LMFDB - Embedded newform 197.10.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,10,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, 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("197.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	197.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:	$101.462059724$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-31.8115 q^{2} +226.712 q^{3} +499.972 q^{4} -1449.41 q^{5} -7212.06 q^{6} +9874.56 q^{7} +382.633 q^{8} +31715.5 q^{9} +46108.1 q^{10} +22839.8 q^{11} +113350. q^{12} -55689.1 q^{13} -314125. q^{14} -328600. q^{15} -268158. q^{16} -45944.5 q^{17} -1.00892e6 q^{18} -592450. q^{19} -724666. q^{20} +2.23868e6 q^{21} -726569. q^{22} +212010. q^{23} +86747.7 q^{24} +147677. q^{25} +1.77155e6 q^{26} +2.72791e6 q^{27} +4.93700e6 q^{28} -4.85128e6 q^{29} +1.04533e7 q^{30} +1.67305e6 q^{31} +8.33459e6 q^{32} +5.17806e6 q^{33} +1.46156e6 q^{34} -1.43123e7 q^{35} +1.58568e7 q^{36} -2.08066e7 q^{37} +1.88467e7 q^{38} -1.26254e7 q^{39} -554594. q^{40} -1.07126e7 q^{41} -7.12159e7 q^{42} -2.66249e6 q^{43} +1.14193e7 q^{44} -4.59688e7 q^{45} -6.74436e6 q^{46} -709244. q^{47} -6.07946e7 q^{48} +5.71534e7 q^{49} -4.69784e6 q^{50} -1.04162e7 q^{51} -2.78430e7 q^{52} -1.71152e7 q^{53} -8.67788e7 q^{54} -3.31043e7 q^{55} +3.77834e6 q^{56} -1.34316e8 q^{57} +1.54327e8 q^{58} +1.01753e8 q^{59} -1.64291e8 q^{60} +6.69100e7 q^{61} -5.32221e7 q^{62} +3.13176e8 q^{63} -1.27839e8 q^{64} +8.07166e7 q^{65} -1.64722e8 q^{66} -2.30667e8 q^{67} -2.29709e7 q^{68} +4.80653e7 q^{69} +4.55297e8 q^{70} -1.98475e8 q^{71} +1.21354e7 q^{72} -5.27407e7 q^{73} +6.61890e8 q^{74} +3.34803e7 q^{75} -2.96208e8 q^{76} +2.25533e8 q^{77} +4.01633e8 q^{78} -1.54549e7 q^{79} +3.88672e8 q^{80} -5.80570e6 q^{81} +3.40784e8 q^{82} +1.07145e8 q^{83} +1.11928e9 q^{84} +6.65926e7 q^{85} +8.46980e7 q^{86} -1.09984e9 q^{87} +8.73927e6 q^{88} -4.82280e8 q^{89} +1.46234e9 q^{90} -5.49905e8 q^{91} +1.05999e8 q^{92} +3.79300e8 q^{93} +2.25621e7 q^{94} +8.58706e8 q^{95} +1.88955e9 q^{96} +1.54578e9 q^{97} -1.81813e9 q^{98} +7.24375e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 32 q^{2} - 892 q^{3} + 16896 q^{4} - 2329 q^{5} - 10272 q^{6} - 37846 q^{7} - 24933 q^{8} + 419903 q^{9} - 138907 q^{10} - 143074 q^{11} - 496640 q^{12} - 433821 q^{13} - 130143 q^{14} - 670126 q^{15}+ \cdots - 6380320552 q^{99}+O(q^{100}) $ 71 * q - 32 * q^2 - 892 * q^3 + 16896 * q^4 - 2329 * q^5 - 10272 * q^6 - 37846 * q^7 - 24933 * q^8 + 419903 * q^9 - 138907 * q^10 - 143074 * q^11 - 496640 * q^12 - 433821 * q^13 - 130143 * q^14 - 670126 * q^15 + 3670016 * q^16 - 226712 * q^17 - 1140455 * q^18 - 4200657 * q^19 - 2522261 * q^20 - 2222620 * q^21 - 5109807 * q^22 - 1576984 * q^23 - 7953747 * q^24 + 20408644 * q^25 - 3606210 * q^26 - 22380322 * q^27 - 28281314 * q^28 - 1600554 * q^29 + 1211083 * q^30 - 27408409 * q^31 - 19842828 * q^32 - 26002786 * q^33 - 33310606 * q^34 - 25745764 * q^35 + 75847738 * q^36 - 56498684 * q^37 - 8523742 * q^38 - 67092176 * q^39 - 69825234 * q^40 - 41524361 * q^41 - 29804525 * q^42 - 103636613 * q^43 - 93059022 * q^44 - 41029851 * q^45 - 35065939 * q^46 - 155481346 * q^47 - 310890046 * q^48 + 274445845 * q^49 - 532508319 * q^50 - 401628576 * q^51 - 638463912 * q^52 - 235002576 * q^53 - 485779441 * q^54 - 274178598 * q^55 - 174143696 * q^56 + 10220750 * q^57 - 54794577 * q^58 - 309204685 * q^59 + 349852813 * q^60 - 172553358 * q^61 + 313207667 * q^62 - 291588072 * q^63 + 1670833437 * q^64 + 394656726 * q^65 + 2405207530 * q^66 - 1034845512 * q^67 + 2160039119 * q^68 + 472060058 * q^69 + 1282221119 * q^70 + 515265617 * q^71 + 1722271619 * q^72 - 667322970 * q^73 + 1111943967 * q^74 - 304507118 * q^75 - 1476894506 * q^76 - 347407724 * q^77 - 99563531 * q^78 - 338475893 * q^79 - 652382330 * q^80 + 1981631951 * q^81 - 2682827483 * q^82 - 2423465319 * q^83 - 1042585800 * q^84 - 2101960924 * q^85 - 2597172884 * q^86 - 2135063354 * q^87 - 5542447545 * q^88 - 2765884440 * q^89 - 6736154529 * q^90 - 6821909968 * q^91 - 4167412114 * q^92 - 4756429190 * q^93 - 5116706209 * q^94 - 4295841932 * q^95 - 14387243887 * q^96 - 6239794299 * q^97 - 8201372742 * q^98 - 6380320552 * q^99

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 $

$2$	−31.8115	−1.40588	−0.702942	−	0.711248i	$-0.748130\pi$
$2$	−31.8115	−1.40588	−0.702942	+	0.711248i	$0.748130\pi$
$3$	226.712	1.61596	0.807978	−	0.589213i	$-0.200562\pi$
$3$	226.712	1.61596	0.807978	+	0.589213i	$0.200562\pi$
$4$	499.972	0.976508
$5$	−1449.41	−1.03712	−0.518558	−	0.855042i	$-0.673531\pi$
$5$	−1449.41	−1.03712	−0.518558	+	0.855042i	$0.673531\pi$
$6$	−7212.06	−2.27184
$7$	9874.56	1.55445	0.777225	−	0.629223i	$-0.216627\pi$
$7$	9874.56	1.55445	0.777225	+	0.629223i	$0.216627\pi$
$8$	382.633	0.0330277
$9$	31715.5	1.61131
$10$	46108.1	1.45806
$11$	22839.8	0.470355	0.235177	−	0.971952i	$-0.424433\pi$
$11$	22839.8	0.470355	0.235177	+	0.971952i	$0.424433\pi$
$12$	113350.	1.57799
$13$	−55689.1	−0.540785	−0.270393	−	0.962750i	$-0.587154\pi$
$13$	−55689.1	−0.540785	−0.270393	+	0.962750i	$0.587154\pi$
$14$	−314125.	−2.18537
$15$	−328600.	−1.67593
$16$	−268158.	−1.02294
$17$	−45944.5	−0.133418	−0.0667088	−	0.997772i	$-0.521250\pi$
$17$	−45944.5	−0.133418	−0.0667088	+	0.997772i	$0.521250\pi$
$18$	−1.00892e6	−2.26532
$19$	−592450.	−1.04294	−0.521471	−	0.853269i	$-0.674617\pi$
$19$	−592450.	−1.04294	−0.521471	+	0.853269i	$0.674617\pi$
$20$	−724666.	−1.01275
$21$	2.23868e6	2.51192
$22$	−726569.	−0.661264
$23$	212010.	0.157972	0.0789862	−	0.996876i	$-0.474832\pi$
$23$	212010.	0.157972	0.0789862	+	0.996876i	$0.474832\pi$
$24$	86747.7	0.0533713
$25$	147677.	0.0756108
$26$	1.77155e6	0.760281
$27$	2.72791e6	0.987853
$28$	4.93700e6	1.51793
$29$	−4.85128e6	−1.27369	−0.636847	−	0.770990i	$-0.719762\pi$
$29$	−4.85128e6	−1.27369	−0.636847	+	0.770990i	$0.719762\pi$
$30$	1.04533e7	2.35617
$31$	1.67305e6	0.325372	0.162686	−	0.986678i	$-0.447984\pi$
$31$	1.67305e6	0.325372	0.162686	+	0.986678i	$0.447984\pi$
$32$	8.33459e6	1.40511
$33$	5.17806e6	0.760072
$34$	1.46156e6	0.187570
$35$	−1.43123e7	−1.61215
$36$	1.58568e7	1.57346
$37$	−2.08066e7	−1.82513	−0.912564	−	0.408933i	$-0.865901\pi$
$37$	−2.08066e7	−1.82513	−0.912564	+	0.408933i	$0.865901\pi$
$38$	1.88467e7	1.46626
$39$	−1.26254e7	−0.873885
$40$	−554594.	−0.0342535
$41$	−1.07126e7	−0.592062	−0.296031	−	0.955178i	$-0.595663\pi$
$41$	−1.07126e7	−0.592062	−0.296031	+	0.955178i	$0.595663\pi$
