LMFDB - Embedded newform 7.18.a.a.1.4

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			1.4
Root			$-32.8226$ 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)

$f(q)$	$=$	$q+465.279 q^{2} +749.859 q^{3} +85412.5 q^{4} -1.54763e6 q^{5} +348894. q^{6} -5.76480e6 q^{7} -2.12444e7 q^{8} -1.28578e8 q^{9} +O(q^{10})$	\(q+465.279 q^{2} +749.859 q^{3} +85412.5 q^{4} -1.54763e6 q^{5} +348894. q^{6} -5.76480e6 q^{7} -2.12444e7 q^{8} -1.28578e8 q^{9} -7.20081e8 q^{10} +1.32989e9 q^{11} +6.40473e7 q^{12} -1.07693e9 q^{13} -2.68224e9 q^{14} -1.16051e9 q^{15} -2.10798e10 q^{16} +1.37139e10 q^{17} -5.98246e10 q^{18} -1.11230e11 q^{19} -1.32187e11 q^{20} -4.32279e9 q^{21} +6.18772e11 q^{22} -1.98008e11 q^{23} -1.59303e10 q^{24} +1.63223e12 q^{25} -5.01071e11 q^{26} -1.93252e11 q^{27} -4.92386e11 q^{28} +2.36257e12 q^{29} -5.39959e11 q^{30} +2.01083e11 q^{31} -7.02342e12 q^{32} +9.97233e11 q^{33} +6.38078e12 q^{34} +8.92180e12 q^{35} -1.09822e13 q^{36} +5.35305e12 q^{37} -5.17529e13 q^{38} -8.07542e11 q^{39} +3.28786e13 q^{40} -6.77967e13 q^{41} -2.01130e12 q^{42} -6.36640e13 q^{43} +1.13590e14 q^{44} +1.98991e14 q^{45} -9.21289e13 q^{46} +2.71873e13 q^{47} -1.58069e13 q^{48} +3.32329e13 q^{49} +7.59442e14 q^{50} +1.02835e13 q^{51} -9.19828e13 q^{52} -2.63554e14 q^{53} -8.99162e13 q^{54} -2.05819e15 q^{55} +1.22470e14 q^{56} -8.34067e13 q^{57} +1.09925e15 q^{58} -1.31652e15 q^{59} -9.91218e13 q^{60} +8.86874e14 q^{61} +9.35599e13 q^{62} +7.41226e14 q^{63} -5.04884e14 q^{64} +1.66669e15 q^{65} +4.63992e14 q^{66} -2.21612e15 q^{67} +1.17134e15 q^{68} -1.48478e14 q^{69} +4.15112e15 q^{70} +3.25484e15 q^{71} +2.73156e15 q^{72} -8.03322e15 q^{73} +2.49066e15 q^{74} +1.22394e15 q^{75} -9.50042e15 q^{76} -7.66657e15 q^{77} -3.75732e14 q^{78} +6.85931e15 q^{79} +3.26237e16 q^{80} +1.64597e16 q^{81} -3.15444e16 q^{82} -1.23496e16 q^{83} -3.69220e14 q^{84} -2.12241e16 q^{85} -2.96215e16 q^{86} +1.77159e15 q^{87} -2.82528e16 q^{88} -5.51807e16 q^{89} +9.25865e16 q^{90} +6.20826e15 q^{91} -1.69124e16 q^{92} +1.50784e14 q^{93} +1.26497e16 q^{94} +1.72143e17 q^{95} -5.26658e15 q^{96} +2.92905e16 q^{97} +1.54626e16 q^{98} -1.70995e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	465.279	1.28516	0.642582	−	0.766217i	$-0.277863\pi$
$2$	465.279	1.28516	0.642582	+	0.766217i	$0.277863\pi$
$3$	749.859	0.0659856	0.0329928	−	0.999456i	$-0.489496\pi$
$3$	749.859	0.0659856	0.0329928	+	0.999456i	$0.489496\pi$
$4$	85412.5	0.651646
$5$	−1.54763e6	−1.77183	−0.885917	−	0.463844i	$-0.846470\pi$
$5$	−1.54763e6	−1.77183	−0.885917	+	0.463844i	$0.846470\pi$
$6$	348894.	0.0848023
$7$	−5.76480e6	−0.377964
$7$	−5.76480e6	−0.377964
$8$	−2.12444e7	−0.447692
$9$	−1.28578e8	−0.995646
$10$	−7.20081e8	−2.27710
$11$	1.32989e9	1.87059	0.935296	−	0.353865i	$-0.115133\pi$
$11$	1.32989e9	1.87059	0.935296	+	0.353865i	$0.115133\pi$
$12$	6.40473e7	0.0429992
$13$	−1.07693e9	−0.366157	−0.183078	−	0.983098i	$-0.558606\pi$
$13$	−1.07693e9	−0.366157	−0.183078	+	0.983098i	$0.558606\pi$
$14$	−2.68224e9	−0.485746
$15$	−1.16051e9	−0.116915
$16$	−2.10798e10	−1.22700
$17$	1.37139e10	0.476809	0.238404	−	0.971166i	$-0.423376\pi$
$17$	1.37139e10	0.476809	0.238404	+	0.971166i	$0.423376\pi$
$18$	−5.98246e10	−1.27957
$19$	−1.11230e11	−1.50250	−0.751252	−	0.660015i	$-0.770550\pi$
$19$	−1.11230e11	−1.50250	−0.751252	+	0.660015i	$0.770550\pi$
$20$	−1.32187e11	−1.15461
$21$	−4.32279e9	−0.0249402
$22$	6.18772e11	2.40402
$23$	−1.98008e11	−0.527225	−0.263613	−	0.964629i	$-0.584914\pi$
$23$	−1.98008e11	−0.527225	−0.263613	+	0.964629i	$0.584914\pi$
$24$	−1.59303e10	−0.0295412
$25$	1.63223e12	2.13940
$26$	−5.01071e11	−0.470571
$27$	−1.93252e11	−0.131684
$28$	−4.92386e11	−0.246299
$29$	2.36257e12	0.877003	0.438502	−	0.898730i	$-0.355509\pi$
$29$	2.36257e12	0.877003	0.438502	+	0.898730i	$0.355509\pi$
$30$	−5.39959e11	−0.150256
$31$	2.01083e11	0.0423450	0.0211725	−	0.999776i	$-0.493260\pi$
$31$	2.01083e11	0.0423450	0.0211725	+	0.999776i	$0.493260\pi$
$32$	−7.02342e12	−1.12921
$33$	9.97233e11	0.123432
$34$	6.38078e12	0.612778
$35$	8.92180e12	0.669690
$36$	−1.09822e13	−0.648808
$37$	5.35305e12	0.250546	0.125273	−	0.992122i	$-0.460019\pi$
$37$	5.35305e12	0.250546	0.125273	+	0.992122i	$0.460019\pi$
$38$	−5.17529e13	−1.93096
$39$	−8.07542e11	−0.0241611
$40$	3.28786e13	0.793237
$41$	−6.77967e13	−1.32601	−0.663004	−	0.748616i	$-0.730719\pi$
$41$	−6.77967e13	−1.32601	−0.663004	+	0.748616i	$0.730719\pi$
$42$	−2.01130e12	−0.0320522
$43$	−6.36640e13	−0.830639	−0.415319	−	0.909676i	$-0.636330\pi$
$43$	−6.36640e13	−0.830639	−0.415319	+	0.909676i	$0.636330\pi$
$44$	1.13590e14	1.21896
$45$	1.98991e14	1.76412
$46$	−9.21289e13	−0.677571
$47$	2.71873e13	0.166546	0.0832729	−	0.996527i	$-0.473463\pi$
$47$	2.71873e13	0.166546	0.0832729	+	0.996527i	$0.473463\pi$
$48$	−1.58069e13	−0.0809645
$49$	3.32329e13	0.142857
$50$	7.59442e14	2.74947
$51$	1.02835e13	0.0314625
$52$	−9.19828e13	−0.238604
$53$	−2.63554e14	−0.581468	−0.290734	−	0.956804i	$-0.593899\pi$
$53$	−2.63554e14	−0.581468	−0.290734	+	0.956804i	$0.593899\pi$
$54$	−8.99162e13	−0.169235
$55$	−2.05819e15	−3.31438
$56$	1.22470e14	0.169212
$57$	−8.34067e13	−0.0991436
$58$	1.09925e15	1.12709
$59$	−1.31652e15	−1.16731	−0.583655	−	0.812002i	$-0.698378\pi$
$59$	−1.31652e15	−1.16731	−0.583655	+	0.812002i	$0.698378\pi$
$60$	−9.91218e13	−0.0761875
$61$	8.86874e14	0.592322	0.296161	−	0.955138i	$-0.404293\pi$
$61$	8.86874e14	0.592322	0.296161	+	0.955138i	$0.404293\pi$
$62$	9.35599e13	0.0544202
$63$	7.41226e14	0.376319
$64$	−5.04884e14	−0.224213
$65$	1.66669e15	0.648769
$66$	4.63992e14	0.158630
$67$	−2.21612e15	−0.666741	−0.333371	−	0.942796i	$-0.608186\pi$
$67$	−2.21612e15	−0.666741	−0.333371	+	0.942796i	$0.608186\pi$
$68$	1.17134e15	0.310710
$69$	−1.48478e14	−0.0347892
$70$	4.15112e15	0.860662
$71$	3.25484e15	0.598183	0.299091	−	0.954224i	$-0.403316\pi$
$71$	3.25484e15	0.598183	0.299091	+	0.954224i	$0.403316\pi$
$72$	2.73156e15	0.445743
$73$	−8.03322e15	−1.16586	−0.582929	−	0.812523i	$-0.698093\pi$
$73$	−8.03322e15	−1.16586	−0.582929	+	0.812523i	$0.698093\pi$
