LMFDB - Embedded newform 37.8.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("37.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 1078 x^{9} + 4966 x^{8} + 379692 x^{7} - 1385588 x^{6} - 48765978 x^{5} + \cdots + 6680404080 $ x^11 - 5x^10 - 1078x^9 + 4966x^8 + 379692x^7 - 1385588x^6 - 48765978x^5 + 87529978x^4 + 2159400643x^3 - 1763707223x^2 - 25456347552x + 6680404080
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$4.43681$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.43681 q^{2} +85.9489 q^{3} -98.4411 q^{4} -143.945 q^{5} +467.288 q^{6} +1592.07 q^{7} -1231.12 q^{8} +5200.21 q^{9} +O(q^{10})$	\(q+5.43681 q^{2} +85.9489 q^{3} -98.4411 q^{4} -143.945 q^{5} +467.288 q^{6} +1592.07 q^{7} -1231.12 q^{8} +5200.21 q^{9} -782.599 q^{10} +6065.58 q^{11} -8460.90 q^{12} -1785.21 q^{13} +8655.77 q^{14} -12371.9 q^{15} +5907.11 q^{16} -24254.8 q^{17} +28272.5 q^{18} -9575.55 q^{19} +14170.1 q^{20} +136836. q^{21} +32977.4 q^{22} +77137.8 q^{23} -105813. q^{24} -57405.0 q^{25} -9705.85 q^{26} +258982. q^{27} -156725. q^{28} -143305. q^{29} -67263.5 q^{30} -283192. q^{31} +189699. q^{32} +521329. q^{33} -131869. q^{34} -229169. q^{35} -511914. q^{36} -50653.0 q^{37} -52060.4 q^{38} -153437. q^{39} +177213. q^{40} +5733.04 q^{41} +743954. q^{42} -106033. q^{43} -597102. q^{44} -748541. q^{45} +419384. q^{46} -93073.8 q^{47} +507709. q^{48} +1.71114e6 q^{49} -312100. q^{50} -2.08467e6 q^{51} +175738. q^{52} -1.28672e6 q^{53} +1.40803e6 q^{54} -873106. q^{55} -1.96002e6 q^{56} -823007. q^{57} -779120. q^{58} -543555. q^{59} +1.21790e6 q^{60} +1.26651e6 q^{61} -1.53966e6 q^{62} +8.27908e6 q^{63} +275247. q^{64} +256971. q^{65} +2.83437e6 q^{66} -2.77522e6 q^{67} +2.38767e6 q^{68} +6.62991e6 q^{69} -1.24595e6 q^{70} +449181. q^{71} -6.40206e6 q^{72} +1.86672e6 q^{73} -275391. q^{74} -4.93389e6 q^{75} +942627. q^{76} +9.65681e6 q^{77} -834207. q^{78} -4.91270e6 q^{79} -850296. q^{80} +1.08863e7 q^{81} +31169.4 q^{82} +1.36787e6 q^{83} -1.34703e7 q^{84} +3.49134e6 q^{85} -576480. q^{86} -1.23169e7 q^{87} -7.46744e6 q^{88} -2.42814e6 q^{89} -4.06968e6 q^{90} -2.84218e6 q^{91} -7.59353e6 q^{92} -2.43400e7 q^{93} -506025. q^{94} +1.37835e6 q^{95} +1.63044e7 q^{96} +7.89343e6 q^{97} +9.30314e6 q^{98} +3.15422e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 16 q^{2} + 121 q^{3} + 794 q^{4} + 376 q^{5} + 519 q^{6} + 2243 q^{7} + 3870 q^{8} + 9826 q^{9}+O(q^{10}) $ 11 * q + 16 * q^2 + 121 * q^3 + 794 * q^4 + 376 * q^5 + 519 * q^6 + 2243 * q^7 + 3870 * q^8 + 9826 * q^9	\( 11 q + 16 q^{2} + 121 q^{3} + 794 q^{4} + 376 q^{5} + 519 q^{6} + 2243 q^{7} + 3870 q^{8} + 9826 q^{9} - 12629 q^{10} + 9415 q^{11} + 27955 q^{12} + 12512 q^{13} + 18260 q^{14} + 25714 q^{15} + 167866 q^{16} + 54312 q^{17} + 163911 q^{18} + 97192 q^{19} + 85625 q^{20} + 97795 q^{21} - 12345 q^{22} + 107342 q^{23} + 163119 q^{24} + 165051 q^{25} + 61531 q^{26} + 446611 q^{27} + 215454 q^{28} + 41748 q^{29} - 1080964 q^{30} - 272248 q^{31} + 593306 q^{32} - 216525 q^{33} - 923600 q^{34} + 436814 q^{35} - 456119 q^{36} - 557183 q^{37} - 175872 q^{38} - 1587326 q^{39} - 3206863 q^{40} + 525465 q^{41} - 3814396 q^{42} - 1376086 q^{43} - 1337377 q^{44} - 2315492 q^{45} - 2037327 q^{46} + 2269179 q^{47} + 1779791 q^{48} + 2282536 q^{49} - 3881347 q^{50} - 103604 q^{51} - 4200495 q^{52} - 346415 q^{53} + 6349248 q^{54} + 4169374 q^{55} - 4307934 q^{56} + 6170792 q^{57} - 1334849 q^{58} + 4598828 q^{59} - 4448200 q^{60} + 6208418 q^{61} + 4732115 q^{62} + 6882994 q^{63} + 12483426 q^{64} + 9330160 q^{65} - 5715150 q^{66} + 2199016 q^{67} + 8095824 q^{68} + 13516268 q^{69} - 6471708 q^{70} + 4653285 q^{71} + 12839097 q^{72} - 1080699 q^{73} - 810448 q^{74} + 16194855 q^{75} + 1331888 q^{76} + 22058153 q^{77} - 23968103 q^{78} - 1336084 q^{79} - 89443 q^{80} + 9585355 q^{81} + 9689125 q^{82} + 28551309 q^{83} - 37602282 q^{84} + 13256012 q^{85} - 47733694 q^{86} - 5826578 q^{87} - 58704117 q^{88} - 8994788 q^{89} - 46526086 q^{90} - 696642 q^{91} - 41894465 q^{92} - 9859184 q^{93} - 26180048 q^{94} + 124152 q^{95} - 19485621 q^{96} - 3968264 q^{97} - 7312590 q^{98} - 14172918 q^{99}+O(q^{100}) \) 11 * q + 16 * q^2 + 121 * q^3 + 794 * q^4 + 376 * q^5 + 519 * q^6 + 2243 * q^7 + 3870 * q^8 + 9826 * q^9 - 12629 * q^10 + 9415 * q^11 + 27955 * q^12 + 12512 * q^13 + 18260 * q^14 + 25714 * q^15 + 167866 * q^16 + 54312 * q^17 + 163911 * q^18 + 97192 * q^19 + 85625 * q^20 + 97795 * q^21 - 12345 * q^22 + 107342 * q^23 + 163119 * q^24 + 165051 * q^25 + 61531 * q^26 + 446611 * q^27 + 215454 * q^28 + 41748 * q^29 - 1080964 * q^30 - 272248 * q^31 + 593306 * q^32 - 216525 * q^33 - 923600 * q^34 + 436814 * q^35 - 456119 * q^36 - 557183 * q^37 - 175872 * q^38 - 1587326 * q^39 - 3206863 * q^40 + 525465 * q^41 - 3814396 * q^42 - 1376086 * q^43 - 1337377 * q^44 - 2315492 * q^45 - 2037327 * q^46 + 2269179 * q^47 + 1779791 * q^48 + 2282536 * q^49 - 3881347 * q^50 - 103604 * q^51 - 4200495 * q^52 - 346415 * q^53 + 6349248 * q^54 + 4169374 * q^55 - 4307934 * q^56 + 6170792 * q^57 - 1334849 * q^58 + 4598828 * q^59 - 4448200 * q^60 + 6208418 * q^61 + 4732115 * q^62 + 6882994 * q^63 + 12483426 * q^64 + 9330160 * q^65 - 5715150 * q^66 + 2199016 * q^67 + 8095824 * q^68 + 13516268 * q^69 - 6471708 * q^70 + 4653285 * q^71 + 12839097 * q^72 - 1080699 * q^73 - 810448 * q^74 + 16194855 * q^75 + 1331888 * q^76 + 22058153 * q^77 - 23968103 * q^78 - 1336084 * q^79 - 89443 * q^80 + 9585355 * q^81 + 9689125 * q^82 + 28551309 * q^83 - 37602282 * q^84 + 13256012 * q^85 - 47733694 * q^86 - 5826578 * q^87 - 58704117 * q^88 - 8994788 * q^89 - 46526086 * q^90 - 696642 * q^91 - 41894465 * q^92 - 9859184 * q^93 - 26180048 * q^94 + 124152 * q^95 - 19485621 * q^96 - 3968264 * q^97 - 7312590 * q^98 - 14172918 * 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 $

$2$	5.43681	0.480551	0.240275	−	0.970705i	$-0.422762\pi$
$2$	5.43681	0.480551	0.240275	+	0.970705i	$0.422762\pi$
$3$	85.9489	1.83787	0.918937	−	0.394404i	$-0.129049\pi$
$3$	85.9489	1.83787	0.918937	+	0.394404i	$0.129049\pi$
$4$	−98.4411	−0.769071
$5$	−143.945	−0.514992	−0.257496	−	0.966279i	$-0.582897\pi$
$5$	−143.945	−0.514992	−0.257496	+	0.966279i	$0.582897\pi$
$6$	467.288	0.883192
$7$	1592.07	1.75436	0.877180	−	0.480162i	$-0.159422\pi$
$7$	1592.07	1.75436	0.877180	+	0.480162i	$0.159422\pi$
$8$	−1231.12	−0.850128
$9$	5200.21	2.37778
$10$	−782.599	−0.247480
$11$	6065.58	1.37403	0.687017	−	0.726641i	$-0.258920\pi$
$11$	6065.58	1.37403	0.687017	+	0.726641i	$0.258920\pi$
$12$	−8460.90	−1.41346
$13$	−1785.21	−0.225366	−0.112683	−	0.993631i	$-0.535944\pi$
$13$	−1785.21	−0.225366	−0.112683	+	0.993631i	$0.535944\pi$
$14$	8655.77	0.843059
$15$	−12371.9	−0.946489
$16$	5907.11	0.360541
