LMFDB - Embedded newform 7.18.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,18,Mod(1,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("7.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	7.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:	$12.8255461141$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 2290x^{2} - 4009x + 1104138 $ x^4 - 2x^3 - 2290x^2 - 4009*x + 1104138
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-32.4553$ of defining polynomial
Character	$\chi$	$=$	7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-404.862 q^{2} -14458.1 q^{3} +32840.9 q^{4} +1.27737e6 q^{5} +5.85352e6 q^{6} -5.76480e6 q^{7} +3.97700e7 q^{8} +7.98958e7 q^{9} +O(q^{10})$	\(q-404.862 q^{2} -14458.1 q^{3} +32840.9 q^{4} +1.27737e6 q^{5} +5.85352e6 q^{6} -5.76480e6 q^{7} +3.97700e7 q^{8} +7.98958e7 q^{9} -5.17159e8 q^{10} +9.48848e8 q^{11} -4.74816e8 q^{12} -5.26224e9 q^{13} +2.33395e9 q^{14} -1.84683e10 q^{15} -2.04059e10 q^{16} +1.14444e10 q^{17} -3.23467e10 q^{18} +4.84720e10 q^{19} +4.19500e10 q^{20} +8.33479e10 q^{21} -3.84152e11 q^{22} -2.59488e11 q^{23} -5.74998e11 q^{24} +8.68740e11 q^{25} +2.13048e12 q^{26} +7.11979e11 q^{27} -1.89321e11 q^{28} -5.77266e11 q^{29} +7.47712e12 q^{30} -3.05156e12 q^{31} +3.04882e12 q^{32} -1.37185e13 q^{33} -4.63338e12 q^{34} -7.36380e12 q^{35} +2.62385e12 q^{36} -3.74633e13 q^{37} -1.96244e13 q^{38} +7.60818e13 q^{39} +5.08011e13 q^{40} -6.58913e13 q^{41} -3.37444e13 q^{42} -5.34485e13 q^{43} +3.11610e13 q^{44} +1.02057e14 q^{45} +1.05057e14 q^{46} +1.05725e13 q^{47} +2.95030e14 q^{48} +3.32329e13 q^{49} -3.51720e14 q^{50} -1.65463e14 q^{51} -1.72816e14 q^{52} +5.93568e13 q^{53} -2.88253e14 q^{54} +1.21203e15 q^{55} -2.29266e14 q^{56} -7.00812e14 q^{57} +2.33713e14 q^{58} +8.69300e13 q^{59} -6.06517e14 q^{60} -2.53511e15 q^{61} +1.23546e15 q^{62} -4.60583e14 q^{63} +1.44029e15 q^{64} -6.72184e15 q^{65} +5.55410e15 q^{66} -9.46111e14 q^{67} +3.75843e14 q^{68} +3.75170e15 q^{69} +2.98132e15 q^{70} +4.24375e15 q^{71} +3.17746e15 q^{72} +3.23795e15 q^{73} +1.51674e16 q^{74} -1.25603e16 q^{75} +1.59186e15 q^{76} -5.46992e15 q^{77} -3.08026e16 q^{78} +1.73428e16 q^{79} -2.60659e16 q^{80} -2.06116e16 q^{81} +2.66769e16 q^{82} -2.79618e16 q^{83} +2.73722e15 q^{84} +1.46187e16 q^{85} +2.16393e16 q^{86} +8.34616e15 q^{87} +3.77357e16 q^{88} -3.32163e16 q^{89} -4.13188e16 q^{90} +3.03357e16 q^{91} -8.52183e15 q^{92} +4.41197e16 q^{93} -4.28040e15 q^{94} +6.19168e16 q^{95} -4.40800e16 q^{96} -9.03701e16 q^{97} -1.34547e16 q^{98} +7.58090e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 186 q^{2} - 2786 q^{3} - 16300 q^{4} + 274722 q^{5} + 1469804 q^{6} - 23059204 q^{7} + 8649336 q^{8} - 2050976 q^{9}+O(q^{10}) $ 4 * q + 186 * q^2 - 2786 * q^3 - 16300 * q^4 + 274722 * q^5 + 1469804 * q^6 - 23059204 * q^7 + 8649336 * q^8 - 2050976 * q^9	\( 4 q + 186 q^{2} - 2786 q^{3} - 16300 q^{4} + 274722 q^{5} + 1469804 q^{6} - 23059204 q^{7} + 8649336 q^{8} - 2050976 q^{9} - 893891656 q^{10} + 610110180 q^{11} - 1826039320 q^{12} - 8514921674 q^{13} - 1072252986 q^{14} - 30645264896 q^{15} - 47269015792 q^{16} - 47762899716 q^{17} - 148424524342 q^{18} - 142813479494 q^{19} - 88080723360 q^{20} + 16060735586 q^{21} - 25116572128 q^{22} + 161322432240 q^{23} + 387147758256 q^{24} + 1921891698992 q^{25} + 2984730379008 q^{26} + 2041714521028 q^{27} + 93966256300 q^{28} + 2470023989364 q^{29} + 6457134393152 q^{30} + 3069063677988 q^{31} - 7036366816032 q^{32} - 14819614563824 q^{33} - 9992374959252 q^{34} - 1583717660322 q^{35} - 18927631502956 q^{36} - 53477713304508 q^{37} - 51421850028780 q^{38} - 4140246547640 q^{39} + 22110911913216 q^{40} - 84856086719628 q^{41} - 8473127569004 q^{42} + 14664094189676 q^{43} + 237550257793824 q^{44} + 160924162333018 q^{45} + 187722899918496 q^{46} + 110590112906028 q^{47} + 428386513367456 q^{48} + 132931722278404 q^{49} + 539831164264974 q^{50} - 229270804715244 q^{51} + 68940623118416 q^{52} - 517697020820328 q^{53} - 32330860930648 q^{54} - 17\!\cdots\!44 q^{55}+ \cdots - 57\!\cdots\!28 q^{99}+O(q^{100}) \) 4 * q + 186 * q^2 - 2786 * q^3 - 16300 * q^4 + 274722 * q^5 + 1469804 * q^6 - 23059204 * q^7 + 8649336 * q^8 - 2050976 * q^9 - 893891656 * q^10 + 610110180 * q^11 - 1826039320 * q^12 - 8514921674 * q^13 - 1072252986 * q^14 - 30645264896 * q^15 - 47269015792 * q^16 - 47762899716 * q^17 - 148424524342 * q^18 - 142813479494 * q^19 - 88080723360 * q^20 + 16060735586 * q^21 - 25116572128 * q^22 + 161322432240 * q^23 + 387147758256 * q^24 + 1921891698992 * q^25 + 2984730379008 * q^26 + 2041714521028 * q^27 + 93966256300 * q^28 + 2470023989364 * q^29 + 6457134393152 * q^30 + 3069063677988 * q^31 - 7036366816032 * q^32 - 14819614563824 * q^33 - 9992374959252 * q^34 - 1583717660322 * q^35 - 18927631502956 * q^36 - 53477713304508 * q^37 - 51421850028780 * q^38 - 4140246547640 * q^39 + 22110911913216 * q^40 - 84856086719628 * q^41 - 8473127569004 * q^42 + 14664094189676 * q^43 + 237550257793824 * q^44 + 160924162333018 * q^45 + 187722899918496 * q^46 + 110590112906028 * q^47 + 428386513367456 * q^48 + 132931722278404 * q^49 + 539831164264974 * q^50 - 229270804715244 * q^51 + 68940623118416 * q^52 - 517697020820328 * q^53 - 32330860930648 * q^54 - 1701016442036744 * q^55 - 49861700822136 * q^56 - 2352229307493836 * q^57 + 1035155400175604 * q^58 - 2778221577040518 * q^59 + 62096128416896 * q^60 - 3329268765288494 * q^61 - 406874975162376 * q^62 + 11823468495776 * q^63 + 3892676387300416 * q^64 - 1795213174093500 * q^65 + 9560762631234080 * q^66 - 1542501737022560 * q^67 + 5553778722869496 * q^68 + 829434613465248 * q^69 + 5153107512400456 * q^70 + 739192660163448 * q^71 + 16950595160647800 * q^72 - 1768956758306304 * q^73 + 24304533536274948 * q^74 - 22124527120060246 * q^75 + 614659296403544 * q^76 - 3517163775774180 * q^77 - 22122617539685488 * q^78 + 1824334397417480 * q^79 - 5329944020335872 * q^80 - 13182300720284792 * q^81 - 36215502923183444 * q^82 - 49183281603250158 * q^83 + 10526753297975320 * q^84 - 44968305361101900 * q^85 - 11999423939098896 * q^86 + 29283570071010892 * q^87 + 47237077355248704 * q^88 - 138655399526807016 * q^89 + 33550243342273112 * q^90 + 49086828981196874 * q^91 - 49994746660573248 * q^92 + 171997447280309016 * q^93 + 97111697039664552 * q^94 + 276760012078126224 * q^95 - 174317142260969792 * q^96 + 73446338844858924 * q^97 + 6181325085945786 * q^98 - 57479877480434828 * 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 $

$2$	−404.862	−1.11828	−0.559141	−	0.829072i	$-0.688869\pi$
$2$	−404.862	−1.11828	−0.559141	+	0.829072i	$0.688869\pi$
$3$	−14458.1	−1.27227	−0.636136	−	0.771577i	$-0.719468\pi$
$3$	−14458.1	−1.27227	−0.636136	+	0.771577i	$0.719468\pi$
$4$	32840.9	0.250556
$5$	1.27737e6	1.46242	0.731211	−	0.682152i	$-0.238956\pi$
$5$	1.27737e6	1.46242	0.731211	+	0.682152i	$0.238956\pi$
$6$	5.85352e6	1.42276
$7$	−5.76480e6	−0.377964
$7$	−5.76480e6	−0.377964
$8$	3.97700e7	0.838090
$9$	7.98958e7	0.618675
$10$	−5.17159e8	−1.63540
