LMFDB - Embedded newform 91.8.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.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:	$28.4270373191$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 957 x^{8} + 1224 x^{7} + 310102 x^{6} - 241884 x^{5} - 40367312 x^{4} + \cdots - 4516262912 $ x^10 - 2x^9 - 957x^8 + 1224x^7 + 310102x^6 - 241884x^5 - 40367312x^4 + 11067840x^3 + 1840757376x^2 + 541859072*x - 4516262912
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.80018$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.80018 q^{2} -76.5407 q^{3} -113.559 q^{4} -339.464 q^{5} +290.868 q^{6} +343.000 q^{7} +917.967 q^{8} +3671.47 q^{9} +O(q^{10})$	\(q-3.80018 q^{2} -76.5407 q^{3} -113.559 q^{4} -339.464 q^{5} +290.868 q^{6} +343.000 q^{7} +917.967 q^{8} +3671.47 q^{9} +1290.03 q^{10} +3399.92 q^{11} +8691.85 q^{12} -2197.00 q^{13} -1303.46 q^{14} +25982.8 q^{15} +11047.1 q^{16} +8096.39 q^{17} -13952.3 q^{18} -49643.5 q^{19} +38549.1 q^{20} -26253.4 q^{21} -12920.3 q^{22} +20612.4 q^{23} -70261.8 q^{24} +37111.1 q^{25} +8349.00 q^{26} -113623. q^{27} -38950.6 q^{28} +138539. q^{29} -98739.5 q^{30} +92549.8 q^{31} -159481. q^{32} -260232. q^{33} -30767.8 q^{34} -116436. q^{35} -416927. q^{36} +40464.8 q^{37} +188654. q^{38} +168160. q^{39} -311617. q^{40} +52424.4 q^{41} +99767.9 q^{42} +696019. q^{43} -386090. q^{44} -1.24633e6 q^{45} -78330.9 q^{46} +77394.2 q^{47} -845550. q^{48} +117649. q^{49} -141029. q^{50} -619703. q^{51} +249488. q^{52} -682352. q^{53} +431786. q^{54} -1.15415e6 q^{55} +314863. q^{56} +3.79975e6 q^{57} -526472. q^{58} -1.73469e6 q^{59} -2.95057e6 q^{60} +2.70508e6 q^{61} -351706. q^{62} +1.25932e6 q^{63} -807969. q^{64} +745803. q^{65} +988929. q^{66} -4.71791e6 q^{67} -919415. q^{68} -1.57769e6 q^{69} +442479. q^{70} +2.79941e6 q^{71} +3.37029e6 q^{72} -3.16613e6 q^{73} -153774. q^{74} -2.84051e6 q^{75} +5.63745e6 q^{76} +1.16617e6 q^{77} -639038. q^{78} +2.13983e6 q^{79} -3.75008e6 q^{80} +667235. q^{81} -199222. q^{82} +5.08233e6 q^{83} +2.98131e6 q^{84} -2.74844e6 q^{85} -2.64500e6 q^{86} -1.06038e7 q^{87} +3.12101e6 q^{88} -1.26416e7 q^{89} +4.73630e6 q^{90} -753571. q^{91} -2.34072e6 q^{92} -7.08382e6 q^{93} -294112. q^{94} +1.68522e7 q^{95} +1.22067e7 q^{96} +1.03648e7 q^{97} -447088. q^{98} +1.24827e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) $ 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9} + 9420 q^{10} + 876 q^{11} - 8765 q^{12} - 21970 q^{13} - 6174 q^{14} - 5320 q^{15} + 41370 q^{16} + 6294 q^{17} - 16027 q^{18} - 97401 q^{19} - 166650 q^{20} - 27440 q^{21} + 74171 q^{22} - 15255 q^{23} + 196187 q^{24} + 162145 q^{25} + 39546 q^{26} - 181820 q^{27} + 229810 q^{28} - 340533 q^{29} - 325020 q^{30} - 148675 q^{31} - 642762 q^{32} - 624400 q^{33} - 1161518 q^{34} - 317961 q^{35} - 773917 q^{36} - 621782 q^{37} - 805092 q^{38} + 175760 q^{39} - 350478 q^{40} - 2043336 q^{41} - 486717 q^{42} - 1801391 q^{43} - 3953667 q^{44} - 1908807 q^{45} - 2707731 q^{46} - 1624701 q^{47} - 6068625 q^{48} + 1176490 q^{49} - 6891516 q^{50} + 1811700 q^{51} - 1471990 q^{52} - 199965 q^{53} - 2895913 q^{54} + 739086 q^{55} - 1673154 q^{56} + 2159088 q^{57} + 2071092 q^{58} - 8098908 q^{59} + 8096436 q^{60} + 2271618 q^{61} - 8910225 q^{62} + 1238916 q^{63} + 8099930 q^{64} + 2036619 q^{65} - 5999191 q^{66} + 1970272 q^{67} - 1766238 q^{68} - 4622962 q^{69} + 3231060 q^{70} - 7145820 q^{71} + 984975 q^{72} + 1409431 q^{73} - 5498643 q^{74} - 8857892 q^{75} - 2749534 q^{76} + 300468 q^{77} + 3117543 q^{78} - 9011055 q^{79} - 23850522 q^{80} + 11613490 q^{81} + 27962597 q^{82} - 15006567 q^{83} - 3006395 q^{84} - 9416628 q^{85} + 38357850 q^{86} - 15828996 q^{87} + 42205269 q^{88} - 11472777 q^{89} + 53425712 q^{90} - 7535710 q^{91} + 16755837 q^{92} + 36339848 q^{93} + 5133371 q^{94} + 29637939 q^{95} + 65329611 q^{96} + 3228571 q^{97} - 2117682 q^{98} + 19367194 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9 + 9420 * q^10 + 876 * q^11 - 8765 * q^12 - 21970 * q^13 - 6174 * q^14 - 5320 * q^15 + 41370 * q^16 + 6294 * q^17 - 16027 * q^18 - 97401 * q^19 - 166650 * q^20 - 27440 * q^21 + 74171 * q^22 - 15255 * q^23 + 196187 * q^24 + 162145 * q^25 + 39546 * q^26 - 181820 * q^27 + 229810 * q^28 - 340533 * q^29 - 325020 * q^30 - 148675 * q^31 - 642762 * q^32 - 624400 * q^33 - 1161518 * q^34 - 317961 * q^35 - 773917 * q^36 - 621782 * q^37 - 805092 * q^38 + 175760 * q^39 - 350478 * q^40 - 2043336 * q^41 - 486717 * q^42 - 1801391 * q^43 - 3953667 * q^44 - 1908807 * q^45 - 2707731 * q^46 - 1624701 * q^47 - 6068625 * q^48 + 1176490 * q^49 - 6891516 * q^50 + 1811700 * q^51 - 1471990 * q^52 - 199965 * q^53 - 2895913 * q^54 + 739086 * q^55 - 1673154 * q^56 + 2159088 * q^57 + 2071092 * q^58 - 8098908 * q^59 + 8096436 * q^60 + 2271618 * q^61 - 8910225 * q^62 + 1238916 * q^63 + 8099930 * q^64 + 2036619 * q^65 - 5999191 * q^66 + 1970272 * q^67 - 1766238 * q^68 - 4622962 * q^69 + 3231060 * q^70 - 7145820 * q^71 + 984975 * q^72 + 1409431 * q^73 - 5498643 * q^74 - 8857892 * q^75 - 2749534 * q^76 + 300468 * q^77 + 3117543 * q^78 - 9011055 * q^79 - 23850522 * q^80 + 11613490 * q^81 + 27962597 * q^82 - 15006567 * q^83 - 3006395 * q^84 - 9416628 * q^85 + 38357850 * q^86 - 15828996 * q^87 + 42205269 * q^88 - 11472777 * q^89 + 53425712 * q^90 - 7535710 * q^91 + 16755837 * q^92 + 36339848 * q^93 + 5133371 * q^94 + 29637939 * q^95 + 65329611 * q^96 + 3228571 * q^97 - 2117682 * q^98 + 19367194 * 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 $

$2$	−3.80018	−0.335892	−0.167946	−	0.985796i	$-0.553713\pi$
$2$	−3.80018	−0.335892	−0.167946	+	0.985796i	$0.553713\pi$
$3$	−76.5407	−1.63670	−0.818348	−	0.574724i	$-0.805110\pi$
$3$	−76.5407	−1.63670	−0.818348	+	0.574724i	$0.805110\pi$
$4$	−113.559	−0.887177
$5$	−339.464	−1.21450	−0.607252	−	0.794509i	$-0.707728\pi$
$5$	−339.464	−1.21450	−0.607252	+	0.794509i	$0.707728\pi$
$6$	290.868	0.549753
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	917.967	0.633887
$9$	3671.47	1.67877
$10$	1290.03	0.407942
$11$	3399.92	0.770184	0.385092	−	0.922878i	$-0.374170\pi$
$11$	3399.92	0.770184	0.385092	+	0.922878i	$0.374170\pi$
$12$	8691.85	1.45204
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−1303.46	−0.126955
$15$	25982.8	1.98777
$16$	11047.1	0.674259
$17$	8096.39	0.399687	0.199844	−	0.979828i	$-0.435957\pi$
$17$	8096.39	0.399687	0.199844	+	0.979828i	$0.435957\pi$
$18$	−13952.3	−0.563886
$19$	−49643.5	−1.66045	−0.830223	−	0.557431i	$-0.811787\pi$
$19$	−49643.5	−1.66045	−0.830223	+	0.557431i	$0.811787\pi$
$20$	38549.1	1.07748
$21$	−26253.4	−0.618613
$22$	−12920.3	−0.258698
