LMFDB - Embedded newform 33.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(1,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("33.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.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:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{313}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 78 $ x^2 - x - 78
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-8.34590$ of defining polynomial
Character	$\chi$	$=$	33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.34590 q^{2} -9.00000 q^{3} +37.6541 q^{4} -107.459 q^{5} +75.1131 q^{6} -26.6918 q^{7} -47.1885 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-8.34590 q^{2} -9.00000 q^{3} +37.6541 q^{4} -107.459 q^{5} +75.1131 q^{6} -26.6918 q^{7} -47.1885 q^{8} +81.0000 q^{9} +896.843 q^{10} +121.000 q^{11} -338.887 q^{12} +904.666 q^{13} +222.767 q^{14} +967.131 q^{15} -811.100 q^{16} -495.384 q^{17} -676.018 q^{18} -1501.38 q^{19} -4046.27 q^{20} +240.226 q^{21} -1009.85 q^{22} +2393.01 q^{23} +424.697 q^{24} +8422.44 q^{25} -7550.25 q^{26} -729.000 q^{27} -1005.06 q^{28} -5132.34 q^{29} -8071.58 q^{30} -410.309 q^{31} +8279.40 q^{32} -1089.00 q^{33} +4134.42 q^{34} +2868.28 q^{35} +3049.98 q^{36} +5828.69 q^{37} +12530.4 q^{38} -8141.99 q^{39} +5070.84 q^{40} +18561.8 q^{41} -2004.91 q^{42} -788.920 q^{43} +4556.15 q^{44} -8704.18 q^{45} -19971.8 q^{46} +3979.11 q^{47} +7299.90 q^{48} -16094.5 q^{49} -70292.9 q^{50} +4458.45 q^{51} +34064.4 q^{52} +15130.5 q^{53} +6084.16 q^{54} -13002.5 q^{55} +1259.55 q^{56} +13512.5 q^{57} +42834.0 q^{58} +41623.5 q^{59} +36416.5 q^{60} -29989.8 q^{61} +3424.40 q^{62} -2162.04 q^{63} -43143.8 q^{64} -97214.5 q^{65} +9088.69 q^{66} +25890.3 q^{67} -18653.2 q^{68} -21537.1 q^{69} -23938.3 q^{70} +58163.0 q^{71} -3822.27 q^{72} +23875.3 q^{73} -48645.7 q^{74} -75802.0 q^{75} -56533.2 q^{76} -3229.71 q^{77} +67952.3 q^{78} +27402.8 q^{79} +87160.0 q^{80} +6561.00 q^{81} -154915. q^{82} +24056.3 q^{83} +9045.50 q^{84} +53233.4 q^{85} +6584.25 q^{86} +46191.1 q^{87} -5709.81 q^{88} -55820.0 q^{89} +72644.3 q^{90} -24147.2 q^{91} +90106.5 q^{92} +3692.78 q^{93} -33209.3 q^{94} +161337. q^{95} -74514.6 q^{96} -101188. q^{97} +134324. q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 18 q^{3} + 93 q^{4} - 38 q^{5} - 9 q^{6} - 18 q^{7} + 171 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q + q^2 - 18 * q^3 + 93 * q^4 - 38 * q^5 - 9 * q^6 - 18 * q^7 + 171 * q^8 + 162 * q^9	\( 2 q + q^{2} - 18 q^{3} + 93 q^{4} - 38 q^{5} - 9 q^{6} - 18 q^{7} + 171 q^{8} + 162 q^{9} + 1546 q^{10} + 242 q^{11} - 837 q^{12} - 66 q^{13} + 304 q^{14} + 342 q^{15} - 543 q^{16} - 920 q^{17} + 81 q^{18} - 2932 q^{19} - 202 q^{20} + 162 q^{21} + 121 q^{22} + 5246 q^{23} - 1539 q^{24} + 10122 q^{25} - 16622 q^{26} - 1458 q^{27} - 524 q^{28} - 12600 q^{29} - 13914 q^{30} + 9936 q^{31} + 3803 q^{32} - 2178 q^{33} + 166 q^{34} + 3472 q^{35} + 7533 q^{36} + 5996 q^{37} - 840 q^{38} + 594 q^{39} + 20226 q^{40} + 24244 q^{41} - 2736 q^{42} + 20360 q^{43} + 11253 q^{44} - 3078 q^{45} + 6692 q^{46} - 5806 q^{47} + 4887 q^{48} - 32826 q^{49} - 54409 q^{50} + 8280 q^{51} - 19658 q^{52} + 40770 q^{53} - 729 q^{54} - 4598 q^{55} + 3156 q^{56} + 26388 q^{57} - 26958 q^{58} + 18212 q^{59} + 1818 q^{60} - 11398 q^{61} + 100120 q^{62} - 1458 q^{63} - 93559 q^{64} - 164636 q^{65} - 1089 q^{66} + 65368 q^{67} - 42154 q^{68} - 47214 q^{69} - 18296 q^{70} + 61446 q^{71} + 13851 q^{72} + 53412 q^{73} - 47082 q^{74} - 91098 q^{75} - 135712 q^{76} - 2178 q^{77} + 149598 q^{78} + 17122 q^{79} + 105782 q^{80} + 13122 q^{81} - 101810 q^{82} - 14304 q^{83} + 4716 q^{84} + 23740 q^{85} + 204240 q^{86} + 113400 q^{87} + 20691 q^{88} - 58140 q^{89} + 125226 q^{90} - 32584 q^{91} + 248008 q^{92} - 89424 q^{93} - 124660 q^{94} + 61968 q^{95} - 34227 q^{96} - 183056 q^{97} - 22047 q^{98} + 19602 q^{99}+O(q^{100}) \) 2 * q + q^2 - 18 * q^3 + 93 * q^4 - 38 * q^5 - 9 * q^6 - 18 * q^7 + 171 * q^8 + 162 * q^9 + 1546 * q^10 + 242 * q^11 - 837 * q^12 - 66 * q^13 + 304 * q^14 + 342 * q^15 - 543 * q^16 - 920 * q^17 + 81 * q^18 - 2932 * q^19 - 202 * q^20 + 162 * q^21 + 121 * q^22 + 5246 * q^23 - 1539 * q^24 + 10122 * q^25 - 16622 * q^26 - 1458 * q^27 - 524 * q^28 - 12600 * q^29 - 13914 * q^30 + 9936 * q^31 + 3803 * q^32 - 2178 * q^33 + 166 * q^34 + 3472 * q^35 + 7533 * q^36 + 5996 * q^37 - 840 * q^38 + 594 * q^39 + 20226 * q^40 + 24244 * q^41 - 2736 * q^42 + 20360 * q^43 + 11253 * q^44 - 3078 * q^45 + 6692 * q^46 - 5806 * q^47 + 4887 * q^48 - 32826 * q^49 - 54409 * q^50 + 8280 * q^51 - 19658 * q^52 + 40770 * q^53 - 729 * q^54 - 4598 * q^55 + 3156 * q^56 + 26388 * q^57 - 26958 * q^58 + 18212 * q^59 + 1818 * q^60 - 11398 * q^61 + 100120 * q^62 - 1458 * q^63 - 93559 * q^64 - 164636 * q^65 - 1089 * q^66 + 65368 * q^67 - 42154 * q^68 - 47214 * q^69 - 18296 * q^70 + 61446 * q^71 + 13851 * q^72 + 53412 * q^73 - 47082 * q^74 - 91098 * q^75 - 135712 * q^76 - 2178 * q^77 + 149598 * q^78 + 17122 * q^79 + 105782 * q^80 + 13122 * q^81 - 101810 * q^82 - 14304 * q^83 + 4716 * q^84 + 23740 * q^85 + 204240 * q^86 + 113400 * q^87 + 20691 * q^88 - 58140 * q^89 + 125226 * q^90 - 32584 * q^91 + 248008 * q^92 - 89424 * q^93 - 124660 * q^94 + 61968 * q^95 - 34227 * q^96 - 183056 * q^97 - 22047 * q^98 + 19602 * 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 $

$2$	−8.34590	−1.47536	−0.737681	−	0.675150i	$-0.764079\pi$
$2$	−8.34590	−1.47536	−0.737681	+	0.675150i	$0.764079\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	37.6541	1.17669
$5$	−107.459	−1.92229	−0.961143	−	0.276052i	$-0.910974\pi$
$5$	−107.459	−1.92229	−0.961143	+	0.276052i	$0.910974\pi$
$6$	75.1131	0.851800
$7$	−26.6918	−0.205889	−0.102944	−	0.994687i	$-0.532826\pi$
$7$	−26.6918	−0.205889	−0.102944	+	0.994687i	$0.532826\pi$
$8$	−47.1885	−0.260682
$9$	81.0000	0.333333
$10$	896.843	2.83607
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−338.887	−0.679363
$13$	904.666	1.48467	0.742335	−	0.670029i	$-0.233718\pi$
$13$	904.666	1.48467	0.742335	+	0.670029i	$0.233718\pi$
$14$	222.767	0.303760
$15$	967.131	1.10983
$16$	−811.100	−0.792090
$17$	−495.384	−0.415738	−0.207869	−	0.978157i	$-0.566653\pi$
$17$	−495.384	−0.415738	−0.207869	+	0.978157i	$0.566653\pi$
$18$	−676.018	−0.491787
$19$	−1501.38	−0.954130	−0.477065	−	0.878868i	$-0.658299\pi$
$19$	−1501.38	−0.954130	−0.477065	+	0.878868i	$0.658299\pi$
$20$	−4046.27	−2.26194
$21$	240.226	0.118870
$22$	−1009.85	−0.444838