$11$	9.48848e8	1.33462	0.667312	−	0.744778i	$-0.267445\pi$
$11$	9.48848e8	1.33462	0.667312	+	0.744778i	$0.267445\pi$
$12$	−4.74816e8	−0.318775
$13$	−5.26224e9	−1.78917	−0.894586	−	0.446897i	$-0.852529\pi$
$13$	−5.26224e9	−1.78917	−0.894586	+	0.446897i	$0.852529\pi$
$14$	2.33395e9	0.422671
$15$	−1.84683e10	−1.86060
$16$	−2.04059e10	−1.18778
$17$	1.14444e10	0.397902	0.198951	−	0.980009i	$-0.436247\pi$
$17$	1.14444e10	0.397902	0.198951	+	0.980009i	$0.436247\pi$
$18$	−3.23467e10	−0.691853
$19$	4.84720e10	0.654765	0.327382	−	0.944892i	$-0.393834\pi$
$19$	4.84720e10	0.654765	0.327382	+	0.944892i	$0.393834\pi$
$20$	4.19500e10	0.366418
$21$	8.33479e10	0.480873
$22$	−3.84152e11	−1.49249
$23$	−2.59488e11	−0.690926	−0.345463	−	0.938432i	$-0.612278\pi$
$23$	−2.59488e11	−0.690926	−0.345463	+	0.938432i	$0.612278\pi$
$24$	−5.74998e11	−1.06628
$25$	8.68740e11	1.13868
$26$	2.13048e12	2.00080
$27$	7.11979e11	0.485149
$28$	−1.89321e11	−0.0947013
$29$	−5.77266e11	−0.214286	−0.107143	−	0.994244i	$-0.534170\pi$
$29$	−5.77266e11	−0.214286	−0.107143	+	0.994244i	$0.534170\pi$
$30$	7.47712e12	2.08067
$31$	−3.05156e12	−0.642611	−0.321305	−	0.946976i	$-0.604122\pi$
$31$	−3.05156e12	−0.642611	−0.321305	+	0.946976i	$0.604122\pi$
$32$	3.04882e12	0.490181
$33$	−1.37185e13	−1.69800
$34$	−4.63338e12	−0.444966
$35$	−7.36380e12	−0.552743
$36$	2.62385e12	0.155013
$37$	−3.74633e13	−1.75344	−0.876721	−	0.481000i	$-0.840274\pi$
$37$	−3.74633e13	−1.75344	−0.876721	+	0.481000i	$0.840274\pi$
$38$	−1.96244e13	−0.732212
$39$	7.60818e13	2.27631
$40$	5.08011e13	1.22564
$41$	−6.58913e13	−1.28874	−0.644370	−	0.764714i	$-0.722880\pi$
$41$	−6.58913e13	−1.28874	−0.644370	+	0.764714i	$0.722880\pi$
$42$	−3.37444e13	−0.537752
$43$	−5.34485e13	−0.697355	−0.348677	−	0.937243i	$-0.613369\pi$
$43$	−5.34485e13	−0.697355	−0.348677	+	0.937243i	$0.613369\pi$
$44$	3.11610e13	0.334398
$45$	1.02057e14	0.904763
$46$	1.05057e14	0.772650
$47$	1.05725e13	0.0647658	0.0323829	−	0.999476i	$-0.489690\pi$
$47$	1.05725e13	0.0647658	0.0323829	+	0.999476i	$0.489690\pi$
$48$	2.95030e14	1.51118
$49$	3.32329e13	0.142857
$50$	−3.51720e14	−1.27336
$51$	−1.65463e14	−0.506239
$52$	−1.72816e14	−0.448288
$53$	5.93568e13	0.130956	0.0654781	−	0.997854i	$-0.479143\pi$
$53$	5.93568e13	0.130956	0.0654781	+	0.997854i	$0.479143\pi$
$54$	−2.88253e14	−0.542534
$55$	1.21203e15	1.95178
$56$	−2.29266e14	−0.316768
$57$	−7.00812e14	−0.833038
$58$	2.33713e14	0.239632
$59$	8.69300e13	0.0770775	0.0385387	−	0.999257i	$-0.487730\pi$
$59$	8.69300e13	0.0770775	0.0385387	+	0.999257i	$0.487730\pi$
$60$	−6.06517e14	−0.466184
$61$	−2.53511e15	−1.69314	−0.846571	−	0.532276i	$-0.821337\pi$
$61$	−2.53511e15	−1.69314	−0.846571	+	0.532276i	$0.821337\pi$
$62$	1.23546e15	0.718620
$63$	−4.60583e14	−0.233837
$64$	1.44029e15	0.639617
$65$	−6.72184e15	−2.61652
$66$	5.55410e15	1.89885
$67$	−9.46111e14	−0.284647	−0.142323	−	0.989820i	$-0.545457\pi$
$67$	−9.46111e14	−0.284647	−0.142323	+	0.989820i	$0.545457\pi$
$68$	3.75843e14	0.0996966
$69$	3.75170e15	0.879045
$70$	2.98132e15	0.618123
$71$	4.24375e15	0.779928	0.389964	−	0.920830i	$-0.372488\pi$
$71$	4.24375e15	0.779928	0.389964	+	0.920830i	$0.372488\pi$
$72$	3.17746e15	0.518505
$73$	3.23795e15	0.469921	0.234961	−	0.972005i	$-0.424504\pi$
$73$	3.23795e15	0.469921	0.234961	+	0.972005i	$0.424504\pi$
$74$	1.51674e16	1.96084
$75$	−1.25603e16	−1.44870
$76$	1.59186e15	0.164055
$77$	−5.46992e15	−0.504441
$78$	−3.08026e16	−2.54556
$79$	1.73428e16	1.28614	0.643070	−	0.765808i	$-0.277661\pi$
$79$	1.73428e16	1.28614	0.643070	+	0.765808i	$0.277661\pi$
$80$	−2.60659e16	−1.73703
$81$	−2.06116e16	−1.23592
$82$	2.66769e16	1.44118
$83$	−2.79618e16	−1.36270	−0.681351	−	0.731957i	$-0.738607\pi$
$83$	−2.79618e16	−1.36270	−0.681351	+	0.731957i	$0.738607\pi$
$84$	2.73722e15	0.120486
$85$	1.46187e16	0.581900
$86$	2.16393e16	0.779840
$87$	8.34616e15	0.272630
$88$	3.77357e16	1.11854
$89$	−3.32163e16	−0.894409	−0.447204	−	0.894432i	$-0.647580\pi$
$89$	−3.32163e16	−0.894409	−0.447204	+	0.894432i	$0.647580\pi$
$90$	−4.13188e16	−1.01178
$91$	3.03357e16	0.676243
$92$	−8.52183e15	−0.173116
$93$	4.41197e16	0.817575
$94$	−4.28040e15	−0.0724265
$95$	6.19168e16	0.957542
$96$	−4.40800e16	−0.623643
$97$	−9.03701e16	−1.17075	−0.585376	−	0.810762i	$-0.699053\pi$
$97$	−9.03701e16	−1.17075	−0.585376	+	0.810762i	$0.699053\pi$
$98$	−1.34547e16	−0.159755
$99$	7.58090e16	0.825698
$100$	2.85302e16	0.285302
$101$	1.61224e17	1.48149	0.740743	−	0.671788i	$-0.234474\pi$
$101$	1.61224e17	1.48149	0.740743	+	0.671788i	$0.234474\pi$
$102$	6.69898e16	0.566118
$103$	−7.27359e16	−0.565760	−0.282880	−	0.959155i	$-0.591290\pi$
$103$	−7.27359e16	−0.565760	−0.282880	+	0.959155i	$0.591290\pi$
$104$	−2.09279e17	−1.49949
$105$	1.06466e17	0.703239
$106$	−2.40313e16	−0.146446
$107$	6.47413e16	0.364266	0.182133	−	0.983274i	$-0.441700\pi$
$107$	6.47413e16	0.364266	0.182133	+	0.983274i	$0.441700\pi$
$108$	2.33820e16	0.121557
$109$	−3.12669e17	−1.50300	−0.751502	−	0.659731i	$-0.770670\pi$
$109$	−3.12669e17	−1.50300	−0.751502	+	0.659731i	$0.770670\pi$
$110$	−4.90705e17	−2.18264
$111$	5.41647e17	2.23085
$112$	1.17636e17	0.448938
$113$	−1.74707e17	−0.618222	−0.309111	−	0.951026i	$-0.600031\pi$
$113$	−1.74707e17	−0.618222	−0.309111	+	0.951026i	$0.600031\pi$
$114$	2.83732e17	0.931572
$115$	−3.31463e17	−1.01042
$116$	−1.89579e16	−0.0536906
$117$	−4.20431e17	−1.10692
$118$	−3.51946e16	−0.0861944
$119$	−6.59744e16	−0.150393
$120$	−7.34486e17	−1.55935
$121$	3.94866e17	0.781222
$122$	1.02637e18	1.89341
$123$	9.52662e17	1.63963
$124$	−1.00216e17	−0.161010
$125$	1.35147e17	0.202802
$126$	1.86472e17	0.261496
$127$	−7.99677e17	−1.04854	−0.524268	−	0.851554i	$-0.675661\pi$
$127$	−7.99677e17	−1.04854	−0.524268	+	0.851554i	$0.675661\pi$
$128$	−9.82732e17	−1.20545
$129$	7.72763e17	0.887225
$130$	2.72141e18	2.92601
$131$	−1.17049e18	−1.17913	−0.589567	−	0.807720i	$-0.700702\pi$
$131$	−1.17049e18	−1.17913	−0.589567	+	0.807720i	$0.700702\pi$
$132$	−4.50528e17	−0.425445
$133$	−2.79431e17	−0.247478
$134$	3.83044e17	0.318315
$135$	9.09462e17	0.709492
$136$	4.55142e17	0.333477
$137$	−1.18005e17	−0.0812409	−0.0406205	−	0.999175i	$-0.512933\pi$
$137$	−1.18005e17	−0.0812409	−0.0406205	+	0.999175i	$0.512933\pi$
$138$	−1.51892e18	−0.983021
$139$	6.03963e16	0.0367608	0.0183804	−	0.999831i	$-0.494149\pi$
$139$	6.03963e16	0.0367608	0.0183804	+	0.999831i	$0.494149\pi$
$140$	−2.41834e17	−0.138493
$141$	−1.52858e17	−0.0823997
$142$	−1.71813e18	−0.872179
$143$	−4.99306e18	−2.38787
$144$	−1.63034e18	−0.734848
$145$	−7.37384e17	−0.313376
$146$	−1.31092e18	−0.525505
$147$	−4.80484e17	−0.181753
$148$	−1.23033e18	−0.439335
$149$	5.11523e18	1.72497	0.862486	−	0.506082i	$-0.168907\pi$
$149$	5.11523e18	1.72497	0.862486	+	0.506082i	$0.168907\pi$
$150$	5.08519e18	1.62006
$151$	5.67942e18	1.71001	0.855007	−	0.518616i	$-0.173552\pi$
$151$	5.67942e18	1.71001	0.855007	+	0.518616i	$0.173552\pi$
$152$	1.92773e18	0.548752
$153$	9.14356e17	0.246172
$154$	2.21456e18	0.564107
$155$	−3.89798e18	−0.939767
$156$	2.49859e18	0.570343
$157$	−1.27614e18	−0.275900	−0.137950	−	0.990439i	$-0.544051\pi$
