LMFDB - Embedded newform 177.8.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.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:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$6.43791$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.43791 q^{2} +27.0000 q^{3} -72.6775 q^{4} +171.827 q^{5} +200.824 q^{6} +1529.87 q^{7} -1492.62 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+7.43791 q^{2} +27.0000 q^{3} -72.6775 q^{4} +171.827 q^{5} +200.824 q^{6} +1529.87 q^{7} -1492.62 q^{8} +729.000 q^{9} +1278.03 q^{10} -1638.92 q^{11} -1962.29 q^{12} -7315.98 q^{13} +11379.0 q^{14} +4639.33 q^{15} -1799.27 q^{16} +33214.7 q^{17} +5422.24 q^{18} +55570.3 q^{19} -12488.0 q^{20} +41306.4 q^{21} -12190.1 q^{22} -51886.9 q^{23} -40300.8 q^{24} -48600.5 q^{25} -54415.6 q^{26} +19683.0 q^{27} -111187. q^{28} +10383.5 q^{29} +34506.9 q^{30} +92770.0 q^{31} +177673. q^{32} -44250.7 q^{33} +247048. q^{34} +262873. q^{35} -52981.9 q^{36} -504232. q^{37} +413327. q^{38} -197531. q^{39} -256473. q^{40} +635489. q^{41} +307234. q^{42} +101770. q^{43} +119112. q^{44} +125262. q^{45} -385930. q^{46} -72413.1 q^{47} -48580.2 q^{48} +1.51695e6 q^{49} -361486. q^{50} +896798. q^{51} +531707. q^{52} +1.67234e6 q^{53} +146400. q^{54} -281610. q^{55} -2.28351e6 q^{56} +1.50040e6 q^{57} +77231.8 q^{58} +205379. q^{59} -337175. q^{60} +727353. q^{61} +690015. q^{62} +1.11527e6 q^{63} +1.55182e6 q^{64} -1.25708e6 q^{65} -329133. q^{66} +2.81505e6 q^{67} -2.41396e6 q^{68} -1.40095e6 q^{69} +1.95522e6 q^{70} -850222. q^{71} -1.08812e6 q^{72} +5.84245e6 q^{73} -3.75043e6 q^{74} -1.31221e6 q^{75} -4.03871e6 q^{76} -2.50732e6 q^{77} -1.46922e6 q^{78} +2.74755e6 q^{79} -309162. q^{80} +531441. q^{81} +4.72671e6 q^{82} +2.78632e6 q^{83} -3.00205e6 q^{84} +5.70719e6 q^{85} +756957. q^{86} +280355. q^{87} +2.44628e6 q^{88} -6.16092e6 q^{89} +931687. q^{90} -1.11925e7 q^{91} +3.77101e6 q^{92} +2.50479e6 q^{93} -538602. q^{94} +9.54849e6 q^{95} +4.79716e6 q^{96} -1.67686e7 q^{97} +1.12830e7 q^{98} -1.19477e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) $ 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * 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 $

$2$	7.43791	0.657425	0.328712	−	0.944430i	$-0.393385\pi$
$2$	7.43791	0.657425	0.328712	+	0.944430i	$0.393385\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−72.6775	−0.567793
$5$	171.827	0.614747	0.307374	−	0.951589i	$-0.400550\pi$
$5$	171.827	0.614747	0.307374	+	0.951589i	$0.400550\pi$
$6$	200.824	0.379564
$7$	1529.87	1.68582	0.842909	−	0.538056i	$-0.180841\pi$
$7$	1529.87	1.68582	0.842909	+	0.538056i	$0.180841\pi$
$8$	−1492.62	−1.03071
$9$	729.000	0.333333
$10$	1278.03	0.404150
$11$	−1638.92	−0.371263	−0.185632	−	0.982619i	$-0.559433\pi$
$11$	−1638.92	−0.371263	−0.185632	+	0.982619i	$0.559433\pi$
$12$	−1962.29	−0.327815
$13$	−7315.98	−0.923572	−0.461786	−	0.886991i	$-0.652791\pi$
$13$	−7315.98	−0.923572	−0.461786	+	0.886991i	$0.652791\pi$
$14$	11379.0	1.10830
$15$	4639.33	0.354924
$16$	−1799.27	−0.109818
$17$	33214.7	1.63968	0.819841	−	0.572592i	$-0.194062\pi$
$17$	33214.7	1.63968	0.819841	+	0.572592i	$0.194062\pi$
$18$	5422.24	0.219142
$19$	55570.3	1.85868	0.929342	−	0.369221i	$-0.120375\pi$
$19$	55570.3	1.85868	0.929342	+	0.369221i	$0.120375\pi$
$20$	−12488.0	−0.349049
$21$	41306.4	0.973308
$22$	−12190.1	−0.244078
$23$	−51886.9	−0.889222	−0.444611	−	0.895724i	$-0.646658\pi$
$23$	−51886.9	−0.889222	−0.444611	+	0.895724i	$0.646658\pi$
$24$	−40300.8	−0.595078
$25$	−48600.5	−0.622086
$26$	−54415.6	−0.607179
$27$	19683.0	0.192450
$28$	−111187.	−0.957196
$29$	10383.5	0.0790591	0.0395296	−	0.999218i	$-0.487414\pi$
$29$	10383.5	0.0790591	0.0395296	+	0.999218i	$0.487414\pi$
$30$	34506.9	0.233336
$31$	92770.0	0.559296	0.279648	−	0.960103i	$-0.409782\pi$
$31$	92770.0	0.559296	0.279648	+	0.960103i	$0.409782\pi$
$32$	177673.	0.958508
$33$	−44250.7	−0.214349
$34$	247048.	1.07797
$35$	262873.	1.03635
$36$	−52981.9	−0.189264
$37$	−504232.	−1.63653	−0.818266	−	0.574840i	$-0.805064\pi$
$37$	−504232.	−1.63653	−0.818266	+	0.574840i	$0.805064\pi$
$38$	413327.	1.22194
$39$	−197531.	−0.533224
$40$	−256473.	−0.633623
$41$	635489.	1.44001	0.720003	−	0.693971i	$-0.244140\pi$
$41$	635489.	1.44001	0.720003	+	0.693971i	$0.244140\pi$
$42$	307234.	0.639877
$43$	101770.	0.195200	0.0976002	−	0.995226i	$-0.468883\pi$
$43$	101770.	0.195200	0.0976002	+	0.995226i	$0.468883\pi$
$44$	119112.	0.210801
$45$	125262.	0.204916
$46$	−385930.	−0.584597
$47$	−72413.1	−0.101736	−0.0508680	−	0.998705i	$-0.516199\pi$
$47$	−72413.1	−0.101736	−0.0508680	+	0.998705i	$0.516199\pi$
$48$	−48580.2	−0.0634037
$49$	1.51695e6	1.84198
$50$	−361486.	−0.408975
$51$	896798.	0.946671
$52$	531707.	0.524397
$53$	1.67234e6	1.54297	0.771487	−	0.636245i	$-0.219513\pi$
$53$	1.67234e6	1.54297	0.771487	+	0.636245i	$0.219513\pi$
$54$	146400.	0.126521
$55$	−281610.	−0.228233
$56$	−2.28351e6	−1.73758
$57$	1.50040e6	1.07311
$58$	77231.8	0.0519754
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−337175.	−0.201524
$61$	727353.	0.410290	0.205145	−	0.978732i	$-0.434233\pi$
$61$	727353.	0.410290	0.205145	+	0.978732i	$0.434233\pi$
$62$	690015.	0.367695
$63$	1.11527e6	0.561940
$64$	1.55182e6	0.739965
$65$	−1.25708e6	−0.567763
$66$	−329133.	−0.140918
$67$	2.81505e6	1.14347	0.571735	−	0.820439i	$-0.306271\pi$
$67$	2.81505e6	1.14347	0.571735	+	0.820439i	$0.306271\pi$
$68$	−2.41396e6	−0.930999
$69$	−1.40095e6	−0.513393
$70$	1.95522e6	0.681323
$71$	−850222.	−0.281921	−0.140961	−	0.990015i	$-0.545019\pi$
$71$	−850222.	−0.281921	−0.140961	+	0.990015i	$0.545019\pi$
$72$	−1.08812e6	−0.343569
$73$	5.84245e6	1.75778	0.878891	−	0.477023i	$-0.158284\pi$
$73$	5.84245e6	1.75778	0.878891	+	0.477023i	$0.158284\pi$
$74$	−3.75043e6	−1.07590
$75$	−1.31221e6	−0.359161
$76$	−4.03871e6	−1.05535
$77$	−2.50732e6	−0.625883
