LMFDB - Embedded newform 91.8.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + \cdots - 7335224320 $ x^10 - 3x^9 - 816x^8 + 2298x^7 + 213848x^6 - 507132x^5 - 19919976x^4 + 24331248x^3 + 727257184x^2 - 56397312*x - 7335224320
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$17.3557$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.3557 q^{2} -89.1399 q^{3} +173.221 q^{4} -9.67118 q^{5} +1547.09 q^{6} -343.000 q^{7} -784.843 q^{8} +5758.93 q^{9} +O(q^{10})$	\(q-17.3557 q^{2} -89.1399 q^{3} +173.221 q^{4} -9.67118 q^{5} +1547.09 q^{6} -343.000 q^{7} -784.843 q^{8} +5758.93 q^{9} +167.850 q^{10} -4810.17 q^{11} -15440.9 q^{12} -2197.00 q^{13} +5953.01 q^{14} +862.088 q^{15} -8550.77 q^{16} -13227.6 q^{17} -99950.4 q^{18} -21690.7 q^{19} -1675.25 q^{20} +30575.0 q^{21} +83484.0 q^{22} -87446.5 q^{23} +69960.9 q^{24} -78031.5 q^{25} +38130.5 q^{26} -318402. q^{27} -59414.8 q^{28} +195594. q^{29} -14962.2 q^{30} -166788. q^{31} +248865. q^{32} +428778. q^{33} +229574. q^{34} +3317.21 q^{35} +997567. q^{36} +52502.8 q^{37} +376458. q^{38} +195840. q^{39} +7590.36 q^{40} -440897. q^{41} -530651. q^{42} -697845. q^{43} -833223. q^{44} -55695.6 q^{45} +1.51770e6 q^{46} -41717.8 q^{47} +762215. q^{48} +117649. q^{49} +1.35429e6 q^{50} +1.17911e6 q^{51} -380567. q^{52} -1.88875e6 q^{53} +5.52609e6 q^{54} +46520.0 q^{55} +269201. q^{56} +1.93351e6 q^{57} -3.39467e6 q^{58} -3452.66 q^{59} +149332. q^{60} -164870. q^{61} +2.89472e6 q^{62} -1.97531e6 q^{63} -3.22473e6 q^{64} +21247.6 q^{65} -7.44176e6 q^{66} -98035.1 q^{67} -2.29130e6 q^{68} +7.79498e6 q^{69} -57572.6 q^{70} +1.68643e6 q^{71} -4.51986e6 q^{72} -6.15276e6 q^{73} -911224. q^{74} +6.95572e6 q^{75} -3.75729e6 q^{76} +1.64989e6 q^{77} -3.39895e6 q^{78} -171958. q^{79} +82696.0 q^{80} +1.57875e7 q^{81} +7.65209e6 q^{82} -7.99418e6 q^{83} +5.29623e6 q^{84} +127926. q^{85} +1.21116e7 q^{86} -1.74352e7 q^{87} +3.77523e6 q^{88} +5.25354e6 q^{89} +966638. q^{90} +753571. q^{91} -1.51476e7 q^{92} +1.48674e7 q^{93} +724042. q^{94} +209775. q^{95} -2.21838e7 q^{96} -5.31437e6 q^{97} -2.04188e6 q^{98} -2.77014e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9} + 2548 q^{10} + 451 q^{11} - 16241 q^{12} - 21970 q^{13} + 1029 q^{14} + 27184 q^{15} + 11897 q^{16} - 8654 q^{17} + 159348 q^{18} + 10130 q^{19} - 82012 q^{20} + 34643 q^{21} - 57863 q^{22} - 52155 q^{23} - 49227 q^{24} + 47190 q^{25} + 6591 q^{26} - 155171 q^{27} - 123823 q^{28} + 520154 q^{29} + 1070236 q^{30} + 692605 q^{31} + 149835 q^{32} + 436053 q^{33} + 1059060 q^{34} - 77518 q^{35} + 2843742 q^{36} - 20511 q^{37} + 1905286 q^{38} + 221897 q^{39} + 636320 q^{40} + 355049 q^{41} - 379015 q^{42} + 1256772 q^{43} - 687913 q^{44} + 1259926 q^{45} + 4043075 q^{46} + 1260721 q^{47} + 1128551 q^{48} + 1176490 q^{49} + 609035 q^{50} + 1411976 q^{51} - 793117 q^{52} + 928854 q^{53} + 6642607 q^{54} + 3423196 q^{55} - 99813 q^{56} + 3014966 q^{57} + 1612588 q^{58} + 3144446 q^{59} + 7738848 q^{60} + 6322923 q^{61} + 6545331 q^{62} - 4200721 q^{63} - 6629943 q^{64} - 496522 q^{65} - 14343317 q^{66} + 3944507 q^{67} - 1787356 q^{68} - 148281 q^{69} - 873964 q^{70} + 6032248 q^{71} + 9760866 q^{72} + 1248533 q^{73} - 8263279 q^{74} + 1573413 q^{75} + 1788254 q^{76} - 154693 q^{77} - 2427685 q^{78} - 14947605 q^{79} - 9147616 q^{80} + 25716334 q^{81} - 6987095 q^{82} - 14177784 q^{83} + 5570663 q^{84} - 11788444 q^{85} + 8748840 q^{86} - 29484448 q^{87} - 15390723 q^{88} + 6734836 q^{89} + 5994972 q^{90} + 7535710 q^{91} - 24493215 q^{92} + 17307847 q^{93} - 22760149 q^{94} - 9329708 q^{95} - 36488483 q^{96} - 12365397 q^{97} - 352947 q^{98} - 43198042 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9 + 2548 * q^10 + 451 * q^11 - 16241 * q^12 - 21970 * q^13 + 1029 * q^14 + 27184 * q^15 + 11897 * q^16 - 8654 * q^17 + 159348 * q^18 + 10130 * q^19 - 82012 * q^20 + 34643 * q^21 - 57863 * q^22 - 52155 * q^23 - 49227 * q^24 + 47190 * q^25 + 6591 * q^26 - 155171 * q^27 - 123823 * q^28 + 520154 * q^29 + 1070236 * q^30 + 692605 * q^31 + 149835 * q^32 + 436053 * q^33 + 1059060 * q^34 - 77518 * q^35 + 2843742 * q^36 - 20511 * q^37 + 1905286 * q^38 + 221897 * q^39 + 636320 * q^40 + 355049 * q^41 - 379015 * q^42 + 1256772 * q^43 - 687913 * q^44 + 1259926 * q^45 + 4043075 * q^46 + 1260721 * q^47 + 1128551 * q^48 + 1176490 * q^49 + 609035 * q^50 + 1411976 * q^51 - 793117 * q^52 + 928854 * q^53 + 6642607 * q^54 + 3423196 * q^55 - 99813 * q^56 + 3014966 * q^57 + 1612588 * q^58 + 3144446 * q^59 + 7738848 * q^60 + 6322923 * q^61 + 6545331 * q^62 - 4200721 * q^63 - 6629943 * q^64 - 496522 * q^65 - 14343317 * q^66 + 3944507 * q^67 - 1787356 * q^68 - 148281 * q^69 - 873964 * q^70 + 6032248 * q^71 + 9760866 * q^72 + 1248533 * q^73 - 8263279 * q^74 + 1573413 * q^75 + 1788254 * q^76 - 154693 * q^77 - 2427685 * q^78 - 14947605 * q^79 - 9147616 * q^80 + 25716334 * q^81 - 6987095 * q^82 - 14177784 * q^83 + 5570663 * q^84 - 11788444 * q^85 + 8748840 * q^86 - 29484448 * q^87 - 15390723 * q^88 + 6734836 * q^89 + 5994972 * q^90 + 7535710 * q^91 - 24493215 * q^92 + 17307847 * q^93 - 22760149 * q^94 - 9329708 * q^95 - 36488483 * q^96 - 12365397 * q^97 - 352947 * q^98 - 43198042 * 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 $

$2$	−17.3557	−1.53404	−0.767022	−	0.641621i	$-0.778262\pi$
$2$	−17.3557	−1.53404	−0.767022	+	0.641621i	$0.778262\pi$
$3$	−89.1399	−1.90611	−0.953055	−	0.302797i	$-0.902079\pi$
$3$	−89.1399	−1.90611	−0.953055	+	0.302797i	$0.902079\pi$
$4$	173.221	1.35329
$5$	−9.67118	−0.0346007	−0.0173003	−	0.999850i	$-0.505507\pi$
$5$	−9.67118	−0.0346007	−0.0173003	+	0.999850i	$0.505507\pi$
$6$	1547.09	2.92406
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−784.843	−0.541961
$9$	5758.93	2.63326
$10$	167.850	0.0530789
$11$	−4810.17	−1.08965	−0.544824	−	0.838551i	$-0.683403\pi$
$11$	−4810.17	−1.08965	−0.544824	+	0.838551i	$0.683403\pi$
$12$	−15440.9	−2.57952
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	5953.01	0.579814
$15$	862.088	0.0659527
$16$	−8550.77	−0.521898
$17$	−13227.6	−0.652995	−0.326497	−	0.945198i	$-0.605868\pi$
$17$	−13227.6	−0.652995	−0.326497	+	0.945198i	$0.605868\pi$
$18$	−99950.4	−4.03953
$19$	−21690.7	−0.725499	−0.362749	−	0.931887i	$-0.618162\pi$
$19$	−21690.7	−0.725499	−0.362749	+	0.931887i	$0.618162\pi$
$20$	−1675.25	−0.0468247
$21$	30575.0	0.720442
$22$	83484.0	1.67157
$23$	−87446.5	−1.49863	−0.749316	−	0.662212i	$-0.769618\pi$
$23$	−87446.5	−1.49863	−0.749316	+	0.662212i	$0.769618\pi$
$24$	69960.9	1.03304
$25$	−78031.5	−0.998803
$26$	38130.5	0.425467
$27$	−318402.	−3.11316
$28$	−59414.8	−0.511495
