 q^{23} +42397.5 q^{24} +15625.0 q^{25} +127812. q^{26} +19683.0 q^{27} -68666.1 q^{28} -10705.4 q^{29} -29557.1 q^{30} +178691. q^{31} -138071. q^{32} +200112. q^{33} -126239. q^{34} +167304. q^{35} -37400.3 q^{36} -427962. q^{37} -3588.27 q^{38} -394046. q^{39} +196285. q^{40} +53370.3 q^{41} -316480. q^{42} +89349.4 q^{43} -380239. q^{44} +91125.0 q^{45} +156883. q^{46} -161273. q^{47} -193997. q^{48} +967848. q^{49} -136838. q^{50} +389197. q^{51} +748740. q^{52} -121833. q^{53} -172377. q^{54} +926444. q^{55} +2.10170e6 q^{56} +11062.7 q^{57} +93754.2 q^{58} -1.69229e6 q^{59} -173149. q^{60} -1.23924e6 q^{61} -1.56491e6 q^{62} +975714. q^{63} +2.12887e6 q^{64} -1.82429e6 q^{65} -1.75251e6 q^{66} -944402. q^{67} -739526. q^{68} -483674. q^{69} -1.46519e6 q^{70} -936943. q^{71} +1.14473e6 q^{72} -5.49712e6 q^{73} +3.74794e6 q^{74} +421875. q^{75} -21020.6 q^{76} +9.91983e6 q^{77} +3.45092e6 q^{78} -3.29987e6 q^{79} -898136. q^{80} +531441. q^{81} -467399. q^{82} -4.16260e6 q^{83} -1.85399e6 q^{84} +1.80184e6 q^{85} -782491. q^{86} -289046. q^{87} +1.16382e7 q^{88} +8.50941e6 q^{89} -798041. q^{90} -1.95334e7 q^{91} +919044. q^{92} +4.82465e6 q^{93} +1.41237e6 q^{94} +51216.2 q^{95} -3.72792e6 q^{96} +6.61583e6 q^{97} -8.47607e6 q^{98} +5.40302e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 7 q^{2} + 54 q^{3} + 69 q^{4} + 250 q^{5} + 189 q^{6} + 1304 q^{7} + 1449 q^{8} + 1458 q^{9}+O(q^{10}) $ 2 * q + 7 * q^2 + 54 * q^3 + 69 * q^4 + 250 * q^5 + 189 * q^6 + 1304 * q^7 + 1449 * q^8 + 1458 * q^9	\( 2 q + 7 q^{2} + 54 q^{3} + 69 q^{4} + 250 q^{5} + 189 q^{6} + 1304 q^{7} + 1449 q^{8} + 1458 q^{9} + 875 q^{10} + 3448 q^{11} + 1863 q^{12} - 8988 q^{13} - 12264 q^{14} + 6750 q^{15} - 24495 q^{16} - 5492 q^{17} + 5103 q^{18} - 49584 q^{19} + 8625 q^{20} + 35208 q^{21} - 127364 q^{22} + 91848 q^{23} + 39123 q^{24} + 31250 q^{25} + 216154 q^{26} + 39366 q^{27} - 72808 q^{28} + 181772 q^{29} + 23625 q^{30} + 304232 q^{31} - 395311 q^{32} + 93096 q^{33} - 439922 q^{34} + 163000 q^{35} + 50301 q^{36} - 502316 q^{37} - 791372 q^{38} - 242676 q^{39} + 181125 q^{40} + 631172 q^{41} - 331128 q^{42} + 353640 q^{43} - 857068 q^{44} + 182250 q^{45} + 1886472 q^{46} - 467480 q^{47} - 661365 q^{48} + 145490 q^{49} + 109375 q^{50} - 148284 q^{51} + 1423198 q^{52} - 568052 q^{53} + 137781 q^{54} + 431000 q^{55} + 2105880 q^{56} - 1338768 q^{57} + 3126746 q^{58} + 287224 q^{59} + 232875 q^{60} - 2514180 q^{61} + 413328 q^{62} + 950616 q^{63} + 291041 q^{64} - 1123500 q^{65} - 3438828 q^{66} - 5073832 q^{67} - 3134374 q^{68} + 2479896 q^{69} - 1533000 q^{70} - 3748816 q^{71} + 1056321 q^{72} - 1477212 q^{73} + 2576306 q^{74} + 843750 q^{75} - 6035444 q^{76} + 10056288 q^{77} + 5836158 q^{78} - 4627720 q^{79} - 3061875 q^{80} + 1062882 q^{81} + 8637398 q^{82} - 6072936 q^{83} - 1965816 q^{84} - 686500 q^{85} + 3382108 q^{86} + 4907844 q^{87} + 12118884 q^{88} + 16516356 q^{89} + 637875 q^{90} - 19726448 q^{91} + 14123784 q^{92} + 8214264 q^{93} - 3412736 q^{94} - 6198000 q^{95} - 10673397 q^{96} + 2723428 q^{97} - 21434497 q^{98} + 2513592 q^{99}+O(q^{100}) \) 2 * q + 7 * q^2 + 54 * q^3 + 69 * q^4 + 250 * q^5 + 189 * q^6 + 1304 * q^7 + 1449 * q^8 + 1458 * q^9 + 875 * q^10 + 3448 * q^11 + 1863 * q^12 - 8988 * q^13 - 12264 * q^14 + 6750 * q^15 - 24495 * q^16 - 5492 * q^17 + 5103 * q^18 - 49584 * q^19 + 8625 * q^20 + 35208 * q^21 - 127364 * q^22 + 91848 * q^23 + 39123 * q^24 + 31250 * q^25 + 216154 * q^26 + 39366 * q^27 - 72808 * q^28 + 181772 * q^29 + 23625 * q^30 + 304232 * q^31 - 395311 * q^32 + 93096 * q^33 - 439922 * q^34 + 163000 * q^35 + 50301 * q^36 - 502316 * q^37 - 791372 * q^38 - 242676 * q^39 + 181125 * q^40 + 631172 * q^41 - 331128 * q^42 + 353640 * q^43 - 857068 * q^44 + 182250 * q^45 + 1886472 * q^46 - 467480 * q^47 - 661365 * q^48 + 145490 * q^49 + 109375 * q^50 - 148284 * q^51 + 1423198 * q^52 - 568052 * q^53 + 137781 * q^54 + 431000 * q^55 + 2105880 * q^56 - 1338768 * q^57 + 3126746 * q^58 + 287224 * q^59 + 232875 * q^60 - 2514180 * q^61 + 413328 * q^62 + 950616 * q^63 + 291041 * q^64 - 1123500 * q^65 - 3438828 * q^66 - 5073832 * q^67 - 3134374 * q^68 + 2479896 * q^69 - 1533000 * q^70 - 3748816 * q^71 + 1056321 * q^72 - 1477212 * q^73 + 2576306 * q^74 + 843750 * q^75 - 6035444 * q^76 + 10056288 * q^77 + 5836158 * q^78 - 4627720 * q^79 - 3061875 * q^80 + 1062882 * q^81 + 8637398 * q^82 - 6072936 * q^83 - 1965816 * q^84 - 686500 * q^85 + 3382108 * q^86 + 4907844 * q^87 + 12118884 * q^88 + 16516356 * q^89 + 637875 * q^90 - 19726448 * q^91 + 14123784 * q^92 + 8214264 * q^93 - 3412736 * q^94 - 6198000 * q^95 - 10673397 * q^96 + 2723428 * q^97 - 21434497 * q^98 + 2513592 * 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 $

$2$	−8.75765	−0.774074	−0.387037	−	0.922064i	$-0.626501\pi$
$2$	−8.75765	−0.774074	−0.387037	+	0.922064i	$0.626501\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−51.3036	−0.400809
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	−236.457	−0.446912
$7$	1338.43	1.47486	0.737432	−	0.675421i	$-0.236038\pi$
$7$	1338.43	1.47486	0.737432	+	0.675421i	$0.236038\pi$
$8$	1570.28	1.08433
$9$	729.000	0.333333
$10$	−1094.71	−0.346177
$11$	7411.55	1.67894	0.839469	−	0.543408i	$-0.182866\pi$
$11$	7411.55	1.67894	0.839469	+	0.543408i	$0.182866\pi$
$12$	−1385.20	−0.231407
$13$	−14594.3	−1.84239	−0.921195	−	0.389101i	$-0.872786\pi$
$13$	−14594.3	−1.84239	−0.921195	+	0.389101i	$0.872786\pi$
$14$	−11721.5	−1.14165
$15$	3375.00	0.258199
$16$	−7185.09	−0.438543
$17$	14414.7	0.711598	0.355799	−	0.934563i	$-0.384209\pi$
$17$	14414.7	0.711598	0.355799	+	0.934563i	$0.384209\pi$
$18$	−6384.33	−0.258025
$19$	409.730	0.0137044	0.00685220	−	0.999977i	$-0.497819\pi$
$19$	409.730	0.0137044	0.00685220	+	0.999977i	$0.497819\pi$
$20$	−6412.94	−0.179247
$21$	36137.6	0.851513
$22$	−64907.8	−1.29962
$23$	−17913.8	−0.307002	−0.153501	−	0.988148i	$-0.549055\pi$
$23$	−17913.8	−0.307002	−0.153501	+	0.988148i	$0.549055\pi$
$24$	42397.5	0.626038
$25$	15625.0	0.200000
$26$	127812.	1.42615
$27$	19683.0	0.192450
$28$	−68666.1	−0.591139
$29$	−10705.4	−0.0815099	−0.0407549	−	0.999169i	$-0.512976\pi$
$29$	−10705.4	−0.0815099	−0.0407549	+	0.999169i	$0.512976\pi$
$30$	−29557.1	−0.199865
$31$	178691.	1.07730	0.538649	−	0.842530i	$-0.318935\pi$
$31$	178691.	1.07730	0.538649	+	0.842530i	$0.318935\pi$
$32$	−138071.	−0.744865
$33$	200112.	0.969335
$34$	−126239.	−0.550830
$35$	167304.	0.659579
$36$	−37400.3	−0.133603
$37$	−427962.	−1.38899	−0.694496	−	0.719497i	$-0.744372\pi$
$37$	−427962.	−1.38899	−0.694496	+	0.719497i	$0.744372\pi$
$38$	−3588.27	−0.0106082
$39$	−394046.	−1.06370
$40$	196285.	0.484927
