LMFDB - Embedded newform 289.10.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-37.5513 q^{2} +70.9462 q^{3} +898.103 q^{4} -98.5382 q^{5} -2664.12 q^{6} -4159.85 q^{7} -14498.7 q^{8} -14649.6 q^{9} +O(q^{10})$	\(q-37.5513 q^{2} +70.9462 q^{3} +898.103 q^{4} -98.5382 q^{5} -2664.12 q^{6} -4159.85 q^{7} -14498.7 q^{8} -14649.6 q^{9} +3700.24 q^{10} -17666.5 q^{11} +63717.0 q^{12} +125323. q^{13} +156208. q^{14} -6990.91 q^{15} +84616.0 q^{16} +550113. q^{18} +186769. q^{19} -88497.5 q^{20} -295126. q^{21} +663401. q^{22} -880420. q^{23} -1.02863e6 q^{24} -1.94342e6 q^{25} -4.70603e6 q^{26} -2.43577e6 q^{27} -3.73598e6 q^{28} -472555. q^{29} +262518. q^{30} -5.47929e6 q^{31} +4.24588e6 q^{32} -1.25337e6 q^{33} +409905. q^{35} -1.31569e7 q^{36} +1.99919e7 q^{37} -7.01344e6 q^{38} +8.89116e6 q^{39} +1.42867e6 q^{40} +1.70530e7 q^{41} +1.10824e7 q^{42} -2.41245e7 q^{43} -1.58663e7 q^{44} +1.44355e6 q^{45} +3.30609e7 q^{46} -3.99422e7 q^{47} +6.00318e6 q^{48} -2.30492e7 q^{49} +7.29778e7 q^{50} +1.12553e8 q^{52} -3.20031e7 q^{53} +9.14664e7 q^{54} +1.74083e6 q^{55} +6.03124e7 q^{56} +1.32506e7 q^{57} +1.77451e7 q^{58} +1.43681e8 q^{59} -6.27856e6 q^{60} -9.63074e7 q^{61} +2.05755e8 q^{62} +6.09404e7 q^{63} -2.02762e8 q^{64} -1.23491e7 q^{65} +4.70658e7 q^{66} +1.54095e8 q^{67} -6.24624e7 q^{69} -1.53925e7 q^{70} +3.43693e8 q^{71} +2.12400e8 q^{72} +1.81429e8 q^{73} -7.50721e8 q^{74} -1.37878e8 q^{75} +1.67738e8 q^{76} +7.34901e7 q^{77} -3.33875e8 q^{78} -4.31537e8 q^{79} -8.33791e6 q^{80} +1.15540e8 q^{81} -6.40364e8 q^{82} -3.37832e8 q^{83} -2.65053e8 q^{84} +9.05906e8 q^{86} -3.35260e7 q^{87} +2.56141e8 q^{88} -2.13172e8 q^{89} -5.42072e7 q^{90} -5.21324e8 q^{91} -7.90707e8 q^{92} -3.88735e8 q^{93} +1.49988e9 q^{94} -1.84039e7 q^{95} +3.01229e8 q^{96} -5.74705e8 q^{97} +8.65529e8 q^{98} +2.58808e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * 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 $

$2$	−37.5513	−1.65955	−0.829775	−	0.558098i	$-0.811531\pi$
$2$	−37.5513	−1.65955	−0.829775	+	0.558098i	$0.811531\pi$
$3$	70.9462	0.505689	0.252845	−	0.967507i	$-0.418634\pi$
$3$	70.9462	0.505689	0.252845	+	0.967507i	$0.418634\pi$
$4$	898.103	1.75411
$5$	−98.5382	−0.0705082	−0.0352541	−	0.999378i	$-0.511224\pi$
$5$	−98.5382	−0.0705082	−0.0352541	+	0.999378i	$0.511224\pi$
$6$	−2664.12	−0.839216
$7$	−4159.85	−0.654843	−0.327421	−	0.944878i	$-0.606180\pi$
$7$	−4159.85	−0.654843	−0.327421	+	0.944878i	$0.606180\pi$
$8$	−14498.7	−1.25148
$9$	−14649.6	−0.744279
$10$	3700.24	0.117012
$11$	−17666.5	−0.363817	−0.181909	−	0.983315i	$-0.558228\pi$
$11$	−17666.5	−0.363817	−0.181909	+	0.983315i	$0.558228\pi$
$12$	63717.0	0.887033
$13$	125323.	1.21698	0.608491	−	0.793561i	$-0.291775\pi$
$13$	125323.	1.21698	0.608491	+	0.793561i	$0.291775\pi$
$14$	156208.	1.08674
$15$	−6990.91	−0.0356552
$16$	84616.0	0.322784
$17$	0	0
$17$	0	0
$18$	550113.	1.23517
$19$	186769.	0.328787	0.164393	−	0.986395i	$-0.447433\pi$
$19$	186769.	0.328787	0.164393	+	0.986395i	$0.447433\pi$
$20$	−88497.5	−0.123679
$21$	−295126.	−0.331147
$22$	663401.	0.603773
$23$	−880420.	−0.656016	−0.328008	−	0.944675i	$-0.606377\pi$
$23$	−880420.	−0.656016	−0.328008	+	0.944675i	$0.606377\pi$
$24$	−1.02863e6	−0.632859
$25$	−1.94342e6	−0.995029
$26$	−4.70603e6	−2.01964
$27$	−2.43577e6	−0.882063
$28$	−3.73598e6	−1.14866
$29$	−472555.	−0.124069	−0.0620343	−	0.998074i	$-0.519759\pi$
$29$	−472555.	−0.124069	−0.0620343	+	0.998074i	$0.519759\pi$
$30$	262518.	0.0591717
$31$	−5.47929e6	−1.06561	−0.532803	−	0.846240i	$-0.678861\pi$
$31$	−5.47929e6	−1.06561	−0.532803	+	0.846240i	$0.678861\pi$
$32$	4.24588e6	0.715802
$33$	−1.25337e6	−0.183978
$34$	0	0
$35$	409905.	0.0461718
$36$	−1.31569e7	−1.30554
$37$	1.99919e7	1.75366	0.876830	−	0.480801i	$-0.159654\pi$
$37$	1.99919e7	1.75366	0.876830	+	0.480801i	$0.159654\pi$
$38$	−7.01344e6	−0.545638
$39$	8.89116e6	0.615415
$40$	1.42867e6	0.0882395
$41$	1.70530e7	0.942484	0.471242	−	0.882004i	$-0.343806\pi$
$41$	1.70530e7	0.942484	0.471242	+	0.882004i	$0.343806\pi$
$42$	1.10824e7	0.549555
$43$	−2.41245e7	−1.07609	−0.538046	−	0.842915i	$-0.680837\pi$
$43$	−2.41245e7	−1.07609	−0.538046	+	0.842915i	$0.680837\pi$
$44$	−1.58663e7	−0.638175
$45$	1.44355e6	0.0524778
$46$	3.30609e7	1.08869
$47$	−3.99422e7	−1.19397	−0.596983	−	0.802254i	$-0.703634\pi$
$47$	−3.99422e7	−1.19397	−0.596983	+	0.802254i	$0.703634\pi$
$48$	6.00318e6	0.163228
$49$	−2.30492e7	−0.571181
$50$	7.29778e7	1.65130
$51$	0	0
$52$	1.12553e8	2.13472
$53$	−3.20031e7	−0.557123	−0.278561	−	0.960418i	$-0.589858\pi$
$53$	−3.20031e7	−0.557123	−0.278561	+	0.960418i	$0.589858\pi$
$54$	9.14664e7	1.46383
$55$	1.74083e6	0.0256521
$56$	6.03124e7	0.819522
$57$	1.32506e7	0.166264
$58$	1.77451e7	0.205898
$59$	1.43681e8	1.54371	0.771856	−	0.635797i	$-0.219328\pi$
$59$	1.43681e8	1.54371	0.771856	+	0.635797i	$0.219328\pi$
$60$	−6.27856e6	−0.0625431
$61$	−9.63074e7	−0.890585	−0.445293	−	0.895385i	$-0.646900\pi$
$61$	−9.63074e7	−0.890585	−0.445293	+	0.895385i	$0.646900\pi$
$62$	2.05755e8	1.76843
$63$	6.09404e7	0.487385
$64$	−2.02762e8	−1.51069
$65$	−1.23491e7	−0.0858073
$66$	4.70658e7	0.305321
$67$	1.54095e8	0.934224	0.467112	−	0.884198i	$-0.345294\pi$
$67$	1.54095e8	0.934224	0.467112	+	0.884198i	$0.345294\pi$
$68$	0	0
$69$	−6.24624e7	−0.331740
$70$	−1.53925e7	−0.0766244
$71$	3.43693e8	1.60512	0.802562	−	0.596568i	$-0.203470\pi$
$71$	3.43693e8	1.60512	0.802562	+	0.596568i	$0.203470\pi$
$72$	2.12400e8	0.931449
$73$	1.81429e8	0.747748	0.373874	−	0.927480i	$-0.378029\pi$
$73$	1.81429e8	0.747748	0.373874	+	0.927480i	$0.378029\pi$
$74$	−7.50721e8	−2.91029
$75$	−1.37878e8	−0.503175
$76$	1.67738e8	0.576727
$77$	7.34901e7	0.238243
$78$	−3.33875e8	−1.02131
$79$	−4.31537e8	−1.24651	−0.623255	−	0.782019i	$-0.714190\pi$
