LMFDB - Embedded newform 1045.6.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.58272 q^{2} +22.1703 q^{3} +25.4976 q^{4} -25.0000 q^{5} -168.111 q^{6} +53.6476 q^{7} +49.3055 q^{8} +248.522 q^{9} +O(q^{10})$	\(q-7.58272 q^{2} +22.1703 q^{3} +25.4976 q^{4} -25.0000 q^{5} -168.111 q^{6} +53.6476 q^{7} +49.3055 q^{8} +248.522 q^{9} +189.568 q^{10} +121.000 q^{11} +565.290 q^{12} +540.898 q^{13} -406.795 q^{14} -554.257 q^{15} -1189.79 q^{16} +1194.99 q^{17} -1884.47 q^{18} +361.000 q^{19} -637.441 q^{20} +1189.38 q^{21} -917.509 q^{22} -2766.35 q^{23} +1093.12 q^{24} +625.000 q^{25} -4101.48 q^{26} +122.424 q^{27} +1367.89 q^{28} +809.228 q^{29} +4202.78 q^{30} -9152.69 q^{31} +7444.10 q^{32} +2682.61 q^{33} -9061.25 q^{34} -1341.19 q^{35} +6336.73 q^{36} -14606.5 q^{37} -2737.36 q^{38} +11991.9 q^{39} -1232.64 q^{40} -13954.0 q^{41} -9018.76 q^{42} +8454.75 q^{43} +3085.22 q^{44} -6213.05 q^{45} +20976.4 q^{46} -17326.1 q^{47} -26378.1 q^{48} -13928.9 q^{49} -4739.20 q^{50} +26493.2 q^{51} +13791.6 q^{52} -6118.14 q^{53} -928.309 q^{54} -3025.00 q^{55} +2645.12 q^{56} +8003.48 q^{57} -6136.15 q^{58} +18129.0 q^{59} -14132.3 q^{60} +12250.1 q^{61} +69402.3 q^{62} +13332.6 q^{63} -18373.1 q^{64} -13522.5 q^{65} -20341.4 q^{66} +43721.6 q^{67} +30469.4 q^{68} -61330.8 q^{69} +10169.9 q^{70} +53567.1 q^{71} +12253.5 q^{72} -14952.0 q^{73} +110757. q^{74} +13856.4 q^{75} +9204.65 q^{76} +6491.36 q^{77} -90931.0 q^{78} -45838.4 q^{79} +29744.9 q^{80} -57676.7 q^{81} +105809. q^{82} -68951.2 q^{83} +30326.5 q^{84} -29874.7 q^{85} -64110.0 q^{86} +17940.8 q^{87} +5965.97 q^{88} +87062.5 q^{89} +47111.8 q^{90} +29017.9 q^{91} -70535.4 q^{92} -202918. q^{93} +131379. q^{94} -9025.00 q^{95} +165038. q^{96} -84468.2 q^{97} +105619. q^{98} +30071.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) $ 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * 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 $

$2$	−7.58272	−1.34045	−0.670224	−	0.742159i	$-0.733802\pi$
$2$	−7.58272	−1.34045	−0.670224	+	0.742159i	$0.733802\pi$
$3$	22.1703	1.42223	0.711113	−	0.703078i	$-0.248192\pi$
$3$	22.1703	1.42223	0.711113	+	0.703078i	$0.248192\pi$
$4$	25.4976	0.796802
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−168.111	−1.90642
$7$	53.6476	0.413814	0.206907	−	0.978361i	$-0.433660\pi$
$7$	53.6476	0.413814	0.206907	+	0.978361i	$0.433660\pi$
$8$	49.3055	0.272377
$9$	248.522	1.02272
$10$	189.568	0.599467
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	565.290	1.13323
$13$	540.898	0.887682	0.443841	−	0.896106i	$-0.353616\pi$
$13$	540.898	0.887682	0.443841	+	0.896106i	$0.353616\pi$
$14$	−406.795	−0.554697
$15$	−554.257	−0.636038
$16$	−1189.79	−1.16191
$17$	1194.99	1.00286	0.501431	−	0.865198i	$-0.332807\pi$
$17$	1194.99	1.00286	0.501431	+	0.865198i	$0.332807\pi$
$18$	−1884.47	−1.37091
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−637.441	−0.356340
$21$	1189.38	0.588537
$22$	−917.509	−0.404160
$23$	−2766.35	−1.09040	−0.545202	−	0.838305i	$-0.683547\pi$
$23$	−2766.35	−1.09040	−0.545202	+	0.838305i	$0.683547\pi$
$24$	1093.12	0.387381
$25$	625.000	0.200000
$26$	−4101.48	−1.18989
$27$	122.424	0.0323190
$28$	1367.89	0.329728
$29$	809.228	0.178680	0.0893400	−	0.996001i	$-0.471524\pi$
$29$	809.228	0.178680	0.0893400	+	0.996001i	$0.471524\pi$
$30$	4202.78	0.852577
$31$	−9152.69	−1.71058	−0.855292	−	0.518146i	$-0.826622\pi$
$31$	−9152.69	−1.71058	−0.855292	+	0.518146i	$0.826622\pi$
$32$	7444.10	1.28510
$33$	2682.61	0.428817
$34$	−9061.25	−1.34428
$35$	−1341.19	−0.185063
$36$	6336.73	0.814908
$37$	−14606.5	−1.75404	−0.877022	−	0.480450i	$-0.840473\pi$
$37$	−14606.5	−1.75404	−0.877022	+	0.480450i	$0.840473\pi$
$38$	−2737.36	−0.307520
$39$	11991.9	1.26248
$40$	−1232.64	−0.121811
$41$	−13954.0	−1.29640	−0.648198	−	0.761472i	$-0.724477\pi$
$41$	−13954.0	−1.29640	−0.648198	+	0.761472i	$0.724477\pi$
$42$	−9018.76	−0.788903
$43$	8454.75	0.697316	0.348658	−	0.937250i	$-0.386637\pi$
$43$	8454.75	0.697316	0.348658	+	0.937250i	$0.386637\pi$
$44$	3085.22	0.240245
$45$	−6213.05	−0.457376
$46$	20976.4	1.46163
$47$	−17326.1	−1.14408	−0.572041	−	0.820225i	$-0.693848\pi$
$47$	−17326.1	−1.14408	−0.572041	+	0.820225i	$0.693848\pi$
$48$	−26378.1	−1.65250
$49$	−13928.9	−0.828758
$50$	−4739.20	−0.268090
$51$	26493.2	1.42629
$52$	13791.6	0.707306
$53$	−6118.14	−0.299178	−0.149589	−	0.988748i	$-0.547795\pi$
$53$	−6118.14	−0.299178	−0.149589	+	0.988748i	$0.547795\pi$
$54$	−928.309	−0.0433220
$55$	−3025.00	−0.134840
$56$	2645.12	0.112713
$57$	8003.48	0.326281
$58$	−6136.15	−0.239511
$59$	18129.0	0.678021	0.339011	−	0.940783i	$-0.389908\pi$
$59$	18129.0	0.678021	0.339011	+	0.940783i	$0.389908\pi$
$60$	−14132.3	−0.506796
$61$	12250.1	0.421517	0.210759	−	0.977538i	$-0.432407\pi$
$61$	12250.1	0.421517	0.210759	+	0.977538i	$0.432407\pi$
$62$	69402.3	2.29295
$63$	13332.6	0.423218
$64$	−18373.1	−0.560703
$65$	−13522.5	−0.396983
$66$	−20341.4	−0.574807
$67$	43721.6	1.18990	0.594948	−	0.803764i	$-0.297173\pi$
$67$	43721.6	1.18990	0.594948	+	0.803764i	$0.297173\pi$
$68$	30469.4	0.799082
$69$	−61330.8	−1.55080
$70$	10169.9	0.248068
$71$	53567.1	1.26111	0.630554	−	0.776145i	$-0.282828\pi$
$71$	53567.1	1.26111	0.630554	+	0.776145i	$0.282828\pi$
$72$	12253.5	0.278567
$73$	−14952.0	−0.328392	−0.164196	−	0.986428i	$-0.552503\pi$
$73$	−14952.0	−0.328392	−0.164196	+	0.986428i	$0.552503\pi$
$74$	110757.	2.35121
$75$	13856.4	0.284445
$76$	9204.65	0.182799
$77$	6491.36	0.124770
$78$	−90931.0	−1.69229
$79$	−45838.4	−0.826346	−0.413173	−	0.910653i	$-0.635579\pi$
$79$	−45838.4	−0.826346	−0.413173	+	0.910653i	$0.635579\pi$
$80$	29744.9	0.519621
$81$	−57676.7	−0.976759