$74$	2.49066e15	0.321992
$75$	1.22394e15	0.141169
$76$	−9.50042e15	−0.979100
$77$	−7.66657e15	−0.707018
$78$	−3.75732e14	−0.0310509
$79$	6.85931e15	0.508687	0.254343	−	0.967114i	$-0.418141\pi$
$79$	6.85931e15	0.508687	0.254343	+	0.967114i	$0.418141\pi$
$80$	3.26237e16	2.17405
$81$	1.64597e16	0.986957
$82$	−3.15444e16	−1.70414
$83$	−1.23496e16	−0.601851	−0.300926	−	0.953648i	$-0.597296\pi$
$83$	−1.23496e16	−0.601851	−0.300926	+	0.953648i	$0.597296\pi$
$84$	−3.69220e14	−0.0162522
$85$	−2.12241e16	−0.844826
$86$	−2.96215e16	−1.06751
$87$	1.77159e15	0.0578696
$88$	−2.82528e16	−0.837450
$89$	−5.51807e16	−1.48584	−0.742920	−	0.669380i	$-0.766560\pi$
$89$	−5.51807e16	−1.48584	−0.742920	+	0.669380i	$0.766560\pi$
$90$	9.25865e16	2.26718
$91$	6.20826e15	0.138394
$92$	−1.69124e16	−0.343564
$93$	1.50784e14	0.00279416
$94$	1.26497e16	0.214039
$95$	1.72143e17	2.66219
$96$	−5.26658e15	−0.0745114
$97$	2.92905e16	0.379461	0.189731	−	0.981836i	$-0.439239\pi$
$97$	2.92905e16	0.379461	0.189731	+	0.981836i	$0.439239\pi$
$98$	1.54626e16	0.183595
$99$	−1.70995e17	−1.86245
$100$	1.39413e17	1.39413
$101$	1.89051e16	0.173719	0.0868595	−	0.996221i	$-0.472317\pi$
$101$	1.89051e16	0.173719	0.0868595	+	0.996221i	$0.472317\pi$
$102$	4.78468e15	0.0404345
$103$	4.43270e16	0.344788	0.172394	−	0.985028i	$-0.444850\pi$
$103$	4.43270e16	0.344788	0.172394	+	0.985028i	$0.444850\pi$
$104$	2.28786e16	0.163926
$105$	6.69009e15	0.0441899
$106$	−1.22626e17	−0.747281
$107$	−1.42299e17	−0.800646	−0.400323	−	0.916374i	$-0.631102\pi$
$107$	−1.42299e17	−0.800646	−0.400323	+	0.916374i	$0.631102\pi$
$108$	−1.65062e16	−0.0858112
$109$	1.57889e17	0.758975	0.379488	−	0.925197i	$-0.376100\pi$
$109$	1.57889e17	0.758975	0.379488	+	0.925197i	$0.376100\pi$
$110$	−9.57632e17	−4.25952
$111$	4.01403e15	0.0165324
$112$	1.21521e17	0.463764
$113$	2.33144e17	0.825007	0.412503	−	0.910956i	$-0.364655\pi$
$113$	2.33144e17	0.825007	0.412503	+	0.910956i	$0.364655\pi$
$114$	−3.88074e16	−0.127416
$115$	3.06444e17	0.934155
$116$	2.01793e17	0.571495
$117$	1.38469e17	0.364562
$118$	−6.12550e17	−1.50018
$119$	−7.90578e16	−0.180217
$120$	2.46543e16	0.0523422
$121$	1.26317e18	2.49912
$122$	4.12644e17	0.761231
$123$	−5.08380e16	−0.0874973
$124$	1.71750e16	0.0275939
$125$	−1.34534e18	−2.01882
$126$	3.44877e17	0.483631
$127$	−2.52229e17	−0.330722	−0.165361	−	0.986233i	$-0.552879\pi$
$127$	−2.52229e17	−0.330722	−0.165361	+	0.986233i	$0.552879\pi$
$128$	6.85662e17	0.841057
$129$	−4.77390e16	−0.0548102
$130$	7.75474e17	0.833774
$131$	−6.73780e17	−0.678754	−0.339377	−	0.940650i	$-0.610216\pi$
$131$	−6.73780e17	−0.678754	−0.339377	+	0.940650i	$0.610216\pi$
$132$	8.51762e16	0.0804340
$133$	6.41218e17	0.567893
$134$	−1.03111e18	−0.856872
$135$	2.99084e17	0.233322
$136$	−2.91343e17	−0.213464
$137$	−2.04921e18	−1.41079	−0.705394	−	0.708815i	$-0.749230\pi$
$137$	−2.04921e18	−1.41079	−0.705394	+	0.708815i	$0.749230\pi$
$138$	−6.90837e16	−0.0447099
$139$	1.81878e18	1.10702	0.553509	−	0.832843i	$-0.313289\pi$
$139$	1.81878e18	1.10702	0.553509	+	0.832843i	$0.313289\pi$
$140$	7.62033e17	0.436401
$141$	2.03866e16	0.0109896
$142$	1.51441e18	0.768763
$143$	−1.43220e18	−0.684930
$144$	2.71039e18	1.22166
$145$	−3.65639e18	−1.55390
$146$	−3.73769e18	−1.49832
$147$	2.49200e16	0.00942651
$148$	4.57217e17	0.163267
$149$	−2.78229e18	−0.938252	−0.469126	−	0.883131i	$-0.655431\pi$
$149$	−2.78229e18	−0.938252	−0.469126	+	0.883131i	$0.655431\pi$
$150$	5.69475e17	0.181426
$151$	7.81424e17	0.235279	0.117639	−	0.993056i	$-0.462467\pi$
$151$	7.81424e17	0.235279	0.117639	+	0.993056i	$0.462467\pi$
$152$	2.36301e18	0.672660
$153$	−1.76330e18	−0.474733
$154$	−3.56710e18	−0.908633
$155$	−3.11203e17	−0.0750283
$156$	−6.89742e16	−0.0157444
$157$	6.17912e18	1.33592	0.667959	−	0.744198i	$-0.267168\pi$
$157$	6.17912e18	1.33592	0.667959	+	0.744198i	$0.267168\pi$
$158$	3.19149e18	0.653746
$159$	−1.97629e17	−0.0383685
$160$	1.08697e19	2.00077
$161$	1.14148e18	0.199272
$162$	7.65833e18	1.26840
$163$	−3.74440e18	−0.588556	−0.294278	−	0.955720i	$-0.595079\pi$
$163$	−3.74440e18	−0.588556	−0.294278	+	0.955720i	$0.595079\pi$
$164$	−5.79069e18	−0.864087
$165$	−1.54335e18	−0.218701
$166$	−5.74601e18	−0.773478
$167$	1.01080e19	1.29293	0.646465	−	0.762944i	$-0.276247\pi$
$167$	1.01080e19	1.29293	0.646465	+	0.762944i	$0.276247\pi$
$168$	9.18351e16	0.0111655
$169$	−7.49065e18	−0.865929
$170$	−9.87510e18	−1.08574
$171$	1.43017e19	1.49596
$172$	−5.43770e18	−0.541282
$173$	1.48327e19	1.40549	0.702744	−	0.711443i	$-0.251958\pi$
$173$	1.48327e19	1.40549	0.702744	+	0.711443i	$0.251958\pi$
$174$	8.24285e17	0.0743719
$175$	−9.40948e18	−0.808616
$176$	−2.80339e19	−2.29522
$177$	−9.87207e17	−0.0770256
$178$	−2.56744e19	−1.90955
$179$	−1.04723e19	−0.742659	−0.371330	−	0.928501i	$-0.621098\pi$
$179$	−1.04723e19	−0.742659	−0.371330	+	0.928501i	$0.621098\pi$
$180$	1.69964e19	1.14958
$181$	−4.33572e18	−0.279765	−0.139883	−	0.990168i	$-0.544672\pi$
$181$	−4.33572e18	−0.279765	−0.139883	+	0.990168i	$0.544672\pi$
$182$	2.88857e18	0.177859
$183$	6.65030e17	0.0390847
$184$	4.20656e18	0.236035
$185$	−8.28456e18	−0.443925
$186$	7.01567e16	0.00359095
$187$	1.82380e19	0.891915
$188$	2.32213e18	0.108529
$189$	1.11406e18	0.0497718
$190$	8.00945e19	3.42135
$191$	1.00097e18	0.0408919	0.0204460	−	0.999791i	$-0.493491\pi$
$191$	1.00097e18	0.0408919	0.0204460	+	0.999791i	$0.493491\pi$
$192$	−3.78592e17	−0.0147948
$193$	−1.73634e19	−0.649230	−0.324615	−	0.945846i	$-0.605235\pi$
$193$	−1.73634e19	−0.649230	−0.324615	+	0.945846i	$0.605235\pi$
$194$	1.36283e19	0.487670
$195$	1.24978e18	0.0428094
$196$	2.83851e18	0.0930922
$197$	3.42729e19	1.07644	0.538218	−	0.842805i	$-0.319098\pi$
$197$	3.42729e19	1.07644	0.538218	+	0.842805i	$0.319098\pi$
$198$	−7.95604e19	−2.39355
$199$	−1.35620e19	−0.390906	−0.195453	−	0.980713i	$-0.562618\pi$
$199$	−1.35620e19	−0.390906	−0.195453	+	0.980713i	$0.562618\pi$
$200$	−3.46758e19	−0.957792
$201$	−1.66178e18	−0.0439953
$202$	8.79614e18	0.223257
$203$	−1.36197e19	−0.331476
$204$	8.78337e17	0.0205024
$205$	1.04924e20	2.34946
$206$	2.06244e19	0.443108