$78$	−1.46922e6	−0.350555
$79$	2.74755e6	0.626977	0.313488	−	0.949592i	$-0.398502\pi$
$79$	2.74755e6	0.626977	0.313488	+	0.949592i	$0.398502\pi$
$80$	−309162.	−0.0675106
$81$	531441.	0.111111
$82$	4.72671e6	0.946695
$83$	2.78632e6	0.534882	0.267441	−	0.963574i	$-0.413822\pi$
$83$	2.78632e6	0.534882	0.267441	+	0.963574i	$0.413822\pi$
$84$	−3.00205e6	−0.552637
$85$	5.70719e6	1.00799
$86$	756957.	0.128330
$87$	280355.	0.0456448
$88$	2.44628e6	0.382663
$89$	−6.16092e6	−0.926361	−0.463181	−	0.886264i	$-0.653292\pi$
$89$	−6.16092e6	−0.926361	−0.463181	+	0.886264i	$0.653292\pi$
$90$	931687.	0.134717
$91$	−1.11925e7	−1.55697
$92$	3.77101e6	0.504894
$93$	2.50479e6	0.322910
$94$	−538602.	−0.0668838
$95$	9.54849e6	1.14262
$96$	4.79716e6	0.553395
$97$	−1.67686e7	−1.86550	−0.932751	−	0.360521i	$-0.882599\pi$
$97$	−1.67686e7	−1.86550	−0.932751	+	0.360521i	$0.882599\pi$
$98$	1.12830e7	1.21097
$99$	−1.19477e6	−0.123754
$100$	3.53216e6	0.353216
$101$	7.93944e6	0.766770	0.383385	−	0.923589i	$-0.374758\pi$
$101$	7.93944e6	0.766770	0.383385	+	0.923589i	$0.374758\pi$
$102$	6.67030e6	0.622365
$103$	1.76750e7	1.59378	0.796889	−	0.604125i	$-0.206477\pi$
$103$	1.76750e7	1.59378	0.796889	+	0.604125i	$0.206477\pi$
$104$	1.09200e7	0.951931
$105$	7.09756e6	0.598338
$106$	1.24387e7	1.01439
$107$	−9.16951e6	−0.723607	−0.361803	−	0.932254i	$-0.617839\pi$
$107$	−9.16951e6	−0.723607	−0.361803	+	0.932254i	$0.617839\pi$
$108$	−1.43051e6	−0.109272
$109$	1.32228e7	0.977982	0.488991	−	0.872289i	$-0.337365\pi$
$109$	1.32228e7	0.977982	0.488991	+	0.872289i	$0.337365\pi$
$110$	−2.09459e6	−0.150046
$111$	−1.36143e7	−0.944852
$112$	−2.75264e6	−0.185134
$113$	−2.66031e7	−1.73443	−0.867216	−	0.497932i	$-0.834093\pi$
$113$	−2.66031e7	−1.73443	−0.867216	+	0.497932i	$0.834093\pi$
$114$	1.11598e7	0.705490
$115$	−8.91557e6	−0.546647
$116$	−754649.	−0.0448892
$117$	−5.33335e6	−0.307857
$118$	1.52759e6	0.0855894
$119$	5.08142e7	2.76421
$120$	−6.92476e6	−0.365823
$121$	−1.68011e7	−0.862163
$122$	5.40999e6	0.269735
$123$	1.71582e7	0.831388
$124$	−6.74229e6	−0.317564
$125$	−2.17749e7	−0.997173
$126$	8.29531e6	0.369433
$127$	−2.04342e7	−0.885209	−0.442604	−	0.896717i	$-0.645945\pi$
$127$	−2.04342e7	−0.885209	−0.442604	+	0.896717i	$0.645945\pi$
$128$	−1.11998e7	−0.472037
$129$	2.74779e6	0.112699
$130$	−9.35007e6	−0.373261
$131$	−4.18739e7	−1.62740	−0.813699	−	0.581286i	$-0.802550\pi$
$131$	−4.18739e7	−1.62740	−0.813699	+	0.581286i	$0.802550\pi$
$132$	3.21603e6	0.121706
$133$	8.50153e7	3.13340
$134$	2.09381e7	0.751745
$135$	3.38207e6	0.118308
$136$	−4.95770e7	−1.69003
$137$	5.60709e7	1.86301	0.931506	−	0.363725i	$-0.118495\pi$
$137$	5.60709e7	1.86301	0.931506	+	0.363725i	$0.118495\pi$
$138$	−1.04201e7	−0.337517
$139$	−3.90420e7	−1.23305	−0.616524	−	0.787336i	$-0.711460\pi$
$139$	−3.90420e7	−1.23305	−0.616524	+	0.787336i	$0.711460\pi$
$140$	−1.91049e7	−0.588433
$141$	−1.95515e6	−0.0587373
$142$	−6.32387e6	−0.185342
$143$	1.19903e7	0.342888
$144$	−1.31166e6	−0.0366062
$145$	1.78417e6	0.0486014
$146$	4.34556e7	1.15561
$147$	4.09577e7	1.06347
$148$	3.66463e7	0.929211
$149$	5.58520e7	1.38320	0.691602	−	0.722278i	$-0.256905\pi$
$149$	5.58520e7	1.38320	0.691602	+	0.722278i	$0.256905\pi$
$150$	−9.76012e6	−0.236122
$151$	−6.78120e7	−1.60283	−0.801414	−	0.598110i	$-0.795919\pi$
$151$	−6.78120e7	−1.60283	−0.801414	+	0.598110i	$0.795919\pi$
$152$	−8.29455e7	−1.91576
$153$	2.42135e7	0.546561
$154$	−1.86493e7	−0.411471
$155$	1.59404e7	0.343826
$156$	1.43561e7	0.302761
$157$	4.45770e7	0.919310	0.459655	−	0.888098i	$-0.347973\pi$
$157$	4.45770e7	0.919310	0.459655	+	0.888098i	$0.347973\pi$
$158$	2.04361e7	0.412190
$159$	4.51532e7	0.890837
$160$	3.05290e7	0.589240
$161$	−7.93801e7	−1.49907
$162$	3.95281e6	0.0730472
$163$	−9.62679e7	−1.74111	−0.870553	−	0.492075i	$-0.836238\pi$
$163$	−9.62679e7	−1.74111	−0.870553	+	0.492075i	$0.836238\pi$
$164$	−4.61857e7	−0.817625
$165$	−7.60347e6	−0.131770
$166$	2.07244e7	0.351645
$167$	−3.06157e7	−0.508671	−0.254335	−	0.967116i	$-0.581857\pi$
$167$	−3.06157e7	−0.508671	−0.254335	+	0.967116i	$0.581857\pi$
$168$	−6.16549e7	−1.00319
$169$	−9.22500e6	−0.147015
$170$	4.24496e7	0.662677
$171$	4.05108e7	0.619561
$172$	−7.39640e6	−0.110833
$173$	−1.60370e7	−0.235484	−0.117742	−	0.993044i	$-0.537566\pi$
$173$	−1.60370e7	−0.235484	−0.117742	+	0.993044i	$0.537566\pi$
$174$	2.08526e6	0.0300080
$175$	−7.43523e7	−1.04872
$176$	2.94884e6	0.0407716
$177$	5.54523e6	0.0751646
$178$	−4.58244e7	−0.609013
$179$	−2.33939e7	−0.304872	−0.152436	−	0.988313i	$-0.548712\pi$
$179$	−2.33939e7	−0.304872	−0.152436	+	0.988313i	$0.548712\pi$
$180$	−9.10372e6	−0.116350
$181$	−9.84290e7	−1.23381	−0.616904	−	0.787038i	$-0.711614\pi$
$181$	−9.84290e7	−1.23381	−0.616904	+	0.787038i	$0.711614\pi$
$182$	−8.32487e7	−1.02359
$183$	1.96385e7	0.236881
$184$	7.74475e7	0.916527
$185$	−8.66407e7	−1.00605
$186$	1.86304e7	0.212289
$187$	−5.44361e7	−0.608754
$188$	5.26280e6	0.0577650
$189$	3.01124e7	0.324436
$190$	7.10208e7	0.751187
$191$	3.21552e7	0.333914	0.166957	−	0.985964i	$-0.446606\pi$
$191$	3.21552e7	0.333914	0.166957	+	0.985964i	$0.446606\pi$
$192$	4.18991e7	0.427219
$193$	2.59381e7	0.259709	0.129854	−	0.991533i	$-0.458549\pi$
$193$	2.59381e7	0.259709	0.129854	+	0.991533i	$0.458549\pi$
$194$	−1.24723e8	−1.22643
$195$	−3.39412e7	−0.327798
$196$	−1.10248e8	−1.04587
$197$	−1.60676e7	−0.149733	−0.0748666	−	0.997194i	$-0.523853\pi$
$197$	−1.60676e7	−0.149733	−0.0748666	+	0.997194i	$0.523853\pi$
$198$	−8.88659e6	−0.0813592
$199$	6.47444e7	0.582394	0.291197	−	0.956663i	$-0.405947\pi$
$199$	6.47444e7	0.582394	0.291197	+	0.956663i	$0.405947\pi$
$200$	7.25421e7	0.641187
$201$	7.60064e7	0.660182
$202$	5.90529e7	0.504094
$203$	1.58854e7	0.133279
$204$	−6.51770e7	−0.537513
$205$	1.09194e8	0.885240
$206$	1.31465e8	1.04779
$207$	−3.78256e7	−0.296407
$208$	1.31634e7	0.101425
