LMFDB - Embedded newform 7.18.a.a.1.3

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			1.3
Root			$43.3902$ 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)

$f(q)$	$=$	$q+307.439 q^{2} -5612.83 q^{3} -36553.2 q^{4} +904274. q^{5} -1.72560e6 q^{6} -5.76480e6 q^{7} -5.15345e7 q^{8} -9.76363e7 q^{9} +O(q^{10})$	\(q+307.439 q^{2} -5612.83 q^{3} -36553.2 q^{4} +904274. q^{5} -1.72560e6 q^{6} -5.76480e6 q^{7} -5.15345e7 q^{8} -9.76363e7 q^{9} +2.78009e8 q^{10} -1.15102e9 q^{11} +2.05167e8 q^{12} +1.96128e9 q^{13} -1.77233e9 q^{14} -5.07553e9 q^{15} -1.10526e10 q^{16} -5.10958e10 q^{17} -3.00172e10 q^{18} +1.10299e10 q^{19} -3.30541e10 q^{20} +3.23568e10 q^{21} -3.53868e11 q^{22} +5.87234e11 q^{23} +2.89254e11 q^{24} +5.47714e10 q^{25} +6.02975e11 q^{26} +1.27286e12 q^{27} +2.10722e11 q^{28} -3.54160e11 q^{29} -1.56042e12 q^{30} -1.34763e12 q^{31} +3.35672e12 q^{32} +6.46046e12 q^{33} -1.57089e13 q^{34} -5.21296e12 q^{35} +3.56892e12 q^{36} +5.64201e12 q^{37} +3.39102e12 q^{38} -1.10083e13 q^{39} -4.66013e13 q^{40} -4.59182e13 q^{41} +9.94776e12 q^{42} +4.07673e13 q^{43} +4.20733e13 q^{44} -8.82900e13 q^{45} +1.80539e14 q^{46} +2.08437e14 q^{47} +6.20365e13 q^{48} +3.32329e13 q^{49} +1.68389e13 q^{50} +2.86792e14 q^{51} -7.16911e13 q^{52} -8.47178e14 q^{53} +3.91326e14 q^{54} -1.04083e15 q^{55} +2.97086e14 q^{56} -6.19088e13 q^{57} -1.08883e14 q^{58} -1.87074e14 q^{59} +1.85527e14 q^{60} -2.03988e15 q^{61} -4.14313e14 q^{62} +5.62854e14 q^{63} +2.48068e15 q^{64} +1.77354e15 q^{65} +1.98620e15 q^{66} -2.00475e15 q^{67} +1.86771e15 q^{68} -3.29604e15 q^{69} -1.60267e15 q^{70} +1.45191e15 q^{71} +5.03164e15 q^{72} +1.33364e15 q^{73} +1.73458e15 q^{74} -3.07422e14 q^{75} -4.03177e14 q^{76} +6.63539e15 q^{77} -3.38440e15 q^{78} -8.31801e15 q^{79} -9.99461e15 q^{80} +5.46445e15 q^{81} -1.41171e16 q^{82} +1.24141e16 q^{83} -1.18274e15 q^{84} -4.62046e16 q^{85} +1.25335e16 q^{86} +1.98784e15 q^{87} +5.93171e16 q^{88} -4.08624e16 q^{89} -2.71438e16 q^{90} -1.13064e16 q^{91} -2.14653e16 q^{92} +7.56399e15 q^{93} +6.40816e16 q^{94} +9.97403e15 q^{95} -1.88407e16 q^{96} +1.17994e17 q^{97} +1.02171e16 q^{98} +1.12381e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	307.439	0.849189	0.424594	−	0.905384i	$-0.360417\pi$
$2$	307.439	0.849189	0.424594	+	0.905384i	$0.360417\pi$
$3$	−5612.83	−0.493914	−0.246957	−	0.969026i	$-0.579431\pi$
$3$	−5612.83	−0.493914	−0.246957	+	0.969026i	$0.579431\pi$
$4$	−36553.2	−0.278878
$5$	904274.	1.03527	0.517636	−	0.855601i	$-0.326812\pi$
$5$	904274.	1.03527	0.517636	+	0.855601i	$0.326812\pi$
$6$	−1.72560e6	−0.419426
$7$	−5.76480e6	−0.377964
$7$	−5.76480e6	−0.377964
$8$	−5.15345e7	−1.08601
$9$	−9.76363e7	−0.756049
$10$	2.78009e8	0.879142
$11$	−1.15102e9	−1.61899	−0.809495	−	0.587127i	$-0.800259\pi$
$11$	−1.15102e9	−1.61899	−0.809495	+	0.587127i	$0.800259\pi$
$12$	2.05167e8	0.137742
$13$	1.96128e9	0.666840	0.333420	−	0.942778i	$-0.391797\pi$
$13$	1.96128e9	0.666840	0.333420	+	0.942778i	$0.391797\pi$
$14$	−1.77233e9	−0.320963
$15$	−5.07553e9	−0.511335
$16$	−1.10526e10	−0.643348
$17$	−5.10958e10	−1.77652	−0.888259	−	0.459344i	$-0.848085\pi$
$17$	−5.10958e10	−1.77652	−0.888259	+	0.459344i	$0.848085\pi$
$18$	−3.00172e10	−0.642029
$19$	1.10299e10	0.148993	0.0744964	−	0.997221i	$-0.476265\pi$
$19$	1.10299e10	0.148993	0.0744964	+	0.997221i	$0.476265\pi$
$20$	−3.30541e10	−0.288715
$21$	3.23568e10	0.186682
$22$	−3.53868e11	−1.37483
$23$	5.87234e11	1.56360	0.781798	−	0.623531i	$-0.214303\pi$
$23$	5.87234e11	1.56360	0.781798	+	0.623531i	$0.214303\pi$
$24$	2.89254e11	0.536395
$25$	5.47714e10	0.0717900
$26$	6.02975e11	0.566273
$27$	1.27286e12	0.867337
$28$	2.10722e11	0.105406
$29$	−3.54160e11	−0.131467	−0.0657335	−	0.997837i	$-0.520939\pi$
$29$	−3.54160e11	−0.131467	−0.0657335	+	0.997837i	$0.520939\pi$
$30$	−1.56042e12	−0.434220
$31$	−1.34763e12	−0.283789	−0.141894	−	0.989882i	$-0.545319\pi$
$31$	−1.34763e12	−0.283789	−0.141894	+	0.989882i	$0.545319\pi$
$32$	3.35672e12	0.539685
$33$	6.46046e12	0.799641
$34$	−1.57089e13	−1.50860
$35$	−5.21296e12	−0.391296
$36$	3.56892e12	0.210846
$37$	5.64201e12	0.264070	0.132035	−	0.991245i	$-0.457849\pi$
$37$	5.64201e12	0.264070	0.132035	+	0.991245i	$0.457849\pi$
$38$	3.39102e12	0.126523
$39$	−1.10083e13	−0.329361
$40$	−4.66013e13	−1.12432
$41$	−4.59182e13	−0.898095	−0.449047	−	0.893508i	$-0.648237\pi$
$41$	−4.59182e13	−0.898095	−0.449047	+	0.893508i	$0.648237\pi$
$42$	9.94776e12	0.158528
$43$	4.07673e13	0.531901	0.265950	−	0.963987i	$-0.414314\pi$
$43$	4.07673e13	0.531901	0.265950	+	0.963987i	$0.414314\pi$
$44$	4.20733e13	0.451501
$45$	−8.82900e13	−0.782717
$46$	1.80539e14	1.32779
$47$	2.08437e14	1.27686	0.638428	−	0.769681i	$-0.279585\pi$
$47$	2.08437e14	1.27686	0.638428	+	0.769681i	$0.279585\pi$
$48$	6.20365e13	0.317758
$49$	3.32329e13	0.142857
$50$	1.68389e13	0.0609632
$51$	2.86792e14	0.877446
$52$	−7.16911e13	−0.185967
$53$	−8.47178e14	−1.86909	−0.934544	−	0.355846i	$-0.884193\pi$
$53$	−8.47178e14	−1.86909	−0.934544	+	0.355846i	$0.884193\pi$
$54$	3.91326e14	0.736532
$55$	−1.04083e15	−1.67610
$56$	2.97086e14	0.410473
$57$	−6.19088e13	−0.0735896
$58$	−1.08883e14	−0.111640
$59$	−1.87074e14	−0.165871	−0.0829355	−	0.996555i	$-0.526430\pi$
$59$	−1.87074e14	−0.165871	−0.0829355	+	0.996555i	$0.526430\pi$
$60$	1.85527e14	0.142600
$61$	−2.03988e15	−1.36239	−0.681195	−	0.732102i	$-0.738540\pi$
$61$	−2.03988e15	−1.36239	−0.681195	+	0.732102i	$0.738540\pi$
$62$	−4.14313e14	−0.240990
$63$	5.62854e14	0.285760
$64$	2.48068e15	1.10164
$65$	1.77354e15	0.690362
$66$	1.98620e15	0.679046
$67$	−2.00475e15	−0.603150	−0.301575	−	0.953442i	$-0.597512\pi$
$67$	−2.00475e15	−0.603150	−0.301575	+	0.953442i	$0.597512\pi$
$68$	1.86771e15	0.495432
$69$	−3.29604e15	−0.772282
$70$	−1.60267e15	−0.332284
$71$	1.45191e15	0.266836	0.133418	−	0.991060i	$-0.457405\pi$
$71$	1.45191e15	0.266836	0.133418	+	0.991060i	$0.457405\pi$
$72$	5.03164e15	0.821077
$73$	1.33364e15	0.193550	0.0967751	−	0.995306i	$-0.469147\pi$
$73$	1.33364e15	0.193550	0.0967751	+	0.995306i	$0.469147\pi$
$74$	1.73458e15	0.224245