$17$	−24254.8	−1.19736	−0.598682	−	0.800987i	$-0.704309\pi$
$17$	−24254.8	−1.19736	−0.598682	+	0.800987i	$0.704309\pi$
$18$	28272.5	1.14264
$19$	−9575.55	−0.320277	−0.160139	−	0.987095i	$-0.551194\pi$
$19$	−9575.55	−0.320277	−0.160139	+	0.987095i	$0.551194\pi$
$20$	14170.1	0.396065
$21$	136836.	3.22429
$22$	32977.4	0.660293
$23$	77137.8	1.32197	0.660983	−	0.750401i	$-0.270140\pi$
$23$	77137.8	1.32197	0.660983	+	0.750401i	$0.270140\pi$
$24$	−105813.	−1.56243
$25$	−57405.0	−0.734784
$26$	−9705.85	−0.108300
$27$	258982.	2.53219
$28$	−156725.	−1.34923
$29$	−143305.	−1.09111	−0.545553	−	0.838076i	$-0.683680\pi$
$29$	−143305.	−1.09111	−0.545553	+	0.838076i	$0.683680\pi$
$30$	−67263.5	−0.454836
$31$	−283192.	−1.70732	−0.853660	−	0.520831i	$-0.825622\pi$
$31$	−283192.	−1.70732	−0.853660	+	0.520831i	$0.825622\pi$
$32$	189699.	1.02339
$33$	521329.	2.52530
$34$	−131869.	−0.575394
$35$	−229169.	−0.903480
$36$	−511914.	−1.82868
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	−52060.4	−0.153909
$39$	−153437.	−0.414193
$40$	177213.	0.437809
$41$	5733.04	0.0129910	0.00649548	−	0.999979i	$-0.497932\pi$
$41$	5733.04	0.0129910	0.00649548	+	0.999979i	$0.497932\pi$
$42$	743954.	1.54944
$43$	−106033.	−0.203376	−0.101688	−	0.994816i	$-0.532424\pi$
$43$	−106033.	−0.203376	−0.101688	+	0.994816i	$0.532424\pi$
$44$	−597102.	−1.05673
$45$	−748541.	−1.22454
$46$	419384.	0.635271
$47$	−93073.8	−0.130763	−0.0653815	−	0.997860i	$-0.520826\pi$
$47$	−93073.8	−0.130763	−0.0653815	+	0.997860i	$0.520826\pi$
$48$	507709.	0.662629
$49$	1.71114e6	2.07778
$50$	−312100.	−0.353101
$51$	−2.08467e6	−2.20060
$52$	175738.	0.173322
$53$	−1.28672e6	−1.18718	−0.593592	−	0.804766i	$-0.702291\pi$
$53$	−1.28672e6	−1.18718	−0.593592	+	0.804766i	$0.702291\pi$
$54$	1.40803e6	1.21684
$55$	−873106.	−0.707616
$56$	−1.96002e6	−1.49143
$57$	−823007.	−0.588629
$58$	−779120.	−0.524332
$59$	−543555.	−0.344557	−0.172279	−	0.985048i	$-0.555113\pi$
$59$	−543555.	−0.344557	−0.172279	+	0.985048i	$0.555113\pi$
$60$	1.21790e6	0.727918
$61$	1.26651e6	0.714423	0.357212	−	0.934023i	$-0.383728\pi$
$61$	1.26651e6	0.714423	0.357212	+	0.934023i	$0.383728\pi$
$62$	−1.53966e6	−0.820454
$63$	8.27908e6	4.17148
$64$	275247.	0.131248
$65$	256971.	0.116061
$66$	2.83437e6	1.21354
$67$	−2.77522e6	−1.12729	−0.563646	−	0.826017i	$-0.690602\pi$
$67$	−2.77522e6	−1.12729	−0.563646	+	0.826017i	$0.690602\pi$
$68$	2.38767e6	0.920858
$69$	6.62991e6	2.42961
$70$	−1.24595e6	−0.434168
$71$	449181.	0.148942	0.0744710	−	0.997223i	$-0.476273\pi$
$71$	449181.	0.148942	0.0744710	+	0.997223i	$0.476273\pi$
$72$	−6.40206e6	−2.02142
$73$	1.86672e6	0.561630	0.280815	−	0.959762i	$-0.409395\pi$
$73$	1.86672e6	0.561630	0.280815	+	0.959762i	$0.409395\pi$
$74$	−275391.	−0.0790020
$75$	−4.93389e6	−1.35044
$76$	942627.	0.246316
$77$	9.65681e6	2.41055
$78$	−834207.	−0.199041
$79$	−4.91270e6	−1.12105	−0.560526	−	0.828137i	$-0.689401\pi$
$79$	−4.91270e6	−1.12105	−0.560526	+	0.828137i	$0.689401\pi$
$80$	−850296.	−0.185676
$81$	1.08863e7	2.27606
$82$	31169.4	0.00624282
$83$	1.36787e6	0.262587	0.131293	−	0.991344i	$-0.458087\pi$
$83$	1.36787e6	0.262587	0.131293	+	0.991344i	$0.458087\pi$
$84$	−1.34703e7	−2.47971
$85$	3.49134e6	0.616632
$86$	−576480.	−0.0977326
$87$	−1.23169e7	−2.00532
$88$	−7.46744e6	−1.16811
$89$	−2.42814e6	−0.365097	−0.182548	−	0.983197i	$-0.558435\pi$
$89$	−2.42814e6	−0.365097	−0.182548	+	0.983197i	$0.558435\pi$
$90$	−4.06968e6	−0.588452
$91$	−2.84218e6	−0.395372
$92$	−7.59353e6	−1.01669
$93$	−2.43400e7	−3.13784
$94$	−506025.	−0.0628383
$95$	1.37835e6	0.164940
$96$	1.63044e7	1.88086
$97$	7.89343e6	0.878141	0.439071	−	0.898453i	$-0.355308\pi$
$97$	7.89343e6	0.878141	0.439071	+	0.898453i	$0.355308\pi$
$98$	9.30314e6	0.998477
$99$	3.15422e7	3.26715
$100$	5.65101e6	0.565101
$101$	7.81178e6	0.754441	0.377220	−	0.926124i	$-0.376880\pi$
$101$	7.81178e6	0.754441	0.377220	+	0.926124i	$0.376880\pi$
$102$	−1.13340e7	−1.05750
$103$	1.80778e6	0.163010	0.0815050	−	0.996673i	$-0.474027\pi$
$103$	1.80778e6	0.163010	0.0815050	+	0.996673i	$0.474027\pi$
$104$	2.19780e6	0.191590
$105$	−1.96969e7	−1.66048
$106$	−6.99565e6	−0.570502
$107$	1.45714e7	1.14989	0.574947	−	0.818191i	$-0.305023\pi$
$107$	1.45714e7	1.14989	0.574947	+	0.818191i	$0.305023\pi$
$108$	−2.54944e7	−1.94743
$109$	5.15404e6	0.381202	0.190601	−	0.981668i	$-0.438956\pi$
$109$	5.15404e6	0.381202	0.190601	+	0.981668i	$0.438956\pi$
$110$	−4.74691e6	−0.340045
$111$	−4.35357e6	−0.302145
$112$	9.40452e6	0.632519
$113$	6.03162e6	0.393241	0.196621	−	0.980480i	$-0.437003\pi$
$113$	6.03162e6	0.393241	0.196621	+	0.980480i	$0.437003\pi$
$114$	−4.47453e6	−0.282866
$115$	−1.11036e7	−0.680801
$116$	1.41071e7	0.839138
$117$	−9.28346e6	−0.535870
$118$	−2.95521e6	−0.165577
$119$	−3.86153e7	−2.10061
$120$	1.52312e7	0.804638
$121$	1.73040e7	0.887971
$122$	6.88580e6	0.343317
$123$	492748.	0.0238758
$124$	2.78777e7	1.31305
$125$	1.95088e7	0.893399
$126$	4.50118e7	2.00461
$127$	−1.92641e7	−0.834519	−0.417259	−	0.908787i	$-0.637009\pi$
$127$	−1.92641e7	−0.834519	−0.417259	+	0.908787i	$0.637009\pi$
$128$	−2.27850e7	−0.960315
$129$	−9.11339e6	−0.373780
$130$	1.39710e6	0.0557734
$131$	4.86103e7	1.88920	0.944601	−	0.328221i	$-0.106449\pi$
$131$	4.86103e7	1.88920	0.944601	+	0.328221i	$0.106449\pi$
$132$	−5.13202e7	−1.94214
$133$	−1.52449e7	−0.561881
$134$	−1.50884e7	−0.541721
$135$	−3.72790e7	−1.30405
$136$	2.98605e7	1.01791
$137$	2.03860e7	0.677344	0.338672	−	0.940905i	$-0.390022\pi$
$137$	2.03860e7	0.677344	0.338672	+	0.940905i	$0.390022\pi$
$138$	3.60456e7	1.16755
$139$	−5.48190e7	−1.73133	−0.865665	−	0.500624i	$-0.833104\pi$
$139$	−5.48190e7	−1.73133	−0.865665	+	0.500624i	$0.833104\pi$
$140$	2.25597e7	0.694840
$141$	−7.99959e6	−0.240326
$142$	2.44211e6	0.0715741
$143$	−1.08283e7	−0.309660
$144$	3.07182e7	0.857288
$145$	2.06279e7	0.561910
$146$	1.01490e7	0.269892
$147$	1.47070e8	3.81869
$148$	4.98634e6	0.126434
$149$	−2.26734e6	−0.0561519	−0.0280759	−	0.999606i	$-0.508938\pi$
$149$	−2.26734e6	−0.0561519	−0.0280759	+	0.999606i	$0.508938\pi$
$150$	−2.68246e7	−0.648955
$151$	−5.31275e7	−1.25574	−0.627871	−	0.778317i	$-0.716073\pi$
$151$	−5.31275e7	−1.25574	−0.627871	+	0.778317i	$0.716073\pi$
$152$	1.17886e7	0.272277
$153$	−1.26130e8	−2.84707
$154$	5.25023e7	1.15839
$155$	4.07639e7	0.879255
$156$	1.51045e7	0.318544
$157$	−1.60071e7	−0.330115	−0.165057	−	0.986284i	$-0.552781\pi$
$157$	−1.60071e7	−0.330115	−0.165057	+	0.986284i	$0.552781\pi$
$158$	−2.67094e7	−0.538722
$159$	−1.10592e8	−2.18190
$160$	−2.73061e7	−0.527035
$161$	1.22809e8	2.31920
$162$	5.91869e7	1.09376
$163$	1.69340e7	0.306269	0.153134	−	0.988205i	$-0.451063\pi$
$163$	1.69340e7	0.306269	0.153134	+	0.988205i	$0.451063\pi$
$164$	−564367.	−0.00999097
