LMFDB - Embedded newform 37.8.a.b.1.11

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			1.11
Root			$20.9474$ 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)

$f(q)$	$=$	$q+21.9474 q^{2} -34.0550 q^{3} +353.689 q^{4} +19.5004 q^{5} -747.419 q^{6} +1140.68 q^{7} +4953.28 q^{8} -1027.26 q^{9} +O(q^{10})$	\(q+21.9474 q^{2} -34.0550 q^{3} +353.689 q^{4} +19.5004 q^{5} -747.419 q^{6} +1140.68 q^{7} +4953.28 q^{8} -1027.26 q^{9} +427.983 q^{10} -509.540 q^{11} -12044.9 q^{12} +6511.39 q^{13} +25034.9 q^{14} -664.085 q^{15} +63439.6 q^{16} -1214.06 q^{17} -22545.6 q^{18} -12262.4 q^{19} +6897.06 q^{20} -38845.7 q^{21} -11183.1 q^{22} -89398.1 q^{23} -168684. q^{24} -77744.7 q^{25} +142908. q^{26} +109462. q^{27} +403444. q^{28} -67161.2 q^{29} -14574.9 q^{30} -246761. q^{31} +758315. q^{32} +17352.4 q^{33} -26645.5 q^{34} +22243.6 q^{35} -363329. q^{36} -50653.0 q^{37} -269127. q^{38} -221745. q^{39} +96590.9 q^{40} +866417. q^{41} -852564. q^{42} -880011. q^{43} -180219. q^{44} -20031.9 q^{45} -1.96206e6 q^{46} +1.07927e6 q^{47} -2.16044e6 q^{48} +477600. q^{49} -1.70630e6 q^{50} +41344.8 q^{51} +2.30300e6 q^{52} -1.41778e6 q^{53} +2.40240e6 q^{54} -9936.22 q^{55} +5.65010e6 q^{56} +417595. q^{57} -1.47401e6 q^{58} +110096. q^{59} -234879. q^{60} -147392. q^{61} -5.41577e6 q^{62} -1.17177e6 q^{63} +8.52277e6 q^{64} +126974. q^{65} +380840. q^{66} +94484.7 q^{67} -429399. q^{68} +3.04445e6 q^{69} +488190. q^{70} +4.43876e6 q^{71} -5.08829e6 q^{72} +427386. q^{73} -1.11170e6 q^{74} +2.64760e6 q^{75} -4.33706e6 q^{76} -581220. q^{77} -4.86674e6 q^{78} +6.99423e6 q^{79} +1.23710e6 q^{80} -1.48110e6 q^{81} +1.90156e7 q^{82} +1.43810e6 q^{83} -1.37393e7 q^{84} -23674.6 q^{85} -1.93140e7 q^{86} +2.28717e6 q^{87} -2.52390e6 q^{88} -4.98866e6 q^{89} -439648. q^{90} +7.42739e6 q^{91} -3.16191e7 q^{92} +8.40346e6 q^{93} +2.36872e7 q^{94} -239120. q^{95} -2.58244e7 q^{96} -1.39302e7 q^{97} +1.04821e7 q^{98} +523428. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.9474	1.93990	0.969948	−	0.243314i	$-0.0782344\pi$
$2$	21.9474	1.93990	0.969948	+	0.243314i	$0.0782344\pi$
$3$	−34.0550	−0.728210	−0.364105	−	0.931358i	$-0.618625\pi$
$3$	−34.0550	−0.728210	−0.364105	+	0.931358i	$0.618625\pi$
$4$	353.689	2.76319
$5$	19.5004	0.0697666	0.0348833	−	0.999391i	$-0.488894\pi$
$5$	19.5004	0.0697666	0.0348833	+	0.999391i	$0.488894\pi$
$6$	−747.419	−1.41265
$7$	1140.68	1.25695	0.628477	−	0.777828i	$-0.283679\pi$
$7$	1140.68	1.25695	0.628477	+	0.777828i	$0.283679\pi$
$8$	4953.28	3.42041
$9$	−1027.26	−0.469710
$10$	427.983	0.135340
$11$	−509.540	−0.115426	−0.0577130	−	0.998333i	$-0.518381\pi$
$11$	−509.540	−0.115426	−0.0577130	+	0.998333i	$0.518381\pi$
$12$	−12044.9	−2.01219
$13$	6511.39	0.822000	0.411000	−	0.911635i	$-0.365180\pi$
$13$	6511.39	0.822000	0.411000	+	0.911635i	$0.365180\pi$
$14$	25034.9	2.43836
$15$	−664.085	−0.0508048
$16$	63439.6	3.87205
$17$	−1214.06	−0.0599334	−0.0299667	−	0.999551i	$-0.509540\pi$
$17$	−1214.06	−0.0599334	−0.0299667	+	0.999551i	$0.509540\pi$
$18$	−22545.6	−0.911189
$19$	−12262.4	−0.410144	−0.205072	−	0.978747i	$-0.565743\pi$
$19$	−12262.4	−0.410144	−0.205072	+	0.978747i	$0.565743\pi$
$20$	6897.06	0.192779
$21$	−38845.7	−0.915326
$22$	−11183.1	−0.223914
$23$	−89398.1	−1.53208	−0.766039	−	0.642794i	$-0.777775\pi$
$23$	−89398.1	−1.53208	−0.766039	+	0.642794i	$0.777775\pi$
$24$	−168684.	−2.49078
$25$	−77744.7	−0.995133
$26$	142908.	1.59459
$27$	109462.	1.07026
$28$	403444.	3.47321
$29$	−67161.2	−0.511358	−0.255679	−	0.966762i	$-0.582299\pi$
$29$	−67161.2	−0.511358	−0.255679	+	0.966762i	$0.582299\pi$
$30$	−14574.9	−0.0985559
$31$	−246761.	−1.48769	−0.743843	−	0.668354i	$-0.766999\pi$
$31$	−246761.	−1.48769	−0.743843	+	0.668354i	$0.766999\pi$
$32$	758315.	4.09095
$33$	17352.4	0.0840544
$34$	−26645.5	−0.116264
$35$	22243.6	0.0876934
$36$	−363329.	−1.29790
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	−269127.	−0.795637
$39$	−221745.	−0.598589
$40$	96590.9	0.238631
$41$	866417.	1.96329	0.981643	−	0.190726i	$-0.0610842\pi$
$41$	866417.	1.96329	0.981643	+	0.190726i	$0.0610842\pi$
$42$	−852564.	−1.77564
$43$	−880011.	−1.68791	−0.843954	−	0.536416i	$-0.819778\pi$
$43$	−880011.	−1.68791	−0.843954	+	0.536416i	$0.819778\pi$
$44$	−180219.	−0.318945
$45$	−20031.9	−0.0327701
$46$	−1.96206e6	−2.97207
$47$	1.07927e6	1.51631	0.758156	−	0.652073i	$-0.226100\pi$
$47$	1.07927e6	1.51631	0.758156	+	0.652073i	$0.226100\pi$
$48$	−2.16044e6	−2.81966
$49$	477600.	0.579933
$50$	−1.70630e6	−1.93045
$51$	41344.8	0.0436441
$52$	2.30300e6	2.27135
$53$	−1.41778e6	−1.30811	−0.654054	−	0.756448i	$-0.726933\pi$
$53$	−1.41778e6	−1.30811	−0.654054	+	0.756448i	$0.726933\pi$
$54$	2.40240e6	2.07619
$55$	−9936.22	−0.00805289
$56$	5.65010e6	4.29930
$57$	417595.	0.298671
$58$	−1.47401e6	−0.991982
$59$	110096.	0.0697895	0.0348948	−	0.999391i	$-0.488890\pi$
$59$	110096.	0.0697895	0.0348948	+	0.999391i	$0.488890\pi$
$60$	−234879.	−0.140383
$61$	−147392.	−0.0831418	−0.0415709	−	0.999136i	$-0.513236\pi$
$61$	−147392.	−0.0831418	−0.0415709	+	0.999136i	$0.513236\pi$
$62$	−5.41577e6	−2.88596
$63$	−1.17177e6	−0.590404
$64$	8.52277e6	4.06397
$65$	126974.	0.0573482
$66$	380840.	0.163057
$67$	94484.7	0.0383795	0.0191898	−	0.999816i	$-0.493891\pi$
$67$	94484.7	0.0383795	0.0191898	+	0.999816i	$0.493891\pi$
$68$	−429399.	−0.165608
$69$	3.04445e6	1.11567
$70$	488190.	0.170116
$71$	4.43876e6	1.47183	0.735914	−	0.677075i	$-0.236753\pi$
$71$	4.43876e6	1.47183	0.735914	+	0.677075i	$0.236753\pi$
$72$	−5.08829e6	−1.60660
$73$	427386.	0.128585	0.0642925	−	0.997931i	$-0.479521\pi$
$73$	427386.	0.128585	0.0642925	+	0.997931i	$0.479521\pi$
$74$	−1.11170e6	−0.318917
$75$	2.64760e6	0.724665
$76$	−4.33706e6	−1.13331
$77$	−581220.	−0.145085
$78$	−4.86674e6	−1.16120
$79$	6.99423e6	1.59605	0.798023	−	0.602627i	$-0.205879\pi$
