# Properties

 Label 26.6.b.b.25.1 Level $26$ Weight $6$ Character 26.25 Analytic conductor $4.170$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,6,Mod(25,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("26.25");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 26.b (of order $$2$$, degree $$1$$, minimal)

## 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: no Analytic conductor: $$4.16997931514$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 25.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 26.25 Dual form 26.6.b.b.25.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-4.00000i q^{2} +4.00000 q^{3} -16.0000 q^{4} -68.0000i q^{5} -16.0000i q^{6} -82.0000i q^{7} +64.0000i q^{8} -227.000 q^{9} +O(q^{10})$$ $$q-4.00000i q^{2} +4.00000 q^{3} -16.0000 q^{4} -68.0000i q^{5} -16.0000i q^{6} -82.0000i q^{7} +64.0000i q^{8} -227.000 q^{9} -272.000 q^{10} -390.000i q^{11} -64.0000 q^{12} +(507.000 + 338.000i) q^{13} -328.000 q^{14} -272.000i q^{15} +256.000 q^{16} +1738.00 q^{17} +908.000i q^{18} +1074.00i q^{19} +1088.00i q^{20} -328.000i q^{21} -1560.00 q^{22} +2104.00 q^{23} +256.000i q^{24} -1499.00 q^{25} +(1352.00 - 2028.00i) q^{26} -1880.00 q^{27} +1312.00i q^{28} -1690.00 q^{29} -1088.00 q^{30} +1430.00i q^{31} -1024.00i q^{32} -1560.00i q^{33} -6952.00i q^{34} -5576.00 q^{35} +3632.00 q^{36} -8852.00i q^{37} +4296.00 q^{38} +(2028.00 + 1352.00i) q^{39} +4352.00 q^{40} -6760.00i q^{41} -1312.00 q^{42} -16916.0 q^{43} +6240.00i q^{44} +15436.0i q^{45} -8416.00i q^{46} +25158.0i q^{47} +1024.00 q^{48} +10083.0 q^{49} +5996.00i q^{50} +6952.00 q^{51} +(-8112.00 - 5408.00i) q^{52} +38214.0 q^{53} +7520.00i q^{54} -26520.0 q^{55} +5248.00 q^{56} +4296.00i q^{57} +6760.00i q^{58} -21286.0i q^{59} +4352.00i q^{60} -5458.00 q^{61} +5720.00 q^{62} +18614.0i q^{63} -4096.00 q^{64} +(22984.0 - 34476.0i) q^{65} -6240.00 q^{66} -44542.0i q^{67} -27808.0 q^{68} +8416.00 q^{69} +22304.0i q^{70} +17790.0i q^{71} -14528.0i q^{72} -31064.0i q^{73} -35408.0 q^{74} -5996.00 q^{75} -17184.0i q^{76} -31980.0 q^{77} +(5408.00 - 8112.00i) q^{78} -45360.0 q^{79} -17408.0i q^{80} +47641.0 q^{81} -27040.0 q^{82} +124546. i q^{83} +5248.00i q^{84} -118184. i q^{85} +67664.0i q^{86} -6760.00 q^{87} +24960.0 q^{88} +18744.0i q^{89} +61744.0 q^{90} +(27716.0 - 41574.0i) q^{91} -33664.0 q^{92} +5720.00i q^{93} +100632. q^{94} +73032.0 q^{95} -4096.00i q^{96} +121488. i q^{97} -40332.0i q^{98} +88530.0i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 8 q^{3} - 32 q^{4} - 454 q^{9}+O(q^{10})$$ 2 * q + 8 * q^3 - 32 * q^4 - 454 * q^9 $$2 q + 8 q^{3} - 32 q^{4} - 454 q^{9} - 544 q^{10} - 128 q^{12} + 1014 q^{13} - 656 q^{14} + 512 q^{16} + 3476 q^{17} - 3120 q^{22} + 4208 q^{23} - 2998 q^{25} + 2704 q^{26} - 3760 q^{27} - 3380 q^{29} - 2176 q^{30} - 11152 q^{35} + 7264 q^{36} + 8592 q^{38} + 4056 q^{39} + 8704 q^{40} - 2624 q^{42} - 33832 q^{43} + 2048 q^{48} + 20166 q^{49} + 13904 q^{51} - 16224 q^{52} + 76428 q^{53} - 53040 q^{55} + 10496 q^{56} - 10916 q^{61} + 11440 q^{62} - 8192 q^{64} + 45968 q^{65} - 12480 q^{66} - 55616 q^{68} + 16832 q^{69} - 70816 q^{74} - 11992 q^{75} - 63960 q^{77} + 10816 q^{78} - 90720 q^{79} + 95282 q^{81} - 54080 q^{82} - 13520 q^{87} + 49920 q^{88} + 123488 q^{90} + 55432 q^{91} - 67328 q^{92} + 201264 q^{94} + 146064 q^{95}+O(q^{100})$$ 2 * q + 8 * q^3 - 32 * q^4 - 454 * q^9 - 544 * q^10 - 128 * q^12 + 1014 * q^13 - 656 * q^14 + 512 * q^16 + 3476 * q^17 - 3120 * q^22 + 4208 * q^23 - 2998 * q^25 + 2704 * q^26 - 3760 * q^27 - 3380 * q^29 - 2176 * q^30 - 11152 * q^35 + 7264 * q^36 + 8592 * q^38 + 4056 * q^39 + 8704 * q^40 - 2624 * q^42 - 33832 * q^43 + 2048 * q^48 + 20166 * q^49 + 13904 * q^51 - 16224 * q^52 + 76428 * q^53 - 53040 * q^55 + 10496 * q^56 - 10916 * q^61 + 11440 * q^62 - 8192 * q^64 + 45968 * q^65 - 12480 * q^66 - 55616 * q^68 + 16832 * q^69 - 70816 * q^74 - 11992 * q^75 - 63960 * q^77 + 10816 * q^78 - 90720 * q^79 + 95282 * q^81 - 54080 * q^82 - 13520 * q^87 + 49920 * q^88 + 123488 * q^90 + 55432 * q^91 - 67328 * q^92 + 201264 * q^94 + 146064 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$$.