$42$	−7.12159e7	−3.53147
$43$	−2.66249e6	−0.118763	−0.0593814	−	0.998235i	$-0.518913\pi$
$43$	−2.66249e6	−0.118763	−0.0593814	+	0.998235i	$0.518913\pi$
$44$	1.14193e7	0.459305
$45$	−4.59688e7	−1.67112
$46$	−6.74436e6	−0.222091
$47$	−709244.	−0.0212009	−0.0106005	−	0.999944i	$-0.503374\pi$
$47$	−709244.	−0.0212009	−0.0106005	+	0.999944i	$0.503374\pi$
$48$	−6.07946e7	−1.65303
$49$	5.71534e7	1.41631
$50$	−4.69784e6	−0.106300
$51$	−1.04162e7	−0.215597
$52$	−2.78430e7	−0.528081
$53$	−1.71152e7	−0.297949	−0.148974	−	0.988841i	$-0.547597\pi$
$53$	−1.71152e7	−0.297949	−0.148974	+	0.988841i	$0.547597\pi$
$54$	−8.67788e7	−1.38881
$55$	−3.31043e7	−0.487813
$56$	3.77834e6	0.0513399
$57$	−1.34316e8	−1.68535
$58$	1.54327e8	1.79067
$59$	1.01753e8	1.09323	0.546614	−	0.837384i	$-0.315916\pi$
$59$	1.01753e8	1.09323	0.546614	+	0.837384i	$0.315916\pi$
$60$	−1.64291e8	−1.63656
$61$	6.69100e7	0.618738	0.309369	−	0.950942i	$-0.399882\pi$
$61$	6.69100e7	0.618738	0.309369	+	0.950942i	$0.399882\pi$
$62$	−5.32221e7	−0.457435
$63$	3.13176e8	2.50470
$64$	−1.27839e8	−0.952476
$65$	8.07166e7	0.560857
$66$	−1.64722e8	−1.06857
$67$	−2.30667e8	−1.39846	−0.699229	−	0.714898i	$-0.746473\pi$
$67$	−2.30667e8	−1.39846	−0.699229	+	0.714898i	$0.746473\pi$
$68$	−2.29709e7	−0.130283
$69$	4.80653e7	0.255276
$70$	4.55297e8	2.26649
$71$	−1.98475e8	−0.926921	−0.463460	−	0.886118i	$-0.653392\pi$
$71$	−1.98475e8	−0.926921	−0.463460	+	0.886118i	$0.653392\pi$
$72$	1.21354e7	0.0532179
$73$	−5.27407e7	−0.217367	−0.108683	−	0.994076i	$-0.534663\pi$
$73$	−5.27407e7	−0.217367	−0.108683	+	0.994076i	$0.534663\pi$
$74$	6.61890e8	2.56592
$75$	3.34803e7	0.122184
$76$	−2.96208e8	−1.01844
$77$	2.25533e8	0.731142
$78$	4.01633e8	1.22858
$79$	−1.54549e7	−0.0446420	−0.0223210	−	0.999751i	$-0.507106\pi$
$79$	−1.54549e7	−0.0446420	−0.0223210	+	0.999751i	$0.507106\pi$
$80$	3.88672e8	1.06091
$81$	−5.80570e6	−0.0149855
$82$	3.40784e8	0.832370
$83$	1.07145e8	0.247811	0.123906	−	0.992294i	$-0.460458\pi$
$83$	1.07145e8	0.247811	0.123906	+	0.992294i	$0.460458\pi$
$84$	1.11928e9	2.45291
$85$	6.65926e7	0.138370
$86$	8.46980e7	0.166967
$87$	−1.09984e9	−2.05823
$88$	8.73927e6	0.0155347
$89$	−4.82280e8	−0.814787	−0.407393	−	0.913253i	$-0.633562\pi$
$89$	−4.82280e8	−0.814787	−0.407393	+	0.913253i	$0.633562\pi$
$90$	1.46234e9	2.34940
$91$	−5.49905e8	−0.840624
$92$	1.05999e8	0.154261
$93$	3.79300e8	0.525787
$94$	2.25621e7	0.0298061
$95$	8.58706e8	1.08165
$96$	1.88955e9	2.27059
$97$	1.54578e9	1.77286	0.886431	−	0.462860i	$-0.153177\pi$
$97$	1.54578e9	1.77286	0.886431	+	0.462860i	$0.153177\pi$
$98$	−1.81813e9	−1.99117
$99$	7.24375e8	0.757888
$100$	7.38345e7	0.0738345
$101$	1.06860e9	1.02181	0.510903	−	0.859638i	$-0.329311\pi$
$101$	1.06860e9	1.02181	0.510903	+	0.859638i	$0.329311\pi$
$102$	3.31354e8	0.303104
$103$	1.04264e8	0.0912778	0.0456389	−	0.998958i	$-0.485468\pi$
$103$	1.04264e8	0.0912778	0.0456389	+	0.998958i	$0.485468\pi$
$104$	−2.13085e7	−0.0178609
$105$	−3.24478e9	−2.60516
$106$	5.44462e8	0.418881
$107$	−1.11846e9	−0.824887	−0.412443	−	0.910983i	$-0.635325\pi$
$107$	−1.11846e9	−0.824887	−0.412443	+	0.910983i	$0.635325\pi$
$108$	1.36388e9	0.964646
$109$	−1.55330e8	−0.105399	−0.0526994	−	0.998610i	$-0.516783\pi$
$109$	−1.55330e8	−0.105399	−0.0526994	+	0.998610i	$0.516783\pi$
$110$	1.05310e9	0.685807
$111$	−4.71711e9	−2.94933
$112$	−2.64794e9	−1.59011
$113$	1.04099e9	0.600610	0.300305	−	0.953843i	$-0.402912\pi$
$113$	1.04099e9	0.600610	0.300305	+	0.953843i	$0.402912\pi$
$114$	4.27278e9	2.36940
$115$	−3.07290e8	−0.163836
$116$	−2.42550e9	−1.24377
$117$	−1.76620e9	−0.871374
$118$	−3.23690e9	−1.53695
$119$	−4.53681e8	−0.207391
$120$	−1.25733e8	−0.0553522
$121$	−1.83629e9	−0.778767
$122$	−2.12851e9	−0.869873
$123$	−2.42868e9	−0.956746
$124$	8.36476e8	0.317728
$125$	2.61684e9	0.958699
$126$	−9.96261e9	−3.52132
$127$	−4.17361e7	−0.0142362	−0.00711812	−	0.999975i	$-0.502266\pi$
$127$	−4.17361e7	−0.0142362	−0.00711812	+	0.999975i	$0.502266\pi$
$128$	−2.00555e8	−0.0660371
$129$	−6.03620e8	−0.191916
$130$	−2.56772e9	−0.788500
$131$	1.80732e9	0.536186	0.268093	−	0.963393i	$-0.413607\pi$
$131$	1.80732e9	0.536186	0.268093	+	0.963393i	$0.413607\pi$
$132$	2.58889e9	0.742216
$133$	−5.85018e9	−1.62120
$134$	7.33787e9	1.96607
$135$	−3.95387e9	−1.02452
$136$	−1.75799e7	−0.00440647
$137$	4.84892e9	1.17599	0.587994	−	0.808865i	$-0.299918\pi$
$137$	4.84892e9	1.17599	0.587994	+	0.808865i	$0.299918\pi$
$138$	−1.52903e9	−0.358889
$139$	−6.95317e9	−1.57985	−0.789925	−	0.613203i	$-0.789881\pi$
$139$	−6.95317e9	−1.57985	−0.789925	+	0.613203i	$0.789881\pi$
$140$	−7.15576e9	−1.57427
$141$	−1.60794e8	−0.0342598
$142$	6.31378e9	1.30314
$143$	−1.27193e9	−0.254361
$144$	−8.50474e9	−1.64828
$145$	7.03151e9	1.32097
$146$	1.67776e9	0.305592
$147$	1.29574e10	2.28870
$148$	−1.04027e10	−1.78225
$149$	3.74749e9	0.622877	0.311438	−	0.950266i	$-0.399189\pi$
$149$	3.74749e9	0.622877	0.311438	+	0.950266i	$0.399189\pi$
$150$	−1.06506e9	−0.171776
$151$	−3.54145e9	−0.554351	−0.277176	−	0.960819i	$-0.589398\pi$
$151$	−3.54145e9	−0.554351	−0.277176	+	0.960819i	$0.589398\pi$
$152$	−2.26691e8	−0.0344460
$153$	−1.45715e9	−0.214977
$154$	−7.17455e9	−1.02790
$155$	−2.42494e9	−0.337449
$156$	−6.31234e9	−0.853355
$157$	−7.86228e9	−1.03276	−0.516380	−	0.856359i	$-0.672721\pi$
$157$	−7.86228e9	−1.03276	−0.516380	+	0.856359i	$0.672721\pi$
$158$	4.91643e8	0.0627614
$159$	−3.88024e9	−0.481472
$160$	−1.20803e10	−1.45726
$161$	2.09351e9	0.245560
$162$	1.84688e8	0.0210679
$163$	−1.08952e10	−1.20890	−0.604452	−	0.796641i	$-0.706608\pi$
$163$	−1.08952e10	−1.20890	−0.604452	+	0.796641i	$0.706608\pi$
$164$	−5.35599e9	−0.578153
$165$	−7.50516e9	−0.788283
$166$	−3.40844e9	−0.348393
$167$	−9.27387e9	−0.922650	−0.461325	−	0.887231i	$-0.652626\pi$
$167$	−9.27387e9	−0.922650	−0.461325	+	0.887231i	$0.652626\pi$
$168$	8.56595e8	0.0829629
$169$	−7.50323e9	−0.707551
$170$	−2.11841e9	−0.194531
$171$	−1.87898e10	−1.68051
$172$	−1.33117e9	−0.115973
$173$	5.32028e9	0.451572	0.225786	−	0.974177i	$-0.427505\pi$
$173$	5.32028e9	0.451572	0.225786	+	0.974177i	$0.427505\pi$
$174$	3.49877e10	2.89364
$175$	1.45825e9	0.117533
$176$	−6.12467e9	−0.481145
$177$	2.30685e10	1.76661
$178$	1.53420e10	1.14549
$179$	−2.54999e10	−1.85652	−0.928262	−	0.371927i	$-0.878697\pi$
$179$	−2.54999e10	−1.85652	−0.928262	+	0.371927i	$0.878697\pi$
$180$	−2.29831e10	−1.63186
$181$	−1.71854e10	−1.19016	−0.595082	−	0.803665i	$-0.702881\pi$