$75$	−3.07422e14	−0.0354580
$76$	−4.03177e14	−0.0415509
$77$	6.63539e15	0.611920
$78$	−3.38440e15	−0.279690
$79$	−8.31801e15	−0.616864	−0.308432	−	0.951246i	$-0.599804\pi$
$79$	−8.31801e15	−0.616864	−0.308432	+	0.951246i	$0.599804\pi$
$80$	−9.99461e15	−0.666041
$81$	5.46445e15	0.327660
$82$	−1.41171e16	−0.762652
$83$	1.24141e16	0.604996	0.302498	−	0.953150i	$-0.402179\pi$
$83$	1.24141e16	0.604996	0.302498	+	0.953150i	$0.402179\pi$
$84$	−1.18274e15	−0.0520615
$85$	−4.62046e16	−1.83918
$86$	1.25335e16	0.451684
$87$	1.98784e15	0.0649333
$88$	5.93171e16	1.75824
$89$	−4.08624e16	−1.10029	−0.550147	−	0.835068i	$-0.685429\pi$
$89$	−4.08624e16	−1.10029	−0.550147	+	0.835068i	$0.685429\pi$
$90$	−2.71438e16	−0.664675
$91$	−1.13064e16	−0.252042
$92$	−2.14653e16	−0.436054
$93$	7.56399e15	0.140167
$94$	6.40816e16	1.08429
$95$	9.97403e15	0.154248
$96$	−1.88407e16	−0.266558
$97$	1.17994e17	1.52862	0.764310	−	0.644849i	$-0.223080\pi$
$97$	1.17994e17	1.52862	0.764310	+	0.644849i	$0.223080\pi$
$98$	1.02171e16	0.121313
$99$	1.12381e17	1.22404
$100$	−2.00207e15	−0.0200207
$101$	7.31416e16	0.672098	0.336049	−	0.941844i	$-0.390909\pi$
$101$	7.31416e16	0.672098	0.336049	+	0.941844i	$0.390909\pi$
$102$	8.81711e16	0.745117
$103$	−2.34793e17	−1.82629	−0.913144	−	0.407638i	$-0.866353\pi$
$103$	−2.34793e17	−1.82629	−0.913144	+	0.407638i	$0.866353\pi$
$104$	−1.01074e17	−0.724195
$105$	2.92594e16	0.193267
$106$	−2.60456e17	−1.58721
$107$	1.21399e17	0.683052	0.341526	−	0.939872i	$-0.389056\pi$
$107$	1.21399e17	0.683052	0.341526	+	0.939872i	$0.389056\pi$
$108$	−4.65270e16	−0.241882
$109$	9.54850e16	0.458997	0.229498	−	0.973309i	$-0.426291\pi$
$109$	9.54850e16	0.458997	0.229498	+	0.973309i	$0.426291\pi$
$110$	−3.19993e17	−1.42332
$111$	−3.16676e16	−0.130428
$112$	6.37163e16	0.243163
$113$	−4.43963e17	−1.57101	−0.785506	−	0.618854i	$-0.787597\pi$
$113$	−4.43963e17	−1.57101	−0.785506	+	0.618854i	$0.787597\pi$
$114$	−1.90332e16	−0.0624914
$115$	5.31020e17	1.61875
$116$	1.29457e16	0.0366633
$117$	−1.91493e17	−0.504164
$118$	−5.75137e16	−0.140856
$119$	2.94557e17	0.671460
$120$	2.61565e17	0.555315
$121$	8.19394e17	1.62113
$122$	−6.27140e17	−1.15693
$123$	2.57731e17	0.443581
$124$	4.92600e16	0.0791425
$125$	−6.40378e17	−0.960951
$126$	1.73043e17	0.242664
$127$	5.94409e17	0.779387	0.389694	−	0.920945i	$-0.372581\pi$
$127$	5.94409e17	0.779387	0.389694	+	0.920945i	$0.372581\pi$
$128$	3.22686e17	0.395818
$129$	−2.28820e17	−0.262713
$130$	5.45255e17	0.586247
$131$	−1.38323e18	−1.39344	−0.696722	−	0.717341i	$-0.745359\pi$
$131$	−1.38323e18	−1.39344	−0.696722	+	0.717341i	$0.745359\pi$
$132$	−2.36150e17	−0.223003
$133$	−6.35851e16	−0.0563140
$134$	−6.16340e17	−0.512188
$135$	1.15101e18	0.897930
$136$	2.63320e18	1.92931
$137$	9.31577e17	0.641348	0.320674	−	0.947190i	$-0.396091\pi$
$137$	9.31577e17	0.641348	0.320674	+	0.947190i	$0.396091\pi$
$138$	−1.01333e18	−0.655813
$139$	−3.11984e18	−1.89892	−0.949458	−	0.313893i	$-0.898367\pi$
$139$	−3.11984e18	−1.89892	−0.949458	+	0.313893i	$0.898367\pi$
$140$	1.90550e17	0.109124
$141$	−1.16992e18	−0.630657
$142$	4.46375e17	0.226594
$143$	−2.25747e18	−1.07961
$144$	1.07914e18	0.486403
$145$	−3.20258e17	−0.136104
$146$	4.10012e17	0.164361
$147$	−1.86531e17	−0.0705591
$148$	−2.06233e17	−0.0736435
$149$	−1.87186e18	−0.631233	−0.315616	−	0.948887i	$-0.602211\pi$
$149$	−1.87186e18	−0.631233	−0.315616	+	0.948887i	$0.602211\pi$
$150$	−9.45137e16	−0.0301106
$151$	−1.96512e18	−0.591677	−0.295839	−	0.955238i	$-0.595599\pi$
$151$	−1.96512e18	−0.591677	−0.295839	+	0.955238i	$0.595599\pi$
$152$	−5.68420e17	−0.161808
$153$	4.98881e18	1.34313
$154$	2.03998e18	0.519636
$155$	−1.21862e18	−0.293799
$156$	4.02390e17	0.0918518
$157$	1.91480e18	0.413978	0.206989	−	0.978343i	$-0.433634\pi$
$157$	1.91480e18	0.413978	0.206989	+	0.978343i	$0.433634\pi$
$158$	−2.55728e18	−0.523834
$159$	4.75506e18	0.923168
$160$	3.03539e18	0.558721
$161$	−3.38529e18	−0.590984
$162$	1.67999e18	0.278245
$163$	1.38278e18	0.217349	0.108674	−	0.994077i	$-0.465339\pi$
$163$	1.38278e18	0.217349	0.108674	+	0.994077i	$0.465339\pi$
$164$	1.67846e18	0.250459
$165$	5.84202e18	0.827846
$166$	3.81659e18	0.513756
$167$	7.23858e18	0.925898	0.462949	−	0.886385i	$-0.346791\pi$
$167$	7.23858e18	0.925898	0.462949	+	0.886385i	$0.346791\pi$
$168$	−1.66749e18	−0.202738
$169$	−4.80378e18	−0.555324
$170$	−1.42051e19	−1.56181
$171$	−1.07692e18	−0.112646
$172$	−1.49018e18	−0.148336
$173$	−1.47276e19	−1.39553	−0.697767	−	0.716325i	$-0.745823\pi$
$173$	−1.47276e19	−1.39553	−0.697767	+	0.716325i	$0.745823\pi$
$174$	6.11139e17	0.0551406
$175$	−3.15746e17	−0.0271341
$176$	1.27218e19	1.04157
$177$	1.05001e18	0.0819259
$178$	−1.25627e19	−0.934358
$179$	−1.96552e19	−1.39389	−0.696943	−	0.717127i	$-0.745457\pi$
$179$	−1.96552e19	−1.39389	−0.696943	+	0.717127i	$0.745457\pi$
$180$	3.22728e18	0.218283
$181$	−1.23148e18	−0.0794620	−0.0397310	−	0.999210i	$-0.512650\pi$
$181$	−1.23148e18	−0.0794620	−0.0397310	+	0.999210i	$0.512650\pi$
$182$	−3.47603e18	−0.214031
$183$	1.14495e19	0.672903
$184$	−3.02628e19	−1.69808
$185$	5.10192e18	0.273385
$186$	2.32547e18	0.119028
$187$	5.88121e19	2.87616
$188$	−7.61902e18	−0.356088
$189$	−7.33777e18	−0.327822
$190$	3.06641e18	0.130986
$191$	1.89305e19	0.773354	0.386677	−	0.922215i	$-0.373623\pi$
$191$	1.89305e19	0.773354	0.386677	+	0.922215i	$0.373623\pi$
$192$	−1.39236e19	−0.544116
$193$	−9.89140e18	−0.369846	−0.184923	−	0.982753i	$-0.559204\pi$
$193$	−9.89140e18	−0.369846	−0.184923	+	0.982753i	$0.559204\pi$
$194$	3.62759e19	1.29809
$195$	−9.95455e18	−0.340979
$196$	−1.21477e18	−0.0398398
$197$	−2.26223e18	−0.0710517	−0.0355258	−	0.999369i	$-0.511311\pi$
$197$	−2.26223e18	−0.0710517	−0.0355258	+	0.999369i	$0.511311\pi$
$198$	3.45504e19	1.03944
$199$	1.38368e19	0.398827	0.199413	−	0.979915i	$-0.436096\pi$
$199$	1.38368e19	0.398827	0.199413	+	0.979915i	$0.436096\pi$
$200$	−2.82262e18	−0.0779646
$201$	1.12523e19	0.297904
$202$	2.24866e19	0.570738
$203$	2.04166e18	0.0496898
$204$	−1.04831e19	−0.244701
$205$	−4.15226e19	−0.929773
$206$	−7.21846e19	−1.55086