$41$	53370.3	0.120936	0.0604681	−	0.998170i	$-0.480741\pi$
$41$	53370.3	0.120936	0.0604681	+	0.998170i	$0.480741\pi$
$42$	−316480.	−0.659134
$43$	89349.4	0.171377	0.0856884	−	0.996322i	$-0.472691\pi$
$43$	89349.4	0.171377	0.0856884	+	0.996322i	$0.472691\pi$
$44$	−380239.	−0.672933
$45$	91125.0	0.149071
$46$	156883.	0.237642
$47$	−161273.	−0.226578	−0.113289	−	0.993562i	$-0.536139\pi$
$47$	−161273.	−0.226578	−0.113289	+	0.993562i	$0.536139\pi$
$48$	−193997.	−0.253193
$49$	967848.	1.17522
$50$	−136838.	−0.154815
$51$	389197.	0.410841
$52$	748740.	0.738447
$53$	−121833.	−0.112408	−0.0562042	−	0.998419i	$-0.517900\pi$
$53$	−121833.	−0.112408	−0.0562042	+	0.998419i	$0.517900\pi$
$54$	−172377.	−0.148971
$55$	926444.	0.750844
$56$	2.10170e6	1.59924
$57$	11062.7	0.00791224
$58$	93754.2	0.0630947
$59$	−1.69229e6	−1.07274	−0.536368	−	0.843984i	$-0.680204\pi$
$59$	−1.69229e6	−1.07274	−0.536368	+	0.843984i	$0.680204\pi$
$60$	−173149.	−0.103488
$61$	−1.23924e6	−0.699040	−0.349520	−	0.936929i	$-0.613655\pi$
$61$	−1.23924e6	−0.699040	−0.349520	+	0.936929i	$0.613655\pi$
$62$	−1.56491e6	−0.833908
$63$	975714.	0.491621
$64$	2.12887e6	1.01512
$65$	−1.82429e6	−0.823942
$66$	−1.75251e6	−0.750337
$67$	−944402.	−0.383615	−0.191807	−	0.981433i	$-0.561435\pi$
$67$	−944402.	−0.383615	−0.191807	+	0.981433i	$0.561435\pi$
$68$	−739526.	−0.285215
$69$	−483674.	−0.177248
$70$	−1.46519e6	−0.510563
$71$	−936943.	−0.310677	−0.155338	−	0.987861i	$-0.549647\pi$
$71$	−936943.	−0.310677	−0.155338	+	0.987861i	$0.549647\pi$
$72$	1.14473e6	0.361443
$73$	−5.49712e6	−1.65389	−0.826943	−	0.562286i	$-0.809922\pi$
$73$	−5.49712e6	−1.65389	−0.826943	+	0.562286i	$0.809922\pi$
$74$	3.74794e6	1.07518
$75$	421875.	0.115470
$76$	−21020.6	−0.00549285
$77$	9.91983e6	2.47621
$78$	3.45092e6	0.823386
$79$	−3.29987e6	−0.753011	−0.376506	−	0.926414i	$-0.622874\pi$
$79$	−3.29987e6	−0.753011	−0.376506	+	0.926414i	$0.622874\pi$
$80$	−898136.	−0.196122
$81$	531441.	0.111111
$82$	−467399.	−0.0936136
$83$	−4.16260e6	−0.799083	−0.399541	−	0.916715i	$-0.630831\pi$
$83$	−4.16260e6	−0.799083	−0.399541	+	0.916715i	$0.630831\pi$
$84$	−1.85399e6	−0.341294
$85$	1.80184e6	0.318236
$86$	−782491.	−0.132658
$87$	−289046.	−0.0470598
$88$	1.16382e7	1.82052
$89$	8.50941e6	1.27948	0.639741	−	0.768590i	$-0.279041\pi$
$89$	8.50941e6	1.27948	0.639741	+	0.768590i	$0.279041\pi$
$90$	−798041.	−0.115392
$91$	−1.95334e7	−2.71728
$92$	919044.	0.123049
$93$	4.82465e6	0.621978
$94$	1.41237e6	0.175389
$95$	51216.2	0.00612879
$96$	−3.72792e6	−0.430048
$97$	6.61583e6	0.736010	0.368005	−	0.929824i	$-0.380041\pi$
$97$	6.61583e6	0.736010	0.368005	+	0.929824i	$0.380041\pi$
$98$	−8.47607e6	−0.909711
$99$	5.40302e6	0.559646
$100$	−801618.	−0.0801618
$101$	1.05637e7	1.02022	0.510108	−	0.860110i	$-0.329605\pi$
$101$	1.05637e7	1.02022	0.510108	+	0.860110i	$0.329605\pi$
$102$	−3.40845e6	−0.318022
$103$	8.46118e6	0.762958	0.381479	−	0.924377i	$-0.375415\pi$
$103$	8.46118e6	0.762958	0.381479	+	0.924377i	$0.375415\pi$
$104$	−2.29171e7	−1.99776
$105$	4.51720e6	0.380808
$106$	1.06697e6	0.0870124
$107$	−2.74027e6	−0.216247	−0.108123	−	0.994137i	$-0.534484\pi$
$107$	−2.74027e6	−0.216247	−0.108123	+	0.994137i	$0.534484\pi$
$108$	−1.00981e6	−0.0771357
$109$	2.66853e6	0.197369	0.0986846	−	0.995119i	$-0.468536\pi$
$109$	2.66853e6	0.197369	0.0986846	+	0.995119i	$0.468536\pi$
$110$	−8.11347e6	−0.581209
$111$	−1.15550e7	−0.801935
$112$	−9.61673e6	−0.646792
$113$	−1.77381e7	−1.15646	−0.578232	−	0.815872i	$-0.696257\pi$
$113$	−1.77381e7	−1.15646	−0.578232	+	0.815872i	$0.696257\pi$
$114$	−96883.3	−0.00612466
$115$	−2.23923e6	−0.137296
$116$	549226.	0.0326699
$117$	−1.06392e7	−0.614130
$118$	1.48205e7	0.830377
$119$	1.92931e7	1.04951
$120$	5.29969e6	0.279973
$121$	3.54439e7	1.81883
$122$	1.08529e7	0.541109
$123$	1.44100e6	0.0698226
$124$	−9.16746e6	−0.431791
$125$	1.95312e6	0.0894427
$126$	−8.54497e6	−0.380551
$127$	−1.39230e7	−0.603142	−0.301571	−	0.953444i	$-0.597511\pi$
$127$	−1.39230e7	−0.603142	−0.301571	+	0.953444i	$0.597511\pi$
$128$	−970801.	−0.0409162
$129$	2.41243e6	0.0989445
$130$	1.59765e7	0.637792
$131$	4.73774e7	1.84129	0.920644	−	0.390403i	$-0.127664\pi$
$131$	4.73774e7	1.84129	0.920644	+	0.390403i	$0.127664\pi$
$132$	−1.02664e7	−0.388518
$133$	548394.	0.0202121
$134$	8.27074e6	0.296946
$135$	2.46038e6	0.0860663
$136$	2.26351e7	0.771607
$137$	−1.37766e7	−0.457740	−0.228870	−	0.973457i	$-0.573503\pi$
$137$	−1.37766e7	−0.457740	−0.228870	+	0.973457i	$0.573503\pi$
$138$	4.23585e6	0.137203
$139$	−2.99177e7	−0.944881	−0.472440	−	0.881363i	$-0.656627\pi$
$139$	−2.99177e7	−0.944881	−0.472440	+	0.881363i	$0.656627\pi$
$140$	−8.58327e6	−0.264365
$141$	−4.35436e6	−0.130815
$142$	8.20542e6	0.240487
$143$	−1.08166e8	−3.09326
$144$	−5.23793e6	−0.146181
$145$	−1.33818e6	−0.0364523
$146$	4.81419e7	1.28023
$147$	2.61319e7	0.678516
$148$	2.19560e7	0.556720
$149$	1.53461e7	0.380056	0.190028	−	0.981779i	$-0.439142\pi$
$149$	1.53461e7	0.380056	0.190028	+	0.981779i	$0.439142\pi$
$150$	−3.69463e6	−0.0893824
$151$	−8.10081e7	−1.91474	−0.957368	−	0.288871i	$-0.906720\pi$
$151$	−8.10081e7	−1.91474	−0.957368	+	0.288871i	$0.906720\pi$
$152$	643390.	0.0148601
$153$	1.05083e7	0.237199
$154$	−8.68744e7	−1.91677
$155$	2.23363e7	0.481782
$156$	2.02160e7	0.426342
$157$	−4.04242e7	−0.833667	−0.416834	−	0.908983i	$-0.636860\pi$
$157$	−4.04242e7	−0.833667	−0.416834	+	0.908983i	$0.636860\pi$
$158$	2.88991e7	0.582887
$159$	−3.28948e6	−0.0648990
$160$	−1.72589e7	−0.333114
$161$	−2.39764e7	−0.452786
$162$	−4.65417e6	−0.0860083
$163$	2.71649e7	0.491305	0.245652	−	0.969358i	$-0.420998\pi$
$163$	2.71649e7	0.491305	0.245652	+	0.969358i	$0.420998\pi$
$164$	−2.73809e6	−0.0484723
$165$	2.50140e7	0.433500
$166$	3.64546e7	0.618549
$167$	−4.96738e7	−0.825315	−0.412658	−	0.910886i	$-0.635399\pi$
$167$	−4.96738e7	−0.825315	−0.412658	+	0.910886i	$0.635399\pi$
$168$	5.67460e7	0.923322
$169$	1.50245e8	2.39440
$170$	−1.57799e7	−0.246339
$171$	298693.	0.00456813
$172$	−4.58394e6	−0.0686894
$173$	1.18247e8	1.73632	0.868161	−	0.496283i	$-0.165302\pi$
$173$	1.18247e8	1.73632	0.868161	+	0.496283i	$0.165302\pi$
$174$	2.53136e6	0.0364277
$175$	2.09129e7	0.294973
$176$	−5.32527e7	−0.736287
$177$	−4.56918e7	−0.619344
$178$	−7.45224e7	−0.990415
$179$	−9.22014e6	−0.120158	−0.0600789	−	0.998194i	$-0.519135\pi$
$179$	−9.22014e6	−0.120158	−0.0600789	+	0.998194i	$0.519135\pi$
$180$	−4.67504e6	−0.0597491
$181$	−7.95194e7	−0.996778	−0.498389	−	0.866954i	$-0.666075\pi$
$181$	−7.95194e7	−0.996778	−0.498389	+	0.866954i	$0.666075\pi$
$182$	1.71067e8	2.10337
$183$	−3.34596e7	−0.403591
$184$	−2.81297e7	−0.332892
$185$	−5.34953e7	−0.621176