$29$	195594.	1.48923	0.744615	−	0.667495i	$-0.232633\pi$
$29$	195594.	1.48923	0.744615	+	0.667495i	$0.232633\pi$
$30$	−14962.2	−0.101174
$31$	−166788.	−1.00554	−0.502768	−	0.864421i	$-0.667685\pi$
$31$	−166788.	−1.00554	−0.502768	+	0.864421i	$0.667685\pi$
$32$	248865.	1.34257
$33$	428778.	2.07699
$34$	229574.	1.00172
$35$	3317.21	0.0130778
$36$	997567.	3.56356
$37$	52502.8	0.170403	0.0852013	−	0.996364i	$-0.472847\pi$
$37$	52502.8	0.170403	0.0852013	+	0.996364i	$0.472847\pi$
$38$	376458.	1.11295
$39$	195840.	0.528660
$40$	7590.36	0.0187522
$41$	−440897.	−0.999065	−0.499532	−	0.866295i	$-0.666495\pi$
$41$	−440897.	−0.999065	−0.499532	+	0.866295i	$0.666495\pi$
$42$	−530651.	−1.10519
$43$	−697845.	−1.33850	−0.669252	−	0.743036i	$-0.733385\pi$
$43$	−697845.	−1.33850	−0.669252	+	0.743036i	$0.733385\pi$
$44$	−833223.	−1.47461
$45$	−55695.6	−0.0911124
$46$	1.51770e6	2.29897
$47$	−41717.8	−0.0586109	−0.0293055	−	0.999571i	$-0.509330\pi$
$47$	−41717.8	−0.0586109	−0.0293055	+	0.999571i	$0.509330\pi$
$48$	762215.	0.994794
$49$	117649.	0.142857
$50$	1.35429e6	1.53221
$51$	1.17911e6	1.24468
$52$	−380567.	−0.375335
$53$	−1.88875e6	−1.74265	−0.871324	−	0.490709i	$-0.836738\pi$
$53$	−1.88875e6	−1.74265	−0.871324	+	0.490709i	$0.836738\pi$
$54$	5.52609e6	4.77573
$55$	46520.0	0.0377025
$56$	269201.	0.204842
$57$	1.93351e6	1.38288
$58$	−3.39467e6	−2.28454
$59$	−3452.66	−0.00218863	−0.00109431	−	0.999999i	$-0.500348\pi$
$59$	−3452.66	−0.00218863	−0.00109431	+	0.999999i	$0.500348\pi$
$60$	149332.	0.0892530
$61$	−164870.	−0.0930011	−0.0465005	−	0.998918i	$-0.514807\pi$
$61$	−164870.	−0.0930011	−0.0465005	+	0.998918i	$0.514807\pi$
$62$	2.89472e6	1.54254
$63$	−1.97531e6	−0.995277
$64$	−3.22473e6	−1.53767
$65$	21247.6	0.00959650
$66$	−7.44176e6	−3.18619
$67$	−98035.1	−0.0398217	−0.0199109	−	0.999802i	$-0.506338\pi$
$67$	−98035.1	−0.0398217	−0.0199109	+	0.999802i	$0.506338\pi$
$68$	−2.29130e6	−0.883691
$69$	7.79498e6	2.85656
$70$	−57572.6	−0.0200619
$71$	1.68643e6	0.559196	0.279598	−	0.960117i	$-0.409799\pi$
$71$	1.68643e6	0.559196	0.279598	+	0.960117i	$0.409799\pi$
$72$	−4.51986e6	−1.42712
$73$	−6.15276e6	−1.85114	−0.925572	−	0.378573i	$-0.876415\pi$
$73$	−6.15276e6	−1.85114	−0.925572	+	0.378573i	$0.876415\pi$
$74$	−911224.	−0.261405
$75$	6.95572e6	1.90383
$76$	−3.75729e6	−0.981809
$77$	1.64989e6	0.411848
$78$	−3.39895e6	−0.810987
$79$	−171958.	−0.0392399	−0.0196200	−	0.999808i	$-0.506246\pi$
$79$	−171958.	−0.0392399	−0.0196200	+	0.999808i	$0.506246\pi$
$80$	82696.0	0.0180580
$81$	1.57875e7	3.30078
$82$	7.65209e6	1.53261
$83$	−7.99418e6	−1.53462	−0.767309	−	0.641277i	$-0.778405\pi$
$83$	−7.99418e6	−1.53462	−0.767309	+	0.641277i	$0.778405\pi$
$84$	5.29623e6	0.974966
$85$	127926.	0.0225940
$86$	1.21116e7	2.05332
$87$	−1.74352e7	−2.83863
$88$	3.77523e6	0.590546
$89$	5.25354e6	0.789928	0.394964	−	0.918697i	$-0.370757\pi$
$89$	5.25354e6	0.789928	0.394964	+	0.918697i	$0.370757\pi$
$90$	966638.	0.139770
$91$	753571.	0.104828
$92$	−1.51476e7	−2.02808
$93$	1.48674e7	1.91666
$94$	724042.	0.0899117
$95$	209775.	0.0251027
$96$	−2.21838e7	−2.55909
$97$	−5.31437e6	−0.591223	−0.295611	−	0.955308i	$-0.595523\pi$
$97$	−5.31437e6	−0.591223	−0.295611	+	0.955308i	$0.595523\pi$
$98$	−2.04188e6	−0.219149
$99$	−2.77014e7	−2.86932
$100$	−1.35167e7	−1.35167
$101$	−7.20787e6	−0.696117	−0.348058	−	0.937473i	$-0.613159\pi$
$101$	−7.20787e6	−0.696117	−0.348058	+	0.937473i	$0.613159\pi$
$102$	−2.04642e7	−1.90939
$103$	−8.59221e6	−0.774774	−0.387387	−	0.921917i	$-0.626622\pi$
$103$	−8.59221e6	−0.774774	−0.387387	+	0.921917i	$0.626622\pi$
$104$	1.72430e6	0.150313
$105$	−295696.	−0.0249278
$106$	3.27807e7	2.67330
$107$	1.72130e7	1.35835	0.679176	−	0.733975i	$-0.262337\pi$
$107$	1.72130e7	1.35835	0.679176	+	0.733975i	$0.262337\pi$
$108$	−5.51538e7	−4.21301
$109$	925472.	0.0684496	0.0342248	−	0.999414i	$-0.489104\pi$
$109$	925472.	0.0684496	0.0342248	+	0.999414i	$0.489104\pi$
$110$	−807388.	−0.0578373
$111$	−4.68010e6	−0.324806
$112$	2.93291e6	0.197259
$113$	1.85205e7	1.20748	0.603738	−	0.797183i	$-0.293677\pi$
$113$	1.85205e7	1.20748	0.603738	+	0.797183i	$0.293677\pi$
$114$	−3.35575e7	−2.12140
$115$	845711.	0.0518537
$116$	3.38809e7	2.01536
$117$	−1.26524e7	−0.730334
$118$	59923.5	0.00335745
$119$	4.53706e6	0.246809
$120$	−676604.	−0.0357438
$121$	3.65057e6	0.187332
$122$	2.86144e6	0.142668
$123$	3.93015e7	1.90433
$124$	−2.88911e7	−1.36078
$125$	1.51022e6	0.0691599
$126$	3.42830e7	1.52680
$127$	−1.44961e7	−0.627970	−0.313985	−	0.949428i	$-0.601664\pi$
$127$	−1.44961e7	−0.627970	−0.313985	+	0.949428i	$0.601664\pi$
$128$	2.41128e7	1.01628
$129$	6.22059e7	2.55134
$130$	−368767.	−0.0147214
$131$	4.29766e7	1.67025	0.835127	−	0.550057i	$-0.185394\pi$
$131$	4.29766e7	1.67025	0.835127	+	0.550057i	$0.185394\pi$
$132$	7.42734e7	2.81077
$133$	7.43992e6	0.274213
$134$	1.70147e6	0.0610882
$135$	3.07932e6	0.107718
$136$	1.03816e7	0.353898
$137$	5.36809e7	1.78360	0.891801	−	0.452428i	$-0.149442\pi$
$137$	5.36809e7	1.78360	0.891801	+	0.452428i	$0.149442\pi$
$138$	−1.35287e8	−4.38208
$139$	6.63333e6	0.209498	0.104749	−	0.994499i	$-0.466596\pi$
$139$	6.63333e6	0.209498	0.104749	+	0.994499i	$0.466596\pi$
$140$	574611.	0.0176981
$141$	3.71872e6	0.111719
$142$	−2.92692e7	−0.857830
$143$	1.05679e7	0.302214
$144$	−4.92433e7	−1.37429
$145$	−1.89162e6	−0.0515283
$146$	1.06786e8	2.83973
$147$	−1.04872e7	−0.272301
$148$	9.09459e6	0.230604
$149$	4.29602e6	0.106393	0.0531967	−	0.998584i	$-0.483059\pi$
$149$	4.29602e6	0.106393	0.0531967	+	0.998584i	$0.483059\pi$
$150$	−1.20722e8	−2.92055
$151$	3.44589e6	0.0814483	0.0407242	−	0.999170i	$-0.487034\pi$
$151$	3.44589e6	0.0814483	0.0407242	+	0.999170i	$0.487034\pi$
$152$	1.70238e7	0.393192
$153$	−7.61768e7	−1.71950
$154$	−2.86350e7	−0.631793
$155$	1.61303e6	0.0347922
$156$	3.39237e7	0.715430
$157$	−996112.	−0.0205428	−0.0102714	−	0.999947i	$-0.503270\pi$
$157$	−996112.	−0.0205428	−0.0102714	+	0.999947i	$0.503270\pi$
$158$	2.98446e6	0.0601957
$159$	1.68363e8	3.32168
$160$	−2.40681e6	−0.0464540
$161$	2.99942e7	0.566430
$162$	−2.74004e8	−5.06354
$163$	2.16231e7	0.391076	0.195538	−	0.980696i	$-0.437355\pi$
$163$	2.16231e7	0.391076	0.195538	+	0.980696i	$0.437355\pi$
$164$	−7.63726e7	−1.35202
$165$	−4.14679e6	−0.0718652
$166$	1.38745e8	2.35417
$167$	−5.31098e7	−0.882403	−0.441201	−	0.897408i	$-0.645448\pi$
$167$	−5.31098e7	−0.882403	−0.441201	+	0.897408i	$0.645448\pi$
$168$	−2.39966e7	−0.390451
$169$	4.82681e6	0.0769231
$170$	−2.22025e6	−0.0346602
$171$	−1.24915e8	−1.91042
$172$	−1.20881e8	−1.81138
$173$	2.03323e7	0.298556	0.149278	−	0.988795i	$-0.452305\pi$
