LMFDB - Embedded newform 690.6.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,6,Mod(1,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, 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("690.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	690.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:	$110.664835671$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 1159x^{2} - 10254x - 22896 $ x^4 - 1159x^2 - 10254x - 22896
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$38.0083$ of defining polynomial
Character	$\chi$	$=$	690.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -77.1586 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -77.1586 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -42.5530 q^{11} +144.000 q^{12} +180.429 q^{13} +308.634 q^{14} +225.000 q^{15} +256.000 q^{16} +381.547 q^{17} -324.000 q^{18} -1983.76 q^{19} +400.000 q^{20} -694.427 q^{21} +170.212 q^{22} -529.000 q^{23} -576.000 q^{24} +625.000 q^{25} -721.716 q^{26} +729.000 q^{27} -1234.54 q^{28} +4856.52 q^{29} -900.000 q^{30} -1996.50 q^{31} -1024.00 q^{32} -382.977 q^{33} -1526.19 q^{34} -1928.96 q^{35} +1296.00 q^{36} +6448.80 q^{37} +7935.06 q^{38} +1623.86 q^{39} -1600.00 q^{40} +9294.14 q^{41} +2777.71 q^{42} -3900.67 q^{43} -680.848 q^{44} +2025.00 q^{45} +2116.00 q^{46} -19766.1 q^{47} +2304.00 q^{48} -10853.6 q^{49} -2500.00 q^{50} +3433.92 q^{51} +2886.87 q^{52} -29600.3 q^{53} -2916.00 q^{54} -1063.82 q^{55} +4938.15 q^{56} -17853.9 q^{57} -19426.1 q^{58} +5669.15 q^{59} +3600.00 q^{60} +7852.98 q^{61} +7985.99 q^{62} -6249.84 q^{63} +4096.00 q^{64} +4510.73 q^{65} +1531.91 q^{66} -17551.9 q^{67} +6104.75 q^{68} -4761.00 q^{69} +7715.86 q^{70} -61879.1 q^{71} -5184.00 q^{72} +22641.8 q^{73} -25795.2 q^{74} +5625.00 q^{75} -31740.2 q^{76} +3283.33 q^{77} -6495.45 q^{78} -96828.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} -37176.6 q^{82} -11074.5 q^{83} -11110.8 q^{84} +9538.67 q^{85} +15602.7 q^{86} +43708.7 q^{87} +2723.39 q^{88} +109915. q^{89} -8100.00 q^{90} -13921.7 q^{91} -8464.00 q^{92} -17968.5 q^{93} +79064.6 q^{94} -49594.1 q^{95} -9216.00 q^{96} +156936. q^{97} +43414.2 q^{98} -3446.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 730 q^{11} + 576 q^{12} - 828 q^{13} - 100 q^{14} + 900 q^{15} + 1024 q^{16} - 179 q^{17} - 1296 q^{18} + 1568 q^{19} + 1600 q^{20} + 225 q^{21} + 2920 q^{22} - 2116 q^{23} - 2304 q^{24} + 2500 q^{25} + 3312 q^{26} + 2916 q^{27} + 400 q^{28} - 1917 q^{29} - 3600 q^{30} - 6331 q^{31} - 4096 q^{32} - 6570 q^{33} + 716 q^{34} + 625 q^{35} + 5184 q^{36} + 10127 q^{37} - 6272 q^{38} - 7452 q^{39} - 6400 q^{40} - 14527 q^{41} - 900 q^{42} - 18052 q^{43} - 11680 q^{44} + 8100 q^{45} + 8464 q^{46} - 13208 q^{47} + 9216 q^{48} - 52681 q^{49} - 10000 q^{50} - 1611 q^{51} - 13248 q^{52} - 39327 q^{53} - 11664 q^{54} - 18250 q^{55} - 1600 q^{56} + 14112 q^{57} + 7668 q^{58} - 43301 q^{59} + 14400 q^{60} - 25154 q^{61} + 25324 q^{62} + 2025 q^{63} + 16384 q^{64} - 20700 q^{65} + 26280 q^{66} - 15827 q^{67} - 2864 q^{68} - 19044 q^{69} - 2500 q^{70} - 20999 q^{71} - 20736 q^{72} - 35844 q^{73} - 40508 q^{74} + 22500 q^{75} + 25088 q^{76} - 16142 q^{77} + 29808 q^{78} - 100414 q^{79} + 25600 q^{80} + 26244 q^{81} + 58108 q^{82} - 140015 q^{83} + 3600 q^{84} - 4475 q^{85} + 72208 q^{86} - 17253 q^{87} + 46720 q^{88} - 26030 q^{89} - 32400 q^{90} + 34190 q^{91} - 33856 q^{92} - 56979 q^{93} + 52832 q^{94} + 39200 q^{95} - 36864 q^{96} - 16946 q^{97} + 210724 q^{98} - 59130 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 730 * q^11 + 576 * q^12 - 828 * q^13 - 100 * q^14 + 900 * q^15 + 1024 * q^16 - 179 * q^17 - 1296 * q^18 + 1568 * q^19 + 1600 * q^20 + 225 * q^21 + 2920 * q^22 - 2116 * q^23 - 2304 * q^24 + 2500 * q^25 + 3312 * q^26 + 2916 * q^27 + 400 * q^28 - 1917 * q^29 - 3600 * q^30 - 6331 * q^31 - 4096 * q^32 - 6570 * q^33 + 716 * q^34 + 625 * q^35 + 5184 * q^36 + 10127 * q^37 - 6272 * q^38 - 7452 * q^39 - 6400 * q^40 - 14527 * q^41 - 900 * q^42 - 18052 * q^43 - 11680 * q^44 + 8100 * q^45 + 8464 * q^46 - 13208 * q^47 + 9216 * q^48 - 52681 * q^49 - 10000 * q^50 - 1611 * q^51 - 13248 * q^52 - 39327 * q^53 - 11664 * q^54 - 18250 * q^55 - 1600 * q^56 + 14112 * q^57 + 7668 * q^58 - 43301 * q^59 + 14400 * q^60 - 25154 * q^61 + 25324 * q^62 + 2025 * q^63 + 16384 * q^64 - 20700 * q^65 + 26280 * q^66 - 15827 * q^67 - 2864 * q^68 - 19044 * q^69 - 2500 * q^70 - 20999 * q^71 - 20736 * q^72 - 35844 * q^73 - 40508 * q^74 + 22500 * q^75 + 25088 * q^76 - 16142 * q^77 + 29808 * q^78 - 100414 * q^79 + 25600 * q^80 + 26244 * q^81 + 58108 * q^82 - 140015 * q^83 + 3600 * q^84 - 4475 * q^85 + 72208 * q^86 - 17253 * q^87 + 46720 * q^88 - 26030 * q^89 - 32400 * q^90 + 34190 * q^91 - 33856 * q^92 - 56979 * q^93 + 52832 * q^94 + 39200 * q^95 - 36864 * q^96 - 16946 * q^97 + 210724 * q^98 - 59130 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−36.0000	−0.408248
$7$	−77.1586	−0.595167	−0.297584	−	0.954696i	$-0.596181\pi$
$7$	−77.1586	−0.595167	−0.297584	+	0.954696i	$0.596181\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−42.5530	−0.106035	−0.0530174	−	0.998594i	$-0.516884\pi$
$11$	−42.5530	−0.106035	−0.0530174	+	0.998594i	$0.516884\pi$
$12$	144.000	0.288675
$13$	180.429	0.296107	0.148053	−	0.988979i	$-0.452699\pi$
$13$	180.429	0.296107	0.148053	+	0.988979i	$0.452699\pi$
$14$	308.634	0.420847
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	381.547	0.320203	0.160101	−	0.987101i	$-0.448818\pi$
$17$	381.547	0.320203	0.160101	+	0.987101i	$0.448818\pi$
$18$	−324.000	−0.235702
$19$	−1983.76	−1.26068	−0.630342	−	0.776318i	$-0.717085\pi$
$19$	−1983.76	−1.26068	−0.630342	+	0.776318i	$0.717085\pi$
$20$	400.000	0.223607
$21$	−694.427	−0.343620
$22$	170.212	0.0749779
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	−721.716	−0.209379
$27$	729.000	0.192450
$28$	−1234.54	−0.297584
$29$	4856.52	1.07233	0.536167	−	0.844112i	$-0.319872\pi$
$29$	4856.52	1.07233	0.536167	+	0.844112i	$0.319872\pi$
$30$	−900.000	−0.182574
$31$	−1996.50	−0.373134	−0.186567	−	0.982442i	$-0.559736\pi$
$31$	−1996.50	−0.373134	−0.186567	+	0.982442i	$0.559736\pi$
$32$	−1024.00	−0.176777
$33$	−382.977	−0.0612192
$34$	−1526.19	−0.226418
$35$	−1928.96	−0.266167
$36$	1296.00	0.166667
$37$	6448.80	0.774417	0.387208	−	0.921992i	$-0.373439\pi$