$186$	−4.22526e7	−0.481457
$187$	1.06835e8	1.19473
$188$	8.27387e6	0.0908147
$189$	2.63443e7	0.283838
$190$	−448534.	−0.00474414
$191$	−7.45248e6	−0.0773899	−0.0386950	−	0.999251i	$-0.512320\pi$
$191$	−7.45248e6	−0.0773899	−0.0386950	+	0.999251i	$0.512320\pi$
$192$	5.74795e7	0.586082
$193$	−5.72075e7	−0.572800	−0.286400	−	0.958110i	$-0.592459\pi$
$193$	−5.72075e7	−0.572800	−0.286400	+	0.958110i	$0.592459\pi$
$194$	−5.79392e7	−0.569726
$195$	−4.92558e7	−0.475703
$196$	−4.96540e7	−0.471040
$197$	−6.10094e7	−0.568545	−0.284273	−	0.958743i	$-0.591752\pi$
$197$	−6.10094e7	−0.568545	−0.284273	+	0.958743i	$0.591752\pi$
$198$	−4.73178e7	−0.433208
$199$	1.51883e8	1.36622	0.683112	−	0.730313i	$-0.260626\pi$
$199$	1.51883e8	1.36622	0.683112	+	0.730313i	$0.260626\pi$
$200$	2.45356e7	0.216866
$201$	−2.54989e7	−0.221480
$202$	−9.25135e7	−0.789724
$203$	−1.43284e7	−0.120216
$204$	−1.99672e7	−0.164669
$205$	6.67129e6	0.0540843
$206$	−7.41001e7	−0.590586
$207$	−1.30592e7	−0.102334
$208$	1.04861e8	0.807968
$209$	3.03673e6	0.0230088
$210$	−3.95600e7	−0.294774
$211$	3.14356e7	0.230374	0.115187	−	0.993344i	$-0.463253\pi$
$211$	3.14356e7	0.230374	0.115187	+	0.993344i	$0.463253\pi$
$212$	6.25045e6	0.0450543
$213$	−2.52975e7	−0.179369
$214$	2.39983e7	0.167391
$215$	1.11687e7	0.0766420
$216$	3.09078e7	0.208679
$217$	2.39165e8	1.58887
$218$	−2.33701e7	−0.152778
$219$	−1.48422e8	−0.954871
$220$	−4.75299e7	−0.300945
$221$	−2.10373e8	−1.31104
$222$	1.01195e8	0.620757
$223$	−1.55318e8	−0.937899	−0.468949	−	0.883225i	$-0.655367\pi$
$223$	−1.55318e8	−0.937899	−0.468949	+	0.883225i	$0.655367\pi$
$224$	−1.84798e8	−1.09858
$225$	1.13906e7	0.0666667
$226$	1.55344e8	0.895189
$227$	1.06573e8	0.604721	0.302361	−	0.953194i	$-0.402225\pi$
$227$	1.06573e8	0.604721	0.302361	+	0.953194i	$0.402225\pi$
$228$	−567556.	−0.00317130
$229$	3.09602e7	0.170365	0.0851825	−	0.996365i	$-0.472853\pi$
$229$	3.09602e7	0.170365	0.0851825	+	0.996365i	$0.472853\pi$
$230$	1.96104e7	0.106277
$231$	2.67835e8	1.42964
$232$	−1.68105e7	−0.0883836
$233$	1.29584e8	0.671128	0.335564	−	0.942017i	$-0.391073\pi$
$233$	1.29584e8	0.671128	0.335564	+	0.942017i	$0.391073\pi$
$234$	9.31748e7	0.475382
$235$	−2.01591e7	−0.101329
$236$	8.68205e7	0.429962
$237$	−8.90964e7	−0.434751
$238$	−1.68962e8	−0.812399
$239$	3.32406e8	1.57498	0.787492	−	0.616325i	$-0.211379\pi$
$239$	3.32406e8	1.57498	0.787492	+	0.616325i	$0.211379\pi$
$240$	−2.42497e7	−0.113231
$241$	2.28413e8	1.05114	0.525570	−	0.850750i	$-0.323852\pi$
$241$	2.28413e8	1.05114	0.525570	+	0.850750i	$0.323852\pi$
$242$	−3.10405e8	−1.40791
$243$	1.43489e7	0.0641500
$244$	6.35776e7	0.280182
$245$	1.20981e8	0.525576
$246$	−1.26198e7	−0.0540479
$247$	−5.97972e6	−0.0252488
$248$	2.80594e8	1.16815
$249$	−1.12390e8	−0.461351
$250$	−1.71048e7	−0.0692353
$251$	−9.68540e7	−0.386598	−0.193299	−	0.981140i	$-0.561919\pi$
$251$	−9.68540e7	−0.386598	−0.193299	+	0.981140i	$0.561919\pi$
$252$	−5.00576e7	−0.197046
$253$	−1.32769e8	−0.515438
$254$	1.21933e8	0.466876
$255$	4.86496e7	0.183734
$256$	−2.63993e8	−0.983452
$257$	−3.58302e8	−1.31669	−0.658345	−	0.752717i	$-0.728743\pi$
$257$	−3.58302e8	−1.31669	−0.658345	+	0.752717i	$0.728743\pi$
$258$	−2.11273e7	−0.0765904
$259$	−5.72797e8	−2.04857
$260$	9.35925e7	0.330243
$261$	−7.80424e6	−0.0271700
$262$	−4.14915e8	−1.42529
$263$	3.55854e8	1.20622	0.603111	−	0.797657i	$-0.293928\pi$
$263$	3.55854e8	1.20622	0.603111	+	0.797657i	$0.293928\pi$
$264$	3.14231e8	1.05108
$265$	−1.52291e7	−0.0502705
$266$	−4.80264e6	−0.0156457
$267$	2.29754e8	0.738710
$268$	4.84512e7	0.153756
$269$	−6.05263e8	−1.89588	−0.947941	−	0.318445i	$-0.896839\pi$
$269$	−6.05263e8	−1.89588	−0.947941	+	0.318445i	$0.896839\pi$
$270$	−2.15471e7	−0.0666217
$271$	−1.40319e8	−0.428277	−0.214138	−	0.976803i	$-0.568694\pi$
$271$	−1.40319e8	−0.428277	−0.214138	+	0.976803i	$0.568694\pi$
$272$	−1.03571e8	−0.312066
$273$	−5.27403e8	−1.56882
$274$	1.20650e8	0.354325
$275$	1.15805e8	0.335788
$276$	2.48142e7	0.0710425
$277$	−2.91107e8	−0.822950	−0.411475	−	0.911421i	$-0.634986\pi$
$277$	−2.91107e8	−0.822950	−0.411475	+	0.911421i	$0.634986\pi$
$278$	2.62009e8	0.731408
$279$	1.30265e8	0.359099
$280$	2.62713e8	0.715202
$281$	5.10230e8	1.37181	0.685905	−	0.727691i	$-0.259406\pi$
$281$	5.10230e8	1.37181	0.685905	+	0.727691i	$0.259406\pi$
$282$	3.81340e7	0.101261
$283$	2.28117e8	0.598281	0.299141	−	0.954209i	$-0.403300\pi$
$283$	2.28117e8	0.598281	0.299141	+	0.954209i	$0.403300\pi$
$284$	4.80685e7	0.124522
$285$	1.38284e6	0.00353846
$286$	9.47284e8	2.39441
$287$	7.14324e7	0.178365
$288$	−1.00654e8	−0.248288
$289$	−2.02555e8	−0.493628
$290$	1.17193e7	0.0282168
$291$	1.78628e8	0.424935
$292$	2.82022e8	0.662892
$293$	−1.68215e8	−0.390687	−0.195343	−	0.980735i	$-0.562582\pi$
$293$	−1.68215e8	−0.390687	−0.195343	+	0.980735i	$0.562582\pi$
$294$	−2.28854e8	−0.525222
$295$	−2.11536e8	−0.479742
$296$	−6.72020e8	−1.50613
$297$	1.45882e8	0.323112
$298$	−1.34396e8	−0.294191
$299$	2.61440e8	0.565618
$300$	−2.16437e7	−0.0462814
$301$	1.19588e8	0.252758
$302$	7.09440e8	1.48215
$303$	2.85221e8	0.589023
$304$	−2.94395e6	−0.00600997
$305$	−1.54905e8	−0.312620
$306$	−9.20282e7	−0.183610
$307$	5.67876e8	1.12013	0.560066	−	0.828448i	$-0.310776\pi$
$307$	5.67876e8	1.12013	0.560066	+	0.828448i	$0.310776\pi$
$308$	−5.08922e8	−0.992485
$309$	2.28452e8	0.440494
$310$	−1.95614e8	−0.372935
$311$	−6.68026e8	−1.25931	−0.629654	−	0.776876i	$-0.716803\pi$
$311$	−6.68026e8	−1.25931	−0.629654	+	0.776876i	$0.716803\pi$
$312$	−6.18762e8	−1.15341
$313$	2.41610e8	0.445358	0.222679	−	0.974892i	$-0.428520\pi$
$313$	2.41610e8	0.445358	0.222679	+	0.974892i	$0.428520\pi$
$314$	3.54021e8	0.645321
$315$	1.21964e8	0.219860
$316$	1.69295e8	0.301814
$317$	−9.73867e8	−1.71709	−0.858544	−	0.512740i	$-0.828630\pi$
$317$	−9.73867e8	−1.71709	−0.858544	+	0.512740i	$0.828630\pi$
$318$	2.88082e7	0.0502366
$319$	−7.93437e7	−0.136850
$320$	2.66109e8	0.453977
$321$	−7.39872e7	−0.124850
$322$	2.09977e8	0.350490
$323$	5.90614e6	0.00975202
$324$	−2.72648e7	−0.0445343
$325$	−2.28036e8	−0.368478
$326$	−2.37901e8	−0.380307
$327$	7.20504e7	0.113951
$328$	8.38063e7	0.131135
$329$	−2.15852e8	−0.334172
$330$	−2.19064e8	−0.335561
$331$	−4.25946e8	−0.645590	−0.322795	−	0.946469i	$-0.604622\pi$
$331$	−4.25946e8	−0.645590	−0.322795	+	0.946469i	$0.604622\pi$
$332$	2.13556e8	0.320280
$333$	−3.11985e8	−0.462997
$334$	4.35026e8	0.638855
$335$	−1.18050e8	−0.171558
$336$	−2.59652e8	−0.373425
$337$	8.64429e8	1.23034	0.615170	−	0.788395i	$-0.289088\pi$
$337$	8.64429e8	1.23034	0.615170	+	0.788395i	$0.289088\pi$
$338$	−1.31579e9	−1.85345
$339$	−4.78928e8	−0.667685
$340$	−9.24407e7	−0.127552
$341$	1.32437e9	1.80872
