LMFDB - Embedded newform 1045.6.a.h.1.20

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:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+0.237841 q^{2} +14.0227 q^{3} -31.9434 q^{4} +25.0000 q^{5} +3.33516 q^{6} +13.4367 q^{7} -15.2083 q^{8} -46.3651 q^{9} +O(q^{10})$	\(q+0.237841 q^{2} +14.0227 q^{3} -31.9434 q^{4} +25.0000 q^{5} +3.33516 q^{6} +13.4367 q^{7} -15.2083 q^{8} -46.3651 q^{9} +5.94602 q^{10} +121.000 q^{11} -447.932 q^{12} +762.757 q^{13} +3.19579 q^{14} +350.566 q^{15} +1018.57 q^{16} -2001.75 q^{17} -11.0275 q^{18} +361.000 q^{19} -798.586 q^{20} +188.418 q^{21} +28.7787 q^{22} +706.337 q^{23} -213.261 q^{24} +625.000 q^{25} +181.415 q^{26} -4057.67 q^{27} -429.214 q^{28} -3930.79 q^{29} +83.3789 q^{30} +8531.06 q^{31} +728.925 q^{32} +1696.74 q^{33} -476.098 q^{34} +335.918 q^{35} +1481.06 q^{36} +880.717 q^{37} +85.8605 q^{38} +10695.9 q^{39} -380.209 q^{40} +2489.76 q^{41} +44.8135 q^{42} +12748.2 q^{43} -3865.16 q^{44} -1159.13 q^{45} +167.996 q^{46} +2796.12 q^{47} +14283.1 q^{48} -16626.5 q^{49} +148.650 q^{50} -28069.9 q^{51} -24365.1 q^{52} -4387.76 q^{53} -965.078 q^{54} +3025.00 q^{55} -204.350 q^{56} +5062.18 q^{57} -934.901 q^{58} -29458.7 q^{59} -11198.3 q^{60} -18677.7 q^{61} +2029.03 q^{62} -622.994 q^{63} -32421.0 q^{64} +19068.9 q^{65} +403.554 q^{66} +16856.4 q^{67} +63942.8 q^{68} +9904.73 q^{69} +79.8948 q^{70} +72654.0 q^{71} +705.137 q^{72} +70264.7 q^{73} +209.470 q^{74} +8764.16 q^{75} -11531.6 q^{76} +1625.84 q^{77} +2543.92 q^{78} -33466.3 q^{79} +25464.3 q^{80} -45632.5 q^{81} +592.167 q^{82} -2916.82 q^{83} -6018.72 q^{84} -50043.8 q^{85} +3032.05 q^{86} -55120.0 q^{87} -1840.21 q^{88} -23748.6 q^{89} -275.688 q^{90} +10248.9 q^{91} -22562.8 q^{92} +119628. q^{93} +665.032 q^{94} +9025.00 q^{95} +10221.5 q^{96} -13529.3 q^{97} -3954.45 q^{98} -5610.18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * 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 $

$2$	0.237841	0.0420447	0.0210223	−	0.999779i	$-0.493308\pi$
$2$	0.237841	0.0420447	0.0210223	+	0.999779i	$0.493308\pi$
$3$	14.0227	0.899554	0.449777	−	0.893141i	$-0.351503\pi$
$3$	14.0227	0.899554	0.449777	+	0.893141i	$0.351503\pi$
$4$	−31.9434	−0.998232
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	3.33516	0.0378215
$7$	13.4367	0.103645	0.0518224	−	0.998656i	$-0.483497\pi$
$7$	13.4367	0.103645	0.0518224	+	0.998656i	$0.483497\pi$
$8$	−15.2083	−0.0840151
$9$	−46.3651	−0.190803
$10$	5.94602	0.0188030
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−447.932	−0.897964
$13$	762.757	1.25178	0.625890	−	0.779911i	$-0.284736\pi$
$13$	762.757	1.25178	0.625890	+	0.779911i	$0.284736\pi$
$14$	3.19579	0.00435771
$15$	350.566	0.402293
$16$	1018.57	0.994700
$17$	−2001.75	−1.67992	−0.839958	−	0.542651i	$-0.817421\pi$
$17$	−2001.75	−1.67992	−0.839958	+	0.542651i	$0.817421\pi$
$18$	−11.0275	−0.00802225
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−798.586	−0.446423
$21$	188.418	0.0932341
$22$	28.7787	0.0126770
$23$	706.337	0.278415	0.139207	−	0.990263i	$-0.455545\pi$
$23$	706.337	0.278415	0.139207	+	0.990263i	$0.455545\pi$
$24$	−213.261	−0.0755761
$25$	625.000	0.200000
$26$	181.415	0.0526307
$27$	−4057.67	−1.07119
$28$	−429.214	−0.103462
$29$	−3930.79	−0.867929	−0.433965	−	0.900930i	$-0.642886\pi$
$29$	−3930.79	−0.867929	−0.433965	+	0.900930i	$0.642886\pi$
$30$	83.3789	0.0169143
$31$	8531.06	1.59441	0.797203	−	0.603711i	$-0.206312\pi$
$31$	8531.06	1.59441	0.797203	+	0.603711i	$0.206312\pi$
$32$	728.925	0.125837
$33$	1696.74	0.271226
$34$	−476.098	−0.0706316
$35$	335.918	0.0463514
$36$	1481.06	0.190466
$37$	880.717	0.105763	0.0528813	−	0.998601i	$-0.483160\pi$
$37$	880.717	0.105763	0.0528813	+	0.998601i	$0.483160\pi$
$38$	85.8605	0.00964571
$39$	10695.9	1.12604
$40$	−380.209	−0.0375727
$41$	2489.76	0.231312	0.115656	−	0.993289i	$-0.463103\pi$
$41$	2489.76	0.231312	0.115656	+	0.993289i	$0.463103\pi$
$42$	44.8135	0.00392000
$43$	12748.2	1.05143	0.525713	−	0.850662i	$-0.323798\pi$
$43$	12748.2	1.05143	0.525713	+	0.850662i	$0.323798\pi$
$44$	−3865.16	−0.300978
$45$	−1159.13	−0.0853297
$46$	167.996	0.0117059
$47$	2796.12	0.184634	0.0923170	−	0.995730i	$-0.470573\pi$
$47$	2796.12	0.184634	0.0923170	+	0.995730i	$0.470573\pi$
$48$	14283.1	0.894786
$49$	−16626.5	−0.989258
$50$	148.650	0.00840894
$51$	−28069.9	−1.51118
$52$	−24365.1	−1.24957
$53$	−4387.76	−0.214562	−0.107281	−	0.994229i	$-0.534214\pi$
$53$	−4387.76	−0.214562	−0.107281	+	0.994229i	$0.534214\pi$
$54$	−965.078	−0.0450379
$55$	3025.00	0.134840
$56$	−204.350	−0.00870772
$57$	5062.18	0.206372
$58$	−934.901	−0.0364918
$59$	−29458.7	−1.10175	−0.550876	−	0.834587i	$-0.685706\pi$
$59$	−29458.7	−1.10175	−0.550876	+	0.834587i	$0.685706\pi$
$60$	−11198.3	−0.401582
$61$	−18677.7	−0.642686	−0.321343	−	0.946963i	$-0.604134\pi$
$61$	−18677.7	−0.642686	−0.321343	+	0.946963i	$0.604134\pi$
$62$	2029.03	0.0670363
$63$	−622.994	−0.0197757
$64$	−32421.0	−0.989409
$65$	19068.9	0.559813
$66$	403.554	0.0114036
$67$	16856.4	0.458753	0.229376	−	0.973338i	$-0.426331\pi$
$67$	16856.4	0.458753	0.229376	+	0.973338i	$0.426331\pi$
$68$	63942.8	1.67695
$69$	9904.73	0.250449
$70$	79.8948	0.00194883
$71$	72654.0	1.71046	0.855231	−	0.518247i	$-0.173415\pi$
$71$	72654.0	1.71046	0.855231	+	0.518247i	$0.173415\pi$
$72$	705.137	0.0160303
$73$	70264.7	1.54323	0.771614	−	0.636092i	$-0.219450\pi$
$73$	70264.7	1.54323	0.771614	+	0.636092i	$0.219450\pi$
$74$	209.470	0.00444675
$75$	8764.16	0.179911
$76$	−11531.6	−0.229010
$77$	1625.84	0.0312501
$78$	2543.92	0.0473441
$79$	−33466.3	−0.603309	−0.301654	−	0.953417i	$-0.597539\pi$
$79$	−33466.3	−0.603309	−0.301654	+	0.953417i	$0.597539\pi$