$157$	−1.27614e18	−0.275900	−0.137950	+	0.990439i	$0.544051\pi$
$158$	−7.02142e18	−1.43827
$159$	−8.58186e17	−0.166612
$160$	3.89447e18	0.716851
$161$	1.49590e18	0.261145
$162$	8.34484e18	1.38210
$163$	−4.86488e18	−0.764676	−0.382338	−	0.924023i	$-0.624881\pi$
$163$	−4.86488e18	−0.764676	−0.382338	+	0.924023i	$0.624881\pi$
$164$	−2.16393e18	−0.322902
$165$	−1.75237e19	−2.48320
$166$	1.13207e19	1.52389
$167$	−9.66843e18	−1.23670	−0.618352	−	0.785901i	$-0.712199\pi$
$167$	−9.66843e18	−1.23670	−0.618352	+	0.785901i	$0.712199\pi$
$168$	3.31475e18	0.403015
$169$	1.90407e19	2.20113
$170$	−5.91855e18	−0.650728
$171$	3.87271e18	0.405086
$172$	−1.75530e18	−0.174726
$173$	1.98002e18	0.187619	0.0938096	−	0.995590i	$-0.470096\pi$
$173$	1.98002e18	0.187619	0.0938096	+	0.995590i	$0.470096\pi$
$174$	−3.37904e18	−0.304877
$175$	−5.00812e18	−0.430379
$176$	−1.93621e19	−1.58524
$177$	−1.25684e18	−0.0980635
$178$	1.34480e19	1.00020
$179$	8.80755e18	0.624603	0.312302	−	0.949983i	$-0.398900\pi$
$179$	8.80755e18	0.624603	0.312302	+	0.949983i	$0.398900\pi$
$180$	3.35163e18	0.226694
$181$	−8.58290e18	−0.553817	−0.276909	−	0.960896i	$-0.589310\pi$
$181$	−8.58290e18	−0.553817	−0.276909	+	0.960896i	$0.589310\pi$
$182$	−1.22818e19	−0.756231
$183$	3.66528e19	2.15414
$184$	−1.03199e19	−0.579058
$185$	−4.78546e19	−2.56427
$186$	−1.78624e19	−0.914280
$187$	1.08590e19	0.531049
$188$	3.47210e17	0.0162275
$189$	−4.10442e18	−0.183369
$190$	−2.50677e19	−1.07080
$191$	2.72111e19	1.11164	0.555818	−	0.831304i	$-0.312405\pi$
$191$	2.72111e19	1.11164	0.555818	+	0.831304i	$0.312405\pi$
$192$	−2.08238e19	−0.813766
$193$	1.50530e19	0.562840	0.281420	−	0.959585i	$-0.409195\pi$
$193$	1.50530e19	0.562840	0.281420	+	0.959585i	$0.409195\pi$
$194$	3.65874e19	1.30923
$195$	9.71848e19	3.32893
$196$	1.09140e18	0.0357937
$197$	−3.18656e18	−0.100083	−0.0500413	−	0.998747i	$-0.515935\pi$
$197$	−3.18656e18	−0.100083	−0.0500413	+	0.998747i	$0.515935\pi$
$198$	−3.06921e19	−0.923364
$199$	2.48446e19	0.716112	0.358056	−	0.933700i	$-0.383440\pi$
$199$	2.48446e19	0.716112	0.358056	+	0.933700i	$0.383440\pi$
$200$	3.45498e19	0.954313
$201$	1.36789e19	0.362148
$202$	−6.52733e19	−1.65672
$203$	3.32783e18	0.0809924
$204$	−5.43396e18	−0.126841
$205$	−8.41678e19	−1.88468
$206$	2.94480e19	0.632680
$207$	−2.07320e19	−0.427458
$208$	1.07380e20	2.12514
$209$	4.59926e19	0.873865
$210$	−4.31041e19	−0.786420
$211$	−9.38713e19	−1.64487	−0.822436	−	0.568857i	$-0.807386\pi$
$211$	−9.38713e19	−1.64487	−0.822436	+	0.568857i	$0.807386\pi$
$212$	1.94933e18	0.0328118
$213$	−6.13565e19	−0.992280
$214$	−2.62113e19	−0.407353
$215$	−6.82737e19	−1.01983
$216$	2.83154e19	0.406599
$217$	1.75917e19	0.242884
$218$	1.26588e20	1.68078
$219$	−4.68145e19	−0.597868
$220$	3.98042e19	0.489031
$221$	−6.02229e19	−0.711914
$222$	−2.19292e20	−2.49472
$223$	−2.34186e19	−0.256431	−0.128215	−	0.991746i	$-0.540925\pi$
$223$	−2.34186e19	−0.256431	−0.128215	+	0.991746i	$0.540925\pi$
$224$	−1.75758e19	−0.185271
$225$	6.94087e19	0.704470
$226$	7.07323e19	0.691347
$227$	7.51144e19	0.707137	0.353569	−	0.935409i	$-0.384968\pi$
$227$	7.51144e19	0.707137	0.353569	+	0.935409i	$0.384968\pi$
$228$	−2.30153e19	−0.208723
$229$	−9.54194e18	−0.0833748	−0.0416874	−	0.999131i	$-0.513273\pi$
$229$	−9.54194e18	−0.0833748	−0.0416874	+	0.999131i	$0.513273\pi$
$230$	1.34197e20	1.12994
$231$	7.90845e19	0.641785
$232$	−2.29579e19	−0.179591
$233$	4.55075e19	0.343208	0.171604	−	0.985166i	$-0.445105\pi$
$233$	4.55075e19	0.343208	0.171604	+	0.985166i	$0.445105\pi$
$234$	1.70216e20	1.23784
$235$	1.35050e19	0.0947149
$236$	2.85486e18	0.0193122
$237$	−2.50743e20	−1.63632
$238$	2.67105e19	0.168181
$239$	1.98095e20	1.20363	0.601814	−	0.798636i	$-0.294445\pi$
$239$	1.98095e20	1.20363	0.601814	+	0.798636i	$0.294445\pi$
$240$	3.76863e20	2.20998
$241$	−2.03513e20	−1.15199	−0.575994	−	0.817454i	$-0.695385\pi$
$241$	−2.03513e20	−1.15199	−0.575994	+	0.817454i	$0.695385\pi$
$242$	−1.59866e20	−0.873626
$243$	2.06059e20	1.08727
$244$	−8.32553e19	−0.424227
$245$	4.24508e19	0.208917
$246$	−3.85696e20	−1.83357
$247$	−2.55071e20	−1.17149
$248$	−1.21361e20	−0.538566
$249$	4.04274e20	1.73373
$250$	−5.47159e19	−0.226790
$251$	−2.17066e20	−0.869690	−0.434845	−	0.900505i	$-0.643197\pi$
$251$	−2.17066e20	−0.869690	−0.434845	+	0.900505i	$0.643197\pi$
$252$	−1.51260e19	−0.0585893
$253$	−2.46215e20	−0.922126
$254$	3.23759e20	1.17256
$255$	−2.11358e20	−0.740334
$256$	2.09089e20	0.708421
$257$	−1.80503e20	−0.591634	−0.295817	−	0.955245i	$-0.595592\pi$
$257$	−1.80503e20	−0.591634	−0.295817	+	0.955245i	$0.595592\pi$
$258$	−3.12862e20	−0.992168
$259$	2.15968e20	0.662738
$260$	−2.20751e20	−0.655585
$261$	−4.61212e19	−0.132573
$262$	4.73888e20	1.31860
$263$	5.01028e20	1.34970	0.674851	−	0.737954i	$-0.264208\pi$
$263$	5.01028e20	1.34970	0.674851	+	0.737954i	$0.264208\pi$
$264$	−5.45586e20	−1.42308
$265$	7.58208e19	0.191513
$266$	1.13131e20	0.276750
$267$	4.80244e20	1.13793
$268$	−3.10711e19	−0.0713199
$269$	−2.72209e19	−0.0605353	−0.0302677	−	0.999542i	$-0.509636\pi$
$269$	−2.72209e19	−0.0605353	−0.0302677	+	0.999542i	$0.509636\pi$
$270$	−3.68206e20	−0.793413
$271$	−2.43194e20	−0.507825	−0.253912	−	0.967227i	$-0.581717\pi$
$271$	−2.43194e20	−0.507825	−0.253912	+	0.967227i	$0.581717\pi$
$272$	−2.33532e20	−0.472619
$273$	−4.38597e20	−0.860365
$274$	4.77756e19	0.0908503
$275$	8.24303e20	1.51970
$276$	1.23209e20	0.220250
$277$	1.68776e20	0.292572	0.146286	−	0.989242i	$-0.453268\pi$
$277$	1.68776e20	0.292572	0.146286	+	0.989242i	$0.453268\pi$
$278$	−2.44521e19	−0.0411089
$279$	−2.43807e20	−0.397567
$280$	−2.92858e20	−0.463249
$281$	−4.66624e20	−0.716082	−0.358041	−	0.933706i	$-0.616555\pi$
$281$	−4.66624e20	−0.716082	−0.358041	+	0.933706i	$0.616555\pi$
$282$	6.18863e19	0.0921461
$283$	2.97236e20	0.429453	0.214727	−	0.976674i	$-0.431114\pi$
$283$	2.97236e20	0.429453	0.214727	+	0.976674i	$0.431114\pi$
$284$	1.39369e20	0.195415
$285$	−8.95197e20	−1.21825
$286$	2.02150e21	2.67031
$287$	3.79850e20	0.487098
$288$	2.43588e20	0.303263
$289$	−6.96267e20	−0.841674
$290$	2.98538e20	0.350443
$291$	1.30658e21	1.48952
$292$	1.06337e20	0.117742
$293$	9.04984e20	0.973343	0.486672	−	0.873585i	$-0.338211\pi$
$293$	9.04984e20	0.973343	0.486672	+	0.873585i	$0.338211\pi$
$294$	1.94530e20	0.203251
$295$	1.11042e20	0.112720
$296$	−1.48992e21	−1.46954
$297$	6.75560e20	0.647492
$298$	−2.07096e21	−1.92901
$299$	1.36549e21	1.23618
$300$	−4.12492e20	−0.362981
$301$	3.08120e20	0.263575
$302$	−2.29938e21	−1.91228
$303$	−2.33099e21	−1.88485
$304$	−9.89113e20	−0.777715
$305$	−3.23828e21	−2.47609
$306$	−3.70188e20	−0.275290
$307$	3.73819e20	0.270386	0.135193	−	0.990819i	$-0.456834\pi$
$307$	3.73819e20	0.270386	0.135193	+	0.990819i	$0.456834\pi$
$308$	−1.79637e20	−0.126391
$309$	1.05162e21	0.719801
$310$	1.57814e21	1.05093
$311$	1.33106e19	0.00862449	0.00431225	−	0.999991i	$-0.498627\pi$
$311$	1.33106e19	0.00862449	0.00431225	+	0.999991i	$0.498627\pi$
$312$	3.02577e21	1.90775
$313$	−4.32716e20	−0.265507	−0.132754	−	0.991149i	$-0.542382\pi$