$173$	2.03323e7	0.298556	0.149278	+	0.988795i	$0.452305\pi$
$174$	3.02600e8	4.35459
$175$	2.67648e7	0.377512
$176$	4.11307e7	0.568684
$177$	307770.	0.00417177
$178$	−9.11790e7	−1.21178
$179$	2.10751e7	0.274653	0.137326	−	0.990526i	$-0.456149\pi$
$179$	2.10751e7	0.274653	0.137326	+	0.990526i	$0.456149\pi$
$180$	−9.64765e6	−0.123301
$181$	−7.51426e7	−0.941914	−0.470957	−	0.882156i	$-0.656091\pi$
$181$	−7.51426e7	−0.941914	−0.470957	+	0.882156i	$0.656091\pi$
$182$	−1.30788e7	−0.160811
$183$	1.46965e7	0.177270
$184$	6.86318e7	0.812200
$185$	−507764.	−0.00589604
$186$	−2.58035e8	−2.94024
$187$	6.36270e7	0.711534
$188$	−7.22640e6	−0.0793176
$189$	1.09212e8	1.17667
$190$	−3.64079e6	−0.0385087
$191$	−5.82631e7	−0.605030	−0.302515	−	0.953145i	$-0.597826\pi$
$191$	−5.82631e7	−0.605030	−0.302515	+	0.953145i	$0.597826\pi$
$192$	2.87452e8	2.93097
$193$	−1.77411e8	−1.77636	−0.888179	−	0.459498i	$-0.848029\pi$
$193$	−1.77411e8	−1.77636	−0.888179	+	0.459498i	$0.848029\pi$
$194$	9.22348e7	0.906961
$195$	−1.89401e6	−0.0182920
$196$	2.03793e7	0.193327
$197$	1.07532e8	1.00209	0.501046	−	0.865421i	$-0.332949\pi$
$197$	1.07532e8	1.00209	0.501046	+	0.865421i	$0.332949\pi$
$198$	4.80778e8	4.40166
$199$	−5.06953e7	−0.456018	−0.228009	−	0.973659i	$-0.573222\pi$
$199$	−5.06953e7	−0.456018	−0.228009	+	0.973659i	$0.573222\pi$
$200$	6.12425e7	0.541312
$201$	8.73884e6	0.0759045
$202$	1.25098e8	1.06787
$203$	−6.70886e7	−0.562876
$204$	2.04246e8	1.68441
$205$	4.26399e6	0.0345683
$206$	1.49124e8	1.18854
$207$	−5.03598e8	−3.94628
$208$	1.87860e7	0.144748
$209$	1.04336e8	0.790538
$210$	5.13202e6	0.0382403
$211$	−2.12543e8	−1.55761	−0.778804	−	0.627267i	$-0.784173\pi$
$211$	−2.12543e8	−1.55761	−0.778804	+	0.627267i	$0.784173\pi$
$212$	−3.27172e8	−2.35831
$213$	−1.50328e8	−1.06589
$214$	−2.98743e8	−2.08377
$215$	6.74899e6	0.0463131
$216$	2.49895e8	1.68721
$217$	5.72082e7	0.380057
$218$	−1.60622e7	−0.105005
$219$	5.48457e8	3.52848
$220$	8.05824e6	0.0510224
$221$	2.90610e7	0.181108
$222$	8.12264e7	0.498267
$223$	1.28517e8	0.776055	0.388028	−	0.921648i	$-0.373157\pi$
$223$	1.28517e8	0.776055	0.388028	+	0.921648i	$0.373157\pi$
$224$	−8.53606e7	−0.507445
$225$	−4.49378e8	−2.63010
$226$	−3.21437e8	−1.85232
$227$	6.92336e7	0.392849	0.196425	−	0.980519i	$-0.437067\pi$
$227$	6.92336e7	0.392849	0.196425	+	0.980519i	$0.437067\pi$
$228$	3.34925e8	1.87144
$229$	3.14258e8	1.72927	0.864634	−	0.502402i	$-0.167550\pi$
$229$	3.14258e8	1.72927	0.864634	+	0.502402i	$0.167550\pi$
$230$	−1.46779e7	−0.0795458
$231$	−1.47071e8	−0.785028
$232$	−1.53510e8	−0.807104
$233$	−1.91790e8	−0.993302	−0.496651	−	0.867950i	$-0.665437\pi$
$233$	−1.91790e8	−0.993302	−0.496651	+	0.867950i	$0.665437\pi$
$234$	2.19591e8	1.12036
$235$	403460.	0.00202798
$236$	−598074.	−0.00296185
$237$	1.53283e7	0.0747956
$238$	−7.87440e7	−0.378615
$239$	3.66028e8	1.73429	0.867145	−	0.498055i	$-0.165952\pi$
$239$	3.66028e8	1.73429	0.867145	+	0.498055i	$0.165952\pi$
$240$	−7.37152e6	−0.0344205
$241$	−9.86705e7	−0.454075	−0.227038	−	0.973886i	$-0.572904\pi$
$241$	−9.86705e7	−0.454075	−0.227038	+	0.973886i	$0.572904\pi$
$242$	−6.33582e7	−0.287375
$243$	−7.10954e8	−3.17848
$244$	−2.85590e7	−0.125857
$245$	−1.13780e6	−0.00494295
$246$	−6.82107e8	−2.92132
$247$	4.76545e7	0.201217
$248$	1.30902e8	0.544962
$249$	7.12600e8	2.92515
$250$	−2.62109e7	−0.106094
$251$	−3.40854e8	−1.36054	−0.680268	−	0.732963i	$-0.738137\pi$
$251$	−3.40854e8	−1.36054	−0.680268	+	0.732963i	$0.738137\pi$
$252$	−3.42166e8	−1.34690
$253$	4.20633e8	1.63298
$254$	2.51591e8	0.963333
$255$	−1.14034e7	−0.0430667
$256$	−5.72962e6	−0.0213445
$257$	−2.76765e8	−1.01706	−0.508528	−	0.861045i	$-0.669810\pi$
$257$	−2.76765e8	−1.01706	−0.508528	+	0.861045i	$0.669810\pi$
$258$	−1.07963e9	−3.91386
$259$	−1.80085e7	−0.0644062
$260$	3.68053e6	0.0129868
$261$	1.12641e9	3.92152
$262$	−7.45890e8	−2.56224
$263$	−4.06428e8	−1.37765	−0.688824	−	0.724928i	$-0.741873\pi$
$263$	−4.06428e8	−1.37765	−0.688824	+	0.724928i	$0.741873\pi$
$264$	−3.36524e8	−1.12565
$265$	1.82665e7	0.0602967
$266$	−1.29125e8	−0.420654
$267$	−4.68301e8	−1.50569
$268$	−1.69817e7	−0.0538903
$269$	−5.54000e8	−1.73531	−0.867654	−	0.497168i	$-0.834373\pi$
$269$	−5.54000e8	−1.73531	−0.867654	+	0.497168i	$0.834373\pi$
$270$	−5.34438e7	−0.165243
$271$	−6.27567e8	−1.91544	−0.957718	−	0.287708i	$-0.907107\pi$
$271$	−6.27567e8	−1.91544	−0.957718	+	0.287708i	$0.907107\pi$
$272$	1.13106e8	0.340796
$273$	−6.71733e7	−0.199815
$274$	−9.31671e8	−2.73612
$275$	3.75345e8	1.08834
$276$	1.35025e9	3.86575
$277$	5.81261e8	1.64321	0.821604	−	0.570059i	$-0.193080\pi$
$277$	5.81261e8	1.64321	0.821604	+	0.570059i	$0.193080\pi$
$278$	−1.15126e8	−0.321379
$279$	−9.60518e8	−2.64783
$280$	−2.60349e6	−0.00708767
$281$	1.90995e8	0.513512	0.256756	−	0.966476i	$-0.417346\pi$
$281$	1.90995e8	0.513512	0.256756	+	0.966476i	$0.417346\pi$
$282$	−6.45411e7	−0.171382
$283$	−1.94383e8	−0.509808	−0.254904	−	0.966966i	$-0.582044\pi$
$283$	−1.94383e8	−0.509808	−0.254904	+	0.966966i	$0.582044\pi$
$284$	2.92125e8	0.756753
$285$	−1.86993e7	−0.0478486
$286$	−1.83414e8	−0.463609
$287$	1.51228e8	0.377611
$288$	1.43319e9	3.53534
$289$	−2.35369e8	−0.573598
$290$	3.28304e7	0.0790467
$291$	4.73723e8	1.12694
$292$	−1.06579e9	−2.50513
$293$	6.41323e8	1.48950	0.744750	−	0.667344i	$-0.232569\pi$
$293$	6.41323e8	1.48950	0.744750	+	0.667344i	$0.232569\pi$
$294$	1.82013e8	0.417722
$295$	33391.3	7.57280e−5 0
$296$	−4.12065e7	−0.0923516
$297$	1.53157e9	3.39225
$298$	−7.45605e7	−0.163212
$299$	1.92120e8	0.415646
$300$	1.20488e9	2.57643
$301$	2.39361e8	0.505907
$302$	−5.98059e7	−0.124945
$303$	6.42509e8	1.32687
$304$	1.85472e8	0.378636
$305$	1.59449e6	0.00321790
$306$	1.32210e9	2.63779
$307$	6.02627e7	0.118868	0.0594339	−	0.998232i	$-0.481070\pi$
$307$	6.02627e7	0.118868	0.0594339	+	0.998232i	$0.481070\pi$
$308$	2.85795e8	0.557350
$309$	7.65909e8	1.47680
$310$	−2.79953e7	−0.0533728
$311$	8.95977e8	1.68902	0.844511	−	0.535538i	$-0.179891\pi$
$311$	8.95977e8	1.68902	0.844511	+	0.535538i	$0.179891\pi$
$312$	−1.53704e8	−0.286513
$313$	3.18196e7	0.0586530	0.0293265	−	0.999570i	$-0.490664\pi$
$313$	3.18196e7	0.0586530	0.0293265	+	0.999570i	$0.490664\pi$
$314$	1.72882e7	0.0315135
$315$	1.91036e7	0.0344372
$316$	−2.97868e7	−0.0531029
$317$	−5.00344e8	−0.882187	−0.441094	−	0.897461i	$-0.645409\pi$
$317$	−5.00344e8	−0.882187	−0.441094	+	0.897461i	$0.645409\pi$
$318$	−2.92207e9	−5.09560
$319$	−9.40838e8	−1.62273
$320$	3.11869e7	0.0532044
$321$	−1.53436e9	−2.58917
$322$	−5.20570e8	−0.868928
$323$	2.86916e8	0.473747
$324$	2.73473e9	4.46691
$325$	1.71435e8	0.277018
$326$	−3.75285e8	−0.599928
$327$	−8.24966e7	−0.130472