$37$	6448.80	0.774417	0.387208	+	0.921992i	$0.373439\pi$
$38$	7935.06	0.891438
$39$	1623.86	0.170957
$40$	−1600.00	−0.158114
$41$	9294.14	0.863475	0.431737	−	0.901999i	$-0.357901\pi$
$41$	9294.14	0.863475	0.431737	+	0.901999i	$0.357901\pi$
$42$	2777.71	0.242976
$43$	−3900.67	−0.321712	−0.160856	−	0.986978i	$-0.551426\pi$
$43$	−3900.67	−0.321712	−0.160856	+	0.986978i	$0.551426\pi$
$44$	−680.848	−0.0530174
$45$	2025.00	0.149071
$46$	2116.00	0.147442
$47$	−19766.1	−1.30520	−0.652600	−	0.757702i	$-0.726322\pi$
$47$	−19766.1	−1.30520	−0.652600	+	0.757702i	$0.726322\pi$
$48$	2304.00	0.144338
$49$	−10853.6	−0.645776
$50$	−2500.00	−0.141421
$51$	3433.92	0.184869
$52$	2886.87	0.148053
$53$	−29600.3	−1.44746	−0.723729	−	0.690084i	$-0.757573\pi$
$53$	−29600.3	−1.44746	−0.723729	+	0.690084i	$0.757573\pi$
$54$	−2916.00	−0.136083
$55$	−1063.82	−0.0474202
$56$	4938.15	0.210423
$57$	−17853.9	−0.727856
$58$	−19426.1	−0.758255
$59$	5669.15	0.212026	0.106013	−	0.994365i	$-0.466192\pi$
$59$	5669.15	0.212026	0.106013	+	0.994365i	$0.466192\pi$
$60$	3600.00	0.129099
$61$	7852.98	0.270215	0.135108	−	0.990831i	$-0.456862\pi$
$61$	7852.98	0.270215	0.135108	+	0.990831i	$0.456862\pi$
$62$	7985.99	0.263846
$63$	−6249.84	−0.198389
$64$	4096.00	0.125000
$65$	4510.73	0.132423
$66$	1531.91	0.0432885
$67$	−17551.9	−0.477680	−0.238840	−	0.971059i	$-0.576767\pi$
$67$	−17551.9	−0.477680	−0.238840	+	0.971059i	$0.576767\pi$
$68$	6104.75	0.160101
$69$	−4761.00	−0.120386
$70$	7715.86	0.188208
$71$	−61879.1	−1.45679	−0.728397	−	0.685155i	$-0.759734\pi$
$71$	−61879.1	−1.45679	−0.728397	+	0.685155i	$0.759734\pi$
$72$	−5184.00	−0.117851
$73$	22641.8	0.497283	0.248642	−	0.968596i	$-0.420016\pi$
$73$	22641.8	0.497283	0.248642	+	0.968596i	$0.420016\pi$
$74$	−25795.2	−0.547595
$75$	5625.00	0.115470
$76$	−31740.2	−0.630342
$77$	3283.33	0.0631084
$78$	−6495.45	−0.120885
$79$	−96828.4	−1.74556	−0.872780	−	0.488114i	$-0.837685\pi$
$79$	−96828.4	−1.74556	−0.872780	+	0.488114i	$0.837685\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	−37176.6	−0.610569
$83$	−11074.5	−0.176453	−0.0882266	−	0.996100i	$-0.528120\pi$
$83$	−11074.5	−0.176453	−0.0882266	+	0.996100i	$0.528120\pi$
$84$	−11110.8	−0.171810
$85$	9538.67	0.143199
$86$	15602.7	0.227485
$87$	43708.7	0.619113
$88$	2723.39	0.0374890
$89$	109915.	1.47090	0.735449	−	0.677580i	$-0.236971\pi$
$89$	109915.	1.47090	0.735449	+	0.677580i	$0.236971\pi$
$90$	−8100.00	−0.105409
$91$	−13921.7	−0.176233
$92$	−8464.00	−0.104257
$93$	−17968.5	−0.215429
$94$	79064.6	0.922916
$95$	−49594.1	−0.563795
$96$	−9216.00	−0.102062
$97$	156936.	1.69354	0.846768	−	0.531963i	$-0.178545\pi$
$97$	156936.	1.69354	0.846768	+	0.531963i	$0.178545\pi$
$98$	43414.2	0.456632
$99$	−3446.79	−0.0353449
$100$	10000.0	0.100000
$101$	−58461.8	−0.570255	−0.285127	−	0.958490i	$-0.592036\pi$
$101$	−58461.8	−0.570255	−0.285127	+	0.958490i	$0.592036\pi$
$102$	−13735.7	−0.130722
$103$	112501.	1.04487	0.522437	−	0.852678i	$-0.325023\pi$
$103$	112501.	1.04487	0.522437	+	0.852678i	$0.325023\pi$
$104$	−11547.5	−0.104690
$105$	−17360.7	−0.153672
$106$	118401.	1.02351
$107$	−46690.1	−0.394244	−0.197122	−	0.980379i	$-0.563160\pi$
$107$	−46690.1	−0.394244	−0.197122	+	0.980379i	$0.563160\pi$
$108$	11664.0	0.0962250
$109$	−135783.	−1.09466	−0.547332	−	0.836916i	$-0.684356\pi$
$109$	−135783.	−1.09466	−0.547332	+	0.836916i	$0.684356\pi$
$110$	4255.30	0.0335311
$111$	58039.2	0.447110
$112$	−19752.6	−0.148792
$113$	49428.2	0.364149	0.182074	−	0.983285i	$-0.441719\pi$
$113$	49428.2	0.364149	0.182074	+	0.983285i	$0.441719\pi$
$114$	71415.5	0.514672
$115$	−13225.0	−0.0932505
$116$	77704.4	0.536167
$117$	14614.8	0.0987022
$118$	−22676.6	−0.149925
$119$	−29439.6	−0.190574
$120$	−14400.0	−0.0912871
$121$	−159240.	−0.988757
$122$	−31411.9	−0.191071
$123$	83647.3	0.498527
$124$	−31944.0	−0.186567
$125$	15625.0	0.0894427
$126$	24999.4	0.140282
$127$	−187783.	−1.03311	−0.516555	−	0.856254i	$-0.672786\pi$
$127$	−187783.	−1.03311	−0.516555	+	0.856254i	$0.672786\pi$
$128$	−16384.0	−0.0883883
$129$	−35106.0	−0.185741
$130$	−18042.9	−0.0936371
$131$	211306.	1.07581	0.537903	−	0.843007i	$-0.319217\pi$
$131$	211306.	1.07581	0.537903	+	0.843007i	$0.319217\pi$
$132$	−6127.63	−0.0306096
$133$	153064.	0.750318
$134$	70207.5	0.337770
$135$	18225.0	0.0860663
$136$	−24419.0	−0.113209
$137$	−328217.	−1.49403	−0.747017	−	0.664805i	$-0.768514\pi$
$137$	−328217.	−1.49403	−0.747017	+	0.664805i	$0.768514\pi$
$138$	19044.0	0.0851257
$139$	−57969.9	−0.254487	−0.127244	−	0.991871i	$-0.540613\pi$
$139$	−57969.9	−0.254487	−0.127244	+	0.991871i	$0.540613\pi$
$140$	−30863.4	−0.133083
$141$	−177895.	−0.753558
$142$	247516.	1.03011
$143$	−7677.80	−0.0313976
$144$	20736.0	0.0833333
$145$	121413.	0.479563
$146$	−90567.2	−0.351632
$147$	−97682.0	−0.372839
$148$	103181.	0.387208
$149$	−179396.	−0.661985	−0.330993	−	0.943633i	$-0.607384\pi$
$149$	−179396.	−0.661985	−0.330993	+	0.943633i	$0.607384\pi$
$150$	−22500.0	−0.0816497
$151$	373971.	1.33474	0.667369	−	0.744727i	$-0.267420\pi$
$151$	373971.	1.33474	0.667369	+	0.744727i	$0.267420\pi$
$152$	126961.	0.445719
$153$	30905.3	0.106734
$154$	−13133.3	−0.0446244
$155$	−49912.5	−0.166871
$156$	25981.8	0.0854786
$157$	159036.	0.514927	0.257464	−	0.966288i	$-0.417113\pi$
$157$	159036.	0.514927	0.257464	+	0.966288i	$0.417113\pi$
$158$	387313.	1.23430
$159$	−266402.	−0.835690
$160$	−25600.0	−0.0790569
$161$	40816.9	0.124101
$162$	−26244.0	−0.0785674
$163$	−357408.	−1.05365	−0.526824	−	0.849974i	$-0.676617\pi$
$163$	−357408.	−1.05365	−0.526824	+	0.849974i	$0.676617\pi$
$164$	148706.	0.431737
$165$	−9574.42	−0.0273781
$166$	44298.1	0.124771
$167$	−142576.	−0.395599	−0.197799	−	0.980243i	$-0.563379\pi$
$167$	−142576.	−0.395599	−0.197799	+	0.980243i	$0.563379\pi$
$168$	44443.3	0.121488
$169$	−338738.	−0.912321
$170$	−38154.7	−0.101257
$171$	−160685.	−0.420228
$172$	−62410.7	−0.160856
$173$	662392.	1.68267	0.841336	−	0.540512i	$-0.181769\pi$
$173$	662392.	1.68267	0.841336	+	0.540512i	$0.181769\pi$
$174$	−174835.	−0.437779
$175$	−48224.1	−0.119033
$176$	−10893.6	−0.0265087
$177$	51022.4	0.122413
$178$	−439661.	−1.04008
$179$	−631932.	−1.47414	−0.737068	−	0.675818i	$-0.763790\pi$
$179$	−631932.	−1.47414	−0.737068	+	0.675818i	$0.763790\pi$
$180$	32400.0	0.0745356
$181$	−101355.	−0.229959	−0.114979	−	0.993368i	$-0.536680\pi$