$165$	−7.50425e7	−1.30051
$166$	7.43687e6	0.126186
$167$	3.48453e7	0.578944	0.289472	−	0.957187i	$-0.406520\pi$
$167$	3.48453e7	0.578944	0.289472	+	0.957187i	$0.406520\pi$
$168$	−1.68462e8	−2.74106
$169$	−5.95615e7	−0.949210
$170$	1.89818e7	0.296323
$171$	−4.97948e7	−0.761549
$172$	1.04380e7	0.156411
$173$	−5.61721e7	−0.824820	−0.412410	−	0.910998i	$-0.635313\pi$
$173$	−5.61721e7	−0.824820	−0.412410	+	0.910998i	$0.635313\pi$
$174$	−6.69644e7	−0.963656
$175$	−9.13926e7	−1.28907
$176$	3.58300e7	0.495396
$177$	−4.67179e7	−0.633253
$178$	−1.32013e7	−0.175447
$179$	1.86775e7	0.243406	0.121703	−	0.992567i	$-0.461164\pi$
$179$	1.86775e7	0.243406	0.121703	+	0.992567i	$0.461164\pi$
$180$	7.36872e7	0.941756
$181$	9.98345e7	1.25143	0.625714	−	0.780053i	$-0.284808\pi$
$181$	9.98345e7	1.25143	0.625714	+	0.780053i	$0.284808\pi$
$182$	−1.54524e7	−0.189996
$183$	1.08855e8	1.31302
$184$	−9.49657e7	−1.12384
$185$	7.29122e6	0.0846641
$186$	−1.32332e8	−1.50789
$187$	−1.47119e8	−1.64522
$188$	9.16229e6	0.100566
$189$	4.12316e8	4.44237
$190$	7.49381e6	0.0792620
$191$	5.37812e7	0.558488	0.279244	−	0.960220i	$-0.409916\pi$
$191$	5.37812e7	0.558488	0.279244	+	0.960220i	$0.409916\pi$
$192$	2.36572e7	0.241217
$193$	5.97040e7	0.597796	0.298898	−	0.954285i	$-0.403381\pi$
$193$	5.97040e7	0.597796	0.298898	+	0.954285i	$0.403381\pi$
$194$	4.29151e7	0.421991
$195$	2.20864e7	0.213306
$196$	−1.68446e8	−1.59796
$197$	−1.54744e8	−1.44206	−0.721029	−	0.692905i	$-0.756330\pi$
$197$	−1.54744e8	−1.44206	−0.721029	+	0.692905i	$0.756330\pi$
$198$	1.71489e8	1.57003
$199$	4.53596e7	0.408022	0.204011	−	0.978969i	$-0.434602\pi$
$199$	4.53596e7	0.408022	0.204011	+	0.978969i	$0.434602\pi$
$200$	7.06723e7	0.624660
$201$	−2.38527e8	−2.07182
$202$	4.24712e7	0.362547
$203$	−2.28151e8	−1.91419
$204$	2.05217e8	1.69242
$205$	−825240.	−0.00669024
$206$	9.82853e6	0.0783346
$207$	4.01133e8	3.14334
$208$	−1.05454e7	−0.0812536
$209$	−5.80812e7	−0.440072
$210$	−1.07088e8	−0.797946
$211$	1.92510e8	1.41080	0.705399	−	0.708811i	$-0.250768\pi$
$211$	1.92510e8	1.41080	0.705399	+	0.708811i	$0.250768\pi$
$212$	1.26666e8	0.913029
$213$	3.86066e7	0.273736
$214$	7.92219e7	0.552583
$215$	1.52628e7	0.104737
$216$	−3.18837e8	−2.15268
$217$	−4.50861e8	−2.99525
$218$	2.80215e7	0.183187
$219$	1.60443e8	1.03221
$220$	8.59495e7	0.544207
$221$	4.32999e7	0.269845
$222$	−2.36695e7	−0.145196
$223$	−2.25471e8	−1.36152	−0.680759	−	0.732508i	$-0.738350\pi$
$223$	−2.25471e8	−1.36152	−0.680759	+	0.732508i	$0.738350\pi$
$224$	3.02014e8	1.79539
$225$	−2.98518e8	−1.74715
$226$	3.27928e7	0.188972
$227$	1.41445e8	0.802599	0.401299	−	0.915947i	$-0.368559\pi$
$227$	1.41445e8	0.802599	0.401299	+	0.915947i	$0.368559\pi$
$228$	8.10177e7	0.452698
$229$	−2.24676e8	−1.23633	−0.618163	−	0.786050i	$-0.712123\pi$
$229$	−2.24676e8	−1.23633	−0.618163	+	0.786050i	$0.712123\pi$
$230$	−6.03680e7	−0.327159
$231$	8.29992e8	4.43029
$232$	1.76425e8	0.927580
$233$	−6.55559e7	−0.339521	−0.169760	−	0.985485i	$-0.554299\pi$
$233$	−6.55559e7	−0.339521	−0.169760	+	0.985485i	$0.554299\pi$
$234$	−5.04724e7	−0.257513
$235$	1.33975e7	0.0673419
$236$	5.35082e7	0.264989
$237$	−4.22241e8	−2.06035
$238$	−2.09944e8	−1.00945
$239$	−5.11355e7	−0.242287	−0.121144	−	0.992635i	$-0.538656\pi$
$239$	−5.11355e7	−0.242287	−0.121144	+	0.992635i	$0.538656\pi$
$240$	−7.30819e7	−0.341248
$241$	−1.89918e8	−0.873988	−0.436994	−	0.899464i	$-0.643957\pi$
$241$	−1.89918e8	−0.873988	−0.436994	+	0.899464i	$0.643957\pi$
$242$	9.40788e7	0.426715
$243$	3.69274e8	1.65092
$244$	−1.24677e8	−0.549442
$245$	−2.46309e8	−1.07004
$246$	2.67898e6	0.0114735
$247$	1.70944e7	0.0721794
$248$	3.48643e8	1.45144
$249$	1.17567e8	0.482601
$250$	1.06066e8	0.429323
$251$	2.28210e8	0.910912	0.455456	−	0.890258i	$-0.349476\pi$
$251$	2.28210e8	0.910912	0.455456	+	0.890258i	$0.349476\pi$
$252$	−8.15002e8	−3.20817
$253$	4.67885e8	1.81643
$254$	−1.04735e8	−0.401028
$255$	3.00077e8	1.13329
$256$	−1.59109e8	−0.592728
$257$	1.25588e8	0.461511	0.230756	−	0.973012i	$-0.425880\pi$
$257$	1.25588e8	0.461511	0.230756	+	0.973012i	$0.425880\pi$
$258$	−4.95478e7	−0.179620
$259$	−8.06430e7	−0.288415
$260$	−2.52965e7	−0.0892594
$261$	−7.45213e8	−2.59441
$262$	2.64285e8	0.907857
$263$	−1.42153e8	−0.481850	−0.240925	−	0.970544i	$-0.577451\pi$
$263$	−1.42153e8	−0.481850	−0.240925	+	0.970544i	$0.577451\pi$
$264$	−6.41818e8	−2.14683
$265$	1.85216e8	0.611390
$266$	−8.28838e7	−0.270012
$267$	−2.08695e8	−0.671002
$268$	2.73196e8	0.866967
$269$	2.44418e8	0.765597	0.382799	−	0.923832i	$-0.374960\pi$
$269$	2.44418e8	0.765597	0.382799	+	0.923832i	$0.374960\pi$
$270$	−2.02679e8	−0.626664
$271$	3.46623e8	1.05795	0.528975	−	0.848637i	$-0.322576\pi$
$271$	3.46623e8	1.05795	0.528975	+	0.848637i	$0.322576\pi$
$272$	−1.43276e8	−0.431699
$273$	−2.44282e8	−0.726644
$274$	1.10835e8	0.325498
$275$	−3.48194e8	−1.00962
$276$	−6.52655e8	−1.86854
$277$	−6.77505e8	−1.91529	−0.957643	−	0.287959i	$-0.907023\pi$
$277$	−6.77505e8	−1.91529	−0.957643	+	0.287959i	$0.907023\pi$
$278$	−2.98041e8	−0.831991
$279$	−1.47266e9	−4.05963
$280$	2.82135e8	0.768074
$281$	7.36490e8	1.98014	0.990068	−	0.140590i	$-0.0448998\pi$
$281$	7.36490e8	1.98014	0.990068	+	0.140590i	$0.0448998\pi$
$282$	−4.34923e7	−0.115489
$283$	6.41865e8	1.68341	0.841707	−	0.539935i	$-0.181551\pi$
$283$	6.41865e8	1.68341	0.841707	+	0.539935i	$0.181551\pi$
$284$	−4.42178e7	−0.114547
$285$	1.18467e8	0.303139
$286$	−5.88716e7	−0.148807
$287$	9.12739e6	0.0227908
$288$	9.86473e8	2.43339
$289$	1.77956e8	0.433680
$290$	1.12150e8	0.270026
$291$	6.78431e8	1.61391
$292$	−1.83762e8	−0.431933
$293$	1.23201e8	0.286139	0.143070	−	0.989713i	$-0.454303\pi$
$293$	1.23201e8	0.286139	0.143070	+	0.989713i	$0.454303\pi$
$294$	7.99594e8	1.83507
$295$	7.82418e7	0.177444
$296$	6.23598e7	0.139760
$297$	1.57087e9	3.47931
$298$	−1.23271e7	−0.0269838
$299$	−1.37707e8	−0.297925
$300$	4.85698e8	1.03858
$301$	−1.68811e8	−0.356795
$302$	−2.88844e8	−0.603448
$303$	6.71413e8	1.38657
$304$	−5.65638e7	−0.115473
$305$	−1.82308e8	−0.367922
$306$	−6.85744e8	−1.36816
$307$	5.43894e7	0.107283	0.0536413	−	0.998560i	$-0.482917\pi$
$307$	5.43894e7	0.107283	0.0536413	+	0.998560i	$0.482917\pi$
$308$	−9.50627e8	−1.85388
$309$	1.55376e8	0.299592
$310$	2.21626e8	0.422527
$311$	1.20150e8	0.226497	0.113248	−	0.993567i	$-0.463874\pi$
$311$	1.20150e8	0.226497	0.113248	+	0.993567i	$0.463874\pi$
$312$	1.88899e8	0.352118
$313$	5.54228e8	1.02161	0.510803	−	0.859698i	$-0.329348\pi$
$313$	5.54228e8	1.02161	0.510803	+	0.859698i	$0.329348\pi$
$314$	−8.70278e7	−0.158637
$315$	−1.19173e9	−2.14828
$316$	4.83612e8	0.862169
$317$	−2.91473e8	−0.513914	−0.256957	−	0.966423i	$-0.582720\pi$
$317$	−2.91473e8	−0.513914	−0.256957	+	0.966423i	$0.582720\pi$
$318$	−6.01268e8	−1.04851
$319$	−8.69225e8	−1.49922