$82$	105809.	1.73775
$83$	−68951.2	−1.09862	−0.549309	−	0.835620i	$-0.685109\pi$
$83$	−68951.2	−1.09862	−0.549309	+	0.835620i	$0.685109\pi$
$84$	30326.5	0.468947
$85$	−29874.7	−0.448493
$86$	−64110.0	−0.934716
$87$	17940.8	0.254123
$88$	5965.97	0.0821248
$89$	87062.5	1.16508	0.582541	−	0.812801i	$-0.302059\pi$
$89$	87062.5	1.16508	0.582541	+	0.812801i	$0.302059\pi$
$90$	47111.8	0.613089
$91$	29017.9	0.367335
$92$	−70535.4	−0.868835
$93$	−202918.	−2.43284
$94$	131379.	1.53358
$95$	−9025.00	−0.102598
$96$	165038.	1.82770
$97$	−84468.2	−0.911515	−0.455757	−	0.890104i	$-0.650632\pi$
$97$	−84468.2	−0.911515	−0.455757	+	0.890104i	$0.650632\pi$
$98$	105619.	1.11091
$99$	30071.2	0.308363
$100$	15936.0	0.159360
$101$	−137442.	−1.34065	−0.670326	−	0.742066i	$-0.733846\pi$
$101$	−137442.	−1.34065	−0.670326	+	0.742066i	$0.733846\pi$
$102$	−200891.	−1.91187
$103$	−16924.5	−0.157190	−0.0785948	−	0.996907i	$-0.525043\pi$
$103$	−16924.5	−0.157190	−0.0785948	+	0.996907i	$0.525043\pi$
$104$	26669.3	0.241784
$105$	−29734.6	−0.263202
$106$	46392.1	0.401032
$107$	−47979.6	−0.405133	−0.202566	−	0.979269i	$-0.564928\pi$
$107$	−47979.6	−0.405133	−0.202566	+	0.979269i	$0.564928\pi$
$108$	3121.53	0.0257518
$109$	84464.3	0.680937	0.340468	−	0.940256i	$-0.389414\pi$
$109$	84464.3	0.680937	0.340468	+	0.940256i	$0.389414\pi$
$110$	22937.7	0.180746
$111$	−323830.	−2.49465
$112$	−63829.7	−0.480814
$113$	−161916.	−1.19287	−0.596435	−	0.802661i	$-0.703417\pi$
$113$	−161916.	−1.19287	−0.596435	+	0.802661i	$0.703417\pi$
$114$	−60688.1	−0.437363
$115$	69158.7	0.487643
$116$	20633.4	0.142373
$117$	134425.	0.907854
$118$	−137467.	−0.908852
$119$	64108.2	0.414998
$120$	−27327.9	−0.173242
$121$	14641.0	0.0909091
$122$	−92889.1	−0.565022
$123$	−309363.	−1.84377
$124$	−233372.	−1.36300
$125$	−15625.0	−0.0894427
$126$	−101097.	−0.567302
$127$	233566.	1.28499	0.642497	−	0.766288i	$-0.277898\pi$
$127$	233566.	1.28499	0.642497	+	0.766288i	$0.277898\pi$
$128$	−98893.0	−0.533508
$129$	187444.	0.991741
$130$	102537.	0.532136
$131$	25108.4	0.127832	0.0639161	−	0.997955i	$-0.479641\pi$
$131$	25108.4	0.127832	0.0639161	+	0.997955i	$0.479641\pi$
$132$	68400.1	0.341682
$133$	19366.8	0.0949355
$134$	−331529.	−1.59499
$135$	−3060.61	−0.0144535
$136$	58919.5	0.273156
$137$	−67917.6	−0.309158	−0.154579	−	0.987980i	$-0.549402\pi$
$137$	−67917.6	−0.309158	−0.154579	+	0.987980i	$0.549402\pi$
$138$	465054.	2.07877
$139$	−89020.1	−0.390797	−0.195398	−	0.980724i	$-0.562600\pi$
$139$	−89020.1	−0.390797	−0.195398	+	0.980724i	$0.562600\pi$
$140$	−34197.2	−0.147459
$141$	−384125.	−1.62714
$142$	−406185.	−1.69045
$143$	65448.7	0.267646
$144$	−295690.	−1.18831
$145$	−20230.7	−0.0799081
$146$	113377.	0.440193
$147$	−308809.	−1.17868
$148$	−372430.	−1.39763
$149$	69139.5	0.255129	0.127565	−	0.991830i	$-0.459284\pi$
$149$	69139.5	0.255129	0.127565	+	0.991830i	$0.459284\pi$
$150$	−105069.	−0.381284
$151$	−89862.3	−0.320727	−0.160363	−	0.987058i	$-0.551267\pi$
$151$	−89862.3	−0.320727	−0.160363	+	0.987058i	$0.551267\pi$
$152$	17799.3	0.0624876
$153$	296981.	1.02565
$154$	−49222.2	−0.167247
$155$	228817.	0.764997
$156$	305765.	1.00595
$157$	194590.	0.630044	0.315022	−	0.949084i	$-0.397988\pi$
$157$	194590.	0.630044	0.315022	+	0.949084i	$0.397988\pi$
$158$	347580.	1.10767
$159$	−135641.	−0.425498
$160$	−186103.	−0.574715
$161$	−148408.	−0.451225
$162$	437346.	1.30930
$163$	−431219.	−1.27124	−0.635622	−	0.772000i	$-0.719256\pi$
$163$	−431219.	−1.27124	−0.635622	+	0.772000i	$0.719256\pi$
$164$	−355793.	−1.03297
$165$	−67065.1	−0.191773
$166$	522837.	1.47264
$167$	−69370.8	−0.192480	−0.0962400	−	0.995358i	$-0.530682\pi$
$167$	−69370.8	−0.192480	−0.0962400	+	0.995358i	$0.530682\pi$
$168$	58643.2	0.160304
$169$	−78722.0	−0.212021
$170$	226531.	0.601182
$171$	89716.4	0.234629
$172$	215576.	0.555623
$173$	144385.	0.366782	0.183391	−	0.983040i	$-0.441293\pi$
$173$	144385.	0.366782	0.183391	+	0.983040i	$0.441293\pi$
$174$	−136040.	−0.340639
$175$	33529.8	0.0827628
$176$	−143965.	−0.350329
$177$	401925.	0.964299
$178$	−660171.	−1.56173
$179$	−214515.	−0.500410	−0.250205	−	0.968193i	$-0.580498\pi$
$179$	−214515.	−0.500410	−0.250205	+	0.968193i	$0.580498\pi$
$180$	−158418.	−0.364438
$181$	529413.	1.20115	0.600577	−	0.799567i	$-0.294938\pi$
$181$	529413.	1.20115	0.600577	+	0.799567i	$0.294938\pi$
$182$	−220035.	−0.492394
$183$	271588.	0.599492
$184$	−136396.	−0.297001
$185$	365161.	0.784433
$186$	1.53867e6	3.26109
$187$	144593.	0.302374
$188$	−441775.	−0.911606
$189$	6567.77	0.0133741
$190$	68434.1	0.137527
$191$	130648.	0.259130	0.129565	−	0.991571i	$-0.458642\pi$
$191$	130648.	0.259130	0.129565	+	0.991571i	$0.458642\pi$
$192$	−407338.	−0.797446
$193$	−328883.	−0.635547	−0.317774	−	0.948167i	$-0.602935\pi$
$193$	−328883.	−0.635547	−0.317774	+	0.948167i	$0.602935\pi$
$194$	640499.	1.22184
$195$	−299797.	−0.564600
$196$	−355155.	−0.660355
$197$	55910.8	0.102643	0.0513216	−	0.998682i	$-0.483657\pi$
$197$	55910.8	0.102643	0.0513216	+	0.998682i	$0.483657\pi$
$198$	−228021.	−0.413345
$199$	767713.	1.37425	0.687126	−	0.726538i	$-0.258872\pi$
$199$	767713.	1.37425	0.687126	+	0.726538i	$0.258872\pi$
$200$	30815.9	0.0544754
$201$	969320.	1.69230
$202$	1.04219e6	1.79708
$203$	43413.2	0.0739403
$204$	675515.	1.13647
$205$	348849.	0.579766
$206$	128334.	0.210704
$207$	−687498.	−1.11518
$208$	−643558.	−1.03141
$209$	43681.0	0.0691714
$210$	225469.	0.352808
$211$	−437147.	−0.675960	−0.337980	−	0.941153i	$-0.609744\pi$
$211$	−437147.	−0.675960	−0.337980	+	0.941153i	$0.609744\pi$
$212$	−155998.	−0.238385
$213$	1.18760e6	1.79358
$214$	363816.	0.543060
$215$	−211369.	−0.311849
$216$	6036.19	0.00880296
$217$	−491020.	−0.707864