$207$	−5.73354e19	−1.18216
$208$	−2.16774e19	−0.429011
$209$	−1.26956e19	−0.241218
$210$	8.99549e18	0.164120
$211$	6.49265e19	1.13768	0.568842	−	0.822447i	$-0.307392\pi$
$211$	6.49265e19	1.13768	0.568842	+	0.822447i	$0.307392\pi$
$212$	3.09670e19	0.521249
$213$	−8.14934e18	−0.131794
$214$	3.73229e19	0.580040
$215$	3.68648e19	0.550662
$216$	−6.55961e19	−0.941936
$217$	7.76880e18	0.107262
$218$	2.93558e19	0.389775
$219$	−7.48548e18	−0.0955971
$220$	3.80458e19	0.467427
$221$	−1.00213e20	−1.18465
$222$	−9.73587e18	−0.110758
$223$	−4.95731e19	−0.542818	−0.271409	−	0.962464i	$-0.587490\pi$
$223$	−4.95731e19	−0.542818	−0.271409	+	0.962464i	$0.587490\pi$
$224$	−1.93508e19	−0.203982
$225$	−5.34768e18	−0.0542768
$226$	−1.36491e20	−1.33409
$227$	1.06120e20	0.999031	0.499516	−	0.866305i	$-0.333511\pi$
$227$	1.06120e20	0.999031	0.499516	+	0.866305i	$0.333511\pi$
$228$	2.26296e18	0.0205226
$229$	−9.94384e19	−0.868866	−0.434433	−	0.900704i	$-0.643051\pi$
$229$	−9.94384e19	−0.868866	−0.434433	+	0.900704i	$0.643051\pi$
$230$	1.63256e20	1.37462
$231$	−3.72433e19	−0.302236
$232$	1.82515e19	0.142774
$233$	1.06053e20	0.799830	0.399915	−	0.916552i	$-0.369040\pi$
$233$	1.06053e20	0.799830	0.399915	+	0.916552i	$0.369040\pi$
$234$	−5.88723e19	−0.428131
$235$	1.88484e20	1.32189
$236$	6.83813e18	0.0462578
$237$	4.66875e19	0.304677
$238$	9.05584e19	0.570197
$239$	−2.03599e20	−1.23707	−0.618535	−	0.785758i	$-0.712273\pi$
$239$	−2.03599e20	−1.23707	−0.618535	+	0.785758i	$0.712273\pi$
$240$	5.60980e19	0.328967
$241$	6.25026e19	0.353796	0.176898	−	0.984229i	$-0.443394\pi$
$241$	6.25026e19	0.353796	0.176898	+	0.984229i	$0.443394\pi$
$242$	2.51914e20	1.37664
$243$	−1.95048e20	−1.02917
$244$	7.45642e19	0.379941
$245$	3.00517e19	0.147896
$246$	7.92366e19	0.376684
$247$	2.16327e19	0.0993544
$248$	6.94493e19	0.308197
$249$	−6.96784e19	−0.298816
$250$	−1.96877e20	−0.816028
$251$	5.98686e19	0.239868	0.119934	−	0.992782i	$-0.461732\pi$
$251$	5.98686e19	0.239868	0.119934	+	0.992782i	$0.461732\pi$
$252$	−2.05741e19	−0.0796923
$253$	−6.75917e20	−2.53145
$254$	1.82744e20	0.661847
$255$	2.59338e20	0.908396
$256$	−2.25941e20	−0.765519
$257$	−1.70513e20	−0.558889	−0.279444	−	0.960162i	$-0.590150\pi$
$257$	−1.70513e20	−0.558889	−0.279444	+	0.960162i	$0.590150\pi$
$258$	−7.03482e19	−0.223093
$259$	−3.25251e19	−0.0998091
$260$	−6.48284e19	−0.192527
$261$	3.45789e19	0.0993955
$262$	−4.25260e20	−1.18330
$263$	6.27902e20	1.69148	0.845742	−	0.533592i	$-0.179158\pi$
$263$	6.27902e20	1.69148	0.845742	+	0.533592i	$0.179158\pi$
$264$	−3.32937e20	−0.868417
$265$	−7.66081e20	−1.93502
$266$	−1.95485e19	−0.0478212
$267$	2.29354e20	0.543451
$268$	7.32801e19	0.168206
$269$	1.12016e20	0.249107	0.124554	−	0.992213i	$-0.460250\pi$
$269$	1.12016e20	0.249107	0.124554	+	0.992213i	$0.460250\pi$
$270$	3.53866e20	0.762512
$271$	5.06820e20	1.05831	0.529157	−	0.848524i	$-0.322508\pi$
$271$	5.06820e20	1.05831	0.529157	+	0.848524i	$0.322508\pi$
$272$	5.64744e20	1.14292
$273$	6.34609e19	0.124487
$274$	2.86403e20	0.544626
$275$	−6.30428e19	−0.116227
$276$	1.20481e20	0.215373
$277$	−7.95531e18	−0.0137905	−0.00689524	−	0.999976i	$-0.502195\pi$
$277$	−7.95531e18	−0.0137905	−0.00689524	+	0.999976i	$0.502195\pi$
$278$	−9.59160e20	−1.61254
$279$	1.31577e20	0.214558
$280$	2.68647e20	0.424951
$281$	5.93229e20	0.910371	0.455186	−	0.890397i	$-0.349573\pi$
$281$	5.93229e20	0.910371	0.455186	+	0.890397i	$0.349573\pi$
$282$	−3.59679e20	−0.535547
$283$	8.90418e20	1.28650	0.643249	−	0.765657i	$-0.277586\pi$
$283$	8.90418e20	1.28650	0.643249	+	0.765657i	$0.277586\pi$
$284$	−5.30720e19	−0.0744149
$285$	−5.59825e19	−0.0761853
$286$	−6.94035e20	−0.916790
$287$	2.64709e20	0.339448
$288$	−3.27738e20	−0.408029
$289$	1.78354e21	2.15601
$290$	−9.84597e19	−0.115578
$291$	−6.62279e20	−0.755006
$292$	−4.87487e19	−0.0539770
$293$	−9.31988e20	−1.00239	−0.501194	−	0.865335i	$-0.667106\pi$
$293$	−9.31988e20	−1.00239	−0.501194	+	0.865335i	$0.667106\pi$
$294$	−5.73468e19	−0.0599180
$295$	−1.69166e20	−0.171722
$296$	−2.90758e20	−0.286783
$297$	−1.46508e21	−1.40421
$298$	−5.75482e20	−0.536036
$299$	1.15173e21	1.04267
$300$	1.12373e19	0.00988849
$301$	−2.35016e20	−0.201040
$302$	−6.04155e20	−0.502446
$303$	−4.10531e20	−0.331958
$304$	−1.21909e20	−0.0958543
$305$	−1.84461e21	−1.41045
$306$	1.53375e21	1.14057
$307$	1.46154e21	1.05714	0.528572	−	0.848888i	$-0.322728\pi$
$307$	1.46154e21	1.05714	0.528572	+	0.848888i	$0.322728\pi$
$308$	−2.42544e20	−0.170651
$309$	1.31785e21	0.902028
$310$	−3.74652e20	−0.249491
$311$	−9.89505e20	−0.641143	−0.320571	−	0.947224i	$-0.603875\pi$
$311$	−9.89505e20	−0.641143	−0.320571	+	0.947224i	$0.603875\pi$
$312$	5.67310e20	0.357690
$313$	−6.80648e20	−0.417634	−0.208817	−	0.977955i	$-0.566961\pi$
$313$	−6.80648e20	−0.417634	−0.208817	+	0.977955i	$0.566961\pi$
$314$	5.88686e20	0.351546
$315$	5.08974e20	0.295839
$316$	3.04050e20	0.172030
$317$	−2.35206e21	−1.29552	−0.647760	−	0.761844i	$-0.724294\pi$
$317$	−2.35206e21	−1.29552	−0.647760	+	0.761844i	$0.724294\pi$
$318$	1.46189e21	0.783944
$319$	4.07644e20	0.212844
$320$	2.24321e21	1.14050
$321$	−6.81393e20	−0.337369
$322$	−1.04077e21	−0.501857
$323$	−5.63581e20	−0.264688
$324$	−1.99743e20	−0.0913774
$325$	1.07422e20	0.0478724
$326$	4.25119e20	0.184570
$327$	−5.35940e20	−0.226705
$328$	2.36637e21	0.975339
$329$	−1.20160e21	−0.482606
$330$	1.79607e21	0.702998
$331$	7.24815e20	0.276496	0.138248	−	0.990398i	$-0.455853\pi$
$331$	7.24815e20	0.276496	0.138248	+	0.990398i	$0.455853\pi$
$332$	−4.53776e20	−0.168720
$333$	−5.50865e20	−0.199650
$334$	2.22542e21	0.786262
$335$	−1.81285e21	−0.624425
$336$	−3.57628e20	−0.120101
$337$	1.54530e21	0.506009	0.253005	−	0.967465i	$-0.418581\pi$
$337$	1.54530e21	0.506009	0.253005	+	0.967465i	$0.418581\pi$
$338$	−1.47687e21	−0.471575
$339$	2.49188e21	0.775944
$340$	1.68892e21	0.512908
$341$	1.55114e21	0.459451
$342$	−3.31087e20	−0.0956577
$343$	−1.91581e20	−0.0539949
$344$	−2.10093e21	−0.577649
$345$	−2.98053e21	−0.799522
$346$	−4.52784e21	−1.18507
$347$	−1.35086e21	−0.344993	−0.172496	−	0.985010i	$-0.555183\pi$