$23$	20612.4	0.353249	0.176625	−	0.984278i	$-0.443482\pi$
$23$	20612.4	0.353249	0.176625	+	0.984278i	$0.443482\pi$
$24$	−70261.8	−1.03748
$25$	37111.1	0.475022
$26$	8349.00	0.0931596
$27$	−113623.	−1.11094
$28$	−38950.6	−0.335321
$29$	138539.	1.05482	0.527409	−	0.849611i	$-0.323163\pi$
$29$	138539.	1.05482	0.527409	+	0.849611i	$0.323163\pi$
$30$	−98739.5	−0.667677
$31$	92549.8	0.557968	0.278984	−	0.960296i	$-0.410002\pi$
$31$	92549.8	0.557968	0.278984	+	0.960296i	$0.410002\pi$
$32$	−159481.	−0.860365
$33$	−260232.	−1.26056
$34$	−30767.8	−0.134252
$35$	−116436.	−0.459040
$36$	−416927.	−1.48937
$37$	40464.8	0.131332	0.0656662	−	0.997842i	$-0.479083\pi$
$37$	40464.8	0.131332	0.0656662	+	0.997842i	$0.479083\pi$
$38$	188654.	0.557730
$39$	168160.	0.453938
$40$	−311617.	−0.769859
$41$	52424.4	0.118793	0.0593963	−	0.998234i	$-0.481082\pi$
$41$	52424.4	0.118793	0.0593963	+	0.998234i	$0.481082\pi$
$42$	99767.9	0.207787
$43$	696019.	1.33500	0.667501	−	0.744609i	$-0.267364\pi$
$43$	696019.	1.33500	0.667501	+	0.744609i	$0.267364\pi$
$44$	−386090.	−0.683289
$45$	−1.24633e6	−2.03888
$46$	−78330.9	−0.118654
$47$	77394.2	0.108734	0.0543670	−	0.998521i	$-0.482686\pi$
$47$	77394.2	0.108734	0.0543670	+	0.998521i	$0.482686\pi$
$48$	−845550.	−1.10356
$49$	117649.	0.142857
$50$	−141029.	−0.159556
$51$	−619703.	−0.654166
$52$	249488.	0.246059
$53$	−682352.	−0.629568	−0.314784	−	0.949163i	$-0.601932\pi$
$53$	−682352.	−0.629568	−0.314784	+	0.949163i	$0.601932\pi$
$54$	431786.	0.373156
$55$	−1.15415e6	−0.935392
$56$	314863.	0.239587
$57$	3.79975e6	2.71765
$58$	−526472.	−0.354305
$59$	−1.73469e6	−1.09961	−0.549807	−	0.835292i	$-0.685299\pi$
$59$	−1.73469e6	−1.09961	−0.549807	+	0.835292i	$0.685299\pi$
$60$	−2.95057e6	−1.76351
$61$	2.70508e6	1.52590	0.762950	−	0.646458i	$-0.223750\pi$
$61$	2.70508e6	1.52590	0.762950	+	0.646458i	$0.223750\pi$
$62$	−351706.	−0.187417
$63$	1.25932e6	0.634516
$64$	−807969.	−0.385270
$65$	745803.	0.336843
$66$	988929.	0.423410
$67$	−4.71791e6	−1.91641	−0.958203	−	0.286090i	$-0.907644\pi$
$67$	−4.71791e6	−1.91641	−0.958203	+	0.286090i	$0.907644\pi$
$68$	−919415.	−0.354593
$69$	−1.57769e6	−0.578162
$70$	442479.	0.154188
$71$	2.79941e6	0.928245	0.464122	−	0.885771i	$-0.346370\pi$
$71$	2.79941e6	0.928245	0.464122	+	0.885771i	$0.346370\pi$
$72$	3.37029e6	1.06415
$73$	−3.16613e6	−0.952573	−0.476287	−	0.879290i	$-0.658018\pi$
$73$	−3.16613e6	−0.952573	−0.476287	+	0.879290i	$0.658018\pi$
$74$	−153774.	−0.0441134
$75$	−2.84051e6	−0.777466
$76$	5.63745e6	1.47311
$77$	1.16617e6	0.291102
$78$	−639038.	−0.152474
$79$	2.13983e6	0.488298	0.244149	−	0.969738i	$-0.421491\pi$
$79$	2.13983e6	0.488298	0.244149	+	0.969738i	$0.421491\pi$
$80$	−3.75008e6	−0.818891
$81$	667235.	0.139502
$82$	−199222.	−0.0399015
$83$	5.08233e6	0.975640	0.487820	−	0.872944i	$-0.337792\pi$
$83$	5.08233e6	0.975640	0.487820	+	0.872944i	$0.337792\pi$
$84$	2.98131e6	0.548819
$85$	−2.74844e6	−0.485422
$86$	−2.64500e6	−0.448416
$87$	−1.06038e7	−1.72642
$88$	3.12101e6	0.488210
$89$	−1.26416e7	−1.90081	−0.950403	−	0.311020i	$-0.899329\pi$
$89$	−1.26416e7	−1.90081	−0.950403	+	0.311020i	$0.899329\pi$
$90$	4.73630e6	0.684842
$91$	−753571.	−0.104828
$92$	−2.34072e6	−0.313395
$93$	−7.08382e6	−0.913224
$94$	−294112.	−0.0365229
$95$	1.68522e7	2.01662
$96$	1.22067e7	1.40816
$97$	1.03648e7	1.15308	0.576541	−	0.817069i	$-0.304402\pi$
$97$	1.03648e7	1.15308	0.576541	+	0.817069i	$0.304402\pi$
$98$	−447088.	−0.0479845
$99$	1.24827e7	1.29296
$100$	−4.21428e6	−0.421428
$101$	4.83651e6	0.467097	0.233549	−	0.972345i	$-0.424966\pi$
$101$	4.83651e6	0.467097	0.233549	+	0.972345i	$0.424966\pi$
$102$	2.35499e6	0.219729
$103$	1.25305e7	1.12990	0.564948	−	0.825126i	$-0.308896\pi$
$103$	1.25305e7	1.12990	0.564948	+	0.825126i	$0.308896\pi$
$104$	−2.01677e6	−0.175809
$105$	8.91211e6	0.751308
$106$	2.59306e6	0.211467
$107$	−2.03751e6	−0.160789	−0.0803946	−	0.996763i	$-0.525618\pi$
$107$	−2.03751e6	−0.160789	−0.0803946	+	0.996763i	$0.525618\pi$
$108$	1.29028e7	0.985602
$109$	1.59876e7	1.18247	0.591235	−	0.806499i	$-0.298641\pi$
$109$	1.59876e7	1.18247	0.591235	+	0.806499i	$0.298641\pi$
$110$	4.38599e6	0.314190
$111$	−3.09720e6	−0.214951
$112$	3.78914e6	0.254846
$113$	3.34020e6	0.217770	0.108885	−	0.994054i	$-0.465272\pi$
$113$	3.34020e6	0.217770	0.108885	+	0.994054i	$0.465272\pi$
$114$	−1.44397e7	−0.912835
$115$	−6.99718e6	−0.429023
$116$	−1.57322e7	−0.935810
$117$	−8.06623e6	−0.465607
$118$	6.59214e6	0.369351
$119$	2.77706e6	0.151068
$120$	2.38514e7	1.26002
$121$	−7.92771e6	−0.406817
$122$	−1.02798e7	−0.512537
$123$	−4.01259e6	−0.194427
$124$	−1.05098e7	−0.495016
$125$	1.39228e7	0.637588
$126$	−4.78563e6	−0.213129
$127$	−4.66494e6	−0.202085	−0.101042	−	0.994882i	$-0.532218\pi$
$127$	−4.66494e6	−0.202085	−0.101042	+	0.994882i	$0.532218\pi$
$128$	2.34839e7	0.989774
$129$	−5.32738e7	−2.18499
$130$	−2.83419e6	−0.113143
$131$	−5.09818e7	−1.98137	−0.990684	−	0.136177i	$-0.956518\pi$
$131$	−5.09818e7	−1.98137	−0.990684	+	0.136177i	$0.956518\pi$
$132$	2.95516e7	1.11834
$133$	−1.70277e7	−0.627590
$134$	1.79289e7	0.643705
$135$	3.85708e7	1.34924
$136$	7.43222e6	0.253357
$137$	5.34985e6	0.177754	0.0888771	−	0.996043i	$-0.471672\pi$
$137$	5.34985e6	0.177754	0.0888771	+	0.996043i	$0.471672\pi$
$138$	5.99550e6	0.194200
$139$	−5.72070e7	−1.80675	−0.903374	−	0.428854i	$-0.858917\pi$
$139$	−5.72070e7	−1.80675	−0.903374	+	0.428854i	$0.858917\pi$
$140$	1.32223e7	0.407249
$141$	−5.92380e6	−0.177965
$142$	−1.06383e7	−0.311790
$143$	−7.46962e6	−0.213611
$144$	4.05590e7	1.13193
$145$	−4.70289e7	−1.28108
$146$	1.20319e7	0.319962
$147$	−9.00493e6	−0.233814
$148$	−4.59513e6	−0.116515
$149$	−5.34532e7	−1.32380	−0.661899	−	0.749593i	$-0.730249\pi$
$149$	−5.34532e7	−1.32380	−0.661899	+	0.749593i	$0.730249\pi$
$150$	1.07944e7	0.261144
$151$	−53852.3	−0.00127287	−0.000636436	−	1.00000i	$-0.500203\pi$
$151$	−53852.3	−0.00127287	−0.000636436		1.00000i	$0.500203\pi$
$152$	−4.55711e7	−1.05254
$153$	2.97257e7	0.670984
$154$	−4.43167e6	−0.0977788
$155$	−3.14173e7	−0.677655
$156$	−1.90960e7	−0.402723
$157$	−7.46784e7	−1.54009	−0.770045	−	0.637989i	$-0.779766\pi$
$157$	−7.46784e7	−1.54009	−0.770045	+	0.637989i	$0.779766\pi$
$158$	−8.13175e6	−0.164015
$159$	5.22277e7	1.03041
$160$	5.41380e7	1.04492
$161$	7.07006e6	0.133516
$162$	−2.53562e6	−0.0468577
$163$	1.75999e7	0.318312	0.159156	−	0.987253i	$-0.449123\pi$
$163$	1.75999e7	0.318312	0.159156	+	0.987253i	$0.449123\pi$
$164$	−5.95324e6	−0.105390
$165$	8.83395e7	1.53095
$166$	−1.93138e7	−0.327709
$167$	6.95017e7	1.15475	0.577375	−	0.816479i	$-0.304077\pi$
$167$	6.95017e7	1.15475	0.577375	+	0.816479i	$0.304077\pi$