$218$	−640469.	−0.912761
$219$	−331491.	−0.467048
$220$	−77130.4	−0.107441
$221$	646367.	0.890222
$222$	2.45551e6	3.34394
$223$	−357673.	−0.481642	−0.240821	−	0.970570i	$-0.577417\pi$
$223$	−357673.	−0.481642	−0.240821	+	0.970570i	$0.577417\pi$
$224$	399358.	0.531793
$225$	155326.	0.204545
$226$	1.22776e6	1.59898
$227$	−891220.	−1.14794	−0.573972	−	0.818875i	$-0.694598\pi$
$227$	−891220.	−1.14794	−0.573972	+	0.818875i	$0.694598\pi$
$228$	204070.	0.259981
$229$	1.14545e6	1.44340	0.721699	−	0.692207i	$-0.243361\pi$
$229$	1.14545e6	1.44340	0.721699	+	0.692207i	$0.243361\pi$
$230$	−524411.	−0.653661
$231$	143915.	0.177451
$232$	39899.4	0.0486683
$233$	282893.	0.341375	0.170688	−	0.985325i	$-0.445401\pi$
$233$	282893.	0.341375	0.170688	+	0.985325i	$0.445401\pi$
$234$	−1.01931e6	−1.21693
$235$	433153.	0.511649
$236$	462246.	0.540248
$237$	−1.01625e6	−1.17525
$238$	−486115.	−0.556284
$239$	−7848.37	−0.00888760	−0.00444380	−	0.999990i	$-0.501415\pi$
$239$	−7848.37	−0.00888760	−0.00444380	+	0.999990i	$0.501415\pi$
$240$	659452.	0.739019
$241$	87357.0	0.0968846	0.0484423	−	0.998826i	$-0.484574\pi$
$241$	87357.0	0.0968846	0.0484423	+	0.998826i	$0.484574\pi$
$242$	−111019.	−0.121859
$243$	−1.30846e6	−1.42149
$244$	312349.	0.335865
$245$	348223.	0.370632
$246$	2.34582e6	2.47147
$247$	195264.	0.203648
$248$	−451278.	−0.465924
$249$	−1.52867e6	−1.56248
$250$	118480.	0.119893
$251$	−734095.	−0.735475	−0.367738	−	0.929930i	$-0.619868\pi$
$251$	−734095.	−0.735475	−0.367738	+	0.929930i	$0.619868\pi$
$252$	339950.	0.337221
$253$	−334728.	−0.328769
$254$	−1.77107e6	−1.72247
$255$	−662330.	−0.637858
$256$	1.33782e6	1.27584
$257$	−469688.	−0.443585	−0.221792	−	0.975094i	$-0.571191\pi$
$257$	−469688.	−0.443585	−0.221792	+	0.975094i	$0.571191\pi$
$258$	−1.42134e6	−1.32938
$259$	−783602.	−0.725849
$260$	−344791.	−0.316317
$261$	201111.	0.182740
$262$	−190390.	−0.171353
$263$	−313511.	−0.279488	−0.139744	−	0.990188i	$-0.544628\pi$
$263$	−313511.	−0.279488	−0.139744	+	0.990188i	$0.544628\pi$
$264$	132267.	0.116800
$265$	152953.	0.133796
$266$	−146853.	−0.127256
$267$	1.93020e6	1.65701
$268$	1.11480e6	0.948111
$269$	−554647.	−0.467343	−0.233671	−	0.972316i	$-0.575074\pi$
$269$	−554647.	−0.467343	−0.233671	+	0.972316i	$0.575074\pi$
$270$	23207.7	0.0193742
$271$	1.05910e6	0.876019	0.438009	−	0.898970i	$-0.355684\pi$
$271$	1.05910e6	0.876019	0.438009	+	0.898970i	$0.355684\pi$
$272$	−1.42179e6	−1.16523
$273$	643336.	0.522433
$274$	515000.	0.414411
$275$	75625.0	0.0603023
$276$	−1.56379e6	−1.23568
$277$	1.81259e6	1.41938	0.709692	−	0.704512i	$-0.248834\pi$
$277$	1.81259e6	1.41938	0.709692	+	0.704512i	$0.248834\pi$
$278$	675015.	0.523843
$279$	−2.27464e6	−1.74946
$280$	−66128.1	−0.0504070
$281$	−1.37033e6	−1.03529	−0.517643	−	0.855597i	$-0.673190\pi$
$281$	−1.37033e6	−1.03529	−0.517643	+	0.855597i	$0.673190\pi$
$282$	2.91272e6	2.18110
$283$	−39484.6	−0.0293063	−0.0146532	−	0.999893i	$-0.504664\pi$
$283$	−39484.6	−0.0293063	−0.0146532	+	0.999893i	$0.504664\pi$
$284$	1.36584e6	1.00485
$285$	−200087.	−0.145917
$286$	−496279.	−0.358766
$287$	−748597.	−0.536467
$288$	1.85002e6	1.31430
$289$	8137.28	0.00573105
$290$	153404.	0.107113
$291$	−1.87268e6	−1.29638
$292$	−381241.	−0.261663
$293$	1.52189e6	1.03566	0.517828	−	0.855485i	$-0.326741\pi$
$293$	1.52189e6	1.03566	0.517828	+	0.855485i	$0.326741\pi$
$294$	2.34161e6	1.57996
$295$	−453224.	−0.303220
$296$	−720179.	−0.477762
$297$	14813.3	0.00974455
$298$	−524265.	−0.341988
$299$	−1.49631e6	−0.967931
$300$	353306.	0.226646
$301$	453577.	0.288559
$302$	681401.	0.429918
$303$	−3.04713e6	−1.90671
$304$	−429516.	−0.266560
$305$	−306253.	−0.188508
$306$	−2.25192e6	−1.37483
$307$	−828155.	−0.501494	−0.250747	−	0.968053i	$-0.580676\pi$
$307$	−828155.	−0.501494	−0.250747	+	0.968053i	$0.580676\pi$
$308$	165514.	0.0994167
$309$	−375222.	−0.223559
$310$	−1.73506e6	−1.02544
$311$	992687.	0.581984	0.290992	−	0.956725i	$-0.406015\pi$
$311$	992687.	0.581984	0.290992	+	0.956725i	$0.406015\pi$
$312$	591266.	0.343871
$313$	−1.53875e6	−0.887783	−0.443892	−	0.896080i	$-0.646403\pi$
$313$	−1.53875e6	−0.887783	−0.443892	+	0.896080i	$0.646403\pi$
$314$	−1.47552e6	−0.844541
$315$	−333315.	−0.189269
$316$	−1.16877e6	−0.658433
$317$	1.24528e6	0.696017	0.348008	−	0.937491i	$-0.386858\pi$
$317$	1.24528e6	0.696017	0.348008	+	0.937491i	$0.386858\pi$
$318$	1.02853e6	0.570358
$319$	97916.6	0.0538741
$320$	459328.	0.250754
$321$	−1.06372e6	−0.576190
$322$	1.12534e6	0.604843
$323$	431390.	0.230072
$324$	−1.47062e6	−0.778283
$325$	338061.	0.177536
$326$	3.26981e6	1.70404
$327$	1.87260e6	0.968446
$328$	−688007.	−0.353109
$329$	−929506.	−0.473437
$330$	508536.	0.257062
$331$	1.07695e6	0.540290	0.270145	−	0.962820i	$-0.412928\pi$
$331$	1.07695e6	0.540290	0.270145	+	0.962820i	$0.412928\pi$
$332$	−1.75809e6	−0.875380
$333$	−3.63003e6	−1.79390
$334$	526020.	0.258010
$335$	−1.09304e6	−0.532137
$336$	−1.41512e6	−0.683826
$337$	−841307.	−0.403534	−0.201767	−	0.979434i	$-0.564668\pi$
$337$	−841307.	−0.403534	−0.201767	+	0.979434i	$0.564668\pi$
$338$	596927.	0.284203
$339$	−3.58972e6	−1.69653
$340$	−761734.	−0.357360
$341$	−1.10748e6	−0.515761
$342$	−680295.	−0.314508
$343$	−1.64891e6	−0.756766
$344$	416866.	0.189933
$345$	1.53327e6	0.693539
$346$	−1.09483e6	−0.491652
$347$	−1.41670e6	−0.631619	−0.315809	−	0.948823i	$-0.602276\pi$
$347$	−1.41670e6	−0.631619	−0.315809	+	0.948823i	$0.602276\pi$
$348$	457449.	0.202486
$349$	−2.13689e6	−0.939115	−0.469558	−	0.882902i	$-0.655587\pi$
$349$	−2.13689e6	−0.939115	−0.469558	+	0.882902i	$0.655587\pi$
$350$	−254247.	−0.110939
$351$	66219.1	0.0286890
$352$	900737.	0.387473