 $$n$$ $$15$$ $$\chi(n)$$ $$-1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.00000i 0.707107i
$$3$$ 4.00000 0.256600 0.128300 0.991735i $$-0.459048\pi$$
0.128300 + 0.991735i $$0.459048\pi$$
$$4$$ −16.0000 −0.500000
$$5$$ 68.0000i 1.21642i −0.793776 0.608210i $$-0.791888\pi$$
0.793776 0.608210i $$-0.208112\pi$$
$$6$$ 16.0000i 0.181444i
$$7$$ 82.0000i 0.632512i −0.948674 0.316256i $$-0.897574\pi$$
0.948674 0.316256i $$-0.102426\pi$$
$$8$$ 64.0000i 0.353553i
$$9$$ −227.000 −0.934156
$$10$$ −272.000 −0.860140
$$11$$ 390.000i 0.971813i −0.874011 0.485907i $$-0.838489\pi$$
0.874011 0.485907i $$-0.161511\pi$$
$$12$$ −64.0000 −0.128300
$$13$$ 507.000 + 338.000i 0.832050 + 0.554700i
$$14$$ −328.000 −0.447254
$$15$$ 272.000i 0.312134i
$$16$$ 256.000 0.250000
$$17$$ 1738.00 1.45857 0.729285 0.684210i $$-0.239853\pi$$
0.729285 + 0.684210i $$0.239853\pi$$
$$18$$ 908.000i 0.660548i
$$19$$ 1074.00i 0.682528i 0.939968 + 0.341264i $$0.110855\pi$$
−0.939968 + 0.341264i $$0.889145\pi$$
$$20$$ 1088.00i 0.608210i
$$21$$ 328.000i 0.162303i
$$22$$ −1560.00 −0.687176
$$23$$ 2104.00 0.829328 0.414664 0.909975i $$-0.363899\pi$$
0.414664 + 0.909975i $$0.363899\pi$$
$$24$$ 256.000i 0.0907218i
$$25$$ −1499.00 −0.479680
$$26$$ 1352.00 2028.00i 0.392232 0.588348i
$$27$$ −1880.00 −0.496305
$$28$$ 1312.00i 0.316256i
$$29$$ −1690.00 −0.373157 −0.186579 0.982440i $$-0.559740\pi$$
−0.186579 + 0.982440i $$0.559740\pi$$
$$30$$ −1088.00 −0.220712
$$31$$ 1430.00i 0.267259i 0.991031 + 0.133629i $$0.0426632\pi$$
−0.991031 + 0.133629i $$0.957337\pi$$
$$32$$ 1024.00i 0.176777i
$$33$$ 1560.00i 0.249367i
$$34$$ 6952.00i 1.03137i
$$35$$ −5576.00 −0.769401
$$36$$ 3632.00 0.467078
$$37$$ 8852.00i 1.06301i −0.847055 0.531505i $$-0.821627\pi$$
0.847055 0.531505i $$-0.178373\pi$$
$$38$$ 4296.00 0.482620
$$39$$ 2028.00 + 1352.00i 0.213504 + 0.142336i
$$40$$ 4352.00 0.430070
$$41$$ 6760.00i 0.628040i −0.949416 0.314020i $$-0.898324\pi$$
0.949416 0.314020i $$-0.101676\pi$$
$$42$$ −1312.00 −0.114765
$$43$$ −16916.0 −1.39517 −0.697584 0.716503i $$-0.745742\pi$$
−0.697584 + 0.716503i $$0.745742\pi$$
$$44$$ 6240.00i 0.485907i
$$45$$ 15436.0i 1.13633i
$$46$$ 8416.00i 0.586423i
$$47$$ 25158.0i 1.66124i 0.556842 + 0.830618i $$0.312013\pi$$
−0.556842 + 0.830618i $$0.687987\pi$$
$$48$$ 1024.00 0.0641500
$$49$$ 10083.0 0.599929
$$50$$ 5996.00i 0.339185i
$$51$$ 6952.00 0.374269
$$52$$ −8112.00 5408.00i −0.416025 0.277350i
$$53$$ 38214.0 1.86867 0.934335 0.356395i $$-0.115994\pi$$
0.934335 + 0.356395i $$0.115994\pi$$
$$54$$ 7520.00i 0.350940i
$$55$$ −26520.0 −1.18213
$$56$$ 5248.00 0.223627
$$57$$ 4296.00i 0.175137i
$$58$$ 6760.00i 0.263862i
$$59$$ 21286.0i 0.796093i −0.917365 0.398047i $$-0.869688\pi$$
0.917365 0.398047i $$-0.130312\pi$$
$$60$$ 4352.00i 0.156067i
$$61$$ −5458.00 −0.187806 −0.0939029 0.995581i $$-0.529934\pi$$
−0.0939029 + 0.995581i $$0.529934\pi$$
$$62$$ 5720.00 0.188980
$$63$$ 18614.0i 0.590865i
$$64$$ −4096.00 −0.125000
$$65$$ 22984.0 34476.0i 0.674749 1.01212i
$$66$$ −6240.00 −0.176329
$$67$$ 44542.0i 1.21222i −0.795379 0.606112i $$-0.792728\pi$$
0.795379 0.606112i $$-0.207272\pi$$
$$68$$ −27808.0 −0.729285
$$69$$ 8416.00 0.212806
$$70$$ 22304.0i 0.544049i
$$71$$ 17790.0i 0.418823i 0.977828 + 0.209411i $$0.0671547\pi$$
−0.977828 + 0.209411i $$0.932845\pi$$
$$72$$ 14528.0i 0.330274i
$$73$$ 31064.0i 0.682260i −0.940016 0.341130i $$-0.889190\pi$$
0.940016 0.341130i $$-0.110810\pi$$
$$74$$ −35408.0 −0.751661
$$75$$ −5996.00 −0.123086
$$76$$ 17184.0i 0.341264i
$$77$$ −31980.0 −0.614684
$$78$$ 5408.00 8112.00i 0.100647 0.150970i
$$79$$ −45360.0 −0.817721 −0.408861 0.912597i $$-0.634074\pi$$
−0.408861 + 0.912597i $$0.634074\pi$$
$$80$$ 17408.0i 0.304105i
$$81$$ 47641.0 0.806805
$$82$$ −27040.0 −0.444091
$$83$$ 124546.i 1.98442i 0.124559 + 0.992212i $$0.460248\pi$$
−0.124559 + 0.992212i $$0.539752\pi$$
$$84$$ 5248.00i 0.0811513i
$$85$$ 118184.i 1.77424i
$$86$$ 67664.0i 0.986533i
$$87$$ −6760.00 −0.0957522
$$88$$ 24960.0 0.343588
$$89$$ 18744.0i 0.250834i 0.992104 + 0.125417i $$0.0400270\pi$$
−0.992104 + 0.125417i $$0.959973\pi$$
$$90$$ 61744.0 0.803505
$$91$$ 27716.0 41574.0i 0.350855 0.526282i
$$92$$ −33664.0 −0.414664
$$93$$ 5720.00i 0.0685786i
$$94$$ 100632. 1.17467
$$95$$ 73032.0 0.830241
$$96$$ 4096.00i 0.0453609i
$$97$$ 121488.i 1.31100i 0.755193 + 0.655502i $$0.227543\pi$$
−0.755193 + 0.655502i $$0.772457\pi$$
$$98$$ 40332.0i 0.424214i
$$99$$ 88530.0i 0.907826i
$$100$$ 23984.0 0.239840
$$101$$ −14218.0 −0.138687 −0.0693434 0.997593i $$-0.522090\pi$$
−0.0693434 + 0.997593i $$0.522090\pi$$
$$102$$ 27808.0i 0.264648i
$$103$$ −62776.0 −0.583043 −0.291521 0.956564i $$-0.594161\pi$$
−0.291521 + 0.956564i $$0.594161\pi$$