$168$	−2.40998e7	−0.392131
$169$	4.82681e6	0.0769231
$170$	1.04446e7	0.163049
$171$	−1.82265e8	−2.78751
$172$	−7.90390e7	−1.18438
$173$	−5.15949e6	−0.0757610	−0.0378805	−	0.999282i	$-0.512061\pi$
$173$	−5.15949e6	−0.0757610	−0.0378805	+	0.999282i	$0.512061\pi$
$174$	4.02965e7	0.579889
$175$	1.27291e7	0.179541
$176$	3.75591e7	0.519303
$177$	1.32774e8	1.79973
$178$	4.80405e7	0.638465
$179$	−8.80205e7	−1.14709	−0.573546	−	0.819173i	$-0.694433\pi$
$179$	−8.80205e7	−1.14709	−0.573546	+	0.819173i	$0.694433\pi$
$180$	1.41532e8	1.80884
$181$	−3.23048e7	−0.404941	−0.202470	−	0.979288i	$-0.564897\pi$
$181$	−3.23048e7	−0.404941	−0.202470	+	0.979288i	$0.564897\pi$
$182$	2.86371e6	0.0352110
$183$	−2.07049e8	−2.49743
$184$	1.89215e7	0.223920
$185$	−1.37364e7	−0.159504
$186$	2.69198e7	0.306744
$187$	2.75271e7	0.307833
$188$	−8.78877e6	−0.0964664
$189$	−3.89725e7	−0.419897
$190$	−6.40414e7	−0.677366
$191$	−2.06430e7	−0.214366	−0.107183	−	0.994239i	$-0.534183\pi$
$191$	−2.06430e7	−0.214366	−0.107183	+	0.994239i	$0.534183\pi$
$192$	6.18425e7	0.630569
$193$	−3.31896e7	−0.332316	−0.166158	−	0.986099i	$-0.553136\pi$
$193$	−3.31896e7	−0.332316	−0.166158	+	0.986099i	$0.553136\pi$
$194$	−3.93881e7	−0.387311
$195$	−5.70843e7	−0.551309
$196$	−1.33601e7	−0.126740
$197$	−1.95827e8	−1.82490	−0.912452	−	0.409185i	$-0.865813\pi$
$197$	−1.95827e8	−1.82490	−0.912452	+	0.409185i	$0.865813\pi$
$198$	−4.74366e7	−0.434295
$199$	2.03382e8	1.82947	0.914737	−	0.404049i	$-0.132397\pi$
$199$	2.03382e8	1.82947	0.914737	+	0.404049i	$0.132397\pi$
$200$	3.40667e7	0.301110
$201$	3.61112e8	3.13657
$202$	−1.83796e7	−0.156894
$203$	4.75187e7	0.398684
$204$	7.03727e7	0.580361
$205$	−1.77962e7	−0.144274
$206$	−4.76183e7	−0.379523
$207$	7.56779e7	0.593025
$208$	−2.42704e7	−0.187006
$209$	−1.68784e8	−1.27885
$210$	−3.38676e7	−0.252358
$211$	6.29200e7	0.461105	0.230553	−	0.973060i	$-0.425947\pi$
$211$	6.29200e7	0.461105	0.230553	+	0.973060i	$0.425947\pi$
$212$	7.74869e7	0.558538
$213$	−2.14269e8	−1.51925
$214$	7.74292e6	0.0540078
$215$	−2.36274e8	−1.62137
$216$	−1.04302e8	−0.704212
$217$	3.17446e7	0.210892
$218$	−6.07557e7	−0.397182
$219$	2.42338e8	1.55907
$220$	1.31064e8	0.829858
$221$	−1.77878e7	−0.110853
$222$	1.17699e7	0.0722003
$223$	1.12770e8	0.680970	0.340485	−	0.940250i	$-0.389409\pi$
$223$	1.12770e8	0.680970	0.340485	+	0.940250i	$0.389409\pi$
$224$	−5.47018e7	−0.325188
$225$	1.36252e8	0.797453
$226$	−1.26934e7	−0.0731471
$227$	1.06587e7	0.0604804	0.0302402	−	0.999543i	$-0.490373\pi$
$227$	1.06587e7	0.0604804	0.0302402	+	0.999543i	$0.490373\pi$
$228$	−4.31494e8	−2.41103
$229$	−2.35163e8	−1.29403	−0.647016	−	0.762477i	$-0.723983\pi$
$229$	−2.35163e8	−1.29403	−0.647016	+	0.762477i	$0.723983\pi$
$230$	2.65906e7	0.144105
$231$	−8.92596e7	−0.476445
$232$	1.27174e8	0.668636
$233$	3.48398e8	1.80439	0.902193	−	0.431332i	$-0.141956\pi$
$233$	3.48398e8	1.80439	0.902193	+	0.431332i	$0.141956\pi$
$234$	3.06531e7	0.156394
$235$	−2.62726e7	−0.132058
$236$	1.96989e8	0.975551
$237$	−1.63784e8	−0.799194
$238$	−1.05533e7	−0.0507424
$239$	9.32918e7	0.442029	0.221015	−	0.975270i	$-0.429063\pi$
$239$	9.32918e7	0.442029	0.221015	+	0.975270i	$0.429063\pi$
$240$	2.87034e8	1.34028
$241$	2.36583e8	1.08874	0.544369	−	0.838846i	$-0.316769\pi$
$241$	2.36583e8	1.08874	0.544369	+	0.838846i	$0.316769\pi$
$242$	3.01268e7	0.136647
$243$	1.97422e8	0.882619
$244$	−3.07185e8	−1.35374
$245$	−3.99376e7	−0.173501
$246$	1.52486e7	0.0653066
$247$	1.09067e8	0.460525
$248$	8.49576e7	0.353689
$249$	−3.89005e8	−1.59682
$250$	−5.29090e7	−0.214161
$251$	1.65859e8	0.662034	0.331017	−	0.943625i	$-0.392608\pi$
$251$	1.65859e8	0.662034	0.331017	+	0.943625i	$0.392608\pi$
$252$	−1.43006e8	−0.562928
$253$	7.00806e7	0.272067
$254$	1.77276e7	0.0678786
$255$	2.10367e8	0.794488
$256$	1.41767e7	0.0528125
$257$	−3.95785e8	−1.45443	−0.727217	−	0.686408i	$-0.759187\pi$
$257$	−3.95785e8	−1.45443	−0.727217	+	0.686408i	$0.759187\pi$
$258$	2.02450e8	0.733920
$259$	1.38794e7	0.0496390
$260$	−8.46924e7	−0.298839
$261$	5.08641e8	1.77080
$262$	1.93740e8	0.665526
$263$	−5.23975e7	−0.177609	−0.0888046	−	0.996049i	$-0.528305\pi$
$263$	−5.23975e7	−0.177609	−0.0888046	+	0.996049i	$0.528305\pi$
$264$	−2.38884e8	−0.799050
$265$	2.31634e8	0.764614
$266$	6.47085e7	0.210802
$267$	9.67599e8	3.11104
$268$	5.35759e8	1.70019
$269$	−2.80171e8	−0.877586	−0.438793	−	0.898588i	$-0.644594\pi$
$269$	−2.80171e8	−0.877586	−0.438793	+	0.898588i	$0.644594\pi$
$270$	−1.46576e8	−0.453200
$271$	3.35906e8	1.02524	0.512620	−	0.858616i	$-0.328675\pi$
$271$	3.35906e8	1.02524	0.512620	+	0.858616i	$0.328675\pi$
$272$	8.94414e7	0.269493
$273$	5.76788e7	0.171572
$274$	−2.03304e7	−0.0597062
$275$	1.26175e8	0.365854
$276$	1.79160e8	0.512932
$277$	5.40118e8	1.52689	0.763447	−	0.645870i	$-0.223505\pi$
$277$	5.40118e8	1.52689	0.763447	+	0.645870i	$0.223505\pi$
$278$	2.17397e8	0.606872
$279$	3.39794e8	0.936701
$280$	−1.06885e8	−0.290979
$281$	−4.45375e8	−1.19744	−0.598719	−	0.800959i	$-0.704324\pi$
$281$	−4.45375e8	−1.19744	−0.598719	+	0.800959i	$0.704324\pi$
$282$	2.25115e7	0.0597768
$283$	3.95539e7	0.103738	0.0518689	−	0.998654i	$-0.483482\pi$
$283$	3.95539e7	0.103738	0.0518689	+	0.998654i	$0.483482\pi$
$284$	−3.17897e8	−0.823517
$285$	−1.28988e9	−3.30059
$286$	2.83859e7	0.0717500
$287$	1.79816e7	0.0448994
$288$	−5.85529e8	−1.44436
$289$	−3.44787e8	−0.840250
$290$	1.78718e8	0.430305
$291$	−7.93329e8	−1.88724
$292$	3.59541e8	0.845101
$293$	−6.83430e8	−1.58729	−0.793647	−	0.608379i	$-0.791820\pi$
$293$	−6.83430e8	−1.58729	−0.793647	+	0.608379i	$0.791820\pi$
$294$	3.42204e7	0.0785361
$295$	5.88866e8	1.33549
$296$	3.71454e7	0.0832499
$297$	−3.86308e8	−0.855630
$298$	2.03132e8	0.444653
$299$	−4.52855e7	−0.0979738
$300$	3.22564e8	0.689750
$301$	2.38735e8	0.504583
$302$	204648.	0.000427547 0
$303$	−3.70190e8	−0.764496
$304$	−5.48415e8	−1.11957
$305$	−9.18279e8	−1.85321
$306$	−1.12963e8	−0.225378
$307$	4.62744e8	0.912760	0.456380	−	0.889785i	$-0.349146\pi$
$307$	4.62744e8	0.912760	0.456380	+	0.889785i	$0.349146\pi$
$308$	−1.32429e8	−0.258259
$309$	−9.59094e8	−1.84930
$310$	1.19392e8	0.227619
$311$	−2.11511e8	−0.398723	−0.199361	−	0.979926i	$-0.563887\pi$
$311$	−2.11511e8	−0.398723	−0.199361	+	0.979926i	$0.563887\pi$
$312$	1.54365e8	0.287745
$313$	−1.07114e9	−1.97442	−0.987211	−	0.159419i	$-0.949038\pi$
$313$	−1.07114e9	−1.97442	−0.987211	+	0.159419i	$0.949038\pi$
$314$	2.83792e8	0.517304
$315$	−4.27493e8	−0.770623
$316$	−2.42996e8	−0.433206
$317$	−9.20889e8	−1.62368	−0.811839	−	0.583881i	$-0.801533\pi$
$317$	−9.20889e8	−1.62368	−0.811839	+	0.583881i	$0.801533\pi$
$318$	−1.98475e8	−0.346107
$319$	4.71020e8	0.812404