$181$	−101355.	−0.229959	−0.114979	+	0.993368i	$0.536680\pi$
$182$	55686.6	0.124616
$183$	70676.8	0.156009
$184$	33856.0	0.0737210
$185$	161220.	0.346330
$186$	71873.9	0.152331
$187$	−16235.9	−0.0339526
$188$	−316258.	−0.652600
$189$	−56248.6	−0.114540
$190$	198376.	0.398663
$191$	−439997.	−0.872704	−0.436352	−	0.899776i	$-0.643730\pi$
$191$	−439997.	−0.872704	−0.436352	+	0.899776i	$0.643730\pi$
$192$	36864.0	0.0721688
$193$	241686.	0.467045	0.233523	−	0.972351i	$-0.424975\pi$
$193$	241686.	0.467045	0.233523	+	0.972351i	$0.424975\pi$
$194$	−627746.	−1.19751
$195$	40596.5	0.0764544
$196$	−173657.	−0.322888
$197$	−903847.	−1.65932	−0.829658	−	0.558272i	$-0.811465\pi$
$197$	−903847.	−1.65932	−0.829658	+	0.558272i	$0.811465\pi$
$198$	13787.2	0.0249926
$199$	532425.	0.953071	0.476536	−	0.879155i	$-0.341892\pi$
$199$	532425.	0.953071	0.476536	+	0.879155i	$0.341892\pi$
$200$	−40000.0	−0.0707107
$201$	−157967.	−0.275788
$202$	233847.	0.403231
$203$	−374722.	−0.638219
$204$	54942.7	0.0924346
$205$	232354.	0.386158
$206$	−450004.	−0.738837
$207$	−42849.0	−0.0695048
$208$	46189.8	0.0740267
$209$	84415.1	0.133676
$210$	69442.7	0.108662
$211$	−948183.	−1.46618	−0.733088	−	0.680134i	$-0.761922\pi$
$211$	−948183.	−1.46618	−0.733088	+	0.680134i	$0.761922\pi$
$212$	−473604.	−0.723729
$213$	−556912.	−0.841081
$214$	186760.	0.278773
$215$	−97516.7	−0.143874
$216$	−46656.0	−0.0680414
$217$	154047.	0.222077
$218$	543134.	0.774044
$219$	203776.	0.287107
$220$	−17021.2	−0.0237101
$221$	68842.1	0.0948142
$222$	−232157.	−0.316154
$223$	−261000.	−0.351462	−0.175731	−	0.984438i	$-0.556229\pi$
$223$	−261000.	−0.351462	−0.175731	+	0.984438i	$0.556229\pi$
$224$	79010.4	0.105212
$225$	50625.0	0.0666667
$226$	−197713.	−0.257492
$227$	−1.30435e6	−1.68008	−0.840040	−	0.542525i	$-0.817468\pi$
$227$	−1.30435e6	−1.68008	−0.840040	+	0.542525i	$0.817468\pi$
$228$	−285662.	−0.363928
$229$	793571.	0.999993	0.499997	−	0.866027i	$-0.333335\pi$
$229$	793571.	0.999993	0.499997	+	0.866027i	$0.333335\pi$
$230$	52900.0	0.0659380
$231$	29550.0	0.0364357
$232$	−310817.	−0.379128
$233$	−1.36110e6	−1.64248	−0.821239	−	0.570584i	$-0.806717\pi$
$233$	−1.36110e6	−1.64248	−0.821239	+	0.570584i	$0.806717\pi$
$234$	−58459.0	−0.0697930
$235$	−494153.	−0.583703
$236$	90706.5	0.106013
$237$	−871455.	−1.00780
$238$	117758.	0.134756
$239$	−964776.	−1.09253	−0.546263	−	0.837614i	$-0.683950\pi$
$239$	−964776.	−1.09253	−0.546263	+	0.837614i	$0.683950\pi$
$240$	57600.0	0.0645497
$241$	−261607.	−0.290140	−0.145070	−	0.989421i	$-0.546341\pi$
$241$	−261607.	−0.290140	−0.145070	+	0.989421i	$0.546341\pi$
$242$	636961.	0.699157
$243$	59049.0	0.0641500
$244$	125648.	0.135108
$245$	−271339.	−0.288800
$246$	−334589.	−0.352512
$247$	−357929.	−0.373297
$248$	127776.	0.131923
$249$	−99670.7	−0.101875
$250$	−62500.0	−0.0632456
$251$	−334427.	−0.335055	−0.167528	−	0.985867i	$-0.553578\pi$
$251$	−334427.	−0.335055	−0.167528	+	0.985867i	$0.553578\pi$
$252$	−99997.5	−0.0991946
$253$	22510.5	0.0221098
$254$	751132.	0.730520
$255$	85848.0	0.0826760
$256$	65536.0	0.0625000
$257$	−816089.	−0.770734	−0.385367	−	0.922763i	$-0.625925\pi$
$257$	−816089.	−0.770734	−0.385367	+	0.922763i	$0.625925\pi$
$258$	140424.	0.131339
$259$	−497580.	−0.460908
$260$	72171.6	0.0662115
$261$	393378.	0.357445
$262$	−845224.	−0.760709
$263$	155214.	0.138370	0.0691849	−	0.997604i	$-0.477960\pi$
$263$	155214.	0.138370	0.0691849	+	0.997604i	$0.477960\pi$
$264$	24510.5	0.0216443
$265$	−740007.	−0.647323
$266$	−612258.	−0.530555
$267$	989237.	0.849224
$268$	−280830.	−0.238840
$269$	−973762.	−0.820487	−0.410244	−	0.911976i	$-0.634556\pi$
$269$	−973762.	−0.820487	−0.410244	+	0.911976i	$0.634556\pi$
$270$	−72900.0	−0.0608581
$271$	321438.	0.265873	0.132936	−	0.991125i	$-0.457559\pi$
$271$	321438.	0.265873	0.132936	+	0.991125i	$0.457559\pi$
$272$	97675.9	0.0800507
$273$	−125295.	−0.101748
$274$	1.31287e6	1.05644
$275$	−26595.6	−0.0212070
$276$	−76176.0	−0.0601929
$277$	1.08912e6	0.852855	0.426427	−	0.904522i	$-0.359772\pi$
$277$	1.08912e6	0.852855	0.426427	+	0.904522i	$0.359772\pi$
$278$	231880.	0.179950
$279$	−161716.	−0.124378
$280$	123454.	0.0941042
$281$	−413383.	−0.312310	−0.156155	−	0.987733i	$-0.549910\pi$
$281$	−413383.	−0.312310	−0.156155	+	0.987733i	$0.549910\pi$
$282$	711581.	0.532846
$283$	2.05863e6	1.52796	0.763981	−	0.645239i	$-0.223242\pi$
$283$	2.05863e6	1.52796	0.763981	+	0.645239i	$0.223242\pi$
$284$	−990066.	−0.728397
$285$	−446347.	−0.325507
$286$	30711.2	0.0222015
$287$	−717123.	−0.513912
$288$	−82944.0	−0.0589256
$289$	−1.27428e6	−0.897470
$290$	−485652.	−0.339102
$291$	1.41243e6	0.977763
$292$	362269.	0.248642
$293$	−583417.	−0.397018	−0.198509	−	0.980099i	$-0.563610\pi$
$293$	−583417.	−0.397018	−0.198509	+	0.980099i	$0.563610\pi$
$294$	390728.	0.263637
$295$	141729.	0.0948207
$296$	−412723.	−0.273798
$297$	−31021.1	−0.0204064
$298$	717586.	0.468094
$299$	−95447.0	−0.0617425
$300$	90000.0	0.0577350
$301$	300970.	0.191473
$302$	−1.49589e6	−0.943802
$303$	−526156.	−0.329237
$304$	−507844.	−0.315171
$305$	196324.	0.120844
$306$	−123621.	−0.0754726
$307$	−674508.	−0.408452	−0.204226	−	0.978924i	$-0.565468\pi$
$307$	−674508.	−0.408452	−0.204226	+	0.978924i	$0.565468\pi$
$308$	52533.3	0.0315542
$309$	1.01251e6	0.603258
$310$	199650.	0.117995
$311$	−3.36009e6	−1.96992	−0.984962	−	0.172773i	$-0.944727\pi$
$311$	−3.36009e6	−1.96992	−0.984962	+	0.172773i	$0.944727\pi$
$312$	−103927.	−0.0604425
$313$	−1.30242e6	−0.751431	−0.375715	−	0.926735i	$-0.622603\pi$
$313$	−1.30242e6	−0.751431	−0.375715	+	0.926735i	$0.622603\pi$
$314$	−636143.	−0.364108
$315$	−156246.	−0.0887223
$316$	−1.54925e6	−0.872780
$317$	1.96290e6	1.09711	0.548555	−	0.836115i	$-0.315178\pi$
$317$	1.96290e6	1.09711	0.548555	+	0.836115i	$0.315178\pi$
$318$	1.06561e6	0.590922
$319$	−206660.	−0.113705
$320$	102400.	0.0559017
$321$	−420211.	−0.227617
$322$	−163268.	−0.0877526
$323$	−756899.	−0.403675
$324$	104976.	0.0555556
$325$	112768.	0.0592213
$326$	1.42963e6	0.745042
$327$	−1.22205e6	−0.632004
$328$	−594825.	−0.305284
$329$	1.52513e6	0.776813
$330$	38297.7	0.0193592
$331$	1.41758e6	0.711175	0.355587	−	0.934643i	$-0.384281\pi$
$331$	1.41758e6	0.711175	0.355587	+	0.934643i	$0.384281\pi$
$332$	−177192.	−0.0882266
$333$	522353.	0.258139
$334$	570303.	0.279730
$335$	−438797.	−0.213625
$336$	−177773.	−0.0859050