$80$	25464.3	0.444843
$81$	−45632.5	−0.772791
$82$	592.167	0.00972545
$83$	−2916.82	−0.0464745	−0.0232373	−	0.999730i	$-0.507397\pi$
$83$	−2916.82	−0.0464745	−0.0232373	+	0.999730i	$0.507397\pi$
$84$	−6018.72	−0.0930693
$85$	−50043.8	−0.751281
$86$	3032.05	0.0442069
$87$	−55120.0	−0.780749
$88$	−1840.21	−0.0253315
$89$	−23748.6	−0.317807	−0.158904	−	0.987294i	$-0.550796\pi$
$89$	−23748.6	−0.317807	−0.158904	+	0.987294i	$0.550796\pi$
$90$	−275.688	−0.00358766
$91$	10248.9	0.129740
$92$	−22562.8	−0.277923
$93$	119628.	1.43425
$94$	665.032	0.00776288
$95$	9025.00	0.102598
$96$	10221.5	0.113197
$97$	−13529.3	−0.145997	−0.0729986	−	0.997332i	$-0.523257\pi$
$97$	−13529.3	−0.145997	−0.0729986	+	0.997332i	$0.523257\pi$
$98$	−3954.45	−0.0415930
$99$	−5610.18	−0.0575293
$100$	−19964.6	−0.199646
$101$	141198.	1.37729	0.688645	−	0.725098i	$-0.258206\pi$
$101$	141198.	1.37729	0.688645	+	0.725098i	$0.258206\pi$
$102$	−6676.15	−0.0635369
$103$	−135486.	−1.25835	−0.629174	−	0.777265i	$-0.716607\pi$
$103$	−135486.	−1.25835	−0.629174	+	0.777265i	$0.716607\pi$
$104$	−11600.3	−0.105168
$105$	4710.46	0.0416955
$106$	−1043.59	−0.00902120
$107$	60023.8	0.506832	0.253416	−	0.967357i	$-0.418446\pi$
$107$	60023.8	0.506832	0.253416	+	0.967357i	$0.418446\pi$
$108$	129616.	1.06930
$109$	81401.3	0.656244	0.328122	−	0.944635i	$-0.393584\pi$
$109$	81401.3	0.656244	0.328122	+	0.944635i	$0.393584\pi$
$110$	719.468	0.00566930
$111$	12350.0	0.0951391
$112$	13686.3	0.103095
$113$	134294.	0.989371	0.494685	−	0.869072i	$-0.335283\pi$
$113$	134294.	0.989371	0.494685	+	0.869072i	$0.335283\pi$
$114$	1203.99	0.00867684
$115$	17658.4	0.124511
$116$	125563.	0.866395
$117$	−35365.3	−0.238843
$118$	−7006.49	−0.0463229
$119$	−26896.9	−0.174115
$120$	−5331.54	−0.0337986
$121$	14641.0	0.0909091
$122$	−4442.32	−0.0270215
$123$	34913.1	0.208078
$124$	−272511.	−1.59159
$125$	15625.0	0.0894427
$126$	−148.173	−0.000831465 0
$127$	−232790.	−1.28072	−0.640361	−	0.768074i	$-0.721215\pi$
$127$	−232790.	−1.28072	−0.640361	+	0.768074i	$0.721215\pi$
$128$	−31036.6	−0.167436
$129$	178764.	0.945815
$130$	4535.37	0.0235372
$131$	148739.	0.757262	0.378631	−	0.925548i	$-0.376395\pi$
$131$	148739.	0.757262	0.378631	+	0.925548i	$0.376395\pi$
$132$	−54199.7	−0.270746
$133$	4850.65	0.0237777
$134$	4009.15	0.0192881
$135$	−101442.	−0.479051
$136$	30443.3	0.141138
$137$	286694.	1.30502	0.652510	−	0.757780i	$-0.273716\pi$
$137$	286694.	1.30502	0.652510	+	0.757780i	$0.273716\pi$
$138$	2355.75	0.0105301
$139$	15407.2	0.0676374	0.0338187	−	0.999428i	$-0.489233\pi$
$139$	15407.2	0.0676374	0.0338187	+	0.999428i	$0.489233\pi$
$140$	−10730.4	−0.0462694
$141$	39209.1	0.166088
$142$	17280.1	0.0719158
$143$	92293.6	0.377426
$144$	−47226.3	−0.189792
$145$	−98269.6	−0.388150
$146$	16711.8	0.0648845
$147$	−233147.	−0.889891
$148$	−28133.1	−0.105576
$149$	−58380.9	−0.215430	−0.107715	−	0.994182i	$-0.534353\pi$
$149$	−58380.9	−0.215430	−0.107715	+	0.994182i	$0.534353\pi$
$150$	2084.47	0.00756429
$151$	361236.	1.28928	0.644641	−	0.764485i	$-0.277007\pi$
$151$	361236.	1.28928	0.644641	+	0.764485i	$0.277007\pi$
$152$	−5490.21	−0.0192744
$153$	92811.4	0.320533
$154$	386.691	0.00131390
$155$	213277.	0.713040
$156$	−341663.	−1.12405
$157$	426364.	1.38048	0.690241	−	0.723579i	$-0.257504\pi$
$157$	426364.	1.38048	0.690241	+	0.723579i	$0.257504\pi$
$158$	−7959.64	−0.0253659
$159$	−61528.0	−0.193010
$160$	18223.1	0.0562760
$161$	9490.84	0.0288563
$162$	−10853.3	−0.0324918
$163$	−238502.	−0.703110	−0.351555	−	0.936167i	$-0.614347\pi$
$163$	−238502.	−0.703110	−0.351555	+	0.936167i	$0.614347\pi$
$164$	−79531.6	−0.230903
$165$	42418.5	0.121296
$166$	−693.739	−0.00195401
$167$	412948.	1.14579	0.572894	−	0.819629i	$-0.305821\pi$
$167$	412948.	1.14579	0.572894	+	0.819629i	$0.305821\pi$
$168$	−2865.53	−0.00783307
$169$	210506.	0.566953
$170$	−11902.4	−0.0315874
$171$	−16737.8	−0.0437732
$172$	−407222.	−1.04957
$173$	107449.	0.272951	0.136476	−	0.990643i	$-0.456422\pi$
$173$	107449.	0.272951	0.136476	+	0.990643i	$0.456422\pi$
$174$	−13109.8	−0.0328263
$175$	8397.94	0.0207290
$176$	123247.	0.299913
$177$	−413090.	−0.991086
$178$	−5648.39	−0.0133621
$179$	359439.	0.838480	0.419240	−	0.907875i	$-0.362297\pi$
$179$	359439.	0.838480	0.419240	+	0.907875i	$0.362297\pi$
$180$	37026.5	0.0851788
$181$	−146510.	−0.332407	−0.166204	−	0.986091i	$-0.553151\pi$
$181$	−146510.	−0.332407	−0.166204	+	0.986091i	$0.553151\pi$
$182$	2437.61	0.00545490
$183$	−261911.	−0.578131
$184$	−10742.2	−0.0233910
$185$	22017.9	0.0472985
$186$	28452.4	0.0603028
$187$	−242212.	−0.506514
$188$	−89317.8	−0.184308
$189$	−54521.7	−0.111023
$190$	2146.51	0.00431369
$191$	581639.	1.15364	0.576820	−	0.816871i	$-0.304294\pi$
$191$	581639.	1.15364	0.576820	+	0.816871i	$0.304294\pi$
$192$	−454628.	−0.890027
$193$	795485.	1.53723	0.768615	−	0.639712i	$-0.220946\pi$
$193$	795485.	1.53723	0.768615	+	0.639712i	$0.220946\pi$
$194$	−3217.81	−0.00613841
$195$	267397.	0.503582
$196$	531106.	0.987509
$197$	563252.	1.03404	0.517020	−	0.855973i	$-0.327041\pi$
$197$	563252.	1.03404	0.517020	+	0.855973i	$0.327041\pi$
$198$	−1334.33	−0.00241880
$199$	−431989.	−0.773287	−0.386643	−	0.922229i	$-0.626366\pi$
$199$	−431989.	−0.773287	−0.386643	+	0.922229i	$0.626366\pi$
$200$	−9505.22	−0.0168030
$201$	236372.	0.412673
$202$	33582.7	0.0579078
$203$	−52816.8	−0.0899564
$204$	896648.	1.50850
$205$	62244.1	0.103446
$206$	−32224.0	−0.0529068
$207$	−32749.4	−0.0531224
$208$	776924.	1.24515
$209$	43681.0	0.0691714
$210$	1120.34	0.00175308
$211$	−660940.	−1.02201	−0.511006	−	0.859577i	$-0.670727\pi$
$211$	−660940.	−1.02201	−0.511006	+	0.859577i	$0.670727\pi$
$212$	140160.	0.214183
$213$	1.01880e6	1.53865