$347$	−1.35086e21	−0.344993	−0.172496	+	0.985010i	$0.555183\pi$
$348$	−7.26618e19	−0.0181085
$349$	7.48862e21	1.82132	0.910658	−	0.413160i	$-0.135575\pi$
$349$	7.48862e21	1.82132	0.910658	+	0.413160i	$0.135575\pi$
$350$	−9.70728e19	−0.0230419
$351$	2.49643e21	0.578375
$352$	−3.86364e21	−0.873744
$353$	−8.09321e21	−1.78664	−0.893318	−	0.449426i	$-0.851629\pi$
$353$	−8.09321e21	−1.78664	−0.893318	+	0.449426i	$0.851629\pi$
$354$	3.22815e20	0.0695706
$355$	1.31293e21	0.276248
$356$	1.49365e21	0.306849
$357$	−1.65330e21	−0.331643
$358$	−6.04278e21	−1.18367
$359$	−1.53955e21	−0.294503	−0.147252	−	0.989099i	$-0.547043\pi$
$359$	−1.53955e21	−0.294503	−0.147252	+	0.989099i	$0.547043\pi$
$360$	4.54998e21	0.850038
$361$	−5.35873e21	−0.977801
$362$	−3.78605e20	−0.0674782
$363$	−4.59911e21	−0.800696
$364$	4.13285e20	0.0702891
$365$	1.20597e21	0.200377
$366$	3.52003e21	0.571422
$367$	−1.15378e21	−0.183005	−0.0915024	−	0.995805i	$-0.529167\pi$
$367$	−1.15378e21	−0.183005	−0.0915024	+	0.995805i	$0.529167\pi$
$368$	−6.49049e21	−1.00594
$369$	4.48329e21	0.679004
$370$	1.56853e21	0.232155
$371$	4.88381e21	0.706449
$372$	−2.76488e20	−0.0390896
$373$	1.36646e22	1.88831	0.944153	−	0.329507i	$-0.106883\pi$
$373$	1.36646e22	1.88831	0.944153	+	0.329507i	$0.106883\pi$
$374$	1.80812e22	2.44240
$375$	3.59433e21	0.474627
$376$	−1.07417e22	−1.38668
$377$	−6.94608e20	−0.0876674
$378$	−2.25592e21	−0.278383
$379$	6.36167e21	0.767605	0.383802	−	0.923415i	$-0.374614\pi$
$379$	6.36167e21	0.767605	0.383802	+	0.923415i	$0.374614\pi$
$380$	−3.64583e20	−0.0430165
$381$	−3.33631e21	−0.384950
$382$	5.81998e21	0.656724
$383$	5.22429e21	0.576551	0.288276	−	0.957547i	$-0.406918\pi$
$383$	5.22429e21	0.576551	0.288276	+	0.957547i	$0.406918\pi$
$384$	−1.81118e21	−0.195500
$385$	6.00020e21	0.633505
$386$	−3.04101e21	−0.314069
$387$	−3.98037e21	−0.402143
$388$	−4.31305e21	−0.426299
$389$	1.19697e22	1.15747	0.578737	−	0.815514i	$-0.303546\pi$
$389$	1.19697e22	1.15747	0.578737	+	0.815514i	$0.303546\pi$
$390$	−3.06042e21	−0.289555
$391$	−3.00052e22	−2.77776
$392$	−1.71264e21	−0.155144
$393$	7.76385e21	0.688241
$394$	−6.95499e20	−0.0603363
$395$	−7.52176e21	−0.638622
$396$	−4.10788e21	−0.341357
$397$	−2.02447e22	−1.64661	−0.823307	−	0.567596i	$-0.807873\pi$
$397$	−2.02447e22	−1.64661	−0.823307	+	0.567596i	$0.807873\pi$
$398$	4.25397e21	0.338679
$399$	3.56892e20	0.0278142
$400$	−6.05369e20	−0.0461860
$401$	1.89731e22	1.41714	0.708568	−	0.705643i	$-0.249342\pi$
$401$	1.89731e22	1.41714	0.708568	+	0.705643i	$0.249342\pi$
$402$	3.45941e21	0.252977
$403$	−2.64308e21	−0.189242
$404$	−2.67356e21	−0.187434
$405$	4.94136e21	0.339218
$406$	6.27687e20	0.0421960
$407$	−6.49405e21	−0.427527
$408$	−1.47797e22	−0.952914
$409$	8.06945e21	0.509561	0.254780	−	0.966999i	$-0.417997\pi$
$409$	8.06945e21	0.509561	0.254780	+	0.966999i	$0.417997\pi$
$410$	−1.27657e22	−0.789553
$411$	−5.22878e21	−0.316771
$412$	8.58243e21	0.509312
$413$	1.07844e21	0.0626933
$414$	−1.76271e22	−1.00387
$415$	1.12258e22	0.626336
$416$	6.58348e21	0.359884
$417$	1.75111e22	0.937901
$418$	−3.90312e21	−0.204839
$419$	−6.29915e21	−0.323939	−0.161969	−	0.986796i	$-0.551785\pi$
$419$	−6.29915e21	−0.323939	−0.161969	+	0.986796i	$0.551785\pi$
$420$	−1.06952e21	−0.0538979
$421$	−1.42713e22	−0.704799	−0.352399	−	0.935850i	$-0.614634\pi$
$421$	−1.42713e22	−0.704799	−0.352399	+	0.935850i	$0.614634\pi$
$422$	1.99610e22	0.966108
$423$	−2.03510e22	−0.965367
$424$	4.36589e22	2.02985
$425$	−2.79859e21	−0.127536
$426$	−2.50543e21	−0.111918
$427$	1.17595e22	0.514935
$428$	−4.43753e21	−0.190489
$429$	1.26708e22	0.533233
$430$	1.13337e22	0.467616
$431$	1.35027e22	0.546216	0.273108	−	0.961983i	$-0.411948\pi$
$431$	1.35027e22	0.546216	0.273108	+	0.961983i	$0.411948\pi$
$432$	−1.40684e22	−0.558000
$433$	−1.35210e22	−0.525850	−0.262925	−	0.964816i	$-0.584687\pi$
$433$	−1.35210e22	−0.525850	−0.262925	+	0.964816i	$0.584687\pi$
$434$	2.38843e21	0.0910857
$435$	1.79755e21	0.0672237
$436$	−3.49028e21	−0.128004
$437$	6.47713e21	0.232965
$438$	−2.30133e21	−0.0811799
$439$	5.16501e21	0.178699	0.0893497	−	0.996000i	$-0.471521\pi$
$439$	5.16501e21	0.178699	0.0893497	+	0.996000i	$0.471521\pi$
$440$	5.36389e22	1.82026
$441$	−3.24474e21	−0.108007
$442$	−3.08095e22	−1.00599
$443$	−5.52076e22	−1.76834	−0.884172	−	0.467161i	$-0.845277\pi$
$443$	−5.52076e22	−1.76834	−0.884172	+	0.467161i	$0.845277\pi$
$444$	1.15755e21	0.0363735
$445$	−3.69508e22	−1.13911
$446$	−1.52407e22	−0.460955
$447$	1.05064e22	0.311774
$448$	−1.43006e22	−0.416382
$449$	5.80467e22	1.65838	0.829189	−	0.558969i	$-0.188803\pi$
$449$	5.80467e22	1.65838	0.829189	+	0.558969i	$0.188803\pi$
$450$	−1.64409e21	−0.0460912
$451$	5.28526e22	1.45401
$452$	1.62282e22	0.438122
$453$	1.10299e22	0.292237
$454$	3.26256e22	0.848366
$455$	−1.02241e22	−0.260932
$456$	3.19044e21	0.0799190
$457$	−1.49314e22	−0.367125	−0.183563	−	0.983008i	$-0.558763\pi$
$457$	−1.49314e22	−0.367125	−0.183563	+	0.983008i	$0.558763\pi$
$458$	−3.05713e22	−0.737831
$459$	−6.50377e22	−1.54084
$460$	−1.94105e22	−0.451434
$461$	−6.23698e22	−1.42402	−0.712011	−	0.702169i	$-0.752215\pi$
$461$	−6.23698e22	−1.42402	−0.712011	+	0.702169i	$0.752215\pi$
$462$	−1.14500e22	−0.256655
$463$	−6.60682e22	−1.45397	−0.726983	−	0.686655i	$-0.759078\pi$
$463$	−6.60682e22	−1.45397	−0.726983	+	0.686655i	$0.759078\pi$
$464$	3.91440e21	0.0845790
$465$	6.83992e21	0.145111
$466$	3.26049e22	0.679207
$467$	3.73065e22	0.763117	0.381558	−	0.924345i	$-0.375388\pi$
$467$	3.73065e22	0.763117	0.381558	+	0.924345i	$0.375388\pi$
$468$	6.99966e21	0.140601
$469$	1.15570e22	0.227969
$470$	5.79473e22	1.12254
$471$	−1.07475e22	−0.204469
$472$	9.64075e21	0.180137
$473$	−4.69239e22	−0.861142
$474$	1.43536e22	0.258728
$475$	6.04122e20	0.0106962
$476$	−1.07670e22	−0.187256
$477$	8.27154e22	1.41312
$478$	−6.25944e22	−1.05051
$479$	−9.51799e22	−1.56925	−0.784627	−	0.619968i	$-0.787146\pi$
$479$	−9.51799e22	−1.56925	−0.784627	+	0.619968i	$0.787146\pi$
$480$	−1.70371e22	−0.275960
$481$	1.10656e22	0.176093
$482$	1.92157e22	0.300440
$483$	1.90010e22	0.291895