$181$	−1.71854e10	−1.19016	−0.595082	+	0.803665i	$0.702881\pi$
$182$	1.74933e10	1.18182
$183$	1.51693e10	0.999853
$184$	8.11221e7	0.00521746
$185$	3.01574e10	1.89287
$186$	−1.20661e10	−0.739195
$187$	−1.04936e9	−0.0627536
$188$	−3.54602e8	−0.0207029
$189$	2.69369e10	1.53557
$190$	−2.73167e10	−1.52068
$191$	3.23747e10	1.76017	0.880086	−	0.474813i	$-0.157484\pi$
$191$	3.23747e10	1.76017	0.880086	+	0.474813i	$0.157484\pi$
$192$	−2.89827e10	−1.53916
$193$	−2.47967e10	−1.28643	−0.643214	−	0.765686i	$-0.722400\pi$
$193$	−2.47967e10	−1.28643	−0.643214	+	0.765686i	$0.722400\pi$
$194$	−4.91736e10	−2.49244
$195$	1.82994e10	0.906321
$196$	2.85751e10	1.38304
$197$	−1.50614e9	−0.0712470
$197$	−1.50614e9	−0.0712470
$198$	−2.30435e10	−1.06550
$199$	−4.38462e9	−0.198195	−0.0990976	−	0.995078i	$-0.531596\pi$
$199$	−4.38462e9	−0.198195	−0.0990976	+	0.995078i	$0.531596\pi$
$200$	5.65063e7	0.00249725
$201$	−5.22951e10	−2.25984
$202$	−3.39938e10	−1.43654
$203$	−4.79043e10	−1.97989
$204$	−5.20779e9	−0.210532
$205$	1.55270e10	0.614037
$206$	−3.31678e9	−0.128326
$207$	6.72399e9	0.254543
$208$	1.49335e10	0.553191
$209$	−1.35314e10	−0.490553
$210$	1.03221e11	3.66254
$211$	−2.01589e10	−0.700157	−0.350078	−	0.936720i	$-0.613845\pi$
$211$	−2.01589e10	−0.700157	−0.350078	+	0.936720i	$0.613845\pi$
$212$	−8.55714e9	−0.290949
$213$	−4.49966e10	−1.49786
$214$	3.55800e10	1.15969
$215$	3.85906e9	0.123171
$216$	1.04379e9	0.0326265
$217$	1.65206e10	0.505774
$218$	4.94127e9	0.148178
$219$	−1.19570e10	−0.351255
$220$	−1.65512e10	−0.476353
$221$	2.55860e9	0.0721503
$222$	1.50058e11	4.14641
$223$	−4.04449e9	−0.109520	−0.0547599	−	0.998500i	$-0.517439\pi$
$223$	−4.04449e9	−0.109520	−0.0547599	+	0.998500i	$0.517439\pi$
$224$	8.23004e10	2.18417
$225$	4.68365e9	0.121833
$226$	−3.31154e10	−0.844387
$227$	6.97082e10	1.74248	0.871239	−	0.490859i	$-0.163317\pi$
$227$	6.97082e10	1.74248	0.871239	+	0.490859i	$0.163317\pi$
$228$	−6.71541e10	−1.64576
$229$	9.62661e9	0.231320	0.115660	−	0.993289i	$-0.463102\pi$
$229$	9.62661e9	0.231320	0.115660	+	0.993289i	$0.463102\pi$
$230$	9.77537e9	0.230334
$231$	5.11311e10	1.18149
$232$	−1.85626e9	−0.0420672
$233$	−4.31272e10	−0.958628	−0.479314	−	0.877644i	$-0.659114\pi$
$233$	−4.31272e10	−0.958628	−0.479314	+	0.877644i	$0.659114\pi$
$234$	5.61856e10	1.22505
$235$	1.02799e9	0.0219879
$236$	5.08734e10	1.06755
$237$	−3.50381e9	−0.0721394
$238$	1.44323e10	0.291567
$239$	5.30551e10	1.05181	0.525904	−	0.850544i	$-0.323727\pi$
$239$	5.30551e10	1.05181	0.525904	+	0.850544i	$0.323727\pi$
$240$	8.81166e10	1.71438
$241$	1.84165e10	0.351665	0.175833	−	0.984420i	$-0.443738\pi$
$241$	1.84165e10	0.351665	0.175833	+	0.984420i	$0.443738\pi$
$242$	5.84152e10	1.09485
$243$	−5.50096e10	−1.01207
$244$	3.34531e10	0.604202
$245$	−8.28389e10	−1.46888
$246$	7.72598e10	1.34507
$247$	3.29930e10	0.564008
$248$	6.40163e8	0.0107463
$249$	2.42911e10	0.400452
$250$	−8.32457e10	−1.34782
$251$	8.68512e10	1.38116	0.690580	−	0.723256i	$-0.257355\pi$
$251$	8.68512e10	1.38116	0.690580	+	0.723256i	$0.257355\pi$
$252$	1.56579e11	2.44586
$253$	4.84227e9	0.0743030
$254$	1.32769e9	0.0200145
$255$	1.50974e10	0.223599
$256$	7.18336e10	1.04532
$257$	−9.81614e10	−1.40359	−0.701797	−	0.712377i	$-0.747619\pi$
$257$	−9.81614e10	−1.40359	−0.701797	+	0.712377i	$0.747619\pi$
$258$	1.92021e10	0.269811
$259$	−2.05456e11	−2.83707
$260$	4.03560e10	0.547682
$261$	−1.53861e11	−2.05232
$262$	−5.74937e10	−0.753815
$263$	−2.85914e10	−0.368498	−0.184249	−	0.982880i	$-0.558985\pi$
$263$	−2.85914e10	−0.368498	−0.184249	+	0.982880i	$0.558985\pi$
$264$	1.98130e9	0.0251034
$265$	2.48071e10	0.309008
$266$	1.86103e11	2.27922
$267$	−1.09339e11	−1.31666
$268$	−1.15327e11	−1.36560
$269$	1.32052e10	0.153766	0.0768830	−	0.997040i	$-0.475503\pi$
$269$	1.32052e10	0.153766	0.0768830	+	0.997040i	$0.475503\pi$
$270$	1.25778e11	1.44035
$271$	2.43678e10	0.274444	0.137222	−	0.990540i	$-0.456183\pi$
$271$	2.43678e10	0.274444	0.137222	+	0.990540i	$0.456183\pi$
$272$	1.23204e10	0.136478
$273$	−1.24670e11	−1.35841
$274$	−1.54252e11	−1.65330
$275$	3.37292e9	0.0355639
$276$	2.40313e10	0.249279
$277$	−1.29647e11	−1.32313	−0.661565	−	0.749887i	$-0.730108\pi$
$277$	−1.29647e11	−1.32313	−0.661565	+	0.749887i	$0.730108\pi$
$278$	2.21191e11	2.22109
$279$	5.30614e10	0.524276
$280$	−5.47638e9	−0.0532454
$281$	−1.47068e11	−1.40715	−0.703575	−	0.710621i	$-0.748414\pi$
$281$	−1.47068e11	−1.40715	−0.703575	+	0.710621i	$0.748414\pi$
$282$	5.11511e9	0.0481653
$283$	−2.58242e10	−0.239325	−0.119662	−	0.992815i	$-0.538181\pi$
$283$	−2.58242e10	−0.239325	−0.119662	+	0.992815i	$0.538181\pi$
$284$	−9.92318e10	−0.905145
$285$	1.94679e11	1.74790
$286$	4.04619e10	0.357602
$287$	−1.05782e11	−0.920330
$288$	2.64335e11	2.26407
$289$	−1.16477e11	−0.982200
$290$	−2.23683e11	−1.85713
$291$	3.50447e11	2.86487
$292$	−2.63689e10	−0.212260
$293$	−1.73204e11	−1.37295	−0.686473	−	0.727155i	$-0.740842\pi$
$293$	−1.73204e11	−1.37295	−0.686473	+	0.727155i	$0.740842\pi$
$294$	−4.12193e11	−3.21764
$295$	−1.47482e11	−1.13381
$296$	−7.96130e9	−0.0602798
$297$	6.23048e10	0.464641
$298$	−1.19213e11	−0.875692
$299$	−1.18066e10	−0.0854291
$300$	1.67392e10	0.119313
$301$	−2.62910e10	−0.184611
$302$	1.12659e11	0.779353
$303$	2.42265e11	1.65119
$304$	1.58870e11	1.06687
$305$	−9.69803e10	−0.641704
$306$	4.63541e10	0.302233
$307$	3.24017e10	0.208183	0.104091	−	0.994568i	$-0.466807\pi$
$307$	3.24017e10	0.208183	0.104091	+	0.994568i	$0.466807\pi$
$308$	1.12760e11	0.713966
$309$	2.36378e10	0.147501
$310$	7.71409e10	0.474414
$311$	−1.57812e11	−0.956571	−0.478285	−	0.878205i	$-0.658742\pi$
$311$	−1.57812e11	−0.956571	−0.478285	+	0.878205i	$0.658742\pi$
$312$	−4.83090e9	−0.0288624
$313$	2.42108e11	1.42580	0.712901	−	0.701265i	$-0.247381\pi$
$313$	2.42108e11	1.42580	0.712901	+	0.701265i	$0.247381\pi$
$314$	2.50111e11	1.45194
$315$	−4.53922e11	−2.59767
$316$	−7.72700e9	−0.0435932
$317$	1.56550e11	0.870734	0.435367	−	0.900253i	$-0.356619\pi$
$317$	1.56550e11	0.870734	0.435367	+	0.900253i	$0.356619\pi$
$318$	1.23436e11	0.676893
$319$	−1.10802e11	−0.599088
$320$	1.85292e11	0.987829
$321$	−2.53569e11	−1.33298
$322$	−6.65976e10	−0.345229
$323$	2.72198e10	0.139147
$324$	−2.90269e9	−0.0146335
$325$	−8.22401e9	−0.0408892
$326$	3.46594e11	1.69958
$327$	−3.52152e10	−0.170320
$328$	−4.09900e9	−0.0195544
$329$	−7.00347e9	−0.0329558
$330$	2.38751e11	1.10823
$331$	−5.53303e10	−0.253360	−0.126680	−	0.991944i	$-0.540432\pi$
$331$	−5.53303e10	−0.253360	−0.126680	+	0.991944i	$0.540432\pi$