$214$	14276.1	0.0213096
$215$	318706.	0.470212
$216$	61710.4	0.0899962
$217$	114629.	0.165252
$218$	19360.5	0.0275916
$219$	985297.	1.38822
$220$	−96628.9	−0.134602
$221$	−1.52685e6	−2.10289
$222$	2937.33	0.00400009
$223$	−460376.	−0.619942	−0.309971	−	0.950746i	$-0.600319\pi$
$223$	−460376.	−0.619942	−0.309971	+	0.950746i	$0.600319\pi$
$224$	9794.35	0.0130423
$225$	−28978.2	−0.0381606
$226$	31940.5	0.0415978
$227$	−416351.	−0.536285	−0.268142	−	0.963379i	$-0.586410\pi$
$227$	−416351.	−0.536285	−0.268142	+	0.963379i	$0.586410\pi$
$228$	−161703.	−0.206007
$229$	833444.	1.05024	0.525119	−	0.851029i	$-0.324021\pi$
$229$	833444.	1.05024	0.525119	+	0.851029i	$0.324021\pi$
$230$	4199.89	0.00523502
$231$	22798.6	0.0281111
$232$	59780.8	0.0729191
$233$	−835699.	−1.00846	−0.504232	−	0.863568i	$-0.668224\pi$
$233$	−835699.	−1.00846	−0.504232	+	0.863568i	$0.668224\pi$
$234$	−8411.32	−0.0100421
$235$	69903.1	0.0825709
$236$	941013.	1.09981
$237$	−469286.	−0.542709
$238$	−6397.18	−0.00732059
$239$	1.25316e6	1.41910	0.709550	−	0.704655i	$-0.248898\pi$
$239$	1.25316e6	1.41910	0.709550	+	0.704655i	$0.248898\pi$
$240$	357077.	0.400160
$241$	203482.	0.225675	0.112838	−	0.993613i	$-0.464006\pi$
$241$	203482.	0.225675	0.112838	+	0.993613i	$0.464006\pi$
$242$	3482.23	0.00382224
$243$	346124.	0.376024
$244$	596630.	0.641550
$245$	−415661.	−0.442410
$246$	8303.75	0.00874856
$247$	275355.	0.287178
$248$	−129743.	−0.133954
$249$	−40901.6	−0.0418063
$250$	3716.26	0.00376059
$251$	594133.	0.595250	0.297625	−	0.954683i	$-0.403806\pi$
$251$	594133.	0.595250	0.297625	+	0.954683i	$0.403806\pi$
$252$	19900.6	0.0197408
$253$	85466.8	0.0839453
$254$	−55367.0	−0.0538476
$255$	−701746.	−0.675818
$256$	1.03009e6	0.982369
$257$	1.19242e6	1.12615	0.563076	−	0.826405i	$-0.309618\pi$
$257$	1.19242e6	1.12615	0.563076	+	0.826405i	$0.309618\pi$
$258$	42517.4	0.0397665
$259$	11833.9	0.0109617
$260$	−609127.	−0.558823
$261$	182251.	0.165603
$262$	35376.2	0.0318389
$263$	735505.	0.655687	0.327843	−	0.944732i	$-0.393678\pi$
$263$	735505.	0.655687	0.327843	+	0.944732i	$0.393678\pi$
$264$	−25804.6	−0.0227870
$265$	−109694.	−0.0959551
$266$	1153.68	0.000999728 0
$267$	−333019.	−0.285885
$268$	−538452.	−0.457942
$269$	1.17187e6	0.987410	0.493705	−	0.869629i	$-0.335642\pi$
$269$	1.17187e6	0.987410	0.493705	+	0.869629i	$0.335642\pi$
$270$	−24127.0	−0.0201416
$271$	−1.88984e6	−1.56315	−0.781576	−	0.623810i	$-0.785584\pi$
$271$	−1.88984e6	−1.56315	−0.781576	+	0.623810i	$0.785584\pi$
$272$	−2.03893e6	−1.67101
$273$	143717.	0.116709
$274$	68187.5	0.0548692
$275$	75625.0	0.0603023
$276$	−316391.	−0.250007
$277$	−48565.1	−0.0380298	−0.0190149	−	0.999819i	$-0.506053\pi$
$277$	−48565.1	−0.0380298	−0.0190149	+	0.999819i	$0.506053\pi$
$278$	3664.46	0.00284379
$279$	−395544.	−0.304217
$280$	−5108.75	−0.00389421
$281$	−379736.	−0.286890	−0.143445	−	0.989658i	$-0.545818\pi$
$281$	−379736.	−0.286890	−0.143445	+	0.989658i	$0.545818\pi$
$282$	9325.52	0.00698313
$283$	−2.61231e6	−1.93891	−0.969457	−	0.245263i	$-0.921126\pi$
$283$	−2.61231e6	−1.93891	−0.969457	+	0.245263i	$0.921126\pi$
$284$	−2.32082e6	−1.70744
$285$	126554.	0.0922923
$286$	21951.2	0.0158688
$287$	33454.2	0.0239743
$288$	−33796.7	−0.0240101
$289$	2.58715e6	1.82212
$290$	−23372.5	−0.0163196
$291$	−189716.	−0.131332
$292$	−2.24449e6	−1.54050
$293$	1.56047e6	1.06191	0.530954	−	0.847401i	$-0.321834\pi$
$293$	1.56047e6	1.06191	0.530954	+	0.847401i	$0.321834\pi$
$294$	−55451.9	−0.0374152
$295$	−736469.	−0.492719
$296$	−13394.2	−0.00888565
$297$	−490978.	−0.322976
$298$	−13885.4	−0.00905767
$299$	538764.	0.348514
$300$	−279957.	−0.179593
$301$	171294.	0.108975
$302$	85916.5	0.0542075
$303$	1.97997e6	1.23895
$304$	367705.	0.228200
$305$	−466943.	−0.287418
$306$	22074.3	0.0134767
$307$	2.63622e6	1.59638	0.798189	−	0.602407i	$-0.205792\pi$
$307$	2.63622e6	1.59638	0.798189	+	0.602407i	$0.205792\pi$
$308$	−51934.9	−0.0311948
$309$	−1.89987e6	−1.13195
$310$	50725.9	0.0299796
$311$	2.44311e6	1.43233	0.716163	−	0.697933i	$-0.245897\pi$
$311$	2.44311e6	1.43233	0.716163	+	0.697933i	$0.245897\pi$
$312$	−162667.	−0.0946046
$313$	−3.05748e6	−1.76402	−0.882008	−	0.471234i	$-0.843809\pi$
$313$	−3.05748e6	−1.76402	−0.882008	+	0.471234i	$0.843809\pi$
$314$	101407.	0.0580420
$315$	−15574.9	−0.00884398
$316$	1.06903e6	0.602242
$317$	1.87160e6	1.04608	0.523041	−	0.852307i	$-0.324797\pi$
$317$	1.87160e6	1.04608	0.523041	+	0.852307i	$0.324797\pi$
$318$	−14633.9	−0.00811505
$319$	−475625.	−0.261691
$320$	−810524.	−0.442477
$321$	841693.	0.455923
$322$	2257.31	0.00121325
$323$	−722632.	−0.385399
$324$	1.45766e6	0.771425
$325$	476723.	0.250356
$326$	−56725.5	−0.0295620
$327$	1.14146e6	0.590327
$328$	−37865.2	−0.0194337
$329$	37570.7	0.0191364
$330$	10088.9	0.00509984
$331$	2.95191e6	1.48093	0.740463	−	0.672097i	$-0.234606\pi$
$331$	2.95191e6	1.48093	0.740463	+	0.672097i	$0.234606\pi$
$332$	93173.4	0.0463924
$333$	−40834.5	−0.0201798
$334$	98215.9	0.0481743
$335$	421411.	0.205161
$336$	191918.	0.0927399
$337$	−1.09405e6	−0.524761	−0.262381	−	0.964964i	$-0.584508\pi$
$337$	−1.09405e6	−0.524761	−0.262381	+	0.964964i	$0.584508\pi$
$338$	50066.8	0.0238374
$339$	1.88315e6	0.889992
$340$	1.59857e6	0.749953
$341$	1.03226e6	0.480732
$342$	−3980.93	−0.00184043
$343$	−449235.	−0.206176
$344$	−193880.	−0.0883357
$345$	247618.	0.112004
$346$	25555.6	0.0114762
$347$	−3.39515e6	−1.51368	−0.756841	−	0.653599i	$-0.773259\pi$
$347$	−3.39515e6	−1.51368	−0.756841	+	0.653599i	$0.773259\pi$
$348$	1.76072e6	0.779369
$349$	3.42781e6	1.50644	0.753221	−	0.657767i	$-0.228499\pi$
$349$	3.42781e6	1.50644	0.753221	+	0.657767i	$0.228499\pi$
$350$	1997.37	0.000871543 0
$351$	−3.09502e6	−1.34090