$79$	6.99423e6	1.59605	0.798023	+	0.602627i	$0.205879\pi$
$80$	1.23710e6	0.270140
$81$	−1.48110e6	−0.309662
$82$	1.90156e7	3.80857
$83$	1.43810e6	0.276067	0.138034	−	0.990428i	$-0.455922\pi$
$83$	1.43810e6	0.276067	0.138034	+	0.990428i	$0.455922\pi$
$84$	−1.37393e7	−2.52922
$85$	−23674.6	−0.00418135
$86$	−1.93140e7	−3.27436
$87$	2.28717e6	0.372376
$88$	−2.52390e6	−0.394805
$89$	−4.98866e6	−0.750099	−0.375049	−	0.927005i	$-0.622374\pi$
$89$	−4.98866e6	−0.750099	−0.375049	+	0.927005i	$0.622374\pi$
$90$	−439648.	−0.0635706
$91$	7.42739e6	1.03322
$92$	−3.16191e7	−4.23343
$93$	8.40346e6	1.08335
$94$	2.36872e7	2.94149
$95$	−239120.	−0.0286144
$96$	−2.58244e7	−2.97907
$97$	−1.39302e7	−1.54973	−0.774863	−	0.632129i	$-0.782181\pi$
$97$	−1.39302e7	−1.54973	−0.774863	+	0.632129i	$0.782181\pi$
$98$	1.04821e7	1.12501
$99$	523428.	0.0542168
$100$	−2.74974e7	−2.74974
$101$	8.66754e6	0.837088	0.418544	−	0.908196i	$-0.362541\pi$
$101$	8.66754e6	0.837088	0.418544	+	0.908196i	$0.362541\pi$
$102$	907411.	0.0846649
$103$	6.58210e6	0.593518	0.296759	−	0.954952i	$-0.404094\pi$
$103$	6.58210e6	0.593518	0.296759	+	0.954952i	$0.404094\pi$
$104$	3.22528e7	2.81158
$105$	−757506.	−0.0638592
$106$	−3.11166e7	−2.53759
$107$	1.06872e7	0.843374	0.421687	−	0.906742i	$-0.361438\pi$
$107$	1.06872e7	0.843374	0.421687	+	0.906742i	$0.361438\pi$
$108$	3.87153e7	2.95733
$109$	8.76441e6	0.648231	0.324116	−	0.946017i	$-0.394933\pi$
$109$	8.76441e6	0.648231	0.324116	+	0.946017i	$0.394933\pi$
$110$	−218074.	−0.0156218
$111$	1.72499e6	0.119717
$112$	7.23641e7	4.86698
$113$	−1.88470e7	−1.22876	−0.614381	−	0.789010i	$-0.710594\pi$
$113$	−1.88470e7	−1.22876	−0.614381	+	0.789010i	$0.710594\pi$
$114$	9.16512e6	0.579390
$115$	−1.74330e6	−0.106888
$116$	−2.37542e7	−1.41298
$117$	−6.68886e6	−0.386102
$118$	2.41633e6	0.135384
$119$	−1.38485e6	−0.0753335
$120$	−3.28940e6	−0.173773
$121$	−1.92275e7	−0.986677
$122$	−3.23487e6	−0.161286
$123$	−2.95059e7	−1.42968
$124$	−8.72767e7	−4.11076
$125$	−3.03952e6	−0.139194
$126$	−2.57173e7	−1.14532
$127$	1.31849e7	0.571168	0.285584	−	0.958354i	$-0.407812\pi$
$127$	1.31849e7	0.571168	0.285584	+	0.958354i	$0.407812\pi$
$128$	8.99885e7	3.79273
$129$	2.99688e7	1.22915
$130$	2.78676e6	0.111249
$131$	−3.56129e7	−1.38407	−0.692034	−	0.721864i	$-0.743285\pi$
$131$	−3.56129e7	−1.38407	−0.692034	+	0.721864i	$0.743285\pi$
$132$	6.13735e6	0.232259
$133$	−1.39874e7	−0.515532
$134$	2.07369e6	0.0744523
$135$	2.13454e6	0.0746683
$136$	−6.01358e6	−0.204997
$137$	1.41524e7	0.470228	0.235114	−	0.971968i	$-0.424454\pi$
$137$	1.41524e7	0.470228	0.235114	+	0.971968i	$0.424454\pi$
$138$	6.68179e7	2.16429
$139$	1.37857e7	0.435388	0.217694	−	0.976017i	$-0.430146\pi$
$139$	1.37857e7	0.435388	0.217694	+	0.976017i	$0.430146\pi$
$140$	7.86732e6	0.242314
$141$	−3.67547e7	−1.10419
$142$	9.74192e7	2.85519
$143$	−3.31781e6	−0.0948802
$144$	−6.51687e7	−1.81874
$145$	−1.30967e6	−0.0356757
$146$	9.38002e6	0.249442
$147$	−1.62647e7	−0.422313
$148$	−1.79154e7	−0.454266
$149$	2.59033e7	0.641510	0.320755	−	0.947162i	$-0.396063\pi$
$149$	2.59033e7	0.641510	0.320755	+	0.947162i	$0.396063\pi$
$150$	5.81079e7	1.40578
$151$	−4.03302e7	−0.953260	−0.476630	−	0.879104i	$-0.658142\pi$
$151$	−4.03302e7	−0.953260	−0.476630	+	0.879104i	$0.658142\pi$
$152$	−6.07390e7	−1.40286
$153$	1.24715e6	0.0281513
$154$	−1.27563e7	−0.281450
$155$	−4.81194e6	−0.103791
$156$	−7.84289e7	−1.65402
$157$	−5.07919e7	−1.04748	−0.523740	−	0.851878i	$-0.675464\pi$
$157$	−5.07919e7	−1.04748	−0.523740	+	0.851878i	$0.675464\pi$
$158$	1.53505e8	3.09616
$159$	4.82825e7	0.952577
$160$	1.47874e7	0.285412
$161$	−1.01974e8	−1.92575
$162$	−3.25064e7	−0.600712
$163$	1.24454e7	0.225088	0.112544	−	0.993647i	$-0.464100\pi$
$163$	1.24454e7	0.225088	0.112544	+	0.993647i	$0.464100\pi$
$164$	3.06442e8	5.42494
$165$	338378.	0.00586419
$166$	3.15625e7	0.535541
$167$	4.66102e7	0.774415	0.387207	−	0.921993i	$-0.373440\pi$
$167$	4.66102e7	0.774415	0.387207	+	0.921993i	$0.373440\pi$
$168$	−1.92414e8	−3.13079
$169$	−2.03503e7	−0.324316
$170$	−519596.	−0.00811138
$171$	1.25966e7	0.192649
$172$	−3.11250e8	−4.66402
$173$	2.04477e7	0.300251	0.150125	−	0.988667i	$-0.452032\pi$
$173$	2.04477e7	0.300251	0.150125	+	0.988667i	$0.452032\pi$
$174$	5.01976e7	0.722371
$175$	−8.86816e7	−1.25084
$176$	−3.23250e7	−0.446935
$177$	−3.74933e6	−0.0508214
$178$	−1.09488e8	−1.45511
$179$	2.73156e7	0.355980	0.177990	−	0.984032i	$-0.443041\pi$
$179$	2.73156e7	0.355980	0.177990	+	0.984032i	$0.443041\pi$
$180$	−7.08505e6	−0.0905501
$181$	7.64151e7	0.957864	0.478932	−	0.877852i	$-0.341024\pi$
$181$	7.64151e7	0.957864	0.478932	+	0.877852i	$0.341024\pi$
$182$	1.63012e8	2.00433
$183$	5.01943e6	0.0605447
$184$	−4.42814e8	−5.24034
$185$	−987752.	−0.0114696
$186$	1.84434e8	2.10158
$187$	618612.	0.00691787
$188$	3.81727e8	4.18987
$189$	1.24860e8	1.34526
$190$	−5.24808e6	−0.0555089
$191$	7.45080e7	0.773724	0.386862	−	0.922138i	$-0.373559\pi$
$191$	7.45080e7	0.773724	0.386862	+	0.922138i	$0.373559\pi$
$192$	−2.90243e8	−2.95943
$193$	−6.62343e7	−0.663181	−0.331591	−	0.943423i	$-0.607585\pi$
$193$	−6.62343e7	−0.663181	−0.331591	+	0.943423i	$0.607585\pi$
$194$	−3.05731e8	−3.00631
$195$	−4.32412e6	−0.0417615
$196$	1.68922e8	1.60247
$197$	2.80902e7	0.261772	0.130886	−	0.991397i	$-0.458218\pi$
$197$	2.80902e7	0.261772	0.130886	+	0.991397i	$0.458218\pi$
$198$	1.14879e7	0.105175
$199$	−1.18540e8	−1.06630	−0.533151	−	0.846020i	$-0.678992\pi$
$199$	−1.18540e8	−1.06630	−0.533151	+	0.846020i	$0.678992\pi$
$200$	−3.85092e8	−3.40376
$201$	−3.21768e6	−0.0279484
$202$	1.90230e8	1.62386
$203$	−7.66092e7	−0.642754
$204$	1.46232e7	0.120597
$205$	1.68955e7	0.136972
$206$	1.44460e8	1.15136
$207$	9.18348e7	0.719633
$208$	4.13080e8	3.18282
$209$	6.24816e6	0.0473413
$210$	−1.66253e7	−0.123880
$211$	2.46660e8	1.80763	0.903815	−	0.427924i	$-0.140755\pi$