$313$	−4.32716e20	−0.265507	−0.132754	+	0.991149i	$0.542382\pi$
$314$	5.16661e20	0.308534
$315$	−5.88336e20	−0.341968
$316$	5.69552e20	0.322250
$317$	2.33408e21	1.28562	0.642810	−	0.766026i	$-0.277768\pi$
$317$	2.33408e21	1.28562	0.642810	+	0.766026i	$0.277768\pi$
$318$	3.47446e20	0.186319
$319$	−5.47738e20	−0.285991
$320$	1.83979e21	0.935389
$321$	−9.36034e20	−0.463446
$322$	−6.05632e20	−0.292034
$323$	5.54731e20	0.260532
$324$	−6.76903e20	−0.309666
$325$	−4.57152e21	−2.03729
$326$	1.96960e21	0.855124
$327$	4.52060e21	1.91223
$328$	−2.62050e21	−1.08008
$329$	−6.09483e19	−0.0244792
$330$	7.09465e21	2.77692
$331$	2.02249e21	0.771521	0.385761	−	0.922599i	$-0.373939\pi$
$331$	2.02249e21	0.771521	0.385761	+	0.922599i	$0.373939\pi$
$332$	−9.18289e20	−0.341433
$333$	−2.99316e21	−1.08481
$334$	3.91438e21	1.38299
$335$	−1.20854e21	−0.416273
$336$	−1.70079e21	−0.571171
$337$	1.07102e21	0.350705	0.175352	−	0.984506i	$-0.443894\pi$
$337$	1.07102e21	0.350705	0.175352	+	0.984506i	$0.443894\pi$
$338$	−7.70886e21	−2.46149
$339$	2.52593e21	0.786546
$340$	4.80091e20	0.145798
$341$	−2.89547e21	−0.857644
$342$	−1.56791e21	−0.453001
$343$	−1.91581e20	−0.0539949
$344$	−2.12565e21	−0.584446
$345$	4.79232e21	1.28553
$346$	−8.01633e20	−0.209811
$347$	−5.39782e21	−1.37854	−0.689268	−	0.724507i	$-0.742068\pi$
$347$	−5.39782e21	−1.37854	−0.689268	+	0.724507i	$0.742068\pi$
$348$	2.74095e20	0.0683090
$349$	−5.00451e20	−0.121715	−0.0608577	−	0.998146i	$-0.519384\pi$
$349$	−5.00451e20	−0.121715	−0.0608577	+	0.998146i	$0.519384\pi$
$350$	2.02759e21	0.481285
$351$	−3.74660e21	−0.868015
$352$	2.89286e21	0.654207
$353$	−3.34725e21	−0.738931	−0.369465	−	0.929244i	$-0.620459\pi$
$353$	−3.34725e21	−0.738931	−0.369465	+	0.929244i	$0.620459\pi$
$354$	5.08846e20	0.109663
$355$	5.42085e21	1.14058
$356$	−1.09085e21	−0.224099
$357$	9.53864e20	0.191340
$358$	−3.56584e21	−0.698483
$359$	−1.26671e20	−0.0242312	−0.0121156	−	0.999927i	$-0.503857\pi$
$359$	−1.26671e20	−0.0242312	−0.0121156	+	0.999927i	$0.503857\pi$
$360$	4.05879e21	0.758273
$361$	−3.13085e21	−0.571283
$362$	3.47489e21	0.619324
$363$	−5.70900e21	−0.993926
$364$	9.96252e20	0.169437
$365$	4.13606e21	0.687223
$366$	−1.48393e22	−2.40893
$367$	−6.78439e20	−0.107609	−0.0538046	−	0.998551i	$-0.517135\pi$
$367$	−6.78439e20	−0.107609	−0.0538046	+	0.998551i	$0.517135\pi$
$368$	5.29509e21	0.820666
$369$	−5.26444e21	−0.797312
$370$	1.93745e22	2.86758
$371$	−3.42180e20	−0.0494968
$372$	1.44893e21	0.204848
$373$	1.07006e22	1.47871	0.739354	−	0.673317i	$-0.235131\pi$
$373$	1.07006e22	1.47871	0.739354	+	0.673317i	$0.235131\pi$
$374$	−4.39638e21	−0.593863
$375$	−1.95397e21	−0.258019
$376$	4.20468e20	0.0542796
$377$	3.03771e21	0.383394
$378$	1.66172e21	0.205058
$379$	6.19448e20	0.0747432	0.0373716	−	0.999301i	$-0.488101\pi$
$379$	6.19448e20	0.0747432	0.0373716	+	0.999301i	$0.488101\pi$
$380$	2.03340e21	0.239918
$381$	1.15618e22	1.33402
$382$	−1.10167e22	−1.24312
$383$	−1.14148e22	−1.25973	−0.629866	−	0.776704i	$-0.716890\pi$
$383$	−1.14148e22	−1.25973	−0.629866	+	0.776704i	$0.716890\pi$
$384$	1.42084e22	1.53366
$385$	−6.98713e21	−0.737704
$386$	−6.09436e21	−0.629414
$387$	−4.27031e21	−0.431436
$388$	−2.96783e21	−0.293339
$389$	1.65408e22	1.59950	0.799750	−	0.600333i	$-0.204965\pi$
$389$	1.65408e22	1.59950	0.799750	+	0.600333i	$0.204965\pi$
$390$	−3.93464e22	−3.72268
$391$	−2.96968e21	−0.274920
$392$	1.32167e21	0.119727
$393$	1.69231e22	1.50018
$394$	1.29011e21	0.111921
$395$	2.21532e22	1.88088
$396$	2.48963e21	0.206884
$397$	1.50473e22	1.22388	0.611940	−	0.790904i	$-0.290389\pi$
$397$	1.50473e22	1.22388	0.611940	+	0.790904i	$0.290389\pi$
$398$	−1.00586e22	−0.800816
$399$	4.04004e21	0.314859
$400$	−1.77274e22	−1.35249
$401$	1.12094e22	0.837249	0.418624	−	0.908159i	$-0.362512\pi$
$401$	1.12094e22	0.837249	0.418624	+	0.908159i	$0.362512\pi$
$402$	−5.53808e21	−0.404984
$403$	1.60580e22	1.14974
$404$	5.29473e21	0.371195
$405$	−2.63287e22	−1.80743
$406$	−1.34731e21	−0.0905724
$407$	−3.55470e22	−2.34018
$408$	−6.58048e21	−0.424274
$409$	−7.61568e21	−0.480907	−0.240453	−	0.970661i	$-0.577296\pi$
$409$	−7.61568e21	−0.480907	−0.240453	+	0.970661i	$0.577296\pi$
$410$	3.40763e22	2.10761
$411$	1.70612e21	0.103361
$412$	−2.38871e21	−0.141755
$413$	−5.01134e20	−0.0291326
$414$	8.39360e21	0.478019
$415$	−3.57176e22	−1.99285
$416$	−1.60436e22	−0.877018
$417$	−8.73214e20	−0.0467697
$418$	−1.86206e22	−0.977228
$419$	−5.92619e21	−0.304759	−0.152380	−	0.988322i	$-0.548694\pi$
$419$	−5.92619e21	−0.304759	−0.152380	+	0.988322i	$0.548694\pi$
$420$	3.49645e21	0.176201
$421$	−1.60117e22	−0.790749	−0.395374	−	0.918520i	$-0.629385\pi$
$421$	−1.60117e22	−0.790749	−0.395374	+	0.918520i	$0.629385\pi$
$422$	3.80049e22	1.83943
$423$	8.44698e20	0.0400690
$424$	2.36062e21	0.109753
$425$	9.94218e21	0.453081
$426$	2.48409e22	1.10965
$427$	1.46144e22	0.639948
$428$	2.12616e21	0.0912691
$429$	7.21901e22	3.03802
$430$	2.76414e22	1.14045
$431$	−3.82323e22	−1.54658	−0.773292	−	0.634051i	$-0.781391\pi$
$431$	−3.82323e22	−1.54658	−0.773292	+	0.634051i	$0.781391\pi$
$432$	−1.45285e22	−0.576249
$433$	−2.90350e22	−1.12921	−0.564606	−	0.825361i	$-0.690972\pi$
$433$	−2.90350e22	−1.12921	−0.564606	+	0.825361i	$0.690972\pi$
$434$	−7.12218e21	−0.271613
$435$	1.06612e22	0.398699
$436$	−1.02683e22	−0.376587
$437$	−1.25779e22	−0.452394
$438$	1.89534e22	0.668585
$439$	4.24152e22	1.46748	0.733741	−	0.679429i	$-0.237772\pi$
$439$	4.24152e22	1.46748	0.733741	+	0.679429i	$0.237772\pi$
$440$	4.82025e22	1.63577
$441$	2.65517e21	0.0883821
$442$	2.43819e22	0.796121
$443$	1.29578e22	0.415049	0.207525	−	0.978230i	$-0.433459\pi$
$443$	1.29578e22	0.415049	0.207525	+	0.978230i	$0.433459\pi$
$444$	1.77882e22	0.558954
$445$	−4.24296e22	−1.30800
$446$	9.48130e21	0.286762
$447$	−7.39564e22	−2.19463
$448$	−8.30298e21	−0.241752
$449$	4.25387e22	1.21532	0.607659	−	0.794198i	$-0.292109\pi$
$449$	4.25387e22	1.21532	0.607659	+	0.794198i	$0.292109\pi$
$450$	−2.81009e22	−0.787796
$451$	−6.25209e22	−1.71998
$452$	−5.73754e21	−0.154899
$453$	−8.21135e22	−2.17560
$454$	−3.04110e22	−0.790779
$455$	3.87500e22	0.988952
$456$	−2.78713e22	−0.698161
$457$	−5.22151e22	−1.28383	−0.641917	−	0.766774i	$-0.721860\pi$
$457$	−5.22151e22	−1.28383	−0.641917	+	0.766774i	$0.721860\pi$
$458$	3.86316e21	0.0932366
$459$	8.14814e21	0.193042
$460$	−1.08855e22	−0.253168
$461$	2.68638e22	0.613352	0.306676	−	0.951814i	$-0.400783\pi$
$461$	2.68638e22	0.613352	0.306676	+	0.951814i	$0.400783\pi$
$462$	−3.20183e22	−0.717697
$463$	6.81783e22	1.50040	0.750201	−	0.661210i	$-0.229957\pi$
$463$	6.81783e22	1.50040	0.750201	+	0.661210i	$0.229957\pi$
$464$	1.17796e22	0.254524
$465$	5.63573e22	1.19564
$466$	−1.84242e22	−0.383804
$467$	−2.51493e22	−0.514438	−0.257219	−	0.966353i	$-0.582806\pi$
$467$	−2.51493e22	−0.514438	−0.257219	+	0.966353i	$0.582806\pi$
$468$	−1.38073e22	−0.277344
$469$	5.45414e21	0.107586
$470$	−5.46766e21	−0.105918
$471$	1.84506e22	0.351020
$472$	3.45721e21	0.0645979
$473$	−5.07145e22	−0.930707
$474$	1.01516e23	1.82987
$475$	4.21096e22	0.745564
$476$	−2.16666e21	−0.0376818