$23$	2393.01	0.943245	0.471622	−	0.881801i	$-0.343669\pi$
$23$	2393.01	0.943245	0.471622	+	0.881801i	$0.343669\pi$
$24$	424.697	0.150505
$25$	8422.44	2.69518
$26$	−7550.25	−2.19042
$27$	−729.000	−0.192450
$28$	−1005.06	−0.242267
$29$	−5132.34	−1.13324	−0.566618	−	0.823980i	$-0.691749\pi$
$29$	−5132.34	−1.13324	−0.566618	+	0.823980i	$0.691749\pi$
$30$	−8071.58	−1.63740
$31$	−410.309	−0.0766844	−0.0383422	−	0.999265i	$-0.512208\pi$
$31$	−410.309	−0.0766844	−0.0383422	+	0.999265i	$0.512208\pi$
$32$	8279.40	1.42930
$33$	−1089.00	−0.174078
$34$	4134.42	0.613363
$35$	2868.28	0.395777
$36$	3049.98	0.392230
$37$	5828.69	0.699949	0.349975	−	0.936759i	$-0.386190\pi$
$37$	5828.69	0.699949	0.349975	+	0.936759i	$0.386190\pi$
$38$	12530.4	1.40769
$39$	−8141.99	−0.857174
$40$	5070.84	0.501106
$41$	18561.8	1.72449	0.862245	−	0.506491i	$-0.169058\pi$
$41$	18561.8	1.72449	0.862245	+	0.506491i	$0.169058\pi$
$42$	−2004.91	−0.175376
$43$	−788.920	−0.0650671	−0.0325336	−	0.999471i	$-0.510358\pi$
$43$	−788.920	−0.0650671	−0.0325336	+	0.999471i	$0.510358\pi$
$44$	4556.15	0.354786
$45$	−8704.18	−0.640762
$46$	−19971.8	−1.39163
$47$	3979.11	0.262749	0.131375	−	0.991333i	$-0.458061\pi$
$47$	3979.11	0.262749	0.131375	+	0.991333i	$0.458061\pi$
$48$	7299.90	0.457313
$49$	−16094.5	−0.957610
$50$	−70292.9	−3.97637
$51$	4458.45	0.240026
$52$	34064.4	1.74700
$53$	15130.5	0.739886	0.369943	−	0.929055i	$-0.379377\pi$
$53$	15130.5	0.739886	0.369943	+	0.929055i	$0.379377\pi$
$54$	6084.16	0.283933
$55$	−13002.5	−0.579591
$56$	1259.55	0.0536716
$57$	13512.5	0.550867
$58$	42834.0	1.67193
$59$	41623.5	1.55671	0.778357	−	0.627822i	$-0.216053\pi$
$59$	41623.5	1.55671	0.778357	+	0.627822i	$0.216053\pi$
$60$	36416.5	1.30593
$61$	−29989.8	−1.03193	−0.515964	−	0.856610i	$-0.672566\pi$
$61$	−29989.8	−1.03193	−0.515964	+	0.856610i	$0.672566\pi$
$62$	3424.40	0.113137
$63$	−2162.04	−0.0686296
$64$	−43143.8	−1.31665
$65$	−97214.5	−2.85396
$66$	9088.69	0.256827
$67$	25890.3	0.704613	0.352307	−	0.935885i	$-0.385397\pi$
$67$	25890.3	0.704613	0.352307	+	0.935885i	$0.385397\pi$
$68$	−18653.2	−0.489195
$69$	−21537.1	−0.544582
$70$	−23938.3	−0.583914
$71$	58163.0	1.36931	0.684654	−	0.728869i	$-0.259954\pi$
$71$	58163.0	1.36931	0.684654	+	0.728869i	$0.259954\pi$
$72$	−3822.27	−0.0868941
$73$	23875.3	0.524375	0.262187	−	0.965017i	$-0.415556\pi$
$73$	23875.3	0.524375	0.262187	+	0.965017i	$0.415556\pi$
$74$	−48645.7	−1.03268
$75$	−75802.0	−1.55606
$76$	−56533.2	−1.12272
$77$	−3229.71	−0.0620778
$78$	67952.3	1.26464
$79$	27402.8	0.494000	0.247000	−	0.969016i	$-0.420555\pi$
$79$	27402.8	0.494000	0.247000	+	0.969016i	$0.420555\pi$
$80$	87160.0	1.52262
$81$	6561.00	0.111111
$82$	−154915.	−2.54425
$83$	24056.3	0.383296	0.191648	−	0.981464i	$-0.438617\pi$
$83$	24056.3	0.383296	0.191648	+	0.981464i	$0.438617\pi$
$84$	9045.50	0.139873
$85$	53233.4	0.799166
$86$	6584.25	0.0959975
$87$	46191.1	0.654274
$88$	−5709.81	−0.0785987
$89$	−55820.0	−0.746990	−0.373495	−	0.927632i	$-0.621841\pi$
$89$	−55820.0	−0.746990	−0.373495	+	0.927632i	$0.621841\pi$
$90$	72644.3	0.945355
$91$	−24147.2	−0.305677
$92$	90106.5	1.10991
$93$	3692.78	0.0442737
$94$	−33209.3	−0.387650
$95$	161337.	1.83411
$96$	−74514.6	−0.825207
$97$	−101188.	−1.09194	−0.545970	−	0.837805i	$-0.683839\pi$
$97$	−101188.	−1.09194	−0.545970	+	0.837805i	$0.683839\pi$
$98$	134324.	1.41282
$99$	9801.00	0.100504
$100$	317139.	3.17139
$101$	−75190.1	−0.733428	−0.366714	−	0.930334i	$-0.619517\pi$
$101$	−75190.1	−0.733428	−0.366714	+	0.930334i	$0.619517\pi$
$102$	−37209.8	−0.354125
$103$	176059.	1.63518	0.817590	−	0.575801i	$-0.195310\pi$
$103$	176059.	1.63518	0.817590	+	0.575801i	$0.195310\pi$
$104$	−42689.9	−0.387027
$105$	−25814.5	−0.228502
$106$	−126278.	−1.09160
$107$	−124963.	−1.05517	−0.527586	−	0.849501i	$-0.676903\pi$
$107$	−124963.	−1.05517	−0.527586	+	0.849501i	$0.676903\pi$
$108$	−27449.8	−0.226454
$109$	48001.5	0.386980	0.193490	−	0.981102i	$-0.438019\pi$
$109$	48001.5	0.386980	0.193490	+	0.981102i	$0.438019\pi$
$110$	108518.	0.855106
$111$	−52458.2	−0.404116
$112$	21649.7	0.163082
$113$	38955.6	0.286995	0.143497	−	0.989651i	$-0.454165\pi$
$113$	38955.6	0.286995	0.143497	+	0.989651i	$0.454165\pi$
$114$	−112774.	−0.812728
$115$	−257150.	−1.81319
$116$	−193254.	−1.33347
$117$	73277.9	0.494890
$118$	−347386.	−2.29672
$119$	13222.7	0.0855957
$120$	−45637.5	−0.289314
$121$	14641.0	0.0909091
$122$	250292.	1.52247
$123$	−167056.	−0.995635
$124$	−15449.8	−0.0902338
$125$	−569258.	−3.25862
$126$	18044.1	0.101253
$127$	186757.	1.02746	0.513732	−	0.857951i	$-0.328262\pi$
$127$	186757.	1.02746	0.513732	+	0.857951i	$0.328262\pi$
$128$	95133.6	0.513226
$129$	7100.28	0.0375665
$130$	811343.	4.21062
$131$	−363603.	−1.85118	−0.925592	−	0.378523i	$-0.876432\pi$
$131$	−363603.	−1.85118	−0.925592	+	0.378523i	$0.876432\pi$
$132$	−41005.3	−0.204836
$133$	40074.6	0.196445
$134$	−216078.	−1.03956
$135$	78337.6	0.369944
$136$	23376.4	0.108375
$137$	−74002.6	−0.336857	−0.168429	−	0.985714i	$-0.553869\pi$
$137$	−74002.6	−0.336857	−0.168429	+	0.985714i	$0.553869\pi$
$138$	179746.	0.803456
$139$	70042.3	0.307485	0.153742	−	0.988111i	$-0.450867\pi$
$139$	70042.3	0.307485	0.153742	+	0.988111i	$0.450867\pi$
$140$	108002.	0.465707
$141$	−35812.0	−0.151698
$142$	−485423.	−2.02022
$143$	109465.	0.447645
$144$	−65699.1	−0.264030
$145$	551516.	2.17840
$146$	−199261.	−0.773642
$147$	144851.	0.552876
$148$	219474.	0.823624
$149$	327767.	1.20948	0.604741	−	0.796422i	$-0.293276\pi$
$149$	327767.	1.20948	0.604741	+	0.796422i	$0.293276\pi$
$150$	632636.	2.29576
$151$	519.828	0.00185531	0.000927656	−	1.00000i	$-0.499705\pi$
$151$	519.828	0.00185531	0.000927656		1.00000i	$0.499705\pi$
$152$	70848.1	0.248725
$153$	−40126.1	−0.138579
$154$	26954.8	0.0915872
$155$	44091.4	0.147409
$156$	−306579.	−1.00863
$157$	−119470.	−0.386821	−0.193411	−	0.981118i	$-0.561955\pi$
$157$	−119470.	−0.386821	−0.193411	+	0.981118i	$0.561955\pi$
$158$	−228701.	−0.728828
$159$	−136175.	−0.427173
$160$	−889696.	−2.74752
$161$	−63873.7	−0.194204
$162$	−54757.5	−0.163929
$163$	314012.	0.925716	0.462858	−	0.886432i	$-0.346824\pi$
$163$	314012.	0.925716	0.462858	+	0.886432i	$0.346824\pi$
$164$	698928.	2.02919
$165$	117023.	0.334627
$166$	−200772.	−0.565500
$167$	281877.	0.782111	0.391056	−	0.920367i	$-0.372110\pi$
$167$	281877.	0.782111	0.391056	+	0.920367i	$0.372110\pi$
$168$	−11335.9	−0.0309873
$169$	447127.	1.20424
$170$	−444281.	−1.17906
$171$	−121612.	−0.318043
$172$	−29706.1	−0.0765639
$173$	154131.	0.391538	0.195769	−	0.980650i	$-0.437280\pi$