$209$	−9.10751e7	−0.690061
$210$	5.27910e7	0.393362
$211$	−4.05485e7	−0.297157	−0.148578	−	0.988901i	$-0.547470\pi$
$211$	−4.05485e7	−0.297157	−0.148578	+	0.988901i	$0.547470\pi$
$212$	−1.21541e8	−0.876090
$213$	−2.29560e7	−0.162767
$214$	−6.82020e7	−0.475717
$215$	1.74869e7	0.119999
$216$	−2.93793e7	−0.198359
$217$	1.41926e8	0.942872
$218$	9.83501e7	0.642950
$219$	1.57746e8	1.01486
$220$	2.04667e7	0.129589
$221$	−2.42998e8	−1.51436
$222$	−1.01262e8	−0.621169
$223$	−6.68937e7	−0.403941	−0.201971	−	0.979392i	$-0.564735\pi$
$223$	−6.68937e7	−0.403941	−0.201971	+	0.979392i	$0.564735\pi$
$224$	2.71816e8	1.61587
$225$	−3.54297e7	−0.207362
$226$	−1.97871e8	−1.14026
$227$	1.22298e8	0.693949	0.346975	−	0.937875i	$-0.387209\pi$
$227$	1.22298e8	0.693949	0.346975	+	0.937875i	$0.387209\pi$
$228$	−1.09045e8	−0.609305
$229$	−2.32389e8	−1.27876	−0.639382	−	0.768889i	$-0.720810\pi$
$229$	−2.32389e8	−1.27876	−0.639382	+	0.768889i	$0.720810\pi$
$230$	−6.63132e7	−0.359379
$231$	−6.76978e7	−0.361354
$232$	−1.54987e7	−0.0814867
$233$	7.69697e7	0.398634	0.199317	−	0.979935i	$-0.436128\pi$
$233$	7.69697e7	0.398634	0.199317	+	0.979935i	$0.436128\pi$
$234$	−3.96690e7	−0.202393
$235$	−1.24425e7	−0.0625419
$236$	−1.49264e7	−0.0739203
$237$	7.41839e7	0.361985
$238$	3.77951e8	1.81726
$239$	−1.06849e7	−0.0506264	−0.0253132	−	0.999680i	$-0.508058\pi$
$239$	−1.06849e7	−0.0506264	−0.0253132	+	0.999680i	$0.508058\pi$
$240$	−8.34739e6	−0.0389773
$241$	−3.74132e8	−1.72173	−0.860866	−	0.508831i	$-0.830078\pi$
$241$	−3.74132e8	−1.72173	−0.860866	+	0.508831i	$0.830078\pi$
$242$	−1.24965e8	−0.566808
$243$	1.43489e7	0.0641500
$244$	−5.28622e7	−0.232960
$245$	2.60654e8	1.13235
$246$	1.27621e8	0.546575
$247$	−4.06551e8	−1.71663
$248$	−1.38470e8	−0.576470
$249$	7.52307e7	0.308814
$250$	−1.61959e8	−0.655566
$251$	2.63434e8	1.05151	0.525755	−	0.850636i	$-0.323783\pi$
$251$	2.63434e8	1.05151	0.525755	+	0.850636i	$0.323783\pi$
$252$	−8.10553e7	−0.319065
$253$	8.50383e7	0.330136
$254$	−1.51988e8	−0.581958
$255$	1.54094e8	0.581963
$256$	−2.81936e8	−1.05029
$257$	−3.92808e8	−1.44349	−0.721746	−	0.692158i	$-0.756660\pi$
$257$	−3.92808e8	−1.44349	−0.721746	+	0.692158i	$0.756660\pi$
$258$	2.04378e7	0.0740911
$259$	−7.71409e8	−2.75890
$260$	9.13616e7	0.322372
$261$	7.56959e6	0.0263530
$262$	−3.11454e8	−1.06989
$263$	−2.41410e8	−0.818297	−0.409148	−	0.912468i	$-0.634174\pi$
$263$	−2.41410e8	−0.818297	−0.409148	+	0.912468i	$0.634174\pi$
$264$	6.60496e7	0.220931
$265$	2.87353e8	0.948539
$266$	6.32336e8	2.05998
$267$	−1.66345e8	−0.534835
$268$	−2.04591e8	−0.649254
$269$	2.35755e8	0.738463	0.369231	−	0.929337i	$-0.379621\pi$
$269$	2.35755e8	0.738463	0.369231	+	0.929337i	$0.379621\pi$
$270$	2.51555e7	0.0777787
$271$	−1.49957e8	−0.457692	−0.228846	−	0.973463i	$-0.573495\pi$
$271$	−1.49957e8	−0.457692	−0.228846	+	0.973463i	$0.573495\pi$
$272$	−5.97621e7	−0.180067
$273$	−3.02197e8	−0.898920
$274$	4.17051e8	1.22479
$275$	7.96521e7	0.230958
$276$	1.01817e8	0.291501
$277$	−9.52984e7	−0.269406	−0.134703	−	0.990886i	$-0.543008\pi$
$277$	−9.52984e7	−0.269406	−0.134703	+	0.990886i	$0.543008\pi$
$278$	−2.90391e8	−0.810637
$279$	6.76293e7	0.186432
$280$	−3.92369e8	−1.06817
$281$	−7.30263e7	−0.196339	−0.0981696	−	0.995170i	$-0.531299\pi$
$281$	−7.30263e7	−0.196339	−0.0981696	+	0.995170i	$0.531299\pi$
$282$	−1.45423e7	−0.0386154
$283$	1.79740e8	0.471404	0.235702	−	0.971825i	$-0.424261\pi$
$283$	1.79740e8	0.471404	0.235702	+	0.971825i	$0.424261\pi$
$284$	6.17920e7	0.160073
$285$	2.57809e8	0.659692
$286$	8.91825e7	0.225423
$287$	9.72214e8	2.42759
$288$	1.29523e8	0.319503
$289$	6.92880e8	1.68856
$290$	1.32705e7	0.0319517
$291$	−4.52752e8	−1.07705
$292$	−4.24614e8	−0.998056
$293$	8.12673e8	1.88747	0.943733	−	0.330709i	$-0.107288\pi$
$293$	8.12673e8	1.88747	0.943733	+	0.330709i	$0.107288\pi$
$294$	3.04640e8	0.699152
$295$	3.52897e7	0.0800333
$296$	7.52628e8	1.68678
$297$	−3.22588e7	−0.0714497
$298$	4.15422e8	0.909353
$299$	3.79603e8	0.821261
$300$	9.53683e7	0.203929
$301$	1.55695e8	0.329073
$302$	−5.04379e8	−1.05374
$303$	2.14365e8	0.442695
$304$	−9.99858e7	−0.204118
$305$	1.24979e8	0.252225
$306$	1.80098e8	0.359322
$307$	−1.93647e8	−0.381968	−0.190984	−	0.981593i	$-0.561168\pi$
$307$	−1.93647e8	−0.381968	−0.190984	+	0.981593i	$0.561168\pi$
$308$	1.82226e8	0.355372
$309$	4.77224e8	0.920168
$310$	1.18563e8	0.226039
$311$	1.76764e8	0.333220	0.166610	−	0.986023i	$-0.446718\pi$
$311$	1.76764e8	0.333220	0.166610	+	0.986023i	$0.446718\pi$
$312$	2.94840e8	0.549597
$313$	1.36535e8	0.251675	0.125837	−	0.992051i	$-0.459838\pi$
$313$	1.36535e8	0.251675	0.125837	+	0.992051i	$0.459838\pi$
$314$	3.31560e8	0.604377
$315$	1.91634e8	0.345451
$316$	−1.99685e8	−0.355993
$317$	−1.67078e8	−0.294586	−0.147293	−	0.989093i	$-0.547056\pi$
$317$	−1.67078e8	−0.294586	−0.147293	+	0.989093i	$0.547056\pi$
$318$	3.35845e8	0.585658
$319$	−1.70177e7	−0.0293518
$320$	2.66645e8	0.454892
$321$	−2.47577e8	−0.417775
$322$	−5.90422e8	−0.985524
$323$	1.84575e9	3.04765
$324$	−3.86238e7	−0.0630881
$325$	3.55560e8	0.574541
$326$	−7.16032e8	−1.14465
$327$	3.57016e8	0.564638
$328$	−9.48544e8	−1.48422
$329$	−1.10783e8	−0.171508
$330$	−5.65539e7	−0.0866291
$331$	3.82887e8	0.580327	0.290163	−	0.956977i	$-0.406290\pi$
$331$	3.82887e8	0.580327	0.290163	+	0.956977i	$0.406290\pi$
$332$	−2.02503e8	−0.303702
$333$	−3.67585e8	−0.545511
$334$	−2.27717e8	−0.334413
$335$	4.83702e8	0.702944
$336$	−7.43213e7	−0.106887
$337$	7.71340e8	1.09785	0.548923	−	0.835873i	$-0.315038\pi$
$337$	7.71340e8	1.09785	0.548923	+	0.835873i	$0.315038\pi$
$338$	−6.86147e7	−0.0966515
$339$	−7.18283e8	−1.00137
$340$	−4.14784e8	−0.572329
$341$	−1.52042e8	−0.207646
$342$	3.01316e8	0.407315
$343$	1.06083e9	1.41943
$344$	−1.51904e8	−0.201194
$345$	−2.40721e8	−0.315607
$346$	−1.19281e8	−0.154813
$347$	−1.31263e9	−1.68651	−0.843257	−	0.537511i	$-0.819365\pi$