$342$	−2.61585e6	−0.00353607
$343$	1.93141e8	0.258432
$344$	1.40303e8	0.185829
$345$	−6.04592e7	−0.0792676
$346$	−1.03557e9	−1.34404
$347$	8.95674e8	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$347$	8.95674e8	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$348$	1.48291e7	0.0188620
$349$	2.98991e8	0.376503	0.188252	−	0.982121i	$-0.439718\pi$
$349$	2.98991e8	0.376503	0.188252	+	0.982121i	$0.439718\pi$
$350$	−1.83148e8	−0.228331
$351$	−2.87260e8	−0.354568
$352$	−1.02332e9	−1.25058
$353$	9.92149e8	1.20051	0.600254	−	0.799809i	$-0.295066\pi$
$353$	9.92149e8	1.20051	0.600254	+	0.799809i	$0.295066\pi$
$354$	4.00153e8	0.479418
$355$	−1.17118e8	−0.138939
$356$	−4.36563e8	−0.512828
$357$	5.20913e8	0.605935
$358$	8.07468e7	0.0930111
$359$	7.94667e8	0.906473	0.453236	−	0.891390i	$-0.350269\pi$
$359$	7.94667e8	0.906473	0.453236	+	0.891390i	$0.350269\pi$
$360$	1.43092e8	0.161642
$361$	−8.93704e8	−0.999812
$362$	6.96403e8	0.771580
$363$	9.56985e8	1.05010
$364$	1.00213e9	1.08911
$365$	−6.87141e8	−0.739640
$366$	2.93027e8	0.312409
$367$	−5.76769e8	−0.609074	−0.304537	−	0.952500i	$-0.598502\pi$
$367$	−5.76769e8	−0.609074	−0.304537	+	0.952500i	$0.598502\pi$
$368$	1.28713e8	0.134634
$369$	3.89070e7	0.0403121
$370$	4.68493e8	0.480836
$371$	−1.63064e8	−0.165787
$372$	−2.47521e8	−0.249294
$373$	7.49247e8	0.747557	0.373779	−	0.927518i	$-0.378062\pi$
$373$	7.49247e8	0.747557	0.373779	+	0.927518i	$0.378062\pi$
$374$	−9.35627e8	−0.924809
$375$	5.27344e7	0.0516398
$376$	−2.53243e8	−0.245686
$377$	1.56238e8	0.150173
$378$	−2.30714e8	−0.219711
$379$	−1.93999e9	−1.83047	−0.915233	−	0.402926i	$-0.867993\pi$
$379$	−1.93999e9	−1.83047	−0.915233	+	0.402926i	$0.867993\pi$
$380$	−2.62757e6	−0.00245648
$381$	−3.75921e8	−0.348224
$382$	6.52663e7	0.0599055
$383$	1.08549e9	0.987254	0.493627	−	0.869674i	$-0.335671\pi$
$383$	1.08549e9	0.987254	0.493627	+	0.869674i	$0.335671\pi$
$384$	−2.62116e7	−0.0236230
$385$	1.23998e9	1.10739
$386$	5.01004e8	0.443389
$387$	6.51357e7	0.0571256
$388$	−3.39416e8	−0.294999
$389$	−7.18963e8	−0.619274	−0.309637	−	0.950855i	$-0.600208\pi$
$389$	−7.18963e8	−0.619274	−0.309637	+	0.950855i	$0.600208\pi$
$390$	4.31365e8	0.368230
$391$	−2.58223e8	−0.218462
$392$	1.51979e9	1.27433
$393$	1.27919e9	1.06307
$394$	5.34299e8	0.440096
$395$	−4.12483e8	−0.336757
$396$	−2.77194e8	−0.224311
$397$	−7.87080e7	−0.0631324	−0.0315662	−	0.999502i	$-0.510049\pi$
$397$	−7.87080e7	−0.0631324	−0.0315662	+	0.999502i	$0.510049\pi$
$398$	−1.33013e9	−1.05756
$399$	1.48066e7	0.0116695
$400$	−1.12267e8	−0.0877086
$401$	4.28246e8	0.331656	0.165828	−	0.986155i	$-0.446970\pi$
$401$	4.28246e8	0.331656	0.165828	+	0.986155i	$0.446970\pi$
$402$	2.23310e8	0.171442
$403$	−2.60786e9	−1.98480
$404$	−5.41957e8	−0.408912
$405$	6.64301e7	0.0496904
$406$	1.25483e8	0.0930561
$407$	−3.17186e9	−2.33203
$408$	6.11148e8	0.445488
$409$	4.98651e8	0.360384	0.180192	−	0.983631i	$-0.442328\pi$
$409$	4.98651e8	0.360384	0.180192	+	0.983631i	$0.442328\pi$
$410$	−5.84248e7	−0.0418653
$411$	−3.71967e8	−0.264276
$412$	−4.34089e8	−0.305800
$413$	−2.26501e9	−1.58214
$414$	1.14368e8	0.0792141
$415$	−5.20325e8	−0.357361
$416$	2.01505e9	1.37233
$417$	−8.07779e8	−0.545527
$418$	−2.65946e7	−0.0178105
$419$	2.31115e9	1.53489	0.767447	−	0.641112i	$-0.221527\pi$
$419$	2.31115e9	1.53489	0.767447	+	0.641112i	$0.221527\pi$
$420$	−2.31748e8	−0.152631
$421$	1.06460e9	0.695344	0.347672	−	0.937616i	$-0.386972\pi$
$421$	1.06460e9	0.695344	0.347672	+	0.937616i	$0.386972\pi$
$422$	−2.75302e8	−0.178326
$423$	−1.17568e8	−0.0755261
$424$	−1.91311e8	−0.121888
$425$	2.25230e8	0.142320
$426$	2.21546e8	0.138845
$427$	−1.65864e9	−1.03099
$428$	1.40586e8	0.0866737
$429$	−2.92049e9	−1.78589
$430$	−9.78114e7	−0.0593266
$431$	2.79013e9	1.67863	0.839313	−	0.543649i	$-0.182958\pi$
$431$	2.79013e9	1.67863	0.839313	+	0.543649i	$0.182958\pi$
$432$	−1.41424e8	−0.0843977
$433$	2.27098e9	1.34433	0.672164	−	0.740403i	$-0.265365\pi$
$433$	2.27098e9	1.34433	0.672164	+	0.740403i	$0.265365\pi$
$434$	−2.09452e9	−1.22990
$435$	−3.61308e7	−0.0210458
$436$	−1.36905e8	−0.0791074
$437$	−7.33984e6	−0.00420728
$438$	1.29983e9	0.739141
$439$	2.10307e9	1.18639	0.593195	−	0.805059i	$-0.297866\pi$
$439$	2.10307e9	1.18639	0.593195	+	0.805059i	$0.297866\pi$
$440$	1.45477e9	0.814163
$441$	7.05561e8	0.391741
$442$	1.84237e9	1.01484
$443$	−2.70576e9	−1.47869	−0.739343	−	0.673329i	$-0.764864\pi$
$443$	−2.70576e9	−1.47869	−0.739343	+	0.673329i	$0.764864\pi$
$444$	5.92812e8	0.321423
$445$	1.06368e9	0.572202
$446$	1.36022e9	0.726003
$447$	4.14346e8	0.219425
$448$	2.84934e9	1.49717
$449$	2.11008e9	1.10011	0.550055	−	0.835128i	$-0.314607\pi$
$449$	2.11008e9	1.10011	0.550055	+	0.835128i	$0.314607\pi$
$450$	−9.97551e7	−0.0516050
$451$	3.95557e8	0.203044
$452$	9.10027e8	0.463521
$453$	−2.18722e9	−1.10547
$454$	−9.33326e8	−0.468099
$455$	−2.44168e9	−1.21520
$456$	1.73715e7	0.00857948
$457$	−2.27404e8	−0.111453	−0.0557264	−	0.998446i	$-0.517747\pi$
$457$	−2.27404e8	−0.111453	−0.0557264	+	0.998446i	$0.517747\pi$
$458$	−2.71139e8	−0.131875
$459$	2.83725e8	0.136947
$460$	1.14880e8	0.0550293
$461$	−5.48876e8	−0.260928	−0.130464	−	0.991453i	$-0.541647\pi$
$461$	−5.48876e8	−0.260928	−0.130464	+	0.991453i	$0.541647\pi$
$462$	−2.34561e9	−1.10665
$463$	4.99899e8	0.234072	0.117036	−	0.993128i	$-0.462661\pi$
$463$	4.99899e8	0.234072	0.117036	+	0.993128i	$0.462661\pi$
$464$	7.69193e7	0.0357456
$465$	6.03081e8	0.278157
$466$	−1.13485e9	−0.519503
$467$	2.23313e9	1.01462	0.507311	−	0.861763i	$-0.330639\pi$
$467$	2.23313e9	1.01462	0.507311	+	0.861763i	$0.330639\pi$
$468$	5.45831e8	0.246149
$469$	−1.26401e9	−0.565779
$470$	1.76546e8	0.0784361
$471$	−1.09145e9	−0.481318
$472$	−2.65737e9	−1.16320
$473$	6.62218e8	0.287731
$474$	7.80275e8	0.336530
$475$	6.40203e6	0.00274088
$476$	−9.89803e8	−0.420653
$477$	−8.88161e7	−0.0374694
$478$	−2.91109e9	−1.21915
$479$	−3.53414e9	−1.46929	−0.734647	−	0.678449i	$-0.762652\pi$
$479$	−3.53414e9	−1.46929	−0.734647	+	0.678449i	$0.762652\pi$
$480$	−4.65990e8	−0.192323
$481$	6.24581e9	2.55906
$482$	−2.00036e9	−0.813660
$483$	−6.47363e8	−0.261416
$484$	−1.81840e9	−0.729004
$485$	8.26979e8	0.329154
$486$	−1.25663e8	−0.0496569
$487$	2.72597e9	1.06947	0.534737	−	0.845019i	$-0.320411\pi$
$487$	2.72597e9	1.06947	0.534737	+	0.845019i	$0.320411\pi$
$488$	−1.94596e9	−0.757990
$489$	7.33452e8	0.283655
$490$	−1.05951e9	−0.406835
$491$	−4.86034e9	−1.85302	−0.926512	−	0.376265i	$-0.877208\pi$
$491$	−4.86034e9	−1.85302	−0.926512	+	0.376265i	$0.877208\pi$
$492$	−7.39284e7	−0.0279855
$493$	−1.54315e8	−0.0580023
$494$	5.23683e7	0.0195445
$495$	6.75377e8	0.250281
$496$	−1.28391e9	−0.472441