$328$	3.46035e8	0.541454
$329$	1.43092e7	0.0221529
$330$	7.19705e7	0.110244
$331$	7.43225e8	1.12648	0.563238	−	0.826294i	$-0.309555\pi$
$331$	7.43225e8	1.12648	0.563238	+	0.826294i	$0.309555\pi$
$332$	−1.38476e9	−2.07678
$333$	3.02360e8	0.448714
$334$	9.21759e8	1.35364
$335$	948115.	0.00137786
$336$	−2.61440e8	−0.375997
$337$	3.82555e8	0.544488	0.272244	−	0.962228i	$-0.412234\pi$
$337$	3.82555e8	0.544488	0.272244	+	0.962228i	$0.412234\pi$
$338$	−8.37727e7	−0.118003
$339$	−1.65092e9	−2.30158
$340$	2.21595e7	0.0305763
$341$	8.02277e8	1.09568
$342$	2.16800e9	2.93067
$343$	−4.03536e7	−0.0539949
$344$	5.47699e8	0.725417
$345$	−7.53866e7	−0.0988388
$346$	−3.52882e8	−0.457997
$347$	1.27004e9	1.63179	0.815897	−	0.578197i	$-0.196244\pi$
$347$	1.27004e9	1.63179	0.815897	+	0.578197i	$0.196244\pi$
$348$	−3.02014e9	−3.84149
$349$	1.01756e9	1.28136	0.640680	−	0.767808i	$-0.278653\pi$
$349$	1.01756e9	1.28136	0.640680	+	0.767808i	$0.278653\pi$
$350$	−4.64522e8	−0.579120
$351$	6.99528e8	0.863436
$352$	−1.19708e9	−1.46293
$353$	1.01873e9	1.23267	0.616335	−	0.787484i	$-0.288617\pi$
$353$	1.01873e9	1.23267	0.616335	+	0.787484i	$0.288617\pi$
$354$	−5.34157e6	−0.00639967
$355$	−1.63097e7	−0.0193485
$356$	9.10024e8	1.06900
$357$	−4.04434e8	−0.470445
$358$	−3.65774e8	−0.421330
$359$	−6.44985e8	−0.735731	−0.367865	−	0.929879i	$-0.619911\pi$
$359$	−6.44985e8	−0.735731	−0.367865	+	0.929879i	$0.619911\pi$
$360$	4.37123e7	0.0493793
$361$	−4.23384e8	−0.473652
$362$	1.30415e9	1.44494
$363$	−3.25411e8	−0.357075
$364$	1.30534e8	0.141863
$365$	5.95044e7	0.0640508
$366$	−2.55069e8	−0.271940
$367$	−1.21524e9	−1.28331	−0.641653	−	0.766995i	$-0.721751\pi$
$367$	−1.21524e9	−1.28331	−0.641653	+	0.766995i	$0.721751\pi$
$368$	7.47735e8	0.782133
$369$	−2.53910e9	−2.63079
$370$	8.81261e6	0.00904479
$371$	6.47842e8	0.658659
$372$	2.57535e9	2.59380
$373$	4.76152e8	0.475078	0.237539	−	0.971378i	$-0.423659\pi$
$373$	4.76152e8	0.475078	0.237539	+	0.971378i	$0.423659\pi$
$374$	−1.10429e9	−1.09152
$375$	−1.34621e8	−0.131826
$376$	3.27419e7	0.0317648
$377$	−4.29719e8	−0.413038
$378$	−1.89545e9	−1.80506
$379$	2.05317e9	1.93726	0.968628	−	0.248516i	$-0.0799428\pi$
$379$	2.05317e9	1.93726	0.968628	+	0.248516i	$0.0799428\pi$
$380$	3.63374e7	0.0339713
$381$	1.29218e9	1.19698
$382$	1.01120e9	0.928142
$383$	−6.47837e8	−0.589210	−0.294605	−	0.955619i	$-0.595188\pi$
$383$	−6.47837e8	−0.589210	−0.294605	+	0.955619i	$0.595188\pi$
$384$	−2.14941e9	−1.93714
$385$	−1.59564e7	−0.0142502
$386$	3.07910e9	2.72501
$387$	−4.01884e9	−3.52462
$388$	−9.20561e8	−0.800095
$389$	−1.77218e8	−0.152645	−0.0763226	−	0.997083i	$-0.524318\pi$
$389$	−1.77218e8	−0.152645	−0.0763226	+	0.997083i	$0.524318\pi$
$390$	3.28719e7	0.0280607
$391$	1.15671e9	0.978599
$392$	−9.23360e7	−0.0774230
$393$	−3.83093e9	−3.18369
$394$	−1.86630e9	−1.53725
$395$	1.66304e6	0.00135773
$396$	−4.79847e9	−3.88302
$397$	1.86008e9	1.49199	0.745993	−	0.665954i	$-0.231975\pi$
$397$	1.86008e9	1.49199	0.745993	+	0.665954i	$0.231975\pi$
$398$	8.79854e8	0.699552
$399$	−6.63194e8	−0.522680
$400$	6.67229e8	0.521273
$401$	−1.70783e9	−1.32263	−0.661315	−	0.750108i	$-0.730001\pi$
$401$	−1.70783e9	−1.32263	−0.661315	+	0.750108i	$0.730001\pi$
$402$	−1.51669e8	−0.116441
$403$	3.66432e8	0.278886
$404$	−1.24855e9	−0.942047
$405$	−1.52684e8	−0.114209
$406$	1.16437e9	0.863476
$407$	−2.52547e8	−0.185679
$408$	−9.25414e8	−0.674568
$409$	−7.13105e8	−0.515373	−0.257687	−	0.966229i	$-0.582960\pi$
$409$	−7.13105e8	−0.515373	−0.257687	+	0.966229i	$0.582960\pi$
$410$	−7.40047e7	−0.0530293
$411$	−4.78511e9	−3.39974
$412$	−1.48835e9	−1.04849
$413$	1.18426e6	0.000827224 0
$414$	8.74031e9	6.05377
$415$	7.73131e7	0.0530988
$416$	−5.46756e8	−0.372363
$417$	−5.91295e8	−0.399326
$418$	−1.81083e9	−1.21272
$419$	8.13873e8	0.540515	0.270257	−	0.962788i	$-0.412891\pi$
$419$	8.13873e8	0.540515	0.270257	+	0.962788i	$0.412891\pi$
$420$	−5.12208e7	−0.0337345
$421$	−2.10577e9	−1.37538	−0.687692	−	0.726003i	$-0.741376\pi$
$421$	−2.10577e9	−1.37538	−0.687692	+	0.726003i	$0.741376\pi$
$422$	3.68884e9	2.38944
$423$	−2.40250e8	−0.154338
$424$	1.48237e9	0.944447
$425$	1.03217e9	0.652213
$426$	2.60905e9	1.63512
$427$	5.65505e7	0.0351511
$428$	2.98165e9	1.83824
$429$	−9.42026e8	−0.576053
$430$	−1.17134e8	−0.0710463
$431$	8.75667e8	0.526828	0.263414	−	0.964683i	$-0.415152\pi$
$431$	8.75667e8	0.526828	0.263414	+	0.964683i	$0.415152\pi$
$432$	2.72258e9	1.62475
$433$	8.83882e8	0.523223	0.261611	−	0.965173i	$-0.415746\pi$
$433$	8.83882e8	0.523223	0.261611	+	0.965173i	$0.415746\pi$
$434$	−9.92889e8	−0.583024
$435$	1.68619e8	0.0982186
$436$	1.60311e8	0.0926321
$437$	1.89678e9	1.08726
$438$	−9.51886e9	−5.41284
$439$	−7.07932e8	−0.399361	−0.199681	−	0.979861i	$-0.563990\pi$
$439$	−7.07932e8	−0.399361	−0.199681	+	0.979861i	$0.563990\pi$
$440$	−3.65109e7	−0.0204333
$441$	6.77532e8	0.376179
$442$	−5.04375e8	−0.277828
$443$	3.03959e9	1.66112	0.830561	−	0.556928i	$-0.188020\pi$
$443$	3.03959e9	1.66112	0.830561	+	0.556928i	$0.188020\pi$
$444$	−8.10691e8	−0.439557
$445$	−5.08080e7	−0.0273320
$446$	−2.23050e9	−1.19050
$447$	−3.82947e8	−0.202797
$448$	1.10608e9	0.581185
$449$	9.63068e8	0.502106	0.251053	−	0.967973i	$-0.419223\pi$
$449$	9.63068e8	0.502106	0.251053	+	0.967973i	$0.419223\pi$
$450$	7.79927e9	4.03469
$451$	2.12079e9	1.08863
$452$	3.20814e9	1.63406
$453$	−3.07166e8	−0.155249
$454$	−1.20160e9	−0.602648
$455$	−7.28792e6	−0.00362713
$456$	−1.51750e9	−0.749467
$457$	2.02027e8	0.0990154	0.0495077	−	0.998774i	$-0.484235\pi$
$457$	2.02027e8	0.0990154	0.0495077	+	0.998774i	$0.484235\pi$
$458$	−5.45418e9	−2.65277
$459$	4.21169e9	2.03288
$460$	1.46495e8	0.0701730
$461$	−2.79434e9	−1.32839	−0.664196	−	0.747558i	$-0.731226\pi$
$461$	−2.79434e9	−1.32839	−0.664196	+	0.747558i	$0.731226\pi$
$462$	2.55252e9	1.20427
$463$	6.87061e8	0.321708	0.160854	−	0.986978i	$-0.448575\pi$
$463$	6.87061e8	0.321708	0.160854	+	0.986978i	$0.448575\pi$
$464$	−1.67248e9	−0.777225
$465$	−1.43786e8	−0.0663178
$466$	3.32866e9	1.52377
$467$	−3.84537e9	−1.74715	−0.873573	−	0.486693i	$-0.838203\pi$
$467$	−3.84537e9	−1.74715	−0.873573	+	0.486693i	$0.838203\pi$
$468$	−2.19166e9	−0.988352
$469$	3.36260e7	0.0150512
$470$	−7.00234e6	−0.00311101
$471$	8.87934e7	0.0391568
$472$	2.70980e6	0.00118615
$473$	3.35676e9	1.45850
$474$	−2.66034e8	−0.114740
$475$	1.69256e9	0.724630
$476$	7.85915e8	0.334004
$477$	−1.08772e10	−4.58883
$478$	−6.35268e9	−2.66048
$479$	−3.45060e9	−1.43457	−0.717283	−	0.696782i	$-0.754615\pi$
$479$	−3.45060e9	−1.43457	−0.717283	+	0.696782i	$0.754615\pi$
$480$	2.14543e8	0.0885464
$481$	−1.15349e8	−0.0472612