$352$	88199.9	0.0379413
$353$	−535037.	−0.228532	−0.114266	−	0.993450i	$-0.536452\pi$
$353$	−535037.	−0.228532	−0.114266	+	0.993450i	$0.536452\pi$
$354$	−98249.6	−0.0416699
$355$	1.81635e6	0.764942
$356$	758613.	0.317245
$357$	−377166.	−0.156625
$358$	85489.2	0.0352536
$359$	−725648.	−0.297160	−0.148580	−	0.988900i	$-0.547470\pi$
$359$	−725648.	−0.297160	−0.148580	+	0.988900i	$0.547470\pi$
$360$	17628.4	0.00716898
$361$	130321.	0.0526316
$362$	−34846.0	−0.0139760
$363$	205306.	0.0817776
$364$	−327386.	−0.129511
$365$	1.75662e6	0.690152
$366$	−62293.1	−0.0243073
$367$	2.75169e6	1.06644	0.533218	−	0.845978i	$-0.320982\pi$
$367$	2.75169e6	1.06644	0.533218	+	0.845978i	$0.320982\pi$
$368$	719456.	0.276939
$369$	−115438.	−0.0441350
$370$	5236.76	0.00198865
$371$	−58957.0	−0.0222383
$372$	−3.82133e6	−1.43172
$373$	1.67257e6	0.622463	0.311231	−	0.950334i	$-0.399259\pi$
$373$	1.67257e6	0.622463	0.311231	+	0.950334i	$0.399259\pi$
$374$	−57607.8	−0.0212962
$375$	219104.	0.0804585
$376$	−42524.4	−0.0155120
$377$	−2.99823e6	−1.08646
$378$	−12967.5	−0.00466795
$379$	−3.18070e6	−1.13743	−0.568715	−	0.822535i	$-0.692559\pi$
$379$	−3.18070e6	−1.13743	−0.568715	+	0.822535i	$0.692559\pi$
$380$	−288289.	−0.102416
$381$	−3.26434e6	−1.15208
$382$	138337.	0.0485044
$383$	−1.98368e6	−0.690994	−0.345497	−	0.938420i	$-0.612290\pi$
$383$	−1.98368e6	−0.690994	−0.345497	+	0.938420i	$0.612290\pi$
$384$	−435216.	−0.150618
$385$	40646.0	0.0139755
$386$	189199.	0.0646323
$387$	−591074.	−0.200615
$388$	432171.	0.145739
$389$	3.25286e6	1.08991	0.544956	−	0.838464i	$-0.316546\pi$
$389$	3.25286e6	1.08991	0.544956	+	0.838464i	$0.316546\pi$
$390$	63597.9	0.0211729
$391$	−1.41391e6	−0.467714
$392$	252861.	0.0831125
$393$	2.08571e6	0.681198
$394$	133964.	0.0434759
$395$	−836657.	−0.269808
$396$	179208.	0.0574276
$397$	2.96793e6	0.945100	0.472550	−	0.881304i	$-0.343334\pi$
$397$	2.96793e6	0.945100	0.472550	+	0.881304i	$0.343334\pi$
$398$	−102745.	−0.0325126
$399$	68019.0	0.0213894
$400$	636608.	0.198940
$401$	−2.20884e6	−0.685966	−0.342983	−	0.939342i	$-0.611437\pi$
$401$	−2.20884e6	−0.685966	−0.342983	+	0.939342i	$0.611437\pi$
$402$	56218.9	0.0173507
$403$	6.50713e6	1.99585
$404$	−4.51035e6	−1.37486
$405$	−1.14081e6	−0.345603
$406$	−12562.0	−0.00378219
$407$	106567.	0.0318886
$408$	426896.	0.126961
$409$	−3.01941e6	−0.892510	−0.446255	−	0.894906i	$-0.647243\pi$
$409$	−3.01941e6	−0.892510	−0.446255	+	0.894906i	$0.647243\pi$
$410$	14804.2	0.00434935
$411$	4.02021e6	1.17394
$412$	4.32788e6	1.25612
$413$	−395828.	−0.114191
$414$	−7789.14	−0.00223352
$415$	−72920.6	−0.0207840
$416$	555993.	0.157520
$417$	216050.	0.0608435
$418$	10389.1	0.00290829
$419$	4.61737e6	1.28487	0.642436	−	0.766339i	$-0.277924\pi$
$419$	4.61737e6	1.28487	0.642436	+	0.766339i	$0.277924\pi$
$420$	−150468.	−0.0416218
$421$	3.73590e6	1.02728	0.513642	−	0.858005i	$-0.328296\pi$
$421$	3.73590e6	1.02728	0.513642	+	0.858005i	$0.328296\pi$
$422$	−157198.	−0.0429702
$423$	−129643.	−0.0352287
$424$	66730.6	0.0180265
$425$	−1.25109e6	−0.335983
$426$	242312.	0.0646922
$427$	−250967.	−0.0666111
$428$	−1.91737e6	−0.505936
$429$	1.29420e6	0.339515
$430$	75801.2	0.0197699
$431$	3.42690e6	0.888604	0.444302	−	0.895877i	$-0.353452\pi$
$431$	3.42690e6	0.888604	0.444302	+	0.895877i	$0.353452\pi$
$432$	−4.13303e6	−1.06551
$433$	−3.40551e6	−0.872897	−0.436448	−	0.899729i	$-0.643764\pi$
$433$	−3.40551e6	−0.872897	−0.436448	+	0.899729i	$0.643764\pi$
$434$	27263.5	0.00694797
$435$	−1.37800e6	−0.349162
$436$	−2.60024e6	−0.655084
$437$	254988.	0.0638728
$438$	234344.	0.0583671
$439$	2.01604e6	0.499274	0.249637	−	0.968340i	$-0.419689\pi$
$439$	2.01604e6	0.499274	0.249637	+	0.968340i	$0.419689\pi$
$440$	−46005.3	−0.0113286
$441$	770888.	0.188753
$442$	−363147.	−0.0884152
$443$	2.62765e6	0.636147	0.318074	−	0.948066i	$-0.396964\pi$
$443$	2.62765e6	0.636147	0.318074	+	0.948066i	$0.396964\pi$
$444$	−394501.	−0.0949709
$445$	−593716.	−0.142128
$446$	−109496.	−0.0260653
$447$	−818655.	−0.193790
$448$	−435631.	−0.102547
$449$	501196.	0.117325	0.0586626	−	0.998278i	$-0.481316\pi$
$449$	501196.	0.117325	0.0586626	+	0.998278i	$0.481316\pi$
$450$	−6892.20	−0.00160445
$451$	301261.	0.0697432
$452$	−4.28980e6	−0.987622
$453$	5.06548e6	1.15978
$454$	−99025.3	−0.0225479
$455$	256224.	0.0580217
$456$	−76987.4	−0.0173383
$457$	−1.95026e6	−0.436820	−0.218410	−	0.975857i	$-0.570087\pi$
$457$	−1.95026e6	−0.436820	−0.218410	+	0.975857i	$0.570087\pi$
$458$	198227.	0.0441570
$459$	8.12244e6	1.79951
$460$	−564071.	−0.124291
$461$	−14514.4	−0.00318087	−0.00159043	−	0.999999i	$-0.500506\pi$
$461$	−14514.4	−0.00318087	−0.00159043	+	0.999999i	$0.500506\pi$
$462$	5422.44	0.00118192
$463$	6.72963e6	1.45894	0.729472	−	0.684011i	$-0.239766\pi$
$463$	6.72963e6	1.45894	0.729472	+	0.684011i	$0.239766\pi$
$464$	−4.00379e6	−0.863329
$465$	2.99070e6	0.641418
$466$	−198763.	−0.0424005
$467$	−4.14046e6	−0.878530	−0.439265	−	0.898357i	$-0.644761\pi$
$467$	−4.14046e6	−0.878530	−0.439265	+	0.898357i	$0.644761\pi$
$468$	1.12969e6	0.238421
$469$	226495.	0.0475474
$470$	16625.8	0.00347167
$471$	5.97875e6	1.24182
$472$	448019.	0.0925638
$473$	1.54254e6	0.317017
$474$	−111615.	−0.0228180
$475$	225625.	0.0458831
$476$	859180.	0.173807
$477$	203439.	0.0409391
$478$	298053.	0.0596657
$479$	1.99457e6	0.397202	0.198601	−	0.980080i	$-0.436360\pi$
$479$	1.99457e6	0.397202	0.198601	+	0.980080i	$0.436360\pi$
$480$	255537.	0.0506233
$481$	671773.	0.132391
$482$	48396.4	0.00948845
$483$	133087.	0.0259578
$484$	−467684.	−0.0907484
$485$	−338231.	−0.0652919
$486$	82322.3	0.0158098
$487$	−832253.	−0.159013	−0.0795065	−	0.996834i	$-0.525334\pi$
$487$	−832253.	−0.159013	−0.0795065	+	0.996834i	$0.525334\pi$