$$104$$ −21632.0 + 32448.0i −0.196116 + 0.294174i
$$105$$ −22304.0 −0.197428
$$106$$ 152856.i 1.32135i
$$107$$ −79252.0 −0.669192 −0.334596 0.942362i $$-0.608600\pi$$
−0.334596 + 0.942362i $$0.608600\pi$$
$$108$$ 30080.0 0.248152
$$109$$ 218084.i 1.75816i 0.476677 + 0.879078i $$0.341841\pi$$
−0.476677 + 0.879078i $$0.658159\pi$$
$$110$$ 106080.i 0.835895i
$$111$$ 35408.0i 0.272768i
$$112$$ 20992.0i 0.158128i
$$113$$ 44234.0 0.325882 0.162941 0.986636i $$-0.447902\pi$$
0.162941 + 0.986636i $$0.447902\pi$$
$$114$$ 17184.0 0.123840
$$115$$ 143072.i 1.00881i
$$116$$ 27040.0 0.186579
$$117$$ −115089. 76726.0i −0.777265 0.518177i
$$118$$ −85144.0 −0.562923
$$119$$ 142516.i 0.922563i
$$120$$ 17408.0 0.110356
$$121$$ 8951.00 0.0555787
$$122$$ 21832.0i 0.132799i
$$123$$ 27040.0i 0.161155i
$$124$$ 22880.0i 0.133629i
$$125$$ 110568.i 0.632928i
$$126$$ 74456.0 0.417805
$$127$$ −310432. −1.70788 −0.853940 0.520372i $$-0.825793\pi$$
−0.853940 + 0.520372i $$0.825793\pi$$
$$128$$ 16384.0i 0.0883883i
$$129$$ −67664.0 −0.358000
$$130$$ −137904. 91936.0i −0.715679 0.477120i
$$131$$ 310372. 1.58017 0.790086 0.612996i $$-0.210036\pi$$
0.790086 + 0.612996i $$0.210036\pi$$
$$132$$ 24960.0i 0.124684i
$$133$$ 88068.0 0.431707
$$134$$ −178168. −0.857171
$$135$$ 127840.i 0.603716i
$$136$$ 111232.i 0.515683i
$$137$$ 281032.i 1.27925i −0.768688 0.639623i $$-0.779090\pi$$
0.768688 0.639623i $$-0.220910\pi$$
$$138$$ 33664.0i 0.150476i
$$139$$ 363820. 1.59716 0.798582 0.601886i $$-0.205584\pi$$
0.798582 + 0.601886i $$0.205584\pi$$
$$140$$ 89216.0 0.384700
$$141$$ 100632.i 0.426273i
$$142$$ 71160.0 0.296152
$$143$$ 131820. 197730.i 0.539065 0.808598i
$$144$$ −58112.0 −0.233539
$$145$$ 114920.i 0.453916i
$$146$$ −124256. −0.482431
$$147$$ 40332.0 0.153942
$$148$$ 141632.i 0.531505i
$$149$$ 274204.i 1.01183i 0.862583 + 0.505916i $$0.168845\pi$$
−0.862583 + 0.505916i $$0.831155\pi$$
$$150$$ 23984.0i 0.0870349i
$$151$$ 344030.i 1.22787i 0.789355 + 0.613937i $$0.210415\pi$$
−0.789355 + 0.613937i $$0.789585\pi$$
$$152$$ −68736.0 −0.241310
$$153$$ −394526. −1.36253
$$154$$ 127920.i 0.434647i
$$155$$ 97240.0 0.325099
$$156$$ −32448.0 21632.0i −0.106752 0.0711681i
$$157$$ 20518.0 0.0664333 0.0332167 0.999448i $$-0.489425\pi$$
0.0332167 + 0.999448i $$0.489425\pi$$
$$158$$ 181440.i 0.578216i
$$159$$ 152856. 0.479501
$$160$$ −69632.0 −0.215035
$$161$$ 172528.i 0.524560i
$$162$$ 190564.i 0.570497i
$$163$$ 36626.0i 0.107974i 0.998542 + 0.0539872i $$0.0171930\pi$$
−0.998542 + 0.0539872i $$0.982807\pi$$
$$164$$ 108160.i 0.314020i
$$165$$ −106080. −0.303336
$$166$$ 498184. 1.40320
$$167$$ 269442.i 0.747608i −0.927508 0.373804i $$-0.878053\pi$$
0.927508 0.373804i $$-0.121947\pi$$
$$168$$ 20992.0 0.0573827
$$169$$ 142805. + 342732.i 0.384615 + 0.923077i
$$170$$ −472736. −1.25457
$$171$$ 243798.i 0.637588i
$$172$$ 270656. 0.697584
$$173$$ 282654. 0.718026 0.359013 0.933333i $$-0.383113\pi$$
0.359013 + 0.933333i $$0.383113\pi$$
$$174$$ 27040.0i 0.0677070i
$$175$$ 122918.i 0.303403i
$$176$$ 99840.0i 0.242953i
$$177$$ 85144.0i 0.204278i
$$178$$ 74976.0 0.177367
$$179$$ 333780. 0.778624 0.389312 0.921106i $$-0.372713\pi$$
0.389312 + 0.921106i $$0.372713\pi$$
$$180$$ 246976.i 0.568164i
$$181$$ −459938. −1.04352 −0.521762 0.853091i $$-0.674725\pi$$
−0.521762 + 0.853091i $$0.674725\pi$$
$$182$$ −166296. 110864.i −0.372137 0.248092i
$$183$$ −21832.0 −0.0481910
$$184$$ 134656.i 0.293212i
$$185$$ −601936. −1.29307
$$186$$ 22880.0 0.0484924
$$187$$ 677820.i 1.41746i
$$188$$ 402528.i 0.830618i
$$189$$ 154160.i 0.313919i
$$190$$ 292128.i 0.587069i
$$191$$ −917088. −1.81898 −0.909489 0.415727i $$-0.863527\pi$$
−0.909489 + 0.415727i $$0.863527\pi$$
$$192$$ −16384.0 −0.0320750
$$193$$ 639056.i 1.23494i 0.786595 + 0.617470i $$0.211842\pi$$
−0.786595 + 0.617470i $$0.788158\pi$$
$$194$$ 485952. 0.927020
$$195$$ 91936.0 137904.i 0.173141 0.259711i
$$196$$ −161328. −0.299964
$$197$$ 358292.i 0.657766i −0.944371 0.328883i $$-0.893328\pi$$
0.944371 0.328883i $$-0.106672\pi$$
$$198$$ 354120. 0.641930
$$199$$ 370440. 0.663109 0.331555 0.943436i $$-0.392427\pi$$
0.331555 + 0.943436i $$0.392427\pi$$
$$200$$ 95936.0i 0.169592i
$$201$$ 178168.i 0.311057i
$$202$$ 56872.0i 0.0980664i
$$203$$ 138580.i 0.236026i
$$204$$ −111232. −0.187135
$$205$$ −459680. −0.763961
$$206$$ 251104.i 0.412274i
$$207$$ −477608. −0.774722
$$208$$ 129792. + 86528.0i 0.208013 + 0.138675i
$$209$$ 418860. 0.663290
$$210$$ 89216.0i 0.139603i
$$211$$ −177228. −0.274048 −0.137024 0.990568i $$-0.543754\pi$$
−0.137024 + 0.990568i $$0.543754\pi$$
$$212$$ −611424. −0.934335
$$213$$ 71160.0i 0.107470i
$$214$$ 317008.i 0.473190i
$$215$$ 1.15029e6i 1.69711i