$320$	−3.96203e7	−0.0675916
$321$	1.25239e9	2.11336
$322$	6.67688e8	1.11449
$323$	2.32253e8	0.383488
$324$	−1.07166e9	−1.75045
$325$	1.02480e8	0.165595
$326$	9.20669e7	0.147178
$327$	4.42984e8	0.700601
$328$	−7.05804e6	−0.0110440
$329$	−1.48180e8	−0.229405
$330$	−4.07992e8	−0.624961
$331$	−8.16983e8	−1.23827	−0.619134	−	0.785285i	$-0.712516\pi$
$331$	−8.16983e8	−1.23827	−0.619134	+	0.785285i	$0.712516\pi$
$332$	−1.34655e8	−0.201948
$333$	−2.63406e8	−0.390905
$334$	1.89447e8	0.278212
$335$	3.99478e8	0.580546
$336$	8.08308e8	1.16249
$337$	6.34471e8	0.903041	0.451520	−	0.892261i	$-0.350882\pi$
$337$	6.34471e8	0.903041	0.451520	+	0.892261i	$0.350882\pi$
$338$	−3.23825e8	−0.456144
$339$	5.18411e8	0.722728
$340$	−3.43692e8	−0.474234
$341$	−1.71772e9	−2.34592
$342$	−2.70725e8	−0.365963
$343$	1.41311e9	1.89081
$344$	1.30539e8	0.172896
$345$	−9.54339e8	−1.25123
$346$	−3.05397e8	−0.396368
$347$	−3.01581e8	−0.387481	−0.193741	−	0.981053i	$-0.562062\pi$
$347$	−3.01581e8	−0.387481	−0.193741	+	0.981053i	$0.562062\pi$
$348$	1.21249e9	1.54223
$349$	2.41816e8	0.304506	0.152253	−	0.988342i	$-0.451347\pi$
$349$	2.41816e8	0.304506	0.152253	+	0.988342i	$0.451347\pi$
$350$	−4.96885e8	−0.619466
$351$	−4.62336e8	−0.570668
$352$	1.15063e9	1.40617
$353$	1.85829e8	0.224855	0.112427	−	0.993660i	$-0.464137\pi$
$353$	1.85829e8	0.224855	0.112427	+	0.993660i	$0.464137\pi$
$354$	−2.53997e8	−0.304310
$355$	−6.46571e7	−0.0767038
$356$	2.39028e8	0.280785
$357$	−3.31894e9	−3.86065
$358$	1.01546e8	0.116969
$359$	1.51997e8	0.173383	0.0866913	−	0.996235i	$-0.472371\pi$
$359$	1.51997e8	0.173383	0.0866913	+	0.996235i	$0.472371\pi$
$360$	9.21542e8	1.04101
$361$	−8.02181e8	−0.897423
$362$	5.42781e8	0.601374
$363$	1.48726e9	1.63198
$364$	2.79787e8	0.304069
$365$	−2.68705e8	−0.289235
$366$	5.91826e8	0.630973
$367$	4.86426e8	0.513672	0.256836	−	0.966455i	$-0.417320\pi$
$367$	4.86426e8	0.513672	0.256836	+	0.966455i	$0.417320\pi$
$368$	4.55662e8	0.476623
$369$	2.98130e7	0.0308897
$370$	3.96410e7	0.0406854
$371$	−2.04854e9	−2.08275
$372$	2.39606e9	2.41322
$373$	−1.41614e9	−1.41294	−0.706470	−	0.707743i	$-0.749714\pi$
$373$	−1.41614e9	−1.41294	−0.706470	+	0.707743i	$0.749714\pi$
$374$	−7.99859e8	−0.790611
$375$	1.67676e9	1.64195
$376$	1.14585e8	0.111165
$377$	2.55829e8	0.245898
$378$	2.24169e9	2.13478
$379$	−9.82343e8	−0.926885	−0.463443	−	0.886127i	$-0.653386\pi$
$379$	−9.82343e8	−0.926885	−0.463443	+	0.886127i	$0.653386\pi$
$380$	−1.35686e8	−0.126851
$381$	−1.65573e9	−1.53374
$382$	2.92398e8	0.268382
$383$	−9.07028e8	−0.824945	−0.412472	−	0.910970i	$-0.635335\pi$
$383$	−9.07028e8	−0.824945	−0.412472	+	0.910970i	$0.635335\pi$
$384$	−1.95834e9	−1.76494
$385$	−1.39004e9	−1.24141
$386$	3.24599e8	0.287271
$387$	−5.51392e8	−0.483584
$388$	−7.77037e8	−0.675353
$389$	2.24564e9	1.93427	0.967134	−	0.254269i	$-0.0818348\pi$
$389$	2.24564e9	1.93427	0.967134	+	0.254269i	$0.0818348\pi$
$390$	1.20079e8	0.102504
$391$	−1.87096e9	−1.58287
$392$	−2.10661e9	−1.76638
$393$	4.17800e9	3.47211
$394$	−8.41315e8	−0.692982
$395$	7.07157e8	0.577332
$396$	−3.10505e9	−2.51267
$397$	9.94740e8	0.797889	0.398945	−	0.916975i	$-0.369377\pi$
$397$	9.94740e8	0.797889	0.398945	+	0.916975i	$0.369377\pi$
$398$	2.46611e8	0.196075
$399$	−1.31028e9	−1.03267
$400$	−3.39097e8	−0.264920
$401$	1.40824e9	1.09062	0.545308	−	0.838235i	$-0.316413\pi$
$401$	1.40824e9	1.09062	0.545308	+	0.838235i	$0.316413\pi$
$402$	−1.29683e9	−0.995614
$403$	5.05557e8	0.384771
$404$	−7.69000e8	−0.580218
$405$	−1.56703e9	−1.17215
$406$	−1.24041e9	−0.919866
$407$	−3.07240e8	−0.225890
$408$	2.56647e9	1.87080
$409$	−1.07390e9	−0.776125	−0.388062	−	0.921633i	$-0.626855\pi$
$409$	−1.07390e9	−0.776125	−0.388062	+	0.921633i	$0.626855\pi$
$410$	−4.48667e6	−0.00321500
$411$	1.75215e9	1.24487
$412$	−1.77959e8	−0.125366
$413$	−8.65377e8	−0.604477
$414$	2.18088e9	1.51054
$415$	−1.96898e8	−0.135230
$416$	−3.38652e8	−0.230636
$417$	−4.71163e9	−3.18196
$418$	−3.15777e8	−0.211477
$419$	2.16351e9	1.43685	0.718423	−	0.695607i	$-0.244864\pi$
$419$	2.16351e9	1.43685	0.718423	+	0.695607i	$0.244864\pi$
$420$	1.93898e9	1.27703
$421$	2.82762e9	1.84686	0.923430	−	0.383767i	$-0.125373\pi$
$421$	2.82762e9	1.84686	0.923430	+	0.383767i	$0.125373\pi$
$422$	1.04664e9	0.677960
$423$	−4.84003e8	−0.310926
$424$	1.58410e9	1.00926
$425$	1.39234e9	0.879803
$426$	2.09897e8	0.131544
$427$	2.01638e9	1.25335
$428$	−1.43442e9	−0.884350
$429$	−9.30682e8	−0.569116
$430$	8.29811e7	0.0503315
$431$	9.21317e8	0.554292	0.277146	−	0.960828i	$-0.410611\pi$
$431$	9.21317e8	0.554292	0.277146	+	0.960828i	$0.410611\pi$
$432$	1.52983e9	0.912958
$433$	−1.67403e9	−0.990958	−0.495479	−	0.868620i	$-0.665007\pi$
$433$	−1.67403e9	−0.990958	−0.495479	+	0.868620i	$0.665007\pi$
$434$	−2.45125e9	−1.43937
$435$	1.77294e9	1.03272
$436$	−5.07369e8	−0.293171
$437$	−7.38637e8	−0.423395
$438$	8.72297e8	0.496027
$439$	2.01775e9	1.13826	0.569131	−	0.822247i	$-0.307280\pi$
$439$	2.01775e9	1.13826	0.569131	+	0.822247i	$0.307280\pi$
$440$	1.07490e9	0.601564
$441$	8.89827e9	4.94050
$442$	2.35413e8	0.129674
$443$	−4.65015e8	−0.254129	−0.127064	−	0.991894i	$-0.540556\pi$
$443$	−4.65015e8	−0.254129	−0.127064	+	0.991894i	$0.540556\pi$
$444$	4.28570e8	0.232371
$445$	3.49517e8	0.188022
$446$	−1.22584e9	−0.654278
$447$	−1.94875e8	−0.103200
$448$	4.38212e8	0.230256
$449$	2.58637e8	0.134843	0.0674215	−	0.997725i	$-0.478523\pi$
$449$	2.58637e8	0.134843	0.0674215	+	0.997725i	$0.478523\pi$
$450$	−1.62298e9	−0.839596
$451$	3.47742e7	0.0178500
$452$	−5.93759e8	−0.302431
$453$	−4.56625e9	−2.30790
$454$	7.69012e8	0.385689
$455$	4.09116e8	0.203613
$456$	1.01322e9	0.500410
$457$	1.39986e9	0.686085	0.343042	−	0.939320i	$-0.388543\pi$
$457$	1.39986e9	0.686085	0.343042	+	0.939320i	$0.388543\pi$
$458$	−1.22152e9	−0.594117
$459$	−6.28154e9	−3.03195
$460$	1.09305e9	0.523584
$461$	8.74250e8	0.415607	0.207803	−	0.978171i	$-0.433369\pi$
$461$	8.74250e8	0.415607	0.207803	+	0.978171i	$0.433369\pi$
$462$	4.51251e9	2.12898
$463$	−2.38594e9	−1.11719	−0.558593	−	0.829442i	$-0.688659\pi$
$463$	−2.38594e9	−1.11719	−0.558593	+	0.829442i	$0.688659\pi$
$464$	−8.46515e8	−0.393389
$465$	3.50361e9	1.61596
$466$	−3.56415e8	−0.163157
$467$	−3.08694e9	−1.40255	−0.701276	−	0.712890i	$-0.747386\pi$
$467$	−3.08694e9	−1.40255	−0.701276	+	0.712890i	$0.747386\pi$
$468$	9.13874e8	0.412122
$469$	−4.41835e9	−1.97767
$470$	7.28395e7	0.0323612
$471$	−1.37579e9	−0.606709
$472$	6.69180e8	0.292918
$473$	−6.43149e8	−0.279446
$474$	−2.29565e9	−0.990104
$475$	5.49684e8	0.235334
$476$	3.80133e9	1.61552
$477$	−6.69120e9	−2.82286
$478$	−2.78014e8	−0.116431
$479$	−2.52475e9	−1.04965	−0.524825	−	0.851210i	$-0.675869\pi$
$479$	−2.52475e9	−1.04965	−0.524825	+	0.851210i	$0.675869\pi$