$173$	154131.	0.391538	0.195769	+	0.980650i	$0.437280\pi$
$174$	−385506.	−0.965291
$175$	−224810.	−0.554908
$176$	−98143.1	−0.238824
$177$	−374612.	−0.898770
$178$	465868.	1.10208
$179$	603292.	1.40733	0.703664	−	0.710533i	$-0.251546\pi$
$179$	603292.	1.40733	0.703664	+	0.710533i	$0.251546\pi$
$180$	−327748.	−0.753978
$181$	−560418.	−1.27150	−0.635749	−	0.771896i	$-0.719309\pi$
$181$	−560418.	−1.27150	−0.635749	+	0.771896i	$0.719309\pi$
$182$	201530.	0.450984
$183$	269909.	0.595784
$184$	−112922.	−0.245887
$185$	−626345.	−1.34550
$186$	−30819.6	−0.0653198
$187$	−59941.4	−0.125350
$188$	149830.	0.309175
$189$	19458.3	0.0396233
$190$	−1.34650e6	−2.70598
$191$	337255.	0.668921	0.334461	−	0.942410i	$-0.391446\pi$
$191$	337255.	0.668921	0.334461	+	0.942410i	$0.391446\pi$
$192$	388295.	0.760166
$193$	427002.	0.825158	0.412579	−	0.910922i	$-0.364628\pi$
$193$	427002.	0.825158	0.412579	+	0.910922i	$0.364628\pi$
$194$	844503.	1.61100
$195$	874931.	1.64773
$196$	−606026.	−1.12681
$197$	387552.	0.711483	0.355741	−	0.934584i	$-0.384228\pi$
$197$	387552.	0.711483	0.355741	+	0.934584i	$0.384228\pi$
$198$	−81798.2	−0.148279
$199$	564409.	1.01033	0.505163	−	0.863024i	$-0.331432\pi$
$199$	564409.	1.01033	0.505163	+	0.863024i	$0.331432\pi$
$200$	−397443.	−0.702586
$201$	−233013.	−0.406809
$202$	627529.	1.08207
$203$	136991.	0.233321
$204$	167879.	0.282437
$205$	−1.99463e6	−3.31496
$206$	−1.46937e6	−2.41248
$207$	193834.	0.314415
$208$	−733774.	−1.17599
$209$	−181667.	−0.287681
$210$	215445.	0.337123
$211$	495448.	0.766112	0.383056	−	0.923725i	$-0.374872\pi$
$211$	495448.	0.766112	0.383056	+	0.923725i	$0.374872\pi$
$212$	569727.	0.870616
$213$	−523467.	−0.790570
$214$	1.04293e6	1.55676
$215$	84776.5	0.125078
$216$	34400.4	0.0501683
$217$	10951.9	0.0157885
$218$	−400616.	−0.570935
$219$	−214878.	−0.302748
$220$	−489599.	−0.681999
$221$	−448157.	−0.617233
$222$	437811.	0.596217
$223$	1.23517e6	1.66327	0.831637	−	0.555320i	$-0.187404\pi$
$223$	1.23517e6	1.66327	0.831637	+	0.555320i	$0.187404\pi$
$224$	−220992.	−0.294277
$225$	682218.	0.898394
$226$	−325120.	−0.423421
$227$	−802179.	−1.03325	−0.516627	−	0.856211i	$-0.672812\pi$
$227$	−802179.	−1.03325	−0.516627	+	0.856211i	$0.672812\pi$
$228$	508799.	0.648200
$229$	−162526.	−0.204802	−0.102401	−	0.994743i	$-0.532652\pi$
$229$	−162526.	−0.204802	−0.102401	+	0.994743i	$0.532652\pi$
$230$	2.14615e6	2.67510
$231$	29067.4	0.0358407
$232$	242188.	0.295415
$233$	−1.45802e6	−1.75944	−0.879718	−	0.475496i	$-0.842269\pi$
$233$	−1.45802e6	−1.75944	−0.879718	+	0.475496i	$0.842269\pi$
$234$	−611570.	−0.730141
$235$	−427592.	−0.505079
$236$	1.56730e6	1.83177
$237$	−246625.	−0.285211
$238$	−110355.	−0.126285
$239$	−582475.	−0.659603	−0.329802	−	0.944050i	$-0.606982\pi$
$239$	−582475.	−0.659603	−0.329802	+	0.944050i	$0.606982\pi$
$240$	−784440.	−0.879087
$241$	434564.	0.481961	0.240980	−	0.970530i	$-0.422531\pi$
$241$	434564.	0.481961	0.240980	+	0.970530i	$0.422531\pi$
$242$	−122192.	−0.134124
$243$	−59049.0	−0.0641500
$244$	−1.12924e6	−1.21426
$245$	1.72950e6	1.84080
$246$	1.39424e6	1.46892
$247$	−1.35825e6	−1.41657
$248$	19361.9	0.0199903
$249$	−216507.	−0.221296
$250$	4.75097e6	4.80765
$251$	−948184.	−0.949967	−0.474983	−	0.879995i	$-0.657546\pi$
$251$	−948184.	−0.949967	−0.474983	+	0.879995i	$0.657546\pi$
$252$	−81409.5	−0.0807558
$253$	289554.	0.284399
$254$	−1.55865e6	−1.51588
$255$	−479101.	−0.461399
$256$	586627.	0.559451
$257$	1.14089e6	1.07749	0.538744	−	0.842470i	$-0.318899\pi$
$257$	1.14089e6	1.07749	0.538744	+	0.842470i	$0.318899\pi$
$258$	−59258.2	−0.0554242
$259$	−155578.	−0.144112
$260$	−3.66052e6	−3.35823
$261$	−415720.	−0.377745
$262$	3.03460e6	2.73116
$263$	280915.	0.250430	0.125215	−	0.992130i	$-0.460038\pi$
$263$	280915.	0.250430	0.125215	+	0.992130i	$0.460038\pi$
$264$	51388.3	0.0453790
$265$	−1.62591e6	−1.42227
$266$	−334459.	−0.289827
$267$	502380.	0.431275
$268$	974878.	0.829112
$269$	1.08759e6	0.916397	0.458198	−	0.888850i	$-0.348495\pi$
$269$	1.08759e6	0.916397	0.458198	+	0.888850i	$0.348495\pi$
$270$	−653798.	−0.545801
$271$	1.17929e6	0.975431	0.487716	−	0.873003i	$-0.337830\pi$
$271$	1.17929e6	0.975431	0.487716	+	0.873003i	$0.337830\pi$
$272$	401806.	0.329302
$273$	217324.	0.176483
$274$	617619.	0.496986
$275$	1.01912e6	0.812628
$276$	−810958.	−0.640805
$277$	−621357.	−0.486566	−0.243283	−	0.969955i	$-0.578224\pi$
$277$	−621357.	−0.486566	−0.243283	+	0.969955i	$0.578224\pi$
$278$	−584566.	−0.453651
$279$	−33235.0	−0.0255615
$280$	−135350.	−0.103172
$281$	−243988.	−0.184333	−0.0921666	−	0.995744i	$-0.529379\pi$
$281$	−243988.	−0.184333	−0.0921666	+	0.995744i	$0.529379\pi$
$282$	298884.	0.223810
$283$	−1.84579e6	−1.36999	−0.684993	−	0.728549i	$-0.740195\pi$
$283$	−1.84579e6	−1.36999	−0.684993	+	0.728549i	$0.740195\pi$
$284$	2.19007e6	1.61125
$285$	−1.45204e6	−1.05892
$286$	−913581.	−0.660438
$287$	−495448.	−0.355053
$288$	670631.	0.476434
$289$	−1.17445e6	−0.827162
$290$	−4.60290e6	−3.21393
$291$	910690.	0.630431
$292$	899003.	0.617027
$293$	−1.34899e6	−0.917995	−0.458998	−	0.888437i	$-0.651791\pi$
$293$	−1.34899e6	−0.917995	−0.458998	+	0.888437i	$0.651791\pi$
$294$	−1.20891e6	−0.815692
$295$	−4.47283e6	−2.99245
$296$	−275047.	−0.182464
$297$	−88209.0	−0.0580259
$298$	−2.73551e6	−1.78442
$299$	2.16487e6	1.40041
$300$	−2.85426e6	−1.83101
$301$	21057.7	0.0133966
$302$	−4338.43	−0.00273726
$303$	676711.	0.423445
$304$	1.21777e6	0.755757
$305$	3.22268e6	1.98366
$306$	334888.	0.204454
$307$	−1.20545e6	−0.729970	−0.364985	−	0.931013i	$-0.618926\pi$
$307$	−1.20545e6	−0.729970	−0.364985	+	0.931013i	$0.618926\pi$
$308$	−121612.	−0.0730464
$309$	−1.58453e6	−0.944072
$310$	−367983.	−0.217482
$311$	636875.	0.373382	0.186691	−	0.982419i	$-0.440224\pi$
$311$	636875.	0.373382	0.186691	+	0.982419i	$0.440224\pi$
$312$	384209.	0.223450
$313$	1.86526e6	1.07616	0.538081	−	0.842893i	$-0.319150\pi$
$313$	1.86526e6	1.07616	0.538081	+	0.842893i	$0.319150\pi$
$314$	997086.	0.570701
$315$	232330.	0.131926
$316$	1.03183e6	0.581285
$317$	2.35417e6	1.31580	0.657900	−	0.753105i	$-0.271445\pi$
$317$	2.35417e6	1.31580	0.657900	+	0.753105i	$0.271445\pi$
$318$	1.13650e6	0.630235
$319$	−621013.	−0.341684
$320$	4.63619e6	2.53097
$321$	1.12467e6	0.609204
$322$	533083.	0.286520
$323$	743761.	0.396668
$324$	247049.	0.130743
$325$	7.61950e6	4.00145
$326$	−2.62072e6	−1.36577
$327$	−432013.	−0.223423
$328$	−875905.	−0.449544
$329$	−106210.	−0.0540972
$330$	−976662.	−0.493696
$331$	1.97887e6	0.992768	0.496384	−	0.868103i	$-0.334661\pi$