$347$	−1.31263e9	−1.68651	−0.843257	+	0.537511i	$0.819365\pi$
$348$	−2.03755e7	−0.0259168
$349$	−5.67291e8	−0.714360	−0.357180	−	0.934036i	$-0.616262\pi$
$349$	−5.67291e8	−0.714360	−0.357180	+	0.934036i	$0.616262\pi$
$350$	−5.53026e8	−0.689457
$351$	−1.44000e8	−0.177741
$352$	−2.91191e8	−0.355859
$353$	1.79304e8	0.216959	0.108480	−	0.994099i	$-0.465402\pi$
$353$	1.79304e8	0.216959	0.108480	+	0.994099i	$0.465402\pi$
$354$	4.12449e7	0.0494151
$355$	−1.46091e8	−0.173310
$356$	4.47760e8	0.525981
$357$	1.37198e9	1.59592
$358$	−1.74002e8	−0.200430
$359$	−1.28294e9	−1.46344	−0.731722	−	0.681603i	$-0.761283\pi$
$359$	−1.28294e9	−1.46344	−0.731722	+	0.681603i	$0.761283\pi$
$360$	−1.86969e8	−0.211208
$361$	2.19419e9	2.45470
$362$	−7.32106e8	−0.811136
$363$	−4.53630e8	−0.497770
$364$	8.13441e8	0.884039
$365$	1.00389e9	1.08059
$366$	1.46070e8	0.155731
$367$	1.71884e7	0.0181512	0.00907560	−	0.999959i	$-0.497111\pi$
$367$	1.71884e7	0.0181512	0.00907560	+	0.999959i	$0.497111\pi$
$368$	9.33583e7	0.0976530
$369$	4.63271e8	0.480002
$370$	−6.44426e8	−0.661404
$371$	2.55846e9	2.60118
$372$	−1.82042e8	−0.183346
$373$	−8.02127e8	−0.800318	−0.400159	−	0.916446i	$-0.631045\pi$
$373$	−8.02127e8	−0.800318	−0.400159	+	0.916446i	$0.631045\pi$
$374$	−4.04891e8	−0.400210
$375$	−5.87921e8	−0.575718
$376$	1.08085e8	0.104860
$377$	−7.59657e7	−0.0730168
$378$	2.23973e8	0.213292
$379$	9.63664e6	0.00909261	0.00454630	−	0.999990i	$-0.498553\pi$
$379$	9.63664e6	0.00909261	0.00454630	+	0.999990i	$0.498553\pi$
$380$	−6.93960e8	−0.648772
$381$	−5.51725e8	−0.511075
$382$	2.39168e8	0.219523
$383$	8.26495e8	0.751700	0.375850	−	0.926681i	$-0.377351\pi$
$383$	8.26495e8	0.751700	0.375850	+	0.926681i	$0.377351\pi$
$384$	−3.02395e8	−0.272531
$385$	−4.30826e8	−0.384760
$386$	1.92925e8	0.170739
$387$	7.41904e7	0.0650668
$388$	1.21870e9	1.05922
$389$	7.27469e8	0.626601	0.313300	−	0.949654i	$-0.398565\pi$
$389$	7.27469e8	0.626601	0.313300	+	0.949654i	$0.398565\pi$
$390$	−2.52452e8	−0.215503
$391$	−1.72341e9	−1.45804
$392$	−2.26424e9	−1.89854
$393$	−1.13060e9	−0.939579
$394$	−1.19509e8	−0.0984383
$395$	4.72104e8	0.385432
$396$	8.68328e7	0.0702669
$397$	−1.15679e9	−0.927871	−0.463936	−	0.885869i	$-0.653563\pi$
$397$	−1.15679e9	−0.927871	−0.463936	+	0.885869i	$0.653563\pi$
$398$	4.81563e8	0.382880
$399$	2.29541e9	1.80907
$400$	8.74451e7	0.0683165
$401$	9.57807e7	0.0741776	0.0370888	−	0.999312i	$-0.488192\pi$
$401$	9.57807e7	0.0741776	0.0370888	+	0.999312i	$0.488192\pi$
$402$	5.65329e8	0.434020
$403$	−6.78703e8	−0.516550
$404$	−5.77019e8	−0.435367
$405$	9.13159e7	0.0683052
$406$	1.18154e8	0.0876211
$407$	8.26394e8	0.607585
$408$	−1.33858e9	−0.975739
$409$	−1.12641e9	−0.814079	−0.407040	−	0.913410i	$-0.633439\pi$
$409$	−1.12641e9	−0.814079	−0.407040	+	0.913410i	$0.633439\pi$
$410$	8.12176e8	0.581978
$411$	1.51392e9	1.07561
$412$	−1.28457e9	−0.904936
$413$	3.14203e8	0.219475
$414$	−2.81343e8	−0.194866
$415$	4.78766e8	0.328817
$416$	−1.29985e9	−0.885251
$417$	−1.05413e9	−0.711901
$418$	−6.77408e8	−0.453663
$419$	−2.46333e9	−1.63596	−0.817981	−	0.575245i	$-0.804907\pi$
$419$	−2.46333e9	−1.63596	−0.817981	+	0.575245i	$0.804907\pi$
$420$	−5.15833e8	−0.339732
$421$	6.02698e8	0.393652	0.196826	−	0.980438i	$-0.436937\pi$
$421$	6.02698e8	0.393652	0.196826	+	0.980438i	$0.436937\pi$
$422$	−3.01596e8	−0.195358
$423$	−5.27892e7	−0.0339120
$424$	−2.49617e9	−1.59035
$425$	−1.61425e9	−1.02002
$426$	−1.70745e8	−0.107007
$427$	1.11275e9	0.691674
$428$	6.66417e8	0.410859
$429$	3.23737e8	0.197967
$430$	1.30066e8	0.0788902
$431$	1.69548e9	1.02005	0.510027	−	0.860159i	$-0.329636\pi$
$431$	1.69548e9	1.02005	0.510027	+	0.860159i	$0.329636\pi$
$432$	−3.54149e7	−0.0211346
$433$	−5.31537e8	−0.314649	−0.157324	−	0.987547i	$-0.550287\pi$
$433$	−5.31537e8	−0.314649	−0.157324	+	0.987547i	$0.550287\pi$
$434$	1.05563e9	0.619867
$435$	4.81726e7	0.0280600
$436$	−9.61000e8	−0.555291
$437$	−2.88337e9	−1.65278
$438$	1.17330e9	0.667191
$439$	−2.39663e9	−1.35200	−0.675998	−	0.736904i	$-0.736287\pi$
$439$	−2.39663e9	−1.35200	−0.675998	+	0.736904i	$0.736287\pi$
$440$	4.20337e8	0.235241
$441$	1.10586e9	0.613995
$442$	−1.80740e9	−0.995580
$443$	−2.03310e9	−1.11108	−0.555542	−	0.831489i	$-0.687489\pi$
$443$	−2.03310e9	−1.11108	−0.555542	+	0.831489i	$0.687489\pi$
$444$	9.89451e8	0.536480
$445$	−1.05861e9	−0.569478
$446$	−4.97550e8	−0.265561
$447$	1.50800e9	0.798594
$448$	2.37408e9	1.24745
$449$	3.46417e9	1.80608	0.903040	−	0.429557i	$-0.141330\pi$
$449$	3.46417e9	1.80608	0.903040	+	0.429557i	$0.141330\pi$
$450$	−2.63523e8	−0.136325
$451$	−1.04151e9	−0.534622
$452$	1.93344e9	0.984798
$453$	−1.83092e9	−0.925393
$454$	9.09639e8	0.456219
$455$	−1.92317e9	−0.957146
$456$	−2.23953e9	−1.10606
$457$	−2.70035e8	−0.132347	−0.0661735	−	0.997808i	$-0.521079\pi$
$457$	−2.70035e8	−0.132347	−0.0661735	+	0.997808i	$0.521079\pi$
$458$	−1.72849e9	−0.840692
$459$	6.53766e8	0.315557
$460$	6.47962e8	0.310382
$461$	−1.94305e9	−0.923698	−0.461849	−	0.886959i	$-0.652814\pi$
$461$	−1.94305e9	−0.923698	−0.461849	+	0.886959i	$0.652814\pi$
$462$	−5.03530e8	−0.237563
$463$	−1.57266e8	−0.0736378	−0.0368189	−	0.999322i	$-0.511722\pi$
$463$	−1.57266e8	−0.0736378	−0.0368189	+	0.999322i	$0.511722\pi$
$464$	−1.86827e7	−0.00868215
$465$	4.30391e8	0.198508
$466$	5.72494e8	0.262072
$467$	−1.00777e9	−0.457881	−0.228941	−	0.973440i	$-0.573526\pi$
$467$	−1.00777e9	−0.457881	−0.228941	+	0.973440i	$0.573526\pi$
$468$	3.87614e8	0.174799
$469$	4.30666e9	1.92768
$470$	−9.25465e7	−0.0411166
$471$	1.20358e9	0.530764
$472$	−3.06553e8	−0.134186
$473$	−1.66793e8	−0.0724708
$474$	5.51773e8	0.237978
$475$	−2.70074e9	−1.15626
$476$	−3.69305e9	−1.56950
$477$	1.21914e9	0.514325
$478$	−7.94732e7	−0.0332830
$479$	1.14824e9	0.477372	0.238686	−	0.971097i	$-0.423283\pi$
$479$	1.14824e9	0.477372	0.238686	+	0.971097i	$0.423283\pi$
$480$	8.24283e8	0.340198