$207$	2.54594e19	0.524930
$208$	2.27013e19	0.449276
$209$	−1.47924e20	−2.81057
$210$	3.11276e18	0.0567913
$211$	−2.80278e19	−0.491121	−0.245560	−	0.969381i	$-0.578972\pi$
$211$	−2.80278e19	−0.491121	−0.245560	+	0.969381i	$0.578972\pi$
$212$	−2.25108e19	−0.378911
$213$	2.44067e18	0.0394714
$214$	−6.62089e19	−1.02896
$215$	9.85285e19	1.47175
$216$	4.10553e18	0.0589539
$217$	−1.15921e18	−0.0160049
$218$	7.34626e19	0.975407
$219$	−6.02379e18	−0.0769298
$220$	−1.75795e20	−2.15980
$221$	−1.47688e19	−0.174587
$222$	1.86765e18	0.0212468
$223$	8.41954e19	0.921928	0.460964	−	0.887419i	$-0.347504\pi$
$223$	8.41954e19	0.921928	0.460964	+	0.887419i	$0.347504\pi$
$224$	4.04886e19	0.426800
$225$	−2.09869e20	−2.13008
$226$	1.08477e20	1.06027
$227$	1.64163e20	1.54545	0.772725	−	0.634741i	$-0.218893\pi$
$227$	1.64163e20	1.54545	0.772725	+	0.634741i	$0.218893\pi$
$228$	−7.12398e18	−0.0646065
$229$	−1.03358e20	−0.903117	−0.451558	−	0.892242i	$-0.649132\pi$
$229$	−1.03358e20	−0.903117	−0.451558	+	0.892242i	$0.649132\pi$
$230$	1.42582e20	1.20054
$231$	−5.74885e18	−0.0466530
$232$	−5.01913e19	−0.392628
$233$	−1.59667e20	−1.20417	−0.602086	−	0.798431i	$-0.705664\pi$
$233$	−1.59667e20	−1.20417	−0.602086	+	0.798431i	$0.705664\pi$
$234$	6.44266e19	0.468522
$235$	−4.20759e19	−0.295091
$236$	−1.12447e20	−0.760672
$237$	5.14352e18	0.0335660
$238$	−3.67839e19	−0.231608
$239$	1.16789e20	0.709612	0.354806	−	0.934940i	$-0.384547\pi$
$239$	1.16789e20	0.709612	0.354806	+	0.934940i	$0.384547\pi$
$240$	2.44632e19	0.143456
$241$	1.47720e20	0.836170	0.418085	−	0.908408i	$-0.362701\pi$
$241$	1.47720e20	0.836170	0.418085	+	0.908408i	$0.362701\pi$
$242$	5.87727e20	3.21177
$243$	3.72990e19	0.196809
$244$	7.57501e19	0.385984
$245$	−5.14324e19	−0.253119
$246$	−2.36538e19	−0.112448
$247$	1.19786e20	0.550152
$248$	−4.27190e18	−0.0189575
$249$	−9.26046e18	−0.0397135
$250$	−6.25960e20	−2.59452
$251$	−1.55508e20	−0.623053	−0.311526	−	0.950237i	$-0.600840\pi$
$251$	−1.55508e20	−0.623053	−0.311526	+	0.950237i	$0.600840\pi$
$252$	6.33099e19	0.245226
$253$	−2.63330e20	−0.986223
$254$	−1.17357e20	−0.425031
$255$	−1.59150e19	−0.0557463
$256$	3.85200e20	1.30511
$257$	−3.21984e20	−1.05537	−0.527683	−	0.849442i	$-0.676939\pi$
$257$	−3.21984e20	−1.05537	−0.527683	+	0.849442i	$0.676939\pi$
$258$	−2.22120e19	−0.0704400
$259$	−3.08593e19	−0.0946973
$260$	1.42356e20	0.422767
$261$	−3.03774e20	−0.873185
$262$	−3.13496e20	−0.872310
$263$	−6.40953e20	−1.72664	−0.863321	−	0.504655i	$-0.831620\pi$
$263$	−6.40953e20	−1.72664	−0.863321	+	0.504655i	$0.831620\pi$
$264$	−2.11856e19	−0.0552596
$265$	4.07886e20	1.03026
$266$	2.98345e20	0.729836
$267$	−4.13777e19	−0.0980440
$268$	−1.89284e20	−0.434479
$269$	7.35147e20	1.63486	0.817429	−	0.576030i	$-0.195399\pi$
$269$	7.35147e20	1.63486	0.817429	+	0.576030i	$0.195399\pi$
$270$	1.39157e20	0.299857
$271$	−1.53576e20	−0.320688	−0.160344	−	0.987061i	$-0.551260\pi$
$271$	−1.53576e20	−0.320688	−0.160344	+	0.987061i	$0.551260\pi$
$272$	−2.89085e20	−0.585046
$273$	4.65532e18	0.00913202
$274$	−9.53455e20	−1.81309
$275$	2.17069e21	4.00194
$276$	−1.26819e19	−0.0226703
$277$	2.43681e20	0.422419	0.211210	−	0.977441i	$-0.432260\pi$
$277$	2.43681e20	0.422419	0.211210	+	0.977441i	$0.432260\pi$
$278$	8.46240e20	1.42270
$279$	−2.58549e19	−0.0421606
$280$	−1.89538e20	−0.299815
$281$	−4.74614e20	−0.728344	−0.364172	−	0.931332i	$-0.618648\pi$
$281$	−4.74614e20	−0.728344	−0.364172	+	0.931332i	$0.618648\pi$
$282$	9.48546e18	0.0141235
$283$	5.03809e20	0.727916	0.363958	−	0.931415i	$-0.381425\pi$
$283$	5.03809e20	0.727916	0.363958	+	0.931415i	$0.381425\pi$
$284$	2.78004e20	0.389803
$285$	1.29083e20	0.175666
$286$	−6.66371e20	−0.880247
$287$	3.90835e20	0.501184
$288$	9.03057e20	1.12429
$289$	−6.39170e20	−0.772653
$290$	−1.70124e21	−1.99702
$291$	2.19638e19	0.0250390
$292$	−6.86138e20	−0.759726
$293$	−1.74476e21	−1.87655	−0.938276	−	0.345886i	$-0.887578\pi$
$293$	−1.74476e21	−1.87655	−0.938276	+	0.345886i	$0.887578\pi$
$294$	1.15948e19	0.0121146
$295$	2.03749e21	2.06828
$296$	−1.13722e20	−0.112167
$297$	−2.57005e20	−0.246327
$298$	−1.29454e21	−1.20581
$299$	2.13240e20	0.193047
$300$	1.04540e20	0.0919923
$301$	3.67010e20	0.313952
$302$	3.63580e20	0.302372
$303$	1.41762e19	0.0114629
$304$	2.34470e21	1.84358
$305$	−1.37256e21	−1.04950
$306$	−8.20427e20	−0.610109
$307$	−6.26704e20	−0.453300	−0.226650	−	0.973976i	$-0.572777\pi$
$307$	−6.26704e20	−0.453300	−0.226650	+	0.973976i	$0.572777\pi$
$308$	−6.54821e20	−0.460725
$309$	3.32390e19	0.0227510
$310$	−1.44796e20	−0.0964236
$311$	−2.07324e21	−1.34334	−0.671671	−	0.740849i	$-0.734423\pi$
$311$	−2.07324e21	−1.34334	−0.671671	+	0.740849i	$0.734423\pi$
$312$	1.71558e19	0.0108167
$313$	2.88951e21	1.77295	0.886476	−	0.462775i	$-0.153146\pi$
$313$	2.88951e21	1.77295	0.886476	+	0.462775i	$0.153146\pi$
$314$	2.87501e21	1.71687
$315$	−1.14715e21	−0.666774
$316$	5.85871e20	0.331483
$317$	−3.48578e21	−1.91998	−0.959989	−	0.280038i	$-0.909653\pi$
$317$	−3.48578e21	−1.91998	−0.959989	+	0.280038i	$0.909653\pi$
$318$	−9.19525e19	−0.0493098
$319$	3.14196e21	1.64052
$320$	7.81375e20	0.397269
$321$	−1.06704e20	−0.0528311
$322$	5.31105e20	0.256098
$323$	−1.52539e21	−0.716408
$324$	1.40586e21	0.643146
$325$	−1.75779e21	−0.783354
$326$	−1.74219e21	−0.756391
$327$	1.18395e20	0.0500814
$328$	1.44030e21	0.593643
$329$	−1.56729e20	−0.0629484
$330$	−7.18089e20	−0.281067
$331$	9.92801e20	0.378725	0.189363	−	0.981907i	$-0.439358\pi$
$331$	9.92801e20	0.378725	0.189363	+	0.981907i	$0.439358\pi$
$332$	−1.05481e21	−0.392194
$333$	−6.88284e20	−0.249455
$334$	4.70304e21	1.66163
$335$	3.42974e21	1.18136
$336$	9.11233e19	0.0306017
$337$	−1.57640e21	−0.516194	−0.258097	−	0.966119i	$-0.583095\pi$
$337$	−1.57640e21	−0.516194	−0.258097	+	0.966119i	$0.583095\pi$
$338$	−3.48524e21	−1.11286
$339$	1.74825e20	0.0544385
$340$	−1.81280e21	−0.550527
$341$	2.67420e20	0.0792102
$342$	6.65428e21	1.92256
$343$	−1.91581e20	−0.0539949
$344$	1.35250e21	0.371871
$345$	2.29790e20	0.0616408
$346$	6.90132e21	1.80628
$347$	−4.26241e21	−1.08856	−0.544282	−	0.838902i	$-0.683198\pi$