$480$	−2.34693e9	−0.968625
$481$	9.04262e7	0.0370499
$482$	−1.03255e9	−0.419996
$483$	1.05553e10	4.26240
$484$	−1.70343e9	−0.682913
$485$	−1.13622e9	−0.452235
$486$	2.00767e9	0.793352
$487$	1.74515e9	0.684669	0.342334	−	0.939578i	$-0.388782\pi$
$487$	1.74515e9	0.684669	0.342334	+	0.939578i	$0.388782\pi$
$488$	−1.55923e9	−0.607351
$489$	1.45546e9	0.562883
$490$	−1.33914e9	−0.514207
$491$	−1.12480e9	−0.428836	−0.214418	−	0.976742i	$-0.568785\pi$
$491$	−1.12480e9	−0.428836	−0.214418	+	0.976742i	$0.568785\pi$
$492$	−4.85067e7	−0.0183622
$493$	3.47582e9	1.30645
$494$	9.29388e7	0.0346859
$495$	−4.54033e9	−1.68256
$496$	−1.67285e9	−0.615559
$497$	7.15127e8	0.261298
$498$	6.39191e8	0.231914
$499$	1.46864e9	0.529133	0.264566	−	0.964368i	$-0.414771\pi$
$499$	1.46864e9	0.529133	0.264566	+	0.964368i	$0.414771\pi$
$500$	−1.92047e9	−0.687087
$501$	2.99491e9	1.06403
$502$	1.24073e9	0.437740
$503$	−2.97882e9	−1.04365	−0.521827	−	0.853052i	$-0.674749\pi$
$503$	−2.97882e9	−1.04365	−0.521827	+	0.853052i	$0.674749\pi$
$504$	−1.01925e10	−3.54629
$505$	−1.12446e9	−0.388531
$506$	2.54380e9	0.872885
$507$	−5.11925e9	−1.74453
$508$	1.89638e9	0.641804
$509$	3.44118e9	1.15663	0.578315	−	0.815813i	$-0.303710\pi$
$509$	3.44118e9	1.15663	0.578315	+	0.815813i	$0.303710\pi$
$510$	1.63146e9	0.544604
$511$	2.97195e9	0.985301
$512$	2.05143e9	0.675479
$513$	−2.47989e9	−0.811002
$514$	6.82798e8	0.221779
$515$	−2.60219e8	−0.0839488
$516$	8.97132e8	0.287463
$517$	−5.64546e8	−0.179673
$518$	−4.38441e8	−0.138598
$519$	−4.82793e9	−1.51591
$520$	−3.16362e8	−0.0986670
$521$	5.84832e9	1.81175	0.905877	−	0.423541i	$-0.139213\pi$
$521$	5.84832e9	1.81175	0.905877	+	0.423541i	$0.139213\pi$
$522$	−4.05158e9	−1.24675
$523$	2.53873e9	0.775998	0.387999	−	0.921660i	$-0.373166\pi$
$523$	2.53873e9	0.775998	0.387999	+	0.921660i	$0.373166\pi$
$524$	−4.78525e9	−1.45293
$525$	−7.85509e9	−2.36916
$526$	−7.72861e8	−0.231554
$527$	6.86876e9	2.04428
$528$	3.07955e9	0.910476
$529$	2.54542e9	0.747592
$530$	1.00699e9	0.293804
$531$	−2.82660e9	−0.819282
$532$	1.50073e9	0.432127
$533$	−1.02347e7	−0.00292772
$534$	−1.13464e9	−0.322450
$535$	−2.09747e9	−0.592186
$536$	3.41663e9	0.958342
$537$	1.60531e9	0.447350
$538$	1.32885e9	0.367908
$539$	1.03790e10	2.85494
$540$	3.66978e9	1.00291
$541$	−4.86365e9	−1.32060	−0.660302	−	0.751001i	$-0.729572\pi$
$541$	−4.86365e9	−1.32060	−0.660302	+	0.751001i	$0.729572\pi$
$542$	1.88453e9	0.508399
$543$	8.58066e9	2.29997
$544$	−4.60110e9	−1.22537
$545$	−7.41896e8	−0.196316
$546$	−1.32811e9	−0.349189
$547$	−4.36104e9	−1.13929	−0.569646	−	0.821890i	$-0.692920\pi$
$547$	−4.36104e9	−1.13929	−0.569646	+	0.821890i	$0.692920\pi$
$548$	−2.00682e9	−0.520925
$549$	6.58613e9	1.69874
$550$	−1.89307e9	−0.485173
$551$	1.37222e9	0.349456
$552$	−8.16220e9	−2.06548
$553$	−7.82136e9	−1.96673
$554$	−3.68347e9	−0.920392
$555$	6.26672e8	0.155602
$556$	5.39645e9	1.33152
$557$	3.57855e9	0.877433	0.438717	−	0.898626i	$-0.355433\pi$
$557$	3.57855e9	0.877433	0.438717	+	0.898626i	$0.355433\pi$
$558$	−8.00655e9	−1.95086
$559$	1.89291e8	0.0458340
$560$	−1.35373e9	−0.325742
$561$	−1.26447e10	−3.02370
$562$	4.00416e9	0.951556
$563$	4.57230e9	1.07983	0.539914	−	0.841720i	$-0.318457\pi$
$563$	4.57230e9	1.07983	0.539914	+	0.841720i	$0.318457\pi$
$564$	7.87488e8	0.184828
$565$	−8.68218e8	−0.202516
$566$	3.48970e9	0.808966
$567$	1.73318e10	3.99303
$568$	−5.52994e8	−0.126620
$569$	−5.74766e9	−1.30797	−0.653986	−	0.756507i	$-0.726904\pi$
$569$	−5.74766e9	−1.30797	−0.653986	+	0.756507i	$0.726904\pi$
$570$	6.44085e8	0.145674
$571$	5.87820e9	1.32135	0.660675	−	0.750672i	$-0.270270\pi$
$571$	5.87820e9	1.32135	0.660675	+	0.750672i	$0.270270\pi$
$572$	1.06595e9	0.238151
$573$	4.62243e9	1.02643
$574$	4.96239e7	0.0109521
$575$	−4.42810e9	−0.971359
$576$	1.43134e9	0.312079
$577$	3.96361e9	0.858966	0.429483	−	0.903075i	$-0.358696\pi$
$577$	3.96361e9	0.858966	0.429483	+	0.903075i	$0.358696\pi$
$578$	9.67511e8	0.208405
$579$	5.13149e9	1.09867
$580$	−2.03063e9	−0.432149
$581$	2.17775e9	0.460672
$582$	3.68850e9	0.775567
$583$	−7.80469e9	−1.63123
$584$	−2.29816e9	−0.477458
$585$	1.33630e9	0.275968
$586$	6.69821e8	0.137504
$587$	8.32515e9	1.69886	0.849432	−	0.527697i	$-0.176944\pi$
$587$	8.32515e9	1.69886	0.849432	+	0.527697i	$0.176944\pi$
$588$	−1.44778e10	−2.93684
$589$	2.71172e9	0.546816
$590$	4.25386e8	0.0852709
$591$	−1.33001e10	−2.65032
$592$	−2.99213e8	−0.0592726
$593$	5.32031e9	1.04772	0.523861	−	0.851804i	$-0.324491\pi$
$593$	5.32031e9	1.04772	0.523861	+	0.851804i	$0.324491\pi$
$594$	8.54054e9	1.67199
$595$	5.55845e9	1.08179
$596$	2.23199e8	0.0431848
$597$	3.89860e9	0.749893
$598$	−7.48688e8	−0.143168
$599$	3.50731e9	0.666776	0.333388	−	0.942790i	$-0.391808\pi$
$599$	3.50731e9	0.666776	0.333388	+	0.942790i	$0.391808\pi$
$600$	6.07420e9	1.14805
$601$	1.37911e9	0.259143	0.129572	−	0.991570i	$-0.458640\pi$
$601$	1.37911e9	0.259143	0.129572	+	0.991570i	$0.458640\pi$
$602$	−9.17795e8	−0.171458
$603$	−1.44317e10	−2.68045
$604$	5.22993e9	0.965755
$605$	−2.49082e9	−0.457297
$606$	3.65035e9	0.666316
$607$	4.24708e9	0.770780	0.385390	−	0.922754i	$-0.374067\pi$
$607$	4.24708e9	0.770780	0.385390	+	0.922754i	$0.374067\pi$
$608$	−1.81647e9	−0.327767
$609$	−1.96093e10	−3.51804
$610$	−9.91173e8	−0.176805
$611$	1.66156e8	0.0294695
$612$	1.24164e10	2.18960
$613$	−2.25754e9	−0.395843	−0.197922	−	0.980218i	$-0.563419\pi$
$613$	−2.25754e9	−0.395843	−0.197922	+	0.980218i	$0.563419\pi$
$614$	2.95705e8	0.0515548
$615$	−7.09284e7	−0.0122958
$616$	−1.18887e10	−2.04928
$617$	−3.77957e9	−0.647805	−0.323902	−	0.946091i	$-0.604995\pi$
$617$	−3.77957e9	−0.647805	−0.323902	+	0.946091i	$0.604995\pi$
$618$	8.44751e8	0.143969
$619$	−9.77460e9	−1.65646	−0.828232	−	0.560386i	$-0.810653\pi$
$619$	−9.77460e9	−1.65646	−0.828232	+	0.560386i	$0.810653\pi$
$620$	−4.01285e9	−0.676210
$621$	1.99773e10	3.34746
$622$	6.53232e8	0.108843
$623$	−3.86576e9	−0.640511
$624$	−9.06367e8	−0.149334
$625$	1.67658e9	0.274691
$626$	3.01323e9	0.490933
$627$	−4.99201e9	−0.808797
$628$	1.57576e9	0.253882
$629$	1.22858e9	0.196845
$630$	−6.47920e9	−1.03236
$631$	−1.03769e10	−1.64424	−0.822121	−	0.569313i	$-0.807209\pi$
$631$	−1.03769e10	−1.64424	−0.822121	+	0.569313i	$0.807209\pi$
$632$	6.04812e9	0.953038
$633$	1.65460e10	2.59287
$634$	−1.58468e9	−0.246962
$635$	2.77296e9	0.429770
$636$	1.08868e10	1.67803
$637$	−3.05474e9	−0.468259
$638$	−4.72581e9	−0.720450
$639$	2.33583e9	0.354151
$640$	3.27977e9	0.494554
$641$	−7.69434e9	−1.15390	−0.576950	−	0.816780i	$-0.695757\pi$
$641$	−7.69434e9	−1.15390	−0.576950	+	0.816780i	$0.695757\pi$
$642$	6.80903e9	1.01558
$643$	2.33235e9	0.345983	0.172991	−	0.984923i	$-0.444657\pi$
$643$	2.33235e9	0.345983	0.172991	+	0.984923i	$0.444657\pi$
$644$	−1.20894e10	−1.78363