$481$	3.68895e9	1.51145
$482$	−2.78276e9	−1.13191
$483$	−2.14326e9	−0.865487
$484$	1.22106e9	0.489530
$485$	−2.88130e9	−1.14681
$486$	1.06726e8	0.0421738
$487$	2.65456e9	1.04146	0.520729	−	0.853722i	$-0.325660\pi$
$487$	2.65456e9	1.04146	0.520729	+	0.853722i	$0.325660\pi$
$488$	−1.08566e9	−0.422888
$489$	−2.59923e9	−1.00523
$490$	1.93872e9	0.744438
$491$	−2.25039e9	−0.857971	−0.428986	−	0.903311i	$-0.641129\pi$
$491$	−2.25039e9	−0.857971	−0.428986	+	0.903311i	$0.641129\pi$
$492$	−1.24701e9	−0.472056
$493$	3.44886e8	0.129632
$494$	−3.02389e9	−1.12855
$495$	−2.05294e8	−0.0760777
$496$	−1.66918e8	−0.0614210
$497$	−1.30073e9	−0.475268
$498$	5.59559e8	0.203022
$499$	7.47962e8	0.269481	0.134740	−	0.990881i	$-0.456980\pi$
$499$	7.47962e8	0.269481	0.134740	+	0.990881i	$0.456980\pi$
$500$	1.58254e9	0.566188
$501$	−8.26624e8	−0.293681
$502$	1.95940e9	0.691288
$503$	5.29706e9	1.85587	0.927933	−	0.372746i	$-0.121584\pi$
$503$	5.29706e9	1.85587	0.927933	+	0.372746i	$0.121584\pi$
$504$	−1.66468e9	−0.579194
$505$	1.36421e9	0.471370
$506$	6.32507e8	0.217039
$507$	−2.49075e8	−0.0848794
$508$	1.48511e9	0.502615
$509$	2.52094e9	0.847327	0.423663	−	0.905820i	$-0.360744\pi$
$509$	2.52094e9	0.847327	0.423663	+	0.905820i	$0.360744\pi$
$510$	1.14614e9	0.382597
$511$	8.93818e9	2.96330
$512$	−6.63440e8	−0.218452
$513$	1.09379e9	0.357704
$514$	−2.92167e9	−0.948988
$515$	3.03703e9	0.979771
$516$	−1.99703e8	−0.0639897
$517$	1.18679e8	0.0377709
$518$	−5.73767e9	−1.81377
$519$	−4.32998e8	−0.135957
$520$	1.87635e9	0.585197
$521$	6.27028e9	1.94247	0.971236	−	0.238118i	$-0.0765305\pi$
$521$	6.27028e9	1.94247	0.971236	+	0.238118i	$0.0765305\pi$
$522$	5.63020e7	0.0173251
$523$	−6.45997e8	−0.197458	−0.0987289	−	0.995114i	$-0.531478\pi$
$523$	−6.45997e8	−0.197458	−0.0987289	+	0.995114i	$0.531478\pi$
$524$	3.04329e9	0.924025
$525$	−2.00751e9	−0.605481
$526$	−1.79559e9	−0.537969
$527$	3.08133e9	0.917067
$528$	7.96188e7	0.0235395
$529$	−7.12574e8	−0.209284
$530$	2.13731e9	0.623593
$531$	1.49721e8	0.0433963
$532$	−6.17870e9	−1.77912
$533$	−4.64922e9	−1.32995
$534$	−1.23726e9	−0.351614
$535$	−1.57557e9	−0.444835
$536$	−4.20181e9	−1.17858
$537$	−6.31635e8	−0.176018
$538$	1.75353e9	0.485484
$539$	−2.48616e9	−0.683861
$540$	−2.45800e8	−0.0671745
$541$	−3.10398e9	−0.842807	−0.421404	−	0.906873i	$-0.638462\pi$
$541$	−3.10398e9	−0.842807	−0.421404	+	0.906873i	$0.638462\pi$
$542$	−1.11536e9	−0.300898
$543$	−2.65758e9	−0.712340
$544$	5.90135e9	1.57165
$545$	2.27204e9	0.601212
$546$	−2.24771e9	−0.590972
$547$	−2.73990e9	−0.715779	−0.357890	−	0.933764i	$-0.616504\pi$
$547$	−2.73990e9	−0.715779	−0.357890	+	0.933764i	$0.616504\pi$
$548$	−4.07509e9	−1.05781
$549$	5.30240e8	0.136763
$550$	5.92445e8	0.151837
$551$	5.77016e8	0.146946
$552$	2.09108e9	0.529157
$553$	4.20339e9	1.05697
$554$	−7.08821e8	−0.177114
$555$	−2.33930e9	−0.580845
$556$	2.83747e9	0.700116
$557$	2.13952e9	0.524595	0.262297	−	0.964987i	$-0.415520\pi$
$557$	2.13952e9	0.524595	0.262297	+	0.964987i	$0.415520\pi$
$558$	5.03021e8	0.122565
$559$	−7.44548e8	−0.180282
$560$	−4.72978e8	−0.113811
$561$	−1.46978e9	−0.351464
$562$	−5.43163e8	−0.129078
$563$	−2.85723e9	−0.674786	−0.337393	−	0.941364i	$-0.609545\pi$
$563$	−2.85723e9	−0.674786	−0.337393	+	0.941364i	$0.609545\pi$
$564$	1.42096e8	0.0333506
$565$	−4.57113e9	−1.06624
$566$	1.33689e9	0.309912
$567$	8.13035e8	0.187313
$568$	1.26906e9	0.290578
$569$	−3.13031e9	−0.712352	−0.356176	−	0.934419i	$-0.615920\pi$
$569$	−3.13031e9	−0.712352	−0.356176	+	0.934419i	$0.615920\pi$
$570$	1.91756e9	0.433698
$571$	−4.57416e9	−1.02822	−0.514109	−	0.857725i	$-0.671877\pi$
$571$	−4.57416e9	−1.02822	−0.514109	+	0.857725i	$0.671877\pi$
$572$	−8.71422e8	−0.194690
$573$	8.68191e8	0.192785
$574$	7.23124e9	1.59596
$575$	2.52173e9	0.553173
$576$	1.13128e9	0.246655
$577$	−5.19496e9	−1.12581	−0.562907	−	0.826520i	$-0.690317\pi$
$577$	−5.19496e9	−1.12581	−0.562907	+	0.826520i	$0.690317\pi$
$578$	5.15358e9	1.11010
$579$	7.00328e8	0.149943
$580$	−1.29669e8	−0.0275955
$581$	4.26271e9	0.901714
$582$	−3.36753e9	−0.708078
$583$	−2.74082e9	−0.572850
$584$	−8.72056e9	−1.81176
$585$	−9.16413e8	−0.189254
$586$	6.04459e9	1.24087
$587$	2.60032e9	0.530632	0.265316	−	0.964162i	$-0.414524\pi$
$587$	2.60032e9	0.530632	0.265316	+	0.964162i	$0.414524\pi$
$588$	−2.97671e9	−0.603831
$589$	5.15526e9	1.03955
$590$	2.62481e8	0.0526158
$591$	−4.33824e8	−0.0864485
$592$	9.07248e8	0.179721
$593$	7.30947e9	1.43944	0.719721	−	0.694263i	$-0.244269\pi$
$593$	7.30947e9	1.43944	0.719721	+	0.694263i	$0.244269\pi$
$594$	−2.39938e8	−0.0469728
$595$	8.73125e9	1.69929
$596$	−4.05918e9	−0.785374
$597$	1.74810e9	0.336245
$598$	2.82346e9	0.539917
$599$	1.02859e9	0.195545	0.0977725	−	0.995209i	$-0.468828\pi$
$599$	1.02859e9	0.195545	0.0977725	+	0.995209i	$0.468828\pi$
$600$	1.95864e9	0.370190
$601$	−2.84013e9	−0.533676	−0.266838	−	0.963741i	$-0.585979\pi$
$601$	−2.84013e9	−0.533676	−0.266838	+	0.963741i	$0.585979\pi$
$602$	1.15804e9	0.216340
$603$	2.05217e9	0.381156
$604$	4.92840e9	0.910074
$605$	−2.88689e9	−0.530013
$606$	1.59443e9	0.291039
$607$	8.39067e9	1.52278	0.761388	−	0.648296i	$-0.224518\pi$
$607$	8.39067e9	1.52278	0.761388	+	0.648296i	$0.224518\pi$
$608$	9.87333e9	1.78156
$609$	4.28907e8	0.0769489
$610$	9.29582e8	0.165819
$611$	5.29773e8	0.0939605
$612$	−1.75978e9	−0.310333
$613$	−2.69978e9	−0.473388	−0.236694	−	0.971584i	$-0.576064\pi$
$613$	−2.69978e9	−0.473388	−0.236694	+	0.971584i	$0.576064\pi$
$614$	−1.44033e9	−0.251115
$615$	2.94824e9	0.511093
$616$	3.74249e9	0.645101
$617$	3.54215e9	0.607112	0.303556	−	0.952814i	$-0.401826\pi$
$617$	3.54215e9	0.607112	0.303556	+	0.952814i	$0.401826\pi$
$618$	3.54955e9	0.604941
$619$	−7.53401e9	−1.27676	−0.638380	−	0.769721i	$-0.720395\pi$
$619$	−7.53401e9	−1.27676	−0.638380	+	0.769721i	$0.720395\pi$
$620$	−1.15851e9	−0.195222
$621$	−1.02129e9	−0.171131