$347$	−4.26241e21	−1.08856	−0.544282	+	0.838902i	$0.683198\pi$
$348$	1.51316e20	0.0377104
$349$	−3.75476e21	−0.913200	−0.456600	−	0.889672i	$-0.650933\pi$
$349$	−3.75476e21	−0.913200	−0.456600	+	0.889672i	$0.650933\pi$
$350$	−4.37803e21	−1.03920
$351$	2.08118e20	0.0482169
$352$	−9.34041e21	−2.11229
$353$	3.18901e20	0.0703998	0.0351999	−	0.999380i	$-0.488793\pi$
$353$	3.18901e20	0.0703998	0.0351999	+	0.999380i	$0.488793\pi$
$354$	−4.59326e20	−0.0989905
$355$	−5.03730e21	−1.05988
$356$	−4.71312e21	−0.968241
$357$	−5.92822e19	−0.0118917
$358$	−4.87252e21	−0.954439
$359$	4.86841e21	0.931289	0.465644	−	0.884972i	$-0.345823\pi$
$359$	4.86841e21	0.931289	0.465644	+	0.884972i	$0.345823\pi$
$360$	−4.22746e21	−0.789783
$361$	6.89170e21	1.25752
$362$	−2.01732e21	−0.359544
$363$	9.47200e20	0.164906
$364$	5.30263e20	0.0901840
$365$	1.24325e22	2.06571
$366$	3.09425e20	0.0502303
$367$	−8.97341e21	−1.42330	−0.711649	−	0.702535i	$-0.752052\pi$
$367$	−8.97341e21	−1.42330	−0.711649	+	0.702535i	$0.752052\pi$
$368$	4.17396e21	0.646907
$369$	8.71716e21	1.32023
$370$	−3.85463e21	−0.570517
$371$	1.51934e21	0.219774
$372$	1.28789e19	0.00182080
$373$	−3.60949e21	−0.498794	−0.249397	−	0.968401i	$-0.580232\pi$
$373$	−3.60949e21	−0.498794	−0.249397	+	0.968401i	$0.580232\pi$
$374$	8.48576e21	1.14626
$375$	−1.00882e21	−0.133213
$376$	−5.77577e20	−0.0745613
$377$	−2.54431e21	−0.321121
$378$	5.18349e20	0.0639649
$379$	7.79019e21	0.939972	0.469986	−	0.882674i	$-0.344259\pi$
$379$	7.79019e21	0.939972	0.469986	+	0.882674i	$0.344259\pi$
$380$	1.47032e22	1.73480
$381$	−1.89136e20	−0.0218229
$382$	4.65731e20	0.0525528
$383$	−1.02337e22	−1.12939	−0.564694	−	0.825300i	$-0.691006\pi$
$383$	−1.02337e22	−1.12939	−0.564694	+	0.825300i	$0.691006\pi$
$384$	5.14150e20	0.0554976
$385$	1.18650e22	1.25272
$386$	−8.07885e21	−0.834367
$387$	8.18578e21	0.827022
$388$	2.50178e21	0.247274
$389$	−7.22837e21	−0.698987	−0.349493	−	0.936939i	$-0.613646\pi$
$389$	−7.22837e21	−0.698987	−0.349493	+	0.936939i	$0.613646\pi$
$390$	5.81496e20	0.0550171
$391$	−2.71546e21	−0.251386
$392$	−7.06014e20	−0.0639561
$393$	−5.05240e20	−0.0447880
$394$	1.59465e22	1.38340
$395$	−1.06157e22	−0.901309
$396$	−1.46051e22	−1.21366
$397$	1.30171e21	0.105875	0.0529377	−	0.998598i	$-0.483142\pi$
$397$	1.30171e21	0.105875	0.0529377	+	0.998598i	$0.483142\pi$
$398$	−6.31011e21	−0.502378
$399$	4.80823e20	0.0374728
$400$	−3.44070e22	−2.62505
$401$	−1.37644e22	−1.02809	−0.514044	−	0.857764i	$-0.671853\pi$
$401$	−1.37644e22	−1.02809	−0.514044	+	0.857764i	$0.671853\pi$
$402$	−7.73190e20	−0.0565412
$403$	−2.16552e20	−0.0155049
$404$	1.61473e21	0.113203
$405$	−2.54735e22	−1.74872
$406$	−6.33697e21	−0.426001
$407$	7.11899e21	0.468669
$408$	−2.18466e20	−0.0140855
$409$	1.13861e22	0.718996	0.359498	−	0.933146i	$-0.382948\pi$
$409$	1.13861e22	0.718996	0.359498	+	0.933146i	$0.382948\pi$
$410$	4.88191e22	3.01945
$411$	−1.53662e21	−0.0930917
$412$	3.78608e21	0.224679
$413$	7.58949e21	0.441202
$414$	1.18457e22	0.674620
$415$	1.91127e22	1.06638
$416$	7.56370e21	0.413467
$417$	1.36383e21	0.0730472
$418$	−6.88259e22	−3.61205
$419$	1.84138e22	0.946946	0.473473	−	0.880808i	$-0.343000\pi$
$419$	1.84138e22	0.946946	0.473473	+	0.880808i	$0.343000\pi$
$420$	5.71417e20	0.0287962
$421$	1.63841e22	0.809144	0.404572	−	0.914506i	$-0.367421\pi$
$421$	1.63841e22	0.809144	0.404572	+	0.914506i	$0.367421\pi$
$422$	−1.30407e22	−0.631170
$423$	−3.49568e21	−0.165821
$424$	5.59906e21	0.260319
$425$	2.23842e22	1.02008
$426$	1.13559e21	0.0507272
$427$	−5.11265e21	−0.223877
$428$	−1.21541e22	−0.521738
$429$	−1.07395e21	−0.0451955
$430$	4.58433e22	1.89144
$431$	−4.09149e22	−1.65510	−0.827551	−	0.561391i	$-0.810266\pi$
$431$	−4.09149e22	−1.65510	−0.827551	+	0.561391i	$0.810266\pi$
$432$	4.07371e21	0.161577
$433$	−1.62847e22	−0.633333	−0.316666	−	0.948537i	$-0.602564\pi$
$433$	−1.62847e22	−0.633333	−0.316666	+	0.948537i	$0.602564\pi$
$434$	−5.39354e20	−0.0205689
$435$	−2.74178e21	−0.102535
$436$	1.34857e22	0.494583
$437$	2.20244e22	0.792158
$438$	−2.80274e21	−0.0988674
$439$	−5.29627e22	−1.83240	−0.916202	−	0.400716i	$-0.868761\pi$
$439$	−5.29627e22	−1.83240	−0.916202	+	0.400716i	$0.868761\pi$
$440$	4.37250e22	1.48382
$441$	−4.27302e21	−0.142235
$442$	−6.87162e21	−0.224373
$443$	1.42402e21	0.0456127	0.0228064	−	0.999740i	$-0.492740\pi$
$443$	1.42402e21	0.0456127	0.0228064	+	0.999740i	$0.492740\pi$
$444$	3.42849e20	0.0107733
$445$	8.53995e22	2.63266
$446$	3.91743e22	1.18483
$447$	−2.08633e21	−0.0619111
$448$	2.91055e21	0.0847447
$449$	−4.49500e22	−1.28421	−0.642104	−	0.766617i	$-0.721938\pi$
$449$	−4.49500e22	−1.28421	−0.642104	+	0.766617i	$0.721938\pi$
$450$	−9.76475e22	−2.73750
$451$	−9.01624e22	−2.48042
$452$	1.99134e22	0.537612
$453$	5.85958e20	0.0155250
$454$	7.63815e22	1.98616
$455$	−9.60811e21	−0.245212
$456$	1.77193e21	0.0443859
$457$	6.28849e22	1.54617	0.773087	−	0.634300i	$-0.218711\pi$
$457$	6.28849e22	1.54617	0.773087	+	0.634300i	$0.218711\pi$
$458$	−4.80905e22	−1.16065
$459$	−2.65024e21	−0.0627880
$460$	2.61741e22	0.608738
$461$	1.81575e22	0.414570	0.207285	−	0.978281i	$-0.433537\pi$
$461$	1.81575e22	0.414570	0.207285	+	0.978281i	$0.433537\pi$
$462$	−2.67482e21	−0.0599567
$463$	−1.23298e22	−0.271341	−0.135671	−	0.990754i	$-0.543319\pi$
$463$	−1.23298e22	−0.271341	−0.135671	+	0.990754i	$0.543319\pi$
$464$	−4.98024e22	−1.07609
$465$	−2.33359e20	−0.00495078
$466$	−7.42895e22	−1.54756
$467$	5.52860e22	1.13089	0.565447	−	0.824785i	$-0.308704\pi$
$467$	5.52860e22	1.13089	0.565447	+	0.824785i	$0.308704\pi$
$468$	1.18270e22	0.237565
$469$	1.27755e22	0.252005
$470$	−1.95770e22	−0.379241
$471$	4.63347e21	0.0881513
$472$	2.79688e22	0.522596
$473$	−8.46664e22	−1.55379
$474$	2.39317e21	0.0431378
$475$	−1.81553e23	−3.21445
$476$	−6.75252e21	−0.117438
$477$	3.38873e22	0.578936
$478$	5.43396e22	0.911968
$479$	6.10024e22	1.00576	0.502880	−	0.864356i	$-0.332274\pi$
$479$	6.10024e22	1.00576	0.502880	+	0.864356i	$0.332274\pi$
$480$	8.15073e21	0.132022
$481$	−5.76484e21	−0.0917389
$482$	6.87311e22	1.07462
$483$	8.55947e20	0.0131491