$211$	2.46660e8	1.80763	0.903815	+	0.427924i	$0.140755\pi$
$212$	−5.01453e8	−3.61456
$213$	−1.51162e8	−1.07180
$214$	2.34556e8	1.63606
$215$	−1.71605e7	−0.117760
$216$	5.42194e8	3.66072
$217$	−2.81475e8	−1.86995
$218$	1.92356e8	1.25750
$219$	−1.45546e7	−0.0936369
$220$	−3.51433e6	−0.0222517
$221$	−7.90521e6	−0.0492652
$222$	3.78590e7	0.232238
$223$	1.78015e8	1.07496	0.537478	−	0.843278i	$-0.319377\pi$
$223$	1.78015e8	1.07496	0.537478	+	0.843278i	$0.319377\pi$
$224$	8.64992e8	5.14214
$225$	7.98638e7	0.467424
$226$	−4.13643e8	−2.38367
$227$	3.05025e8	1.73079	0.865397	−	0.501087i	$-0.167066\pi$
$227$	3.05025e8	1.73079	0.865397	+	0.501087i	$0.167066\pi$
$228$	1.47699e8	0.825286
$229$	3.06270e8	1.68531	0.842655	−	0.538454i	$-0.180992\pi$
$229$	3.06270e8	1.68531	0.842655	+	0.538454i	$0.180992\pi$
$230$	−3.82608e7	−0.207351
$231$	1.97935e7	0.105652
$232$	−3.32668e8	−1.74906
$233$	−7.27020e7	−0.376531	−0.188265	−	0.982118i	$-0.560286\pi$
$233$	−7.27020e7	−0.376531	−0.188265	+	0.982118i	$0.560286\pi$
$234$	−1.46803e8	−0.748997
$235$	2.10462e7	0.105788
$236$	3.89398e7	0.192842
$237$	−2.38189e8	−1.16226
$238$	−3.03938e7	−0.146139
$239$	−1.68209e8	−0.796996	−0.398498	−	0.917169i	$-0.630468\pi$
$239$	−1.68209e8	−0.796996	−0.398498	+	0.917169i	$0.630468\pi$
$240$	−4.21293e7	−0.196718
$241$	5.03908e7	0.231895	0.115948	−	0.993255i	$-0.463010\pi$
$241$	5.03908e7	0.231895	0.115948	+	0.993255i	$0.463010\pi$
$242$	−4.21995e8	−1.91405
$243$	−1.88953e8	−0.844759
$244$	−5.21309e7	−0.229737
$245$	9.31337e6	0.0404600
$246$	−6.47577e8	−2.77344
$247$	−7.98450e7	−0.337138
$248$	−1.22228e9	−5.08850
$249$	−4.89744e7	−0.201035
$250$	−6.67095e7	−0.270021
$251$	3.45420e7	0.137876	0.0689382	−	0.997621i	$-0.478039\pi$
$251$	3.45420e7	0.137876	0.0689382	+	0.997621i	$0.478039\pi$
$252$	−4.14441e8	−1.63140
$253$	4.55519e7	0.176842
$254$	2.89375e8	1.10801
$255$	806239.	0.00304490
$256$	8.84100e8	3.29353
$257$	6.26541e7	0.230242	0.115121	−	0.993351i	$-0.463274\pi$
$257$	6.26541e7	0.230242	0.115121	+	0.993351i	$0.463274\pi$
$258$	6.57737e8	2.38442
$259$	−5.77787e7	−0.206642
$260$	4.49094e7	0.158464
$261$	6.89918e7	0.240190
$262$	−7.81611e8	−2.68495
$263$	−1.37469e8	−0.465970	−0.232985	−	0.972480i	$-0.574849\pi$
$263$	−1.37469e8	−0.465970	−0.232985	+	0.972480i	$0.574849\pi$
$264$	8.59513e7	0.287501
$265$	−2.76472e7	−0.0912623
$266$	−3.06987e8	−1.00008
$267$	1.69889e8	0.546230
$268$	3.34182e7	0.106050
$269$	−2.37952e8	−0.745344	−0.372672	−	0.927963i	$-0.621558\pi$
$269$	−2.37952e8	−0.745344	−0.372672	+	0.927963i	$0.621558\pi$
$270$	4.68476e7	0.144849
$271$	−1.99834e8	−0.609925	−0.304962	−	0.952364i	$-0.598644\pi$
$271$	−1.99834e8	−0.609925	−0.304962	+	0.952364i	$0.598644\pi$
$272$	−7.70195e7	−0.232065
$273$	−2.52940e8	−0.752398
$274$	3.10609e8	0.912193
$275$	3.96140e7	0.114864
$276$	1.07679e9	3.08283
$277$	1.59939e8	0.452141	0.226071	−	0.974111i	$-0.427412\pi$
$277$	1.59939e8	0.452141	0.226071	+	0.974111i	$0.427412\pi$
$278$	3.02560e8	0.844607
$279$	2.53487e8	0.698781
$280$	1.10179e8	0.299948
$281$	−3.34772e8	−0.900071	−0.450035	−	0.893011i	$-0.648589\pi$
$281$	−3.34772e8	−0.900071	−0.450035	+	0.893011i	$0.648589\pi$
$282$	−8.06669e8	−2.14202
$283$	1.76813e8	0.463728	0.231864	−	0.972748i	$-0.425518\pi$
$283$	1.76813e8	0.463728	0.231864	+	0.972748i	$0.425518\pi$
$284$	1.56994e9	4.06695
$285$	8.14325e6	0.0208373
$286$	−7.28174e7	−0.184058
$287$	9.88302e8	2.46776
$288$	−7.78983e8	−1.92156
$289$	−4.08865e8	−0.996408
$290$	−2.87438e7	−0.0692072
$291$	4.74392e8	1.12853
$292$	1.51162e8	0.355305
$293$	6.50418e8	1.51062	0.755311	−	0.655366i	$-0.227486\pi$
$293$	6.50418e8	1.51062	0.755311	+	0.655366i	$0.227486\pi$
$294$	−3.56967e8	−0.819243
$295$	2.14692e6	0.00486898
$296$	−2.50899e8	−0.562312
$297$	−5.57750e7	−0.123536
$298$	5.68511e8	1.24446
$299$	−5.82106e8	−1.25937
$300$	9.36426e8	2.00239
$301$	−1.00381e9	−2.12162
$302$	−8.85144e8	−1.84922
$303$	−2.95173e8	−0.609576
$304$	−7.77919e8	−1.58810
$305$	−2.87420e6	−0.00580052
$306$	2.73717e7	0.0546106
$307$	−3.37178e8	−0.665081	−0.332541	−	0.943089i	$-0.607906\pi$
$307$	−3.37178e8	−0.665081	−0.332541	+	0.943089i	$0.607906\pi$
$308$	−2.05571e8	−0.400899
$309$	−2.24153e8	−0.432206
$310$	−1.05610e8	−0.201343
$311$	7.72697e8	1.45663	0.728313	−	0.685245i	$-0.240305\pi$
$311$	7.72697e8	1.45663	0.728313	+	0.685245i	$0.240305\pi$
$312$	−1.09837e9	−2.04742
$313$	3.15004e8	0.580646	0.290323	−	0.956929i	$-0.406237\pi$
$313$	3.15004e8	0.580646	0.290323	+	0.956929i	$0.406237\pi$
$314$	−1.11475e9	−2.03200
$315$	−2.28499e7	−0.0411905
$316$	2.47378e9	4.41018
$317$	6.19543e8	1.09236	0.546178	−	0.837669i	$-0.316082\pi$
$317$	6.19543e8	1.09236	0.546178	+	0.837669i	$0.316082\pi$
$318$	1.05968e9	1.84790
$319$	3.42213e7	0.0590241
$320$	1.66197e8	0.283530
$321$	−3.63952e8	−0.614153
$322$	−2.23807e9	−3.73576
$323$	1.48872e7	0.0245813
$324$	−5.23850e8	−0.855656
$325$	−5.06226e8	−0.817999
$326$	2.73144e8	0.436646
$327$	−2.98472e8	−0.472048
$328$	4.29161e9	6.71525
$329$	1.23110e9	1.90594
$330$	7.42652e6	0.0113759
$331$	2.39925e8	0.363645	0.181823	−	0.983331i	$-0.441800\pi$
$331$	2.39925e8	0.363645	0.181823	+	0.983331i	$0.441800\pi$
$332$	5.08639e8	0.762827
$333$	5.20336e7	0.0772199
$334$	1.02297e9	1.50228
$335$	1.84249e6	0.00267761
$336$	−2.46436e9	−3.54419
$337$	−1.47402e8	−0.209796	−0.104898	−	0.994483i	$-0.533452\pi$
$337$	−1.47402e8	−0.209796	−0.104898	+	0.994483i	$0.533452\pi$
$338$	−4.46637e8	−0.629139
$339$	6.41835e8	0.894796
$340$	−8.37344e6	−0.0115539
$341$	1.25735e8	0.171718
$342$	2.76462e8	0.373719
$343$	−3.94609e8	−0.528005
$344$	−4.35895e9	−5.77334
$345$	5.93680e7	0.0778369
$346$	4.48775e8	0.582455
$347$	9.16280e8	1.17727	0.588634	−	0.808400i	$-0.299666\pi$
$347$	9.16280e8	1.17727	0.588634	+	0.808400i	$0.299666\pi$
$348$	8.08948e8	1.02895
$349$	−8.02526e8	−1.01058	−0.505289	−	0.862950i	$-0.668614\pi$