$488$	284057.	0.0539953
$489$	−3.34443e6	−0.632485
$490$	−98861.2	−0.0186010
$491$	−2.73598e6	−0.512165	−0.256082	−	0.966655i	$-0.582432\pi$
$491$	−2.73598e6	−0.512165	−0.256082	+	0.966655i	$0.582432\pi$
$492$	−1.11524e6	−0.207710
$493$	7.86845e6	1.45805
$494$	65490.7	0.0120743
$495$	−140255.	−0.0257279
$496$	8.68951e6	1.58596
$497$	976229.	0.177280
$498$	−9728.07	−0.00175773
$499$	−3.85719e6	−0.693458	−0.346729	−	0.937965i	$-0.612708\pi$
$499$	−3.85719e6	−0.693458	−0.346729	+	0.937965i	$0.612708\pi$
$500$	−499116.	−0.0892846
$501$	5.79063e6	1.03070
$502$	141309.	0.0250271
$503$	1.84439e6	0.325038	0.162519	−	0.986705i	$-0.448038\pi$
$503$	1.84439e6	0.325038	0.162519	+	0.986705i	$0.448038\pi$
$504$	9474.72	0.00166146
$505$	3.52995e6	0.615943
$506$	20327.5	0.00352945
$507$	2.95185e6	0.510004
$508$	7.43611e6	1.27846
$509$	7.89689e6	1.35102	0.675509	−	0.737351i	$-0.263924\pi$
$509$	7.89689e6	1.35102	0.675509	+	0.737351i	$0.263924\pi$
$510$	−166904.	−0.0284146
$511$	944125.	0.159947
$512$	1.23817e6	0.208740
$513$	−1.46482e6	−0.245748
$514$	283606.	0.0473487
$515$	−3.38714e6	−0.562750
$516$	−5.71034e6	−0.944143
$517$	338331.	0.0556693
$518$	2814.59	0.000460883 0
$519$	1.50671e6	0.245534
$520$	−290007.	−0.0470327
$521$	6.41862e6	1.03597	0.517986	−	0.855389i	$-0.326682\pi$
$521$	6.41862e6	1.03597	0.517986	+	0.855389i	$0.326682\pi$
$522$	43346.8	0.00696275
$523$	−2.64741e6	−0.423220	−0.211610	−	0.977354i	$-0.567871\pi$
$523$	−2.64741e6	−0.423220	−0.211610	+	0.977354i	$0.567871\pi$
$524$	−4.75123e6	−0.755924
$525$	117761.	0.0186468
$526$	174933.	0.0275681
$527$	−1.70771e7	−2.67847
$528$	1.72825e6	0.269788
$529$	−5.93743e6	−0.922485
$530$	−26089.7	−0.00403440
$531$	1.36586e6	0.210218
$532$	−154946.	−0.0237357
$533$	1.89908e6	0.289552
$534$	−79205.4	−0.0120199
$535$	1.50059e6	0.226662
$536$	−256359.	−0.0385421
$537$	5.04029e6	0.754258
$538$	278718.	0.0415154
$539$	−2.01180e6	−0.298272
$540$	3.24040e6	0.478204
$541$	9.91923e6	1.45708	0.728542	−	0.685001i	$-0.240198\pi$
$541$	9.91923e6	1.45708	0.728542	+	0.685001i	$0.240198\pi$
$542$	−449480.	−0.0657222
$543$	−2.05446e6	−0.299018
$544$	−1.45913e6	−0.211395
$545$	2.03503e6	0.293481
$546$	34181.8	0.00490697
$547$	−9.93545e6	−1.41977	−0.709887	−	0.704315i	$-0.751254\pi$
$547$	−9.93545e6	−1.41977	−0.709887	+	0.704315i	$0.751254\pi$
$548$	−9.15799e6	−1.30271
$549$	865994.	0.122626
$550$	17986.7	0.00253539
$551$	−1.41901e6	−0.199117
$552$	−150635.	−0.0210415
$553$	−449676.	−0.0625298
$554$	−11550.7	−0.00159895
$555$	308750.	0.0425475
$556$	−492159.	−0.0675179
$557$	−3.13866e6	−0.428653	−0.214327	−	0.976762i	$-0.568756\pi$
$557$	−3.13866e6	−0.428653	−0.214327	+	0.976762i	$0.568756\pi$
$558$	−94076.4	−0.0127907
$559$	9.72381e6	1.31615
$560$	342156.	0.0461057
$561$	−3.39645e6	−0.455636
$562$	−90316.6	−0.0120622
$563$	6.58190e6	0.875145	0.437572	−	0.899183i	$-0.355838\pi$
$563$	6.58190e6	0.875145	0.437572	+	0.899183i	$0.355838\pi$
$564$	−1.25247e6	−0.165795
$565$	3.35734e6	0.442460
$566$	−621313.	−0.0815210
$567$	−613151.	−0.0800958
$568$	−1.10495e6	−0.143705
$569$	−2.23838e6	−0.289837	−0.144918	−	0.989444i	$-0.546292\pi$
$569$	−2.23838e6	−0.289837	−0.144918	+	0.989444i	$0.546292\pi$
$570$	30099.8	0.00388040
$571$	1.00359e7	1.28815	0.644077	−	0.764961i	$-0.277242\pi$
$571$	1.00359e7	1.28815	0.644077	+	0.764961i	$0.277242\pi$
$572$	−2.94818e6	−0.376759
$573$	8.15612e6	1.03776
$574$	7956.77	0.00100799
$575$	441461.	0.0556830
$576$	1.50320e6	0.188782
$577$	−1.31917e7	−1.64953	−0.824764	−	0.565477i	$-0.808692\pi$
$577$	−1.31917e7	−1.64953	−0.824764	+	0.565477i	$0.808692\pi$
$578$	615329.	0.0766104
$579$	1.11548e7	1.38282
$580$	3.13907e6	0.387464
$581$	−39192.5	−0.00481684
$582$	−45122.2	−0.00552183
$583$	−530919.	−0.0646929
$584$	−1.06861e6	−0.129654
$585$	−884133.	−0.106814
$586$	371143.	0.0446476
$587$	−2.64077e6	−0.316326	−0.158163	−	0.987413i	$-0.550557\pi$
$587$	−2.64077e6	−0.316326	−0.158163	+	0.987413i	$0.550557\pi$
$588$	7.44752e6	0.888317
$589$	3.07971e6	0.365782
$590$	−175162.	−0.0207162
$591$	7.89829e6	0.930175
$592$	897074.	0.105202
$593$	−3.07163e6	−0.358701	−0.179351	−	0.983785i	$-0.557400\pi$
$593$	−3.07163e6	−0.358701	−0.179351	+	0.983785i	$0.557400\pi$
$594$	−116774.	−0.0135794
$595$	−672423.	−0.0778664
$596$	1.86489e6	0.215049
$597$	−6.05764e6	−0.695613
$598$	128140.	0.0146532
$599$	−9.95471e6	−1.13360	−0.566802	−	0.823854i	$-0.691820\pi$
$599$	−9.95471e6	−1.13360	−0.566802	+	0.823854i	$0.691820\pi$
$600$	−133288.	−0.0151152
$601$	2.54692e6	0.287627	0.143813	−	0.989605i	$-0.454064\pi$
$601$	2.54692e6	0.287627	0.143813	+	0.989605i	$0.454064\pi$
$602$	40740.7	0.00458182
$603$	−781551.	−0.0875314
$604$	−1.15391e7	−1.28700
$605$	366025.	0.0406558
$606$	470918.	0.0520912
$607$	1.26844e7	1.39733	0.698664	−	0.715450i	$-0.253778\pi$
$607$	1.26844e7	1.39733	0.698664	+	0.715450i	$0.253778\pi$
$608$	263142.	0.0288690
$609$	−740632.	−0.0809206
$610$	−111058.	−0.0120844
$611$	2.13276e6	0.231121
$612$	−2.96472e6	−0.319966
$613$	−7.37808e6	−0.793035	−0.396518	−	0.918027i	$-0.629781\pi$
$613$	−7.37808e6	−0.793035	−0.396518	+	0.918027i	$0.629781\pi$
$614$	627000.	0.0671192
$615$	872827.	0.0930552
$616$	−24726.4	−0.00262548
$617$	9.02256e6	0.954151	0.477075	−	0.878862i	$-0.341697\pi$
$617$	9.02256e6	0.954151	0.477075	+	0.878862i	$0.341697\pi$
$618$	−451866.	−0.0475925
$619$	−2.58008e6	−0.270649	−0.135325	−	0.990801i	$-0.543208\pi$
$619$	−2.58008e6	−0.270649	−0.135325	+	0.990801i	$0.543208\pi$
$620$	−6.81279e6	−0.711780
$621$	−2.86608e6	−0.298236
$622$	581071.	0.0602217
$623$	−319103.	−0.0329391
$624$	1.08945e7	1.12008
$625$	390625.	0.0400000
$626$	−727193.	−0.0741675