$$216$$ 120320.i 0.175470i
$$217$$ 117260. 0.169044
$$218$$ 872336. 1.24320
$$219$$ 124256.i 0.175068i
$$220$$ 424320. 0.591067
$$221$$ 881166. + 587444.i 1.21360 + 0.809069i
$$222$$ −141632. −0.192876
$$223$$ 1.11297e6i 1.49872i 0.662164 + 0.749359i $$0.269638\pi$$
−0.662164 + 0.749359i $$0.730362\pi$$
$$224$$ −83968.0 −0.111813
$$225$$ 340273. 0.448096
$$226$$ 176936.i 0.230433i
$$227$$ 1.39158e6i 1.79244i −0.443612 0.896219i $$-0.646303\pi$$
0.443612 0.896219i $$-0.353697\pi$$
$$228$$ 68736.0i 0.0875683i
$$229$$ 909796.i 1.14645i −0.819398 0.573225i $$-0.805692\pi$$
0.819398 0.573225i $$-0.194308\pi$$
$$230$$ −572288. −0.713337
$$231$$ −127920. −0.157728
$$232$$ 108160.i 0.131931i
$$233$$ 266154. 0.321176 0.160588 0.987022i $$-0.448661\pi$$
0.160588 + 0.987022i $$0.448661\pi$$
$$234$$ −306904. + 460356.i −0.366406 + 0.549609i
$$235$$ 1.71074e6 2.02076
$$236$$ 340576.i 0.398047i
$$237$$ −181440. −0.209827
$$238$$ −570064. −0.652351
$$239$$ 254614.i 0.288328i 0.989554 + 0.144164i $$0.0460494\pi$$
−0.989554 + 0.144164i $$0.953951\pi$$
$$240$$ 69632.0i 0.0780334i
$$241$$ 313600.i 0.347803i 0.984763 + 0.173902i $$0.0556375\pi$$
−0.984763 + 0.173902i $$0.944363\pi$$
$$242$$ 35804.0i 0.0393001i
$$243$$ 647404. 0.703331
$$244$$ 87328.0 0.0939029
$$245$$ 685644.i 0.729766i
$$246$$ −108160. −0.113954
$$247$$ −363012. + 544518.i −0.378598 + 0.567897i
$$248$$ −91520.0 −0.0944902
$$249$$ 498184.i 0.509204i
$$250$$ −442272. −0.447548
$$251$$ −1.07127e6 −1.07328 −0.536641 0.843811i $$-0.680307\pi$$
−0.536641 + 0.843811i $$0.680307\pi$$
$$252$$ 297824.i 0.295433i
$$253$$ 820560.i 0.805952i
$$254$$ 1.24173e6i 1.20765i
$$255$$ 472736.i 0.455269i
$$256$$ 65536.0 0.0625000
$$257$$ −188382. −0.177913 −0.0889563 0.996036i $$-0.528353\pi$$
−0.0889563 + 0.996036i $$0.528353\pi$$
$$258$$ 270656.i 0.253144i
$$259$$ −725864. −0.672366
$$260$$ −367744. + 551616.i −0.337374 + 0.506062i
$$261$$ 383630. 0.348587
$$262$$ 1.24149e6i 1.11735i
$$263$$ −1.48678e6 −1.32543 −0.662714 0.748873i $$-0.730596\pi$$
−0.662714 + 0.748873i $$0.730596\pi$$
$$264$$ 99840.0 0.0881647
$$265$$ 2.59855e6i 2.27309i
$$266$$ 352272.i 0.305263i
$$267$$ 74976.0i 0.0643642i
$$268$$ 712672.i 0.606112i
$$269$$ 743990. 0.626883 0.313441 0.949608i $$-0.398518\pi$$
0.313441 + 0.949608i $$0.398518\pi$$
$$270$$ 511360. 0.426891
$$271$$ 455590.i 0.376835i 0.982089 + 0.188417i $$0.0603358\pi$$
−0.982089 + 0.188417i $$0.939664\pi$$
$$272$$ 444928. 0.364643
$$273$$ 110864. 166296.i 0.0900293 0.135044i
$$274$$ −1.12413e6 −0.904564
$$275$$ 584610.i 0.466159i
$$276$$ −134656. −0.106403
$$277$$ 460198. 0.360367 0.180184 0.983633i $$-0.442331\pi$$
0.180184 + 0.983633i $$0.442331\pi$$
$$278$$ 1.45528e6i 1.12937i
$$279$$ 324610.i 0.249661i
$$280$$ 356864.i 0.272024i
$$281$$ 49240.0i 0.0372008i 0.999827 + 0.0186004i $$0.00592103\pi$$
−0.999827 + 0.0186004i $$0.994079\pi$$
$$282$$ 402528. 0.301421
$$283$$ −544196. −0.403914 −0.201957 0.979394i $$-0.564730\pi$$
−0.201957 + 0.979394i $$0.564730\pi$$
$$284$$ 284640.i 0.209411i
$$285$$ 292128. 0.213040
$$286$$ −790920. 527280.i −0.571765 0.381177i
$$287$$ −554320. −0.397243
$$288$$ 232448.i 0.165137i
$$289$$ 1.60079e6 1.12743
$$290$$ 459680. 0.320967
$$291$$ 485952.i 0.336404i
$$292$$ 497024.i 0.341130i
$$293$$ 1.02504e6i 0.697542i 0.937208 + 0.348771i $$0.113401\pi$$
−0.937208 + 0.348771i $$0.886599\pi$$
$$294$$ 161328.i 0.108853i
$$295$$ −1.44745e6 −0.968385
$$296$$ 566528. 0.375831
$$297$$ 733200.i 0.482316i
$$298$$ 1.09682e6 0.715473
$$299$$ 1.06673e6 + 711152.i 0.690042 + 0.460028i
$$300$$ 95936.0 0.0615430
$$301$$ 1.38711e6i 0.882461i
$$302$$ 1.37612e6 0.868238
$$303$$ −56872.0 −0.0355870
$$304$$ 274944.i 0.170632i
$$305$$ 371144.i 0.228451i
$$306$$ 1.57810e6i 0.963456i
$$307$$ 1.57766e6i 0.955362i −0.878533 0.477681i $$-0.841477\pi$$
0.878533 0.477681i $$-0.158523\pi$$
$$308$$ 511680. 0.307342
$$309$$ −251104. −0.149609
$$310$$ 388960.i 0.229880i
$$311$$ −330088. −0.193521 −0.0967606 0.995308i $$-0.530848\pi$$
−0.0967606 + 0.995308i $$0.530848\pi$$
$$312$$ −86528.0 + 129792.i −0.0503234 + 0.0754851i
$$313$$ −1.78677e6 −1.03088 −0.515438 0.856927i $$-0.672371\pi$$
−0.515438 + 0.856927i $$0.672371\pi$$
$$314$$ 82072.0i 0.0469754i
$$315$$ 1.26575e6 0.718741
$$316$$ 725760. 0.408861
$$317$$ 182148.i 0.101807i 0.998704 + 0.0509033i $$0.0162100\pi$$
−0.998704 + 0.0509033i $$0.983790\pi$$
$$318$$ 611424.i 0.339059i
$$319$$ 659100.i 0.362639i
$$320$$ 278528.i 0.152053i
$$321$$ −317008. −0.171715
$$322$$ −690112. −0.370920
$$323$$ 1.86661e6i 0.995515i
$$324$$ −762256. −0.403402
$$325$$ −759993. 506662.i −0.399118 0.266079i
$$326$$ 146504. 0.0763494
$$327$$ 872336.i 0.451143i
$$328$$ 432640. 0.222046