$484$	1.07891e23	1.62854
$485$	−4.53310e22	−0.672342
$486$	1.73545e22	0.252931
$487$	−7.45003e22	−1.06699	−0.533497	−	0.845802i	$-0.679123\pi$
$487$	−7.45003e22	−1.06699	−0.533497	+	0.845802i	$0.679123\pi$
$488$	−1.88411e22	−0.265178
$489$	−2.80777e21	−0.0388362
$490$	−2.39304e22	−0.325300
$491$	1.41363e23	1.88862	0.944308	−	0.329063i	$-0.106733\pi$
$491$	1.41363e23	1.88862	0.944308	+	0.329063i	$0.106733\pi$
$492$	−4.34220e21	−0.0570172
$493$	3.24000e22	0.418163
$494$	5.57340e22	0.707036
$495$	2.64638e23	3.29995
$496$	−4.23879e21	−0.0519574
$497$	−1.87635e22	−0.226092
$498$	−4.30870e21	−0.0510384
$499$	9.89380e22	1.15215	0.576074	−	0.817397i	$-0.304584\pi$
$499$	9.89380e22	1.15215	0.576074	+	0.817397i	$0.304584\pi$
$500$	−1.14909e23	−1.31556
$501$	7.57957e21	0.0853147
$502$	−7.23544e22	−0.800725
$503$	−1.48681e23	−1.61781	−0.808905	−	0.587939i	$-0.799940\pi$
$503$	−1.48681e23	−1.61781	−0.808905	+	0.587939i	$0.799940\pi$
$504$	−1.57469e22	−0.168475
$505$	−2.92582e22	−0.307801
$506$	−1.22522e23	−1.26746
$507$	−5.61693e21	−0.0571388
$508$	−2.15435e22	−0.215513
$509$	5.94577e22	0.584934	0.292467	−	0.956276i	$-0.405524\pi$
$509$	5.94577e22	0.584934	0.292467	+	0.956276i	$0.405524\pi$
$510$	−7.40494e21	−0.0716432
$511$	4.63099e22	0.440653
$512$	8.93545e22	0.836222
$513$	2.14954e22	0.197856
$514$	−1.49812e23	−1.35632
$515$	−6.86019e22	−0.610906
$516$	−4.07751e21	−0.0357168
$517$	3.61562e22	0.311539
$518$	−1.43582e22	−0.121702
$519$	1.11224e22	0.0927419
$520$	−3.54077e22	−0.290449
$521$	−1.56747e22	−0.126496	−0.0632482	−	0.997998i	$-0.520146\pi$
$521$	−1.56747e22	−0.126496	−0.0632482	+	0.997998i	$0.520146\pi$
$522$	−1.41340e23	−1.12219
$523$	−8.69704e22	−0.679371	−0.339686	−	0.940539i	$-0.610321\pi$
$523$	−8.69704e22	−0.679371	−0.339686	+	0.940539i	$0.610321\pi$
$524$	−5.75493e22	−0.442307
$525$	−7.05578e21	−0.0533570
$526$	−2.98222e23	−2.21902
$527$	2.75763e21	0.0201905
$528$	−2.10214e22	−0.151452
$529$	−1.01843e23	−0.722034
$530$	1.89781e23	1.32406
$531$	1.69276e23	1.16223
$532$	5.47680e22	0.370065
$533$	7.30120e22	0.485526
$534$	−1.92522e22	−0.126003
$535$	2.20227e23	1.41861
$536$	4.70802e22	0.298495
$537$	−7.85272e21	−0.0490048
$538$	3.42048e23	2.10106
$539$	4.41963e22	0.267228
$540$	2.55455e22	0.152043
$541$	2.08084e23	1.21916	0.609580	−	0.792724i	$-0.291338\pi$
$541$	2.08084e23	1.21916	0.609580	+	0.792724i	$0.291338\pi$
$542$	−7.14555e22	−0.412137
$543$	−3.25118e21	−0.0184605
$544$	−9.63183e22	−0.538416
$545$	−2.44355e23	−1.34478
$546$	2.16602e21	0.0117361
$547$	−1.78764e23	−0.953645	−0.476822	−	0.879000i	$-0.658212\pi$
$547$	−1.78764e23	−0.953645	−0.476822	+	0.879000i	$0.658212\pi$
$548$	−1.75028e23	−0.919334
$549$	−1.14032e23	−0.589743
$550$	1.00998e24	5.14315
$551$	−2.62788e23	−1.31770
$552$	3.15433e21	0.0155749
$553$	−3.95426e22	−0.192266
$554$	1.13380e23	0.542878
$555$	−6.21225e21	−0.0292927
$556$	1.55347e23	0.721383
$557$	−3.57210e23	−1.63363	−0.816816	−	0.576898i	$-0.804263\pi$
$557$	−3.57210e23	−1.63363	−0.816816	+	0.576898i	$0.804263\pi$
$558$	−1.20297e22	−0.0541833
$559$	6.85614e22	0.304144
$560$	−1.88069e23	−0.821712
$561$	1.36759e22	0.0588535
$562$	−2.20828e23	−0.936041
$563$	1.12350e23	0.469085	0.234543	−	0.972106i	$-0.424641\pi$
$563$	1.12350e23	0.469085	0.234543	+	0.972106i	$0.424641\pi$
$564$	1.74127e21	0.00716133
$565$	−3.60821e23	−1.46177
$566$	2.34412e23	0.935491
$567$	−9.48866e22	−0.373035
$568$	−6.91472e22	−0.267802
$569$	1.43918e23	0.549110	0.274555	−	0.961571i	$-0.411469\pi$
$569$	1.43918e23	0.549110	0.274555	+	0.961571i	$0.411469\pi$
$570$	6.00596e22	0.225760
$571$	2.79666e23	1.03570	0.517848	−	0.855473i	$-0.326733\pi$
$571$	2.79666e23	1.03570	0.517848	+	0.855473i	$0.326733\pi$
$572$	−1.22327e23	−0.446332
$573$	7.50587e20	0.00269828
$574$	1.81847e23	0.644103
$575$	−3.23195e23	−1.12794
$576$	6.49169e22	0.223237
$577$	5.19840e23	1.76147	0.880734	−	0.473610i	$-0.157050\pi$
$577$	5.19840e23	1.76147	0.880734	+	0.473610i	$0.157050\pi$
$578$	−2.97392e23	−0.992986
$579$	−1.30201e22	−0.0428398
$580$	−3.12301e23	−1.01259
$581$	7.11930e22	0.227478
$582$	1.02193e22	0.0321792
$583$	−3.50500e23	−1.08769
$584$	1.70661e23	0.521946
$585$	−2.14299e23	−0.645944
$586$	−8.11800e23	−2.41168
$587$	−7.53472e22	−0.220619	−0.110310	−	0.993897i	$-0.535184\pi$
$587$	−7.53472e22	−0.220619	−0.110310	+	0.993897i	$0.535184\pi$
$588$	2.12848e21	0.00614274
$589$	−2.23665e22	−0.0636235
$590$	9.48003e23	2.65808
$591$	2.56999e22	0.0710293
$592$	−1.12841e23	−0.307420
$593$	5.01094e23	1.34572	0.672860	−	0.739770i	$-0.265066\pi$
$593$	5.01094e23	1.34572	0.672860	+	0.739770i	$0.265066\pi$
$594$	−1.19579e23	−0.316570
$595$	1.22352e23	0.319314
$596$	−2.37642e23	−0.611408
$597$	−1.01696e22	−0.0257941
$598$	9.92160e22	0.248097
$599$	6.18716e23	1.52533	0.762664	−	0.646795i	$-0.223891\pi$
$599$	6.18716e23	1.52533	0.762664	+	0.646795i	$0.223891\pi$
$600$	−2.60019e22	−0.0632004
$601$	−5.02644e23	−1.20456	−0.602278	−	0.798286i	$-0.705740\pi$
$601$	−5.02644e23	−1.20456	−0.602278	+	0.798286i	$0.705740\pi$
$602$	1.70762e23	0.403480
$603$	2.84944e23	0.663838
$604$	6.67434e22	0.153318
$605$	−1.95493e24	−4.42802
$606$	6.59587e21	0.0147318
$607$	4.38165e23	0.965014	0.482507	−	0.875892i	$-0.339726\pi$
$607$	4.38165e23	0.965014	0.482507	+	0.875892i	$0.339726\pi$
$608$	7.81214e23	1.69664
$609$	−1.02129e22	−0.0218726
$610$	−6.38621e23	−1.34878
$611$	−2.92786e22	−0.0609818
$612$	−1.50608e23	−0.309358
$613$	4.18811e23	0.848406	0.424203	−	0.905567i	$-0.360554\pi$
$613$	4.18811e23	0.848406	0.424203	+	0.905567i	$0.360554\pi$
$614$	−2.91592e23	−0.582565
$615$	7.86786e22	0.155031
$616$	1.62872e23	0.316526
$617$	3.18614e23	0.610718	0.305359	−	0.952237i	$-0.401224\pi$
$617$	3.18614e23	0.610718	0.305359	+	0.952237i	$0.401224\pi$
$618$	1.54654e22	0.0292388
$619$	8.77483e23	1.63632	0.818160	−	0.574991i	$-0.194994\pi$
$619$	8.77483e23	1.63632	0.818160	+	0.574991i	$0.194994\pi$
$620$	−2.65807e22	−0.0488918
$621$	3.82655e22	0.0694270
$622$	−9.64636e23	−1.72642
$623$	3.18106e23	0.561595
$624$	1.70228e22	0.0296457
$625$	8.36805e23	1.43762
$626$	1.34443e24	2.27853