$645$	1.31182e9	0.192493
$646$	1.26271e9	0.184286
$647$	−9.76964e9	−1.41812	−0.709061	−	0.705147i	$-0.750881\pi$
$647$	−9.76964e9	−1.41812	−0.709061	+	0.705147i	$0.750881\pi$
$648$	−1.34023e10	−1.93494
$649$	−3.29697e9	−0.473434
$650$	5.57164e8	0.0795768
$651$	−3.87510e10	−5.50490
$652$	−1.66700e9	−0.235542
$653$	1.13417e10	1.59398	0.796989	−	0.603994i	$-0.206425\pi$
$653$	1.13417e10	1.59398	0.796989	+	0.603994i	$0.206425\pi$
$654$	2.40842e9	0.336674
$655$	−6.99718e9	−0.972923
$656$	3.38657e7	0.00468378
$657$	9.70735e9	1.33543
$658$	−8.05626e8	−0.110241
$659$	1.71587e9	0.233553	0.116777	−	0.993158i	$-0.462744\pi$
$659$	1.71587e9	0.233553	0.116777	+	0.993158i	$0.462744\pi$
$660$	7.38726e9	1.00018
$661$	−2.79167e9	−0.375974	−0.187987	−	0.982171i	$-0.560196\pi$
$661$	−2.79167e9	−0.375974	−0.187987	+	0.982171i	$0.560196\pi$
$662$	−4.44178e9	−0.595051
$663$	3.72157e9	0.495940
$664$	−1.68401e9	−0.223232
$665$	2.19442e9	0.289364
$666$	−1.43209e9	−0.187850
$667$	−1.10542e10	−1.44240
$668$	−3.43021e9	−0.445249
$669$	−1.93790e10	−2.50230
$670$	2.17189e9	0.278982
$671$	7.68214e9	0.981642
$672$	2.59577e10	3.29970
$673$	1.27636e10	1.61407	0.807033	−	0.590507i	$-0.201072\pi$
$673$	1.27636e10	1.61407	0.807033	+	0.590507i	$0.201072\pi$
$674$	3.44950e9	0.433957
$675$	−1.48668e10	−1.86061
$676$	5.86330e9	0.730010
$677$	−9.91993e9	−1.22871	−0.614353	−	0.789031i	$-0.710583\pi$
$677$	−9.91993e9	−1.22871	−0.614353	+	0.789031i	$0.710583\pi$
$678$	2.81850e9	0.347308
$679$	1.25669e10	1.54058
$680$	−4.29825e9	−0.524216
$681$	1.21571e10	1.47508
$682$	−9.33893e9	−1.12733
$683$	−6.46468e9	−0.776381	−0.388190	−	0.921579i	$-0.626900\pi$
$683$	−6.46468e9	−0.776381	−0.388190	+	0.921579i	$0.626900\pi$
$684$	4.90186e9	0.585685
$685$	−2.93445e9	−0.348826
$686$	7.68283e9	0.908629
$687$	−1.93107e10	−2.27221
$688$	−6.26347e8	−0.0733255
$689$	2.29706e9	0.267550
$690$	−5.18856e9	−0.601278
$691$	1.05139e10	1.21224	0.606121	−	0.795372i	$-0.292725\pi$
$691$	1.05139e10	1.21224	0.606121	+	0.795372i	$0.292725\pi$
$692$	5.52964e9	0.634345
$693$	5.02174e10	5.73176
$694$	−1.63964e9	−0.186204
$695$	7.89090e9	0.891620
$696$	1.51635e10	1.70478
$697$	−1.39054e8	−0.0155549
$698$	1.31471e9	0.146331
$699$	−5.63446e9	−0.623996
$700$	8.99679e9	0.991390
$701$	6.05190e8	0.0663557	0.0331779	−	0.999449i	$-0.489437\pi$
$701$	6.05190e8	0.0663557	0.0331779	+	0.999449i	$0.489437\pi$
$702$	−2.51364e9	−0.274235
$703$	4.85030e8	0.0526532
$704$	1.66953e9	0.180339
$705$	1.15150e9	0.123766
$706$	1.01032e9	0.108054
$707$	1.24369e10	1.32356
$708$	4.59896e9	0.487017
$709$	−1.12730e10	−1.18789	−0.593946	−	0.804505i	$-0.702431\pi$
$709$	−1.12730e10	−1.18789	−0.593946	+	0.804505i	$0.702431\pi$
$710$	−3.51528e8	−0.0368601
$711$	−2.55471e10	−2.66562
$712$	2.98932e9	0.310379
$713$	−2.18448e10	−2.25702
$714$	−1.80444e10	−1.85524
$715$	1.55868e9	0.159472
$716$	−1.83863e9	−0.187197
$717$	−4.39504e9	−0.445293
$718$	8.26381e8	0.0833191
$719$	5.45602e9	0.547425	0.273713	−	0.961812i	$-0.411748\pi$
$719$	5.45602e9	0.547425	0.273713	+	0.961812i	$0.411748\pi$
$720$	−4.42171e9	−0.441496
$721$	2.87810e9	0.285978
$722$	−4.36130e9	−0.431257
$723$	−1.63232e10	−1.60628
$724$	−9.82782e9	−0.962437
$725$	8.22639e9	0.801727
$726$	8.08596e9	0.784248
$727$	−1.26650e10	−1.22246	−0.611229	−	0.791454i	$-0.709325\pi$
$727$	−1.26650e10	−1.22246	−0.611229	+	0.791454i	$0.709325\pi$
$728$	3.49905e9	0.336117
$729$	7.93030e9	0.758130
$730$	−1.46090e9	−0.138992
$731$	2.57180e9	0.243515
$732$	−1.07158e10	−1.00981
$733$	1.13202e10	1.06167	0.530836	−	0.847475i	$-0.321878\pi$
$733$	1.13202e10	1.06167	0.530836	+	0.847475i	$0.321878\pi$
$734$	2.64461e9	0.246845
$735$	−2.11700e10	−1.96659
$736$	1.46330e10	1.35288
$737$	−1.68333e10	−1.54894
$738$	1.62088e8	0.0148440
$739$	−2.94649e8	−0.0268565	−0.0134282	−	0.999910i	$-0.504274\pi$
$739$	−2.94649e8	−0.0268565	−0.0134282	+	0.999910i	$0.504274\pi$
$740$	−7.17756e8	−0.0651127
$741$	1.46924e9	0.132657
$742$	−1.11375e10	−1.00087
$743$	1.02172e9	0.0913838	0.0456919	−	0.998956i	$-0.485451\pi$
$743$	1.02172e9	0.0913838	0.0456919	+	0.998956i	$0.485451\pi$
$744$	2.99654e10	2.66757
$745$	3.26371e8	0.0289177
$746$	−7.69926e9	−0.678990
$747$	7.11323e9	0.624374
$748$	1.44826e10	1.26529
$749$	2.31987e10	2.01733
$750$	9.11622e9	0.789042
$751$	1.84800e9	0.159207	0.0796036	−	0.996827i	$-0.474635\pi$
$751$	1.84800e9	0.159207	0.0796036	+	0.996827i	$0.474635\pi$
$752$	−5.49797e8	−0.0471455
$753$	1.96144e10	1.67414
$754$	1.39089e9	0.118166
$755$	7.64742e9	0.646697
$756$	−4.05889e10	−3.41649
$757$	−1.39360e10	−1.16762	−0.583810	−	0.811890i	$-0.698439\pi$
$757$	−1.39360e10	−1.16762	−0.583810	+	0.811890i	$0.698439\pi$
$758$	−5.34081e9	−0.445415
$759$	4.02142e10	3.33836
$760$	−1.69691e9	−0.140220
$761$	2.09458e10	1.72286	0.861430	−	0.507877i	$-0.169570\pi$
$761$	2.09458e10	1.72286	0.861430	+	0.507877i	$0.169570\pi$
$762$	−9.00188e9	−0.737040
$763$	8.20559e9	0.668765
$764$	−5.29428e9	−0.429517
$765$	1.81557e10	1.46622
$766$	−4.93134e9	−0.396428
$767$	9.70360e8	0.0776514
$768$	−1.36753e10	−1.08936
$769$	−5.59950e9	−0.444025	−0.222012	−	0.975044i	$-0.571263\pi$
$769$	−5.59950e9	−0.444025	−0.222012	+	0.975044i	$0.571263\pi$
$770$	−7.55741e9	−0.596562
$771$	1.07941e10	0.848199
$772$	−5.87733e9	−0.459747
$773$	−7.30068e9	−0.568506	−0.284253	−	0.958749i	$-0.591746\pi$
$773$	−7.30068e9	−0.568506	−0.284253	+	0.958749i	$0.591746\pi$
$774$	−2.99781e9	−0.232387
$775$	1.62566e10	1.25451
$776$	−9.71773e9	−0.746533
$777$	−6.93118e9	−0.530070
$778$	1.22091e10	0.929513
$779$	−5.48970e7	−0.00416071
$780$	−2.17421e9	−0.164048
$781$	2.72454e9	0.204651
$782$	−1.01721e10	−0.760651
$783$	−3.71132e10	−2.76288
$784$	1.01079e10	0.749124
$785$	2.30414e9	0.170006
$786$	2.27150e10	1.66853
$787$	−9.87828e9	−0.722387	−0.361193	−	0.932491i	$-0.617631\pi$
$787$	−9.87828e9	−0.722387	−0.361193	+	0.932491i	$0.617631\pi$
$788$	1.52332e10	1.10904
$789$	−1.22179e10	−0.885580
$790$	3.84468e9	0.277437
$791$	9.60275e9	0.689887
$792$	−3.88322e10	−2.77750
$793$	−2.26099e9	−0.161006
$794$	5.40821e9	0.383426
$795$	1.59191e10	1.12366
$796$	−4.46525e9	−0.313798
$797$	−1.00836e9	−0.0705527	−0.0352763	−	0.999378i	$-0.511231\pi$
$797$	−1.00836e9	−0.0705527	−0.0352763	+	0.999378i	$0.511231\pi$
$798$	−7.12377e9	−0.496249
$799$	2.25749e9	0.156571
$800$	−1.08897e10	−0.751968
$801$	−1.26268e10	−0.868120
$802$	7.65635e9	0.524097
$803$	1.13228e10	0.771699
$804$	2.34809e10	1.59338
$805$	−1.76776e10	−1.19437
$806$	2.74862e9	0.184902
$807$	2.10075e10	1.40707
$808$	−9.61721e9	−0.641371
$809$	6.68960e9	0.444202	0.222101	−	0.975024i	$-0.428709\pi$
$809$	6.68960e9	0.444202	0.222101	+	0.975024i	$0.428709\pi$
$810$	−8.51962e9	−0.563278
$811$	9.22476e9	0.607271	0.303635	−	0.952788i	$-0.401800\pi$