$622$	1.31475e9	0.219067
$623$	−9.42539e9	−1.56168
$624$	3.55411e8	0.0585579
$625$	5.54007e7	0.00907685
$626$	1.01554e9	0.165457
$627$	−2.45903e9	−0.398407
$628$	−3.23974e9	−0.521978
$629$	−1.67479e10	−2.68339
$630$	1.42536e9	0.227108
$631$	1.21541e10	1.92584	0.962920	−	0.269787i	$-0.0869533\pi$
$631$	1.21541e10	1.92584	0.962920	+	0.269787i	$0.0869533\pi$
$632$	−4.10106e9	−0.646228
$633$	−1.09481e9	−0.171564
$634$	−1.24271e9	−0.193668
$635$	−3.51116e9	−0.544179
$636$	−3.28162e9	−0.505811
$637$	−1.10980e10	−1.70120
$638$	−1.26576e8	−0.0192966
$639$	−6.19812e8	−0.0939738
$640$	−1.92443e9	−0.290183
$641$	6.74739e9	1.01189	0.505944	−	0.862566i	$-0.331144\pi$
$641$	6.74739e9	1.01189	0.505944	+	0.862566i	$0.331144\pi$
$642$	−1.84145e9	−0.274655
$643$	−8.85998e9	−1.31430	−0.657150	−	0.753760i	$-0.728238\pi$
$643$	−8.85998e9	−1.31430	−0.657150	+	0.753760i	$0.728238\pi$
$644$	5.76915e9	0.851160
$645$	4.72145e8	0.0692814
$646$	1.37286e10	2.00360
$647$	−5.90409e9	−0.857015	−0.428507	−	0.903538i	$-0.640960\pi$
$647$	−5.90409e9	−0.857015	−0.428507	+	0.903538i	$0.640960\pi$
$648$	−7.93240e8	−0.114523
$649$	−3.36599e8	−0.0483344
$650$	2.64462e9	0.377717
$651$	3.83200e9	0.544367
$652$	6.99651e9	0.988587
$653$	−8.95278e9	−1.25823	−0.629117	−	0.777310i	$-0.716584\pi$
$653$	−8.95278e9	−1.25823	−0.629117	+	0.777310i	$0.716584\pi$
$654$	2.65545e9	0.371207
$655$	−7.19507e9	−1.00044
$656$	−1.14341e9	−0.158139
$657$	4.25914e9	0.585927
$658$	−8.23991e8	−0.112754
$659$	1.19309e10	1.62396	0.811979	−	0.583687i	$-0.198391\pi$
$659$	1.19309e10	1.62396	0.811979	+	0.583687i	$0.198391\pi$
$660$	5.52601e8	0.0748183
$661$	−3.52536e9	−0.474786	−0.237393	−	0.971414i	$-0.576293\pi$
$661$	−3.52536e9	−0.474786	−0.237393	+	0.971414i	$0.576293\pi$
$662$	2.84788e9	0.381521
$663$	−6.56095e9	−0.874318
$664$	−4.15892e9	−0.551306
$665$	1.46079e10	1.92625
$666$	−2.73407e9	−0.358632
$667$	−5.38769e8	−0.0703011
$668$	2.22507e9	0.288820
$669$	−1.80613e9	−0.233216
$670$	3.59773e9	0.462133
$671$	−1.19207e9	−0.152326
$672$	7.33903e9	0.932924
$673$	2.13472e9	0.269953	0.134976	−	0.990849i	$-0.456904\pi$
$673$	2.13472e9	0.269953	0.134976	+	0.990849i	$0.456904\pi$
$674$	5.73716e9	0.721751
$675$	−9.56603e8	−0.119720
$676$	6.70450e8	0.0834743
$677$	1.03034e10	1.27621	0.638103	−	0.769951i	$-0.279719\pi$
$677$	1.03034e10	1.27621	0.638103	+	0.769951i	$0.279719\pi$
$678$	−5.34253e9	−0.658329
$679$	−2.56537e10	−3.14490
$680$	−8.51867e9	−1.03894
$681$	3.30204e9	0.400652
$682$	−1.13088e9	−0.136512
$683$	4.34566e9	0.521895	0.260947	−	0.965353i	$-0.415965\pi$
$683$	4.34566e9	0.521895	0.260947	+	0.965353i	$0.415965\pi$
$684$	−2.94422e9	−0.351782
$685$	9.63450e9	1.14528
$686$	7.89033e9	0.933170
$687$	−6.27449e9	−0.738295
$688$	−1.83112e8	−0.0214366
$689$	−1.22348e10	−1.42505
$690$	−1.79046e9	−0.207488
$691$	1.26968e9	0.146393	0.0731965	−	0.997318i	$-0.476680\pi$
$691$	1.26968e9	0.146393	0.0731965	+	0.997318i	$0.476680\pi$
$692$	1.16553e9	0.133706
$693$	−1.82784e9	−0.208628
$694$	−9.76324e9	−1.10876
$695$	−6.70847e9	−0.758013
$696$	−4.18464e8	−0.0470464
$697$	2.11076e10	2.36115
$698$	−4.21946e9	−0.469638
$699$	2.07818e9	0.230151
$700$	5.40374e9	0.595458
$701$	−1.71178e9	−0.187687	−0.0938435	−	0.995587i	$-0.529915\pi$
$701$	−1.71178e9	−0.187687	−0.0938435	+	0.995587i	$0.529915\pi$
$702$	−1.07106e9	−0.116852
$703$	−2.80204e10	−3.04180
$704$	−2.54330e9	−0.274722
$705$	−3.35948e8	−0.0361086
$706$	1.33365e9	0.142634
$707$	1.21463e10	1.29264
$708$	−4.03014e8	−0.0426779
$709$	1.22235e10	1.28805	0.644025	−	0.765004i	$-0.277263\pi$
$709$	1.22235e10	1.28805	0.644025	+	0.765004i	$0.277263\pi$
$710$	−1.08661e9	−0.113938
$711$	2.00297e9	0.208992
$712$	9.19592e9	0.954806
$713$	−4.81355e9	−0.497338
$714$	1.02047e10	1.04919
$715$	2.06025e9	0.210790
$716$	1.70021e9	0.173104
$717$	−2.88492e8	−0.0292292
$718$	−9.54240e9	−0.962104
$719$	−5.76282e8	−0.0578207	−0.0289104	−	0.999582i	$-0.509204\pi$
$719$	−5.76282e8	−0.0578207	−0.0289104	+	0.999582i	$0.509204\pi$
$720$	−2.25379e8	−0.0225035
$721$	2.70403e10	2.68682
$722$	1.63202e10	1.61378
$723$	−1.01016e10	−0.994043
$724$	7.15357e9	0.700548
$725$	−5.04644e8	−0.0491816
$726$	−3.37406e9	−0.327246
$727$	3.68604e9	0.355787	0.177894	−	0.984050i	$-0.443072\pi$
$727$	3.68604e9	0.355787	0.177894	+	0.984050i	$0.443072\pi$
$728$	1.67061e10	1.60478
$729$	3.87420e8	0.0370370
$730$	7.46685e9	0.710407
$731$	3.38027e9	0.320067
$732$	−1.42728e9	−0.134499
$733$	−5.75370e9	−0.539614	−0.269807	−	0.962914i	$-0.586960\pi$
$733$	−5.75370e9	−0.539614	−0.269807	+	0.962914i	$0.586960\pi$
$734$	1.27846e8	0.0119331
$735$	7.03765e9	0.653765
$736$	−9.21889e9	−0.852327
$737$	−4.61363e9	−0.424528
$738$	3.44577e9	0.315565
$739$	−7.57514e9	−0.690455	−0.345227	−	0.938519i	$-0.612198\pi$
$739$	−7.57514e9	−0.690455	−0.345227	+	0.938519i	$0.612198\pi$
$740$	6.29683e9	0.571230
$741$	−1.09769e10	−0.991095
$742$	1.90296e10	1.71008
$743$	9.30976e9	0.832679	0.416340	−	0.909209i	$-0.363313\pi$
$743$	9.30976e9	0.832679	0.416340	+	0.909209i	$0.363313\pi$
$744$	−3.73870e9	−0.332825
$745$	9.59688e9	0.850321
$746$	−5.96615e9	−0.526149
$747$	2.03123e9	0.178294
$748$	3.95628e9	0.345646
$749$	−1.40281e10	−1.21987
$750$	−4.37291e9	−0.378491
$751$	1.04130e10	0.897091	0.448546	−	0.893760i	$-0.351942\pi$
$751$	1.04130e10	0.897091	0.448546	+	0.893760i	$0.351942\pi$
$752$	1.30290e8	0.0111725
$753$	7.11271e9	0.607089
$754$	−5.65026e8	−0.0480030
$755$	−1.16519e10	−0.985334
$756$	−2.18849e9	−0.184212
$757$	−5.37115e9	−0.450020	−0.225010	−	0.974356i	$-0.572241\pi$
$757$	−5.37115e9	−0.450020	−0.225010	+	0.974356i	$0.572241\pi$
$758$	7.16765e7	0.00597771
$759$	2.29603e9	0.190604
$760$	−1.42523e10	−1.17771
$761$	−2.00035e10	−1.64535	−0.822677	−	0.568509i	$-0.807521\pi$
$761$	−2.00035e10	−1.64535	−0.822677	+	0.568509i	$0.807521\pi$
$762$	−4.10368e9	−0.335994
$763$	2.02292e10	1.64870