$331$	1.97887e6	0.992768	0.496384	+	0.868103i	$0.334661\pi$
$332$	905820.	0.451021
$333$	472124.	0.233316
$334$	−2.35252e6	−1.15390
$335$	−2.78215e6	−1.35447
$336$	−194848.	−0.0941557
$337$	2.86225e6	1.37288	0.686439	−	0.727187i	$-0.259173\pi$
$337$	2.86225e6	1.37288	0.686439	+	0.727187i	$0.259173\pi$
$338$	−3.73168e6	−1.77669
$339$	−350601.	−0.165697
$340$	2.00446e6	0.940372
$341$	−49647.4	−0.0231212
$342$	1.01496e6	0.469229
$343$	878202.	0.403050
$344$	37228.0	0.0169619
$345$	2.31435e6	1.04684
$346$	−1.28636e6	−0.577660
$347$	−1.81514e6	−0.809257	−0.404629	−	0.914481i	$-0.632599\pi$
$347$	−1.81514e6	−0.809257	−0.404629	+	0.914481i	$0.632599\pi$
$348$	1.73928e6	0.769878
$349$	−1.77907e6	−0.781861	−0.390930	−	0.920420i	$-0.627847\pi$
$349$	−1.77907e6	−0.781861	−0.390930	+	0.920420i	$0.627847\pi$
$350$	1.87624e6	0.818690
$351$	−659501.	−0.285725
$352$	1.00181e6	0.430950
$353$	−4.18817e6	−1.78890	−0.894452	−	0.447164i	$-0.852434\pi$
$353$	−4.18817e6	−1.78890	−0.894452	+	0.447164i	$0.852434\pi$
$354$	3.12647e6	1.32601
$355$	−6.25014e6	−2.63220
$356$	−2.10185e6	−0.878976
$357$	−119004.	−0.0494187
$358$	−5.03502e6	−2.07632
$359$	1.13143e6	0.463329	0.231665	−	0.972796i	$-0.425583\pi$
$359$	1.13143e6	0.463329	0.231665	+	0.972796i	$0.425583\pi$
$360$	410738.	0.167035
$361$	−221946.	−0.0896355
$362$	4.67720e6	1.87592
$363$	−131769.	−0.0524864
$364$	−909240.	−0.359687
$365$	−2.56562e6	−1.00800
$366$	−2.25263e6	−0.878997
$367$	1.31924e6	0.511279	0.255639	−	0.966772i	$-0.417714\pi$
$367$	1.31924e6	0.511279	0.255639	+	0.966772i	$0.417714\pi$
$368$	−1.94097e6	−0.747134
$369$	1.50351e6	0.574830
$370$	5.22742e6	1.98510
$371$	−403861.	−0.152334
$372$	139048.	0.0520965
$373$	741.945	0.000276121 0	0.000138061	−	1.00000i	$-0.499956\pi$
$373$	741.945	0.000276121 0	0.000138061		1.00000i	$0.499956\pi$
$374$	500265.	0.184936
$375$	5.12332e6	1.88137
$376$	−187769.	−0.0684941
$377$	−4.64305e6	−1.68248
$378$	−162397.	−0.0584587
$379$	−567437.	−0.202917	−0.101459	−	0.994840i	$-0.532351\pi$
$379$	−567437.	−0.202917	−0.101459	+	0.994840i	$0.532351\pi$
$380$	6.07501e6	2.15818
$381$	−1.68081e6	−0.593207
$382$	−2.81470e6	−0.986900
$383$	3.54829e6	1.23601	0.618006	−	0.786174i	$-0.287941\pi$
$383$	3.54829e6	1.23601	0.618006	+	0.786174i	$0.287941\pi$
$384$	−856202.	−0.296311
$385$	347061.	0.119331
$386$	−3.56372e6	−1.21741
$387$	−63902.5	−0.0216890
$388$	−3.81013e6	−1.28487
$389$	4.09335e6	1.37153	0.685764	−	0.727824i	$-0.259468\pi$
$389$	4.09335e6	1.37153	0.685764	+	0.727824i	$0.259468\pi$
$390$	−7.30209e6	−2.43100
$391$	−1.18546e6	−0.392142
$392$	759478.	0.249632
$393$	3.27243e6	1.06878
$394$	−3.23447e6	−1.04969
$395$	−2.94468e6	−0.949609
$396$	369048.	0.118262
$397$	153511.	0.0488835	0.0244417	−	0.999701i	$-0.492219\pi$
$397$	153511.	0.0488835	0.0244417	+	0.999701i	$0.492219\pi$
$398$	−4.71050e6	−1.49059
$399$	−360672.	−0.113417
$400$	−6.83144e6	−2.13483
$401$	474424.	0.147335	0.0736674	−	0.997283i	$-0.476530\pi$
$401$	474424.	0.147335	0.0736674	+	0.997283i	$0.476530\pi$
$402$	1.94470e6	0.600190
$403$	−371193.	−0.113851
$404$	−2.83122e6	−0.863017
$405$	−705039.	−0.213587
$406$	−1.14332e6	−0.344232
$407$	705271.	0.211043
$408$	−210388.	−0.0625706
$409$	2.85246e6	0.843164	0.421582	−	0.906790i	$-0.361475\pi$
$409$	2.85246e6	0.843164	0.421582	+	0.906790i	$0.361475\pi$
$410$	1.66470e7	4.89077
$411$	666023.	0.194484
$412$	6.62935e6	1.92410
$413$	−1.11101e6	−0.320510
$414$	−1.61772e6	−0.463875
$415$	−2.58507e6	−0.736805
$416$	7.49009e6	2.12204
$417$	−630381.	−0.177526
$418$	1.51618e6	0.424434
$419$	6.61913e6	1.84190	0.920950	−	0.389681i	$-0.127415\pi$
$419$	6.61913e6	1.84190	0.920950	+	0.389681i	$0.127415\pi$
$420$	−972021.	−0.268876
$421$	1.67579e6	0.460802	0.230401	−	0.973096i	$-0.425996\pi$
$421$	1.67579e6	0.460802	0.230401	+	0.973096i	$0.425996\pi$
$422$	−4.13496e6	−1.13029
$423$	322308.	0.0875831
$424$	−713988.	−0.192875
$425$	−4.17234e6	−1.12049
$426$	4.36880e6	1.16638
$427$	800483.	0.212463
$428$	−4.70539e6	−1.24161
$429$	−985181.	−0.258448
$430$	−707537.	−0.184535
$431$	−4.53856e6	−1.17686	−0.588430	−	0.808548i	$-0.700254\pi$
$431$	−4.53856e6	−1.17686	−0.588430	+	0.808548i	$0.700254\pi$
$432$	591292.	0.152438
$433$	379605.	0.0972999	0.0486500	−	0.998816i	$-0.484508\pi$
$433$	379605.	0.0972999	0.0486500	+	0.998816i	$0.484508\pi$
$434$	−91403.4	−0.0232937
$435$	−4.96365e6	−1.25770
$436$	1.80745e6	0.455355
$437$	−3.59282e6	−0.899978
$438$	1.79335e6	0.446663
$439$	−1.97778e6	−0.489797	−0.244899	−	0.969549i	$-0.578755\pi$
$439$	−1.97778e6	−0.489797	−0.244899	+	0.969549i	$0.578755\pi$
$440$	613571.	0.151089
$441$	−1.30366e6	−0.319203
$442$	3.74027e6	0.910641
$443$	3.58373e6	0.867613	0.433807	−	0.901006i	$-0.357170\pi$
$443$	3.58373e6	0.867613	0.433807	+	0.901006i	$0.357170\pi$
$444$	−1.97527e6	−0.475519
$445$	5.99836e6	1.43593
$446$	−1.03086e7	−2.45393
$447$	−2.94990e6	−0.698295
$448$	1.15159e6	0.271083
$449$	−1.05735e6	−0.247515	−0.123758	−	0.992312i	$-0.539495\pi$
$449$	−1.05735e6	−0.247515	−0.123758	+	0.992312i	$0.539495\pi$
$450$	−5.69372e6	−1.32546
$451$	2.24598e6	0.519954
$452$	1.46684e6	0.337704
$453$	−4678.45	−0.00107117
$454$	6.69491e6	1.52442
$455$	2.59483e6	0.587598
$456$	−637633.	−0.143601
$457$	1.39016e6	0.311368	0.155684	−	0.987807i	$-0.450242\pi$
$457$	1.39016e6	0.311368	0.155684	+	0.987807i	$0.450242\pi$
$458$	1.35643e6	0.302157
$459$	361135.	0.0800087
$460$	−9.68276e6	−2.13356
$461$	−1.09360e6	−0.239666	−0.119833	−	0.992794i	$-0.538236\pi$
$461$	−1.09360e6	−0.239666	−0.119833	+	0.992794i	$0.538236\pi$
$462$	−242594.	−0.0528779
$463$	1.94891e6	0.422513	0.211256	−	0.977431i	$-0.432244\pi$
$463$	1.94891e6	0.422513	0.211256	+	0.977431i	$0.432244\pi$
$464$	4.16284e6	0.897625
$465$	−396823.	−0.0851068
$466$	1.21685e7	2.59580
$467$	−4.69017e6	−0.995169	−0.497584	−	0.867416i	$-0.665780\pi$
$467$	−4.69017e6	−0.995169	−0.497584	+	0.867416i	$0.665780\pi$
$468$	2.75921e6	0.582332
$469$	−691060.	−0.145072
$470$	3.56864e6	0.745174
$471$	1.07523e6	0.223331
$472$	−1.96415e6	−0.405808
$473$	−95459.3	−0.0196185
$474$	2.05831e6	0.420789
$475$	−1.26453e7	−2.57155
$476$	497888.	0.100720
$477$	1.22557e6	0.246629
$478$	4.86128e6	0.973153
$479$	4.15576e6	0.827584	0.413792	−	0.910372i	$-0.364204\pi$
$479$	4.15576e6	0.827584	0.413792	+	0.910372i	$0.364204\pi$
$480$	8.00726e6	1.58628
$481$	5.27302e6	1.03919
$482$	−3.62683e6	−0.711066
$483$	574863.	0.112123
$484$	551294.	0.106972
$485$	1.08735e7	2.09902
$486$	492817.	0.0946445
$487$	−2.37242e6	−0.453282	−0.226641	−	0.973978i	$-0.572774\pi$