$$329$$ 2.06296e6 1.05075
$$330$$ 424320.i 0.214491i
$$331$$ 216230.i 0.108479i −0.998528 0.0542395i $$-0.982727\pi$$
0.998528 0.0542395i $$-0.0172735\pi$$
$$332$$ 1.99274e6i 0.992212i
$$333$$ 2.00940e6i 0.993017i
$$334$$ −1.07777e6 −0.528639
$$335$$ −3.02886e6 −1.47457
$$336$$ 83968.0i 0.0405757i
$$337$$ −2.05314e6 −0.984791 −0.492396 0.870371i $$-0.663879\pi$$
−0.492396 + 0.870371i $$0.663879\pi$$
$$338$$ 1.37093e6 571220.i 0.652714 0.271964i
$$339$$ 176936. 0.0836213
$$340$$ 1.89094e6i 0.887118i
$$341$$ 557700. 0.259726
$$342$$ −975192. −0.450843
$$343$$ 2.20498e6i 1.01197i
$$344$$ 1.08262e6i 0.493266i
$$345$$ 572288.i 0.258861i
$$346$$ 1.13062e6i 0.507721i
$$347$$ 4.28819e6 1.91183 0.955917 0.293637i $$-0.0948658\pi$$
0.955917 + 0.293637i $$0.0948658\pi$$
$$348$$ 108160. 0.0478761
$$349$$ 3.55152e6i 1.56081i −0.625274 0.780405i $$-0.715013\pi$$
0.625274 0.780405i $$-0.284987\pi$$
$$350$$ 491672. 0.214539
$$351$$ −953160. 635440.i −0.412951 0.275300i
$$352$$ −399360. −0.171794
$$353$$ 2.08678e6i 0.891335i −0.895199 0.445667i $$-0.852966\pi$$
0.895199 0.445667i $$-0.147034\pi$$
$$354$$ −340576. −0.144446
$$355$$ 1.20972e6 0.509465
$$356$$ 299904.i 0.125417i
$$357$$ 570064.i 0.236730i
$$358$$ 1.33512e6i 0.550570i
$$359$$ 500654.i 0.205023i 0.994732 + 0.102511i $$0.0326878\pi$$
−0.994732 + 0.102511i $$0.967312\pi$$
$$360$$ −987904. −0.401752
$$361$$ 1.32262e6 0.534156
$$362$$ 1.83975e6i 0.737884i
$$363$$ 35804.0 0.0142615
$$364$$ −443456. + 665184.i −0.175427 + 0.263141i
$$365$$ −2.11235e6 −0.829916
$$366$$ 87328.0i 0.0340762i
$$367$$ −1.28027e6 −0.496178 −0.248089 0.968737i $$-0.579802\pi$$
−0.248089 + 0.968737i $$0.579802\pi$$
$$368$$ 538624. 0.207332
$$369$$ 1.53452e6i 0.586687i
$$370$$ 2.40774e6i 0.914336i
$$371$$ 3.13355e6i 1.18196i
$$372$$ 91520.0i 0.0342893i
$$373$$ −405666. −0.150972 −0.0754860 0.997147i $$-0.524051\pi$$
−0.0754860 + 0.997147i $$0.524051\pi$$
$$374$$ −2.71128e6 −1.00229
$$375$$ 442272.i 0.162409i
$$376$$ −1.61011e6 −0.587336
$$377$$ −856830. 571220.i −0.310485 0.206990i
$$378$$ 616640. 0.221974
$$379$$ 4.66217e6i 1.66721i −0.552363 0.833604i $$-0.686274\pi$$
0.552363 0.833604i $$-0.313726\pi$$
$$380$$ −1.16851e6 −0.415121
$$381$$ −1.24173e6 −0.438242
$$382$$ 3.66835e6i 1.28621i
$$383$$ 4.35473e6i 1.51692i 0.651717 + 0.758462i $$0.274049\pi$$
−0.651717 + 0.758462i $$0.725951\pi$$
$$384$$ 65536.0i 0.0226805i
$$385$$ 2.17464e6i 0.747714i
$$386$$ 2.55622e6 0.873234
$$387$$ 3.83993e6 1.30331
$$388$$ 1.94381e6i 0.655502i
$$389$$ 786990. 0.263691 0.131845 0.991270i $$-0.457910\pi$$
0.131845 + 0.991270i $$0.457910\pi$$
$$390$$ −551616. 367744.i −0.183643 0.122429i
$$391$$ 3.65675e6 1.20963
$$392$$ 645312.i 0.212107i
$$393$$ 1.24149e6 0.405472
$$394$$ −1.43317e6 −0.465111
$$395$$ 3.08448e6i 0.994693i
$$396$$ 1.41648e6i 0.453913i
$$397$$ 3.97023e6i 1.26427i 0.774859 + 0.632134i $$0.217821\pi$$
−0.774859 + 0.632134i $$0.782179\pi$$
$$398$$ 1.48176e6i 0.468889i
$$399$$ 352272. 0.110776
$$400$$ −383744. −0.119920
$$401$$ 344640.i 0.107030i 0.998567 + 0.0535149i $$0.0170425\pi$$
−0.998567 + 0.0535149i $$0.982958\pi$$
$$402$$ −712672. −0.219950
$$403$$ −483340. + 725010.i −0.148248 + 0.222373i
$$404$$ 227488. 0.0693434
$$405$$ 3.23959e6i 0.981414i
$$406$$ 554320. 0.166896
$$407$$ −3.45228e6 −1.03305
$$408$$ 444928.i 0.132324i
$$409$$ 2.55466e6i 0.755137i 0.925982 + 0.377568i $$0.123240\pi$$
−0.925982 + 0.377568i $$0.876760\pi$$
$$410$$ 1.83872e6i 0.540202i
$$411$$ 1.12413e6i 0.328255i
$$412$$ 1.00442e6 0.291521
$$413$$ −1.74545e6 −0.503539
$$414$$ 1.91043e6i 0.547811i
$$415$$ 8.46913e6 2.41390
$$416$$ 346112. 519168.i 0.0980581 0.147087i
$$417$$ 1.45528e6 0.409833
$$418$$ 1.67544e6i 0.469017i
$$419$$ −2.51894e6 −0.700943 −0.350472 0.936573i $$-0.613979\pi$$
−0.350472 + 0.936573i $$0.613979\pi$$
$$420$$ 356864. 0.0987142
$$421$$ 4.83670e6i 1.32998i 0.746854 + 0.664988i $$0.231563\pi$$
−0.746854 + 0.664988i $$0.768437\pi$$
$$422$$ 708912.i 0.193781i
$$423$$ 5.71087e6i 1.55185i
$$424$$ 2.44570e6i 0.660675i
$$425$$ −2.60526e6 −0.699647
$$426$$ 284640. 0.0759927
$$427$$ 447556.i 0.118789i
$$428$$ 1.26803e6 0.334596
$$429$$ 527280. 790920.i 0.138324 0.207486i
$$430$$ 4.60115e6 1.20004
$$431$$ 219110.i 0.0568158i 0.999596 + 0.0284079i $$0.00904373\pi$$
−0.999596 + 0.0284079i $$0.990956\pi$$
$$432$$ −481280. −0.124076
$$433$$ −3.03477e6 −0.777867 −0.388934 0.921266i $$-0.627156\pi$$
−0.388934 + 0.921266i $$0.627156\pi$$
$$434$$ 469040.i 0.119532i
$$435$$ 459680.i 0.116475i
$$436$$ 3.48934e6i 0.879078i
$$437$$ 2.25970e6i 0.566039i
$$438$$ −497024. −0.123792
$$439$$ 4.16940e6 1.03255 0.516276 0.856422i $$-0.327318\pi$$
0.516276 + 0.856422i $$0.327318\pi$$