$484$	−2.99514e22	−0.452097
$485$	1.06699e23	1.58254
$486$	−5.99654e22	−0.873962
$487$	1.81999e22	0.260659	0.130330	−	0.991471i	$-0.458396\pi$
$487$	1.81999e22	0.260659	0.130330	+	0.991471i	$0.458396\pi$
$488$	1.05124e23	1.47957
$489$	−7.76128e21	−0.107351
$490$	9.23906e21	0.125592
$491$	3.46182e22	0.462500	0.231250	−	0.972894i	$-0.425718\pi$
$491$	3.46182e22	0.462500	0.231250	+	0.972894i	$0.425718\pi$
$492$	−9.42088e21	−0.123705
$493$	1.80961e22	0.233553
$494$	6.65075e21	0.0843707
$495$	1.01623e23	1.26721
$496$	1.48948e22	0.182575
$497$	−8.36999e21	−0.100855
$498$	−2.14219e22	−0.253751
$499$	9.64344e22	1.12299	0.561497	−	0.827479i	$-0.310226\pi$
$499$	9.64344e22	1.12299	0.561497	+	0.827479i	$0.310226\pi$
$500$	2.34078e22	0.267988
$501$	−4.06289e22	−0.457314
$502$	1.84060e22	0.203693
$503$	−5.93417e22	−0.645702	−0.322851	−	0.946450i	$-0.604641\pi$
$503$	−5.93417e22	−0.645702	−0.322851	+	0.946450i	$0.604641\pi$
$504$	−2.90064e22	−0.310338
$505$	6.61400e22	0.695805
$506$	−2.07803e23	−2.14968
$507$	2.69628e22	0.274282
$508$	−2.17275e22	−0.217354
$509$	1.33748e23	1.31579	0.657893	−	0.753111i	$-0.271448\pi$
$509$	1.33748e23	1.31579	0.657893	+	0.753111i	$0.271448\pi$
$510$	7.97308e22	0.771400
$511$	−7.68816e21	−0.0731551
$512$	−1.11758e23	−1.04589
$513$	1.40395e22	0.129227
$514$	−5.24223e22	−0.474602
$515$	−2.12317e23	−1.89071
$516$	8.36410e21	0.0732650
$517$	−2.39914e23	−2.06722
$518$	−9.99948e21	−0.0847568
$519$	8.26635e22	0.689273
$520$	−9.13984e22	−0.749739
$521$	−1.04188e23	−0.840812	−0.420406	−	0.907336i	$-0.638112\pi$
$521$	−1.04188e23	−0.840812	−0.420406	+	0.907336i	$0.638112\pi$
$522$	1.06309e22	0.0844055
$523$	−6.27210e22	−0.489946	−0.244973	−	0.969530i	$-0.578779\pi$
$523$	−6.27210e22	−0.489946	−0.244973	+	0.969530i	$0.578779\pi$
$524$	5.05616e22	0.388602
$525$	1.77223e21	0.0134019
$526$	1.93042e23	1.43639
$527$	6.88580e22	0.504155
$528$	−7.14051e22	−0.514448
$529$	2.03794e23	1.44484
$530$	−2.35523e23	−1.64319
$531$	1.82652e22	0.125407
$532$	2.32424e21	0.0157048
$533$	−9.00586e22	−0.598886
$534$	7.05123e22	0.461492
$535$	1.09778e23	0.707146
$536$	1.03314e23	0.655027
$537$	1.10321e23	0.688459
$538$	3.44381e22	0.211539
$539$	−3.82517e22	−0.231284
$540$	−4.20731e22	−0.250413
$541$	7.93926e22	0.465161	0.232581	−	0.972577i	$-0.425283\pi$
$541$	7.93926e22	0.465161	0.232581	+	0.972577i	$0.425283\pi$
$542$	1.55816e23	0.898709
$543$	6.91208e21	0.0392473
$544$	−1.71514e23	−0.958760
$545$	8.63445e22	0.475187
$546$	1.95104e22	0.105713
$547$	−7.40616e22	−0.395094	−0.197547	−	0.980293i	$-0.563298\pi$
$547$	−7.40616e22	−0.395094	−0.197547	+	0.980293i	$0.563298\pi$
$548$	−3.40521e22	−0.178858
$549$	1.99167e23	1.03003
$550$	−1.93818e22	−0.0986988
$551$	−3.90634e21	−0.0195876
$552$	1.69860e23	0.838705
$553$	4.79517e22	0.233153
$554$	−2.44577e21	−0.0117107
$555$	−2.86362e22	−0.135028
$556$	1.14040e23	0.529567
$557$	−2.08675e23	−0.954338	−0.477169	−	0.878812i	$-0.658337\pi$
$557$	−2.08675e23	−0.954338	−0.477169	+	0.878812i	$0.658337\pi$
$558$	4.04520e22	0.182200
$559$	7.99563e22	0.354693
$560$	5.76169e22	0.251740
$561$	−3.30102e23	−1.42058
$562$	1.82382e23	0.773077
$563$	−8.53880e22	−0.356513	−0.178256	−	0.983984i	$-0.557046\pi$
$563$	−8.53880e22	−0.356513	−0.178256	+	0.983984i	$0.557046\pi$
$564$	4.27642e22	0.175877
$565$	−4.01464e23	−1.62643
$566$	2.73749e23	1.09248
$567$	−3.15015e22	−0.123844
$568$	−7.48237e22	−0.289787
$569$	−4.75498e23	−1.81424	−0.907119	−	0.420875i	$-0.861723\pi$
$569$	−4.75498e23	−1.81424	−0.907119	+	0.420875i	$0.861723\pi$
$570$	−1.72112e22	−0.0646957
$571$	3.08401e23	1.14211	0.571056	−	0.820911i	$-0.306534\pi$
$571$	3.08401e23	1.14211	0.571056	+	0.820911i	$0.306534\pi$
$572$	8.25177e22	0.301079
$573$	−1.06254e23	−0.381970
$574$	8.13820e22	0.288255
$575$	3.21636e22	0.112251
$576$	−2.42204e23	−0.832896
$577$	−2.98883e23	−1.01276	−0.506381	−	0.862310i	$-0.669017\pi$
$577$	−2.98883e23	−1.01276	−0.506381	+	0.862310i	$0.669017\pi$
$578$	5.48330e23	1.83086
$579$	5.55187e22	0.182672
$580$	1.17064e22	0.0379565
$581$	−7.15650e22	−0.228667
$582$	−2.03610e23	−0.641143
$583$	9.75117e23	3.02604
$584$	−6.87284e22	−0.210197
$585$	−1.73162e23	−0.521948
$586$	−2.86530e23	−0.851216
$587$	−4.72700e23	−1.38408	−0.692041	−	0.721858i	$-0.743288\pi$
$587$	−4.72700e23	−1.38408	−0.692041	+	0.721858i	$0.743288\pi$
$588$	6.81829e21	0.0196774
$589$	−1.48642e22	−0.0422825
$590$	−5.20082e22	−0.145824
$591$	1.26975e22	0.0350934
$592$	−6.23591e22	−0.169889
$593$	−5.30563e23	−1.42486	−0.712430	−	0.701744i	$-0.752405\pi$
$593$	−5.30563e23	−1.42486	−0.712430	+	0.701744i	$0.752405\pi$
$594$	−4.50423e23	−1.19244
$595$	2.66360e23	0.695145
$596$	6.84223e22	0.176037
$597$	−7.76636e22	−0.196986
$598$	3.54088e23	0.885423
$599$	1.31742e23	0.324786	0.162393	−	0.986726i	$-0.448079\pi$
$599$	1.31742e23	0.324786	0.162393	+	0.986726i	$0.448079\pi$
$600$	1.58429e22	0.0385078
$601$	−5.23046e22	−0.125345	−0.0626725	−	0.998034i	$-0.519962\pi$
$601$	−5.23046e22	−0.125345	−0.0626725	+	0.998034i	$0.519962\pi$
$602$	−7.22530e22	−0.170721
$603$	1.95737e23	0.456011
$604$	7.18313e22	0.165006
$605$	7.40956e23	1.67831
$606$	−1.26213e23	−0.281895
$607$	−5.08636e23	−1.12022	−0.560109	−	0.828419i	$-0.689241\pi$
$607$	−5.08636e23	−1.12022	−0.560109	+	0.828419i	$0.689241\pi$
$608$	3.70242e22	0.0804092
$609$	−1.14595e22	−0.0245425
$610$	−5.67106e23	−1.19773
$611$	4.08803e23	0.851459
$612$	−1.82357e23	−0.374571
$613$	2.98843e23	0.605382	0.302691	−	0.953089i	$-0.402115\pi$
$613$	2.98843e23	0.605382	0.302691	+	0.953089i	$0.402115\pi$
$614$	4.49334e23	0.897715
$615$	2.33059e23	0.459227
$616$	−3.41952e23	−0.664551
$617$	9.70789e23	1.86081	0.930403	−	0.366539i	$-0.119457\pi$
$617$	9.70789e23	1.86081	0.930403	+	0.366539i	$0.119457\pi$
$618$	4.05160e23	0.765992
$619$	−3.96945e23	−0.740219	−0.370109	−	0.928988i	$-0.620680\pi$
$619$	−3.96945e23	−0.740219	−0.370109	+	0.928988i	$0.620680\pi$
$620$	4.45445e22	0.0819341
$621$	7.47465e23	1.35616
$622$	−3.04213e23	−0.544451
$623$	2.35564e23	0.415872
$624$	1.21671e23	0.211894
$625$	−6.20864e23	−1.06664
$626$	−2.09258e23	−0.354650