$79$	−4.31537e8	−1.24651	−0.623255	+	0.782019i	$0.714190\pi$
$80$	−8.33791e6	−0.0227589
$81$	1.15540e8	0.298229
$82$	−6.40364e8	−1.56410
$83$	−3.37832e8	−0.781357	−0.390678	−	0.920527i	$-0.627760\pi$
$83$	−3.37832e8	−0.781357	−0.390678	+	0.920527i	$0.627760\pi$
$84$	−2.65053e8	−0.580867
$85$	0	0
$86$	9.05906e8	1.78583
$87$	−3.35260e7	−0.0627401
$88$	2.56141e8	0.455310
$89$	−2.13172e8	−0.360144	−0.180072	−	0.983653i	$-0.557633\pi$
$89$	−2.13172e8	−0.360144	−0.180072	+	0.983653i	$0.557633\pi$
$90$	−5.42072e7	−0.0870895
$91$	−5.21324e8	−0.796932
$92$	−7.90707e8	−1.15072
$93$	−3.88735e8	−0.538865
$94$	1.49988e9	1.98145
$95$	−1.84039e7	−0.0231822
$96$	3.01229e8	0.361973
$97$	−5.74705e8	−0.659131	−0.329566	−	0.944133i	$-0.606902\pi$
$97$	−5.74705e8	−0.659131	−0.329566	+	0.944133i	$0.606902\pi$
$98$	8.65529e8	0.947904
$99$	2.58808e8	0.270781
$100$	−1.74539e9	−1.74539
$101$	−1.61579e9	−1.54504	−0.772518	−	0.634993i	$-0.781003\pi$
$101$	−1.61579e9	−1.54504	−0.772518	+	0.634993i	$0.781003\pi$
$102$	0	0
$103$	1.58557e9	1.38809	0.694044	−	0.719932i	$-0.255827\pi$
$103$	1.58557e9	1.38809	0.694044	+	0.719932i	$0.255827\pi$
$104$	−1.81701e9	−1.52303
$105$	2.90812e7	0.0233486
$106$	1.20176e9	0.924573
$107$	−1.83230e9	−1.35135	−0.675676	−	0.737199i	$-0.736148\pi$
$107$	−1.83230e9	−1.35135	−0.675676	+	0.737199i	$0.736148\pi$
$108$	−2.18757e9	−1.54723
$109$	−2.76044e9	−1.87309	−0.936546	−	0.350546i	$-0.885996\pi$
$109$	−2.76044e9	−1.87309	−0.936546	+	0.350546i	$0.885996\pi$
$110$	−6.53703e7	−0.0425710
$111$	1.41835e9	0.886807
$112$	−3.51990e8	−0.211373
$113$	1.15966e9	0.669082	0.334541	−	0.942381i	$-0.391419\pi$
$113$	1.15966e9	0.669082	0.334541	+	0.942381i	$0.391419\pi$
$114$	−4.97577e8	−0.275923
$115$	8.67550e7	0.0462545
$116$	−4.24403e8	−0.217629
$117$	−1.83593e9	−0.905774
$118$	−5.39543e9	−2.56187
$119$	0	0
$120$	1.01359e8	0.0446218
$121$	−2.04584e9	−0.867637
$122$	3.61647e9	1.47797
$123$	1.20985e9	0.476604
$124$	−4.92096e9	−1.86919
$125$	3.83958e8	0.140666
$126$	−2.28839e9	−0.808841
$127$	1.74470e9	0.595118	0.297559	−	0.954703i	$-0.403827\pi$
$127$	1.74470e9	0.595118	0.297559	+	0.954703i	$0.403827\pi$
$128$	5.44009e9	1.79127
$129$	−1.71154e9	−0.544168
$130$	4.63724e8	0.142402
$131$	−1.59935e9	−0.474485	−0.237242	−	0.971450i	$-0.576244\pi$
$131$	−1.59935e9	−0.474485	−0.237242	+	0.971450i	$0.576244\pi$
$132$	−1.12566e9	−0.322718
$133$	−7.76934e8	−0.215304
$134$	−5.78646e9	−1.55039
$135$	2.40017e8	0.0621927
$136$	0	0
$137$	2.42729e9	0.588681	0.294340	−	0.955701i	$-0.404900\pi$
$137$	2.42729e9	0.588681	0.294340	+	0.955701i	$0.404900\pi$
$138$	2.34555e9	0.550539
$139$	1.63994e9	0.372616	0.186308	−	0.982491i	$-0.440348\pi$
$139$	1.63994e9	0.372616	0.186308	+	0.982491i	$0.440348\pi$
$140$	3.68137e8	0.0809903
$141$	−2.83375e9	−0.603776
$142$	−1.29061e10	−2.66378
$143$	−2.21401e9	−0.442759
$144$	−1.23959e9	−0.240241
$145$	4.65648e7	0.00874785
$146$	−6.81292e9	−1.24092
$147$	−1.63525e9	−0.288840
$148$	1.79547e10	3.07611
$149$	2.74370e9	0.456036	0.228018	−	0.973657i	$-0.426776\pi$
$149$	2.74370e9	0.456036	0.228018	+	0.973657i	$0.426776\pi$
$150$	5.17750e9	0.835044
$151$	8.07933e9	1.26467	0.632337	−	0.774693i	$-0.282096\pi$
$151$	8.07933e9	1.26467	0.632337	+	0.774693i	$0.282096\pi$
$152$	−2.70791e9	−0.411470
$153$	0	0
$154$	−2.75965e9	−0.395376
$155$	5.39919e8	0.0751339
$156$	7.98518e9	1.07950
$157$	−7.87840e9	−1.03488	−0.517440	−	0.855720i	$-0.673115\pi$
$157$	−7.87840e9	−1.03488	−0.517440	+	0.855720i	$0.673115\pi$
$158$	1.62048e10	2.06865
$159$	−2.27050e9	−0.281731
$160$	−4.18381e8	−0.0504699
$161$	3.66242e9	0.429587
$162$	−4.33869e9	−0.494927
$163$	−7.99073e9	−0.886630	−0.443315	−	0.896366i	$-0.646198\pi$
$163$	−7.99073e9	−0.886630	−0.443315	+	0.896366i	$0.646198\pi$
$164$	1.53154e10	1.65322
$165$	1.23505e8	0.0129720
$166$	1.26860e10	1.29670
$167$	−3.09907e9	−0.308324	−0.154162	−	0.988046i	$-0.549268\pi$
$167$	−3.09907e9	−0.308324	−0.154162	+	0.988046i	$0.549268\pi$
$168$	4.27893e9	0.414423
$169$	5.10126e9	0.481047
$170$	0	0
$171$	−2.73610e9	−0.244709
$172$	−2.16662e10	−1.88758
$173$	1.63993e10	1.39193	0.695967	−	0.718073i	$-0.254976\pi$
$173$	1.63993e10	1.39193	0.695967	+	0.718073i	$0.254976\pi$
$174$	1.25895e9	0.104120
$175$	8.08433e9	0.651587
$176$	−1.49487e9	−0.117435
$177$	1.01936e10	0.780639
$178$	8.00490e9	0.597676
$179$	−1.11112e10	−0.808950	−0.404475	−	0.914549i	$-0.632546\pi$
$179$	−1.11112e10	−0.808950	−0.404475	+	0.914549i	$0.632546\pi$
$180$	1.29646e9	0.0920516
$181$	8.54950e9	0.592090	0.296045	−	0.955174i	$-0.404332\pi$
$181$	8.54950e9	0.592090	0.296045	+	0.955174i	$0.404332\pi$
$182$	1.95764e10	1.32255
$183$	−6.83265e9	−0.450359
$184$	1.27649e10	0.820990
$185$	−1.96996e9	−0.123647
$186$	1.45975e10	0.894273
$187$	0	0
$188$	−3.58722e10	−2.09434
$189$	1.01325e10	0.577612
$190$	6.91092e8	0.0384720
$191$	8.58739e8	0.0466886	0.0233443	−	0.999727i	$-0.492569\pi$
$191$	8.58739e8	0.0466886	0.0233443	+	0.999727i	$0.492569\pi$
$192$	−1.43852e10	−0.763941
$193$	1.58649e10	0.823055	0.411527	−	0.911397i	$-0.364995\pi$
$193$	1.58649e10	0.823055	0.411527	+	0.911397i	$0.364995\pi$
$194$	2.15809e10	1.09386
$195$	−8.76120e8	−0.0433918
$196$	−2.07006e10	−1.00191
$197$	3.61603e10	1.71054	0.855271	−	0.518180i	$-0.173390\pi$
$197$	3.61603e10	1.71054	0.855271	+	0.518180i	$0.173390\pi$
$198$	−9.71858e9	−0.449375
$199$	1.67380e10	0.756595	0.378298	−	0.925684i	$-0.376510\pi$
$199$	1.67380e10	0.756595	0.378298	+	0.925684i	$0.376510\pi$
$200$	2.81769e10	1.24526
$201$	1.09324e10	0.472427
$202$	6.06750e10	2.56406
$203$	1.96576e9	0.0812454
$204$	0	0
$205$	−1.68038e9	−0.0664529
$206$	−5.95402e10	−2.30360
$207$	1.28978e10	0.488259
$208$	1.06043e10	0.392823
$209$	−3.29956e9	−0.119618
$210$	−1.09204e9	−0.0387481
$211$	7.73670e9	0.268711	0.134355	−	0.990933i	$-0.457104\pi$