$811$	9.22476e9	0.607271	0.303635	+	0.952788i	$0.401800\pi$
$812$	2.24594e10	1.47215
$813$	2.97919e10	1.94438
$814$	−1.67040e9	−0.108552
$815$	−2.43755e9	−0.157726
$816$	−1.23144e10	−0.793408
$817$	1.01532e9	0.0651368
$818$	−5.83858e9	−0.372967
$819$	−1.47799e10	−0.940108
$820$	8.12375e7	0.00514527
$821$	−4.26294e9	−0.268849	−0.134424	−	0.990924i	$-0.542919\pi$
$821$	−4.26294e9	−0.268849	−0.134424	+	0.990924i	$0.542919\pi$
$822$	9.52611e9	0.598224
$823$	−1.08165e10	−0.676375	−0.338188	−	0.941079i	$-0.609814\pi$
$823$	−1.08165e10	−0.676375	−0.338188	+	0.941079i	$0.609814\pi$
$824$	−2.22558e9	−0.138579
$825$	−2.99269e10	−1.85555
$826$	−4.70489e9	−0.290482
$827$	−6.47845e9	−0.398292	−0.199146	−	0.979970i	$-0.563817\pi$
$827$	−6.47845e9	−0.398292	−0.199146	+	0.979970i	$0.563817\pi$
$828$	−3.94879e10	−2.41745
$829$	−1.37814e10	−0.840144	−0.420072	−	0.907491i	$-0.637995\pi$
$829$	−1.37814e10	−0.840144	−0.420072	+	0.907491i	$0.637995\pi$
$830$	−1.07050e9	−0.0649848
$831$	−5.82308e10	−3.52005
$832$	−4.91373e8	−0.0295788
$833$	−4.15033e10	−2.48785
$834$	−2.56163e10	−1.52910
$835$	−5.01579e9	−0.298151
$836$	5.71758e9	0.338447
$837$	−7.33415e10	−4.32325
$838$	1.17626e10	0.690477
$839$	−2.37172e10	−1.38642	−0.693211	−	0.720734i	$-0.743805\pi$
$839$	−2.37172e10	−1.38642	−0.693211	+	0.720734i	$0.743805\pi$
$840$	2.42491e10	1.41162
$841$	3.28632e9	0.190512
$842$	1.53732e10	0.887510
$843$	6.33005e10	3.63924
$844$	−1.89509e10	−1.08500
$845$	8.57356e9	0.488835
$846$	−2.63143e9	−0.149416
$847$	2.75492e10	1.55782
$848$	−7.60079e9	−0.428029
$849$	5.51675e10	3.09390
$850$	7.56992e9	0.422790
$851$	−3.90726e9	−0.217330
$852$	−3.80047e9	−0.210523
$853$	2.37644e10	1.31101	0.655503	−	0.755192i	$-0.272457\pi$
$853$	2.37644e10	1.31101	0.655503	+	0.755192i	$0.272457\pi$
$854$	1.09627e10	0.602301
$855$	7.16769e9	0.392191
$856$	−1.79391e10	−0.977558
$857$	−2.55545e10	−1.38687	−0.693433	−	0.720521i	$-0.743903\pi$
$857$	−2.55545e10	−1.38687	−0.693433	+	0.720521i	$0.743903\pi$
$858$	−5.05994e9	−0.273489
$859$	−9.72129e9	−0.523296	−0.261648	−	0.965163i	$-0.584266\pi$
$859$	−9.72129e9	−0.523296	−0.261648	+	0.965163i	$0.584266\pi$
$860$	−1.50249e9	−0.0805502
$861$	7.84489e8	0.0418867
$862$	5.00903e9	0.266365
$863$	−5.76409e9	−0.305276	−0.152638	−	0.988282i	$-0.548777\pi$
$863$	−5.76409e9	−0.305276	−0.152638	+	0.988282i	$0.548777\pi$
$864$	4.91285e10	2.59141
$865$	8.08566e9	0.424775
$866$	−9.10138e9	−0.476206
$867$	1.52951e10	0.797049
$868$	4.43832e10	2.30356
$869$	−2.97984e10	−1.54036
$870$	9.63916e9	0.496275
$871$	4.95436e9	0.254053
$872$	−6.34523e9	−0.324071
$873$	4.10474e10	2.08803
$874$	−4.01583e9	−0.203463
$875$	3.10593e10	1.56734
$876$	−1.57942e10	−0.793839
$877$	1.78806e10	0.895124	0.447562	−	0.894253i	$-0.352292\pi$
$877$	1.78806e10	0.895124	0.447562	+	0.894253i	$0.352292\pi$
$878$	1.09701e10	0.546993
$879$	1.05890e10	0.525888
$880$	−5.15753e9	−0.255125
$881$	−2.44483e10	−1.20457	−0.602287	−	0.798280i	$-0.705744\pi$
$881$	−2.44483e10	−1.20457	−0.602287	+	0.798280i	$0.705744\pi$
$882$	4.83782e10	2.37416
$883$	−3.19663e10	−1.56254	−0.781268	−	0.624196i	$-0.785427\pi$
$883$	−3.19663e10	−1.56254	−0.781268	+	0.624196i	$0.785427\pi$
$884$	−4.26249e9	−0.207530
$885$	6.72479e9	0.326120
$886$	−2.52820e9	−0.122122
$887$	−2.08748e10	−1.00436	−0.502181	−	0.864763i	$-0.667469\pi$
$887$	−2.08748e10	−1.00436	−0.502181	+	0.864763i	$0.667469\pi$
$888$	5.35975e9	0.256862
$889$	−3.06698e10	−1.46405
$890$	1.90026e9	0.0903540
$891$	6.60318e10	3.12738
$892$	2.21956e10	1.04710
$893$	8.91233e8	0.0418804
$894$	−1.05950e9	−0.0495929
$895$	−2.68852e9	−0.125352
$896$	−3.62753e10	−1.68474
$897$	−1.18358e10	−0.547549
$898$	1.40616e9	0.0647989
$899$	4.05827e10	1.86287
$900$	2.93864e10	1.34369
$901$	3.12091e10	1.42149
$902$	1.89061e8	0.00857785
$903$	−1.45091e10	−0.655744
$904$	−7.42563e9	−0.334306
$905$	−1.43706e10	−0.644475
$906$	−2.48258e10	−1.10906
$907$	−1.20573e9	−0.0536566	−0.0268283	−	0.999640i	$-0.508541\pi$
$907$	−1.20573e9	−0.0536566	−0.0268283	+	0.999640i	$0.508541\pi$
$908$	−1.39240e10	−0.617255
$909$	4.06229e10	1.79389
$910$	2.22428e9	0.0978465
$911$	−4.43668e10	−1.94421	−0.972107	−	0.234539i	$-0.924642\pi$
$911$	−4.43668e10	−1.94421	−0.972107	+	0.234539i	$0.924642\pi$
$912$	−4.86159e9	−0.212225
$913$	8.29694e9	0.360803
$914$	7.61077e9	0.329699
$915$	−1.56691e10	−0.676194
$916$	2.21174e10	0.950822
$917$	7.73908e10	3.31434
$918$	−3.41515e10	−1.45700
$919$	−7.89432e8	−0.0335514	−0.0167757	−	0.999859i	$-0.505340\pi$
$919$	−7.89432e8	−0.0335514	−0.0167757	+	0.999859i	$0.505340\pi$
$920$	1.36698e10	0.578768
$921$	4.67470e9	0.197172
$922$	4.75313e9	0.199720
$923$	−8.01882e8	−0.0335664
$924$	−8.17053e10	−3.40721
$925$	2.90773e9	0.120798
$926$	−1.29719e10	−0.536865
$927$	9.40081e9	0.387602
$928$	−2.71847e10	−1.11662
$929$	−3.33802e10	−1.36595	−0.682973	−	0.730443i	$-0.739313\pi$
$929$	−3.33802e10	−1.36595	−0.682973	+	0.730443i	$0.739313\pi$
$930$	1.90485e10	0.776551
$931$	−1.63851e10	−0.665464
$932$	6.45340e9	0.261116
$933$	1.03267e10	0.416272
$934$	−1.67831e10	−0.673998
$935$	2.11770e10	0.847274
$936$	1.14290e10	0.455558
$937$	3.90787e9	0.155186	0.0775928	−	0.996985i	$-0.475277\pi$
$937$	3.90787e9	0.155186	0.0775928	+	0.996985i	$0.475277\pi$
$938$	−2.40217e10	−0.950373
$939$	4.76353e10	1.87758
$940$	−1.31886e9	−0.0517907
$941$	−3.24442e10	−1.26933	−0.634664	−	0.772788i	$-0.718861\pi$
$941$	−3.24442e10	−1.26933	−0.634664	+	0.772788i	$0.718861\pi$
$942$	−7.47994e9	−0.291554
$943$	4.42234e8	0.0171736
$944$	−3.21084e9	−0.124227
$945$	−5.93507e10	−2.28778
$946$	−3.49668e9	−0.134288
$947$	−1.81618e10	−0.694918	−0.347459	−	0.937695i	$-0.612955\pi$
$947$	−1.81618e10	−0.694918	−0.347459	+	0.937695i	$0.612955\pi$
$948$	4.15659e10	1.58456
$949$	−3.33250e9	−0.126572
$950$	2.98853e9	0.113090
$951$	−2.50517e10	−0.944509
$952$	4.75399e10	1.78578
$953$	−4.18523e10	−1.56637	−0.783186	−	0.621788i	$-0.786407\pi$
$953$	−4.18523e10	−1.56637	−0.783186	+	0.621788i	$0.786407\pi$
$954$	−3.63788e10	−1.35653
$955$	−7.74151e9	−0.287617
$956$	5.03384e9	0.186336
$957$	−7.47089e10	−2.75537
$958$	−1.37266e10	−0.504410
$959$	3.24558e10	1.18830
$960$	−3.40532e9	−0.124225
$961$	5.26851e10	1.91494
$962$	4.91630e8	0.0178043
$963$	7.57743e10	2.73420
$964$	1.86957e10	0.672159
$965$	−8.59406e9	−0.307860
$966$	5.73870e10	2.04830
$967$	3.82386e10	1.35991	0.679953	−	0.733255i	$-0.262000\pi$
$967$	3.82386e10	1.35991	0.679953	+	0.733255i	$0.262000\pi$
$968$	−2.13033e10	−0.754889
$969$	1.99619e10	0.704803
$970$	−6.17739e9	−0.217322
$971$	3.05093e10	1.06946	0.534730	−	0.845023i	$-0.320413\pi$
$971$	3.05093e10	1.06946	0.534730	+	0.845023i	$0.320413\pi$
$972$	−3.63517e10	−1.26968
$973$	−8.72757e10	−3.03737
$974$	9.48803e9	0.329018
$975$	8.80803e9	0.304343