$337$	−1.64299e6	−0.788061	−0.394030	−	0.919097i	$-0.628920\pi$
$337$	−1.64299e6	−0.788061	−0.394030	+	0.919097i	$0.628920\pi$
$338$	1.35495e6	0.645108
$339$	444854.	0.210241
$340$	152619.	0.0715995
$341$	84957.0	0.0395652
$342$	642740.	0.297146
$343$	2.13425e6	0.979512
$344$	249643.	0.113743
$345$	−119025.	−0.0538382
$346$	−2.64957e6	−1.18983
$347$	−2.94758e6	−1.31414	−0.657071	−	0.753828i	$-0.728205\pi$
$347$	−2.94758e6	−1.31414	−0.657071	+	0.753828i	$0.728205\pi$
$348$	699339.	0.309556
$349$	−1.77834e6	−0.781540	−0.390770	−	0.920488i	$-0.627791\pi$
$349$	−1.77834e6	−0.781540	−0.390770	+	0.920488i	$0.627791\pi$
$350$	192896.	0.0841694
$351$	131533.	0.0569857
$352$	43574.3	0.0187445
$353$	−665015.	−0.284050	−0.142025	−	0.989863i	$-0.545361\pi$
$353$	−665015.	−0.284050	−0.142025	+	0.989863i	$0.545361\pi$
$354$	−204090.	−0.0865591
$355$	−1.54698e6	−0.651498
$356$	1.75864e6	0.735449
$357$	−264956.	−0.110028
$358$	2.52773e6	1.04237
$359$	−1.62032e6	−0.663538	−0.331769	−	0.943361i	$-0.607646\pi$
$359$	−1.62032e6	−0.663538	−0.331769	+	0.943361i	$0.607646\pi$
$360$	−129600.	−0.0527046
$361$	1.45922e6	0.589324
$362$	405421.	0.162605
$363$	−1.43316e6	−0.570859
$364$	−222746.	−0.0881165
$365$	566045.	0.222392
$366$	−282707.	−0.110315
$367$	−1.55202e6	−0.601494	−0.300747	−	0.953704i	$-0.597236\pi$
$367$	−1.55202e6	−0.601494	−0.300747	+	0.953704i	$0.597236\pi$
$368$	−135424.	−0.0521286
$369$	752825.	0.287825
$370$	−644880.	−0.244892
$371$	2.28391e6	0.861480
$372$	−287496.	−0.107714
$373$	2.32252e6	0.864345	0.432172	−	0.901791i	$-0.357747\pi$
$373$	2.32252e6	0.864345	0.432172	+	0.901791i	$0.357747\pi$
$374$	64943.8	0.0240081
$375$	140625.	0.0516398
$376$	1.26503e6	0.461458
$377$	876258.	0.317525
$378$	224994.	0.0809920
$379$	1.71855e6	0.614562	0.307281	−	0.951619i	$-0.400581\pi$
$379$	1.71855e6	0.614562	0.307281	+	0.951619i	$0.400581\pi$
$380$	−793506.	−0.281897
$381$	−1.69005e6	−0.596467
$382$	1.75999e6	0.617095
$383$	3.13617e6	1.09245	0.546226	−	0.837638i	$-0.316064\pi$
$383$	3.13617e6	1.09245	0.546226	+	0.837638i	$0.316064\pi$
$384$	−147456.	−0.0510310
$385$	82083.2	0.0282230
$386$	−966745.	−0.330251
$387$	−315954.	−0.107237
$388$	2.51098e6	0.846768
$389$	−4.41205e6	−1.47831	−0.739156	−	0.673534i	$-0.764775\pi$
$389$	−4.41205e6	−1.47831	−0.739156	+	0.673534i	$0.764775\pi$
$390$	−162386.	−0.0540614
$391$	−201838.	−0.0667669
$392$	694627.	0.228316
$393$	1.90175e6	0.621116
$394$	3.61539e6	1.17331
$395$	−2.42071e6	−0.780638
$396$	−55148.7	−0.0176725
$397$	1.23746e6	0.394052	0.197026	−	0.980398i	$-0.436872\pi$
$397$	1.23746e6	0.394052	0.197026	+	0.980398i	$0.436872\pi$
$398$	−2.12970e6	−0.673923
$399$	1.37758e6	0.433196
$400$	160000.	0.0500000
$401$	−872653.	−0.271007	−0.135504	−	0.990777i	$-0.543265\pi$
$401$	−872653.	−0.271007	−0.135504	+	0.990777i	$0.543265\pi$
$402$	631868.	0.195012
$403$	−360226.	−0.110487
$404$	−935389.	−0.285127
$405$	164025.	0.0496904
$406$	1.49889e6	0.451289
$407$	−274416.	−0.0821151
$408$	−219771.	−0.0653611
$409$	190064.	0.0561812	0.0280906	−	0.999605i	$-0.491057\pi$
$409$	190064.	0.0561812	0.0280906	+	0.999605i	$0.491057\pi$
$410$	−929414.	−0.273055
$411$	−2.95396e6	−0.862580
$412$	1.80002e6	0.522437
$413$	−437424.	−0.126191
$414$	171396.	0.0491473
$415$	−276863.	−0.0789123
$416$	−184759.	−0.0523448
$417$	−521730.	−0.146928
$418$	−337661.	−0.0945235
$419$	150315.	0.0418281	0.0209140	−	0.999781i	$-0.493342\pi$
$419$	150315.	0.0418281	0.0209140	+	0.999781i	$0.493342\pi$
$420$	−277771.	−0.0768358
$421$	1.21956e6	0.335349	0.167675	−	0.985842i	$-0.446374\pi$
$421$	1.21956e6	0.335349	0.167675	+	0.985842i	$0.446374\pi$
$422$	3.79273e6	1.03674
$423$	−1.60106e6	−0.435067
$424$	1.89442e6	0.511754
$425$	238467.	0.0640406
$426$	2.22765e6	0.594734
$427$	−605924.	−0.160823
$428$	−747042.	−0.197122
$429$	−69100.2	−0.0181274
$430$	390067.	0.101734
$431$	−4.83459e6	−1.25362	−0.626811	−	0.779171i	$-0.715640\pi$
$431$	−4.83459e6	−1.25362	−0.626811	+	0.779171i	$0.715640\pi$
$432$	186624.	0.0481125
$433$	−722912.	−0.185296	−0.0926479	−	0.995699i	$-0.529533\pi$
$433$	−722912.	−0.185296	−0.0926479	+	0.995699i	$0.529533\pi$
$434$	−616188.	−0.157032
$435$	1.09272e6	0.276876
$436$	−2.17253e6	−0.547332
$437$	1.04941e6	0.262871
$438$	−815105.	−0.203015
$439$	7.48135e6	1.85276	0.926379	−	0.376593i	$-0.122905\pi$
$439$	7.48135e6	1.85276	0.926379	+	0.376593i	$0.122905\pi$
$440$	68084.8	0.0167656
$441$	−879138.	−0.215259
$442$	−275368.	−0.0670438
$443$	7.64878e6	1.85175	0.925877	−	0.377826i	$-0.123328\pi$
$443$	7.64878e6	1.85175	0.925877	+	0.377826i	$0.123328\pi$
$444$	928628.	0.223555
$445$	2.74788e6	0.657806
$446$	1.04400e6	0.248521
$447$	−1.61457e6	−0.382197
$448$	−316042.	−0.0743959
$449$	1.23027e6	0.287994	0.143997	−	0.989578i	$-0.454004\pi$
$449$	1.23027e6	0.287994	0.143997	+	0.989578i	$0.454004\pi$
$450$	−202500.	−0.0471405
$451$	−395494.	−0.0915584
$452$	790851.	0.182074
$453$	3.36574e6	0.770611
$454$	5.21740e6	1.18800
$455$	−348041.	−0.0788138
$456$	1.14265e6	0.257336
$457$	780159.	0.174740	0.0873701	−	0.996176i	$-0.472154\pi$
$457$	780159.	0.174740	0.0873701	+	0.996176i	$0.472154\pi$
$458$	−3.17428e6	−0.707102
$459$	278147.	0.0616231
$460$	−211600.	−0.0466252
$461$	−4.10773e6	−0.900221	−0.450111	−	0.892973i	$-0.648615\pi$
$461$	−4.10773e6	−0.900221	−0.450111	+	0.892973i	$0.648615\pi$
$462$	−118200.	−0.0257639
$463$	−1.72523e6	−0.374019	−0.187010	−	0.982358i	$-0.559880\pi$
$463$	−1.72523e6	−0.374019	−0.187010	+	0.982358i	$0.559880\pi$
$464$	1.24327e6	0.268084
$465$	−449212.	−0.0963428
$466$	5.44439e6	1.16141
$467$	595454.	0.126344	0.0631721	−	0.998003i	$-0.479878\pi$
$467$	595454.	0.126344	0.0631721	+	0.998003i	$0.479878\pi$
$468$	233836.	0.0493511
$469$	1.35428e6	0.284299
$470$	1.97661e6	0.412741
$471$	1.43132e6	0.297293
$472$	−362826.	−0.0749624
$473$	165985.	0.0341127
$474$	3.48582e6	0.712622
$475$	−1.23985e6	−0.252137
$476$	−471033.	−0.0952872
$477$	−2.39762e6	−0.482486
$478$	3.85910e6	0.772533
$479$	8.64913e6	1.72240	0.861199	−	0.508268i	$-0.169714\pi$
$479$	8.64913e6	1.72240	0.861199	+	0.508268i	$0.169714\pi$
$480$	−230400.	−0.0456435
$481$	1.16355e6	0.229310
$482$	1.04643e6	0.205160
$483$	367352.	0.0716497
$484$	−2.54784e6	−0.494378
$485$	3.92341e6	0.757372
$486$	−236196.	−0.0453609
$487$	5.39631e6	1.03104	0.515518	−	0.856879i	$-0.327599\pi$