$482$	1.71250e9	0.696571
$483$	−2.67368e9	−1.07968
$484$	6.32355e8	0.253514
$485$	5.13963e7	0.0204567
$486$	1.23391e10	4.87593
$487$	−2.18947e8	−0.0858989	−0.0429495	−	0.999077i	$-0.513675\pi$
$487$	−2.18947e8	−0.0858989	−0.0429495	+	0.999077i	$0.513675\pi$
$488$	1.29397e8	0.0504029
$489$	−1.92748e9	−0.745434
$490$	1.97474e7	0.00758270
$491$	−5.32188e8	−0.202899	−0.101449	−	0.994841i	$-0.532348\pi$
$491$	−5.32188e8	−0.202899	−0.101449	+	0.994841i	$0.532348\pi$
$492$	6.80785e9	2.57711
$493$	−2.58723e9	−0.972459
$494$	−8.27079e8	−0.308676
$495$	2.67905e8	0.0992804
$496$	1.42616e9	0.524787
$497$	−5.78445e8	−0.211356
$498$	−1.23677e10	−4.48731
$499$	3.19449e9	1.15093	0.575466	−	0.817826i	$-0.304821\pi$
$499$	3.19449e9	1.15093	0.575466	+	0.817826i	$0.304821\pi$
$500$	2.61601e8	0.0935933
$501$	4.73420e9	1.68196
$502$	5.91576e9	2.08712
$503$	−3.24820e9	−1.13803	−0.569016	−	0.822326i	$-0.692676\pi$
$503$	−3.24820e9	−1.13803	−0.569016	+	0.822326i	$0.692676\pi$
$504$	1.55031e9	0.539401
$505$	6.97086e7	0.0240861
$506$	−7.30038e9	−2.50506
$507$	−4.30261e8	−0.146624
$508$	−2.51103e9	−0.849825
$509$	−1.11805e9	−0.375794	−0.187897	−	0.982189i	$-0.560167\pi$
$509$	−1.11805e9	−0.375794	−0.187897	+	0.982189i	$0.560167\pi$
$510$	1.97913e8	0.0660662
$511$	2.11040e9	0.699666
$512$	−2.98699e9	−0.983535
$513$	6.90636e9	2.25860
$514$	4.80345e9	1.56021
$515$	8.30968e7	0.0268077
$516$	1.07754e10	3.45269
$517$	2.00670e8	0.0638653
$518$	3.12550e8	0.0988018
$519$	−1.81242e9	−0.569080
$520$	−1.66760e7	−0.00520093
$521$	−2.63448e9	−0.816138	−0.408069	−	0.912951i	$-0.633798\pi$
$521$	−2.63448e9	−0.816138	−0.408069	+	0.912951i	$0.633798\pi$
$522$	−1.95496e10	−6.01578
$523$	−5.56509e9	−1.70105	−0.850523	−	0.525938i	$-0.823714\pi$
$523$	−5.56509e9	−1.70105	−0.850523	+	0.525938i	$0.823714\pi$
$524$	7.44445e9	2.26034
$525$	−2.38581e9	−0.719579
$526$	7.05385e9	2.11337
$527$	2.20620e9	0.656610
$528$	−3.66638e9	−1.08398
$529$	4.24207e9	1.24590
$530$	−3.17028e8	−0.0924978
$531$	−1.98836e7	−0.00576322
$532$	1.28875e9	0.371089
$533$	9.68651e8	0.277091
$534$	8.12769e9	2.30979
$535$	−1.66470e8	−0.0469999
$536$	7.69422e7	0.0215818
$537$	−1.87863e9	−0.523519
$538$	9.61506e9	2.66204
$539$	−5.65912e8	−0.155664
$540$	5.33403e8	0.145773
$541$	−1.68303e9	−0.456985	−0.228493	−	0.973546i	$-0.573380\pi$
$541$	−1.68303e9	−0.456985	−0.228493	+	0.973546i	$0.573380\pi$
$542$	1.08919e10	2.93836
$543$	6.69821e9	1.79539
$544$	−3.29188e9	−0.876694
$545$	−8.95041e6	−0.00236840
$546$	1.16584e9	0.306524
$547$	−6.60056e9	−1.72435	−0.862174	−	0.506612i	$-0.830898\pi$
$547$	−6.60056e9	−1.72435	−0.862174	+	0.506612i	$0.830898\pi$
$548$	9.29866e9	2.41373
$549$	−9.49476e8	−0.244896
$550$	−6.51438e9	−1.66957
$551$	−4.24257e9	−1.08043
$552$	−6.11783e9	−1.54814
$553$	5.89816e7	0.0148313
$554$	−1.00882e10	−2.52075
$555$	4.52620e7	0.0112385
$556$	1.14903e9	0.283511
$557$	4.97604e9	1.22009	0.610044	−	0.792368i	$-0.291152\pi$
$557$	4.97604e9	1.22009	0.610044	+	0.792368i	$0.291152\pi$
$558$	1.66705e10	4.06189
$559$	1.53317e9	0.371234
$560$	−2.83647e7	−0.00682528
$561$	−5.67170e9	−1.35626
$562$	−3.31486e9	−0.787750
$563$	9.88221e8	0.233386	0.116693	−	0.993168i	$-0.462771\pi$
$563$	9.88221e8	0.233386	0.116693	+	0.993168i	$0.462771\pi$
$564$	6.44161e8	0.151188
$565$	−1.79115e8	−0.0417795
$566$	3.37366e9	0.782067
$567$	−5.41512e9	−1.24758
$568$	−1.32358e9	−0.303062
$569$	−7.44589e9	−1.69443	−0.847215	−	0.531250i	$-0.821723\pi$
$569$	−7.44589e9	−1.69443	−0.847215	+	0.531250i	$0.821723\pi$
$570$	3.24540e8	0.0734018
$571$	5.47301e9	1.23027	0.615134	−	0.788422i	$-0.289102\pi$
$571$	5.47301e9	1.23027	0.615134	+	0.788422i	$0.289102\pi$
$572$	1.83059e9	0.408983
$573$	5.19357e9	1.15325
$574$	−2.62467e9	−0.579272
$575$	6.82358e9	1.49684
$576$	−1.85710e10	−4.04908
$577$	1.63003e9	0.353248	0.176624	−	0.984278i	$-0.443482\pi$
$577$	1.63003e9	0.353248	0.176624	+	0.984278i	$0.443482\pi$
$578$	4.08501e9	0.879924
$579$	1.58144e10	3.38593
$580$	−3.27668e8	−0.0697327
$581$	2.74200e9	0.580031
$582$	−8.22180e9	−1.72877
$583$	9.08522e9	1.89887
$584$	4.82895e9	1.00325
$585$	1.22363e8	0.0252700
$586$	−1.11306e10	−2.28496
$587$	−3.63952e9	−0.742695	−0.371347	−	0.928494i	$-0.621104\pi$
$587$	−3.63952e9	−0.742695	−0.371347	+	0.928494i	$0.621104\pi$
$588$	−1.81661e9	−0.368503
$589$	3.61775e9	0.729515
$590$	−579530.	−0.000116170 0
$591$	−9.58543e9	−1.91010
$592$	−4.48939e8	−0.0889328
$593$	1.76713e9	0.347998	0.173999	−	0.984746i	$-0.444331\pi$
$593$	1.76713e9	0.347998	0.173999	+	0.984746i	$0.444331\pi$
$594$	−2.65814e10	−5.20386
$595$	−4.38788e7	−0.00853975
$596$	7.44161e8	0.143981
$597$	4.51898e9	0.869221
$598$	−3.33438e9	−0.637619
$599$	3.07060e9	0.583753	0.291877	−	0.956456i	$-0.405720\pi$
$599$	3.07060e9	0.583753	0.291877	+	0.956456i	$0.405720\pi$
$600$	−5.45915e9	−1.03180
$601$	−7.99662e8	−0.150261	−0.0751304	−	0.997174i	$-0.523937\pi$
$601$	−7.99662e8	−0.150261	−0.0751304	+	0.997174i	$0.523937\pi$
$602$	−4.15428e9	−0.776083
$603$	−5.64577e8	−0.104861
$604$	5.96901e8	0.110223
$605$	−3.53053e7	−0.00648181
$606$	−1.11512e10	−2.03548
$607$	4.24468e9	0.770344	0.385172	−	0.922845i	$-0.374142\pi$
$607$	4.24468e9	0.770344	0.385172	+	0.922845i	$0.374142\pi$
$608$	−5.39806e9	−0.974036
$609$	5.98027e9	1.07290
$610$	−2.76735e7	−0.00493640
$611$	9.16540e7	0.0162558
$612$	−1.31954e10	−2.32698
$613$	7.49949e8	0.131498	0.0657492	−	0.997836i	$-0.479056\pi$
$613$	7.49949e8	0.131498	0.0657492	+	0.997836i	$0.479056\pi$
$614$	−1.04590e9	−0.182348
$615$	−3.80092e8	−0.0658910
$616$	−1.29490e9	−0.223206
$617$	2.47397e9	0.424029	0.212015	−	0.977266i	$-0.431998\pi$
$617$	2.47397e9	0.424029	0.212015	+	0.977266i	$0.431998\pi$
$618$	−1.32929e10	−2.26548
$619$	−5.14688e9	−0.872222	−0.436111	−	0.899893i	$-0.643645\pi$
$619$	−5.14688e9	−0.872222	−0.436111	+	0.899893i	$0.643645\pi$
$620$	2.79411e8	0.0470839
$621$	2.78431e10	4.66549
$622$	−1.55503e10	−2.59103
$623$	−1.80197e9	−0.298565
$624$	−1.67459e9	−0.275906
$625$	6.08160e9	0.996410
$626$	−5.52253e8	−0.0899762
$627$	−9.30052e9	−1.50685
$628$	−1.72548e8	−0.0278003
$629$	−6.94486e8	−0.111272
$630$	−3.31557e8	−0.0528282
$631$	−1.27962e9	−0.202758	−0.101379	−	0.994848i	$-0.532326\pi$
$631$	−1.27962e9	−0.202758	−0.101379	+	0.994848i	$0.532326\pi$
$632$	1.34960e8	0.0212665
$633$	1.89461e10	2.96897
$634$	8.68382e9	1.35331
$635$	1.40195e8	0.0217282
$636$	2.91641e10	4.49519
$637$	−2.58475e8	−0.0396214
$638$	1.63289e10	2.48935
$639$	9.71202e9	1.47250
$640$	−2.33199e8	−0.0351639
$641$	7.63788e9	1.14543	0.572716	−	0.819754i	$-0.305890\pi$
$641$	7.63788e9	1.14543	0.572716	+	0.819754i	$0.305890\pi$
$642$	2.66300e10	3.97190