$976$	7.48143e9	0.257579
$977$	−1.03617e10	−0.355469	−0.177734	−	0.984079i	$-0.556877\pi$
$977$	−1.03617e10	−0.355469	−0.177734	+	0.984079i	$0.556877\pi$
$978$	7.91304e9	0.270494
$979$	−1.47280e10	−0.501655
$980$	2.42469e10	0.822935
$981$	2.68021e10	0.906415
$982$	−6.11534e9	−0.206077
$983$	3.89408e10	1.30758	0.653788	−	0.756678i	$-0.273179\pi$
$983$	3.89408e10	1.30758	0.653788	+	0.756678i	$0.273179\pi$
$984$	−6.06631e8	−0.0202975
$985$	2.22746e10	0.742647
$986$	1.88974e10	0.627816
$987$	−1.27359e10	−0.421618
$988$	−1.68279e9	−0.0555111
$989$	−8.17913e9	−0.268856
$990$	−2.46849e10	−0.808553
$991$	−5.90872e10	−1.92857	−0.964286	−	0.264864i	$-0.914673\pi$
$991$	−5.90872e10	−1.92857	−0.964286	+	0.264864i	$0.914673\pi$
$992$	−5.37212e10	−1.74725
$993$	−7.02187e10	−2.27578
$994$	3.88801e9	0.125567
$995$	−6.52926e9	−0.210128
$996$	−1.15734e10	−0.371155
$997$	−1.19995e10	−0.383467	−0.191734	−	0.981447i	$-0.561411\pi$
$997$	−1.19995e10	−0.383467	−0.191734	+	0.981447i	$0.561411\pi$
$998$	7.98474e9	0.254275
$999$	−1.31182e10	−0.416289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.a.b.1.7	✓	11
3.2	odd	2		333.8.a.d.1.5		11
4.3	odd	2		592.8.a.g.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.a.b.1.7	✓	11	1.1	even	1	trivial
333.8.a.d.1.5		11	3.2	odd	2
592.8.a.g.1.1		11	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q+5.43681 q^{2} +85.9489 q^{3} -98.4411 q^{4} -143.945 q^{5} +467.288 q^{6} +1592.07 q^{7} -1231.12 q^{8} +5200.21 q^{9} +O(q^{10})\)	\(q+5.43681 q^{2} +85.9489 q^{3} -98.4411 q^{4} -143.945 q^{5} +467.288 q^{6} +1592.07 q^{7} -1231.12 q^{8} +5200.21 q^{9} -782.599 q^{10} +6065.58 q^{11} -8460.90 q^{12} -1785.21 q^{13} +8655.77 q^{14} -12371.9 q^{15} +5907.11 q^{16} -24254.8 q^{17} +28272.5 q^{18} -9575.55 q^{19} +14170.1 q^{20} +136836. q^{21} +32977.4 q^{22} +77137.8 q^{23} -105813. q^{24} -57405.0 q^{25} -9705.85 q^{26} +258982. q^{27} -156725. q^{28} -143305. q^{29} -67263.5 q^{30} -283192. q^{31} +189699. q^{32} +521329. q^{33} -131869. q^{34} -229169. q^{35} -511914. q^{36} -50653.0 q^{37} -52060.4 q^{38} -153437. q^{39} +177213. q^{40} +5733.04 q^{41} +743954. q^{42} -106033. q^{43} -597102. q^{44} -748541. q^{45} +419384. q^{46} -93073.8 q^{47} +507709. q^{48} +1.71114e6 q^{49} -312100. q^{50} -2.08467e6 q^{51} +175738. q^{52} -1.28672e6 q^{53} +1.40803e6 q^{54} -873106. q^{55} -1.96002e6 q^{56} -823007. q^{57} -779120. q^{58} -543555. q^{59} +1.21790e6 q^{60} +1.26651e6 q^{61} -1.53966e6 q^{62} +8.27908e6 q^{63} +275247. q^{64} +256971. q^{65} +2.83437e6 q^{66} -2.77522e6 q^{67} +2.38767e6 q^{68} +6.62991e6 q^{69} -1.24595e6 q^{70} +449181. q^{71} -6.40206e6 q^{72} +1.86672e6 q^{73} -275391. q^{74} -4.93389e6 q^{75} +942627. q^{76} +9.65681e6 q^{77} -834207. q^{78} -4.91270e6 q^{79} -850296. q^{80} +1.08863e7 q^{81} +31169.4 q^{82} +1.36787e6 q^{83} -1.34703e7 q^{84} +3.49134e6 q^{85} -576480. q^{86} -1.23169e7 q^{87} -7.46744e6 q^{88} -2.42814e6 q^{89} -4.06968e6 q^{90} -2.84218e6 q^{91} -7.59353e6 q^{92} -2.43400e7 q^{93} -506025. q^{94} +1.37835e6 q^{95} +1.63044e7 q^{96} +7.89343e6 q^{97} +9.30314e6 q^{98} +3.15422e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 16 q^{2} + 121 q^{3} + 794 q^{4} + 376 q^{5} + 519 q^{6} + 2243 q^{7} + 3870 q^{8} + 9826 q^{9}+O(q^{10}) \) 11 * q + 16 * q^2 + 121 * q^3 + 794 * q^4 + 376 * q^5 + 519 * q^6 + 2243 * q^7 + 3870 * q^8 + 9826 * q^9	\( 11 q + 16 q^{2} + 121 q^{3} + 794 q^{4} + 376 q^{5} + 519 q^{6} + 2243 q^{7} + 3870 q^{8} + 9826 q^{9} - 12629 q^{10} + 9415 q^{11} + 27955 q^{12} + 12512 q^{13} + 18260 q^{14} + 25714 q^{15} + 167866 q^{16} + 54312 q^{17} + 163911 q^{18} + 97192 q^{19} + 85625 q^{20} + 97795 q^{21} - 12345 q^{22} + 107342 q^{23} + 163119 q^{24} + 165051 q^{25} + 61531 q^{26} + 446611 q^{27} + 215454 q^{28} + 41748 q^{29} - 1080964 q^{30} - 272248 q^{31} + 593306 q^{32} - 216525 q^{33} - 923600 q^{34} + 436814 q^{35} - 456119 q^{36} - 557183 q^{37} - 175872 q^{38} - 1587326 q^{39} - 3206863 q^{40} + 525465 q^{41} - 3814396 q^{42} - 1376086 q^{43} - 1337377 q^{44} - 2315492 q^{45} - 2037327 q^{46} + 2269179 q^{47} + 1779791 q^{48} + 2282536 q^{49} - 3881347 q^{50} - 103604 q^{51} - 4200495 q^{52} - 346415 q^{53} + 6349248 q^{54} + 4169374 q^{55} - 4307934 q^{56} + 6170792 q^{57} - 1334849 q^{58} + 4598828 q^{59} - 4448200 q^{60} + 6208418 q^{61} + 4732115 q^{62} + 6882994 q^{63} + 12483426 q^{64} + 9330160 q^{65} - 5715150 q^{66} + 2199016 q^{67} + 8095824 q^{68} + 13516268 q^{69} - 6471708 q^{70} + 4653285 q^{71} + 12839097 q^{72} - 1080699 q^{73} - 810448 q^{74} + 16194855 q^{75} + 1331888 q^{76} + 22058153 q^{77} - 23968103 q^{78} - 1336084 q^{79} - 89443 q^{80} + 9585355 q^{81} + 9689125 q^{82} + 28551309 q^{83} - 37602282 q^{84} + 13256012 q^{85} - 47733694 q^{86} - 5826578 q^{87} - 58704117 q^{88} - 8994788 q^{89} - 46526086 q^{90} - 696642 q^{91} - 41894465 q^{92} - 9859184 q^{93} - 26180048 q^{94} + 124152 q^{95} - 19485621 q^{96} - 3968264 q^{97} - 7312590 q^{98} - 14172918 q^{99}+O(q^{100}) \) 11 * q + 16 * q^2 + 121 * q^3 + 794 * q^4 + 376 * q^5 + 519 * q^6 + 2243 * q^7 + 3870 * q^8 + 9826 * q^9 - 12629 * q^10 + 9415 * q^11 + 27955 * q^12 + 12512 * q^13 + 18260 * q^14 + 25714 * q^15 + 167866 * q^16 + 54312 * q^17 + 163911 * q^18 + 97192 * q^19 + 85625 * q^20 + 97795 * q^21 - 12345 * q^22 + 107342 * q^23 + 163119 * q^24 + 165051 * q^25 + 61531 * q^26 + 446611 * q^27 + 215454 * q^28 + 41748 * q^29 - 1080964 * q^30 - 272248 * q^31 + 593306 * q^32 - 216525 * q^33 - 923600 * q^34 + 436814 * q^35 - 456119 * q^36 - 557183 * q^37 - 175872 * q^38 - 1587326 * q^39 - 3206863 * q^40 + 525465 * q^41 - 3814396 * q^42 - 1376086 * q^43 - 1337377 * q^44 - 2315492 * q^45 - 2037327 * q^46 + 2269179 * q^47 + 1779791 * q^48 + 2282536 * q^49 - 3881347 * q^50 - 103604 * q^51 - 4200495 * q^52 - 346415 * q^53 + 6349248 * q^54 + 4169374 * q^55 - 4307934 * q^56 + 6170792 * q^57 - 1334849 * q^58 + 4598828 * q^59 - 4448200 * q^60 + 6208418 * q^61 + 4732115 * q^62 + 6882994 * q^63 + 12483426 * q^64 + 9330160 * q^65 - 5715150 * q^66 + 2199016 * q^67 + 8095824 * q^68 + 13516268 * q^69 - 6471708 * q^70 + 4653285 * q^71 + 12839097 * q^72 - 1080699 * q^73 - 810448 * q^74 + 16194855 * q^75 + 1331888 * q^76 + 22058153 * q^77 - 23968103 * q^78 - 1336084 * q^79 - 89443 * q^80 + 9585355 * q^81 + 9689125 * q^82 + 28551309 * q^83 - 37602282 * q^84 + 13256012 * q^85 - 47733694 * q^86 - 5826578 * q^87 - 58704117 * q^88 - 8994788 * q^89 - 46526086 * q^90 - 696642 * q^91 - 41894465 * q^92 - 9859184 * q^93 - 26180048 * q^94 + 124152 * q^95 - 19485621 * q^96 - 3968264 * q^97 - 7312590 * q^98 - 14172918 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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