$353$	−3.47612e6	−1.48477	−0.742383	−	0.669976i	$-0.766305\pi$
$353$	−3.47612e6	−1.48477	−0.742383	+	0.669976i	$0.766305\pi$
$354$	−3.04768e6	−1.29259
$355$	−1.33918e6	−0.563985
$356$	2.21989e6	0.928339
$357$	1.42130e6	0.590221
$358$	1.62661e6	0.670774
$359$	−4.26844e6	−1.74797	−0.873983	−	0.485956i	$-0.838471\pi$
$359$	−4.26844e6	−1.74797	−0.873983	+	0.485956i	$0.838471\pi$
$360$	−306338.	−0.124579
$361$	130321.	0.0526316
$362$	−4.01439e6	−1.61008
$363$	324595.	0.129293
$364$	739888.	0.292693
$365$	373801.	0.146861
$366$	−2.05938e6	−0.803588
$367$	−830925.	−0.322030	−0.161015	−	0.986952i	$-0.551477\pi$
$367$	−830925.	−0.322030	−0.161015	+	0.986952i	$0.551477\pi$
$368$	3.29139e6	1.26695
$369$	−3.46787e6	−1.32586
$370$	−2.76892e6	−1.05149
$371$	−328223.	−0.123804
$372$	−5.17393e6	−1.93849
$373$	1.91676e6	0.713339	0.356670	−	0.934231i	$-0.383912\pi$
$373$	1.91676e6	0.713339	0.356670	+	0.934231i	$0.383912\pi$
$374$	−1.09641e6	−0.405317
$375$	−346411.	−0.127208
$376$	−854274.	−0.311621
$377$	437710.	0.158611
$378$	−49801.6	−0.0179272
$379$	−4.55948e6	−1.63049	−0.815243	−	0.579118i	$-0.803397\pi$
$379$	−4.55948e6	−1.63049	−0.815243	+	0.579118i	$0.803397\pi$
$380$	−230116.	−0.0817501
$381$	5.17824e6	1.82755
$382$	−990664.	−0.347351
$383$	−709216.	−0.247048	−0.123524	−	0.992342i	$-0.539420\pi$
$383$	−709216.	−0.247048	−0.123524	+	0.992342i	$0.539420\pi$
$384$	−2.19249e6	−0.758768
$385$	−162284.	−0.0557987
$386$	2.49383e6	0.851918
$387$	2.10119e6	0.713162
$388$	−2.15374e6	−0.726296
$389$	−3.31273e6	−1.10997	−0.554987	−	0.831859i	$-0.687277\pi$
$389$	−3.31273e6	−1.10997	−0.554987	+	0.831859i	$0.687277\pi$
$390$	2.27328e6	0.756817
$391$	−3.30575e6	−1.09352
$392$	−686773.	−0.225735
$393$	556660.	0.181806
$394$	−423956.	−0.137588
$395$	1.14596e6	0.369553
$396$	766744.	0.245704
$397$	−3.34118e6	−1.06395	−0.531977	−	0.846759i	$-0.678551\pi$
$397$	−3.34118e6	−1.06395	−0.531977	+	0.846759i	$0.678551\pi$
$398$	−5.82136e6	−1.84211
$399$	429367.	0.135020
$400$	−743622.	−0.232382
$401$	−1.23077e6	−0.382222	−0.191111	−	0.981568i	$-0.561209\pi$
$401$	−1.23077e6	−0.382222	−0.191111	+	0.981568i	$0.561209\pi$
$402$	−7.35009e6	−2.26844
$403$	−4.95068e6	−1.51845
$404$	−3.50445e6	−1.06823
$405$	1.44192e6	0.436820
$406$	−329190.	−0.0991132
$407$	−1.76738e6	−0.528864
$408$	1.30626e6	0.388490
$409$	−2.70060e6	−0.798273	−0.399136	−	0.916892i	$-0.630690\pi$
$409$	−2.70060e6	−0.798273	−0.399136	+	0.916892i	$0.630690\pi$
$410$	−2.64522e6	−0.777146
$411$	−1.50575e6	−0.439693
$412$	−431536.	−0.125249
$413$	972577.	0.280575
$414$	5.21311e6	1.49484
$415$	1.72378e6	0.491317
$416$	4.02650e6	1.14076
$417$	−1.97360e6	−0.555801
$418$	−331221.	−0.0927207
$419$	6.51169e6	1.81200	0.906001	−	0.423276i	$-0.139120\pi$
$419$	6.51169e6	1.81200	0.906001	+	0.423276i	$0.139120\pi$
$420$	−758162.	−0.209720
$421$	3.06167e6	0.841885	0.420942	−	0.907087i	$-0.361699\pi$
$421$	3.06167e6	0.841885	0.420942	+	0.907087i	$0.361699\pi$
$422$	3.31476e6	0.906089
$423$	−4.30592e6	−1.17008
$424$	−301658.	−0.0814892
$425$	746867.	0.200572
$426$	−9.00523e6	−2.40420
$427$	657189.	0.174430
$428$	−1.22337e6	−0.322811
$429$	1.45102e6	0.380653
$430$	1.60275e6	0.418018
$431$	1.86035e6	0.482395	0.241197	−	0.970476i	$-0.422460\pi$
$431$	1.86035e6	0.482395	0.241197	+	0.970476i	$0.422460\pi$
$432$	−145660.	−0.0375518
$433$	−6.06544e6	−1.55469	−0.777343	−	0.629077i	$-0.783433\pi$
$433$	−6.06544e6	−1.55469	−0.777343	+	0.629077i	$0.783433\pi$
$434$	3.72327e6	0.948855
$435$	−448521.	−0.113647
$436$	2.15364e6	0.542572
$437$	−998652.	−0.250156
$438$	2.51360e6	0.626053
$439$	2.03325e6	0.503534	0.251767	−	0.967788i	$-0.418988\pi$
$439$	2.03325e6	0.503534	0.251767	+	0.967788i	$0.418988\pi$
$440$	−149149.	−0.0367273
$441$	−3.46165e6	−0.847591
$442$	−4.90122e6	−1.19330
$443$	−1.16098e6	−0.281071	−0.140535	−	0.990076i	$-0.544882\pi$
$443$	−1.16098e6	−0.281071	−0.140535	+	0.990076i	$0.544882\pi$
$444$	−8.25689e6	−1.98774
$445$	−2.17656e6	−0.521040
$446$	2.71214e6	0.645616
$447$	1.53284e6	0.362851
$448$	−985675.	−0.232027
$449$	616197.	0.144246	0.0721230	−	0.997396i	$-0.477023\pi$
$449$	616197.	0.144246	0.0721230	+	0.997396i	$0.477023\pi$
$450$	−1.17780e6	−0.274182
$451$	−1.68843e6	−0.390878
$452$	−4.12847e6	−0.950481
$453$	−1.99227e6	−0.456146
$454$	6.75787e6	1.53876
$455$	−725448.	−0.164277
$456$	394616.	0.0888714
$457$	6.31931e6	1.41540	0.707700	−	0.706513i	$-0.249733\pi$
$457$	6.31931e6	1.41540	0.707700	+	0.706513i	$0.249733\pi$
$458$	−8.68561e6	−1.93480
$459$	146295.	0.0324115
$460$	1.76338e6	0.388555
$461$	−2.98097e6	−0.653290	−0.326645	−	0.945147i	$-0.605918\pi$
$461$	−2.98097e6	−0.653290	−0.326645	+	0.945147i	$0.605918\pi$
$462$	−1.09127e6	−0.237863
$463$	4.66648e6	1.01167	0.505833	−	0.862632i	$-0.331185\pi$
$463$	4.66648e6	1.01167	0.505833	+	0.862632i	$0.331185\pi$
$464$	−962815.	−0.207610
$465$	5.07295e6	1.08800
$466$	−2.14510e6	−0.457596
$467$	−5.83314e6	−1.23768	−0.618842	−	0.785515i	$-0.712398\pi$
$467$	−5.83314e6	−1.23768	−0.618842	+	0.785515i	$0.712398\pi$
$468$	3.42752e6	0.723379
$469$	2.34556e6	0.492396
$470$	−3.28448e6	−0.685839
$471$	4.31411e6	0.896064
$472$	893859.	0.184677
$473$	1.02303e6	0.210249
$474$	7.70595e6	1.57536
$475$	225625.	0.0458831
$476$	1.63461e6	0.330671
$477$	−1.52049e6	−0.305976
$478$	59512.0	0.0119134
$479$	−9.16851e6	−1.82583	−0.912915	−	0.408151i	$-0.866174\pi$
$479$	−9.16851e6	−1.82583	−0.912915	+	0.408151i	$0.866174\pi$
$480$	−4.12595e6	−0.817374
$481$	−7.90061e6	−1.55703
$482$	−662403.	−0.129869
$483$	−3.29025e6	−0.641743
$484$	373311.	0.0724365
$485$	2.11170e6	0.407642
$486$	9.92167e6	1.90543
$487$	7.29147e6	1.39313	0.696566	−	0.717492i	$-0.254710\pi$
$487$	7.29147e6	1.39313	0.696566	+	0.717492i	$0.254710\pi$