$349$	−8.02526e8	−1.01058	−0.505289	+	0.862950i	$0.668614\pi$
$350$	−1.94633e9	−2.42649
$351$	7.12746e8	0.879752
$352$	−3.86392e8	−0.472203
$353$	−8.00581e7	−0.0968710	−0.0484355	−	0.998826i	$-0.515424\pi$
$353$	−8.00581e7	−0.0968710	−0.0484355	+	0.998826i	$0.515424\pi$
$354$	−8.22880e7	−0.0985882
$355$	8.65574e7	0.102685
$356$	−1.76443e9	−2.07267
$357$	4.71610e7	0.0548586
$358$	5.99507e8	0.690563
$359$	1.13788e9	1.29797	0.648984	−	0.760802i	$-0.275194\pi$
$359$	1.13788e9	1.29797	0.648984	+	0.760802i	$0.275194\pi$
$360$	−9.92236e7	−0.112087
$361$	−7.43506e8	−0.831782
$362$	1.67711e9	1.85816
$363$	6.54794e8	0.718508
$364$	2.62698e9	2.85498
$365$	8.33419e6	0.00897095
$366$	1.10164e8	0.117450
$367$	−5.49343e8	−0.580113	−0.290056	−	0.957010i	$-0.593674\pi$
$367$	−5.49343e8	−0.580113	−0.290056	+	0.957010i	$0.593674\pi$
$368$	−5.67138e9	−5.93228
$369$	−8.90033e8	−0.922176
$370$	−2.16786e7	−0.0222498
$371$	−1.61723e9	−1.64423
$372$	2.97221e9	2.99350
$373$	−4.46127e8	−0.445120	−0.222560	−	0.974919i	$-0.571441\pi$
$373$	−4.46127e8	−0.445120	−0.222560	+	0.974919i	$0.571441\pi$
$374$	1.35769e7	0.0134199
$375$	1.03511e8	0.101362
$376$	5.34595e9	5.18641
$377$	−4.37313e8	−0.420337
$378$	2.74036e9	2.60967
$379$	1.59198e9	1.50211	0.751053	−	0.660242i	$-0.229546\pi$
$379$	1.59198e9	1.50211	0.751053	+	0.660242i	$0.229546\pi$
$380$	−8.45742e7	−0.0790670
$381$	−4.49012e8	−0.415931
$382$	1.63526e9	1.50094
$383$	7.80053e8	0.709461	0.354730	−	0.934969i	$-0.384573\pi$
$383$	7.80053e8	0.709461	0.354730	+	0.934969i	$0.384573\pi$
$384$	−3.06456e9	−2.76191
$385$	−1.13340e7	−0.0101221
$386$	−1.45367e9	−1.28650
$387$	9.03997e8	0.792827
$388$	−4.92694e9	−4.28219
$389$	−8.49446e8	−0.731665	−0.365832	−	0.930681i	$-0.619216\pi$
$389$	−8.49446e8	−0.731665	−0.365832	+	0.930681i	$0.619216\pi$
$390$	−9.49031e7	−0.0810130
$391$	1.08535e8	0.0918226
$392$	2.36569e9	1.98361
$393$	1.21280e9	1.00789
$394$	6.16508e8	0.507810
$395$	1.36390e8	0.111351
$396$	1.85131e8	0.149812
$397$	−1.80575e9	−1.44841	−0.724203	−	0.689587i	$-0.757792\pi$
$397$	−1.80575e9	−1.44841	−0.724203	+	0.689587i	$0.757792\pi$
$398$	−2.60165e9	−2.06851
$399$	4.76340e8	0.375416
$400$	−4.93210e9	−3.85320
$401$	−9.54063e8	−0.738876	−0.369438	−	0.929255i	$-0.620450\pi$
$401$	−9.54063e8	−0.738876	−0.369438	+	0.929255i	$0.620450\pi$
$402$	−7.06197e7	−0.0542169
$403$	−1.60676e9	−1.22288
$404$	3.06561e9	2.31304
$405$	−2.88821e7	−0.0216041
$406$	−1.68137e9	−1.24688
$407$	2.58097e7	0.0189759
$408$	2.04793e8	0.149281
$409$	−1.83232e9	−1.32425	−0.662126	−	0.749392i	$-0.730346\pi$
$409$	−1.83232e9	−1.32425	−0.662126	+	0.749392i	$0.730346\pi$
$410$	3.70812e8	0.265711
$411$	−4.81960e8	−0.342425
$412$	2.32801e9	1.64001
$413$	1.25584e8	0.0877222
$414$	2.01554e9	1.39601
$415$	2.80434e7	0.0192603
$416$	4.93768e9	3.36276
$417$	−4.69472e8	−0.317054
$418$	1.37131e8	0.0918372
$419$	1.27659e9	0.847817	0.423908	−	0.905705i	$-0.360658\pi$
$419$	1.27659e9	0.847817	0.423908	+	0.905705i	$0.360658\pi$
$420$	−2.67921e8	−0.176455
$421$	−1.11085e9	−0.725548	−0.362774	−	0.931877i	$-0.618170\pi$
$421$	−1.11085e9	−0.725548	−0.362774	+	0.931877i	$0.618170\pi$
$422$	5.41354e9	3.50661
$423$	−1.10869e9	−0.712228
$424$	−7.02267e9	−4.47427
$425$	9.43867e7	0.0596417
$426$	−3.31761e9	−2.07918
$427$	−1.68126e8	−0.104505
$428$	3.77994e9	2.33040
$429$	1.12988e8	0.0690927
$430$	−3.76629e8	−0.228441
$431$	−3.08376e9	−1.85528	−0.927641	−	0.373474i	$-0.878167\pi$
$431$	−3.08376e9	−1.85528	−0.927641	+	0.373474i	$0.878167\pi$
$432$	6.94420e9	4.14409
$433$	−2.04002e9	−1.20761	−0.603805	−	0.797132i	$-0.706349\pi$
$433$	−2.04002e9	−1.20761	−0.603805	+	0.797132i	$0.706349\pi$
$434$	−6.17764e9	−3.62751
$435$	4.46007e7	0.0259794
$436$	3.09987e9	1.79119
$437$	1.09623e9	0.628373
$438$	−3.19437e8	−0.181646
$439$	4.67584e8	0.263775	0.131887	−	0.991265i	$-0.457896\pi$
$439$	4.67584e8	0.263775	0.131887	+	0.991265i	$0.457896\pi$
$440$	−4.92169e7	−0.0275442
$441$	−4.90617e8	−0.272400
$442$	−1.73499e8	−0.0955694
$443$	−1.56407e9	−0.854757	−0.427379	−	0.904073i	$-0.640563\pi$
$443$	−1.56407e9	−0.854757	−0.427379	+	0.904073i	$0.640563\pi$
$444$	6.10109e8	0.330801
$445$	−9.72806e7	−0.0523319
$446$	3.90698e9	2.08530
$447$	−8.82138e8	−0.467154
$448$	9.72173e9	5.10823
$449$	3.29544e8	0.171811	0.0859056	−	0.996303i	$-0.472622\pi$
$449$	3.29544e8	0.171811	0.0859056	+	0.996303i	$0.472622\pi$
$450$	1.75280e9	0.906754
$451$	−4.41474e8	−0.226614
$452$	−6.66597e9	−3.39531
$453$	1.37345e9	0.694173
$454$	6.69451e9	3.35756
$455$	1.44837e8	0.0720840
$456$	2.06847e9	1.02158
$457$	−3.02546e8	−0.148281	−0.0741403	−	0.997248i	$-0.523621\pi$
$457$	−3.02546e8	−0.148281	−0.0741403	+	0.997248i	$0.523621\pi$
$458$	6.72182e9	3.26932
$459$	−1.32893e8	−0.0641441
$460$	−6.16584e8	−0.295352
$461$	3.43809e9	1.63442	0.817212	−	0.576338i	$-0.195519\pi$
$461$	3.43809e9	1.63442	0.817212	+	0.576338i	$0.195519\pi$
$462$	4.34415e8	0.204955
$463$	−2.23289e9	−1.04552	−0.522762	−	0.852479i	$-0.675098\pi$
$463$	−2.23289e9	−1.04552	−0.522762	+	0.852479i	$0.675098\pi$
$464$	−4.26068e9	−1.98000
$465$	1.63871e8	0.0755815
$466$	−1.59562e9	−0.730430
$467$	4.28244e8	0.194573	0.0972865	−	0.995256i	$-0.468984\pi$
$467$	4.28244e8	0.194573	0.0972865	+	0.995256i	$0.468984\pi$
$468$	−2.36578e9	−1.06687
$469$	1.07776e8	0.0482413
$470$	4.61910e8	0.205218
$471$	1.72972e9	0.762786
$472$	5.45338e8	0.238709
$473$	4.48401e8	0.194828
$474$	−5.22763e9	−2.25466
$475$	9.53334e8	0.408148
$476$	−4.89806e8	−0.208161
$477$	1.45642e9	0.614432
$478$	−3.69175e9	−1.54609
$479$	−3.56899e9	−1.48378	−0.741892	−	0.670520i	$-0.766071\pi$
$479$	−3.56899e9	−1.48378	−0.741892	+	0.670520i	$0.766071\pi$
$480$	−5.03585e8	−0.207840
$481$	−3.29821e8	−0.135136
$482$	1.10595e9	0.449852
$483$	3.47274e9	1.40235
$484$	−6.80057e9	−2.72638
$485$	−2.71643e8	−0.108119
$486$	−4.14704e9	−1.63874
$487$	3.68461e9	1.44557	0.722786	−	0.691072i	$-0.242861\pi$