$477$	4.74236e21	0.0810193
$478$	−8.02012e22	−1.34600
$479$	5.26863e22	0.868653	0.434326	−	0.900756i	$-0.356986\pi$
$479$	5.26863e22	0.868653	0.434326	+	0.900756i	$0.356986\pi$
$480$	−5.63066e22	−0.912029
$481$	1.97141e23	3.13721
$482$	8.23947e22	1.28825
$483$	−2.16278e22	−0.332248
$484$	1.29677e22	0.195740
$485$	−1.15436e23	−1.71213
$486$	−8.34254e22	−1.21588
$487$	−9.19543e21	−0.131697	−0.0658485	−	0.997830i	$-0.520975\pi$
$487$	−9.19543e21	−0.131697	−0.0658485	+	0.997830i	$0.520975\pi$
$488$	−1.00821e23	−1.41901
$489$	7.03368e22	0.972875
$490$	−1.71867e22	−0.233629
$491$	−1.14657e23	−1.53182	−0.765909	−	0.642949i	$-0.777711\pi$
$491$	−1.14657e23	−1.53182	−0.765909	+	0.642949i	$0.777711\pi$
$492$	3.12863e22	0.410819
$493$	−6.60644e21	−0.0852646
$494$	1.03268e23	1.31005
$495$	9.68363e22	1.20752
$496$	6.22698e22	0.763279
$497$	−2.44644e22	−0.294785
$498$	−1.63675e23	−1.93880
$499$	7.15678e22	0.833418	0.416709	−	0.909040i	$-0.363183\pi$
$499$	7.15678e22	0.833418	0.416709	+	0.909040i	$0.363183\pi$
$500$	4.43835e21	0.0508132
$501$	1.39787e23	1.57342
$502$	8.78816e22	0.972560
$503$	−1.37084e23	−1.49162	−0.745812	−	0.666157i	$-0.767938\pi$
$503$	−1.37084e23	−1.49162	−0.745812	+	0.666157i	$0.767938\pi$
$504$	−1.83174e22	−0.195977
$505$	2.05943e23	2.16656
$506$	9.96831e22	1.03120
$507$	−2.75292e23	−2.80044
$508$	−2.62621e22	−0.262717
$509$	−1.69438e23	−1.66690	−0.833451	−	0.552593i	$-0.813638\pi$
$509$	−1.69438e23	−1.66690	−0.833451	+	0.552593i	$0.813638\pi$
$510$	8.55709e22	0.827903
$511$	−1.86661e22	−0.177614
$512$	4.41566e22	0.413239
$513$	3.45110e22	0.317658
$514$	7.30787e22	0.661614
$515$	−9.29108e22	−0.827380
$516$	2.53782e22	0.222299
$517$	1.00317e22	0.0864380
$518$	−8.74373e22	−0.741129
$519$	−2.86273e22	−0.238703
$520$	−2.67327e23	−2.19288
$521$	−4.71952e22	−0.380870	−0.190435	−	0.981700i	$-0.560990\pi$
$521$	−4.71952e22	−0.380870	−0.190435	+	0.981700i	$0.560990\pi$
$522$	1.86727e22	0.148254
$523$	1.02297e23	0.799094	0.399547	−	0.916713i	$-0.369167\pi$
$523$	1.02297e23	0.799094	0.399547	+	0.916713i	$0.369167\pi$
$524$	−3.84400e22	−0.295439
$525$	7.24077e22	0.547559
$526$	−2.02847e23	−1.50935
$527$	−3.49232e22	−0.255696
$528$	2.79938e23	2.01685
$529$	−7.37158e22	−0.522621
$530$	−3.06969e22	−0.214166
$531$	6.94534e21	0.0476859
$532$	−9.17677e21	−0.0620070
$533$	3.46736e23	2.30578
$534$	−1.94432e23	−1.27253
$535$	8.26987e22	0.532711
$536$	−3.76268e22	−0.238560
$537$	−1.27340e23	−0.794665
$538$	1.10207e22	0.0676956
$539$	3.15330e22	0.190661
$540$	2.98675e22	0.177768
$541$	4.15577e22	0.243486	0.121743	−	0.992562i	$-0.461152\pi$
$541$	4.15577e22	0.243486	0.121743	+	0.992562i	$0.461152\pi$
$542$	9.84599e22	0.567892
$543$	1.24092e23	0.704606
$544$	3.48917e22	0.195044
$545$	−3.99395e23	−2.19802
$546$	1.77571e23	0.962131
$547$	9.78497e22	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$547$	9.78497e22	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$548$	−3.87538e21	−0.0203554
$549$	−2.02545e23	−1.04750
$550$	−3.33729e23	−1.69946
$551$	−2.79812e22	−0.140307
$552$	1.49205e23	0.736719
$553$	−9.99776e22	−0.486115
$554$	−6.83309e22	−0.327178
$555$	6.91885e23	3.26245
$556$	1.98347e21	0.00921063
$557$	2.55236e23	1.16727	0.583637	−	0.812015i	$-0.301629\pi$
$557$	2.55236e23	1.16727	0.583637	+	0.812015i	$0.301629\pi$
$558$	9.87081e22	0.444592
$559$	2.81259e23	1.24769
$560$	1.50265e23	0.656536
$561$	−1.57000e23	−0.675639
$562$	1.88918e23	0.800783
$563$	−2.45666e23	−1.02571	−0.512855	−	0.858475i	$-0.671412\pi$
$563$	−2.45666e23	−1.02571	−0.512855	+	0.858475i	$0.671412\pi$
$564$	−5.01999e21	−0.0206457
$565$	−2.23166e23	−0.904101
$566$	−1.20339e23	−0.480250
$567$	1.18822e23	0.467132
$568$	1.68774e23	0.653650
$569$	−2.09273e22	−0.0798471	−0.0399236	−	0.999203i	$-0.512711\pi$
$569$	−2.09273e22	−0.0798471	−0.0399236	+	0.999203i	$0.512711\pi$
$570$	3.62431e23	1.36235
$571$	−3.51209e23	−1.30065	−0.650323	−	0.759658i	$-0.725366\pi$
$571$	−3.51209e23	−1.30065	−0.650323	+	0.759658i	$0.725366\pi$
$572$	−1.63977e23	−0.598295
$573$	−3.93420e23	−1.41430
$574$	−1.53787e23	−0.544713
$575$	−2.25428e23	−0.786740
$576$	1.15073e23	0.395715
$577$	−8.03696e21	−0.0272331	−0.0136166	−	0.999907i	$-0.504334\pi$
$577$	−8.03696e21	−0.0272331	−0.0136166	+	0.999907i	$0.504334\pi$
$578$	2.81892e23	0.941230
$579$	−2.17637e23	−0.716085
$580$	−2.42163e22	−0.0785182
$581$	1.61194e23	0.515053
$582$	−5.28983e23	−1.66570
$583$	5.63206e22	0.174777
$584$	1.28773e23	0.393837
$585$	−5.37046e23	−1.61878
$586$	−3.66393e23	−1.08847
$587$	2.71492e23	0.794939	0.397470	−	0.917615i	$-0.369888\pi$
$587$	2.71492e23	0.794939	0.397470	+	0.917615i	$0.369888\pi$
$588$	−1.57795e22	−0.0455393
$589$	−1.47915e23	−0.420759
$590$	−4.49566e22	−0.126053
$591$	4.60715e22	0.127332
$592$	7.64471e23	2.08270
$593$	1.36029e23	0.365315	0.182658	−	0.983177i	$-0.441530\pi$
$593$	1.36029e23	0.365315	0.182658	+	0.983177i	$0.441530\pi$
$594$	−2.73508e23	−0.724079
$595$	−8.42739e22	−0.219937
$596$	1.67989e23	0.432202
$597$	−3.59205e23	−0.911089
$598$	−5.52834e23	−1.38240
$599$	5.13277e23	1.26539	0.632694	−	0.774402i	$-0.281949\pi$
$599$	5.13277e23	1.26539	0.632694	+	0.774402i	$0.281949\pi$
$600$	−4.99524e23	−1.21414
$601$	−7.54483e23	−1.80807	−0.904037	−	0.427453i	$-0.859411\pi$
$601$	−7.54483e23	−1.80807	−0.904037	+	0.427453i	$0.859411\pi$
$602$	−1.24746e23	−0.294752
$603$	−7.55903e22	−0.176104
$604$	1.86517e23	0.428454
$605$	5.04391e23	1.14247
$606$	9.43727e23	2.10780
$607$	8.53372e23	1.87947	0.939733	−	0.341910i	$-0.111074\pi$
$607$	8.53372e23	1.87947	0.939733	+	0.341910i	$0.111074\pi$
$608$	1.47782e23	0.320953
$609$	−4.81140e22	−0.103044
$610$	1.31106e24	2.76896
$611$	−5.56350e22	−0.115877
$612$	3.00282e22	0.0616798
$613$	5.86452e23	1.18801	0.594003	−	0.804463i	$-0.297547\pi$
$613$	5.86452e23	1.18801	0.594003	+	0.804463i	$0.297547\pi$
$614$	−1.51345e23	−0.302368
$615$	1.21690e24	2.39783
$616$	−2.17539e23	−0.422767
$617$	−3.81916e23	−0.732055	−0.366027	−	0.930604i	$-0.619282\pi$
$617$	−3.81916e23	−0.732055	−0.366027	+	0.930604i	$0.619282\pi$
$618$	−4.25761e23	−0.804941
$619$	−1.17274e23	−0.218692	−0.109346	−	0.994004i	$-0.534876\pi$
$619$	−1.17274e23	−0.218692	−0.109346	+	0.994004i	$0.534876\pi$
$620$	−1.28013e23	−0.235464
$621$	−1.84750e23	−0.335202
$622$	−5.38894e21	−0.00964462
$623$	1.91485e23	0.338055
$624$	−1.55252e24	−2.70375
$625$	−4.90163e23	−0.842094
$626$	1.75190e23	0.296912
$627$	−6.64964e23	−1.11179
$628$	−4.19096e22	−0.0691284
$629$	−4.28743e23	−0.697697
$630$	2.38195e23	0.382417
$631$	−4.13524e23	−0.655014	−0.327507	−	0.944849i	$-0.606209\pi$
$631$	−4.13524e23	−0.655014	−0.327507	+	0.944849i	$0.606209\pi$
$632$	6.89722e23	1.07790
$633$	1.35720e24	2.09272
$634$	−9.44981e23	−1.43769
$635$	−1.02149e24	−1.53340
$636$	−2.81836e22	−0.0417456
$637$	−1.74880e23	−0.255596
$638$	2.21758e23	0.319819
$639$	3.39058e23	0.482522
$640$	−1.25531e24	−1.76288
$641$	3.41874e23	0.473776	0.236888	−	0.971537i	$-0.423873\pi$
$641$	3.41874e23	0.473776	0.236888	+	0.971537i	$0.423873\pi$
$642$	3.78964e23	0.518263
$643$	1.25846e24	1.69842	0.849211	−	0.528054i	$-0.177078\pi$