$497$	−1.25403e9	−0.458206
$498$	9.84275e8	0.357120
$499$	2.41002e8	0.0868297	0.0434149	−	0.999057i	$-0.486176\pi$
$499$	2.41002e8	0.0868297	0.0434149	+	0.999057i	$0.486176\pi$
$500$	−1.00202e8	−0.0358494
$501$	−1.34119e9	−0.476496
$502$	8.48214e8	0.299256
$503$	3.91762e9	1.37257	0.686285	−	0.727333i	$-0.259240\pi$
$503$	3.91762e9	1.37257	0.686285	+	0.727333i	$0.259240\pi$
$504$	1.53214e9	0.533080
$505$	1.32047e9	0.456255
$506$	1.16275e9	0.398987
$507$	4.05662e9	1.38241
$508$	7.14299e8	0.241745
$509$	1.53452e9	0.515775	0.257888	−	0.966175i	$-0.416974\pi$
$509$	1.53452e9	0.515775	0.257888	+	0.966175i	$0.416974\pi$
$510$	−4.26057e8	−0.142224
$511$	−7.35751e9	−2.43926
$512$	2.43622e9	0.802181
$513$	8.06471e6	0.00263741
$514$	3.13788e9	1.01922
$515$	1.05765e9	0.341205
$516$	−1.23766e8	−0.0396578
$517$	−1.19528e9	−0.380411
$518$	5.01636e9	1.58575
$519$	3.19268e9	1.00247
$520$	−2.86464e9	−0.893425
$521$	−2.45259e9	−0.759790	−0.379895	−	0.925030i	$-0.624040\pi$
$521$	−2.45259e9	−0.759790	−0.379895	+	0.925030i	$0.624040\pi$
$522$	6.83468e7	0.0210316
$523$	−2.27819e8	−0.0696362	−0.0348181	−	0.999394i	$-0.511085\pi$
$523$	−2.27819e8	−0.0696362	−0.0348181	+	0.999394i	$0.511085\pi$
$524$	−2.43063e9	−0.738005
$525$	5.64649e8	0.170303
$526$	−3.11645e9	−0.933706
$527$	2.57577e9	0.766603
$528$	−1.43782e9	−0.425095
$529$	−3.08392e9	−0.905750
$530$	1.33371e8	0.0389131
$531$	−1.23368e9	−0.357579
$532$	−2.81346e7	−0.00810120
$533$	−7.78903e8	−0.222812
$534$	−2.01211e9	−0.571816
$535$	−3.42534e8	−0.0967086
$536$	−1.48297e9	−0.415965
$537$	−2.48944e8	−0.0693731
$538$	5.30069e9	1.46755
$539$	7.17325e9	1.97313
$540$	−1.26226e8	−0.0344961
$541$	3.79946e9	1.03165	0.515824	−	0.856694i	$-0.327486\pi$
$541$	3.79946e9	1.03165	0.515824	+	0.856694i	$0.327486\pi$
$542$	1.22887e9	0.331518
$543$	−2.14702e9	−0.575490
$544$	−1.99025e9	−0.530045
$545$	3.33566e8	0.0882662
$546$	4.61881e9	1.21438
$547$	5.31117e9	1.38751	0.693753	−	0.720213i	$-0.255956\pi$
$547$	5.31117e9	1.38751	0.693753	+	0.720213i	$0.255956\pi$
$548$	7.06787e8	0.183466
$549$	−9.03408e8	−0.233013
$550$	−1.01418e9	−0.259925
$551$	−4.38632e6	−0.00111704
$552$	−7.59502e8	−0.192195
$553$	−4.41663e9	−1.11059
$554$	2.54941e9	0.637024
$555$	−1.44437e9	−0.358636
$556$	1.53489e9	0.378717
$557$	−7.38937e9	−1.81182	−0.905909	−	0.423473i	$-0.860811\pi$
$557$	−7.38937e9	−1.81182	−0.905909	+	0.423473i	$0.860811\pi$
$558$	−1.14082e9	−0.277969
$559$	−1.30399e9	−0.315743
$560$	−1.20209e9	−0.289254
$561$	2.88455e9	0.689777
$562$	−4.46842e9	−1.06188
$563$	−2.33548e9	−0.551564	−0.275782	−	0.961220i	$-0.588937\pi$
$563$	−2.33548e9	−0.551564	−0.275782	+	0.961220i	$0.588937\pi$
$564$	2.23394e8	0.0524319
$565$	−2.21726e9	−0.517187
$566$	−1.99777e9	−0.463114
$567$	7.11296e8	0.163874
$568$	−1.47126e9	−0.336876
$569$	6.66096e9	1.51581	0.757903	−	0.652367i	$-0.226224\pi$
$569$	6.66096e9	1.51581	0.757903	+	0.652367i	$0.226224\pi$
$570$	−1.21104e7	−0.00273903
$571$	−2.11804e9	−0.476110	−0.238055	−	0.971252i	$-0.576510\pi$
$571$	−2.11804e9	−0.476110	−0.238055	+	0.971252i	$0.576510\pi$
$572$	5.54932e9	1.23981
$573$	−2.01217e8	−0.0446811
$574$	−6.25580e8	−0.138067
$575$	−2.79904e8	−0.0614004
$576$	1.55195e9	0.338375
$577$	4.63211e9	1.00384	0.501919	−	0.864915i	$-0.332628\pi$
$577$	4.63211e9	1.00384	0.501919	+	0.864915i	$0.332628\pi$
$578$	1.77390e9	0.382105
$579$	−1.54460e9	−0.330706
$580$	6.86532e7	0.0146104
$581$	−5.57135e9	−1.17854
$582$	−1.56436e9	−0.328932
$583$	−9.02970e8	−0.188727
$584$	−8.63201e9	−1.79336
$585$	−1.32991e9	−0.274647
$586$	1.47317e9	0.302420
$587$	−7.08115e9	−1.44501	−0.722504	−	0.691367i	$-0.757009\pi$
$587$	−7.08115e9	−1.44501	−0.722504	+	0.691367i	$0.757009\pi$
$588$	−1.34066e9	−0.271955
$589$	7.32149e7	0.0147637
$590$	1.85256e9	0.371356
$591$	−1.64725e9	−0.328250
$592$	3.07495e9	0.609133
$593$	2.25289e9	0.443657	0.221829	−	0.975086i	$-0.428797\pi$
$593$	2.25289e9	0.443657	0.221829	+	0.975086i	$0.428797\pi$
$594$	−1.27758e9	−0.250112
$595$	2.41163e9	0.469355
$596$	−7.87312e8	−0.152330
$597$	4.10083e9	0.788790
$598$	−2.28960e9	−0.437830
$599$	−4.50218e9	−0.855912	−0.427956	−	0.903799i	$-0.640766\pi$
$599$	−4.50218e9	−0.855912	−0.427956	+	0.903799i	$0.640766\pi$
$600$	6.62461e8	0.125208
$601$	5.26755e9	0.989802	0.494901	−	0.868949i	$-0.335204\pi$
$601$	5.26755e9	0.989802	0.494901	+	0.868949i	$0.335204\pi$
$602$	−1.04731e9	−0.195653
$603$	−6.88469e8	−0.127872
$604$	4.15600e9	0.767444
$605$	4.43049e9	0.813407
$606$	−2.49786e9	−0.455947
$607$	−2.39522e9	−0.434696	−0.217348	−	0.976094i	$-0.569741\pi$
$607$	−2.39522e9	−0.434696	−0.217348	+	0.976094i	$0.569741\pi$
$608$	−5.65718e7	−0.0102079
$609$	−3.86867e8	−0.0694067
$610$	1.35661e9	0.241991
$611$	2.35366e9	0.417446
$612$	−5.39114e8	−0.0950716
$613$	−9.90842e9	−1.73737	−0.868686	−	0.495363i	$-0.835035\pi$
$613$	−9.90842e9	−1.73737	−0.868686	+	0.495363i	$0.835035\pi$
$614$	−4.97326e9	−0.867066
$615$	1.80125e8	0.0312256
$616$	1.55769e10	2.68502
$617$	−2.05272e9	−0.351829	−0.175915	−	0.984405i	$-0.556288\pi$
$617$	−2.05272e9	−0.351829	−0.175915	+	0.984405i	$0.556288\pi$
$618$	−2.00070e9	−0.340975
$619$	8.57333e9	1.45289	0.726444	−	0.687225i	$-0.241172\pi$
$619$	8.57333e9	1.45289	0.726444	+	0.687225i	$0.241172\pi$
$620$	−1.14593e9	−0.193103
$621$	−3.52598e8	−0.0590826
$622$	5.85034e9	0.974798
$623$	1.13892e10	1.88706
$624$	2.83126e9	0.466480
$625$	2.44141e8	0.0400000
$626$	−2.11593e9	−0.344740
$627$	8.19918e7	0.0132842
$628$	2.07391e9	0.334141
$629$	−6.16895e9	−0.988403
$630$	−1.06812e9	−0.170188
$631$	−2.15662e9	−0.341720	−0.170860	−	0.985295i	$-0.554655\pi$
$631$	−2.15662e9	−0.341720	−0.170860	+	0.985295i	$0.554655\pi$
$632$	−5.18171e9	−0.816513
$633$	8.48761e8	0.133006
$634$	8.52879e9	1.32915
$635$	−1.74037e9	−0.269733
$636$	1.68762e8	0.0260121
$637$	−1.41251e10	−2.16522
$638$	6.94864e8	0.105932
$639$	−6.83031e8	−0.103559
$640$	−1.21350e8	−0.0182983
$641$	1.09316e10	1.63938	0.819689	−	0.572809i	$-0.194146\pi$
$641$	1.09316e10	1.63938	0.819689	+	0.572809i	$0.194146\pi$
$642$	6.47954e8	0.0966433
$643$	5.34196e9	0.792432	0.396216	−	0.918157i	$-0.370323\pi$
$643$	5.34196e9	0.792432	0.396216	+	0.918157i	$0.370323\pi$
$644$	1.23007e9	0.181481
$645$	3.01554e8	0.0442493
$646$	−5.17239e7	−0.00754879
$647$	4.77656e9	0.693346	0.346673	−	0.937986i	$-0.387311\pi$
$647$	4.77656e9	0.693346	0.346673	+	0.937986i	$0.387311\pi$
$648$	8.34510e8	0.120481
$649$	−1.25425e10	−1.80106
$650$	1.99706e9	0.285229
$651$	6.45744e9	0.917333
$652$	−1.39365e9	−0.196919
$653$	−1.50855e9	−0.212013	−0.106006	−	0.994365i	$-0.533806\pi$
$653$	−1.50855e9	−0.212013	−0.106006	+	0.994365i	$0.533806\pi$
$654$	−6.30992e8	−0.0882067
$655$	5.92218e9	0.823449