$488$	603998.	0.114812
$489$	−9.56025e6	−1.80800
$490$	−2.64048e6	−0.496813
$491$	9.11341e6	1.70599	0.852997	−	0.521917i	$-0.174783\pi$
$491$	9.11341e6	1.70599	0.852997	+	0.521917i	$0.174783\pi$
$492$	−7.88804e6	−1.46912
$493$	967017.	0.179191
$494$	−1.48063e6	−0.272980
$495$	−751779.	−0.137904
$496$	1.08898e7	1.98754
$497$	2.87375e6	0.521865
$498$	1.15915e7	2.09442
$499$	4.35743e6	0.783392	0.391696	−	0.920095i	$-0.371888\pi$
$499$	4.35743e6	0.783392	0.391696	+	0.920095i	$0.371888\pi$
$500$	−398401.	−0.0712681
$501$	−1.53797e6	−0.273750
$502$	5.56644e6	0.985867
$503$	2.80453e6	0.494242	0.247121	−	0.968985i	$-0.420516\pi$
$503$	2.80453e6	0.494242	0.247121	+	0.968985i	$0.420516\pi$
$504$	657371.	0.115275
$505$	3.43605e6	0.599558
$506$	2.53815e6	0.440698
$507$	−1.74529e6	−0.301542
$508$	5.95540e6	1.02389
$509$	−9.10809e6	−1.55824	−0.779118	−	0.626878i	$-0.784333\pi$
$509$	−9.10809e6	−1.55824	−0.779118	+	0.626878i	$0.784333\pi$
$510$	5.02227e6	0.855016
$511$	−802140.	−0.135893
$512$	−6.97973e6	−1.17669
$513$	44195.2	0.00741449
$514$	3.56151e6	0.594602
$515$	423113.	0.0702973
$516$	4.77939e6	0.790221
$517$	−2.09646e6	−0.344953
$518$	5.94183e6	0.972962
$519$	3.20107e6	0.521646
$520$	−666732.	−0.108129
$521$	−1.61886e6	−0.261286	−0.130643	−	0.991429i	$-0.541704\pi$
$521$	−1.61886e6	−0.261286	−0.130643	+	0.991429i	$0.541704\pi$
$522$	−1.52497e6	−0.244954
$523$	3.07704e6	0.491903	0.245951	−	0.969282i	$-0.420900\pi$
$523$	3.07704e6	0.491903	0.245951	+	0.969282i	$0.420900\pi$
$524$	640205.	0.101857
$525$	743365.	0.117707
$526$	2.37726e6	0.374639
$527$	−1.09373e7	−1.71548
$528$	−3.19175e6	−0.498246
$529$	1.21634e6	0.188980
$530$	−1.15980e6	−0.179347
$531$	4.50545e6	0.693429
$532$	493808.	0.0756447
$533$	−7.54767e6	−1.15079
$534$	−1.46362e7	−2.22113
$535$	1.19949e6	0.181181
$536$	2.15572e6	0.324100
$537$	−4.75587e6	−0.711695
$538$	4.20573e6	0.626449
$539$	−1.68540e6	−0.249880
$540$	−78038.3	−0.0115166
$541$	6.46447e6	0.949597	0.474799	−	0.880094i	$-0.342521\pi$
$541$	6.46447e6	0.949597	0.474799	+	0.880094i	$0.342521\pi$
$542$	−8.03085e6	−1.17426
$543$	1.17373e7	1.70831
$544$	8.89561e6	1.28878
$545$	−2.11161e6	−0.304524
$546$	−4.87823e6	−0.700295
$547$	−8.81369e6	−1.25947	−0.629737	−	0.776808i	$-0.716837\pi$
$547$	−8.81369e6	−1.25947	−0.629737	+	0.776808i	$0.716837\pi$
$548$	−1.73174e6	−0.246338
$549$	3.04442e6	0.431096
$550$	−573443.	−0.0808321
$551$	292131.	0.0409920
$552$	−3.02394e6	−0.422402
$553$	−2.45912e6	−0.341953
$554$	−1.37444e7	−1.90261
$555$	8.09574e6	1.11564
$556$	−2.26980e6	−0.311388
$557$	8.51313e6	1.16266	0.581328	−	0.813669i	$-0.302533\pi$
$557$	8.51313e6	1.16266	0.581328	+	0.813669i	$0.302533\pi$
$558$	1.72480e7	2.34506
$559$	4.57316e6	0.618995
$560$	1.59574e6	0.215027
$561$	3.20568e6	0.430044
$562$	1.03908e7	1.38775
$563$	2.90438e6	0.386174	0.193087	−	0.981182i	$-0.438150\pi$
$563$	2.90438e6	0.386174	0.193087	+	0.981182i	$0.438150\pi$
$564$	−9.79429e6	−1.29651
$565$	4.04790e6	0.533468
$566$	299400.	0.0392836
$567$	−3.09422e6	−0.404197
$568$	2.64116e6	0.343497
$569$	−6.24399e6	−0.808503	−0.404252	−	0.914648i	$-0.632468\pi$
$569$	−6.24399e6	−0.808503	−0.404252	+	0.914648i	$0.632468\pi$
$570$	1.51720e6	0.195594
$571$	1.10042e7	1.41243	0.706215	−	0.707997i	$-0.250401\pi$
$571$	1.10042e7	1.41243	0.706215	+	0.707997i	$0.250401\pi$
$572$	1.66879e6	0.213261
$573$	2.89650e6	0.368542
$574$	5.67640e6	0.719106
$575$	−1.72897e6	−0.218081
$576$	−4.56613e6	−0.573445
$577$	−1.32962e7	−1.66260	−0.831298	−	0.555827i	$-0.812402\pi$
$577$	−1.32962e7	−1.66260	−0.831298	+	0.555827i	$0.812402\pi$
$578$	−61702.7	−0.00768218
$579$	−7.29143e6	−0.903891
$580$	−515835.	−0.0636709
$581$	−3.69907e6	−0.454623
$582$	1.42000e7	1.73773
$583$	−740294.	−0.0902055
$584$	−737217.	−0.0894465
$585$	−3.36063e6	−0.406004
$586$	−1.15401e7	−1.38824
$587$	−8.08895e6	−0.968940	−0.484470	−	0.874808i	$-0.660988\pi$
$587$	−8.08895e6	−0.968940	−0.484470	+	0.874808i	$0.660988\pi$
$588$	−7.87389e6	−0.939174
$589$	−3.30412e6	−0.392435
$590$	3.43667e6	0.406451
$591$	1.23956e6	0.145982
$592$	1.73787e7	2.03804
$593$	105237.	0.0122895	0.00614473	−	0.999981i	$-0.498044\pi$
$593$	105237.	0.0122895	0.00614473	+	0.999981i	$0.498044\pi$
$594$	−112325.	−0.0130621
$595$	−1.60271e6	−0.185593
$596$	1.76289e6	0.203287
$597$	1.70204e7	1.95450
$598$	1.13461e7	1.29746
$599$	−7.47270e6	−0.850962	−0.425481	−	0.904967i	$-0.639895\pi$
$599$	−7.47270e6	−0.850962	−0.425481	+	0.904967i	$0.639895\pi$
$600$	683199.	0.0774763
$601$	1.77349e6	0.200282	0.100141	−	0.994973i	$-0.468071\pi$
$601$	1.77349e6	0.200282	0.100141	+	0.994973i	$0.468071\pi$
$602$	−3.43935e6	−0.386799
$603$	1.08658e7	1.21694
$604$	−2.29128e6	−0.255556
$605$	−366025.	−0.0406558
$606$	2.31056e7	2.55585
$607$	−1.08008e7	−1.18983	−0.594913	−	0.803790i	$-0.702814\pi$
$607$	−1.08008e7	−1.18983	−0.594913	+	0.803790i	$0.702814\pi$
$608$	2.68732e6	0.294823
$609$	962483.	0.105160
$610$	2.32223e6	0.252685
$611$	−9.37167e6	−1.01558
$612$	7.57231e6	0.817240
$613$	5.54811e6	0.596340	0.298170	−	0.954513i	$-0.403624\pi$
$613$	5.54811e6	0.596340	0.298170	+	0.954513i	$0.403624\pi$
$614$	6.27967e6	0.672227
$615$	7.73408e6	0.824558
$616$	320060.	0.0339844
$617$	−3.19290e6	−0.337654	−0.168827	−	0.985646i	$-0.553998\pi$
$617$	−3.19290e6	−0.337654	−0.168827	+	0.985646i	$0.553998\pi$
$618$	2.84520e6	0.299669
$619$	5.53538e6	0.580658	0.290329	−	0.956927i	$-0.406235\pi$
$619$	5.53538e6	0.580658	0.290329	+	0.956927i	$0.406235\pi$
$620$	5.83430e6	0.609551
$621$	−338668.	−0.0352408
$622$	−7.52727e6	−0.780120
$623$	4.67070e6	0.482127
$624$	−1.42679e7	−1.46689
$625$	390625.	0.0400000
$626$	1.16679e7	1.19003
$627$	968421.	0.0983774