$627$	7.12581e22	0.119141
$628$	−6.99922e22	−0.115450
$629$	−2.88283e23	−0.469125
$630$	1.56479e23	0.251223
$631$	−1.48840e23	−0.235761	−0.117880	−	0.993028i	$-0.537610\pi$
$631$	−1.48840e23	−0.235761	−0.117880	+	0.993028i	$0.537610\pi$
$632$	4.28665e23	0.669919
$633$	−3.64421e23	−0.561917
$634$	−7.23115e23	−1.10014
$635$	5.37508e23	0.806879
$636$	−1.73813e23	−0.257452
$637$	6.51792e22	0.0952629
$638$	1.25326e23	0.180744
$639$	−1.41760e23	−0.201741
$640$	2.91796e23	0.409779
$641$	−2.74376e23	−0.380236	−0.190118	−	0.981761i	$-0.560887\pi$
$641$	−2.74376e23	−0.380236	−0.190118	+	0.981761i	$0.560887\pi$
$642$	−2.09487e23	−0.286490
$643$	5.59221e23	0.754728	0.377364	−	0.926065i	$-0.376831\pi$
$643$	5.59221e23	0.754728	0.377364	+	0.926065i	$0.376831\pi$
$644$	1.23743e23	0.164813
$645$	−2.06916e23	−0.271980
$646$	−1.73267e23	−0.224770
$647$	−7.60914e23	−0.974203	−0.487101	−	0.873346i	$-0.661946\pi$
$647$	−7.60914e23	−0.974203	−0.487101	+	0.873346i	$0.661946\pi$
$648$	−2.81608e23	−0.355842
$649$	2.15325e23	0.268543
$650$	3.30258e22	0.0406527
$651$	−4.36049e22	−0.0529782
$652$	−5.05448e22	−0.0606139
$653$	−1.00542e24	−1.19010	−0.595051	−	0.803688i	$-0.702868\pi$
$653$	−1.00542e24	−1.19010	−0.595051	+	0.803688i	$0.702868\pi$
$654$	−1.64769e23	−0.192515
$655$	−1.25082e24	−1.44260
$656$	5.07517e23	0.577788
$657$	−1.30212e23	−0.146333
$658$	−3.69417e23	−0.409824
$659$	−6.28207e23	−0.687981	−0.343991	−	0.938973i	$-0.611779\pi$
$659$	−6.28207e23	−0.687981	−0.343991	+	0.938973i	$0.611779\pi$
$660$	−2.13544e23	−0.230869
$661$	9.61538e23	1.02625	0.513126	−	0.858313i	$-0.328487\pi$
$661$	9.61538e23	1.02625	0.513126	+	0.858313i	$0.328487\pi$
$662$	2.22836e23	0.234797
$663$	5.62480e23	0.585116
$664$	−6.39757e23	−0.657031
$665$	−5.74983e22	−0.0583004
$666$	−1.69358e23	−0.169541
$667$	−2.07975e23	−0.205561
$668$	−2.64593e23	−0.258213
$669$	2.78245e23	0.268105
$670$	−5.57340e23	−0.530255
$671$	2.34794e24	2.20570
$672$	1.08613e23	0.100749
$673$	8.05256e23	0.737574	0.368787	−	0.929514i	$-0.379773\pi$
$673$	8.05256e23	0.737574	0.368787	+	0.929514i	$0.379773\pi$
$674$	4.75086e23	0.429697
$675$	6.97162e22	0.0622661
$676$	1.75594e23	0.154868
$677$	−1.58712e23	−0.138231	−0.0691157	−	0.997609i	$-0.522018\pi$
$677$	−1.58712e23	−0.138231	−0.0691157	+	0.997609i	$0.522018\pi$
$678$	7.66103e23	0.658923
$679$	−6.80211e23	−0.577764
$680$	2.38113e24	1.99737
$681$	−5.95635e23	−0.493435
$682$	4.76881e23	0.390160
$683$	6.17169e23	0.498687	0.249343	−	0.968415i	$-0.419785\pi$
$683$	6.17169e23	0.498687	0.249343	+	0.968415i	$0.419785\pi$
$684$	3.93647e22	0.0314145
$685$	8.42400e23	0.663970
$686$	−5.88996e22	−0.0458519
$687$	5.58131e23	0.429145
$688$	−4.50587e23	−0.342197
$689$	−1.66156e24	−1.24638
$690$	−9.16330e23	−0.678945
$691$	1.54202e24	1.12856	0.564281	−	0.825583i	$-0.309154\pi$
$691$	1.54202e24	1.12856	0.564281	+	0.825583i	$0.309154\pi$
$692$	5.38340e23	0.389184
$693$	−6.47855e23	−0.462642
$694$	−4.15308e23	−0.292964
$695$	−2.82118e24	−1.96590
$696$	−1.02442e23	−0.0705182
$697$	2.34623e24	1.59548
$698$	2.30229e24	1.54664
$699$	−5.95257e23	−0.395047
$700$	1.15415e22	0.00756711
$701$	−1.16911e24	−0.757273	−0.378636	−	0.925545i	$-0.623607\pi$
$701$	−1.16911e24	−0.757273	−0.378636	+	0.925545i	$0.623607\pi$
$702$	7.67501e23	0.491149
$703$	6.22307e22	0.0393446
$704$	−2.85530e24	−1.78355
$705$	−1.05793e24	−0.652902
$706$	−2.48817e24	−1.51719
$707$	−4.21647e23	−0.254029
$708$	−3.83812e22	−0.0228474
$709$	7.92029e23	0.465852	0.232926	−	0.972494i	$-0.425170\pi$
$709$	7.92029e23	0.465852	0.232926	+	0.972494i	$0.425170\pi$
$710$	4.03645e23	0.234587
$711$	8.12140e23	0.466379
$712$	2.10583e24	1.19493
$713$	−7.91372e23	−0.443731
$714$	−5.08289e23	−0.281628
$715$	−2.04137e24	−1.11769
$716$	7.18460e23	0.388725
$717$	1.14277e24	0.611005
$718$	−4.73317e23	−0.250089
$719$	−3.11282e24	−1.62540	−0.812698	−	0.582686i	$-0.802002\pi$
$719$	−3.11282e24	−1.62540	−0.812698	+	0.582686i	$0.802002\pi$
$720$	9.75837e23	0.503560
$721$	1.35354e24	0.690272
$722$	−1.64748e24	−0.830338
$723$	−3.50816e23	−0.174745
$724$	4.50145e22	0.0221602
$725$	−1.93978e22	−0.00943801
$726$	−1.41395e24	−0.679942
$727$	1.84525e24	0.877027	0.438513	−	0.898725i	$-0.355505\pi$
$727$	1.84525e24	0.877027	0.438513	+	0.898725i	$0.355505\pi$
$728$	5.82670e23	0.273720
$729$	3.89091e23	0.180662
$730$	3.70763e23	0.170158
$731$	−2.08304e24	−0.944931
$732$	−4.18516e23	−0.187658
$733$	1.52549e24	0.676124	0.338062	−	0.941124i	$-0.390229\pi$
$733$	1.52549e24	0.676124	0.338062	+	0.941124i	$0.390229\pi$
$734$	−3.54718e23	−0.155406
$735$	−1.68675e23	−0.0730479
$736$	1.97118e24	0.843850
$737$	2.30751e24	0.976494
$738$	1.37834e24	0.576603
$739$	−6.15712e23	−0.254624	−0.127312	−	0.991863i	$-0.540635\pi$
$739$	−6.15712e23	−0.254624	−0.127312	+	0.991863i	$0.540635\pi$
$740$	−1.86491e23	−0.0762411
$741$	−1.21421e23	−0.0490725
$742$	1.50148e24	0.599909
$743$	−2.37210e23	−0.0936974	−0.0468487	−	0.998902i	$-0.514918\pi$
$743$	−2.37210e23	−0.0936974	−0.0468487	+	0.998902i	$0.514918\pi$
$744$	−3.89807e23	−0.152223
$745$	−1.69267e24	−0.653498
$746$	4.20104e24	1.60353
$747$	−1.21207e24	−0.457407
$748$	−2.14977e24	−0.802100
$749$	−6.99843e23	−0.258170
$750$	1.10504e24	0.403048
$751$	−1.07498e24	−0.387670	−0.193835	−	0.981034i	$-0.562093\pi$
$751$	−1.07498e24	−0.387670	−0.193835	+	0.981034i	$0.562093\pi$
$752$	−2.30377e24	−0.821463
$753$	−3.36032e23	−0.118474
$754$	−2.13550e23	−0.0744462
$755$	−1.77701e24	−0.612548
$756$	2.68219e23	0.0914226
$757$	5.62882e23	0.189715	0.0948577	−	0.995491i	$-0.469760\pi$
$757$	5.62882e23	0.189715	0.0948577	+	0.995491i	$0.469760\pi$
$758$	1.95583e24	0.651841
$759$	3.79380e24	1.25032
$760$	−5.14007e23	−0.167515
$761$	−2.07826e24	−0.669777	−0.334889	−	0.942258i	$-0.608699\pi$
$761$	−2.07826e24	−0.669777	−0.334889	+	0.942258i	$0.608699\pi$
$762$	−1.02571e24	−0.326895
$763$	−5.50452e23	−0.173485
$764$	−6.91970e23	−0.215672
$765$	4.51125e24	1.39051
$766$	1.60615e24	0.489601
$767$	−3.66904e23	−0.110609
$768$	1.26817e24	0.378100
$769$	3.01894e24	0.890186	0.445093	−	0.895484i	$-0.353171\pi$