$656$	−3.83471e8	−0.0530358
$657$	−4.00740e9	−0.551295
$658$	1.89036e9	0.258674
$659$	2.78418e9	0.378965	0.189482	−	0.981884i	$-0.439319\pi$
$659$	2.78418e9	0.378965	0.189482	+	0.981884i	$0.439319\pi$
$660$	−1.28331e9	−0.173751
$661$	−9.29515e9	−1.25185	−0.625924	−	0.779884i	$-0.715278\pi$
$661$	−9.29515e9	−1.25185	−0.625924	+	0.779884i	$0.715278\pi$
$662$	3.73029e9	0.499735
$663$	−5.68006e9	−0.756930
$664$	−6.53644e9	−0.866469
$665$	6.85492e7	0.00903914
$666$	2.73225e9	0.358394
$667$	1.91775e8	0.0250237
$668$	2.54844e9	0.330794
$669$	−4.19360e9	−0.541496
$670$	1.03384e9	0.132798
$671$	−9.18471e9	−1.17364
$672$	−4.98955e9	−0.634263
$673$	−7.87291e9	−0.995595	−0.497798	−	0.867293i	$-0.665858\pi$
$673$	−7.87291e9	−0.995595	−0.497798	+	0.867293i	$0.665858\pi$
$674$	−7.57037e9	−0.952374
$675$	3.07547e8	0.0384900
$676$	−7.70811e9	−0.959698
$677$	−7.50679e9	−0.929810	−0.464905	−	0.885361i	$-0.653911\pi$
$677$	−7.50679e9	−0.929810	−0.464905	+	0.885361i	$0.653911\pi$
$678$	4.19429e9	0.516838
$679$	8.85482e9	1.08551
$680$	2.82939e9	0.345073
$681$	2.87746e9	0.349136
$682$	−1.15984e10	−1.40008
$683$	7.93522e9	0.952985	0.476493	−	0.879178i	$-0.341908\pi$
$683$	7.93522e9	0.952985	0.476493	+	0.879178i	$0.341908\pi$
$684$	−1.53240e7	−0.00183095
$685$	−1.72207e9	−0.204708
$686$	−1.69147e9	−0.200046
$687$	8.35927e8	0.0983603
$688$	−6.41984e8	−0.0751561
$689$	1.77806e9	0.207100
$690$	5.29481e8	0.0613590
$691$	−7.23622e8	−0.0834332	−0.0417166	−	0.999129i	$-0.513283\pi$
$691$	−7.23622e8	−0.0834332	−0.0417166	+	0.999129i	$0.513283\pi$
$692$	−6.06651e9	−0.695934
$693$	7.23156e9	0.825402
$694$	−7.84400e9	−0.890799
$695$	−3.73972e9	−0.422564
$696$	−4.53883e8	−0.0510283
$697$	7.69318e8	0.0860580
$698$	−2.61846e9	−0.291442
$699$	3.49876e9	0.387476
$700$	−1.07291e9	−0.118228
$701$	1.37209e10	1.50442	0.752211	−	0.658923i	$-0.228988\pi$
$701$	1.37209e10	1.50442	0.752211	+	0.658923i	$0.228988\pi$
$702$	2.51572e9	0.274462
$703$	−1.75349e8	−0.0190353
$704$	1.57782e10	1.70433
$705$	−5.44296e8	−0.0585023
$706$	−8.68889e9	−0.929283
$707$	1.41388e10	1.50468
$708$	2.34415e9	0.248239
$709$	1.20390e10	1.26861	0.634304	−	0.773084i	$-0.281287\pi$
$709$	1.20390e10	1.26861	0.634304	+	0.773084i	$0.281287\pi$
$710$	1.02568e9	0.107549
$711$	−2.40560e9	−0.251004
$712$	1.33621e10	1.38738
$713$	−3.20104e9	−0.330733
$714$	−4.56197e9	−0.469039
$715$	−1.35208e10	−1.38335
$716$	4.73026e8	0.0481603
$717$	8.97496e9	0.909317
$718$	−6.95942e9	−0.701677
$719$	−1.84411e8	−0.0185027	−0.00925137	−	0.999957i	$-0.502945\pi$
$719$	−1.84411e8	−0.0185027	−0.00925137	+	0.999957i	$0.502945\pi$
$720$	−6.54741e8	−0.0653741
$721$	1.13247e10	1.12526
$722$	7.82675e9	0.773929
$723$	6.16714e9	0.606876
$724$	4.07963e9	0.399517
$725$	−1.67272e8	−0.0163020
$726$	−8.38094e9	−0.812858
$727$	1.10078e10	1.06250	0.531251	−	0.847215i	$-0.321722\pi$
$727$	1.10078e10	1.06250	0.531251	+	0.847215i	$0.321722\pi$
$728$	−3.06729e10	−2.94642
$729$	3.87420e8	0.0370370
$730$	6.01774e9	0.572536
$731$	1.28795e9	0.121951
$732$	1.71659e9	0.161763
$733$	1.57261e10	1.47488	0.737439	−	0.675414i	$-0.236035\pi$
$733$	1.57261e10	1.47488	0.737439	+	0.675414i	$0.236035\pi$
$734$	5.05114e9	0.471469
$735$	3.26649e9	0.303442
$736$	2.47338e9	0.228675
$737$	−6.99948e9	−0.644065
$738$	−3.40734e8	−0.0312045
$739$	−1.66376e10	−1.51647	−0.758236	−	0.651980i	$-0.773939\pi$
$739$	−1.66376e10	−1.51647	−0.758236	+	0.651980i	$0.773939\pi$
$740$	2.74450e9	0.248973
$741$	−1.61452e8	−0.0145774
$742$	1.42806e9	0.128331
$743$	−1.32975e10	−1.18935	−0.594673	−	0.803967i	$-0.702719\pi$
$743$	−1.32975e10	−1.18935	−0.594673	+	0.803967i	$0.702719\pi$
$744$	7.57603e9	0.674430
$745$	1.91827e9	0.169966
$746$	−6.56165e9	−0.578665
$747$	−3.03454e9	−0.266361
$748$	−5.48103e9	−0.478858
$749$	−3.66765e9	−0.318935
$750$	−4.61829e8	−0.0399730
$751$	−4.12057e8	−0.0354991	−0.0177495	−	0.999842i	$-0.505650\pi$
$751$	−4.12057e8	−0.0354991	−0.0177495	+	0.999842i	$0.505650\pi$
$752$	1.15876e9	0.0993644
$753$	−2.61506e9	−0.223202
$754$	−1.36828e9	−0.116245
$755$	−1.01260e10	−0.856296
$756$	−1.35156e9	−0.113765
$757$	−6.86113e9	−0.574857	−0.287428	−	0.957802i	$-0.592800\pi$
$757$	−6.86113e9	−0.574857	−0.287428	+	0.957802i	$0.592800\pi$
$758$	1.69897e10	1.41692
$759$	−3.58477e9	−0.297588
$760$	8.04237e7	0.00664564
$761$	−6.71798e9	−0.552576	−0.276288	−	0.961075i	$-0.589104\pi$
$761$	−6.71798e9	−0.552576	−0.276288	+	0.961075i	$0.589104\pi$
$762$	3.29218e9	0.269551
$763$	3.57164e9	0.291093
$764$	3.82339e8	0.0310186
$765$	1.31354e9	0.106079
$766$	−9.50632e9	−0.764208
$767$	2.46978e10	1.97640
$768$	−7.12782e9	−0.567796
$769$	2.89464e9	0.229537	0.114768	−	0.993392i	$-0.463387\pi$
$769$	2.89464e9	0.229537	0.114768	+	0.993392i	$0.463387\pi$
$770$	−1.08593e10	−0.857204
$771$	−9.67416e9	−0.760191
$772$	2.93495e9	0.229583
$773$	8.52286e9	0.663677	0.331839	−	0.943336i	$-0.392331\pi$
$773$	8.52286e9	0.663677	0.331839	+	0.943336i	$0.392331\pi$
$774$	−5.70436e8	−0.0442195
$775$	2.79204e9	0.215460
$776$	1.03887e10	0.798077
$777$	−1.54655e10	−1.18274
$778$	6.29643e9	0.479364
$779$	2.18674e7	0.00165736
$780$	2.52700e9	0.190666
$781$	−6.94420e9	−0.521607
$782$	2.26143e9	0.169106
$783$	−2.10715e8	−0.0156866
$784$	−6.95407e9	−0.515386
$785$	−5.05303e9	−0.372827
$786$	−1.12027e10	−0.822894
$787$	7.66305e9	0.560390	0.280195	−	0.959943i	$-0.409601\pi$
$787$	7.66305e9	0.560390	0.280195	+	0.959943i	$0.409601\pi$
$788$	3.13000e9	0.227878
$789$	9.60807e9	0.696413
$790$	3.61238e9	0.260675
$791$	−2.37412e10	−1.70563
$792$	8.48424e9	0.606841
$793$	1.80859e10	1.28790
$794$	6.89297e8	0.0488691
$795$	−4.11186e8	−0.0290237
$796$	−7.79211e9	−0.547595
$797$	−1.16737e10	−0.816780	−0.408390	−	0.912807i	$-0.633910\pi$
$797$	−1.16737e10	−0.816780	−0.408390	+	0.912807i	$0.633910\pi$
$798$	−1.29671e8	−0.00903304
$799$	−2.32470e9	−0.161233
$800$	−2.15736e9	−0.148973
$801$	6.20336e9	0.426494
$802$	−3.75043e9	−0.256726
$803$	−4.07422e10	−2.77677
$804$	1.30818e9	0.0887712
$805$	−2.99705e9	−0.202492
$806$	2.28388e10	1.53638
$807$	−1.63421e10	−1.09459
$808$	1.65880e10	1.10625
$809$	2.70449e8	0.0179583	0.00897917	−	0.999960i	$-0.497142\pi$
$809$	2.70449e8	0.0179583	0.00897917	+	0.999960i	$0.497142\pi$
$810$	−5.81772e8	−0.0384641
$811$	−1.73776e9	−0.114398	−0.0571989	−	0.998363i	$-0.518217\pi$
$811$	−1.73776e9	−0.114398	−0.0571989	+	0.998363i	$0.518217\pi$
$812$	7.35099e8	0.0481837
$813$	−3.78862e9	−0.247266
$814$	2.77781e10	1.80516
$815$	3.39561e9	0.219718
$816$	−2.79642e9	−0.180172
$817$	3.66091e7	0.00234862
$818$	−4.36701e9	−0.278964
$819$	−1.42399e10	−0.905759
$820$	−3.42261e8	−0.0216775
$821$	2.90103e10	1.82958	0.914791	−	0.403928i	$-0.132355\pi$