$487$	−2.37242e6	−0.453282	−0.226641	+	0.973978i	$0.572774\pi$
$488$	1.41518e6	0.269006
$489$	−2.82611e6	−0.534463
$490$	−1.44343e7	−2.71584
$491$	−1.18797e6	−0.222384	−0.111192	−	0.993799i	$-0.535467\pi$
$491$	−1.18797e6	−0.222384	−0.111192	+	0.993799i	$0.535467\pi$
$492$	−6.29036e6	−1.17155
$493$	2.54248e6	0.471129
$494$	1.13358e7	2.08995
$495$	−1.05321e6	−0.193197
$496$	332802.	0.0607409
$497$	−1.55248e6	−0.281925
$498$	1.80695e6	0.326492
$499$	710493.	0.127735	0.0638673	−	0.997958i	$-0.479657\pi$
$499$	710493.	0.127735	0.0638673	+	0.997958i	$0.479657\pi$
$500$	−2.14349e7	−3.83439
$501$	−2.53689e6	−0.451552
$502$	7.91345e6	1.40154
$503$	4.75381e6	0.837765	0.418882	−	0.908041i	$-0.362422\pi$
$503$	4.75381e6	0.837765	0.418882	+	0.908041i	$0.362422\pi$
$504$	102023.	0.0178905
$505$	8.07986e6	1.40986
$506$	−2.41659e6	−0.419591
$507$	−4.02414e6	−0.695270
$508$	7.03215e6	1.20901
$509$	−5.05479e6	−0.864787	−0.432393	−	0.901685i	$-0.642331\pi$
$509$	−5.05479e6	−0.864787	−0.432393	+	0.901685i	$0.642331\pi$
$510$	3.99853e6	0.680730
$511$	−637275.	−0.107963
$512$	−7.94021e6	−1.33862
$513$	1.09451e6	0.183622
$514$	−9.52179e6	−1.58968
$515$	−1.89191e7	−3.14328
$516$	267355.	0.0442042
$517$	481473.	0.0792219
$518$	1.29844e6	0.212617
$519$	−1.38718e6	−0.226055
$520$	4.58741e6	0.743977
$521$	−4.69775e6	−0.758220	−0.379110	−	0.925352i	$-0.623770\pi$
$521$	−4.69775e6	−0.758220	−0.379110	+	0.925352i	$0.623770\pi$
$522$	3.46956e6	0.557311
$523$	−1.97083e6	−0.315062	−0.157531	−	0.987514i	$-0.550353\pi$
$523$	−1.97083e6	−0.315062	−0.157531	+	0.987514i	$0.550353\pi$
$524$	−1.36912e7	−2.17827
$525$	2.02329e6	0.320376
$526$	−2.34449e6	−0.369474
$527$	203260.	0.0318806
$528$	883288.	0.137885
$529$	−709863.	−0.110290
$530$	1.35697e7	2.09836
$531$	3.37151e6	0.518905
$532$	1.50897e6	0.231155
$533$	1.67922e7	2.56030
$534$	−4.19282e6	−0.636286
$535$	1.34285e7	2.02834
$536$	−1.22173e6	−0.183680
$537$	−5.42963e6	−0.812521
$538$	−9.07690e6	−1.35202
$539$	−1.94744e6	−0.288730
$540$	2.94973e6	0.435310
$541$	−5.76437e6	−0.846757	−0.423378	−	0.905953i	$-0.639156\pi$
$541$	−5.76437e6	−0.846757	−0.423378	+	0.905953i	$0.639156\pi$
$542$	−9.84222e6	−1.43911
$543$	5.04377e6	0.734100
$544$	−4.10148e6	−0.594214
$545$	−5.15819e6	−0.743886
$546$	−1.81377e6	−0.260376
$547$	−4.65202e6	−0.664772	−0.332386	−	0.943143i	$-0.607854\pi$
$547$	−4.65202e6	−0.664772	−0.332386	+	0.943143i	$0.607854\pi$
$548$	−2.78650e6	−0.396376
$549$	−2.42918e6	−0.343976
$550$	−8.50544e6	−1.19892
$551$	7.70561e6	1.08126
$552$	1.01630e6	0.141963
$553$	−731430.	−0.101709
$554$	5.18578e6	0.717860
$555$	5.63711e6	0.776826
$556$	2.63738e6	0.361814
$557$	−4.24834e6	−0.580204	−0.290102	−	0.956996i	$-0.593689\pi$
$557$	−4.24834e6	−0.580204	−0.290102	+	0.956996i	$0.593689\pi$
$558$	277376.	0.0377124
$559$	−713709.	−0.0966032
$560$	−2.32646e6	−0.313491
$561$	539473.	0.0723706
$562$	2.03630e6	0.271958
$563$	−3.09512e6	−0.411534	−0.205767	−	0.978601i	$-0.565969\pi$
$563$	−3.09512e6	−0.411534	−0.205767	+	0.978601i	$0.565969\pi$
$564$	−1.34847e6	−0.178502
$565$	−4.18613e6	−0.551686
$566$	1.54048e7	2.02122
$567$	−175125.	−0.0228765
$568$	−2.74463e6	−0.356954
$569$	−7.60568e6	−0.984821	−0.492411	−	0.870363i	$-0.663884\pi$
$569$	−7.60568e6	−0.984821	−0.492411	+	0.870363i	$0.663884\pi$
$570$	1.21185e7	1.56230
$571$	−2.28582e6	−0.293395	−0.146697	−	0.989181i	$-0.546864\pi$
$571$	−2.28582e6	−0.293395	−0.146697	+	0.989181i	$0.546864\pi$
$572$	4.12179e6	0.526739
$573$	−3.03529e6	−0.386202
$574$	4.13496e6	0.523832
$575$	2.01550e7	2.54222
$576$	−3.49465e6	−0.438882
$577$	−6.27770e6	−0.784984	−0.392492	−	0.919755i	$-0.628387\pi$
$577$	−6.27770e6	−0.784984	−0.392492	+	0.919755i	$0.628387\pi$
$578$	9.80186e6	1.22036
$579$	−3.84302e6	−0.476405
$580$	2.07669e7	2.56331
$581$	−642107.	−0.0789164
$582$	−7.60053e6	−0.930114
$583$	1.83079e6	0.223084
$584$	−1.12664e6	−0.136695
$585$	−7.87437e6	−0.951320
$586$	1.12586e7	1.35437
$587$	−1.48651e6	−0.178063	−0.0890314	−	0.996029i	$-0.528377\pi$
$587$	−1.48651e6	−0.178063	−0.0890314	+	0.996029i	$0.528377\pi$
$588$	5.45423e6	0.650564
$589$	616031.	0.0731669
$590$	3.73298e7	4.41494
$591$	−3.48797e6	−0.410775
$592$	−4.72765e6	−0.554423
$593$	4.72874e6	0.552216	0.276108	−	0.961127i	$-0.410955\pi$
$593$	4.72874e6	0.552216	0.276108	+	0.961127i	$0.410955\pi$
$594$	736184.	0.0856091
$595$	−1.42090e6	−0.164539
$596$	1.23418e7	1.42319
$597$	−5.07968e6	−0.583312
$598$	−1.80678e7	−2.06611
$599$	−325927.	−0.0371153	−0.0185577	−	0.999828i	$-0.505907\pi$
$599$	−325927.	−0.0371153	−0.0185577	+	0.999828i	$0.505907\pi$
$600$	3.57699e6	0.405638
$601$	−1.30291e7	−1.47140	−0.735698	−	0.677310i	$-0.763146\pi$
$601$	−1.30291e7	−1.47140	−0.735698	+	0.677310i	$0.763146\pi$
$602$	−175745.	−0.0197648
$603$	2.09712e6	0.234871
$604$	19573.6	0.00218313
$605$	−1.57331e6	−0.174753
$606$	−5.64776e6	−0.624734
$607$	−1.45956e6	−0.160787	−0.0803933	−	0.996763i	$-0.525618\pi$
$607$	−1.45956e6	−0.160787	−0.0803933	+	0.996763i	$0.525618\pi$
$608$	−1.24305e7	−1.36374
$609$	−1.23292e6	−0.134708
$610$	−2.68962e7	−2.92662
$611$	3.59977e6	0.390096
$612$	−1.51091e6	−0.163065
$613$	1.26574e7	1.36048	0.680241	−	0.732989i	$-0.261875\pi$
$613$	1.26574e7	1.36048	0.680241	+	0.732989i	$0.261875\pi$
$614$	1.00606e7	1.07697
$615$	1.79517e7	1.91390
$616$	152405.	0.0161826
$617$	2.57472e6	0.272281	0.136140	−	0.990690i	$-0.456530\pi$
$617$	2.57472e6	0.272281	0.136140	+	0.990690i	$0.456530\pi$
$618$	1.32244e7	1.39285
$619$	−1.82556e7	−1.91500	−0.957500	−	0.288434i	$-0.906866\pi$
$619$	−1.82556e7	−1.91500	−0.957500	+	0.288434i	$0.906866\pi$
$620$	1.66022e6	0.173455
$621$	−1.74450e6	−0.181527
$622$	−5.31530e6	−0.550873
$623$	1.48994e6	0.153797
$624$	6.60397e6	0.678959
$625$	3.48518e7	3.56882
$626$	−1.55672e7	−1.58773
$627$	1.63501e6	0.166093
$628$	−4.49854e6	−0.455169
$629$	−2.88744e6	−0.290995
$630$	−1.93901e6	−0.194638
$631$	7.91613e6	0.791480	0.395740	−	0.918363i	$-0.370488\pi$
$631$	7.91613e6	0.791480	0.395740	+	0.918363i	$0.370488\pi$
$632$	−1.29310e6	−0.128777
$633$	−4.45903e6	−0.442315
$634$	−1.96477e7	−1.94128
$635$	−2.00687e7	−1.97508
$636$	−5.12754e6	−0.502651
$637$	−1.45602e7	−1.42173
$638$	5.18292e6	0.504107
$639$	4.71120e6	0.456436
$640$	−1.02230e7	−0.986568
$641$	−3.40205e6	−0.327036	−0.163518	−	0.986540i	$-0.552284\pi$
$641$	−3.40205e6	−0.327036	−0.163518	+	0.986540i	$0.552284\pi$
$642$	−9.38640e6	−0.898796
$643$	−6.92901e6	−0.660912	−0.330456	−	0.943821i	$-0.607203\pi$
$643$	−6.92901e6	−0.660912	−0.330456	+	0.943821i	$0.607203\pi$