$487$	3.68461e9	1.44557	0.722786	+	0.691072i	$0.242861\pi$
$488$	−7.30074e8	−0.284379
$489$	−4.23828e8	−0.163911
$490$	2.04404e8	0.0784881
$491$	−2.11559e9	−0.806578	−0.403289	−	0.915073i	$-0.632133\pi$
$491$	−2.11559e9	−0.806578	−0.403289	+	0.915073i	$0.632133\pi$
$492$	−1.04359e10	−3.95050
$493$	8.15377e7	0.0306474
$494$	−1.75239e9	−0.654013
$495$	1.02070e7	0.00378252
$496$	−1.56544e10	−5.76039
$497$	5.06319e9	1.85002
$498$	−1.07486e9	−0.389987
$499$	3.85228e9	1.38792	0.693962	−	0.720012i	$-0.255864\pi$
$499$	3.85228e9	1.38792	0.693962	+	0.720012i	$0.255864\pi$
$500$	−1.07504e9	−0.384619
$501$	−1.58731e9	−0.563937
$502$	7.58109e8	0.267466
$503$	2.46964e9	0.865259	0.432629	−	0.901572i	$-0.357586\pi$
$503$	2.46964e9	0.865259	0.432629	+	0.901572i	$0.357586\pi$
$504$	−5.80410e9	−2.01942
$505$	1.69020e8	0.0584008
$506$	9.99746e8	0.343054
$507$	6.93031e8	0.236170
$508$	4.66336e9	1.57825
$509$	3.91697e9	1.31655	0.658276	−	0.752777i	$-0.271286\pi$
$509$	3.91697e9	1.31655	0.658276	+	0.752777i	$0.271286\pi$
$510$	1.76949e7	0.00590679
$511$	4.87509e8	0.161625
$512$	7.88517e9	2.59637
$513$	−1.34226e9	−0.438960
$514$	1.37510e9	0.446645
$515$	1.28353e8	0.0414078
$516$	1.05996e10	3.39638
$517$	−5.49933e8	−0.175022
$518$	−1.26809e9	−0.400864
$519$	−6.96348e8	−0.218646
$520$	6.28941e8	0.196154
$521$	−1.65951e8	−0.0514101	−0.0257050	−	0.999670i	$-0.508183\pi$
$521$	−1.65951e8	−0.0514101	−0.0257050	+	0.999670i	$0.508183\pi$
$522$	1.51419e9	0.465944
$523$	−4.36428e9	−1.33400	−0.667001	−	0.745056i	$-0.732423\pi$
$523$	−4.36428e9	−1.33400	−0.667001	+	0.745056i	$0.732423\pi$
$524$	−1.25959e10	−3.82445
$525$	3.02005e9	0.910871
$526$	−3.01708e9	−0.903934
$527$	2.99583e8	0.0891620
$528$	1.10083e9	0.325463
$529$	4.58720e9	1.34726
$530$	−6.06785e8	−0.177039
$531$	−1.13097e8	−0.0327809
$532$	−4.94718e9	−1.42452
$533$	5.64158e9	1.61382
$534$	3.72862e9	1.05963
$535$	2.08404e8	0.0588393
$536$	4.68010e8	0.131274
$537$	−9.30233e8	−0.259228
$538$	−5.22243e9	−1.44589
$539$	−2.43356e8	−0.0669394
$540$	7.54963e8	0.206323
$541$	2.36183e9	0.641295	0.320648	−	0.947199i	$-0.396099\pi$
$541$	2.36183e9	0.641295	0.320648	+	0.947199i	$0.396099\pi$
$542$	−4.38583e9	−1.18319
$543$	−2.60232e9	−0.697526
$544$	−9.20639e8	−0.245185
$545$	1.70909e8	0.0452249
$546$	−5.55137e9	−1.45957
$547$	1.32177e9	0.345303	0.172651	−	0.984983i	$-0.444767\pi$
$547$	1.32177e9	0.345303	0.172651	+	0.984983i	$0.444767\pi$
$548$	5.00555e9	1.29933
$549$	1.51409e8	0.0390525
$550$	8.69426e8	0.222825
$551$	8.23555e8	0.209731
$552$	1.50800e10	3.81607
$553$	7.97816e9	2.00616
$554$	3.51024e9	0.877107
$555$	3.36379e7	0.00835225
$556$	4.87584e9	1.20306
$557$	−3.71117e9	−0.909949	−0.454975	−	0.890504i	$-0.650352\pi$
$557$	−3.71117e9	−0.909949	−0.454975	+	0.890504i	$0.650352\pi$
$558$	5.56339e9	1.35556
$559$	−5.73009e9	−1.38746
$560$	1.41113e9	0.339553
$561$	−2.10668e7	−0.00503766
$562$	−7.34737e9	−1.74604
$563$	1.75416e9	0.414276	0.207138	−	0.978312i	$-0.433585\pi$
$563$	1.75416e9	0.414276	0.207138	+	0.978312i	$0.433585\pi$
$564$	−1.29997e10	−3.05110
$565$	−3.67523e8	−0.0857266
$566$	3.88060e9	0.899583
$567$	−1.68946e9	−0.389231
$568$	2.19864e10	5.03426
$569$	−6.48080e9	−1.47481	−0.737404	−	0.675452i	$-0.763949\pi$
$569$	−6.48080e9	−1.47481	−0.737404	+	0.675452i	$0.763949\pi$
$570$	1.78723e8	0.0404221
$571$	−8.24336e9	−1.85301	−0.926505	−	0.376283i	$-0.877202\pi$
$571$	−8.24336e9	−1.85301	−0.926505	+	0.376283i	$0.877202\pi$
$572$	−1.17347e9	−0.262172
$573$	−2.53737e9	−0.563433
$574$	2.16907e10	4.78720
$575$	6.95023e9	1.52462
$576$	−8.75507e9	−1.90889
$577$	−6.53740e9	−1.41674	−0.708370	−	0.705842i	$-0.750569\pi$
$577$	−6.53740e9	−1.41674	−0.708370	+	0.705842i	$0.750569\pi$
$578$	−8.97352e9	−1.93293
$579$	2.25561e9	0.482935
$580$	−4.63215e8	−0.0985790
$581$	1.64040e9	0.347004
$582$	1.04117e10	2.18922
$583$	7.22416e8	0.150990
$584$	2.11697e9	0.439814
$585$	−1.30435e8	−0.0269370
$586$	1.42750e10	2.93045
$587$	−7.98063e9	−1.62856	−0.814280	−	0.580472i	$-0.802868\pi$
$587$	−7.98063e9	−1.62856	−0.814280	+	0.580472i	$0.802868\pi$
$588$	−5.75263e9	−1.16693
$589$	3.02588e9	0.610166
$590$	4.71192e7	0.00944531
$591$	−9.56613e8	−0.190625
$592$	−3.21341e9	−0.636561
$593$	2.55820e9	0.503783	0.251891	−	0.967756i	$-0.418947\pi$
$593$	2.55820e9	0.503783	0.251891	+	0.967756i	$0.418947\pi$
$594$	−1.22412e9	−0.239646
$595$	−2.70051e7	−0.00525576
$596$	9.16172e9	1.77262
$597$	4.03689e9	0.776491
$598$	−1.27757e10	−2.44304
$599$	5.36491e8	0.101993	0.0509963	−	0.998699i	$-0.483760\pi$
$599$	5.36491e8	0.101993	0.0509963	+	0.998699i	$0.483760\pi$
$600$	1.31143e10	2.47865
$601$	−2.86639e9	−0.538610	−0.269305	−	0.963055i	$-0.586794\pi$
$601$	−2.86639e9	−0.538610	−0.269305	+	0.963055i	$0.586794\pi$
$602$	−2.20310e10	−4.11572
$603$	−9.70600e7	−0.0180273
$604$	−1.42643e10	−2.63404
$605$	−3.74944e8	−0.0688371
$606$	−6.47829e9	−1.18251
$607$	−2.05203e8	−0.0372411	−0.0186205	−	0.999827i	$-0.505927\pi$
$607$	−2.05203e8	−0.0372411	−0.0186205	+	0.999827i	$0.505927\pi$
$608$	−9.29873e9	−1.67788
$609$	2.60893e9	0.468060
$610$	−6.30812e7	−0.0112524
$611$	7.02757e9	1.24641
$612$	4.41103e8	0.0777875
$613$	4.22323e9	0.740513	0.370257	−	0.928929i	$-0.379270\pi$
$613$	4.22323e9	0.740513	0.370257	+	0.928929i	$0.379270\pi$
$614$	−7.40018e9	−1.29019
$615$	−5.75375e8	−0.0997443
$616$	−2.87895e9	−0.496251
$617$	−4.10351e9	−0.703326	−0.351663	−	0.936127i	$-0.614384\pi$
$617$	−4.10351e9	−0.703326	−0.351663	+	0.936127i	$0.614384\pi$
$618$	−4.91959e9	−0.838434
$619$	−5.01312e9	−0.849553	−0.424776	−	0.905298i	$-0.639647\pi$
$619$	−5.01312e9	−0.849553	−0.424776	+	0.905298i	$0.639647\pi$
$620$	−1.70193e9	−0.286794
$621$	−9.78565e9	−1.63972
$622$	1.69587e10	2.82570
$623$	−5.69044e9	−0.942840
$624$	−1.40674e10	−2.31776
$625$	6.01454e9	0.985422
$626$	6.91353e9	1.12639
$627$	−2.12781e8	−0.0344744
$628$	−1.79645e10	−2.89439