$627$	612524.	0.0622234
$628$	−1.36195e7	−1.37804
$629$	−1.76298e6	−0.177672
$630$	−3704.33	−0.000371842 0
$631$	−1.31123e7	−1.31101	−0.655504	−	0.755192i	$-0.727544\pi$
$631$	−1.31123e7	−1.31101	−0.655504	+	0.755192i	$0.727544\pi$
$632$	508967.	0.0506870
$633$	−9.26813e6	−0.919355
$634$	445144.	0.0439822
$635$	−5.81975e6	−0.572757
$636$	1.96542e6	0.192669
$637$	−1.26819e7	−1.23833
$638$	−113123.	−0.0110027
$639$	−3.36861e6	−0.326361
$640$	−775916.	−0.0748798
$641$	−1.64330e7	−1.57969	−0.789845	−	0.613306i	$-0.789839\pi$
$641$	−1.64330e7	−1.57969	−0.789845	+	0.613306i	$0.789839\pi$
$642$	200189.	0.0191691
$643$	−4.28158e6	−0.408392	−0.204196	−	0.978930i	$-0.565458\pi$
$643$	−4.28158e6	−0.408392	−0.204196	+	0.978930i	$0.565458\pi$
$644$	−303170.	−0.0288053
$645$	4.46910e6	0.422981
$646$	−171871.	−0.0162040
$647$	−1.04162e7	−0.978251	−0.489125	−	0.872213i	$-0.662684\pi$
$647$	−1.04162e7	−0.978251	−0.489125	+	0.872213i	$0.662684\pi$
$648$	693996.	0.0649261
$649$	−3.56451e6	−0.332191
$650$	113384.	0.0105261
$651$	1.60741e6	0.148653
$652$	7.61857e6	0.701867
$653$	4.78986e6	0.439582	0.219791	−	0.975547i	$-0.429463\pi$
$653$	4.78986e6	0.439582	0.219791	+	0.975547i	$0.429463\pi$
$654$	271486.	0.0248201
$655$	3.71847e6	0.338658
$656$	2.53600e6	0.230086
$657$	−3.25783e6	−0.294452
$658$	8935.84	0.000804582 0
$659$	−6.78319e6	−0.608444	−0.304222	−	0.952601i	$-0.598397\pi$
$659$	−6.78319e6	−0.608444	−0.304222	+	0.952601i	$0.598397\pi$
$660$	−1.35499e6	−0.121081
$661$	2.77654e6	0.247172	0.123586	−	0.992334i	$-0.460560\pi$
$661$	2.77654e6	0.247172	0.123586	+	0.992334i	$0.460560\pi$
$662$	702085.	0.0622651
$663$	−2.14105e7	−1.89166
$664$	44360.1	0.00390456
$665$	121266.	0.0106337
$666$	−9712.12	−0.000848454 0
$667$	−2.77646e6	−0.241644
$668$	−1.31910e7	−1.14376
$669$	−6.45570e6	−0.557671
$670$	100229.	0.00862591
$671$	−2.26000e6	−0.193777
$672$	137343.	0.0117323
$673$	−1.59547e7	−1.35785	−0.678923	−	0.734209i	$-0.737553\pi$
$673$	−1.59547e7	−1.35785	−0.678923	+	0.734209i	$0.737553\pi$
$674$	−260209.	−0.0220634
$675$	−2.53604e6	−0.214238
$676$	−6.72427e6	−0.565950
$677$	9566.55	0.000802202 0	0.000401101	−	1.00000i	$-0.499872\pi$
$677$	9566.55	0.000802202 0	0.000401101		1.00000i	$0.499872\pi$
$678$	447890.	0.0374195
$679$	−181789.	−0.0151318
$680$	761083.	0.0631189
$681$	−5.83835e6	−0.482417
$682$	245513.	0.0202122
$683$	−1.92293e7	−1.57729	−0.788644	−	0.614850i	$-0.789217\pi$
$683$	−1.92293e7	−1.57729	−0.788644	+	0.614850i	$0.789217\pi$
$684$	534663.	0.0436958
$685$	7.16735e6	0.583623
$686$	−106846.	−0.00866862
$687$	1.16871e7	0.944746
$688$	1.29850e7	1.04585
$689$	−3.34680e6	−0.268585
$690$	58893.7	0.00470919
$691$	−3.69107e6	−0.294074	−0.147037	−	0.989131i	$-0.546974\pi$
$691$	−3.69107e6	−0.294074	−0.147037	+	0.989131i	$0.546974\pi$
$692$	−3.43227e6	−0.272469
$693$	−75382.3	−0.00596261
$694$	−807504.	−0.0636423
$695$	385180.	0.0302484
$696$	838285.	0.0655947
$697$	−4.98388e6	−0.388585
$698$	815272.	0.0633379
$699$	−1.17187e7	−0.907167
$700$	−268259.	−0.0206923
$701$	−6.16999e6	−0.474230	−0.237115	−	0.971482i	$-0.576202\pi$
$701$	−6.16999e6	−0.474230	−0.237115	+	0.971482i	$0.576202\pi$
$702$	−736121.	−0.0563775
$703$	317939.	0.0242636
$704$	−3.92294e6	−0.298318
$705$	980227.	0.0742769
$706$	−127254.	−0.00960857
$707$	1.89724e6	0.142749
$708$	1.31955e7	0.989334
$709$	−1.61376e7	−1.20565	−0.602827	−	0.797872i	$-0.705959\pi$
$709$	−1.61376e7	−1.20565	−0.602827	+	0.797872i	$0.705959\pi$
$710$	432002.	0.0321617
$711$	1.55167e6	0.115113
$712$	361178.	0.0267006
$713$	6.02581e6	0.443907
$714$	−89705.5	−0.00658527
$715$	2.30734e6	0.168790
$716$	−1.14817e7	−0.836998
$717$	1.75727e7	1.27656
$718$	−172589.	−0.0124940
$719$	2.06581e7	1.49028	0.745142	−	0.666906i	$-0.232382\pi$
$719$	2.06581e7	1.49028	0.745142	+	0.666906i	$0.232382\pi$
$720$	−1.18066e6	−0.0848774
$721$	−1.82048e6	−0.130421
$722$	30995.6	0.00221288
$723$	2.85336e6	0.203007
$724$	4.68003e6	0.331820
$725$	−2.45674e6	−0.173586
$726$	48830.0	0.00343831
$727$	−1.80431e7	−1.26612	−0.633060	−	0.774103i	$-0.718201\pi$
$727$	−1.80431e7	−1.26612	−0.633060	+	0.774103i	$0.718201\pi$
$728$	−155869.	−0.0109002
$729$	1.59423e7	1.11105
$730$	417795.	0.0290172
$731$	−2.55188e7	−1.76631
$732$	8.36634e6	0.577109
$733$	−3.18991e6	−0.219290	−0.109645	−	0.993971i	$-0.534971\pi$
$733$	−3.18991e6	−0.219290	−0.109645	+	0.993971i	$0.534971\pi$
$734$	654465.	0.0448380
$735$	−5.82868e6	−0.397971
$736$	514867.	0.0350349
$737$	2.03963e6	0.138319
$738$	−27455.9	−0.00185564
$739$	5.03450e6	0.339114	0.169557	−	0.985520i	$-0.445766\pi$
$739$	5.03450e6	0.339114	0.169557	+	0.985520i	$0.445766\pi$
$740$	−703328.	−0.0472148
$741$	3.86121e6	0.258332
$742$	−14022.4	−0.000935001 0
$743$	1.29496e7	0.860569	0.430284	−	0.902693i	$-0.358413\pi$
$743$	1.29496e7	0.860569	0.430284	+	0.902693i	$0.358413\pi$
$744$	−1.81935e6	−0.120499
$745$	−1.45952e6	−0.0963430
$746$	397806.	0.0261712
$747$	135239.	0.00886748
$748$	7.73708e6	0.505618
$749$	806522.	0.0525305
$750$	52111.8	0.00338285
$751$	−2.56649e7	−1.66050	−0.830251	−	0.557390i	$-0.811803\pi$
$751$	−2.56649e7	−1.66050	−0.830251	+	0.557390i	$0.811803\pi$
$752$	2.84806e6	0.183655
$753$	8.33132e6	0.535459
$754$	−713102.	−0.0456797
$755$	9.03089e6	0.576585
$756$	1.74161e6	0.110827
$757$	−9.78629e6	−0.620695	−0.310347	−	0.950623i	$-0.600445\pi$
$757$	−9.78629e6	−0.620695	−0.310347	+	0.950623i	$0.600445\pi$
$758$	−756500.	−0.0478229
$759$	1.19847e6	0.0755133
$760$	−137255.	−0.00861976
$761$	1.22546e7	0.767073	0.383536	−	0.923526i	$-0.374706\pi$
$761$	1.22546e7	0.767073	0.383536	+	0.923526i	$0.374706\pi$
$762$	−776392.	−0.0484388
$763$	1.09377e6	0.0680163
$764$	−1.85795e7	−1.15160