$644$	−2.40511e6	−0.228517
$645$	−762989.	−0.0722136
$646$	−6.20736e6	−0.585228
$647$	1.11125e7	1.04364	0.521819	−	0.853056i	$-0.325254\pi$
$647$	1.11125e7	1.04364	0.521819	+	0.853056i	$0.325254\pi$
$648$	−309604.	−0.0289647
$649$	5.03645e6	0.469367
$650$	−6.35916e7	−5.90359
$651$	−98567.0	−0.00911547
$652$	1.18239e7	1.08928
$653$	6.61748e6	0.607309	0.303654	−	0.952782i	$-0.401793\pi$
$653$	6.61748e6	0.607309	0.303654	+	0.952782i	$0.401793\pi$
$654$	3.60554e6	0.329629
$655$	3.90725e7	3.55850
$656$	−1.50555e7	−1.36595
$657$	1.93390e6	0.174792
$658$	886416.	0.0798128
$659$	1.88838e7	1.69385	0.846926	−	0.531711i	$-0.178451\pi$
$659$	1.88838e7	1.69385	0.846926	+	0.531711i	$0.178451\pi$
$660$	4.40639e6	0.393752
$661$	7.10304e6	0.632326	0.316163	−	0.948705i	$-0.397605\pi$
$661$	7.10304e6	0.632326	0.316163	+	0.948705i	$0.397605\pi$
$662$	−1.65155e7	−1.46469
$663$	4.03341e6	0.356360
$664$	−1.13518e6	−0.0999185
$665$	−4.30638e6	−0.377623
$666$	−3.94030e6	−0.344226
$667$	−1.22817e7	−1.06892
$668$	1.06138e7	0.920303
$669$	−1.11165e7	−0.960291
$670$	2.32196e7	1.99833
$671$	−3.62877e6	−0.311138
$672$	1.98893e6	0.169901
$673$	−1.79739e7	−1.52970	−0.764849	−	0.644209i	$-0.777187\pi$
$673$	−1.79739e7	−1.52970	−0.764849	+	0.644209i	$0.777187\pi$
$674$	−2.38880e7	−2.02549
$675$	−6.13996e6	−0.518688
$676$	1.68362e7	1.41702
$677$	−617034.	−0.0517413	−0.0258706	−	0.999665i	$-0.508236\pi$
$677$	−617034.	−0.0517413	−0.0258706	+	0.999665i	$0.508236\pi$
$678$	2.92608e6	0.244462
$679$	2.70088e6	0.224818
$680$	−2.51201e6	−0.208329
$681$	7.21961e6	0.596549
$682$	414352.	0.0341121
$683$	924287.	0.0758150	0.0379075	−	0.999281i	$-0.487931\pi$
$683$	924287.	0.0758150	0.0379075	+	0.999281i	$0.487931\pi$
$684$	−4.57919e6	−0.374239
$685$	7.95225e6	0.647535
$686$	−7.32939e6	−0.594644
$687$	1.46273e6	0.118242
$688$	639893.	0.0515390
$689$	1.36881e7	1.09849
$690$	−1.93154e7	−1.54447
$691$	2.33550e7	1.86074	0.930368	−	0.366627i	$-0.119487\pi$
$691$	2.33550e7	1.86074	0.930368	+	0.366627i	$0.119487\pi$
$692$	5.80365e6	0.460719
$693$	−261606.	−0.0206926
$694$	1.51490e7	1.19395
$695$	−7.52668e6	−0.591073
$696$	−2.17969e6	−0.170558
$697$	−9.19522e6	−0.716936
$698$	1.48479e7	1.15353
$699$	1.31222e7	1.01581
$700$	−8.46503e6	−0.652955
$701$	1.15300e7	0.886206	0.443103	−	0.896471i	$-0.353878\pi$
$701$	1.15300e7	0.886206	0.443103	+	0.896471i	$0.353878\pi$
$702$	5.50413e6	0.421547
$703$	−8.75110e6	−0.667843
$704$	−5.22040e6	−0.396984
$705$	3.84832e6	0.291608
$706$	3.49540e7	2.63928
$707$	2.00696e6	0.151005
$708$	−1.41057e7	−1.05757
$709$	−1.13035e7	−0.844497	−0.422248	−	0.906480i	$-0.638759\pi$
$709$	−1.13035e7	−0.844497	−0.422248	+	0.906480i	$0.638759\pi$
$710$	5.21631e7	3.88344
$711$	2.21962e6	0.164667
$712$	2.63407e6	0.194727
$713$	−981872.	−0.0723321
$714$	993197.	0.0729105
$715$	−1.17630e7	−0.860501
$716$	2.27164e7	1.65599
$717$	5.24228e6	0.380822
$718$	−9.44276e6	−0.683578
$719$	406909.	0.0293545	0.0146773	−	0.999892i	$-0.495328\pi$
$719$	406909.	0.0293545	0.0146773	+	0.999892i	$0.495328\pi$
$720$	7.05996e6	0.507541
$721$	−4.69934e6	−0.336665
$722$	1.85234e6	0.132245
$723$	−3.91108e6	−0.278260
$724$	−2.11020e7	−1.49616
$725$	−4.32268e7	−3.05428
$726$	1.09973e6	0.0774364
$727$	1.93239e6	0.135600	0.0678000	−	0.997699i	$-0.478402\pi$
$727$	1.93239e6	0.135600	0.0678000	+	0.997699i	$0.478402\pi$
$728$	1.13947e6	0.0796846
$729$	531441.	0.0370370
$730$	2.14124e7	1.48716
$731$	390818.	0.0270509
$732$	1.01632e7	0.701054
$733$	357394.	0.0245690	0.0122845	−	0.999925i	$-0.496090\pi$
$733$	357394.	0.0245690	0.0122845	+	0.999925i	$0.496090\pi$
$734$	−1.10102e7	−0.754320
$735$	−1.55655e7	−1.06279
$736$	1.98126e7	1.34818
$737$	3.13273e6	0.212449
$738$	−1.25481e7	−0.848082
$739$	2.22117e7	1.49613	0.748066	−	0.663624i	$-0.230983\pi$
$739$	2.22117e7	1.49613	0.748066	+	0.663624i	$0.230983\pi$
$740$	−2.35845e7	−1.58324
$741$	1.22243e7	0.817856
$742$	3.37059e6	0.224748
$743$	−2.10894e7	−1.40149	−0.700747	−	0.713410i	$-0.747150\pi$
$743$	−2.10894e7	−1.40149	−0.700747	+	0.713410i	$0.747150\pi$
$744$	−174257.	−0.0115414
$745$	−3.52215e7	−2.32497
$746$	−6192.20	−0.000407378 0
$747$	1.94856e6	0.127765
$748$	−2.25704e6	−0.147498
$749$	3.33550e6	0.217248
$750$	−4.27588e7	−2.77570
$751$	−3.08277e7	−1.99453	−0.997267	−	0.0738774i	$-0.976463\pi$
$751$	−3.08277e7	−1.99453	−0.997267	+	0.0738774i	$0.976463\pi$
$752$	−3.22746e6	−0.208121
$753$	8.53366e6	0.548464
$754$	3.87505e7	2.48227
$755$	−55860.2	−0.00356644
$756$	732686.	0.0466244
$757$	3.26795e6	0.207270	0.103635	−	0.994615i	$-0.466953\pi$
$757$	3.26795e6	0.207270	0.103635	+	0.994615i	$0.466953\pi$
$758$	4.73577e6	0.299376
$759$	−2.60598e6	−0.164198
$760$	−7.61327e6	−0.478120
$761$	1.01120e7	0.632961	0.316480	−	0.948599i	$-0.397499\pi$
$761$	1.01120e7	0.632961	0.316480	+	0.948599i	$0.397499\pi$
$762$	1.40279e7	0.875194
$763$	−1.28125e6	−0.0796748
$764$	1.26990e7	0.787113
$765$	4.31191e6	0.266389
$766$	−2.96137e7	−1.82356
$767$	3.76554e7	2.31121
$768$	−5.27964e6	−0.322999
$769$	2.14392e7	1.30735	0.653676	−	0.756775i	$-0.273226\pi$
$769$	2.14392e7	1.30735	0.653676	+	0.756775i	$0.273226\pi$
$770$	−2.89654e6	−0.176057
$771$	−1.02680e7	−0.622088
$772$	1.60784e7	0.970955
$773$	−1.89394e7	−1.14003	−0.570017	−	0.821633i	$-0.693063\pi$
$773$	−1.89394e7	−1.14003	−0.570017	+	0.821633i	$0.693063\pi$
$774$	533324.	0.0319992
$775$	−3.45580e6	−0.206678
$776$	4.77490e6	0.284649
$777$	1.40020e6	0.0832030
$778$	−3.41627e7	−2.02350
$779$	−2.78684e7	−1.64539
$780$	3.29447e7	1.93887
$781$	7.03772e6	0.412862
$782$	9.89370e6	0.578551
$783$	3.74148e6	0.218091
$784$	1.30543e7	0.758513
$785$	1.28381e7	0.743580
$786$	−2.73114e7	−1.57684
$787$	−1.10351e7	−0.635096	−0.317548	−	0.948242i	$-0.602859\pi$
$787$	−1.10351e7	−0.635096	−0.317548	+	0.948242i	$0.602859\pi$
$788$	1.45929e7	0.837195
$789$	−2.52824e6	−0.144586
$790$	2.45760e7	1.40102
$791$	−1.03980e6	−0.0590890
$792$	−462495.	−0.0261996
$793$	−2.71308e7	−1.53207
$794$	−1.28118e6	−0.0721208
$795$	1.46332e7	0.821149
$796$	2.12523e7	1.18884
$797$	−1.22483e7	−0.683015	−0.341507	−	0.939879i	$-0.610937\pi$
$797$	−1.22483e7	−0.683015	−0.341507	+	0.939879i	$0.610937\pi$
$798$	3.01013e6	0.167332
$799$	−1.97119e6	−0.109235
$800$	6.97327e7	3.85223
$801$	−4.52142e6	−0.248997
$802$	−3.95949e6	−0.217372
$803$	2.88891e6	0.158105
$804$	−8.77390e6	−0.478688
$805$	6.86380e6	0.373315
$806$	3.09794e6	0.167971
$807$	−9.78829e6	−0.529082
$808$	3.54811e6	0.191192
$809$	−2.42528e7	−1.30284	−0.651421	−	0.758717i	$-0.725827\pi$
$809$	−2.42528e7	−1.30284	−0.651421	+	0.758717i	$0.725827\pi$