$487$	5.39631e6	1.03104	0.515518	+	0.856879i	$0.327599\pi$
$488$	−502590.	−0.0955355
$489$	−3.21667e6	−0.608324
$490$	1.08536e6	0.204212
$491$	1.68658e6	0.315722	0.157861	−	0.987461i	$-0.449540\pi$
$491$	1.68658e6	0.315722	0.157861	+	0.987461i	$0.449540\pi$
$492$	1.33836e6	0.249264
$493$	1.85299e6	0.343365
$494$	1.43172e6	0.263961
$495$	−86169.8	−0.0158067
$496$	−511104.	−0.0932835
$497$	4.77450e6	0.867036
$498$	398683.	0.0720367
$499$	−1.19034e6	−0.214003	−0.107001	−	0.994259i	$-0.534125\pi$
$499$	−1.19034e6	−0.214003	−0.107001	+	0.994259i	$0.534125\pi$
$500$	250000.	0.0447214
$501$	−1.28318e6	−0.228399
$502$	1.33771e6	0.236920
$503$	5.60570e6	0.987894	0.493947	−	0.869492i	$-0.335554\pi$
$503$	5.60570e6	0.987894	0.493947	+	0.869492i	$0.335554\pi$
$504$	399990.	0.0701411
$505$	−1.46155e6	−0.255026
$506$	−90042.1	−0.0156340
$507$	−3.04865e6	−0.526729
$508$	−3.00453e6	−0.516555
$509$	−7.75363e6	−1.32651	−0.663255	−	0.748393i	$-0.730826\pi$
$509$	−7.75363e6	−1.32651	−0.663255	+	0.748393i	$0.730826\pi$
$510$	−343392.	−0.0584608
$511$	−1.74701e6	−0.295967
$512$	−262144.	−0.0441942
$513$	−1.44616e6	−0.242619
$514$	3.26435e6	0.544991
$515$	2.81253e6	0.467282
$516$	−561696.	−0.0928704
$517$	841108.	0.138397
$518$	1.99032e6	0.325911
$519$	5.96153e6	0.971492
$520$	−288687.	−0.0468186
$521$	5.83967e6	0.942527	0.471263	−	0.881993i	$-0.343798\pi$
$521$	5.83967e6	0.942527	0.471263	+	0.881993i	$0.343798\pi$
$522$	−1.57351e6	−0.252752
$523$	8.03048e6	1.28377	0.641885	−	0.766801i	$-0.278153\pi$
$523$	8.03048e6	1.28377	0.641885	+	0.766801i	$0.278153\pi$
$524$	3.38090e6	0.537903
$525$	−434017.	−0.0687240
$526$	−620856.	−0.0978422
$527$	−761757.	−0.119479
$528$	−98042.1	−0.0153048
$529$	279841.	0.0434783
$530$	2.96003e6	0.457726
$531$	459202.	0.0706752
$532$	2.44903e6	0.375159
$533$	1.67693e6	0.255681
$534$	−3.95695e6	−0.600492
$535$	−1.16725e6	−0.176311
$536$	1.12332e6	0.168885
$537$	−5.68739e6	−0.851093
$538$	3.89505e6	0.580172
$539$	461851.	0.0684747
$540$	291600.	0.0430331
$541$	−9.88586e6	−1.45218	−0.726092	−	0.687598i	$-0.758665\pi$
$541$	−9.88586e6	−1.45218	−0.726092	+	0.687598i	$0.758665\pi$
$542$	−1.28575e6	−0.188000
$543$	−912198.	−0.132767
$544$	−390704.	−0.0566044
$545$	−3.39459e6	−0.489548
$546$	501179.	0.0719468
$547$	7.24962e6	1.03597	0.517985	−	0.855390i	$-0.326682\pi$
$547$	7.24962e6	1.03597	0.517985	+	0.855390i	$0.326682\pi$
$548$	−5.25148e6	−0.747017
$549$	636091.	0.0900717
$550$	106382.	0.0149956
$551$	−9.63420e6	−1.35188
$552$	304704.	0.0425628
$553$	7.47114e6	1.03890
$554$	−4.35647e6	−0.603059
$555$	1.45098e6	0.199954
$556$	−927519.	−0.127244
$557$	1.07930e7	1.47403	0.737013	−	0.675879i	$-0.236236\pi$
$557$	1.07930e7	1.47403	0.737013	+	0.675879i	$0.236236\pi$
$558$	646866.	0.0879485
$559$	−703794.	−0.0952612
$560$	−493815.	−0.0665417
$561$	−146124.	−0.0196026
$562$	1.65353e6	0.220837
$563$	5.67088e6	0.754014	0.377007	−	0.926210i	$-0.376953\pi$
$563$	5.67088e6	0.754014	0.377007	+	0.926210i	$0.376953\pi$
$564$	−2.84632e6	−0.376779
$565$	1.23570e6	0.162852
$566$	−8.23452e6	−1.08043
$567$	−506237.	−0.0661297
$568$	3.96026e6	0.515055
$569$	4.43942e6	0.574837	0.287419	−	0.957805i	$-0.407203\pi$
$569$	4.43942e6	0.574837	0.287419	+	0.957805i	$0.407203\pi$
$570$	1.78539e6	0.230168
$571$	−8.25080e6	−1.05902	−0.529512	−	0.848302i	$-0.677625\pi$
$571$	−8.25080e6	−1.05902	−0.529512	+	0.848302i	$0.677625\pi$
$572$	−122845.	−0.0156988
$573$	−3.95998e6	−0.503856
$574$	2.86849e6	0.363391
$575$	−330625.	−0.0417029
$576$	331776.	0.0416667
$577$	5.63562e6	0.704697	0.352348	−	0.935869i	$-0.385383\pi$
$577$	5.63562e6	0.704697	0.352348	+	0.935869i	$0.385383\pi$
$578$	5.09712e6	0.634607
$579$	2.17518e6	0.269649
$580$	1.94261e6	0.239781
$581$	854494.	0.105019
$582$	−5.64971e6	−0.691383
$583$	1.25958e6	0.153481
$584$	−1.44908e6	−0.175816
$585$	365369.	0.0441410
$586$	2.33367e6	0.280734
$587$	−436511.	−0.0522877	−0.0261439	−	0.999658i	$-0.508323\pi$
$587$	−436511.	−0.0522877	−0.0261439	+	0.999658i	$0.508323\pi$
$588$	−1.56291e6	−0.186419
$589$	3.96058e6	0.470404
$590$	−566915.	−0.0670484
$591$	−8.13462e6	−0.958007
$592$	1.65089e6	0.193604
$593$	−29479.6	−0.00344259	−0.00172129	−	0.999999i	$-0.500548\pi$
$593$	−29479.6	−0.00344259	−0.00172129	+	0.999999i	$0.500548\pi$
$594$	124085.	0.0144295
$595$	−735990.	−0.0852274
$596$	−2.87034e6	−0.330993
$597$	4.79182e6	0.550256
$598$	381788.	0.0436585
$599$	−1.10133e7	−1.25416	−0.627079	−	0.778956i	$-0.715750\pi$
$599$	−1.10133e7	−1.25416	−0.627079	+	0.778956i	$0.715750\pi$
$600$	−360000.	−0.0408248
$601$	−1.60363e7	−1.81100	−0.905498	−	0.424351i	$-0.860502\pi$
$601$	−1.60363e7	−1.81100	−0.905498	+	0.424351i	$0.860502\pi$
$602$	−1.20388e6	−0.135392
$603$	−1.42170e6	−0.159227
$604$	5.98354e6	0.667369
$605$	−3.98101e6	−0.442185
$606$	2.10463e6	0.232806
$607$	−2.67319e6	−0.294482	−0.147241	−	0.989101i	$-0.547039\pi$
$607$	−2.67319e6	−0.294482	−0.147241	+	0.989101i	$0.547039\pi$
$608$	2.03138e6	0.222860
$609$	−3.37250e6	−0.368476
$610$	−785298.	−0.0854495
$611$	−3.56639e6	−0.386478
$612$	494484.	0.0533672
$613$	6.69430e6	0.719538	0.359769	−	0.933041i	$-0.382855\pi$
$613$	6.69430e6	0.719538	0.359769	+	0.933041i	$0.382855\pi$
$614$	2.69803e6	0.288819
$615$	2.09118e6	0.222948
$616$	−210133.	−0.0223122
$617$	−9.69098e6	−1.02484	−0.512418	−	0.858736i	$-0.671250\pi$
$617$	−9.69098e6	−1.02484	−0.512418	+	0.858736i	$0.671250\pi$
$618$	−4.05004e6	−0.426568
$619$	7.59391e6	0.796597	0.398299	−	0.917256i	$-0.369601\pi$
$619$	7.59391e6	0.796597	0.398299	+	0.917256i	$0.369601\pi$
$620$	−798599.	−0.0834353
$621$	−385641.	−0.0401286
$622$	1.34403e7	1.39295
$623$	−8.48090e6	−0.875431
$624$	415709.	0.0427393
$625$	390625.	0.0400000
$626$	5.20967e6	0.531342
$627$	759736.	0.0771781
$628$	2.54457e6	0.257464
$629$	2.46052e6	0.247971
$630$	624984.	0.0627361
$631$	1.59372e7	1.59345	0.796727	−	0.604340i	$-0.206563\pi$
$631$	1.59372e7	1.59345	0.796727	+	0.604340i	$0.206563\pi$
$632$	6.19702e6	0.617149
$633$	−8.53365e6	−0.846497
$634$	−7.85160e6	−0.775774
$635$	−4.69458e6	−0.462021
$636$	−4.26244e6	−0.417845
$637$	−1.95830e6	−0.191219
$638$	826638.	0.0804014
$639$	−5.01221e6	−0.485598
$640$	−409600.	−0.0395285
$641$	−6.80007e6	−0.653685	−0.326842	−	0.945079i	$-0.605985\pi$
$641$	−6.80007e6	−0.653685	−0.326842	+	0.945079i	$0.605985\pi$
$642$	1.68084e6	0.160950