$211$	7.73670e9	0.268711	0.134355	+	0.990933i	$0.457104\pi$
$212$	−2.87421e10	−0.977253
$213$	2.43837e10	0.811694
$214$	6.88052e10	2.24264
$215$	2.37718e9	0.0758734
$216$	3.53154e10	1.10388
$217$	2.27930e10	0.697804
$218$	1.03658e11	3.10849
$219$	1.28717e10	0.378128
$220$	1.56344e9	0.0449966
$221$	0	0
$222$	−5.32608e10	−1.47170
$223$	3.19556e9	0.0865315	0.0432658	−	0.999064i	$-0.486224\pi$
$223$	3.19556e9	0.0865315	0.0432658	+	0.999064i	$0.486224\pi$
$224$	−1.76622e10	−0.468738
$225$	2.84703e10	0.740579
$226$	−4.35470e10	−1.11038
$227$	4.05926e10	1.01468	0.507341	−	0.861745i	$-0.330628\pi$
$227$	4.05926e10	1.01468	0.507341	+	0.861745i	$0.330628\pi$
$228$	1.19004e10	0.291645
$229$	−5.91362e10	−1.42100	−0.710500	−	0.703697i	$-0.751531\pi$
$229$	−5.91362e10	−1.42100	−0.710500	+	0.703697i	$0.751531\pi$
$230$	−3.25777e9	−0.0767617
$231$	5.21384e9	0.120477
$232$	6.85143e9	0.155269
$233$	−4.52505e10	−1.00582	−0.502912	−	0.864338i	$-0.667738\pi$
$233$	−4.52505e10	−1.00582	−0.502912	+	0.864338i	$0.667738\pi$
$234$	6.89417e10	1.50318
$235$	3.93584e9	0.0841844
$236$	1.29041e11	2.70784
$237$	−3.06159e10	−0.630346
$238$	0	0
$239$	−5.33414e10	−1.05748	−0.528742	−	0.848783i	$-0.677336\pi$
$239$	−5.33414e10	−1.05748	−0.528742	+	0.848783i	$0.677336\pi$
$240$	−5.91543e8	−0.0115089
$241$	−1.03808e11	−1.98222	−0.991111	−	0.133034i	$-0.957528\pi$
$241$	−1.03808e11	−1.98222	−0.991111	+	0.133034i	$0.957528\pi$
$242$	7.68241e10	1.43989
$243$	5.61404e10	1.03287
$244$	−8.64940e10	−1.56218
$245$	2.27123e9	0.0402730
$246$	−4.54314e10	−0.790948
$247$	2.34064e10	0.400128
$248$	7.94424e10	1.33358
$249$	−2.39679e10	−0.395123
$250$	−1.44181e10	−0.233442
$251$	8.18530e10	1.30168	0.650838	−	0.759217i	$-0.274418\pi$
$251$	8.18530e10	1.30168	0.650838	+	0.759217i	$0.274418\pi$
$252$	5.47307e10	0.854926
$253$	1.55539e10	0.238670
$254$	−6.55157e10	−0.987629
$255$	0	0
$256$	−1.00468e11	−1.46201
$257$	−3.14222e10	−0.449301	−0.224650	−	0.974439i	$-0.572124\pi$
$257$	−3.14222e10	−0.449301	−0.224650	+	0.974439i	$0.572124\pi$
$258$	6.42706e10	0.903074
$259$	−8.31632e10	−1.14837
$260$	−1.10907e10	−0.150515
$261$	6.92276e9	0.0923416
$262$	6.00577e10	0.787432
$263$	5.82416e10	0.750641	0.375320	−	0.926895i	$-0.377533\pi$
$263$	5.82416e10	0.750641	0.375320	+	0.926895i	$0.377533\pi$
$264$	1.81722e10	0.230245
$265$	3.15353e9	0.0392817
$266$	2.91749e10	0.357307
$267$	−1.51238e10	−0.182121
$268$	1.38393e11	1.63873
$269$	−6.48636e9	−0.0755294	−0.0377647	−	0.999287i	$-0.512024\pi$
$269$	−6.48636e9	−0.0755294	−0.0377647	+	0.999287i	$0.512024\pi$
$270$	−9.01294e9	−0.103212
$271$	1.14924e11	1.29435	0.647173	−	0.762343i	$-0.275951\pi$
$271$	1.14924e11	1.29435	0.647173	+	0.762343i	$0.275951\pi$
$272$	0	0
$273$	−3.69860e10	−0.403000
$274$	−9.11481e10	−0.976945
$275$	3.43333e10	0.362009
$276$	−5.60977e10	−0.581908
$277$	−4.72845e10	−0.482570	−0.241285	−	0.970454i	$-0.577569\pi$
$277$	−4.72845e10	−0.482570	−0.241285	+	0.970454i	$0.577569\pi$
$278$	−6.15819e10	−0.618374
$279$	8.02696e10	0.793107
$280$	−5.94308e9	−0.0577830
$281$	6.88901e10	0.659141	0.329570	−	0.944131i	$-0.393096\pi$
$281$	6.88901e10	0.659141	0.329570	+	0.944131i	$0.393096\pi$
$282$	1.06411e11	1.00200
$283$	1.62716e11	1.50797	0.753983	−	0.656894i	$-0.228130\pi$
$283$	1.62716e11	1.50797	0.753983	+	0.656894i	$0.228130\pi$
$284$	3.08672e11	2.81556
$285$	−1.30569e9	−0.0117230
$286$	8.31391e10	0.734781
$287$	−7.09381e10	−0.617179
$288$	−6.22006e10	−0.532756
$289$	0	0
$290$	−1.74857e9	−0.0145175
$291$	−4.07731e10	−0.333315
$292$	1.62942e11	1.31163
$293$	1.10593e11	0.876646	0.438323	−	0.898818i	$-0.355573\pi$
$293$	1.10593e11	0.876646	0.438323	+	0.898818i	$0.355573\pi$
$294$	6.14060e10	0.479344
$295$	−1.41581e10	−0.108844
$296$	−2.89855e11	−2.19467
$297$	4.30315e10	0.320910
$298$	−1.03030e11	−0.756814
$299$	−1.10336e11	−0.798360
$300$	−1.23829e11	−0.882623
$301$	1.00354e11	0.704671
$302$	−3.03389e11	−2.09879
$303$	−1.14634e11	−0.781307
$304$	1.58037e10	0.106127
$305$	9.48996e9	0.0627936
$306$	0	0
$307$	2.01516e11	1.29476	0.647378	−	0.762169i	$-0.275866\pi$
$307$	2.01516e11	1.29476	0.647378	+	0.762169i	$0.275866\pi$
$308$	6.60016e10	0.417904
$309$	1.12490e11	0.701941
$310$	−2.02747e10	−0.124689
$311$	1.00156e11	0.607091	0.303545	−	0.952817i	$-0.401830\pi$
$311$	1.00156e11	0.607091	0.303545	+	0.952817i	$0.401830\pi$
$312$	−1.28910e11	−0.770178
$313$	−1.11324e10	−0.0655602	−0.0327801	−	0.999463i	$-0.510436\pi$
$313$	−1.11324e10	−0.0655602	−0.0327801	+	0.999463i	$0.510436\pi$
$314$	2.95844e11	1.71743
$315$	−6.00496e9	−0.0343647
$316$	−3.87564e11	−2.18651
$317$	2.14276e11	1.19181	0.595906	−	0.803054i	$-0.296793\pi$
$317$	2.14276e11	1.19181	0.595906	+	0.803054i	$0.296793\pi$
$318$	8.52603e10	0.467546
$319$	8.34840e9	0.0451383
$320$	1.99798e10	0.106516
$321$	−1.29994e11	−0.683364
$322$	−1.37529e11	−0.712922
$323$	0	0
$324$	1.03767e11	0.523126
$325$	−2.43554e11	−1.21093
$326$	3.00063e11	1.47141
$327$	−1.95843e11	−0.947202
$328$	−2.47246e11	−1.17950
$329$	1.66154e11	0.781860
$330$	−4.63778e9	−0.0215277
$331$	−1.34835e11	−0.617413	−0.308707	−	0.951157i	$-0.599896\pi$
$331$	−1.34835e11	−0.617413	−0.308707	+	0.951157i	$0.599896\pi$
$332$	−3.03408e11	−1.37058
$333$	−2.92873e11	−1.30521
$334$	1.16374e11	0.511679
$335$	−1.51842e10	−0.0658705
$336$	−2.49724e10	−0.106889
$337$	−3.74106e10	−0.158001	−0.0790005	−	0.996875i	$-0.525173\pi$
$337$	−3.74106e10	−0.158001	−0.0790005	+	0.996875i	$0.525173\pi$
$338$	−1.91559e11	−0.798321
$339$	8.22738e10	0.338348
$340$	0	0
$341$	9.67998e10	0.387686
$342$	1.02744e11	0.406107
$343$	2.63747e11	1.02888
$344$	3.49773e11	1.34671
$345$	6.15494e9	0.0233904
$346$	−6.15817e11	−2.30999
$347$	8.04529e10	0.297892	0.148946	−	0.988845i	$-0.452412\pi$
$347$	8.04529e10	0.297892	0.148946	+	0.988845i	$0.452412\pi$
$348$	−3.01098e10	−0.110053