$810$	5.88418e6	0.315118
$811$	3.64893e7	1.94811	0.974055	−	0.226311i	$-0.0726664\pi$
$811$	3.64893e7	1.94811	0.974055	+	0.226311i	$0.0726664\pi$
$812$	5.15829e6	0.274546
$813$	−1.06136e7	−0.563166
$814$	−5.88613e6	−0.311364
$815$	−3.37435e7	−1.77949
$816$	−3.61625e6	−0.190122
$817$	1.18447e6	0.0620825
$818$	−2.38064e7	−1.24397
$819$	−1.95592e6	−0.101892
$820$	−7.51062e7	−3.90069
$821$	2.40297e7	1.24420	0.622100	−	0.782938i	$-0.286280\pi$
$821$	2.40297e7	1.24420	0.622100	+	0.782938i	$0.286280\pi$
$822$	−5.55857e6	−0.286935
$823$	−1.16283e7	−0.598432	−0.299216	−	0.954185i	$-0.596725\pi$
$823$	−1.16283e7	−0.598432	−0.299216	+	0.954185i	$0.596725\pi$
$824$	−8.30798e6	−0.426263
$825$	−9.17204e6	−0.469171
$826$	9.27236e6	0.472868
$827$	1.01425e7	0.515680	0.257840	−	0.966188i	$-0.416989\pi$
$827$	1.01425e7	0.515680	0.257840	+	0.966188i	$0.416989\pi$
$828$	7.29863e6	0.369969
$829$	1.51928e7	0.767804	0.383902	−	0.923374i	$-0.374580\pi$
$829$	1.51928e7	0.767804	0.383902	+	0.923374i	$0.374580\pi$
$830$	2.15748e7	1.08705
$831$	5.59221e6	0.280919
$832$	−3.90307e7	−1.95478
$833$	7.97298e6	0.398114
$834$	5.26110e6	0.261916
$835$	−3.02902e7	−1.50344
$836$	−6.84052e6	−0.338512
$837$	299115.	0.0147579
$838$	−5.52426e7	−2.71747
$839$	−9.62729e6	−0.472171	−0.236085	−	0.971732i	$-0.575864\pi$
$839$	−9.62729e6	−0.472171	−0.236085	+	0.971732i	$0.575864\pi$
$840$	1.21815e6	0.0595665
$841$	5.82977e6	0.284225
$842$	−1.39860e7	−0.679849
$843$	2.19590e6	0.106425
$844$	1.86557e7	0.901477
$845$	−4.80478e7	−2.31490
$846$	−2.68995e6	−0.129217
$847$	−390795.	−0.0187172
$848$	−1.22724e7	−0.586056
$849$	1.66121e7	0.790962
$850$	3.48219e7	1.65313
$851$	1.39481e7	0.660223
$852$	−1.97107e7	−0.930256
$853$	7.49543e6	0.352715	0.176358	−	0.984326i	$-0.443568\pi$
$853$	7.49543e6	0.352715	0.176358	+	0.984326i	$0.443568\pi$
$854$	−6.68076e6	−0.313459
$855$	1.30683e7	0.611370
$856$	5.89684e6	0.275065
$857$	−2.69493e6	−0.125342	−0.0626708	−	0.998034i	$-0.519962\pi$
$857$	−2.69493e6	−0.125342	−0.0626708	+	0.998034i	$0.519962\pi$
$858$	8.22222e6	0.381304
$859$	−3.28791e7	−1.52033	−0.760164	−	0.649731i	$-0.774882\pi$
$859$	−3.28791e7	−1.52033	−0.760164	+	0.649731i	$0.774882\pi$
$860$	3.19218e6	0.147178
$861$	4.45904e6	0.204990
$862$	3.78784e7	1.73629
$863$	3.03331e7	1.38640	0.693202	−	0.720744i	$-0.256199\pi$
$863$	3.03331e7	1.38640	0.693202	+	0.720744i	$0.256199\pi$
$864$	−6.03568e6	−0.275069
$865$	−1.65627e7	−0.752648
$866$	−3.16815e6	−0.143553
$867$	1.05701e7	0.477562
$868$	412383.	0.0185781
$869$	3.31574e6	0.148947
$870$	4.14261e7	1.85556
$871$	2.34221e7	1.04612
$872$	−2.26512e6	−0.100879
$873$	−8.19621e6	−0.363980
$874$	2.99853e7	1.32779
$875$	1.51945e7	0.670914
$876$	−8.09103e6	−0.356241
$877$	−3.81826e7	−1.67636	−0.838178	−	0.545396i	$-0.816379\pi$
$877$	−3.81826e7	−1.67636	−0.838178	+	0.545396i	$0.816379\pi$
$878$	1.65064e7	0.722628
$879$	1.21409e7	0.530005
$880$	1.05464e7	0.459088
$881$	−8.09402e6	−0.351338	−0.175669	−	0.984449i	$-0.556209\pi$
$881$	−8.09402e6	−0.351338	−0.175669	+	0.984449i	$0.556209\pi$
$882$	1.08802e7	0.470940
$883$	1.90914e7	0.824018	0.412009	−	0.911180i	$-0.364827\pi$
$883$	1.90914e7	0.824018	0.412009	+	0.911180i	$0.364827\pi$
$884$	−1.68749e7	−0.726292
$885$	4.02554e7	1.72769
$886$	−2.99095e7	−1.28004
$887$	1.40640e7	0.600205	0.300102	−	0.953907i	$-0.402979\pi$
$887$	1.40640e7	0.600205	0.300102	+	0.953907i	$0.402979\pi$
$888$	2.47543e6	0.105346
$889$	−4.98487e6	−0.211543
$890$	−5.00618e7	−2.11851
$891$	793881.	0.0335013
$892$	4.65091e7	1.95716
$893$	−5.97417e6	−0.250697
$894$	2.46196e7	1.03024
$895$	−6.48292e7	−2.70529
$896$	−2.53929e6	−0.105668
$897$	−1.94838e7	−0.808525
$898$	8.82452e6	0.365174
$899$	2.10585e6	0.0869015
$900$	2.56883e7	1.05713
$901$	−7.49542e6	−0.307598
$902$	−1.87447e7	−0.767119
$903$	−189519.	−0.00773453
$904$	−1.83826e6	−0.0748145
$905$	6.02220e7	2.44418
$906$	39045.9	0.00158036
$907$	1.37464e7	0.554845	0.277423	−	0.960748i	$-0.410520\pi$
$907$	1.37464e7	0.554845	0.277423	+	0.960748i	$0.410520\pi$
$908$	−3.02053e7	−1.21582
$909$	−6.09040e6	−0.244476
$910$	−2.16562e7	−0.866920
$911$	3.83931e7	1.53270	0.766350	−	0.642423i	$-0.222071\pi$
$911$	3.83931e7	1.53270	0.766350	+	0.642423i	$0.222071\pi$
$912$	−1.09600e7	−0.436336
$913$	2.91082e6	0.115568
$914$	−1.16021e7	−0.459381
$915$	−2.90041e7	−1.14527
$916$	−6.11977e6	−0.240988
$917$	9.70523e6	0.381138
$918$	−3.01399e6	−0.118042
$919$	1.85935e7	0.726227	0.363114	−	0.931745i	$-0.381714\pi$
$919$	1.85935e7	0.726227	0.363114	+	0.931745i	$0.381714\pi$
$920$	1.21345e7	0.472665
$921$	1.08491e7	0.421448
$922$	9.12710e6	0.353595
$923$	5.26181e7	2.03297
$924$	1.09451e6	0.0421734
$925$	4.90918e7	1.88649
$926$	−1.62654e7	−0.623359
$927$	1.42608e7	0.545060
$928$	−4.24927e7	−1.61974
$929$	−2.77987e7	−1.05678	−0.528391	−	0.849001i	$-0.677204\pi$
$929$	−2.77987e7	−1.05678	−0.528391	+	0.849001i	$0.677204\pi$
$930$	3.31184e6	0.125563
$931$	2.41641e7	0.913684
$932$	−5.49004e7	−2.07031
$933$	−5.73187e6	−0.215572
$934$	3.91437e7	1.46823
$935$	6.44125e6	0.240958
$936$	−3.45788e6	−0.129009
$937$	4.55794e7	1.69598	0.847988	−	0.530015i	$-0.177814\pi$
$937$	4.55794e7	1.69598	0.847988	+	0.530015i	$0.177814\pi$
$938$	5.76752e6	0.214034
$939$	−1.67873e7	−0.621322
$940$	−1.61006e7	−0.594322
$941$	−2.38944e7	−0.879676	−0.439838	−	0.898077i	$-0.644964\pi$
$941$	−2.38944e7	−0.879676	−0.439838	+	0.898077i	$0.644964\pi$
$942$	−8.97377e6	−0.329494
$943$	4.44186e7	1.62662
$944$	−3.37609e7	−1.23306
$945$	−2.09097e6	−0.0761674
$946$	796694.	0.0289443
$947$	3.52637e7	1.27777	0.638885	−	0.769302i	$-0.279396\pi$
$947$	3.52637e7	1.27777	0.638885	+	0.769302i	$0.279396\pi$
$948$	−9.28644e6	−0.335605
$949$	2.15992e7	0.778523
$950$	1.05537e8	3.79397
$951$	−2.11875e7	−0.759678
$952$	−623959.	−0.0223133
$953$	5.08550e7	1.81385	0.906924	−	0.421293i	$-0.138424\pi$
$953$	5.08550e7	1.81385	0.906924	+	0.421293i	$0.138424\pi$
$954$	−1.02285e7	−0.363866
$955$	−3.62411e7	−1.28586
$956$	−2.19326e7	−0.776149
$957$	5.58912e6	0.197271
$958$	−3.46836e7	−1.22098
$959$	1.97526e6	0.0693551
$960$	−4.17258e7	−1.46126
$961$	−2.84608e7	−0.994120
$962$	−4.40081e7	−1.53319
$963$	−1.01220e7	−0.351724
$964$	1.63631e7	0.567119
$965$	−4.58853e7	−1.58619
$966$	−4.79775e6	−0.165423
$967$	2.33318e7	0.802384	0.401192	−	0.915994i	$-0.368596\pi$
$967$	2.33318e7	0.802384	0.401192	+	0.915994i	$0.368596\pi$
$968$	−690887.	−0.0236984
$969$	−6.69385e6	−0.229016
$970$	−9.07495e7	−3.09681
$971$	−2.99725e7	−1.02017	−0.510087	−	0.860123i	$-0.670387\pi$