$643$	9.01009e9	1.33657	0.668283	−	0.743907i	$-0.267029\pi$
$643$	9.01009e9	1.33657	0.668283	+	0.743907i	$0.267029\pi$
$644$	5.19562e9	0.766543
$645$	−6.01604e8	−0.0882779
$646$	−4.97964e9	−0.726748
$647$	1.53382e9	0.222644	0.111322	−	0.993784i	$-0.464492\pi$
$647$	1.53382e9	0.222644	0.111322	+	0.993784i	$0.464492\pi$
$648$	−1.23907e10	−1.78889
$649$	1.66079e7	0.00238483
$650$	−2.97538e9	−0.424958
$651$	−5.09953e9	−0.724431
$652$	3.74558e9	0.529239
$653$	−9.14623e9	−1.28542	−0.642711	−	0.766109i	$-0.722190\pi$
$653$	−9.14623e9	−1.28542	−0.642711	+	0.766109i	$0.722190\pi$
$654$	1.43179e9	0.200150
$655$	−4.15634e8	−0.0577919
$656$	3.77001e9	0.521410
$657$	−3.54333e10	−4.87453
$658$	−2.48346e8	−0.0339834
$659$	−3.20337e9	−0.436022	−0.218011	−	0.975946i	$-0.569957\pi$
$659$	−3.20337e9	−0.436022	−0.218011	+	0.975946i	$0.569957\pi$
$660$	−7.18311e8	−0.0972543
$661$	−2.32121e9	−0.312614	−0.156307	−	0.987708i	$-0.549959\pi$
$661$	−2.32121e9	−0.312614	−0.156307	+	0.987708i	$0.549959\pi$
$662$	−1.28992e10	−1.72806
$663$	−2.59050e9	−0.345212
$664$	6.27417e9	0.831703
$665$	−7.19528e7	−0.00948794
$666$	−5.24767e9	−0.688346
$667$	−1.71040e10	−2.23181
$668$	−9.19973e9	−1.19415
$669$	−1.14560e10	−1.47925
$670$	−1.64552e7	−0.00211369
$671$	7.93054e8	0.101338
$672$	7.60904e9	0.967247
$673$	1.45621e9	0.184149	0.0920747	−	0.995752i	$-0.470650\pi$
$673$	1.45621e9	0.184149	0.0920747	+	0.995752i	$0.470650\pi$
$674$	−6.63951e9	−0.835269
$675$	2.48453e10	3.10944
$676$	8.36105e8	0.104099
$677$	−6.26351e9	−0.775814	−0.387907	−	0.921698i	$-0.626802\pi$
$677$	−6.26351e9	−0.775814	−0.387907	+	0.921698i	$0.626802\pi$
$678$	2.86529e10	3.53073
$679$	1.82283e9	0.223461
$680$	−1.00402e8	−0.0122451
$681$	−6.17148e9	−0.748814
$682$	−1.39241e10	−1.68082
$683$	2.56035e9	0.307487	0.153744	−	0.988111i	$-0.450867\pi$
$683$	2.56035e9	0.307487	0.153744	+	0.988111i	$0.450867\pi$
$684$	−2.16380e10	−2.58535
$685$	−5.19158e8	−0.0617138
$686$	7.00366e8	0.0828306
$687$	−2.80130e10	−3.29618
$688$	5.96712e9	0.698562
$689$	4.14959e9	0.483323
$690$	1.30839e9	0.151623
$691$	7.27918e9	0.839284	0.419642	−	0.907690i	$-0.362156\pi$
$691$	7.27918e9	0.839284	0.419642	+	0.907690i	$0.362156\pi$
$692$	3.52198e9	0.404032
$693$	9.50159e9	1.08450
$694$	−2.20425e10	−2.50324
$695$	−6.41521e7	−0.00724877
$696$	1.36839e10	1.53843
$697$	5.83201e9	0.652384
$698$	−1.76605e10	−1.96566
$699$	1.70962e10	1.89334
$700$	4.63622e9	0.510883
$701$	9.40973e9	1.03173	0.515863	−	0.856671i	$-0.327471\pi$
$701$	9.40973e9	1.03173	0.515863	+	0.856671i	$0.327471\pi$
$702$	−1.21408e10	−1.32455
$703$	−1.13882e9	−0.123627
$704$	1.55115e10	1.67552
$705$	−3.59644e7	−0.00386555
$706$	−1.76808e10	−1.89097
$707$	2.47230e9	0.263107
$708$	5.33123e7	0.00564561
$709$	−1.39670e10	−1.47178	−0.735889	−	0.677103i	$-0.763235\pi$
$709$	−1.39670e10	−1.47178	−0.735889	+	0.677103i	$0.763235\pi$
$710$	2.83067e8	0.0296815
$711$	−9.90295e8	−0.103329
$712$	−4.12321e9	−0.428110
$713$	1.45850e10	1.50693
$714$	7.01924e9	0.721682
$715$	−1.02204e8	−0.0104568
$716$	3.65065e9	0.371685
$717$	−3.26277e10	−3.30575
$718$	1.11942e10	1.12864
$719$	−1.78331e10	−1.78927	−0.894633	−	0.446801i	$-0.852563\pi$
$719$	−1.78331e10	−1.78927	−0.894633	+	0.446801i	$0.852563\pi$
$720$	4.76241e8	0.0475513
$721$	2.94713e9	0.292837
$722$	7.34813e9	0.726602
$723$	8.79549e9	0.865517
$724$	−1.30163e10	−1.27468
$725$	−1.52625e10	−1.48745
$726$	5.64775e9	0.547769
$727$	−6.66437e9	−0.643264	−0.321632	−	0.946865i	$-0.604231\pi$
$727$	−6.66437e9	−0.643264	−0.321632	+	0.946865i	$0.604231\pi$
$728$	−5.91435e8	−0.0568129
$729$	2.88471e10	2.75776
$730$	−1.03274e9	−0.0982567
$731$	9.23082e9	0.874036
$732$	2.54575e9	0.239898
$733$	−8.90855e9	−0.835493	−0.417747	−	0.908564i	$-0.637180\pi$
$733$	−8.90855e9	−0.835493	−0.417747	+	0.908564i	$0.637180\pi$
$734$	2.10913e10	1.96865
$735$	1.01424e8	0.00942181
$736$	−2.17624e10	−2.01203
$737$	4.71566e8	0.0433916
$738$	4.40678e10	4.03575
$739$	−6.30362e9	−0.574559	−0.287280	−	0.957847i	$-0.592751\pi$
$739$	−6.30362e9	−0.574559	−0.287280	+	0.957847i	$0.592751\pi$
$740$	−8.79554e7	−0.00797905
$741$	−4.24792e9	−0.383542
$742$	−1.12438e10	−1.01041
$743$	1.71064e10	1.53002	0.765011	−	0.644017i	$-0.222733\pi$
$743$	1.71064e10	1.53002	0.765011	+	0.644017i	$0.222733\pi$
$744$	−1.16686e10	−1.03876
$745$	−4.15476e7	−0.00368128
$746$	−8.26397e9	−0.728790
$747$	−4.60379e10	−4.04104
$748$	1.10215e10	0.962911
$749$	−5.90405e9	−0.513409
$750$	2.33644e9	0.202227
$751$	−1.59756e9	−0.137632	−0.0688158	−	0.997629i	$-0.521922\pi$
$751$	−1.59756e9	−0.137632	−0.0688158	+	0.997629i	$0.521922\pi$
$752$	3.56719e8	0.0305889
$753$	3.03837e10	2.59333
$754$	7.45808e9	0.633618
$755$	−3.33258e7	−0.00281817
$756$	1.89178e10	1.59237
$757$	−9.52163e9	−0.797767	−0.398883	−	0.917002i	$-0.630602\pi$
$757$	−9.52163e9	−0.797767	−0.398883	+	0.917002i	$0.630602\pi$
$758$	−3.56342e10	−2.97183
$759$	−3.74952e10	−3.11264
$760$	−1.64640e8	−0.0136047
$761$	2.92422e9	0.240527	0.120263	−	0.992742i	$-0.461626\pi$
$761$	2.92422e9	0.240527	0.120263	+	0.992742i	$0.461626\pi$
$762$	−2.24268e10	−1.83622
$763$	−3.17437e8	−0.0258715
$764$	−1.00924e10	−0.818780
$765$	7.36719e8	0.0594959
$766$	1.12437e10	0.903873
$767$	7.58550e6	0.000607017 0
$768$	5.10738e8	0.0406850
$769$	1.31606e10	1.04360	0.521799	−	0.853069i	$-0.325261\pi$
$769$	1.31606e10	1.04360	0.521799	+	0.853069i	$0.325261\pi$
$770$	2.76934e8	0.0218604
$771$	2.46708e10	1.93862
$772$	−3.07313e10	−2.40393
$773$	2.71953e9	0.211770	0.105885	−	0.994378i	$-0.466232\pi$
$773$	2.71953e9	0.211770	0.105885	+	0.994378i	$0.466232\pi$
$774$	6.97499e10	5.40692
$775$	1.30147e10	1.00433
$776$	4.17095e9	0.320420
$777$	1.60527e9	0.122765
$778$	3.07574e9	0.234164
$779$	9.56338e9	0.724820
$780$	−3.28082e8	−0.0247543
$781$	−8.11201e9	−0.609326
$782$	−2.00755e10	−1.50121
$783$	−6.22773e10	−4.63621
$784$	−1.00599e9	−0.0745568
$785$	9.63358e6	0.000710794 0
$786$	6.64886e10	4.88392
$787$	5.29011e9	0.386859	0.193430	−	0.981114i	$-0.438039\pi$
$787$	5.29011e9	0.386859	0.193430	+	0.981114i	$0.438039\pi$
$788$	1.86269e10	1.35612
$789$	3.62290e10	2.62595
$790$	−2.88632e7	−0.00208281
$791$	−6.35254e9	−0.456383
$792$	2.17413e10	1.55506
$793$	3.62220e8	0.0257939
$794$	−3.22830e10	−2.28877
$795$	−1.62827e9	−0.114932
$796$	−8.78150e9	−0.617125
$797$	−7.86647e9	−0.550396	−0.275198	−	0.961388i	$-0.588743\pi$
$797$	−7.86647e9	−0.550396	−0.275198	+	0.961388i	$0.588743\pi$
$798$	1.15102e10	0.801813
$799$	5.51826e8	0.0382726
$800$	−1.94193e10	−1.34097
$801$	3.02548e10	2.08008
$802$	2.96406e10	2.02897
$803$	2.95958e10	2.01709
$804$	1.51375e9	0.102721
$805$	−2.90079e8	−0.0195988
$806$	−6.35970e9	−0.427823