$349$	4.32246e11	1.55961	0.779806	−	0.626021i	$-0.215318\pi$
$349$	4.32246e11	1.55961	0.779806	+	0.626021i	$0.215318\pi$
$350$	−3.03577e11	−1.08134
$351$	−3.05257e11	−1.07345
$352$	−7.50098e10	−0.260421
$353$	−1.09770e11	−0.376269	−0.188135	−	0.982143i	$-0.560244\pi$
$353$	−1.09770e11	−0.376269	−0.188135	+	0.982143i	$0.560244\pi$
$354$	−3.82785e11	−1.29551
$355$	−3.38670e10	−0.113174
$356$	−1.91451e11	−0.631730
$357$	0	0
$358$	4.17240e11	1.34249
$359$	−4.96246e10	−0.157678	−0.0788391	−	0.996887i	$-0.525121\pi$
$359$	−4.96246e10	−0.157678	−0.0788391	+	0.996887i	$0.525121\pi$
$360$	−2.09296e10	−0.0656748
$361$	−2.87805e11	−0.891899
$362$	−3.21045e11	−0.982602
$363$	−1.45145e11	−0.438754
$364$	−4.68202e11	−1.39790
$365$	−1.78777e10	−0.0527224
$366$	2.56575e11	0.747394
$367$	−1.92703e11	−0.554487	−0.277243	−	0.960800i	$-0.589421\pi$
$367$	−1.92703e11	−0.554487	−0.277243	+	0.960800i	$0.589421\pi$
$368$	−7.44975e10	−0.211752
$369$	−2.49821e11	−0.701471
$370$	7.39747e10	0.205199
$371$	1.33128e11	0.364828
$372$	−3.49124e11	−0.945227
$373$	−2.91248e11	−0.779065	−0.389533	−	0.921013i	$-0.627363\pi$
$373$	−2.91248e11	−0.779065	−0.389533	+	0.921013i	$0.627363\pi$
$374$	0	0
$375$	2.72404e10	0.0711332
$376$	5.79110e11	1.49422
$377$	−5.92219e10	−0.150989
$378$	−3.80487e11	−0.958577
$379$	4.17979e11	1.04059	0.520293	−	0.853988i	$-0.325823\pi$
$379$	4.17979e11	1.04059	0.520293	+	0.853988i	$0.325823\pi$
$380$	−1.65286e10	−0.0406640
$381$	1.23780e11	0.300945
$382$	−3.22468e10	−0.0774821
$383$	6.50085e11	1.54374	0.771872	−	0.635778i	$-0.219321\pi$
$383$	6.50085e11	1.54374	0.771872	+	0.635778i	$0.219321\pi$
$384$	3.85953e11	0.905825
$385$	−7.24158e9	−0.0167981
$386$	−5.95747e11	−1.36590
$387$	3.53415e11	0.800912
$388$	−5.16144e11	−1.15619
$389$	−6.79183e11	−1.50388	−0.751941	−	0.659231i	$-0.770882\pi$
$389$	−6.79183e11	−1.50388	−0.751941	+	0.659231i	$0.770882\pi$
$390$	3.28995e10	0.0720109
$391$	0	0
$392$	3.34183e11	0.714821
$393$	−1.13468e11	−0.239942
$394$	−1.35787e12	−2.83873
$395$	4.25228e10	0.0878892
$396$	2.32436e11	0.474980
$397$	8.45189e11	1.70764	0.853820	−	0.520568i	$-0.174280\pi$
$397$	8.45189e11	1.70764	0.853820	+	0.520568i	$0.174280\pi$
$398$	−6.28533e11	−1.25561
$399$	−5.51205e10	−0.108877
$400$	−1.64444e11	−0.321180
$401$	9.27527e11	1.79134	0.895668	−	0.444723i	$-0.146698\pi$
$401$	9.27527e11	1.79134	0.895668	+	0.444723i	$0.146698\pi$
$402$	−4.10527e11	−0.784016
$403$	−6.86679e11	−1.29682
$404$	−1.45114e12	−2.71016
$405$	−1.13851e10	−0.0210276
$406$	−7.38170e10	−0.134831
$407$	−3.53186e11	−0.638012
$408$	0	0
$409$	2.00626e11	0.354514	0.177257	−	0.984165i	$-0.443278\pi$
$409$	2.00626e11	0.354514	0.177257	+	0.984165i	$0.443278\pi$
$410$	6.31003e10	0.110282
$411$	1.72207e11	0.297689
$412$	1.42400e12	2.43486
$413$	−5.97694e11	−1.01089
$414$	−4.84331e11	−0.810290
$415$	3.32894e10	0.0550921
$416$	5.32105e11	0.871118
$417$	1.16347e11	0.188428
$418$	1.23903e11	0.198513
$419$	1.21669e12	1.92848	0.964240	−	0.265031i	$-0.0853822\pi$
$419$	1.21669e12	1.92848	0.964240	+	0.265031i	$0.0853822\pi$
$420$	2.61179e10	0.0409559
$421$	8.68283e11	1.34708	0.673538	−	0.739153i	$-0.264774\pi$
$421$	8.68283e11	1.34708	0.673538	+	0.739153i	$0.264774\pi$
$422$	−2.90524e11	−0.445939
$423$	5.85139e11	0.888644
$424$	4.64003e11	0.697227
$425$	0	0
$426$	−9.15642e11	−1.34705
$427$	4.00625e11	0.583193
$428$	−1.64559e12	−2.37042
$429$	−1.57076e11	−0.223899
$430$	−8.92663e10	−0.125916
$431$	9.10662e11	1.27119	0.635594	−	0.772024i	$-0.280755\pi$
$431$	9.10662e11	1.27119	0.635594	+	0.772024i	$0.280755\pi$
$432$	−2.06105e11	−0.284716
$433$	3.19740e10	0.0437121	0.0218560	−	0.999761i	$-0.493042\pi$
$433$	3.19740e10	0.0437121	0.0218560	+	0.999761i	$0.493042\pi$
$434$	−8.55909e11	−1.15804
$435$	3.30359e9	0.00442369
$436$	−2.47916e12	−3.28560
$437$	−1.64435e11	−0.215690
$438$	−4.83351e11	−0.627522
$439$	−9.65386e10	−0.124054	−0.0620270	−	0.998074i	$-0.519756\pi$
$439$	−9.65386e10	−0.124054	−0.0620270	+	0.998074i	$0.519756\pi$
$440$	−2.52397e10	−0.0321031
$441$	3.37663e11	0.425118
$442$	0	0
$443$	4.55197e11	0.561542	0.280771	−	0.959775i	$-0.409410\pi$
$443$	4.55197e11	0.561542	0.280771	+	0.959775i	$0.409410\pi$
$444$	1.27382e12	1.55555
$445$	2.10056e10	0.0253931
$446$	−1.19997e11	−0.143603
$447$	1.94655e11	0.230612
$448$	8.43460e11	0.989266
$449$	1.54092e12	1.78926	0.894628	−	0.446812i	$-0.147441\pi$
$449$	1.54092e12	1.78926	0.894628	+	0.446812i	$0.147441\pi$
$450$	−1.06910e12	−1.22903
$451$	−3.01267e11	−0.342892
$452$	1.04150e12	1.17364
$453$	5.73197e11	0.639532
$454$	−1.52431e12	−1.68392
$455$	5.13703e10	0.0561903
$456$	−1.92116e11	−0.208076
$457$	−5.52148e10	−0.0592151	−0.0296076	−	0.999562i	$-0.509426\pi$
$457$	−5.52148e10	−0.0592151	−0.0296076	+	0.999562i	$0.509426\pi$
$458$	2.22064e12	2.35822
$459$	0	0
$460$	7.79149e10	0.0811354
$461$	−9.04347e11	−0.932568	−0.466284	−	0.884635i	$-0.654408\pi$
$461$	−9.04347e11	−0.932568	−0.466284	+	0.884635i	$0.654408\pi$
$462$	−1.95787e11	−0.199938
$463$	−1.69193e12	−1.71107	−0.855535	−	0.517745i	$-0.826772\pi$
$463$	−1.69193e12	−1.71107	−0.855535	+	0.517745i	$0.826772\pi$
$464$	−3.99857e10	−0.0400474
$465$	3.83052e10	0.0379944
$466$	1.69922e12	1.66922
$467$	5.51847e11	0.536899	0.268450	−	0.963294i	$-0.413489\pi$
$467$	5.51847e11	0.536899	0.268450	+	0.963294i	$0.413489\pi$
$468$	−1.64885e12	−1.58882
$469$	−6.41012e11	−0.611770
$470$	−1.47796e11	−0.139708
$471$	−5.58943e11	−0.523327
$472$	−2.08319e12	−1.93192
$473$	4.26195e11	0.391501
$474$	1.14967e12	1.04609
$475$	−3.62971e11	−0.327152
$476$	0	0
$477$	4.68834e11	0.414655
$478$	2.00304e12	1.75495
$479$	2.30106e11	0.199719	0.0998594	−	0.995002i	$-0.468161\pi$
$479$	2.30106e11	0.199719	0.0998594	+	0.995002i	$0.468161\pi$
$480$	−2.96826e10	−0.0255221
$481$	2.50543e12	2.13417
$482$	3.89811e12	3.28960