$643$	1.25846e24	1.69842	0.849211	+	0.528054i	$0.177078\pi$
$644$	4.91266e22	0.0654315
$645$	9.87106e23	1.29750
$646$	−2.24589e23	−0.291348
$647$	−2.82254e23	−0.361371	−0.180686	−	0.983541i	$-0.557832\pi$
$647$	−2.82254e23	−0.361371	−0.180686	+	0.983541i	$0.557832\pi$
$648$	−8.19723e23	−1.03581
$649$	8.24834e22	0.102869
$650$	1.85083e24	2.27826
$651$	−2.54341e23	−0.309014
$652$	−1.59767e23	−0.191594
$653$	−4.98277e23	−0.589806	−0.294903	−	0.955527i	$-0.595287\pi$
$653$	−4.98277e23	−0.589806	−0.294903	+	0.955527i	$0.595287\pi$
$654$	−1.83022e24	−2.13841
$655$	−1.49516e24	−1.72439
$656$	1.34457e24	1.53074
$657$	2.58698e23	0.290729
$658$	2.46756e22	0.0273746
$659$	3.14704e22	0.0344649	0.0172324	−	0.999852i	$-0.494514\pi$
$659$	3.14704e22	0.0344649	0.0172324	+	0.999852i	$0.494514\pi$
$660$	−5.75492e23	−0.622180
$661$	1.32928e24	1.41874	0.709370	−	0.704837i	$-0.248980\pi$
$661$	1.32928e24	1.41874	0.709370	+	0.704837i	$0.248980\pi$
$662$	−8.18828e23	−0.862779
$663$	8.70708e23	0.905748
$664$	−1.11204e24	−1.14207
$665$	−3.56938e23	−0.361917
$666$	1.21181e24	1.21312
$667$	1.49794e23	0.148056
$668$	−3.17520e23	−0.309864
$669$	3.38588e23	0.326249
$670$	4.89290e23	0.465511
$671$	−2.40544e24	−2.25971
$672$	2.54112e23	0.235715
$673$	1.29456e23	0.118575	0.0592875	−	0.998241i	$-0.481117\pi$
$673$	1.29456e23	0.118575	0.0592875	+	0.998241i	$0.481117\pi$
$674$	−4.33613e23	−0.392187
$675$	6.18525e23	0.552427
$676$	6.25314e23	0.551507
$677$	3.67295e23	0.319898	0.159949	−	0.987125i	$-0.448867\pi$
$677$	3.67295e23	0.319898	0.159949	+	0.987125i	$0.448867\pi$
$678$	−1.02265e24	−0.879581
$679$	5.20966e23	0.442503
$680$	5.81386e23	0.487684
$681$	−1.08601e24	−0.899671
$682$	1.17226e24	0.959088
$683$	8.32688e23	0.672832	0.336416	−	0.941714i	$-0.390785\pi$
$683$	8.32688e23	0.672832	0.336416	+	0.941714i	$0.390785\pi$
$684$	1.27183e23	0.101497
$685$	−1.50736e23	−0.118808
$686$	7.75639e22	0.0603816
$687$	1.37958e23	0.106075
$688$	1.09066e24	0.828303
$689$	−3.12350e23	−0.234303
$690$	−1.94023e24	−1.43759
$691$	2.07024e24	1.51516	0.757578	−	0.652745i	$-0.226383\pi$
$691$	2.07024e24	1.51516	0.757578	+	0.652745i	$0.226383\pi$
$692$	6.50255e22	0.0470091
$693$	−4.37024e23	−0.312085
$694$	2.18537e24	1.54159
$695$	7.71485e22	0.0537597
$696$	3.31927e23	0.228488
$697$	−7.54084e23	−0.512792
$698$	2.02613e23	0.136112
$699$	−6.57951e23	−0.436654
$700$	−1.64471e23	−0.107834
$701$	1.88605e24	1.22166	0.610830	−	0.791762i	$-0.290836\pi$
$701$	1.88605e24	1.22166	0.610830	+	0.791762i	$0.290836\pi$
$702$	1.51686e24	0.970686
$703$	−1.81592e24	−1.14809
$704$	1.36662e24	0.853648
$705$	−1.95257e23	−0.120503
$706$	1.35517e24	0.826333
$707$	−9.29424e23	−0.559949
$708$	−4.12757e22	−0.0245704
$709$	−1.62008e24	−0.952890	−0.476445	−	0.879204i	$-0.658075\pi$
$709$	−1.62008e24	−0.952890	−0.476445	+	0.879204i	$0.658075\pi$
$710$	−2.19470e24	−1.27549
$711$	1.38561e24	0.795702
$712$	−1.32101e24	−0.749595
$713$	7.91845e23	0.443996
$714$	−3.86183e23	−0.213973
$715$	−6.37800e24	−3.49207
$716$	2.89247e23	0.156498
$717$	−2.86408e24	−1.53134
$718$	5.12842e22	0.0270973
$719$	4.69470e22	0.0245139	0.0122569	−	0.999925i	$-0.496098\pi$
$719$	4.69470e22	0.0245139	0.0122569	+	0.999925i	$0.496098\pi$
$720$	−2.08255e24	−1.07466
$721$	4.19308e23	0.213837
$722$	1.26756e24	0.638856
$723$	2.94241e24	1.46564
$724$	−2.81870e23	−0.138762
$725$	−5.01495e23	−0.244002
$726$	2.31136e24	1.11149
$727$	−9.54670e23	−0.453744	−0.226872	−	0.973925i	$-0.572850\pi$
$727$	−9.54670e23	−0.453744	−0.226872	+	0.973925i	$0.572850\pi$
$728$	1.20645e24	0.566753
$729$	−3.17431e23	−0.147389
$730$	−1.67453e24	−0.768510
$731$	−6.11684e23	−0.277479
$732$	1.20371e24	0.539732
$733$	6.99048e23	0.309830	0.154915	−	0.987928i	$-0.450490\pi$
$733$	6.99048e23	0.309830	0.154915	+	0.987928i	$0.450490\pi$
$734$	2.74674e23	0.120337
$735$	−6.13757e23	−0.265800
$736$	−7.91133e23	−0.338679
$737$	−8.97716e23	−0.379896
$738$	2.13137e24	0.891620
$739$	4.16451e23	0.172221	0.0861105	−	0.996286i	$-0.472556\pi$
$739$	4.16451e23	0.172221	0.0861105	+	0.996286i	$0.472556\pi$
$740$	−1.57159e24	−0.642493
$741$	3.68784e24	1.49045
$742$	1.38536e23	0.0553514
$743$	−3.43477e24	−1.35673	−0.678363	−	0.734727i	$-0.737310\pi$
$743$	−3.43477e24	−1.35673	−0.678363	+	0.734727i	$0.737310\pi$
$744$	1.75464e24	0.685202
$745$	6.53405e24	2.52263
$746$	−4.33226e24	−1.65361
$747$	−2.23403e24	−0.843070
$748$	3.56618e23	0.133057
$749$	−3.73221e23	−0.137680
$750$	7.91086e23	0.288538
$751$	−3.29500e24	−1.18827	−0.594136	−	0.804364i	$-0.702506\pi$
$751$	−3.29500e24	−1.18827	−0.594136	+	0.804364i	$0.702506\pi$
$752$	−2.15741e23	−0.0769274
$753$	3.13835e24	1.10648
$754$	−1.22985e24	−0.428743
$755$	7.25473e24	2.50076
$756$	−1.34793e23	−0.0459442
$757$	2.49908e24	0.842296	0.421148	−	0.906992i	$-0.361627\pi$
$757$	2.49908e24	0.842296	0.421148	+	0.906992i	$0.361627\pi$
$758$	−2.50791e23	−0.0835840
$759$	3.55980e24	1.17320
$760$	2.46243e24	0.802506
$761$	−6.00617e24	−1.93566	−0.967828	−	0.251612i	$-0.919039\pi$
$761$	−6.00617e24	−1.93566	−0.967828	+	0.251612i	$0.919039\pi$
$762$	−4.68093e24	−1.49181
$763$	1.80248e24	0.568082
$764$	8.93636e23	0.278527
$765$	1.16797e24	0.360007
$766$	4.62141e24	1.40874
$767$	−4.57446e23	−0.137905
$768$	−3.02302e24	−0.901303
$769$	3.75620e24	1.10758	0.553790	−	0.832657i	$-0.313181\pi$
$769$	3.75620e24	1.10758	0.553790	+	0.832657i	$0.313181\pi$
$770$	2.82882e24	0.824962
$771$	2.60973e24	0.752719
$772$	4.94352e23	0.141023
$773$	−3.50675e24	−0.989417	−0.494709	−	0.869059i	$-0.664725\pi$
$773$	−3.50675e24	−0.989417	−0.494709	+	0.869059i	$0.664725\pi$
$774$	1.72888e24	0.482467
$775$	−2.65102e24	−0.731725
$776$	−3.59402e24	−0.981196
$777$	−3.12249e24	−0.843183
$778$	−6.69672e24	−1.78869
$779$	−3.19388e24	−0.843822
$780$	3.19163e24	0.834082
$781$	4.02668e24	1.04091
$782$	1.20231e24	0.307439
$783$	−4.11002e23	−0.103961
$784$	−6.78147e23	−0.169683
$785$	−1.63011e24	−0.403482
$786$	−6.85151e24	−1.67762
$787$	−2.55712e24	−0.619391	−0.309696	−	0.950836i	$-0.600227\pi$
$787$	−2.55712e24	−0.619391	−0.309696	+	0.950836i	$0.600227\pi$
$788$	−1.04649e23	−0.0250763
$789$	−7.24389e24	−1.71719
$790$	−8.96897e24	−2.10335
$791$	1.00715e24	0.233666
$792$	3.01492e24	0.692010
$793$	1.33404e25	3.02932
$794$	−6.09207e24	−1.36864
$795$	−1.09622e24	−0.243657
$796$	8.15919e23	0.179426
$797$	5.92910e24	1.29001	0.645004	−	0.764179i	$-0.276856\pi$
$797$	5.92910e24	1.29001	0.645004	+	0.764179i	$0.276856\pi$
$798$	−1.63566e24	−0.352101
$799$	1.20995e23	0.0257704
$800$	2.64863e24	0.558157
$801$	−2.65384e24	−0.553348
$802$	−4.53825e24	−0.936281
$803$	3.07232e24	0.627169
$804$	4.49228e23	0.0907383
$805$	1.91082e24	0.381905
$806$	−6.50129e24	−1.28573
$807$	3.93562e23	0.0770174
$808$	6.41187e24	1.24162
$809$	−3.50028e24	−0.670719	−0.335359	−	0.942090i	$-0.608858\pi$
$809$	−3.50028e24	−0.670719	−0.335359	+	0.942090i	$0.608858\pi$
$810$	1.06595e25	2.02122
$811$	−5.66446e23	−0.106287	−0.0531436	−	0.998587i	$-0.516924\pi$
$811$	−5.66446e23	−0.106287	−0.0531436	+	0.998587i	$0.516924\pi$
$812$	1.09289e23	0.0202931