$643$	6.95827e6	0.663703	0.331852	−	0.943332i	$-0.392327\pi$
$643$	6.95827e6	0.663703	0.331852	+	0.943332i	$0.392327\pi$
$644$	653070.	0.0620505
$645$	−877650.	−0.0830658
$646$	3.02759e6	0.285441
$647$	7.74025e6	0.726933	0.363467	−	0.931607i	$-0.381593\pi$
$647$	7.74025e6	0.726933	0.363467	+	0.931607i	$0.381593\pi$
$648$	−419904.	−0.0392837
$649$	−241240.	−0.0224821
$650$	−451073.	−0.0418758
$651$	1.38642e6	0.128216
$652$	−5.71853e6	−0.526824
$653$	−5.95091e6	−0.546135	−0.273068	−	0.961995i	$-0.588038\pi$
$653$	−5.95091e6	−0.546135	−0.273068	+	0.961995i	$0.588038\pi$
$654$	4.88820e6	0.446894
$655$	5.28265e6	0.481115
$656$	2.37930e6	0.215869
$657$	1.83399e6	0.165761
$658$	−6.10051e6	−0.549289
$659$	−9.90847e6	−0.888778	−0.444389	−	0.895834i	$-0.646579\pi$
$659$	−9.90847e6	−0.888778	−0.444389	+	0.895834i	$0.646579\pi$
$660$	−153191.	−0.0136890
$661$	1.57197e7	1.39939	0.699697	−	0.714440i	$-0.253318\pi$
$661$	1.57197e7	1.39939	0.699697	+	0.714440i	$0.253318\pi$
$662$	−5.67030e6	−0.502877
$663$	619579.	0.0547410
$664$	708769.	0.0623856
$665$	3.82661e6	0.335552
$666$	−2.08941e6	−0.182532
$667$	−2.56910e6	−0.223597
$668$	−2.28121e6	−0.197799
$669$	−2.34900e6	−0.202917
$670$	1.75519e6	0.151056
$671$	−334168.	−0.0286522
$672$	711093.	0.0607440
$673$	2.02204e7	1.72089	0.860444	−	0.509546i	$-0.170187\pi$
$673$	2.02204e7	1.72089	0.860444	+	0.509546i	$0.170187\pi$
$674$	6.57195e6	0.557243
$675$	455625.	0.0384900
$676$	−5.41981e6	−0.456160
$677$	−1.28279e7	−1.07568	−0.537842	−	0.843045i	$-0.680760\pi$
$677$	−1.28279e7	−1.07568	−0.537842	+	0.843045i	$0.680760\pi$
$678$	−1.77941e6	−0.148663
$679$	−1.21090e7	−1.00794
$680$	−610475.	−0.0506285
$681$	−1.17392e7	−0.969994
$682$	−339828.	−0.0279768
$683$	2.05046e7	1.68190	0.840951	−	0.541112i	$-0.181996\pi$
$683$	2.05046e7	1.68190	0.840951	+	0.541112i	$0.181996\pi$
$684$	−2.57096e6	−0.210114
$685$	−8.20544e6	−0.668152
$686$	−8.53700e6	−0.692620
$687$	7.14214e6	0.577346
$688$	−998571.	−0.0804281
$689$	−5.34075e6	−0.428602
$690$	476100.	0.0380693
$691$	−9.48903e6	−0.756009	−0.378004	−	0.925804i	$-0.623390\pi$
$691$	−9.48903e6	−0.756009	−0.378004	+	0.925804i	$0.623390\pi$
$692$	1.05983e7	0.841336
$693$	265950.	0.0210361
$694$	1.17903e7	0.929239
$695$	−1.44925e6	−0.113810
$696$	−2.79736e6	−0.218889
$697$	3.54615e6	0.276487
$698$	7.11336e6	0.552632
$699$	−1.22499e7	−0.948286
$700$	−771586.	−0.0595167
$701$	−2.14723e7	−1.65038	−0.825188	−	0.564858i	$-0.808931\pi$
$701$	−2.14723e7	−1.65038	−0.825188	+	0.564858i	$0.808931\pi$
$702$	−526131.	−0.0402950
$703$	−1.27929e7	−0.976295
$704$	−174297.	−0.0132543
$705$	−4.44738e6	−0.337001
$706$	2.66006e6	0.200854
$707$	4.51083e6	0.339397
$708$	816358.	0.0612065
$709$	1.37970e7	1.03079	0.515393	−	0.856954i	$-0.327646\pi$
$709$	1.37970e7	1.03079	0.515393	+	0.856954i	$0.327646\pi$
$710$	6.18791e6	0.460679
$711$	−7.84310e6	−0.581853
$712$	−7.03457e6	−0.520041
$713$	1.05615e6	0.0778038
$714$	1.05983e6	0.0778016
$715$	−191945.	−0.0140414
$716$	−1.01109e7	−0.737068
$717$	−8.68298e6	−0.630770
$718$	6.48130e6	0.469192
$719$	1.35919e7	0.980525	0.490262	−	0.871575i	$-0.336901\pi$
$719$	1.35919e7	0.980525	0.490262	+	0.871575i	$0.336901\pi$
$720$	518400.	0.0372678
$721$	−8.68042e6	−0.621874
$722$	−5.83690e6	−0.416715
$723$	−2.35447e6	−0.167512
$724$	−1.62169e6	−0.114979
$725$	3.03533e6	0.214467
$726$	5.73265e6	0.403658
$727$	6.70621e6	0.470588	0.235294	−	0.971924i	$-0.424395\pi$
$727$	6.70621e6	0.470588	0.235294	+	0.971924i	$0.424395\pi$
$728$	890986.	0.0623078
$729$	531441.	0.0370370
$730$	−2.26418e6	−0.157255
$731$	−1.48829e6	−0.103013
$732$	1.13083e6	0.0780044
$733$	−2.35635e7	−1.61987	−0.809934	−	0.586522i	$-0.800497\pi$
$733$	−2.35635e7	−1.61987	−0.809934	+	0.586522i	$0.800497\pi$
$734$	6.20806e6	0.425320
$735$	−2.44205e6	−0.166739
$736$	541696.	0.0368605
$737$	746885.	0.0506507
$738$	−3.01130e6	−0.203523
$739$	2.61039e6	0.175830	0.0879152	−	0.996128i	$-0.471980\pi$
$739$	2.61039e6	0.175830	0.0879152	+	0.996128i	$0.471980\pi$
$740$	2.57952e6	0.173165
$741$	−3.22136e6	−0.215523
$742$	−9.13566e6	−0.609158
$743$	−8.27676e6	−0.550032	−0.275016	−	0.961440i	$-0.588683\pi$
$743$	−8.27676e6	−0.550032	−0.275016	+	0.961440i	$0.588683\pi$
$744$	1.14998e6	0.0761656
$745$	−4.48491e6	−0.296049
$746$	−9.29007e6	−0.611184
$747$	−897036.	−0.0588177
$748$	−259775.	−0.0169763
$749$	3.60254e6	0.234641
$750$	−562500.	−0.0365148
$751$	6.51908e6	0.421781	0.210890	−	0.977510i	$-0.432364\pi$
$751$	6.51908e6	0.421781	0.210890	+	0.977510i	$0.432364\pi$
$752$	−5.06013e6	−0.326300
$753$	−3.00984e6	−0.193444
$754$	−3.50503e6	−0.224524
$755$	9.34928e6	0.596913
$756$	−899978.	−0.0572700
$757$	−1.62010e7	−1.02755	−0.513773	−	0.857926i	$-0.671753\pi$
$757$	−1.62010e7	−1.02755	−0.513773	+	0.857926i	$0.671753\pi$
$758$	−6.87422e6	−0.434561
$759$	202595.	0.0127651
$760$	3.17402e6	0.199332
$761$	2.77397e6	0.173636	0.0868181	−	0.996224i	$-0.472330\pi$
$761$	2.77397e6	0.173636	0.0868181	+	0.996224i	$0.472330\pi$
$762$	6.76019e6	0.421766
$763$	1.04769e7	0.651508
$764$	−7.03996e6	−0.436352
$765$	772632.	0.0477330
$766$	−1.25447e7	−0.772480
$767$	1.02288e6	0.0627822
$768$	589824.	0.0360844
$769$	1.84092e7	1.12259	0.561294	−	0.827617i	$-0.310304\pi$
$769$	1.84092e7	1.12259	0.561294	+	0.827617i	$0.310304\pi$
$770$	−328333.	−0.0199566
$771$	−7.34480e6	−0.444984
$772$	3.86698e6	0.233523
$773$	−4.41900e6	−0.265996	−0.132998	−	0.991116i	$-0.542460\pi$
$773$	−4.41900e6	−0.265996	−0.132998	+	0.991116i	$0.542460\pi$
$774$	1.26382e6	0.0758283
$775$	−1.24781e6	−0.0746268
$776$	−1.00439e7	−0.598755
$777$	−4.47822e6	−0.266105
$778$	1.76482e7	1.04532
$779$	−1.84374e7	−1.08857
$780$	649545.	0.0382272
$781$	2.63314e6	0.154471
$782$	807353.	0.0472113
$783$	3.54040e6	0.206371
$784$	−2.77851e6	−0.161444
$785$	3.97589e6	0.230282
$786$	−7.60702e6	−0.439196
$787$	−5.80700e6	−0.334206	−0.167103	−	0.985939i	$-0.553441\pi$
$787$	−5.80700e6	−0.334206	−0.167103	+	0.985939i	$0.553441\pi$
$788$	−1.44615e7	−0.829658
$789$	1.39693e6	0.0798878
$790$	9.68284e6	0.551995
$791$	−3.81381e6	−0.216729
$792$	220595.	0.0124963
$793$	1.41691e6	0.0800125
$794$	−4.94983e6	−0.278637
$795$	−6.66006e6	−0.373732
$796$	8.51879e6	0.476536
$797$	2.73241e7	1.52370	0.761852	−	0.647751i	$-0.224290\pi$
$797$	2.73241e7	1.52370	0.761852	+	0.647751i	$0.224290\pi$
$798$	−5.51032e6	−0.306316
$799$	−7.54170e6	−0.417929