$821$	2.90103e10	1.82958	0.914791	+	0.403928i	$0.132355\pi$
$822$	3.25756e9	0.204570
$823$	1.99700e10	1.24876	0.624379	−	0.781122i	$-0.285352\pi$
$823$	1.99700e10	1.24876	0.624379	+	0.781122i	$0.285352\pi$
$824$	1.32864e10	0.827299
$825$	3.12675e9	0.193867
$826$	1.98362e10	1.22469
$827$	−1.04944e10	−0.645193	−0.322597	−	0.946537i	$-0.604556\pi$
$827$	−1.04944e10	−0.645193	−0.322597	+	0.946537i	$0.604556\pi$
$828$	6.69983e8	0.0410164
$829$	−2.15421e10	−1.31325	−0.656625	−	0.754218i	$-0.728016\pi$
$829$	−2.15421e10	−1.31325	−0.656625	+	0.754218i	$0.728016\pi$
$830$	4.55683e9	0.276624
$831$	−7.85988e9	−0.475130
$832$	−3.10694e10	−1.87026
$833$	1.39512e10	0.836287
$834$	7.07425e9	0.422279
$835$	−6.20923e9	−0.369092
$836$	−1.55795e8	−0.00922215
$837$	3.51717e9	0.207326
$838$	−2.02402e10	−1.18812
$839$	−1.14187e10	−0.667498	−0.333749	−	0.942662i	$-0.608314\pi$
$839$	−1.14187e10	−0.667498	−0.333749	+	0.942662i	$0.608314\pi$
$840$	7.09325e9	0.412922
$841$	−1.71353e10	−0.993356
$842$	−9.32340e9	−0.538248
$843$	1.37762e10	0.792015
$844$	−1.61276e9	−0.0923358
$845$	1.87806e10	1.07081
$846$	1.02962e9	0.0584628
$847$	4.74391e10	2.68253
$848$	8.75379e8	0.0492959
$849$	6.15916e9	0.345418
$850$	−1.97248e9	−0.110166
$851$	7.66645e9	0.426423
$852$	1.29785e9	0.0718929
$853$	9.38139e9	0.517542	0.258771	−	0.965939i	$-0.416682\pi$
$853$	9.38139e9	0.517542	0.258771	+	0.965939i	$0.416682\pi$
$854$	1.45258e10	0.798062
$855$	3.73366e7	0.00204293
$856$	−4.30298e9	−0.234483
$857$	1.57142e10	0.852826	0.426413	−	0.904529i	$-0.359777\pi$
$857$	1.57142e10	0.852826	0.426413	+	0.904529i	$0.359777\pi$
$858$	2.55767e10	1.38241
$859$	−8.67241e9	−0.466835	−0.233418	−	0.972377i	$-0.574991\pi$
$859$	−8.67241e9	−0.466835	−0.233418	+	0.972377i	$0.574991\pi$
$860$	−5.72993e8	−0.0307188
$861$	1.92867e9	0.102979
$862$	−2.44350e10	−1.29938
$863$	−1.44436e10	−0.764961	−0.382480	−	0.923964i	$-0.624930\pi$
$863$	−1.44436e10	−0.764961	−0.382480	+	0.923964i	$0.624930\pi$
$864$	−2.71765e9	−0.143349
$865$	1.47809e10	0.776507
$866$	−1.98884e10	−1.04061
$867$	−5.46898e9	−0.284996
$868$	−1.22700e10	−0.636833
$869$	−2.44571e10	−1.26426
$870$	3.16421e8	0.0162910
$871$	1.37829e10	0.706768
$872$	4.19034e9	0.214013
$873$	4.82294e9	0.245337
$874$	6.42797e7	0.00325675
$875$	2.61412e9	0.131916
$876$	7.61459e9	0.382721
$877$	−3.05357e10	−1.52865	−0.764327	−	0.644829i	$-0.776929\pi$
$877$	−3.05357e10	−1.52865	−0.764327	+	0.644829i	$0.776929\pi$
$878$	−1.84179e10	−0.918354
$879$	−4.54181e9	−0.225563
$880$	−6.65658e9	−0.329277
$881$	1.64615e10	0.811063	0.405532	−	0.914081i	$-0.367086\pi$
$881$	1.64615e10	0.811063	0.405532	+	0.914081i	$0.367086\pi$
$882$	−6.17906e9	−0.303237
$883$	6.48699e8	0.0317089	0.0158544	−	0.999874i	$-0.494953\pi$
$883$	6.48699e8	0.0317089	0.0158544	+	0.999874i	$0.494953\pi$
$884$	1.07929e10	0.525477
$885$	−5.71148e9	−0.276979
$886$	2.36961e10	1.14461
$887$	−3.02429e10	−1.45509	−0.727547	−	0.686058i	$-0.759340\pi$
$887$	−3.02429e10	−1.45509	−0.727547	+	0.686058i	$0.759340\pi$
$888$	−1.81445e10	−0.869562
$889$	−1.86349e10	−0.889552
$890$	−9.31531e9	−0.442927
$891$	3.93880e9	0.186549
$892$	7.96839e9	0.375918
$893$	−6.60783e7	−0.00310512
$894$	−3.62870e9	−0.169851
$895$	−1.15252e9	−0.0537362
$896$	−1.29935e9	−0.0603459
$897$	7.05888e9	0.326560
$898$	−1.84793e10	−0.851567
$899$	−1.91296e9	−0.0878104
$900$	−5.84380e8	−0.0267206
$901$	−1.75618e9	−0.0799896
$902$	−3.46415e9	−0.157171
$903$	3.22887e9	0.145930
$904$	−2.78537e10	−1.25399
$905$	−9.93993e9	−0.445772
$906$	1.91549e10	0.855719
$907$	−3.51061e10	−1.56227	−0.781136	−	0.624361i	$-0.785359\pi$
$907$	−3.51061e10	−1.56227	−0.781136	+	0.624361i	$0.785359\pi$
$908$	−5.46755e9	−0.242378
$909$	7.70096e9	0.340072
$910$	2.13834e10	0.940657
$911$	1.98834e10	0.871318	0.435659	−	0.900112i	$-0.356515\pi$
$911$	1.98834e10	0.871318	0.435659	+	0.900112i	$0.356515\pi$
$912$	−7.94865e7	−0.00346986
$913$	−3.08513e10	−1.34161
$914$	1.99152e9	0.0862727
$915$	−4.18244e9	−0.180491
$916$	−1.58837e9	−0.0682838
$917$	6.34113e10	2.71565
$918$	−2.48476e9	−0.106007
$919$	3.04145e10	1.29263	0.646317	−	0.763069i	$-0.276308\pi$
$919$	3.04145e10	1.29263	0.646317	+	0.763069i	$0.276308\pi$
$920$	−3.51621e9	−0.148874
$921$	1.53327e10	0.646709
$922$	4.80686e9	0.201978
$923$	1.36740e10	0.572388
$924$	−1.37409e10	−0.573012
$925$	−6.68691e9	−0.277798
$926$	−4.37794e9	−0.181189
$927$	6.16820e9	0.254319
$928$	1.47811e9	0.0607139
$929$	−1.54054e10	−0.630402	−0.315201	−	0.949025i	$-0.602072\pi$
$929$	−1.54054e10	−0.630402	−0.315201	+	0.949025i	$0.602072\pi$
$930$	−5.28157e9	−0.215314
$931$	3.96556e8	0.0161057
$932$	−6.64811e9	−0.268994
$933$	−1.80367e10	−0.727062
$934$	−1.95570e10	−0.785393
$935$	1.33544e10	0.534299
$936$	−1.67066e10	−0.665920
$937$	1.59155e10	0.632022	0.316011	−	0.948755i	$-0.397656\pi$
$937$	1.59155e10	0.632022	0.316011	+	0.948755i	$0.397656\pi$
$938$	1.10698e10	0.437955
$939$	6.52346e9	0.257128
$940$	1.03423e9	0.0406136
$941$	2.40112e10	0.939400	0.469700	−	0.882826i	$-0.344362\pi$
$941$	2.40112e10	0.939400	0.469700	+	0.882826i	$0.344362\pi$
$942$	9.55857e9	0.372576
$943$	−9.56068e8	−0.0371277
$944$	1.21593e10	0.470441
$945$	3.29304e9	0.126936
$946$	−5.79947e9	−0.222725
$947$	8.05811e8	0.0308325	0.0154162	−	0.999881i	$-0.495093\pi$
$947$	8.05811e8	0.0308325	0.0154162	+	0.999881i	$0.495093\pi$
$948$	4.57096e9	0.174252
$949$	8.02267e10	3.04710
$950$	−5.60667e7	−0.00212164
$951$	−2.62944e10	−0.991361
$952$	3.02955e10	1.13802
$953$	2.64373e10	0.989447	0.494723	−	0.869050i	$-0.335269\pi$
$953$	2.64373e10	0.989447	0.494723	+	0.869050i	$0.335269\pi$
$954$	7.77820e8	0.0290041
$955$	−9.31561e8	−0.0346098
$956$	−1.70536e10	−0.631268
$957$	−2.14228e9	−0.0790104
$958$	3.09507e10	1.13734
$959$	−1.84390e10	−0.675105
$960$	7.18494e9	0.262104
$961$	4.41771e9	0.160570
$962$	−5.46986e10	−1.98091
$963$	−1.99766e9	−0.0720823
$964$	−1.17184e10	−0.421306
$965$	−7.15094e9	−0.256164
$966$	5.66938e9	0.202356
$967$	−5.21065e10	−1.85310	−0.926552	−	0.376167i	$-0.877242\pi$
$967$	−5.21065e10	−1.85310	−0.926552	+	0.376167i	$0.877242\pi$
$968$	5.56568e10	1.97222
$969$	1.59466e8	0.00563033
$970$	−7.24239e9	−0.254789
$971$	7.86045e9	0.275537	0.137769	−	0.990464i	$-0.456007\pi$
$971$	7.86045e9	0.275537	0.137769	+	0.990464i	$0.456007\pi$
$972$	−7.36150e8	−0.0257119
$973$	−4.00428e10	−1.39357
$974$	−2.38731e10	−0.827852
$975$	−6.15697e9	−0.212741
$976$	8.90407e9	0.306559
$977$	−1.16546e10	−0.399822	−0.199911	−	0.979814i	$-0.564065\pi$
$977$	−1.16546e10	−0.399822	−0.199911	+	0.979814i	$0.564065\pi$
$978$	−6.42331e9	−0.219570
$979$	6.30679e10	2.14817
$980$	−6.20675e9	−0.210656
$981$	1.94536e9	0.0657898
$982$	4.25651e10	1.43438