$813$	3.51612e24	0.646091
$814$	1.43916e25	2.61699
$815$	−6.21426e24	−1.11828
$816$	3.37642e24	0.601299
$817$	−2.59076e24	−0.456603
$818$	3.08330e24	0.537790
$819$	2.42370e24	0.418375
$820$	−2.76414e24	−0.472218
$821$	−4.42177e24	−0.747618	−0.373809	−	0.927506i	$-0.621948\pi$
$821$	−4.42177e24	−0.747618	−0.373809	+	0.927506i	$0.621948\pi$
$822$	−6.90743e23	−0.115586
$823$	1.96420e24	0.325302	0.162651	−	0.986684i	$-0.447996\pi$
$823$	1.96420e24	0.325302	0.162651	+	0.986684i	$0.447996\pi$
$824$	−2.89271e24	−0.474158
$825$	−1.19178e25	−1.93348
$826$	2.02890e23	0.0325784
$827$	6.45831e24	1.02641	0.513206	−	0.858265i	$-0.328458\pi$
$827$	6.45831e24	1.02641	0.513206	+	0.858265i	$0.328458\pi$
$828$	−6.80858e23	−0.107102
$829$	−4.64676e24	−0.723497	−0.361749	−	0.932276i	$-0.617820\pi$
$829$	−4.64676e24	−0.723497	−0.361749	+	0.932276i	$0.617820\pi$
$830$	1.44607e25	2.22856
$831$	−2.44018e24	−0.372231
$832$	−7.57914e24	−1.14438
$833$	3.80330e23	0.0568431
$834$	3.53531e23	0.0523017
$835$	−1.23502e25	−1.80858
$836$	1.51044e24	0.218952
$837$	−2.17265e24	−0.311762
$838$	2.39929e24	0.340807
$839$	−1.78363e24	−0.250800	−0.125400	−	0.992106i	$-0.540021\pi$
$839$	−1.78363e24	−0.250800	−0.125400	+	0.992106i	$0.540021\pi$
$840$	4.23417e24	0.589378
$841$	−6.92391e24	−0.954082
$842$	6.48250e24	0.884281
$843$	6.74648e24	0.911051
$844$	−3.08282e24	−0.412133
$845$	2.43221e25	3.21898
$846$	−3.41986e23	−0.0448084
$847$	−2.27632e24	−0.295274
$848$	−1.21123e24	−0.155547
$849$	−4.29745e24	−0.546381
$850$	−4.02520e24	−0.506672
$851$	9.72129e24	1.21150
$852$	−2.01500e24	−0.248622
$853$	2.39767e24	0.292902	0.146451	−	0.989218i	$-0.453215\pi$
$853$	2.39767e24	0.292902	0.146451	+	0.989218i	$0.453215\pi$
$854$	−5.91681e24	−0.715642
$855$	4.94689e24	0.592407
$856$	2.57476e24	0.305288
$857$	4.13190e24	0.485080	0.242540	−	0.970141i	$-0.422019\pi$
$857$	4.13190e24	0.485080	0.242540	+	0.970141i	$0.422019\pi$
$858$	−2.92270e25	−3.39737
$859$	−7.26097e24	−0.835705	−0.417852	−	0.908515i	$-0.637217\pi$
$859$	−7.26097e24	−0.835705	−0.417852	+	0.908515i	$0.637217\pi$
$860$	−2.24217e24	−0.255524
$861$	−5.49191e24	−0.619721
$862$	1.54788e25	1.72952
$863$	−1.22790e25	−1.35853	−0.679267	−	0.733891i	$-0.737702\pi$
$863$	−1.22790e25	−1.35853	−0.679267	+	0.733891i	$0.737702\pi$
$864$	2.17069e24	0.237811
$865$	2.52922e24	0.274378
$866$	1.17552e25	1.26278
$867$	1.00667e25	1.07084
$868$	5.77725e23	0.0608560
$869$	1.64557e25	1.71651
$870$	−4.31629e24	−0.445859
$871$	4.97866e24	0.509282
$872$	−1.24349e25	−1.25965
$873$	−7.22019e24	−0.724315
$874$	5.09232e24	0.505904
$875$	−7.79096e23	−0.0766519
$876$	−1.53743e24	−0.149799
$877$	1.54858e25	1.49430	0.747150	−	0.664655i	$-0.231422\pi$
$877$	1.54858e25	1.49430	0.747150	+	0.664655i	$0.231422\pi$
$878$	−1.71723e25	−1.64106
$879$	−1.30843e25	−1.23836
$880$	−2.47326e25	−2.31828
$881$	−9.03292e24	−0.838558	−0.419279	−	0.907857i	$-0.637717\pi$
$881$	−9.03292e24	−0.838558	−0.419279	+	0.907857i	$0.637717\pi$
$882$	−1.07498e24	−0.0988362
$883$	−1.77124e25	−1.61291	−0.806456	−	0.591294i	$-0.798617\pi$
$883$	−1.77124e25	−1.61291	−0.806456	+	0.591294i	$0.798617\pi$
$884$	−1.97777e24	−0.178374
$885$	−1.60545e24	−0.143410
$886$	−5.24611e24	−0.464142
$887$	−5.09620e24	−0.446576	−0.223288	−	0.974753i	$-0.571679\pi$
$887$	−5.09620e24	−0.446576	−0.223288	+	0.974753i	$0.571679\pi$
$888$	2.15413e25	1.86966
$889$	4.60998e24	0.396309
$890$	1.71781e25	1.46272
$891$	−1.95573e25	−1.64948
$892$	−7.69088e23	−0.0642502
$893$	5.12470e23	0.0424064
$894$	2.99421e25	2.45422
$895$	1.12505e25	0.913433
$896$	5.66526e24	0.455619
$897$	−1.97424e25	−1.57276
$898$	−1.72223e25	−1.35907
$899$	1.76156e24	0.137702
$900$	2.27944e24	0.176509
$901$	6.79301e23	0.0521076
$902$	2.53123e25	1.92343
$903$	−4.45482e24	−0.335339
$904$	−6.94811e24	−0.518126
$905$	−1.09636e25	−0.809914
$906$	3.32446e25	2.43294
$907$	1.49463e25	1.08360	0.541802	−	0.840506i	$-0.317742\pi$
$907$	1.49463e25	1.08360	0.541802	+	0.840506i	$0.317742\pi$
$908$	2.46682e24	0.177177
$909$	1.28811e25	0.916559
$910$	−1.56884e25	−1.10593
$911$	1.37957e25	0.963470	0.481735	−	0.876317i	$-0.340007\pi$
$911$	1.37957e25	0.963470	0.481735	+	0.876317i	$0.340007\pi$
$912$	1.43007e25	0.989464
$913$	−2.65315e25	−1.81870
$914$	2.11399e25	1.43569
$915$	4.68193e25	3.15025
$916$	−3.13365e23	−0.0208901
$917$	6.74766e24	0.445671
$918$	−3.29887e24	−0.215875
$919$	2.86219e25	1.85574	0.927869	−	0.372906i	$-0.121639\pi$
$919$	2.86219e25	1.85574	0.927869	+	0.372906i	$0.121639\pi$
$920$	−1.31823e25	−0.846827
$921$	−5.40470e24	−0.344005
$922$	−1.08761e25	−0.685901
$923$	−2.23316e25	−1.39542
$924$	2.59721e24	0.160803
$925$	−3.25459e25	−1.99660
$926$	−2.76028e25	−1.67787
$927$	−5.81129e24	−0.350022
$928$	−1.75998e24	−0.105039
$929$	−1.62901e25	−0.963364	−0.481682	−	0.876346i	$-0.659974\pi$
$929$	−1.62901e25	−0.963364	−0.481682	+	0.876346i	$0.659974\pi$
$930$	−2.28169e25	−1.33706
$931$	1.61087e24	0.0935378
$932$	1.49451e24	0.0859928
$933$	−1.92445e23	−0.0109727
$934$	1.01820e25	0.575287
$935$	1.38709e25	0.776617
$936$	−1.67205e25	−0.927695
$937$	5.38791e24	0.296233	0.148117	−	0.988970i	$-0.452679\pi$
$937$	5.38791e24	0.296233	0.148117	+	0.988970i	$0.452679\pi$
$938$	−2.20817e24	−0.120312
$939$	6.25624e24	0.337797
$940$	4.43516e23	0.0237314
$941$	1.29675e25	0.687613	0.343807	−	0.939040i	$-0.388284\pi$
$941$	1.29675e25	0.687613	0.343807	+	0.939040i	$0.388284\pi$
$942$	−7.46992e24	−0.392539
$943$	1.70980e25	0.890424
$944$	−1.77388e24	−0.0915509
$945$	−5.24287e24	−0.268163
$946$	2.05324e25	1.04079
$947$	−1.96020e24	−0.0984750	−0.0492375	−	0.998787i	$-0.515679\pi$
$947$	−1.96020e24	−0.0984750	−0.0492375	+	0.998787i	$0.515679\pi$
$948$	−8.23462e24	−0.409989
$949$	−1.70388e25	−0.840770
$950$	−1.70485e25	−0.833752
$951$	−3.37464e25	−1.63566
$952$	−2.62380e24	−0.126043
$953$	1.87969e25	0.894945	0.447473	−	0.894298i	$-0.352324\pi$
$953$	1.87969e25	0.894945	0.447473	+	0.894298i	$0.352324\pi$
$954$	−1.92000e24	−0.0906024
$955$	3.47587e25	1.62568
$956$	6.50563e24	0.301576
$957$	7.91924e24	0.363858
$958$	−2.13307e25	−0.971399
$959$	6.80274e23	0.0307062
$960$	−2.65998e25	−1.19007
$961$	−1.32381e25	−0.587052
$962$	−7.98147e25	−3.50828
$963$	5.17256e24	0.225363
$964$	−6.68355e24	−0.288637
$965$	1.92282e25	0.823109
$966$	8.75627e24	0.371547
$967$	2.99031e25	1.25774	0.628871	−	0.777509i	$-0.283517\pi$
$967$	2.99031e25	1.25774	0.628871	+	0.777509i	$0.283517\pi$
$968$	1.57038e25	0.654734
$969$	−8.02034e24	−0.331467
$970$	4.67357e25	1.91465
$971$	−1.99759e25	−0.811226	−0.405613	−	0.914045i	$-0.632942\pi$
$971$	−1.99759e25	−0.811226	−0.405613	+	0.914045i	$0.632942\pi$
$972$	6.76716e24	0.272422
$973$	−3.48173e23	−0.0138943
$974$	3.72288e24	0.147275
$975$	6.60953e25	2.59198
$976$	5.17311e25	2.01108
$977$	−3.44614e25	−1.32810	−0.664048	−	0.747690i	$-0.731163\pi$
$977$	−3.44614e25	−1.32810	−0.664048	+	0.747690i	$0.731163\pi$
$978$	−2.84767e25	−1.08795
$979$	−3.15172e25	−1.19370
$980$	1.39412e24	0.0523455
$981$	−2.49810e25	−0.929871
$982$	4.64201e25	1.71301
$983$	3.22256e25	1.17895	0.589477	−	0.807785i	$-0.299334\pi$