$765$	2.32029e6	0.143347
$766$	−471799.	−0.0290526
$767$	−2.24699e7	−1.37915
$768$	1.44446e7	0.883694
$769$	−3.08185e7	−1.87930	−0.939650	−	0.342138i	$-0.888849\pi$
$769$	−3.08185e7	−1.87930	−0.939650	+	0.342138i	$0.888849\pi$
$770$	9667.28	0.000587594 0
$771$	1.67209e7	1.01303
$772$	−2.54105e7	−1.53451
$773$	−2.39580e7	−1.44212	−0.721061	−	0.692871i	$-0.756345\pi$
$773$	−2.39580e7	−1.44212	−0.721061	+	0.692871i	$0.756345\pi$
$774$	−140581.	−0.00843481
$775$	5.33192e6	0.318881
$776$	205758.	0.0122660
$777$	165943.	0.00986068
$778$	773663.	0.0458250
$779$	898804.	0.0530666
$780$	−8.54158e6	−0.502692
$781$	8.79113e6	0.515724
$782$	−336286.	−0.0196649
$783$	1.59498e7	0.929718
$784$	−1.69353e7	−0.984015
$785$	1.06591e7	0.617371
$786$	496068.	0.0286408
$787$	−1.06543e7	−0.613178	−0.306589	−	0.951842i	$-0.599188\pi$
$787$	−1.06543e7	−0.613178	−0.306589	+	0.951842i	$0.599188\pi$
$788$	−1.79922e7	−1.03221
$789$	1.03137e7	0.589825
$790$	−198991.	−0.0113440
$791$	1.80446e6	0.102543
$792$	85321.6	0.00483332
$793$	−1.42466e7	−0.804502
$794$	705895.	0.0397364
$795$	−1.53820e6	−0.0863168
$796$	1.37992e7	0.771920
$797$	−2.29416e7	−1.27932	−0.639658	−	0.768660i	$-0.720924\pi$
$797$	−2.29416e7	−1.27932	−0.639658	+	0.768660i	$0.720924\pi$
$798$	16177.7	0.000899309 0
$799$	−5.59714e6	−0.310170
$800$	455578.	0.0251674
$801$	1.10111e6	0.0606385
$802$	−525351.	−0.0288412
$803$	8.50202e6	0.465300
$804$	−7.55053e6	−0.411943
$805$	237271.	0.0129049
$806$	1.54766e6	0.0839147
$807$	1.64327e7	0.888229
$808$	−2.14739e6	−0.115713
$809$	−2.22454e7	−1.19500	−0.597501	−	0.801868i	$-0.703840\pi$
$809$	−2.22454e7	−1.19500	−0.597501	+	0.801868i	$0.703840\pi$
$810$	−271332.	−0.0145308
$811$	−3.11364e7	−1.66232	−0.831162	−	0.556030i	$-0.812324\pi$
$811$	−3.11364e7	−1.66232	−0.831162	+	0.556030i	$0.812324\pi$
$812$	1.68715e6	0.0897973
$813$	−2.65005e7	−1.40614
$814$	25345.9	0.00134075
$815$	−5.96255e6	−0.314440
$816$	−2.85912e7	−1.50317
$817$	4.60211e6	0.241214
$818$	−718138.	−0.0375253
$819$	−475193.	−0.0247549
$820$	−1.98829e6	−0.103263
$821$	−2.75160e7	−1.42471	−0.712357	−	0.701817i	$-0.752372\pi$
$821$	−2.75160e7	−1.42471	−0.712357	+	0.701817i	$0.752372\pi$
$822$	956170.	0.0493578
$823$	1.81038e7	0.931690	0.465845	−	0.884866i	$-0.345750\pi$
$823$	1.81038e7	0.931690	0.465845	+	0.884866i	$0.345750\pi$
$824$	2.06051e6	0.105720
$825$	1.06046e6	0.0542451
$826$	−94144.1	−0.00480112
$827$	2.27756e7	1.15799	0.578996	−	0.815330i	$-0.303445\pi$
$827$	2.27756e7	1.15799	0.578996	+	0.815330i	$0.303445\pi$
$828$	1.04613e6	0.0530285
$829$	−9.39704e6	−0.474903	−0.237451	−	0.971399i	$-0.576312\pi$
$829$	−9.39704e6	−0.474903	−0.237451	+	0.971399i	$0.576312\pi$
$830$	−17343.5	−0.000873858 0
$831$	−681011.	−0.0342099
$832$	−2.47293e7	−1.23852
$833$	3.32820e7	1.66187
$834$	51385.5	0.00255815
$835$	1.03237e7	0.512412
$836$	−1.39532e6	−0.0690492
$837$	−3.46162e7	−1.70791
$838$	1.09820e6	0.0540220
$839$	3.68860e7	1.80907	0.904537	−	0.426395i	$-0.140216\pi$
$839$	3.68860e7	1.80907	0.904537	+	0.426395i	$0.140216\pi$
$840$	−71638.3	−0.00350305
$841$	−5.06008e6	−0.246699
$842$	888550.	0.0431918
$843$	−5.32490e6	−0.258073
$844$	2.11127e7	1.02021
$845$	5.26264e6	0.253549
$846$	−30834.3	−0.00148118
$847$	196727.	0.00942225
$848$	−4.46925e6	−0.213425
$849$	−3.66315e7	−1.74416
$850$	−297561.	−0.0141263
$851$	622083.	0.0294459
$852$	−3.25440e7	−1.53593
$853$	1.29325e7	0.608570	0.304285	−	0.952581i	$-0.401583\pi$
$853$	1.29325e7	0.608570	0.304285	+	0.952581i	$0.401583\pi$
$854$	−59690.1	−0.00280064
$855$	−418445.	−0.0195760
$856$	−912863.	−0.0425815
$857$	3.74701e7	1.74274	0.871371	−	0.490624i	$-0.163231\pi$
$857$	3.74701e7	1.74274	0.871371	+	0.490624i	$0.163231\pi$
$858$	307814.	0.0142748
$859$	3.07350e6	0.142118	0.0710592	−	0.997472i	$-0.477362\pi$
$859$	3.07350e6	0.142118	0.0710592	+	0.997472i	$0.477362\pi$
$860$	−1.01806e7	−0.469381
$861$	469117.	0.0215662
$862$	815057.	0.0373611
$863$	7.51629e6	0.343539	0.171770	−	0.985137i	$-0.445052\pi$
$863$	7.51629e6	0.343539	0.171770	+	0.985137i	$0.445052\pi$
$864$	−2.95774e6	−0.134795
$865$	2.68621e6	0.122068
$866$	−809970.	−0.0367007
$867$	3.62787e7	1.63909
$868$	−3.66166e6	−0.164960
$869$	−4.04942e6	−0.181904
$870$	−327745.	−0.0146804
$871$	1.28574e7	0.574258
$872$	−1.23798e6	−0.0551344
$873$	627286.	0.0278567
$874$	60646.5	0.00268551
$875$	209948.	0.00927027
$876$	−3.14738e7	−1.38576
$877$	6.35147e6	0.278853	0.139427	−	0.990232i	$-0.455474\pi$
$877$	6.35147e6	0.278853	0.139427	+	0.990232i	$0.455474\pi$
$878$	479497.	0.0209918
$879$	2.18819e7	0.955243
$880$	3.08118e6	0.134125
$881$	−4.09407e7	−1.77711	−0.888556	−	0.458767i	$-0.848291\pi$
$881$	−4.09407e7	−1.77711	−0.888556	+	0.458767i	$0.848291\pi$
$882$	183348.	0.00793608
$883$	−3.72230e7	−1.60661	−0.803303	−	0.595570i	$-0.796926\pi$
$883$	−3.72230e7	−1.60661	−0.803303	+	0.595570i	$0.796926\pi$
$884$	4.87728e7	2.09917
$885$	−1.03272e7	−0.443227
$886$	624961.	0.0267466
$887$	6.01716e6	0.256792	0.128396	−	0.991723i	$-0.459017\pi$
$887$	6.01716e6	0.256792	0.128396	+	0.991723i	$0.459017\pi$
$888$	−187823.	−0.00799312
$889$	−3.12793e6	−0.132740
$890$	−141210.	−0.00597571
$891$	−5.52154e6	−0.233005
$892$	1.47060e7	0.618846
$893$	1.00940e6	0.0423580
$894$	−194710.	−0.00814786
$895$	8.98598e6	0.374980
$896$	−417030.	−0.0173539
$897$	7.55490e6	0.313507
$898$	119205.	0.00493290
$899$	−3.35338e7	−1.38383
$900$	925663.	0.0380931
$901$	8.78320e6	0.360446
$902$	71652.2	0.00293233
$903$	2.40200e6	0.0980288
$904$	−2.04238e6	−0.0831220
$905$	−3.66275e6	−0.148657
$906$	1.20478e6	0.0487626
$907$	−3.16493e7	−1.27746	−0.638728	−	0.769432i	$-0.720539\pi$
$907$	−3.16493e7	−1.27746	−0.638728	+	0.769432i	$0.720539\pi$