$483$	2.59835e11	0.217238
$484$	−1.83738e12	−1.52193
$485$	5.66304e10	0.0464742
$486$	−2.10815e12	−1.71411
$487$	−1.20979e12	−0.974608	−0.487304	−	0.873232i	$-0.662020\pi$
$487$	−1.20979e12	−0.974608	−0.487304	+	0.873232i	$0.662020\pi$
$488$	1.39633e12	1.11455
$489$	−5.66912e11	−0.448359
$490$	−8.52877e10	−0.0668350
$491$	1.11945e12	0.869234	0.434617	−	0.900615i	$-0.356884\pi$
$491$	1.11945e12	0.869234	0.434617	+	0.900615i	$0.356884\pi$
$492$	1.08657e12	0.836014
$493$	0	0
$494$	−8.78943e11	−0.664033
$495$	−2.55025e10	−0.0190923
$496$	−4.63635e11	−0.343961
$497$	−1.42972e12	−1.05110
$498$	9.00026e11	0.655727
$499$	9.47198e11	0.683893	0.341947	−	0.939719i	$-0.388914\pi$
$499$	9.47198e11	0.683893	0.341947	+	0.939719i	$0.388914\pi$
$500$	3.44834e11	0.246743
$501$	−2.19867e11	−0.155916
$502$	−3.07369e12	−2.16020
$503$	8.69721e11	0.605793	0.302896	−	0.953023i	$-0.402046\pi$
$503$	8.69721e11	0.605793	0.302896	+	0.953023i	$0.402046\pi$
$504$	−8.83554e11	−0.609952
$505$	1.59217e11	0.108938
$506$	−5.84071e11	−0.396085
$507$	3.61915e11	0.243260
$508$	1.56692e12	1.04390
$509$	2.54306e12	1.67929	0.839646	−	0.543134i	$-0.182762\pi$
$509$	2.54306e12	1.67929	0.839646	+	0.543134i	$0.182762\pi$
$510$	0	0
$511$	−7.54720e11	−0.489657
$512$	9.87401e11	0.635007
$513$	−4.54927e11	−0.290011
$514$	1.17994e12	0.745637
$515$	−1.56239e11	−0.0978717
$516$	−1.53714e12	−0.954529
$517$	7.05639e11	0.434386
$518$	3.12289e12	1.90578
$519$	1.16347e12	0.703886
$520$	1.79045e11	0.107386
$521$	3.03890e12	1.80695	0.903477	−	0.428638i	$-0.141006\pi$
$521$	3.03890e12	1.80695	0.903477	+	0.428638i	$0.141006\pi$
$522$	−2.59959e11	−0.153245
$523$	2.02927e12	1.18599	0.592995	−	0.805206i	$-0.297945\pi$
$523$	2.02927e12	1.18599	0.592995	+	0.805206i	$0.297945\pi$
$524$	−1.43638e12	−0.832297
$525$	5.73552e11	0.329501
$526$	−2.18705e12	−1.24573
$527$	0	0
$528$	−1.06055e11	−0.0593853
$529$	−1.02601e12	−0.569643
$530$	−1.18419e11	−0.0651900
$531$	−2.10488e12	−1.14895
$532$	−6.97766e11	−0.377666
$533$	2.13713e12	1.14699
$534$	5.67918e11	0.302238
$535$	1.80551e11	0.0952815
$536$	−2.23417e12	−1.16916
$537$	−7.88296e11	−0.409077
$538$	2.43572e11	0.125345
$539$	4.07199e11	0.207806
$540$	2.15559e11	0.109093
$541$	1.14736e12	0.575855	0.287927	−	0.957652i	$-0.407034\pi$
$541$	1.14736e12	0.575855	0.287927	+	0.957652i	$0.407034\pi$
$542$	−4.31557e12	−2.14803
$543$	6.06555e11	0.299413
$544$	0	0
$545$	2.72009e11	0.132068
$546$	1.38887e12	0.668799
$547$	−1.20725e12	−0.576573	−0.288287	−	0.957544i	$-0.593086\pi$
$547$	−1.20725e12	−0.576573	−0.288287	+	0.957544i	$0.593086\pi$
$548$	2.17996e12	1.03261
$549$	1.41087e12	0.662844
$550$	−1.28926e12	−0.600772
$551$	−8.82589e10	−0.0407921
$552$	9.05622e11	0.415166
$553$	1.79513e12	0.816268
$554$	1.77560e12	0.800849
$555$	−1.39761e11	−0.0625272
$556$	1.47283e12	0.653608
$557$	−3.91673e12	−1.72415	−0.862074	−	0.506782i	$-0.830835\pi$
$557$	−3.91673e12	−1.72415	−0.862074	+	0.506782i	$0.830835\pi$
$558$	−3.01423e12	−1.31620
$559$	−3.02334e12	−1.30959
$560$	3.46845e10	0.0149035
$561$	0	0
$562$	−2.58691e12	−1.09388
$563$	2.78380e11	0.116775	0.0583875	−	0.998294i	$-0.481404\pi$
$563$	2.78380e11	0.116775	0.0583875	+	0.998294i	$0.481404\pi$
$564$	−2.54500e12	−1.05909
$565$	−1.14271e11	−0.0471758
$566$	−6.11020e12	−2.50254
$567$	−4.80630e11	−0.195293
$568$	−4.98310e12	−2.00878
$569$	1.05967e12	0.423804	0.211902	−	0.977291i	$-0.432034\pi$
$569$	1.05967e12	0.423804	0.211902	+	0.977291i	$0.432034\pi$
$570$	4.90304e10	0.0194549
$571$	2.19847e12	0.865481	0.432740	−	0.901519i	$-0.357547\pi$
$571$	2.19847e12	0.865481	0.432740	+	0.901519i	$0.357547\pi$
$572$	−1.98841e12	−0.776647
$573$	6.09243e10	0.0236099
$574$	2.66382e12	1.02424
$575$	1.71102e12	0.652755
$576$	2.97039e12	1.12438
$577$	−3.27165e12	−1.22878	−0.614392	−	0.789001i	$-0.710599\pi$
$577$	−3.27165e12	−1.22878	−0.614392	+	0.789001i	$0.710599\pi$
$578$	0	0
$579$	1.12555e12	0.416210
$580$	4.18199e10	0.0153447
$581$	1.40533e12	0.511666
$582$	1.53108e12	0.553154
$583$	5.65383e11	0.202691
$584$	−2.63049e12	−0.935790
$585$	1.80909e11	0.0638645
$586$	−4.15292e12	−1.45484
$587$	4.69052e12	1.63061	0.815304	−	0.579033i	$-0.196570\pi$
$587$	4.69052e12	1.63061	0.815304	+	0.579033i	$0.196570\pi$
$588$	−1.46863e12	−0.506656
$589$	−1.02336e12	−0.350357
$590$	5.31656e11	0.180633
$591$	2.56544e12	0.865003
$592$	1.69163e12	0.566054
$593$	−3.23030e12	−1.07274	−0.536372	−	0.843982i	$-0.680206\pi$
$593$	−3.23030e12	−1.07274	−0.536372	+	0.843982i	$0.680206\pi$
$594$	−1.61589e12	−0.532566
$595$	0	0
$596$	2.46413e12	0.799936
$597$	1.18749e12	0.382602
$598$	4.14328e12	1.32492
$599$	−7.65685e11	−0.243013	−0.121507	−	0.992591i	$-0.538773\pi$
$599$	−7.65685e11	−0.243013	−0.121507	+	0.992591i	$0.538773\pi$
$600$	1.99905e12	0.629713
$601$	−4.21877e12	−1.31902	−0.659510	−	0.751696i	$-0.729236\pi$
$601$	−4.21877e12	−1.31902	−0.659510	+	0.751696i	$0.729236\pi$
$602$	−3.76844e12	−1.16944
$603$	−2.25743e12	−0.695323
$604$	7.25606e12	2.21837
$605$	2.01594e11	0.0611755
$606$	4.30466e12	1.29662
$607$	−6.53092e12	−1.95265	−0.976327	−	0.216301i	$-0.930601\pi$
$607$	−6.53092e12	−1.95265	−0.976327	+	0.216301i	$0.930601\pi$
$608$	7.93000e11	0.235346
$609$	1.39463e11	0.0410849
$610$	−3.56361e11	−0.104209
$611$	−5.00567e12	−1.45304
$612$	0	0
$613$	1.11938e12	0.320189	0.160095	−	0.987102i	$-0.448820\pi$
$613$	1.11938e12	0.320189	0.160095	+	0.987102i	$0.448820\pi$
$614$	−7.56721e12	−2.14871
$615$	−1.19216e11	−0.0336045
$616$	−1.06551e12	−0.298156
$617$	−2.37749e11	−0.0660442	−0.0330221	−	0.999455i	$-0.510513\pi$
$617$	−2.37749e11	−0.0660442	−0.0330221	+	0.999455i	$0.510513\pi$
$618$	−4.22415e12	−1.16491
$619$	−1.01284e12	−0.277288	−0.138644	−	0.990342i	$-0.544274\pi$
$619$	−1.01284e12	−0.277288	−0.138644	+	0.990342i	$0.544274\pi$
$620$	4.84903e11	0.131793
$621$	2.14450e12	0.578647