$983$	3.22256e25	1.17895	0.589477	+	0.807785i	$0.299334\pi$
$984$	3.78874e25	1.37416
$985$	−4.07042e24	−0.146363
$986$	2.67470e24	0.0953500
$987$	8.81196e23	0.0311442
$988$	−8.37676e24	−0.293523
$989$	1.38693e25	0.481820
$990$	−3.92053e25	−1.35035
$991$	−2.85327e25	−0.974353	−0.487176	−	0.873304i	$-0.661973\pi$
$991$	−2.85327e25	−0.974353	−0.487176	+	0.873304i	$0.661973\pi$
$992$	−9.30365e24	−0.314995
$993$	−2.92413e25	−0.981585
$994$	9.90469e24	0.329653
$995$	3.17358e25	1.04726
$996$	1.32767e25	0.434396
$997$	5.15252e25	1.67152	0.835759	−	0.549096i	$-0.185028\pi$
$997$	5.15252e25	1.67152	0.835759	+	0.549096i	$0.185028\pi$
$998$	−2.89751e25	−0.931997
$999$	−2.66731e25	−0.850680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.a.a.1.1	✓	4
3.2	odd	2		63.18.a.b.1.4		4
4.3	odd	2		112.18.a.f.1.4		4
7.6	odd	2		49.18.a.c.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.a.a.1.1	✓	4	1.1	even	1	trivial
49.18.a.c.1.1		4	7.6	odd	2
63.18.a.b.1.4		4	3.2	odd	2
112.18.a.f.1.4		4	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q-404.862 q^{2} -14458.1 q^{3} +32840.9 q^{4} +1.27737e6 q^{5} +5.85352e6 q^{6} -5.76480e6 q^{7} +3.97700e7 q^{8} +7.98958e7 q^{9} +O(q^{10})\)	\(q-404.862 q^{2} -14458.1 q^{3} +32840.9 q^{4} +1.27737e6 q^{5} +5.85352e6 q^{6} -5.76480e6 q^{7} +3.97700e7 q^{8} +7.98958e7 q^{9} -5.17159e8 q^{10} +9.48848e8 q^{11} -4.74816e8 q^{12} -5.26224e9 q^{13} +2.33395e9 q^{14} -1.84683e10 q^{15} -2.04059e10 q^{16} +1.14444e10 q^{17} -3.23467e10 q^{18} +4.84720e10 q^{19} +4.19500e10 q^{20} +8.33479e10 q^{21} -3.84152e11 q^{22} -2.59488e11 q^{23} -5.74998e11 q^{24} +8.68740e11 q^{25} +2.13048e12 q^{26} +7.11979e11 q^{27} -1.89321e11 q^{28} -5.77266e11 q^{29} +7.47712e12 q^{30} -3.05156e12 q^{31} +3.04882e12 q^{32} -1.37185e13 q^{33} -4.63338e12 q^{34} -7.36380e12 q^{35} +2.62385e12 q^{36} -3.74633e13 q^{37} -1.96244e13 q^{38} +7.60818e13 q^{39} +5.08011e13 q^{40} -6.58913e13 q^{41} -3.37444e13 q^{42} -5.34485e13 q^{43} +3.11610e13 q^{44} +1.02057e14 q^{45} +1.05057e14 q^{46} +1.05725e13 q^{47} +2.95030e14 q^{48} +3.32329e13 q^{49} -3.51720e14 q^{50} -1.65463e14 q^{51} -1.72816e14 q^{52} +5.93568e13 q^{53} -2.88253e14 q^{54} +1.21203e15 q^{55} -2.29266e14 q^{56} -7.00812e14 q^{57} +2.33713e14 q^{58} +8.69300e13 q^{59} -6.06517e14 q^{60} -2.53511e15 q^{61} +1.23546e15 q^{62} -4.60583e14 q^{63} +1.44029e15 q^{64} -6.72184e15 q^{65} +5.55410e15 q^{66} -9.46111e14 q^{67} +3.75843e14 q^{68} +3.75170e15 q^{69} +2.98132e15 q^{70} +4.24375e15 q^{71} +3.17746e15 q^{72} +3.23795e15 q^{73} +1.51674e16 q^{74} -1.25603e16 q^{75} +1.59186e15 q^{76} -5.46992e15 q^{77} -3.08026e16 q^{78} +1.73428e16 q^{79} -2.60659e16 q^{80} -2.06116e16 q^{81} +2.66769e16 q^{82} -2.79618e16 q^{83} +2.73722e15 q^{84} +1.46187e16 q^{85} +2.16393e16 q^{86} +8.34616e15 q^{87} +3.77357e16 q^{88} -3.32163e16 q^{89} -4.13188e16 q^{90} +3.03357e16 q^{91} -8.52183e15 q^{92} +4.41197e16 q^{93} -4.28040e15 q^{94} +6.19168e16 q^{95} -4.40800e16 q^{96} -9.03701e16 q^{97} -1.34547e16 q^{98} +7.58090e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 186 q^{2} - 2786 q^{3} - 16300 q^{4} + 274722 q^{5} + 1469804 q^{6} - 23059204 q^{7} + 8649336 q^{8} - 2050976 q^{9}+O(q^{10}) \) 4 * q + 186 * q^2 - 2786 * q^3 - 16300 * q^4 + 274722 * q^5 + 1469804 * q^6 - 23059204 * q^7 + 8649336 * q^8 - 2050976 * q^9	\( 4 q + 186 q^{2} - 2786 q^{3} - 16300 q^{4} + 274722 q^{5} + 1469804 q^{6} - 23059204 q^{7} + 8649336 q^{8} - 2050976 q^{9} - 893891656 q^{10} + 610110180 q^{11} - 1826039320 q^{12} - 8514921674 q^{13} - 1072252986 q^{14} - 30645264896 q^{15} - 47269015792 q^{16} - 47762899716 q^{17} - 148424524342 q^{18} - 142813479494 q^{19} - 88080723360 q^{20} + 16060735586 q^{21} - 25116572128 q^{22} + 161322432240 q^{23} + 387147758256 q^{24} + 1921891698992 q^{25} + 2984730379008 q^{26} + 2041714521028 q^{27} + 93966256300 q^{28} + 2470023989364 q^{29} + 6457134393152 q^{30} + 3069063677988 q^{31} - 7036366816032 q^{32} - 14819614563824 q^{33} - 9992374959252 q^{34} - 1583717660322 q^{35} - 18927631502956 q^{36} - 53477713304508 q^{37} - 51421850028780 q^{38} - 4140246547640 q^{39} + 22110911913216 q^{40} - 84856086719628 q^{41} - 8473127569004 q^{42} + 14664094189676 q^{43} + 237550257793824 q^{44} + 160924162333018 q^{45} + 187722899918496 q^{46} + 110590112906028 q^{47} + 428386513367456 q^{48} + 132931722278404 q^{49} + 539831164264974 q^{50} - 229270804715244 q^{51} + 68940623118416 q^{52} - 517697020820328 q^{53} - 32330860930648 q^{54} - 17\!\cdots\!44 q^{55}+ \cdots - 57\!\cdots\!28 q^{99}+O(q^{100}) \) 4 * q + 186 * q^2 - 2786 * q^3 - 16300 * q^4 + 274722 * q^5 + 1469804 * q^6 - 23059204 * q^7 + 8649336 * q^8 - 2050976 * q^9 - 893891656 * q^10 + 610110180 * q^11 - 1826039320 * q^12 - 8514921674 * q^13 - 1072252986 * q^14 - 30645264896 * q^15 - 47269015792 * q^16 - 47762899716 * q^17 - 148424524342 * q^18 - 142813479494 * q^19 - 88080723360 * q^20 + 16060735586 * q^21 - 25116572128 * q^22 + 161322432240 * q^23 + 387147758256 * q^24 + 1921891698992 * q^25 + 2984730379008 * q^26 + 2041714521028 * q^27 + 93966256300 * q^28 + 2470023989364 * q^29 + 6457134393152 * q^30 + 3069063677988 * q^31 - 7036366816032 * q^32 - 14819614563824 * q^33 - 9992374959252 * q^34 - 1583717660322 * q^35 - 18927631502956 * q^36 - 53477713304508 * q^37 - 51421850028780 * q^38 - 4140246547640 * q^39 + 22110911913216 * q^40 - 84856086719628 * q^41 - 8473127569004 * q^42 + 14664094189676 * q^43 + 237550257793824 * q^44 + 160924162333018 * q^45 + 187722899918496 * q^46 + 110590112906028 * q^47 + 428386513367456 * q^48 + 132931722278404 * q^49 + 539831164264974 * q^50 - 229270804715244 * q^51 + 68940623118416 * q^52 - 517697020820328 * q^53 - 32330860930648 * q^54 - 1701016442036744 * q^55 - 49861700822136 * q^56 - 2352229307493836 * q^57 + 1035155400175604 * q^58 - 2778221577040518 * q^59 + 62096128416896 * q^60 - 3329268765288494 * q^61 - 406874975162376 * q^62 + 11823468495776 * q^63 + 3892676387300416 * q^64 - 1795213174093500 * q^65 + 9560762631234080 * q^66 - 1542501737022560 * q^67 + 5553778722869496 * q^68 + 829434613465248 * q^69 + 5153107512400456 * q^70 + 739192660163448 * q^71 + 16950595160647800 * q^72 - 1768956758306304 * q^73 + 24304533536274948 * q^74 - 22124527120060246 * q^75 + 614659296403544 * q^76 - 3517163775774180 * q^77 - 22122617539685488 * q^78 + 1824334397417480 * q^79 - 5329944020335872 * q^80 - 13182300720284792 * q^81 - 36215502923183444 * q^82 - 49183281603250158 * q^83 + 10526753297975320 * q^84 - 44968305361101900 * q^85 - 11999423939098896 * q^86 + 29283570071010892 * q^87 + 47237077355248704 * q^88 - 138655399526807016 * q^89 + 33550243342273112 * q^90 + 49086828981196874 * q^91 - 49994746660573248 * q^92 + 171997447280309016 * q^93 + 97111697039664552 * q^94 + 276760012078126224 * q^95 - 174317142260969792 * q^96 + 73446338844858924 * q^97 + 6181325085945786 * q^98 - 57479877480434828 * q^99

Introduction

L-functions

Modular forms

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