$332$	5.35695e10	0.241989
$333$	−6.59891e11	−2.94085
$334$	2.95016e11	1.29714
$335$	3.34332e11	1.45036
$336$	−6.00320e11	−2.56955
$337$	1.45508e11	0.614542	0.307271	−	0.951622i	$-0.400584\pi$
$337$	1.45508e11	0.614542	0.307271	+	0.951622i	$0.400584\pi$
$338$	2.38689e11	0.994734
$339$	2.36005e11	0.970559
$340$	3.32944e10	0.135119
$341$	3.82121e10	0.153040
$342$	5.97732e11	2.36260
$343$	1.65890e11	0.647138
$344$	−1.01876e9	−0.00392246
$345$	−6.96665e10	−0.264751
$346$	−1.69246e11	−0.634857
$347$	−6.39428e10	−0.236761	−0.118380	−	0.992968i	$-0.537770\pi$
$347$	−6.39428e10	−0.236761	−0.118380	+	0.992968i	$0.537770\pi$
$348$	−5.49891e11	−2.00988
$349$	−1.14191e11	−0.412020	−0.206010	−	0.978550i	$-0.566048\pi$
$349$	−1.14191e11	−0.412020	−0.206010	+	0.978550i	$0.566048\pi$
$350$	−4.63891e10	−0.165238
$351$	−1.51915e11	−0.534216
$352$	1.90361e11	0.660899
$353$	−1.16026e10	−0.0397712	−0.0198856	−	0.999802i	$-0.506330\pi$
$353$	−1.16026e10	−0.0397712	−0.0198856	+	0.999802i	$0.506330\pi$
$354$	−7.33845e11	−2.48365
$355$	2.87672e11	0.961325
$356$	−2.41126e11	−0.795645
$357$	−1.02855e11	−0.335134
$358$	8.11192e11	2.61006
$359$	−1.71039e11	−0.543462	−0.271731	−	0.962373i	$-0.587596\pi$
$359$	−1.71039e11	−0.543462	−0.271731	+	0.962373i	$0.587596\pi$
$360$	−1.75892e10	−0.0551932
$361$	2.83093e10	0.0877297
$362$	5.46695e11	1.67323
$363$	−4.16310e11	−1.25845
$364$	−2.74937e11	−0.820875
$365$	7.64431e10	0.225435
$366$	−4.82559e11	−1.40568
$367$	3.24996e11	0.935150	0.467575	−	0.883953i	$-0.345128\pi$
$367$	3.24996e11	0.935150	0.467575	+	0.883953i	$0.345128\pi$
$368$	−5.68521e10	−0.161596
$369$	−3.39755e11	−0.953996
$370$	−9.59352e11	−2.66116
$371$	−1.69006e11	−0.463146
$372$	1.89639e11	0.513435
$373$	7.12429e11	1.90569	0.952844	−	0.303459i	$-0.0981416\pi$
$373$	7.12429e11	1.90569	0.952844	+	0.303459i	$0.0981416\pi$
$374$	3.33818e10	0.0882242
$375$	5.93270e11	1.54922
$376$	−2.71380e8	−0.000700218 0
$377$	2.70163e11	0.688795
$378$	−8.56902e11	−2.15883
$379$	−2.74595e11	−0.683623	−0.341812	−	0.939768i	$-0.611040\pi$
$379$	−2.74595e11	−0.683623	−0.341812	+	0.939768i	$0.611040\pi$
$380$	4.29329e11	1.05624
$381$	−9.46209e9	−0.0230051
$382$	−1.02989e12	−2.47460
$383$	5.67014e11	1.34648	0.673239	−	0.739425i	$-0.264903\pi$
$383$	5.67014e11	1.34648	0.673239	+	0.739425i	$0.264903\pi$
$384$	−4.54682e10	−0.106713
$385$	−3.26891e11	−0.758280
$386$	7.88820e11	1.80857
$387$	−8.44422e10	−0.191364
$388$	7.72847e11	1.73121
$389$	−1.13858e11	−0.252109	−0.126055	−	0.992023i	$-0.540231\pi$
$389$	−1.13858e11	−0.252109	−0.126055	+	0.992023i	$0.540231\pi$
$390$	−5.82133e11	−1.27418
$391$	−9.74069e9	−0.0210763
$392$	2.18688e10	0.0467775
$393$	4.09743e11	0.866452
$394$	4.79125e10	0.100165
$395$	2.24005e10	0.0462989
$396$	3.62167e11	0.740083
$397$	9.79495e11	1.97900	0.989498	−	0.144544i	$-0.0461716\pi$
$397$	9.79495e11	1.97900	0.989498	+	0.144544i	$0.0461716\pi$
$398$	1.39481e11	0.278639
$399$	−1.32631e12	−2.61979
$400$	−3.96008e10	−0.0773453
$401$	5.14376e11	0.993415	0.496708	−	0.867918i	$-0.334542\pi$
$401$	5.14376e11	0.993415	0.496708	+	0.867918i	$0.334542\pi$
$402$	1.66359e12	3.17708
$403$	−9.31704e10	−0.175956
$404$	5.34270e11	0.997802
$405$	8.41486e9	0.0155417
$406$	1.52391e12	2.78350
$407$	−4.75219e11	−0.858458
$408$	−3.98558e9	−0.00712066
$409$	−6.04978e11	−1.06902	−0.534509	−	0.845163i	$-0.679503\pi$
$409$	−6.04978e11	−1.06902	−0.534509	+	0.845163i	$0.679503\pi$
$410$	−4.93937e11	−0.863265
$411$	1.09931e12	1.90034
$412$	5.21288e10	0.0891334
$413$	1.00476e12	1.69937
$414$	−2.13900e11	−0.357857
$415$	−1.55298e11	−0.257009
$416$	−4.64146e11	−0.759861
$417$	−1.57637e12	−2.55297
$418$	4.30456e11	0.689660
$419$	8.82181e11	1.39828	0.699141	−	0.714984i	$-0.253566\pi$
$419$	8.82181e11	1.39828	0.699141	+	0.714984i	$0.253566\pi$
$420$	−1.62230e12	−2.54395
$421$	−1.22008e12	−1.89287	−0.946434	−	0.322898i	$-0.895343\pi$
$421$	−1.22008e12	−1.89287	−0.946434	+	0.322898i	$0.895343\pi$
$422$	6.41284e11	0.984339
$423$	−2.24940e10	−0.0341613
$424$	−6.54886e9	−0.00984056
$425$	−6.78496e9	−0.0100878
$426$	1.43141e12	2.10582
$427$	6.60707e11	0.961797
$428$	−5.59200e11	−0.805508
$429$	−2.88362e11	−0.411036
$430$	−1.22762e11	−0.173164
$431$	−1.10357e12	−1.54046	−0.770232	−	0.637764i	$-0.779860\pi$
$431$	−1.10357e12	−1.54046	−0.770232	+	0.637764i	$0.779860\pi$
$432$	−7.31509e11	−1.01051
$433$	5.88410e11	0.804423	0.402212	−	0.915547i	$-0.368242\pi$
$433$	5.88410e11	0.804423	0.402212	+	0.915547i	$0.368242\pi$
$434$	−5.25545e11	−0.711060
$435$	1.59413e12	2.13463
$436$	−7.76605e10	−0.102923
$437$	−1.25605e11	−0.164756
$438$	3.80369e11	0.493823
$439$	5.62966e11	0.723422	0.361711	−	0.932290i	$-0.382193\pi$
$439$	5.62966e11	0.723422	0.361711	+	0.932290i	$0.382193\pi$
$440$	−1.26668e10	−0.0161113
$441$	1.81264e12	2.28212
$442$	−8.13931e10	−0.101435
$443$	3.96636e11	0.489300	0.244650	−	0.969611i	$-0.421327\pi$
$443$	3.96636e11	0.489300	0.244650	+	0.969611i	$0.421327\pi$
$444$	−2.35842e12	−2.88004
$445$	6.99023e11	0.845029
$446$	1.28661e11	0.153972
$447$	8.49602e11	1.00654
$448$	−1.26236e12	−1.48058
$449$	−2.23119e11	−0.259076	−0.129538	−	0.991574i	$-0.541349\pi$
$449$	−2.23119e11	−0.259076	−0.129538	+	0.991574i	$0.541349\pi$
$450$	−1.48994e11	−0.171282
$451$	−2.44673e11	−0.278479
$452$	5.20464e11	0.586500
$453$	−8.02891e11	−0.895807
$454$	−2.21752e12	−2.44972
$455$	7.97041e11	0.871825
$456$	−5.13937e10	−0.0556632
$457$	1.18873e12	1.27486	0.637428	−	0.770510i	$-0.279998\pi$
$457$	1.18873e12	1.27486	0.637428	+	0.770510i	$0.279998\pi$
$458$	−3.06237e11	−0.325209
$459$	−1.25332e11	−0.131797
$460$	−1.53637e11	−0.159987
$461$	3.10028e11	0.319703	0.159852	−	0.987141i	$-0.448898\pi$
$461$	3.10028e11	0.319703	0.159852	+	0.987141i	$0.448898\pi$
$462$	−1.62656e12	−1.66104
$463$	−1.04982e12	−1.06169	−0.530847	−	0.847468i	$-0.678126\pi$
$463$	−1.04982e12	−1.06169	−0.530847	+	0.847468i	$0.678126\pi$
$464$	1.30091e12	1.30291
$465$	−5.49763e11	−0.545302
$466$	1.37194e12	1.34772
$467$	−2.00259e11	−0.194835	−0.0974173	−	0.995244i	$-0.531058\pi$
$467$	−2.00259e11	−0.194835	−0.0974173	+	0.995244i	$0.531058\pi$
$468$	−8.83052e11	−0.850903
$469$	−2.27774e12	−2.17383
$470$	−3.27019e10	−0.0309124
$471$	−1.78247e12	−1.66890
$472$	3.89339e10	0.0361068
$473$	−6.08109e10	−0.0558607
$474$	1.11461e11	0.101420
$475$	−8.74914e10	−0.0788577
$476$	−2.26828e11	−0.202519
$477$	−5.42818e11	−0.480088
$478$	−1.68776e12	−1.47872
$479$	2.03940e10	0.0177008	0.00885040	−	0.999961i	$-0.497183\pi$