$764$	−2.33696e9	−0.189594
$765$	4.16054e9	0.335997
$766$	6.14740e9	0.494186
$767$	−1.50255e9	−0.120239
$768$	−7.61228e9	−0.606388
$769$	−1.99672e10	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$769$	−1.99672e10	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$770$	−3.20445e9	−0.252950
$771$	−1.06058e10	−0.833401
$772$	−1.88511e9	−0.147461
$773$	−1.32942e10	−1.03522	−0.517611	−	0.855616i	$-0.673179\pi$
$773$	−1.32942e10	−1.03522	−0.517611	+	0.855616i	$0.673179\pi$
$774$	5.51822e8	0.0427765
$775$	−4.50867e9	−0.347930
$776$	2.50292e10	1.92278
$777$	−2.08280e10	−1.59285
$778$	5.41085e9	0.411943
$779$	3.53143e10	2.67652
$780$	2.46676e9	0.186121
$781$	1.39344e9	0.104667
$782$	−1.28186e10	−0.958552
$783$	2.04379e8	0.0152149
$784$	−2.72940e9	−0.202284
$785$	7.65954e9	0.565143
$786$	−8.40927e9	−0.617702
$787$	−1.67731e10	−1.22659	−0.613297	−	0.789853i	$-0.710157\pi$
$787$	−1.67731e10	−1.22659	−0.613297	+	0.789853i	$0.710157\pi$
$788$	1.16775e9	0.0850174
$789$	−6.51808e9	−0.472444
$790$	3.51147e9	0.253393
$791$	−4.06992e10	−2.92394
$792$	1.78334e9	0.127554
$793$	−5.32130e9	−0.378932
$794$	−8.60410e9	−0.610005
$795$	7.75854e9	0.547640
$796$	−4.70546e9	−0.330679
$797$	−1.36721e10	−0.956603	−0.478301	−	0.878196i	$-0.658747\pi$
$797$	−1.36721e10	−0.956603	−0.478301	+	0.878196i	$0.658747\pi$
$798$	1.70731e10	1.18933
$799$	−2.40518e9	−0.166815
$800$	−8.63498e9	−0.596275
$801$	−4.49131e9	−0.308787
$802$	7.12408e8	0.0487662
$803$	−9.57528e9	−0.652600
$804$	−5.52395e9	−0.374847
$805$	−1.36397e10	−0.921548
$806$	−5.04813e9	−0.339593
$807$	6.36540e9	0.426352
$808$	−1.18506e10	−0.790314
$809$	2.47296e10	1.64209	0.821046	−	0.570862i	$-0.193391\pi$
$809$	2.47296e10	1.64209	0.821046	+	0.570862i	$0.193391\pi$
$810$	6.79200e8	0.0449055
$811$	−5.97641e9	−0.393430	−0.196715	−	0.980461i	$-0.563027\pi$
$811$	−5.97641e9	−0.393430	−0.196715	+	0.980461i	$0.563027\pi$
$812$	−1.15451e9	−0.0756751
$813$	−4.04883e9	−0.264248
$814$	6.14664e9	0.399441
$815$	−1.65414e10	−1.07034
$816$	−1.61358e9	−0.103962
$817$	5.65540e9	0.362816
$818$	−8.37817e9	−0.535196
$819$	−8.15932e9	−0.518991
$820$	−7.93596e9	−0.502633
$821$	6.86651e9	0.433047	0.216523	−	0.976277i	$-0.430528\pi$
$821$	6.86651e9	0.433047	0.216523	+	0.976277i	$0.430528\pi$
$822$	1.12604e10	0.707133
$823$	−1.06812e10	−0.667916	−0.333958	−	0.942588i	$-0.608384\pi$
$823$	−1.06812e10	−0.667916	−0.333958	+	0.942588i	$0.608384\pi$
$824$	−2.63820e10	−1.64272
$825$	2.15061e9	0.133344
$826$	2.33701e9	0.144288
$827$	1.28871e10	0.792291	0.396146	−	0.918188i	$-0.370348\pi$
$827$	1.28871e10	0.792291	0.396146	+	0.918188i	$0.370348\pi$
$828$	2.74907e9	0.168298
$829$	2.54525e10	1.55164	0.775819	−	0.630956i	$-0.217337\pi$
$829$	2.54525e10	1.55164	0.775819	+	0.630956i	$0.217337\pi$
$830$	3.56102e9	0.216173
$831$	−2.57306e9	−0.155541
$832$	−1.13531e10	−0.683411
$833$	5.03852e10	3.02027
$834$	−7.84056e9	−0.468021
$835$	−5.26061e9	−0.312704
$836$	6.61911e9	0.391812
$837$	1.82599e9	0.107637
$838$	−1.83220e10	−1.07552
$839$	1.16543e10	0.681269	0.340635	−	0.940196i	$-0.389358\pi$
$839$	1.16543e10	0.681269	0.340635	+	0.940196i	$0.389358\pi$
$840$	−1.05940e10	−0.616711
$841$	−1.71421e10	−0.993750
$842$	4.48282e9	0.258797
$843$	−1.97171e9	−0.113356
$844$	2.94696e9	0.168724
$845$	−1.58510e9	−0.0903773
$846$	−3.92641e8	−0.0222946
$847$	−2.57035e10	−1.45345
$848$	−3.00898e9	−0.169447
$849$	4.85299e9	0.272165
$850$	−1.20067e10	−0.670588
$851$	2.61631e10	1.45524
$852$	1.66838e9	0.0924181
$853$	−8.84397e9	−0.487894	−0.243947	−	0.969789i	$-0.578442\pi$
$853$	−8.84397e9	−0.487894	−0.243947	+	0.969789i	$0.578442\pi$
$854$	8.27657e9	0.454724
$855$	6.96085e9	0.380873
$856$	1.36866e10	0.745826
$857$	−9.53214e9	−0.517318	−0.258659	−	0.965969i	$-0.583281\pi$
$857$	−9.53214e9	−0.517318	−0.258659	+	0.965969i	$0.583281\pi$
$858$	2.40793e9	0.130148
$859$	−1.01239e10	−0.544971	−0.272485	−	0.962160i	$-0.587846\pi$
$859$	−1.01239e10	−0.544971	−0.272485	+	0.962160i	$0.587846\pi$
$860$	−1.27090e9	−0.0681345
$861$	2.62498e10	1.40157
$862$	1.26108e10	0.670608
$863$	3.34111e9	0.176951	0.0884755	−	0.996078i	$-0.471801\pi$
$863$	3.34111e9	0.176951	0.0884755	+	0.996078i	$0.471801\pi$
$864$	3.49713e9	0.184465
$865$	−2.75558e9	−0.144763
$866$	−3.95353e9	−0.206858
$867$	1.87078e10	0.974888
$868$	−1.03148e10	−0.535356
$869$	−4.50301e9	−0.232773
$870$	3.58304e8	0.0184473
$871$	−2.05948e10	−1.05608
$872$	−1.97366e10	−1.00801
$873$	−1.22243e10	−0.621834
$874$	−2.14463e10	−1.08658
$875$	−3.33127e10	−1.68105
$876$	−1.14646e10	−0.576228
$877$	−1.70327e10	−0.852679	−0.426339	−	0.904563i	$-0.640197\pi$
$877$	−1.70327e10	−0.852679	−0.426339	+	0.904563i	$0.640197\pi$
$878$	−1.78259e10	−0.888835
$879$	2.19422e10	1.08973
$880$	5.06691e8	0.0250642
$881$	−6.92335e9	−0.341115	−0.170558	−	0.985348i	$-0.554557\pi$
$881$	−6.92335e9	−0.341115	−0.170558	+	0.985348i	$0.554557\pi$
$882$	8.22528e9	0.403655
$883$	−2.45719e9	−0.120109	−0.0600547	−	0.998195i	$-0.519128\pi$
$883$	−2.45719e9	−0.120109	−0.0600547	+	0.998195i	$0.519128\pi$
$884$	1.76605e10	0.859845
$885$	9.52821e8	0.0462072
$886$	−1.51220e10	−0.730453
$887$	1.99592e10	0.960307	0.480154	−	0.877184i	$-0.340581\pi$
$887$	1.99592e10	0.960307	0.480154	+	0.877184i	$0.340581\pi$
$888$	2.03209e10	0.973865
$889$	−3.12617e10	−1.49230
$890$	−7.87387e9	−0.374389
$891$	−8.70987e8	−0.0412515
$892$	4.86167e9	0.229355
$893$	−4.02402e9	−0.189095
$894$	1.12164e10	0.525015
$895$	−4.01971e9	−0.187419
$896$	−1.71342e10	−0.795768
$897$	1.02493e10	0.474155
$898$	2.57662e10	1.18736
$899$	9.63280e8	0.0442174
$900$	2.57494e9	0.117739
$901$	5.55463e10	2.52999
$902$	−7.74667e9	−0.351473
$903$	4.20376e9	0.189990
$904$	3.97083e10	1.78769
$905$	−1.69128e10	−0.758481
$906$	−1.36182e10	−0.608376
$907$	1.22070e10	0.543227	0.271614	−	0.962406i	$-0.412443\pi$
$907$	1.22070e10	0.543227	0.271614	+	0.962406i	$0.412443\pi$