$769$	3.01894e24	0.890186	0.445093	+	0.895484i	$0.353171\pi$
$770$	1.84470e24	0.537965
$771$	9.57059e23	0.276043
$772$	3.61562e23	0.103142
$773$	2.97846e24	0.840362	0.420181	−	0.907440i	$-0.361967\pi$
$773$	2.97846e24	0.840362	0.420181	+	0.907440i	$0.361967\pi$
$774$	−1.22372e24	−0.341496
$775$	−7.38114e22	−0.0203732
$776$	−6.08076e24	−1.66010
$777$	1.82558e23	0.0492971
$778$	3.67995e24	0.982913
$779$	−5.06473e23	−0.133810
$780$	3.63870e23	0.0950917
$781$	−1.67118e24	−0.432005
$782$	−9.22478e24	−2.35884
$783$	−4.50795e23	−0.114026
$784$	−3.67312e23	−0.0919069
$785$	1.73151e24	0.428580
$786$	2.38691e24	0.584447
$787$	2.45332e24	0.594251	0.297125	−	0.954838i	$-0.403972\pi$
$787$	2.45332e24	0.594251	0.297125	+	0.954838i	$0.403972\pi$
$788$	8.26917e22	0.0198148
$789$	−3.52431e24	−0.835447
$790$	−2.31248e24	−0.542311
$791$	2.55936e24	0.593787
$792$	−5.79151e24	−1.32931
$793$	−4.00079e24	−0.908497
$794$	−6.22401e24	−1.39829
$795$	4.29988e24	0.955731
$796$	−5.05779e23	−0.111224
$797$	5.45083e24	1.18595	0.592976	−	0.805220i	$-0.297953\pi$
$797$	5.45083e24	1.18595	0.592976	+	0.805220i	$0.297953\pi$
$798$	1.09723e23	0.0236195
$799$	−1.06502e25	−2.26836
$800$	1.83852e23	0.0387440
$801$	3.98966e24	0.831877
$802$	5.83308e24	1.20342
$803$	−1.53504e24	−0.313356
$804$	−4.11309e23	−0.0830790
$805$	−3.06123e24	−0.611830
$806$	−8.12585e23	−0.160702
$807$	−6.28727e23	−0.123037
$808$	−3.76932e24	−0.729905
$809$	6.41394e24	1.22903	0.614515	−	0.788905i	$-0.289352\pi$
$809$	6.41394e24	1.22903	0.614515	+	0.788905i	$0.289352\pi$
$810$	1.51917e24	0.288060
$811$	8.43409e23	0.158256	0.0791281	−	0.996864i	$-0.474786\pi$
$811$	8.43409e23	0.158256	0.0791281	+	0.996864i	$0.474786\pi$
$812$	−7.46292e22	−0.0138574
$813$	−2.84469e24	−0.522716
$814$	−1.99653e24	−0.363051
$815$	1.25041e24	0.225015
$816$	−3.16981e24	−0.564503
$817$	4.49659e23	0.0792494
$818$	2.48087e24	0.432713
$819$	1.10392e24	0.190556
$820$	1.51778e24	0.259294
$821$	2.36220e24	0.399393	0.199696	−	0.979858i	$-0.436004\pi$
$821$	2.36220e24	0.399393	0.199696	+	0.979858i	$0.436004\pi$
$822$	−1.60753e24	−0.268998
$823$	−5.10762e24	−0.845902	−0.422951	−	0.906153i	$-0.639006\pi$
$823$	−5.10762e24	−0.845902	−0.422951	+	0.906153i	$0.639006\pi$
$824$	1.21000e25	1.98336
$825$	3.53848e23	0.0574062
$826$	3.31555e23	0.0532385
$827$	1.19926e24	0.190597	0.0952983	−	0.995449i	$-0.469620\pi$
$827$	1.19926e24	0.190597	0.0952983	+	0.995449i	$0.469620\pi$
$828$	2.09579e24	0.329678
$829$	7.17384e24	1.11696	0.558481	−	0.829517i	$-0.311384\pi$
$829$	7.17384e24	1.11696	0.558481	+	0.829517i	$0.311384\pi$
$830$	3.45124e24	0.531878
$831$	4.46518e22	0.00681130
$832$	4.86531e24	0.734620
$833$	−1.69806e24	−0.253788
$834$	5.38360e24	0.796455
$835$	6.54566e24	0.958557
$836$	4.64064e23	0.0672705
$837$	−1.71534e24	−0.246140
$838$	−1.93661e24	−0.275085
$839$	5.99860e24	0.843476	0.421738	−	0.906718i	$-0.361420\pi$
$839$	5.99860e24	0.843476	0.421738	+	0.906718i	$0.361420\pi$
$840$	−1.50787e24	−0.209889
$841$	−7.13172e24	−0.982716
$842$	−4.38755e24	−0.598507
$843$	−3.32969e24	−0.449645
$844$	−2.37327e24	−0.317275
$845$	−4.34394e24	−0.574912
$846$	−6.25669e24	−0.819778
$847$	−4.72364e24	−0.612728
$848$	9.36356e24	1.20248
$849$	−4.99776e24	−0.635419
$850$	−8.60396e23	−0.108302
$851$	3.31318e24	0.412899
$852$	2.97884e23	0.0367545
$853$	6.59831e24	0.806057	0.403029	−	0.915187i	$-0.367958\pi$
$853$	6.59831e24	0.806057	0.403029	+	0.915187i	$0.367958\pi$
$854$	3.61534e24	0.437277
$855$	−9.73828e23	−0.116619
$856$	−6.25626e24	−0.741801
$857$	−1.03313e25	−1.21289	−0.606443	−	0.795127i	$-0.707404\pi$
$857$	−1.03313e25	−1.21289	−0.606443	+	0.795127i	$0.707404\pi$
$858$	3.89550e24	0.452815
$859$	8.90994e24	1.02549	0.512747	−	0.858540i	$-0.328628\pi$
$859$	8.90994e24	1.02549	0.512747	+	0.858540i	$0.328628\pi$
$860$	−1.34753e24	−0.153568
$861$	−1.48577e24	−0.167658
$862$	4.15127e24	0.463841
$863$	−1.48974e25	−1.64823	−0.824116	−	0.566421i	$-0.808328\pi$
$863$	−1.48974e25	−1.64823	−0.824116	+	0.566421i	$0.808328\pi$
$864$	4.27263e24	0.468089
$865$	−1.33178e25	−1.44476
$866$	−4.15689e24	−0.446546
$867$	−1.00107e25	−1.06488
$868$	−2.83974e23	−0.0299131
$869$	9.57417e24	0.998695
$870$	5.52637e23	0.0570856
$871$	−3.93189e24	−0.402205
$872$	−4.92077e24	−0.498475
$873$	−1.15205e25	−1.15571
$874$	1.99132e24	0.197831
$875$	3.69165e24	0.363205
$876$	2.73618e23	0.0266600
$877$	1.14446e24	0.110434	0.0552170	−	0.998474i	$-0.482415\pi$
$877$	1.14446e24	0.110434	0.0552170	+	0.998474i	$0.482415\pi$
$878$	1.58793e24	0.151750
$879$	5.23109e24	0.495093
$880$	1.15040e25	1.07831
$881$	3.50796e24	0.325656	0.162828	−	0.986654i	$-0.447938\pi$
$881$	3.50796e24	0.325656	0.162828	+	0.986654i	$0.447938\pi$
$882$	−9.97561e23	−0.0917184
$883$	4.23812e24	0.385929	0.192965	−	0.981206i	$-0.438190\pi$
$883$	4.23812e24	0.385929	0.192965	+	0.981206i	$0.438190\pi$
$884$	3.66311e24	0.330374
$885$	9.49498e23	0.0848157
$886$	−1.69730e25	−1.50166
$887$	1.19109e25	1.04374	0.521872	−	0.853024i	$-0.325234\pi$
$887$	1.19109e25	1.04374	0.521872	+	0.853024i	$0.325234\pi$
$888$	1.63198e24	0.141646
$889$	−3.42665e24	−0.294581
$890$	−1.13601e25	−0.967316
$891$	−6.28967e24	−0.530478
$892$	1.81205e24	0.151380
$893$	2.29903e24	0.190242
$894$	3.23008e24	0.264755
$895$	−1.77737e25	−1.44305
$896$	−1.86022e24	−0.149605
$897$	−6.46448e24	−0.514988
$898$	1.78458e25	1.40828
$899$	4.77275e23	0.0373088
$900$	1.95475e23	0.0151366
$901$	4.32873e25	3.32047
$902$	1.62490e25	1.23473
$903$	1.31910e24	0.0992962
$904$	2.28794e25	1.70613
$905$	−1.11359e24	−0.0822648
$906$	3.39102e24	0.248165
$907$	−2.39520e25	−1.73652	−0.868262	−	0.496106i	$-0.834763\pi$
$907$	−2.39520e25	−1.73652	−0.868262	+	0.496106i	$0.834763\pi$
$908$	−3.87904e24	−0.278608
$909$	−7.14128e24	−0.508139
$910$	−3.14328e24	−0.221581
$911$	2.22981e25	1.55726	0.778632	−	0.627481i	$-0.215914\pi$
$911$	2.22981e25	1.55726	0.778632	+	0.627481i	$0.215914\pi$
$912$	6.84256e23	0.0473437
$913$	−1.42889e25	−0.979482
$914$	−4.59051e24	−0.311759
$915$	1.03535e25	0.696638
$916$	3.63479e24	0.242308
$917$	7.97407e24	0.526673
$918$	−1.99951e25	−1.30846