$479$	2.03940e10	0.0177008	0.00885040	+	0.999961i	$0.497183\pi$
$480$	−2.73875e12	−2.35487
$481$	1.15870e12	0.987003
$482$	−5.85855e11	−0.494400
$483$	4.74623e11	0.396814
$484$	−9.18094e11	−0.760471
$485$	−2.24048e12	−1.83867
$486$	1.74994e12	1.42285
$487$	2.33165e12	1.87838	0.939190	−	0.343397i	$-0.111578\pi$
$487$	2.33165e12	1.87838	0.939190	+	0.343397i	$0.111578\pi$
$488$	2.56020e10	0.0204355
$489$	−2.47008e12	−1.95354
$490$	2.63523e12	2.06508
$491$	1.71540e12	1.33199	0.665993	−	0.745958i	$-0.268008\pi$
$491$	1.71540e12	1.33199	0.665993	+	0.745958i	$0.268008\pi$
$492$	−1.21427e12	−0.934269
$493$	2.22889e11	0.169933
$494$	−1.04956e12	−0.792930
$495$	−1.04992e12	−0.786018
$496$	−4.48640e11	−0.332836
$497$	−1.95985e12	−1.44085
$498$	−7.72736e11	−0.562988
$499$	3.25362e11	0.234917	0.117459	−	0.993078i	$-0.462525\pi$
$499$	3.25362e11	0.234917	0.117459	+	0.993078i	$0.462525\pi$
$500$	1.30835e12	0.936177
$501$	−2.10250e12	−1.49096
$502$	−2.76287e12	−1.94175
$503$	3.65217e11	0.254387	0.127193	−	0.991878i	$-0.459403\pi$
$503$	3.65217e11	0.254387	0.127193	+	0.991878i	$0.459403\pi$
$504$	1.19832e11	0.0827245
$505$	−1.54884e12	−1.05973
$506$	−1.54040e11	−0.104461
$507$	−1.70107e12	−1.14337
$508$	−2.08669e10	−0.0139018
$509$	−2.41548e12	−1.59505	−0.797525	−	0.603286i	$-0.793858\pi$
$509$	−2.41548e12	−1.59505	−0.797525	+	0.603286i	$0.793858\pi$
$510$	−4.80270e11	−0.314354
$511$	−5.20791e11	−0.337886
$512$	−2.18245e12	−1.40356
$513$	−1.61615e12	−1.03027
$514$	3.12266e12	1.97329
$515$	−1.51121e11	−0.0946657
$516$	−3.01793e11	−0.187407
$517$	−1.61990e10	−0.00997196
$518$	6.53587e12	3.98859
$519$	1.20617e12	0.729720
$520$	3.08849e10	0.0185238
$521$	−5.50115e11	−0.327103	−0.163551	−	0.986535i	$-0.552295\pi$
$521$	−5.50115e11	−0.327103	−0.163551	+	0.986535i	$0.552295\pi$
$522$	4.89454e12	2.88532
$523$	2.27108e12	1.32732	0.663658	−	0.748036i	$-0.269003\pi$
$523$	2.27108e12	1.32732	0.663658	+	0.748036i	$0.269003\pi$
$524$	9.03611e11	0.523589
$525$	3.30603e11	0.189928
$526$	9.09536e11	0.518065
$527$	−7.68672e10	−0.0434104
$528$	−1.38854e12	−0.777509
$529$	−1.75620e12	−0.975045
$530$	−7.89151e11	−0.434429
$531$	3.22713e12	1.76153
$532$	−2.92493e12	−1.58312
$533$	5.96574e11	0.320178
$534$	3.47823e12	1.85107
$535$	1.62112e12	0.855504
$536$	−8.82610e10	−0.0461878
$537$	−5.78115e12	−3.00006
$538$	−4.20078e11	−0.216177
$539$	1.30537e12	0.666169
$540$	−1.97682e12	−1.00045
$541$	−1.60456e12	−0.805320	−0.402660	−	0.915350i	$-0.631914\pi$
$541$	−1.60456e12	−0.805320	−0.402660	+	0.915350i	$0.631914\pi$
$542$	−7.75175e11	−0.385836
$543$	−3.89615e12	−1.92325
$544$	−3.82928e11	−0.187466
$545$	2.25137e11	0.109311
$546$	3.96595e12	1.90977
$547$	2.15732e10	0.0103032	0.00515159	−	0.999987i	$-0.498360\pi$
$547$	2.15732e10	0.0103032	0.00515159	+	0.999987i	$0.498360\pi$
$548$	2.42432e12	1.14836
$549$	2.12208e12	0.996980
$550$	−1.07298e11	−0.0499987
$551$	2.87414e12	1.32839
$552$	1.83914e10	0.00843118
$553$	−1.52610e11	−0.0693937
$554$	4.12426e12	1.86017
$555$	6.83705e12	3.05880
$556$	−3.47639e12	−1.54274
$557$	−3.19479e12	−1.40635	−0.703176	−	0.711015i	$-0.748236\pi$
$557$	−3.19479e12	−1.40635	−0.703176	+	0.711015i	$0.748236\pi$
$558$	−1.68796e12	−0.737071
$559$	1.48272e11	0.0642252
$560$	3.83796e12	1.64913
$561$	−2.37903e11	−0.101407
$562$	4.67846e12	1.97829
$563$	2.47417e12	1.03787	0.518933	−	0.854815i	$-0.326329\pi$
$563$	2.47417e12	1.03787	0.518933	+	0.854815i	$0.326329\pi$
$564$	−8.03926e10	−0.0334549
$565$	−1.50882e12	−0.622902
$566$	8.21506e11	0.336463
$567$	−5.73287e10	−0.0232942
$568$	−7.59431e10	−0.0306140
$569$	2.14218e11	0.0856745	0.0428373	−	0.999082i	$-0.486360\pi$
$569$	2.14218e11	0.0856745	0.0428373	+	0.999082i	$0.486360\pi$
$570$	−6.19304e12	−2.45735
$571$	−1.17952e12	−0.464348	−0.232174	−	0.972674i	$-0.574584\pi$
$571$	−1.17952e12	−0.464348	−0.232174	+	0.972674i	$0.574584\pi$
$572$	−6.35928e11	−0.248385
$573$	7.33974e12	2.84436
$574$	3.36509e12	1.29388
$575$	3.13091e10	0.0119444
$576$	−4.05448e12	−1.53474
$577$	−2.55613e12	−0.960044	−0.480022	−	0.877256i	$-0.659371\pi$
$577$	−2.55613e12	−0.960044	−0.480022	+	0.877256i	$0.659371\pi$
$578$	3.70531e12	1.38086
$579$	−5.62171e12	−2.07881
$580$	3.51556e12	1.28994
$581$	1.05801e12	0.385210
$582$	−1.11483e13	−4.02767
$583$	−3.90909e11	−0.140142
$584$	−2.01804e10	−0.00717912
$585$	2.55996e12	0.903716
$586$	5.50988e12	1.93020
$587$	1.41133e12	0.490632	0.245316	−	0.969443i	$-0.421108\pi$
$587$	1.41133e12	0.490632	0.245316	+	0.969443i	$0.421108\pi$
$588$	6.47832e12	2.23493
$589$	−9.91196e11	−0.339344
$590$	4.69161e12	1.59400
$591$	−3.41460e11	−0.115132
$592$	5.57945e12	1.86700
$593$	3.41543e12	1.13423	0.567113	−	0.823640i	$-0.308060\pi$
$593$	3.41543e12	1.13423	0.567113	+	0.823640i	$0.308060\pi$
$594$	−1.98201e12	−0.653231
$595$	6.57572e11	0.215089
$596$	1.87364e12	0.608244
$597$	−9.94047e11	−0.320275
$598$	3.75587e11	0.120103
$599$	−4.06951e12	−1.29158	−0.645790	−	0.763515i	$-0.723472\pi$
$599$	−4.06951e12	−1.29158	−0.645790	+	0.763515i	$0.723472\pi$
$600$	1.28107e10	0.00403544
$601$	3.72234e12	1.16381	0.581904	−	0.813258i	$-0.302308\pi$
$601$	3.72234e12	1.16381	0.581904	+	0.813258i	$0.302308\pi$
$602$	8.36355e11	0.259541
$603$	−7.31572e12	−2.25335
$604$	−1.77063e12	−0.541328
$605$	2.66155e12	0.807672
$606$	−7.70680e12	−2.32139
$607$	−5.57137e12	−1.66576	−0.832881	−	0.553452i	$-0.813310\pi$
$607$	−5.57137e12	−1.66576	−0.832881	+	0.553452i	$0.813310\pi$
$608$	−4.93783e12	−1.46545
$609$	−1.08605e13	−3.19942
$610$	3.08509e12	0.902160
$611$	3.94971e10	0.0114652
$612$	−7.28534e11	−0.209927
$613$	−4.09603e12	−1.17163	−0.585816	−	0.810444i	$-0.699226\pi$
$613$	−4.09603e12	−1.17163	−0.585816	+	0.810444i	$0.699226\pi$
$614$	−1.03075e12	−0.292680
$615$	3.52016e12	0.992257
$616$	8.62965e10	0.0241479
$617$	1.31949e11	0.0366541	0.0183270	−	0.999832i	$-0.494166\pi$
$617$	1.31949e11	0.0366541	0.0183270	+	0.999832i	$0.494166\pi$
$618$	−7.51955e11	−0.207369
$619$	−4.89034e12	−1.33885	−0.669424	−	0.742880i	$-0.733459\pi$
$619$	−4.89034e12	−1.33885	−0.669424	+	0.742880i	$0.733459\pi$
$620$	−1.21240e12	−0.329521
$621$	5.78343e11	0.156053
$622$	5.02022e12	1.34483
$623$	−4.76230e12	−1.26654
$624$	3.38560e12	0.893932
$625$	−4.08132e12	−1.06989
$626$	−7.70181e12	−2.00451
$627$	−3.06774e12	−0.792712
$628$	−3.93092e12	−1.00850
$629$	9.55949e11	0.243504
$630$	1.44399e13	3.65202
$631$	7.13746e11	0.179230	0.0896152	−	0.995976i	$-0.471436\pi$