$983$	1.58904e10	0.533576	0.266788	−	0.963755i	$-0.414038\pi$
$983$	1.58904e10	0.533576	0.266788	+	0.963755i	$0.414038\pi$
$984$	2.26277e9	0.0757107
$985$	−7.62618e9	−0.254261
$986$	1.35144e9	0.0448981
$987$	−5.82801e9	−0.192935
$988$	3.06781e8	0.0101200
$989$	−1.60059e9	−0.0526130
$990$	−5.91472e9	−0.193736
$991$	−3.50706e10	−1.14468	−0.572342	−	0.820015i	$-0.693965\pi$
$991$	−3.50706e10	−1.14468	−0.572342	+	0.820015i	$0.693965\pi$
$992$	−2.46720e10	−0.802442
$993$	−1.15006e10	−0.372732
$994$	1.09824e10	0.354686
$995$	1.89853e10	0.610994
$996$	5.76602e9	0.184913
$997$	5.92011e10	1.89189	0.945947	−	0.324322i	$-0.105136\pi$
$997$	5.92011e10	1.89189	0.945947	+	0.324322i	$0.105136\pi$
$998$	−2.11061e9	−0.0672126
$999$	−8.42358e9	−0.267312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.8.a.c.1.1	✓	2
3.2	odd	2		45.8.a.i.1.2		2
4.3	odd	2		240.8.a.p.1.1		2
5.2	odd	4		75.8.b.d.49.2		4
5.3	odd	4		75.8.b.d.49.3		4
5.4	even	2		75.8.a.e.1.2		2
15.2	even	4		225.8.b.n.199.3		4
15.8	even	4		225.8.b.n.199.2		4
15.14	odd	2		225.8.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.8.a.c.1.1	✓	2	1.1	even	1	trivial
45.8.a.i.1.2		2	3.2	odd	2
75.8.a.e.1.2		2	5.4	even	2
75.8.b.d.49.2		4	5.2	odd	4
75.8.b.d.49.3		4	5.3	odd	4
225.8.a.t.1.1		2	15.14	odd	2
225.8.b.n.199.2		4	15.8	even	4
225.8.b.n.199.3		4	15.2	even	4
240.8.a.p.1.1		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q-8.75765 q^{2} +27.0000 q^{3} -51.3036 q^{4} +125.000 q^{5} -236.457 q^{6} +1338.43 q^{7} +1570.28 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.75765 q^{2} +27.0000 q^{3} -51.3036 q^{4} +125.000 q^{5} -236.457 q^{6} +1338.43 q^{7} +1570.28 q^{8} +729.000 q^{9} -1094.71 q^{10} +7411.55 q^{11} -1385.20 q^{12} -14594.3 q^{13} -11721.5 q^{14} +3375.00 q^{15} -7185.09 q^{16} +14414.7 q^{17} -6384.33 q^{18} +409.730 q^{19} -6412.94 q^{20} +36137.6 q^{21} -64907.8 q^{22} -17913.8 q^{23} +42397.5 q^{24} +15625.0 q^{25} +127812. q^{26} +19683.0 q^{27} -68666.1 q^{28} -10705.4 q^{29} -29557.1 q^{30} +178691. q^{31} -138071. q^{32} +200112. q^{33} -126239. q^{34} +167304. q^{35} -37400.3 q^{36} -427962. q^{37} -3588.27 q^{38} -394046. q^{39} +196285. q^{40} +53370.3 q^{41} -316480. q^{42} +89349.4 q^{43} -380239. q^{44} +91125.0 q^{45} +156883. q^{46} -161273. q^{47} -193997. q^{48} +967848. q^{49} -136838. q^{50} +389197. q^{51} +748740. q^{52} -121833. q^{53} -172377. q^{54} +926444. q^{55} +2.10170e6 q^{56} +11062.7 q^{57} +93754.2 q^{58} -1.69229e6 q^{59} -173149. q^{60} -1.23924e6 q^{61} -1.56491e6 q^{62} +975714. q^{63} +2.12887e6 q^{64} -1.82429e6 q^{65} -1.75251e6 q^{66} -944402. q^{67} -739526. q^{68} -483674. q^{69} -1.46519e6 q^{70} -936943. q^{71} +1.14473e6 q^{72} -5.49712e6 q^{73} +3.74794e6 q^{74} +421875. q^{75} -21020.6 q^{76} +9.91983e6 q^{77} +3.45092e6 q^{78} -3.29987e6 q^{79} -898136. q^{80} +531441. q^{81} -467399. q^{82} -4.16260e6 q^{83} -1.85399e6 q^{84} +1.80184e6 q^{85} -782491. q^{86} -289046. q^{87} +1.16382e7 q^{88} +8.50941e6 q^{89} -798041. q^{90} -1.95334e7 q^{91} +919044. q^{92} +4.82465e6 q^{93} +1.41237e6 q^{94} +51216.2 q^{95} -3.72792e6 q^{96} +6.61583e6 q^{97} -8.47607e6 q^{98} +5.40302e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 7 q^{2} + 54 q^{3} + 69 q^{4} + 250 q^{5} + 189 q^{6} + 1304 q^{7} + 1449 q^{8} + 1458 q^{9}+O(q^{10}) \) 2 * q + 7 * q^2 + 54 * q^3 + 69 * q^4 + 250 * q^5 + 189 * q^6 + 1304 * q^7 + 1449 * q^8 + 1458 * q^9	\( 2 q + 7 q^{2} + 54 q^{3} + 69 q^{4} + 250 q^{5} + 189 q^{6} + 1304 q^{7} + 1449 q^{8} + 1458 q^{9} + 875 q^{10} + 3448 q^{11} + 1863 q^{12} - 8988 q^{13} - 12264 q^{14} + 6750 q^{15} - 24495 q^{16} - 5492 q^{17} + 5103 q^{18} - 49584 q^{19} + 8625 q^{20} + 35208 q^{21} - 127364 q^{22} + 91848 q^{23} + 39123 q^{24} + 31250 q^{25} + 216154 q^{26} + 39366 q^{27} - 72808 q^{28} + 181772 q^{29} + 23625 q^{30} + 304232 q^{31} - 395311 q^{32} + 93096 q^{33} - 439922 q^{34} + 163000 q^{35} + 50301 q^{36} - 502316 q^{37} - 791372 q^{38} - 242676 q^{39} + 181125 q^{40} + 631172 q^{41} - 331128 q^{42} + 353640 q^{43} - 857068 q^{44} + 182250 q^{45} + 1886472 q^{46} - 467480 q^{47} - 661365 q^{48} + 145490 q^{49} + 109375 q^{50} - 148284 q^{51} + 1423198 q^{52} - 568052 q^{53} + 137781 q^{54} + 431000 q^{55} + 2105880 q^{56} - 1338768 q^{57} + 3126746 q^{58} + 287224 q^{59} + 232875 q^{60} - 2514180 q^{61} + 413328 q^{62} + 950616 q^{63} + 291041 q^{64} - 1123500 q^{65} - 3438828 q^{66} - 5073832 q^{67} - 3134374 q^{68} + 2479896 q^{69} - 1533000 q^{70} - 3748816 q^{71} + 1056321 q^{72} - 1477212 q^{73} + 2576306 q^{74} + 843750 q^{75} - 6035444 q^{76} + 10056288 q^{77} + 5836158 q^{78} - 4627720 q^{79} - 3061875 q^{80} + 1062882 q^{81} + 8637398 q^{82} - 6072936 q^{83} - 1965816 q^{84} - 686500 q^{85} + 3382108 q^{86} + 4907844 q^{87} + 12118884 q^{88} + 16516356 q^{89} + 637875 q^{90} - 19726448 q^{91} + 14123784 q^{92} + 8214264 q^{93} - 3412736 q^{94} - 6198000 q^{95} - 10673397 q^{96} + 2723428 q^{97} - 21434497 q^{98} + 2513592 q^{99}+O(q^{100}) \) 2 * q + 7 * q^2 + 54 * q^3 + 69 * q^4 + 250 * q^5 + 189 * q^6 + 1304 * q^7 + 1449 * q^8 + 1458 * q^9 + 875 * q^10 + 3448 * q^11 + 1863 * q^12 - 8988 * q^13 - 12264 * q^14 + 6750 * q^15 - 24495 * q^16 - 5492 * q^17 + 5103 * q^18 - 49584 * q^19 + 8625 * q^20 + 35208 * q^21 - 127364 * q^22 + 91848 * q^23 + 39123 * q^24 + 31250 * q^25 + 216154 * q^26 + 39366 * q^27 - 72808 * q^28 + 181772 * q^29 + 23625 * q^30 + 304232 * q^31 - 395311 * q^32 + 93096 * q^33 - 439922 * q^34 + 163000 * q^35 + 50301 * q^36 - 502316 * q^37 - 791372 * q^38 - 242676 * q^39 + 181125 * q^40 + 631172 * q^41 - 331128 * q^42 + 353640 * q^43 - 857068 * q^44 + 182250 * q^45 + 1886472 * q^46 - 467480 * q^47 - 661365 * q^48 + 145490 * q^49 + 109375 * q^50 - 148284 * q^51 + 1423198 * q^52 - 568052 * q^53 + 137781 * q^54 + 431000 * q^55 + 2105880 * q^56 - 1338768 * q^57 + 3126746 * q^58 + 287224 * q^59 + 232875 * q^60 - 2514180 * q^61 + 413328 * q^62 + 950616 * q^63 + 291041 * q^64 - 1123500 * q^65 - 3438828 * q^66 - 5073832 * q^67 - 3134374 * q^68 + 2479896 * q^69 - 1533000 * q^70 - 3748816 * q^71 + 1056321 * q^72 - 1477212 * q^73 + 2576306 * q^74 + 843750 * q^75 - 6035444 * q^76 + 10056288 * q^77 + 5836158 * q^78 - 4627720 * q^79 - 3061875 * q^80 + 1062882 * q^81 + 8637398 * q^82 - 6072936 * q^83 - 1965816 * q^84 - 686500 * q^85 + 3382108 * q^86 + 4907844 * q^87 + 12118884 * q^88 + 16516356 * q^89 + 637875 * q^90 - 19726448 * q^91 + 14123784 * q^92 + 8214264 * q^93 - 3412736 * q^94 - 6198000 * q^95 - 10673397 * q^96 + 2723428 * q^97 - 21434497 * q^98 + 2513592 * q^99

Introduction

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