$622$	−3.76098e12	−1.00750
$623$	8.86766e11	0.235837
$624$	7.52334e11	0.198646
$625$	3.75790e12	0.985110
$626$	4.18038e11	0.108800
$627$	−2.34091e11	−0.0604897
$628$	−7.07561e12	−1.81529
$629$	0	0
$630$	2.25494e11	0.0570299
$631$	−4.57844e12	−1.14970	−0.574851	−	0.818258i	$-0.694940\pi$
$631$	−4.57844e12	−1.14970	−0.574851	+	0.818258i	$0.694940\pi$
$632$	6.25671e12	1.55998
$633$	5.48890e11	0.135884
$634$	−8.04636e12	−1.97787
$635$	−1.71919e11	−0.0419607
$636$	−2.03914e12	−0.494186
$637$	−2.88859e12	−0.695117
$638$	−3.13493e11	−0.0749092
$639$	−5.03498e12	−1.19466
$640$	−5.36057e11	−0.126299
$641$	6.84749e12	1.60203	0.801014	−	0.598645i	$-0.204294\pi$
$641$	6.84749e12	1.60203	0.801014	+	0.598645i	$0.204294\pi$
$642$	4.88146e12	1.13408
$643$	2.56550e11	0.0591864	0.0295932	−	0.999562i	$-0.490579\pi$
$643$	2.56550e11	0.0591864	0.0295932	+	0.999562i	$0.490579\pi$
$644$	3.28923e12	0.753542
$645$	1.68652e11	0.0383683
$646$	0	0
$647$	4.79815e12	1.07648	0.538238	−	0.842793i	$-0.319090\pi$
$647$	4.79815e12	1.07648	0.538238	+	0.842793i	$0.319090\pi$
$648$	−1.67518e12	−0.373228
$649$	−2.53835e12	−0.561629
$650$	9.14577e12	2.00960
$651$	1.61708e12	0.352872
$652$	−7.17650e12	−1.55524
$653$	2.65352e12	0.571101	0.285550	−	0.958364i	$-0.407824\pi$
$653$	2.65352e12	0.571101	0.285550	+	0.958364i	$0.407824\pi$
$654$	7.35415e12	1.57193
$655$	1.57597e11	0.0334551
$656$	1.44296e12	0.304219
$657$	−2.65788e12	−0.556533
$658$	−6.23930e12	−1.29754
$659$	−6.71596e12	−1.38715	−0.693575	−	0.720384i	$-0.743965\pi$
$659$	−6.71596e12	−1.38715	−0.693575	+	0.720384i	$0.743965\pi$
$660$	1.10920e11	0.0227543
$661$	−8.92190e11	−0.181782	−0.0908910	−	0.995861i	$-0.528971\pi$
$661$	−8.92190e11	−0.181782	−0.0908910	+	0.995861i	$0.528971\pi$
$662$	5.06322e12	1.02463
$663$	0	0
$664$	4.89811e12	0.977851
$665$	7.65577e10	0.0151807
$666$	1.09978e13	2.16606
$667$	4.16047e11	0.0813909
$668$	−2.78328e12	−0.540833
$669$	2.26713e11	0.0437580
$670$	5.70188e11	0.109315
$671$	1.70141e12	0.324010
$672$	−1.25307e12	−0.237035
$673$	−1.94234e12	−0.364970	−0.182485	−	0.983209i	$-0.558414\pi$
$673$	−1.94234e12	−0.364970	−0.182485	+	0.983209i	$0.558414\pi$
$674$	1.40482e12	0.262211
$675$	4.73371e12	0.877677
$676$	4.58146e12	0.843808
$677$	1.48181e12	0.271109	0.135555	−	0.990770i	$-0.456718\pi$
$677$	1.48181e12	0.271109	0.135555	+	0.990770i	$0.456718\pi$
$678$	−3.08949e12	−0.561505
$679$	2.39069e12	0.431627
$680$	0	0
$681$	2.87989e12	0.513114
$682$	−3.63496e12	−0.643384
$683$	6.51135e12	1.14493	0.572464	−	0.819930i	$-0.305988\pi$
$683$	6.51135e12	1.14493	0.572464	+	0.819930i	$0.305988\pi$
$684$	−2.45730e12	−0.429246
$685$	−2.39181e11	−0.0415068
$686$	−9.90403e12	−1.70747
$687$	−4.19549e12	−0.718584
$688$	−2.04131e12	−0.347346
$689$	−4.01071e12	−0.678009
$690$	−2.31126e11	−0.0388176
$691$	5.42411e12	0.905059	0.452530	−	0.891749i	$-0.350522\pi$
$691$	5.42411e12	0.905059	0.452530	+	0.891749i	$0.350522\pi$
$692$	1.47283e13	2.44160
$693$	−1.07660e12	−0.177319
$694$	−3.02111e12	−0.494367
$695$	−1.61597e11	−0.0262725
$696$	4.86083e11	0.0785179
$697$	0	0
$698$	−1.62314e13	−2.58825
$699$	−3.21035e12	−0.508634
$700$	7.26056e12	1.14295
$701$	−1.83146e12	−0.286461	−0.143230	−	0.989689i	$-0.545749\pi$
$701$	−1.83146e12	−0.286461	−0.143230	+	0.989689i	$0.545749\pi$
$702$	1.14628e13	1.78145
$703$	3.73387e12	0.576581
$704$	3.58209e12	0.549616
$705$	2.79233e11	0.0425711
$706$	4.12202e12	0.624438
$707$	6.72145e12	1.01176
$708$	9.15494e12	1.36932
$709$	4.41281e12	0.655854	0.327927	−	0.944703i	$-0.393650\pi$
$709$	4.41281e12	0.655854	0.327927	+	0.944703i	$0.393650\pi$
$710$	1.27175e12	0.187819
$711$	6.32185e12	0.927750
$712$	3.09072e12	0.450712
$713$	4.82407e12	0.699054
$714$	0	0
$715$	2.18165e11	0.0312182
$716$	−9.97898e12	−1.41898
$717$	−3.78437e12	−0.534758
$718$	1.86347e12	0.261675
$719$	6.39579e12	0.892513	0.446256	−	0.894905i	$-0.352757\pi$
$719$	6.39579e12	0.892513	0.446256	+	0.894905i	$0.352757\pi$
$720$	1.22147e11	0.0169390
$721$	−6.59573e12	−0.908980
$722$	1.08075e13	1.48015
$723$	−7.36476e12	−1.00239
$724$	7.67833e12	1.03859
$725$	9.18371e11	0.123452
$726$	5.45038e12	0.728135
$727$	−9.70659e12	−1.28873	−0.644365	−	0.764718i	$-0.722878\pi$
$727$	−9.70659e12	−1.28873	−0.644365	+	0.764718i	$0.722878\pi$
$728$	7.55851e12	0.997343
$729$	1.70877e12	0.224084
$730$	6.71333e11	0.0874954
$731$	0	0
$732$	−6.13642e12	−0.789978
$733$	1.27278e12	0.162849	0.0814246	−	0.996680i	$-0.474053\pi$
$733$	1.27278e12	0.162849	0.0814246	+	0.996680i	$0.474053\pi$
$734$	7.23625e12	0.920198
$735$	1.61135e11	0.0203656
$736$	−3.73815e12	−0.469577
$737$	−2.72231e12	−0.339887
$738$	9.38110e12	1.16413
$739$	−8.07516e12	−0.995982	−0.497991	−	0.867182i	$-0.665929\pi$
$739$	−8.07516e12	−0.995982	−0.497991	+	0.867182i	$0.665929\pi$
$740$	−1.76923e12	−0.216891
$741$	1.66060e12	0.202340
$742$	−4.99915e12	−0.605450
$743$	9.55473e12	1.15019	0.575094	−	0.818088i	$-0.304966\pi$
$743$	9.55473e12	1.15019	0.575094	+	0.818088i	$0.304966\pi$
$744$	5.63614e12	0.674378
$745$	−2.70360e11	−0.0321543
$746$	1.09368e13	1.29290
$747$	4.94911e12	0.581547
$748$	0	0
$749$	7.62209e12	0.884923
$750$	−1.02291e12	−0.118049
$751$	−6.20481e12	−0.711785	−0.355893	−	0.934527i	$-0.615823\pi$
$751$	−6.20481e12	−0.711785	−0.355893	+	0.934527i	$0.615823\pi$
$752$	−3.37975e12	−0.385394
$753$	5.80716e12	0.658243
$754$	2.22386e12	0.250574
$755$	−7.96123e11	−0.0891700
$756$	9.09998e12	1.01319
$757$	2.32006e12	0.256784	0.128392	−	0.991723i	$-0.459018\pi$
$757$	2.32006e12	0.256784	0.128392	+	0.991723i	$0.459018\pi$
$758$	−1.56957e13	−1.72690
$759$	1.10349e12	0.120693
$760$	2.66833e11	0.0290120
$761$	6.55124e12	0.708097	0.354048	−	0.935227i	$-0.384805\pi$
$761$	6.55124e12	0.708097	0.354048	+	0.935227i	$0.384805\pi$
$762$	−4.64809e12	−0.499433
$763$	1.14830e13	1.22658