$320$	2.74277e8	0.467912
$321$	1.55953e8	0.263163
$322$	−2.68675e7	−0.0448468
$323$	−4.01933e8	−0.663659
$324$	−7.57703e7	−0.123763
$325$	−8.15331e7	−0.131747
$326$	−6.68828e7	−0.106919
$327$	−1.22370e9	−1.93534
$328$	4.81238e7	0.0753011
$329$	2.65462e7	0.0410976
$330$	−3.35706e8	−0.514234
$331$	1.06044e9	1.60727	0.803635	−	0.595123i	$-0.202897\pi$
$331$	1.06044e9	1.60727	0.803635	+	0.595123i	$0.202897\pi$
$332$	−5.77142e8	−0.865565
$333$	1.48566e8	0.220477
$334$	−2.64119e8	−0.387871
$335$	1.60156e9	2.32748
$336$	−2.90023e8	−0.417105
$337$	3.67084e8	0.522469	0.261234	−	0.965275i	$-0.415870\pi$
$337$	3.67084e8	0.522469	0.261234	+	0.965275i	$0.415870\pi$
$338$	−1.83428e7	−0.0258378
$339$	−2.55661e8	−0.356423
$340$	3.12109e8	0.430655
$341$	3.14662e8	0.429738
$342$	6.92640e8	0.936302
$343$	4.03536e7	0.0539949
$344$	6.38923e8	0.846240
$345$	5.35569e8	0.702180
$346$	1.96070e7	0.0254475
$347$	4.72177e8	0.606669	0.303334	−	0.952884i	$-0.401900\pi$
$347$	4.72177e8	0.606669	0.303334	+	0.952884i	$0.401900\pi$
$348$	1.20416e9	1.53164
$349$	−1.30323e9	−1.64108	−0.820542	−	0.571587i	$-0.806328\pi$
$349$	−1.30323e9	−1.64108	−0.820542	+	0.571587i	$0.806328\pi$
$350$	−4.83729e7	−0.0603065
$351$	2.49629e8	0.308120
$352$	−5.42221e8	−0.662639
$353$	−3.12446e8	−0.378063	−0.189031	−	0.981971i	$-0.560535\pi$
$353$	−3.12446e8	−0.378063	−0.189031	+	0.981971i	$0.560535\pi$
$354$	−5.04567e8	−0.604515
$355$	−9.50301e8	−1.12736
$356$	1.43557e9	1.68635
$357$	−2.12558e8	−0.247252
$358$	3.34494e8	0.385299
$359$	−2.07105e8	−0.236244	−0.118122	−	0.992999i	$-0.537687\pi$
$359$	−2.07105e8	−0.236244	−0.118122	+	0.992999i	$0.537687\pi$
$360$	−1.14409e9	−1.29242
$361$	1.57061e9	1.75708
$362$	1.22764e8	0.136016
$363$	6.06793e8	0.665836
$364$	8.55745e7	0.0930014
$365$	1.07479e9	1.15690
$366$	7.86823e8	0.838867
$367$	−8.40606e8	−0.887690	−0.443845	−	0.896104i	$-0.646386\pi$
$367$	−8.40606e8	−0.887690	−0.443845	+	0.896104i	$0.646386\pi$
$368$	2.27707e8	0.238182
$369$	1.92475e8	0.199426
$370$	5.22007e7	0.0535760
$371$	−2.34047e8	−0.237954
$372$	8.04429e8	0.810191
$373$	1.82593e9	1.82181	0.910903	−	0.412621i	$-0.135387\pi$
$373$	1.82593e9	1.82181	0.910903	+	0.412621i	$0.135387\pi$
$374$	−1.04608e8	−0.103398
$375$	−1.06566e9	−1.04354
$376$	7.10453e7	0.0689251
$377$	−3.04369e8	−0.292554
$378$	1.48103e8	0.141040
$379$	−1.61714e8	−0.152584	−0.0762922	−	0.997086i	$-0.524308\pi$
$379$	−1.61714e8	−0.152584	−0.0762922	+	0.997086i	$0.524308\pi$
$380$	−1.91371e9	−1.78910
$381$	3.57058e8	0.330751
$382$	7.84472e7	0.0720038
$383$	−2.65588e8	−0.241553	−0.120777	−	0.992680i	$-0.538539\pi$
$383$	−2.65588e8	−0.241553	−0.120777	+	0.992680i	$0.538539\pi$
$384$	−1.79748e9	−1.61996
$385$	−3.95874e8	−0.353545
$386$	1.26126e8	0.111622
$387$	2.55542e9	2.24116
$388$	−1.17701e9	−1.02299
$389$	−1.41972e8	−0.122287	−0.0611434	−	0.998129i	$-0.519475\pi$
$389$	−1.41972e8	−0.122287	−0.0611434	+	0.998129i	$0.519475\pi$
$390$	2.16931e8	0.185180
$391$	1.66886e8	0.141189
$392$	1.07998e8	0.0905553
$393$	3.90218e9	3.24290
$394$	7.44177e8	0.612970
$395$	−7.26396e8	−0.593040
$396$	−1.41752e9	−1.14709
$397$	−7.22873e8	−0.579823	−0.289912	−	0.957053i	$-0.593626\pi$
$397$	−7.22873e8	−0.579823	−0.289912	+	0.957053i	$0.593626\pi$
$398$	−7.72888e8	−0.614506
$399$	1.30331e9	1.02717
$400$	4.09968e8	0.320288
$401$	−8.71880e8	−0.675229	−0.337615	−	0.941284i	$-0.609620\pi$
$401$	−8.71880e8	−0.675229	−0.337615	+	0.941284i	$0.609620\pi$
$402$	−1.37229e9	−1.05355
$403$	−2.03332e8	−0.154753
$404$	−5.49228e8	−0.414398
$405$	−2.26503e8	−0.169426
$406$	−1.80580e8	−0.133915
$407$	1.37577e8	0.101150
$408$	−5.68867e8	−0.414668
$409$	−1.03396e9	−0.747263	−0.373632	−	0.927577i	$-0.621888\pi$
$409$	−1.03396e9	−0.747263	−0.373632	+	0.927577i	$0.621888\pi$
$410$	6.76288e7	0.0484605
$411$	−4.09481e8	−0.290929
$412$	−1.42295e9	−1.00242
$413$	−5.94999e8	−0.415615
$414$	−2.87590e8	−0.199192
$415$	−1.72527e9	−1.18492
$416$	3.50379e8	0.238622
$417$	4.37866e9	2.95709
$418$	6.41410e8	0.429555
$419$	9.75703e8	0.647990	0.323995	−	0.946059i	$-0.394974\pi$
$419$	9.75703e8	0.647990	0.323995	+	0.946059i	$0.394974\pi$
$420$	−1.01205e9	−0.666543
$421$	−1.34931e9	−0.881299	−0.440649	−	0.897679i	$-0.645252\pi$
$421$	−1.34931e9	−0.881299	−0.440649	+	0.897679i	$0.645252\pi$
$422$	−2.39107e8	−0.154881
$423$	2.84151e8	0.182540
$424$	−6.26376e8	−0.399075
$425$	3.00466e8	0.189860
$426$	8.14261e8	0.510305
$427$	9.27843e8	0.576736
$428$	2.31377e8	0.142649
$429$	5.71730e8	0.349615
$430$	8.97883e8	0.544603
$431$	1.24186e8	0.0747143	0.0373572	−	0.999302i	$-0.488106\pi$
$431$	1.24186e8	0.0747143	0.0373572	+	0.999302i	$0.488106\pi$
$432$	−1.25520e9	−0.749063
$433$	1.58640e9	0.939083	0.469542	−	0.882910i	$-0.344419\pi$
$433$	1.58640e9	0.939083	0.469542	+	0.882910i	$0.344419\pi$
$434$	−1.20635e8	−0.0708369
$435$	3.59962e9	2.09674
$436$	−1.81553e9	−1.04906
$437$	−1.02327e9	−0.586552
$438$	−9.20927e8	−0.523680
$439$	−5.98873e8	−0.337838	−0.168919	−	0.985630i	$-0.554028\pi$
$439$	−5.98873e8	−0.337838	−0.168919	+	0.985630i	$0.554028\pi$
$440$	−1.05947e9	−0.592933
$441$	4.31945e8	0.239825
$442$	6.75968e7	0.0372347
$443$	3.01012e9	1.64502	0.822508	−	0.568754i	$-0.192574\pi$
$443$	3.01012e9	1.64502	0.822508	+	0.568754i	$0.192574\pi$
$444$	3.51714e8	0.190700
$445$	4.29138e9	2.30854
$446$	−4.28548e8	−0.228732
$447$	4.09134e9	2.16665
$448$	−2.77133e8	−0.145618
$449$	−3.22007e9	−1.67881	−0.839407	−	0.543503i	$-0.817098\pi$
$449$	−3.22007e9	−1.67881	−0.839407	+	0.543503i	$0.817098\pi$
$450$	−5.17784e8	−0.267858
$451$	1.78239e8	0.0914922
$452$	−3.79308e8	−0.193200
$453$	4.12189e6	0.00208330
$454$	−4.05051e7	−0.0203149
$455$	2.55811e8	0.127315
$456$	3.48804e9	1.72268
$457$	2.83525e9	1.38958	0.694792	−	0.719211i	$-0.255496\pi$
$457$	2.83525e9	1.38958	0.694792	+	0.719211i	$0.255496\pi$
$458$	8.93662e8	0.434654
$459$	−9.19933e8	−0.444030
$460$	7.94590e8	0.380619
$461$	−3.20816e9	−1.52512	−0.762558	−	0.646920i	$-0.776057\pi$
$461$	−3.20816e9	−1.52512	−0.762558	+	0.646920i	$0.776057\pi$
$462$	3.39203e8	0.160034
$463$	−8.94081e8	−0.418642	−0.209321	−	0.977847i	$-0.567125\pi$
$463$	−8.94081e8	−0.418642	−0.209321	+	0.977847i	$0.567125\pi$
$464$	1.53044e9	0.711221
$465$	2.40470e9	1.10911
$466$	−1.32397e9	−0.606079
$467$	−7.58084e8	−0.344436	−0.172218	−	0.985059i	$-0.555093\pi$
$467$	−7.58084e8	−0.344436	−0.172218	+	0.985059i	$0.555093\pi$
$468$	9.15990e8	0.413076
$469$	−1.61824e9	−0.724333
$470$	9.98405e7	0.0443572
$471$	5.71594e9	2.52066
$472$	−1.59239e9	−0.697031
$473$	2.36641e9	1.02820
$474$	6.22409e8	0.268443
$475$	−1.84232e9	−0.788748
$476$	−3.15359e8	−0.134024
$477$	−2.50524e9	−1.05690
$478$	−3.54526e8	−0.148474