$$440$$ 1.69728e6i 0.417948i
$$441$$ −2.28884e6 −0.560427
$$442$$ 2.34978e6 3.52466e6i 0.572098 0.858148i
$$443$$ −6.30548e6 −1.52654 −0.763271 0.646079i $$-0.776408\pi$$
−0.763271 + 0.646079i $$0.776408\pi$$
$$444$$ 566528.i 0.136384i
$$445$$ 1.27459e6 0.305120
$$446$$ 4.45186e6 1.05975
$$447$$ 1.09682e6i 0.259636i
$$448$$ 335872.i 0.0790640i
$$449$$ 7.41586e6i 1.73598i −0.496579 0.867991i $$-0.665411\pi$$
0.496579 0.867991i $$-0.334589\pi$$
$$450$$ 1.36109e6i 0.316852i
$$451$$ −2.63640e6 −0.610337
$$452$$ −707744. −0.162941
$$453$$ 1.37612e6i 0.315073i
$$454$$ −5.56633e6 −1.26745
$$455$$ −2.82703e6 1.88469e6i −0.640180 0.426787i
$$456$$ −274944. −0.0619202
$$457$$ 4.71529e6i 1.05613i 0.849204 + 0.528065i $$0.177082\pi$$
−0.849204 + 0.528065i $$0.822918\pi$$
$$458$$ −3.63918e6 −0.810663
$$459$$ −3.26744e6 −0.723896
$$460$$ 2.28915e6i 0.504406i
$$461$$ 3.34566e6i 0.733212i −0.930376 0.366606i $$-0.880520\pi$$
0.930376 0.366606i $$-0.119480\pi$$
$$462$$ 511680.i 0.111530i
$$463$$ 1.65791e6i 0.359426i −0.983719 0.179713i $$-0.942483\pi$$
0.983719 0.179713i $$-0.0575169\pi$$
$$464$$ −432640. −0.0932893
$$465$$ 388960. 0.0834205
$$466$$ 1.06462e6i 0.227106i
$$467$$ 823668. 0.174767 0.0873836 0.996175i $$-0.472149\pi$$
0.0873836 + 0.996175i $$0.472149\pi$$
$$468$$ 1.84142e6 + 1.22762e6i 0.388633 + 0.259088i
$$469$$ −3.65244e6 −0.766746
$$470$$ 6.84298e6i 1.42890i
$$471$$ 82072.0 0.0170468
$$472$$ 1.36230e6 0.281462
$$473$$ 6.59724e6i 1.35584i
$$474$$ 725760.i 0.148370i
$$475$$ 1.60993e6i 0.327395i
$$476$$ 2.28026e6i 0.461282i
$$477$$ −8.67458e6 −1.74563
$$478$$ 1.01846e6 0.203879
$$479$$ 3.59011e6i 0.714938i −0.933925 0.357469i $$-0.883640\pi$$
0.933925 0.357469i $$-0.116360\pi$$
$$480$$ −278528. −0.0551780
$$481$$ 2.99198e6 4.48796e6i 0.589652 0.884477i
$$482$$ 1.25440e6 0.245934
$$483$$ 690112.i 0.134602i
$$484$$ −143216. −0.0277893
$$485$$ 8.26118e6 1.59473
$$486$$ 2.58962e6i 0.497330i
$$487$$ 9.67688e6i 1.84890i 0.381306 + 0.924449i $$0.375474\pi$$
−0.381306 + 0.924449i $$0.624526\pi$$
$$488$$ 349312.i 0.0663994i
$$489$$ 146504.i 0.0277062i
$$490$$ −2.74258e6 −0.516022
$$491$$ 3.45633e6 0.647011 0.323506 0.946226i $$-0.395139\pi$$
0.323506 + 0.946226i $$0.395139\pi$$
$$492$$ 432640.i 0.0805775i
$$493$$ −2.93722e6 −0.544276
$$494$$ 2.17807e6 + 1.45205e6i 0.401564 + 0.267709i
$$495$$ 6.02004e6 1.10430
$$496$$ 366080.i 0.0668147i
$$497$$ 1.45878e6 0.264910
$$498$$ 1.99274e6 0.360061
$$499$$ 2.09109e6i 0.375942i −0.982175 0.187971i $$-0.939809\pi$$
0.982175 0.187971i $$-0.0601911\pi$$
$$500$$ 1.76909e6i 0.316464i
$$501$$ 1.07777e6i 0.191836i
$$502$$ 4.28507e6i 0.758925i
$$503$$ 5.58626e6 0.984468 0.492234 0.870463i $$-0.336180\pi$$
0.492234 + 0.870463i $$0.336180\pi$$
$$504$$ −1.19130e6 −0.208902
$$505$$ 966824.i 0.168702i
$$506$$ −3.28224e6 −0.569894
$$507$$ 571220. + 1.37093e6i 0.0986924 + 0.236862i
$$508$$ 4.96691e6 0.853940
$$509$$ 4.15504e6i 0.710854i −0.934704 0.355427i $$-0.884335\pi$$
0.934704 0.355427i $$-0.115665\pi$$
$$510$$ −1.89094e6 −0.321924
$$511$$ −2.54725e6 −0.431538
$$512$$ 262144.i 0.0441942i
$$513$$ 2.01912e6i 0.338742i
$$514$$ 753528.i 0.125803i
$$515$$ 4.26877e6i 0.709226i
$$516$$ 1.08262e6 0.179000
$$517$$ 9.81162e6 1.61441
$$518$$ 2.90346e6i 0.475435i
$$519$$ 1.13062e6 0.184245
$$520$$ 2.20646e6 + 1.47098e6i 0.357840 + 0.238560i
$$521$$ −9.84416e6 −1.58886 −0.794428 0.607359i $$-0.792229\pi$$
−0.794428 + 0.607359i $$0.792229\pi$$
$$522$$ 1.53452e6i 0.246488i
$$523$$ 481324. 0.0769455 0.0384728 0.999260i $$-0.487751\pi$$
0.0384728 + 0.999260i $$0.487751\pi$$
$$524$$ −4.96595e6 −0.790086
$$525$$ 491672.i 0.0778533i
$$526$$ 5.94710e6i 0.937219i
$$527$$ 2.48534e6i 0.389816i
$$528$$ 399360.i 0.0623419i
$$529$$ −2.00953e6 −0.312216
$$530$$ −1.03942e7 −1.60732
$$531$$ 4.83192e6i 0.743676i
$$532$$ −1.40909e6 −0.215853
$$533$$ 2.28488e6 3.42732e6i 0.348374 0.522561i
$$534$$ 299904. 0.0455123
$$535$$ 5.38914e6i 0.814019i
$$536$$ 2.85069e6 0.428586
$$537$$ 1.33512e6 0.199795
$$538$$ 2.97596e6i 0.443273i
$$539$$ 3.93237e6i 0.583019i
$$540$$ 2.04544e6i 0.301858i
$$541$$ 263980.i 0.0387773i −0.999812 0.0193887i $$-0.993828\pi$$
0.999812 0.0193887i $$-0.00617199\pi$$
$$542$$ 1.82236e6 0.266462
$$543$$ −1.83975e6 −0.267769
$$544$$ 1.77971e6i 0.257841i
$$545$$ 1.48297e7 2.13866
$$546$$ −665184. 443456.i −0.0954905 0.0636603i
$$547$$ 2.80023e6 0.400152 0.200076 0.979780i $$-0.435881\pi$$
0.200076 + 0.979780i $$0.435881\pi$$
$$548$$ 4.49651e6i 0.639623i
$$549$$ 1.23897e6 0.175440
$$550$$ 2.33844e6 0.329625
$$551$$ 1.81506e6i 0.254690i
$$552$$ 538624.i 0.0752381i
$$553$$ 3.71952e6i 0.517219i
$$554$$ 1.84079e6i 0.254818i
$$555$$ −2.40774e6 −0.331801
$$556$$ −5.82112e6 −0.798582