$800$	−640000.	−0.0353553
$801$	8.90313e6	0.490299
$802$	3.49061e6	0.191631
$803$	−963477.	−0.0527293
$804$	−2.52747e6	−0.137894
$805$	1.02042e6	0.0554996
$806$	1.44091e6	0.0781264
$807$	−8.76385e6	−0.473709
$808$	3.74156e6	0.201616
$809$	1.80683e7	0.970612	0.485306	−	0.874344i	$-0.338708\pi$
$809$	1.80683e7	0.970612	0.485306	+	0.874344i	$0.338708\pi$
$810$	−656100.	−0.0351364
$811$	−1.39602e7	−0.745315	−0.372657	−	0.927969i	$-0.621553\pi$
$811$	−1.39602e7	−0.745315	−0.372657	+	0.927969i	$0.621553\pi$
$812$	−5.99556e6	−0.319109
$813$	2.89294e6	0.153502
$814$	1.09766e6	0.0580642
$815$	−8.93521e6	−0.471206
$816$	879083.	0.0462173
$817$	7.73801e6	0.405578
$818$	−760255.	−0.0397261
$819$	−1.12765e6	−0.0587443
$820$	3.71766e6	0.193079
$821$	−1.02018e7	−0.528227	−0.264114	−	0.964492i	$-0.585079\pi$
$821$	−1.02018e7	−0.528227	−0.264114	+	0.964492i	$0.585079\pi$
$822$	1.18158e7	0.609936
$823$	2.94656e6	0.151641	0.0758204	−	0.997121i	$-0.475842\pi$
$823$	2.94656e6	0.151641	0.0758204	+	0.997121i	$0.475842\pi$
$824$	−7.20007e6	−0.369418
$825$	−239361.	−0.0122438
$826$	1.74970e6	0.0892303
$827$	−8.62601e6	−0.438577	−0.219289	−	0.975660i	$-0.570374\pi$
$827$	−8.62601e6	−0.438577	−0.219289	+	0.975660i	$0.570374\pi$
$828$	−685584.	−0.0347524
$829$	−2.80448e7	−1.41732	−0.708658	−	0.705552i	$-0.750699\pi$
$829$	−2.80448e7	−1.41732	−0.708658	+	0.705552i	$0.750699\pi$
$830$	1.10745e6	0.0557994
$831$	9.80205e6	0.492396
$832$	739037.	0.0370133
$833$	−4.14114e6	−0.206779
$834$	2.08692e6	0.103894
$835$	−3.56440e6	−0.176917
$836$	1.35064e6	0.0668382
$837$	−1.45545e6	−0.0718097
$838$	−601261.	−0.0295769
$839$	3.20266e6	0.157075	0.0785373	−	0.996911i	$-0.474975\pi$
$839$	3.20266e6	0.157075	0.0785373	+	0.996911i	$0.474975\pi$
$840$	1.11108e6	0.0543311
$841$	3.07466e6	0.149902
$842$	−4.87823e6	−0.237128
$843$	−3.72044e6	−0.180312
$844$	−1.51709e7	−0.733088
$845$	−8.46846e6	−0.408002
$846$	6.40423e6	0.307639
$847$	1.22868e7	0.588476
$848$	−7.57767e6	−0.361865
$849$	1.85277e7	0.882169
$850$	−953867.	−0.0452835
$851$	−3.41142e6	−0.161477
$852$	−8.91059e6	−0.420540
$853$	−1.65194e7	−0.777359	−0.388680	−	0.921373i	$-0.627069\pi$
$853$	−1.65194e7	−0.777359	−0.388680	+	0.921373i	$0.627069\pi$
$854$	2.42370e6	0.113719
$855$	−4.01712e6	−0.187932
$856$	2.98817e6	0.139386
$857$	3.03608e7	1.41209	0.706043	−	0.708169i	$-0.250478\pi$
$857$	3.03608e7	1.41209	0.706043	+	0.708169i	$0.250478\pi$
$858$	276401.	0.0128180
$859$	6.43440e6	0.297526	0.148763	−	0.988873i	$-0.452471\pi$
$859$	6.43440e6	0.297526	0.148763	+	0.988873i	$0.452471\pi$
$860$	−1.56027e6	−0.0719371
$861$	−6.45410e6	−0.296707
$862$	1.93384e7	0.886445
$863$	1.22131e7	0.558214	0.279107	−	0.960260i	$-0.409962\pi$
$863$	1.22131e7	0.558214	0.279107	+	0.960260i	$0.409962\pi$
$864$	−746496.	−0.0340207
$865$	1.65598e7	0.752514
$866$	2.89165e6	0.131024
$867$	−1.14685e7	−0.518155
$868$	2.46475e6	0.111039
$869$	4.12034e6	0.185090
$870$	−4.37087e6	−0.195781
$871$	−3.16687e6	−0.141444
$872$	8.69014e6	0.387022
$873$	1.27118e7	0.564512
$874$	−4.19765e6	−0.185878
$875$	−1.20560e6	−0.0532334
$876$	3.26042e6	0.143553
$877$	1.12855e7	0.495477	0.247738	−	0.968827i	$-0.420313\pi$
$877$	1.12855e7	0.495477	0.247738	+	0.968827i	$0.420313\pi$
$878$	−2.99254e7	−1.31010
$879$	−5.25076e6	−0.229219
$880$	−272339.	−0.0118551
$881$	−2.96283e7	−1.28608	−0.643040	−	0.765833i	$-0.722327\pi$
$881$	−2.96283e7	−1.28608	−0.643040	+	0.765833i	$0.722327\pi$
$882$	3.51655e6	0.152211
$883$	−4.56032e6	−0.196831	−0.0984154	−	0.995145i	$-0.531377\pi$
$883$	−4.56032e6	−0.196831	−0.0984154	+	0.995145i	$0.531377\pi$
$884$	1.10147e6	0.0474071
$885$	1.27556e6	0.0547448
$886$	−3.05951e7	−1.30939
$887$	3.77652e7	1.61169	0.805846	−	0.592125i	$-0.201711\pi$
$887$	3.77652e7	1.61169	0.805846	+	0.592125i	$0.201711\pi$
$888$	−3.71451e6	−0.158077
$889$	1.44891e7	0.614874
$890$	−1.09915e7	−0.465139
$891$	−279190.	−0.0117816
$892$	−4.17600e6	−0.175731
$893$	3.92114e7	1.64544
$894$	6.45827e6	0.270254
$895$	−1.57983e7	−0.659254
$896$	1.26417e6	0.0526059
$897$	−859023.	−0.0356471
$898$	−4.92106e6	−0.203642
$899$	−9.69604e6	−0.400125
$900$	810000.	0.0333333
$901$	−1.12939e7	−0.463480
$902$	1.58197e6	0.0647415
$903$	2.70873e6	0.110547
$904$	−3.16340e6	−0.128746
$905$	−2.53388e6	−0.102841
$906$	−1.34630e7	−0.544904
$907$	−2.20530e7	−0.890120	−0.445060	−	0.895501i	$-0.646818\pi$
$907$	−2.20530e7	−0.890120	−0.445060	+	0.895501i	$0.646818\pi$
$908$	−2.08696e7	−0.840040
$909$	−4.73541e6	−0.190085
$910$	1.39217e6	0.0557298
$911$	−1.47228e7	−0.587751	−0.293875	−	0.955844i	$-0.594945\pi$
$911$	−1.47228e7	−0.587751	−0.293875	+	0.955844i	$0.594945\pi$
$912$	−4.57059e6	−0.181964
$913$	471254.	0.0187102
$914$	−3.12064e6	−0.123560
$915$	1.76692e6	0.0697693
$916$	1.26971e7	0.499997
$917$	−1.63041e7	−0.640284
$918$	−1.11259e6	−0.0435741
$919$	1.25403e7	0.489800	0.244900	−	0.969548i	$-0.421245\pi$
$919$	1.25403e7	0.489800	0.244900	+	0.969548i	$0.421245\pi$
$920$	846400.	0.0329690
$921$	−6.07057e6	−0.235820
$922$	1.64309e7	0.636552
$923$	−1.11648e7	−0.431366
$924$	472799.	0.0182178
$925$	4.03050e6	0.154883
$926$	6.90091e6	0.264471
$927$	9.11259e6	0.348291
$928$	−4.97308e6	−0.189564
$929$	2.95361e7	1.12283	0.561416	−	0.827534i	$-0.310257\pi$
$929$	2.95361e7	1.12283	0.561416	+	0.827534i	$0.310257\pi$
$930$	1.79685e6	0.0681246
$931$	2.15309e7	0.814119
$932$	−2.17776e7	−0.821239
$933$	−3.02408e7	−1.13734
$934$	−2.38181e6	−0.0893389
$935$	−405899.	−0.0151841
$936$	−935344.	−0.0348965
$937$	4.31594e7	1.60593	0.802964	−	0.596027i	$-0.203255\pi$
$937$	4.31594e7	1.60593	0.802964	+	0.596027i	$0.203255\pi$
$938$	−5.41711e6	−0.201030
$939$	−1.17217e7	−0.433839
$940$	−7.90646e6	−0.291852
$941$	4.92320e7	1.81248	0.906240	−	0.422764i	$-0.138940\pi$
$941$	4.92320e7	1.81248	0.906240	+	0.422764i	$0.138940\pi$
$942$	−5.72529e6	−0.210218
$943$	−4.91660e6	−0.180047
$944$	1.45130e6	0.0530064
$945$	−1.40622e6	−0.0512239
$946$	−663940.	−0.0241213
$947$	−1.49578e7	−0.541992	−0.270996	−	0.962581i	$-0.587353\pi$
$947$	−1.49578e7	−0.541992	−0.270996	+	0.962581i	$0.587353\pi$
$948$	−1.39433e7	−0.503900
$949$	4.08524e6	0.147249
$950$	4.95941e6	0.178288
$951$	1.76661e7	0.633416
$952$	1.88413e6	0.0673782
$953$	1.14823e7	0.409541	0.204771	−	0.978810i	$-0.434355\pi$
$953$	1.14823e7	0.409541	0.204771	+	0.978810i	$0.434355\pi$
$954$	9.59049e6	0.341169