$807$	4.93835e10	3.30769
$808$	5.65705e9	0.377268
$809$	−1.81417e10	−1.20464	−0.602322	−	0.798253i	$-0.705758\pi$
$809$	−1.81417e10	−1.20464	−0.602322	+	0.798253i	$0.705758\pi$
$810$	2.64994e9	0.175202
$811$	−9.20902e9	−0.606234	−0.303117	−	0.952953i	$-0.598027\pi$
$811$	−9.20902e9	−0.606234	−0.303117	+	0.952953i	$0.598027\pi$
$812$	−1.16212e10	−0.761734
$813$	5.59413e10	3.65103
$814$	4.38314e9	0.284839
$815$	−2.09121e8	−0.0135315
$816$	−1.00823e10	−0.649595
$817$	1.51368e10	0.971083
$818$	1.23765e10	0.790605
$819$	4.33976e9	0.276040
$820$	7.38613e8	0.0467809
$821$	−7.97270e9	−0.502811	−0.251405	−	0.967882i	$-0.580893\pi$
$821$	−7.97270e9	−0.502811	−0.251405	+	0.967882i	$0.580893\pi$
$822$	8.30491e10	5.21535
$823$	−8.16620e9	−0.510646	−0.255323	−	0.966856i	$-0.582182\pi$
$823$	−8.16620e9	−0.510646	−0.255323	+	0.966856i	$0.582182\pi$
$824$	6.74354e9	0.419897
$825$	−3.34582e10	−2.07450
$826$	−2.05537e7	−0.00126900
$827$	1.34044e10	0.824096	0.412048	−	0.911162i	$-0.364814\pi$
$827$	1.34044e10	0.824096	0.412048	+	0.911162i	$0.364814\pi$
$828$	−8.72338e10	−5.34046
$829$	−4.47188e9	−0.272615	−0.136307	−	0.990667i	$-0.543523\pi$
$829$	−4.47188e9	−0.272615	−0.136307	+	0.990667i	$0.543523\pi$
$830$	−1.34182e9	−0.0814559
$831$	−5.18136e10	−3.13213
$832$	7.08473e9	0.426473
$833$	−1.55621e9	−0.0932849
$834$	1.02623e10	0.612584
$835$	5.13634e8	0.0305317
$836$	1.80732e10	1.06983
$837$	5.31054e10	3.13040
$838$	−1.41254e10	−0.829173
$839$	−1.60884e10	−0.940474	−0.470237	−	0.882540i	$-0.655832\pi$
$839$	−1.60884e10	−0.940474	−0.470237	+	0.882540i	$0.655832\pi$
$840$	2.32075e8	0.0135099
$841$	2.10070e10	1.21780
$842$	3.65472e10	2.10990
$843$	−1.70253e10	−0.978811
$844$	−3.68169e10	−2.10789
$845$	−4.66809e7	−0.00266159
$846$	4.16971e9	0.236761
$847$	−1.25214e9	−0.0708048
$848$	1.61503e10	0.909483
$849$	1.73273e10	0.971750
$850$	−1.79140e10	−1.00052
$851$	−4.59119e9	−0.255371
$852$	−2.60400e10	−1.44245
$853$	2.16103e10	1.19217	0.596086	−	0.802920i	$-0.296722\pi$
$853$	2.16103e10	1.19217	0.596086	+	0.802920i	$0.296722\pi$
$854$	−9.81475e8	−0.0539233
$855$	1.20808e9	0.0661019
$856$	−1.35095e10	−0.736174
$857$	9.29534e9	0.504466	0.252233	−	0.967666i	$-0.418835\pi$
$857$	9.29534e9	0.504466	0.252233	+	0.967666i	$0.418835\pi$
$858$	1.63495e10	0.883690
$859$	2.32940e10	1.25392	0.626959	−	0.779053i	$-0.284300\pi$
$859$	2.32940e10	1.25392	0.626959	+	0.779053i	$0.284300\pi$
$860$	1.16907e9	0.0626750
$861$	−1.34804e10	−0.719768
$862$	−1.51978e10	−0.808176
$863$	−2.18333e10	−1.15633	−0.578164	−	0.815921i	$-0.696231\pi$
$863$	−2.18333e10	−1.15633	−0.578164	+	0.815921i	$0.696231\pi$
$864$	−7.92389e10	−4.17965
$865$	−1.96637e8	−0.0103302
$866$	−1.53404e10	−0.802646
$867$	2.09808e10	1.09334
$868$	9.90965e9	0.514327
$869$	8.27148e8	0.0427577
$870$	−2.92650e9	−0.150672
$871$	2.15383e8	0.0110446
$872$	−7.26351e8	−0.0370970
$873$	−3.06051e10	−1.55684
$874$	−3.29200e10	−1.66790
$875$	−5.18004e8	−0.0261400
$876$	9.50042e10	4.77506
$877$	−1.93936e9	−0.0970866	−0.0485433	−	0.998821i	$-0.515458\pi$
$877$	−1.93936e9	−0.0970866	−0.0485433	+	0.998821i	$0.515458\pi$
$878$	1.22867e10	0.612637
$879$	−5.71675e10	−2.83915
$880$	−3.97782e8	−0.0196769
$881$	−2.05356e10	−1.01180	−0.505898	−	0.862594i	$-0.668839\pi$
$881$	−2.05356e10	−1.01180	−0.505898	+	0.862594i	$0.668839\pi$
$882$	−1.17591e10	−0.577075
$883$	−2.03996e10	−0.997149	−0.498574	−	0.866847i	$-0.666143\pi$
$883$	−2.03996e10	−0.997149	−0.498574	+	0.866847i	$0.666143\pi$
$884$	5.03398e9	0.245092
$885$	−2.97650e6	−0.000144346 0
$886$	−5.27542e10	−2.54823
$887$	1.54254e9	0.0742172	0.0371086	−	0.999311i	$-0.488185\pi$
$887$	1.54254e9	0.0742172	0.0371086	+	0.999311i	$0.488185\pi$
$888$	3.67314e9	0.176032
$889$	4.97217e9	0.237350
$890$	8.81809e8	0.0419285
$891$	−7.59406e10	−3.59668
$892$	2.22618e10	1.05023
$893$	9.04889e8	0.0425222
$894$	6.64632e9	0.311100
$895$	−2.03821e8	−0.00950317
$896$	−8.27069e9	−0.384117
$897$	−1.71256e10	−0.792267
$898$	−1.67147e10	−0.770252
$899$	−3.26226e10	−1.49747
$900$	−7.78417e10	−3.55929
$901$	2.49836e10	1.13794
$902$	−3.68078e10	−1.67000
$903$	−2.13366e10	−0.964314
$904$	−1.45357e10	−0.654405
$905$	7.26718e8	0.0325909
$906$	5.33110e9	0.238159
$907$	1.08181e10	0.481422	0.240711	−	0.970597i	$-0.422619\pi$
$907$	1.08181e10	0.481422	0.240711	+	0.970597i	$0.422619\pi$
$908$	1.19927e10	0.531639
$909$	−4.15096e10	−1.83305
$910$	1.26487e8	0.00556418
$911$	−5.51610e9	−0.241723	−0.120861	−	0.992669i	$-0.538566\pi$
$911$	−5.51610e9	−0.241723	−0.120861	+	0.992669i	$0.538566\pi$
$912$	−1.65330e10	−0.721722
$913$	3.84533e10	1.67219
$914$	−3.50632e9	−0.151894
$915$	−1.42133e8	−0.00613367
$916$	5.44361e10	2.34020
$917$	−1.47410e10	−0.631297
$918$	−7.30968e10	−3.11852
$919$	−3.38328e10	−1.43792	−0.718959	−	0.695053i	$-0.755381\pi$
$919$	−3.38328e10	−1.43792	−0.718959	+	0.695053i	$0.755381\pi$
$920$	−6.63750e8	−0.0281027
$921$	−5.37181e9	−0.226575
$922$	4.84978e10	2.03781
$923$	−3.70508e9	−0.155093
$924$	−2.54758e10	−1.06237
$925$	−4.09687e9	−0.170199
$926$	−1.19244e10	−0.493514
$927$	−4.94820e10	−2.04018
$928$	4.86763e10	1.99940
$929$	2.86913e10	1.17407	0.587037	−	0.809560i	$-0.300294\pi$
$929$	2.86913e10	1.17407	0.587037	+	0.809560i	$0.300294\pi$
$930$	2.49550e9	0.101734
$931$	−2.55189e9	−0.103643
$932$	−3.32221e10	−1.34422
$933$	−7.98673e10	−3.21946
$934$	6.67392e10	2.68020
$935$	−6.15348e8	−0.0246195
$936$	9.93012e9	0.395812
$937$	2.33671e10	0.927930	0.463965	−	0.885853i	$-0.346426\pi$
$937$	2.33671e10	0.927930	0.463965	+	0.885853i	$0.346426\pi$
$938$	−5.83604e8	−0.0230892
$939$	−2.83640e9	−0.111799
$940$	6.98878e7	0.00274444
$941$	−2.50407e9	−0.0979677	−0.0489839	−	0.998800i	$-0.515598\pi$
$941$	−2.50407e9	−0.0979677	−0.0489839	+	0.998800i	$0.515598\pi$
$942$	−1.54107e9	−0.0600683
$943$	3.85549e10	1.49723
$944$	2.95229e7	0.00114224
$945$	−1.05621e9	−0.0407134
$946$	−5.82589e10	−2.23740
$947$	2.09057e10	0.799906	0.399953	−	0.916536i	$-0.369026\pi$
$947$	2.09057e10	0.799906	0.399953	+	0.916536i	$0.369026\pi$
$948$	2.65519e9	0.101220
$949$	1.35176e10	0.513415
$950$	−2.93756e10	−1.11161
$951$	4.46006e10	1.68155
$952$	−3.56088e9	−0.133761
$953$	−2.16794e10	−0.811378	−0.405689	−	0.914011i	$-0.632968\pi$
$953$	−2.16794e10	−0.811378	−0.405689	+	0.914011i	$0.632968\pi$
$954$	1.88781e11	7.03947
$955$	5.63472e8	0.0209344
$956$	6.34038e10	2.34700
$957$	8.38663e10	3.09311
$958$	5.98877e10	2.20069
$959$	−1.84126e10	−0.674138
$960$	−2.78000e9	−0.101413
$961$	3.05498e8	0.0111039
$962$	2.00196e9	0.0725007
$963$	9.91282e10	3.57689
$964$	−1.70918e10	−0.614495
$965$	1.71577e9	0.0614631
$966$	4.64036e10	1.65627