$764$	7.71236e11	0.0818968
$765$	0	0
$766$	−2.44115e13	−2.56192
$767$	1.80065e13	1.87867
$768$	−7.12786e12	−0.739322
$769$	−8.34102e12	−0.860104	−0.430052	−	0.902804i	$-0.641505\pi$
$769$	−8.34102e12	−0.860104	−0.430052	+	0.902804i	$0.641505\pi$
$770$	2.71931e11	0.0278773
$771$	−2.22928e12	−0.227206
$772$	1.42483e13	1.44373
$773$	−1.39783e13	−1.40815	−0.704073	−	0.710128i	$-0.748637\pi$
$773$	−1.39783e13	−1.40815	−0.704073	+	0.710128i	$0.748637\pi$
$774$	−1.32712e13	−1.32915
$775$	1.06485e13	1.06031
$776$	8.33245e12	0.824888
$777$	−5.90012e12	−0.580719
$778$	2.55042e13	2.49577
$779$	3.18498e12	0.309877
$780$	−7.86846e11	−0.0761139
$781$	−6.07186e12	−0.583972
$782$	0	0
$783$	1.15104e12	0.109436
$784$	−1.95033e12	−0.184368
$785$	7.76324e11	0.0729675
$786$	4.26087e12	0.398196
$787$	−1.23909e13	−1.15137	−0.575686	−	0.817671i	$-0.695265\pi$
$787$	−1.23909e13	−1.15137	−0.575686	+	0.817671i	$0.695265\pi$
$788$	3.24757e13	3.00048
$789$	4.13202e12	0.379591
$790$	−1.59679e12	−0.145857
$791$	−4.82404e12	−0.438144
$792$	−3.75237e12	−0.338877
$793$	−1.20695e13	−1.08383
$794$	−3.17380e13	−2.83391
$795$	2.23731e11	0.0198643
$796$	1.50324e13	1.32715
$797$	5.26393e12	0.462112	0.231056	−	0.972940i	$-0.425782\pi$
$797$	5.26393e12	0.462112	0.231056	+	0.972940i	$0.425782\pi$
$798$	2.06985e12	0.180686
$799$	0	0
$800$	−8.25151e12	−0.712243
$801$	3.12290e12	0.268047
$802$	−3.48299e13	−2.97281
$803$	−3.20522e12	−0.272044
$804$	9.81845e12	0.828687
$805$	−3.60888e11	−0.0302894
$806$	2.57857e13	2.15214
$807$	−4.60183e11	−0.0381944
$808$	2.34268e13	1.93358
$809$	7.01985e12	0.576182	0.288091	−	0.957603i	$-0.406979\pi$
$809$	7.01985e12	0.576182	0.288091	+	0.957603i	$0.406979\pi$
$810$	4.27527e11	0.0348964
$811$	1.35676e13	1.10131	0.550655	−	0.834733i	$-0.314378\pi$
$811$	1.35676e13	1.10131	0.550655	+	0.834733i	$0.314378\pi$
$812$	1.76546e12	0.142513
$813$	8.15345e12	0.654537
$814$	1.32626e13	1.05881
$815$	7.87393e11	0.0625147
$816$	0	0
$817$	−4.50571e12	−0.353805
$818$	−7.53379e12	−0.588333
$819$	7.63721e12	0.593140
$820$	−1.50915e12	−0.116565
$821$	−1.09555e12	−0.0841565	−0.0420782	−	0.999114i	$-0.513398\pi$
$821$	−1.09555e12	−0.0841565	−0.0420782	+	0.999114i	$0.513398\pi$
$822$	−6.46661e12	−0.494030
$823$	−2.21638e13	−1.68401	−0.842006	−	0.539469i	$-0.818625\pi$
$823$	−2.21638e13	−1.68401	−0.842006	+	0.539469i	$0.818625\pi$
$824$	−2.29886e13	−1.73716
$825$	2.43582e12	0.183064
$826$	2.24442e13	1.67762
$827$	−2.07994e13	−1.54624	−0.773119	−	0.634261i	$-0.781305\pi$
$827$	−2.07994e13	−1.54624	−0.773119	+	0.634261i	$0.781305\pi$
$828$	1.15836e13	0.856458
$829$	4.56048e12	0.335363	0.167682	−	0.985841i	$-0.446372\pi$
$829$	4.56048e12	0.335363	0.167682	+	0.985841i	$0.446372\pi$
$830$	−1.25006e12	−0.0914280
$831$	−3.35466e12	−0.244030
$832$	−2.54106e13	−1.83849
$833$	0	0
$834$	−4.36900e12	−0.312705
$835$	3.05377e11	0.0217394
$836$	−2.96335e12	−0.209823
$837$	1.33463e13	0.939931
$838$	−4.56881e13	−3.20041
$839$	1.02208e13	0.712125	0.356063	−	0.934462i	$-0.384119\pi$
$839$	1.02208e13	0.712125	0.356063	+	0.934462i	$0.384119\pi$
$840$	−4.21639e11	−0.0292202
$841$	−1.42838e13	−0.984607
$842$	−3.26052e13	−2.23554
$843$	4.88749e12	0.333320
$844$	6.94836e12	0.471347
$845$	−5.02669e11	−0.0339178
$846$	−2.19728e13	−1.47475
$847$	8.51041e12	0.568166
$848$	−2.70797e12	−0.179830
$849$	1.15441e13	0.762562
$850$	0	0
$851$	−1.76012e13	−1.15043
$852$	2.18991e13	1.42380
$853$	−1.82858e13	−1.18261	−0.591306	−	0.806447i	$-0.701387\pi$
$853$	−1.82858e13	−1.18261	−0.591306	+	0.806447i	$0.701387\pi$
$854$	−1.50440e13	−0.967838
$855$	2.69611e11	0.0172540
$856$	2.65659e13	1.69119
$857$	−2.38014e13	−1.50726	−0.753632	−	0.657297i	$-0.771700\pi$
$857$	−2.38014e13	−1.50726	−0.753632	+	0.657297i	$0.771700\pi$
$858$	5.89840e12	0.371571
$859$	1.25917e13	0.789070	0.394535	−	0.918881i	$-0.370906\pi$
$859$	1.25917e13	0.789070	0.394535	+	0.918881i	$0.370906\pi$
$860$	2.13495e12	0.133090
$861$	−5.03279e12	−0.312101
$862$	−3.41966e13	−2.10960
$863$	−1.42262e13	−0.873052	−0.436526	−	0.899692i	$-0.643791\pi$
$863$	−1.42262e13	−0.873052	−0.436526	+	0.899692i	$0.643791\pi$
$864$	−1.03420e13	−0.631382
$865$	−1.61596e12	−0.0981429
$866$	−1.20067e12	−0.0725424
$867$	0	0
$868$	2.04705e13	1.22402
$869$	7.62374e12	0.453502
$870$	−1.24054e11	−0.00734134
$871$	1.93116e13	1.13693
$872$	4.00227e13	2.34413
$873$	8.41921e12	0.490577
$874$	6.17477e12	0.357948
$875$	−1.59721e12	−0.0921141
$876$	1.15601e13	0.663276
$877$	1.86781e13	1.06619	0.533096	−	0.846055i	$-0.321028\pi$
$877$	1.86781e13	1.06619	0.533096	+	0.846055i	$0.321028\pi$
$878$	3.62515e12	0.205874
$879$	7.84617e12	0.443310
$880$	1.47302e11	0.00828010
$881$	1.32102e13	0.738783	0.369392	−	0.929274i	$-0.379566\pi$
$881$	1.32102e13	0.738783	0.369392	+	0.929274i	$0.379566\pi$
$882$	−1.26797e13	−0.705504
$883$	5.54927e12	0.307194	0.153597	−	0.988134i	$-0.450914\pi$
$883$	5.54927e12	0.307194	0.153597	+	0.988134i	$0.450914\pi$
$884$	0	0
$885$	−1.00446e12	−0.0550414
$886$	−1.70932e13	−0.931907
$887$	−1.26950e13	−0.688613	−0.344307	−	0.938857i	$-0.611886\pi$
$887$	−1.26950e13	−0.688613	−0.344307	+	0.938857i	$0.611886\pi$
$888$	−2.05641e13	−1.10982
$889$	−7.25769e12	−0.389709
$890$	−7.88789e11	−0.0421411
$891$	−2.04119e12	−0.108501
$892$	2.86994e12	0.151786
$893$	−7.45999e12	−0.392561
$894$	−7.30957e12	−0.382713
$895$	1.09488e12	0.0570376
$896$	−2.26300e13	−1.17300
$897$	−7.82796e12	−0.403722
$898$	−5.78637e13	−2.96936
$899$	2.58927e12	0.132208
$900$	2.55693e13	1.29905
$901$	0	0
$902$	1.13130e13	0.569047
$903$	7.11975e12	0.356344
$904$	−1.68136e13	−0.837342
$905$	−8.42453e11	−0.0417472
$906$	−2.15243e13	−1.06134
$907$	−8.72745e12	−0.428208	−0.214104	−	0.976811i	$-0.568683\pi$
$907$	−8.72745e12	−0.428208	−0.214104	+	0.976811i	$0.568683\pi$
$908$	3.64563e13	1.77986
$909$	2.36707e13	1.14994