$955$	−1.09999e7	−0.390285
$956$	−1.54364e7	−0.546263
$957$	−1.85994e6	−0.0656475
$958$	−3.45965e7	−1.21792
$959$	2.53248e7	0.889200
$960$	921600.	0.0322749
$961$	−2.46431e7	−0.860771
$962$	−4.65421e6	−0.162147
$963$	−3.78190e6	−0.131415
$964$	−4.18572e6	−0.145070
$965$	6.04216e6	0.208869
$966$	−1.46941e6	−0.0506640
$967$	4.70177e7	1.61695	0.808473	−	0.588534i	$-0.200295\pi$
$967$	4.70177e7	1.61695	0.808473	+	0.588534i	$0.200295\pi$
$968$	1.01914e7	0.349578
$969$	−6.81209e6	−0.233062
$970$	−1.56936e7	−0.535543
$971$	−1.37185e7	−0.466939	−0.233469	−	0.972364i	$-0.575008\pi$
$971$	−1.37185e7	−0.466939	−0.233469	+	0.972364i	$0.575008\pi$
$972$	944784.	0.0320750
$973$	4.47288e6	0.151462
$974$	−2.15852e7	−0.729053
$975$	1.01491e6	0.0341914
$976$	2.01036e6	0.0675538
$977$	3.65530e6	0.122514	0.0612571	−	0.998122i	$-0.480489\pi$
$977$	3.65530e6	0.122514	0.0612571	+	0.998122i	$0.480489\pi$
$978$	1.28667e7	0.430150
$979$	−4.67722e6	−0.155966
$980$	−4.34142e6	−0.144400
$981$	−1.09985e7	−0.364888
$982$	−6.74634e6	−0.223249
$983$	−2.08184e7	−0.687169	−0.343584	−	0.939122i	$-0.611641\pi$
$983$	−2.08184e7	−0.687169	−0.343584	+	0.939122i	$0.611641\pi$
$984$	−5.35343e6	−0.176256
$985$	−2.25962e7	−0.742069
$986$	−7.41196e6	−0.242796
$987$	1.37261e7	0.448493
$988$	−5.72686e6	−0.186648
$989$	2.06345e6	0.0670817
$990$	344679.	0.0111770
$991$	−3.18309e7	−1.02959	−0.514796	−	0.857313i	$-0.672132\pi$
$991$	−3.18309e7	−1.02959	−0.514796	+	0.857313i	$0.672132\pi$
$992$	2.04441e6	0.0659614
$993$	1.27582e7	0.410597
$994$	−1.90980e7	−0.613087
$995$	1.33106e7	0.426227
$996$	−1.59473e6	−0.0509377
$997$	4.17660e7	1.33071	0.665357	−	0.746526i	$-0.268279\pi$
$997$	4.17660e7	1.33071	0.665357	+	0.746526i	$0.268279\pi$
$998$	4.76135e6	0.151323
$999$	4.70118e6	0.149037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.6.a.g.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.6.a.g.1.1	✓	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	690.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -77.1586 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -77.1586 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -42.5530 q^{11} +144.000 q^{12} +180.429 q^{13} +308.634 q^{14} +225.000 q^{15} +256.000 q^{16} +381.547 q^{17} -324.000 q^{18} -1983.76 q^{19} +400.000 q^{20} -694.427 q^{21} +170.212 q^{22} -529.000 q^{23} -576.000 q^{24} +625.000 q^{25} -721.716 q^{26} +729.000 q^{27} -1234.54 q^{28} +4856.52 q^{29} -900.000 q^{30} -1996.50 q^{31} -1024.00 q^{32} -382.977 q^{33} -1526.19 q^{34} -1928.96 q^{35} +1296.00 q^{36} +6448.80 q^{37} +7935.06 q^{38} +1623.86 q^{39} -1600.00 q^{40} +9294.14 q^{41} +2777.71 q^{42} -3900.67 q^{43} -680.848 q^{44} +2025.00 q^{45} +2116.00 q^{46} -19766.1 q^{47} +2304.00 q^{48} -10853.6 q^{49} -2500.00 q^{50} +3433.92 q^{51} +2886.87 q^{52} -29600.3 q^{53} -2916.00 q^{54} -1063.82 q^{55} +4938.15 q^{56} -17853.9 q^{57} -19426.1 q^{58} +5669.15 q^{59} +3600.00 q^{60} +7852.98 q^{61} +7985.99 q^{62} -6249.84 q^{63} +4096.00 q^{64} +4510.73 q^{65} +1531.91 q^{66} -17551.9 q^{67} +6104.75 q^{68} -4761.00 q^{69} +7715.86 q^{70} -61879.1 q^{71} -5184.00 q^{72} +22641.8 q^{73} -25795.2 q^{74} +5625.00 q^{75} -31740.2 q^{76} +3283.33 q^{77} -6495.45 q^{78} -96828.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} -37176.6 q^{82} -11074.5 q^{83} -11110.8 q^{84} +9538.67 q^{85} +15602.7 q^{86} +43708.7 q^{87} +2723.39 q^{88} +109915. q^{89} -8100.00 q^{90} -13921.7 q^{91} -8464.00 q^{92} -17968.5 q^{93} +79064.6 q^{94} -49594.1 q^{95} -9216.00 q^{96} +156936. q^{97} +43414.2 q^{98} -3446.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 730 q^{11} + 576 q^{12} - 828 q^{13} - 100 q^{14} + 900 q^{15} + 1024 q^{16} - 179 q^{17} - 1296 q^{18} + 1568 q^{19} + 1600 q^{20} + 225 q^{21} + 2920 q^{22} - 2116 q^{23} - 2304 q^{24} + 2500 q^{25} + 3312 q^{26} + 2916 q^{27} + 400 q^{28} - 1917 q^{29} - 3600 q^{30} - 6331 q^{31} - 4096 q^{32} - 6570 q^{33} + 716 q^{34} + 625 q^{35} + 5184 q^{36} + 10127 q^{37} - 6272 q^{38} - 7452 q^{39} - 6400 q^{40} - 14527 q^{41} - 900 q^{42} - 18052 q^{43} - 11680 q^{44} + 8100 q^{45} + 8464 q^{46} - 13208 q^{47} + 9216 q^{48} - 52681 q^{49} - 10000 q^{50} - 1611 q^{51} - 13248 q^{52} - 39327 q^{53} - 11664 q^{54} - 18250 q^{55} - 1600 q^{56} + 14112 q^{57} + 7668 q^{58} - 43301 q^{59} + 14400 q^{60} - 25154 q^{61} + 25324 q^{62} + 2025 q^{63} + 16384 q^{64} - 20700 q^{65} + 26280 q^{66} - 15827 q^{67} - 2864 q^{68} - 19044 q^{69} - 2500 q^{70} - 20999 q^{71} - 20736 q^{72} - 35844 q^{73} - 40508 q^{74} + 22500 q^{75} + 25088 q^{76} - 16142 q^{77} + 29808 q^{78} - 100414 q^{79} + 25600 q^{80} + 26244 q^{81} + 58108 q^{82} - 140015 q^{83} + 3600 q^{84} - 4475 q^{85} + 72208 q^{86} - 17253 q^{87} + 46720 q^{88} - 26030 q^{89} - 32400 q^{90} + 34190 q^{91} - 33856 q^{92} - 56979 q^{93} + 52832 q^{94} + 39200 q^{95} - 36864 q^{96} - 16946 q^{97} + 210724 q^{98} - 59130 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 730 * q^11 + 576 * q^12 - 828 * q^13 - 100 * q^14 + 900 * q^15 + 1024 * q^16 - 179 * q^17 - 1296 * q^18 + 1568 * q^19 + 1600 * q^20 + 225 * q^21 + 2920 * q^22 - 2116 * q^23 - 2304 * q^24 + 2500 * q^25 + 3312 * q^26 + 2916 * q^27 + 400 * q^28 - 1917 * q^29 - 3600 * q^30 - 6331 * q^31 - 4096 * q^32 - 6570 * q^33 + 716 * q^34 + 625 * q^35 + 5184 * q^36 + 10127 * q^37 - 6272 * q^38 - 7452 * q^39 - 6400 * q^40 - 14527 * q^41 - 900 * q^42 - 18052 * q^43 - 11680 * q^44 + 8100 * q^45 + 8464 * q^46 - 13208 * q^47 + 9216 * q^48 - 52681 * q^49 - 10000 * q^50 - 1611 * q^51 - 13248 * q^52 - 39327 * q^53 - 11664 * q^54 - 18250 * q^55 - 1600 * q^56 + 14112 * q^57 + 7668 * q^58 - 43301 * q^59 + 14400 * q^60 - 25154 * q^61 + 25324 * q^62 + 2025 * q^63 + 16384 * q^64 - 20700 * q^65 + 26280 * q^66 - 15827 * q^67 - 2864 * q^68 - 19044 * q^69 - 2500 * q^70 - 20999 * q^71 - 20736 * q^72 - 35844 * q^73 - 40508 * q^74 + 22500 * q^75 + 25088 * q^76 - 16142 * q^77 + 29808 * q^78 - 100414 * q^79 + 25600 * q^80 + 26244 * q^81 + 58108 * q^82 - 140015 * q^83 + 3600 * q^84 - 4475 * q^85 + 72208 * q^86 - 17253 * q^87 + 46720 * q^88 - 26030 * q^89 - 32400 * q^90 + 34190 * q^91 - 33856 * q^92 - 56979 * q^93 + 52832 * q^94 + 39200 * q^95 - 36864 * q^96 - 16946 * q^97 + 210724 * q^98 - 59130 * q^99

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