$919$	9.12170e24	0.591417	0.295708	−	0.955278i	$-0.404444\pi$
$919$	9.12170e24	0.591417	0.295708	+	0.955278i	$0.404444\pi$
$920$	−2.73659e25	−1.75798
$921$	−8.20336e24	−0.522138
$922$	−1.91749e25	−1.20926
$923$	2.84761e24	0.177937
$924$	1.36136e24	0.0842871
$925$	3.09021e23	0.0189576
$926$	−2.03120e25	−1.23469
$927$	2.29244e25	1.38076
$928$	−1.18882e24	−0.0709507
$929$	−1.01994e25	−0.603170	−0.301585	−	0.953439i	$-0.597516\pi$
$929$	−1.01994e25	−0.603170	−0.301585	+	0.953439i	$0.597516\pi$
$930$	2.10286e24	0.123227
$931$	3.66555e23	0.0212847
$932$	−3.87657e24	−0.223055
$933$	5.55392e24	0.316669
$934$	1.14695e25	0.648030
$935$	5.31823e25	2.97761
$936$	9.86848e24	0.547527
$937$	−1.82779e25	−1.00494	−0.502469	−	0.864595i	$-0.667575\pi$
$937$	−1.82779e25	−1.00494	−0.502469	+	0.864595i	$0.667575\pi$
$938$	3.55308e24	0.193589
$939$	3.82036e24	0.206275
$940$	−6.88967e24	−0.368648
$941$	−1.82285e25	−0.966583	−0.483292	−	0.875459i	$-0.660559\pi$
$941$	−1.82285e25	−0.966583	−0.483292	+	0.875459i	$0.660559\pi$
$942$	−3.30419e24	−0.173633
$943$	−2.69647e25	−1.40426
$944$	2.06766e24	0.106713
$945$	−6.63535e24	−0.339386
$946$	−1.44263e25	−0.731272
$947$	1.54759e25	0.777463	0.388732	−	0.921351i	$-0.372913\pi$
$947$	1.54759e25	0.777463	0.388732	+	0.921351i	$0.372913\pi$
$948$	−1.70658e24	−0.0849679
$949$	2.61564e24	0.129067
$950$	1.85731e23	0.00908309
$951$	1.32017e25	0.639875
$952$	−1.51799e25	−0.729212
$953$	−6.94635e24	−0.330725	−0.165362	−	0.986233i	$-0.552879\pi$
$953$	−6.94635e24	−0.330725	−0.165362	+	0.986233i	$0.552879\pi$
$954$	2.54300e25	1.20001
$955$	1.71184e25	0.800633
$956$	7.44220e24	0.344992
$957$	−2.28804e24	−0.105126
$958$	−2.92620e25	−1.33259
$959$	−5.37036e24	−0.242407
$960$	−1.25908e25	−0.563309
$961$	−2.07340e25	−0.919464
$962$	3.40199e24	0.149536
$963$	−1.18530e25	−0.516421
$964$	−2.28467e24	−0.0986661
$965$	−8.94454e24	−0.382891
$966$	5.84166e24	0.247874
$967$	9.88936e24	0.415952	0.207976	−	0.978134i	$-0.433312\pi$
$967$	9.88936e24	0.415952	0.207976	+	0.978134i	$0.433312\pi$
$968$	−4.22271e25	−1.76056
$969$	3.16328e24	0.130733
$970$	3.28034e25	1.34387
$971$	−4.00389e25	−1.62599	−0.812997	−	0.582268i	$-0.802165\pi$
$971$	−4.00389e25	−1.62599	−0.812997	+	0.582268i	$0.802165\pi$
$972$	7.12962e24	0.287014
$973$	1.79852e25	0.717723
$974$	5.59537e24	0.221349
$975$	−6.02942e23	−0.0236448
$976$	2.25461e25	0.876492
$977$	−8.10888e24	−0.312505	−0.156253	−	0.987717i	$-0.549941\pi$
$977$	−8.10888e24	−0.312505	−0.156253	+	0.987717i	$0.549941\pi$
$978$	−2.38612e24	−0.0911616
$979$	4.70334e25	1.78137
$980$	−1.09848e24	−0.0412450
$981$	−9.32280e24	−0.347024
$982$	1.06430e25	0.392750
$983$	−2.37127e25	−0.867512	−0.433756	−	0.901030i	$-0.642812\pi$
$983$	−2.37127e25	−0.867512	−0.433756	+	0.901030i	$0.642812\pi$
$984$	−1.32820e25	−0.481733
$985$	−2.04568e24	−0.0735579
$986$	5.56345e24	0.198331
$987$	6.74435e24	0.238366
$988$	−7.90745e23	−0.0277078
$989$	2.39400e25	0.831678
$990$	3.12430e25	1.07610
$991$	1.40897e25	0.481145	0.240572	−	0.970631i	$-0.422665\pi$
$991$	1.40897e25	0.481145	0.240572	+	0.970631i	$0.422665\pi$
$992$	−4.52360e24	−0.153156
$993$	−4.06826e24	−0.136565
$994$	−2.57326e24	−0.0856446
$995$	1.25123e25	0.412895
$996$	2.54697e24	0.0833333
$997$	−3.76698e24	−0.122204	−0.0611019	−	0.998132i	$-0.519461\pi$
$997$	−3.76698e24	−0.122204	−0.0611019	+	0.998132i	$0.519461\pi$
$998$	2.96477e25	0.953634
$999$	7.18148e24	0.229038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.a.a.1.3	✓	4
3.2	odd	2		63.18.a.b.1.2		4
4.3	odd	2		112.18.a.f.1.3		4
7.6	odd	2		49.18.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.a.a.1.3	✓	4	1.1	even	1	trivial
49.18.a.c.1.3		4	7.6	odd	2
63.18.a.b.1.2		4	3.2	odd	2
112.18.a.f.1.3		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)

\(f(q)\)	\(=\)	\(q+307.439 q^{2} -5612.83 q^{3} -36553.2 q^{4} +904274. q^{5} -1.72560e6 q^{6} -5.76480e6 q^{7} -5.15345e7 q^{8} -9.76363e7 q^{9} +O(q^{10})\)	\(q+307.439 q^{2} -5612.83 q^{3} -36553.2 q^{4} +904274. q^{5} -1.72560e6 q^{6} -5.76480e6 q^{7} -5.15345e7 q^{8} -9.76363e7 q^{9} +2.78009e8 q^{10} -1.15102e9 q^{11} +2.05167e8 q^{12} +1.96128e9 q^{13} -1.77233e9 q^{14} -5.07553e9 q^{15} -1.10526e10 q^{16} -5.10958e10 q^{17} -3.00172e10 q^{18} +1.10299e10 q^{19} -3.30541e10 q^{20} +3.23568e10 q^{21} -3.53868e11 q^{22} +5.87234e11 q^{23} +2.89254e11 q^{24} +5.47714e10 q^{25} +6.02975e11 q^{26} +1.27286e12 q^{27} +2.10722e11 q^{28} -3.54160e11 q^{29} -1.56042e12 q^{30} -1.34763e12 q^{31} +3.35672e12 q^{32} +6.46046e12 q^{33} -1.57089e13 q^{34} -5.21296e12 q^{35} +3.56892e12 q^{36} +5.64201e12 q^{37} +3.39102e12 q^{38} -1.10083e13 q^{39} -4.66013e13 q^{40} -4.59182e13 q^{41} +9.94776e12 q^{42} +4.07673e13 q^{43} +4.20733e13 q^{44} -8.82900e13 q^{45} +1.80539e14 q^{46} +2.08437e14 q^{47} +6.20365e13 q^{48} +3.32329e13 q^{49} +1.68389e13 q^{50} +2.86792e14 q^{51} -7.16911e13 q^{52} -8.47178e14 q^{53} +3.91326e14 q^{54} -1.04083e15 q^{55} +2.97086e14 q^{56} -6.19088e13 q^{57} -1.08883e14 q^{58} -1.87074e14 q^{59} +1.85527e14 q^{60} -2.03988e15 q^{61} -4.14313e14 q^{62} +5.62854e14 q^{63} +2.48068e15 q^{64} +1.77354e15 q^{65} +1.98620e15 q^{66} -2.00475e15 q^{67} +1.86771e15 q^{68} -3.29604e15 q^{69} -1.60267e15 q^{70} +1.45191e15 q^{71} +5.03164e15 q^{72} +1.33364e15 q^{73} +1.73458e15 q^{74} -3.07422e14 q^{75} -4.03177e14 q^{76} +6.63539e15 q^{77} -3.38440e15 q^{78} -8.31801e15 q^{79} -9.99461e15 q^{80} +5.46445e15 q^{81} -1.41171e16 q^{82} +1.24141e16 q^{83} -1.18274e15 q^{84} -4.62046e16 q^{85} +1.25335e16 q^{86} +1.98784e15 q^{87} +5.93171e16 q^{88} -4.08624e16 q^{89} -2.71438e16 q^{90} -1.13064e16 q^{91} -2.14653e16 q^{92} +7.56399e15 q^{93} +6.40816e16 q^{94} +9.97403e15 q^{95} -1.88407e16 q^{96} +1.17994e17 q^{97} +1.02171e16 q^{98} +1.12381e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 186 q^{2} - 2786 q^{3} - 16300 q^{4} + 274722 q^{5} + 1469804 q^{6} - 23059204 q^{7} + 8649336 q^{8} - 2050976 q^{9}+O(q^{10}) \) 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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