$479$	−4.43815e9	−1.84513	−0.922567	−	0.385838i	$-0.873912\pi$
$479$	−4.43815e9	−1.84513	−0.922567	+	0.385838i	$0.873912\pi$
$480$	−4.14376e9	−1.71021
$481$	−8.89012e7	−0.0364250
$482$	−8.99057e8	−0.365698
$483$	−5.41147e8	−0.218525
$484$	9.00260e8	0.360919
$485$	−3.51848e9	−1.40042
$486$	−7.50239e8	−0.296465
$487$	3.04352e9	1.19405	0.597027	−	0.802221i	$-0.296348\pi$
$487$	3.04352e9	1.19405	0.597027	+	0.802221i	$0.296348\pi$
$488$	2.48318e9	0.967248
$489$	−1.34711e9	−0.520980
$490$	1.51770e8	0.0582775
$491$	−5.11802e9	−1.95127	−0.975634	−	0.219402i	$-0.929589\pi$
$491$	−5.11802e9	−1.95127	−0.975634	+	0.219402i	$0.929589\pi$
$492$	4.55665e8	0.172491
$493$	1.12166e9	0.421598
$494$	−4.14474e8	−0.154687
$495$	−4.23744e9	−1.57031
$496$	1.02240e9	0.376215
$497$	9.60198e8	0.350844
$498$	1.47829e9	0.536360
$499$	−1.85528e8	−0.0668434	−0.0334217	−	0.999441i	$-0.510640\pi$
$499$	−1.85528e8	−0.0668434	−0.0334217	+	0.999441i	$0.510640\pi$
$500$	−1.58105e9	−0.565654
$501$	−5.31971e9	−1.88997
$502$	−6.30294e8	−0.222372
$503$	4.86650e8	0.170502	0.0852509	−	0.996360i	$-0.472831\pi$
$503$	4.86650e8	0.170502	0.0852509	+	0.996360i	$0.472831\pi$
$504$	1.15601e9	0.402212
$505$	−1.64182e9	−0.567292
$506$	−2.66319e8	−0.0913851
$507$	−3.69447e8	−0.125900
$508$	5.29744e8	0.179285
$509$	4.07911e9	1.37105	0.685525	−	0.728049i	$-0.259573\pi$
$509$	4.07911e9	1.37105	0.685525	+	0.728049i	$0.259573\pi$
$510$	−7.99434e8	−0.266862
$511$	−1.08598e9	−0.360039
$512$	−3.05982e9	−1.00751
$513$	5.64062e9	1.84466
$514$	1.50406e9	0.488532
$515$	−4.25367e9	−1.37227
$516$	6.04970e9	1.93847
$517$	2.63134e8	0.0837452
$518$	−5.27444e7	−0.0166733
$519$	3.94911e8	0.123998
$520$	6.84623e8	0.213520
$521$	−1.01981e9	−0.315927	−0.157963	−	0.987445i	$-0.550493\pi$
$521$	−1.01981e9	−0.315927	−0.157963	+	0.987445i	$0.550493\pi$
$522$	−1.93293e9	−0.594797
$523$	−4.78076e9	−1.46131	−0.730653	−	0.682749i	$-0.760784\pi$
$523$	−4.78076e9	−1.46131	−0.730653	+	0.682749i	$0.760784\pi$
$524$	5.78942e9	1.75782
$525$	−9.74294e8	−0.293855
$526$	1.99120e8	0.0596575
$527$	7.49319e8	0.223013
$528$	−2.87480e9	−0.849941
$529$	−2.97995e9	−0.875215
$530$	−8.80252e8	−0.256827
$531$	−6.36887e9	−1.84600
$532$	1.93364e9	0.556783
$533$	−1.15176e8	−0.0329472
$534$	−3.67705e9	−1.04497
$535$	6.91663e8	0.195279
$536$	−4.33088e9	−1.21478
$537$	6.73715e9	1.87744
$538$	1.06470e9	0.294774
$539$	3.99997e8	0.110026
$540$	−4.38005e9	−1.19702
$541$	−5.96266e8	−0.161901	−0.0809505	−	0.996718i	$-0.525796\pi$
$541$	−5.96266e8	−0.161901	−0.0809505	+	0.996718i	$0.525796\pi$
$542$	−1.27650e9	−0.344370
$543$	2.47263e9	0.662765
$544$	−1.29122e9	−0.343877
$545$	−5.42722e9	−1.43612
$546$	−2.19190e8	−0.0576297
$547$	−3.57892e9	−0.934967	−0.467484	−	0.884002i	$-0.654839\pi$
$547$	−3.57892e9	−0.934967	−0.467484	+	0.884002i	$0.654839\pi$
$548$	−6.07522e8	−0.157699
$549$	9.93164e9	2.56164
$550$	−4.79487e8	−0.122887
$551$	−6.87754e9	−1.75147
$552$	−1.44827e9	−0.366489
$553$	7.33962e8	0.184559
$554$	−2.05255e9	−0.512871
$555$	1.05139e9	0.261059
$556$	6.49635e9	1.60290
$557$	−1.71021e7	−0.00419331	−0.00209665	−	0.999998i	$-0.500667\pi$
$557$	−1.71021e7	−0.00419331	−0.00209665	+	0.999998i	$0.500667\pi$
$558$	−1.29128e9	−0.314630
$559$	−1.52915e9	−0.370263
$560$	−1.28628e9	−0.309512
$561$	−2.10694e9	−0.503828
$562$	1.69250e9	0.402210
$563$	5.27373e9	1.24548	0.622742	−	0.782427i	$-0.286019\pi$
$563$	5.27373e9	1.24548	0.622742	+	0.782427i	$0.286019\pi$
$564$	6.72699e8	0.157886
$565$	−1.13388e9	−0.264482
$566$	−1.50312e8	−0.0348447
$567$	2.28862e8	0.0527269
$568$	2.56977e9	0.588402
$569$	−6.49997e9	−1.47917	−0.739585	−	0.673063i	$-0.764978\pi$
$569$	−6.49997e9	−1.47917	−0.739585	+	0.673063i	$0.764978\pi$
$570$	4.90178e9	1.10864
$571$	−5.10445e8	−0.114742	−0.0573710	−	0.998353i	$-0.518272\pi$
$571$	−5.10445e8	−0.114742	−0.0573710	+	0.998353i	$0.518272\pi$
$572$	8.48240e8	0.189510
$573$	1.58003e9	0.350852
$574$	−6.83332e7	−0.0150813
$575$	7.64949e8	0.167801
$576$	−2.96644e9	−0.646780
$577$	6.35150e9	1.37645	0.688226	−	0.725496i	$-0.258390\pi$
$577$	6.35150e9	1.37645	0.688226	+	0.725496i	$0.258390\pi$
$578$	1.31025e9	0.282233
$579$	2.54035e9	0.543900
$580$	5.34054e9	1.13655
$581$	1.74324e9	0.368757
$582$	3.01479e9	0.633909
$583$	−2.31994e9	−0.484883
$584$	−2.90640e9	−0.603824
$585$	2.73820e9	0.565482
$586$	2.59716e9	0.533159
$587$	1.23731e7	0.00252491	0.00126245	−	0.999999i	$-0.499598\pi$
$587$	1.23731e7	0.00252491	0.00126245	+	0.999999i	$0.499598\pi$
$588$	1.02259e9	0.207434
$589$	−4.59450e9	−0.926476
$590$	−2.23780e9	−0.448579
$591$	1.49887e10	2.98681
$592$	4.47017e8	0.0885520
$593$	−1.09632e7	−0.00215898	−0.00107949	−	0.999999i	$-0.500344\pi$
$593$	−1.09632e7	−0.00215898	−0.00107949	+	0.999999i	$0.500344\pi$
$594$	1.46804e9	0.287399
$595$	−9.42714e8	−0.183472
$596$	6.07007e9	1.17444
$597$	−1.55670e10	−2.99429
$598$	1.72093e8	0.0329086
$599$	−4.01930e9	−0.764111	−0.382055	−	0.924139i	$-0.624784\pi$
$599$	−4.01930e9	−0.764111	−0.382055	+	0.924139i	$0.624784\pi$
$600$	−2.60749e9	−0.492826
$601$	1.98736e9	0.373436	0.186718	−	0.982414i	$-0.440215\pi$
$601$	1.98736e9	0.373436	0.186718	+	0.982414i	$0.440215\pi$
$602$	−9.07235e8	−0.169485
$603$	−1.73217e10	−3.21721
$604$	6.11539e6	0.00112926
$605$	2.69118e9	0.494081
$606$	1.40679e9	0.256788
$607$	7.82981e9	1.42099	0.710495	−	0.703703i	$-0.248471\pi$
$607$	7.82981e9	1.42099	0.710495	+	0.703703i	$0.248471\pi$
$608$	7.91718e9	1.42859
$609$	−3.63712e9	−0.652524
$610$	3.48963e9	0.622479
$611$	−1.70035e8	−0.0301574
$612$	−3.37561e9	−0.595281
$613$	−8.53356e9	−1.49630	−0.748150	−	0.663530i	$-0.769058\pi$
$613$	−8.53356e9	−1.49630	−0.748150	+	0.663530i	$0.769058\pi$
$614$	−1.75851e9	−0.306589
$615$	1.36213e9	0.236133
$616$	1.07051e9	0.184526
$617$	7.29223e9	1.24986	0.624932	−	0.780680i	$-0.285127\pi$
$617$	7.29223e9	1.24986	0.624932	+	0.780680i	$0.285127\pi$
$618$	3.64473e9	0.621164
$619$	2.06975e9	0.350752	0.175376	−	0.984501i	$-0.443886\pi$
$619$	2.06975e9	0.350752	0.175376	+	0.984501i	$0.443886\pi$
$620$	3.56771e9	0.601200
$621$	−2.34204e9	−0.392440
$622$	8.03779e8	0.133928
$623$	−4.33608e9	−0.718437
$624$	1.85767e9	0.306072
$625$	−7.62559e9	−1.24938
$626$	4.07052e9	0.663192
$627$	1.29188e10	2.09309
$628$	8.48038e9	1.36633
$629$	3.27619e8	0.0524919
$630$	1.62455e9	0.258846
$631$	−4.58145e9	−0.725940	−0.362970	−	0.931801i	$-0.618237\pi$
$631$	−4.58145e9	−0.725940	−0.362970	+	0.931801i	$0.618237\pi$
$632$	1.96429e9	0.309526
$633$	−4.81594e9	−0.754689
$634$	3.49955e9	0.545380
$635$	1.58358e9	0.245433
$636$	−5.93090e9	−0.914157
$637$	−2.58475e8	−0.0396214
$638$	−1.78996e9	−0.272880
$639$	1.02780e10	1.55831
$640$	−7.97196e9	−1.20209