$631$	7.13746e11	0.179230	0.0896152	+	0.995976i	$0.471436\pi$
$632$	−5.91355e9	−0.00147442
$633$	−4.57027e12	−1.13142
$634$	−4.98008e12	−1.22415
$635$	6.04929e10	0.0147646
$636$	−1.94001e12	−0.470161
$637$	−3.18282e12	−0.765922
$638$	3.52479e12	0.842248
$639$	−6.29471e12	−1.49356
$640$	2.90687e11	0.0684882
$641$	−2.68785e12	−0.628846	−0.314423	−	0.949283i	$-0.601811\pi$
$641$	−2.68785e12	−0.628846	−0.314423	+	0.949283i	$0.601811\pi$
$642$	8.06641e12	1.87401
$643$	5.16853e12	1.19239	0.596194	−	0.802840i	$-0.296679\pi$
$643$	5.16853e12	1.19239	0.596194	+	0.802840i	$0.296679\pi$
$644$	1.04669e12	0.239791
$645$	8.74896e11	0.199039
$646$	−8.65903e11	−0.195624
$647$	8.53833e12	1.91560	0.957798	−	0.287443i	$-0.0928052\pi$
$647$	8.53833e12	1.91560	0.957798	+	0.287443i	$0.0928052\pi$
$648$	−2.22145e9	−0.000494937 0
$649$	2.32401e12	0.514205
$650$	2.61618e11	0.0574854
$651$	3.74542e12	0.817309
$652$	−5.44731e12	−1.18050
$653$	5.27979e12	1.13634	0.568168	−	0.822912i	$-0.307652\pi$
$653$	5.27979e12	1.13634	0.568168	+	0.822912i	$0.307652\pi$
$654$	1.12025e12	0.239450
$655$	−2.61956e12	−0.556087
$656$	2.87266e12	0.605644
$657$	−1.67270e12	−0.350246
$658$	2.22791e11	0.0463320
$659$	−2.34951e12	−0.485280	−0.242640	−	0.970116i	$-0.578013\pi$
$659$	−2.34951e12	−0.485280	−0.242640	+	0.970116i	$0.578013\pi$
$660$	−3.75237e12	−0.769765
$661$	7.26460e12	1.48015	0.740073	−	0.672526i	$-0.234791\pi$
$661$	7.26460e12	1.48015	0.740073	+	0.672526i	$0.234791\pi$
$662$	1.76014e12	0.356194
$663$	5.80067e11	0.116592
$664$	4.09973e10	0.00818462
$665$	8.47934e12	1.68138
$666$	2.09921e13	4.13449
$667$	−1.02852e12	−0.201209
$668$	−4.63667e12	−0.900974
$669$	−9.16937e11	−0.176979
$670$	−1.06356e13	−2.03904
$671$	1.52821e12	0.291026
$672$	1.86585e13	3.52952
$673$	−7.13952e12	−1.34153	−0.670766	−	0.741669i	$-0.734035\pi$
$673$	−7.13952e12	−1.34153	−0.670766	+	0.741669i	$0.734035\pi$
$674$	−4.62882e12	−0.863974
$675$	4.02850e11	0.0746923
$676$	−3.75140e12	−0.690929
$677$	−2.57187e12	−0.470543	−0.235272	−	0.971930i	$-0.575598\pi$
$677$	−2.57187e12	−0.470543	−0.235272	+	0.971930i	$0.575598\pi$
$678$	−7.50766e12	−1.36449
$679$	1.52639e13	2.75583
$680$	2.54805e10	0.00457003
$681$	1.58037e13	2.81577
$682$	−1.21558e12	−0.215157
$683$	−4.88447e12	−0.858864	−0.429432	−	0.903099i	$-0.641286\pi$
$683$	−4.88447e12	−0.858864	−0.429432	+	0.903099i	$0.641286\pi$
$684$	−9.39438e12	−1.64103
$685$	−7.02810e12	−1.21964
$686$	−5.27721e12	−0.909801
$687$	2.18247e12	0.373803
$688$	7.13969e11	0.121487
$689$	9.53132e11	0.161126
$690$	2.21620e12	0.372209
$691$	9.89790e12	1.65155	0.825775	−	0.564000i	$-0.190738\pi$
$691$	9.89790e12	1.65155	0.825775	+	0.564000i	$0.190738\pi$
$692$	2.65999e12	0.440963
$693$	7.15288e12	1.17810
$694$	2.03412e12	0.332858
$695$	1.00780e13	1.63849
$696$	−4.20837e11	−0.0679787
$697$	4.92184e11	0.0789915
$698$	3.63260e12	0.579252
$699$	−9.77747e12	−1.54910
$700$	7.29083e11	0.114772
$701$	6.90991e11	0.108079	0.0540395	−	0.998539i	$-0.482790\pi$
$701$	6.90991e11	0.108079	0.0540395	+	0.998539i	$0.482790\pi$
$702$	4.83263e12	0.751046
$703$	1.23269e13	1.90351
$704$	−2.91982e12	−0.448001
$705$	2.33058e11	0.0355314
$706$	3.69096e11	0.0559137
$707$	1.05520e13	1.58835
$708$	1.15336e13	1.72511
$709$	−1.33929e13	−1.99052	−0.995260	−	0.0972520i	$-0.968995\pi$
$709$	−1.33929e13	−1.99052	−0.995260	+	0.0972520i	$0.968995\pi$
$710$	−9.15128e12	−1.35151
$711$	−4.90158e11	−0.0719322
$712$	−1.84536e11	−0.0269105
$713$	3.54703e11	0.0513998
$714$	3.27198e12	0.471160
$715$	1.84355e12	0.263802
$716$	−1.27493e13	−1.81291
$717$	1.20282e13	1.69967
$718$	5.44099e12	0.764044
$719$	1.04525e13	1.45861	0.729304	−	0.684189i	$-0.239844\pi$
$719$	1.04525e13	1.45861	0.729304	+	0.684189i	$0.239844\pi$
$720$	1.23269e13	1.70945
$721$	1.02956e12	0.141887
$722$	−9.00562e11	−0.123338
$723$	4.17524e12	0.568275
$724$	−8.59224e12	−1.16220
$725$	−7.16424e11	−0.0963050
$726$	1.32434e13	1.76924
$727$	6.95191e12	0.922996	0.461498	−	0.887141i	$-0.347312\pi$
$727$	6.95191e12	0.922996	0.461498	+	0.887141i	$0.347312\pi$
$728$	−2.10412e11	−0.0277638
$729$	−1.23571e13	−1.62047
$730$	−2.43177e12	−0.316935
$731$	1.22327e11	0.0158451
$732$	7.58423e12	0.976364
$733$	4.53224e12	0.579889	0.289944	−	0.957044i	$-0.406363\pi$
$733$	4.53224e12	0.579889	0.289944	+	0.957044i	$0.406363\pi$
$734$	−1.03386e13	−1.31471
$735$	−1.87806e13	−2.37365
$736$	1.76702e12	0.221968
$737$	−5.26839e12	−0.657771
$738$	1.08081e13	1.34121
$739$	−1.36577e13	−1.68452	−0.842261	−	0.539070i	$-0.818776\pi$
$739$	−1.36577e13	−1.68452	−0.842261	+	0.539070i	$0.818776\pi$
$740$	1.50779e13	1.84840
$741$	7.47992e12	0.911412
$742$	5.37632e12	0.651130
$743$	−2.57632e12	−0.310134	−0.155067	−	0.987904i	$-0.549559\pi$
$743$	−2.57632e12	−0.310134	−0.155067	+	0.987904i	$0.549559\pi$
$744$	1.45133e11	0.0173655
$745$	−5.43167e12	−0.645996
$746$	−2.26634e13	−2.67918
$747$	3.39815e12	0.399301
$748$	−5.24652e11	−0.0612793
$749$	−1.10443e13	−1.28224
$750$	−1.88728e13	−2.17802
$751$	1.06543e13	1.22221	0.611106	−	0.791548i	$-0.290725\pi$
$751$	1.06543e13	1.22221	0.611106	+	0.791548i	$0.290725\pi$
$752$	1.90189e11	0.0216873
$753$	1.96902e13	2.23189
$754$	−8.59430e12	−0.968366
$755$	5.13303e12	0.574927
$756$	1.34677e13	1.49949
$757$	9.12478e12	1.00993	0.504964	−	0.863140i	$-0.331506\pi$
$757$	9.12478e12	1.00993	0.504964	+	0.863140i	$0.331506\pi$
$758$	8.73529e12	0.961094
$759$	1.09780e12	0.120070
$760$	3.28569e11	0.0357245
$761$	−3.43279e12	−0.371036	−0.185518	−	0.982641i	$-0.559396\pi$
$761$	−3.43279e12	−0.371036	−0.185518	+	0.982641i	$0.559396\pi$
$762$	3.01003e11	0.0323425
$763$	−1.53381e12	−0.163837
$764$	1.61864e13	1.71882
$765$	2.11201e12	0.222957
$766$	−1.80376e13	−1.89299
$767$	−5.66650e12	−0.591202
$768$	1.62856e13	1.68919
$769$	8.63565e12	0.890484	0.445242	−	0.895410i	$-0.353118\pi$
$769$	8.63565e12	0.890484	0.445242	+	0.895410i	$0.353118\pi$
$770$	1.03989e13	1.06605
$771$	−2.22544e13	−2.26815
$772$	−1.23976e13	−1.25621
$773$	−7.03808e12	−0.709000	−0.354500	−	0.935056i	$-0.615349\pi$
$773$	−7.03808e12	−0.709000	−0.354500	+	0.935056i	$0.615349\pi$
$774$	2.68623e12	0.269035
$775$	2.47071e11	0.0246016
$776$	5.91467e11	0.0585535
$777$	−4.65794e13	−4.58458
$778$	3.62198e12	0.354436
$779$	6.34667e12	0.617487
$780$	9.14920e12	0.885029
$781$	−4.53312e12	−0.435981
$782$	3.09866e11	0.0296308
$783$	−1.32338e13	−1.25822
$784$	−1.53261e13	−1.44880
$785$	1.13957e13	1.07109
$786$	−1.30345e13	−1.21813
$787$	−6.36112e12	−0.591082	−0.295541	−	0.955330i	$-0.595500\pi$