$627$	−1.10922e23	−0.185457
$628$	5.27774e23	0.870544
$629$	7.34111e22	0.119462
$630$	−5.33743e23	−0.856914
$631$	7.40986e23	1.17371	0.586854	−	0.809693i	$-0.300366\pi$
$631$	7.40986e23	1.17371	0.586854	+	0.809693i	$0.300366\pi$
$632$	−1.45722e23	−0.227735
$633$	−2.10169e22	−0.0324069
$634$	−1.62186e24	−2.46749
$635$	3.90357e23	0.585984
$636$	−1.68800e22	−0.0250026
$637$	−3.57894e22	−0.0523081
$638$	1.46189e24	2.10833
$639$	−4.18501e23	−0.595578
$640$	−1.06115e24	−1.49021
$641$	−2.59277e23	−0.359311	−0.179656	−	0.983730i	$-0.557498\pi$
$641$	−2.59277e23	−0.359311	−0.179656	+	0.983730i	$0.557498\pi$
$642$	−4.96473e22	−0.0678966
$643$	−8.69513e23	−1.17350	−0.586749	−	0.809769i	$-0.699593\pi$
$643$	−8.69513e23	−1.17350	−0.586749	+	0.809769i	$0.699593\pi$
$644$	9.74964e22	0.129855
$645$	7.38825e22	0.0971145
$646$	−7.09733e23	−0.920701
$647$	−6.37263e23	−0.815891	−0.407946	−	0.913006i	$-0.633755\pi$
$647$	−6.37263e23	−0.815891	−0.407946	+	0.913006i	$0.633755\pi$
$648$	−3.49676e23	−0.441853
$649$	−1.75084e24	−2.18356
$650$	−8.17862e23	−1.00674
$651$	−8.69241e20	−0.00105609
$652$	−3.19819e23	−0.383530
$653$	−1.08875e23	−0.128874	−0.0644372	−	0.997922i	$-0.520525\pi$
$653$	−1.08875e23	−0.128874	−0.0644372	+	0.997922i	$0.520525\pi$
$654$	5.50866e22	0.0643628
$655$	1.04277e24	1.20264
$656$	1.42914e24	1.62702
$657$	1.03289e24	1.16078
$658$	−7.29228e22	−0.0808990
$659$	−7.22617e23	−0.791374	−0.395687	−	0.918385i	$-0.629494\pi$
$659$	−7.22617e23	−0.791374	−0.395687	+	0.918385i	$0.629494\pi$
$660$	−1.31821e23	−0.142516
$661$	−8.97949e22	−0.0958383	−0.0479192	−	0.998851i	$-0.515259\pi$
$661$	−8.97949e22	−0.0958383	−0.0479192	+	0.998851i	$0.515259\pi$
$662$	4.61929e23	0.486724
$663$	−1.10745e22	−0.0115202
$664$	2.62360e23	0.269444
$665$	−9.92371e23	−1.00621
$666$	−3.20244e23	−0.320590
$667$	−4.67807e23	−0.462378
$668$	8.63349e23	0.842532
$669$	6.31347e22	0.0608339
$670$	1.59579e24	1.51823
$671$	1.17945e24	1.10799
$672$	3.03608e22	0.0281627
$673$	−4.69165e23	−0.429732	−0.214866	−	0.976644i	$-0.568931\pi$
$673$	−4.69165e23	−0.429732	−0.214866	+	0.976644i	$0.568931\pi$
$674$	−7.33467e23	−0.663394
$675$	−3.15432e23	−0.281724
$676$	−6.39795e23	−0.564279
$677$	8.56181e23	0.745696	0.372848	−	0.927892i	$-0.378381\pi$
$677$	8.56181e23	0.745696	0.372848	+	0.927892i	$0.378381\pi$
$678$	8.13424e22	0.0699624
$679$	−1.68854e23	−0.143423
$680$	4.50893e23	0.378222
$681$	1.23099e23	0.101977
$682$	1.24425e23	0.101798
$683$	−5.24073e23	−0.423464	−0.211732	−	0.977328i	$-0.567910\pi$
$683$	−5.24073e23	−0.423464	−0.211732	+	0.977328i	$0.567910\pi$
$684$	1.22154e24	0.974837
$685$	3.17143e24	2.49968
$686$	−8.91387e22	−0.0693923
$687$	−7.75042e22	−0.0595927
$688$	1.34202e24	1.01920
$689$	2.83828e23	0.212908
$690$	1.06916e23	0.0792185
$691$	5.63344e23	0.412297	0.206149	−	0.978521i	$-0.433907\pi$
$691$	5.63344e23	0.412297	0.206149	+	0.978521i	$0.433907\pi$
$692$	1.26689e24	0.915880
$693$	9.85752e23	0.703939
$694$	−1.98321e24	−1.39898
$695$	−2.81480e24	−1.96145
$696$	−3.76364e22	−0.0259078
$697$	−9.29756e23	−0.632252
$698$	−1.74701e24	−1.17361
$699$	−1.19727e23	−0.0794580
$700$	−8.03687e23	−0.526931
$701$	7.87779e23	0.510272	0.255136	−	0.966905i	$-0.417880\pi$
$701$	7.87779e23	0.510272	0.255136	+	0.966905i	$0.417880\pi$
$702$	9.68330e22	0.0619666
$703$	−5.95419e23	−0.376446
$704$	−6.71442e23	−0.419412
$705$	−3.15510e22	−0.0194718
$706$	1.48378e23	0.0904753
$707$	−1.08984e23	−0.0656596
$708$	−8.43198e22	−0.0501934
$709$	−1.71248e24	−1.00724	−0.503619	−	0.863926i	$-0.667998\pi$
$709$	−1.71248e24	−1.00724	−0.503619	+	0.863926i	$0.667998\pi$
$710$	−2.34375e24	−1.36212
$711$	−8.81956e23	−0.506472
$712$	1.17228e24	0.665199
$713$	−3.98161e22	−0.0223253
$714$	−2.75828e22	−0.0152828
$715$	2.21651e24	1.21358
$716$	−8.94462e23	−0.483951
$717$	8.75756e22	0.0468242
$718$	2.26517e24	1.19686
$719$	−2.27774e24	−1.18935	−0.594674	−	0.803967i	$-0.702719\pi$
$719$	−2.27774e24	−1.18935	−0.594674	+	0.803967i	$0.702719\pi$
$720$	−4.19469e24	−2.16458
$721$	−2.55536e23	−0.130317
$722$	3.20656e24	1.61612
$723$	1.10769e23	0.0551752
$724$	−3.70325e23	−0.182308
$725$	3.85625e24	1.87626
$726$	4.40712e23	0.211931
$727$	1.30389e24	0.619724	0.309862	−	0.950782i	$-0.399717\pi$
$727$	1.30389e24	0.619724	0.309862	+	0.950782i	$0.399717\pi$
$728$	−1.31891e23	−0.0619581
$729$	−2.09763e24	−0.973970
$730$	5.78457e24	2.65477
$731$	−8.73080e23	−0.396056
$732$	5.68019e22	0.0254694
$733$	−1.60454e24	−0.711158	−0.355579	−	0.934646i	$-0.615716\pi$
$733$	−1.60454e24	−0.711158	−0.355579	+	0.934646i	$0.615716\pi$
$734$	−4.17514e24	−1.82917
$735$	−3.85670e22	−0.0167022
$736$	1.39069e24	0.595347
$737$	−2.94720e24	−1.24720
$738$	4.05591e24	1.69672
$739$	−2.93894e24	−1.21538	−0.607691	−	0.794173i	$-0.707904\pi$
$739$	−2.93894e24	−1.21538	−0.607691	+	0.794173i	$0.707904\pi$
$740$	−7.07605e23	−0.289282
$741$	8.98228e22	0.0363021
$742$	7.06917e23	0.282446
$743$	−3.72586e24	−1.47171	−0.735854	−	0.677141i	$-0.763219\pi$
$743$	−3.72586e24	−1.47171	−0.735854	+	0.677141i	$0.763219\pi$
$744$	−3.20332e21	−0.00125092
$745$	4.30597e24	1.66243
$746$	−1.67942e24	−0.641032
$747$	1.58789e24	0.599231
$748$	1.55775e24	0.581213
$749$	8.20327e23	0.302616
$750$	−4.69381e23	−0.171201
$751$	2.38800e24	0.861183	0.430591	−	0.902547i	$-0.358305\pi$
$751$	2.38800e24	0.861183	0.430591	+	0.902547i	$0.358305\pi$
$752$	−5.73101e23	−0.204352
$753$	−1.16609e23	−0.0411125
$754$	−1.18381e24	−0.412693
$755$	−1.20936e24	−0.416875
$756$	9.51547e22	0.0324336
$757$	3.27592e24	1.10413	0.552063	−	0.833802i	$-0.313841\pi$
$757$	3.27592e24	1.10413	0.552063	+	0.833802i	$0.313841\pi$
$758$	3.62461e24	1.20802
$759$	−1.97460e23	−0.0650765
$760$	−3.65708e24	−1.19184
$761$	6.93571e22	0.0223523	0.0111761	−	0.999938i	$-0.496442\pi$
$761$	6.93571e22	0.0223523	0.0111761	+	0.999938i	$0.496442\pi$
$762$	−8.80009e22	−0.0280459
$763$	−9.10201e23	−0.286866
$764$	8.54954e22	0.0266471
$765$	2.72894e24	0.841148
$766$	−4.76153e24	−1.45145
$767$	1.41780e24	0.427418
$768$	2.88846e23	0.0861184
$769$	−3.58174e24	−1.05614	−0.528068	−	0.849202i	$-0.677083\pi$