$908$	1.32997e7	0.535337
$909$	−6.54667e6	−0.262791
$910$	60940.4	0.00243950
$911$	−1.65255e7	−0.659719	−0.329860	−	0.944030i	$-0.607001\pi$
$911$	−1.65255e7	−0.659719	−0.329860	+	0.944030i	$0.607001\pi$
$912$	5.15620e6	0.205278
$913$	−352936.	−0.0140126
$914$	−463851.	−0.0183660
$915$	−6.54778e6	−0.258548
$916$	−2.66231e7	−1.04838
$917$	1.99856e6	0.0784863
$918$	1.93185e6	0.0756599
$919$	3.77434e6	0.147419	0.0737093	−	0.997280i	$-0.476516\pi$
$919$	3.77434e6	0.147419	0.0737093	+	0.997280i	$0.476516\pi$
$920$	−268556.	−0.0104608
$921$	3.69668e7	1.43603
$922$	−3452.11	−0.000133739 0
$923$	5.54173e7	2.14112
$924$	−728266.	−0.0280614
$925$	550448.	0.0211525
$926$	1.60058e6	0.0613408
$927$	6.28181e6	0.240096
$928$	−2.86525e6	−0.109218
$929$	−1.04084e7	−0.395679	−0.197840	−	0.980234i	$-0.563392\pi$
$929$	−1.04084e7	−0.395679	−0.197840	+	0.980234i	$0.563392\pi$
$930$	711311.	0.0269682
$931$	−6.00215e6	−0.226951
$932$	2.66951e7	1.00668
$933$	3.42589e7	1.28845
$934$	−984771.	−0.0369375
$935$	−6.05530e6	−0.226520
$936$	537848.	0.0200664
$937$	5.23121e7	1.94649	0.973247	−	0.229763i	$-0.0737950\pi$
$937$	5.23121e7	1.94649	0.973247	+	0.229763i	$0.0737950\pi$
$938$	53869.7	0.00199911
$939$	−4.28740e7	−1.58683
$940$	−2.23295e6	−0.0824249
$941$	−991679.	−0.0365088	−0.0182544	−	0.999833i	$-0.505811\pi$
$941$	−991679.	−0.0365088	−0.0182544	+	0.999833i	$0.505811\pi$
$942$	1.42199e6	0.0522119
$943$	1.75861e6	0.0644008
$944$	−3.00059e7	−1.09591
$945$	−1.36304e6	−0.0496512
$946$	366878.	0.0133289
$947$	−2.12854e7	−0.771269	−0.385635	−	0.922652i	$-0.626017\pi$
$947$	−2.12854e7	−0.771269	−0.385635	+	0.922652i	$0.626017\pi$
$948$	1.49906e7	0.541749
$949$	5.35949e7	1.93178
$950$	53662.8	0.00192914
$951$	2.62449e7	0.941008
$952$	409058.	0.0146282
$953$	3.99471e6	0.142480	0.0712398	−	0.997459i	$-0.477304\pi$
$953$	3.99471e6	0.142480	0.0712398	+	0.997459i	$0.477304\pi$
$954$	48386.1	0.00172127
$955$	1.45410e7	0.515923
$956$	−4.00304e7	−1.41659
$957$	−6.66953e6	−0.235405
$958$	474390.	0.0167002
$959$	3.85222e6	0.135259
$960$	−1.13657e7	−0.398032
$961$	4.41499e7	1.54213
$962$	159775.	0.00556636
$963$	−2.78301e6	−0.0967050
$964$	−6.49993e6	−0.225277
$965$	1.98871e7	0.687470
$966$	31653.5	0.00109139
$967$	3.18059e7	1.09381	0.546905	−	0.837195i	$-0.315806\pi$
$967$	3.18059e7	1.09381	0.546905	+	0.837195i	$0.315806\pi$
$968$	−222665.	−0.00763773
$969$	−1.01332e7	−0.346687
$970$	−80445.2	−0.00274518
$971$	−6.42176e6	−0.218578	−0.109289	−	0.994010i	$-0.534857\pi$
$971$	−6.42176e6	−0.218578	−0.109289	+	0.994010i	$0.534857\pi$
$972$	−1.10564e7	−0.375359
$973$	207022.	0.00701027
$974$	−197944.	−0.00668565
$975$	6.68493e6	0.225209
$976$	−1.90246e7	−0.639280
$977$	7.63925e6	0.256044	0.128022	−	0.991771i	$-0.459137\pi$
$977$	7.63925e6	0.256044	0.128022	+	0.991771i	$0.459137\pi$
$978$	−795442.	−0.0265926
$979$	−2.87358e6	−0.0958224
$980$	1.32777e7	0.441627
$981$	−3.77418e6	−0.125213
$982$	−650728.	−0.0215338
$983$	−4.54880e7	−1.50146	−0.750728	−	0.660611i	$-0.770297\pi$
$983$	−4.54880e7	−1.50146	−0.750728	+	0.660611i	$0.770297\pi$
$984$	−530970.	−0.0174817
$985$	1.40813e7	0.462437
$986$	1.87144e6	0.0613032
$987$	526841.	0.0172142
$988$	−8.79580e6	−0.286670
$989$	9.00455e6	0.292733
$990$	−33358.2	−0.00108172
$991$	3.14083e7	1.01592	0.507961	−	0.861380i	$-0.330399\pi$
$991$	3.14083e7	1.01592	0.507961	+	0.861380i	$0.330399\pi$
$992$	6.21851e6	0.200635
$993$	4.13936e7	1.33217
$994$	232187.	0.00745370
$995$	−1.07997e7	−0.345824
$996$	1.30654e6	0.0417324
$997$	3.37727e7	1.07604	0.538019	−	0.842933i	$-0.319173\pi$
$997$	3.37727e7	1.07604	0.538019	+	0.842933i	$0.319173\pi$
$998$	−917397.	−0.0291562
$999$	−3.57366e6	−0.113292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.20	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.20	✓	40	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)

\(f(q)\)	\(=\)	\(q+0.237841 q^{2} +14.0227 q^{3} -31.9434 q^{4} +25.0000 q^{5} +3.33516 q^{6} +13.4367 q^{7} -15.2083 q^{8} -46.3651 q^{9} +O(q^{10})\)	\(q+0.237841 q^{2} +14.0227 q^{3} -31.9434 q^{4} +25.0000 q^{5} +3.33516 q^{6} +13.4367 q^{7} -15.2083 q^{8} -46.3651 q^{9} +5.94602 q^{10} +121.000 q^{11} -447.932 q^{12} +762.757 q^{13} +3.19579 q^{14} +350.566 q^{15} +1018.57 q^{16} -2001.75 q^{17} -11.0275 q^{18} +361.000 q^{19} -798.586 q^{20} +188.418 q^{21} +28.7787 q^{22} +706.337 q^{23} -213.261 q^{24} +625.000 q^{25} +181.415 q^{26} -4057.67 q^{27} -429.214 q^{28} -3930.79 q^{29} +83.3789 q^{30} +8531.06 q^{31} +728.925 q^{32} +1696.74 q^{33} -476.098 q^{34} +335.918 q^{35} +1481.06 q^{36} +880.717 q^{37} +85.8605 q^{38} +10695.9 q^{39} -380.209 q^{40} +2489.76 q^{41} +44.8135 q^{42} +12748.2 q^{43} -3865.16 q^{44} -1159.13 q^{45} +167.996 q^{46} +2796.12 q^{47} +14283.1 q^{48} -16626.5 q^{49} +148.650 q^{50} -28069.9 q^{51} -24365.1 q^{52} -4387.76 q^{53} -965.078 q^{54} +3025.00 q^{55} -204.350 q^{56} +5062.18 q^{57} -934.901 q^{58} -29458.7 q^{59} -11198.3 q^{60} -18677.7 q^{61} +2029.03 q^{62} -622.994 q^{63} -32421.0 q^{64} +19068.9 q^{65} +403.554 q^{66} +16856.4 q^{67} +63942.8 q^{68} +9904.73 q^{69} +79.8948 q^{70} +72654.0 q^{71} +705.137 q^{72} +70264.7 q^{73} +209.470 q^{74} +8764.16 q^{75} -11531.6 q^{76} +1625.84 q^{77} +2543.92 q^{78} -33466.3 q^{79} +25464.3 q^{80} -45632.5 q^{81} +592.167 q^{82} -2916.82 q^{83} -6018.72 q^{84} -50043.8 q^{85} +3032.05 q^{86} -55120.0 q^{87} -1840.21 q^{88} -23748.6 q^{89} -275.688 q^{90} +10248.9 q^{91} -22562.8 q^{92} +119628. q^{93} +665.032 q^{94} +9025.00 q^{95} +10221.5 q^{96} -13529.3 q^{97} -3954.45 q^{98} -5610.18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

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