$787$	−6.36112e12	−0.591082	−0.295541	+	0.955330i	$0.595500\pi$
$788$	−7.53027e11	−0.0695733
$789$	−6.48202e12	−0.595476
$790$	−7.12594e11	−0.0650909
$791$	1.02793e13	0.933618
$792$	2.77170e11	0.0250313
$793$	−3.72616e12	−0.334605
$794$	−3.11592e13	−2.78224
$795$	5.62407e12	0.499343
$796$	−2.19219e12	−0.193539
$797$	2.33981e12	0.205408	0.102704	−	0.994712i	$-0.467250\pi$
$797$	2.33981e12	0.205408	0.102704	+	0.994712i	$0.467250\pi$
$798$	4.21919e13	3.68312
$799$	3.25858e10	0.00282858
$800$	1.23083e12	0.106241
$801$	−1.52957e13	−1.31288
$802$	−1.63631e13	−1.39663
$803$	−1.20459e12	−0.102239
$804$	−2.61461e13	−2.20676
$805$	−3.03436e12	−0.254674
$806$	2.96389e12	0.247374
$807$	2.99379e12	0.248479
$808$	4.08882e11	0.0337479
$809$	1.07144e13	0.879423	0.439712	−	0.898139i	$-0.355081\pi$
$809$	1.07144e13	0.879423	0.439712	+	0.898139i	$0.355081\pi$
$810$	−2.67689e11	−0.0218499
$811$	−1.85316e13	−1.50425	−0.752125	−	0.659021i	$-0.770971\pi$
$811$	−1.85316e13	−1.50425	−0.752125	+	0.659021i	$0.770971\pi$
$812$	−2.39508e13	−1.93338
$813$	5.52447e12	0.443489
$814$	1.51174e13	1.20689
$815$	1.57917e13	1.25378
$816$	2.79318e12	0.220543
$817$	1.57739e12	0.123863
$818$	1.92453e13	1.50291
$819$	−1.74405e13	−1.35451
$820$	7.76305e12	0.599612
$821$	3.45942e12	0.265741	0.132871	−	0.991133i	$-0.457581\pi$
$821$	3.45942e12	0.265741	0.132871	+	0.991133i	$0.457581\pi$
$822$	−3.49707e13	−2.67166
$823$	−7.96788e12	−0.605402	−0.302701	−	0.953086i	$-0.597888\pi$
$823$	−7.96788e12	−0.605402	−0.302701	+	0.953086i	$0.597888\pi$
$824$	3.98947e10	0.00301469
$825$	7.64683e11	0.0574696
$826$	−3.19630e13	−2.38911
$827$	1.92430e13	1.43053	0.715266	−	0.698852i	$-0.246306\pi$
$827$	1.92430e13	1.43053	0.715266	+	0.698852i	$0.246306\pi$
$828$	3.36181e12	0.248563
$829$	−2.11659e13	−1.55647	−0.778235	−	0.627973i	$-0.783885\pi$
$829$	−2.11659e13	−1.55647	−0.778235	+	0.627973i	$0.783885\pi$
$830$	4.94025e12	0.361324
$831$	−2.93925e13	−2.13812
$832$	7.11925e12	0.515085
$833$	−2.62588e12	−0.188961
$834$	5.01466e13	3.58917
$835$	1.34417e13	0.956895
$836$	−6.76534e12	−0.479029
$837$	4.56391e12	0.321420
$838$	−2.80635e13	−1.96582
$839$	4.74291e12	0.330458	0.165229	−	0.986255i	$-0.447164\pi$
$839$	4.74291e12	0.330458	0.165229	+	0.986255i	$0.447164\pi$
$840$	−1.24156e12	−0.0860422
$841$	9.02777e12	0.622298
$842$	3.88127e13	2.66115
$843$	−3.33422e13	−2.27389
$844$	−1.00789e13	−0.683709
$845$	1.08753e13	0.733813
$846$	7.15568e11	0.0480269
$847$	−1.81326e13	−1.21055
$848$	4.58958e12	0.304784
$849$	−5.85466e12	−0.386738
$850$	2.15840e11	0.0141823
$851$	−4.41121e12	−0.288320
$852$	−2.24971e13	−1.46267
$853$	−2.76410e13	−1.78766	−0.893828	−	0.448411i	$-0.851990\pi$
$853$	−2.76410e13	−1.78766	−0.893828	+	0.448411i	$0.851990\pi$
$854$	−2.10181e13	−1.35217
$855$	2.72342e13	1.74288
$856$	−4.27961e11	−0.0272441
$857$	−2.86262e12	−0.181280	−0.0906399	−	0.995884i	$-0.528891\pi$
$857$	−2.86262e12	−0.181280	−0.0906399	+	0.995884i	$0.528891\pi$
$858$	9.17322e12	0.577868
$859$	−2.04273e13	−1.28009	−0.640046	−	0.768337i	$-0.721085\pi$
$859$	−2.04273e13	−1.28009	−0.640046	+	0.768337i	$0.721085\pi$
$860$	1.92942e12	0.120277
$861$	−2.39821e13	−1.48721
$862$	3.51062e13	2.16571
$863$	3.13209e13	1.92214	0.961072	−	0.276297i	$-0.0891075\pi$
$863$	3.13209e13	1.92214	0.961072	+	0.276297i	$0.0891075\pi$
$864$	2.27360e13	1.38804
$865$	−7.71129e12	−0.468333
$866$	−1.87182e13	−1.13092
$867$	−2.64068e13	−1.58719
$868$	8.25983e12	0.493893
$869$	−3.52986e11	−0.0209976
$870$	−5.07117e13	−3.00104
$871$	1.28456e13	0.756265
$872$	−5.94344e10	−0.00348108
$873$	4.90251e13	2.85663
$874$	3.99569e12	0.231628
$875$	2.58402e13	1.49025
$876$	−5.97814e12	−0.343003
$877$	1.00982e13	0.576430	0.288215	−	0.957566i	$-0.406938\pi$
$877$	1.00982e13	0.576430	0.288215	+	0.957566i	$0.406938\pi$
$878$	−1.79088e13	−1.01705
$879$	−3.92675e13	−2.21862
$880$	8.87719e12	0.499003
$881$	−2.31441e13	−1.29434	−0.647170	−	0.762346i	$-0.724048\pi$
$881$	−2.31441e13	−1.29434	−0.647170	+	0.762346i	$0.724048\pi$
$882$	−5.76630e13	−3.20840
$883$	−2.09580e13	−1.16019	−0.580093	−	0.814550i	$-0.696984\pi$
$883$	−2.09580e13	−1.16019	−0.580093	+	0.814550i	$0.696984\pi$
$884$	1.27923e12	0.0704553
$885$	−3.34359e13	−1.83218
$886$	−1.26176e13	−0.687899
$887$	−9.06620e12	−0.491778	−0.245889	−	0.969298i	$-0.579080\pi$
$887$	−9.06620e12	−0.491778	−0.245889	+	0.969298i	$0.579080\pi$
$888$	−1.80493e12	−0.0974094
$889$	−4.12126e11	−0.0221295
$890$	−2.22370e13	−1.18801
$891$	−1.32601e11	−0.00704851
$892$	−2.02213e12	−0.106947
$893$	4.20192e11	0.0221114
$894$	−2.70271e13	−1.41508
$895$	3.69600e13	1.92543
$896$	−1.98039e12	−0.102651
$897$	−2.67671e12	−0.138050
$898$	7.09775e12	0.364231
$899$	−8.11641e12	−0.414425
$900$	2.34169e12	0.118970
$901$	7.86351e11	0.0397516
$902$	7.78343e12	0.391509
$903$	−5.96048e12	−0.298323
$904$	3.98317e11	0.0198367
$905$	2.49088e13	1.23434
$906$	2.55412e13	1.25940
$907$	2.45443e12	0.120425	0.0602127	−	0.998186i	$-0.480822\pi$
$907$	2.45443e12	0.120425	0.0602127	+	0.998186i	$0.480822\pi$
$908$	3.48521e13	1.70154
$909$	3.38911e13	1.64645
$910$	−2.53551e13	−1.22568
$911$	−9.03552e12	−0.434631	−0.217315	−	0.976101i	$-0.569730\pi$
$911$	−9.03552e12	−0.434631	−0.217315	+	0.976101i	$0.569730\pi$
$912$	3.60178e13	1.72401
$913$	2.44717e12	0.116559
$914$	−3.78153e13	−1.79230
$915$	−2.19866e13	−1.03696
$916$	4.81303e12	0.225886
$917$	1.78465e13	0.833474
$918$	3.98700e12	0.185291
$919$	3.18443e13	1.47269	0.736346	−	0.676605i	$-0.236549\pi$
$919$	3.18443e13	1.47269	0.736346	+	0.676605i	$0.236549\pi$
$920$	−1.17580e11	−0.00541111
$921$	7.34585e12	0.336414
$922$	−9.86247e12	−0.449466
$923$	1.10529e13	0.501265
$924$	2.55641e13	1.15374
$925$	−3.07266e12	−0.137999
$926$	3.33963e13	1.49262
$927$	3.30677e12	0.147077
$928$	−4.04334e13	−1.78968
$929$	3.81113e13	1.67874	0.839368	−	0.543563i	$-0.182925\pi$
$929$	3.81113e13	1.67874	0.839368	+	0.543563i	$0.182925\pi$
$930$	1.74888e13	0.766631
$931$	−3.38605e13	−1.47713
$932$	−2.15624e13	−0.936107
$933$	−3.57778e13	−1.54578
$934$	6.37054e12	0.273915
$935$	1.52096e12	0.0650828
$936$	−6.75809e11	−0.0287795
$937$	−1.23336e13	−0.522709	−0.261355	−	0.965243i	$-0.584169\pi$
$937$	−1.23336e13	−0.522709	−0.261355	+	0.965243i	$0.584169\pi$
$938$	7.24583e13	3.05615
$939$	5.48888e13	2.30403
$940$	5.13965e11	0.0214713
$941$	7.37410e12	0.306588	0.153294	−	0.988181i	$-0.451012\pi$
$941$	7.37410e12	0.306588	0.153294	+	0.988181i	$0.451012\pi$