$769$	−3.58174e24	−1.05614	−0.528068	+	0.849202i	$0.677083\pi$
$770$	5.52056e24	1.60995
$771$	−2.41443e23	−0.0696389
$772$	−1.48306e24	−0.423068
$773$	3.28514e23	0.0926889	0.0463445	−	0.998926i	$-0.485243\pi$
$773$	3.28514e23	0.0926889	0.0463445	+	0.998926i	$0.485243\pi$
$774$	3.80867e24	1.06286
$775$	3.28214e23	0.0905927
$776$	−6.22260e23	−0.169882
$777$	−2.31401e22	−0.00624866
$778$	−3.36321e24	−0.898312
$779$	7.54102e24	1.99233
$780$	1.06747e23	0.0278965
$781$	4.32859e24	1.11896
$782$	−1.26344e24	−0.323072
$783$	−4.56571e23	−0.115487
$784$	−7.00542e23	−0.175286
$785$	−9.56301e24	−2.36702
$786$	−2.35078e23	−0.0575599
$787$	−3.43665e24	−0.832436	−0.416218	−	0.909265i	$-0.636645\pi$
$787$	−3.43665e24	−0.832436	−0.416218	+	0.909265i	$0.636645\pi$
$788$	2.92734e24	0.701455
$789$	−4.80624e23	−0.113933
$790$	−4.93926e24	−1.15833
$791$	−1.34403e24	−0.311823
$792$	3.63269e24	0.833804
$793$	−9.55097e23	−0.216883
$794$	6.05658e23	0.136067
$795$	3.05857e23	0.0679826
$796$	−1.15836e24	−0.254732
$797$	6.38674e24	1.38958	0.694790	−	0.719212i	$-0.255497\pi$
$797$	6.38674e24	1.38958	0.694790	+	0.719212i	$0.255497\pi$
$798$	2.23717e23	0.0481586
$799$	3.72843e23	0.0794105
$800$	−1.14638e25	−2.41582
$801$	7.09502e24	1.47937
$802$	−6.40429e24	−1.32126
$803$	−1.06833e25	−2.18085
$804$	−1.41937e23	−0.0286693
$805$	−1.76659e24	−0.353078
$806$	−1.00757e23	−0.0199263
$807$	5.51257e23	0.107877
$808$	−4.01628e23	−0.0777727
$809$	4.24605e24	0.813622	0.406811	−	0.913512i	$-0.366641\pi$
$809$	4.24605e24	0.813622	0.406811	+	0.913512i	$0.366641\pi$
$810$	−1.18523e25	−2.24740
$811$	2.80844e24	0.526972	0.263486	−	0.964663i	$-0.415128\pi$
$811$	2.80844e24	0.526972	0.263486	+	0.964663i	$0.415128\pi$
$812$	−1.16329e24	−0.216005
$813$	−1.15160e23	−0.0211608
$814$	3.31232e24	0.602316
$815$	5.79496e24	1.04282
$816$	−2.16773e23	−0.0386046
$817$	7.08134e24	1.24804
$818$	5.29771e24	0.924028
$819$	−7.98245e23	−0.137792
$820$	8.96186e24	1.53102
$821$	−2.46315e24	−0.416461	−0.208230	−	0.978080i	$-0.566770\pi$
$821$	−2.46315e24	−0.416461	−0.208230	+	0.978080i	$0.566770\pi$
$822$	−7.14957e23	−0.119638
$823$	1.97971e24	0.327871	0.163936	−	0.986471i	$-0.447581\pi$
$823$	1.97971e24	0.327871	0.163936	+	0.986471i	$0.447581\pi$
$824$	−9.41700e23	−0.154359
$825$	1.62771e24	0.264070
$826$	3.53123e24	0.567016
$827$	5.87046e23	0.0932986	0.0466493	−	0.998911i	$-0.485146\pi$
$827$	5.87046e23	0.0932986	0.0466493	+	0.998911i	$0.485146\pi$
$828$	2.17455e24	0.342068
$829$	3.47007e24	0.540287	0.270144	−	0.962820i	$-0.412929\pi$
$829$	3.47007e24	0.540287	0.270144	+	0.962820i	$0.412929\pi$
$830$	8.89272e24	1.37047
$831$	1.82726e23	0.0278736
$832$	5.43722e23	0.0820972
$833$	4.55752e23	0.0681156
$834$	6.34561e23	0.0938776
$835$	−1.56435e25	−2.29086
$836$	−1.26346e25	−1.83150
$837$	−3.88598e22	−0.00557615
$838$	8.56757e24	1.21698
$839$	1.07122e25	1.50626	0.753131	−	0.657871i	$-0.228543\pi$
$839$	1.07122e25	1.50626	0.753131	+	0.657871i	$0.228543\pi$
$840$	−1.42127e23	−0.0197835
$841$	−1.67542e24	−0.230865
$842$	7.62319e24	1.03988
$843$	−3.55893e23	−0.0480602
$844$	−2.39392e24	−0.320037
$845$	1.15928e25	1.53428
$846$	−1.62647e24	−0.213107
$847$	−7.28193e24	−0.944577
$848$	5.55567e24	0.713463
$849$	3.77786e23	0.0480319
$850$	1.04149e25	1.31097
$851$	−1.05995e24	−0.132094
$852$	2.08464e23	0.0257214
$853$	−1.40685e25	−1.71863	−0.859313	−	0.511450i	$-0.829109\pi$
$853$	−1.40685e25	−1.71863	−0.859313	+	0.511450i	$0.829109\pi$
$854$	−2.37881e24	−0.287718
$855$	−2.21338e25	−2.65060
$856$	3.02307e24	0.358443
$857$	−4.51107e24	−0.529593	−0.264797	−	0.964304i	$-0.585305\pi$
$857$	−4.51107e24	−0.529593	−0.264797	+	0.964304i	$0.585305\pi$
$858$	−4.99684e23	−0.0580836
$859$	1.65234e24	0.190177	0.0950887	−	0.995469i	$-0.469687\pi$
$859$	1.65234e24	0.190177	0.0950887	+	0.995469i	$0.469687\pi$
$860$	8.41557e24	0.959062
$861$	2.93071e23	0.0330709
$862$	−1.90368e25	−2.12708
$863$	4.01430e24	0.444138	0.222069	−	0.975031i	$-0.428719\pi$
$863$	4.01430e24	0.444138	0.222069	+	0.975031i	$0.428719\pi$
$864$	1.35729e24	0.148698
$865$	−2.29555e25	−2.49029
$866$	−7.57692e24	−0.813936
$867$	−4.79287e23	−0.0509840
$868$	−9.90107e22	−0.0104295
$869$	9.12216e24	0.951546
$870$	−1.27569e24	−0.131775
$871$	2.38660e24	0.244132
$872$	−3.35427e24	−0.339788
$873$	−3.76611e24	−0.377809
$874$	1.02475e25	1.01805
$875$	7.75563e24	0.763043
$876$	−5.14507e23	−0.0501310
$877$	−1.74406e25	−1.68293	−0.841464	−	0.540313i	$-0.818306\pi$
$877$	−1.74406e25	−1.68293	−0.841464	+	0.540313i	$0.818306\pi$
$878$	−2.46424e25	−2.35494
$879$	−1.30832e24	−0.123825
$880$	4.33861e25	4.06676
$881$	−1.07521e25	−0.998155	−0.499078	−	0.866557i	$-0.666328\pi$
$881$	−1.07521e25	−0.998155	−0.499078	+	0.866557i	$0.666328\pi$
$882$	−1.98815e24	−0.182795
$883$	1.57828e25	1.43720	0.718600	−	0.695423i	$-0.244783\pi$
$883$	1.57828e25	1.43720	0.718600	+	0.695423i	$0.244783\pi$
$884$	−1.26144e24	−0.113769
$885$	1.52783e24	0.136477
$886$	6.62569e23	0.0586198
$887$	−1.00351e25	−0.879365	−0.439683	−	0.898153i	$-0.644909\pi$
$887$	−1.00351e25	−0.879365	−0.439683	+	0.898153i	$0.644909\pi$
$888$	−8.52758e22	−0.00740143
$889$	1.45405e24	0.125001
$890$	3.97346e25	3.38340
$891$	2.18896e25	1.84619
$892$	7.19134e24	0.600770
$893$	−3.02404e24	−0.250236
$894$	−9.70724e23	−0.0795659
$895$	1.62072e25	1.31587
$896$	−3.95271e24	−0.317890
$897$	1.59900e23	0.0127383
$898$	−2.09143e25	−1.65042
$899$	4.75073e23	0.0371367
$900$	−1.79254e25	−1.38806
$901$	−3.61435e24	−0.277249
$902$	−4.19507e25	−3.18774
$903$	2.75206e23	0.0207163
$904$	−4.95301e24	−0.369349
$905$	6.71011e24	0.495697
$906$	2.72634e23	0.0199522
$907$	9.12638e24	0.661663	0.330831	−	0.943690i	$-0.392671\pi$
$907$	9.12638e24	0.661663	0.330831	+	0.943690i	$0.392671\pi$
$908$	1.40216e25	1.00709
$909$	−2.43078e24	−0.172963
$910$	−4.47045e24	−0.315137
$911$	2.27252e25	1.58709	0.793544	−	0.608513i	$-0.208234\pi$
$911$	2.27252e25	1.58709	0.793544	+	0.608513i	$0.208234\pi$
$912$	1.75819e24	0.121650
$913$	−1.64237e25	−1.12582
$914$	2.92590e25	1.98709
$915$	−1.02922e24	−0.0692517
$916$	−8.82809e24	−0.588512
$917$	3.88421e24	0.256545