$641$	−6.97916e9	−1.04665	−0.523323	−	0.852134i	$-0.675308\pi$
$641$	−6.97916e9	−1.04665	−0.523323	+	0.852134i	$0.675308\pi$
$642$	−5.92648e8	−0.0883943
$643$	1.79438e9	0.266180	0.133090	−	0.991104i	$-0.457510\pi$
$643$	1.79438e9	0.266180	0.133090	+	0.991104i	$0.457510\pi$
$644$	−8.02866e8	−0.118452
$645$	1.80846e10	2.65368
$646$	1.52742e9	0.222918
$647$	−8.25623e9	−1.19844	−0.599221	−	0.800584i	$-0.704523\pi$
$647$	−8.25623e9	−1.19844	−0.599221	+	0.800584i	$0.704523\pi$
$648$	6.12500e8	0.0884288
$649$	−5.89781e9	−0.846904
$650$	3.09840e8	0.0442529
$651$	−2.42975e9	−0.345166
$652$	−1.99862e9	−0.282399
$653$	−3.61339e9	−0.507830	−0.253915	−	0.967227i	$-0.581718\pi$
$653$	−3.61339e9	−0.507830	−0.253915	+	0.967227i	$0.581718\pi$
$654$	4.65028e9	0.650066
$655$	1.73065e10	2.40638
$656$	5.79135e8	0.0800970
$657$	−1.16244e10	−1.59915
$658$	−1.00880e8	−0.0138044
$659$	−7.46935e9	−1.01668	−0.508339	−	0.861157i	$-0.669740\pi$
$659$	−7.46935e9	−1.01668	−0.508339	+	0.861157i	$0.669740\pi$
$660$	−1.00317e10	−1.35822
$661$	9.47073e8	0.127549	0.0637747	−	0.997964i	$-0.479686\pi$
$661$	9.47073e8	0.127549	0.0637747	+	0.997964i	$0.479686\pi$
$662$	−4.02987e9	−0.539869
$663$	1.36149e9	0.181433
$664$	4.66541e9	0.618445
$665$	5.78031e9	0.762211
$666$	−5.64576e8	−0.0740564
$667$	2.85561e9	0.372614
$668$	−7.89252e9	−1.02447
$669$	−8.63152e9	−1.11454
$670$	−6.08622e9	−0.781783
$671$	9.19706e9	1.17522
$672$	4.18692e9	0.532233
$673$	3.21500e9	0.406563	0.203282	−	0.979120i	$-0.434839\pi$
$673$	3.21500e9	0.406563	0.203282	+	0.979120i	$0.434839\pi$
$674$	−1.39498e9	−0.175493
$675$	−4.21666e9	−0.527722
$676$	−5.48126e8	−0.0682444
$677$	1.46998e10	1.82075	0.910375	−	0.413785i	$-0.135793\pi$
$677$	1.46998e10	1.82075	0.910375	+	0.413785i	$0.135793\pi$
$678$	9.71558e8	0.119719
$679$	3.55513e9	0.435824
$680$	−2.52297e9	−0.307703
$681$	−8.15826e8	−0.0989881
$682$	−1.19577e9	−0.144345
$683$	5.76686e9	0.692575	0.346288	−	0.938128i	$-0.387442\pi$
$683$	5.76686e9	0.692575	0.346288	+	0.938128i	$0.387442\pi$
$684$	2.06977e10	2.47301
$685$	−1.81608e9	−0.215883
$686$	−1.53351e8	−0.0181365
$687$	1.79995e10	2.11793
$688$	7.68897e9	0.900137
$689$	1.49913e9	0.174611
$690$	−2.03526e9	−0.235857
$691$	−1.39416e10	−1.60746	−0.803728	−	0.594997i	$-0.797153\pi$
$691$	−1.39416e10	−1.60746	−0.803728	+	0.594997i	$0.797153\pi$
$692$	5.85905e8	0.0672134
$693$	4.28157e9	0.488694
$694$	−1.79436e9	−0.203775
$695$	1.94197e10	2.19430
$696$	−9.73397e9	−1.09435
$697$	4.24448e8	0.0474799
$698$	4.95249e9	0.551226
$699$	−2.66666e10	−2.95323
$700$	−1.44550e9	−0.159285
$701$	−3.04175e9	−0.333511	−0.166756	−	0.985998i	$-0.553329\pi$
$701$	−3.04175e9	−0.333511	−0.166756	+	0.985998i	$0.553329\pi$
$702$	−9.48635e8	−0.103495
$703$	−2.00882e9	−0.218070
$704$	−2.74703e9	−0.296728
$705$	2.01092e9	0.216139
$706$	1.18735e9	0.126988
$707$	1.65892e9	0.176546
$708$	−1.50777e10	−1.59668
$709$	−1.01521e10	−1.06978	−0.534892	−	0.844920i	$-0.679648\pi$
$709$	−1.01521e10	−1.06978	−0.534892	+	0.844920i	$0.679648\pi$
$710$	3.61132e9	0.378670
$711$	7.85633e9	0.819740
$712$	−1.16046e10	−1.20490
$713$	1.90767e9	0.197102
$714$	8.07760e8	0.0830498
$715$	2.53567e9	0.259431
$716$	9.99549e9	1.01767
$717$	−7.14062e9	−0.723467
$718$	7.87038e8	0.0793524
$719$	8.36403e9	0.839198	0.419599	−	0.907709i	$-0.362171\pi$
$719$	8.36403e9	0.839198	0.419599	+	0.907709i	$0.362171\pi$
$720$	−1.37683e10	−1.37473
$721$	4.29797e9	0.427061
$722$	−5.96859e9	−0.590190
$723$	−1.81082e10	−1.78193
$724$	3.66848e9	0.359254
$725$	5.14132e9	0.501062
$726$	−2.30592e9	−0.223649
$727$	−4.99911e8	−0.0482528	−0.0241264	−	0.999709i	$-0.507680\pi$
$727$	−4.99911e8	−0.0482528	−0.0241264	+	0.999709i	$0.507680\pi$
$728$	−6.91753e8	−0.0664494
$729$	−1.65701e10	−1.58408
$730$	−4.08439e9	−0.388595
$731$	5.63525e9	0.533583
$732$	2.35122e10	2.21566
$733$	−1.16182e8	−0.0108962	−0.00544811	−	0.999985i	$-0.501734\pi$
$733$	−1.16182e8	−0.0108962	−0.00544811	+	0.999985i	$0.501734\pi$
$734$	3.19446e9	0.298168
$735$	3.05685e9	0.283968
$736$	−3.28728e9	−0.303924
$737$	−1.60405e10	−1.47598
$738$	−7.31439e8	−0.0669855
$739$	6.85800e9	0.625090	0.312545	−	0.949903i	$-0.398819\pi$
$739$	6.85800e9	0.625090	0.312545	+	0.949903i	$0.398819\pi$
$740$	1.55988e9	0.141508
$741$	−8.34805e9	−0.753739
$742$	8.89420e8	0.0799269
$743$	−1.01255e10	−0.905643	−0.452822	−	0.891601i	$-0.649583\pi$
$743$	−1.01255e10	−0.905643	−0.452822	+	0.891601i	$0.649583\pi$
$744$	−6.50271e9	−0.578881
$745$	1.81455e10	1.60776
$746$	−6.93885e9	−0.611930
$747$	1.86596e10	1.63788
$748$	−3.12594e9	−0.273102
$749$	−6.98867e8	−0.0607726
$750$	4.04969e9	0.350516
$751$	−1.28118e10	−1.10375	−0.551873	−	0.833928i	$-0.686087\pi$
$751$	−1.28118e10	−1.10375	−0.551873	+	0.833928i	$0.686087\pi$
$752$	8.54978e8	0.0733150
$753$	−1.26949e10	−1.08355
$754$	1.15666e9	0.0982665
$755$	1.82809e7	0.00154591
$756$	4.42567e9	0.372523
$757$	3.94851e9	0.330824	0.165412	−	0.986225i	$-0.447105\pi$
$757$	3.94851e9	0.330824	0.165412	+	0.986225i	$0.447105\pi$
$758$	6.14542e8	0.0512518
$759$	−5.36401e9	−0.445291
$760$	1.54698e10	1.27831
$761$	8.86888e9	0.729495	0.364748	−	0.931106i	$-0.381155\pi$
$761$	8.86888e9	0.729495	0.364748	+	0.931106i	$0.381155\pi$
$762$	−1.35688e9	−0.111097
$763$	5.48374e9	0.446932
$764$	2.34419e9	0.190181
$765$	−1.00908e10	−0.814913
$766$	1.00928e9	0.0811358
$767$	3.81111e9	0.304978
$768$	−1.08510e9	−0.0864380
$769$	−2.95572e9	−0.234380	−0.117190	−	0.993110i	$-0.537389\pi$
$769$	−2.95572e9	−0.234380	−0.117190	+	0.993110i	$0.537389\pi$
$770$	1.50439e9	0.118753
$771$	3.02937e10	2.38046
$772$	3.76896e9	0.294823
$773$	−2.21264e10	−1.72299	−0.861493	−	0.507769i	$-0.830470\pi$
$773$	−2.21264e10	−1.72299	−0.861493	+	0.507769i	$0.830470\pi$
$774$	−9.71105e9	−0.752788
$775$	3.43462e9	0.265047
$776$	9.51454e9	0.730923
$777$	−1.06234e9	−0.0812438
$778$	5.39520e8	0.0410751
$779$	−2.60253e9	−0.197249
$780$	6.48241e9	0.489109
$781$	9.51778e9	0.714919
$782$	−6.34198e8	−0.0474243
$783$	−1.57411e10	−1.17184
$784$	1.29968e9	0.0963227
$785$	2.53507e10	1.87045
$786$	−1.48290e10	−1.08926
$787$	−1.42586e10	−1.04272	−0.521359	−	0.853338i	$-0.674575\pi$
$787$	−1.42586e10	−1.04272	−0.521359	+	0.853338i	$0.674575\pi$
$788$	2.22378e10	1.61901
$789$	4.01054e9	0.290692
$790$	2.76044e9	0.199197
$791$	1.14569e9	0.0823092
$792$	1.14587e10	0.819592
$793$	−5.94307e9	−0.423208
$794$	2.74705e9	0.194758
$795$	−1.77294e10	−1.25144
$796$	−2.30958e10	−1.62307
$797$	1.04574e10	0.731678	0.365839	−	0.930678i	$-0.380782\pi$
$797$	1.04574e10	0.731678	0.365839	+	0.930678i	$0.380782\pi$
$798$	−4.95283e9	−0.345019
$799$	6.26614e8	0.0434596
$800$	−5.91850e9	−0.408692