$942$	5.67032e13	2.34627
$943$	−2.27118e12	−0.0935294
$944$	−2.72857e13	−1.11831
$945$	−3.90427e13	−1.59256
$946$	1.93449e12	0.0785336
$947$	−9.64986e12	−0.389894	−0.194947	−	0.980814i	$-0.562453\pi$
$947$	−9.64986e12	−0.389894	−0.194947	+	0.980814i	$0.562453\pi$
$948$	−1.75181e12	−0.0704447
$949$	2.93708e12	0.117549
$950$	2.78323e12	0.110865
$951$	3.54917e13	1.40707
$952$	−1.73594e11	−0.00684964
$953$	1.04239e13	0.409365	0.204683	−	0.978828i	$-0.434384\pi$
$953$	1.04239e13	0.409365	0.204683	+	0.978828i	$0.434384\pi$
$954$	1.72678e13	0.674948
$955$	−4.69243e13	−1.82550
$956$	2.65260e13	1.02710
$957$	−2.51202e13	−0.968100
$958$	−6.48764e11	−0.0248853
$959$	4.78810e13	1.82801
$960$	4.20080e13	1.59629
$961$	−2.36405e13	−0.894133
$962$	−3.68600e13	−1.38761
$963$	−3.54725e13	−1.32915
$964$	9.20771e12	0.343404
$965$	3.59407e13	1.33418
$966$	−1.50985e13	−0.557874
$967$	−2.86459e13	−1.05352	−0.526761	−	0.850014i	$-0.676594\pi$
$967$	−2.86459e13	−1.05352	−0.526761	+	0.850014i	$0.676594\pi$
$968$	−7.02626e11	−0.0257208
$969$	6.17106e12	0.224855
$970$	7.12729e13	2.58495
$971$	−4.99282e13	−1.80243	−0.901217	−	0.433367i	$-0.857325\pi$
$971$	−4.99282e13	−1.80243	−0.901217	+	0.433367i	$0.857325\pi$
$972$	−2.75032e13	−0.988293
$973$	−6.86595e13	−2.45580
$974$	−7.41734e13	−2.64078
$975$	−1.86448e12	−0.0660751
$976$	−1.79424e13	−0.632932
$977$	−4.35658e13	−1.52975	−0.764874	−	0.644180i	$-0.777199\pi$
$977$	−4.35658e13	−1.52975	−0.764874	+	0.644180i	$0.777199\pi$
$978$	7.85770e13	2.74644
$979$	−1.10152e13	−0.383239
$980$	−4.14171e13	−1.43437
$981$	−4.92635e12	−0.169830
$982$	−5.45695e13	−1.87262
$983$	−1.86560e13	−0.637275	−0.318638	−	0.947877i	$-0.603225\pi$
$983$	−1.86560e13	−0.637275	−0.318638	+	0.947877i	$0.603225\pi$
$984$	−9.29293e11	−0.0315991
$985$	2.18302e12	0.0738915
$986$	−7.09045e12	−0.238906
$987$	−1.58777e12	−0.0532551
$988$	1.64956e13	0.550758
$989$	−5.64475e11	−0.0187612
$990$	3.33995e13	1.10505
$991$	4.65500e13	1.53316	0.766582	−	0.642147i	$-0.221956\pi$
$991$	4.65500e13	1.53316	0.766582	+	0.642147i	$0.221956\pi$
$992$	1.39442e13	0.457183
$993$	−1.25441e13	−0.409418
$994$	6.23458e13	2.02567
$995$	6.35513e12	0.205551
$996$	1.21449e13	0.391044
$997$	5.55137e12	0.177939	0.0889697	−	0.996034i	$-0.471643\pi$
$997$	5.55137e12	0.177939	0.0889697	+	0.996034i	$0.471643\pi$
$998$	−1.03503e13	−0.330266
$999$	−5.67585e13	−1.80296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.a.1.11	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.a.1.11	✓	71	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-31.8115 q^{2} +226.712 q^{3} +499.972 q^{4} -1449.41 q^{5} -7212.06 q^{6} +9874.56 q^{7} +382.633 q^{8} +31715.5 q^{9} +46108.1 q^{10} +22839.8 q^{11} +113350. q^{12} -55689.1 q^{13} -314125. q^{14} -328600. q^{15} -268158. q^{16} -45944.5 q^{17} -1.00892e6 q^{18} -592450. q^{19} -724666. q^{20} +2.23868e6 q^{21} -726569. q^{22} +212010. q^{23} +86747.7 q^{24} +147677. q^{25} +1.77155e6 q^{26} +2.72791e6 q^{27} +4.93700e6 q^{28} -4.85128e6 q^{29} +1.04533e7 q^{30} +1.67305e6 q^{31} +8.33459e6 q^{32} +5.17806e6 q^{33} +1.46156e6 q^{34} -1.43123e7 q^{35} +1.58568e7 q^{36} -2.08066e7 q^{37} +1.88467e7 q^{38} -1.26254e7 q^{39} -554594. q^{40} -1.07126e7 q^{41} -7.12159e7 q^{42} -2.66249e6 q^{43} +1.14193e7 q^{44} -4.59688e7 q^{45} -6.74436e6 q^{46} -709244. q^{47} -6.07946e7 q^{48} +5.71534e7 q^{49} -4.69784e6 q^{50} -1.04162e7 q^{51} -2.78430e7 q^{52} -1.71152e7 q^{53} -8.67788e7 q^{54} -3.31043e7 q^{55} +3.77834e6 q^{56} -1.34316e8 q^{57} +1.54327e8 q^{58} +1.01753e8 q^{59} -1.64291e8 q^{60} +6.69100e7 q^{61} -5.32221e7 q^{62} +3.13176e8 q^{63} -1.27839e8 q^{64} +8.07166e7 q^{65} -1.64722e8 q^{66} -2.30667e8 q^{67} -2.29709e7 q^{68} +4.80653e7 q^{69} +4.55297e8 q^{70} -1.98475e8 q^{71} +1.21354e7 q^{72} -5.27407e7 q^{73} +6.61890e8 q^{74} +3.34803e7 q^{75} -2.96208e8 q^{76} +2.25533e8 q^{77} +4.01633e8 q^{78} -1.54549e7 q^{79} +3.88672e8 q^{80} -5.80570e6 q^{81} +3.40784e8 q^{82} +1.07145e8 q^{83} +1.11928e9 q^{84} +6.65926e7 q^{85} +8.46980e7 q^{86} -1.09984e9 q^{87} +8.73927e6 q^{88} -4.82280e8 q^{89} +1.46234e9 q^{90} -5.49905e8 q^{91} +1.05999e8 q^{92} +3.79300e8 q^{93} +2.25621e7 q^{94} +8.58706e8 q^{95} +1.88955e9 q^{96} +1.54578e9 q^{97} -1.81813e9 q^{98} +7.24375e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 32 q^{2} - 892 q^{3} + 16896 q^{4} - 2329 q^{5} - 10272 q^{6} - 37846 q^{7} - 24933 q^{8} + 419903 q^{9} - 138907 q^{10} - 143074 q^{11} - 496640 q^{12} - 433821 q^{13} - 130143 q^{14} - 670126 q^{15}+ \cdots - 6380320552 q^{99}+O(q^{100}) \) 71 * q - 32 * q^2 - 892 * q^3 + 16896 * q^4 - 2329 * q^5 - 10272 * q^6 - 37846 * q^7 - 24933 * q^8 + 419903 * q^9 - 138907 * q^10 - 143074 * q^11 - 496640 * q^12 - 433821 * q^13 - 130143 * q^14 - 670126 * q^15 + 3670016 * q^16 - 226712 * q^17 - 1140455 * q^18 - 4200657 * q^19 - 2522261 * q^20 - 2222620 * q^21 - 5109807 * q^22 - 1576984 * q^23 - 7953747 * q^24 + 20408644 * q^25 - 3606210 * q^26 - 22380322 * q^27 - 28281314 * q^28 - 1600554 * q^29 + 1211083 * q^30 - 27408409 * q^31 - 19842828 * q^32 - 26002786 * q^33 - 33310606 * q^34 - 25745764 * q^35 + 75847738 * q^36 - 56498684 * q^37 - 8523742 * q^38 - 67092176 * q^39 - 69825234 * q^40 - 41524361 * q^41 - 29804525 * q^42 - 103636613 * q^43 - 93059022 * q^44 - 41029851 * q^45 - 35065939 * q^46 - 155481346 * q^47 - 310890046 * q^48 + 274445845 * q^49 - 532508319 * q^50 - 401628576 * q^51 - 638463912 * q^52 - 235002576 * q^53 - 485779441 * q^54 - 274178598 * q^55 - 174143696 * q^56 + 10220750 * q^57 - 54794577 * q^58 - 309204685 * q^59 + 349852813 * q^60 - 172553358 * q^61 + 313207667 * q^62 - 291588072 * q^63 + 1670833437 * q^64 + 394656726 * q^65 + 2405207530 * q^66 - 1034845512 * q^67 + 2160039119 * q^68 + 472060058 * q^69 + 1282221119 * q^70 + 515265617 * q^71 + 1722271619 * q^72 - 667322970 * q^73 + 1111943967 * q^74 - 304507118 * q^75 - 1476894506 * q^76 - 347407724 * q^77 - 99563531 * q^78 - 338475893 * q^79 - 652382330 * q^80 + 1981631951 * q^81 - 2682827483 * q^82 - 2423465319 * q^83 - 1042585800 * q^84 - 2101960924 * q^85 - 2597172884 * q^86 - 2135063354 * q^87 - 5542447545 * q^88 - 2765884440 * q^89 - 6736154529 * q^90 - 6821909968 * q^91 - 4167412114 * q^92 - 4756429190 * q^93 - 5116706209 * q^94 - 4295841932 * q^95 - 14387243887 * q^96 - 6239794299 * q^97 - 8201372742 * q^98 - 6380320552 * q^99

Introduction

L-functions

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