$$557$$ 2.70983e6i 0.370087i 0.982730 + 0.185043i $$0.0592426\pi$$
−0.982730 + 0.185043i $$0.940757\pi$$
$$558$$ −1.29844e6 −0.176537
$$559$$ −8.57641e6 5.71761e6i −1.16085 0.773900i
$$560$$ −1.42746e6 −0.192350
$$561$$ 2.71128e6i 0.363720i
$$562$$ 196960. 0.0263049
$$563$$ −1.14870e7 −1.52733 −0.763667 0.645610i $$-0.776603\pi$$
−0.763667 + 0.645610i $$0.776603\pi$$
$$564$$ 1.61011e6i 0.213137i
$$565$$ 3.00791e6i 0.396409i
$$566$$ 2.17678e6i 0.285611i
$$567$$ 3.90656e6i 0.510314i
$$568$$ −1.13856e6 −0.148076
$$569$$ 7.85065e6 1.01654 0.508271 0.861197i $$-0.330285\pi$$
0.508271 + 0.861197i $$0.330285\pi$$
$$570$$ 1.16851e6i 0.150642i
$$571$$ −6.34071e6 −0.813856 −0.406928 0.913460i $$-0.633400\pi$$
−0.406928 + 0.913460i $$0.633400\pi$$
$$572$$ −2.10912e6 + 3.16368e6i −0.269533 + 0.404299i
$$573$$ −3.66835e6 −0.466750
$$574$$ 2.21728e6i 0.280893i
$$575$$ −3.15390e6 −0.397812
$$576$$ 929792. 0.116770
$$577$$ 7.20867e6i 0.901396i −0.892676 0.450698i $$-0.851175\pi$$
0.892676 0.450698i $$-0.148825\pi$$
$$578$$ 6.40315e6i 0.797212i
$$579$$ 2.55622e6i 0.316886i
$$580$$ 1.83872e6i 0.226958i
$$581$$ 1.02128e7 1.25517
$$582$$ 1.94381e6 0.237873
$$583$$ 1.49035e7i 1.81600i
$$584$$ 1.98810e6 0.241216
$$585$$ −5.21737e6 + 7.82605e6i −0.630321 + 0.945482i
$$586$$ 4.10014e6 0.493236
$$587$$ 2.48138e6i 0.297234i −0.988895 0.148617i $$-0.952518\pi$$
0.988895 0.148617i $$-0.0474821\pi$$
$$588$$ −645312. −0.0769709
$$589$$ −1.53582e6 −0.182411
$$590$$ 5.78979e6i 0.684751i
$$591$$ 1.43317e6i 0.168783i
$$592$$ 2.26611e6i 0.265752i
$$593$$ 1.38811e7i 1.62102i −0.585728 0.810508i $$-0.699191\pi$$
0.585728 0.810508i $$-0.300809\pi$$
$$594$$ 2.93280e6 0.341049
$$595$$ −9.69109e6 −1.12223
$$596$$ 4.38726e6i 0.505916i
$$597$$ 1.48176e6 0.170154
$$598$$ 2.84461e6 4.26691e6i 0.325289 0.487934i
$$599$$ 3.85356e6 0.438829 0.219414 0.975632i $$-0.429585\pi$$
0.219414 + 0.975632i $$0.429585\pi$$
$$600$$ 383744.i 0.0435175i
$$601$$ 1.32728e6 0.149892 0.0749458 0.997188i $$-0.476122\pi$$
0.0749458 + 0.997188i $$0.476122\pi$$
$$602$$ 5.54845e6 0.623994
$$603$$ 1.01110e7i 1.13241i
$$604$$ 5.50448e6i 0.613937i
$$605$$ 608668.i 0.0676071i
$$606$$ 227488.i 0.0251638i
$$607$$ 9.73197e6 1.07208 0.536042 0.844191i $$-0.319919\pi$$
0.536042 + 0.844191i $$0.319919\pi$$
$$608$$ 1.09978e6 0.120655
$$609$$ 554320.i 0.0605644i
$$610$$ 1.48458e6 0.161539
$$611$$ −8.50340e6 + 1.27551e7i −0.921488 + 1.38223i
$$612$$ 6.31242e6 0.681267
$$613$$ 1.40465e7i 1.50979i 0.655846 + 0.754894i $$0.272312\pi$$
−0.655846 + 0.754894i $$0.727688\pi$$
$$614$$ −6.31065e6 −0.675543
$$615$$ −1.83872e6 −0.196032
$$616$$ 2.04672e6i 0.217323i
$$617$$ 3.72561e6i 0.393989i 0.980405 + 0.196995i $$0.0631181\pi$$
−0.980405 + 0.196995i $$0.936882\pi$$
$$618$$ 1.00442e6i 0.105789i
$$619$$ 8.96911e6i 0.940855i 0.882439 + 0.470428i $$0.155900\pi$$
−0.882439 + 0.470428i $$0.844100\pi$$
$$620$$ −1.55584e6 −0.162550
$$621$$ −3.95552e6 −0.411599
$$622$$ 1.32035e6i 0.136840i
$$623$$ 1.53701e6 0.158656
$$624$$ 519168. + 346112.i 0.0533761 + 0.0355840i
$$625$$ −1.22030e7 −1.24959
$$626$$ 7.14706e6i 0.728940i
$$627$$ 1.67544e6 0.170200
$$628$$ −328288. −0.0332167
$$629$$ 1.53848e7i 1.55047i
$$630$$ 5.06301e6i 0.508226i
$$631$$ 1.72189e7i 1.72160i 0.508943 + 0.860800i $$0.330036\pi$$
−0.508943 + 0.860800i $$0.669964\pi$$
$$632$$ 2.90304e6i 0.289108i
$$633$$ −708912. −0.0703207
$$634$$ 728592. 0.0719882
$$635$$ 2.11094e7i 2.07750i
$$636$$ −2.44570e6 −0.239751
$$637$$ 5.11208e6 + 3.40805e6i 0.499171 + 0.332781i
$$638$$ 2.63640e6 0.256425
$$639$$ 4.03833e6i 0.391246i
$$640$$ 1.11411e6 0.107517
$$641$$ 8.51692e6 0.818724 0.409362 0.912372i $$-0.365751\pi$$
0.409362 + 0.912372i $$0.365751\pi$$
$$642$$ 1.26803e6i 0.121421i
$$643$$ 8.14145e6i 0.776559i −0.921542 0.388280i $$-0.873069\pi$$
0.921542 0.388280i $$-0.126931\pi$$
$$644$$ 2.76045e6i 0.262280i
$$645$$ 4.60115e6i 0.435479i
$$646$$ 7.46645e6 0.703935
$$647$$ −2.39391e6 −0.224826 −0.112413 0.993662i $$-0.535858\pi$$
−0.112413 + 0.993662i $$0.535858\pi$$
$$648$$ 3.04902e6i 0.285248i
$$649$$ −8.30154e6 −0.773654
$$650$$ −2.02665e6 + 3.03997e6i −0.188146 + 0.282219i
$$651$$ 469040. 0.0433768
$$652$$ 586016.i 0.0539872i
$$653$$ 1.17900e7 1.08201 0.541003 0.841020i $$-0.318045\pi$$
0.541003 + 0.841020i $$0.318045\pi$$
$$654$$ 3.48934e6 0.319006
$$655$$ 2.11053e7i 1.92215i
$$656$$ 1.73056e6i 0.157010i
$$657$$ 7.05153e6i 0.637338i
$$658$$ 8.25182e6i 0.742994i
$$659$$ 4.84562e6 0.434646 0.217323 0.976100i $$-0.430267\pi$$
0.217323 + 0.976100i $$0.430267\pi$$
$$660$$ 1.69728e6 0.151668
$$661$$ 1.14461e7i 1.01895i −0.860485 0.509476i $$-0.829839\pi$$
0.860485 0.509476i $$-0.170161\pi$$
$$662$$ −864920. −0.0767063