$629$	6.14957e7	0.00985299
$630$	−5.01496e8	−0.0799053
$631$	−2.96749e9	−0.470205	−0.235102	−	0.971971i	$-0.575543\pi$
$631$	−2.96749e9	−0.470205	−0.235102	+	0.971971i	$0.575543\pi$
$632$	3.46444e10	5.45913
$633$	−8.39999e9	−1.31633
$634$	1.35974e10	2.11906
$635$	2.57111e8	0.0398485
$636$	1.70770e10	2.63216
$637$	3.10984e9	0.476705
$638$	7.51069e8	0.114501
$639$	−4.55974e9	−0.691333
$640$	1.75481e9	0.264606
$641$	−1.81524e9	−0.272228	−0.136114	−	0.990693i	$-0.543461\pi$
$641$	−1.81524e9	−0.272228	−0.136114	+	0.990693i	$0.543461\pi$
$642$	−7.98781e9	−1.19139
$643$	6.39809e9	0.949100	0.474550	−	0.880228i	$-0.342611\pi$
$643$	6.39809e9	0.949100	0.474550	+	0.880228i	$0.342611\pi$
$644$	−3.60672e10	−5.32123
$645$	5.84402e8	0.0857537
$646$	3.26736e8	0.0476852
$647$	−2.34923e9	−0.341004	−0.170502	−	0.985357i	$-0.554539\pi$
$647$	−2.34923e9	−0.341004	−0.170502	+	0.985357i	$0.554539\pi$
$648$	−7.33633e9	−1.05917
$649$	−5.60984e7	−0.00805553
$650$	−1.11104e10	−1.58683
$651$	9.58563e9	1.36172
$652$	4.40179e9	0.621961
$653$	−5.09805e9	−0.716487	−0.358243	−	0.933628i	$-0.616624\pi$
$653$	−5.09805e9	−0.716487	−0.358243	+	0.933628i	$0.616624\pi$
$654$	−6.55069e9	−0.915725
$655$	−6.94464e8	−0.0965618
$656$	5.49652e10	7.60194
$657$	−4.39035e8	−0.0603977
$658$	2.70195e10	3.69731
$659$	−6.82099e9	−0.928428	−0.464214	−	0.885723i	$-0.653663\pi$
$659$	−6.82099e9	−0.928428	−0.464214	+	0.885723i	$0.653663\pi$
$660$	1.19680e8	0.0162039
$661$	8.30536e9	1.11855	0.559273	−	0.828984i	$-0.311081\pi$
$661$	8.30536e9	1.11855	0.559273	+	0.828984i	$0.311081\pi$
$662$	5.26574e9	0.705433
$663$	2.69212e8	0.0358754
$664$	7.12330e9	0.944263
$665$	−2.72759e8	−0.0359669
$666$	1.14200e9	0.149799
$667$	6.00408e9	0.783441
$668$	1.64855e10	2.13986
$669$	−6.06232e9	−0.782793
$670$	4.04378e7	0.00519429
$671$	7.51021e7	0.00959673
$672$	−2.94573e10	−3.74456
$673$	8.47639e9	1.07191	0.535955	−	0.844247i	$-0.319952\pi$
$673$	8.47639e9	1.07191	0.535955	+	0.844247i	$0.319952\pi$
$674$	−3.23509e9	−0.406983
$675$	−8.51006e9	−1.06505
$676$	−7.19769e9	−0.896148
$677$	2.69539e9	0.333857	0.166929	−	0.985969i	$-0.446615\pi$
$677$	2.69539e9	0.333857	0.166929	+	0.985969i	$0.446615\pi$
$678$	1.40866e10	1.73581
$679$	−1.58898e10	−1.94793
$680$	−1.17267e8	−0.0143019
$681$	−1.03876e10	−1.26038
$682$	2.75955e9	0.333114
$683$	4.21776e9	0.506535	0.253268	−	0.967396i	$-0.418495\pi$
$683$	4.21776e9	0.506535	0.253268	+	0.967396i	$0.418495\pi$
$684$	4.45527e9	0.532326
$685$	2.75977e8	0.0328062
$686$	−8.66065e9	−1.02427
$687$	−1.04300e10	−1.22726
$688$	−5.58276e10	−6.53566
$689$	−9.23172e9	−1.07526
$690$	1.30297e9	0.150995
$691$	−6.37687e9	−0.735249	−0.367624	−	0.929974i	$-0.619829\pi$
$691$	−6.37687e9	−0.735249	−0.367624	+	0.929974i	$0.619829\pi$
$692$	7.23214e9	0.829651
$693$	5.97062e8	0.0681480
$694$	2.01100e10	2.28378
$695$	2.68826e8	0.0303756
$696$	1.13290e10	1.27368
$697$	−1.05188e9	−0.117666
$698$	−1.76134e10	−1.96042
$699$	2.47587e9	0.274193
$700$	−3.13657e10	−3.45630
$701$	6.21495e9	0.681436	0.340718	−	0.940166i	$-0.389330\pi$
$701$	6.21495e9	0.681436	0.340718	+	0.940166i	$0.389330\pi$
$702$	1.56429e10	1.70663
$703$	6.21125e8	0.0674273
$704$	−4.34269e9	−0.469089
$705$	−7.16729e8	−0.0770359
$706$	−1.75707e9	−0.187920
$707$	9.88686e9	1.05218
$708$	−1.32609e9	−0.140429
$709$	−2.14621e9	−0.226157	−0.113078	−	0.993586i	$-0.536071\pi$
$709$	−2.14621e9	−0.226157	−0.113078	+	0.993586i	$0.536071\pi$
$710$	1.89971e9	0.199197
$711$	−7.18487e9	−0.749679
$712$	−2.47102e10	−2.56565
$713$	2.20600e10	2.27925
$714$	1.03506e9	0.106420
$715$	−6.46985e7	−0.00661947
$716$	9.66122e9	0.983641
$717$	5.72835e9	0.580380
$718$	2.49734e10	2.51792
$719$	3.34890e9	0.336010	0.168005	−	0.985786i	$-0.446268\pi$
$719$	3.34890e9	0.336010	0.168005	+	0.985786i	$0.446268\pi$
$720$	−1.27081e9	−0.126887
$721$	7.50804e9	0.746025
$722$	−1.63180e10	−1.61357
$723$	−1.71606e9	−0.168868
$724$	2.70272e10	2.64677
$725$	5.22143e9	0.508869
$726$	1.43710e10	1.39383
$727$	−1.03971e10	−1.00355	−0.501777	−	0.864997i	$-0.667320\pi$
$727$	−1.03971e10	−1.00355	−0.501777	+	0.864997i	$0.667320\pi$
$728$	3.67900e10	3.53402
$729$	9.67398e9	0.924824
$730$	1.82914e8	0.0174027
$731$	1.06839e9	0.101162
$732$	1.77532e9	0.167297
$733$	−3.38334e9	−0.317309	−0.158654	−	0.987334i	$-0.550716\pi$
$733$	−3.38334e9	−0.317309	−0.158654	+	0.987334i	$0.550716\pi$
$734$	−1.20567e10	−1.12536
$735$	−3.17167e8	−0.0294633
$736$	−6.77919e10	−6.26766
$737$	−4.81437e7	−0.00443000
$738$	−1.95339e10	−1.78892
$739$	2.71654e9	0.247605	0.123803	−	0.992307i	$-0.460491\pi$
$739$	2.71654e9	0.247605	0.123803	+	0.992307i	$0.460491\pi$
$740$	−3.49357e8	−0.0316926
$741$	2.71912e9	0.245508
$742$	−3.54940e10	−3.18964
$743$	2.35963e9	0.211049	0.105525	−	0.994417i	$-0.466348\pi$
$743$	2.35963e9	0.211049	0.105525	+	0.994417i	$0.466348\pi$
$744$	4.16247e10	3.70550
$745$	5.05124e8	0.0447560
$746$	−9.79133e9	−0.863487
$747$	−1.47729e9	−0.129672
$748$	2.18796e8	0.0191154
$749$	1.21906e10	1.06008
$750$	2.27179e9	0.196632
$751$	1.33472e10	1.14987	0.574936	−	0.818198i	$-0.305027\pi$
$751$	1.33472e10	1.14987	0.574936	+	0.818198i	$0.305027\pi$
$752$	6.84687e10	5.87123
$753$	−1.17633e9	−0.100403
$754$	−9.59788e9	−0.815409
$755$	−7.86454e8	−0.0665057
$756$	4.41617e10	3.71723
$757$	−2.30344e10	−1.92993	−0.964966	−	0.262376i	$-0.915494\pi$
$757$	−2.30344e10	−1.92993	−0.964966	+	0.262376i	$0.915494\pi$
$758$	3.49398e10	2.91393
$759$	−1.55127e9	−0.128778
$760$	−1.18443e9	−0.0978729
$761$	−1.86867e10	−1.53704	−0.768522	−	0.639823i	$-0.779008\pi$
$761$	−1.86867e10	−1.53704	−0.768522	+	0.639823i	$0.779008\pi$
$762$	−9.85466e9	−0.806862
$763$	9.99736e9	0.814797
$764$	2.63526e10	2.13795
$765$	2.43199e7	0.00196402
$766$	1.71201e10	1.37628
$767$	7.16879e8	0.0573670
$768$	−3.01080e10	−2.39838
$769$	1.21850e10	0.966233	0.483116	−	0.875556i	$-0.339505\pi$