$628$	4.96158e6	0.502020
$629$	−1.74545e7	−1.75906
$630$	2.52744e6	0.253705
$631$	−1.53874e7	−1.53848	−0.769238	−	0.638963i	$-0.779364\pi$
$631$	−1.53874e7	−1.53848	−0.769238	+	0.638963i	$0.779364\pi$
$632$	−2.26009e6	−0.225078
$633$	−9.69167e6	−0.961367
$634$	−9.44263e6	−0.932975
$635$	−5.83916e6	−0.574667
$636$	−3.45852e6	−0.339038
$637$	−7.53414e6	−0.735673
$638$	−742474.	−0.0722154
$639$	1.33126e7	1.28977
$640$	2.47233e6	0.238592
$641$	2.67896e6	0.257526	0.128763	−	0.991675i	$-0.458899\pi$
$641$	2.67896e6	0.257526	0.128763	+	0.991675i	$0.458899\pi$
$642$	8.06591e6	0.772353
$643$	284413.	0.0271283	0.0135642	−	0.999908i	$-0.495682\pi$
$643$	284413.	0.0271283	0.0135642	+	0.999908i	$0.495682\pi$
$644$	−3.78406e6	−0.359536
$645$	−4.68611e6	−0.443520
$646$	−3.27111e6	−0.308400
$647$	3.69774e6	0.347277	0.173638	−	0.984809i	$-0.444448\pi$
$647$	3.69774e6	0.347277	0.173638	+	0.984809i	$0.444448\pi$
$648$	−2.84378e6	−0.266047
$649$	2.19361e6	0.204431
$650$	−2.56343e6	−0.237978
$651$	−1.08861e7	−1.00674
$652$	−1.09951e7	−1.01293
$653$	3.54839e6	0.325648	0.162824	−	0.986655i	$-0.447940\pi$
$653$	3.54839e6	0.325648	0.162824	+	0.986655i	$0.447940\pi$
$654$	−1.41994e7	−1.29815
$655$	−627709.	−0.0571683
$656$	1.66023e7	1.50629
$657$	−3.71591e6	−0.335855
$658$	7.04818e6	0.634618
$659$	−7.45461e6	−0.668670	−0.334335	−	0.942454i	$-0.608512\pi$
$659$	−7.45461e6	−0.668670	−0.334335	+	0.942454i	$0.608512\pi$
$660$	−1.71000e6	−0.152805
$661$	−5.32579e6	−0.474111	−0.237056	−	0.971496i	$-0.576182\pi$
$661$	−5.32579e6	−0.474111	−0.237056	+	0.971496i	$0.576182\pi$
$662$	−8.16624e6	−0.724231
$663$	1.43301e7	1.26610
$664$	−3.39967e6	−0.299238
$665$	−484170.	−0.0424564
$666$	2.75255e7	2.40464
$667$	−2.23861e6	−0.194833
$668$	−1.76879e6	−0.153368
$669$	−7.92972e6	−0.685003
$670$	8.28821e6	0.713303
$671$	1.48226e6	0.127092
$672$	8.85390e6	0.756330
$673$	1.28946e7	1.09741	0.548706	−	0.836016i	$-0.315121\pi$
$673$	1.28946e7	1.09741	0.548706	+	0.836016i	$0.315121\pi$
$674$	6.37939e6	0.540916
$675$	76515.2	0.00646380
$676$	−2.00723e6	−0.168939
$677$	1.72698e7	1.44815	0.724076	−	0.689720i	$-0.242266\pi$
$677$	1.72698e7	1.44815	0.724076	+	0.689720i	$0.242266\pi$
$678$	2.72199e7	2.27411
$679$	−4.53152e6	−0.377198
$680$	−1.47299e6	−0.122159
$681$	−1.97586e7	−1.63263
$682$	8.39768e6	0.691350
$683$	1.60240e7	1.31438	0.657189	−	0.753726i	$-0.271745\pi$
$683$	1.60240e7	1.31438	0.657189	+	0.753726i	$0.271745\pi$
$684$	2.28756e6	0.186953
$685$	1.69794e6	0.138260
$686$	1.25032e7	1.01441
$687$	2.53949e7	2.05284
$688$	−1.00594e7	−0.810218
$689$	−3.30929e6	−0.265575
$690$	−1.16264e7	−0.929653
$691$	3.50741e6	0.279441	0.139721	−	0.990191i	$-0.455380\pi$
$691$	3.50741e6	0.279441	0.139721	+	0.990191i	$0.455380\pi$
$692$	3.68149e6	0.292252
$693$	1.61325e6	0.127605
$694$	1.07425e7	0.846652
$695$	2.22550e6	0.174770
$696$	884582.	0.0692173
$697$	−1.66748e7	−1.30011
$698$	1.62035e7	1.25884
$699$	6.27182e6	0.485513
$700$	854930.	0.0659456
$701$	−1.98801e7	−1.52800	−0.764000	−	0.645216i	$-0.776767\pi$
$701$	−1.98801e7	−1.52800	−0.764000	+	0.645216i	$0.776767\pi$
$702$	−502121.	−0.0384561
$703$	−5.27293e6	−0.402405
$704$	−2.22315e6	−0.169058
$705$	9.60313e6	0.727680
$706$	2.63585e7	1.99025
$707$	−7.37344e6	−0.554781
$708$	1.02481e7	0.768355
$709$	−1.01873e7	−0.761101	−0.380550	−	0.924760i	$-0.624265\pi$
$709$	−1.01873e7	−0.761101	−0.380550	+	0.924760i	$0.624265\pi$
$710$	1.01546e7	0.755993
$711$	−1.13918e7	−0.845124
$712$	4.29266e6	0.317341
$713$	2.53195e7	1.86523
$714$	−1.07773e7	−0.791161
$715$	−1.63622e6	−0.119695
$716$	−5.46964e6	−0.398727
$717$	−174001.	−0.0126402
$718$	3.23664e7	2.34306
$719$	1.39107e7	1.00352	0.501760	−	0.865007i	$-0.332686\pi$
$719$	1.39107e7	1.00352	0.501760	+	0.865007i	$0.332686\pi$
$720$	7.39225e6	0.531429
$721$	−907961.	−0.0650472
$722$	−988188.	−0.0705499
$723$	1.93673e6	0.137792
$724$	1.34988e7	0.957081
$725$	505768.	0.0357360
$726$	−2.46132e6	−0.173311
$727$	−6.54450e6	−0.459241	−0.229620	−	0.973280i	$-0.573748\pi$
$727$	−6.54450e6	−0.459241	−0.229620	+	0.973280i	$0.573748\pi$
$728$	1.43074e6	0.100054
$729$	−1.49935e7	−1.04492
$730$	−2.83443e6	−0.196860
$731$	1.01033e7	0.699312
$732$	6.92487e6	0.477676
$733$	2.81603e7	1.93587	0.967936	−	0.251195i	$-0.0808236\pi$
$733$	2.81603e7	1.93587	0.967936	+	0.251195i	$0.0808236\pi$
$734$	6.30067e6	0.431665
$735$	7.72021e6	0.527122
$736$	−2.05930e7	−1.40128
$737$	5.29031e6	0.358767
$738$	2.62959e7	1.77724
$739$	−9.41392e6	−0.634103	−0.317051	−	0.948408i	$-0.602693\pi$
$739$	−9.41392e6	−0.634103	−0.317051	+	0.948408i	$0.602693\pi$
$740$	9.31076e6	0.625037
$741$	4.32907e6	0.289634
$742$	2.48883e6	0.165953
$743$	−1.87465e7	−1.24580	−0.622900	−	0.782302i	$-0.714046\pi$
$743$	−1.87465e7	−1.24580	−0.622900	+	0.782302i	$0.714046\pi$
$744$	−1.00050e7	−0.662649
$745$	−1.72849e6	−0.114097
$746$	−1.45343e7	−0.956195
$747$	−1.71359e7	−1.12358
$748$	3.68679e6	0.240932
$749$	−2.57399e6	−0.167650
$750$	2.62674e6	0.170515
$751$	−2.12138e7	−1.37252	−0.686259	−	0.727357i	$-0.740749\pi$
$751$	−2.12138e7	−1.37252	−0.686259	+	0.727357i	$0.740749\pi$
$752$	2.06145e7	1.32932
$753$	−1.62751e7	−1.04601
$754$	−3.31903e6	−0.212610
$755$	2.24656e6	0.143433
$756$	167463.	0.0106565
$757$	1.93886e7	1.22972	0.614859	−	0.788637i	$-0.289213\pi$
$757$	1.93886e7	1.22972	0.614859	+	0.788637i	$0.289213\pi$
$758$	3.45733e7	2.18558
$759$	−7.42102e6	−0.467584
$760$	−444982.	−0.0279453
$761$	−2.37577e7	−1.48711	−0.743553	−	0.668677i	$-0.766861\pi$
$761$	−2.37577e7	−1.48711	−0.743553	+	0.668677i	$0.766861\pi$
$762$	−3.92651e7	−2.44974
$763$	4.53131e6	0.281781
$764$	3.33121e6	0.206475
$765$	−7.42451e6	−0.458685
$766$	5.37778e6	0.331155