$908$	−8.88829e9	−0.394019
$909$	5.78785e9	0.255590
$910$	−1.43044e10	−0.629251
$911$	1.78824e10	0.783629	0.391815	−	0.920044i	$-0.371847\pi$
$911$	1.78824e10	0.783629	0.391815	+	0.920044i	$0.371847\pi$
$912$	−2.69962e9	−0.117847
$913$	−4.56655e9	−0.198582
$914$	−2.00850e9	−0.0870081
$915$	3.37443e9	0.145622
$916$	1.68894e10	0.726074
$917$	−6.40616e10	−2.74350
$918$	4.86265e9	0.207455
$919$	−1.01138e10	−0.429843	−0.214921	−	0.976631i	$-0.568949\pi$
$919$	−1.01138e10	−0.429843	−0.214921	+	0.976631i	$0.568949\pi$
$920$	1.33076e10	0.563432
$921$	−5.22847e9	−0.220529
$922$	−1.44522e10	−0.607262
$923$	6.22020e9	0.260375
$924$	4.92010e9	0.205174
$925$	2.45059e10	1.01806
$926$	−1.16973e9	−0.0484113
$927$	1.28850e10	0.531259
$928$	1.84487e9	0.0757788
$929$	7.28094e9	0.297942	0.148971	−	0.988842i	$-0.452404\pi$
$929$	7.28094e9	0.297942	0.148971	+	0.988842i	$0.452404\pi$
$930$	3.20121e9	0.130504
$931$	8.42976e10	3.42367
$932$	−5.59397e9	−0.226342
$933$	4.77262e9	0.192385
$934$	−7.49571e9	−0.301022
$935$	−9.35360e9	−0.374230
$936$	7.96067e9	0.317310
$937$	−2.64374e10	−1.04986	−0.524928	−	0.851147i	$-0.675908\pi$
$937$	−2.64374e10	−1.04986	−0.524928	+	0.851147i	$0.675908\pi$
$938$	3.20325e10	1.26731
$939$	3.68645e9	0.145304
$940$	9.04292e8	0.0355109
$941$	−7.30500e9	−0.285796	−0.142898	−	0.989737i	$-0.545642\pi$
$941$	−7.30500e9	−0.285796	−0.142898	+	0.989737i	$0.545642\pi$
$942$	8.95211e9	0.348937
$943$	−3.29735e10	−1.28049
$944$	−3.69531e8	−0.0142971
$945$	5.17412e9	0.199446
$946$	−1.24059e9	−0.0476441
$947$	6.35717e9	0.243242	0.121621	−	0.992577i	$-0.461191\pi$
$947$	6.35717e9	0.243242	0.121621	+	0.992577i	$0.461191\pi$
$948$	−5.39150e9	−0.205533
$949$	−4.27432e10	−1.62344
$950$	−2.00879e10	−0.760154
$951$	−4.51111e9	−0.170079
$952$	−7.58463e10	−2.84908
$953$	−6.22176e9	−0.232856	−0.116428	−	0.993199i	$-0.537144\pi$
$953$	−6.22176e9	−0.232856	−0.116428	+	0.993199i	$0.537144\pi$
$954$	9.06782e9	0.338130
$955$	5.52514e9	0.205273
$956$	7.76550e8	0.0287453
$957$	−4.59479e8	−0.0169462
$958$	8.54047e9	0.313836
$959$	8.57811e10	3.14070
$960$	7.19941e9	0.262632
$961$	−1.89063e10	−0.687188
$962$	2.74381e10	0.993668
$963$	−6.68457e9	−0.241202
$964$	2.71910e10	0.977587
$965$	4.45686e9	0.159655
$966$	−1.59414e10	−0.568993
$967$	−3.37902e10	−1.20171	−0.600853	−	0.799360i	$-0.705172\pi$
$967$	−3.37902e10	−1.20171	−0.600853	+	0.799360i	$0.705172\pi$
$968$	2.50777e10	0.888637
$969$	4.98354e10	1.75956
$970$	−2.14308e10	−0.753943
$971$	−4.96021e10	−1.73873	−0.869366	−	0.494169i	$-0.835472\pi$
$971$	−4.96021e10	−1.73873	−0.869366	+	0.494169i	$0.835472\pi$
$972$	−1.04284e9	−0.0364239
$973$	−5.97291e10	−2.07870
$974$	1.97444e10	0.684680
$975$	9.60012e9	0.331711
$976$	−1.30870e9	−0.0450574
$977$	−3.46137e10	−1.18745	−0.593727	−	0.804667i	$-0.702344\pi$
$977$	−3.46137e10	−1.18745	−0.593727	+	0.804667i	$0.702344\pi$
$978$	−1.93329e10	−0.660861
$979$	1.00972e10	0.343924
$980$	−1.89437e10	−0.642943
$981$	9.63943e9	0.325994
$982$	−1.67382e10	−0.564052
$983$	−9.52456e9	−0.319822	−0.159911	−	0.987131i	$-0.551121\pi$
$983$	−9.52456e9	−0.319822	−0.159911	+	0.987131i	$0.551121\pi$
$984$	−2.56107e10	−0.856916
$985$	−2.76084e9	−0.0920480
$986$	2.56523e9	0.0852231
$987$	−2.99113e9	−0.0990205
$988$	2.95471e10	0.974689
$989$	−5.28054e9	−0.173577
$990$	−1.52696e9	−0.0500154
$991$	4.31860e10	1.40956	0.704782	−	0.709424i	$-0.251045\pi$
$991$	4.31860e10	1.40956	0.704782	+	0.709424i	$0.251045\pi$
$992$	1.64827e10	0.536090
$993$	1.03379e10	0.335052
$994$	−9.67469e9	−0.312453
$995$	1.11248e10	0.358025
$996$	−5.46758e9	−0.175343
$997$	5.74177e9	0.183490	0.0917451	−	0.995783i	$-0.470755\pi$
$997$	5.74177e9	0.183490	0.0917451	+	0.995783i	$0.470755\pi$
$998$	5.56327e9	0.177163
$999$	−9.92480e9	−0.314951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.11	✓	18
3.2	odd	2		531.8.a.e.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.11	✓	18	1.1	even	1	trivial
531.8.a.e.1.8		18	3.2	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+7.43791 q^{2} +27.0000 q^{3} -72.6775 q^{4} +171.827 q^{5} +200.824 q^{6} +1529.87 q^{7} -1492.62 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+7.43791 q^{2} +27.0000 q^{3} -72.6775 q^{4} +171.827 q^{5} +200.824 q^{6} +1529.87 q^{7} -1492.62 q^{8} +729.000 q^{9} +1278.03 q^{10} -1638.92 q^{11} -1962.29 q^{12} -7315.98 q^{13} +11379.0 q^{14} +4639.33 q^{15} -1799.27 q^{16} +33214.7 q^{17} +5422.24 q^{18} +55570.3 q^{19} -12488.0 q^{20} +41306.4 q^{21} -12190.1 q^{22} -51886.9 q^{23} -40300.8 q^{24} -48600.5 q^{25} -54415.6 q^{26} +19683.0 q^{27} -111187. q^{28} +10383.5 q^{29} +34506.9 q^{30} +92770.0 q^{31} +177673. q^{32} -44250.7 q^{33} +247048. q^{34} +262873. q^{35} -52981.9 q^{36} -504232. q^{37} +413327. q^{38} -197531. q^{39} -256473. q^{40} +635489. q^{41} +307234. q^{42} +101770. q^{43} +119112. q^{44} +125262. q^{45} -385930. q^{46} -72413.1 q^{47} -48580.2 q^{48} +1.51695e6 q^{49} -361486. q^{50} +896798. q^{51} +531707. q^{52} +1.67234e6 q^{53} +146400. q^{54} -281610. q^{55} -2.28351e6 q^{56} +1.50040e6 q^{57} +77231.8 q^{58} +205379. q^{59} -337175. q^{60} +727353. q^{61} +690015. q^{62} +1.11527e6 q^{63} +1.55182e6 q^{64} -1.25708e6 q^{65} -329133. q^{66} +2.81505e6 q^{67} -2.41396e6 q^{68} -1.40095e6 q^{69} +1.95522e6 q^{70} -850222. q^{71} -1.08812e6 q^{72} +5.84245e6 q^{73} -3.75043e6 q^{74} -1.31221e6 q^{75} -4.03871e6 q^{76} -2.50732e6 q^{77} -1.46922e6 q^{78} +2.74755e6 q^{79} -309162. q^{80} +531441. q^{81} +4.72671e6 q^{82} +2.78632e6 q^{83} -3.00205e6 q^{84} +5.70719e6 q^{85} +756957. q^{86} +280355. q^{87} +2.44628e6 q^{88} -6.16092e6 q^{89} +931687. q^{90} -1.11925e7 q^{91} +3.77101e6 q^{92} +2.50479e6 q^{93} -538602. q^{94} +9.54849e6 q^{95} +4.79716e6 q^{96} -1.67686e7 q^{97} +1.12830e7 q^{98} -1.19477e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more