$801$	−4.64134e10	−3.19102
$802$	3.31330e9	0.226804
$803$	−1.07646e10	−0.733656
$804$	−4.10073e10	−2.78269
$805$	−2.40003e9	−0.162156
$806$	7.72698e8	0.0519801
$807$	2.14445e10	1.43634
$808$	4.43976e9	0.296087
$809$	1.34180e10	0.890977	0.445489	−	0.895288i	$-0.353030\pi$
$809$	1.34180e10	0.890977	0.445489	+	0.895288i	$0.353030\pi$
$810$	8.60751e8	0.0569089
$811$	−2.09601e9	−0.137981	−0.0689905	−	0.997617i	$-0.521978\pi$
$811$	−2.09601e9	−0.137981	−0.0689905	+	0.997617i	$0.521978\pi$
$812$	−5.39616e9	−0.353703
$813$	−2.57105e10	−1.67801
$814$	−5.22818e8	−0.0339755
$815$	−5.97454e9	−0.386592
$816$	−6.84590e9	−0.441078
$817$	−3.45528e10	−2.21670
$818$	3.92925e9	0.251000
$819$	−2.76672e9	−0.175983
$820$	2.02091e9	0.127997
$821$	−2.80182e10	−1.76701	−0.883505	−	0.468421i	$-0.844823\pi$
$821$	−2.80182e10	−1.76701	−0.883505	+	0.468421i	$0.844823\pi$
$822$	1.55610e9	0.0977208
$823$	−1.74157e10	−1.08903	−0.544516	−	0.838750i	$-0.683287\pi$
$823$	−1.74157e10	−1.08903	−0.544516	+	0.838750i	$0.683287\pi$
$824$	1.15026e10	0.716227
$825$	−9.65750e9	−0.598792
$826$	2.26110e9	0.139602
$827$	1.17896e9	0.0724818	0.0362409	−	0.999343i	$-0.488462\pi$
$827$	1.17896e9	0.0724818	0.0362409	+	0.999343i	$0.488462\pi$
$828$	−8.59388e9	−0.526118
$829$	2.62554e10	1.60058	0.800292	−	0.599610i	$-0.204678\pi$
$829$	2.62554e10	1.60058	0.800292	+	0.599610i	$0.204678\pi$
$830$	6.55634e9	0.398005
$831$	−4.13410e10	−2.49906
$832$	1.77511e9	0.106855
$833$	9.52533e8	0.0570982
$834$	−1.66397e10	−0.993264
$835$	−2.35934e10	−1.40245
$836$	1.91669e10	1.13456
$837$	−1.05157e10	−0.619870
$838$	−3.70785e9	−0.217655
$839$	1.55887e10	0.911264	0.455632	−	0.890168i	$-0.349413\pi$
$839$	1.55887e10	0.911264	0.455632	+	0.890168i	$0.349413\pi$
$840$	8.18102e9	0.476245
$841$	1.94306e9	0.112642
$842$	5.12761e9	0.296021
$843$	3.40893e10	1.95984
$844$	−7.14511e9	−0.409082
$845$	−1.63853e9	−0.0934234
$846$	−1.07982e9	−0.0613136
$847$	−2.71921e9	−0.153762
$848$	−7.53798e9	−0.424492
$849$	−3.02749e9	−0.169787
$850$	−1.14183e9	−0.0637725
$851$	8.34078e8	0.0463931
$852$	2.43321e10	1.34785
$853$	−2.08797e9	−0.115187	−0.0575933	−	0.998340i	$-0.518343\pi$
$853$	−2.08797e9	−0.115187	−0.0575933	+	0.998340i	$0.518343\pi$
$854$	−3.52597e9	−0.193721
$855$	6.18724e10	3.38544
$856$	−1.87037e9	−0.101922
$857$	1.54418e10	0.838039	0.419020	−	0.907977i	$-0.362374\pi$
$857$	1.54418e10	0.838039	0.419020	+	0.907977i	$0.362374\pi$
$858$	−2.17268e9	−0.117433
$859$	−1.06055e9	−0.0570896	−0.0285448	−	0.999593i	$-0.509087\pi$
$859$	−1.06055e9	−0.0570896	−0.0285448	+	0.999593i	$0.509087\pi$
$860$	2.68309e10	1.43844
$861$	−1.37632e9	−0.0734866
$862$	−4.71931e8	−0.0250959
$863$	9.61556e9	0.509257	0.254628	−	0.967039i	$-0.418047\pi$
$863$	9.61556e9	0.509257	0.254628	+	0.967039i	$0.418047\pi$
$864$	1.81206e10	0.955816
$865$	1.75146e9	0.0920121
$866$	−6.02860e9	−0.315430
$867$	2.63902e10	1.37523
$868$	−3.60487e9	−0.187099
$869$	7.27525e9	0.376079
$870$	−1.36792e10	−0.704278
$871$	1.03652e10	0.531515
$872$	1.46761e10	0.749553
$873$	3.80541e10	1.93576
$874$	3.88862e9	0.197018
$875$	4.77551e9	0.240986
$876$	−2.75195e10	−1.38317
$877$	−1.91278e9	−0.0957563	−0.0478781	−	0.998853i	$-0.515246\pi$
$877$	−1.91278e9	−0.0957563	−0.0478781	+	0.998853i	$0.515246\pi$
$878$	2.27582e9	0.113477
$879$	5.23102e10	2.59792
$880$	−1.27500e10	−0.630696
$881$	−1.14488e10	−0.564086	−0.282043	−	0.959402i	$-0.591012\pi$
$881$	−1.14488e10	−0.564086	−0.282043	+	0.959402i	$0.591012\pi$
$882$	−1.64147e9	−0.0805551
$883$	−9.61596e8	−0.0470035	−0.0235017	−	0.999724i	$-0.507482\pi$
$883$	−9.61596e8	−0.0470035	−0.0235017	+	0.999724i	$0.507482\pi$
$884$	2.01996e9	0.0983465
$885$	−4.50722e10	−2.18578
$886$	−1.14390e10	−0.552547
$887$	2.68603e10	1.29234	0.646171	−	0.763192i	$-0.276369\pi$
$887$	2.68603e10	1.29234	0.646171	+	0.763192i	$0.276369\pi$
$888$	−2.84313e9	−0.136255
$889$	−1.60008e9	−0.0763808
$890$	−1.63080e10	−0.775419
$891$	2.26855e9	0.107442
$892$	−1.28060e10	−0.604141
$893$	−3.84212e9	−0.180547
$894$	−1.55479e10	−0.727762
$895$	2.98798e10	1.39315
$896$	8.05499e9	0.374099
$897$	3.46618e9	0.160353
$898$	1.22368e10	0.563900
$899$	1.28217e10	0.588555
$900$	−1.54726e10	−0.707482
$901$	−5.52459e9	−0.251630
$902$	−6.77339e8	−0.0307315
$903$	−1.82729e10	−0.825849
$904$	3.06619e9	0.138041
$905$	1.09663e10	0.491803
$906$	−1.56639e7	−0.000699764 0
$907$	3.05483e10	1.35945	0.679723	−	0.733469i	$-0.262100\pi$
$907$	3.05483e10	1.35945	0.679723	+	0.733469i	$0.262100\pi$
$908$	−1.21039e9	−0.0536568
$909$	1.77571e10	0.784150
$910$	−9.72127e8	−0.0427640
$911$	−2.29762e10	−1.00685	−0.503423	−	0.864040i	$-0.667926\pi$
$911$	−2.29762e10	−1.00685	−0.503423	+	0.864040i	$0.667926\pi$
$912$	4.19760e10	1.83240
$913$	1.72795e10	0.751422
$914$	−1.07745e10	−0.466750
$915$	7.02857e10	3.03314
$916$	2.67048e10	1.14803
$917$	−1.74867e10	−0.748887
$918$	3.49591e9	0.149146
$919$	−8.52757e9	−0.362427	−0.181214	−	0.983444i	$-0.558003\pi$
$919$	−8.52757e9	−0.362427	−0.181214	+	0.983444i	$0.558003\pi$
$920$	−6.42318e9	−0.271952
$921$	−3.54188e10	−1.49391
$922$	1.21916e10	0.512274
$923$	−6.15031e9	−0.257449
$924$	1.01362e10	0.422691
$925$	1.50169e9	0.0623857
$926$	3.39767e9	0.140619
$927$	4.60055e10	1.89684
$928$	−2.20942e10	−0.907529
$929$	−8.26112e8	−0.0338052	−0.0169026	−	0.999857i	$-0.505381\pi$
$929$	−8.26112e8	−0.0338052	−0.0169026	+	0.999857i	$0.505381\pi$
$930$	−9.13832e9	−0.372543
$931$	−5.84051e9	−0.237207
$932$	−3.95636e10	−1.60081
$933$	1.61892e10	0.652588
$934$	2.88086e9	0.115693
$935$	−9.34447e9	−0.373864
$936$	−7.40453e9	−0.295143
$937$	−4.34340e10	−1.72481	−0.862404	−	0.506220i	$-0.831042\pi$
$937$	−4.34340e10	−1.72481	−0.862404	+	0.506220i	$0.831042\pi$
$938$	6.14961e9	0.243298
$939$	8.19856e10	3.23153
$940$	2.98348e9	0.117159
$941$	−8.99511e9	−0.351919	−0.175960	−	0.984397i	$-0.556303\pi$
$941$	−8.99511e9	−0.351919	−0.175960	+	0.984397i	$0.556303\pi$
$942$	−2.17216e10	−0.846669
$943$	1.08059e9	0.0419634
$944$	−1.91632e10	−0.741424
$945$	1.32298e10	0.509967
$946$	−8.99279e9	−0.345363
$947$	−1.79765e10	−0.687829	−0.343914	−	0.939001i	$-0.611753\pi$
$947$	−1.79765e10	−0.687829	−0.343914	+	0.939001i	$0.611753\pi$
$948$	1.85991e10	0.709027
$949$	6.95598e9	0.264196
$950$	7.00117e9	0.264934
$951$	7.04855e10	2.65747
$952$	2.54925e9	0.0957598
$953$	−2.08985e10	−0.782150	−0.391075	−	0.920359i	$-0.627897\pi$
$953$	−2.08985e10	−0.782150	−0.391075	+	0.920359i	$0.627897\pi$
$954$	9.52035e9	0.355004
$955$	7.00757e9	0.260349
$956$	−1.05941e10	−0.392158
$957$	−3.60522e10	−1.32966
$958$	1.68658e10	0.619765
$959$	1.83500e9	0.0671848
$960$	−2.09933e10	−0.765829
$961$	−1.89472e10	−0.688672
$962$	3.37841e8	0.0122349