$767$	9.80593e6	0.601867
$768$	2.96598e7	1.81454
$769$	2.58065e7	1.57367	0.786835	−	0.617163i	$-0.211718\pi$
$769$	2.58065e7	1.57367	0.786835	+	0.617163i	$0.211718\pi$
$770$	1.23055e6	0.0747953
$771$	−1.04131e7	−0.630877
$772$	−8.38574e6	−0.506405
$773$	−5.87227e6	−0.353474	−0.176737	−	0.984258i	$-0.556554\pi$
$773$	−5.87227e6	−0.353474	−0.176737	+	0.984258i	$0.556554\pi$
$774$	−1.59328e7	−0.955957
$775$	−5.72043e6	−0.342117
$776$	−4.16475e6	−0.248276
$777$	−1.73727e7	−1.03232
$778$	2.51195e7	1.48786
$779$	−5.03738e6	−0.297414
$780$	−7.64412e6	−0.449874
$781$	6.48162e6	0.380239
$782$	2.50666e7	1.46581
$783$	99069.2	0.00577476
$784$	1.65726e7	0.962941
$785$	−4.86474e6	−0.281764
$786$	−4.22100e6	−0.243702
$787$	8.92319e6	0.513551	0.256775	−	0.966471i	$-0.417340\pi$
$787$	8.92319e6	0.513551	0.256775	+	0.966471i	$0.417340\pi$
$788$	1.42559e6	0.0817862
$789$	−6.95063e6	−0.397495
$790$	−8.68949e6	−0.495367
$791$	−8.68640e6	−0.493627
$792$	1.48267e6	0.0839910
$793$	6.62606e6	0.374173
$794$	2.53352e7	1.42618
$795$	3.39102e6	0.190289
$796$	1.95749e7	1.09501
$797$	−8.20820e6	−0.457723	−0.228861	−	0.973459i	$-0.573500\pi$
$797$	−8.20820e6	−0.457723	−0.228861	+	0.973459i	$0.573500\pi$
$798$	−3.25577e6	−0.180987
$799$	−2.07045e7	−1.14735
$800$	4.65256e6	0.257020
$801$	2.16370e7	1.19156
$802$	9.33257e6	0.512348
$803$	−1.80919e6	−0.0990140
$804$	2.47154e7	1.34843
$805$	3.71020e6	0.201794
$806$	3.75396e7	2.03541
$807$	−1.22967e7	−0.664667
$808$	−6.77665e6	−0.365163
$809$	1.35818e7	0.729602	0.364801	−	0.931085i	$-0.381137\pi$
$809$	1.35818e7	0.729602	0.364801	+	0.931085i	$0.381137\pi$
$810$	−1.09337e7	−0.585535
$811$	5.61013e6	0.299516	0.149758	−	0.988723i	$-0.452150\pi$
$811$	5.61013e6	0.299516	0.149758	+	0.988723i	$0.452150\pi$
$812$	1.10693e6	0.0589158
$813$	2.34805e7	1.24590
$814$	1.34016e7	0.708915
$815$	1.07805e7	0.568518
$816$	−3.15215e7	−1.65722
$817$	3.05217e6	0.159975
$818$	2.04779e7	1.07004
$819$	7.21159e6	0.375683
$820$	8.89483e6	0.461958
$821$	2.43362e6	0.126007	0.0630035	−	0.998013i	$-0.479932\pi$
$821$	2.43362e6	0.126007	0.0630035	+	0.998013i	$0.479932\pi$
$822$	1.14177e7	0.589386
$823$	1.80499e6	0.0928914	0.0464457	−	0.998921i	$-0.485211\pi$
$823$	1.80499e6	0.0928914	0.0464457	+	0.998921i	$0.485211\pi$
$824$	−834473.	−0.0428148
$825$	1.67663e6	0.0857634
$826$	−7.37478e6	−0.376096
$827$	−7.31686e6	−0.372015	−0.186008	−	0.982548i	$-0.559555\pi$
$827$	−7.31686e6	−0.372015	−0.186008	+	0.982548i	$0.559555\pi$
$828$	−1.75296e7	−0.888579
$829$	−8.19081e6	−0.413943	−0.206971	−	0.978347i	$-0.566361\pi$
$829$	−8.19081e6	−0.413943	−0.206971	+	0.978347i	$0.566361\pi$
$830$	−1.30709e7	−0.658584
$831$	4.01856e7	2.01868
$832$	−9.93799e6	−0.497726
$833$	−1.66449e7	−0.831129
$834$	1.49653e7	0.745023
$835$	1.73427e6	0.0860797
$836$	1.11376e6	0.0551159
$837$	−1.12051e6	−0.0552844
$838$	−4.93763e7	−2.42889
$839$	−2.88291e7	−1.41393	−0.706963	−	0.707250i	$-0.749935\pi$
$839$	−2.88291e7	−1.41393	−0.706963	+	0.707250i	$0.749935\pi$
$840$	−1.46608e6	−0.0716901
$841$	−1.98563e7	−0.968073
$842$	−2.32158e7	−1.12850
$843$	−3.03807e7	−1.47241
$844$	−1.11462e7	−0.538606
$845$	1.96805e6	0.0948188
$846$	3.26506e7	1.56843
$847$	785455.	0.0376195
$848$	7.27933e6	0.347617
$849$	−875384.	−0.0416802
$850$	−5.66328e6	−0.268857
$851$	4.04066e7	1.91262
$852$	3.02810e7	1.42913
$853$	−4.10253e6	−0.193054	−0.0965270	−	0.995330i	$-0.530773\pi$
$853$	−4.10253e6	−0.193054	−0.0965270	+	0.995330i	$0.530773\pi$
$854$	−4.98328e6	−0.233814
$855$	−2.24291e6	−0.104929
$856$	−2.36566e6	−0.110349
$857$	−69572.0	−0.00323581	−0.00161790	−	0.999999i	$-0.500515\pi$
$857$	−69572.0	−0.00323581	−0.00161790	+	0.999999i	$0.500515\pi$
$858$	−1.10027e7	−0.510246
$859$	−9.10200e6	−0.420876	−0.210438	−	0.977607i	$-0.567489\pi$
$859$	−9.10200e6	−0.420876	−0.210438	+	0.977607i	$0.567489\pi$
$860$	−5.38941e6	−0.248482
$861$	−1.65966e7	−0.762977
$862$	−1.41066e7	−0.646625
$863$	9.88926e6	0.451998	0.225999	−	0.974127i	$-0.427435\pi$
$863$	9.88926e6	0.451998	0.225999	+	0.974127i	$0.427435\pi$
$864$	911339.	0.0415332
$865$	−3.60963e6	−0.164030
$866$	4.59925e7	2.08398
$867$	180406.	0.00815085
$868$	−1.25199e7	−0.564027
$869$	−5.54645e6	−0.249153
$870$	3.40101e6	0.152338
$871$	2.36489e7	1.05625
$872$	4.16456e6	0.185472
$873$	−2.09922e7	−0.932228
$874$	7.57250e6	0.335321
$875$	−838244.	−0.0370127
$876$	−8.45224e6	−0.372144
$877$	2.98380e7	1.31000	0.654999	−	0.755630i	$-0.272669\pi$
$877$	2.98380e7	1.31000	0.654999	+	0.755630i	$0.272669\pi$
$878$	−1.54175e7	−0.674961
$879$	3.37409e7	1.47294
$880$	3.59913e6	0.156672
$881$	−2.01325e7	−0.873893	−0.436947	−	0.899487i	$-0.643940\pi$
$881$	−2.01325e7	−0.873893	−0.436947	+	0.899487i	$0.643940\pi$
$882$	2.62487e7	1.13615
$883$	3.33067e7	1.43757	0.718787	−	0.695231i	$-0.244698\pi$
$883$	3.33067e7	1.43757	0.718787	+	0.695231i	$0.244698\pi$
$884$	1.64808e7	0.709330
$885$	−1.00481e7	−0.431248
$886$	8.80339e6	0.376761
$887$	−1.52647e7	−0.651447	−0.325724	−	0.945465i	$-0.605608\pi$
$887$	−1.52647e7	−0.651447	−0.325724	+	0.945465i	$0.605608\pi$
$888$	−1.59666e7	−0.679484
$889$	1.25303e7	0.531749
$890$	1.65043e7	0.698428
$891$	−6.97888e6	−0.294504
$892$	−9.11982e6	−0.383773
$893$	−6.25473e6	−0.262470
$894$	−1.16231e7	−0.486383
$895$	5.36288e6	0.223790
$896$	−5.30538e6	−0.220773
$897$	−3.31737e7	−1.37662
$898$	−4.67245e6	−0.193354
$899$	−7.40661e6	−0.305647
$900$	3.96045e6	0.162982
$901$	−7.31109e6	−0.300034
$902$	1.28029e7	0.523952
$903$	1.00559e7	0.410396
$904$	−7.98335e6	−0.324911
$905$	−1.32353e7	−0.537172
$906$	1.51069e7	0.611440
$907$	−1.28670e7	−0.519348	−0.259674	−	0.965696i	$-0.583615\pi$
$907$	−1.28670e7	−0.519348	−0.259674	+	0.965696i	$0.583615\pi$