$967$	−2.51463e10	−0.894296	−0.447148	−	0.894460i	$-0.647560\pi$
$967$	−2.51463e10	−0.894296	−0.447148	+	0.894460i	$0.647560\pi$
$968$	−2.86512e9	−0.101527
$969$	−2.55757e10	−0.903013
$970$	−8.92019e8	−0.0313815
$971$	−2.13281e10	−0.747626	−0.373813	−	0.927504i	$-0.621950\pi$
$971$	−2.13281e10	−0.747626	−0.373813	+	0.927504i	$0.621950\pi$
$972$	−1.23152e11	−4.30140
$973$	−2.27523e9	−0.0791828
$974$	3.79998e9	0.131773
$975$	−1.52817e10	−0.528027
$976$	1.40977e9	0.0485370
$977$	−6.90646e9	−0.236933	−0.118466	−	0.992958i	$-0.537798\pi$
$977$	−6.90646e9	−0.236933	−0.118466	+	0.992958i	$0.537798\pi$
$978$	3.34528e10	1.14353
$979$	−2.52704e10	−0.860743
$980$	−1.97092e8	−0.00668924
$981$	5.32973e9	0.180245
$982$	9.23650e9	0.311256
$983$	1.84577e10	0.619783	0.309892	−	0.950772i	$-0.399707\pi$
$983$	1.84577e10	0.619783	0.309892	+	0.950772i	$0.399707\pi$
$984$	−3.08455e10	−1.03207
$985$	−1.03997e9	−0.0346730
$986$	4.49033e10	1.49179
$987$	−1.27552e9	−0.0422258
$988$	8.25477e9	0.272305
$989$	6.10241e10	2.00593
$990$	−4.64969e9	−0.152300
$991$	2.34045e10	0.763910	0.381955	−	0.924181i	$-0.375251\pi$
$991$	2.34045e10	0.763910	0.381955	+	0.924181i	$0.375251\pi$
$992$	−4.15076e10	−1.35001
$993$	−6.62510e10	−2.14719
$994$	1.00393e10	0.324229
$995$	4.90284e8	0.0157785
$996$	1.23437e11	3.95858
$997$	4.84837e10	1.54940	0.774698	−	0.632332i	$-0.217902\pi$
$997$	4.84837e10	1.54940	0.774698	+	0.632332i	$0.217902\pi$
$998$	−5.54426e10	−1.76558
$999$	−1.67170e10	−0.530491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.d.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.d.1.2	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-17.3557 q^{2} -89.1399 q^{3} +173.221 q^{4} -9.67118 q^{5} +1547.09 q^{6} -343.000 q^{7} -784.843 q^{8} +5758.93 q^{9} +O(q^{10})\)	\(q-17.3557 q^{2} -89.1399 q^{3} +173.221 q^{4} -9.67118 q^{5} +1547.09 q^{6} -343.000 q^{7} -784.843 q^{8} +5758.93 q^{9} +167.850 q^{10} -4810.17 q^{11} -15440.9 q^{12} -2197.00 q^{13} +5953.01 q^{14} +862.088 q^{15} -8550.77 q^{16} -13227.6 q^{17} -99950.4 q^{18} -21690.7 q^{19} -1675.25 q^{20} +30575.0 q^{21} +83484.0 q^{22} -87446.5 q^{23} +69960.9 q^{24} -78031.5 q^{25} +38130.5 q^{26} -318402. q^{27} -59414.8 q^{28} +195594. q^{29} -14962.2 q^{30} -166788. q^{31} +248865. q^{32} +428778. q^{33} +229574. q^{34} +3317.21 q^{35} +997567. q^{36} +52502.8 q^{37} +376458. q^{38} +195840. q^{39} +7590.36 q^{40} -440897. q^{41} -530651. q^{42} -697845. q^{43} -833223. q^{44} -55695.6 q^{45} +1.51770e6 q^{46} -41717.8 q^{47} +762215. q^{48} +117649. q^{49} +1.35429e6 q^{50} +1.17911e6 q^{51} -380567. q^{52} -1.88875e6 q^{53} +5.52609e6 q^{54} +46520.0 q^{55} +269201. q^{56} +1.93351e6 q^{57} -3.39467e6 q^{58} -3452.66 q^{59} +149332. q^{60} -164870. q^{61} +2.89472e6 q^{62} -1.97531e6 q^{63} -3.22473e6 q^{64} +21247.6 q^{65} -7.44176e6 q^{66} -98035.1 q^{67} -2.29130e6 q^{68} +7.79498e6 q^{69} -57572.6 q^{70} +1.68643e6 q^{71} -4.51986e6 q^{72} -6.15276e6 q^{73} -911224. q^{74} +6.95572e6 q^{75} -3.75729e6 q^{76} +1.64989e6 q^{77} -3.39895e6 q^{78} -171958. q^{79} +82696.0 q^{80} +1.57875e7 q^{81} +7.65209e6 q^{82} -7.99418e6 q^{83} +5.29623e6 q^{84} +127926. q^{85} +1.21116e7 q^{86} -1.74352e7 q^{87} +3.77523e6 q^{88} +5.25354e6 q^{89} +966638. q^{90} +753571. q^{91} -1.51476e7 q^{92} +1.48674e7 q^{93} +724042. q^{94} +209775. q^{95} -2.21838e7 q^{96} -5.31437e6 q^{97} -2.04188e6 q^{98} -2.77014e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9} + 2548 q^{10} + 451 q^{11} - 16241 q^{12} - 21970 q^{13} + 1029 q^{14} + 27184 q^{15} + 11897 q^{16} - 8654 q^{17} + 159348 q^{18} + 10130 q^{19} - 82012 q^{20} + 34643 q^{21} - 57863 q^{22} - 52155 q^{23} - 49227 q^{24} + 47190 q^{25} + 6591 q^{26} - 155171 q^{27} - 123823 q^{28} + 520154 q^{29} + 1070236 q^{30} + 692605 q^{31} + 149835 q^{32} + 436053 q^{33} + 1059060 q^{34} - 77518 q^{35} + 2843742 q^{36} - 20511 q^{37} + 1905286 q^{38} + 221897 q^{39} + 636320 q^{40} + 355049 q^{41} - 379015 q^{42} + 1256772 q^{43} - 687913 q^{44} + 1259926 q^{45} + 4043075 q^{46} + 1260721 q^{47} + 1128551 q^{48} + 1176490 q^{49} + 609035 q^{50} + 1411976 q^{51} - 793117 q^{52} + 928854 q^{53} + 6642607 q^{54} + 3423196 q^{55} - 99813 q^{56} + 3014966 q^{57} + 1612588 q^{58} + 3144446 q^{59} + 7738848 q^{60} + 6322923 q^{61} + 6545331 q^{62} - 4200721 q^{63} - 6629943 q^{64} - 496522 q^{65} - 14343317 q^{66} + 3944507 q^{67} - 1787356 q^{68} - 148281 q^{69} - 873964 q^{70} + 6032248 q^{71} + 9760866 q^{72} + 1248533 q^{73} - 8263279 q^{74} + 1573413 q^{75} + 1788254 q^{76} - 154693 q^{77} - 2427685 q^{78} - 14947605 q^{79} - 9147616 q^{80} + 25716334 q^{81} - 6987095 q^{82} - 14177784 q^{83} + 5570663 q^{84} - 11788444 q^{85} + 8748840 q^{86} - 29484448 q^{87} - 15390723 q^{88} + 6734836 q^{89} + 5994972 q^{90} + 7535710 q^{91} - 24493215 q^{92} + 17307847 q^{93} - 22760149 q^{94} - 9329708 q^{95} - 36488483 q^{96} - 12365397 q^{97} - 352947 q^{98} - 43198042 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9 + 2548 * q^10 + 451 * q^11 - 16241 * q^12 - 21970 * q^13 + 1029 * q^14 + 27184 * q^15 + 11897 * q^16 - 8654 * q^17 + 159348 * q^18 + 10130 * q^19 - 82012 * q^20 + 34643 * q^21 - 57863 * q^22 - 52155 * q^23 - 49227 * q^24 + 47190 * q^25 + 6591 * q^26 - 155171 * q^27 - 123823 * q^28 + 520154 * q^29 + 1070236 * q^30 + 692605 * q^31 + 149835 * q^32 + 436053 * q^33 + 1059060 * q^34 - 77518 * q^35 + 2843742 * q^36 - 20511 * q^37 + 1905286 * q^38 + 221897 * q^39 + 636320 * q^40 + 355049 * q^41 - 379015 * q^42 + 1256772 * q^43 - 687913 * q^44 + 1259926 * q^45 + 4043075 * q^46 + 1260721 * q^47 + 1128551 * q^48 + 1176490 * q^49 + 609035 * q^50 + 1411976 * q^51 - 793117 * q^52 + 928854 * q^53 + 6642607 * q^54 + 3423196 * q^55 - 99813 * q^56 + 3014966 * q^57 + 1612588 * q^58 + 3144446 * q^59 + 7738848 * q^60 + 6322923 * q^61 + 6545331 * q^62 - 4200721 * q^63 - 6629943 * q^64 - 496522 * q^65 - 14343317 * q^66 + 3944507 * q^67 - 1787356 * q^68 - 148281 * q^69 - 873964 * q^70 + 6032248 * q^71 + 9760866 * q^72 + 1248533 * q^73 - 8263279 * q^74 + 1573413 * q^75 + 1788254 * q^76 - 154693 * q^77 - 2427685 * q^78 - 14947605 * q^79 - 9147616 * q^80 + 25716334 * q^81 - 6987095 * q^82 - 14177784 * q^83 + 5570663 * q^84 - 11788444 * q^85 + 8748840 * q^86 - 29484448 * q^87 - 15390723 * q^88 + 6734836 * q^89 + 5994972 * q^90 + 7535710 * q^91 - 24493215 * q^92 + 17307847 * q^93 - 22760149 * q^94 - 9329708 * q^95 - 36488483 * q^96 - 12365397 * q^97 - 352947 * q^98 - 43198042 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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