$918$	−1.23310e24	−0.0806929
$919$	8.98037e24	0.582254	0.291127	−	0.956684i	$-0.405970\pi$
$919$	8.98037e24	0.582254	0.291127	+	0.956684i	$0.405970\pi$
$920$	−6.51022e24	−0.418214
$921$	−4.69939e23	−0.0299113
$922$	8.44830e24	0.532791
$923$	−3.50522e24	−0.219029
$924$	−4.91024e23	−0.0304012
$925$	8.73741e24	0.536016
$926$	−5.73677e24	−0.348718
$927$	−5.69947e24	−0.343286
$928$	−1.65933e25	−0.990319
$929$	9.60504e24	0.568022	0.284011	−	0.958821i	$-0.408335\pi$
$929$	9.60504e24	0.568022	0.284011	+	0.958821i	$0.408335\pi$
$930$	−1.08577e23	−0.00636257
$931$	−3.69649e24	−0.214644
$932$	−1.36375e25	−0.784694
$933$	−1.55464e24	−0.0886412
$934$	2.57234e25	1.45338
$935$	−2.82257e25	−1.58033
$936$	−2.94169e24	−0.163212
$937$	5.46544e24	0.300496	0.150248	−	0.988648i	$-0.451993\pi$
$937$	5.46544e24	0.300496	0.150248	+	0.988648i	$0.451993\pi$
$938$	5.94417e24	0.323867
$939$	2.16672e24	0.116989
$940$	−3.59381e24	−0.192295
$941$	9.15810e24	0.485617	0.242808	−	0.970074i	$-0.421931\pi$
$941$	9.15810e24	0.485617	0.242808	+	0.970074i	$0.421931\pi$
$942$	2.15586e24	0.113289
$943$	1.34243e25	0.699104
$944$	2.77520e25	1.43229
$945$	−1.72416e24	−0.0881874
$946$	−3.93935e25	−1.99687
$947$	6.69133e24	0.336154	0.168077	−	0.985774i	$-0.446244\pi$
$947$	6.69133e24	0.336154	0.168077	+	0.985774i	$0.446244\pi$
$948$	4.39321e23	0.0218731
$949$	8.65118e24	0.426887
$950$	−8.44727e25	−4.13110
$951$	−2.61384e24	−0.126691
$952$	1.67954e24	0.0806817
$953$	−1.80291e25	−0.858389	−0.429194	−	0.903212i	$-0.641202\pi$
$953$	−1.80291e25	−0.858389	−0.429194	+	0.903212i	$0.641202\pi$
$954$	1.57670e25	0.744027
$955$	−1.54914e24	−0.0724538
$956$	9.97527e24	0.462416
$957$	2.35603e24	0.108250
$958$	2.83831e25	1.29257
$959$	1.18133e25	0.533228
$960$	5.85921e23	0.0262140
$961$	−2.25097e25	−0.998207
$962$	−2.68226e24	−0.117900
$963$	1.82965e25	0.797160
$964$	1.26171e25	0.544887
$965$	2.68722e25	1.15033
$966$	3.98254e23	0.0168987
$967$	−4.09280e24	−0.172145	−0.0860726	−	0.996289i	$-0.527432\pi$
$967$	−4.09280e24	−0.172145	−0.0860726	+	0.996289i	$0.527432\pi$
$968$	−2.68353e25	−1.11884
$969$	−1.14383e24	−0.0472726
$970$	−2.10916e25	−0.864070
$971$	3.60792e25	1.46519	0.732595	−	0.680665i	$-0.238309\pi$
$971$	3.60792e25	1.46519	0.732595	+	0.680665i	$0.238309\pi$
$972$	3.18580e24	0.128250
$973$	−1.04849e25	−0.418413
$974$	−3.46634e25	−1.37126
$975$	−1.31809e24	−0.0516901
$976$	−1.86951e25	−0.726782
$977$	2.84870e25	1.09785	0.548925	−	0.835872i	$-0.315037\pi$
$977$	2.84870e25	1.09785	0.548925	+	0.835872i	$0.315037\pi$
$978$	−1.30640e24	−0.0499109
$979$	−7.33845e25	−2.77940
$980$	−4.39297e24	−0.164944
$981$	−2.03011e25	−0.755671
$982$	6.57733e25	2.42718
$983$	−3.93479e25	−1.43952	−0.719758	−	0.694225i	$-0.755747\pi$
$983$	−3.93479e25	−1.43952	−0.719758	+	0.694225i	$0.755747\pi$
$984$	1.08002e24	0.0391719
$985$	−5.30420e25	−1.90727
$986$	1.50750e25	0.537408
$987$	−1.17525e23	−0.00415368
$988$	1.02312e25	0.358504
$989$	1.26060e25	0.437934
$990$	1.23130e26	4.24097
$991$	4.30174e25	1.46899	0.734494	−	0.678615i	$-0.237420\pi$
$991$	4.30174e25	1.46899	0.734494	+	0.678615i	$0.237420\pi$
$992$	−1.41229e24	−0.0478163
$993$	7.44461e23	0.0249904
$994$	−8.73027e24	−0.290565
$995$	2.09890e25	0.692620
$996$	−7.90959e23	−0.0258791
$997$	3.14767e25	1.02113	0.510565	−	0.859839i	$-0.329436\pi$
$997$	3.14767e25	1.02113	0.510565	+	0.859839i	$0.329436\pi$
$998$	4.60338e25	1.48070
$999$	−1.03449e24	−0.0329928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.a.a.1.4	✓	4
3.2	odd	2		63.18.a.b.1.1		4
4.3	odd	2		112.18.a.f.1.2		4
7.6	odd	2		49.18.a.c.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.a.a.1.4	✓	4	1.1	even	1	trivial
49.18.a.c.1.4		4	7.6	odd	2
63.18.a.b.1.1		4	3.2	odd	2
112.18.a.f.1.2		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)

\(f(q)\)	\(=\)	\(q+465.279 q^{2} +749.859 q^{3} +85412.5 q^{4} -1.54763e6 q^{5} +348894. q^{6} -5.76480e6 q^{7} -2.12444e7 q^{8} -1.28578e8 q^{9} +O(q^{10})\)	\(q+465.279 q^{2} +749.859 q^{3} +85412.5 q^{4} -1.54763e6 q^{5} +348894. q^{6} -5.76480e6 q^{7} -2.12444e7 q^{8} -1.28578e8 q^{9} -7.20081e8 q^{10} +1.32989e9 q^{11} +6.40473e7 q^{12} -1.07693e9 q^{13} -2.68224e9 q^{14} -1.16051e9 q^{15} -2.10798e10 q^{16} +1.37139e10 q^{17} -5.98246e10 q^{18} -1.11230e11 q^{19} -1.32187e11 q^{20} -4.32279e9 q^{21} +6.18772e11 q^{22} -1.98008e11 q^{23} -1.59303e10 q^{24} +1.63223e12 q^{25} -5.01071e11 q^{26} -1.93252e11 q^{27} -4.92386e11 q^{28} +2.36257e12 q^{29} -5.39959e11 q^{30} +2.01083e11 q^{31} -7.02342e12 q^{32} +9.97233e11 q^{33} +6.38078e12 q^{34} +8.92180e12 q^{35} -1.09822e13 q^{36} +5.35305e12 q^{37} -5.17529e13 q^{38} -8.07542e11 q^{39} +3.28786e13 q^{40} -6.77967e13 q^{41} -2.01130e12 q^{42} -6.36640e13 q^{43} +1.13590e14 q^{44} +1.98991e14 q^{45} -9.21289e13 q^{46} +2.71873e13 q^{47} -1.58069e13 q^{48} +3.32329e13 q^{49} +7.59442e14 q^{50} +1.02835e13 q^{51} -9.19828e13 q^{52} -2.63554e14 q^{53} -8.99162e13 q^{54} -2.05819e15 q^{55} +1.22470e14 q^{56} -8.34067e13 q^{57} +1.09925e15 q^{58} -1.31652e15 q^{59} -9.91218e13 q^{60} +8.86874e14 q^{61} +9.35599e13 q^{62} +7.41226e14 q^{63} -5.04884e14 q^{64} +1.66669e15 q^{65} +4.63992e14 q^{66} -2.21612e15 q^{67} +1.17134e15 q^{68} -1.48478e14 q^{69} +4.15112e15 q^{70} +3.25484e15 q^{71} +2.73156e15 q^{72} -8.03322e15 q^{73} +2.49066e15 q^{74} +1.22394e15 q^{75} -9.50042e15 q^{76} -7.66657e15 q^{77} -3.75732e14 q^{78} +6.85931e15 q^{79} +3.26237e16 q^{80} +1.64597e16 q^{81} -3.15444e16 q^{82} -1.23496e16 q^{83} -3.69220e14 q^{84} -2.12241e16 q^{85} -2.96215e16 q^{86} +1.77159e15 q^{87} -2.82528e16 q^{88} -5.51807e16 q^{89} +9.25865e16 q^{90} +6.20826e15 q^{91} -1.69124e16 q^{92} +1.50784e14 q^{93} +1.26497e16 q^{94} +1.72143e17 q^{95} -5.26658e15 q^{96} +2.92905e16 q^{97} +1.54626e16 q^{98} -1.70995e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 186 q^{2} - 2786 q^{3} - 16300 q^{4} + 274722 q^{5} + 1469804 q^{6} - 23059204 q^{7} + 8649336 q^{8} - 2050976 q^{9}+O(q^{10}) \) 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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