$910$	−1.92903e12	−0.0932506
$911$	−2.60110e13	−1.25119	−0.625596	−	0.780147i	$-0.715144\pi$
$911$	−2.60110e13	−1.25119	−0.625596	+	0.780147i	$0.715144\pi$
$912$	1.12121e12	0.0536674
$913$	5.96831e12	0.284271
$914$	2.07339e12	0.0982704
$915$	6.73277e11	0.0317540
$916$	−5.31104e13	−2.49259
$917$	6.65306e12	0.310713
$918$	0	0
$919$	2.79205e13	1.29123	0.645615	−	0.763663i	$-0.276601\pi$
$919$	2.79205e13	1.29123	0.645615	+	0.763663i	$0.276601\pi$
$920$	−1.25783e12	−0.0578865
$921$	1.42968e13	0.654744
$922$	3.39594e13	1.54764
$923$	4.30726e13	1.95341
$924$	4.68257e12	0.211329
$925$	−3.88525e13	−1.74494
$926$	6.35342e13	2.83961
$927$	−2.32280e13	−1.03312
$928$	−2.00641e12	−0.0888085
$929$	−9.34734e12	−0.411735	−0.205867	−	0.978580i	$-0.566002\pi$
$929$	−9.34734e12	−0.411735	−0.205867	+	0.978580i	$0.566002\pi$
$930$	−1.43841e12	−0.0630536
$931$	−4.30489e12	−0.187797
$932$	−4.06396e13	−1.76432
$933$	7.10566e12	0.306999
$934$	−2.07226e13	−0.891012
$935$	0	0
$936$	2.66186e13	1.13356
$937$	4.53001e13	1.91987	0.959933	−	0.280231i	$-0.0904112\pi$
$937$	4.53001e13	1.91987	0.959933	+	0.280231i	$0.0904112\pi$
$938$	2.40708e13	1.01526
$939$	−7.89804e11	−0.0331531
$940$	3.53479e12	0.147669
$941$	−3.85131e13	−1.60124	−0.800618	−	0.599176i	$-0.795495\pi$
$941$	−3.85131e13	−1.60124	−0.800618	+	0.599176i	$0.795495\pi$
$942$	2.09890e13	0.868487
$943$	−1.50138e13	−0.618285
$944$	1.21577e13	0.498286
$945$	−9.98434e11	−0.0407264
$946$	−1.60042e13	−0.649716
$947$	3.56276e13	1.43950	0.719751	−	0.694233i	$-0.244256\pi$
$947$	3.56276e13	1.43950	0.719751	+	0.694233i	$0.244256\pi$
$948$	−2.74962e13	−1.10569
$949$	2.27372e13	0.909996
$950$	1.36300e13	0.542926
$951$	1.52021e13	0.602686
$952$	0	0
$953$	3.24042e13	1.27257	0.636287	−	0.771452i	$-0.280469\pi$
$953$	3.24042e13	1.27257	0.636287	+	0.771452i	$0.280469\pi$
$954$	−1.76053e13	−0.688140
$955$	−8.46186e10	−0.00329193
$956$	−4.79061e13	−1.85494
$957$	5.92287e11	0.0228259
$958$	−8.64081e12	−0.331443
$959$	−1.00972e13	−0.385493
$960$	1.41749e12	0.0538641
$961$	3.58296e12	0.135515
$962$	−9.40823e13	−3.54177
$963$	2.68425e13	1.00578
$964$	−9.32299e13	−3.47703
$965$	−1.56330e12	−0.0580321
$966$	−9.75714e12	−0.360517
$967$	−1.85067e13	−0.680626	−0.340313	−	0.940312i	$-0.610533\pi$
$967$	−1.85067e13	−0.680626	−0.340313	+	0.940312i	$0.610533\pi$
$968$	2.96620e13	1.08583
$969$	0	0
$970$	−2.12655e12	−0.0771262
$971$	−9.11588e12	−0.329088	−0.164544	−	0.986370i	$-0.552615\pi$
$971$	−9.11588e12	−0.329088	−0.164544	+	0.986370i	$0.552615\pi$
$972$	5.04198e13	1.81177
$973$	−6.82191e12	−0.244005
$974$	4.54293e13	1.61741
$975$	−1.72792e13	−0.612355
$976$	−8.14914e12	−0.287467
$977$	−4.93720e13	−1.73363	−0.866813	−	0.498634i	$-0.833835\pi$
$977$	−4.93720e13	−1.73363	−0.866813	+	0.498634i	$0.833835\pi$
$978$	2.12883e13	0.744074
$979$	3.76601e12	0.131026
$980$	2.03980e12	0.0706431
$981$	4.04394e13	1.39410
$982$	−4.20367e13	−1.44254
$983$	−4.75683e13	−1.62490	−0.812450	−	0.583030i	$-0.801867\pi$
$983$	−4.75683e13	−1.62490	−0.812450	+	0.583030i	$0.801867\pi$
$984$	−1.75412e13	−0.596460
$985$	−3.56317e12	−0.120607
$986$	0	0
$987$	1.17880e13	0.395378
$988$	2.10214e13	0.701867
$989$	2.12396e13	0.705934
$990$	9.57652e11	0.0316847
$991$	2.02242e13	0.666101	0.333050	−	0.942909i	$-0.391922\pi$
$991$	2.02242e13	0.666101	0.333050	+	0.942909i	$0.391922\pi$
$992$	−2.32644e13	−0.762762
$993$	−9.56601e12	−0.312219
$994$	5.36877e13	1.74436
$995$	−1.64933e12	−0.0533462
$996$	−2.15256e13	−0.693089
$997$	−1.55512e13	−0.498467	−0.249233	−	0.968443i	$-0.580179\pi$
$997$	−1.55512e13	−0.498467	−0.249233	+	0.968443i	$0.580179\pi$
$998$	−3.55685e13	−1.13495
$999$	−4.86956e13	−1.54684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.4	yes	36
17.16	even	2		289.10.a.g.1.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.4	✓	36	17.16	even	2
289.10.a.h.1.4	yes	36	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-37.5513 q^{2} +70.9462 q^{3} +898.103 q^{4} -98.5382 q^{5} -2664.12 q^{6} -4159.85 q^{7} -14498.7 q^{8} -14649.6 q^{9} +O(q^{10})\)	\(q-37.5513 q^{2} +70.9462 q^{3} +898.103 q^{4} -98.5382 q^{5} -2664.12 q^{6} -4159.85 q^{7} -14498.7 q^{8} -14649.6 q^{9} +3700.24 q^{10} -17666.5 q^{11} +63717.0 q^{12} +125323. q^{13} +156208. q^{14} -6990.91 q^{15} +84616.0 q^{16} +550113. q^{18} +186769. q^{19} -88497.5 q^{20} -295126. q^{21} +663401. q^{22} -880420. q^{23} -1.02863e6 q^{24} -1.94342e6 q^{25} -4.70603e6 q^{26} -2.43577e6 q^{27} -3.73598e6 q^{28} -472555. q^{29} +262518. q^{30} -5.47929e6 q^{31} +4.24588e6 q^{32} -1.25337e6 q^{33} +409905. q^{35} -1.31569e7 q^{36} +1.99919e7 q^{37} -7.01344e6 q^{38} +8.89116e6 q^{39} +1.42867e6 q^{40} +1.70530e7 q^{41} +1.10824e7 q^{42} -2.41245e7 q^{43} -1.58663e7 q^{44} +1.44355e6 q^{45} +3.30609e7 q^{46} -3.99422e7 q^{47} +6.00318e6 q^{48} -2.30492e7 q^{49} +7.29778e7 q^{50} +1.12553e8 q^{52} -3.20031e7 q^{53} +9.14664e7 q^{54} +1.74083e6 q^{55} +6.03124e7 q^{56} +1.32506e7 q^{57} +1.77451e7 q^{58} +1.43681e8 q^{59} -6.27856e6 q^{60} -9.63074e7 q^{61} +2.05755e8 q^{62} +6.09404e7 q^{63} -2.02762e8 q^{64} -1.23491e7 q^{65} +4.70658e7 q^{66} +1.54095e8 q^{67} -6.24624e7 q^{69} -1.53925e7 q^{70} +3.43693e8 q^{71} +2.12400e8 q^{72} +1.81429e8 q^{73} -7.50721e8 q^{74} -1.37878e8 q^{75} +1.67738e8 q^{76} +7.34901e7 q^{77} -3.33875e8 q^{78} -4.31537e8 q^{79} -8.33791e6 q^{80} +1.15540e8 q^{81} -6.40364e8 q^{82} -3.37832e8 q^{83} -2.65053e8 q^{84} +9.05906e8 q^{86} -3.35260e7 q^{87} +2.56141e8 q^{88} -2.13172e8 q^{89} -5.42072e7 q^{90} -5.21324e8 q^{91} -7.90707e8 q^{92} -3.88735e8 q^{93} +1.49988e9 q^{94} -1.84039e7 q^{95} +3.01229e8 q^{96} -5.74705e8 q^{97} +8.65529e8 q^{98} +2.58808e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Introduction

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