$769$	1.21850e10	0.966233	0.483116	+	0.875556i	$0.339505\pi$
$770$	−2.48752e8	−0.0196358
$771$	−2.13369e9	−0.167664
$772$	−2.34263e10	−1.83250
$773$	−4.21070e9	−0.327888	−0.163944	−	0.986470i	$-0.552422\pi$
$773$	−4.21070e9	−0.327888	−0.163944	+	0.986470i	$0.552422\pi$
$774$	1.98404e10	1.53800
$775$	1.91844e10	1.48044
$776$	−6.90000e10	−5.30070
$777$	1.96765e9	0.150479
$778$	−1.86431e10	−1.41935
$779$	−1.06243e10	−0.805230
$780$	−1.52939e9	−0.115395
$781$	−2.26172e9	−0.169887
$782$	2.38205e9	0.178126
$783$	−7.35157e9	−0.547285
$784$	3.02987e10	2.24553
$785$	−9.90462e8	−0.0730792
$786$	2.66178e10	1.95521
$787$	8.92159e9	0.652425	0.326213	−	0.945296i	$-0.394227\pi$
$787$	8.92159e9	0.652425	0.326213	+	0.945296i	$0.394227\pi$
$788$	9.93520e9	0.723327
$789$	4.68149e9	0.339324
$790$	2.99341e9	0.216009
$791$	−2.14983e10	−1.54450
$792$	2.59269e9	0.185444
$793$	−9.59726e8	−0.0683425
$794$	−3.96315e10	−2.80976
$795$	9.41527e8	0.0664581
$796$	−4.19264e10	−2.94640
$797$	1.32124e10	0.924437	0.462219	−	0.886766i	$-0.347054\pi$
$797$	1.32124e10	0.924437	0.462219	+	0.886766i	$0.347054\pi$
$798$	1.04544e10	0.728267
$799$	−1.31030e9	−0.0908777
$800$	−5.89550e10	−4.07104
$801$	5.12463e9	0.352329
$802$	−2.09392e10	−1.43334
$803$	−2.17770e8	−0.0148421
$804$	−1.13806e9	−0.0772267
$805$	−1.98854e9	−0.134353
$806$	−3.52642e10	−2.37226
$807$	8.10346e9	0.542767
$808$	4.29328e10	2.86319
$809$	9.61165e9	0.638231	0.319116	−	0.947716i	$-0.396614\pi$
$809$	9.61165e9	0.638231	0.319116	+	0.947716i	$0.396614\pi$
$810$	−6.33887e8	−0.0419096
$811$	−1.80562e10	−1.18865	−0.594326	−	0.804224i	$-0.702581\pi$
$811$	−1.80562e10	−1.18865	−0.594326	+	0.804224i	$0.702581\pi$
$812$	−2.70958e10	−1.77605
$813$	6.80534e9	0.444153
$814$	5.66457e8	0.0368113
$815$	2.42689e8	0.0157036
$816$	2.62290e9	0.168992
$817$	1.07910e10	0.692285
$818$	−4.02148e10	−2.56891
$819$	−7.62983e9	−0.485312
$820$	5.97573e9	0.378480
$821$	1.14040e9	0.0719209	0.0359604	−	0.999353i	$-0.488551\pi$
$821$	1.14040e9	0.0719209	0.0359604	+	0.999353i	$0.488551\pi$
$822$	−1.05778e10	−0.664268
$823$	8.91536e9	0.557493	0.278746	−	0.960365i	$-0.410081\pi$
$823$	8.91536e9	0.557493	0.278746	+	0.960365i	$0.410081\pi$
$824$	3.26030e10	2.03008
$825$	−1.34906e9	−0.0836453
$826$	2.75625e9	0.170172
$827$	1.62107e9	0.0996628	0.0498314	−	0.998758i	$-0.484132\pi$
$827$	1.62107e9	0.0996628	0.0498314	+	0.998758i	$0.484132\pi$
$828$	3.24809e10	1.98849
$829$	8.64323e9	0.526908	0.263454	−	0.964672i	$-0.415138\pi$
$829$	8.64323e9	0.526908	0.263454	+	0.964672i	$0.415138\pi$
$830$	6.15480e8	0.0373629
$831$	−5.44671e9	−0.329254
$832$	5.54951e10	3.34059
$833$	−5.79834e8	−0.0347573
$834$	−1.03037e10	−0.615052
$835$	9.08917e8	0.0540283
$836$	2.20990e9	0.130813
$837$	−2.70109e10	−1.59221
$838$	2.80178e10	1.64468
$839$	1.54048e9	0.0900511	0.0450255	−	0.998986i	$-0.485663\pi$
$839$	1.54048e9	0.0900511	0.0450255	+	0.998986i	$0.485663\pi$
$840$	−3.75214e9	−0.218425
$841$	−1.27393e10	−0.738513
$842$	−2.43802e10	−1.40749
$843$	1.14007e10	0.655440
$844$	8.72407e10	4.99483
$845$	−3.96839e8	−0.0226264
$846$	−2.43329e10	−1.38165
$847$	−2.19324e10	−1.24021
$848$	−8.99434e10	−5.06505
$849$	−6.02139e9	−0.337691
$850$	2.07154e9	0.115699
$851$	4.52828e9	0.251872
$852$	−5.34643e10	−2.96159
$853$	1.33583e10	0.736936	0.368468	−	0.929640i	$-0.379882\pi$
$853$	1.33583e10	0.736936	0.368468	+	0.929640i	$0.379882\pi$
$854$	−3.68994e9	−0.202729
$855$	2.45638e8	0.0134405
$856$	5.29367e10	2.88468
$857$	3.37241e10	1.83024	0.915119	−	0.403184i	$-0.132097\pi$
$857$	3.37241e10	1.83024	0.915119	+	0.403184i	$0.132097\pi$
$858$	2.47980e9	0.134033
$859$	4.40362e9	0.237047	0.118523	−	0.992951i	$-0.462184\pi$
$859$	4.40362e9	0.237047	0.118523	+	0.992951i	$0.462184\pi$
$860$	−6.06949e9	−0.325393
$861$	−3.36566e10	−1.79705
$862$	−6.76805e10	−3.59905
$863$	9.69422e9	0.513423	0.256711	−	0.966488i	$-0.417361\pi$
$863$	9.69422e9	0.513423	0.256711	+	0.966488i	$0.417361\pi$
$864$	8.30063e10	4.37837
$865$	3.98738e8	0.0209475
$866$	−4.47731e10	−2.34264
$867$	1.39239e10	0.725594
$868$	−9.95545e10	−5.16704
$869$	−3.56384e9	−0.184225
$870$	9.78871e8	0.0503974
$871$	6.15227e8	0.0315480
$872$	4.34126e10	2.21722
$873$	1.43098e10	0.727922
$874$	2.40594e10	1.21898
$875$	−3.46711e9	−0.174960
$876$	−5.14781e9	−0.258737
$877$	−1.40697e10	−0.704349	−0.352174	−	0.935934i	$-0.614558\pi$
$877$	−1.40697e10	−0.704349	−0.352174	+	0.935934i	$0.614558\pi$
$878$	1.02622e10	0.511696
$879$	−2.21500e10	−1.10005
$880$	−6.30350e8	−0.0311812
$881$	−1.32417e9	−0.0652422	−0.0326211	−	0.999468i	$-0.510385\pi$
$881$	−1.32417e9	−0.0652422	−0.0326211	+	0.999468i	$0.510385\pi$
$882$	−1.07678e10	−0.528428
$883$	2.66725e10	1.30377	0.651885	−	0.758318i	$-0.273979\pi$
$883$	2.66725e10	1.30377	0.651885	+	0.758318i	$0.273979\pi$
$884$	−2.79598e9	−0.136129
$885$	−7.31132e7	−0.00354564
$886$	−3.43273e10	−1.65814
$887$	−1.70663e10	−0.821119	−0.410560	−	0.911834i	$-0.634667\pi$
$887$	−1.70663e10	−0.821119	−0.410560	+	0.911834i	$0.634667\pi$
$888$	8.54436e9	0.409481
$889$	1.50397e10	0.717932
$890$	−2.13506e9	−0.101518
$891$	7.54682e8	0.0357431
$892$	6.29620e10	2.97031
$893$	−1.32344e10	−0.621907
$894$	−1.93606e10	−0.906230
$895$	5.32664e8	0.0248355
$896$	1.02648e11	4.76729
$897$	1.98236e10	0.917085
$898$	7.23264e9	0.333296
$899$	1.65728e10	0.760741
$900$	2.82469e10	1.29158
$901$	1.72127e9	0.0783993
$902$	−9.68922e9	−0.439608
$903$	3.41847e10	1.54499
$904$	−9.33545e10	−4.20287
$905$	1.49012e9	0.0668270
$906$	3.01436e10	1.34662
$907$	1.72359e10	0.767022	0.383511	−	0.923536i	$-0.374715\pi$
$907$	1.72359e10	0.767022	0.383511	+	0.923536i	$0.374715\pi$
$908$	1.07884e11	4.78252
$909$	−8.90379e9	−0.393189
$910$	3.17879e9	0.139835
$911$	2.01121e10	0.881337	0.440669	−	0.897670i	$-0.354741\pi$
$911$	2.01121e10	0.881337	0.440669	+	0.897670i	$0.354741\pi$
$912$	2.64920e10	1.15647
$913$	−7.32768e8	−0.0318653