$971$	−2.99725e7	−1.02017	−0.510087	+	0.860123i	$0.670387\pi$
$972$	−2.22344e6	−0.0754847
$973$	−1.86956e6	−0.0633077
$974$	1.97999e7	0.668754
$975$	−6.85755e7	−2.31024
$976$	2.43248e7	0.817380
$977$	3.06238e7	1.02642	0.513208	−	0.858264i	$-0.328457\pi$
$977$	3.06238e7	1.02642	0.513208	+	0.858264i	$0.328457\pi$
$978$	2.35865e7	0.788525
$979$	−6.75422e6	−0.225226
$980$	6.51229e7	2.16605
$981$	3.88812e6	0.128993
$982$	9.91471e6	0.328096
$983$	2.10228e7	0.693915	0.346958	−	0.937881i	$-0.387215\pi$
$983$	2.10228e7	0.693915	0.346958	+	0.937881i	$0.387215\pi$
$984$	7.88315e6	0.259545
$985$	−4.16460e7	−1.36767
$986$	−2.12193e7	−0.695085
$987$	955887.	0.0312330
$988$	−5.11437e7	−1.66686
$989$	−1.88789e6	−0.0613742
$990$	8.78995e6	0.285035
$991$	−2.43651e7	−0.788103	−0.394052	−	0.919088i	$-0.628927\pi$
$991$	−2.43651e7	−0.788103	−0.394052	+	0.919088i	$0.628927\pi$
$992$	−3.39711e6	−0.109605
$993$	−1.78098e7	−0.573175
$994$	1.29568e7	0.415941
$995$	−6.06508e7	−1.94213
$996$	−8.15238e6	−0.260397
$997$	−1.04094e7	−0.331655	−0.165827	−	0.986155i	$-0.553029\pi$
$997$	−1.04094e7	−0.331655	−0.165827	+	0.986155i	$0.553029\pi$
$998$	−5.92971e6	−0.188455
$999$	−4.24911e6	−0.134705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.a.d.1.1	✓	2
3.2	odd	2		99.6.a.e.1.2		2
4.3	odd	2		528.6.a.q.1.1		2
5.4	even	2		825.6.a.d.1.2		2
11.10	odd	2		363.6.a.g.1.2		2
33.32	even	2		1089.6.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.a.d.1.1	✓	2	1.1	even	1	trivial
99.6.a.e.1.2		2	3.2	odd	2
363.6.a.g.1.2		2	11.10	odd	2
528.6.a.q.1.1		2	4.3	odd	2
825.6.a.d.1.2		2	5.4	even	2
1089.6.a.o.1.1		2	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q-8.34590 q^{2} -9.00000 q^{3} +37.6541 q^{4} -107.459 q^{5} +75.1131 q^{6} -26.6918 q^{7} -47.1885 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-8.34590 q^{2} -9.00000 q^{3} +37.6541 q^{4} -107.459 q^{5} +75.1131 q^{6} -26.6918 q^{7} -47.1885 q^{8} +81.0000 q^{9} +896.843 q^{10} +121.000 q^{11} -338.887 q^{12} +904.666 q^{13} +222.767 q^{14} +967.131 q^{15} -811.100 q^{16} -495.384 q^{17} -676.018 q^{18} -1501.38 q^{19} -4046.27 q^{20} +240.226 q^{21} -1009.85 q^{22} +2393.01 q^{23} +424.697 q^{24} +8422.44 q^{25} -7550.25 q^{26} -729.000 q^{27} -1005.06 q^{28} -5132.34 q^{29} -8071.58 q^{30} -410.309 q^{31} +8279.40 q^{32} -1089.00 q^{33} +4134.42 q^{34} +2868.28 q^{35} +3049.98 q^{36} +5828.69 q^{37} +12530.4 q^{38} -8141.99 q^{39} +5070.84 q^{40} +18561.8 q^{41} -2004.91 q^{42} -788.920 q^{43} +4556.15 q^{44} -8704.18 q^{45} -19971.8 q^{46} +3979.11 q^{47} +7299.90 q^{48} -16094.5 q^{49} -70292.9 q^{50} +4458.45 q^{51} +34064.4 q^{52} +15130.5 q^{53} +6084.16 q^{54} -13002.5 q^{55} +1259.55 q^{56} +13512.5 q^{57} +42834.0 q^{58} +41623.5 q^{59} +36416.5 q^{60} -29989.8 q^{61} +3424.40 q^{62} -2162.04 q^{63} -43143.8 q^{64} -97214.5 q^{65} +9088.69 q^{66} +25890.3 q^{67} -18653.2 q^{68} -21537.1 q^{69} -23938.3 q^{70} +58163.0 q^{71} -3822.27 q^{72} +23875.3 q^{73} -48645.7 q^{74} -75802.0 q^{75} -56533.2 q^{76} -3229.71 q^{77} +67952.3 q^{78} +27402.8 q^{79} +87160.0 q^{80} +6561.00 q^{81} -154915. q^{82} +24056.3 q^{83} +9045.50 q^{84} +53233.4 q^{85} +6584.25 q^{86} +46191.1 q^{87} -5709.81 q^{88} -55820.0 q^{89} +72644.3 q^{90} -24147.2 q^{91} +90106.5 q^{92} +3692.78 q^{93} -33209.3 q^{94} +161337. q^{95} -74514.6 q^{96} -101188. q^{97} +134324. q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 18 q^{3} + 93 q^{4} - 38 q^{5} - 9 q^{6} - 18 q^{7} + 171 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q + q^2 - 18 * q^3 + 93 * q^4 - 38 * q^5 - 9 * q^6 - 18 * q^7 + 171 * q^8 + 162 * q^9	\( 2 q + q^{2} - 18 q^{3} + 93 q^{4} - 38 q^{5} - 9 q^{6} - 18 q^{7} + 171 q^{8} + 162 q^{9} + 1546 q^{10} + 242 q^{11} - 837 q^{12} - 66 q^{13} + 304 q^{14} + 342 q^{15} - 543 q^{16} - 920 q^{17} + 81 q^{18} - 2932 q^{19} - 202 q^{20} + 162 q^{21} + 121 q^{22} + 5246 q^{23} - 1539 q^{24} + 10122 q^{25} - 16622 q^{26} - 1458 q^{27} - 524 q^{28} - 12600 q^{29} - 13914 q^{30} + 9936 q^{31} + 3803 q^{32} - 2178 q^{33} + 166 q^{34} + 3472 q^{35} + 7533 q^{36} + 5996 q^{37} - 840 q^{38} + 594 q^{39} + 20226 q^{40} + 24244 q^{41} - 2736 q^{42} + 20360 q^{43} + 11253 q^{44} - 3078 q^{45} + 6692 q^{46} - 5806 q^{47} + 4887 q^{48} - 32826 q^{49} - 54409 q^{50} + 8280 q^{51} - 19658 q^{52} + 40770 q^{53} - 729 q^{54} - 4598 q^{55} + 3156 q^{56} + 26388 q^{57} - 26958 q^{58} + 18212 q^{59} + 1818 q^{60} - 11398 q^{61} + 100120 q^{62} - 1458 q^{63} - 93559 q^{64} - 164636 q^{65} - 1089 q^{66} + 65368 q^{67} - 42154 q^{68} - 47214 q^{69} - 18296 q^{70} + 61446 q^{71} + 13851 q^{72} + 53412 q^{73} - 47082 q^{74} - 91098 q^{75} - 135712 q^{76} - 2178 q^{77} + 149598 q^{78} + 17122 q^{79} + 105782 q^{80} + 13122 q^{81} - 101810 q^{82} - 14304 q^{83} + 4716 q^{84} + 23740 q^{85} + 204240 q^{86} + 113400 q^{87} + 20691 q^{88} - 58140 q^{89} + 125226 q^{90} - 32584 q^{91} + 248008 q^{92} - 89424 q^{93} - 124660 q^{94} + 61968 q^{95} - 34227 q^{96} - 183056 q^{97} - 22047 q^{98} + 19602 q^{99}+O(q^{100}) \) 2 * q + q^2 - 18 * q^3 + 93 * q^4 - 38 * q^5 - 9 * q^6 - 18 * q^7 + 171 * q^8 + 162 * q^9 + 1546 * q^10 + 242 * q^11 - 837 * q^12 - 66 * q^13 + 304 * q^14 + 342 * q^15 - 543 * q^16 - 920 * q^17 + 81 * q^18 - 2932 * q^19 - 202 * q^20 + 162 * q^21 + 121 * q^22 + 5246 * q^23 - 1539 * q^24 + 10122 * q^25 - 16622 * q^26 - 1458 * q^27 - 524 * q^28 - 12600 * q^29 - 13914 * q^30 + 9936 * q^31 + 3803 * q^32 - 2178 * q^33 + 166 * q^34 + 3472 * q^35 + 7533 * q^36 + 5996 * q^37 - 840 * q^38 + 594 * q^39 + 20226 * q^40 + 24244 * q^41 - 2736 * q^42 + 20360 * q^43 + 11253 * q^44 - 3078 * q^45 + 6692 * q^46 - 5806 * q^47 + 4887 * q^48 - 32826 * q^49 - 54409 * q^50 + 8280 * q^51 - 19658 * q^52 + 40770 * q^53 - 729 * q^54 - 4598 * q^55 + 3156 * q^56 + 26388 * q^57 - 26958 * q^58 + 18212 * q^59 + 1818 * q^60 - 11398 * q^61 + 100120 * q^62 - 1458 * q^63 - 93559 * q^64 - 164636 * q^65 - 1089 * q^66 + 65368 * q^67 - 42154 * q^68 - 47214 * q^69 - 18296 * q^70 + 61446 * q^71 + 13851 * q^72 + 53412 * q^73 - 47082 * q^74 - 91098 * q^75 - 135712 * q^76 - 2178 * q^77 + 149598 * q^78 + 17122 * q^79 + 105782 * q^80 + 13122 * q^81 - 101810 * q^82 - 14304 * q^83 + 4716 * q^84 + 23740 * q^85 + 204240 * q^86 + 113400 * q^87 + 20691 * q^88 - 58140 * q^89 + 125226 * q^90 - 32584 * q^91 + 248008 * q^92 - 89424 * q^93 - 124660 * q^94 + 61968 * q^95 - 34227 * q^96 - 183056 * q^97 - 22047 * q^98 + 19602 * q^99

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