$963$	−7.48067e9	−0.269928
$964$	−2.68660e10	−0.965902
$965$	1.12667e10	0.403599
$966$	2.05646e9	0.0734006
$967$	−2.58736e10	−0.920161	−0.460080	−	0.887877i	$-0.652179\pi$
$967$	−2.58736e10	−0.920161	−0.460080	+	0.887877i	$0.652179\pi$
$968$	−7.27738e9	−0.257876
$969$	3.07643e10	1.08621
$970$	1.33709e10	0.470390
$971$	−1.57586e10	−0.552395	−0.276197	−	0.961101i	$-0.589074\pi$
$971$	−1.57586e10	−0.552395	−0.276197	+	0.961101i	$0.589074\pi$
$972$	−2.24190e10	−0.783039
$973$	−1.96220e10	−0.682886
$974$	−1.15659e10	−0.401073
$975$	6.24059e9	0.215630
$976$	2.98832e10	1.02885
$977$	8.83147e9	0.302972	0.151486	−	0.988459i	$-0.451594\pi$
$977$	8.83147e9	0.302972	0.151486	+	0.988459i	$0.451594\pi$
$978$	5.11926e9	0.174993
$979$	−4.29805e10	−1.46397
$980$	4.53526e9	0.153926
$981$	5.86980e10	1.98510
$982$	1.94494e10	0.655415
$983$	−7.60217e9	−0.255270	−0.127635	−	0.991821i	$-0.540739\pi$
$983$	−7.60217e9	−0.255270	−0.127635	+	0.991821i	$0.540739\pi$
$984$	−3.68343e9	−0.123245
$985$	6.64761e10	2.21635
$986$	−4.26252e9	−0.141611
$987$	−2.03186e9	−0.0672643
$988$	−1.23855e10	−0.408567
$989$	1.43466e10	0.471588
$990$	1.61030e10	0.527454
$991$	−5.10651e10	−1.66673	−0.833367	−	0.552720i	$-0.813590\pi$
$991$	−5.10651e10	−1.66673	−0.833367	+	0.552720i	$0.813590\pi$
$992$	−1.47599e10	−0.480056
$993$	−8.11669e10	−2.63061
$994$	−3.64893e9	−0.117845
$995$	−6.90409e10	−2.22191
$996$	4.41749e10	1.41667
$997$	−1.53172e10	−0.489492	−0.244746	−	0.969587i	$-0.578705\pi$
$997$	−1.53172e10	−0.489492	−0.244746	+	0.969587i	$0.578705\pi$
$998$	7.05041e8	0.0224521
$999$	−4.59772e9	−0.145903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.c.1.5	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-3.80018 q^{2} -76.5407 q^{3} -113.559 q^{4} -339.464 q^{5} +290.868 q^{6} +343.000 q^{7} +917.967 q^{8} +3671.47 q^{9} +O(q^{10})\)	\(q-3.80018 q^{2} -76.5407 q^{3} -113.559 q^{4} -339.464 q^{5} +290.868 q^{6} +343.000 q^{7} +917.967 q^{8} +3671.47 q^{9} +1290.03 q^{10} +3399.92 q^{11} +8691.85 q^{12} -2197.00 q^{13} -1303.46 q^{14} +25982.8 q^{15} +11047.1 q^{16} +8096.39 q^{17} -13952.3 q^{18} -49643.5 q^{19} +38549.1 q^{20} -26253.4 q^{21} -12920.3 q^{22} +20612.4 q^{23} -70261.8 q^{24} +37111.1 q^{25} +8349.00 q^{26} -113623. q^{27} -38950.6 q^{28} +138539. q^{29} -98739.5 q^{30} +92549.8 q^{31} -159481. q^{32} -260232. q^{33} -30767.8 q^{34} -116436. q^{35} -416927. q^{36} +40464.8 q^{37} +188654. q^{38} +168160. q^{39} -311617. q^{40} +52424.4 q^{41} +99767.9 q^{42} +696019. q^{43} -386090. q^{44} -1.24633e6 q^{45} -78330.9 q^{46} +77394.2 q^{47} -845550. q^{48} +117649. q^{49} -141029. q^{50} -619703. q^{51} +249488. q^{52} -682352. q^{53} +431786. q^{54} -1.15415e6 q^{55} +314863. q^{56} +3.79975e6 q^{57} -526472. q^{58} -1.73469e6 q^{59} -2.95057e6 q^{60} +2.70508e6 q^{61} -351706. q^{62} +1.25932e6 q^{63} -807969. q^{64} +745803. q^{65} +988929. q^{66} -4.71791e6 q^{67} -919415. q^{68} -1.57769e6 q^{69} +442479. q^{70} +2.79941e6 q^{71} +3.37029e6 q^{72} -3.16613e6 q^{73} -153774. q^{74} -2.84051e6 q^{75} +5.63745e6 q^{76} +1.16617e6 q^{77} -639038. q^{78} +2.13983e6 q^{79} -3.75008e6 q^{80} +667235. q^{81} -199222. q^{82} +5.08233e6 q^{83} +2.98131e6 q^{84} -2.74844e6 q^{85} -2.64500e6 q^{86} -1.06038e7 q^{87} +3.12101e6 q^{88} -1.26416e7 q^{89} +4.73630e6 q^{90} -753571. q^{91} -2.34072e6 q^{92} -7.08382e6 q^{93} -294112. q^{94} +1.68522e7 q^{95} +1.22067e7 q^{96} +1.03648e7 q^{97} -447088. q^{98} +1.24827e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9} + 9420 q^{10} + 876 q^{11} - 8765 q^{12} - 21970 q^{13} - 6174 q^{14} - 5320 q^{15} + 41370 q^{16} + 6294 q^{17} - 16027 q^{18} - 97401 q^{19} - 166650 q^{20} - 27440 q^{21} + 74171 q^{22} - 15255 q^{23} + 196187 q^{24} + 162145 q^{25} + 39546 q^{26} - 181820 q^{27} + 229810 q^{28} - 340533 q^{29} - 325020 q^{30} - 148675 q^{31} - 642762 q^{32} - 624400 q^{33} - 1161518 q^{34} - 317961 q^{35} - 773917 q^{36} - 621782 q^{37} - 805092 q^{38} + 175760 q^{39} - 350478 q^{40} - 2043336 q^{41} - 486717 q^{42} - 1801391 q^{43} - 3953667 q^{44} - 1908807 q^{45} - 2707731 q^{46} - 1624701 q^{47} - 6068625 q^{48} + 1176490 q^{49} - 6891516 q^{50} + 1811700 q^{51} - 1471990 q^{52} - 199965 q^{53} - 2895913 q^{54} + 739086 q^{55} - 1673154 q^{56} + 2159088 q^{57} + 2071092 q^{58} - 8098908 q^{59} + 8096436 q^{60} + 2271618 q^{61} - 8910225 q^{62} + 1238916 q^{63} + 8099930 q^{64} + 2036619 q^{65} - 5999191 q^{66} + 1970272 q^{67} - 1766238 q^{68} - 4622962 q^{69} + 3231060 q^{70} - 7145820 q^{71} + 984975 q^{72} + 1409431 q^{73} - 5498643 q^{74} - 8857892 q^{75} - 2749534 q^{76} + 300468 q^{77} + 3117543 q^{78} - 9011055 q^{79} - 23850522 q^{80} + 11613490 q^{81} + 27962597 q^{82} - 15006567 q^{83} - 3006395 q^{84} - 9416628 q^{85} + 38357850 q^{86} - 15828996 q^{87} + 42205269 q^{88} - 11472777 q^{89} + 53425712 q^{90} - 7535710 q^{91} + 16755837 q^{92} + 36339848 q^{93} + 5133371 q^{94} + 29637939 q^{95} + 65329611 q^{96} + 3228571 q^{97} - 2117682 q^{98} + 19367194 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9 + 9420 * q^10 + 876 * q^11 - 8765 * q^12 - 21970 * q^13 - 6174 * q^14 - 5320 * q^15 + 41370 * q^16 + 6294 * q^17 - 16027 * q^18 - 97401 * q^19 - 166650 * q^20 - 27440 * q^21 + 74171 * q^22 - 15255 * q^23 + 196187 * q^24 + 162145 * q^25 + 39546 * q^26 - 181820 * q^27 + 229810 * q^28 - 340533 * q^29 - 325020 * q^30 - 148675 * q^31 - 642762 * q^32 - 624400 * q^33 - 1161518 * q^34 - 317961 * q^35 - 773917 * q^36 - 621782 * q^37 - 805092 * q^38 + 175760 * q^39 - 350478 * q^40 - 2043336 * q^41 - 486717 * q^42 - 1801391 * q^43 - 3953667 * q^44 - 1908807 * q^45 - 2707731 * q^46 - 1624701 * q^47 - 6068625 * q^48 + 1176490 * q^49 - 6891516 * q^50 + 1811700 * q^51 - 1471990 * q^52 - 199965 * q^53 - 2895913 * q^54 + 739086 * q^55 - 1673154 * q^56 + 2159088 * q^57 + 2071092 * q^58 - 8098908 * q^59 + 8096436 * q^60 + 2271618 * q^61 - 8910225 * q^62 + 1238916 * q^63 + 8099930 * q^64 + 2036619 * q^65 - 5999191 * q^66 + 1970272 * q^67 - 1766238 * q^68 - 4622962 * q^69 + 3231060 * q^70 - 7145820 * q^71 + 984975 * q^72 + 1409431 * q^73 - 5498643 * q^74 - 8857892 * q^75 - 2749534 * q^76 + 300468 * q^77 + 3117543 * q^78 - 9011055 * q^79 - 23850522 * q^80 + 11613490 * q^81 + 27962597 * q^82 - 15006567 * q^83 - 3006395 * q^84 - 9416628 * q^85 + 38357850 * q^86 - 15828996 * q^87 + 42205269 * q^88 - 11472777 * q^89 + 53425712 * q^90 - 7535710 * q^91 + 16755837 * q^92 + 36339848 * q^93 + 5133371 * q^94 + 29637939 * q^95 + 65329611 * q^96 + 3228571 * q^97 - 2117682 * q^98 + 19367194 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more