$914$	−6.64009e9	−0.287649
$915$	9.78808e7	0.00422400
$916$	1.08324e11	4.65684
$917$	−4.06228e10	−1.73971
$918$	−2.91665e9	−0.124433
$919$	−3.32126e10	−1.41156	−0.705780	−	0.708431i	$-0.749403\pi$
$919$	−3.32126e10	−1.41156	−0.705780	+	0.708431i	$0.749403\pi$
$920$	−8.63504e9	−0.365601
$921$	1.14826e10	0.484319
$922$	7.54573e10	3.17061
$923$	2.89025e10	1.20984
$924$	7.00072e9	0.291938
$925$	3.93800e9	0.163599
$926$	−4.90061e10	−2.02821
$927$	−6.76150e9	−0.278782
$928$	−5.09293e10	−2.09194
$929$	−3.26489e10	−1.33602	−0.668012	−	0.744151i	$-0.732854\pi$
$929$	−3.26489e10	−1.33602	−0.668012	+	0.744151i	$0.732854\pi$
$930$	3.59653e9	0.146620
$931$	−5.85650e9	−0.237856
$932$	−2.57139e10	−1.04043
$933$	−2.63142e10	−1.06073
$934$	9.39886e9	0.377451
$935$	1.20632e7	0.000482637 0
$936$	−3.31318e10	−1.32063
$937$	7.86332e9	0.312261	0.156130	−	0.987736i	$-0.450098\pi$
$937$	7.86332e9	0.312261	0.156130	+	0.987736i	$0.450098\pi$
$938$	2.36541e9	0.0935831
$939$	−1.07275e10	−0.422832
$940$	7.44381e9	0.292313
$941$	−4.82942e10	−1.88943	−0.944715	−	0.327892i	$-0.893662\pi$
$941$	−4.82942e10	−1.88943	−0.944715	+	0.327892i	$0.893662\pi$
$942$	3.79629e10	1.47972
$943$	−7.74561e10	−3.00791
$944$	6.98446e9	0.270228
$945$	2.43482e9	0.0938546
$946$	9.84124e9	0.377947
$947$	3.07850e10	1.17791	0.588957	−	0.808164i	$-0.299539\pi$
$947$	3.07850e10	1.17791	0.588957	+	0.808164i	$0.299539\pi$
$948$	−8.42447e10	−3.21154
$949$	2.78288e9	0.105697
$950$	2.09232e10	0.791764
$951$	−2.10985e10	−0.795464
$952$	−6.85955e9	−0.257671
$953$	6.91558e9	0.258824	0.129412	−	0.991591i	$-0.458691\pi$
$953$	6.91558e9	0.258824	0.129412	+	0.991591i	$0.458691\pi$
$954$	3.19647e10	1.19193
$955$	1.45293e9	0.0539801
$956$	−5.94935e10	−2.20225
$957$	−1.16541e9	−0.0429819
$958$	−7.83300e10	−2.87838
$959$	1.61433e10	0.591055
$960$	−5.65985e9	−0.206469
$961$	3.33786e10	1.21321
$962$	−7.23872e9	−0.262150
$963$	−1.09785e10	−0.396141
$964$	1.78227e10	0.640771
$965$	−1.29159e9	−0.0462679
$966$	7.62176e10	2.72042
$967$	7.55107e9	0.268544	0.134272	−	0.990944i	$-0.457130\pi$
$967$	7.55107e9	0.268544	0.134272	+	0.990944i	$0.457130\pi$
$968$	−9.52395e10	−3.37484
$969$	−5.06985e8	−0.0179004
$970$	−5.96186e9	−0.209740
$971$	2.04306e10	0.716168	0.358084	−	0.933689i	$-0.383430\pi$
$971$	2.04306e10	0.716168	0.358084	+	0.933689i	$0.383430\pi$
$972$	−6.68307e10	−2.33423
$973$	1.57250e10	0.547263
$974$	8.08676e10	2.80426
$975$	1.72395e10	0.595675
$976$	−9.35049e9	−0.321929
$977$	1.38889e10	0.476470	0.238235	−	0.971208i	$-0.423431\pi$
$977$	1.38889e10	0.476470	0.238235	+	0.971208i	$0.423431\pi$
$978$	−9.30192e9	−0.317970
$979$	2.54192e9	0.0865810
$980$	3.29403e9	0.111799
$981$	−9.00330e9	−0.304481
$982$	−4.64317e10	−1.56468
$983$	−2.66740e10	−0.895676	−0.447838	−	0.894115i	$-0.647806\pi$
$983$	−2.66740e10	−0.895676	−0.447838	+	0.894115i	$0.647806\pi$
$984$	−1.46151e11	−4.89011
$985$	5.47770e8	0.0182630
$986$	1.78954e9	0.0594528
$987$	−4.19252e10	−1.38792
$988$	−2.82403e10	−0.931579
$989$	7.86713e10	2.58601
$990$	2.24018e8	0.00733770
$991$	1.03260e10	0.337035	0.168518	−	0.985699i	$-0.446102\pi$
$991$	1.03260e10	0.337035	0.168518	+	0.985699i	$0.446102\pi$
$992$	−1.87123e11	−6.08605
$993$	−8.17065e9	−0.264810
$994$	1.11124e11	3.58885
$995$	−2.31158e9	−0.0743923
$996$	−1.73217e10	−0.555498
$997$	7.89623e9	0.252340	0.126170	−	0.992009i	$-0.459731\pi$
$997$	7.89623e9	0.252340	0.126170	+	0.992009i	$0.459731\pi$
$998$	8.45475e10	2.69243
$999$	−5.54455e9	−0.175949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.a.b.1.11	✓	11
3.2	odd	2		333.8.a.d.1.1		11
4.3	odd	2		592.8.a.g.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.a.b.1.11	✓	11	1.1	even	1	trivial
333.8.a.d.1.1		11	3.2	odd	2
592.8.a.g.1.9		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)

\(f(q)\)	\(=\)	\(q+21.9474 q^{2} -34.0550 q^{3} +353.689 q^{4} +19.5004 q^{5} -747.419 q^{6} +1140.68 q^{7} +4953.28 q^{8} -1027.26 q^{9} +O(q^{10})\)	\(q+21.9474 q^{2} -34.0550 q^{3} +353.689 q^{4} +19.5004 q^{5} -747.419 q^{6} +1140.68 q^{7} +4953.28 q^{8} -1027.26 q^{9} +427.983 q^{10} -509.540 q^{11} -12044.9 q^{12} +6511.39 q^{13} +25034.9 q^{14} -664.085 q^{15} +63439.6 q^{16} -1214.06 q^{17} -22545.6 q^{18} -12262.4 q^{19} +6897.06 q^{20} -38845.7 q^{21} -11183.1 q^{22} -89398.1 q^{23} -168684. q^{24} -77744.7 q^{25} +142908. q^{26} +109462. q^{27} +403444. q^{28} -67161.2 q^{29} -14574.9 q^{30} -246761. q^{31} +758315. q^{32} +17352.4 q^{33} -26645.5 q^{34} +22243.6 q^{35} -363329. q^{36} -50653.0 q^{37} -269127. q^{38} -221745. q^{39} +96590.9 q^{40} +866417. q^{41} -852564. q^{42} -880011. q^{43} -180219. q^{44} -20031.9 q^{45} -1.96206e6 q^{46} +1.07927e6 q^{47} -2.16044e6 q^{48} +477600. q^{49} -1.70630e6 q^{50} +41344.8 q^{51} +2.30300e6 q^{52} -1.41778e6 q^{53} +2.40240e6 q^{54} -9936.22 q^{55} +5.65010e6 q^{56} +417595. q^{57} -1.47401e6 q^{58} +110096. q^{59} -234879. q^{60} -147392. q^{61} -5.41577e6 q^{62} -1.17177e6 q^{63} +8.52277e6 q^{64} +126974. q^{65} +380840. q^{66} +94484.7 q^{67} -429399. q^{68} +3.04445e6 q^{69} +488190. q^{70} +4.43876e6 q^{71} -5.08829e6 q^{72} +427386. q^{73} -1.11170e6 q^{74} +2.64760e6 q^{75} -4.33706e6 q^{76} -581220. q^{77} -4.86674e6 q^{78} +6.99423e6 q^{79} +1.23710e6 q^{80} -1.48110e6 q^{81} +1.90156e7 q^{82} +1.43810e6 q^{83} -1.37393e7 q^{84} -23674.6 q^{85} -1.93140e7 q^{86} +2.28717e6 q^{87} -2.52390e6 q^{88} -4.98866e6 q^{89} -439648. q^{90} +7.42739e6 q^{91} -3.16191e7 q^{92} +8.40346e6 q^{93} +2.36872e7 q^{94} -239120. q^{95} -2.58244e7 q^{96} -1.39302e7 q^{97} +1.04821e7 q^{98} +523428. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 16 q^{2} + 121 q^{3} + 794 q^{4} + 376 q^{5} + 519 q^{6} + 2243 q^{7} + 3870 q^{8} + 9826 q^{9}+O(q^{10}) \) 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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