$908$	−2.27240e7	−0.914683
$909$	−3.41574e7	−1.37112
$910$	5.50087e6	0.220205
$911$	−4.55945e7	−1.82019	−0.910095	−	0.414400i	$-0.863991\pi$
$911$	−4.55945e7	−1.82019	−0.910095	+	0.414400i	$0.863991\pi$
$912$	−9.52249e6	−0.379109
$913$	−8.34309e6	−0.331246
$914$	−4.79176e7	−1.89727
$915$	−6.78971e6	−0.268101
$916$	2.92062e7	1.15010
$917$	1.34700e6	0.0528988
$918$	−1.10932e6	−0.0434459
$919$	−2.63285e7	−1.02834	−0.514171	−	0.857688i	$-0.671900\pi$
$919$	−2.63285e7	−1.02834	−0.514171	+	0.857688i	$0.671900\pi$
$920$	3.40991e6	0.132823
$921$	−1.83604e7	−0.713237
$922$	2.26039e7	0.875701
$923$	2.89744e7	1.11946
$924$	3.66950e6	0.141393
$925$	−9.12904e6	−0.350809
$926$	−3.53846e7	−1.35609
$927$	−4.20612e6	−0.160762
$928$	6.02398e6	0.229622
$929$	375095.	0.0142594	0.00712971	−	0.999975i	$-0.497731\pi$
$929$	375095.	0.0142594	0.00712971	+	0.999975i	$0.497731\pi$
$930$	−3.84667e7	−1.45840
$931$	−5.02834e6	−0.190130
$932$	7.21310e6	0.272008
$933$	2.20082e7	0.827713
$934$	4.42311e7	1.65905
$935$	−3.61484e6	−0.135226
$936$	6.62790e6	0.247278
$937$	2.46178e7	0.916009	0.458004	−	0.888950i	$-0.348564\pi$
$937$	2.46178e7	0.916009	0.458004	+	0.888950i	$0.348564\pi$
$938$	−1.77857e7	−0.660031
$939$	−3.41145e7	−1.26263
$940$	1.10444e7	0.407682
$941$	1.81742e7	0.669085	0.334543	−	0.942381i	$-0.391418\pi$
$941$	1.81742e7	0.669085	0.334543	+	0.942381i	$0.391418\pi$
$942$	−3.27127e7	−1.20113
$943$	3.86015e7	1.41360
$944$	−2.15698e7	−0.787799
$945$	−164194.	−0.00598107
$946$	−7.75731e6	−0.281828
$947$	5.15099e7	1.86645	0.933224	−	0.359295i	$-0.116983\pi$
$947$	5.15099e7	1.86645	0.933224	+	0.359295i	$0.116983\pi$
$948$	−2.59120e7	−0.936440
$949$	−8.08752e6	−0.291508
$950$	−1.71085e6	−0.0615040
$951$	2.76083e7	0.989893
$952$	3.16089e6	0.113036
$953$	−5.20479e7	−1.85640	−0.928199	−	0.372084i	$-0.878643\pi$
$953$	−5.20479e7	−1.85640	−0.928199	+	0.372084i	$0.878643\pi$
$954$	1.15295e7	0.410146
$955$	−3.26619e6	−0.115887
$956$	−200115.	−0.00708165
$957$	2.17084e6	0.0766210
$958$	6.95223e7	2.44743
$959$	−3.64362e6	−0.127934
$960$	1.01834e7	0.356629
$961$	5.51426e7	1.92610
$962$	5.99081e7	2.08712
$963$	−1.19240e7	−0.414339
$964$	2.22740e6	0.0771978
$965$	8.22207e6	0.284225
$966$	2.49490e7	0.860223
$967$	2.83657e7	0.975499	0.487749	−	0.872984i	$-0.337818\pi$
$967$	2.83657e7	0.975499	0.487749	+	0.872984i	$0.337818\pi$
$968$	721882.	0.0247616
$969$	9.56405e6	0.327214
$970$	−1.60125e7	−0.546423
$971$	−1.70328e7	−0.579746	−0.289873	−	0.957065i	$-0.593613\pi$
$971$	−1.70328e7	−0.579746	−0.289873	+	0.957065i	$0.593613\pi$
$972$	−3.33626e7	−1.13265
$973$	−4.77572e6	−0.161717
$974$	−5.52892e7	−1.86742
$975$	7.49492e6	0.252497
$976$	−1.45751e7	−0.489764
$977$	4.77885e7	1.60172	0.800860	−	0.598851i	$-0.204376\pi$
$977$	4.77885e7	1.60172	0.800860	+	0.598851i	$0.204376\pi$
$978$	7.24927e7	2.42352
$979$	1.05346e7	0.351285
$980$	8.87888e6	0.295320
$981$	2.09912e7	0.696411
$982$	−6.91045e7	−2.28680
$983$	1.39142e7	0.459278	0.229639	−	0.973276i	$-0.426245\pi$
$983$	1.39142e7	0.459278	0.229639	+	0.973276i	$0.426245\pi$
$984$	−1.52533e7	−0.502200
$985$	−1.39777e6	−0.0459034
$986$	−7.33262e6	−0.240197
$987$	−2.06074e7	−0.673334
$988$	4.97878e6	0.162267
$989$	−2.33888e7	−0.760356
$990$	5.70053e6	0.184853
$991$	2.56389e7	0.829307	0.414653	−	0.909979i	$-0.363903\pi$
$991$	2.56389e7	0.829307	0.414653	+	0.909979i	$0.363903\pi$
$992$	−6.81336e7	−2.19828
$993$	2.38764e7	0.768414
$994$	−2.17908e7	−0.699533
$995$	−1.91928e7	−0.614584
$996$	−3.89774e7	−1.24499
$997$	5.77728e7	1.84071	0.920356	−	0.391082i	$-0.127899\pi$
$997$	5.77728e7	1.84071	0.920356	+	0.391082i	$0.127899\pi$
$998$	−3.30412e7	−1.05010
$999$	−1.78819e6	−0.0566890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.7	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.7	✓	35	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-7.58272 q^{2} +22.1703 q^{3} +25.4976 q^{4} -25.0000 q^{5} -168.111 q^{6} +53.6476 q^{7} +49.3055 q^{8} +248.522 q^{9} +O(q^{10})\)	\(q-7.58272 q^{2} +22.1703 q^{3} +25.4976 q^{4} -25.0000 q^{5} -168.111 q^{6} +53.6476 q^{7} +49.3055 q^{8} +248.522 q^{9} +189.568 q^{10} +121.000 q^{11} +565.290 q^{12} +540.898 q^{13} -406.795 q^{14} -554.257 q^{15} -1189.79 q^{16} +1194.99 q^{17} -1884.47 q^{18} +361.000 q^{19} -637.441 q^{20} +1189.38 q^{21} -917.509 q^{22} -2766.35 q^{23} +1093.12 q^{24} +625.000 q^{25} -4101.48 q^{26} +122.424 q^{27} +1367.89 q^{28} +809.228 q^{29} +4202.78 q^{30} -9152.69 q^{31} +7444.10 q^{32} +2682.61 q^{33} -9061.25 q^{34} -1341.19 q^{35} +6336.73 q^{36} -14606.5 q^{37} -2737.36 q^{38} +11991.9 q^{39} -1232.64 q^{40} -13954.0 q^{41} -9018.76 q^{42} +8454.75 q^{43} +3085.22 q^{44} -6213.05 q^{45} +20976.4 q^{46} -17326.1 q^{47} -26378.1 q^{48} -13928.9 q^{49} -4739.20 q^{50} +26493.2 q^{51} +13791.6 q^{52} -6118.14 q^{53} -928.309 q^{54} -3025.00 q^{55} +2645.12 q^{56} +8003.48 q^{57} -6136.15 q^{58} +18129.0 q^{59} -14132.3 q^{60} +12250.1 q^{61} +69402.3 q^{62} +13332.6 q^{63} -18373.1 q^{64} -13522.5 q^{65} -20341.4 q^{66} +43721.6 q^{67} +30469.4 q^{68} -61330.8 q^{69} +10169.9 q^{70} +53567.1 q^{71} +12253.5 q^{72} -14952.0 q^{73} +110757. q^{74} +13856.4 q^{75} +9204.65 q^{76} +6491.36 q^{77} -90931.0 q^{78} -45838.4 q^{79} +29744.9 q^{80} -57676.7 q^{81} +105809. q^{82} -68951.2 q^{83} +30326.5 q^{84} -29874.7 q^{85} -64110.0 q^{86} +17940.8 q^{87} +5965.97 q^{88} +87062.5 q^{89} +47111.8 q^{90} +29017.9 q^{91} -70535.4 q^{92} -202918. q^{93} +131379. q^{94} -9025.00 q^{95} +165038. q^{96} -84468.2 q^{97} +105619. q^{98} +30071.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * q^99

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