$$663$$ 3.52466e6 + 2.34978e6i 0.311411 + 0.207607i
$$664$$ −7.97094e6 −0.701600
$$665$$ 5.98862e6i 0.525137i
$$666$$ 8.03762e6 0.702169
$$667$$ −3.55576e6 −0.309470
$$668$$ 4.31107e6i 0.373804i
$$669$$ 4.45186e6i 0.384571i
$$670$$ 1.21154e7i 1.04268i
$$671$$ 2.12862e6i 0.182512i
$$672$$ −335872. −0.0286913
$$673$$ −5.34001e6 −0.454469 −0.227234 0.973840i $$-0.572968\pi$$
−0.227234 + 0.973840i $$0.572968\pi$$
$$674$$ 8.21257e6i 0.696353i
$$675$$ 2.81812e6 0.238067
$$676$$ −2.28488e6 5.48371e6i −0.192308 0.461538i
$$677$$ −7.06132e6 −0.592126 −0.296063 0.955168i $$-0.595674\pi$$
−0.296063 + 0.955168i $$0.595674\pi$$
$$678$$ 707744.i 0.0591292i
$$679$$ 9.96202e6 0.829226
$$680$$ 7.56378e6 0.627287
$$681$$ 5.56633e6i 0.459940i
$$682$$ 2.23080e6i 0.183654i
$$683$$ 3.50035e6i 0.287117i 0.989642 + 0.143559i $$0.0458546\pi$$
−0.989642 + 0.143559i $$0.954145\pi$$
$$684$$ 3.90077e6i 0.318794i
$$685$$ −1.91102e7 −1.55610
$$686$$ −8.81992e6 −0.715574
$$687$$ 3.63918e6i 0.294179i
$$688$$ −4.33050e6 −0.348792
$$689$$ 1.93745e7 + 1.29163e7i 1.55483 + 1.03655i
$$690$$ −2.28915e6 −0.183042
$$691$$ 302510.i 0.0241015i −0.999927 0.0120508i $$-0.996164\pi$$
0.999927 0.0120508i $$-0.00383597\pi$$
$$692$$ −4.52246e6 −0.359013
$$693$$ 7.25946e6 0.574211
$$694$$ 1.71528e7i 1.35187i
$$695$$ 2.47398e7i 1.94282i
$$696$$ 432640.i 0.0338535i
$$697$$ 1.17489e7i 0.916040i
$$698$$ −1.42061e7 −1.10366
$$699$$ 1.06462e6 0.0824138
$$700$$ 1.96669e6i 0.151702i
$$701$$ −1.03212e7 −0.793294 −0.396647 0.917971i $$-0.629826\pi$$
−0.396647 + 0.917971i $$0.629826\pi$$
$$702$$ −2.54176e6 + 3.81264e6i −0.194667 + 0.292000i
$$703$$ 9.50705e6 0.725533
$$704$$ 1.59744e6i 0.121477i
$$705$$ 6.84298e6 0.518528
$$706$$ −8.34714e6 −0.630269
$$707$$ 1.16588e6i 0.0877211i
$$708$$ 1.36230e6i 0.102139i
$$709$$ 5.27524e6i 0.394118i −0.980392 0.197059i $$-0.936861\pi$$
0.980392 0.197059i $$-0.0631391\pi$$
$$710$$ 4.83888e6i 0.360246i
$$711$$ 1.02967e7 0.763880
$$712$$ −1.19962e6 −0.0886834
$$713$$ 3.00872e6i 0.221645i
$$714$$ −2.28026e6 −0.167393
$$715$$ −1.34456e7 8.96376e6i −0.983595 0.655730i
$$716$$ −5.34048e6 −0.389312
$$717$$ 1.01846e6i 0.0739851i
$$718$$ 2.00262e6 0.144973
$$719$$ −5.02216e6 −0.362300 −0.181150 0.983455i $$-0.557982\pi$$
−0.181150 + 0.983455i $$0.557982\pi$$
$$720$$ 3.95162e6i 0.284082i
$$721$$ 5.14763e6i 0.368782i
$$722$$ 5.29049e6i 0.377705i
$$723$$ 1.25440e6i 0.0892463i
$$724$$ 7.35901e6 0.521762
$$725$$ 2.53331e6 0.178996
$$726$$ 143216.i 0.0100844i
$$727$$ 8.80441e6 0.617823 0.308912 0.951091i $$-0.400035\pi$$
0.308912 + 0.951091i $$0.400035\pi$$
$$728$$ 2.66074e6 + 1.77382e6i 0.186069 + 0.124046i
$$729$$ −8.98715e6 −0.626330
$$730$$ 8.44941e6i 0.586839i
$$731$$ −2.94000e7 −2.03495
$$732$$ 349312. 0.0240955
$$733$$ 3.05052e6i 0.209708i −0.994488 0.104854i $$-0.966563\pi$$
0.994488 0.104854i $$-0.0334375\pi$$
$$734$$ 5.12109e6i 0.350850i
$$735$$ 2.74258e6i 0.187258i
$$736$$ 2.15450e6i 0.146606i
$$737$$ −1.73714e7 −1.17806
$$738$$ 6.13808e6 0.414851
$$739$$ 7.62605e6i 0.513675i −0.966455 0.256837i $$-0.917320\pi$$
0.966455 0.256837i $$-0.0826805\pi$$
$$740$$ 9.63098e6 0.646533
$$741$$ −1.45205e6 + 2.17807e6i −0.0971484 + 0.145723i
$$742$$ −1.25342e7 −0.835770
$$743$$ 2.18236e7i 1.45029i 0.688595 + 0.725146i $$0.258228\pi$$
−0.688595 + 0.725146i $$0.741772\pi$$
$$744$$ −366080. −0.0242462
$$745$$ 1.86459e7 1.23081
$$746$$ 1.62266e6i 0.106753i
$$747$$ 2.82719e7i 1.85376i
$$748$$ 1.08451e7i 0.708729i
$$749$$ 6.49866e6i 0.423272i
$$750$$ −1.76909e6 −0.114841
$$751$$ 1.69030e7 1.09361 0.546807 0.837259i $$-0.315843\pi$$
0.546807 + 0.837259i $$0.315843\pi$$
$$752$$ 6.44045e6i 0.415309i
$$753$$ −4.28507e6 −0.275404
$$754$$ −2.28488e6 + 3.42732e6i −0.146364 + 0.219546i
$$755$$ 2.33940e7 1.49361
$$756$$ 2.46656e6i 0.156959i
$$757$$ −8.90252e6 −0.564642 −0.282321 0.959320i $$-0.591104\pi$$
−0.282321 + 0.959320i $$0.591104\pi$$
$$758$$ −1.86487e7 −1.17889
$$759$$ 3.28224e6i 0.206807i
$$760$$ 4.67405e6i 0.293535i
$$761$$ 6.98052e6i 0.436944i 0.975843 + 0.218472i $$0.0701073\pi$$
−0.975843 + 0.218472i $$0.929893\pi$$
$$762$$ 4.96691e6i 0.309884i
$$763$$ 1.78829e7 1.11206
$$764$$ 1.46734e7 0.909489
$$765$$ 2.68278e7i 1.65741i
$$766$$ 1.74189e7 1.07263
$$767$$ 7.19467e6 1.07920e7i 0.441593 0.662390i
$$768$$ 262144. 0.0160375
$$769$$ 2.67789e7i 1.63296i 0.577372 + 0.816481i $$0.304078\pi$$
−0.577372 + 0.816481i $$0.695922\pi$$
$$770$$ 8.69856e6 0.528714
$$771$$ −753528. −0.0456524
$$772$$ 1.02249e7i 0.617470i
$$773$$ 710244.i 0.0427522i −0.999772 0.0213761i $$-0.993195\pi$$
0.999772 0.0213761i $$-0.00680475\pi$$
$$774$$ 1.53597e7i 0.921576i
$$775$$ 2.14357e6i 0.128199i
$$776$$ −7.77523e6 −0.463510